LMFDB - Embedded newform 288.2.w.a.35.2

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			35.2
Character	$\chi$	$=$	288.35
Dual form			288.2.w.a.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33776 - 0.458699i) q^{2} +(1.57919 + 1.22726i) q^{4} +(-2.70076 + 1.11869i) q^{5} +(-1.06647 - 1.06647i) q^{7} +(-1.54963 - 2.36614i) q^{8} +O(q^{10})$	\(q+(-1.33776 - 0.458699i) q^{2} +(1.57919 + 1.22726i) q^{4} +(-2.70076 + 1.11869i) q^{5} +(-1.06647 - 1.06647i) q^{7} +(-1.54963 - 2.36614i) q^{8} +(4.12611 - 0.257702i) q^{10} +(5.29504 - 2.19328i) q^{11} +(1.67540 - 4.04478i) q^{13} +(0.937494 + 1.91588i) q^{14} +(0.987684 + 3.87614i) q^{16} +3.44484 q^{17} +(3.23205 + 1.33876i) q^{19} +(-5.63794 - 1.54790i) q^{20} +(-8.08953 + 0.505243i) q^{22} +(0.703083 + 0.703083i) q^{23} +(2.50711 - 2.50711i) q^{25} +(-4.09662 + 4.64243i) q^{26} +(-0.375329 - 2.99300i) q^{28} +(3.94721 - 9.52941i) q^{29} +4.23846i q^{31} +(0.456702 - 5.63839i) q^{32} +(-4.60837 - 1.58015i) q^{34} +(4.07335 + 1.68724i) q^{35} +(-2.04600 - 4.93947i) q^{37} +(-3.70961 - 3.27347i) q^{38} +(6.83218 + 4.65683i) q^{40} +(-3.53573 + 3.53573i) q^{41} +(-3.38340 - 8.16825i) q^{43} +(11.0536 + 3.03477i) q^{44} +(-0.618051 - 1.26306i) q^{46} +4.33671i q^{47} -4.72526i q^{49} +(-4.50391 + 2.20390i) q^{50} +(7.60977 - 4.33133i) q^{52} +(-0.541366 - 1.30697i) q^{53} +(-11.8470 + 11.8470i) q^{55} +(-0.870790 + 4.17608i) q^{56} +(-9.65155 + 10.9375i) q^{58} +(3.66093 + 8.83827i) q^{59} +(-1.97197 - 0.816817i) q^{61} +(1.94418 - 5.67003i) q^{62} +(-3.19728 + 7.33331i) q^{64} +12.7983i q^{65} +(-3.55849 + 8.59096i) q^{67} +(5.44006 + 4.22771i) q^{68} +(-4.67522 - 4.12556i) q^{70} +(-1.76501 + 1.76501i) q^{71} +(-1.16342 - 1.16342i) q^{73} +(0.471315 + 7.54631i) q^{74} +(3.46102 + 6.08071i) q^{76} +(-7.98610 - 3.30795i) q^{77} +14.4770 q^{79} +(-7.00371 - 9.36362i) q^{80} +(6.35178 - 3.10811i) q^{82} +(4.27230 - 10.3143i) q^{83} +(-9.30371 + 3.85372i) q^{85} +(0.779399 + 12.4791i) q^{86} +(-13.3950 - 9.13005i) q^{88} +(-7.99481 - 7.99481i) q^{89} +(-6.10044 + 2.52688i) q^{91} +(0.247439 + 1.97317i) q^{92} +(1.98925 - 5.80147i) q^{94} -10.2267 q^{95} +12.8450 q^{97} +(-2.16747 + 6.32126i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

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 $

$2$	−1.33776	−	0.458699i	−0.945937	−	0.324349i
$2$	−1.33776	−	0.458699i	−0.945937	−	0.324349i
$3$		0			0
$3$		0			0
$4$	1.57919	+	1.22726i	0.789595	+	0.613628i
$5$	−2.70076	+	1.11869i	−1.20782	+	0.500294i	−0.893517	−	0.449029i	$-0.851770\pi$
$5$	−2.70076	+	1.11869i	−1.20782	+	0.500294i	−0.314300	+	0.949324i	$0.601770\pi$
$6$		0			0
$7$	−1.06647	−	1.06647i	−0.403090	−	0.403090i	0.476231	−	0.879320i	$-0.342003\pi$
$7$	−1.06647	−	1.06647i	−0.403090	−	0.403090i	−0.879320	+	0.476231i	$0.842003\pi$
$8$	−1.54963	−	2.36614i	−0.547878	−	0.836558i
$9$		0			0
$10$	4.12611	−	0.257702i	1.30479	−	0.0814925i
$11$	5.29504	−	2.19328i	1.59651	−	0.661297i	0.605596	−	0.795772i	$-0.292935\pi$
$11$	5.29504	−	2.19328i	1.59651	−	0.661297i	0.990917	+	0.134475i	$0.0429346\pi$
$12$		0			0
$13$	1.67540	−	4.04478i	0.464674	−	1.12182i	−0.501783	−	0.864993i	$-0.667323\pi$
$13$	1.67540	−	4.04478i	0.464674	−	1.12182i	0.966457	−	0.256828i	$-0.0826774\pi$
$14$	0.937494	+	1.91588i	0.250556	+	0.512039i
$15$		0			0
$16$	0.987684	+	3.87614i	0.246921	+	0.969036i
$17$	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	$-0.243563\pi$
$19$	3.23205	+	1.33876i	0.741483	+	0.307132i	0.0202218	+	0.999796i	$0.493563\pi$
$20$	−5.63794	−	1.54790i	−1.26068	−	0.346121i
$21$		0			0
$22$	−8.08953	+	0.505243i	−1.72469	+	0.107718i
$23$	0.703083	+	0.703083i	0.146603	+	0.146603i	0.776599	−	0.629996i	$-0.216943\pi$
$23$	0.703083	+	0.703083i	0.146603	+	0.146603i	−0.629996	+	0.776599i	$0.716943\pi$
$24$		0			0
$25$	2.50711	−	2.50711i	0.501422	−	0.501422i
$26$	−4.09662	+	4.64243i	−0.803414	+	0.910456i
$27$		0			0
$28$	−0.375329	−	2.99300i	−0.0709304	−	0.565625i
$29$	3.94721	−	9.52941i	0.732979	−	1.76957i	0.100574	−	0.994930i	$-0.467932\pi$
$29$	3.94721	−	9.52941i	0.732979	−	1.76957i	0.632405	−	0.774638i	$-0.282068\pi$
$30$		0			0
$31$			4.23846i			0.761250i	0.924729	+	0.380625i	$0.124291\pi$
$31$			4.23846i			0.761250i	−0.924729	+	0.380625i	$0.875709\pi$
$32$	0.456702	−	5.63839i	0.0807343	−	0.996736i
$33$		0			0
$34$	−4.60837	−	1.58015i	−0.790328	−	0.270993i
$35$	4.07335	+	1.68724i	0.688522	+	0.285195i
$36$		0			0
$37$	−2.04600	−	4.93947i	−0.336360	−	0.812044i	−0.998059	−	0.0622749i	$-0.980164\pi$
$37$	−2.04600	−	4.93947i	−0.336360	−	0.812044i	0.661699	−	0.749769i	$-0.269836\pi$
$38$	−3.70961	−	3.27347i	−0.601778	−	0.531027i
$39$		0			0
$40$	6.83218	+	4.65683i	1.08026	+	0.736310i
$41$	−3.53573	+	3.53573i	−0.552188	+	0.552188i	−0.927072	−	0.374884i	$-0.877683\pi$
$41$	−3.53573	+	3.53573i	−0.552188	+	0.552188i	0.374884	+	0.927072i	$0.377683\pi$
$42$		0			0
$43$	−3.38340	−	8.16825i	−0.515963	−	1.24565i	−0.940364	−	0.340171i	$-0.889515\pi$
$43$	−3.38340	−	8.16825i	−0.515963	−	1.24565i	0.424400	−	0.905475i	$-0.360485\pi$
$44$	11.0536	+	3.03477i	1.66639	+	0.457508i
$45$		0			0
$46$	−0.618051	−	1.26306i	−0.0911267	−	0.186228i
$47$			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
$50$	−4.50391	+	2.20390i	−0.636950	+	0.311678i
$51$		0			0
$52$	7.60977	−	4.33133i	1.05529	−	0.600648i
$53$	−0.541366	−	1.30697i	−0.0743624	−	0.179527i	0.882327	−	0.470636i	$-0.155976\pi$
$53$	−0.541366	−	1.30697i	−0.0743624	−	0.179527i	−0.956690	+	0.291110i	$0.905976\pi$
$54$		0			0
$55$	−11.8470	+	11.8470i	−1.59745	+	1.59745i
$56$	−0.870790	+	4.17608i	−0.116364	+	0.558052i
$57$		0			0
$58$	−9.65155	+	10.9375i	−1.26731	+	1.43616i
$59$	3.66093	+	8.83827i	0.476613	+	1.15064i	0.961188	+	0.275895i	$0.0889743\pi$
$59$	3.66093	+	8.83827i	0.476613	+	1.15064i	−0.484575	+	0.874750i	$0.661026\pi$
$60$		0			0
$61$	−1.97197	−	0.816817i	−0.252485	−	0.104583i	0.252851	−	0.967505i	$-0.418632\pi$
$61$	−1.97197	−	0.816817i	−0.252485	−	0.104583i	−0.505336	+	0.862922i	$0.668632\pi$
$62$	1.94418	−	5.67003i	0.246911	−	0.720095i
$63$		0			0
$64$	−3.19728	+	7.33331i	−0.399660	+	0.916663i
$65$			12.7983i			1.58743i
$66$		0			0
$67$	−3.55849	+	8.59096i	−0.434739	+	1.04955i	0.543001	+	0.839732i	$0.317288\pi$
$67$	−3.55849	+	8.59096i	−0.434739	+	1.04955i	−0.977740	+	0.209821i	$0.932712\pi$
$68$	5.44006	+	4.22771i	0.659705	+	0.512685i
$69$		0			0
$70$	−4.67522	−	4.12556i	−0.558796	−	0.493098i
$71$	−1.76501	+	1.76501i	−0.209468	+	0.209468i	−0.804041	−	0.594574i	$-0.797321\pi$
$71$	−1.76501	+	1.76501i	−0.209468	+	0.209468i	0.594574	+	0.804041i	$0.297321\pi$
$72$		0			0
$73$	−1.16342	−	1.16342i	−0.136168	−	0.136168i	0.635737	−	0.771905i	$-0.280696\pi$
$73$	−1.16342	−	1.16342i	−0.136168	−	0.136168i	−0.771905	+	0.635737i	$0.780696\pi$
$74$	0.471315	+	7.54631i	0.0547893	+	0.877241i
$75$		0			0
$76$	3.46102	+	6.08071i	0.397006	+	0.697505i
$77$	−7.98610	−	3.30795i	−0.910100	−	0.376976i
$78$		0			0
$79$	14.4770			1.62879			0.814393	−	0.580314i	$-0.197070\pi$
$79$	14.4770			1.62879			0.814393	+	0.580314i	$0.197070\pi$
$80$	−7.00371	−	9.36362i	−0.783039	−	1.04689i
$81$		0			0
$82$	6.35178	−	3.10811i	0.701437	−	0.343233i
$83$	4.27230	−	10.3143i	0.468946	−	1.13214i	−0.495678	−	0.868507i	$-0.665080\pi$
$83$	4.27230	−	10.3143i	0.468946	−	1.13214i	0.964624	−	0.263630i	$-0.0849197\pi$
$84$		0			0
$85$	−9.30371	+	3.85372i	−1.00913	+	0.417995i
$86$	0.779399	+	12.4791i	0.0840448	+	1.34566i
$87$		0			0
$88$	−13.3950	−	9.13005i	−1.42791	−	0.973267i
$89$	−7.99481	−	7.99481i	−0.847448	−	0.847448i	0.142366	−	0.989814i	$-0.454529\pi$
$89$	−7.99481	−	7.99481i	−0.847448	−	0.847448i	−0.989814	+	0.142366i	$0.954529\pi$
$90$		0			0
$91$	−6.10044	+	2.52688i	−0.639500	+	0.264889i
$92$	0.247439	+	1.97317i	0.0257973	+	0.205717i
$93$		0			0
$94$	1.98925	−	5.80147i	0.205175	−	0.598376i
$95$	−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	$0.273885\pi$
$98$	−2.16747	+	6.32126i	−0.218948	+	0.638543i
$99$		0			0
$100$	7.03607	−	0.882337i	0.703607	−	0.0882337i
$101$	−0.195046	+	0.0807908i	−0.0194078	+	0.00803898i	−0.392366	−	0.919809i	$-0.628343\pi$
$101$	−0.195046	+	0.0807908i	−0.0194078	+	0.00803898i	0.372958	+	0.927848i	$0.378343\pi$
$102$		0			0
$103$	7.52990	+	7.52990i	0.741943	+	0.741943i	0.972952	−	0.231009i	$-0.0742026\pi$
$103$	7.52990	+	7.52990i	0.741943	+	0.741943i	−0.231009	+	0.972952i	$0.574203\pi$
$104$	−12.1668	+	2.30368i	−1.19305	+	0.225894i
$105$		0			0
$106$	0.124709	+	1.99674i	0.0121128	+	0.193940i
$107$	−6.43177	+	2.66413i	−0.621783	+	0.257551i	−0.671257	−	0.741225i	$-0.734245\pi$
$107$	−6.43177	+	2.66413i	−0.621783	+	0.257551i	0.0494744	+	0.998775i	$0.484245\pi$
$108$		0			0
$109$	−4.89484	+	11.8172i	−0.468840	+	1.13188i	0.495830	+	0.868420i	$0.334864\pi$
$109$	−4.89484	+	11.8172i	−0.468840	+	1.13188i	−0.964670	+	0.263461i	$0.915136\pi$
$110$	21.2827	−	10.4142i	2.02922	−	0.992958i
$111$		0			0
$112$	3.08047	−	5.18715i	0.291077	−	0.490139i
$113$	−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
$116$	17.9284	−	10.2045i	1.66461	−	0.947465i
$117$		0			0
$118$	−0.843332	−	13.5027i	−0.0776350	−	1.24303i
$119$	−3.67384	−	3.67384i	−0.336780	−	0.336780i
$120$		0			0
$121$	15.4488	−	15.4488i	1.40443	−	1.40443i
$122$	2.26335	+	1.99724i	0.204914	+	0.180822i
$123$		0			0
$124$	−5.20168	+	6.69334i	−0.467125	+	0.601079i
$125$	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	$-0.0759600\pi$
$128$	7.64097	−	8.34360i	0.675372	−	0.737477i
$129$		0			0
$130$	5.87055	−	17.1210i	0.514882	−	1.50161i
$131$	17.7023	+	7.33252i	1.54666	+	0.640646i	0.982707	−	0.185165i	$-0.0592820\pi$
$131$	17.7023	+	7.33252i	1.54666	+	0.640646i	0.563948	+	0.825811i	$0.309282\pi$
$132$		0			0
$133$	−2.01915	−	4.87465i	−0.175082	−	0.422686i
$134$	8.70107	−	9.86034i	0.751658	−	0.851804i
$135$		0			0
$136$	−5.33824	−	8.15100i	−0.457750	−	0.698943i
$137$	−10.0787	+	10.0787i	−0.861079	+	0.861079i	−0.991464	−	0.130384i	$-0.958379\pi$
$137$	−10.0787	+	10.0787i	−0.861079	+	0.861079i	0.130384	+	0.991464i	$0.458379\pi$
$138$		0			0
$139$	−4.57378	−	11.0421i	−0.387943	−	0.936578i	−0.990375	−	0.138408i	$-0.955802\pi$
$139$	−4.57378	−	11.0421i	−0.387943	−	0.936578i	0.602432	−	0.798170i	$-0.294198\pi$
$140$	4.36192	+	7.66352i	0.368650	+	0.647685i
$141$		0			0
$142$	3.17076	−	1.55154i	0.266084	−	0.130203i
$143$		−	25.0919i		−	2.09829i
$144$		0			0
$145$			30.1524i			2.50402i
$146$	1.02271	+	2.09003i	0.0846404	+	0.172972i
$147$		0			0
$148$	2.83098	−	10.3113i	0.232705	−	0.847586i
$149$	−2.47497	−	5.97511i	−0.202758	−	0.489500i	0.789492	−	0.613761i	$-0.210344\pi$
$149$	−2.47497	−	5.97511i	−0.202758	−	0.489500i	−0.992250	+	0.124261i	$0.960344\pi$
$150$		0			0
$151$	−5.28519	+	5.28519i	−0.430103	+	0.430103i	−0.888663	−	0.458560i	$-0.848365\pi$
$151$	−5.28519	+	5.28519i	−0.430103	+	0.430103i	0.458560	+	0.888663i	$0.348365\pi$
$152$	−1.84079	−	9.72208i	−0.149308	−	0.788565i
$153$		0			0
$154$	9.16611	+	8.08845i	0.738626	+	0.651786i
$155$	−4.74153	−	11.4471i	−0.380849	−	0.919451i
$156$		0			0
$157$	19.9431	+	8.26070i	1.59163	+	0.659276i	0.990201	−	0.139649i	$-0.0445973\pi$
$157$	19.9431	+	8.26070i	1.59163	+	0.659276i	0.601431	+	0.798924i	$0.294597\pi$
$158$	−19.3667	−	6.64057i	−1.54073	−	0.528295i
$159$		0			0
$160$	5.07418	+	15.7389i	0.401149	+	1.24427i
$161$		−	1.49964i		−	0.118188i
$162$		0			0
$163$	4.75817	−	11.4872i	0.372689	−	0.899751i	−0.620604	−	0.784124i	$-0.713112\pi$
$163$	4.75817	−	11.4872i	0.372689	−	0.899751i	0.993293	−	0.115626i	$-0.0368875\pi$
$164$	−9.92283	+	1.24434i	−0.774843	+	0.0971668i
$165$		0			0
$166$	−10.4464	+	11.8383i	−0.810801	+	0.918828i
$167$	−13.4711	+	13.4711i	−1.04243	+	1.04243i	−0.0433679	+	0.999059i	$0.513809\pi$
$167$	−13.4711	+	13.4711i	−1.04243	+	1.04243i	−0.999059	+	0.0433679i	$0.986191\pi$
$168$		0			0
$169$	−4.36092	−	4.36092i	−0.335455	−	0.335455i
$170$	14.2138	−	0.887743i	1.09015	−	0.0680868i
$171$		0			0
$172$	4.68150	−	17.0515i	0.356961	−	1.30017i
$173$	−1.48659	−	0.615768i	−0.113024	−	0.0468160i	0.325455	−	0.945558i	$-0.394483\pi$
$173$	−1.48659	−	0.615768i	−0.113024	−	0.0468160i	−0.438479	+	0.898742i	$0.644483\pi$
$174$		0			0
$175$	−5.34754			−0.404236
$176$	13.7313	+	18.3581i	1.03503	+	1.38379i
$177$		0			0
$178$	7.02791	+	14.3623i	0.526764	+	1.07650i
$179$	0.188898	−	0.456040i	0.0141189	−	0.0340860i	−0.916663	−	0.399661i	$-0.869128\pi$
$179$	0.188898	−	0.456040i	0.0141189	−	0.0340860i	0.930782	+	0.365575i	$0.119128\pi$
$180$		0			0
$181$	−20.2286	+	8.37896i	−1.50358	+	0.622803i	−0.974221	−	0.225596i	$-0.927567\pi$
$181$	−20.2286	+	8.37896i	−1.50358	+	0.622803i	−0.529358	+	0.848398i	$0.677567\pi$
$182$	9.31999	−	0.582093i	0.690843	−	0.0431476i
$183$		0			0
$184$	0.574076	−	2.75312i	0.0423215	−	0.202963i
$185$	11.0515	+	11.0515i	0.812522	+	0.812522i
$186$		0			0
$187$	18.2406	−	7.55549i	1.33388	−	0.552512i
$188$	−5.32226	+	6.84850i	−0.388166	+	0.499478i
$189$		0			0
$190$	13.6808	+	4.69096i	0.992509	+	0.340318i
$191$	−23.3059			−1.68636			−0.843180	−	0.537632i	$-0.819319\pi$
$191$	−23.3059			−1.68636			−0.843180	+	0.537632i	$0.819319\pi$
$192$		0			0
$193$	−27.0699			−1.94854			−0.974268	−	0.225392i	$-0.927634\pi$
$193$	−27.0699			−1.94854			−0.974268	+	0.225392i	$0.927634\pi$
$194$	−17.1835	−	5.89200i	−1.23371	−	0.423021i
$195$		0			0
$196$	5.79911	−	7.46209i	0.414222	−	0.533006i
$197$	0.234504	−	0.0971345i	0.0167077	−	0.00692055i	−0.374314	−	0.927302i	$-0.622122\pi$
$197$	0.234504	−	0.0971345i	0.0167077	−	0.00692055i	0.391022	+	0.920381i	$0.372122\pi$
$198$		0			0
$199$	−2.87064	−	2.87064i	−0.203494	−	0.203494i	0.598001	−	0.801495i	$-0.295962\pi$
$199$	−2.87064	−	2.87064i	−0.203494	−	0.203494i	−0.801495	+	0.598001i	$0.795962\pi$
$200$	−9.81728	−	2.04709i	−0.694187	−	0.144751i
$201$		0			0
$202$	0.297983	−	0.0186110i	0.0209660	−	0.00130946i
$203$	−14.3725	+	5.95328i	−1.00875	+	0.417838i
$204$		0			0
$205$	5.59377	−	13.5045i	0.390686	−	0.943199i
$206$	−6.61922	−	13.5271i	−0.461183	−	0.942480i
$207$		0			0
$208$	17.3329	+	2.49914i	1.20182	+	0.173284i
$209$	20.0501			1.38689
$210$		0			0
$211$	21.3966	+	8.86277i	1.47300	+	0.610138i	0.967542	−	0.252710i	$-0.0813219\pi$
$211$	21.3966	+	8.86277i	1.47300	+	0.610138i	0.505462	+	0.862849i	$0.331322\pi$
$212$	0.749072	−	2.72836i	0.0514465	−	0.187384i
$213$		0			0
$214$	9.82618	−	0.613708i	0.671704	−	0.0419522i
$215$	18.2755	+	18.2755i	1.24638	+	1.24638i
$216$		0			0
$217$	4.52021	−	4.52021i	0.306852	−	0.306852i
$218$	11.9686	−	13.5633i	0.810618	−	0.918620i
$219$		0			0
$220$	−33.2481	+	4.16937i	−2.24158	+	0.281099i
$221$	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	$0.932048\pi$
$224$	−6.50026	+	5.52614i	−0.434317	+	0.369231i
$225$		0			0
$226$	1.31578	+	0.451162i	0.0875241	+	0.0300108i
$227$	−6.62883	−	2.74575i	−0.439971	−	0.182242i	0.151691	−	0.988428i	$-0.451528\pi$
$227$	−6.62883	−	2.74575i	−0.439971	−	0.182242i	−0.591662	+	0.806186i	$0.701528\pi$
$228$		0			0
$229$	−2.56839	−	6.20065i	−0.169724	−	0.409751i	0.816015	−	0.578031i	$-0.196179\pi$
$229$	−2.56839	−	6.20065i	−0.169724	−	0.409751i	−0.985739	+	0.168280i	$0.946179\pi$
$230$	3.08218	+	2.71981i	0.203233	+	0.179339i
$231$		0			0
$232$	−28.6647	+	5.42741i	−1.88193	+	0.356327i
$233$	4.72679	−	4.72679i	0.309662	−	0.309662i	−0.535116	−	0.844779i	$-0.679732\pi$
$233$	4.72679	−	4.72679i	0.309662	−	0.309662i	0.844779	+	0.535116i	$0.179732\pi$
$234$		0			0
$235$	−4.85145	−	11.7124i	−0.316474	−	0.764035i
$236$	−5.06552	+	18.4502i	−0.329737	+	1.20101i
$237$		0			0
$238$	3.22952	+	6.59989i	0.209339	+	0.427808i
$239$			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	$0.225048\pi$
$241$			20.1679i			1.29913i	−0.760308	+	0.649563i	$0.774952\pi$
$242$	−27.7530	+	13.5804i	−1.78403	+	0.872979i
$243$		0			0
$244$	−2.11167	−	3.71002i	−0.135186	−	0.237510i
$245$	5.28612	+	12.7618i	0.337718	+	0.815322i
$246$		0			0
$247$	10.8300	−	10.8300i	0.689095	−	0.689095i
$248$	10.0288	−	6.56806i	0.636830	−	0.417072i
$249$		0			0
$250$	−3.97836	+	4.50842i	−0.251614	+	0.285137i
$251$	0.288817	+	0.697266i	0.0182300	+	0.0440110i	0.932732	−	0.360569i	$-0.117418\pi$
$251$	0.288817	+	0.697266i	0.0182300	+	0.0440110i	−0.914502	+	0.404580i	$0.867418\pi$
$252$		0			0
$253$	5.26491	+	2.18080i	0.331002	+	0.137105i
$254$	−2.44379	+	7.12712i	−0.153337	+	0.447195i
$255$		0			0
$256$	−14.0490	+	7.65681i	−0.878060	+	0.478550i
$257$		−	6.89560i		−	0.430136i	−0.976599	−	0.215068i	$-0.931003\pi$
$257$		−	6.89560i		−	0.430136i	0.976599	−	0.215068i	$-0.0689973\pi$
$258$		0			0
$259$	−3.08582	+	7.44983i	−0.191743	+	0.462910i
$260$	−15.7068	+	20.2109i	−0.974091	+	1.25343i
$261$		0			0
$262$	−20.3179	−	17.9292i	−1.25525	−	1.10767i
$263$	3.11571	−	3.11571i	0.192123	−	0.192123i	−0.604490	−	0.796613i	$-0.706623\pi$
$263$	3.11571	−	3.11571i	0.192123	−	0.192123i	0.796613	+	0.604490i	$0.206623\pi$
$264$		0			0
$265$	2.92420	+	2.92420i	0.179632	+	0.179632i
$266$	0.465130	+	7.44728i	0.0285190	+	0.456622i
$267$		0			0
$268$	−16.1628	+	9.19958i	−0.987303	+	0.561954i
$269$	12.4085	+	5.13977i	0.756560	+	0.313378i	0.727415	−	0.686198i	$-0.240721\pi$
$269$	12.4085	+	5.13977i	0.756560	+	0.313378i	0.0291452	+	0.999575i	$0.490721\pi$
$270$		0			0
$271$	5.94627			0.361210			0.180605	−	0.983556i	$-0.442194\pi$
$271$	5.94627			0.361210			0.180605	+	0.983556i	$0.442194\pi$
$272$	3.40242	+	13.3527i	0.206302	+	0.809627i
$273$		0			0
$274$	18.1059	−	8.85974i	1.09382	−	0.535237i
$275$	7.77645	−	18.7740i	0.468938	−	1.13212i
$276$		0			0
$277$	−8.48544	+	3.51479i	−0.509841	+	0.211183i	−0.622748	−	0.782423i	$-0.713984\pi$
$277$	−8.48544	+	3.51479i	−0.509841	+	0.211183i	0.112907	+	0.993606i	$0.463984\pi$
$278$	1.05362	+	16.8696i	0.0631917	+	1.01177i
$279$		0			0
$280$	−2.31995	−	12.2527i	−0.138643	−	0.732241i
$281$	12.5190	+	12.5190i	0.746823	+	0.746823i	0.973881	−	0.227058i	$-0.0729107\pi$
$281$	12.5190	+	12.5190i	0.746823	+	0.746823i	−0.227058	+	0.973881i	$0.572911\pi$
$282$		0			0
$283$	−16.8466	+	6.97810i	−1.00143	+	0.414805i	−0.822321	−	0.569024i	$-0.807321\pi$
$283$	−16.8466	+	6.97810i	−1.00143	+	0.414805i	−0.179107	+	0.983830i	$0.557321\pi$
$284$	−4.95340	+	0.621166i	−0.293930	+	0.0368594i
$285$		0			0
$286$	−11.5096	+	33.5669i	−0.680579	+	1.98485i
$287$	7.54153			0.445162
$288$		0			0
$289$	−5.13305			−0.301944
$290$	13.8309	−	40.3366i	0.812177	−	2.36865i
$291$		0			0
$292$	−0.409447	−	3.26508i	−0.0239611	−	0.191074i
$293$	1.86190	−	0.771224i	0.108773	−	0.0450554i	−0.327633	−	0.944805i	$-0.606251\pi$
$293$	1.86190	−	0.771224i	0.108773	−	0.0450554i	0.436406	+	0.899750i	$0.356251\pi$
$294$		0			0
$295$	−19.7746	−	19.7746i	−1.15132	−	1.15132i
$296$	−8.51696	+	12.4955i	−0.495038	+	0.726285i
$297$		0			0
$298$	0.570135	+	9.12852i	0.0330270	+	0.528801i
$299$	4.02177	−	1.66587i	0.232585	−	0.0963398i
$300$		0			0
$301$	−5.10292	+	12.3195i	−0.294127	+	0.710086i
$302$	9.49462	−	4.64599i	0.546354	−	0.267347i
$303$		0			0
$304$	−1.99698	+	13.8502i	−0.114534	+	0.794361i
$305$	6.23959			0.357278
$306$		0			0
$307$	−3.70099	−	1.53300i	−0.211227	−	0.0874930i	0.274561	−	0.961570i	$-0.411467\pi$
$307$	−3.70099	−	1.53300i	−0.211227	−	0.0874930i	−0.485788	+	0.874077i	$0.661467\pi$
$308$	−8.55186	−	15.0249i	−0.487288	−	0.856121i
$309$		0			0
$310$	1.09226	+	17.4884i	0.0620362	+	0.993272i
$311$	9.17785	+	9.17785i	0.520428	+	0.520428i	0.917701	−	0.397273i	$-0.130043\pi$
$311$	9.17785	+	9.17785i	0.520428	+	0.520428i	−0.397273	+	0.917701i	$0.630043\pi$
$312$		0			0
$313$	−8.66154	+	8.66154i	−0.489579	+	0.489579i	−0.908173	−	0.418594i	$-0.862523\pi$
$313$	−8.66154	+	8.66154i	−0.489579	+	0.489579i	0.418594	+	0.908173i	$0.362523\pi$
$314$	−22.8899	−	20.1987i	−1.29175	−	1.13988i
$315$		0			0
$316$	22.8619	+	17.7669i	1.28608	+	0.999469i
$317$	−7.41379	+	17.8985i	−0.416400	+	1.00528i	0.566982	+	0.823730i	$0.308111\pi$
$317$	−7.41379	+	17.8985i	−0.416400	+	1.00528i	−0.983382	+	0.181548i	$0.941889\pi$
$318$		0			0
$319$		−	59.1159i		−	3.30986i
$320$	0.431378	−	23.3823i	0.0241148	−	1.30711i
$321$		0			0
$322$	−0.687884	+	2.00616i	−0.0383343	+	0.111799i
$323$	11.1339	+	4.61182i	0.619507	+	0.256608i
$324$		0			0
$325$	−5.94030	−	14.3411i	−0.329508	−	0.795503i
$326$	−11.6345	+	13.1846i	−0.644374	+	0.730226i
$327$		0			0
$328$	13.8451	+	2.88697i	0.764469	+	0.159406i
$329$	4.62500	−	4.62500i	0.254984	−	0.254984i
$330$		0			0
$331$	−3.96293	−	9.56736i	−0.217822	−	0.525870i	0.776763	−	0.629793i	$-0.216860\pi$
$331$	−3.96293	−	9.56736i	−0.217822	−	0.525870i	−0.994585	+	0.103923i	$0.966860\pi$
$332$	19.4050	−	11.0450i	1.06499	−	0.606171i
$333$		0			0
$334$	24.2003	−	11.8419i	1.32418	−	0.647960i
$335$		−	27.1830i		−	1.48517i
$336$		0			0
$337$		−	7.50723i		−	0.408945i	−0.978872	−	0.204472i	$-0.934452\pi$
$337$		−	7.50723i		−	0.408945i	0.978872	−	0.204472i	$-0.0655479\pi$
$338$	3.83350	+	7.83420i	0.208515	+	0.426124i
$339$		0			0
$340$	−19.4218	−	5.33227i	−1.05330	−	0.289183i
$341$	9.29611	+	22.4428i	0.503413	+	1.21535i
$342$		0			0
$343$	−12.5047	+	12.5047i	−0.675190	+	0.675190i
$344$	−14.0842	+	20.6634i	−0.759371	+	1.11410i
$345$		0			0
$346$	1.70625	+	1.50565i	0.0917286	+	0.0809441i
$347$	1.18203	+	2.85368i	0.0634548	+	0.153194i	0.952426	−	0.304769i	$-0.0985793\pi$
$347$	1.18203	+	2.85368i	0.0634548	+	0.153194i	−0.888971	+	0.457963i	$0.848579\pi$
$348$		0			0
$349$	3.41473	+	1.41443i	0.182786	+	0.0757126i	0.472200	−	0.881492i	$-0.343460\pi$
$349$	3.41473	+	1.41443i	0.182786	+	0.0757126i	−0.289413	+	0.957204i	$0.593460\pi$
$350$	7.15371	+	2.45291i	0.382382	+	0.131114i
$351$		0			0
$352$	−9.94829	−	30.8571i	−0.530245	−	1.64469i
$353$			6.81226i			0.362580i	0.983430	+	0.181290i	$0.0580273\pi$
$353$			6.81226i			0.362580i	−0.983430	+	0.181290i	$0.941973\pi$
$354$		0			0
$355$	2.79236	−	6.74136i	0.148203	−	0.357794i
$356$	−2.81365	−	22.4370i	−0.149123	−	1.18916i
$357$		0			0
$358$	−0.461884	+	0.523423i	−0.0244114	+	0.0276638i
$359$	5.31414	−	5.31414i	0.280469	−	0.280469i	−0.552827	−	0.833296i	$-0.686451\pi$
$359$	5.31414	−	5.31414i	0.280469	−	0.280469i	0.833296	+	0.552827i	$0.186451\pi$
$360$		0			0
$361$	−4.78116	−	4.78116i	−0.251640	−	0.251640i
$362$	30.9044	−	1.93018i	1.62430	−	0.101448i
$363$		0			0
$364$	−12.7349	−	3.49637i	−0.667489	−	0.183260i
$365$	4.44363	+	1.84061i	0.232590	+	0.0963420i
$366$		0			0
$367$	29.3775			1.53349			0.766745	−	0.641951i	$-0.221875\pi$
$367$	29.3775			1.53349			0.766745	+	0.641951i	$0.221875\pi$
$368$	−2.03083	+	3.41968i	−0.105864	+	0.178263i
$369$		0			0
$370$	−9.71491	−	19.8535i	−0.505054	−	1.03214i
$371$	−0.816501	+	1.97121i	−0.0423906	+	0.102340i
$372$		0			0
$373$	14.6798	−	6.08058i	0.760092	−	0.314840i	0.0312402	−	0.999512i	$-0.490054\pi$
$373$	14.6798	−	6.08058i	0.760092	−	0.314840i	0.728852	+	0.684671i	$0.240054\pi$
$374$	−27.8672	+	1.74048i	−1.44098	+	0.0899982i
$375$		0			0
$376$	10.2613	−	6.72031i	0.529186	−	0.346574i
$377$	−31.9312	−	31.9312i	−1.64454	−	1.64454i
$378$		0			0
$379$	−1.25001	+	0.517769i	−0.0642085	+	0.0265960i	−0.414557	−	0.910024i	$-0.636063\pi$
$379$	−1.25001	+	0.517769i	−0.0642085	+	0.0265960i	0.350348	+	0.936620i	$0.386063\pi$
$380$	−16.1498	−	12.5507i	−0.828469	−	0.643839i
$381$		0			0
$382$	31.1777	+	10.6904i	1.59519	+	0.546969i
$383$	35.2581			1.80160			0.900802	−	0.434230i	$-0.142980\pi$
$383$	35.2581			1.80160			0.900802	+	0.434230i	$0.142980\pi$
$384$		0			0
$385$	25.2691			1.28783
$386$	36.2130	+	12.4170i	1.84319	+	0.632006i
$387$		0			0
$388$	20.2847	+	15.7641i	1.02980	+	0.800303i
$389$	3.34556	−	1.38578i	0.169627	−	0.0702616i	−0.296254	−	0.955109i	$-0.595738\pi$
$389$	3.34556	−	1.38578i	0.169627	−	0.0702616i	0.465881	+	0.884848i	$0.345738\pi$
$390$		0			0
$391$	2.42201	+	2.42201i	0.122486	+	0.122486i
$392$	−11.1807	+	7.32242i	−0.564708	+	0.369838i
$393$		0			0
$394$	−0.358264	+	0.0223759i	−0.0180491	+	0.00112728i
$395$	−39.0988	+	16.1953i	−1.96728	+	0.814872i
$396$		0			0
$397$	−2.21822	+	5.35526i	−0.111329	+	0.268773i	−0.969718	−	0.244227i	$-0.921466\pi$
$397$	−2.21822	+	5.35526i	−0.111329	+	0.268773i	0.858389	+	0.513000i	$0.171466\pi$
$398$	2.52346	+	5.15698i	0.126490	+	0.258496i
$399$		0			0
$400$	12.1941	+	7.24168i	0.609707	+	0.362084i
$401$	−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
$404$	−0.407166	−	0.111788i	−0.0202573	−	0.00556164i
$405$		0			0
$406$	21.9577	−	1.37140i	1.08974	−	0.0680612i
$407$	−21.6672	−	21.6672i	−1.07401	−	1.07401i
$408$		0			0
$409$	−5.91961	+	5.91961i	−0.292706	+	0.292706i	−0.838148	−	0.545443i	$-0.816362\pi$
$409$	−5.91961	+	5.91961i	−0.292706	+	0.292706i	0.545443	+	0.838148i	$0.316362\pi$
$410$	−13.6776	+	15.5000i	−0.675490	+	0.765488i
$411$		0			0
$412$	2.65003	+	21.1323i	0.130557	+	1.04111i
$413$	5.52150	−	13.3301i	0.271695	−	0.655931i
$414$		0			0
$415$			32.6357i			1.60203i
$416$	−22.0409	−	11.2938i	−1.08064	−	0.553726i
$417$		0			0
$418$	−26.8222	−	9.19696i	−1.31191	−	0.449838i
$419$	−30.7382	−	12.7322i	−1.50166	−	0.622007i	−0.527841	−	0.849343i	$-0.676998\pi$
$419$	−30.7382	−	12.7322i	−1.50166	−	0.622007i	−0.973816	+	0.227336i	$0.926998\pi$
$420$		0			0
$421$	7.98264	+	19.2718i	0.389050	+	0.939249i	0.990142	+	0.140069i	$0.0447326\pi$
$421$	7.98264	+	19.2718i	0.389050	+	0.939249i	−0.601092	+	0.799180i	$0.705267\pi$
$422$	−24.5582	−	21.6709i	−1.19547	−	1.05492i
$423$		0			0
$424$	−2.25357	+	3.30628i	−0.109443	+	0.160567i
$425$	8.63660	−	8.63660i	0.418937	−	0.418937i
$426$		0			0
$427$	1.23194	+	2.97417i	0.0596179	+	0.143930i
$428$	−13.4266	−	3.68627i	−0.648997	−	0.178183i
$429$		0			0
$430$	−16.0652	−	32.8312i	−0.774735	−	1.58326i
$431$			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	$-0.858127\pi$
$433$		−	17.9410i		−	0.862190i	0.902306	−	0.431095i	$-0.141873\pi$
$434$	−8.12037	+	3.97353i	−0.389790	+	0.190736i
$435$		0			0
$436$	−22.2326	+	12.6544i	−1.06475	+	0.606034i
$437$	1.33114	+	3.21366i	0.0636771	+	0.153730i
$438$		0			0
$439$	−8.96708	+	8.96708i	−0.427975	+	0.427975i	−0.887938	−	0.459963i	$-0.847863\pi$
$439$	−8.96708	+	8.96708i	−0.427975	+	0.427975i	0.459963	+	0.887938i	$0.347863\pi$
$440$	46.3903	+	9.67325i	2.21157	+	0.461154i
$441$		0			0
$442$	−14.1122	+	15.9925i	−0.671251	+	0.760684i
$443$	6.09257	+	14.7088i	0.289467	+	0.698835i	0.999988	−	0.00484090i	$-0.00154091\pi$
$443$	6.09257	+	14.7088i	0.289467	+	0.698835i	−0.710522	+	0.703675i	$0.751541\pi$
$444$		0			0
$445$	30.5358	+	12.6484i	1.44754	+	0.599589i
$446$	2.90241	−	8.46464i	0.137433	−	0.400812i
$447$		0			0
$448$	11.2306	−	4.41097i	0.530596	−	0.208399i
$449$			3.66413i			0.172921i	0.996255	+	0.0864604i	$0.0275556\pi$
$449$			3.66413i			0.172921i	−0.996255	+	0.0864604i	$0.972444\pi$
$450$		0			0
$451$	−10.9670	+	26.4766i	−0.516415	+	1.24674i
$452$	−1.55324	−	1.20709i	−0.0730583	−	0.0567767i
$453$		0			0
$454$	7.60829	+	6.71379i	0.357075	+	0.315094i
$455$	13.6490	−	13.6490i	0.639876	−	0.639876i
$456$		0			0
$457$	−13.9728	−	13.9728i	−0.653622	−	0.653622i	0.300241	−	0.953863i	$-0.402933\pi$
$457$	−13.9728	−	13.9728i	−0.653622	−	0.653622i	−0.953863	+	0.300241i	$0.902933\pi$
$458$	0.591655	+	9.47309i	0.0276462	+	0.442648i
$459$		0			0
$460$	−2.87564	−	5.05224i	−0.134077	−	0.235562i
$461$	2.25638	+	0.934623i	0.105090	+	0.0435297i	0.434609	−	0.900619i	$-0.356887\pi$
$461$	2.25638	+	0.934623i	0.105090	+	0.0435297i	−0.329519	+	0.944149i	$0.606887\pi$
$462$		0			0
$463$	16.4302			0.763575			0.381788	−	0.924250i	$-0.375309\pi$
$463$	16.4302			0.763575			0.381788	+	0.924250i	$0.375309\pi$
$464$	40.8360	+	5.88791i	1.89576	+	0.273339i
$465$		0			0
$466$	−8.49148	+	4.15513i	−0.393360	+	0.192482i
$467$	−8.14599	+	19.6662i	−0.376951	+	0.910041i	0.615582	+	0.788072i	$0.288921\pi$
$467$	−8.14599	+	19.6662i	−0.376951	+	0.910041i	−0.992534	+	0.121969i	$0.961079\pi$
$468$		0			0
$469$	12.9571	−	5.36700i	0.598303	−	0.247825i
$470$	1.11758	+	17.8938i	0.0515501	+	0.825377i
$471$		0			0
$472$	15.2395	−	22.3584i	0.701456	−	1.02913i
$473$	−35.8304	−	35.8304i	−1.64748	−	1.64748i
$474$		0			0
$475$	11.4595	−	4.74669i	0.525799	−	0.217793i
$476$	−1.29295	−	10.3104i	−0.0592622	−	0.472578i
$477$		0			0
$478$	2.64614	−	7.71724i	0.121032	−	0.352978i
$479$	4.35772			0.199109			0.0995545	−	0.995032i	$-0.468258\pi$
$479$	4.35772			0.199109			0.0995545	+	0.995032i	$0.468258\pi$
$480$		0			0
$481$	−23.4070			−1.06727
$482$	9.25098	−	26.9797i	0.421370	−	1.22889i
$483$		0			0
$484$	43.3562	−	5.43695i	1.97073	−	0.247134i
$485$	−34.6914	+	14.3696i	−1.57525	+	0.652491i
$486$		0			0
$487$	10.1865	+	10.1865i	0.461594	+	0.461594i	0.899178	−	0.437584i	$-0.144166\pi$
$487$	10.1865	+	10.1865i	0.461594	+	0.461594i	−0.437584	+	0.899178i	$0.644166\pi$
$488$	1.12312	+	5.93174i	0.0508414	+	0.268517i
$489$		0			0
$490$	−1.21771	−	19.4969i	−0.0550105	−	0.880782i
$491$	28.0848	−	11.6331i	1.26745	−	0.524994i	0.355260	−	0.934768i	$-0.384392\pi$
$491$	28.0848	−	11.6331i	1.26745	−	0.524994i	0.912187	+	0.409774i	$0.134392\pi$
$492$		0			0
$493$	13.5975	−	32.8273i	0.612402	−	1.47847i
$494$	−19.4556	+	9.52019i	−0.875349	+	0.428333i
$495$		0			0
$496$	−16.4289	+	4.18626i	−0.737679	+	0.187969i
$497$	3.76467			0.168869
$498$		0			0
$499$	−20.5327	−	8.50493i	−0.919170	−	0.380733i	−0.127610	−	0.991824i	$-0.540731\pi$
$499$	−20.5327	−	8.50493i	−0.919170	−	0.380733i	−0.791560	+	0.611092i	$0.790731\pi$
$500$	7.39009	−	4.20630i	0.330495	−	0.188111i
$501$		0			0
$502$	−0.0665318	−	1.06525i	−0.00296946	−	0.0475446i
$503$	6.66355	+	6.66355i	0.297113	+	0.297113i	0.839882	−	0.542769i	$-0.182624\pi$
$503$	6.66355	+	6.66355i	0.297113	+	0.297113i	−0.542769	+	0.839882i	$0.682624\pi$
$504$		0			0
$505$	0.436393	−	0.436393i	0.0194192	−	0.0194192i
$506$	−6.04284	−	5.33238i	−0.268637	−	0.237053i
$507$		0			0
$508$	6.53841	−	8.41339i	0.290095	−	0.373284i
$509$	4.13590	−	9.98494i	0.183320	−	0.442575i	−0.805327	−	0.592831i	$-0.798010\pi$
$509$	4.13590	−	9.98494i	0.183320	−	0.442575i	0.988647	+	0.150257i	$0.0480101\pi$
$510$		0			0
$511$			2.48152i			0.109776i
$512$	22.3063	−	3.79870i	0.985807	−	0.167881i
$513$		0			0
$514$	−3.16301	+	9.22464i	−0.139514	+	0.406882i
$515$	−28.7601	−	11.9128i	−1.26732	−	0.524942i
$516$		0			0
$517$	9.51161	+	22.9631i	0.418320	+	1.00991i
$518$	7.54531	−	8.55060i	0.331522	−	0.375692i
$519$		0			0
$520$	30.2825	−	19.8326i	1.32798	−	0.869717i
$521$	−2.91587	+	2.91587i	−0.127746	+	0.127746i	−0.768089	−	0.640343i	$-0.778792\pi$
$521$	−2.91587	+	2.91587i	−0.127746	+	0.127746i	0.640343	+	0.768089i	$0.278792\pi$
$522$		0			0
$523$	14.2159	+	34.3201i	0.621616	+	1.50071i	0.849805	+	0.527097i	$0.176720\pi$
$523$	14.2159	+	34.3201i	0.621616	+	1.50071i	−0.228189	+	0.973617i	$0.573280\pi$
$524$	18.9564	+	33.3047i	0.828113	+	1.45492i
$525$		0			0
$526$	−5.59724	+	2.73889i	−0.244051	+	0.119421i
$527$			14.6008i			0.636023i
$528$		0			0
$529$		−	22.0113i		−	0.957015i
$530$	−2.57055	−	5.25320i	−0.111657	−	0.228185i
$531$		0			0
$532$	2.79383	−	10.1760i	0.121128	−	0.441186i
$533$	8.37748	+	20.2250i	0.362869	+	0.876043i
$534$		0			0
$535$	14.3903	−	14.3903i	0.622149	−	0.622149i
$536$	25.8418	−	4.89292i	1.11620	−	0.211342i
$537$		0			0
$538$	−14.2420	−	12.5675i	−0.614015	−	0.541825i
$539$	−10.3638	−	25.0204i	−0.446401	−	1.07771i
$540$		0			0
$541$	−29.5435	−	12.2373i	−1.27017	−	0.526123i	−0.357157	−	0.934044i	$-0.616254\pi$
$541$	−29.5435	−	12.2373i	−1.27017	−	0.526123i	−0.913017	+	0.407921i	$0.866254\pi$
$542$	−7.95467	−	2.72755i	−0.341682	−	0.117158i
$543$		0			0
$544$	1.57327	−	19.4234i	0.0674533	−	0.832770i
$545$		−	37.3912i		−	1.60166i
$546$		0			0
$547$	−11.8740	+	28.6664i	−0.507696	+	1.22569i	0.437510	+	0.899213i	$0.355860\pi$
$547$	−11.8740	+	28.6664i	−0.507696	+	1.22569i	−0.945206	+	0.326474i	$0.894140\pi$
$548$	−28.2853	+	3.54703i	−1.20829	+	0.151521i
$549$		0			0
$550$	−19.0146	+	21.5480i	−0.810787	+	0.918811i
$551$	25.5152	−	25.5152i	1.08698	−	1.08698i
$552$		0			0
$553$	−15.4393	−	15.4393i	−0.656546	−	0.656546i
$554$	12.9637	−	0.809665i	0.550775	−	0.0343994i
$555$		0			0
$556$	6.32860	−	23.0508i	0.268392	−	0.977570i
$557$	−16.2393	−	6.72656i	−0.688083	−	0.285013i	0.0111181	−	0.999938i	$-0.496461\pi$
$557$	−16.2393	−	6.72656i	−0.688083	−	0.285013i	−0.699201	+	0.714925i	$0.746461\pi$
$558$		0			0
$559$	−38.7074			−1.63715
$560$	−2.51679	+	17.4553i	−0.106354	+	0.737623i
$561$		0			0
$562$	−11.0050	−	22.4899i	−0.464216	−	0.948679i
$563$	−15.7698	+	38.0718i	−0.664620	+	1.60453i	0.125862	+	0.992048i	$0.459830\pi$
$563$	−15.7698	+	38.0718i	−0.664620	+	1.60453i	−0.790481	+	0.612486i	$0.790170\pi$
$564$		0			0
$565$	2.65638	−	1.10031i	0.111755	−	0.0462904i
$566$	25.7375	−	1.60747i	1.08183	−	0.0675672i
$567$		0			0
$568$	6.91137	+	1.44115i	0.289995	+	0.0604693i
$569$	11.0276	+	11.0276i	0.462302	+	0.462302i	0.899409	−	0.437107i	$-0.143997\pi$
$569$	11.0276	+	11.0276i	0.462302	+	0.462302i	−0.437107	+	0.899409i	$0.643997\pi$
$570$		0			0
$571$	−31.3409	+	12.9818i	−1.31157	+	0.543272i	−0.925343	−	0.379130i	$-0.876223\pi$
$571$	−31.3409	+	12.9818i	−1.31157	+	0.543272i	−0.386231	+	0.922402i	$0.626223\pi$
$572$	30.7942	−	39.6249i	1.28757	−	1.65680i
$573$		0			0
$574$	−10.0887	−	3.45929i	−0.421096	−	0.144388i
$575$	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	$0.515154\pi$
$578$	6.86677	+	2.35452i	0.285620	+	0.0979353i
$579$		0			0
$580$	−37.0047	+	47.6164i	−1.53654	+	1.97716i
$581$	−15.5562	+	6.44359i	−0.645380	+	0.267325i
$582$		0			0
$583$	−5.73311	−	5.73311i	−0.237441	−	0.237441i
$584$	−0.949947	+	4.55569i	−0.0393091	+	0.188516i
$585$		0			0
$586$	−2.84453	+	0.177659i	−0.117506	+	0.00733903i
$587$	−5.89005	+	2.43974i	−0.243108	+	0.100699i	−0.500911	−	0.865499i	$-0.667002\pi$
$587$	−5.89005	+	2.43974i	−0.243108	+	0.100699i	0.257803	+	0.966198i	$0.417002\pi$
$588$		0			0
$589$	−5.67428	+	13.6989i	−0.233805	+	0.564454i
$590$	17.3830	+	35.5242i	0.715648	+	1.46251i
$591$		0			0
$592$	17.1253	−	12.8092i	0.703845	−	0.526455i
$593$	−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
$596$	3.42454	−	12.4733i	0.140275	−	0.510925i
$597$		0			0
$598$	−6.14429	+	0.383750i	−0.251259	+	0.0156927i
$599$	3.54515	+	3.54515i	0.144851	+	0.144851i	0.775813	−	0.630962i	$-0.217340\pi$
$599$	3.54515	+	3.54515i	0.144851	+	0.144851i	−0.630962	+	0.775813i	$0.717340\pi$
$600$		0			0
$601$	0.844578	−	0.844578i	0.0344511	−	0.0344511i	−0.689671	−	0.724122i	$-0.742245\pi$
$601$	0.844578	−	0.844578i	0.0344511	−	0.0344511i	0.724122	+	0.689671i	$0.242245\pi$
$602$	12.4774	−	14.1398i	0.508542	−	0.576297i
$603$		0			0
$604$	−14.8326	+	1.86004i	−0.603531	+	0.0756839i
$605$	−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	$0.881065\pi$
$608$	9.02453	−	17.6121i	0.365993	−	0.714266i
$609$		0			0
$610$	−8.34706	−	2.86210i	−0.337963	−	0.115883i
$611$	17.5411	+	7.26575i	0.709636	+	0.293941i
$612$		0			0
$613$	−6.72419	−	16.2336i	−0.271588	−	0.655671i	0.727964	−	0.685615i	$-0.240467\pi$
$613$	−6.72419	−	16.2336i	−0.271588	−	0.655671i	−0.999552	+	0.0299448i	$0.990467\pi$
$614$	4.24784	+	3.74843i	0.171429	+	0.151274i
$615$		0			0
$616$	4.54842	+	24.0224i	0.183261	+	0.967888i
$617$	−8.70935	+	8.70935i	−0.350625	+	0.350625i	−0.860342	−	0.509717i	$-0.829750\pi$
$617$	−8.70935	+	8.70935i	−0.350625	+	0.350625i	0.509717	+	0.860342i	$0.329750\pi$
$618$		0			0
$619$	−3.38639	−	8.17546i	−0.136110	−	0.328600i	0.841098	−	0.540883i	$-0.181910\pi$
$619$	−3.38639	−	8.17546i	−0.136110	−	0.328600i	−0.977208	+	0.212284i	$0.931910\pi$
$620$	6.56071	−	23.8962i	0.263485	−	0.959694i
$621$		0			0
$622$	−8.06786	−	16.4876i	−0.323492	−	0.661093i
$623$			17.0525i			0.683195i
$624$		0			0
$625$			30.1567i			1.20627i
$626$	15.5601	−	7.61400i	0.621906	−	0.304317i
$627$		0			0
$628$	21.3559	+	37.5205i	0.852195	+	1.49723i
$629$	−7.04814	−	17.0157i	−0.281028	−	0.678461i
$630$		0			0
$631$	2.69060	−	2.69060i	0.107111	−	0.107111i	−0.651520	−	0.758631i	$-0.725868\pi$
$631$	2.69060	−	2.69060i	0.107111	−	0.107111i	0.758631	+	0.651520i	$0.225868\pi$
$632$	−22.4340	−	34.2546i	−0.892375	−	1.36257i
$633$		0			0
$634$	18.1279	−	20.5431i	0.719949	−	0.815871i
$635$	5.96002	+	14.3888i	0.236516	+	0.571000i
$636$		0			0
$637$	−19.1127	−	7.91673i	−0.757272	−	0.313672i
$638$	−27.1164	+	79.0827i	−1.07355	+	3.13092i
$639$		0			0
$640$	−11.3025	+	31.0820i	−0.446771	+	1.22862i
$641$		−	37.2166i		−	1.46997i	−0.678084	−	0.734984i	$-0.737189\pi$
$641$		−	37.2166i		−	1.46997i	0.678084	−	0.734984i	$-0.262811\pi$
$642$		0			0
$643$	−11.0037	+	26.5652i	−0.433942	+	1.04763i	0.544063	+	0.839044i	$0.316885\pi$
$643$	−11.0037	+	26.5652i	−0.433942	+	1.04763i	−0.978005	+	0.208583i	$0.933115\pi$
$644$	1.84044	−	2.36822i	0.0725237	−	0.0933209i
$645$		0			0
$646$	−12.7790	−	11.2766i	−0.502784	−	0.443672i
$647$	−30.0988	+	30.0988i	−1.18331	+	1.18331i	−0.204426	+	0.978882i	$0.565533\pi$
$647$	−30.0988	+	30.0988i	−1.18331	+	1.18331i	−0.978882	+	0.204426i	$0.934467\pi$
$648$		0			0
$649$	38.7695	+	38.7695i	1.52184	+	1.52184i
$650$	1.36841	+	21.9098i	0.0536733	+	0.859372i
$651$		0			0
$652$	21.6119	−	12.3011i	0.846386	−	0.481746i
$653$	4.00245	+	1.65787i	0.156628	+	0.0648775i	0.459620	−	0.888116i	$-0.347986\pi$
$653$	4.00245	+	1.65787i	0.156628	+	0.0648775i	−0.302992	+	0.952993i	$0.597986\pi$
$654$		0			0
$655$	−56.0125			−2.18859
$656$	−17.1972	−	10.2128i	−0.671436	−	0.398743i
$657$		0			0
$658$	−8.30861	+	4.06564i	−0.323903	+	0.158495i
$659$	2.32569	−	5.61472i	0.0905962	−	0.218719i	−0.872086	−	0.489352i	$-0.837233\pi$
$659$	2.32569	−	5.61472i	0.0905962	−	0.218719i	0.962682	+	0.270634i	$0.0872332\pi$
$660$		0			0
$661$	37.0965	−	15.3659i	1.44288	−	0.597662i	0.482389	−	0.875957i	$-0.339769\pi$
$661$	37.0965	−	15.3659i	1.44288	−	0.597662i	0.960496	+	0.278295i	$0.0897692\pi$
$662$	0.912900	+	14.6166i	0.0354809	+	0.568090i
$663$		0			0
$664$	−31.0255	+	5.87441i	−1.20402	+	0.227971i
$665$	10.9065	+	10.9065i	0.422935	+	0.422935i
$666$		0			0
$667$	9.47519	−	3.92475i	0.366881	−	0.151967i
$668$	−37.8060	+	4.74095i	−1.46276	+	0.183433i
$669$		0			0
$670$	−12.4688	+	36.3643i	−0.481712	+	1.40487i
$671$	−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	$0.584554\pi$
$674$	−3.44356	+	10.0429i	−0.132641	+	0.386836i
$675$		0			0
$676$	−1.53475	−	12.2387i	−0.0590290	−	0.470718i
$677$	11.5314	−	4.77647i	0.443189	−	0.183575i	−0.149918	−	0.988698i	$-0.547901\pi$
$677$	11.5314	−	4.77647i	0.443189	−	0.183575i	0.593107	+	0.805124i	$0.297901\pi$
$678$		0			0
$679$	−13.6989	−	13.6989i	−0.525715	−	0.525715i
$680$	23.5358	+	16.0421i	0.902556	+	0.615185i
$681$		0			0
$682$	−2.14145	−	34.2872i	−0.0820004	−	1.31292i
$683$	37.0003	−	15.3260i	1.41578	−	0.586435i	0.461982	−	0.886889i	$-0.347138\pi$
$683$	37.0003	−	15.3260i	1.41578	−	0.586435i	0.953796	+	0.300454i	$0.0971383\pi$
$684$		0			0
$685$	15.9452	−	38.4950i	0.609233	−	1.47082i
$686$	22.4641	−	10.9924i	0.857685	−	0.419690i
$687$		0			0
$688$	28.3196	−	21.1822i	1.07967	−	0.807563i
$689$	−6.19344			−0.235951
$690$		0			0
$691$	6.40367	+	2.65249i	0.243607	+	0.100905i	0.501147	−	0.865362i	$-0.332912\pi$
$691$	6.40367	+	2.65249i	0.243607	+	0.100905i	−0.257539	+	0.966268i	$0.582912\pi$
$692$	−1.59191	−	2.79685i	−0.0605154	−	0.106320i
$693$		0			0
$694$	−0.272293	−	4.35973i	−0.0103361	−	0.165493i
$695$	24.7054	+	24.7054i	0.937129	+	0.937129i
$696$		0			0
$697$	−12.1800	+	12.1800i	−0.461352	+	0.461352i
$698$	−3.91929	−	3.45850i	−0.148347	−	0.130906i
$699$		0			0
$700$	−8.44478	−	6.56280i	−0.319183	−	0.248051i
$701$	7.95095	−	19.1953i	0.300303	−	0.724996i	−0.699642	−	0.714494i	$-0.746657\pi$
$701$	7.95095	−	19.1953i	0.300303	−	0.724996i	0.999945	−	0.0105021i	$-0.00334297\pi$
$702$		0			0
$703$		−	18.7037i		−	0.705424i
$704$	−0.845748	+	45.8426i	−0.0318753	+	1.72776i
$705$		0			0
$706$	3.12478	−	9.11315i	0.117603	−	0.342978i
$707$	0.294173	+	0.121850i	0.0110635	+	0.00458266i
$708$		0			0
$709$	0.602133	+	1.45368i	0.0226136	+	0.0545940i	0.934783	−	0.355219i	$-0.115594\pi$
$709$	0.602133	+	1.45368i	0.0226136	+	0.0545940i	−0.912169	+	0.409813i	$0.865594\pi$
$710$	−6.82776	+	7.73745i	−0.256241	+	0.290381i
$711$		0			0
$712$	−6.52786	+	31.3059i	−0.244642	+	1.17324i
$713$	−2.97999	+	2.97999i	−0.111602	+	0.111602i
$714$		0			0
$715$	28.0701	+	67.7673i	1.04976	+	2.53435i
$716$	0.857983	−	0.488347i	0.0320643	−	0.0182504i
$717$		0			0
$718$	−9.54662	+	4.67144i	−0.356277	+	0.174337i
$719$		−	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
$722$	4.20292	+	8.58915i	0.156416	+	0.319655i
$723$		0			0
$724$	−42.2279	−	11.5937i	−1.56939	−	0.430876i
$725$	−13.9952	−	33.7874i	−0.519768	−	1.25483i
$726$		0			0
$727$	−3.48345	+	3.48345i	−0.129194	+	0.129194i	−0.768747	−	0.639553i	$-0.779119\pi$
$727$	−3.48345	+	3.48345i	−0.129194	+	0.129194i	0.639553	+	0.768747i	$0.279119\pi$
$728$	15.4324	+	10.5188i	0.571963	+	0.389852i
$729$		0			0
$730$	−5.10021	−	4.50058i	−0.188767	−	0.166574i
$731$	−11.6553	−	28.1383i	−0.431086	−	1.04073i
$732$		0			0
$733$	−9.32567	−	3.86282i	−0.344452	−	0.142677i	0.203750	−	0.979023i	$-0.434687\pi$
$733$	−9.32567	−	3.86282i	−0.344452	−	0.142677i	−0.548201	+	0.836347i	$0.684687\pi$
$734$	−39.2999	−	13.4754i	−1.45059	−	0.497387i
$735$		0			0
$736$	4.28536	−	3.64316i	0.157960	−	0.134289i
$737$			53.2942i			1.96312i
$738$		0			0
$739$	18.2859	−	44.1460i	0.672657	−	1.62394i	−0.104421	−	0.994533i	$-0.533299\pi$
$739$	18.2859	−	44.1460i	0.672657	−	1.62394i	0.777078	−	0.629404i	$-0.216701\pi$
$740$	3.88940	+	31.0154i	0.142977	+	1.14015i
$741$		0			0
$742$	1.99647	−	2.26247i	0.0732928	−	0.0830579i
$743$	26.3660	−	26.3660i	0.967273	−	0.967273i	−0.0322079	−	0.999481i	$-0.510254\pi$
$743$	26.3660	−	26.3660i	0.967273	−	0.967273i	0.999481	+	0.0322079i	$0.0102539\pi$
$744$		0			0
$745$	13.3686	+	13.3686i	0.489789	+	0.489789i
$746$	−22.4272	+	1.40072i	−0.821118	+	0.0512841i
$747$		0			0
$748$	38.0779	+	10.4543i	1.39226	+	0.382247i
$749$	9.70055	+	4.01810i	0.354450	+	0.146818i
$750$		0			0
$751$	31.9193			1.16475			0.582377	−	0.812919i	$-0.302123\pi$
$751$	31.9193			1.16475			0.582377	+	0.812919i	$0.302123\pi$
$752$	−16.8097	+	4.28330i	−0.612988	+	0.156196i
$753$		0			0
$754$	28.0694	+	57.3631i	1.02223	+	2.08904i
$755$	8.36155	−	20.1866i	0.304308	−	0.734664i
$756$		0			0
$757$	25.8156	−	10.6932i	0.938284	−	0.388650i	0.139469	−	0.990226i	$-0.455461\pi$
$757$	25.8156	−	10.6932i	0.938284	−	0.388650i	0.798815	+	0.601577i	$0.205461\pi$
$758$	1.90970	−	0.119273i	0.0693636	−	0.00433220i
$759$		0			0
$760$	15.8476	+	24.1977i	0.574851	+	0.877745i
$761$	14.4436	+	14.4436i	0.523579	+	0.523579i	0.918650	−	0.395072i	$-0.129280\pi$
$761$	14.4436	+	14.4436i	0.523579	+	0.523579i	−0.395072	+	0.918650i	$0.629280\pi$
$762$		0			0
$763$	17.8229	−	7.38250i	0.645234	−	0.267265i
$764$	−36.8045	−	28.6024i	−1.33154	−	1.03480i
$765$		0			0
$766$	−47.1668	−	16.1729i	−1.70420	−	0.584349i
$767$	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	$0.372203\pi$
$770$	−33.8040	−	11.5909i	−1.21821	−	0.417708i
$771$		0			0
$772$	−42.7486	−	33.2217i	−1.53855	−	1.19568i
$773$	−5.45257	+	2.25853i	−0.196115	+	0.0812336i	−0.478580	−	0.878044i	$-0.658848\pi$
$773$	−5.45257	+	2.25853i	−0.196115	+	0.0812336i	0.282464	+	0.959278i	$0.408848\pi$
$774$		0			0
$775$	10.6263	+	10.6263i	0.381708	+	0.381708i
$776$	−19.9051	−	30.3932i	−0.714550	−	1.09105i
$777$		0			0
$778$	−5.11120	+	0.319227i	−0.183245	+	0.0114448i
$779$	−16.1611	+	6.69416i	−0.579033	+	0.239843i
$780$		0			0
$781$	−5.47463	+	13.2169i	−0.195898	+	0.472939i
$782$	−2.12909	−	4.35104i	−0.0761361	−	0.155593i
$783$		0			0
$784$	18.3158	−	4.66707i	0.654135	−	0.166681i
$785$	−63.1027			−2.25223
$786$		0			0
$787$	−38.9288	−	16.1249i	−1.38766	−	0.574789i	−0.441144	−	0.897436i	$-0.645427\pi$
$787$	−38.9288	−	16.1249i	−1.38766	−	0.574789i	−0.946519	+	0.322647i	$0.895427\pi$
$788$	0.489535	+	0.134402i	0.0174389	+	0.00478787i
$789$		0			0
$790$	59.7335	−	3.73074i	2.12522	−	0.132734i
$791$	1.04895	+	1.04895i	0.0372964	+	0.0372964i
$792$		0			0
$793$	−6.60770	+	6.60770i	−0.234646	+	0.234646i
$794$	5.42390	−	6.14654i	0.192487	−	0.218133i
$795$		0			0
$796$	−1.01028	−	8.05630i	−0.0358083	−	0.285548i
$797$	−13.4105	+	32.3759i	−0.475025	+	1.14681i	0.486890	+	0.873463i	$0.338131\pi$
$797$	−13.4105	+	32.3759i	−0.475025	+	1.14681i	−0.961915	+	0.273349i	$0.911869\pi$
$798$		0			0
$799$			14.9393i			0.528515i
$800$	−12.9911	−	15.2811i	−0.459303	−	0.540267i
$801$		0			0
$802$	7.99467	+	2.74126i	0.282301	+	0.0967974i
$803$	−8.71205	−	3.60865i	−0.307442	−	0.127346i
$804$		0			0
$805$	1.67764	+	4.05017i	0.0591289	+	0.142750i
$806$	−19.6768	−	17.3634i	−0.693085	−	0.611599i
$807$		0			0
$808$	0.493412	+	0.336311i	0.0173582	+	0.0118314i
$809$	23.3959	−	23.3959i	0.822557	−	0.822557i	−0.163917	−	0.986474i	$-0.552413\pi$
$809$	23.3959	−	23.3959i	0.822557	−	0.822557i	0.986474	+	0.163917i	$0.0524130\pi$
$810$		0			0
$811$	−14.5916	−	35.2272i	−0.512380	−	1.23699i	−0.942495	−	0.334221i	$-0.891527\pi$
$811$	−14.5916	−	35.2272i	−0.512380	−	1.23699i	0.430115	−	0.902774i	$-0.358473\pi$
$812$	−30.0031	−	8.23736i	−1.05290	−	0.289075i
$813$		0			0
$814$	19.0468	+	38.9243i	0.667589	+	1.36429i
$815$			36.3473i			1.27319i
$816$		0			0
$817$		−	30.9297i		−	1.08209i
$818$	10.6343	−	5.20368i	0.371820	−	0.181942i
$819$		0			0
$820$	25.4072	−	14.4613i	0.887257	−	0.505009i
$821$	−6.11371	−	14.7598i	−0.213370	−	0.515120i	0.780567	−	0.625072i	$-0.214930\pi$
$821$	−6.11371	−	14.7598i	−0.213370	−	0.515120i	−0.993937	+	0.109952i	$0.964930\pi$
$822$		0			0
$823$	17.5536	−	17.5536i	0.611879	−	0.611879i	−0.331557	−	0.943435i	$-0.607574\pi$
$823$	17.5536	−	17.5536i	0.611879	−	0.611879i	0.943435	+	0.331557i	$0.107574\pi$
$824$	6.14825	−	29.4854i	0.214185	−	1.02717i
$825$		0			0
$826$	−13.5009	+	15.2997i	−0.469757	+	0.532345i
$827$	4.15220	+	10.0243i	0.144386	+	0.348579i	0.979484	−	0.201522i	$-0.0645889\pi$
$827$	4.15220	+	10.0243i	0.144386	+	0.348579i	−0.835098	+	0.550102i	$0.814589\pi$
$828$		0			0
$829$	3.68500	+	1.52638i	0.127985	+	0.0530132i	0.445757	−	0.895154i	$-0.352935\pi$
$829$	3.68500	+	1.52638i	0.127985	+	0.0530132i	−0.317772	+	0.948167i	$0.602935\pi$
$830$	14.9700	−	43.6587i	0.519616	−	1.51542i
$831$		0			0
$832$	24.3049	+	25.2186i	0.842621	+	0.874297i
$833$		−	16.2778i		−	0.563992i
$834$		0			0
$835$	21.3123	−	51.4524i	0.737541	−	1.78058i
$836$	31.6629	+	24.6066i	1.09508	+	0.851037i
$837$		0			0
$838$	35.2800	+	31.1321i	1.21873	+	1.07544i
$839$	−4.96619	+	4.96619i	−0.171452	+	0.171452i	−0.787617	−	0.616165i	$-0.788685\pi$
$839$	−4.96619	+	4.96619i	−0.171452	+	0.171452i	0.616165	+	0.787617i	$0.288685\pi$
$840$		0			0
$841$	−54.7231	−	54.7231i	−1.88700	−	1.88700i
$842$	−1.83888	−	29.4426i	−0.0633719	−	1.01466i
$843$		0			0
$844$	22.9124	+	40.2551i	0.788679	+	1.38564i
$845$	16.6563	+	6.89927i	0.572995	+	0.237342i
$846$		0			0
$847$	−32.9514			−1.13223
$848$	4.53132	−	3.38929i	0.155606	−	0.116389i
$849$		0			0
$850$	−15.5153	+	7.59208i	−0.532170	+	0.260406i
$851$	2.03435	−	4.91137i	0.0697368	−	0.168359i
$852$		0			0
$853$	−7.27599	+	3.01381i	−0.249125	+	0.103191i	−0.503752	−	0.863848i	$-0.668047\pi$
$853$	−7.27599	+	3.01381i	−0.249125	+	0.103191i	0.254627	+	0.967039i	$0.418047\pi$
$854$	−0.283790	−	4.54381i	−0.00971110	−	0.155486i
$855$		0			0
$856$	16.2706	+	11.0901i	0.556117	+	0.379051i
$857$	36.1746	+	36.1746i	1.23570	+	1.23570i	0.961741	+	0.273961i	$0.0883341\pi$
$857$	36.1746	+	36.1746i	1.23570	+	1.23570i	0.273961	+	0.961741i	$0.411666\pi$
$858$		0			0
$859$	−28.2133	+	11.6863i	−0.962627	+	0.398733i	−0.807962	−	0.589234i	$-0.799430\pi$
$859$	−28.2133	+	11.6863i	−0.962627	+	0.398733i	−0.154664	+	0.987967i	$0.549430\pi$
$860$	6.43177	+	51.2892i	0.219322	+	1.74895i
$861$		0			0
$862$	13.3999	−	39.0796i	0.456402	−	1.33106i
$863$	−6.56021			−0.223312			−0.111656	−	0.993747i	$-0.535616\pi$
$863$	−6.56021			−0.223312			−0.111656	+	0.993747i	$0.535616\pi$
$864$		0			0
$865$	4.70379			0.159934
$866$	−8.22953	+	24.0007i	−0.279651	+	0.815578i
$867$		0			0
$868$	12.6857	−	1.59082i	0.430582	−	0.0539958i
$869$	76.6560	−	31.7520i	2.60038	−	1.07711i
$870$		0			0
$871$	28.7867	+	28.7867i	0.975399	+	0.975399i
$872$	35.5463	−	6.73039i	1.20375	−	0.227920i
$873$		0			0
$874$	−0.306642	−	4.90969i	−0.0103723	−	0.166073i
$875$	−5.92433	+	2.45394i	−0.200279	+	0.0829582i
$876$		0			0
$877$	−9.62481	+	23.2364i	−0.325007	+	0.784636i	0.673941	+	0.738785i	$0.264600\pi$
$877$	−9.62481	+	23.2364i	−0.325007	+	0.784636i	−0.998948	+	0.0458511i	$0.985400\pi$
$878$	16.1090	−	7.88259i	0.543651	−	0.266024i
$879$		0			0
$880$	−57.6219	−	34.2197i	−1.94243	−	1.15354i
$881$	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	$-0.366842\pi$
$883$	1.40699	+	0.582794i	0.0473489	+	0.0196126i	−0.358883	+	0.933382i	$0.616842\pi$
$884$	26.2145	−	14.9208i	0.881688	−	0.501840i
$885$		0			0
$886$	−1.40348	−	22.4714i	−0.0471510	−	0.754942i
$887$	−32.4795	−	32.4795i	−1.09056	−	1.09056i	−0.995469	−	0.0950860i	$-0.969687\pi$
$887$	−32.4795	−	32.4795i	−1.09056	−	1.09056i	−0.0950860	−	0.995469i	$-0.530313\pi$
$888$		0			0
$889$	−5.68182	+	5.68182i	−0.190562	+	0.190562i
$890$	−35.0477	−	30.9272i	−1.17480	−	1.03668i
$891$		0			0
$892$	−7.76545	+	9.99230i	−0.260006	+	0.334567i
$893$	−5.80581	+	14.0165i	−0.194284	+	0.469044i
$894$		0			0
$895$			1.44297i			0.0482333i
$896$	−17.0471	+	0.749338i	−0.569505	+	0.0250336i
$897$		0			0
$898$	1.68073	−	4.90171i	0.0560867	−	0.163572i
$899$	40.3901	+	16.7301i	1.34708	+	0.557980i
$900$		0			0
$901$	−1.86492	−	4.50232i	−0.0621296	−	0.149994i
$902$	26.8160	−	30.3888i	0.892874	−	1.01184i
$903$		0			0
$904$	1.52417	+	2.32726i	0.0506931	+	0.0774036i
$905$	45.2591	−	45.2591i	1.50446	−	1.50446i
$906$		0			0
$907$	10.6402	+	25.6878i	0.353303	+	0.852950i	0.996208	+	0.0870037i	$0.0277292\pi$
$907$	10.6402	+	25.6878i	0.353303	+	0.852950i	−0.642905	+	0.765946i	$0.722271\pi$
$908$	−7.09844	−	12.4713i	−0.235570	−	0.413876i
$909$		0			0
$910$	−24.5199	+	11.9983i	−0.812826	+	0.397739i
$911$		−	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
$914$	12.2830	+	25.1016i	0.406284	+	0.830288i
$915$		0			0
$916$	3.55381	−	12.9441i	0.117421	−	0.427685i
$917$	−11.0591	−	26.6990i	−0.365203	−	0.881678i
$918$		0			0
$919$	36.1191	−	36.1191i	1.19146	−	1.19146i	0.214803	−	0.976657i	$-0.431089\pi$
$919$	36.1191	−	36.1191i	1.19146	−	1.19146i	0.976657	−	0.214803i	$-0.0689110\pi$
$920$	1.52945	+	8.07773i	0.0504244	+	0.266315i
$921$		0			0
$922$	−2.58978	−	2.28530i	−0.0852898	−	0.0752623i
$923$	4.18197	+	10.0962i	0.137651	+	0.332320i
$924$		0			0
$925$	−17.5133	−	7.25426i	−0.575835	−	0.238519i
$926$	−21.9796	−	7.53651i	−0.722295	−	0.247665i
$927$		0			0
$928$	−51.9278	−	26.6080i	−1.70461	−	0.873451i
$929$		−	16.6303i		−	0.545622i	−0.962068	−	0.272811i	$-0.912047\pi$
$929$		−	16.6303i		−	0.545622i	0.962068	−	0.272811i	$-0.0879534\pi$
$930$		0			0
$931$	6.32599	−	15.2723i	0.207326	−	0.500529i
$932$	13.2655	−	1.66352i	0.434526	−	0.0544903i
$933$		0			0
$934$	19.9182	−	22.5720i	0.651744	−	0.738578i
$935$	−40.8112	+	40.8112i	−1.33467	+	1.33467i
$936$		0			0
$937$	39.4807	+	39.4807i	1.28978	+	1.28978i	0.934920	+	0.354860i	$0.115471\pi$
$937$	39.4807	+	39.4807i	1.28978	+	1.28978i	0.354860	+	0.934920i	$0.384529\pi$
$938$	−19.7953	+	1.23634i	−0.646339	+	0.0403680i
$939$		0			0
$940$	6.71280	−	24.4501i	0.218947	−	0.797475i
$941$	−38.4855	−	15.9412i	−1.25459	−	0.519669i	−0.346347	−	0.938107i	$-0.612578\pi$
$941$	−38.4855	−	15.9412i	−1.25459	−	0.519669i	−0.908246	+	0.418437i	$0.862578\pi$
$942$		0			0
$943$	−4.97182			−0.161905
$944$	−30.6426	+	22.9197i	−0.997330	+	0.745973i
$945$		0			0
$946$	31.4970	+	64.3678i	1.02406	+	2.09278i
$947$	1.88812	−	4.55832i	0.0613556	−	0.148125i	−0.890228	−	0.455515i	$-0.849455\pi$
$947$	1.88812	−	4.55832i	0.0613556	−	0.148125i	0.951584	+	0.307389i	$0.0994553\pi$
$948$		0			0
$949$	−6.65498	+	2.75658i	−0.216030	+	0.0894825i
$950$	−17.5074	+	1.09345i	−0.568014	+	0.0354761i
$951$		0			0
$952$	−2.99974	+	14.3859i	−0.0972220	+	0.466251i
$953$	3.89115	+	3.89115i	0.126047	+	0.126047i	0.767316	−	0.641269i	$-0.221592\pi$
$953$	3.89115	+	3.89115i	0.126047	+	0.126047i	−0.641269	+	0.767316i	$0.721592\pi$
$954$		0			0
$955$	62.9438	−	26.0722i	2.03681	−	0.843676i
$956$	−7.07978	+	9.11001i	−0.228976	+	0.294639i
$957$		0			0
$958$	−5.82957	−	1.99888i	−0.188345	−	0.0645809i
$959$	21.4973			0.694184
$960$		0			0
$961$	13.0354			0.420498
$962$	31.3129	+	10.7368i	1.00957	+	0.346167i
$963$		0			0
$964$	−24.7511	+	31.8489i	−0.797180	+	1.02578i
$965$	73.1094	−	30.2829i	2.35348	−	0.974842i
$966$		0			0
$967$	11.3033	+	11.3033i	0.363488	+	0.363488i	0.865095	−	0.501607i	$-0.167258\pi$
$967$	11.3033	+	11.3033i	0.363488	+	0.363488i	−0.501607	+	0.865095i	$0.667258\pi$
$968$	−60.4939	−	12.6141i	−1.94435	−	0.405433i
$969$		0			0
$970$	53.0000	−	3.31019i	1.70173	−	0.106284i
$971$	−19.3675	+	8.02226i	−0.621531	+	0.257447i	−0.671150	−	0.741322i	$-0.734199\pi$
$971$	−19.3675	+	8.02226i	−0.621531	+	0.257447i	0.0496188	+	0.998768i	$0.484199\pi$
$972$		0			0
$973$	−6.89828	+	16.6539i	−0.221149	+	0.533900i
$974$	−8.95451	−	18.2996i	−0.286921	−	0.586356i
$975$		0			0
$976$	1.21842	−	8.45040i	0.0390006	−	0.270491i
$977$	−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
$980$	−7.31423	+	26.6407i	−0.233645	+	0.851007i
$981$		0			0
$982$	−42.9067	+	2.67980i	−1.36921	+	0.0855157i
$983$	−35.5614	−	35.5614i	−1.13423	−	1.13423i	−0.989466	−	0.144767i	$-0.953757\pi$
$983$	−35.5614	−	35.5614i	−1.13423	−	1.13423i	−0.144767	−	0.989466i	$-0.546243\pi$
$984$		0			0
$985$	−0.524675	+	0.524675i	−0.0167175	+	0.0167175i
$986$	−33.2481	+	37.6779i	−1.05883	+	1.19991i
$987$		0			0
$988$	30.3938	−	3.81144i	0.966955	−	0.121258i
$989$	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	$0.962245\pi$
$992$	23.8981	+	1.93571i	0.758765	+	0.0614590i
$993$		0			0
$994$	−5.03622	−	1.72685i	−0.159739	−	0.0547724i
$995$	10.9643	+	4.54156i	0.347591	+	0.143977i
$996$		0			0
$997$	0.482816	+	1.16562i	0.0152909	+	0.0369156i	0.931341	−	0.364149i	$-0.118640\pi$
$997$	0.482816	+	1.16562i	0.0152909	+	0.0369156i	−0.916050	+	0.401065i	$0.868640\pi$
$998$	23.5666	+	20.7959i	0.745987	+	0.658282i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.2	✓	32	1.1	even	1	trivial
288.2.w.a.107.2	yes	32	96.11	even	8	inner
288.2.w.b.35.7	yes	32	3.2	odd	2
288.2.w.b.107.7	yes	32	32.11	odd	8
1152.2.w.a.431.7		32	12.11	even	2
1152.2.w.a.719.7		32	32.21	even	8
1152.2.w.b.431.2		32	4.3	odd	2
1152.2.w.b.719.2		32	96.53	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.33776 - 0.458699i) q^{2} +(1.57919 + 1.22726i) q^{4} +(-2.70076 + 1.11869i) q^{5} +(-1.06647 - 1.06647i) q^{7} +(-1.54963 - 2.36614i) q^{8} +O(q^{10})\)	\(q+(-1.33776 - 0.458699i) q^{2} +(1.57919 + 1.22726i) q^{4} +(-2.70076 + 1.11869i) q^{5} +(-1.06647 - 1.06647i) q^{7} +(-1.54963 - 2.36614i) q^{8} +(4.12611 - 0.257702i) q^{10} +(5.29504 - 2.19328i) q^{11} +(1.67540 - 4.04478i) q^{13} +(0.937494 + 1.91588i) q^{14} +(0.987684 + 3.87614i) q^{16} +3.44484 q^{17} +(3.23205 + 1.33876i) q^{19} +(-5.63794 - 1.54790i) q^{20} +(-8.08953 + 0.505243i) q^{22} +(0.703083 + 0.703083i) q^{23} +(2.50711 - 2.50711i) q^{25} +(-4.09662 + 4.64243i) q^{26} +(-0.375329 - 2.99300i) q^{28} +(3.94721 - 9.52941i) q^{29} +4.23846i q^{31} +(0.456702 - 5.63839i) q^{32} +(-4.60837 - 1.58015i) q^{34} +(4.07335 + 1.68724i) q^{35} +(-2.04600 - 4.93947i) q^{37} +(-3.70961 - 3.27347i) q^{38} +(6.83218 + 4.65683i) q^{40} +(-3.53573 + 3.53573i) q^{41} +(-3.38340 - 8.16825i) q^{43} +(11.0536 + 3.03477i) q^{44} +(-0.618051 - 1.26306i) q^{46} +4.33671i q^{47} -4.72526i q^{49} +(-4.50391 + 2.20390i) q^{50} +(7.60977 - 4.33133i) q^{52} +(-0.541366 - 1.30697i) q^{53} +(-11.8470 + 11.8470i) q^{55} +(-0.870790 + 4.17608i) q^{56} +(-9.65155 + 10.9375i) q^{58} +(3.66093 + 8.83827i) q^{59} +(-1.97197 - 0.816817i) q^{61} +(1.94418 - 5.67003i) q^{62} +(-3.19728 + 7.33331i) q^{64} +12.7983i q^{65} +(-3.55849 + 8.59096i) q^{67} +(5.44006 + 4.22771i) q^{68} +(-4.67522 - 4.12556i) q^{70} +(-1.76501 + 1.76501i) q^{71} +(-1.16342 - 1.16342i) q^{73} +(0.471315 + 7.54631i) q^{74} +(3.46102 + 6.08071i) q^{76} +(-7.98610 - 3.30795i) q^{77} +14.4770 q^{79} +(-7.00371 - 9.36362i) q^{80} +(6.35178 - 3.10811i) q^{82} +(4.27230 - 10.3143i) q^{83} +(-9.30371 + 3.85372i) q^{85} +(0.779399 + 12.4791i) q^{86} +(-13.3950 - 9.13005i) q^{88} +(-7.99481 - 7.99481i) q^{89} +(-6.10044 + 2.52688i) q^{91} +(0.247439 + 1.97317i) q^{92} +(1.98925 - 5.80147i) q^{94} -10.2267 q^{95} +12.8450 q^{97} +(-2.16747 + 6.32126i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) 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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