LMFDB - Embedded newform 504.2.cj.e.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(37,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("504.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.7
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.e.109.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.491996 + 1.32587i) q^{2} +(-1.51588 - 1.30465i) q^{4} +(3.08781 + 1.78275i) q^{5} +(-2.38336 + 1.14873i) q^{7} +(2.47560 - 1.36799i) q^{8} +O(q^{10})$	\(q+(-0.491996 + 1.32587i) q^{2} +(-1.51588 - 1.30465i) q^{4} +(3.08781 + 1.78275i) q^{5} +(-2.38336 + 1.14873i) q^{7} +(2.47560 - 1.36799i) q^{8} +(-3.88289 + 3.21694i) q^{10} +(-3.52552 + 2.03546i) q^{11} -1.44065i q^{13} +(-0.350472 - 3.72521i) q^{14} +(0.595789 + 3.95538i) q^{16} +(3.49555 + 6.05447i) q^{17} +(0.261102 + 0.150747i) q^{19} +(-2.35490 - 6.73095i) q^{20} +(-0.964222 - 5.67583i) q^{22} +(-1.21250 + 2.10010i) q^{23} +(3.85640 + 6.67947i) q^{25} +(1.91012 + 0.708792i) q^{26} +(5.11158 + 1.36810i) q^{28} -0.151350i q^{29} +(2.37719 + 4.11741i) q^{31} +(-5.53746 - 1.15609i) q^{32} +(-9.74726 + 1.65588i) q^{34} +(-9.40728 - 0.701863i) q^{35} +(-9.82338 - 5.67153i) q^{37} +(-0.328333 + 0.272021i) q^{38} +(10.0830 + 0.189300i) q^{40} +0.239424 q^{41} +1.32831i q^{43} +(7.99983 + 1.51405i) q^{44} +(-2.18793 - 2.64086i) q^{46} +(-3.17936 + 5.50681i) q^{47} +(4.36082 - 5.47569i) q^{49} +(-10.7535 + 1.82682i) q^{50} +(-1.87954 + 2.18385i) q^{52} +(-5.18376 + 2.99285i) q^{53} -14.5149 q^{55} +(-4.32881 + 6.10421i) q^{56} +(0.200671 + 0.0744635i) q^{58} +(9.73654 - 5.62140i) q^{59} +(3.64539 + 2.10467i) q^{61} +(-6.62874 + 1.12610i) q^{62} +(4.25723 - 6.77318i) q^{64} +(2.56831 - 4.44845i) q^{65} +(3.79384 - 2.19037i) q^{67} +(2.60011 - 13.7383i) q^{68} +(5.55892 - 12.1275i) q^{70} +8.46387 q^{71} +(-0.284724 - 0.493156i) q^{73} +(12.3528 - 10.2342i) q^{74} +(-0.199128 - 0.569162i) q^{76} +(6.06439 - 8.90112i) q^{77} +(0.746916 - 1.29370i) q^{79} +(-5.21177 + 13.2756i) q^{80} +(-0.117795 + 0.317446i) q^{82} -10.0352i q^{83} +24.9268i q^{85} +(-1.76117 - 0.653524i) q^{86} +(-5.94331 + 9.86185i) q^{88} +(-1.83434 + 3.17718i) q^{89} +(1.65492 + 3.43358i) q^{91} +(4.57789 - 1.60163i) q^{92} +(-5.73711 - 6.92476i) q^{94} +(0.537490 + 0.930960i) q^{95} +10.4657 q^{97} +(5.11457 + 8.47592i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{49} - 52 q^{50} + 44 q^{52} - 64 q^{55} - 40 q^{56} + 34 q^{58} - 100 q^{62} - 20 q^{64} - 16 q^{68} + 38 q^{70} + 80 q^{71} + 8 q^{73} - 10 q^{74} - 32 q^{76} + 8 q^{79} + 56 q^{80} + 22 q^{86} + 50 q^{88} - 64 q^{92} - 48 q^{94} - 24 q^{95} - 48 q^{97} + 64 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.491996	+	1.32587i	−0.347893	+	0.937534i
$2$	−0.491996	+	1.32587i	−0.347893	+	0.937534i
$3$		0			0
$3$		0			0
$4$	−1.51588	−	1.30465i	−0.757940	−	0.652324i
$5$	3.08781	+	1.78275i	1.38091	+	0.797270i	0.992268	−	0.124118i	$-0.0396100\pi$
$5$	3.08781	+	1.78275i	1.38091	+	0.797270i	0.388645	+	0.921388i	$0.372943\pi$
$6$		0			0
$7$	−2.38336	+	1.14873i	−0.900826	+	0.434180i
$7$	−2.38336	+	1.14873i	−0.900826	+	0.434180i
$8$	2.47560	−	1.36799i	0.875258	−	0.483656i
$9$		0			0
$10$	−3.88289	+	3.21694i	−1.22788	+	1.01729i
$11$	−3.52552	+	2.03546i	−1.06298	+	0.613714i	−0.926256	−	0.376894i	$-0.876992\pi$
$11$	−3.52552	+	2.03546i	−1.06298	+	0.613714i	−0.136728	+	0.990609i	$0.543659\pi$
$12$		0			0
$13$		−	1.44065i		−	0.399564i	−0.979840	−	0.199782i	$-0.935977\pi$
$13$		−	1.44065i		−	0.399564i	0.979840	−	0.199782i	$-0.0640233\pi$
$14$	−0.350472	−	3.72521i	−0.0936675	−	0.995604i
$15$		0			0
$16$	0.595789	+	3.95538i	0.148947	+	0.988845i
$17$	3.49555	+	6.05447i	0.847796	+	1.46843i	0.883171	+	0.469051i	$0.155404\pi$
$17$	3.49555	+	6.05447i	0.847796	+	1.46843i	−0.0353755	+	0.999374i	$0.511263\pi$
$18$		0			0
$19$	0.261102	+	0.150747i	0.0599010	+	0.0345838i	0.529651	−	0.848215i	$-0.322323\pi$
$19$	0.261102	+	0.150747i	0.0599010	+	0.0345838i	−0.469750	+	0.882799i	$0.655656\pi$
$20$	−2.35490	−	6.73095i	−0.526571	−	1.50509i
$21$		0			0
$22$	−0.964222	−	5.67583i	−0.205573	−	1.21009i
$23$	−1.21250	+	2.10010i	−0.252823	+	0.437902i	−0.964302	−	0.264805i	$-0.914692\pi$
$23$	−1.21250	+	2.10010i	−0.252823	+	0.437902i	0.711479	+	0.702707i	$0.248026\pi$
$24$		0			0
$25$	3.85640	+	6.67947i	0.771279	+	1.33589i
$26$	1.91012	+	0.708792i	0.374604	+	0.139006i
$27$		0			0
$28$	5.11158	+	1.36810i	0.965999	+	0.258547i
$29$		−	0.151350i		−	0.0281050i	−0.999901	−	0.0140525i	$-0.995527\pi$
$29$		−	0.151350i		−	0.0281050i	0.999901	−	0.0140525i	$-0.00447319\pi$
$30$		0			0
$31$	2.37719	+	4.11741i	0.426956	+	0.739509i	0.996601	−	0.0823815i	$-0.0262526\pi$
$31$	2.37719	+	4.11741i	0.426956	+	0.739509i	−0.569645	+	0.821891i	$0.692919\pi$
$32$	−5.53746	−	1.15609i	−0.978894	−	0.204370i
$33$		0			0
$34$	−9.74726	+	1.65588i	−1.67164	+	0.283982i
$35$	−9.40728	−	0.701863i	−1.59012	−	0.118637i
$36$		0			0
$37$	−9.82338	−	5.67153i	−1.61495	−	0.932394i	−0.988199	−	0.153178i	$-0.951049\pi$
$37$	−9.82338	−	5.67153i	−1.61495	−	0.932394i	−0.626755	−	0.779216i	$-0.715617\pi$
$38$	−0.328333	+	0.272021i	−0.0532627	+	0.0441277i
$39$		0			0
$40$	10.0830	+	0.189300i	1.59426	+	0.0299310i
$41$	0.239424			0.0373917			0.0186959	−	0.999825i	$-0.494049\pi$
$41$	0.239424			0.0373917			0.0186959	+	0.999825i	$0.494049\pi$
$42$		0			0
$43$			1.32831i			0.202566i	0.994858	+	0.101283i	$0.0322947\pi$
$43$			1.32831i			0.202566i	−0.994858	+	0.101283i	$0.967705\pi$
$44$	7.99983	+	1.51405i	1.20602	+	0.228251i
$45$		0			0
$46$	−2.18793	−	2.64086i	−0.322593	−	0.389373i
$47$	−3.17936	+	5.50681i	−0.463757	+	0.803251i	−0.999144	−	0.0413556i	$-0.986832\pi$
$47$	−3.17936	+	5.50681i	−0.463757	+	0.803251i	0.535387	+	0.844607i	$0.320166\pi$
$48$		0			0
$49$	4.36082	−	5.47569i	0.622975	−	0.782242i
$50$	−10.7535	+	1.82682i	−1.52077	+	0.258352i
$51$		0			0
$52$	−1.87954	+	2.18385i	−0.260645	+	0.302845i
$53$	−5.18376	+	2.99285i	−0.712045	+	0.411099i	−0.811818	−	0.583911i	$-0.801522\pi$
$53$	−5.18376	+	2.99285i	−0.712045	+	0.411099i	0.0997730	+	0.995010i	$0.468188\pi$
$54$		0			0
$55$	−14.5149			−1.95718
$56$	−4.32881	+	6.10421i	−0.578462	+	0.815710i
$57$		0			0
$58$	0.200671	+	0.0744635i	0.0263494	+	0.00977753i
$59$	9.73654	−	5.62140i	1.26759	−	0.731843i	0.293059	−	0.956094i	$-0.405327\pi$
$59$	9.73654	−	5.62140i	1.26759	−	0.731843i	0.974531	+	0.224251i	$0.0719936\pi$
$60$		0			0
$61$	3.64539	+	2.10467i	0.466744	+	0.269475i	0.714876	−	0.699251i	$-0.246483\pi$
$61$	3.64539	+	2.10467i	0.466744	+	0.269475i	−0.248132	+	0.968726i	$0.579817\pi$
$62$	−6.62874	+	1.12610i	−0.841850	+	0.143015i
$63$		0			0
$64$	4.25723	−	6.77318i	0.532154	−	0.846647i
$65$	2.56831	−	4.44845i	0.318560	−	0.551762i
$66$		0			0
$67$	3.79384	−	2.19037i	0.463491	−	0.267597i	−0.250020	−	0.968241i	$-0.580437\pi$
$67$	3.79384	−	2.19037i	0.463491	−	0.267597i	0.713511	+	0.700644i	$0.247104\pi$
$68$	2.60011	−	13.7383i	0.315310	−	1.66602i
$69$		0			0
$70$	5.55892	−	12.1275i	0.664418	−	1.44952i
$71$	8.46387			1.00448			0.502238	−	0.864729i	$-0.332510\pi$
$71$	8.46387			1.00448			0.502238	+	0.864729i	$0.332510\pi$
$72$		0			0
$73$	−0.284724	−	0.493156i	−0.0333244	−	0.0577196i	0.848882	−	0.528582i	$-0.177276\pi$
$73$	−0.284724	−	0.493156i	−0.0333244	−	0.0577196i	−0.882207	+	0.470863i	$0.843943\pi$
$74$	12.3528	−	10.2342i	1.43598	−	1.18970i
$75$		0			0
$76$	−0.199128	−	0.569162i	−0.0228415	−	0.0652873i
$77$	6.06439	−	8.90112i	0.691101	−	1.01438i
$78$		0			0
$79$	0.746916	−	1.29370i	0.0840347	−	0.145552i	−0.820945	−	0.571008i	$-0.806553\pi$
$79$	0.746916	−	1.29370i	0.0840347	−	0.145552i	0.904979	+	0.425455i	$0.139886\pi$
$80$	−5.21177	+	13.2756i	−0.582694	+	1.48426i
$81$		0			0
$82$	−0.117795	+	0.317446i	−0.0130083	+	0.0350560i
$83$		−	10.0352i		−	1.10151i	−0.834668	−	0.550753i	$-0.814340\pi$
$83$		−	10.0352i		−	1.10151i	0.834668	−	0.550753i	$-0.185660\pi$
$84$		0			0
$85$			24.9268i			2.70369i
$86$	−1.76117	−	0.653524i	−0.189912	−	0.0704713i
$87$		0			0
$88$	−5.94331	+	9.86185i	−0.633559	+	1.05128i
$89$	−1.83434	+	3.17718i	−0.194440	+	0.336780i	−0.946717	−	0.322067i	$-0.895622\pi$
$89$	−1.83434	+	3.17718i	−0.194440	+	0.336780i	0.752277	+	0.658847i	$0.228956\pi$
$90$		0			0
$91$	1.65492	+	3.43358i	0.173483	+	0.359937i
$92$	4.57789	−	1.60163i	0.477278	−	0.166981i
$93$		0			0
$94$	−5.73711	−	6.92476i	−0.591737	−	0.714234i
$95$	0.537490	+	0.930960i	0.0551453	+	0.0955145i
$96$		0			0
$97$	10.4657			1.06264			0.531318	−	0.847173i	$-0.321697\pi$
$97$	10.4657			1.06264			0.531318	+	0.847173i	$0.321697\pi$
$98$	5.11457	+	8.47592i	0.516650	+	0.856197i
$99$		0			0
$100$	2.86852	−	15.1565i	0.286852	−	1.51565i
$101$	−11.0277	+	6.36685i	−1.09730	+	0.633526i	−0.935510	−	0.353300i	$-0.885060\pi$
$101$	−11.0277	+	6.36685i	−1.09730	+	0.633526i	−0.161789	+	0.986825i	$0.551726\pi$
$102$		0			0
$103$	3.00437	−	5.20373i	0.296030	−	0.512739i	−0.679194	−	0.733959i	$-0.737671\pi$
$103$	3.00437	−	5.20373i	0.296030	−	0.512739i	0.975224	+	0.221220i	$0.0710039\pi$
$104$	−1.97078	−	3.56647i	−0.193251	−	0.349721i
$105$		0			0
$106$	−1.41775	−	8.34548i	−0.137704	−	0.810585i
$107$	13.8269	+	7.98297i	1.33670	+	0.771743i	0.986316	−	0.164864i	$-0.0527186\pi$
$107$	13.8269	+	7.98297i	1.33670	+	0.771743i	0.350382	+	0.936607i	$0.386052\pi$
$108$		0			0
$109$	12.0127	−	6.93554i	1.15061	−	0.664304i	0.201573	−	0.979474i	$-0.435395\pi$
$109$	12.0127	−	6.93554i	1.15061	−	0.664304i	0.949035	+	0.315170i	$0.102061\pi$
$110$	7.14125	−	19.2449i	0.680891	−	1.83493i
$111$		0			0
$112$	−5.96366	−	8.74270i	−0.563513	−	0.826107i
$113$	16.4495			1.54744			0.773719	−	0.633529i	$-0.218394\pi$
$113$	16.4495			1.54744			0.773719	+	0.633529i	$0.218394\pi$
$114$		0			0
$115$	−7.48792	+	4.32315i	−0.698252	+	0.403136i
$116$	−0.197458	+	0.229428i	−0.0183335	+	0.0213019i
$117$		0			0
$118$	2.66292	+	15.6751i	0.245142	+	1.44301i
$119$	−15.2861	−	10.4145i	−1.40128	−	0.954699i
$120$		0			0
$121$	2.78620	−	4.82583i	0.253291	−	0.438712i
$122$	−4.58404	+	3.79784i	−0.415019	+	0.343840i
$123$		0			0
$124$	1.76824	−	9.34290i	0.158792	−	0.839018i
$125$			9.67245i			0.865131i
$126$		0			0
$127$	−3.33297			−0.295754			−0.147877	−	0.989006i	$-0.547244\pi$
$127$	−3.33297			−0.295754			−0.147877	+	0.989006i	$0.547244\pi$
$128$	6.88584	+	8.97693i	0.608628	+	0.793456i
$129$		0			0
$130$	4.63448	+	5.59387i	0.406471	+	0.490615i
$131$	3.54089	+	2.04433i	0.309369	+	0.178614i	0.646644	−	0.762792i	$-0.276172\pi$
$131$	3.54089	+	2.04433i	0.309369	+	0.178614i	−0.337275	+	0.941406i	$0.609505\pi$
$132$		0			0
$133$	−0.795470	−	0.0593488i	−0.0689760	−	0.00514620i
$134$	1.03761	+	6.10780i	0.0896356	+	0.527634i
$135$		0			0
$136$	16.9360	+	10.2066i	1.45225	+	0.875210i
$137$	4.14368	+	7.17707i	0.354019	+	0.613178i	0.986950	−	0.161030i	$-0.0514816\pi$
$137$	4.14368	+	7.17707i	0.354019	+	0.613178i	−0.632931	+	0.774208i	$0.718148\pi$
$138$		0			0
$139$		−	18.4180i		−	1.56219i	−0.624411	−	0.781096i	$-0.714661\pi$
$139$		−	18.4180i		−	1.56219i	0.624411	−	0.781096i	$-0.285339\pi$
$140$	13.3446	+	13.3371i	1.12783	+	1.12719i
$141$		0			0
$142$	−4.16419	+	11.2220i	−0.349451	+	0.941731i
$143$	2.93238	+	5.07903i	0.245218	+	0.424730i
$144$		0			0
$145$	0.269819	−	0.467340i	0.0224072	−	0.0388105i
$146$	0.793945	−	0.134877i	0.0657074	−	0.0111625i
$147$		0			0
$148$	7.49172	+	21.4134i	0.615816	+	1.76017i
$149$	−4.42715	−	2.55602i	−0.362686	−	0.209397i	0.307572	−	0.951525i	$-0.400483\pi$
$149$	−4.42715	−	2.55602i	−0.362686	−	0.209397i	−0.670258	+	0.742128i	$0.733817\pi$
$150$		0			0
$151$	2.08563	+	3.61242i	0.169726	+	0.293974i	0.938324	−	0.345758i	$-0.112378\pi$
$151$	2.08563	+	3.61242i	0.169726	+	0.293974i	−0.768597	+	0.639733i	$0.779045\pi$
$152$	0.852606	+	0.0160070i	0.0691555	+	0.00129834i
$153$		0			0
$154$	8.81811	+	12.4199i	0.710583	+	1.00083i
$155$			16.9517i			1.36160i
$156$		0			0
$157$	7.83645	−	4.52438i	0.625417	−	0.361084i	−0.153558	−	0.988140i	$-0.549073\pi$
$157$	7.83645	−	4.52438i	0.625417	−	0.361084i	0.778975	+	0.627055i	$0.215740\pi$
$158$	1.34780	+	1.62681i	0.107225	+	0.129422i
$159$		0			0
$160$	−15.0376	−	13.4417i	−1.18883	−	1.06266i
$161$	0.477356	−	6.39814i	0.0376209	−	0.504244i
$162$		0			0
$163$	11.6491	+	6.72560i	0.912426	+	0.526790i	0.881211	−	0.472723i	$-0.156729\pi$
$163$	11.6491	+	6.72560i	0.912426	+	0.526790i	0.0312153	+	0.999513i	$0.490062\pi$
$164$	−0.362938	−	0.312364i	−0.0283407	−	0.0243915i
$165$		0			0
$166$	13.3054	+	4.93728i	1.03270	+	0.383207i
$167$	−17.2099			−1.33174			−0.665872	−	0.746066i	$-0.731940\pi$
$167$	−17.2099			−1.33174			−0.665872	+	0.746066i	$0.731940\pi$
$168$		0			0
$169$	10.9245			0.840349
$170$	−33.0497	−	12.2639i	−2.53480	−	0.940595i
$171$		0			0
$172$	1.73298	−	2.01356i	0.132138	−	0.153533i
$173$	−2.98726	−	1.72470i	−0.227117	−	0.131126i	0.382124	−	0.924111i	$-0.375193\pi$
$173$	−2.98726	−	1.72470i	−0.227117	−	0.131126i	−0.609242	+	0.792985i	$0.708526\pi$
$174$		0			0
$175$	−16.8641	−	11.4896i	−1.27481	−	0.868534i
$176$	−10.1515	−	12.7321i	−0.765197	−	0.959716i
$177$		0			0
$178$	−3.31005	−	3.99526i	−0.248098	−	0.299458i
$179$	−9.78752	+	5.65083i	−0.731554	+	0.422363i	−0.818990	−	0.573807i	$-0.805466\pi$
$179$	−9.78752	+	5.65083i	−0.731554	+	0.422363i	0.0874365	+	0.996170i	$0.472133\pi$
$180$		0			0
$181$		−	10.0566i		−	0.747502i	−0.927529	−	0.373751i	$-0.878071\pi$
$181$		−	10.0566i		−	0.747502i	0.927529	−	0.373751i	$-0.121929\pi$
$182$	−5.36671	+	0.504906i	−0.397807	+	0.0374261i
$183$		0			0
$184$	−0.128748	+	6.85770i	−0.00949144	+	0.505557i
$185$	−20.2218	−	35.0253i	−1.48674	−	2.57511i
$186$		0			0
$187$	−24.6473	−	14.2301i	−1.80239	−	1.04061i
$188$	12.0040	−	4.19973i	0.875480	−	0.306297i
$189$		0			0
$190$	−1.49878	+	0.254616i	−0.108733	+	0.0184718i
$191$	10.7430	−	18.6075i	0.777338	−	1.34639i	−0.156134	−	0.987736i	$-0.549903\pi$
$191$	10.7430	−	18.6075i	0.777338	−	1.34639i	0.933471	−	0.358652i	$-0.116764\pi$
$192$		0			0
$193$	8.20798	+	14.2166i	0.590823	+	1.02334i	0.994122	+	0.108267i	$0.0345302\pi$
$193$	8.20798	+	14.2166i	0.590823	+	1.02334i	−0.403299	+	0.915068i	$0.632136\pi$
$194$	−5.14910	+	13.8763i	−0.369684	+	0.996257i
$195$		0			0
$196$	−13.7543	+	2.61116i	−0.982453	+	0.186511i
$197$		−	15.7045i		−	1.11890i	−0.828864	−	0.559450i	$-0.811012\pi$
$197$		−	15.7045i		−	1.11890i	0.828864	−	0.559450i	$-0.188988\pi$
$198$		0			0
$199$	−3.13717	−	5.43374i	−0.222388	−	0.385188i	0.733144	−	0.680073i	$-0.238052\pi$
$199$	−3.13717	−	5.43374i	−0.222388	−	0.385188i	−0.955533	+	0.294885i	$0.904719\pi$
$200$	18.6843	+	11.2602i	1.32118	+	0.796219i
$201$		0			0
$202$	−3.01606	−	17.7538i	−0.212209	−	1.24915i
$203$	0.173861	+	0.360721i	0.0122026	+	0.0253177i
$204$		0			0
$205$	0.739296	+	0.426833i	0.0516347	+	0.0298113i
$206$	5.42135	+	6.54363i	0.377723	+	0.455916i
$207$		0			0
$208$	5.69831	−	0.858321i	0.395106	−	0.0595139i
$209$	−1.22736			−0.0848984
$210$		0			0
$211$		−	9.40458i		−	0.647438i	−0.946153	−	0.323719i	$-0.895067\pi$
$211$		−	9.40458i		−	0.647438i	0.946153	−	0.323719i	$-0.104933\pi$
$212$	11.7626	+	2.22619i	0.807857	+	0.152895i
$213$		0			0
$214$	−17.3872	+	14.4051i	−1.18856	+	0.984716i
$215$	−2.36805	+	4.10158i	−0.161500	+	0.279726i
$216$		0			0
$217$	−10.3955	−	7.08253i	−0.705693	−	0.480793i
$218$	3.28545	+	19.3396i	0.222519	+	1.30984i
$219$		0			0
$220$	22.0028	+	18.9368i	1.48343	+	1.27672i
$221$	8.72235	−	5.03585i	0.586729	−	0.338748i
$222$		0			0
$223$	4.34741			0.291124			0.145562	−	0.989349i	$-0.453501\pi$
$223$	4.34741			0.291124			0.145562	+	0.989349i	$0.453501\pi$
$224$	14.5258	−	3.60569i	0.970546	−	0.240915i
$225$		0			0
$226$	−8.09307	+	21.8099i	−0.538343	+	1.45078i
$227$	6.30643	−	3.64102i	0.418572	−	0.241663i	−0.275894	−	0.961188i	$-0.588974\pi$
$227$	6.30643	−	3.64102i	0.418572	−	0.241663i	0.694466	+	0.719525i	$0.255641\pi$
$228$		0			0
$229$	0.885272	+	0.511112i	0.0585004	+	0.0337752i	0.528965	−	0.848644i	$-0.322580\pi$
$229$	0.885272	+	0.511112i	0.0585004	+	0.0337752i	−0.470465	+	0.882419i	$0.655914\pi$
$230$	−2.04793	−	12.0550i	−0.135037	−	0.794884i
$231$		0			0
$232$	−0.207044	−	0.374682i	−0.0135931	−	0.0245991i
$233$	−11.0331	+	19.1098i	−0.722800	+	1.25193i	0.237074	+	0.971492i	$0.423812\pi$
$233$	−11.0331	+	19.1098i	−0.722800	+	1.25193i	−0.959873	+	0.280434i	$0.909522\pi$
$234$		0			0
$235$	−19.6345	+	11.3360i	−1.28082	+	0.739480i
$236$	−22.0934	−	4.18139i	−1.43816	−	0.272185i
$237$		0			0
$238$	21.3291	−	15.1436i	1.38256	−	0.981612i
$239$	−4.80475			−0.310794			−0.155397	−	0.987852i	$-0.549666\pi$
$239$	−4.80475			−0.310794			−0.155397	+	0.987852i	$0.549666\pi$
$240$		0			0
$241$	−11.8844	−	20.5844i	−0.765542	−	1.32596i	−0.939960	−	0.341286i	$-0.889138\pi$
$241$	−11.8844	−	20.5844i	−0.765542	−	1.32596i	0.174418	−	0.984672i	$-0.444196\pi$
$242$	5.02765	+	6.06843i	0.323190	+	0.390094i
$243$		0			0
$244$	−2.78013	−	7.94637i	−0.177979	−	0.508714i
$245$	23.2272	−	9.13366i	1.48393	−	0.583528i
$246$		0			0
$247$	0.217174	−	0.376156i	0.0138184	−	0.0239342i
$248$	11.5175	+	6.94113i	0.731365	+	0.440762i
$249$		0			0
$250$	−12.8244	−	4.75880i	−0.811089	−	0.300973i
$251$		−	14.0888i		−	0.889280i	−0.895709	−	0.444640i	$-0.853332\pi$
$251$		−	14.0888i		−	0.889280i	0.895709	−	0.444640i	$-0.146668\pi$
$252$		0			0
$253$		−	9.87195i		−	0.620644i
$254$	1.63981	−	4.41910i	0.102891	−	0.277279i
$255$		0			0
$256$	−15.2901	+	4.71314i	−0.955629	+	0.294572i
$257$	−2.89962	+	5.02229i	−0.180873	+	0.313282i	−0.942178	−	0.335112i	$-0.891226\pi$
$257$	−2.89962	+	5.02229i	−0.180873	+	0.313282i	0.761305	+	0.648394i	$0.224559\pi$
$258$		0			0
$259$	29.9277	+	2.23287i	1.85962	+	0.138743i
$260$	−9.69691	+	3.39257i	−0.601377	+	0.210399i
$261$		0			0
$262$	−4.45263	+	3.68897i	−0.275084	+	0.227905i
$263$	1.21627	+	2.10664i	0.0749983	+	0.129901i	0.901086	−	0.433641i	$-0.142772\pi$
$263$	1.21627	+	2.10664i	0.0749983	+	0.129901i	−0.826087	+	0.563542i	$0.809438\pi$
$264$		0			0
$265$	−21.3420			−1.31103
$266$	0.470057	−	1.02549i	0.0288210	−	0.0628770i
$267$		0			0
$268$	−8.60867	−	1.62928i	−0.525858	−	0.0995240i
$269$	4.98470	−	2.87792i	0.303923	−	0.175470i	−0.340281	−	0.940324i	$-0.610522\pi$
$269$	4.98470	−	2.87792i	0.303923	−	0.175470i	0.644204	+	0.764854i	$0.277189\pi$
$270$		0			0
$271$	−8.50926	+	14.7385i	−0.516901	+	0.895299i	0.482906	+	0.875672i	$0.339581\pi$
$271$	−8.50926	+	14.7385i	−0.516901	+	0.895299i	−0.999807	+	0.0196268i	$0.993752\pi$
$272$	−21.8651	+	17.4334i	−1.32577	+	1.05706i
$273$		0			0
$274$	−11.5546	+	1.96291i	−0.698036	+	0.118584i
$275$	−27.1916	−	15.6991i	−1.63972	−	0.946690i
$276$		0			0
$277$	−19.4599	+	11.2352i	−1.16923	+	0.675057i	−0.953499	−	0.301395i	$-0.902548\pi$
$277$	−19.4599	+	11.2352i	−1.16923	+	0.675057i	−0.215734	+	0.976452i	$0.569214\pi$
$278$	24.4199	+	9.06156i	1.46461	+	0.543476i
$279$		0			0
$280$	−24.2488	+	11.1315i	−1.44915	+	0.665233i
$281$	−7.29261			−0.435041			−0.217520	−	0.976056i	$-0.569797\pi$
$281$	−7.29261			−0.435041			−0.217520	+	0.976056i	$0.569797\pi$
$282$		0			0
$283$	−9.21249	+	5.31883i	−0.547626	+	0.316172i	−0.748164	−	0.663514i	$-0.769064\pi$
$283$	−9.21249	+	5.31883i	−0.547626	+	0.316172i	0.200538	+	0.979686i	$0.435731\pi$
$284$	−12.8302	−	11.0424i	−0.761333	−	0.655244i
$285$		0			0
$286$	−8.17687	+	1.38910i	−0.483508	+	0.0821394i
$287$	−0.570633	+	0.275034i	−0.0336834	+	0.0162348i
$288$		0			0
$289$	−15.9378	+	27.6050i	−0.937515	+	1.62382i
$290$	0.486884	+	0.587675i	0.0285908	+	0.0345095i
$291$		0			0
$292$	−0.211788	+	1.11903i	−0.0123939	+	0.0654863i
$293$			26.4432i			1.54483i	0.635120	+	0.772414i	$0.280951\pi$
$293$			26.4432i			1.54483i	−0.635120	+	0.772414i	$0.719049\pi$
$294$		0			0
$295$	40.0862			2.33391
$296$	−32.0774	−	0.602228i	−1.86446	−	0.0350038i
$297$		0			0
$298$	5.56709	−	4.61229i	0.322493	−	0.267183i
$299$	3.02551	+	1.74678i	0.174970	+	0.101019i
$300$		0			0
$301$	−1.52588	−	3.16585i	−0.0879501	−	0.182477i
$302$	−5.81573	+	0.987988i	−0.334658	+	0.0568523i
$303$		0			0
$304$	−0.440702	+	1.12257i	−0.0252760	+	0.0643839i
$305$	7.50419	+	12.9976i	0.429689	+	0.744243i
$306$		0			0
$307$			23.6553i			1.35008i	0.737780	+	0.675041i	$0.235874\pi$
$307$			23.6553i			1.35008i	−0.737780	+	0.675041i	$0.764126\pi$
$308$	−20.8057	+	5.58115i	−1.18552	+	0.318015i
$309$		0			0
$310$	−22.4759	−	8.34018i	−1.27654	−	0.473691i
$311$	−1.62606	−	2.81643i	−0.0922056	−	0.159705i	0.816233	−	0.577722i	$-0.196058\pi$
$311$	−1.62606	−	2.81643i	−0.0922056	−	0.159705i	−0.908439	+	0.418018i	$0.862725\pi$
$312$		0			0
$313$	−3.47621	+	6.02097i	−0.196487	+	0.340325i	−0.947387	−	0.320091i	$-0.896287\pi$
$313$	−3.47621	+	6.02097i	−0.196487	+	0.340325i	0.750900	+	0.660416i	$0.229620\pi$
$314$	2.14325	+	12.6161i	0.120951	+	0.711968i
$315$		0			0
$316$	−2.82006	+	0.986628i	−0.158641	+	0.0555022i
$317$	5.44303	+	3.14254i	0.305711	+	0.176502i	0.645006	−	0.764178i	$-0.276855\pi$
$317$	5.44303	+	3.14254i	0.305711	+	0.176502i	−0.339295	+	0.940680i	$0.610188\pi$
$318$		0			0
$319$	0.308067	+	0.533587i	0.0172484	+	0.0298751i
$320$	25.2204	−	13.3247i	1.40986	−	0.744875i
$321$		0			0
$322$	8.24827	+	3.78077i	0.459658	+	0.210694i
$323$			2.10778i			0.117280i
$324$		0			0
$325$	9.62276	−	5.55570i	0.533775	−	0.308175i
$326$	−14.6486	+	12.1362i	−0.811310	+	0.672164i
$327$		0			0
$328$	0.592719	−	0.327528i	0.0327274	−	0.0180847i
$329$	1.25170	−	16.7770i	0.0690087	−	0.924944i
$330$		0			0
$331$	21.9584	+	12.6777i	1.20694	+	0.696827i	0.962090	−	0.272733i	$-0.0879277\pi$
$331$	21.9584	+	12.6777i	1.20694	+	0.696827i	0.244851	+	0.969561i	$0.421261\pi$
$332$	−13.0924	+	15.2122i	−0.718539	+	0.834876i
$333$		0			0
$334$	8.46721	−	22.8182i	0.463305	−	1.24856i
$335$	15.6196			0.853388
$336$		0			0
$337$	−18.0761			−0.984668			−0.492334	−	0.870406i	$-0.663856\pi$
$337$	−18.0761			−0.984668			−0.492334	+	0.870406i	$0.663856\pi$
$338$	−5.37482	+	14.4846i	−0.292352	+	0.787856i
$339$		0			0
$340$	32.5207	−	37.7860i	1.76368	−	2.04923i
$341$	−16.7617	−	9.67735i	−0.907695	−	0.524058i
$342$		0			0
$343$	−4.10331	+	18.0600i	−0.221558	+	0.975147i
$344$	1.81711	+	3.28838i	0.0979721	+	0.177297i
$345$		0			0
$346$	3.75645	−	3.11219i	0.201948	−	0.167312i
$347$	6.46167	−	3.73065i	0.346881	−	0.200272i	−0.316430	−	0.948616i	$-0.602484\pi$
$347$	6.46167	−	3.73065i	0.346881	−	0.200272i	0.663311	+	0.748344i	$0.269151\pi$
$348$		0			0
$349$			23.2053i			1.24215i	0.783750	+	0.621077i	$0.213305\pi$
$349$			23.2053i			1.24215i	−0.783750	+	0.621077i	$0.786695\pi$
$350$	23.5309	−	16.7068i	1.25778	−	0.893018i
$351$		0			0
$352$	21.8756	−	7.19546i	1.16597	−	0.383519i
$353$	−2.14531	−	3.71578i	−0.114183	−	0.197771i	0.803270	−	0.595615i	$-0.203092\pi$
$353$	−2.14531	−	3.71578i	−0.114183	−	0.197771i	−0.917453	+	0.397844i	$0.869758\pi$
$354$		0			0
$355$	26.1349	+	15.0890i	1.38709	+	0.800839i
$356$	6.92574	−	2.42305i	0.367064	−	0.128421i
$357$		0			0
$358$	−2.67687	−	15.7572i	−0.141477	−	0.832794i
$359$	3.00706	−	5.20837i	0.158706	−	0.274888i	−0.775696	−	0.631107i	$-0.782601\pi$
$359$	3.00706	−	5.20837i	0.158706	−	0.274888i	0.934402	+	0.356219i	$0.115934\pi$
$360$		0			0
$361$	−9.45455	−	16.3758i	−0.497608	−	0.861882i
$362$	13.3338	+	4.94781i	0.700809	+	0.260051i
$363$		0			0
$364$	1.97095	−	7.36399i	0.103306	−	0.385978i
$365$		−	2.03037i		−	0.106274i
$366$		0			0
$367$	7.78693	+	13.4874i	0.406475	+	0.704035i	0.994492	−	0.104814i	$-0.0334246\pi$
$367$	7.78693	+	13.4874i	0.406475	+	0.704035i	−0.588017	+	0.808848i	$0.700091\pi$
$368$	−9.02910	−	3.54466i	−0.470674	−	0.184778i
$369$		0			0
$370$	56.3881	−	9.57933i	2.93148	−	0.498006i
$371$	8.91680	−	13.0878i	0.462937	−	0.679485i
$372$		0			0
$373$	−9.84545	−	5.68427i	−0.509778	−	0.294320i	0.222964	−	0.974827i	$-0.428427\pi$
$373$	−9.84545	−	5.68427i	−0.509778	−	0.294320i	−0.732742	+	0.680506i	$0.761760\pi$
$374$	30.9937	−	25.6780i	1.60264	−	1.32778i
$375$		0			0
$376$	−0.337598	+	17.9820i	−0.0174103	+	0.927351i
$377$	−0.218042			−0.0112297
$378$		0			0
$379$		−	31.9644i		−	1.64190i	−0.571000	−	0.820950i	$-0.693444\pi$
$379$		−	31.9644i		−	1.64190i	0.571000	−	0.820950i	$-0.306556\pi$
$380$	0.399804	−	2.11246i	0.0205095	−	0.108367i
$381$		0			0
$382$	19.3856	+	23.3987i	0.991854	+	1.19718i
$383$	−4.75224	+	8.23112i	−0.242828	+	0.420590i	−0.961519	−	0.274739i	$-0.911408\pi$
$383$	−4.75224	+	8.23112i	−0.242828	+	0.420590i	0.718691	+	0.695330i	$0.244742\pi$
$384$		0			0
$385$	34.5942	−	16.6737i	1.76308	−	0.849771i
$386$	−22.8877	+	3.88822i	−1.16496	+	0.197905i
$387$		0			0
$388$	−15.8648	−	13.6541i	−0.805415	−	0.693183i
$389$	−9.83845	+	5.68023i	−0.498829	+	0.287999i	−0.728230	−	0.685333i	$-0.759657\pi$
$389$	−9.83845	+	5.68023i	−0.498829	+	0.287999i	0.229401	+	0.973332i	$0.426323\pi$
$390$		0			0
$391$	−16.9534			−0.857368
$392$	3.30501	−	19.5212i	0.166928	−	0.985969i
$393$		0			0
$394$	20.8222	+	7.72655i	1.04901	+	0.389258i
$395$	4.61268	−	2.66313i	0.232089	−	0.133997i
$396$		0			0
$397$	−18.7003	−	10.7967i	−0.938544	−	0.541868i	−0.0490401	−	0.998797i	$-0.515616\pi$
$397$	−18.7003	−	10.7967i	−0.938544	−	0.541868i	−0.889503	+	0.456928i	$0.848950\pi$
$398$	8.74793	−	1.48612i	0.438494	−	0.0744923i
$399$		0			0
$400$	−24.1223	+	19.2331i	−1.20611	+	0.961653i
$401$	14.1230	−	24.4617i	0.705267	−	1.22156i	−0.261329	−	0.965250i	$-0.584161\pi$
$401$	14.1230	−	24.4617i	0.705267	−	1.22156i	0.966595	−	0.256308i	$-0.0825060\pi$
$402$		0			0
$403$	5.93174	−	3.42469i	0.295481	−	0.170596i
$404$	25.0232	+	4.73589i	1.24495	+	0.235619i
$405$		0			0
$406$	−0.563810	+	0.0530438i	−0.0279814	+	0.00263252i
$407$	46.1767			2.28889
$408$		0			0
$409$	−6.74458	−	11.6820i	−0.333498	−	0.577635i	0.649697	−	0.760193i	$-0.274896\pi$
$409$	−6.74458	−	11.6820i	−0.333498	−	0.577635i	−0.983195	+	0.182558i	$0.941562\pi$
$410$	−0.929657	+	0.770213i	−0.0459125	+	0.0380381i
$411$		0			0
$412$	−11.3433	+	3.96858i	−0.558845	+	0.195518i
$413$	−16.7482	+	24.5825i	−0.824126	+	1.20963i
$414$		0			0
$415$	17.8903	−	30.9868i	0.878198	−	1.52108i
$416$	−1.66552	+	7.97752i	−0.0816586	+	0.391130i
$417$		0			0
$418$	0.603857	−	1.62733i	0.0295356	−	0.0795951i
$419$			25.0575i			1.22414i	0.790804	+	0.612069i	$0.209663\pi$
$419$			25.0575i			1.22414i	−0.790804	+	0.612069i	$0.790337\pi$
$420$		0			0
$421$		−	23.0346i		−	1.12264i	−0.827600	−	0.561318i	$-0.810294\pi$
$421$		−	23.0346i		−	1.12264i	0.827600	−	0.561318i	$-0.189706\pi$
$422$	12.4693	+	4.62701i	0.606995	+	0.225239i
$423$		0			0
$424$	−8.73878	+	14.5004i	−0.424392	+	0.704202i
$425$	−26.9604	+	46.6969i	−1.30777	+	2.26513i
$426$		0			0
$427$	−11.1060	−	0.828601i	−0.537456	−	0.0400988i
$428$	−10.5450	−	30.1405i	−0.509711	−	1.45689i
$429$		0			0
$430$	−4.27311	−	5.15769i	−0.206068	−	0.248726i
$431$	0.0929281	+	0.160956i	0.00447619	+	0.00775299i	0.868255	−	0.496118i	$-0.165242\pi$
$431$	0.0929281	+	0.160956i	0.00447619	+	0.00775299i	−0.863779	+	0.503871i	$0.831909\pi$
$432$		0			0
$433$	34.7454			1.66976			0.834878	−	0.550435i	$-0.185538\pi$
$433$	34.7454			1.66976			0.834878	+	0.550435i	$0.185538\pi$
$434$	14.5051	−	10.2986i	0.696266	−	0.494347i
$435$		0			0
$436$	−27.2583	−	5.15890i	−1.30543	−	0.247066i
$437$	−0.633171	+	0.365561i	−0.0302887	+	0.0174872i
$438$		0			0
$439$	13.5890	−	23.5369i	0.648570	−	1.12336i	−0.334895	−	0.942255i	$-0.608701\pi$
$439$	13.5890	−	23.5369i	0.648570	−	1.12336i	0.983465	−	0.181100i	$-0.0579658\pi$
$440$	−35.9331	+	19.8561i	−1.71304	+	0.946604i
$441$		0			0
$442$	2.38555	+	14.0424i	0.113469	+	0.667927i
$443$	−3.43698	−	1.98434i	−0.163296	−	0.0942789i	0.416125	−	0.909307i	$-0.363388\pi$
$443$	−3.43698	−	1.98434i	−0.163296	−	0.0942789i	−0.579421	+	0.815029i	$0.696721\pi$
$444$		0			0
$445$	−11.3282	+	6.54035i	−0.537009	+	0.310042i
$446$	−2.13891	+	5.76411i	−0.101280	+	0.272939i
$447$		0			0
$448$	−2.36595	+	21.0334i	−0.111781	+	0.993733i
$449$	12.1637			0.574040			0.287020	−	0.957925i	$-0.407335\pi$
$449$	12.1637			0.574040			0.287020	+	0.957925i	$0.407335\pi$
$450$		0			0
$451$	−0.844094	+	0.487338i	−0.0397468	+	0.0229478i
$452$	−24.9355	−	21.4608i	−1.17287	−	1.00943i
$453$		0			0
$454$	1.72479	+	10.1529i	0.0809486	+	0.476499i
$455$	−1.01114	+	13.5526i	−0.0474028	+	0.635354i
$456$		0			0
$457$	−12.8791	+	22.3072i	−0.602459	+	1.04349i	0.389989	+	0.920820i	$0.372479\pi$
$457$	−12.8791	+	22.3072i	−0.602459	+	1.04349i	−0.992448	+	0.122670i	$0.960854\pi$
$458$	−1.11322	+	0.922294i	−0.0520173	+	0.0430960i
$459$		0			0
$460$	16.9910	+	3.21571i	0.792209	+	0.149933i
$461$		−	17.0423i		−	0.793737i	−0.917875	−	0.396868i	$-0.870097\pi$
$461$		−	17.0423i		−	0.793737i	0.917875	−	0.396868i	$-0.129903\pi$
$462$		0			0
$463$	34.1343			1.58635			0.793177	−	0.608991i	$-0.208426\pi$
$463$	34.1343			1.58635			0.793177	+	0.608991i	$0.208426\pi$
$464$	0.598646	−	0.0901726i	0.0277915	−	0.00418616i
$465$		0			0
$466$	−19.9090	−	24.0304i	−0.922266	−	1.11319i
$467$	−14.0940	−	8.13715i	−0.652191	−	0.376543i	0.137104	−	0.990557i	$-0.456220\pi$
$467$	−14.0940	−	8.13715i	−0.652191	−	0.376543i	−0.789295	+	0.614014i	$0.789554\pi$
$468$		0			0
$469$	−6.52593	+	9.57856i	−0.301340	+	0.442297i
$470$	−5.37000	−	31.6102i	−0.247700	−	1.45807i
$471$		0			0
$472$	16.4138	−	27.2358i	0.755508	−	1.25363i
$473$	−2.70373	−	4.68299i	−0.124318	−	0.215324i
$474$		0			0
$475$			2.32537i			0.106695i
$476$	9.58465	+	35.7302i	0.439312	+	1.63769i
$477$		0			0
$478$	2.36392	−	6.37050i	0.108123	−	0.291380i
$479$	−10.0045	−	17.3284i	−0.457119	−	0.791754i	0.541688	−	0.840580i	$-0.317785\pi$
$479$	−10.0045	−	17.3284i	−0.457119	−	0.791754i	−0.998807	+	0.0488257i	$0.984452\pi$
$480$		0			0
$481$	−8.17067	+	14.1520i	−0.372551	+	0.645277i
$482$	33.1394	−	5.62979i	1.50946	−	0.256430i
$483$		0			0
$484$	−10.5196	+	3.68038i	−0.478162	+	0.167290i
$485$	32.3163	+	18.6578i	1.46741	+	0.847208i
$486$		0			0
$487$	−8.27889	−	14.3394i	−0.375152	−	0.649782i	0.615198	−	0.788373i	$-0.289076\pi$
$487$	−8.27889	−	14.3394i	−0.375152	−	0.649782i	−0.990350	+	0.138590i	$0.955743\pi$
$488$	11.9037	+	0.223483i	0.538855	+	0.0101166i
$489$		0			0
$490$	0.682399	+	35.2901i	0.0308277	+	1.59424i
$491$			9.49257i			0.428394i	0.976791	+	0.214197i	$0.0687134\pi$
$491$			9.49257i			0.428394i	−0.976791	+	0.214197i	$0.931287\pi$
$492$		0			0
$493$	0.916343	−	0.529051i	0.0412700	−	0.0238273i
$494$	0.391887	+	0.473012i	0.0176318	+	0.0212818i
$495$		0			0
$496$	−14.8696	+	11.8558i	−0.667666	+	0.532341i
$497$	−20.1725	+	9.72273i	−0.904859	+	0.436124i
$498$		0			0
$499$	−29.6441	−	17.1150i	−1.32705	−	0.766174i	−0.342210	−	0.939624i	$-0.611175\pi$
$499$	−29.6441	−	17.1150i	−1.32705	−	0.766174i	−0.984843	+	0.173449i	$0.944509\pi$
$500$	12.6191	−	14.6623i	0.564345	−	0.655717i
$501$		0			0
$502$	18.6800	+	6.93165i	0.833730	+	0.309375i
$503$	21.0469			0.938436			0.469218	−	0.883082i	$-0.344536\pi$
$503$	21.0469			0.938436			0.469218	+	0.883082i	$0.344536\pi$
$504$		0			0
$505$	−45.4020			−2.02036
$506$	13.0890	+	4.85695i	0.581875	+	0.215918i
$507$		0			0
$508$	5.05239	+	4.34836i	0.224164	+	0.192927i
$509$	−13.0298	−	7.52276i	−0.577536	−	0.333440i	0.182618	−	0.983184i	$-0.441543\pi$
$509$	−13.0298	−	7.52276i	−0.577536	−	0.333440i	−0.760153	+	0.649744i	$0.774876\pi$
$510$		0			0
$511$	1.24510	+	0.848298i	0.0550802	+	0.0375265i
$512$	1.27361	−	22.5915i	0.0562863	−	0.998415i
$513$		0			0
$514$	−5.23232	−	6.31547i	−0.230788	−	0.278563i
$515$	18.5539	−	10.7121i	0.817582	−	0.472031i
$516$		0			0
$517$		−	25.8858i		−	1.13846i
$518$	−17.6848	+	38.5818i	−0.777026	+	1.69519i
$519$		0			0
$520$	0.272715	−	14.5260i	0.0119593	−	0.637008i
$521$	−4.48956	−	7.77615i	−0.196691	−	0.340679i	0.750762	−	0.660572i	$-0.229686\pi$
$521$	−4.48956	−	7.77615i	−0.196691	−	0.340679i	−0.947454	+	0.319893i	$0.896353\pi$
$522$		0			0
$523$	8.55073	+	4.93677i	0.373897	+	0.215870i	0.675160	−	0.737672i	$-0.264075\pi$
$523$	8.55073	+	4.93677i	0.373897	+	0.215870i	−0.301262	+	0.953541i	$0.597408\pi$
$524$	−2.70043	−	7.71858i	−0.117969	−	0.337188i
$525$		0			0
$526$	−3.39153	+	0.576161i	−0.147878	+	0.0251218i
$527$	−16.6192	+	28.7853i	−0.723943	+	1.25391i
$528$		0			0
$529$	8.55971	+	14.8259i	0.372161	+	0.644602i
$530$	10.5002	−	28.2968i	0.456098	−	1.22913i
$531$		0			0
$532$	1.12841	+	1.12777i	0.0489227	+	0.0488952i
$533$		−	0.344925i		−	0.0149404i
$534$		0			0
$535$	28.4633	+	49.2998i	1.23057	+	2.13142i
$536$	6.39564	−	10.6124i	0.276250	−	0.458386i
$537$		0			0
$538$	1.36331	+	8.02501i	0.0587763	+	0.345983i
$539$	−4.22862	+	28.1810i	−0.182139	+	1.21384i
$540$		0			0
$541$	17.1313	+	9.89077i	0.736533	+	0.425237i	0.820807	−	0.571205i	$-0.193524\pi$
$541$	17.1313	+	9.89077i	0.736533	+	0.425237i	−0.0842746	+	0.996443i	$0.526857\pi$
$542$	−15.3548	−	18.5335i	−0.659547	−	0.796081i
$543$		0			0
$544$	−12.3570	−	37.5676i	−0.529800	−	1.61070i
$545$	49.4573			2.11852
$546$		0			0
$547$			39.3961i			1.68446i	0.539122	+	0.842228i	$0.318756\pi$
$547$			39.3961i			1.68446i	−0.539122	+	0.842228i	$0.681244\pi$
$548$	3.08222	−	16.2856i	0.131666	−	0.695687i
$549$		0			0
$550$	34.1931	−	28.3287i	1.45800	−	1.20794i
$551$	0.0228156	−	0.0395178i	0.000971977	−	0.00168351i
$552$		0			0
$553$	−0.294059	+	3.94136i	−0.0125047	+	0.167604i
$554$	−5.32225	−	31.3291i	−0.226121	−	1.33104i
$555$		0			0
$556$	−24.0290	+	27.9194i	−1.01905	+	1.18405i
$557$	−5.84611	+	3.37525i	−0.247708	+	0.143014i	−0.618714	−	0.785616i	$-0.712346\pi$
$557$	−5.84611	+	3.37525i	−0.247708	+	0.143014i	0.371006	+	0.928630i	$0.379013\pi$
$558$		0			0
$559$	1.91363			0.0809379
$560$	−2.82862	−	37.6275i	−0.119531	−	1.59005i
$561$		0			0
$562$	3.58793	−	9.66908i	0.151348	−	0.407866i
$563$	−25.1027	+	14.4930i	−1.05795	+	0.610809i	−0.924865	−	0.380296i	$-0.875822\pi$
$563$	−25.1027	+	14.4930i	−1.05795	+	0.610809i	−0.133087	+	0.991104i	$0.542489\pi$
$564$		0			0
$565$	50.7929	+	29.3253i	2.13688	+	1.23373i
$566$	−2.51960	−	14.8314i	−0.105907	−	0.623412i
$567$		0			0
$568$	20.9532	−	11.5785i	0.879177	−	0.485821i
$569$	−19.9834	+	34.6123i	−0.837748	+	1.45102i	0.0540248	+	0.998540i	$0.482795\pi$
$569$	−19.9834	+	34.6123i	−0.837748	+	1.45102i	−0.891773	+	0.452483i	$0.850538\pi$
$570$		0			0
$571$	−7.01347	+	4.04923i	−0.293505	+	0.169455i	−0.639521	−	0.768773i	$-0.720867\pi$
$571$	−7.01347	+	4.04923i	−0.293505	+	0.169455i	0.346017	+	0.938228i	$0.387534\pi$
$572$	2.18121	−	11.5249i	0.0912008	−	0.481881i
$573$		0			0
$574$	−0.0839113	−	0.891903i	−0.00350239	−	0.0372273i
$575$	−18.7034			−0.779988
$576$		0			0
$577$	−23.7611	−	41.1555i	−0.989188	−	1.71332i	−0.621599	−	0.783336i	$-0.713517\pi$
$577$	−23.7611	−	41.1555i	−0.989188	−	1.71332i	−0.367589	−	0.929988i	$-0.619817\pi$
$578$	−28.7594	−	34.7130i	−1.19623	−	1.44387i
$579$		0			0
$580$	−1.01873	+	0.356413i	−0.0423004	+	0.0147993i
$581$	11.5278	+	23.9175i	0.478253	+	0.992266i
$582$		0			0
$583$	12.1836	−	21.1027i	0.504595	−	0.873984i
$584$	−1.37949	−	0.831361i	−0.0570839	−	0.0344020i
$585$		0			0
$586$	−35.0603	−	13.0099i	−1.44833	−	0.537435i
$587$			11.8785i			0.490279i	0.969488	+	0.245140i	$0.0788338\pi$
$587$			11.8785i			0.490279i	−0.969488	+	0.245140i	$0.921166\pi$
$588$		0			0
$589$			1.43342i			0.0590631i
$590$	−19.7222	+	53.1492i	−0.811951	+	2.18812i
$591$		0			0
$592$	16.5804	−	42.2342i	0.681450	−	1.73582i
$593$	16.1160	−	27.9138i	0.661806	−	1.14628i	−0.318335	−	0.947978i	$-0.603124\pi$
$593$	16.1160	−	27.9138i	0.661806	−	1.14628i	0.980141	−	0.198303i	$-0.0635430\pi$
$594$		0			0
$595$	−28.6342	−	59.4095i	−1.17389	−	2.43555i
$596$	3.37633	+	9.65048i	0.138300	+	0.395299i
$597$		0			0
$598$	−3.80454	+	3.15203i	−0.155579	+	0.128896i
$599$	19.8427	+	34.3686i	0.810752	+	1.40426i	0.912338	+	0.409437i	$0.134275\pi$
$599$	19.8427	+	34.3686i	0.810752	+	1.40426i	−0.101586	+	0.994827i	$0.532392\pi$
$600$		0			0
$601$	22.3599			0.912081			0.456040	−	0.889959i	$-0.349267\pi$
$601$	22.3599			0.912081			0.456040	+	0.889959i	$0.349267\pi$
$602$	4.94824	−	0.465536i	0.201675	−	0.0189738i
$603$		0			0
$604$	1.55137	−	8.19701i	0.0631242	−	0.333532i
$605$	17.2065	−	9.93418i	0.699544	−	0.403882i
$606$		0			0
$607$	−7.38757	+	12.7956i	−0.299852	+	0.519359i	−0.976102	−	0.217313i	$-0.930271\pi$
$607$	−7.38757	+	12.7956i	−0.299852	+	0.519359i	0.676250	+	0.736672i	$0.263604\pi$
$608$	−1.27157	−	1.13662i	−0.0515688	−	0.0460958i
$609$		0			0
$610$	−20.9252	+	3.55483i	−0.847239	+	0.143931i
$611$	7.93337	+	4.58033i	0.320950	+	0.185300i
$612$		0			0
$613$	22.7453	−	13.1320i	0.918676	−	0.530398i	0.0354633	−	0.999371i	$-0.488709\pi$
$613$	22.7453	−	13.1320i	0.918676	−	0.530398i	0.883212	+	0.468973i	$0.155376\pi$
$614$	−31.3640	−	11.6383i	−1.26575	−	0.469685i
$615$		0			0
$616$	2.83643	−	30.3316i	0.114283	−	1.22210i
$617$	−33.8882			−1.36429			−0.682144	−	0.731218i	$-0.738952\pi$
$617$	−33.8882			−1.36429			−0.682144	+	0.731218i	$0.738952\pi$
$618$		0			0
$619$	5.24132	−	3.02608i	0.210667	−	0.121628i	−0.390955	−	0.920410i	$-0.627855\pi$
$619$	5.24132	−	3.02608i	0.210667	−	0.121628i	0.601621	+	0.798782i	$0.294522\pi$
$620$	22.1161	−	25.6968i	0.888202	−	1.03201i
$621$		0			0
$622$	4.53424	−	0.770286i	0.181806	−	0.0308857i
$623$	0.722176	−	9.67953i	0.0289334	−	0.387802i
$624$		0			0
$625$	2.03841	−	3.53063i	0.0815364	−	0.141225i
$626$	−6.27277	−	7.57130i	−0.250710	−	0.302610i
$627$		0			0
$628$	−17.7818	−	3.36539i	−0.709573	−	0.134294i
$629$		−	79.3005i		−	3.16192i
$630$		0			0
$631$	−14.6555			−0.583426			−0.291713	−	0.956506i	$-0.594225\pi$
$631$	−14.6555			−0.583426			−0.291713	+	0.956506i	$0.594225\pi$
$632$	0.0793109	−	4.22445i	0.00315482	−	0.168040i
$633$		0			0
$634$	−6.84455	+	5.67066i	−0.271832	+	0.225211i
$635$	−10.2916	−	5.94186i	−0.408410	−	0.235796i
$636$		0			0
$637$	−7.88854	−	6.28241i	−0.312555	−	0.248918i
$638$	−0.859036	+	0.145935i	−0.0340096	+	0.00577762i
$639$		0			0
$640$	5.25857	+	39.9948i	0.207863	+	1.58093i
$641$	7.77488	+	13.4665i	0.307089	+	0.531894i	0.977724	−	0.209893i	$-0.0673117\pi$
$641$	7.77488	+	13.4665i	0.307089	+	0.531894i	−0.670635	+	0.741787i	$0.733978\pi$
$642$		0			0
$643$			28.3180i			1.11675i	0.829587	+	0.558377i	$0.188576\pi$
$643$			28.3180i			1.11675i	−0.829587	+	0.558377i	$0.811424\pi$
$644$	−9.07093	+	9.07604i	−0.357445	+	0.357646i
$645$		0			0
$646$	−2.79465	−	1.03702i	−0.109954	−	0.0408010i
$647$	12.9342	+	22.4026i	0.508495	+	0.880739i	0.999952	+	0.00983684i	$0.00313121\pi$
$647$	12.9342	+	22.4026i	0.508495	+	0.880739i	−0.491457	+	0.870902i	$0.663535\pi$
$648$		0			0
$649$	−22.8843	+	39.6367i	−0.898286	+	1.55588i
$650$	2.63180	+	15.4919i	0.103228	+	0.607644i
$651$		0			0
$652$	−8.88408	−	25.3931i	−0.347927	−	0.994472i
$653$	−24.4781	−	14.1324i	−0.957902	−	0.553045i	−0.0623752	−	0.998053i	$-0.519868\pi$
$653$	−24.4781	−	14.1324i	−0.957902	−	0.553045i	−0.895527	+	0.445008i	$0.853201\pi$
$654$		0			0
$655$	7.28907	+	12.6250i	0.284808	+	0.493301i
$656$	0.142646	+	0.947012i	0.00556939	+	0.0369746i
$657$		0			0
$658$	21.6283	+	9.91379i	0.843159	+	0.386480i
$659$			21.7217i			0.846159i	0.906093	+	0.423079i	$0.139051\pi$
$659$			21.7217i			0.846159i	−0.906093	+	0.423079i	$0.860949\pi$
$660$		0			0
$661$	27.5252	−	15.8917i	1.07061	−	0.618115i	0.142260	−	0.989829i	$-0.454563\pi$
$661$	27.5252	−	15.8917i	1.07061	−	0.618115i	0.928347	+	0.371714i	$0.121230\pi$
$662$	−27.6124	+	22.8766i	−1.07319	+	0.889126i
$663$		0			0
$664$	−13.7280	−	24.8432i	−0.532750	−	0.964103i
$665$	−2.35046	−	1.60138i	−0.0911469	−	0.0620989i
$666$		0			0
$667$	0.317850	+	0.183511i	0.0123072	+	0.00710557i
$668$	26.0882	+	22.4529i	1.00938	+	0.868728i
$669$		0			0
$670$	−7.68475	+	20.7096i	−0.296888	+	0.800080i
$671$	−17.1359			−0.661523
$672$		0			0
$673$	16.1882			0.624009			0.312004	−	0.950081i	$-0.399000\pi$
$673$	16.1882			0.624009			0.312004	+	0.950081i	$0.399000\pi$
$674$	8.89336	−	23.9666i	0.342559	−	0.923159i
$675$		0			0
$676$	−16.5603	−	14.2527i	−0.636934	−	0.548180i
$677$	−20.6873	−	11.9438i	−0.795078	−	0.459038i	0.0466693	−	0.998910i	$-0.485139\pi$
$677$	−20.6873	−	11.9438i	−0.795078	−	0.459038i	−0.841747	+	0.539872i	$0.818473\pi$
$678$		0			0
$679$	−24.9437	+	12.0224i	−0.957250	+	0.461376i
$680$	34.0995	+	61.7088i	1.30765	+	2.36643i
$681$		0			0
$682$	21.0776	−	17.4626i	0.807103	−	0.668679i
$683$	21.8511	−	12.6157i	0.836110	−	0.482728i	−0.0198304	−	0.999803i	$-0.506313\pi$
$683$	21.8511	−	12.6157i	0.836110	−	0.482728i	0.855940	+	0.517075i	$0.172979\pi$
$684$		0			0
$685$			29.5486i			1.12899i
$686$	−21.9264	−	14.3259i	−0.837155	−	0.546965i
$687$		0			0
$688$	−5.25398	+	0.791394i	−0.200306	+	0.0301716i
$689$	4.31164	+	7.46797i	0.164260	+	0.284507i
$690$		0			0
$691$	−13.8089	−	7.97260i	−0.525317	−	0.303292i	0.213790	−	0.976880i	$-0.431419\pi$
$691$	−13.8089	−	7.97260i	−0.525317	−	0.303292i	−0.739107	+	0.673588i	$0.764752\pi$
$692$	2.27821	+	6.51176i	0.0866047	+	0.247540i
$693$		0			0
$694$	1.76725	+	10.4028i	0.0670840	+	0.394886i
$695$	32.8346	−	56.8713i	1.24549	−	2.15725i
$696$		0			0
$697$	0.836918	+	1.44958i	0.0317005	+	0.0549069i
$698$	−30.7674	−	11.4169i	−1.16456	−	0.432137i
$699$		0			0
$700$	10.5741	+	39.4186i	0.399662	+	1.48988i
$701$			46.5568i			1.75842i	0.476430	+	0.879212i	$0.341931\pi$
$701$			46.5568i			1.75842i	−0.476430	+	0.879212i	$0.658069\pi$
$702$		0			0
$703$	−1.70994	−	2.96170i	−0.0644915	−	0.111703i
$704$	−1.22242	+	32.5444i	−0.0460718	+	1.22656i
$705$		0			0
$706$	5.98213	−	1.01626i	0.225141	−	0.0382474i
$707$	18.9692	−	27.8424i	0.713411	−	1.04712i
$708$		0			0
$709$	−4.68128	−	2.70274i	−0.175809	−	0.101503i	0.409513	−	0.912304i	$-0.365699\pi$
$709$	−4.68128	−	2.70274i	−0.175809	−	0.101503i	−0.585322	+	0.810801i	$0.699032\pi$
$710$	−32.8643	+	27.2278i	−1.23337	+	1.02184i
$711$		0			0
$712$	−0.194779	+	10.3748i	−0.00729964	+	0.388812i
$713$	−11.5293			−0.431777
$714$		0			0
$715$			20.9108i			0.782019i
$716$	22.2091	+	4.20329i	0.829992	+	0.157084i
$717$		0			0
$718$	5.42619	+	6.54947i	0.202504	+	0.244424i
$719$	9.74035	−	16.8708i	0.363254	−	0.629174i	−0.625240	−	0.780432i	$-0.714999\pi$
$719$	9.74035	−	16.8708i	0.363254	−	0.629174i	0.988494	+	0.151258i	$0.0483324\pi$
$720$		0			0
$721$	−1.18281	+	15.8536i	−0.0440503	+	0.590419i
$722$	26.3638	−	4.47874i	0.981158	−	0.166681i
$723$		0			0
$724$	−13.1203	+	15.2446i	−0.487613	+	0.566562i
$725$	1.01094	−	0.583665i	0.0375453	−	0.0216768i
$726$		0			0
$727$	22.4025			0.830864			0.415432	−	0.909624i	$-0.363630\pi$
$727$	22.4025			0.830864			0.415432	+	0.909624i	$0.363630\pi$
$728$	8.79401	+	6.23629i	0.325928	+	0.231132i
$729$		0			0
$730$	2.69201	+	0.998931i	0.0996357	+	0.0369721i
$731$	−8.04223	+	4.64318i	−0.297453	+	0.171734i
$732$		0			0
$733$	−40.3059	−	23.2706i	−1.48873	−	0.859520i	−0.488815	−	0.872388i	$-0.662571\pi$
$733$	−40.3059	−	23.2706i	−1.48873	−	0.859520i	−0.999917	+	0.0128680i	$0.995904\pi$
$734$	−21.7137	+	3.68877i	−0.801467	+	0.136155i
$735$		0			0
$736$	9.14205	−	10.2275i	0.336980	−	0.376990i
$737$	−8.91684	+	15.4444i	−0.328456	+	0.568902i
$738$		0			0
$739$	27.6623	−	15.9708i	1.01757	−	0.587497i	0.104174	−	0.994559i	$-0.466780\pi$
$739$	27.6623	−	15.9708i	1.01757	−	0.587497i	0.913400	+	0.407062i	$0.133447\pi$
$740$	−15.0417	+	79.4765i	−0.552945	+	2.92161i
$741$		0			0
$742$	12.9657	+	18.2617i	0.475987	+	0.670407i
$743$	−14.3888			−0.527874			−0.263937	−	0.964540i	$-0.585021\pi$
$743$	−14.3888			−0.527874			−0.263937	+	0.964540i	$0.585021\pi$
$744$		0			0
$745$	−9.11347	−	15.7850i	−0.333892	−	0.578318i
$746$	12.3805	−	10.2572i	0.453284	−	0.375542i
$747$		0			0
$748$	18.7970	+	53.7272i	0.687288	+	1.96446i
$749$	−42.1248	−	3.14287i	−1.53921	−	0.114838i
$750$		0			0
$751$	15.1568	−	26.2524i	0.553080	−	0.957963i	−0.444970	−	0.895546i	$-0.646786\pi$
$751$	15.1568	−	26.2524i	0.553080	−	0.957963i	0.998050	−	0.0624177i	$-0.0198811\pi$
$752$	−23.6758	−	9.29468i	−0.863366	−	0.338942i
$753$		0			0
$754$	0.107276	−	0.289096i	0.00390674	−	0.0105282i
$755$			14.8726i			0.541270i
$756$		0			0
$757$			51.0353i			1.85491i	0.373937	+	0.927454i	$0.378007\pi$
$757$			51.0353i			1.85491i	−0.373937	+	0.927454i	$0.621993\pi$
$758$	42.3807	+	15.7263i	1.53934	+	0.571206i
$759$		0			0
$760$	2.60415	+	1.56941i	0.0944625	+	0.0569285i
$761$	15.1055	−	26.1636i	0.547576	−	0.948429i	−0.450864	−	0.892593i	$-0.648884\pi$
$761$	15.1055	−	26.1636i	0.547576	−	0.948429i	0.998440	−	0.0558364i	$-0.0177825\pi$
$762$		0			0
$763$	−20.6635	+	30.3293i	−0.748070	+	1.09799i
$764$	−40.5613	+	14.1908i	−1.46746	+	0.513406i
$765$		0			0
$766$	−8.57534	−	10.3505i	−0.309840	−	0.373980i
$767$	−8.09845	−	14.0269i	−0.292418	−	0.506483i
$768$		0			0
$769$	4.26448			0.153781			0.0768906	−	0.997040i	$-0.475501\pi$
$769$	4.26448			0.153781			0.0768906	+	0.997040i	$0.475501\pi$
$770$	5.08705	+	54.0709i	0.183325	+	1.94858i
$771$		0			0
$772$	6.10538	−	32.2592i	0.219738	−	1.16104i
$773$	4.66804	−	2.69509i	0.167898	−	0.0969357i	−0.413697	−	0.910415i	$-0.635763\pi$
$773$	4.66804	−	2.69509i	0.167898	−	0.0969357i	0.581594	+	0.813479i	$0.302429\pi$
$774$		0			0
$775$	−18.3348	+	31.7568i	−0.658604	+	1.14074i
$776$	25.9091	−	14.3170i	0.930081	−	0.513950i
$777$		0			0
$778$	−2.69080	−	15.8392i	−0.0964697	−	0.567863i
$779$	0.0625141	+	0.0360925i	0.00223980	+	0.00129315i
$780$		0			0
$781$	−29.8396	+	17.2279i	−1.06774	+	0.616462i
$782$	8.34098	−	22.4780i	0.298273	−	0.803812i
$783$		0			0
$784$	24.2566	+	13.9864i	0.866306	+	0.499513i
$785$	32.2633			1.15153
$786$		0			0
$787$	−5.36826	+	3.09937i	−0.191358	+	0.110480i	−0.592618	−	0.805484i	$-0.701906\pi$
$787$	−5.36826	+	3.09937i	−0.191358	+	0.110480i	0.401260	+	0.915964i	$0.368572\pi$
$788$	−20.4888	+	23.8062i	−0.729885	+	0.848059i
$789$		0			0
$790$	1.26156	+	7.42608i	0.0448842	+	0.264208i
$791$	−39.2051	+	18.8961i	−1.39397	+	0.671867i
$792$		0			0
$793$	3.03208	−	5.25172i	0.107672	−	0.186494i
$794$	23.5155	−	19.4824i	0.834533	−	0.691404i
$795$		0			0
$796$	−2.33354	+	12.3298i	−0.0827101	+	0.437018i
$797$		−	2.24353i		−	0.0794699i	−0.999210	−	0.0397349i	$-0.987349\pi$
$797$		−	2.24353i		−	0.0794699i	0.999210	−	0.0397349i	$-0.0126514\pi$
$798$		0			0
$799$	−44.4545			−1.57269
$800$	−13.6326	−	41.4456i	−0.481984	−	1.46532i
$801$		0			0
$802$	25.4846	+	30.7603i	0.899894	+	1.08618i
$803$	2.00760	+	1.15909i	0.0708466	+	0.0409033i
$804$		0			0
$805$	12.8803	−	18.9053i	0.453970	−	0.666323i
$806$	1.62232	+	9.54967i	0.0571437	+	0.336373i
$807$		0			0
$808$	−18.5905	+	30.8476i	−0.654011	+	1.08521i
$809$	−7.66844	−	13.2821i	−0.269608	−	0.466974i	0.699153	−	0.714972i	$-0.253561\pi$
$809$	−7.66844	−	13.2821i	−0.269608	−	0.466974i	−0.968761	+	0.247998i	$0.920227\pi$
$810$		0			0
$811$		−	15.1509i		−	0.532019i	−0.963970	−	0.266010i	$-0.914295\pi$
$811$		−	15.1509i		−	0.532019i	0.963970	−	0.266010i	$-0.0857053\pi$
$812$	0.207062	−	0.773637i	0.00726646	−	0.0271494i
$813$		0			0
$814$	−22.7187	+	61.2245i	−0.796291	+	2.14592i
$815$	23.9801	+	41.5348i	0.839987	+	1.45490i
$816$		0			0
$817$	−0.200240	+	0.346825i	−0.00700550	+	0.0121339i
$818$	18.8071	−	3.19499i	0.657575	−	0.111710i
$819$		0			0
$820$	−0.563818	−	1.61155i	−0.0196894	−	0.0562777i
$821$	−1.41618	−	0.817631i	−0.0494249	−	0.0285355i	0.475084	−	0.879940i	$-0.342418\pi$
$821$	−1.41618	−	0.817631i	−0.0494249	−	0.0285355i	−0.524509	+	0.851405i	$0.675751\pi$
$822$		0			0
$823$	−22.5067	−	38.9828i	−0.784535	−	1.35886i	−0.929276	−	0.369385i	$-0.879568\pi$
$823$	−22.5067	−	38.9828i	−0.784535	−	1.35886i	0.144741	−	0.989470i	$-0.453765\pi$
$824$	0.319018	−	16.9923i	0.0111135	−	0.591955i
$825$		0			0
$826$	−24.3532	−	34.3005i	−0.847358	−	1.19347i
$827$		−	42.4945i		−	1.47768i	−0.673882	−	0.738839i	$-0.735374\pi$
$827$		−	42.4945i		−	1.47768i	0.673882	−	0.738839i	$-0.264626\pi$
$828$		0			0
$829$	−39.6168	+	22.8728i	−1.37595	+	0.794405i	−0.991669	−	0.128811i	$-0.958884\pi$
$829$	−39.6168	+	22.8728i	−1.37595	+	0.794405i	−0.384281	+	0.923216i	$0.625551\pi$
$830$	32.2827	+	38.9656i	1.12055	+	1.35252i
$831$		0			0
$832$	−9.75776	−	6.13317i	−0.338289	−	0.212629i
$833$	48.3959	+	7.26192i	1.67682	+	0.251611i
$834$		0			0
$835$	−53.1410	−	30.6810i	−1.83902	−	1.06176i
$836$	1.86053	+	1.60127i	0.0643479	+	0.0553812i
$837$		0			0
$838$	−33.2231	−	12.3282i	−1.14767	−	0.425870i
$839$	−30.4207			−1.05024			−0.525120	−	0.851028i	$-0.675980\pi$
$839$	−30.4207			−1.05024			−0.525120	+	0.851028i	$0.675980\pi$
$840$		0			0
$841$	28.9771			0.999210
$842$	30.5409	+	11.3329i	1.05251	+	0.390558i
$843$		0			0
$844$	−12.2697	+	14.2562i	−0.422339	+	0.490719i
$845$	33.7329	+	19.4757i	1.16045	+	0.669985i
$846$		0			0
$847$	−1.09692	+	14.7023i	−0.0376905	+	0.505177i
$848$	−14.9263	−	18.7206i	−0.512570	−	0.642870i
$849$		0			0
$850$	−48.6497	−	58.7208i	−1.66867	−	2.01411i
$851$	23.8216	−	13.7534i	0.816594	−	0.471461i
$852$		0			0
$853$		−	0.386158i		−	0.0132218i	−0.999978	−	0.00661090i	$-0.997896\pi$
$853$		−	0.386158i		−	0.0132218i	0.999978	−	0.00661090i	$-0.00210433\pi$
$854$	6.56271	−	14.3175i	0.224571	−	0.489933i
$855$		0			0
$856$	45.1505	+	0.847667i	1.54321	+	0.0289727i
$857$	−13.1617	−	22.7967i	−0.449595	−	0.778721i	0.548765	−	0.835977i	$-0.315098\pi$
$857$	−13.1617	−	22.7967i	−0.449595	−	0.778721i	−0.998360	+	0.0572556i	$0.981765\pi$
$858$		0			0
$859$	20.1570	+	11.6377i	0.687749	+	0.397072i	0.802768	−	0.596291i	$-0.203360\pi$
$859$	20.1570	+	11.6377i	0.687749	+	0.397072i	−0.115019	+	0.993363i	$0.536693\pi$
$860$	8.94080	−	3.12804i	0.304879	−	0.106665i
$861$		0			0
$862$	−0.259128	+	0.0440212i	−0.00882593	+	0.00149937i
$863$	8.25613	−	14.3000i	0.281042	−	0.486779i	−0.690600	−	0.723237i	$-0.742653\pi$
$863$	8.25613	−	14.3000i	0.281042	−	0.486779i	0.971642	+	0.236458i	$0.0759866\pi$
$864$		0			0
$865$	−6.14941	−	10.6511i	−0.209086	−	0.362148i
$866$	−17.0946	+	46.0680i	−0.580897	+	1.56545i
$867$		0			0
$868$	6.51816	+	24.2988i	0.221241	+	0.824753i
$869$			6.08128i			0.206293i
$870$		0			0
$871$	−3.15555	−	5.46558i	−0.106922	−	0.185194i
$872$	20.2510	−	33.6028i	0.685785	−	1.13794i
$873$		0			0
$874$	−0.173171	−	1.01936i	−0.00585759	−	0.0344803i
$875$	−11.1111	−	23.0530i	−0.375623	−	0.779332i
$876$		0			0
$877$	24.8320	+	14.3368i	0.838518	+	0.484119i	0.856760	−	0.515715i	$-0.172474\pi$
$877$	24.8320	+	14.3368i	0.838518	+	0.484119i	−0.0182421	+	0.999834i	$0.505807\pi$
$878$	24.5212	+	29.5974i	0.827551	+	0.998864i
$879$		0			0
$880$	−8.64780	−	57.4118i	−0.291517	−	1.93535i
$881$	−5.88181			−0.198163			−0.0990816	−	0.995079i	$-0.531590\pi$
$881$	−5.88181			−0.198163			−0.0990816	+	0.995079i	$0.531590\pi$
$882$		0			0
$883$		−	1.69703i		−	0.0571095i	−0.999592	−	0.0285548i	$-0.990910\pi$
$883$		−	1.69703i		−	0.0571095i	0.999592	−	0.0285548i	$-0.00909050\pi$
$884$	−19.7921	−	3.74585i	−0.665679	−	0.125986i
$885$		0			0
$886$	4.32196	−	3.58071i	0.145199	−	0.120296i
$887$	−28.8622	+	49.9909i	−0.969099	+	1.67853i	−0.270926	+	0.962600i	$0.587330\pi$
$887$	−28.8622	+	49.9909i	−0.969099	+	1.67853i	−0.698173	+	0.715929i	$0.746004\pi$
$888$		0			0
$889$	7.94368	−	3.82870i	0.266423	−	0.128410i
$890$	−3.09824	−	18.2376i	−0.103853	−	0.611326i
$891$		0			0
$892$	−6.59015	−	5.67184i	−0.220655	−	0.189907i
$893$	−1.66028	+	0.958561i	−0.0555590	+	0.0320770i
$894$		0			0
$895$	−40.2961			−1.34695
$896$	−26.7235	−	13.4853i	−0.892771	−	0.450511i
$897$		0			0
$898$	−5.98448	+	16.1275i	−0.199705	+	0.538182i
$899$	0.623170	−	0.359787i	0.0207839	−	0.0119996i
$900$		0			0
$901$	−36.2402	−	20.9233i	−1.20734	−	0.697056i
$902$	−0.230858	−	1.35893i	−0.00768672	−	0.0452474i
$903$		0			0
$904$	40.7224	−	22.5027i	1.35441	−	0.748427i
$905$	17.9284	−	31.0529i	0.595961	−	1.03223i
$906$		0			0
$907$	39.2549	−	22.6638i	1.30344	−	0.752540i	0.322446	−	0.946588i	$-0.395495\pi$
$907$	39.2549	−	22.6638i	1.30344	−	0.752540i	0.980992	+	0.194047i	$0.0621615\pi$
$908$	−14.3100	−	2.70832i	−0.474895	−	0.0898786i
$909$		0			0
$910$	−17.4715	−	8.00844i	−0.579175	−	0.265477i
$911$	26.4254			0.875511			0.437755	−	0.899094i	$-0.355774\pi$
$911$	26.4254			0.875511			0.437755	+	0.899094i	$0.355774\pi$
$912$		0			0
$913$	20.4263	+	35.3793i	0.676011	+	1.17088i
$914$	−23.2401	−	28.0511i	−0.768715	−	0.927849i
$915$		0			0
$916$	−0.675146	−	1.92975i	−0.0223074	−	0.0637608i
$917$	−10.7876	−	0.804848i	−0.356238	−	0.0265784i
$918$		0			0
$919$	0.150333	−	0.260384i	0.00495901	−	0.00858926i	−0.863535	−	0.504288i	$-0.831755\pi$
$919$	0.150333	−	0.260384i	0.00495901	−	0.00858926i	0.868494	+	0.495699i	$0.165088\pi$
$920$	−12.6231	+	20.9458i	−0.416172	+	0.690562i
$921$		0			0
$922$	22.5959	+	8.38471i	0.744155	+	0.276136i
$923$		−	12.1934i		−	0.401352i
$924$		0			0
$925$		−	87.4867i		−	2.87654i
$926$	−16.7939	+	45.2577i	−0.551882	+	1.48726i
$927$		0			0
$928$	−0.174974	+	0.838094i	−0.00574380	+	0.0275118i
$929$	−19.3333	+	33.4862i	−0.634304	+	1.09865i	0.352358	+	0.935865i	$0.385380\pi$
$929$	−19.3333	+	33.4862i	−0.634304	+	1.09865i	−0.986662	+	0.162782i	$0.947953\pi$
$930$		0			0
$931$	1.96407	−	0.772333i	0.0643697	−	0.0253122i
$932$	41.6564	−	14.5739i	1.36450	−	0.477386i
$933$		0			0
$934$	17.7230	−	14.6834i	0.579914	−	0.480455i
$935$	−50.7375	−	87.8798i	−1.65929	−	2.87398i
$936$		0			0
$937$	23.9292			0.781734			0.390867	−	0.920447i	$-0.372175\pi$
$937$	23.9292			0.781734			0.390867	+	0.920447i	$0.372175\pi$
$938$	−9.48923	−	13.3652i	−0.309834	−	0.436388i
$939$		0			0
$940$	44.5531	+	8.43212i	1.45316	+	0.275025i
$941$	36.7253	−	21.2034i	1.19721	−	0.691210i	0.237279	−	0.971442i	$-0.423745\pi$
$941$	36.7253	−	21.2034i	1.19721	−	0.691210i	0.959932	+	0.280232i	$0.0904113\pi$
$942$		0			0
$943$	−0.290300	+	0.502815i	−0.00945348	+	0.0163739i
$944$	28.0357	+	35.1626i	0.912484	+	1.14444i
$945$		0			0
$946$	7.53928	−	1.28079i	0.245123	−	0.0416420i
$947$	11.9347	+	6.89051i	0.387826	+	0.223911i	0.681218	−	0.732081i	$-0.261451\pi$
$947$	11.9347	+	6.89051i	0.387826	+	0.223911i	−0.293392	+	0.955992i	$0.594784\pi$
$948$		0			0
$949$	−0.710464	+	0.410186i	−0.0230626	+	0.0133152i
$950$	−3.08314	−	1.14407i	−0.100030	−	0.0371185i
$951$		0			0
$952$	−52.0894	−	4.87107i	−1.68823	−	0.157872i
$953$	−57.0092			−1.84671			−0.923354	−	0.383950i	$-0.874564\pi$
$953$	−57.0092			−1.84671			−0.923354	+	0.383950i	$0.874564\pi$
$954$		0			0
$955$	66.3449	−	38.3042i	2.14687	−	1.23950i
$956$	7.28344	+	6.26851i	0.235563	+	0.202738i
$957$		0			0
$958$	27.8974	−	4.73928i	0.901325	−	0.153119i
$959$	−18.1204	−	12.3456i	−0.585139	−	0.398659i
$960$		0			0
$961$	4.19793	−	7.27103i	0.135417	−	0.234549i
$962$	−14.7439	−	17.7960i	−0.475361	−	0.573766i
$963$		0			0
$964$	−8.84004	+	46.7084i	−0.284719	+	1.50438i
$965$			58.5311i			1.88418i
$966$		0			0
$967$	−20.0555			−0.644941			−0.322470	−	0.946580i	$-0.604513\pi$
$967$	−20.0555			−0.644941			−0.322470	+	0.946580i	$0.604513\pi$
$968$	0.295851	−	15.7583i	0.00950900	−	0.506492i
$969$		0			0
$970$	−40.6374	+	33.6677i	−1.30479	+	1.08101i
$971$	0.979533	+	0.565534i	0.0314347	+	0.0181488i	0.515635	−	0.856808i	$-0.327556\pi$
$971$	0.979533	+	0.565534i	0.0314347	+	0.0181488i	−0.484200	+	0.874957i	$0.660889\pi$
$972$		0			0
$973$	21.1573	+	43.8967i	0.678273	+	1.40726i
$974$	23.0855	−	3.92181i	0.739706	−	0.125663i
$975$		0			0
$976$	−6.15288	+	15.6728i	−0.196949	+	0.501675i
$977$	−15.5033	−	26.8526i	−0.495996	−	0.859089i	0.503994	−	0.863707i	$-0.331863\pi$
$977$	−15.5033	−	26.8526i	−0.495996	−	0.859089i	−0.999989	+	0.00461783i	$0.998530\pi$
$978$		0			0
$979$		−	14.9349i		−	0.477323i
$980$	−47.1259	−	16.4578i	−1.50538	−	0.525724i
$981$		0			0
$982$	−12.5859	−	4.67030i	−0.401634	−	0.149035i
$983$	−4.59402	−	7.95708i	−0.146527	−	0.253791i	0.783415	−	0.621499i	$-0.213476\pi$
$983$	−4.59402	−	7.95708i	−0.146527	−	0.253791i	−0.929941	+	0.367708i	$0.880143\pi$
$984$		0			0
$985$	27.9972	−	48.4926i	0.892065	−	1.54510i
$986$	0.250618	+	1.47525i	0.00798130	+	0.0469814i
$987$		0			0
$988$	−0.819961	+	0.286872i	−0.0260864	+	0.00912663i
$989$	−2.78959	−	1.61057i	−0.0887040	−	0.0512133i
$990$		0			0
$991$	−20.0275	−	34.6886i	−0.636194	−	1.10192i	−0.986261	−	0.165195i	$-0.947175\pi$
$991$	−20.0275	−	34.6886i	−0.636194	−	1.10192i	0.350067	−	0.936725i	$-0.386159\pi$
$992$	−8.40350	−	25.5483i	−0.266811	−	0.811158i
$993$		0			0
$994$	−2.96635	−	31.5297i	−0.0940868	−	1.00006i
$995$		−	22.3712i		−	0.709214i
$996$		0			0
$997$	22.5912	−	13.0430i	0.715470	−	0.413077i	−0.0976129	−	0.995224i	$-0.531121\pi$
$997$	22.5912	−	13.0430i	0.715470	−	0.413077i	0.813083	+	0.582147i	$0.197787\pi$
$998$	37.2771	−	30.8838i	1.17999	−	0.977610i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.e.37.7		32
3.2	odd	2		168.2.bc.a.37.10	✓	32
4.3	odd	2		2016.2.cr.e.1297.15		32
7.4	even	3	inner	504.2.cj.e.109.5		32
8.3	odd	2		2016.2.cr.e.1297.2		32
8.5	even	2	inner	504.2.cj.e.37.5		32
12.11	even	2		672.2.bk.a.625.9		32
21.2	odd	6		1176.2.c.e.589.2		16
21.5	even	6		1176.2.c.f.589.2		16
21.11	odd	6		168.2.bc.a.109.12	yes	32
24.5	odd	2		168.2.bc.a.37.12	yes	32
24.11	even	2		672.2.bk.a.625.8		32
28.11	odd	6		2016.2.cr.e.1873.2		32
56.11	odd	6		2016.2.cr.e.1873.15		32
56.53	even	6	inner	504.2.cj.e.109.7		32
84.11	even	6		672.2.bk.a.529.8		32
84.23	even	6		4704.2.c.e.2353.16		16
84.47	odd	6		4704.2.c.f.2353.1		16
168.5	even	6		1176.2.c.f.589.1		16
168.11	even	6		672.2.bk.a.529.9		32
168.53	odd	6		168.2.bc.a.109.10	yes	32
168.107	even	6		4704.2.c.e.2353.1		16
168.131	odd	6		4704.2.c.f.2353.16		16
168.149	odd	6		1176.2.c.e.589.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.10	✓	32	3.2	odd	2
168.2.bc.a.37.12	yes	32	24.5	odd	2
168.2.bc.a.109.10	yes	32	168.53	odd	6
168.2.bc.a.109.12	yes	32	21.11	odd	6
504.2.cj.e.37.5		32	8.5	even	2	inner
504.2.cj.e.37.7		32	1.1	even	1	trivial
504.2.cj.e.109.5		32	7.4	even	3	inner
504.2.cj.e.109.7		32	56.53	even	6	inner
672.2.bk.a.529.8		32	84.11	even	6
672.2.bk.a.529.9		32	168.11	even	6
672.2.bk.a.625.8		32	24.11	even	2
672.2.bk.a.625.9		32	12.11	even	2
1176.2.c.e.589.1		16	168.149	odd	6
1176.2.c.e.589.2		16	21.2	odd	6
1176.2.c.f.589.1		16	168.5	even	6
1176.2.c.f.589.2		16	21.5	even	6
2016.2.cr.e.1297.2		32	8.3	odd	2
2016.2.cr.e.1297.15		32	4.3	odd	2
2016.2.cr.e.1873.2		32	28.11	odd	6
2016.2.cr.e.1873.15		32	56.11	odd	6
4704.2.c.e.2353.1		16	168.107	even	6
4704.2.c.e.2353.16		16	84.23	even	6
4704.2.c.f.2353.1		16	84.47	odd	6
4704.2.c.f.2353.16		16	168.131	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.491996 + 1.32587i) q^{2} +(-1.51588 - 1.30465i) q^{4} +(3.08781 + 1.78275i) q^{5} +(-2.38336 + 1.14873i) q^{7} +(2.47560 - 1.36799i) q^{8} +O(q^{10})\)	\(q+(-0.491996 + 1.32587i) q^{2} +(-1.51588 - 1.30465i) q^{4} +(3.08781 + 1.78275i) q^{5} +(-2.38336 + 1.14873i) q^{7} +(2.47560 - 1.36799i) q^{8} +(-3.88289 + 3.21694i) q^{10} +(-3.52552 + 2.03546i) q^{11} -1.44065i q^{13} +(-0.350472 - 3.72521i) q^{14} +(0.595789 + 3.95538i) q^{16} +(3.49555 + 6.05447i) q^{17} +(0.261102 + 0.150747i) q^{19} +(-2.35490 - 6.73095i) q^{20} +(-0.964222 - 5.67583i) q^{22} +(-1.21250 + 2.10010i) q^{23} +(3.85640 + 6.67947i) q^{25} +(1.91012 + 0.708792i) q^{26} +(5.11158 + 1.36810i) q^{28} -0.151350i q^{29} +(2.37719 + 4.11741i) q^{31} +(-5.53746 - 1.15609i) q^{32} +(-9.74726 + 1.65588i) q^{34} +(-9.40728 - 0.701863i) q^{35} +(-9.82338 - 5.67153i) q^{37} +(-0.328333 + 0.272021i) q^{38} +(10.0830 + 0.189300i) q^{40} +0.239424 q^{41} +1.32831i q^{43} +(7.99983 + 1.51405i) q^{44} +(-2.18793 - 2.64086i) q^{46} +(-3.17936 + 5.50681i) q^{47} +(4.36082 - 5.47569i) q^{49} +(-10.7535 + 1.82682i) q^{50} +(-1.87954 + 2.18385i) q^{52} +(-5.18376 + 2.99285i) q^{53} -14.5149 q^{55} +(-4.32881 + 6.10421i) q^{56} +(0.200671 + 0.0744635i) q^{58} +(9.73654 - 5.62140i) q^{59} +(3.64539 + 2.10467i) q^{61} +(-6.62874 + 1.12610i) q^{62} +(4.25723 - 6.77318i) q^{64} +(2.56831 - 4.44845i) q^{65} +(3.79384 - 2.19037i) q^{67} +(2.60011 - 13.7383i) q^{68} +(5.55892 - 12.1275i) q^{70} +8.46387 q^{71} +(-0.284724 - 0.493156i) q^{73} +(12.3528 - 10.2342i) q^{74} +(-0.199128 - 0.569162i) q^{76} +(6.06439 - 8.90112i) q^{77} +(0.746916 - 1.29370i) q^{79} +(-5.21177 + 13.2756i) q^{80} +(-0.117795 + 0.317446i) q^{82} -10.0352i q^{83} +24.9268i q^{85} +(-1.76117 - 0.653524i) q^{86} +(-5.94331 + 9.86185i) q^{88} +(-1.83434 + 3.17718i) q^{89} +(1.65492 + 3.43358i) q^{91} +(4.57789 - 1.60163i) q^{92} +(-5.73711 - 6.92476i) q^{94} +(0.537490 + 0.930960i) q^{95} +10.4657 q^{97} +(5.11457 + 8.47592i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{49} - 52 q^{50} + 44 q^{52} - 64 q^{55} - 40 q^{56} + 34 q^{58} - 100 q^{62} - 20 q^{64} - 16 q^{68} + 38 q^{70} + 80 q^{71} + 8 q^{73} - 10 q^{74} - 32 q^{76} + 8 q^{79} + 56 q^{80} + 22 q^{86} + 50 q^{88} - 64 q^{92} - 48 q^{94} - 24 q^{95} - 48 q^{97} + 64 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

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