LMFDB - Embedded newform 756.2.o.a.359.38

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			359.38
Character	$\chi$	$=$	756.359
Dual form			756.2.o.a.179.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30585 + 0.542910i) q^{2} +(1.41050 + 1.41792i) q^{4} +2.45799i q^{5} +(2.25199 + 1.38871i) q^{7} +(1.07210 + 2.61737i) q^{8} +O(q^{10})$	\(q+(1.30585 + 0.542910i) q^{2} +(1.41050 + 1.41792i) q^{4} +2.45799i q^{5} +(2.25199 + 1.38871i) q^{7} +(1.07210 + 2.61737i) q^{8} +(-1.33447 + 3.20977i) q^{10} -3.73252 q^{11} +(-0.708051 - 1.22638i) q^{13} +(2.18682 + 3.03608i) q^{14} +(-0.0209987 + 3.99994i) q^{16} +(3.50791 - 2.02529i) q^{17} +(-1.98185 - 1.14422i) q^{19} +(-3.48523 + 3.46699i) q^{20} +(-4.87411 - 2.02642i) q^{22} -3.61698 q^{23} -1.04171 q^{25} +(-0.258795 - 1.98588i) q^{26} +(1.20735 + 5.15192i) q^{28} +(4.59226 + 2.65135i) q^{29} +(-5.38753 - 3.11049i) q^{31} +(-2.19903 + 5.21193i) q^{32} +(5.68037 - 0.740251i) q^{34} +(-3.41344 + 5.53538i) q^{35} +(2.37386 - 4.11165i) q^{37} +(-1.96679 - 2.57015i) q^{38} +(-6.43346 + 2.63520i) q^{40} +(7.67307 - 4.43005i) q^{41} +(10.5542 + 6.09346i) q^{43} +(-5.26470 - 5.29241i) q^{44} +(-4.72324 - 1.96370i) q^{46} +(-4.33970 - 7.51657i) q^{47} +(3.14296 + 6.25474i) q^{49} +(-1.36032 - 0.565555i) q^{50} +(0.740207 - 2.73377i) q^{52} +(-6.93030 + 4.00121i) q^{53} -9.17448i q^{55} +(-1.22042 + 7.38313i) q^{56} +(4.55737 + 5.95545i) q^{58} +(1.75698 - 3.04317i) q^{59} +(5.23289 + 9.06363i) q^{61} +(-5.34660 - 6.98679i) q^{62} +(-5.70122 + 5.61213i) q^{64} +(3.01443 - 1.74038i) q^{65} +(9.49365 + 5.48116i) q^{67} +(7.81961 + 2.11727i) q^{68} +(-7.46266 + 5.37519i) q^{70} +2.01888 q^{71} +(0.474356 + 0.821609i) q^{73} +(5.33217 - 4.08041i) q^{74} +(-1.17298 - 4.42403i) q^{76} +(-8.40560 - 5.18339i) q^{77} +(-3.49588 + 2.01835i) q^{79} +(-9.83182 - 0.0516145i) q^{80} +(12.4250 - 1.61920i) q^{82} +(-0.112352 + 0.194599i) q^{83} +(4.97815 + 8.62241i) q^{85} +(10.4740 + 13.6871i) q^{86} +(-4.00161 - 9.76936i) q^{88} +(-8.55343 - 4.93832i) q^{89} +(0.108562 - 3.74508i) q^{91} +(-5.10174 - 5.12859i) q^{92} +(-1.58617 - 12.1716i) q^{94} +(2.81249 - 4.87137i) q^{95} +(6.52412 - 11.3001i) q^{97} +(0.708472 + 9.87411i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.30585	+	0.542910i	0.923376	+	0.383896i
$2$	1.30585	+	0.542910i	0.923376	+	0.383896i
$3$		0			0
$3$		0			0
$4$	1.41050	+	1.41792i	0.705248	+	0.708960i
$5$			2.45799i			1.09925i	0.835413	+	0.549623i	$0.185229\pi$
$5$			2.45799i			1.09925i	−0.835413	+	0.549623i	$0.814771\pi$
$6$		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
$10$	−1.33447	+	3.20977i	−0.421996	+	1.01502i
$11$	−3.73252			−1.12540			−0.562698	−	0.826663i	$-0.690237\pi$
$11$	−3.73252			−1.12540			−0.562698	+	0.826663i	$0.690237\pi$
$12$		0			0
$13$	−0.708051	−	1.22638i	−0.196378	−	0.340137i	0.750973	−	0.660332i	$-0.229585\pi$
$13$	−0.708051	−	1.22638i	−0.196378	−	0.340137i	−0.947351	+	0.320196i	$0.896251\pi$
$14$	2.18682	+	3.03608i	0.584453	+	0.811427i
$15$		0			0
$16$	−0.0209987	+	3.99994i	−0.00524967	+	0.999986i
$17$	3.50791	−	2.02529i	0.850794	−	0.491206i	−0.0101248	−	0.999949i	$-0.503223\pi$
$17$	3.50791	−	2.02529i	0.850794	−	0.491206i	0.860919	+	0.508743i	$0.169890\pi$
$18$		0			0
$19$	−1.98185	−	1.14422i	−0.454668	−	0.262503i	0.255132	−	0.966906i	$-0.417881\pi$
$19$	−1.98185	−	1.14422i	−0.454668	−	0.262503i	−0.709800	+	0.704404i	$0.751215\pi$
$20$	−3.48523	+	3.46699i	−0.779322	+	0.775241i
$21$		0			0
$22$	−4.87411	−	2.02642i	−1.03916	−	0.432035i
$23$	−3.61698			−0.754192			−0.377096	−	0.926174i	$-0.623077\pi$
$23$	−3.61698			−0.754192			−0.377096	+	0.926174i	$0.623077\pi$
$24$		0			0
$25$	−1.04171			−0.208342
$26$	−0.258795	−	1.98588i	−0.0507539	−	0.389463i
$27$		0			0
$28$	1.20735	+	5.15192i	0.228167	+	0.973622i
$29$	4.59226	+	2.65135i	0.852762	+	0.492342i	0.861582	−	0.507619i	$-0.169474\pi$
$29$	4.59226	+	2.65135i	0.852762	+	0.492342i	−0.00881973	+	0.999961i	$0.502807\pi$
$30$		0			0
$31$	−5.38753	−	3.11049i	−0.967629	−	0.558661i	−0.0691164	−	0.997609i	$-0.522018\pi$
$31$	−5.38753	−	3.11049i	−0.967629	−	0.558661i	−0.898513	+	0.438948i	$0.855351\pi$
$32$	−2.19903	+	5.21193i	−0.388738	+	0.921348i
$33$		0			0
$34$	5.68037	−	0.740251i	0.974175	−	0.126952i
$35$	−3.41344	+	5.53538i	−0.576976	+	0.935650i
$36$		0			0
$37$	2.37386	−	4.11165i	0.390261	−	0.675952i	−0.602223	−	0.798328i	$-0.705718\pi$
$37$	2.37386	−	4.11165i	0.390261	−	0.675952i	0.992484	+	0.122376i	$0.0390515\pi$
$38$	−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	0.238149	−	0.971229i	$-0.423459\pi$
$41$	7.67307	−	4.43005i	1.19833	−	0.691857i	0.960183	+	0.279372i	$0.0901261\pi$
$42$		0			0
$43$	10.5542	+	6.09346i	1.60950	+	0.929244i	0.989482	+	0.144654i	$0.0462070\pi$
$43$	10.5542	+	6.09346i	1.60950	+	0.929244i	0.620016	+	0.784590i	$0.287126\pi$
$44$	−5.26470	−	5.29241i	−0.793683	−	0.797861i
$45$		0			0
$46$	−4.72324	−	1.96370i	−0.696403	−	0.289531i
$47$	−4.33970	−	7.51657i	−0.633010	−	1.09640i	−0.986933	−	0.161130i	$-0.948486\pi$
$47$	−4.33970	−	7.51657i	−0.633010	−	1.09640i	0.353923	−	0.935274i	$-0.384847\pi$
$48$		0			0
$49$	3.14296	+	6.25474i	0.448994	+	0.893535i
$50$	−1.36032	−	0.565555i	−0.192378	−	0.0799816i
$51$		0			0
$52$	0.740207	−	2.73377i	0.102648	−	0.379105i
$53$	−6.93030	+	4.00121i	−0.951950	+	0.549609i	−0.893686	−	0.448693i	$-0.851890\pi$
$53$	−6.93030	+	4.00121i	−0.951950	+	0.549609i	−0.0582640	+	0.998301i	$0.518557\pi$
$54$		0			0
$55$		−	9.17448i		−	1.23709i
$56$	−1.22042	+	7.38313i	−0.163085	+	0.986612i
$57$		0			0
$58$	4.55737	+	5.95545i	0.598412	+	0.781989i
$59$	1.75698	−	3.04317i	0.228739	−	0.396187i	−0.728696	−	0.684838i	$-0.759873\pi$
$59$	1.75698	−	3.04317i	0.228739	−	0.396187i	0.957435	+	0.288650i	$0.0932065\pi$
$60$		0			0
$61$	5.23289	+	9.06363i	0.670003	+	1.16048i	0.977903	+	0.209060i	$0.0670404\pi$
$61$	5.23289	+	9.06363i	0.670003	+	1.16048i	−0.307900	+	0.951419i	$0.599626\pi$
$62$	−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	$-0.0997859\pi$
$67$	9.49365	+	5.48116i	1.15983	+	0.669630i	0.208570	+	0.978008i	$0.433119\pi$
$68$	7.81961	+	2.11727i	0.948266	+	0.256757i
$69$		0			0
$70$	−7.46266	+	5.37519i	−0.891958	+	0.642458i
$71$	2.01888			0.239597			0.119799	−	0.992798i	$-0.461775\pi$
$71$	2.01888			0.239597			0.119799	+	0.992798i	$0.461775\pi$
$72$		0			0
$73$	0.474356	+	0.821609i	0.0555192	+	0.0961621i	0.892449	−	0.451148i	$-0.148985\pi$
$73$	0.474356	+	0.821609i	0.0555192	+	0.0961621i	−0.836930	+	0.547310i	$0.815652\pi$
$74$	5.33217	−	4.08041i	0.619853	−	0.474338i
$75$		0			0
$76$	−1.17298	−	4.42403i	−0.134550	−	0.507471i
$77$	−8.40560	−	5.18339i	−0.957908	−	0.590702i
$78$		0			0
$79$	−3.49588	+	2.01835i	−0.393318	+	0.227082i	−0.683597	−	0.729860i	$-0.739585\pi$
$79$	−3.49588	+	2.01835i	−0.393318	+	0.227082i	0.290279	+	0.956942i	$0.406252\pi$
$80$	−9.83182	−	0.0516145i	−1.09923	−	0.00577068i
$81$		0			0
$82$	12.4250	−	1.61920i	1.37211	−	0.178810i
$83$	−0.112352	+	0.194599i	−0.0123322	+	0.0213601i	−0.872126	−	0.489282i	$-0.837259\pi$
$83$	−0.112352	+	0.194599i	−0.0123322	+	0.0213601i	0.859793	+	0.510642i	$0.170592\pi$
$84$		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	−0.0273061	−	0.999627i	$-0.508693\pi$
$89$	−8.55343	−	4.93832i	−0.906662	−	0.523461i	−0.879356	+	0.476166i	$0.842026\pi$
$90$		0			0
$91$	0.108562	−	3.74508i	0.0113804	−	0.392591i
$92$	−5.10174	−	5.12859i	−0.531893	−	0.534692i
$93$		0			0
$94$	−1.58617	−	12.1716i	−0.163601	−	1.25540i
$95$	2.81249	−	4.87137i	0.288555	−	0.499792i
$96$		0			0
$97$	6.52412	−	11.3001i	0.662424	−	1.14735i	−0.317553	−	0.948241i	$-0.602861\pi$
$97$	6.52412	−	11.3001i	0.662424	−	1.14735i	0.979977	−	0.199111i	$-0.0638056\pi$
$98$	0.708472	+	9.87411i	0.0715665	+	0.997436i
$99$		0			0
$100$	−1.46933	−	1.47706i	−0.146933	−	0.147706i
$101$		−	5.48128i		−	0.545408i	−0.962098	−	0.272704i	$-0.912082\pi$
$101$		−	5.48128i		−	0.545408i	0.962098	−	0.272704i	$-0.0879180\pi$
$102$		0			0
$103$		−	16.4461i		−	1.62048i	−0.586097	−	0.810241i	$-0.699336\pi$
$103$		−	16.4461i		−	1.62048i	0.586097	−	0.810241i	$-0.300664\pi$
$104$	2.45079	−	3.16803i	0.240320	−	0.310650i
$105$		0			0
$106$	−11.2222	+	1.46246i	−1.09000	+	0.142046i
$107$	4.38000	−	7.58638i	0.423431	−	0.733404i	−0.572842	−	0.819666i	$-0.694159\pi$
$107$	4.38000	−	7.58638i	0.423431	−	0.733404i	0.996272	+	0.0862625i	$0.0274924\pi$
$108$		0			0
$109$	−5.83206	−	10.1014i	−0.558610	−	0.967541i	−0.997613	−	0.0690550i	$-0.978002\pi$
$109$	−5.83206	−	10.1014i	−0.558610	−	0.967541i	0.439003	−	0.898486i	$-0.355332\pi$
$110$	4.98092	−	11.9805i	0.474912	−	1.14230i
$111$		0			0
$112$	−5.60206	+	8.97869i	−0.529345	+	0.848407i
$113$	8.35926	−	4.82622i	0.786373	−	0.454013i	−0.0523109	−	0.998631i	$-0.516659\pi$
$113$	8.35926	−	4.82622i	0.786373	−	0.454013i	0.838684	+	0.544618i	$0.183325\pi$
$114$		0			0
$115$		−	8.89049i		−	0.829043i
$116$	2.71798	+	10.2512i	0.252358	+	0.951798i
$117$		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
$122$	1.91264	+	14.6767i	0.173162	+	1.32877i
$123$		0			0
$124$	−3.18866	−	12.0264i	−0.286350	−	1.08001i
$125$			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	$0.986749\pi$
$128$	−10.4918	+	4.23336i	−0.927356	+	0.374180i
$129$		0			0
$130$	4.88127	−	0.636115i	0.428116	−	0.0557910i
$131$	−6.97190			−0.609138			−0.304569	−	0.952490i	$-0.598512\pi$
$131$	−6.97190			−0.609138			−0.304569	+	0.952490i	$0.598512\pi$
$132$		0			0
$133$	−2.87412	−	5.32900i	−0.249218	−	0.462083i
$134$	9.42152	+	12.3118i	0.813895	+	1.06358i
$135$		0			0
$136$	9.06176	+	7.01019i	0.777039	+	0.601119i
$137$		−	14.5675i		−	1.24459i	−0.782784	−	0.622293i	$-0.786201\pi$
$137$		−	14.5675i		−	1.24459i	0.782784	−	0.622293i	$-0.213799\pi$
$138$		0			0
$139$	−11.2990	+	6.52347i	−0.958368	+	0.553314i	−0.895670	−	0.444719i	$-0.853304\pi$
$139$	−11.2990	+	6.52347i	−0.958368	+	0.553314i	−0.0626973	+	0.998033i	$0.519970\pi$
$140$	−12.6634	+	2.96765i	−1.07025	+	0.250812i
$141$		0			0
$142$	2.63636	+	1.09607i	0.221239	+	0.0919804i
$143$	2.64281	+	4.57748i	0.221003	+	0.382788i
$144$		0			0
$145$	−6.51698	+	11.2877i	−0.541205	+	0.937395i
$146$	0.173379	+	1.33043i	0.0143489	+	0.110107i
$147$		0			0
$148$	9.17833	−	2.43352i	0.754454	−	0.200034i
$149$			22.2238i			1.82064i	0.413902	+	0.910321i	$0.364166\pi$
$149$			22.2238i			1.82064i	−0.413902	+	0.910321i	$0.635834\pi$
$150$		0			0
$151$			2.25709i			0.183679i	0.995774	+	0.0918395i	$0.0292747\pi$
$151$			2.25709i			0.183679i	−0.995774	+	0.0918395i	$0.970725\pi$
$152$	0.870117	−	6.41395i	0.0705758	−	0.520240i
$153$		0			0
$154$	−8.16236	−	11.3322i	−0.657741	−	0.913177i
$155$	7.64556	−	13.2425i	0.614106	−	1.06366i
$156$		0			0
$157$	1.11181	−	1.92570i	0.0887317	−	0.153688i	−0.818244	−	0.574872i	$-0.805052\pi$
$157$	1.11181	−	1.92570i	0.0887317	−	0.153688i	0.906975	+	0.421184i	$0.138385\pi$
$158$	−5.66089	+	0.737713i	−0.450356	+	0.0586893i
$159$		0			0
$160$	−12.8109	−	5.40520i	−1.01279	−	0.427318i
$161$	−8.14542	−	5.02294i	−0.641949	−	0.395863i
$162$		0			0
$163$	−0.479974	−	0.277113i	−0.0375945	−	0.0217052i	0.481085	−	0.876674i	$-0.340243\pi$
$163$	−0.479974	−	0.277113i	−0.0375945	−	0.0217052i	−0.518679	+	0.854969i	$0.673576\pi$
$164$	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	$-0.314519\pi$
$167$	−5.78903	−	10.0269i	−0.447968	−	0.775904i	−0.998254	+	0.0590727i	$0.981186\pi$
$168$		0			0
$169$	5.49733	−	9.52165i	0.422871	−	0.732435i
$170$	1.81953	+	13.9623i	0.139552	+	1.07086i
$171$		0			0
$172$	6.24659	+	23.5598i	0.476298	+	1.79642i
$173$	9.23186	−	5.33002i	0.701886	−	0.405234i	−0.106164	−	0.994349i	$-0.533857\pi$
$173$	9.23186	−	5.33002i	0.701886	−	0.405234i	0.808049	+	0.589115i	$0.200523\pi$
$174$		0			0
$175$	−2.34592	−	1.44663i	−0.177335	−	0.109355i
$176$	0.0783779	−	14.9299i	0.00590795	−	1.12538i
$177$		0			0
$178$	−8.48844	−	11.0925i	−0.636235	−	0.831415i
$179$	−10.5947	−	18.3506i	−0.791886	−	1.37159i	−0.924798	−	0.380459i	$-0.875766\pi$
$179$	−10.5947	−	18.3506i	−0.791886	−	1.37159i	0.132911	−	0.991128i	$-0.457567\pi$
$180$		0			0
$181$	−16.5889			−1.23304			−0.616521	−	0.787338i	$-0.711459\pi$
$181$	−16.5889			−1.23304			−0.616521	+	0.787338i	$0.711459\pi$
$182$	2.17501	−	4.83158i	0.161222	−	0.358141i
$183$		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	0.993344	+	0.115182i	$0.0367451\pi$
$191$	8.24273	+	14.2768i	0.596423	+	1.03303i	−0.396922	+	0.917853i	$0.629922\pi$
$192$		0			0
$193$	−11.5854	+	20.0665i	−0.833936	+	1.44442i	0.0609572	+	0.998140i	$0.480585\pi$
$193$	−11.5854	+	20.0665i	−0.833936	+	1.44442i	−0.894894	+	0.446280i	$0.852749\pi$
$194$	14.6545	−	11.2142i	1.05213	−	0.805136i
$195$		0			0
$196$	−4.43560	+	13.2788i	−0.316828	+	0.948483i
$197$		−	14.4116i		−	1.02679i	−0.858154	−	0.513393i	$-0.828389\pi$
$197$		−	14.4116i		−	1.02679i	0.858154	−	0.513393i	$-0.171611\pi$
$198$		0			0
$199$	2.36477	−	1.36530i	0.167634	−	0.0967837i	−0.413836	−	0.910352i	$-0.635811\pi$
$199$	2.36477	−	1.36530i	0.167634	−	0.0967837i	0.581470	+	0.813568i	$0.302478\pi$
$200$	−1.11681	−	2.72654i	−0.0789705	−	0.192795i
$201$		0			0
$202$	2.97585	−	7.15774i	0.209380	−	0.503617i
$203$	6.65980	+	12.3481i	0.467426	+	0.866670i
$204$		0			0
$205$	10.8890	+	18.8603i	0.760521	+	1.31726i
$206$	8.92876	−	21.4762i	0.622096	−	1.49632i
$207$		0			0
$208$	4.92032	−	2.80641i	0.341163	−	0.194590i
$209$	7.39729	+	4.27083i	0.511681	+	0.295419i
$210$		0			0
$211$	−7.91848	+	4.57174i	−0.545131	+	0.314731i	−0.747156	−	0.664649i	$-0.768581\pi$
$211$	−7.91848	+	4.57174i	−0.545131	+	0.314731i	0.202025	+	0.979380i	$0.435248\pi$
$212$	−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
$218$	−2.13164	−	16.3572i	−0.144373	−	1.10785i
$219$		0			0
$220$	13.0087	−	12.9406i	0.877046	−	0.872453i
$221$	−4.96756	−	2.86802i	−0.334154	−	0.192924i
$222$		0			0
$223$	−7.77997	−	4.49177i	−0.520985	−	0.300791i	0.216352	−	0.976315i	$-0.430584\pi$
$223$	−7.77997	−	4.49177i	−0.520985	−	0.300791i	−0.737338	+	0.675524i	$0.763917\pi$
$224$	−12.1901	+	8.68342i	−0.814484	+	0.580186i
$225$		0			0
$226$	13.5362	−	1.76400i	0.900412	−	0.117340i
$227$	−10.3688			−0.688198			−0.344099	−	0.938933i	$-0.611816\pi$
$227$	−10.3688			−0.688198			−0.344099	+	0.938933i	$0.611816\pi$
$228$		0			0
$229$	−3.71000			−0.245164			−0.122582	−	0.992458i	$-0.539117\pi$
$229$	−3.71000			−0.245164			−0.122582	+	0.992458i	$0.539117\pi$
$230$	4.82674	−	11.6097i	0.318266	−	0.765519i
$231$		0			0
$232$	−2.01620	+	14.8621i	−0.132370	+	0.975747i
$233$	12.9602	+	7.48260i	0.849054	+	0.490201i	0.860331	−	0.509735i	$-0.170257\pi$
$233$	12.9602	+	7.48260i	0.849054	+	0.490201i	−0.0112778	+	0.999936i	$0.503590\pi$
$234$		0			0
$235$	18.4757	−	10.6669i	1.20522	−	0.695833i
$236$	6.79319	−	1.80113i	0.442199	−	0.117244i
$237$		0			0
$238$	13.8202	+	6.22135i	0.895827	+	0.403270i
$239$	6.84478	+	11.8555i	0.442752	+	0.766869i	0.997893	−	0.0648877i	$-0.0206689\pi$
$239$	6.84478	+	11.8555i	0.442752	+	0.766869i	−0.555141	+	0.831756i	$0.687336\pi$
$240$		0			0
$241$	11.7384			0.756135			0.378067	−	0.925778i	$-0.376589\pi$
$241$	11.7384			0.756135			0.378067	+	0.925778i	$0.376589\pi$
$242$	3.82833	+	1.59164i	0.246094	+	0.102314i
$243$		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
$248$	2.36535	−	17.4359i	0.150200	−	1.10718i
$249$		0			0
$250$	−5.28221	+	12.7052i	−0.334076	+	0.803547i
$251$	17.6466			1.11384			0.556922	−	0.830565i	$-0.311982\pi$
$251$	17.6466			1.11384			0.556922	+	0.830565i	$0.311982\pi$
$252$		0			0
$253$	13.5004			0.848765
$254$	−0.509239	+	1.22486i	−0.0319525	+	0.0768547i
$255$		0			0
$256$	−15.9991	−	0.167987i	−0.999945	−	0.0104992i
$257$			14.9206i			0.930720i	0.885121	+	0.465360i	$0.154075\pi$
$257$			14.9206i			0.930720i	−0.885121	+	0.465360i	$0.845925\pi$
$258$		0			0
$259$	11.0558	−	5.96281i	0.686976	−	0.370511i
$260$	6.71956	+	1.81942i	0.416730	+	0.112836i
$261$		0			0
$262$	−9.10426	−	3.78512i	−0.562463	−	0.233845i
$263$	−0.853210			−0.0526112			−0.0263056	−	0.999654i	$-0.508374\pi$
$263$	−0.853210			−0.0526112			−0.0263056	+	0.999654i	$0.508374\pi$
$264$		0			0
$265$	−9.83493	−	17.0346i	−0.604155	−	1.04643i
$266$	−0.860007	−	8.51928i	−0.0527304	−	0.522351i
$267$		0			0
$268$	5.61891	+	21.1924i	0.343229	+	1.29453i
$269$	6.98964	−	4.03547i	0.426166	−	0.246047i	−0.271546	−	0.962425i	$-0.587535\pi$
$269$	6.98964	−	4.03547i	0.426166	−	0.246047i	0.697712	+	0.716378i	$0.254202\pi$
$270$		0			0
$271$	13.5435	+	7.81935i	0.822710	+	0.474992i	0.851350	−	0.524598i	$-0.175784\pi$
$271$	13.5435	+	7.81935i	0.822710	+	0.474992i	−0.0286401	+	0.999590i	$0.509118\pi$
$272$	8.02740	+	14.0740i	0.486733	+	0.853361i
$273$		0			0
$274$	7.90885	−	19.0230i	0.477791	−	1.14922i
$275$	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	$0.708132\pi$
$278$	−18.2965	+	2.38435i	−1.09735	+	0.143004i
$279$		0			0
$280$	−18.1476	−	2.99977i	−1.08453	−	0.179271i
$281$	−5.50545	−	3.17857i	−0.328428	−	0.189618i	0.326715	−	0.945123i	$-0.394058\pi$
$281$	−5.50545	−	3.17857i	−0.328428	−	0.189618i	−0.655143	+	0.755505i	$0.727392\pi$
$282$		0			0
$283$	8.85659	+	5.11336i	0.526470	+	0.303958i	0.739578	−	0.673071i	$-0.235025\pi$
$283$	8.85659	+	5.11336i	0.526470	+	0.303958i	−0.213108	+	0.977029i	$0.568359\pi$
$284$	2.84763	+	2.86262i	0.168976	+	0.169865i
$285$		0			0
$286$	0.965956	+	7.41232i	0.0571182	+	0.438300i
$287$	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	−0.962094	−	0.272716i	$-0.912078\pi$
$293$	−20.6599	+	11.9280i	−1.20696	+	0.696840i	−0.244868	+	0.969556i	$0.578745\pi$
$294$		0			0
$295$	7.48009	+	4.31863i	0.435507	+	0.251440i
$296$	13.3067	+	1.80519i	0.773437	+	0.104925i
$297$		0			0
$298$	−12.0655	+	29.0210i	−0.698937	+	1.68114i
$299$	2.56101	+	4.43579i	0.148107	+	0.256528i
$300$		0			0
$301$	15.3059	+	28.3792i	0.882217	+	1.63575i
$302$	−1.22540	+	2.94742i	−0.0705136	+	0.169605i
$303$		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	$0.941077\pi$
$308$	−4.50644	−	19.2296i	−0.256778	−	1.09571i
$309$		0			0
$310$	17.1734	−	13.1419i	0.975386	−	0.746408i
$311$	−0.253074	+	0.438337i	−0.0143505	+	0.0248558i	−0.873111	−	0.487521i	$-0.837901\pi$
$311$	−0.253074	+	0.438337i	−0.0143505	+	0.0248558i	0.858761	+	0.512376i	$0.171235\pi$
$312$		0			0
$313$	−12.6914	−	21.9822i	−0.717362	−	1.24251i	−0.962041	−	0.272904i	$-0.912016\pi$
$313$	−12.6914	−	21.9822i	−0.717362	−	1.24251i	0.244679	−	0.969604i	$-0.421317\pi$
$314$	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	−0.953792	−	0.300468i	$-0.902857\pi$
$317$	−20.8397	+	12.0318i	−1.17048	+	0.675774i	−0.216683	+	0.976242i	$0.569524\pi$
$318$		0			0
$319$	−17.1407	−	9.89619i	−0.959695	−	0.554080i
$320$	−13.7946	−	14.0135i	−0.771140	−	0.783381i
$321$		0			0
$322$	−7.90970	−	10.9814i	−0.440790	−	0.611972i
$323$	−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
$328$	19.8213	+	15.3338i	1.09445	+	0.846668i
$329$	0.665384	−	22.9539i	0.0366838	−	1.26549i
$330$		0			0
$331$	−5.80713	+	3.35275i	−0.319189	+	0.184284i	−0.651031	−	0.759051i	$-0.725663\pi$
$331$	−5.80713	+	3.35275i	−0.319189	+	0.184284i	0.331842	+	0.943335i	$0.392330\pi$
$332$	−0.434399	+	0.115176i	−0.0238407	+	0.00632108i
$333$		0			0
$334$	−2.11591	−	16.2366i	−0.115777	−	0.888425i
$335$	−13.4726	+	23.3353i	−0.736089	+	1.27494i
$336$		0			0
$337$	−15.3334	−	26.5582i	−0.835263	−	1.44672i	−0.893816	−	0.448434i	$-0.851982\pi$
$337$	−15.3334	−	26.5582i	−0.835263	−	1.44672i	0.0585525	−	0.998284i	$-0.481351\pi$
$338$	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
$344$	−4.63373	+	34.1569i	−0.249834	+	1.84162i
$345$		0			0
$346$	14.9492	−	1.94814i	0.803672	−	0.104733i
$347$	−4.51700	+	7.82368i	−0.242485	+	0.419997i	−0.961422	−	0.275079i	$-0.911296\pi$
$347$	−4.51700	+	7.82368i	−0.242485	+	0.419997i	0.718936	+	0.695076i	$0.244629\pi$
$348$		0			0
$349$	10.9004	−	18.8800i	0.583485	−	1.01063i	−0.411578	−	0.911375i	$-0.635022\pi$
$349$	10.9004	−	18.8800i	0.583485	−	1.01063i	0.995062	−	0.0992507i	$-0.0316446\pi$
$350$	−2.27804	−	3.16272i	−0.121766	−	0.169054i
$351$		0			0
$352$	8.20792	−	19.4536i	0.437484	−	1.03688i
$353$			11.9218i			0.634536i	0.948336	+	0.317268i	$0.102765\pi$
$353$			11.9218i			0.634536i	−0.948336	+	0.317268i	$0.897235\pi$
$354$		0			0
$355$			4.96239i			0.263376i
$356$	−5.06243	−	19.0936i	−0.268308	−	1.01196i
$357$		0			0
$358$	−3.87240	−	29.7151i	−0.204663	−	1.57049i
$359$	5.13759	−	8.89857i	0.271152	−	0.469649i	−0.698005	−	0.716093i	$-0.745929\pi$
$359$	5.13759	−	8.89857i	0.271152	−	0.469649i	0.969157	+	0.246444i	$0.0792621\pi$
$360$		0			0
$361$	−6.88151	−	11.9191i	−0.362185	−	0.627322i
$362$	−21.6626	−	9.00628i	−1.13856	−	0.473360i
$363$		0			0
$364$	5.46335	−	5.12849i	0.286358	−	0.268806i
$365$	−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	$0.745905\pi$
$368$	0.0759517	−	14.4677i	0.00395926	−	0.754182i
$369$		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	$0.541862\pi$
$374$	−21.2021	+	2.76300i	−1.09633	+	0.142871i
$375$		0			0
$376$	15.0211	−	19.4171i	0.774652	−	1.00136i
$377$		−	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	$-0.00838790\pi$
$380$	10.8742	−	2.88317i	0.557836	−	0.147903i
$381$		0			0
$382$	3.01274	+	23.1185i	0.154145	+	1.18284i
$383$	25.2687			1.29117			0.645584	−	0.763689i	$-0.276614\pi$
$383$	25.2687			1.29117			0.645584	+	0.763689i	$0.276614\pi$
$384$		0			0
$385$	12.7407	−	20.6609i	0.649327	−	1.05298i
$386$	−26.0232	+	19.9141i	−1.32454	+	1.01360i
$387$		0			0
$388$	25.2249	−	6.68808i	1.28060	−	0.339536i
$389$			9.30821i			0.471945i	0.971760	+	0.235973i	$0.0758276\pi$
$389$			9.30821i			0.471945i	−0.971760	+	0.235973i	$0.924172\pi$
$390$		0			0
$391$	−12.6880	+	7.32545i	−0.641662	+	0.370464i
$392$	−13.0014	+	14.9320i	−0.656670	+	0.754178i
$393$		0			0
$394$	7.82422	−	18.8194i	0.394178	−	0.948109i
$395$	−4.96108	−	8.59284i	−0.249619	−	0.432353i
$396$		0			0
$397$	−7.25979	+	12.5743i	−0.364358	+	0.631087i	−0.988673	−	0.150086i	$-0.952045\pi$
$397$	−7.25979	+	12.5743i	−0.364358	+	0.631087i	0.624315	+	0.781173i	$0.285378\pi$
$398$	3.82928	−	0.499022i	0.191944	−	0.0250137i
$399$		0			0
$400$	0.0218745	−	4.16678i	0.00109373	−	0.208339i
$401$		−	17.9574i		−	0.896748i	−0.893846	−	0.448374i	$-0.852003\pi$
$401$		−	17.9574i		−	0.896748i	0.893846	−	0.448374i	$-0.147997\pi$
$402$		0			0
$403$			8.80955i			0.438835i
$404$	7.77203	−	7.73133i	0.386673	−	0.384648i
$405$		0			0
$406$	1.99277	+	19.7405i	0.0988996	+	0.979706i
$407$	−8.86048	+	15.3468i	−0.439198	+	0.760713i
$408$		0			0
$409$	0.158417	−	0.274386i	0.00783322	−	0.0135675i	−0.862082	−	0.506768i	$-0.830840\pi$
$409$	0.158417	−	0.274386i	0.00783322	−	0.0135675i	0.869915	+	0.493201i	$0.164173\pi$
$410$	3.97997	+	30.5405i	0.196557	+	1.50829i
$411$		0			0
$412$	23.3193	−	23.1972i	1.14886	−	1.14284i
$413$	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	$-0.308124\pi$
$419$	−8.80022	−	15.2424i	−0.429919	−	0.744641i	−0.996866	+	0.0791133i	$0.974791\pi$
$420$		0			0
$421$	−11.4743	+	19.8741i	−0.559224	+	0.968605i	0.438337	+	0.898811i	$0.355568\pi$
$421$	−11.4743	+	19.8741i	−0.559224	+	0.968605i	−0.997561	+	0.0697943i	$0.977766\pi$
$422$	−12.8224	+	1.67099i	−0.624185	+	0.0813423i
$423$		0			0
$424$	−17.9026	−	13.8495i	−0.869426	−	0.672590i
$425$	−3.65423	+	2.10977i	−0.177256	+	0.102339i
$426$		0			0
$427$	−0.802333	+	27.6782i	−0.0388276	+	1.33944i
$428$	16.9349	−	4.49008i	0.818578	−	0.217036i
$429$		0			0
$430$	−33.6428	+	25.7450i	−1.62240	+	1.24153i
$431$	−11.3929	−	19.7331i	−0.548778	−	0.950512i	−0.998359	−	0.0572722i	$-0.981760\pi$
$431$	−11.3929	−	19.7331i	−0.548778	−	0.950512i	0.449580	−	0.893240i	$-0.351574\pi$
$432$		0			0
$433$	−25.9567			−1.24740			−0.623700	−	0.781664i	$-0.714371\pi$
$433$	−25.9567			−1.24740			−0.623700	+	0.781664i	$0.714371\pi$
$434$	−2.33787	−	23.1591i	−0.112221	−	1.11167i
$435$		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	$-0.696531\pi$
$439$	−3.39989	+	1.96293i	−0.162268	+	0.0936854i	0.416667	+	0.909059i	$0.363198\pi$
$440$	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	$-0.0798632\pi$
$443$	5.66882	+	9.81868i	0.269334	+	0.466500i	−0.699356	+	0.714773i	$0.746530\pi$
$444$		0			0
$445$	12.1383	−	21.0242i	0.575413	−	0.996644i
$446$	−7.72086	−	10.0894i	−0.365593	−	0.477747i
$447$		0			0
$448$	−20.6328	+	4.72114i	−0.974806	+	0.223053i
$449$		−	15.6718i		−	0.739600i	−0.929111	−	0.369800i	$-0.879426\pi$
$449$		−	15.6718i		−	0.739600i	0.929111	−	0.369800i	$-0.120574\pi$
$450$		0			0
$451$	−28.6398	+	16.5352i	−1.34860	+	0.778613i
$452$	18.6339	+	5.04540i	0.876466	+	0.237316i
$453$		0			0
$454$	−13.5401	−	5.62930i	−0.635466	−	0.264196i
$455$	9.20537	+	0.266844i	0.431554	+	0.0125098i
$456$		0			0
$457$	8.74272	+	15.1428i	0.408967	+	0.708352i	0.994774	−	0.102099i	$-0.0325557\pi$
$457$	8.74272	+	15.1428i	0.408967	+	0.708352i	−0.585807	+	0.810451i	$0.699222\pi$
$458$	−4.84471	−	2.01420i	−0.226379	−	0.0941174i
$459$		0			0
$460$	12.6060	−	12.5400i	0.587759	−	0.584681i
$461$	−2.17782	−	1.25736i	−0.101431	−	0.0585613i	0.448426	−	0.893820i	$-0.351985\pi$
$461$	−2.17782	−	1.25736i	−0.101431	−	0.0585613i	−0.549857	+	0.835259i	$0.685318\pi$
$462$		0			0
$463$	−15.3322	+	8.85204i	−0.712547	+	0.411389i	−0.812003	−	0.583653i	$-0.801623\pi$
$463$	−15.3322	+	8.85204i	−0.712547	+	0.411389i	0.0994566	+	0.995042i	$0.468290\pi$
$464$	−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	0.446460	+	0.894804i	$0.352685\pi$
$467$	−11.9222	+	20.6498i	−0.551693	+	0.955560i	−0.998153	+	0.0607566i	$0.980649\pi$
$468$		0			0
$469$	13.7679	+	25.5275i	0.635742	+	1.17875i
$470$	29.9176	−	3.89879i	1.38000	−	0.179838i
$471$		0			0
$472$	9.84875	+	1.33608i	0.453325	+	0.0614982i
$473$	−39.3937	−	22.7439i	−1.81132	−	1.04577i
$474$		0			0
$475$	2.06451	+	1.19195i	0.0947264	+	0.0546903i
$476$	14.6694	+	15.6273i	0.672372	+	0.716274i
$477$		0			0
$478$	2.50179	+	19.1976i	0.114429	+	0.878079i
$479$	−1.78481			−0.0815499			−0.0407750	−	0.999168i	$-0.512983\pi$
$479$	−1.78481			−0.0815499			−0.0407750	+	0.999168i	$0.512983\pi$
$480$		0			0
$481$	−6.72327			−0.306555
$482$	15.3286	+	6.37288i	0.698197	+	0.290277i
$483$		0			0
$484$	4.13511	+	4.15688i	0.187960	+	0.188949i
$485$	27.7755	+	16.0362i	1.26122	+	0.728167i
$486$		0			0
$487$	14.2958	−	8.25366i	0.647803	−	0.374009i	−0.139811	−	0.990178i	$-0.544649\pi$
$487$	14.2958	−	8.25366i	0.647803	−	0.374009i	0.787614	+	0.616169i	$0.211316\pi$
$488$	−18.1127	+	23.4135i	−0.819923	+	1.05988i
$489$		0			0
$490$	−24.2705	+	1.74142i	−1.09643	+	0.0786692i
$491$	16.6450	+	28.8300i	0.751179	+	1.30108i	0.947252	+	0.320491i	$0.103848\pi$
$491$	16.6450	+	28.8300i	0.751179	+	1.30108i	−0.196072	+	0.980589i	$0.562819\pi$
$492$		0			0
$493$	21.4790			0.967366
$494$	−1.75939	+	4.23184i	−0.0791589	+	0.190399i
$495$		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	$-0.215071\pi$
$500$	−13.7956	+	13.7233i	−0.616956	+	0.613726i
$501$		0			0
$502$	23.0438	+	9.58052i	1.02850	+	0.427600i
$503$	1.00731			0.0449138			0.0224569	−	0.999748i	$-0.492851\pi$
$503$	1.00731			0.0449138			0.0224569	+	0.999748i	$0.492851\pi$
$504$		0			0
$505$	13.4729			0.599538
$506$	17.6296	+	7.32952i	0.783729	+	0.325837i
$507$		0			0
$508$	−1.32998	+	1.32302i	−0.0590083	+	0.0586994i
$509$		−	5.35143i		−	0.237198i	−0.992942	−	0.118599i	$-0.962160\pi$
$509$		−	5.35143i		−	0.237198i	0.992942	−	0.118599i	$-0.0378403\pi$
$510$		0			0
$511$	−0.0727307	+	2.50900i	−0.00321742	+	0.110992i
$512$	−20.8013	−	8.90545i	−0.919295	−	0.393569i
$513$		0			0
$514$	−8.10054	+	19.4841i	−0.357299	+	0.859405i
$515$	40.4243			1.78131
$516$		0			0
$517$	16.1980	+	28.0557i	0.712386	+	1.23389i
$518$	17.6745	−	1.78422i	0.776575	−	0.0783939i
$519$		0			0
$520$	7.78697	+	6.02401i	0.341481	+	0.264170i
$521$	0.0326842	−	0.0188702i	0.00143192	−	0.000826719i	−0.499284	−	0.866438i	$-0.666404\pi$
$521$	0.0326842	−	0.0188702i	0.00143192	−	0.000826719i	0.500716	+	0.865612i	$0.333070\pi$
$522$		0			0
$523$	−22.6882	−	13.0990i	−0.992086	−	0.572781i	−0.0861890	−	0.996279i	$-0.527469\pi$
$523$	−22.6882	−	13.0990i	−0.992086	−	0.572781i	−0.905897	+	0.423498i	$0.860802\pi$
$524$	−9.83384	−	9.88560i	−0.429593	−	0.431854i
$525$		0			0
$526$	−1.11417	−	0.463217i	−0.0485799	−	0.0201972i
$527$	−25.1986			−1.09767
$528$		0			0
$529$	−9.91746			−0.431194
$530$	−3.59470	−	27.5842i	−0.156144	−	1.19818i
$531$		0			0
$532$	3.50216	−	11.5918i	0.151838	−	0.502569i
$533$	−10.8658	−	6.27340i	−0.470652	−	0.271731i
$534$		0			0
$535$	18.6473	+	10.7660i	0.806191	+	0.465455i
$536$	−4.16812	+	30.7247i	−0.180035	+	1.32710i
$537$		0			0
$538$	11.3183	−	1.47498i	0.487968	−	0.0635908i
$539$	−11.7311	−	23.3459i	−0.505296	−	1.00558i
$540$		0			0
$541$	3.71877	−	6.44110i	0.159882	−	0.276925i	−0.774944	−	0.632030i	$-0.782222\pi$
$541$	3.71877	−	6.44110i	0.159882	−	0.276925i	0.934826	+	0.355106i	$0.115555\pi$
$542$	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	$-0.346121\pi$
$547$	−1.62692	−	0.939303i	−0.0695621	−	0.0401617i	−0.534378	+	0.845246i	$0.679454\pi$
$548$	20.6556	−	20.5474i	0.882362	−	0.877742i
$549$		0			0
$550$	5.07741	+	2.11094i	0.216501	+	0.0900109i
$551$	−6.06746	−	10.5091i	−0.258482	−	0.447705i
$552$		0			0
$553$	−10.6756	−	0.309464i	−0.453973	−	0.0131597i
$554$	−26.4394	−	10.9922i	−1.12330	−	0.467016i
$555$		0			0
$556$	−25.1870	−	6.81973i	−1.06816	−	0.289221i
$557$	−8.36838	+	4.83149i	−0.354580	+	0.204717i	−0.666700	−	0.745326i	$-0.732294\pi$
$557$	−8.36838	+	4.83149i	−0.354580	+	0.204717i	0.312121	+	0.950042i	$0.398961\pi$
$558$		0			0
$559$		−	17.2579i		−	0.729932i
$560$	−22.0695	−	13.7698i	−0.932608	−	0.581880i
$561$		0			0
$562$	−5.46362	−	7.13971i	−0.230469	−	0.301171i
$563$	−7.44672	+	12.8981i	−0.313842	+	0.543590i	−0.979191	−	0.202943i	$-0.934949\pi$
$563$	−7.44672	+	12.8981i	−0.313842	+	0.543590i	0.665349	+	0.746533i	$0.268283\pi$
$564$		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	−0.567714	−	0.823226i	$-0.692172\pi$
$569$	−3.30697	+	1.90928i	−0.138635	+	0.0800412i	0.429078	+	0.903267i	$0.358839\pi$
$570$		0			0
$571$	3.92146	+	2.26406i	0.164108	+	0.0947478i	0.579805	−	0.814756i	$-0.303129\pi$
$571$	3.92146	+	2.26406i	0.164108	+	0.0947478i	−0.415697	+	0.909503i	$0.636462\pi$
$572$	−2.76283	+	10.2038i	−0.115520	+	0.426643i
$573$		0			0
$574$	30.2296	+	13.6083i	1.26176	+	0.568001i
$575$	3.76784			0.157130
$576$		0			0
$577$	11.9152	+	20.6378i	0.496038	+	0.859162i	0.999990	−	0.00456937i	$-0.00145448\pi$
$577$	11.9152	+	20.6378i	0.496038	+	0.859162i	−0.503952	+	0.863732i	$0.668121\pi$
$578$	−0.665698	+	0.509421i	−0.0276894	+	0.0211891i
$579$		0			0
$580$	−25.1973	+	6.68076i	−1.04626	+	0.277403i
$581$	−0.523259	+	0.282212i	−0.0217084	+	0.0117081i
$582$		0			0
$583$	25.8675	−	14.9346i	1.07132	−	0.618527i
$584$	−1.64190	+	2.12241i	−0.0679422	+	0.0878259i
$585$		0			0
$586$	−33.4545	+	4.35971i	−1.38199	+	0.180098i
$587$	8.04599	−	13.9361i	0.332094	−	0.575203i	−0.650829	−	0.759225i	$-0.725578\pi$
$587$	8.04599	−	13.9361i	0.332094	−	0.575203i	0.982922	+	0.184022i	$0.0589117\pi$
$588$		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	0.872621	−	0.488398i	$-0.162419\pi$
$593$	21.5747	+	12.4561i	0.885966	+	0.511513i	0.0133450	+	0.999911i	$0.495752\pi$
$594$		0			0
$595$	−0.763275	+	26.3308i	−0.0312912	+	1.07946i
$596$	−31.5116	+	31.3466i	−1.29076	+	1.28401i
$597$		0			0
$598$	0.936056	+	7.18288i	0.0382782	+	0.293730i
$599$	5.20340	−	9.01255i	0.212605	−	0.368243i	−0.739924	−	0.672691i	$-0.765139\pi$
$599$	5.20340	−	9.01255i	0.212605	−	0.368243i	0.952529	+	0.304448i	$0.0984719\pi$
$600$		0			0
$601$	−19.7275	+	34.1690i	−0.804701	+	1.39378i	0.111791	+	0.993732i	$0.464341\pi$
$601$	−19.7275	+	34.1690i	−0.804701	+	1.39378i	−0.916493	+	0.400052i	$0.868992\pi$
$602$	4.57989	+	45.3687i	0.186663	+	1.84909i
$603$		0			0
$604$	−3.20037	+	3.18361i	−0.130221	+	0.129539i
$605$			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	$-0.0673323\pi$
$608$	10.3218	−	7.81310i	0.418603	−	0.316863i
$609$		0			0
$610$	−36.0753	+	4.70124i	−1.46064	+	0.190348i
$611$	−6.14545	+	10.6442i	−0.248618	+	0.430620i
$612$		0			0
$613$	−18.1531	−	31.4421i	−0.733196	−	1.26993i	−0.955510	−	0.294958i	$-0.904694\pi$
$613$	−18.1531	−	31.4421i	−0.733196	−	1.26993i	0.222314	−	0.974975i	$-0.428639\pi$
$614$	−3.50168	+	8.42251i	−0.141316	+	0.339905i
$615$		0			0
$616$	4.55522	−	27.5576i	0.183535	−	1.11033i
$617$	5.74103	−	3.31459i	0.231125	−	0.133440i	−0.379966	−	0.925001i	$-0.624064\pi$
$617$	5.74103	−	3.31459i	0.231125	−	0.133440i	0.611091	+	0.791560i	$0.290731\pi$
$618$		0			0
$619$		−	38.3693i		−	1.54219i	−0.636717	−	0.771097i	$-0.719708\pi$
$619$		−	38.3693i		−	1.54219i	0.636717	−	0.771097i	$-0.280292\pi$
$620$	29.5608	−	7.83770i	1.18719	−	0.314769i
$621$		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
$626$	−4.63876	−	35.5958i	−0.185402	−	1.42270i
$627$		0			0
$628$	4.29869	−	1.13975i	0.171537	−	0.0454808i
$629$		−	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	$-0.165560\pi$
$632$	−9.03068	−	6.98615i	−0.359221	−	0.277894i
$633$		0			0
$634$	−33.7458	+	4.39767i	−1.34022	+	0.174654i
$635$	−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
$640$	−10.4056	−	25.7888i	−0.411316	−	1.01939i
$641$			7.58006i			0.299394i	0.988732	+	0.149697i	$0.0478299\pi$
$641$			7.58006i			0.299394i	−0.988732	+	0.149697i	$0.952170\pi$
$642$		0			0
$643$	29.8134	−	17.2128i	1.17573	−	0.678806i	0.220705	−	0.975341i	$-0.429164\pi$
$643$	29.8134	−	17.2128i	1.17573	−	0.678806i	0.955022	+	0.296535i	$0.0958310\pi$
$644$	−4.36695	−	18.6344i	−0.172082	−	0.734298i
$645$		0			0
$646$	−12.1047	−	5.03254i	−0.476251	−	0.198002i
$647$	18.3282	+	31.7454i	0.720557	+	1.24804i	0.960777	+	0.277323i	$0.0894472\pi$
$647$	18.3282	+	31.7454i	0.720557	+	1.24804i	−0.240220	+	0.970719i	$0.577220\pi$
$648$		0			0
$649$	−6.55794	+	11.3587i	−0.257422	+	0.445868i
$650$	0.269589	+	2.06871i	0.0105742	+	0.0811414i
$651$		0			0
$652$	−0.284077	−	1.07143i	−0.0111253	−	0.0419605i
$653$			14.7474i			0.577110i	0.957463	+	0.288555i	$0.0931748\pi$
$653$			14.7474i			0.577110i	−0.957463	+	0.288555i	$0.906825\pi$
$654$		0			0
$655$		−	17.1368i		−	0.669592i
$656$	17.5588	+	30.7849i	0.685557	+	1.20195i
$657$		0			0
$658$	13.3308	−	29.6131i	0.519688	−	1.15444i
$659$	14.0724	−	24.3742i	0.548184	−	0.949483i	−0.450215	−	0.892920i	$-0.648653\pi$
$659$	14.0724	−	24.3742i	0.548184	−	0.949483i	0.998399	−	0.0565626i	$-0.0180141\pi$
$660$		0			0
$661$	−0.520581	+	0.901673i	−0.0202483	+	0.0350710i	−0.875972	−	0.482362i	$-0.839779\pi$
$661$	−0.520581	+	0.901673i	−0.0202483	+	0.0350710i	0.855724	+	0.517433i	$0.173112\pi$
$662$	−9.40349	+	1.22544i	−0.365477	+	0.0476281i
$663$		0			0
$664$	−0.629790	−	0.0854374i	−0.0244406	−	0.00331562i
$665$	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	−0.722809	−	0.691047i	$-0.757150\pi$
$673$	6.14987	−	10.6519i	0.237060	−	0.410600i	0.959869	+	0.280448i	$0.0904829\pi$
$674$	−5.60441	−	43.0058i	−0.215874	−	1.65652i
$675$		0			0
$676$	21.2549	−	5.63548i	0.817496	−	0.216749i
$677$	−8.08976	+	4.67062i	−0.310915	+	0.179507i	−0.647336	−	0.762205i	$-0.724117\pi$
$677$	−8.08976	+	4.67062i	−0.310915	+	0.179507i	0.336421	+	0.941712i	$0.390783\pi$
$678$		0			0
$679$	30.3849	−	16.3877i	1.16606	−	0.628900i
$680$	−17.2310	+	22.2737i	−0.660777	+	0.854157i
$681$		0			0
$682$	19.9563	+	26.0783i	0.764165	+	0.998589i
$683$	10.8870	+	18.8568i	0.416578	+	0.721535i	0.995593	−	0.0937826i	$-0.0298959\pi$
$683$	10.8870	+	18.8568i	0.416578	+	0.721535i	−0.579014	+	0.815317i	$0.696563\pi$
$684$		0			0
$685$	35.8068			1.36811
$686$	−12.1168	+	23.2203i	−0.462622	+	0.886555i
$687$		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	$-0.820672\pi$
$691$	−21.1790	+	12.2277i	−0.805689	+	0.465165i	0.0397677	+	0.999209i	$0.487338\pi$
$692$	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
$700$	−1.25771	−	5.36681i	−0.0475368	−	0.202846i
$701$			10.4921i			0.396279i	0.980174	+	0.198140i	$0.0634900\pi$
$701$			10.4921i			0.396279i	−0.980174	+	0.198140i	$0.936510\pi$
$702$		0			0
$703$	−9.40929	+	5.43246i	−0.354878	+	0.204889i
$704$	21.2799	−	20.9474i	0.802017	−	0.789484i
$705$		0			0
$706$	−6.47249	+	15.5682i	−0.243596	+	0.585915i
$707$	7.61192	−	12.3438i	0.286276	−	0.464237i
$708$		0			0
$709$	−3.34723	−	5.79758i	−0.125708	−	0.217733i	0.796301	−	0.604900i	$-0.206787\pi$
$709$	−3.34723	−	5.79758i	−0.125708	−	0.217733i	−0.922009	+	0.387167i	$0.873454\pi$
$710$	−2.69413	+	6.48015i	−0.101109	+	0.243196i
$711$		0			0
$712$	3.75532	−	27.6818i	0.140737	−	1.03742i
$713$	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	$-0.728546\pi$
$719$	8.66863	−	15.0145i	0.323285	−	0.559947i	0.981164	+	0.193177i	$0.0618793\pi$
$720$		0			0
$721$	22.8389	−	37.0365i	0.850565	−	1.37931i
$722$	−2.51521	−	19.3006i	−0.0936065	−	0.718296i
$723$		0			0
$724$	−23.3986	−	23.5217i	−0.869601	−	0.874178i
$725$	−4.78381	−	2.76193i	−0.177666	−	0.102576i
$726$		0			0
$727$	18.0236	+	10.4059i	0.668458	+	0.385934i	0.795492	−	0.605964i	$-0.207213\pi$
$727$	18.0236	+	10.4059i	0.668458	+	0.385934i	−0.127034	+	0.991898i	$0.540546\pi$
$728$	9.91864	−	3.73094i	0.367609	−	0.138278i
$729$		0			0
$730$	−3.27019	+	0.426163i	−0.121035	+	0.0157730i
$731$	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	$0.490030\pi$
$734$	−14.8968	+	35.8309i	−0.549850	+	1.32254i
$735$		0			0
$736$	7.95386	−	18.8515i	0.293183	−	0.694874i
$737$	−35.4352	−	20.4585i	−1.30527	−	0.753599i
$738$		0			0
$739$	42.4863	−	24.5295i	1.56288	−	0.902331i	0.565920	−	0.824460i	$-0.308521\pi$
$739$	42.4863	−	24.5295i	1.56288	−	0.902331i	0.996963	−	0.0778716i	$-0.0248124\pi$
$740$	5.98157	+	22.5602i	0.219887	+	0.829330i
$741$		0			0
$742$	−27.3034	−	12.2910i	−1.00234	−	0.451218i
$743$	−13.4749	−	23.3392i	−0.494346	−	0.856232i	0.505633	−	0.862749i	$-0.331259\pi$
$743$	−13.4749	−	23.3392i	−0.494346	−	0.856232i	−0.999979	+	0.00651646i	$0.997926\pi$
$744$		0			0
$745$	−54.6258			−2.00133
$746$	−6.61441	−	2.74995i	−0.242171	−	0.100683i
$747$		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	$0.789844\pi$
$752$	30.1570	−	17.2007i	1.09971	−	0.627245i
$753$		0			0
$754$	4.07680	−	9.80584i	0.148468	−	0.357107i
$755$	−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	$0.315271\pi$
$758$	0.556968	−	1.33967i	0.0202300	−	0.0486588i
$759$		0			0
$760$	15.7654	+	2.13874i	0.571872	+	0.0775802i
$761$		−	15.9088i		−	0.576694i	−0.957526	−	0.288347i	$-0.906894\pi$
$761$		−	15.9088i		−	0.576694i	0.957526	−	0.288347i	$-0.0931056\pi$
$762$		0			0
$763$	0.894201	−	30.8474i	0.0323722	−	1.11675i
$764$	−8.61706	+	31.8249i	−0.311754	+	1.15139i
$765$		0			0
$766$	32.9971	+	13.7186i	1.19223	+	0.495674i
$767$	−4.97612			−0.179677
$768$		0			0
$769$	−2.11592	−	3.66489i	−0.0763022	−	0.132159i	0.825350	−	0.564622i	$-0.190978\pi$
$769$	−2.11592	−	3.66489i	−0.0763022	−	0.132159i	−0.901652	+	0.432463i	$0.857645\pi$
$770$	27.8545	−	20.0630i	1.00381	−	0.723020i
$771$		0			0
$772$	−44.7939	+	11.8766i	−1.61217	+	0.427447i
$773$	−24.1708	+	13.9550i	−0.869362	+	0.501927i	−0.867136	−	0.498071i	$-0.834042\pi$
$773$	−24.1708	+	13.9550i	−0.869362	+	0.501927i	−0.00222598	+	0.999998i	$0.500709\pi$
$774$		0			0
$775$	5.61224	+	3.24023i	0.201598	+	0.116392i
$776$	36.5710	+	4.96123i	1.31282	+	0.178098i
$777$		0			0
$778$	−5.05353	+	12.1551i	−0.181178	+	0.435783i
$779$	−20.2758			−0.726457
$780$		0			0
$781$	−7.53551			−0.269642
$782$	−20.5458	+	2.67747i	−0.734715	+	0.0957463i
$783$		0			0
$784$	−25.0846	+	12.4403i	−0.895879	+	0.444297i
$785$	4.73336	+	2.73281i	0.168941	+	0.0975380i
$786$		0			0
$787$	−5.59132	−	3.22815i	−0.199309	−	0.115071i	0.397024	−	0.917808i	$-0.370043\pi$
$787$	−5.59132	−	3.22815i	−0.199309	−	0.115071i	−0.596333	+	0.802737i	$0.703376\pi$
$788$	20.4345	−	20.3275i	0.727950	−	0.724138i
$789$		0			0
$790$	−1.81329	−	13.9144i	−0.0645140	−	0.495052i
$791$	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	−0.919383	−	0.393363i	$-0.871312\pi$
$797$	−29.3156	+	16.9254i	−1.03841	+	0.599528i	−0.119029	+	0.992891i	$0.537978\pi$
$798$		0			0
$799$	−30.4465	−	17.5783i	−1.07712	−	0.621876i
$800$	2.29075	−	5.42932i	0.0809904	−	0.191956i
$801$		0			0
$802$	9.74924	−	23.4497i	0.344258	−	0.828036i
$803$	−1.77054	−	3.06667i	−0.0624811	−	0.108220i
$804$		0			0
$805$	12.3463	−	20.0213i	0.435151	−	0.705660i
$806$	−4.78280	+	11.5040i	−0.168467	+	0.405210i
$807$		0			0
$808$	14.3465	−	5.87646i	0.504709	−	0.206733i
$809$	6.11435	−	3.53012i	0.214969	−	0.124112i	−0.388650	−	0.921386i	$-0.627058\pi$
$809$	6.11435	−	3.53012i	0.214969	−	0.124112i	0.603619	+	0.797273i	$0.293725\pi$
$810$		0			0
$811$		−	40.7979i		−	1.43261i	−0.697789	−	0.716304i	$-0.745833\pi$
$811$		−	40.7979i		−	1.43261i	0.697789	−	0.716304i	$-0.254167\pi$
$812$	−8.11507	+	26.8601i	−0.284783	+	0.942604i
$813$		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	0.178125	−	0.984008i	$-0.442997\pi$
$821$	32.0732	−	18.5175i	1.11936	−	0.646265i	0.941238	+	0.337743i	$0.109663\pi$
$822$		0			0
$823$	−10.2150	−	5.89764i	−0.356073	−	0.205579i	0.311284	−	0.950317i	$-0.399241\pi$
$823$	−10.2150	−	5.89764i	−0.356073	−	0.205579i	−0.667357	+	0.744738i	$0.732574\pi$
$824$	43.0455	−	17.6318i	1.49956	−	0.614232i
$825$		0			0
$826$	13.0815	−	1.32056i	0.455164	−	0.0459481i
$827$	−9.85297			−0.342621			−0.171311	−	0.985217i	$-0.554800\pi$
$827$	−9.85297			−0.342621			−0.171311	+	0.985217i	$0.554800\pi$
$828$		0			0
$829$	−6.91019	−	11.9688i	−0.240001	−	0.415693i	0.720713	−	0.693233i	$-0.243814\pi$
$829$	−6.91019	−	11.9688i	−0.240001	−	0.415693i	−0.960714	+	0.277540i	$0.910481\pi$
$830$	−0.474689	−	0.620311i	−0.0164767	−	0.0215313i
$831$		0			0
$832$	10.9194	+	3.01819i	0.378561	+	0.104637i
$833$	23.6929	+	15.5757i	0.820911	+	0.539665i
$834$		0			0
$835$	24.6460	−	14.2294i	0.852909	−	0.492428i
$836$	4.37816	+	16.5128i	0.151422	+	0.571106i
$837$		0			0
$838$	−3.21651	−	24.6821i	−0.111112	−	0.852628i
$839$	−21.5036	+	37.2454i	−0.742388	+	1.28585i	0.209017	+	0.977912i	$0.432974\pi$
$839$	−21.5036	+	37.2454i	−0.742388	+	1.28585i	−0.951405	+	0.307942i	$0.900360\pi$
$840$		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
$848$	−15.8591	−	27.8048i	−0.544604	−	0.954822i
$849$		0			0
$850$	−5.91729	+	0.771127i	−0.202961	+	0.0264494i
$851$	−8.58622	+	14.8718i	−0.294332	+	0.509797i
$852$		0			0
$853$	−27.0808	+	46.9054i	−0.927230	+	1.60601i	−0.139296	+	0.990251i	$0.544484\pi$
$853$	−27.0808	+	46.9054i	−0.927230	+	1.60601i	−0.787935	+	0.615759i	$0.788849\pi$
$854$	−16.0745	+	35.7080i	−0.550059	+	1.22190i
$855$		0			0
$856$	24.5521	+	3.33075i	0.839175	+	0.113843i
$857$		−	35.0389i		−	1.19691i	−0.801158	−	0.598453i	$-0.795782\pi$
$857$		−	35.0389i		−	1.19691i	0.801158	−	0.598453i	$-0.204218\pi$
$858$		0			0
$859$		−	32.4153i		−	1.10600i	−0.833182	−	0.552999i	$-0.813483\pi$
$859$		−	32.4153i		−	1.10600i	0.833182	−	0.552999i	$-0.186517\pi$
$860$	−57.9097	+	15.3541i	−1.97471	+	0.523569i
$861$		0			0
$862$	−4.16415	−	31.9539i	−0.141832	−	1.08835i
$863$	−0.619701	+	1.07335i	−0.0210949	+	0.0365374i	−0.876380	−	0.481620i	$-0.840049\pi$
$863$	−0.619701	+	1.07335i	−0.0210949	+	0.0365374i	0.855285	+	0.518157i	$0.173382\pi$
$864$		0			0
$865$	13.1011	+	22.6918i	0.445452	+	0.771545i
$866$	−33.8956	−	14.0922i	−1.15182	−	0.478871i
$867$		0			0
$868$	9.52040	−	31.5116i	0.323143	−	1.06957i
$869$	13.0484	−	7.53352i	0.442638	−	0.255557i
$870$		0			0
$871$		−	15.5238i		−	0.526003i
$872$	20.1866	−	26.0943i	0.683605	−	0.883665i
$873$		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	$0.198359\pi$
$878$	−5.50544	+	0.717456i	−0.185800	+	0.0242130i
$879$		0			0
$880$	36.6974	+	0.192652i	1.23707	+	0.00649429i
$881$			5.79121i			0.195111i	0.995230	+	0.0975554i	$0.0311023\pi$
$881$			5.79121i			0.195111i	−0.995230	+	0.0975554i	$0.968898\pi$
$882$		0			0
$883$			52.6107i			1.77049i	0.465125	+	0.885245i	$0.346009\pi$
$883$			52.6107i			1.77049i	−0.465125	+	0.885245i	$0.653991\pi$
$884$	−2.94010	−	11.0889i	−0.0988862	−	0.372962i
$885$		0			0
$886$	2.07197	+	15.8994i	0.0696092	+	0.534151i
$887$	−47.6931			−1.60138			−0.800689	−	0.599080i	$-0.795533\pi$
$887$	−47.6931			−1.60138			−0.800689	+	0.599080i	$0.795533\pi$
$888$		0			0
$889$	−1.30258	+	2.11232i	−0.0436872	+	0.0708451i
$890$	27.2652	−	20.8645i	0.913930	−	0.699379i
$891$		0			0
$892$	−4.60465	−	17.3670i	−0.154175	−	0.581490i
$893$			19.8623i			0.664667i
$894$		0			0
$895$	45.1055	−	26.0417i	1.50771	−	0.870478i
$896$	−29.5065	−	5.03663i	−0.985742	−	0.168262i
$897$		0			0
$898$	8.50840	−	20.4651i	0.283929	−	0.682929i
$899$	−16.4940	−	28.5684i	−0.550105	−	0.952810i
$900$		0			0
$901$	−16.2073	+	28.0718i	−0.539942	+	0.935207i
$902$	−46.3765	+	6.04368i	−1.54417	+	0.201232i
$903$		0			0
$904$	21.5939	+	16.7051i	0.718203	+	0.555603i
$905$		−	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	$0.968240\pi$
$908$	−14.6251	−	14.7021i	−0.485351	−	0.487905i
$909$		0			0
$910$	11.8760	+	5.34615i	0.393685	+	0.177223i
$911$	8.56559	−	14.8360i	0.283791	−	0.491540i	−0.688525	−	0.725213i	$-0.741741\pi$
$911$	8.56559	−	14.8360i	0.283791	−	0.491540i	0.972315	+	0.233673i	$0.0750746\pi$
$912$		0			0
$913$	0.419356	−	0.726346i	0.0138787	−	0.0240385i
$914$	3.19549	+	24.5208i	0.105697	+	0.811076i
$915$		0			0
$916$	−5.23295	−	5.26049i	−0.172901	−	0.173812i
$917$	−15.7007	−	9.68196i	−0.518482	−	0.319726i
$918$		0			0
$919$	−7.67873	−	4.43332i	−0.253298	−	0.146242i	0.367975	−	0.929836i	$-0.380051\pi$
$919$	−7.67873	−	4.43332i	−0.253298	−	0.146242i	−0.621273	+	0.783594i	$0.713384\pi$
$920$	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
$926$	−24.8274	+	3.23545i	−0.815879	+	0.106323i
$927$		0			0
$928$	−23.9172	+	18.1042i	−0.785120	+	0.594299i
$929$	9.29468	−	5.36629i	0.304949	−	0.176062i	−0.339715	−	0.940528i	$-0.610331\pi$
$929$	9.29468	−	5.36629i	0.304949	−	0.176062i	0.644664	+	0.764466i	$0.276997\pi$
$930$		0			0
$931$	0.927941	−	15.9922i	0.0304120	−	0.524124i
$932$	7.67064	+	28.9308i	0.251260	+	0.947659i
$933$		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	$0.614519\pi$
$938$	4.11968	+	40.8098i	0.134512	+	1.33249i
$939$		0			0
$940$	41.1847	+	11.1514i	1.34330	+	0.363717i
$941$	8.80806	+	5.08533i	0.287134	+	0.165777i	0.636649	−	0.771154i	$-0.280320\pi$
$941$	8.80806	+	5.08533i	0.287134	+	0.165777i	−0.349514	+	0.936931i	$0.613653\pi$
$942$		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	$-0.198956\pi$
$947$	−3.11631	−	5.39761i	−0.101267	−	0.175399i	−0.912207	+	0.409730i	$0.865623\pi$
$948$		0			0
$949$	0.671737	−	1.16348i	0.0218055	−	0.0377682i
$950$	2.04883	+	2.67735i	0.0664728	+	0.0868648i
$951$		0			0
$952$	10.6719	+	28.3711i	0.345878	+	0.919512i
$953$		−	24.0752i		−	0.779871i	−0.920842	−	0.389936i	$-0.872497\pi$
$953$		−	24.0752i		−	0.779871i	0.920842	−	0.389936i	$-0.127503\pi$
$954$		0			0
$955$	−35.0923	+	20.2605i	−1.13556	+	0.655615i
$956$	−7.15563	+	26.4275i	−0.231430	+	0.854726i
$957$		0			0
$958$	−2.33069	−	0.968990i	−0.0753013	−	0.0313067i
$959$	20.2301	−	32.8059i	0.653263	−	1.05936i
$960$		0			0
$961$	3.85032	+	6.66896i	0.124204	+	0.215128i
$962$	−8.77959	−	3.65013i	−0.283065	−	0.117685i
$963$		0			0
$964$	16.5569	+	16.6441i	0.533263	+	0.536069i
$965$	−49.3233	−	28.4768i	−1.58777	−	0.916701i
$966$		0			0
$967$	−1.08046	+	0.623806i	−0.0347454	+	0.0200603i	−0.517272	−	0.855821i	$-0.673052\pi$
$967$	−1.08046	+	0.623806i	−0.0347454	+	0.0200603i	0.482527	+	0.875881i	$0.339719\pi$
$968$	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	$-0.757715\pi$
$971$	7.33316	−	12.7014i	0.235332	−	0.407608i	0.959369	+	0.282154i	$0.0910488\pi$
$972$		0			0
$973$	−34.5045	−	1.00021i	−1.10616	−	0.0320653i
$974$	23.1491	−	3.01674i	0.741747	−	0.0966626i
$975$		0			0
$976$	−36.3639	+	20.7409i	−1.16398	+	0.663901i
$977$	36.4261	+	21.0306i	1.16538	+	0.672830i	0.952586	−	0.304268i	$-0.0984120\pi$
$977$	36.4261	+	21.0306i	1.16538	+	0.672830i	0.212789	+	0.977098i	$0.431745\pi$
$978$		0			0
$979$	31.9258	+	18.4324i	1.02035	+	0.589101i
$980$	−32.6390	−	10.9027i	−1.04262	−	0.348272i
$981$		0			0
$982$	6.08381	+	46.6845i	0.194142	+	1.48976i
$983$	−7.02310			−0.224002			−0.112001	−	0.993708i	$-0.535726\pi$
$983$	−7.02310			−0.224002			−0.112001	+	0.993708i	$0.535726\pi$
$984$		0			0
$985$	35.4236			1.12869
$986$	28.0484	+	11.6612i	0.893243	+	0.371368i
$987$		0			0
$988$	−4.59502	+	4.57096i	−0.146187	+	0.145422i
$989$	−38.1743	−	22.0399i	−1.21387	−	0.700829i
$990$		0			0
$991$	−34.0177	+	19.6402i	−1.08061	+	0.623890i	−0.931061	−	0.364864i	$-0.881115\pi$
$991$	−34.0177	+	19.6402i	−1.08061	+	0.623890i	−0.149548	+	0.988754i	$0.547782\pi$
$992$	28.0590	−	21.2394i	0.890875	−	0.674351i
$993$		0			0
$994$	4.41494	+	6.12950i	0.140034	+	0.194416i
$995$	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	$0.522908\pi$
$998$	15.1697	−	36.4874i	0.480189	−	1.15499i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.o.a.359.38		88
3.2	odd	2		252.2.o.a.191.7	yes	88
4.3	odd	2	inner	756.2.o.a.359.24		88
7.4	even	3		756.2.bb.a.683.9		88
9.4	even	3		252.2.bb.a.23.9	yes	88
9.5	odd	6		756.2.bb.a.611.36		88
12.11	even	2		252.2.o.a.191.21	yes	88
21.11	odd	6		252.2.bb.a.11.36	yes	88
28.11	odd	6		756.2.bb.a.683.36		88
36.23	even	6		756.2.bb.a.611.9		88
36.31	odd	6		252.2.bb.a.23.36	yes	88
63.4	even	3		252.2.o.a.95.21	yes	88
63.32	odd	6	inner	756.2.o.a.179.24		88
84.11	even	6		252.2.bb.a.11.9	yes	88
252.67	odd	6		252.2.o.a.95.7	✓	88
252.95	even	6	inner	756.2.o.a.179.38		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.7	✓	88	252.67	odd	6
252.2.o.a.95.21	yes	88	63.4	even	3
252.2.o.a.191.7	yes	88	3.2	odd	2
252.2.o.a.191.21	yes	88	12.11	even	2
252.2.bb.a.11.9	yes	88	84.11	even	6
252.2.bb.a.11.36	yes	88	21.11	odd	6
252.2.bb.a.23.9	yes	88	9.4	even	3
252.2.bb.a.23.36	yes	88	36.31	odd	6
756.2.o.a.179.24		88	63.32	odd	6	inner
756.2.o.a.179.38		88	252.95	even	6	inner
756.2.o.a.359.24		88	4.3	odd	2	inner
756.2.o.a.359.38		88	1.1	even	1	trivial
756.2.bb.a.611.9		88	36.23	even	6
756.2.bb.a.611.36		88	9.5	odd	6
756.2.bb.a.683.9		88	7.4	even	3
756.2.bb.a.683.36		88	28.11	odd	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)

\(f(q)\)	\(=\)	\(q+(1.30585 + 0.542910i) q^{2} +(1.41050 + 1.41792i) q^{4} +2.45799i q^{5} +(2.25199 + 1.38871i) q^{7} +(1.07210 + 2.61737i) q^{8} +O(q^{10})\)	\(q+(1.30585 + 0.542910i) q^{2} +(1.41050 + 1.41792i) q^{4} +2.45799i q^{5} +(2.25199 + 1.38871i) q^{7} +(1.07210 + 2.61737i) q^{8} +(-1.33447 + 3.20977i) q^{10} -3.73252 q^{11} +(-0.708051 - 1.22638i) q^{13} +(2.18682 + 3.03608i) q^{14} +(-0.0209987 + 3.99994i) q^{16} +(3.50791 - 2.02529i) q^{17} +(-1.98185 - 1.14422i) q^{19} +(-3.48523 + 3.46699i) q^{20} +(-4.87411 - 2.02642i) q^{22} -3.61698 q^{23} -1.04171 q^{25} +(-0.258795 - 1.98588i) q^{26} +(1.20735 + 5.15192i) q^{28} +(4.59226 + 2.65135i) q^{29} +(-5.38753 - 3.11049i) q^{31} +(-2.19903 + 5.21193i) q^{32} +(5.68037 - 0.740251i) q^{34} +(-3.41344 + 5.53538i) q^{35} +(2.37386 - 4.11165i) q^{37} +(-1.96679 - 2.57015i) q^{38} +(-6.43346 + 2.63520i) q^{40} +(7.67307 - 4.43005i) q^{41} +(10.5542 + 6.09346i) q^{43} +(-5.26470 - 5.29241i) q^{44} +(-4.72324 - 1.96370i) q^{46} +(-4.33970 - 7.51657i) q^{47} +(3.14296 + 6.25474i) q^{49} +(-1.36032 - 0.565555i) q^{50} +(0.740207 - 2.73377i) q^{52} +(-6.93030 + 4.00121i) q^{53} -9.17448i q^{55} +(-1.22042 + 7.38313i) q^{56} +(4.55737 + 5.95545i) q^{58} +(1.75698 - 3.04317i) q^{59} +(5.23289 + 9.06363i) q^{61} +(-5.34660 - 6.98679i) q^{62} +(-5.70122 + 5.61213i) q^{64} +(3.01443 - 1.74038i) q^{65} +(9.49365 + 5.48116i) q^{67} +(7.81961 + 2.11727i) q^{68} +(-7.46266 + 5.37519i) q^{70} +2.01888 q^{71} +(0.474356 + 0.821609i) q^{73} +(5.33217 - 4.08041i) q^{74} +(-1.17298 - 4.42403i) q^{76} +(-8.40560 - 5.18339i) q^{77} +(-3.49588 + 2.01835i) q^{79} +(-9.83182 - 0.0516145i) q^{80} +(12.4250 - 1.61920i) q^{82} +(-0.112352 + 0.194599i) q^{83} +(4.97815 + 8.62241i) q^{85} +(10.4740 + 13.6871i) q^{86} +(-4.00161 - 9.76936i) q^{88} +(-8.55343 - 4.93832i) q^{89} +(0.108562 - 3.74508i) q^{91} +(-5.10174 - 5.12859i) q^{92} +(-1.58617 - 12.1716i) q^{94} +(2.81249 - 4.87137i) q^{95} +(6.52412 - 11.3001i) q^{97} +(0.708472 + 9.87411i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 3 q^{2} + q^{4}+O(q^{10}) \) 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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