LMFDB - Embedded newform 756.2.o.a.179.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(179,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 4]))

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

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

chi := DirichletCharacter("756.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.24
Character	$\chi$	$=$	756.179
Dual form			756.2.o.a.359.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.182752 + 1.40236i) q^{2} +(-1.93320 + 0.512566i) q^{4} -2.45799i q^{5} +(-2.25199 + 1.38871i) q^{7} +(-1.07210 - 2.61737i) q^{8} +O(q^{10})$	\(q+(0.182752 + 1.40236i) q^{2} +(-1.93320 + 0.512566i) q^{4} -2.45799i q^{5} +(-2.25199 + 1.38871i) q^{7} +(-1.07210 - 2.61737i) q^{8} +(3.44698 - 0.449201i) q^{10} +3.73252 q^{11} +(-0.708051 + 1.22638i) q^{13} +(-2.35902 - 2.90431i) q^{14} +(3.47455 - 1.98179i) q^{16} +(3.50791 + 2.02529i) q^{17} +(1.98185 - 1.14422i) q^{19} +(1.25988 + 4.75179i) q^{20} +(0.682123 + 5.23432i) q^{22} +3.61698 q^{23} -1.04171 q^{25} +(-1.84922 - 0.768816i) q^{26} +(3.64176 - 3.83896i) q^{28} +(4.59226 - 2.65135i) q^{29} +(5.38753 - 3.11049i) q^{31} +(3.41415 + 4.51039i) q^{32} +(-2.19911 + 5.28947i) q^{34} +(3.41344 + 5.53538i) q^{35} +(2.37386 + 4.11165i) q^{37} +(1.96679 + 2.57015i) q^{38} +(-6.43346 + 2.63520i) q^{40} +(7.67307 + 4.43005i) q^{41} +(-10.5542 + 6.09346i) q^{43} +(-7.21571 + 1.91316i) q^{44} +(0.661009 + 5.07229i) q^{46} +(4.33970 - 7.51657i) q^{47} +(3.14296 - 6.25474i) q^{49} +(-0.190374 - 1.46085i) q^{50} +(0.740207 - 2.73377i) q^{52} +(-6.93030 - 4.00121i) q^{53} -9.17448i q^{55} +(6.04912 + 4.40547i) q^{56} +(4.55737 + 5.95545i) q^{58} +(-1.75698 - 3.04317i) q^{59} +(5.23289 - 9.06363i) q^{61} +(5.34660 + 6.98679i) q^{62} +(-5.70122 + 5.61213i) q^{64} +(3.01443 + 1.74038i) q^{65} +(-9.49365 + 5.48116i) q^{67} +(-7.81961 - 2.11727i) q^{68} +(-7.13876 + 5.79845i) q^{70} -2.01888 q^{71} +(0.474356 - 0.821609i) q^{73} +(-5.33217 + 4.08041i) q^{74} +(-3.24483 + 3.22784i) q^{76} +(-8.40560 + 5.18339i) q^{77} +(3.49588 + 2.01835i) q^{79} +(-4.87121 - 8.54041i) q^{80} +(-4.81024 + 11.5700i) q^{82} +(0.112352 + 0.194599i) q^{83} +(4.97815 - 8.62241i) q^{85} +(-10.4740 - 13.6871i) q^{86} +(-4.00161 - 9.76936i) q^{88} +(-8.55343 + 4.93832i) q^{89} +(-0.108562 - 3.74508i) q^{91} +(-6.99236 + 1.85394i) q^{92} +(11.3340 + 4.71213i) q^{94} +(-2.81249 - 4.87137i) q^{95} +(6.52412 + 11.3001i) q^{97} +(9.34576 + 3.26448i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 3 q^{2} + q^{4}+O(q^{10}) $ 88 * q + 3 * q^2 + q^4	$ 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) $ 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.182752	+	1.40236i	0.129225	+	0.991615i
$2$	0.182752	+	1.40236i	0.129225	+	0.991615i
$3$		0			0
$3$		0			0
$4$	−1.93320	+	0.512566i	−0.966602	+	0.256283i
$5$		−	2.45799i		−	1.09925i	−0.835413	−	0.549623i	$-0.814771\pi$
$5$		−	2.45799i		−	1.09925i	0.835413	−	0.549623i	$-0.185229\pi$
$6$		0			0
$7$	−2.25199	+	1.38871i	−0.851174	+	0.524884i
$7$	−2.25199	+	1.38871i	−0.851174	+	0.524884i
$8$	−1.07210	−	2.61737i	−0.379043	−	0.925379i
$9$		0			0
$10$	3.44698	−	0.449201i	1.09003	−	0.142050i
$11$	3.73252			1.12540			0.562698	−	0.826663i	$-0.309763\pi$
$11$	3.73252			1.12540			0.562698	+	0.826663i	$0.309763\pi$
$12$		0			0
$13$	−0.708051	+	1.22638i	−0.196378	+	0.340137i	−0.947351	−	0.320196i	$-0.896251\pi$
$13$	−0.708051	+	1.22638i	−0.196378	+	0.340137i	0.750973	+	0.660332i	$0.229585\pi$
$14$	−2.35902	−	2.90431i	−0.630476	−	0.776209i
$15$		0			0
$16$	3.47455	−	1.98179i	0.868638	−	0.495447i
$17$	3.50791	+	2.02529i	0.850794	+	0.491206i	0.860919	−	0.508743i	$-0.169890\pi$
$17$	3.50791	+	2.02529i	0.850794	+	0.491206i	−0.0101248	+	0.999949i	$0.503223\pi$
$18$		0			0
$19$	1.98185	−	1.14422i	0.454668	−	0.262503i	−0.255132	−	0.966906i	$-0.582119\pi$
$19$	1.98185	−	1.14422i	0.454668	−	0.262503i	0.709800	+	0.704404i	$0.248785\pi$
$20$	1.25988	+	4.75179i	0.281718	+	1.06253i
$21$		0			0
$22$	0.682123	+	5.23432i	0.145429	+	1.11596i
$23$	3.61698			0.754192			0.377096	−	0.926174i	$-0.376923\pi$
$23$	3.61698			0.754192			0.377096	+	0.926174i	$0.376923\pi$
$24$		0			0
$25$	−1.04171			−0.208342
$26$	−1.84922	−	0.768816i	−0.362662	−	0.150777i
$27$		0			0
$28$	3.64176	−	3.83896i	0.688228	−	0.725495i
$29$	4.59226	−	2.65135i	0.852762	−	0.492342i	−0.00881973	−	0.999961i	$-0.502807\pi$
$29$	4.59226	−	2.65135i	0.852762	−	0.492342i	0.861582	+	0.507619i	$0.169474\pi$
$30$		0			0
$31$	5.38753	−	3.11049i	0.967629	−	0.558661i	0.0691164	−	0.997609i	$-0.477982\pi$
$31$	5.38753	−	3.11049i	0.967629	−	0.558661i	0.898513	+	0.438948i	$0.144649\pi$
$32$	3.41415	+	4.51039i	0.603542	+	0.797331i
$33$		0			0
$34$	−2.19911	+	5.28947i	−0.377144	+	0.907136i
$35$	3.41344	+	5.53538i	0.576976	+	0.935650i
$36$		0			0
$37$	2.37386	+	4.11165i	0.390261	+	0.675952i	0.992484	−	0.122376i	$-0.0390515\pi$
$37$	2.37386	+	4.11165i	0.390261	+	0.675952i	−0.602223	+	0.798328i	$0.705718\pi$
$38$	1.96679	+	2.57015i	0.319056	+	0.416934i
$39$		0			0
$40$	−6.43346	+	2.63520i	−1.01722	+	0.416661i
$41$	7.67307	+	4.43005i	1.19833	+	0.691857i	0.960183	−	0.279372i	$-0.0901261\pi$
$41$	7.67307	+	4.43005i	1.19833	+	0.691857i	0.238149	+	0.971229i	$0.423459\pi$
$42$		0			0
$43$	−10.5542	+	6.09346i	−1.60950	+	0.929244i	−0.620016	+	0.784590i	$0.712874\pi$
$43$	−10.5542	+	6.09346i	−1.60950	+	0.929244i	−0.989482	+	0.144654i	$0.953793\pi$
$44$	−7.21571	+	1.91316i	−1.08781	+	0.288420i
$45$		0			0
$46$	0.661009	+	5.07229i	0.0974604	+	0.747869i
$47$	4.33970	−	7.51657i	0.633010	−	1.09640i	−0.353923	−	0.935274i	$-0.615153\pi$
$47$	4.33970	−	7.51657i	0.633010	−	1.09640i	0.986933	−	0.161130i	$-0.0515140\pi$
$48$		0			0
$49$	3.14296	−	6.25474i	0.448994	−	0.893535i
$50$	−0.190374	−	1.46085i	−0.0269230	−	0.206595i
$51$		0			0
$52$	0.740207	−	2.73377i	0.102648	−	0.379105i
$53$	−6.93030	−	4.00121i	−0.951950	−	0.549609i	−0.0582640	−	0.998301i	$-0.518557\pi$
$53$	−6.93030	−	4.00121i	−0.951950	−	0.549609i	−0.893686	+	0.448693i	$0.851890\pi$
$54$		0			0
$55$		−	9.17448i		−	1.23709i
$56$	6.04912	+	4.40547i	0.808348	+	0.588705i
$57$		0			0
$58$	4.55737	+	5.95545i	0.598412	+	0.781989i
$59$	−1.75698	−	3.04317i	−0.228739	−	0.396187i	0.728696	−	0.684838i	$-0.240127\pi$
$59$	−1.75698	−	3.04317i	−0.228739	−	0.396187i	−0.957435	+	0.288650i	$0.906794\pi$
$60$		0			0
$61$	5.23289	−	9.06363i	0.670003	−	1.16048i	−0.307900	−	0.951419i	$-0.599626\pi$
$61$	5.23289	−	9.06363i	0.670003	−	1.16048i	0.977903	−	0.209060i	$-0.0670404\pi$
$62$	5.34660	+	6.98679i	0.679018	+	0.887323i
$63$		0			0
$64$	−5.70122	+	5.61213i	−0.712653	+	0.701517i
$65$	3.01443	+	1.74038i	0.373894	+	0.215868i
$66$		0			0
$67$	−9.49365	+	5.48116i	−1.15983	+	0.669630i	−0.951264	−	0.308377i	$-0.900214\pi$
$67$	−9.49365	+	5.48116i	−1.15983	+	0.669630i	−0.208570	+	0.978008i	$0.566881\pi$
$68$	−7.81961	−	2.11727i	−0.948266	−	0.256757i
$69$		0			0
$70$	−7.13876	+	5.79845i	−0.853245	+	0.693048i
$71$	−2.01888			−0.239597			−0.119799	−	0.992798i	$-0.538225\pi$
$71$	−2.01888			−0.239597			−0.119799	+	0.992798i	$0.538225\pi$
$72$		0			0
$73$	0.474356	−	0.821609i	0.0555192	−	0.0961621i	−0.836930	−	0.547310i	$-0.815652\pi$
$73$	0.474356	−	0.821609i	0.0555192	−	0.0961621i	0.892449	+	0.451148i	$0.148985\pi$
$74$	−5.33217	+	4.08041i	−0.619853	+	0.474338i
$75$		0			0
$76$	−3.24483	+	3.22784i	−0.372208	+	0.370259i
$77$	−8.40560	+	5.18339i	−0.957908	+	0.590702i
$78$		0			0
$79$	3.49588	+	2.01835i	0.393318	+	0.227082i	0.683597	−	0.729860i	$-0.260415\pi$
$79$	3.49588	+	2.01835i	0.393318	+	0.227082i	−0.290279	+	0.956942i	$0.593748\pi$
$80$	−4.87121	−	8.54041i	−0.544618	−	0.954847i
$81$		0			0
$82$	−4.81024	+	11.5700i	−0.531202	+	1.27769i
$83$	0.112352	+	0.194599i	0.0123322	+	0.0213601i	0.872126	−	0.489282i	$-0.162741\pi$
$83$	0.112352	+	0.194599i	0.0123322	+	0.0213601i	−0.859793	+	0.510642i	$0.829408\pi$
$84$		0			0
$85$	4.97815	−	8.62241i	0.539956	−	0.935232i
$86$	−10.4740	−	13.6871i	−1.12944	−	1.47592i
$87$		0			0
$88$	−4.00161	−	9.76936i	−0.426573	−	1.04142i
$89$	−8.55343	+	4.93832i	−0.906662	+	0.523461i	−0.879356	−	0.476166i	$-0.842026\pi$
$89$	−8.55343	+	4.93832i	−0.906662	+	0.523461i	−0.0273061	+	0.999627i	$0.508693\pi$
$90$		0			0
$91$	−0.108562	−	3.74508i	−0.0113804	−	0.392591i
$92$	−6.99236	+	1.85394i	−0.729004	+	0.193286i
$93$		0			0
$94$	11.3340	+	4.71213i	1.16901	+	0.486019i
$95$	−2.81249	−	4.87137i	−0.288555	−	0.499792i
$96$		0			0
$97$	6.52412	+	11.3001i	0.662424	+	1.14735i	0.979977	+	0.199111i	$0.0638056\pi$
$97$	6.52412	+	11.3001i	0.662424	+	1.14735i	−0.317553	+	0.948241i	$0.602861\pi$
$98$	9.34576	+	3.26448i	0.944064	+	0.329762i
$99$		0			0
$100$	2.01384	−	0.533944i	0.201384	−	0.0533944i
$101$			5.48128i			0.545408i	0.962098	+	0.272704i	$0.0879180\pi$
$101$			5.48128i			0.545408i	−0.962098	+	0.272704i	$0.912082\pi$
$102$		0			0
$103$		−	16.4461i		−	1.62048i	−0.586097	−	0.810241i	$-0.699336\pi$
$103$		−	16.4461i		−	1.62048i	0.586097	−	0.810241i	$-0.300664\pi$
$104$	3.96899	+	0.538433i	0.389191	+	0.0527977i
$105$		0			0
$106$	4.34460	−	10.4500i	0.421985	−	1.01499i
$107$	−4.38000	−	7.58638i	−0.423431	−	0.733404i	0.572842	−	0.819666i	$-0.305841\pi$
$107$	−4.38000	−	7.58638i	−0.423431	−	0.733404i	−0.996272	+	0.0862625i	$0.972508\pi$
$108$		0			0
$109$	−5.83206	+	10.1014i	−0.558610	+	0.967541i	0.439003	+	0.898486i	$0.355332\pi$
$109$	−5.83206	+	10.1014i	−0.558610	+	0.967541i	−0.997613	+	0.0690550i	$0.978002\pi$
$110$	12.8659	−	1.67665i	1.22671	−	0.159862i
$111$		0			0
$112$	−5.07254	+	9.28813i	−0.479310	+	0.877646i
$113$	8.35926	+	4.82622i	0.786373	+	0.454013i	0.838684	−	0.544618i	$-0.183325\pi$
$113$	8.35926	+	4.82622i	0.786373	+	0.454013i	−0.0523109	+	0.998631i	$0.516659\pi$
$114$		0			0
$115$		−	8.89049i		−	0.829043i
$116$	−7.51879	+	7.47943i	−0.698103	+	0.694447i
$117$		0			0
$118$	3.94652	−	3.02005i	0.363307	−	0.278018i
$119$	−10.7124	+	0.310528i	−0.982000	+	0.0284661i
$120$		0			0
$121$	2.93167			0.266516
$122$	13.6667	+	5.68198i	1.23733	+	0.514422i
$123$		0			0
$124$	−8.82086	+	8.77468i	−0.792137	+	0.787989i
$125$		−	9.72943i		−	0.870227i
$126$		0			0
$127$			0.937979i			0.0832322i	0.999134	+	0.0416161i	$0.0132506\pi$
$127$			0.937979i			0.0832322i	−0.999134	+	0.0416161i	$0.986749\pi$
$128$	−8.91212	−	6.96952i	−0.787727	−	0.616024i
$129$		0			0
$130$	−1.88974	+	4.54536i	−0.165741	+	0.398654i
$131$	6.97190			0.609138			0.304569	−	0.952490i	$-0.401488\pi$
$131$	6.97190			0.609138			0.304569	+	0.952490i	$0.401488\pi$
$132$		0			0
$133$	−2.87412	+	5.32900i	−0.249218	+	0.462083i
$134$	−9.42152	−	12.3118i	−0.813895	−	1.06358i
$135$		0			0
$136$	1.54012	−	11.3528i	0.132064	−	0.973495i
$137$			14.5675i			1.24459i	0.782784	+	0.622293i	$0.213799\pi$
$137$			14.5675i			1.24459i	−0.782784	+	0.622293i	$0.786201\pi$
$138$		0			0
$139$	11.2990	+	6.52347i	0.958368	+	0.553314i	0.895670	−	0.444719i	$-0.146696\pi$
$139$	11.2990	+	6.52347i	0.958368	+	0.553314i	0.0626973	+	0.998033i	$0.480030\pi$
$140$	−9.43612	−	8.95140i	−0.797497	−	0.756532i
$141$		0			0
$142$	−0.368954	−	2.83119i	−0.0309619	−	0.237588i
$143$	−2.64281	+	4.57748i	−0.221003	+	0.382788i
$144$		0			0
$145$	−6.51698	−	11.2877i	−0.541205	−	0.937395i
$146$	1.23888	+	0.515066i	0.102530	+	0.0426272i
$147$		0			0
$148$	−6.69665	−	6.73190i	−0.550462	−	0.553359i
$149$		−	22.2238i		−	1.82064i	−0.413902	−	0.910321i	$-0.635834\pi$
$149$		−	22.2238i		−	1.82064i	0.413902	−	0.910321i	$-0.364166\pi$
$150$		0			0
$151$			2.25709i			0.183679i	0.995774	+	0.0918395i	$0.0292747\pi$
$151$			2.25709i			0.183679i	−0.995774	+	0.0918395i	$0.970725\pi$
$152$	−5.11958	−	3.96052i	−0.415253	−	0.321240i
$153$		0			0
$154$	−8.80509	−	10.8404i	−0.709535	−	0.873542i
$155$	−7.64556	−	13.2425i	−0.614106	−	1.06366i
$156$		0			0
$157$	1.11181	+	1.92570i	0.0887317	+	0.153688i	0.906975	−	0.421184i	$-0.138385\pi$
$157$	1.11181	+	1.92570i	0.0887317	+	0.153688i	−0.818244	+	0.574872i	$0.805052\pi$
$158$	−2.19157	+	5.27133i	−0.174352	+	0.419364i
$159$		0			0
$160$	11.0865	−	8.39194i	0.876463	−	0.663441i
$161$	−8.14542	+	5.02294i	−0.641949	+	0.395863i
$162$		0			0
$163$	0.479974	−	0.277113i	0.0375945	−	0.0217052i	−0.481085	−	0.876674i	$-0.659757\pi$
$163$	0.479974	−	0.277113i	0.0375945	−	0.0217052i	0.518679	+	0.854969i	$0.326424\pi$
$164$	−17.1043	−	4.63123i	−1.33562	−	0.361639i
$165$		0			0
$166$	−0.252365	+	0.193121i	−0.0195873	+	0.0149891i
$167$	5.78903	−	10.0269i	0.447968	−	0.775904i	−0.550285	−	0.834977i	$-0.685481\pi$
$167$	5.78903	−	10.0269i	0.447968	−	0.775904i	0.998254	+	0.0590727i	$0.0188144\pi$
$168$		0			0
$169$	5.49733	+	9.52165i	0.422871	+	0.732435i
$170$	13.0015	+	5.40538i	0.997166	+	0.414574i
$171$		0			0
$172$	17.2801	−	17.1896i	1.31759	−	1.31070i
$173$	9.23186	+	5.33002i	0.701886	+	0.405234i	0.808049	−	0.589115i	$-0.200523\pi$
$173$	9.23186	+	5.33002i	0.701886	+	0.405234i	−0.106164	+	0.994349i	$0.533857\pi$
$174$		0			0
$175$	2.34592	−	1.44663i	0.177335	−	0.109355i
$176$	12.9688	−	7.39705i	0.977562	−	0.557574i
$177$		0			0
$178$	−8.48844	−	11.0925i	−0.636235	−	0.831415i
$179$	10.5947	−	18.3506i	0.791886	−	1.37159i	−0.132911	−	0.991128i	$-0.542433\pi$
$179$	10.5947	−	18.3506i	0.791886	−	1.37159i	0.924798	−	0.380459i	$-0.124234\pi$
$180$		0			0
$181$	−16.5889			−1.23304			−0.616521	−	0.787338i	$-0.711459\pi$
$181$	−16.5889			−1.23304			−0.616521	+	0.787338i	$0.711459\pi$
$182$	5.23210	−	0.836662i	0.387829	−	0.0620175i
$183$		0			0
$184$	−3.87775	−	9.46696i	−0.285871	−	0.697914i
$185$	10.1064	−	5.83493i	0.743037	−	0.428993i
$186$		0			0
$187$	13.0933	+	7.55944i	0.957480	+	0.552801i
$188$	−4.53678	+	16.7554i	−0.330879	+	1.22202i
$189$		0			0
$190$	6.31741	−	4.83436i	0.458313	−	0.350721i
$191$	−8.24273	+	14.2768i	−0.596423	+	1.03303i	0.396922	+	0.917853i	$0.370078\pi$
$191$	−8.24273	+	14.2768i	−0.596423	+	1.03303i	−0.993344	+	0.115182i	$0.963255\pi$
$192$		0			0
$193$	−11.5854	−	20.0665i	−0.833936	−	1.44442i	−0.894894	−	0.446280i	$-0.852749\pi$
$193$	−11.5854	−	20.0665i	−0.833936	−	1.44442i	0.0609572	−	0.998140i	$-0.480585\pi$
$194$	−14.6545	+	11.2142i	−1.05213	+	0.805136i
$195$		0			0
$196$	−2.87001	+	13.7027i	−0.205001	+	0.978762i
$197$			14.4116i			1.02679i	0.858154	+	0.513393i	$0.171611\pi$
$197$			14.4116i			1.02679i	−0.858154	+	0.513393i	$0.828389\pi$
$198$		0			0
$199$	−2.36477	−	1.36530i	−0.167634	−	0.0967837i	0.413836	−	0.910352i	$-0.364189\pi$
$199$	−2.36477	−	1.36530i	−0.167634	−	0.0967837i	−0.581470	+	0.813568i	$0.697522\pi$
$200$	1.11681	+	2.72654i	0.0789705	+	0.192795i
$201$		0			0
$202$	−7.68671	+	1.00171i	−0.540835	+	0.0704803i
$203$	−6.65980	+	12.3481i	−0.467426	+	0.866670i
$204$		0			0
$205$	10.8890	−	18.8603i	0.760521	−	1.31726i
$206$	23.0633	−	3.00555i	1.60689	−	0.209407i
$207$		0			0
$208$	−0.0297363	+	5.66433i	−0.00206184	+	0.392751i
$209$	7.39729	−	4.27083i	0.511681	−	0.295419i
$210$		0			0
$211$	7.91848	+	4.57174i	0.545131	+	0.314731i	0.747156	−	0.664649i	$-0.231419\pi$
$211$	7.91848	+	4.57174i	0.545131	+	0.314731i	−0.202025	+	0.979380i	$0.564752\pi$
$212$	15.4486	+	4.18292i	1.06101	+	0.287284i
$213$		0			0
$214$	9.83836	−	7.52874i	0.672536	−	0.514654i
$215$	14.9777	+	25.9421i	1.02147	+	1.76923i
$216$		0			0
$217$	−7.81311	+	14.4865i	−0.530389	+	0.983410i
$218$	−15.2316	−	6.33257i	−1.03161	−	0.428896i
$219$		0			0
$220$	4.70252	+	17.7361i	0.317044	+	1.19577i
$221$	−4.96756	+	2.86802i	−0.334154	+	0.192924i
$222$		0			0
$223$	7.77997	−	4.49177i	0.520985	−	0.300791i	−0.216352	−	0.976315i	$-0.569416\pi$
$223$	7.77997	−	4.49177i	0.520985	−	0.300791i	0.737338	+	0.675524i	$0.236083\pi$
$224$	−13.9523	−	5.41609i	−0.932226	−	0.361878i
$225$		0			0
$226$	−5.24041	+	12.6047i	−0.348587	+	0.838450i
$227$	10.3688			0.688198			0.344099	−	0.938933i	$-0.388184\pi$
$227$	10.3688			0.688198			0.344099	+	0.938933i	$0.388184\pi$
$228$		0			0
$229$	−3.71000			−0.245164			−0.122582	−	0.992458i	$-0.539117\pi$
$229$	−3.71000			−0.245164			−0.122582	+	0.992458i	$0.539117\pi$
$230$	12.4676	−	1.62475i	0.822092	−	0.107133i
$231$		0			0
$232$	−11.8629	−	9.17715i	−0.778837	−	0.602509i
$233$	12.9602	−	7.48260i	0.849054	−	0.490201i	−0.0112778	−	0.999936i	$-0.503590\pi$
$233$	12.9602	−	7.48260i	0.849054	−	0.490201i	0.860331	+	0.509735i	$0.170257\pi$
$234$		0			0
$235$	−18.4757	−	10.6669i	−1.20522	−	0.695833i
$236$	4.95642	+	4.98251i	0.322635	+	0.324334i
$237$		0			0
$238$	−2.39317	−	14.9658i	−0.155126	−	0.970087i
$239$	−6.84478	+	11.8555i	−0.442752	+	0.766869i	−0.997893	−	0.0648877i	$-0.979331\pi$
$239$	−6.84478	+	11.8555i	−0.442752	+	0.766869i	0.555141	+	0.831756i	$0.312664\pi$
$240$		0			0
$241$	11.7384			0.756135			0.378067	−	0.925778i	$-0.376589\pi$
$241$	11.7384			0.756135			0.378067	+	0.925778i	$0.376589\pi$
$242$	0.535768	+	4.11125i	0.0344405	+	0.264281i
$243$		0			0
$244$	−5.47054	+	20.2040i	−0.350215	+	1.29343i
$245$	−15.3741	−	7.72536i	−0.982215	−	0.493555i
$246$		0			0
$247$			3.24067i			0.206199i
$248$	−13.9172	−	10.7664i	−0.883746	−	0.683667i
$249$		0			0
$250$	13.6441	−	1.77807i	0.862930	−	0.112455i
$251$	−17.6466			−1.11384			−0.556922	−	0.830565i	$-0.688018\pi$
$251$	−17.6466			−1.11384			−0.556922	+	0.830565i	$0.688018\pi$
$252$		0			0
$253$	13.5004			0.848765
$254$	−1.31538	+	0.171417i	−0.0825343	+	0.0107557i
$255$		0			0
$256$	8.14504	−	13.7716i	0.509065	−	0.860728i
$257$		−	14.9206i		−	0.930720i	−0.885121	−	0.465360i	$-0.845925\pi$
$257$		−	14.9206i		−	0.930720i	0.885121	−	0.465360i	$-0.154075\pi$
$258$		0			0
$259$	−11.0558	−	5.96281i	−0.686976	−	0.370511i
$260$	−6.71956	−	1.81942i	−0.416730	−	0.112836i
$261$		0			0
$262$	1.27413	+	9.77708i	0.0787157	+	0.604030i
$263$	0.853210			0.0526112			0.0263056	−	0.999654i	$-0.491626\pi$
$263$	0.853210			0.0526112			0.0263056	+	0.999654i	$0.491626\pi$
$264$		0			0
$265$	−9.83493	+	17.0346i	−0.604155	+	1.04643i
$266$	−7.99841	−	3.05666i	−0.490414	−	0.187416i
$267$		0			0
$268$	15.5437	−	15.4623i	0.949483	−	0.944511i
$269$	6.98964	+	4.03547i	0.426166	+	0.246047i	0.697712	−	0.716378i	$-0.254202\pi$
$269$	6.98964	+	4.03547i	0.426166	+	0.246047i	−0.271546	+	0.962425i	$0.587535\pi$
$270$		0			0
$271$	−13.5435	+	7.81935i	−0.822710	+	0.474992i	−0.851350	−	0.524598i	$-0.824216\pi$
$271$	−13.5435	+	7.81935i	−0.822710	+	0.474992i	0.0286401	+	0.999590i	$0.490882\pi$
$272$	16.2021	+	0.0850570i	0.982398	+	0.00515734i
$273$		0			0
$274$	−20.4288	+	2.66223i	−1.23415	+	0.160831i
$275$	−3.88820			−0.234467
$276$		0			0
$277$	−20.2469			−1.21652			−0.608259	−	0.793739i	$-0.708132\pi$
$277$	−20.2469			−1.21652			−0.608259	+	0.793739i	$0.708132\pi$
$278$	−7.08332	+	17.0374i	−0.424829	+	1.02183i
$279$		0			0
$280$	10.8286	−	14.8687i	0.647132	−	0.888573i
$281$	−5.50545	+	3.17857i	−0.328428	+	0.189618i	−0.655143	−	0.755505i	$-0.727392\pi$
$281$	−5.50545	+	3.17857i	−0.328428	+	0.189618i	0.326715	+	0.945123i	$0.394058\pi$
$282$		0			0
$283$	−8.85659	+	5.11336i	−0.526470	+	0.303958i	−0.739578	−	0.673071i	$-0.764975\pi$
$283$	−8.85659	+	5.11336i	−0.526470	+	0.303958i	0.213108	+	0.977029i	$0.431641\pi$
$284$	3.90291	−	1.03481i	0.231595	−	0.0614047i
$285$		0			0
$286$	−6.90224	−	2.86962i	−0.408138	−	0.169684i
$287$	−23.4318	+	0.679237i	−1.38313	+	0.0400941i
$288$		0			0
$289$	−0.296366	−	0.513321i	−0.0174333	−	0.0301954i
$290$	14.6384	−	11.2020i	0.859598	−	0.657802i
$291$		0			0
$292$	−0.495899	+	1.83148i	−0.0290203	+	0.107179i
$293$	−20.6599	−	11.9280i	−1.20696	−	0.696840i	−0.244868	−	0.969556i	$-0.578745\pi$
$293$	−20.6599	−	11.9280i	−1.20696	−	0.696840i	−0.962094	+	0.272716i	$0.912078\pi$
$294$		0			0
$295$	−7.48009	+	4.31863i	−0.435507	+	0.251440i
$296$	8.21670	−	10.6214i	0.477586	−	0.617354i
$297$		0			0
$298$	31.1656	−	4.06143i	1.80538	−	0.235272i
$299$	−2.56101	+	4.43579i	−0.148107	+	0.256528i
$300$		0			0
$301$	15.3059	−	28.3792i	0.882217	−	1.63575i
$302$	−3.16524	+	0.412486i	−0.182139	+	0.0237359i
$303$		0			0
$304$	4.61844	−	7.90327i	0.264886	−	0.453284i
$305$	−22.2783	−	12.8624i	−1.27565	−	0.736498i
$306$		0			0
$307$			6.44982i			0.368111i	0.982916	+	0.184055i	$0.0589226\pi$
$307$			6.44982i			0.368111i	−0.982916	+	0.184055i	$0.941077\pi$
$308$	13.5929	−	14.3290i	0.774528	−	0.816469i
$309$		0			0
$310$	17.1734	−	13.1419i	0.975386	−	0.746408i
$311$	0.253074	+	0.438337i	0.0143505	+	0.0248558i	0.873111	−	0.487521i	$-0.162099\pi$
$311$	0.253074	+	0.438337i	0.0143505	+	0.0248558i	−0.858761	+	0.512376i	$0.828765\pi$
$312$		0			0
$313$	−12.6914	+	21.9822i	−0.717362	+	1.24251i	0.244679	+	0.969604i	$0.421317\pi$
$313$	−12.6914	+	21.9822i	−0.717362	+	1.24251i	−0.962041	+	0.272904i	$0.912016\pi$
$314$	−2.49734	+	1.91107i	−0.140933	+	0.107848i
$315$		0			0
$316$	−7.79279	−	2.11001i	−0.438379	−	0.118697i
$317$	−20.8397	−	12.0318i	−1.17048	−	0.675774i	−0.216683	−	0.976242i	$-0.569524\pi$
$317$	−20.8397	−	12.0318i	−1.17048	−	0.675774i	−0.953792	+	0.300468i	$0.902857\pi$
$318$		0			0
$319$	17.1407	−	9.89619i	0.959695	−	0.554080i
$320$	13.7946	+	14.0135i	0.771140	+	0.783381i
$321$		0			0
$322$	−8.53254	−	10.5048i	−0.475500	−	0.585411i
$323$	9.26955			0.515772
$324$		0			0
$325$	0.737584	−	1.27753i	0.0409138	−	0.0708647i
$326$	0.476327	+	0.622451i	0.0263813	+	0.0344744i
$327$		0			0
$328$	3.36880	−	24.8327i	0.186011	−	1.37115i
$329$	0.665384	+	22.9539i	0.0366838	+	1.26549i
$330$		0			0
$331$	5.80713	+	3.35275i	0.319189	+	0.184284i	0.651031	−	0.759051i	$-0.274337\pi$
$331$	5.80713	+	3.35275i	0.319189	+	0.184284i	−0.331842	+	0.943335i	$0.607670\pi$
$332$	−0.316944	−	0.318613i	−0.0173946	−	0.0174861i
$333$		0			0
$334$	15.1192	+	6.28585i	0.827287	+	0.343946i
$335$	13.4726	+	23.3353i	0.736089	+	1.27494i
$336$		0			0
$337$	−15.3334	+	26.5582i	−0.835263	+	1.44672i	0.0585525	+	0.998284i	$0.481351\pi$
$337$	−15.3334	+	26.5582i	−0.835263	+	1.44672i	−0.893816	+	0.448434i	$0.851982\pi$
$338$	−12.3481	+	9.44931i	−0.671648	+	0.513975i
$339$		0			0
$340$	−5.20423	+	19.2205i	−0.282239	+	1.04238i
$341$	20.1090	−	11.6100i	1.08897	−	0.628715i
$342$		0			0
$343$	1.60811	+	18.4503i	0.0868298	+	0.996223i
$344$	27.2639	+	21.0914i	1.46997	+	1.13717i
$345$		0			0
$346$	−5.78745	+	13.9204i	−0.311135	+	0.748367i
$347$	4.51700	+	7.82368i	0.242485	+	0.419997i	0.961422	−	0.275079i	$-0.0887040\pi$
$347$	4.51700	+	7.82368i	0.242485	+	0.419997i	−0.718936	+	0.695076i	$0.755371\pi$
$348$		0			0
$349$	10.9004	+	18.8800i	0.583485	+	1.01063i	0.995062	+	0.0992507i	$0.0316446\pi$
$349$	10.9004	+	18.8800i	0.583485	+	1.01063i	−0.411578	+	0.911375i	$0.635022\pi$
$350$	2.45742	+	3.02545i	0.131355	+	0.161717i
$351$		0			0
$352$	12.7434	+	16.8351i	0.679224	+	0.897313i
$353$		−	11.9218i		−	0.634536i	−0.948336	−	0.317268i	$-0.897235\pi$
$353$		−	11.9218i		−	0.634536i	0.948336	−	0.317268i	$-0.102765\pi$
$354$		0			0
$355$			4.96239i			0.263376i
$356$	14.0043	−	13.9310i	0.742227	−	0.738340i
$357$		0			0
$358$	27.6703	+	11.5040i	1.46242	+	0.608003i
$359$	−5.13759	−	8.89857i	−0.271152	−	0.469649i	0.698005	−	0.716093i	$-0.254071\pi$
$359$	−5.13759	−	8.89857i	−0.271152	−	0.469649i	−0.969157	+	0.246444i	$0.920738\pi$
$360$		0			0
$361$	−6.88151	+	11.9191i	−0.362185	+	0.627322i
$362$	−3.03165	−	23.2635i	−0.159340	−	1.22270i
$363$		0			0
$364$	2.12947	+	7.18436i	0.111615	+	0.376563i
$365$	−2.01951	−	1.16596i	−0.105706	−	0.0610293i
$366$		0			0
$367$			27.4387i			1.43229i	0.697951	+	0.716145i	$0.254095\pi$
$367$			27.4387i			1.43229i	−0.697951	+	0.716145i	$0.745905\pi$
$368$	12.5674	−	7.16808i	0.655120	−	0.373662i
$369$		0			0
$370$	10.0296	+	13.1064i	0.521415	+	0.681371i
$371$	21.1635	−	0.613486i	1.09876	−	0.0318506i
$372$		0			0
$373$	−5.06521			−0.262266			−0.131133	−	0.991365i	$-0.541862\pi$
$373$	−5.06521			−0.262266			−0.131133	+	0.991365i	$0.541862\pi$
$374$	−8.20820	+	19.7430i	−0.424436	+	1.02089i
$375$		0			0
$376$	−24.3262	−	3.30009i	−1.25453	−	0.170189i
$377$			7.50915i			0.386741i
$378$		0			0
$379$		−	1.02589i		−	0.0526966i	−0.999653	−	0.0263483i	$-0.991612\pi$
$379$		−	1.02589i		−	0.0526966i	0.999653	−	0.0263483i	$-0.00838790\pi$
$380$	7.93401	+	7.97577i	0.407006	+	0.409148i
$381$		0			0
$382$	−21.5276	−	8.95012i	−1.10145	−	0.457928i
$383$	−25.2687			−1.29117			−0.645584	−	0.763689i	$-0.723386\pi$
$383$	−25.2687			−1.29117			−0.645584	+	0.763689i	$0.723386\pi$
$384$		0			0
$385$	12.7407	+	20.6609i	0.649327	+	1.05298i
$386$	26.0232	−	19.9141i	1.32454	−	1.01360i
$387$		0			0
$388$	−18.4045	−	18.5014i	−0.934347	−	0.939265i
$389$		−	9.30821i		−	0.471945i	−0.971760	−	0.235973i	$-0.924172\pi$
$389$		−	9.30821i		−	0.471945i	0.971760	−	0.235973i	$-0.0758276\pi$
$390$		0			0
$391$	12.6880	+	7.32545i	0.641662	+	0.370464i
$392$	−19.7405	−	1.52060i	−0.997046	−	0.0768017i
$393$		0			0
$394$	−20.2102	+	2.63375i	−1.01818	+	0.132686i
$395$	4.96108	−	8.59284i	0.249619	−	0.432353i
$396$		0			0
$397$	−7.25979	−	12.5743i	−0.364358	−	0.631087i	0.624315	−	0.781173i	$-0.285378\pi$
$397$	−7.25979	−	12.5743i	−0.364358	−	0.631087i	−0.988673	+	0.150086i	$0.952045\pi$
$398$	1.48247	−	3.56576i	0.0743096	−	0.178736i
$399$		0			0
$400$	−3.61948	+	2.06445i	−0.180974	+	0.103222i
$401$			17.9574i			0.896748i	0.893846	+	0.448374i	$0.147997\pi$
$401$			17.9574i			0.896748i	−0.893846	+	0.448374i	$0.852003\pi$
$402$		0			0
$403$			8.80955i			0.438835i
$404$	−2.80952	−	10.5964i	−0.139779	−	0.527193i
$405$		0			0
$406$	−18.5336	−	7.08277i	−0.919806	−	0.351512i
$407$	8.86048	+	15.3468i	0.439198	+	0.760713i
$408$		0			0
$409$	0.158417	+	0.274386i	0.00783322	+	0.0135675i	0.869915	−	0.493201i	$-0.164173\pi$
$409$	0.158417	+	0.274386i	0.00783322	+	0.0135675i	−0.862082	+	0.506768i	$0.830840\pi$
$410$	28.4389	+	11.8235i	1.40449	+	0.583922i
$411$		0			0
$412$	8.42970	+	31.7937i	0.415302	+	1.56636i
$413$	8.18279	+	4.41327i	0.402649	+	0.217163i
$414$		0			0
$415$	0.478323	−	0.276160i	0.0234800	−	0.0135562i
$416$	−7.94884	+	0.993464i	−0.389724	+	0.0487086i
$417$		0			0
$418$	7.34109	+	9.59314i	0.359064	+	0.469216i
$419$	8.80022	−	15.2424i	0.429919	−	0.744641i	−0.566947	−	0.823754i	$-0.691876\pi$
$419$	8.80022	−	15.2424i	0.429919	−	0.744641i	0.996866	+	0.0791133i	$0.0252089\pi$
$420$		0			0
$421$	−11.4743	−	19.8741i	−0.559224	−	0.968605i	−0.997561	−	0.0697943i	$-0.977766\pi$
$421$	−11.4743	−	19.8741i	−0.559224	−	0.968605i	0.438337	−	0.898811i	$-0.355568\pi$
$422$	−4.96409	+	11.9400i	−0.241648	+	0.581231i
$423$		0			0
$424$	−3.04270	+	22.4288i	−0.147766	+	1.08924i
$425$	−3.65423	−	2.10977i	−0.177256	−	0.102339i
$426$		0			0
$427$	0.802333	+	27.6782i	0.0388276	+	1.33944i
$428$	12.3560	+	12.4210i	0.597248	+	0.600391i
$429$		0			0
$430$	−33.6428	+	25.7450i	−1.62240	+	1.24153i
$431$	11.3929	−	19.7331i	0.548778	−	0.950512i	−0.449580	−	0.893240i	$-0.648426\pi$
$431$	11.3929	−	19.7331i	0.548778	−	0.950512i	0.998359	−	0.0572722i	$-0.0182403\pi$
$432$		0			0
$433$	−25.9567			−1.24740			−0.623700	−	0.781664i	$-0.714371\pi$
$433$	−25.9567			−1.24740			−0.623700	+	0.781664i	$0.714371\pi$
$434$	−21.7431	−	8.30932i	−1.04370	−	0.398860i
$435$		0			0
$436$	6.09692	−	22.5174i	0.291989	−	1.07839i
$437$	7.16832	−	4.13863i	0.342907	−	0.197977i
$438$		0			0
$439$	3.39989	+	1.96293i	0.162268	+	0.0936854i	0.578935	−	0.815374i	$-0.303469\pi$
$439$	3.39989	+	1.96293i	0.162268	+	0.0936854i	−0.416667	+	0.909059i	$0.636802\pi$
$440$	−24.0130	+	9.83592i	−1.14477	+	0.468909i
$441$		0			0
$442$	−4.92982	−	6.44215i	−0.234488	−	0.306422i
$443$	−5.66882	+	9.81868i	−0.269334	+	0.466500i	−0.968690	−	0.248274i	$-0.920137\pi$
$443$	−5.66882	+	9.81868i	−0.269334	+	0.466500i	0.699356	+	0.714773i	$0.253470\pi$
$444$		0			0
$445$	12.1383	+	21.0242i	0.575413	+	0.996644i
$446$	7.72086	+	10.0894i	0.365593	+	0.477747i
$447$		0			0
$448$	5.04549	−	20.5559i	0.238377	−	0.971173i
$449$			15.6718i			0.739600i	0.929111	+	0.369800i	$0.120574\pi$
$449$			15.6718i			0.739600i	−0.929111	+	0.369800i	$0.879426\pi$
$450$		0			0
$451$	28.6398	+	16.5352i	1.34860	+	0.778613i
$452$	−18.6339	−	5.04540i	−0.876466	−	0.237316i
$453$		0			0
$454$	1.89491	+	14.5407i	0.0889323	+	0.682428i
$455$	−9.20537	+	0.266844i	−0.431554	+	0.0125098i
$456$		0			0
$457$	8.74272	−	15.1428i	0.408967	−	0.708352i	−0.585807	−	0.810451i	$-0.699222\pi$
$457$	8.74272	−	15.1428i	0.408967	−	0.708352i	0.994774	+	0.102099i	$0.0325557\pi$
$458$	−0.678009	−	5.20275i	−0.0316813	−	0.243108i
$459$		0			0
$460$	4.55696	+	17.1871i	0.212469	+	0.801354i
$461$	−2.17782	+	1.25736i	−0.101431	+	0.0585613i	−0.549857	−	0.835259i	$-0.685318\pi$
$461$	−2.17782	+	1.25736i	−0.101431	+	0.0585613i	0.448426	+	0.893820i	$0.351985\pi$
$462$		0			0
$463$	15.3322	+	8.85204i	0.712547	+	0.411389i	0.812003	−	0.583653i	$-0.198377\pi$
$463$	15.3322	+	8.85204i	0.712547	+	0.411389i	−0.0994566	+	0.995042i	$0.531710\pi$
$464$	10.7017	−	18.3131i	0.496812	−	0.850166i
$465$		0			0
$466$	12.8618	+	16.8074i	0.595810	+	0.778588i
$467$	11.9222	+	20.6498i	0.551693	+	0.955560i	0.998153	+	0.0607566i	$0.0193514\pi$
$467$	11.9222	+	20.6498i	0.551693	+	0.955560i	−0.446460	+	0.894804i	$0.647315\pi$
$468$		0			0
$469$	13.7679	−	25.5275i	0.635742	−	1.17875i
$470$	11.5824	−	27.8588i	0.534255	−	1.28503i
$471$		0			0
$472$	−6.08146	+	7.86123i	−0.279922	+	0.361842i
$473$	−39.3937	+	22.7439i	−1.81132	+	1.04577i
$474$		0			0
$475$	−2.06451	+	1.19195i	−0.0947264	+	0.0546903i
$476$	20.5500	−	6.09110i	0.941907	−	0.279185i
$477$		0			0
$478$	−17.8765	−	7.43220i	−0.817653	−	0.339941i
$479$	1.78481			0.0815499			0.0407750	−	0.999168i	$-0.487017\pi$
$479$	1.78481			0.0815499			0.0407750	+	0.999168i	$0.487017\pi$
$480$		0			0
$481$	−6.72327			−0.306555
$482$	2.14521	+	16.4614i	0.0977114	+	0.749795i
$483$		0			0
$484$	−5.66752	+	1.50267i	−0.257615	+	0.0683034i
$485$	27.7755	−	16.0362i	1.26122	−	0.728167i
$486$		0			0
$487$	−14.2958	−	8.25366i	−0.647803	−	0.374009i	0.139811	−	0.990178i	$-0.455351\pi$
$487$	−14.2958	−	8.25366i	−0.647803	−	0.374009i	−0.787614	+	0.616169i	$0.788684\pi$
$488$	−29.3330	−	3.97932i	−1.32784	−	0.180135i
$489$		0			0
$490$	8.02406	−	22.9718i	0.362490	−	1.03776i
$491$	−16.6450	+	28.8300i	−0.751179	+	1.30108i	0.196072	+	0.980589i	$0.437181\pi$
$491$	−16.6450	+	28.8300i	−0.751179	+	1.30108i	−0.947252	+	0.320491i	$0.896152\pi$
$492$		0			0
$493$	21.4790			0.967366
$494$	−4.54458	+	0.592238i	−0.204470	+	0.0266460i
$495$		0			0
$496$	12.5549	−	21.4845i	0.563733	−	0.964683i
$497$	4.54651	−	2.80365i	0.203939	−	0.125761i
$498$		0			0
$499$		−	27.9415i		−	1.25083i	−0.780291	−	0.625417i	$-0.784929\pi$
$499$		−	27.9415i		−	1.25083i	0.780291	−	0.625417i	$-0.215071\pi$
$500$	4.98697	+	18.8090i	0.223024	+	0.841163i
$501$		0			0
$502$	−3.22494	−	24.7468i	−0.143936	−	1.10450i
$503$	−1.00731			−0.0449138			−0.0224569	−	0.999748i	$-0.507149\pi$
$503$	−1.00731			−0.0449138			−0.0224569	+	0.999748i	$0.507149\pi$
$504$		0			0
$505$	13.4729			0.599538
$506$	2.46723	+	18.9324i	0.109682	+	0.841648i
$507$		0			0
$508$	−0.480776	−	1.81331i	−0.0213310	−	0.0804524i
$509$			5.35143i			0.237198i	0.992942	+	0.118599i	$0.0378403\pi$
$509$			5.35143i			0.237198i	−0.992942	+	0.118599i	$0.962160\pi$
$510$		0			0
$511$	0.0727307	+	2.50900i	0.00321742	+	0.110992i
$512$	20.8013	+	8.90545i	0.919295	+	0.393569i
$513$		0			0
$514$	20.9240	−	2.72676i	0.922916	−	0.120272i
$515$	−40.4243			−1.78131
$516$		0			0
$517$	16.1980	−	28.0557i	0.712386	−	1.23389i
$518$	6.34151	−	16.5939i	0.278630	−	0.729095i
$519$		0			0
$520$	1.32346	−	9.75572i	0.0580377	−	0.427817i
$521$	0.0326842	+	0.0188702i	0.00143192	+	0.000826719i	0.500716	−	0.865612i	$-0.333070\pi$
$521$	0.0326842	+	0.0188702i	0.00143192	+	0.000826719i	−0.499284	+	0.866438i	$0.666404\pi$
$522$		0			0
$523$	22.6882	−	13.0990i	0.992086	−	0.572781i	0.0861890	−	0.996279i	$-0.472531\pi$
$523$	22.6882	−	13.0990i	0.992086	−	0.572781i	0.905897	+	0.423498i	$0.139198\pi$
$524$	−13.4781	+	3.57355i	−0.588794	+	0.156111i
$525$		0			0
$526$	0.155926	+	1.19650i	0.00679867	+	0.0521701i
$527$	25.1986			1.09767
$528$		0			0
$529$	−9.91746			−0.431194
$530$	−25.6859	−	10.6790i	−1.11573	−	0.463865i
$531$		0			0
$532$	2.82480	−	11.7752i	0.122471	−	0.510521i
$533$	−10.8658	+	6.27340i	−0.470652	+	0.271731i
$534$		0			0
$535$	−18.6473	+	10.7660i	−0.806191	+	0.465455i
$536$	24.5243	+	18.9720i	1.05929	+	0.819467i
$537$		0			0
$538$	−4.38180	+	10.5395i	−0.188913	+	0.454388i
$539$	11.7311	−	23.3459i	0.505296	−	1.00558i
$540$		0			0
$541$	3.71877	+	6.44110i	0.159882	+	0.276925i	0.934826	−	0.355106i	$-0.115555\pi$
$541$	3.71877	+	6.44110i	0.159882	+	0.276925i	−0.774944	+	0.632030i	$0.782222\pi$
$542$	−13.4406	−	17.5638i	−0.577324	−	0.754431i
$543$		0			0
$544$	2.84168	+	22.7367i	0.121836	+	0.974828i
$545$	24.8292	+	14.3351i	1.06357	+	0.614050i
$546$		0			0
$547$	1.62692	−	0.939303i	0.0695621	−	0.0401617i	−0.464816	−	0.885408i	$-0.653879\pi$
$547$	1.62692	−	0.939303i	0.0695621	−	0.0401617i	0.534378	+	0.845246i	$0.320546\pi$
$548$	−7.46680	−	28.1620i	−0.318966	−	1.20302i
$549$		0			0
$550$	−0.710574	−	5.45264i	−0.0302990	−	0.232501i
$551$	6.06746	−	10.5091i	0.258482	−	0.447705i
$552$		0			0
$553$	−10.6756	+	0.309464i	−0.453973	+	0.0131597i
$554$	−3.70015	−	28.3933i	−0.157204	−	1.20632i
$555$		0			0
$556$	−25.1870	−	6.81973i	−1.06816	−	0.289221i
$557$	−8.36838	−	4.83149i	−0.354580	−	0.204717i	0.312121	−	0.950042i	$-0.398961\pi$
$557$	−8.36838	−	4.83149i	−0.354580	−	0.204717i	−0.666700	+	0.745326i	$0.732294\pi$
$558$		0			0
$559$		−	17.2579i		−	0.729932i
$560$	22.8301	+	12.4683i	0.964748	+	0.526880i
$561$		0			0
$562$	−5.46362	−	7.13971i	−0.230469	−	0.301171i
$563$	7.44672	+	12.8981i	0.313842	+	0.543590i	0.979191	−	0.202943i	$-0.0650505\pi$
$563$	7.44672	+	12.8981i	0.313842	+	0.543590i	−0.665349	+	0.746533i	$0.731717\pi$
$564$		0			0
$565$	11.8628	−	20.5470i	0.499072	−	0.864418i
$566$	−8.78930	−	11.4856i	−0.369442	−	0.482777i
$567$		0			0
$568$	2.16444	+	5.28416i	0.0908177	+	0.221718i
$569$	−3.30697	−	1.90928i	−0.138635	−	0.0800412i	0.429078	−	0.903267i	$-0.358839\pi$
$569$	−3.30697	−	1.90928i	−0.138635	−	0.0800412i	−0.567714	+	0.823226i	$0.692172\pi$
$570$		0			0
$571$	−3.92146	+	2.26406i	−0.164108	+	0.0947478i	−0.579805	−	0.814756i	$-0.696871\pi$
$571$	−3.92146	+	2.26406i	−0.164108	+	0.0947478i	0.415697	+	0.909503i	$0.363538\pi$
$572$	2.76283	−	10.2038i	0.115520	−	0.426643i
$573$		0			0
$574$	−5.23472	−	32.7355i	−0.218493	−	1.36635i
$575$	−3.76784			−0.157130
$576$		0			0
$577$	11.9152	−	20.6378i	0.496038	−	0.859162i	−0.503952	−	0.863732i	$-0.668121\pi$
$577$	11.9152	−	20.6378i	0.496038	−	0.859162i	0.999990	+	0.00456937i	$0.00145448\pi$
$578$	0.665698	−	0.509421i	0.0276894	−	0.0211891i
$579$		0			0
$580$	18.3843	+	18.4811i	0.763369	+	0.767387i
$581$	−0.523259	−	0.282212i	−0.0217084	−	0.0117081i
$582$		0			0
$583$	−25.8675	−	14.9346i	−1.07132	−	0.618527i
$584$	−2.65901	−	0.360721i	−0.110031	−	0.0149268i
$585$		0			0
$586$	12.9516	−	31.1523i	0.535028	−	1.28689i
$587$	−8.04599	−	13.9361i	−0.332094	−	0.575203i	0.650829	−	0.759225i	$-0.274422\pi$
$587$	−8.04599	−	13.9361i	−0.332094	−	0.575203i	−0.982922	+	0.184022i	$0.941088\pi$
$588$		0			0
$589$	7.11819	−	12.3291i	0.293300	−	0.508010i
$590$	−7.42325	−	9.70051i	−0.305610	−	0.399364i
$591$		0			0
$592$	16.3965	+	9.58166i	0.673894	+	0.393804i
$593$	21.5747	−	12.4561i	0.885966	−	0.511513i	0.0133450	−	0.999911i	$-0.495752\pi$
$593$	21.5747	−	12.4561i	0.885966	−	0.511513i	0.872621	+	0.488398i	$0.162419\pi$
$594$		0			0
$595$	0.763275	+	26.3308i	0.0312912	+	1.07946i
$596$	11.3911	+	42.9631i	0.466599	+	1.75984i
$597$		0			0
$598$	−6.68859	−	2.78079i	−0.273517	−	0.113715i
$599$	−5.20340	−	9.01255i	−0.212605	−	0.368243i	0.739924	−	0.672691i	$-0.234861\pi$
$599$	−5.20340	−	9.01255i	−0.212605	−	0.368243i	−0.952529	+	0.304448i	$0.901528\pi$
$600$		0			0
$601$	−19.7275	−	34.1690i	−0.804701	−	1.39378i	−0.916493	−	0.400052i	$-0.868992\pi$
$601$	−19.7275	−	34.1690i	−0.804701	−	1.39378i	0.111791	−	0.993732i	$-0.464341\pi$
$602$	42.5949	+	16.2780i	1.73604	+	0.663441i
$603$		0			0
$604$	−1.15690	−	4.36341i	−0.0470738	−	0.177545i
$605$		−	7.20602i		−	0.292966i
$606$		0			0
$607$		−	10.3456i		−	0.419914i	−0.977711	−	0.209957i	$-0.932668\pi$
$607$		−	10.3456i		−	0.419914i	0.977711	−	0.209957i	$-0.0673323\pi$
$608$	11.9272	+	5.03237i	0.483713	+	0.204089i
$609$		0			0
$610$	13.9662	−	33.5927i	0.565477	−	1.36013i
$611$	6.14545	+	10.6442i	0.248618	+	0.430620i
$612$		0			0
$613$	−18.1531	+	31.4421i	−0.733196	+	1.26993i	0.222314	+	0.974975i	$0.428639\pi$
$613$	−18.1531	+	31.4421i	−0.733196	+	1.26993i	−0.955510	+	0.294958i	$0.904694\pi$
$614$	−9.04495	+	1.17872i	−0.365024	+	0.0475691i
$615$		0			0
$616$	22.5784	+	16.4435i	0.909711	+	0.662526i
$617$	5.74103	+	3.31459i	0.231125	+	0.133440i	0.611091	−	0.791560i	$-0.290731\pi$
$617$	5.74103	+	3.31459i	0.231125	+	0.133440i	−0.379966	+	0.925001i	$0.624064\pi$
$618$		0			0
$619$		−	38.3693i		−	1.54219i	−0.636717	−	0.771097i	$-0.719708\pi$
$619$		−	38.3693i		−	1.54219i	0.636717	−	0.771097i	$-0.280292\pi$
$620$	21.5681	+	21.6816i	0.866194	+	0.870753i
$621$		0			0
$622$	−0.568455	+	0.435007i	−0.0227930	+	0.0174422i
$623$	12.4044	−	22.9993i	0.496970	−	0.921449i
$624$		0			0
$625$	−29.1234			−1.16494
$626$	−33.1463	−	13.7806i	−1.32479	−	0.550785i
$627$		0			0
$628$	−3.13640	−	3.15290i	−0.125156	−	0.125815i
$629$			19.2311i			0.766794i
$630$		0			0
$631$		−	24.9683i		−	0.993973i	−0.867758	−	0.496986i	$-0.834440\pi$
$631$		−	24.9683i		−	0.993973i	0.867758	−	0.496986i	$-0.165560\pi$
$632$	1.53484	−	11.3139i	0.0610527	−	0.450042i
$633$		0			0
$634$	13.0644	−	31.4235i	0.518854	−	1.24799i
$635$	2.30554			0.0914927
$636$		0			0
$637$	5.44532	+	8.28314i	0.215751	+	0.328190i
$638$	17.0105	+	22.2288i	0.673451	+	0.880047i
$639$		0			0
$640$	−17.1310	+	21.9059i	−0.677162	+	0.865906i
$641$		−	7.58006i		−	0.299394i	−0.988732	−	0.149697i	$-0.952170\pi$
$641$		−	7.58006i		−	0.299394i	0.988732	−	0.149697i	$-0.0478299\pi$
$642$		0			0
$643$	−29.8134	−	17.2128i	−1.17573	−	0.678806i	−0.220705	−	0.975341i	$-0.570836\pi$
$643$	−29.8134	−	17.2128i	−1.17573	−	0.678806i	−0.955022	+	0.296535i	$0.904169\pi$
$644$	13.1722	−	13.8854i	0.519056	−	0.547163i
$645$		0			0
$646$	1.69403	+	12.9992i	0.0666505	+	0.511447i
$647$	−18.3282	+	31.7454i	−0.720557	+	1.24804i	0.240220	+	0.970719i	$0.422780\pi$
$647$	−18.3282	+	31.7454i	−0.720557	+	1.24804i	−0.960777	+	0.277323i	$0.910553\pi$
$648$		0			0
$649$	−6.55794	−	11.3587i	−0.257422	−	0.445868i
$650$	1.92635	+	0.800884i	0.0755576	+	0.0314132i
$651$		0			0
$652$	−0.785849	+	0.781734i	−0.0307762	+	0.0306151i
$653$		−	14.7474i		−	0.577110i	−0.957463	−	0.288555i	$-0.906825\pi$
$653$		−	14.7474i		−	0.577110i	0.957463	−	0.288555i	$-0.0931748\pi$
$654$		0			0
$655$		−	17.1368i		−	0.669592i
$656$	35.4399	+	0.186050i	1.38370	+	0.00726404i
$657$		0			0
$658$	−32.0679	+	5.12796i	−1.25014	+	0.199909i
$659$	−14.0724	−	24.3742i	−0.548184	−	0.949483i	−0.998399	−	0.0565626i	$-0.981986\pi$
$659$	−14.0724	−	24.3742i	−0.548184	−	0.949483i	0.450215	−	0.892920i	$-0.351347\pi$
$660$		0			0
$661$	−0.520581	−	0.901673i	−0.0202483	−	0.0350710i	0.855724	−	0.517433i	$-0.173112\pi$
$661$	−0.520581	−	0.901673i	−0.0202483	−	0.0350710i	−0.875972	+	0.482362i	$0.839779\pi$
$662$	−3.64048	+	8.75639i	−0.141491	+	0.340327i
$663$		0			0
$664$	0.388886	−	0.502696i	0.0150917	−	0.0195084i
$665$	13.0986	+	7.06456i	0.507943	+	0.273952i
$666$		0			0
$667$	16.6101	−	9.58986i	0.643147	−	0.371321i
$668$	−6.05193	+	22.3513i	−0.234156	+	0.864797i
$669$		0			0
$670$	−30.2622	+	23.1580i	−1.16913	+	0.894671i
$671$	19.5318	−	33.8301i	0.754018	−	1.30600i
$672$		0			0
$673$	6.14987	+	10.6519i	0.237060	+	0.410600i	0.959869	−	0.280448i	$-0.0904829\pi$
$673$	6.14987	+	10.6519i	0.237060	+	0.410600i	−0.722809	+	0.691047i	$0.757150\pi$
$674$	−40.0463	−	16.6493i	−1.54253	−	0.641308i
$675$		0			0
$676$	−15.5079	−	15.5896i	−0.596459	−	0.599598i
$677$	−8.08976	−	4.67062i	−0.310915	−	0.179507i	0.336421	−	0.941712i	$-0.390783\pi$
$677$	−8.08976	−	4.67062i	−0.310915	−	0.179507i	−0.647336	+	0.762205i	$0.724117\pi$
$678$		0			0
$679$	−30.3849	−	16.3877i	−1.16606	−	0.628900i
$680$	−27.9051	−	3.78560i	−1.07011	−	0.145171i
$681$		0			0
$682$	19.9563	+	26.0783i	0.764165	+	0.998589i
$683$	−10.8870	+	18.8568i	−0.416578	+	0.721535i	−0.995593	−	0.0937826i	$-0.970104\pi$
$683$	−10.8870	+	18.8568i	−0.416578	+	0.721535i	0.579014	+	0.815317i	$0.303437\pi$
$684$		0			0
$685$	35.8068			1.36811
$686$	−25.5800	+	5.62697i	−0.976650	+	0.214839i
$687$		0			0
$688$	−24.5951	+	42.0882i	−0.937680	+	1.60460i
$689$	9.81401	−	5.66612i	0.373884	−	0.215862i
$690$		0			0
$691$	21.1790	+	12.2277i	0.805689	+	0.465165i	0.845456	−	0.534044i	$-0.179328\pi$
$691$	21.1790	+	12.2277i	0.805689	+	0.465165i	−0.0397677	+	0.999209i	$0.512662\pi$
$692$	−20.5791	−	5.57208i	−0.782298	−	0.211819i
$693$		0			0
$694$	−10.1461	+	7.76423i	−0.385140	+	0.294726i
$695$	16.0346	−	27.7728i	0.608228	−	1.05348i
$696$		0			0
$697$	17.9443	+	31.0804i	0.679689	+	1.17726i
$698$	−24.4845	+	18.7366i	−0.926751	+	0.709190i
$699$		0			0
$700$	−3.79365	+	3.99908i	−0.143387	+	0.151151i
$701$		−	10.4921i		−	0.396279i	−0.980174	−	0.198140i	$-0.936510\pi$
$701$		−	10.4921i		−	0.396279i	0.980174	−	0.198140i	$-0.0634900\pi$
$702$		0			0
$703$	9.40929	+	5.43246i	0.354878	+	0.204889i
$704$	−21.2799	+	20.9474i	−0.802017	+	0.789484i
$705$		0			0
$706$	16.7187	−	2.17874i	0.629215	−	0.0819978i
$707$	−7.61192	−	12.3438i	−0.286276	−	0.464237i
$708$		0			0
$709$	−3.34723	+	5.79758i	−0.125708	+	0.217733i	−0.922009	−	0.387167i	$-0.873454\pi$
$709$	−3.34723	+	5.79758i	−0.125708	+	0.217733i	0.796301	+	0.604900i	$0.206787\pi$
$710$	−6.95904	+	0.906885i	−0.261168	+	0.0340348i
$711$		0			0
$712$	22.0955	+	17.0931i	0.828064	+	0.640591i
$713$	19.4866	−	11.2506i	0.729778	−	0.421338i
$714$		0			0
$715$	11.2514	+	6.49600i	0.420779	+	0.242937i
$716$	−11.0759	+	40.9059i	−0.413925	+	1.52873i
$717$		0			0
$718$	11.5401	−	8.83096i	0.430671	−	0.329569i
$719$	−8.66863	−	15.0145i	−0.323285	−	0.559947i	0.657879	−	0.753124i	$-0.271454\pi$
$719$	−8.66863	−	15.0145i	−0.323285	−	0.559947i	−0.981164	+	0.193177i	$0.938121\pi$
$720$		0			0
$721$	22.8389	+	37.0365i	0.850565	+	1.37931i
$722$	−17.9725	−	7.47209i	−0.668866	−	0.278082i
$723$		0			0
$724$	32.0697	−	8.50289i	1.19186	−	0.316008i
$725$	−4.78381	+	2.76193i	−0.177666	+	0.102576i
$726$		0			0
$727$	−18.0236	+	10.4059i	−0.668458	+	0.385934i	−0.795492	−	0.605964i	$-0.792787\pi$
$727$	−18.0236	+	10.4059i	−0.668458	+	0.385934i	0.127034	+	0.991898i	$0.459454\pi$
$728$	−9.68586	+	4.29923i	−0.358982	+	0.159340i
$729$		0			0
$730$	1.26603	−	3.04515i	0.0468577	−	0.112706i
$731$	−49.3642			−1.82580
$732$		0			0
$733$	1.69574			0.0626336			0.0313168	−	0.999510i	$-0.490030\pi$
$733$	1.69574			0.0626336			0.0313168	+	0.999510i	$0.490030\pi$
$734$	−38.4789	+	5.01447i	−1.42028	+	0.185088i
$735$		0			0
$736$	12.3489	+	16.3140i	0.455187	+	0.601341i
$737$	−35.4352	+	20.4585i	−1.30527	+	0.753599i
$738$		0			0
$739$	−42.4863	−	24.5295i	−1.56288	−	0.902331i	−0.996963	−	0.0778716i	$-0.975188\pi$
$739$	−42.4863	−	24.5295i	−1.56288	−	0.902331i	−0.565920	−	0.824460i	$-0.691479\pi$
$740$	−16.5469	+	16.4603i	−0.608278	+	0.605093i
$741$		0			0
$742$	4.72799	+	29.5667i	0.173570	+	1.08543i
$743$	13.4749	−	23.3392i	0.494346	−	0.856232i	−0.505633	−	0.862749i	$-0.668741\pi$
$743$	13.4749	−	23.3392i	0.494346	−	0.856232i	0.999979	+	0.00651646i	$0.00207427\pi$
$744$		0			0
$745$	−54.6258			−2.00133
$746$	−0.925674	−	7.10322i	−0.0338913	−	0.260067i
$747$		0			0
$748$	−29.1868	−	7.90275i	−1.06718	−	0.288953i
$749$	20.3990	+	11.0019i	0.745365	+	0.402002i
$750$		0			0
$751$			33.6139i			1.22659i	0.789855	+	0.613294i	$0.210156\pi$
$751$			33.6139i			1.22659i	−0.789855	+	0.613294i	$0.789844\pi$
$752$	0.182256	−	34.7171i	0.00664618	−	1.26600i
$753$		0			0
$754$	−10.5305	+	1.37231i	−0.383498	+	0.0499765i
$755$	5.54789			0.201908
$756$		0			0
$757$	30.1721			1.09662			0.548312	−	0.836274i	$-0.315271\pi$
$757$	30.1721			1.09662			0.548312	+	0.836274i	$0.315271\pi$
$758$	1.43867	−	0.187484i	0.0522548	−	0.00680972i
$759$		0			0
$760$	−9.73491	+	12.5839i	−0.353122	+	0.456465i
$761$			15.9088i			0.576694i	0.957526	+	0.288347i	$0.0931056\pi$
$761$			15.9088i			0.576694i	−0.957526	+	0.288347i	$0.906894\pi$
$762$		0			0
$763$	−0.894201	−	30.8474i	−0.0323722	−	1.11675i
$764$	8.61706	−	31.8249i	0.311754	−	1.15139i
$765$		0			0
$766$	−4.61789	−	35.4356i	−0.166851	−	1.28034i
$767$	4.97612			0.179677
$768$		0			0
$769$	−2.11592	+	3.66489i	−0.0763022	+	0.132159i	−0.901652	−	0.432463i	$-0.857645\pi$
$769$	−2.11592	+	3.66489i	−0.0763022	+	0.132159i	0.825350	+	0.564622i	$0.190978\pi$
$770$	−26.6455	+	21.6428i	−0.960238	+	0.779953i
$771$		0			0
$772$	32.6824	+	32.8544i	1.17626	+	1.18246i
$773$	−24.1708	−	13.9550i	−0.869362	−	0.501927i	−0.00222598	−	0.999998i	$-0.500709\pi$
$773$	−24.1708	−	13.9550i	−0.869362	−	0.501927i	−0.867136	+	0.498071i	$0.834042\pi$
$774$		0			0
$775$	−5.61224	+	3.24023i	−0.201598	+	0.116392i
$776$	22.5821	−	29.1908i	0.810648	−	1.04789i
$777$		0			0
$778$	13.0534	−	1.70109i	0.467988	−	0.0609871i
$779$	20.2758			0.726457
$780$		0			0
$781$	−7.53551			−0.269642
$782$	−7.95412	+	19.1319i	−0.284439	+	0.684155i
$783$		0			0
$784$	−1.47519	−	27.9611i	−0.0526855	−	0.998611i
$785$	4.73336	−	2.73281i	0.168941	−	0.0975380i
$786$		0			0
$787$	5.59132	−	3.22815i	0.199309	−	0.115071i	−0.397024	−	0.917808i	$-0.629957\pi$
$787$	5.59132	−	3.22815i	0.199309	−	0.115071i	0.596333	+	0.802737i	$0.296624\pi$
$788$	−7.38690	−	27.8606i	−0.263147	−	0.992492i
$789$		0			0
$790$	12.9569	+	5.38684i	0.460985	+	0.191655i
$791$	−25.5272	+	0.739981i	−0.907644	+	0.0263107i
$792$		0			0
$793$	7.41030	+	12.8350i	0.263148	+	0.455785i
$794$	16.3069	−	12.4788i	0.578712	−	0.442856i
$795$		0			0
$796$	5.27139	+	1.42731i	0.186840	+	0.0505895i
$797$	−29.3156	−	16.9254i	−1.03841	−	0.599528i	−0.119029	−	0.992891i	$-0.537978\pi$
$797$	−29.3156	−	16.9254i	−1.03841	−	0.599528i	−0.919383	+	0.393363i	$0.871312\pi$
$798$		0			0
$799$	30.4465	−	17.5783i	1.07712	−	0.621876i
$800$	−3.55655	−	4.69851i	−0.125743	−	0.166117i
$801$		0			0
$802$	−25.1826	+	3.28174i	−0.889229	+	0.115882i
$803$	1.77054	−	3.06667i	0.0624811	−	0.108220i
$804$		0			0
$805$	12.3463	+	20.0213i	0.435151	+	0.705660i
$806$	−12.3541	+	1.60996i	−0.435155	+	0.0567084i
$807$		0			0
$808$	14.3465	−	5.87646i	0.504709	−	0.206733i
$809$	6.11435	+	3.53012i	0.214969	+	0.124112i	0.603619	−	0.797273i	$-0.293725\pi$
$809$	6.11435	+	3.53012i	0.214969	+	0.124112i	−0.388650	+	0.921386i	$0.627058\pi$
$810$		0			0
$811$		−	40.7979i		−	1.43261i	−0.697789	−	0.716304i	$-0.745833\pi$
$811$		−	40.7979i		−	1.43261i	0.697789	−	0.716304i	$-0.254167\pi$
$812$	6.54552	−	27.2851i	0.229703	−	0.957518i
$813$		0			0
$814$	−19.9024	+	15.2302i	−0.697579	+	0.533818i
$815$	−0.681141	−	1.17977i	−0.0238593	−	0.0413256i
$816$		0			0
$817$	−13.9446	+	24.1527i	−0.487858	+	0.844995i
$818$	−0.355836	+	0.272302i	−0.0124415	+	0.00952081i
$819$		0			0
$820$	−11.3835	+	42.0422i	−0.397530	+	1.46818i
$821$	32.0732	+	18.5175i	1.11936	+	0.646265i	0.941238	−	0.337743i	$-0.109663\pi$
$821$	32.0732	+	18.5175i	1.11936	+	0.646265i	0.178125	+	0.984008i	$0.442997\pi$
$822$		0			0
$823$	10.2150	−	5.89764i	0.356073	−	0.205579i	−0.311284	−	0.950317i	$-0.600759\pi$
$823$	10.2150	−	5.89764i	0.356073	−	0.205579i	0.667357	+	0.744738i	$0.267426\pi$
$824$	−43.0455	+	17.6318i	−1.49956	+	0.614232i
$825$		0			0
$826$	−4.69356	+	12.2817i	−0.163310	+	0.427336i
$827$	9.85297			0.342621			0.171311	−	0.985217i	$-0.445200\pi$
$827$	9.85297			0.342621			0.171311	+	0.985217i	$0.445200\pi$
$828$		0			0
$829$	−6.91019	+	11.9688i	−0.240001	+	0.415693i	−0.960714	−	0.277540i	$-0.910481\pi$
$829$	−6.91019	+	11.9688i	−0.240001	+	0.415693i	0.720713	+	0.693233i	$0.243814\pi$
$830$	0.474689	+	0.620311i	0.0164767	+	0.0215313i
$831$		0			0
$832$	−2.84585	−	10.9655i	−0.0986622	−	0.380162i
$833$	23.6929	−	15.5757i	0.820911	−	0.539665i
$834$		0			0
$835$	−24.6460	−	14.2294i	−0.852909	−	0.492428i
$836$	−12.1114	+	12.0480i	−0.418881	+	0.416688i
$837$		0			0
$838$	22.9836	+	9.55546i	0.793954	+	0.330088i
$839$	21.5036	+	37.2454i	0.742388	+	1.28585i	0.951405	+	0.307942i	$0.0996402\pi$
$839$	21.5036	+	37.2454i	0.742388	+	1.28585i	−0.209017	+	0.977912i	$0.567026\pi$
$840$		0			0
$841$	−0.440737	+	0.763379i	−0.0151978	+	0.0263234i
$842$	25.7736	−	19.7231i	0.888218	−	0.679703i
$843$		0			0
$844$	−17.6514	−	4.77936i	−0.607585	−	0.164512i
$845$	23.4041	−	13.5124i	0.805126	−	0.464840i
$846$		0			0
$847$	−6.60211	+	4.07125i	−0.226851	+	0.139890i
$848$	−32.0093	−	0.168040i	−1.09920	−	0.00577053i
$849$		0			0
$850$	2.29083	−	5.51009i	0.0785748	−	0.188994i
$851$	8.58622	+	14.8718i	0.294332	+	0.509797i
$852$		0			0
$853$	−27.0808	−	46.9054i	−0.927230	−	1.60601i	−0.787935	−	0.615759i	$-0.788849\pi$
$853$	−27.0808	−	46.9054i	−0.927230	−	1.60601i	−0.139296	−	0.990251i	$-0.544484\pi$
$854$	−38.6681	+	6.18339i	−1.32319	+	0.211591i
$855$		0			0
$856$	−15.1606	+	19.5974i	−0.518178	+	0.669825i
$857$			35.0389i			1.19691i	0.801158	+	0.598453i	$0.204218\pi$
$857$			35.0389i			1.19691i	−0.801158	+	0.598453i	$0.795782\pi$
$858$		0			0
$859$		−	32.4153i		−	1.10600i	−0.833182	−	0.552999i	$-0.813483\pi$
$859$		−	32.4153i		−	1.10600i	0.833182	−	0.552999i	$-0.186517\pi$
$860$	−42.2519	−	42.4743i	−1.44078	−	1.44836i
$861$		0			0
$862$	29.7550	+	12.3707i	1.01346	+	0.421347i
$863$	0.619701	+	1.07335i	0.0210949	+	0.0365374i	0.876380	−	0.481620i	$-0.159951\pi$
$863$	0.619701	+	1.07335i	0.0210949	+	0.0365374i	−0.855285	+	0.518157i	$0.826618\pi$
$864$		0			0
$865$	13.1011	−	22.6918i	0.445452	−	0.771545i
$866$	−4.74363	−	36.4005i	−0.161195	−	1.23694i
$867$		0			0
$868$	7.67904	−	32.0102i	0.260643	−	1.08650i
$869$	13.0484	+	7.53352i	0.442638	+	0.255557i
$870$		0			0
$871$		−	15.5238i		−	0.526003i
$872$	32.6917	+	4.43495i	1.10708	+	0.150186i
$873$		0			0
$874$	7.11385	+	9.29619i	0.240630	+	0.314448i
$875$	13.5114	+	21.9106i	0.456768	+	0.740715i
$876$		0			0
$877$	48.0956			1.62407			0.812037	−	0.583606i	$-0.198359\pi$
$877$	48.0956			1.62407			0.812037	+	0.583606i	$0.198359\pi$
$878$	−2.13139	+	5.12658i	−0.0719308	+	0.173014i
$879$		0			0
$880$	−18.1819	−	31.8772i	−0.612911	−	1.07458i
$881$		−	5.79121i		−	0.195111i	−0.995230	−	0.0975554i	$-0.968898\pi$
$881$		−	5.79121i		−	0.195111i	0.995230	−	0.0975554i	$-0.0311023\pi$
$882$		0			0
$883$			52.6107i			1.77049i	0.465125	+	0.885245i	$0.346009\pi$
$883$			52.6107i			1.77049i	−0.465125	+	0.885245i	$0.653991\pi$
$884$	8.13326	−	8.09067i	0.273551	−	0.272119i
$885$		0			0
$886$	−14.8053	−	6.15532i	−0.497393	−	0.206792i
$887$	47.6931			1.60138			0.800689	−	0.599080i	$-0.204467\pi$
$887$	47.6931			1.60138			0.800689	+	0.599080i	$0.204467\pi$
$888$		0			0
$889$	−1.30258	−	2.11232i	−0.0436872	−	0.0708451i
$890$	−27.2652	+	20.8645i	−0.913930	+	0.699379i
$891$		0			0
$892$	−12.7379	+	12.6712i	−0.426498	+	0.424265i
$893$		−	19.8623i		−	0.664667i
$894$		0			0
$895$	−45.1055	−	26.0417i	−1.50771	−	0.870478i
$896$	29.7487	+	3.31895i	0.993834	+	0.110878i
$897$		0			0
$898$	−21.9775	+	2.86405i	−0.733398	+	0.0955747i
$899$	16.4940	−	28.5684i	0.550105	−	0.952810i
$900$		0			0
$901$	−16.2073	−	28.0718i	−0.539942	−	0.935207i
$902$	−17.9543	+	43.1851i	−0.597812	+	1.43791i
$903$		0			0
$904$	3.67007	−	27.0534i	0.122065	−	0.899784i
$905$			40.7753i			1.35542i
$906$		0			0
$907$			5.99987i			0.199223i	0.995026	+	0.0996113i	$0.0317599\pi$
$907$			5.99987i			0.199223i	−0.995026	+	0.0996113i	$0.968240\pi$
$908$	−20.0449	+	5.31466i	−0.665214	+	0.176373i
$909$		0			0
$910$	−2.05651	−	12.8604i	−0.0681725	−	0.426319i
$911$	−8.56559	−	14.8360i	−0.283791	−	0.491540i	0.688525	−	0.725213i	$-0.258259\pi$
$911$	−8.56559	−	14.8360i	−0.283791	−	0.491540i	−0.972315	+	0.233673i	$0.924925\pi$
$912$		0			0
$913$	0.419356	+	0.726346i	0.0138787	+	0.0240385i
$914$	22.8334	+	9.49303i	0.755261	+	0.314001i
$915$		0			0
$916$	7.17219	−	1.90162i	0.236976	−	0.0628313i
$917$	−15.7007	+	9.68196i	−0.518482	+	0.319726i
$918$		0			0
$919$	7.67873	−	4.43332i	0.253298	−	0.146242i	−0.367975	−	0.929836i	$-0.619949\pi$
$919$	7.67873	−	4.43332i	0.253298	−	0.146242i	0.621273	+	0.783594i	$0.286616\pi$
$920$	−23.2697	+	9.53146i	−0.767179	+	0.314243i
$921$		0			0
$922$	−2.16127	−	2.82429i	−0.0711777	−	0.0930130i
$923$	1.42947	−	2.47592i	0.0470517	−	0.0814959i
$924$		0			0
$925$	−2.47288	−	4.28315i	−0.0813077	−	0.140829i
$926$	−9.61172	+	23.1189i	−0.315861	+	0.759734i
$927$		0			0
$928$	27.6373	+	11.6608i	0.907238	+	0.382784i
$929$	9.29468	+	5.36629i	0.304949	+	0.176062i	0.644664	−	0.764466i	$-0.276997\pi$
$929$	9.29468	+	5.36629i	0.304949	+	0.176062i	−0.339715	+	0.940528i	$0.610331\pi$
$930$		0			0
$931$	−0.927941	−	15.9922i	−0.0304120	−	0.524124i
$932$	−21.2195	+	21.1084i	−0.695067	+	0.691427i
$933$		0			0
$934$	−26.7796	+	20.4929i	−0.876256	+	0.670550i
$935$	18.5810	−	32.1833i	0.607665	−	1.05251i
$936$		0			0
$937$	−21.5535			−0.704121			−0.352061	−	0.935977i	$-0.614519\pi$
$937$	−21.5535			−0.704121			−0.352061	+	0.935977i	$0.614519\pi$
$938$	38.3147	+	14.6423i	1.25102	+	0.478088i
$939$		0			0
$940$	41.1847	+	11.1514i	1.34330	+	0.363717i
$941$	8.80806	−	5.08533i	0.287134	−	0.165777i	−0.349514	−	0.936931i	$-0.613653\pi$
$941$	8.80806	−	5.08533i	0.287134	−	0.165777i	0.636649	+	0.771154i	$0.280320\pi$
$942$		0			0
$943$	27.7533	+	16.0234i	0.903772	+	0.521793i
$944$	−12.1356	−	7.09171i	−0.394981	−	0.230816i
$945$		0			0
$946$	−39.0943	−	51.0874i	−1.27107	−	1.66100i
$947$	3.11631	−	5.39761i	0.101267	−	0.175399i	−0.810940	−	0.585129i	$-0.801044\pi$
$947$	3.11631	−	5.39761i	0.101267	−	0.175399i	0.912207	+	0.409730i	$0.134377\pi$
$948$		0			0
$949$	0.671737	+	1.16348i	0.0218055	+	0.0377682i
$950$	−2.04883	−	2.67735i	−0.0664728	−	0.0868648i
$951$		0			0
$952$	12.2974	+	27.7052i	0.398562	+	0.897932i
$953$			24.0752i			0.779871i	0.920842	+	0.389936i	$0.127503\pi$
$953$			24.0752i			0.779871i	−0.920842	+	0.389936i	$0.872497\pi$
$954$		0			0
$955$	35.0923	+	20.2605i	1.13556	+	0.655615i
$956$	7.15563	−	26.4275i	0.231430	−	0.854726i
$957$		0			0
$958$	0.326176	+	2.50294i	0.0105383	+	0.0808662i
$959$	−20.2301	−	32.8059i	−0.653263	−	1.05936i
$960$		0			0
$961$	3.85032	−	6.66896i	0.124204	−	0.215128i
$962$	−1.22869	−	9.42841i	−0.0396145	−	0.303984i
$963$		0			0
$964$	−22.6927	+	6.01668i	−0.730881	+	0.193784i
$965$	−49.3233	+	28.4768i	−1.58777	+	0.916701i
$966$		0			0
$967$	1.08046	+	0.623806i	0.0347454	+	0.0200603i	0.517272	−	0.855821i	$-0.326948\pi$
$967$	1.08046	+	0.623806i	0.0347454	+	0.0200603i	−0.482527	+	0.875881i	$0.660281\pi$
$968$	−3.14303	−	7.67326i	−0.101021	−	0.246628i
$969$		0			0
$970$	27.5645	+	36.0205i	0.885043	+	1.15655i
$971$	−7.33316	−	12.7014i	−0.235332	−	0.407608i	0.724037	−	0.689761i	$-0.242285\pi$
$971$	−7.33316	−	12.7014i	−0.235332	−	0.407608i	−0.959369	+	0.282154i	$0.908951\pi$
$972$		0			0
$973$	−34.5045	+	1.00021i	−1.10616	+	0.0320653i
$974$	8.96200	−	21.5561i	0.287161	−	0.690703i
$975$		0			0
$976$	0.219767	−	41.8625i	0.00703458	−	1.33999i
$977$	36.4261	−	21.0306i	1.16538	−	0.672830i	0.212789	−	0.977098i	$-0.431745\pi$
$977$	36.4261	−	21.0306i	1.16538	−	0.672830i	0.952586	+	0.304268i	$0.0984120\pi$
$978$		0			0
$979$	−31.9258	+	18.4324i	−1.02035	+	0.589101i
$980$	33.6810	+	7.05446i	1.07590	+	0.225346i
$981$		0			0
$982$	−43.4718	−	18.0735i	−1.38724	−	0.576749i
$983$	7.02310			0.224002			0.112001	−	0.993708i	$-0.464274\pi$
$983$	7.02310			0.224002			0.112001	+	0.993708i	$0.464274\pi$
$984$		0			0
$985$	35.4236			1.12869
$986$	3.92532	+	30.1212i	0.125008	+	0.959255i
$987$		0			0
$988$	−1.66106	−	6.26488i	−0.0528452	−	0.199312i
$989$	−38.1743	+	22.0399i	−1.21387	+	0.700829i
$990$		0			0
$991$	34.0177	+	19.6402i	1.08061	+	0.623890i	0.931061	−	0.364864i	$-0.118885\pi$
$991$	34.0177	+	19.6402i	1.08061	+	0.623890i	0.149548	+	0.988754i	$0.452218\pi$
$992$	32.4234	+	13.6801i	1.02944	+	0.434345i
$993$		0			0
$994$	4.76259	+	5.86346i	0.151060	+	0.185978i
$995$	−3.35590	+	5.81258i	−0.106389	+	0.184271i
$996$		0			0
$997$	−4.54078			−0.143808			−0.0719039	−	0.997412i	$-0.522908\pi$
$997$	−4.54078			−0.143808			−0.0719039	+	0.997412i	$0.522908\pi$
$998$	39.1839	−	5.10635i	1.24035	−	0.161639i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.o.a.179.24		88
3.2	odd	2		252.2.o.a.95.21	yes	88
4.3	odd	2	inner	756.2.o.a.179.38		88
7.2	even	3		756.2.bb.a.611.36		88
9.2	odd	6		756.2.bb.a.683.9		88
9.7	even	3		252.2.bb.a.11.36	yes	88
12.11	even	2		252.2.o.a.95.7	✓	88
21.2	odd	6		252.2.bb.a.23.9	yes	88
28.23	odd	6		756.2.bb.a.611.9		88
36.7	odd	6		252.2.bb.a.11.9	yes	88
36.11	even	6		756.2.bb.a.683.36		88
63.2	odd	6	inner	756.2.o.a.359.38		88
63.16	even	3		252.2.o.a.191.7	yes	88
84.23	even	6		252.2.bb.a.23.36	yes	88
252.79	odd	6		252.2.o.a.191.21	yes	88
252.191	even	6	inner	756.2.o.a.359.24		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.7	✓	88	12.11	even	2
252.2.o.a.95.21	yes	88	3.2	odd	2
252.2.o.a.191.7	yes	88	63.16	even	3
252.2.o.a.191.21	yes	88	252.79	odd	6
252.2.bb.a.11.9	yes	88	36.7	odd	6
252.2.bb.a.11.36	yes	88	9.7	even	3
252.2.bb.a.23.9	yes	88	21.2	odd	6
252.2.bb.a.23.36	yes	88	84.23	even	6
756.2.o.a.179.24		88	1.1	even	1	trivial
756.2.o.a.179.38		88	4.3	odd	2	inner
756.2.o.a.359.24		88	252.191	even	6	inner
756.2.o.a.359.38		88	63.2	odd	6	inner
756.2.bb.a.611.9		88	28.23	odd	6
756.2.bb.a.611.36		88	7.2	even	3
756.2.bb.a.683.9		88	9.2	odd	6
756.2.bb.a.683.36		88	36.11	even	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.182752 + 1.40236i) q^{2} +(-1.93320 + 0.512566i) q^{4} -2.45799i q^{5} +(-2.25199 + 1.38871i) q^{7} +(-1.07210 - 2.61737i) q^{8} +O(q^{10})\)	\(q+(0.182752 + 1.40236i) q^{2} +(-1.93320 + 0.512566i) q^{4} -2.45799i q^{5} +(-2.25199 + 1.38871i) q^{7} +(-1.07210 - 2.61737i) q^{8} +(3.44698 - 0.449201i) q^{10} +3.73252 q^{11} +(-0.708051 + 1.22638i) q^{13} +(-2.35902 - 2.90431i) q^{14} +(3.47455 - 1.98179i) q^{16} +(3.50791 + 2.02529i) q^{17} +(1.98185 - 1.14422i) q^{19} +(1.25988 + 4.75179i) q^{20} +(0.682123 + 5.23432i) q^{22} +3.61698 q^{23} -1.04171 q^{25} +(-1.84922 - 0.768816i) q^{26} +(3.64176 - 3.83896i) q^{28} +(4.59226 - 2.65135i) q^{29} +(5.38753 - 3.11049i) q^{31} +(3.41415 + 4.51039i) q^{32} +(-2.19911 + 5.28947i) q^{34} +(3.41344 + 5.53538i) q^{35} +(2.37386 + 4.11165i) q^{37} +(1.96679 + 2.57015i) q^{38} +(-6.43346 + 2.63520i) q^{40} +(7.67307 + 4.43005i) q^{41} +(-10.5542 + 6.09346i) q^{43} +(-7.21571 + 1.91316i) q^{44} +(0.661009 + 5.07229i) q^{46} +(4.33970 - 7.51657i) q^{47} +(3.14296 - 6.25474i) q^{49} +(-0.190374 - 1.46085i) q^{50} +(0.740207 - 2.73377i) q^{52} +(-6.93030 - 4.00121i) q^{53} -9.17448i q^{55} +(6.04912 + 4.40547i) q^{56} +(4.55737 + 5.95545i) q^{58} +(-1.75698 - 3.04317i) q^{59} +(5.23289 - 9.06363i) q^{61} +(5.34660 + 6.98679i) q^{62} +(-5.70122 + 5.61213i) q^{64} +(3.01443 + 1.74038i) q^{65} +(-9.49365 + 5.48116i) q^{67} +(-7.81961 - 2.11727i) q^{68} +(-7.13876 + 5.79845i) q^{70} -2.01888 q^{71} +(0.474356 - 0.821609i) q^{73} +(-5.33217 + 4.08041i) q^{74} +(-3.24483 + 3.22784i) q^{76} +(-8.40560 + 5.18339i) q^{77} +(3.49588 + 2.01835i) q^{79} +(-4.87121 - 8.54041i) q^{80} +(-4.81024 + 11.5700i) q^{82} +(0.112352 + 0.194599i) q^{83} +(4.97815 - 8.62241i) q^{85} +(-10.4740 - 13.6871i) q^{86} +(-4.00161 - 9.76936i) q^{88} +(-8.55343 + 4.93832i) q^{89} +(-0.108562 - 3.74508i) q^{91} +(-6.99236 + 1.85394i) q^{92} +(11.3340 + 4.71213i) q^{94} +(-2.81249 - 4.87137i) q^{95} +(6.52412 + 11.3001i) q^{97} +(9.34576 + 3.26448i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 3 q^{2} + q^{4}+O(q^{10}) \) 88 * q + 3 * q^2 + q^4	\( 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) \) 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

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