LMFDB - Embedded newform 936.2.ed.e.19.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(19,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.ed (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	936.19
Dual form			936.2.ed.e.739.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25675 + 0.648526i) q^{2} +(1.15883 + 1.63007i) q^{4} +(-0.513065 - 0.513065i) q^{5} +(1.43100 + 0.383434i) q^{7} +(0.399211 + 2.80011i) q^{8} +(-0.312057 - 0.977529i) q^{10} +(-1.43129 + 0.383513i) q^{11} +(0.967164 + 3.47341i) q^{13} +(1.54973 + 1.40992i) q^{14} +(-1.31424 + 3.77793i) q^{16} +(-1.08804 + 0.628178i) q^{17} +(6.19113 + 1.65891i) q^{19} +(0.241777 - 1.43088i) q^{20} +(-2.04749 - 0.446251i) q^{22} +(-1.68941 + 2.92615i) q^{23} -4.47353i q^{25} +(-1.03712 + 4.99243i) q^{26} +(1.03325 + 2.77695i) q^{28} +(5.98829 + 3.45734i) q^{29} +(-1.65000 - 1.65000i) q^{31} +(-4.10176 + 3.89559i) q^{32} +(-1.77478 + 0.0838407i) q^{34} +(-0.537467 - 0.930920i) q^{35} +(0.944898 + 3.52641i) q^{37} +(6.70484 + 6.09994i) q^{38} +(1.23182 - 1.64146i) q^{40} +(-0.503062 - 1.87745i) q^{41} +(7.93214 - 4.57963i) q^{43} +(-2.28377 - 1.88867i) q^{44} +(-4.02085 + 2.58180i) q^{46} +(-2.96711 + 2.96711i) q^{47} +(-4.16145 - 2.40261i) q^{49} +(2.90120 - 5.62210i) q^{50} +(-4.54112 + 5.60163i) q^{52} -0.513310i q^{53} +(0.931112 + 0.537578i) q^{55} +(-0.502390 + 4.16002i) q^{56} +(5.28359 + 8.22856i) q^{58} +(3.60773 - 13.4642i) q^{59} +(-12.2267 + 7.05906i) q^{61} +(-1.00357 - 3.14371i) q^{62} +(-7.68126 + 2.23567i) q^{64} +(1.28587 - 2.27830i) q^{65} +(1.88176 + 7.02284i) q^{67} +(-2.28482 - 1.04562i) q^{68} +(-0.0717338 - 1.51849i) q^{70} +(0.979852 - 3.65686i) q^{71} +(-4.42114 - 4.42114i) q^{73} +(-1.09947 + 5.04459i) q^{74} +(4.47032 + 12.0143i) q^{76} -2.19522 q^{77} -3.24902i q^{79} +(2.61261 - 1.26403i) q^{80} +(0.585356 - 2.68573i) q^{82} +(2.89926 - 2.89926i) q^{83} +(0.880529 + 0.235937i) q^{85} +(12.9387 - 0.611226i) q^{86} +(-1.64527 - 3.85467i) q^{88} +(2.05252 - 0.549972i) q^{89} +(0.0521823 + 5.34128i) q^{91} +(-6.72756 + 0.637043i) q^{92} +(-5.65316 + 1.80466i) q^{94} +(-2.32532 - 4.02758i) q^{95} +(1.09430 + 0.293217i) q^{97} +(-3.67173 - 5.71829i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{8} + 28 q^{14} + 12 q^{16} - 8 q^{19} + 4 q^{20} + 10 q^{22} - 34 q^{26} - 14 q^{28} + 30 q^{32} + 56 q^{34} - 28 q^{40} - 40 q^{41} + 44 q^{44} - 18 q^{46} + 24 q^{49} + 72 q^{50} + 32 q^{52}+ \cdots - 4 q^{98}+O(q^{100}) $ 56 * q + 12 * q^8 + 28 * q^14 + 12 * q^16 - 8 * q^19 + 4 * q^20 + 10 * q^22 - 34 * q^26 - 14 * q^28 + 30 * q^32 + 56 * q^34 - 28 * q^40 - 40 * q^41 + 44 * q^44 - 18 * q^46 + 24 * q^49 + 72 * q^50 + 32 * q^52 + 54 * q^56 - 16 * q^58 - 32 * q^59 - 48 * q^65 - 24 * q^67 + 26 * q^68 + 64 * q^70 + 44 * q^73 + 6 * q^74 + 6 * q^76 + 4 * q^80 - 30 * q^82 - 40 * q^83 + 28 * q^86 + 126 * q^88 + 68 * q^89 - 72 * q^91 - 52 * q^92 + 34 * q^94 - 4 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$	$-1$	$-1$

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 $

$2$	1.25675	+	0.648526i	0.888654	+	0.458577i
$2$	1.25675	+	0.648526i	0.888654	+	0.458577i
$3$		0			0
$3$		0			0
$4$	1.15883	+	1.63007i	0.579413	+	0.815034i
$5$	−0.513065	−	0.513065i	−0.229449	−	0.229449i	0.583013	−	0.812463i	$-0.301874\pi$
$5$	−0.513065	−	0.513065i	−0.229449	−	0.229449i	−0.812463	+	0.583013i	$0.801874\pi$
$6$		0			0
$7$	1.43100	+	0.383434i	0.540866	+	0.144925i	0.518901	−	0.854834i	$-0.326341\pi$
$7$	1.43100	+	0.383434i	0.540866	+	0.144925i	0.0219645	+	0.999759i	$0.493008\pi$
$8$	0.399211	+	2.80011i	0.141142	+	0.989989i
$9$		0			0
$10$	−0.312057	−	0.977529i	−0.0986809	−	0.309122i
$11$	−1.43129	+	0.383513i	−0.431550	+	0.115634i	−0.468054	−	0.883700i	$-0.655045\pi$
$11$	−1.43129	+	0.383513i	−0.431550	+	0.115634i	0.0365035	+	0.999334i	$0.488378\pi$
$12$		0			0
$13$	0.967164	+	3.47341i	0.268243	+	0.963351i
$13$	0.967164	+	3.47341i	0.268243	+	0.963351i
$14$	1.54973	+	1.40992i	0.414184	+	0.376817i
$15$		0			0
$16$	−1.31424	+	3.77793i	−0.328560	+	0.944483i
$17$	−1.08804	+	0.628178i	−0.263888	+	0.152356i	−0.626107	−	0.779737i	$-0.715353\pi$
$17$	−1.08804	+	0.628178i	−0.263888	+	0.152356i	0.362219	+	0.932093i	$0.382019\pi$
$18$		0			0
$19$	6.19113	+	1.65891i	1.42034	+	0.380580i	0.885605	−	0.464439i	$-0.153744\pi$
$19$	6.19113	+	1.65891i	1.42034	+	0.380580i	0.534737	+	0.845018i	$0.320411\pi$
$20$	0.241777	−	1.43088i	0.0540630	−	0.319955i
$21$		0			0
$22$	−2.04749	−	0.446251i	−0.436526	−	0.0951410i
$23$	−1.68941	+	2.92615i	−0.352267	+	0.610144i	−0.986646	−	0.162878i	$-0.947922\pi$
$23$	−1.68941	+	2.92615i	−0.352267	+	0.610144i	0.634379	+	0.773022i	$0.281256\pi$
$24$		0			0
$25$		−	4.47353i		−	0.894706i
$26$	−1.03712	+	4.99243i	−0.203396	+	0.979097i
$27$		0			0
$28$	1.03325	+	2.77695i	0.195266	+	0.524795i
$29$	5.98829	+	3.45734i	1.11200	+	0.642012i	0.939346	−	0.342971i	$-0.111433\pi$
$29$	5.98829	+	3.45734i	1.11200	+	0.642012i	0.172651	+	0.984983i	$0.444767\pi$
$30$		0			0
$31$	−1.65000	−	1.65000i	−0.296349	−	0.296349i	0.543233	−	0.839582i	$-0.317200\pi$
$31$	−1.65000	−	1.65000i	−0.296349	−	0.296349i	−0.839582	+	0.543233i	$0.817200\pi$
$32$	−4.10176	+	3.89559i	−0.725095	+	0.688649i
$33$		0			0
$34$	−1.77478	+	0.0838407i	−0.304372	+	0.0143786i
$35$	−0.537467	−	0.930920i	−0.0908485	−	0.157354i
$36$		0			0
$37$	0.944898	+	3.52641i	0.155340	+	0.579738i	0.999076	+	0.0429788i	$0.0136848\pi$
$37$	0.944898	+	3.52641i	0.155340	+	0.579738i	−0.843736	+	0.536759i	$0.819649\pi$
$38$	6.70484	+	6.09994i	1.08767	+	0.989541i
$39$		0			0
$40$	1.23182	−	1.64146i	0.194768	−	0.259538i
$41$	−0.503062	−	1.87745i	−0.0785651	−	0.293209i	0.915453	−	0.402425i	$-0.131833\pi$
$41$	−0.503062	−	1.87745i	−0.0785651	−	0.293209i	−0.994018	+	0.109216i	$0.965166\pi$
$42$		0			0
$43$	7.93214	−	4.57963i	1.20964	−	0.698386i	0.246960	−	0.969026i	$-0.420568\pi$
$43$	7.93214	−	4.57963i	1.20964	−	0.698386i	0.962681	+	0.270639i	$0.0872351\pi$
$44$	−2.28377	−	1.88867i	−0.344291	−	0.284728i
$45$		0			0
$46$	−4.02085	+	2.58180i	−0.592842	+	0.380666i
$47$	−2.96711	+	2.96711i	−0.432797	+	0.432797i	−0.889579	−	0.456781i	$-0.849002\pi$
$47$	−2.96711	+	2.96711i	−0.432797	+	0.432797i	0.456781	+	0.889579i	$0.349002\pi$
$48$		0			0
$49$	−4.16145	−	2.40261i	−0.594493	−	0.343231i
$50$	2.90120	−	5.62210i	0.410292	−	0.795084i
$51$		0			0
$52$	−4.54112	+	5.60163i	−0.629740	+	0.776806i
$53$		−	0.513310i		−	0.0705086i	−0.999378	−	0.0352543i	$-0.988776\pi$
$53$		−	0.513310i		−	0.0705086i	0.999378	−	0.0352543i	$-0.0112241\pi$
$54$		0			0
$55$	0.931112	+	0.537578i	0.125551	+	0.0724869i
$56$	−0.502390	+	4.16002i	−0.0671347	+	0.555906i
$57$		0			0
$58$	5.28359	+	8.22856i	0.693769	+	1.08046i
$59$	3.60773	−	13.4642i	0.469687	−	1.75290i	−0.171176	−	0.985241i	$-0.554757\pi$
$59$	3.60773	−	13.4642i	0.469687	−	1.75290i	0.640863	−	0.767655i	$-0.278577\pi$
$60$		0			0
$61$	−12.2267	+	7.05906i	−1.56546	+	0.903820i	−0.568775	+	0.822493i	$0.692583\pi$
$61$	−12.2267	+	7.05906i	−1.56546	+	0.903820i	−0.996687	+	0.0813276i	$0.974084\pi$
$62$	−1.00357	−	3.14371i	−0.127453	−	0.399251i
$63$		0			0
$64$	−7.68126	+	2.23567i	−0.960158	+	0.279459i
$65$	1.28587	−	2.27830i	0.159492	−	0.282589i
$66$		0			0
$67$	1.88176	+	7.02284i	0.229894	+	0.857977i	0.980384	+	0.197095i	$0.0631507\pi$
$67$	1.88176	+	7.02284i	0.229894	+	0.857977i	−0.750490	+	0.660881i	$0.770183\pi$
$68$	−2.28482	−	1.04562i	−0.277075	−	0.126800i
$69$		0			0
$70$	−0.0717338	−	1.51849i	−0.00857383	−	0.181495i
$71$	0.979852	−	3.65686i	0.116287	−	0.433989i	−0.883093	−	0.469198i	$-0.844543\pi$
$71$	0.979852	−	3.65686i	0.116287	−	0.433989i	0.999380	+	0.0352090i	$0.0112097\pi$
$72$		0			0
$73$	−4.42114	−	4.42114i	−0.517455	−	0.517455i	0.399345	−	0.916801i	$-0.369237\pi$
$73$	−4.42114	−	4.42114i	−0.517455	−	0.517455i	−0.916801	+	0.399345i	$0.869237\pi$
$74$	−1.09947	+	5.04459i	−0.127811	+	0.586422i
$75$		0			0
$76$	4.47032	+	12.0143i	0.512780	+	1.37814i
$77$	−2.19522			−0.250169
$78$		0			0
$79$		−	3.24902i		−	0.365543i	−0.983155	−	0.182771i	$-0.941493\pi$
$79$		−	3.24902i		−	0.365543i	0.983155	−	0.182771i	$-0.0585068\pi$
$80$	2.61261	−	1.26403i	0.292099	−	0.141323i
$81$		0			0
$82$	0.585356	−	2.68573i	0.0646418	−	0.296590i
$83$	2.89926	−	2.89926i	0.318235	−	0.318235i	−0.529854	−	0.848089i	$-0.677753\pi$
$83$	2.89926	−	2.89926i	0.318235	−	0.318235i	0.848089	+	0.529854i	$0.177753\pi$
$84$		0			0
$85$	0.880529	+	0.235937i	0.0955068	+	0.0255910i
$86$	12.9387	−	0.611226i	1.39522	−	0.0659102i
$87$		0			0
$88$	−1.64527	−	3.85467i	−0.175386	−	0.410909i
$89$	2.05252	−	0.549972i	0.217567	−	0.0582969i	−0.148389	−	0.988929i	$-0.547409\pi$
$89$	2.05252	−	0.549972i	0.217567	−	0.0582969i	0.365956	+	0.930632i	$0.380742\pi$
$90$		0			0
$91$	0.0521823	+	5.34128i	0.00547019	+	0.559919i
$92$	−6.72756	+	0.637043i	−0.701396	+	0.0664163i
$93$		0			0
$94$	−5.65316	+	1.80466i	−0.583079	+	0.186136i
$95$	−2.32532	−	4.02758i	−0.238573	−	0.413221i
$96$		0			0
$97$	1.09430	+	0.293217i	0.111109	+	0.0297716i	0.313945	−	0.949441i	$-0.398349\pi$
$97$	1.09430	+	0.293217i	0.111109	+	0.0297716i	−0.202836	+	0.979213i	$0.565016\pi$
$98$	−3.67173	−	5.71829i	−0.370901	−	0.577634i
$99$		0			0
$100$	7.29215	−	5.18405i	0.729215	−	0.518405i
$101$	5.72724	−	9.91986i	0.569881	−	0.987063i	−0.426696	−	0.904395i	$-0.640323\pi$
$101$	5.72724	−	9.91986i	0.569881	−	0.987063i	0.996577	−	0.0826680i	$-0.0263441\pi$
$102$		0			0
$103$	−2.48901			−0.245249			−0.122625	−	0.992453i	$-0.539131\pi$
$103$	−2.48901			−0.245249			−0.122625	+	0.992453i	$0.539131\pi$
$104$	−9.33984	+	4.09479i	−0.915847	+	0.401527i
$105$		0			0
$106$	0.332895	−	0.645101i	0.0323337	−	0.0626578i
$107$	5.13018	−	8.88572i	0.495953	−	0.859015i	−0.504036	−	0.863682i	$-0.668152\pi$
$107$	5.13018	−	8.88572i	0.495953	−	0.859015i	0.999989	+	0.00466706i	$0.00148558\pi$
$108$		0			0
$109$	−7.21056	−	7.21056i	−0.690646	−	0.690646i	0.271728	−	0.962374i	$-0.412405\pi$
$109$	−7.21056	−	7.21056i	−0.690646	−	0.690646i	−0.962374	+	0.271728i	$0.912405\pi$
$110$	0.821539	+	1.27945i	0.0783306	+	0.121991i
$111$		0			0
$112$	−3.32926	+	4.90228i	−0.314586	+	0.463222i
$113$	2.37145	+	4.10748i	0.223088	+	0.386399i	0.955744	−	0.294200i	$-0.0950531\pi$
$113$	2.37145	+	4.10748i	0.223088	+	0.386399i	−0.732656	+	0.680599i	$0.761720\pi$
$114$		0			0
$115$	2.36808	−	0.634526i	0.220825	−	0.0591698i
$116$	1.30369	+	13.7678i	0.121045	+	1.27831i
$117$		0			0
$118$	13.2659	−	14.5814i	1.22123	−	1.34233i
$119$	−1.79784	+	0.481730i	−0.164808	+	0.0441601i
$120$		0			0
$121$	−7.62477	+	4.40216i	−0.693161	+	0.400197i
$122$	−19.9438	+	0.942148i	−1.80563	+	0.0852981i
$123$		0			0
$124$	0.777549	−	4.60169i	0.0698259	−	0.413244i
$125$	−4.86053	+	4.86053i	−0.434739	+	0.434739i
$126$		0			0
$127$	9.40686	−	16.2932i	0.834724	−	1.44578i	−0.0595311	−	0.998226i	$-0.518961\pi$
$127$	9.40686	−	16.2932i	0.834724	−	1.44578i	0.894255	−	0.447558i	$-0.147706\pi$
$128$	−11.1033	−	2.17183i	−0.981402	−	0.191964i
$129$		0			0
$130$	3.09355	−	2.02933i	0.271322	−	0.177984i
$131$	1.40105			0.122410			0.0612050	−	0.998125i	$-0.480506\pi$
$131$	1.40105			0.122410			0.0612050	+	0.998125i	$0.480506\pi$
$132$		0			0
$133$	8.22340	+	4.74778i	0.713059	+	0.411685i
$134$	−2.18960	+	10.0463i	−0.189152	+	0.867869i
$135$		0			0
$136$	−2.19333	−	2.79585i	−0.188076	−	0.239742i
$137$	4.33906	−	16.1936i	0.370711	−	1.38351i	−0.488800	−	0.872396i	$-0.662565\pi$
$137$	4.33906	−	16.1936i	0.370711	−	1.38351i	0.859511	−	0.511117i	$-0.170768\pi$
$138$		0			0
$139$	−7.57593	−	13.1219i	−0.642582	−	1.11298i	−0.984854	−	0.173384i	$-0.944530\pi$
$139$	−7.57593	−	13.1219i	−0.642582	−	1.11298i	0.342273	−	0.939601i	$-0.388803\pi$
$140$	0.894631	−	1.95488i	0.0756101	−	0.165218i
$141$		0			0
$142$	3.60299	−	3.96028i	0.302357	−	0.332340i
$143$	−2.71639	−	4.60054i	−0.227156	−	0.384717i
$144$		0			0
$145$	−1.29854	−	4.84622i	−0.107838	−	0.402456i
$146$	−2.68903	−	8.42348i	−0.222546	−	0.697132i
$147$		0			0
$148$	−4.65331	+	5.62674i	−0.382499	+	0.462515i
$149$	−2.01396	+	7.51621i	−0.164990	+	0.615752i	0.833051	+	0.553196i	$0.186592\pi$
$149$	−2.01396	+	7.51621i	−0.164990	+	0.615752i	−0.998041	+	0.0625561i	$0.980075\pi$
$150$		0			0
$151$	6.96070	−	6.96070i	0.566453	−	0.566453i	−0.364680	−	0.931133i	$-0.618822\pi$
$151$	6.96070	−	6.96070i	0.566453	−	0.566453i	0.931133	+	0.364680i	$0.118822\pi$
$152$	−2.17357	+	17.9981i	−0.176299	+	1.45984i
$153$		0			0
$154$	−2.75884	−	1.42366i	−0.222314	−	0.114722i
$155$			1.69312i			0.135994i
$156$		0			0
$157$			10.6185i			0.847450i	0.905791	+	0.423725i	$0.139278\pi$
$157$			10.6185i			0.847450i	−0.905791	+	0.423725i	$0.860722\pi$
$158$	2.10707	−	4.08319i	0.167630	−	0.324841i
$159$		0			0
$160$	4.10315	+	0.105779i	0.324383	+	0.00836255i
$161$	−3.53953	+	3.53953i	−0.278954	+	0.278954i
$162$		0			0
$163$	2.99986	−	11.1956i	0.234967	−	0.876908i	−0.743197	−	0.669073i	$-0.766692\pi$
$163$	2.99986	−	11.1956i	0.234967	−	0.876908i	0.978164	−	0.207835i	$-0.0666418\pi$
$164$	2.47741	−	2.99567i	0.193453	−	0.233922i
$165$		0			0
$166$	5.52388	−	1.76339i	0.428736	−	0.136866i
$167$	−2.32855	−	8.69026i	−0.180189	−	0.672473i	−0.995609	−	0.0936043i	$-0.970161\pi$
$167$	−2.32855	−	8.69026i	−0.180189	−	0.672473i	0.815421	−	0.578868i	$-0.196506\pi$
$168$		0			0
$169$	−11.1292	+	6.71872i	−0.856091	+	0.516824i
$170$	0.953591	+	0.867560i	0.0731371	+	0.0665388i
$171$		0			0
$172$	16.6571	+	7.62294i	1.27009	+	0.581243i
$173$	6.97351	+	12.0785i	0.530186	+	0.918309i	0.999380	+	0.0352137i	$0.0112112\pi$
$173$	6.97351	+	12.0785i	0.530186	+	0.918309i	−0.469194	+	0.883095i	$0.655455\pi$
$174$		0			0
$175$	1.71530	−	6.40160i	0.129665	−	0.483916i
$176$	0.432173	−	5.91135i	0.0325763	−	0.445585i
$177$		0			0
$178$	2.93617	+	0.639940i	0.220076	+	0.0479655i
$179$	8.03592	+	4.63954i	0.600633	+	0.346776i	0.769291	−	0.638899i	$-0.220610\pi$
$179$	8.03592	+	4.63954i	0.600633	+	0.346776i	−0.168658	+	0.985675i	$0.553943\pi$
$180$		0			0
$181$	20.7868			1.54507			0.772535	−	0.634973i	$-0.218989\pi$
$181$	20.7868			1.54507			0.772535	+	0.634973i	$0.218989\pi$
$182$	−3.39838	+	6.74648i	−0.251905	+	0.500083i
$183$		0			0
$184$	−8.86798	−	3.56240i	−0.653756	−	0.262623i
$185$	1.32448	−	2.29407i	0.0973778	−	0.168663i
$186$		0			0
$187$	1.31638	−	1.31638i	0.0962634	−	0.0962634i
$188$	−8.27496	−	1.39822i	−0.603513	−	0.101976i
$189$		0			0
$190$	−0.310353	−	6.56968i	−0.0225153	−	0.476615i
$191$	22.5621	−	13.0262i	1.63254	−	0.942545i	0.649228	−	0.760593i	$-0.275092\pi$
$191$	22.5621	−	13.0262i	1.63254	−	0.942545i	0.983307	−	0.181952i	$-0.0582414\pi$
$192$		0			0
$193$	−14.5165	+	3.88969i	−1.04492	+	0.279986i	−0.740152	−	0.672439i	$-0.765247\pi$
$193$	−14.5165	+	3.88969i	−1.04492	+	0.279986i	−0.304771	+	0.952426i	$0.598580\pi$
$194$	1.18510	+	1.07818i	0.0850851	+	0.0774089i
$195$		0			0
$196$	−0.905977	−	9.56766i	−0.0647126	−	0.683404i
$197$	−19.2785	+	5.16566i	−1.37354	+	0.368038i	−0.868769	−	0.495217i	$-0.835088\pi$
$197$	−19.2785	+	5.16566i	−1.37354	+	0.368038i	−0.504767	+	0.863255i	$0.668422\pi$
$198$		0			0
$199$	−5.62998	−	9.75141i	−0.399098	−	0.691259i	0.594516	−	0.804083i	$-0.297344\pi$
$199$	−5.62998	−	9.75141i	−0.399098	−	0.691259i	−0.993615	+	0.112825i	$0.964010\pi$
$200$	12.5264	−	1.78588i	0.885749	−	0.126281i
$201$		0			0
$202$	13.6310	−	8.75250i	0.959072	−	0.615823i
$203$	7.24355	+	7.24355i	0.508398	+	0.508398i
$204$		0			0
$205$	−0.705151	+	1.22136i	−0.0492499	+	0.0853033i
$206$	−3.12806	−	1.61419i	−0.217942	−	0.112466i
$207$		0			0
$208$	−14.3934	−	0.911019i	−0.998003	−	0.0631678i
$209$	−9.49752			−0.656957
$210$		0			0
$211$	0.571787	−	0.990365i	0.0393635	−	0.0681795i	−0.845672	−	0.533702i	$-0.820800\pi$
$211$	0.571787	−	0.990365i	0.0393635	−	0.0681795i	0.885036	+	0.465523i	$0.154134\pi$
$212$	0.836731	−	0.594838i	0.0574669	−	0.0408536i
$213$		0			0
$214$	12.2100	−	7.84005i	0.834656	−	0.535935i
$215$	−6.41935	−	1.72006i	−0.437796	−	0.117307i
$216$		0			0
$217$	−1.72848	−	2.99382i	−0.117337	−	0.203233i
$218$	−4.38561	−	13.7381i	−0.297031	−	0.930460i
$219$		0			0
$220$	0.202710	+	2.14073i	0.0136667	+	0.144328i
$221$	−3.23423	−	3.17165i	−0.217558	−	0.213348i
$222$		0			0
$223$	−14.1824	+	3.80017i	−0.949726	+	0.254478i	−0.700246	−	0.713902i	$-0.746926\pi$
$223$	−14.1824	+	3.80017i	−0.949726	+	0.254478i	−0.249480	+	0.968380i	$0.580260\pi$
$224$	−7.36330	+	4.00181i	−0.491981	+	0.267382i
$225$		0			0
$226$	0.316509	+	6.70001i	0.0210539	+	0.445678i
$227$	8.65489	+	2.31907i	0.574445	+	0.153922i	0.534334	−	0.845273i	$-0.320562\pi$
$227$	8.65489	+	2.31907i	0.574445	+	0.153922i	0.0401107	+	0.999195i	$0.487229\pi$
$228$		0			0
$229$	−1.63656	+	1.63656i	−0.108147	+	0.108147i	−0.759110	−	0.650963i	$-0.774365\pi$
$229$	−1.63656	+	1.63656i	−0.108147	+	0.108147i	0.650963	+	0.759110i	$0.274365\pi$
$230$	3.38759	+	0.738325i	0.223371	+	0.0486837i
$231$		0			0
$232$	−7.29035	+	18.1481i	−0.478635	+	1.19148i
$233$			15.2245i			0.997391i	0.866777	+	0.498695i	$0.166187\pi$
$233$			15.2245i			0.997391i	−0.866777	+	0.498695i	$0.833813\pi$
$234$		0			0
$235$	3.04464			0.198610
$236$	26.1284	−	9.72188i	1.70081	−	0.632841i
$237$		0			0
$238$	−2.57185	−	0.560534i	−0.166708	−	0.0363341i
$239$	20.1260	+	20.1260i	1.30184	+	1.30184i	0.927149	+	0.374693i	$0.122252\pi$
$239$	20.1260	+	20.1260i	1.30184	+	1.30184i	0.374693	+	0.927149i	$0.377748\pi$
$240$		0			0
$241$	0.968043	−	3.61278i	0.0623571	−	0.232720i	−0.927713	−	0.373294i	$-0.878228\pi$
$241$	0.968043	−	3.61278i	0.0623571	−	0.232720i	0.990070	+	0.140574i	$0.0448949\pi$
$242$	−12.4373	+	0.587541i	−0.799502	+	0.0377686i
$243$		0			0
$244$	−25.6753	−	11.7500i	−1.64369	−	0.752219i
$245$	0.902396	+	3.36779i	0.0576520	+	0.215160i
$246$		0			0
$247$	0.225764	+	23.1088i	0.0143650	+	1.47038i
$248$	3.96150	−	5.27889i	0.251555	−	0.335210i
$249$		0			0
$250$	−9.26065	+	2.95628i	−0.585695	+	0.186971i
$251$	−19.4389	+	11.2231i	−1.22697	+	0.708393i	−0.966395	−	0.257060i	$-0.917246\pi$
$251$	−19.4389	+	11.2231i	−1.22697	+	0.708393i	−0.260577	+	0.965453i	$0.583913\pi$
$252$		0			0
$253$	1.29582	−	4.83608i	0.0814678	−	0.304042i
$254$	22.3886	−	14.3758i	1.40479	−	0.902017i
$255$		0			0
$256$	−12.5455	−	9.93022i	−0.784097	−	0.620639i
$257$	−25.8091	−	14.9009i	−1.60993	−	0.929494i	−0.989384	−	0.145324i	$-0.953578\pi$
$257$	−25.8091	−	14.9009i	−1.60993	−	0.929494i	−0.620546	−	0.784170i	$-0.713089\pi$
$258$		0			0
$259$			5.40858i			0.336073i
$260$	5.20389	−	0.544108i	0.322731	−	0.0337441i
$261$		0			0
$262$	1.76076	+	0.908616i	0.108780	+	0.0561345i
$263$	−2.11644	−	1.22193i	−0.130506	−	0.0753474i	0.433326	−	0.901237i	$-0.357340\pi$
$263$	−2.11644	−	1.22193i	−0.130506	−	0.0753474i	−0.563831	+	0.825890i	$0.690673\pi$
$264$		0			0
$265$	−0.263361	+	0.263361i	−0.0161782	+	0.0161782i
$266$	7.25567	+	11.2999i	0.444874	+	0.692838i
$267$		0			0
$268$	−9.26706	+	11.2057i	−0.566076	+	0.684495i
$269$	22.9614	−	13.2568i	1.39998	−	0.808280i	0.405592	−	0.914054i	$-0.367065\pi$
$269$	22.9614	−	13.2568i	1.39998	−	0.808280i	0.994390	+	0.105774i	$0.0337320\pi$
$270$		0			0
$271$	−1.72024	−	6.42004i	−0.104497	−	0.389990i	0.893790	−	0.448485i	$-0.148036\pi$
$271$	−1.72024	−	6.42004i	−0.104497	−	0.389990i	−0.998288	+	0.0584956i	$0.981370\pi$
$272$	−0.943273	−	4.93610i	−0.0571943	−	0.299295i
$273$		0			0
$274$	15.9551	−	17.5373i	0.963882	−	1.05946i
$275$	1.71566	+	6.40292i	0.103458	+	0.386111i
$276$		0			0
$277$	0.878646	+	1.52186i	0.0527927	+	0.0914397i	0.891214	−	0.453583i	$-0.149854\pi$
$277$	0.878646	+	1.52186i	0.0527927	+	0.0914397i	−0.838421	+	0.545023i	$0.816521\pi$
$278$	−1.01113	−	21.4041i	−0.0606437	−	1.28373i
$279$		0			0
$280$	2.39212	−	1.87660i	0.142956	−	0.112148i
$281$	−17.3570	−	17.3570i	−1.03543	−	1.03543i	−0.999349	−	0.0360826i	$-0.988512\pi$
$281$	−17.3570	−	17.3570i	−1.03543	−	1.03543i	−0.0360826	−	0.999349i	$-0.511488\pi$
$282$		0			0
$283$	−3.46233	−	1.99897i	−0.205814	−	0.118827i	0.393551	−	0.919303i	$-0.371247\pi$
$283$	−3.46233	−	1.99897i	−0.205814	−	0.118827i	−0.599364	+	0.800476i	$0.704580\pi$
$284$	7.09640	−	2.64044i	0.421094	−	0.156681i
$285$		0			0
$286$	−0.430244	−	7.54337i	−0.0254409	−	0.446049i
$287$		−	2.87952i		−	0.169973i
$288$		0			0
$289$	−7.71078	+	13.3555i	−0.453576	+	0.785616i
$290$	1.51096	−	6.93261i	0.0887268	−	0.407097i
$291$		0			0
$292$	2.08342	−	12.3301i	0.121923	−	0.721564i
$293$	−20.3123	−	5.44266i	−1.18666	−	0.317963i	−0.389093	−	0.921199i	$-0.627211\pi$
$293$	−20.3123	−	5.44266i	−1.18666	−	0.317963i	−0.797563	+	0.603235i	$0.793878\pi$
$294$		0			0
$295$	−8.75903	+	5.05703i	−0.509971	+	0.294432i
$296$	−9.49712	+	4.05360i	−0.552009	+	0.235611i
$297$		0			0
$298$	−7.40550	+	8.13987i	−0.428989	+	0.471530i
$299$	−11.7977	−	3.03796i	−0.682276	−	0.175690i
$300$		0			0
$301$	13.1069	−	3.51197i	0.755466	−	0.202427i
$302$	13.2620	−	4.23364i	0.763144	−	0.243619i
$303$		0			0
$304$	−14.4039	+	21.2095i	−0.826119	+	1.21645i
$305$	9.89482	+	2.65131i	0.566576	+	0.151814i
$306$		0			0
$307$	−1.73231	−	1.73231i	−0.0988683	−	0.0988683i	0.655943	−	0.754811i	$-0.272271\pi$
$307$	−1.73231	−	1.73231i	−0.0988683	−	0.0988683i	−0.754811	+	0.655943i	$0.772271\pi$
$308$	−2.54388	−	3.57836i	−0.144951	−	0.203896i
$309$		0			0
$310$	−1.09803	+	2.12782i	−0.0623640	+	0.120852i
$311$	2.28061			0.129321			0.0646606	−	0.997907i	$-0.479404\pi$
$311$	2.28061			0.129321			0.0646606	+	0.997907i	$0.479404\pi$
$312$		0			0
$313$	32.2565			1.82325			0.911623	−	0.411028i	$-0.134830\pi$
$313$	32.2565			1.82325			0.911623	+	0.411028i	$0.134830\pi$
$314$	−6.88639	+	13.3448i	−0.388621	+	0.753090i
$315$		0			0
$316$	5.29612	−	3.76505i	0.297930	−	0.211800i
$317$	17.9781	+	17.9781i	1.00975	+	1.00975i	0.999952	+	0.00979695i	$0.00311852\pi$
$317$	17.9781	+	17.9781i	1.00975	+	1.00975i	0.00979695	+	0.999952i	$0.496881\pi$
$318$		0			0
$319$	−9.89691	−	2.65187i	−0.554121	−	0.148476i
$320$	5.08803	+	2.79394i	0.284429	+	0.156186i
$321$		0			0
$322$	−6.74377	+	2.15281i	−0.375816	+	0.119972i
$323$	−7.77826	+	2.08418i	−0.432794	+	0.115967i
$324$		0			0
$325$	15.5384	−	4.32664i	0.861916	−	0.239999i
$326$	11.0307	−	12.1246i	0.610934	−	0.671518i
$327$		0			0
$328$	5.05625	−	2.15813i	0.279185	−	0.119163i
$329$	−5.38361	+	3.10823i	−0.296808	+	0.171362i
$330$		0			0
$331$	28.0985	+	7.52896i	1.54443	+	0.413829i	0.927694	−	0.373341i	$-0.121788\pi$
$331$	28.0985	+	7.52896i	1.54443	+	0.413829i	0.616736	+	0.787170i	$0.288454\pi$
$332$	8.08573	+	1.36625i	0.443762	+	0.0749826i
$333$		0			0
$334$	2.70947	−	12.4316i	0.148255	−	0.680226i
$335$	2.63770	−	4.56864i	0.144113	−	0.249611i
$336$		0			0
$337$			13.9376i			0.759229i	0.925145	+	0.379615i	$0.123943\pi$
$337$			13.9376i			0.759229i	−0.925145	+	0.379615i	$0.876057\pi$
$338$	−18.3438	+	1.22616i	−0.997773	+	0.0666941i
$339$		0			0
$340$	0.635787	+	1.70873i	0.0344804	+	0.0926690i
$341$	2.99443	+	1.72884i	0.162158	+	0.0936217i
$342$		0			0
$343$	−12.3667	−	12.3667i	−0.667739	−	0.667739i
$344$	15.9901	+	20.3827i	0.862126	+	1.09896i
$345$		0			0
$346$	0.930729	+	19.7021i	0.0500363	+	1.05919i
$347$	14.4501	+	25.0283i	0.775720	+	1.34359i	0.934389	+	0.356255i	$0.115947\pi$
$347$	14.4501	+	25.0283i	0.775720	+	1.34359i	−0.158668	+	0.987332i	$0.550720\pi$
$348$		0			0
$349$	−5.08095	−	18.9624i	−0.271977	−	1.01503i	−0.957840	−	0.287302i	$-0.907242\pi$
$349$	−5.08095	−	18.9624i	−0.271977	−	1.01503i	0.685863	−	0.727731i	$-0.259425\pi$
$350$	6.30731	−	6.93278i	0.337140	−	0.370572i
$351$		0			0
$352$	4.37680	−	7.14879i	0.233284	−	0.381032i
$353$	4.83344	+	18.0387i	0.257258	+	0.960101i	0.966820	+	0.255458i	$0.0822262\pi$
$353$	4.83344	+	18.0387i	0.257258	+	0.960101i	−0.709562	+	0.704643i	$0.751107\pi$
$354$		0			0
$355$	−2.37893	+	1.37348i	−0.126261	+	0.0728966i
$356$	3.27501	+	2.70843i	0.173575	+	0.143546i
$357$		0			0
$358$	7.09026	+	11.0422i	0.374732	+	0.583600i
$359$	−16.3844	+	16.3844i	−0.864734	+	0.864734i	−0.991884	−	0.127149i	$-0.959417\pi$
$359$	−16.3844	+	16.3844i	−0.864734	+	0.864734i	0.127149	+	0.991884i	$0.459417\pi$
$360$		0			0
$361$	19.1236	+	11.0410i	1.00651	+	0.581107i
$362$	26.1237	+	13.4808i	1.37303	+	0.708534i
$363$		0			0
$364$	−8.64618	+	6.27468i	−0.453183	+	0.328883i
$365$			4.53666i			0.237460i
$366$		0			0
$367$	25.4992	+	14.7220i	1.33105	+	0.768480i	0.985460	−	0.169907i	$-0.0543466\pi$
$367$	25.4992	+	14.7220i	1.33105	+	0.768480i	0.345587	+	0.938387i	$0.387680\pi$
$368$	−8.83450	−	10.2282i	−0.460530	−	0.533179i
$369$		0			0
$370$	3.15230	−	2.02410i	0.163880	−	0.105228i
$371$	0.196821	−	0.734545i	0.0102184	−	0.0381357i
$372$		0			0
$373$	−20.6658	+	11.9314i	−1.07003	+	0.617785i	−0.928191	−	0.372104i	$-0.878636\pi$
$373$	−20.6658	+	11.9314i	−1.07003	+	0.617785i	−0.141844	+	0.989889i	$0.545303\pi$
$374$	2.50807	−	0.800651i	0.129689	−	0.0414007i
$375$		0			0
$376$	−9.49274	−	7.12374i	−0.489551	−	0.367379i
$377$	−6.21711	+	24.1436i	−0.320197	+	1.24346i
$378$		0			0
$379$	3.24058	+	12.0940i	0.166457	+	0.621227i	0.997850	+	0.0655416i	$0.0208775\pi$
$379$	3.24058	+	12.0940i	0.166457	+	0.621227i	−0.831393	+	0.555686i	$0.812456\pi$
$380$	3.87058	−	8.45770i	0.198556	−	0.433871i
$381$		0			0
$382$	36.8027	−	1.73856i	1.88299	−	0.0889527i
$383$	8.74431	−	32.6342i	0.446814	−	1.66753i	−0.264290	−	0.964443i	$-0.585138\pi$
$383$	8.74431	−	32.6342i	0.446814	−	1.66753i	0.711103	−	0.703088i	$-0.248196\pi$
$384$		0			0
$385$	1.12629	+	1.12629i	0.0574011	+	0.0574011i
$386$	−20.7662	−	4.52600i	−1.05697	−	0.230367i
$387$		0			0
$388$	0.790141	+	2.12357i	0.0401133	+	0.107808i
$389$	−29.5448			−1.49798			−0.748990	−	0.662581i	$-0.769461\pi$
$389$	−29.5448			−1.49798			−0.748990	+	0.662581i	$0.769461\pi$
$390$		0			0
$391$		−	4.24501i		−	0.214679i
$392$	5.06630	−	12.6117i	0.255887	−	0.636986i
$393$		0			0
$394$	−27.5783	−	6.01069i	−1.38937	−	0.302814i
$395$	−1.66696	+	1.66696i	−0.0838736	+	0.0838736i
$396$		0			0
$397$	−28.0508	−	7.51619i	−1.40783	−	0.377227i	−0.526679	−	0.850064i	$-0.676563\pi$
$397$	−28.0508	−	7.51619i	−1.40783	−	0.377227i	−0.881150	+	0.472838i	$0.843230\pi$
$398$	−0.751413	−	15.9062i	−0.0376649	−	0.797308i
$399$		0			0
$400$	16.9007	+	5.87929i	0.845035	+	0.293965i
$401$	5.34143	−	1.43123i	0.266738	−	0.0714723i	−0.122971	−	0.992410i	$-0.539242\pi$
$401$	5.34143	−	1.43123i	0.266738	−	0.0714723i	0.389709	+	0.920938i	$0.372576\pi$
$402$		0			0
$403$	4.13532	−	7.32697i	0.205995	−	0.364982i
$404$	22.8069	−	2.15962i	1.13469	−	0.107445i
$405$		0			0
$406$	4.40568	+	13.8009i	0.218650	+	0.684930i
$407$	−2.70485	−	4.68493i	−0.134074	−	0.232223i
$408$		0			0
$409$	−17.8385	−	4.77981i	−0.882056	−	0.236346i	−0.210762	−	0.977537i	$-0.567595\pi$
$409$	−17.8385	−	4.77981i	−0.882056	−	0.236346i	−0.671294	+	0.741191i	$0.734261\pi$
$410$	−1.67828	+	1.07763i	−0.0828843	+	0.0532203i
$411$		0			0
$412$	−2.88433	−	4.05725i	−0.142101	−	0.199887i
$413$	10.3253	−	17.8840i	0.508075	−	0.880012i
$414$		0			0
$415$	−2.97501			−0.146038
$416$	−17.4980	−	10.4794i	−0.857912	−	0.513796i
$417$		0			0
$418$	−11.9360	−	6.15939i	−0.583808	−	0.301266i
$419$	−14.1415	+	24.4939i	−0.690859	+	1.19660i	0.280698	+	0.959796i	$0.409434\pi$
$419$	−14.1415	+	24.4939i	−0.690859	+	1.19660i	−0.971557	+	0.236807i	$0.923899\pi$
$420$		0			0
$421$	19.6915	+	19.6915i	0.959704	+	0.959704i	0.999219	−	0.0395149i	$-0.0125812\pi$
$421$	19.6915	+	19.6915i	0.959704	+	0.959704i	−0.0395149	+	0.999219i	$0.512581\pi$
$422$	1.36087	−	0.873819i	0.0662461	−	0.0425368i
$423$		0			0
$424$	1.43733	−	0.204919i	0.0698028	−	0.00995174i
$425$	2.81017	+	4.86736i	0.136313	+	0.236102i
$426$		0			0
$427$	−20.2030	+	5.41337i	−0.977691	+	0.261971i
$428$	20.4293	−	1.93448i	0.987488	−	0.0935068i
$429$		0			0
$430$	−6.95199	−	6.32479i	−0.335255	−	0.305009i
$431$	−30.7854	+	8.24891i	−1.48288	+	0.397336i	−0.907326	−	0.420428i	$-0.861880\pi$
$431$	−30.7854	+	8.24891i	−1.48288	+	0.397336i	−0.575553	+	0.817764i	$0.695213\pi$
$432$		0			0
$433$	13.1701	−	7.60376i	0.632915	−	0.365414i	−0.148965	−	0.988842i	$-0.547594\pi$
$433$	13.1701	−	7.60376i	0.632915	−	0.365414i	0.781880	+	0.623429i	$0.214261\pi$
$434$	−0.230694	−	4.88344i	−0.0110737	−	0.234412i
$435$		0			0
$436$	3.39791	−	20.1095i	0.162730	−	0.963069i
$437$	−15.3136	+	15.3136i	−0.732548	+	0.732548i
$438$		0			0
$439$	1.65131	−	2.86016i	0.0788129	−	0.136508i	−0.823925	−	0.566699i	$-0.808220\pi$
$439$	1.65131	−	2.86016i	0.0788129	−	0.136508i	0.902738	+	0.430191i	$0.141554\pi$
$440$	−1.13357	+	2.82182i	−0.0540407	+	0.134525i
$441$		0			0
$442$	−2.00771	−	6.08344i	−0.0954972	−	0.289360i
$443$	12.1161			0.575654			0.287827	−	0.957682i	$-0.407067\pi$
$443$	12.1161			0.575654			0.287827	+	0.957682i	$0.407067\pi$
$444$		0			0
$445$	−1.33525	−	0.770906i	−0.0632968	−	0.0365444i
$446$	−20.2882	−	4.42183i	−0.960676	−	0.209380i
$447$		0			0
$448$	−11.8491	+	0.253975i	−0.559817	+	0.0119992i
$449$	−2.46287	+	9.19155i	−0.116230	+	0.433776i	−0.999376	−	0.0353221i	$-0.988754\pi$
$449$	−2.46287	+	9.19155i	−0.116230	+	0.433776i	0.883146	+	0.469098i	$0.155421\pi$
$450$		0			0
$451$	1.44006	+	2.49425i	0.0678096	+	0.117450i
$452$	−3.94736	+	8.62548i	−0.185668	+	0.405709i
$453$		0			0
$454$	9.37303	+	8.52741i	0.439898	+	0.400211i
$455$	2.71365	−	2.76720i	0.127218	−	0.129728i
$456$		0			0
$457$	−3.13824	−	11.7121i	−0.146800	−	0.547867i	−0.999669	−	0.0257405i	$-0.991806\pi$
$457$	−3.13824	−	11.7121i	−0.146800	−	0.547867i	0.852868	−	0.522126i	$-0.174861\pi$
$458$	−3.11809	+	0.995387i	−0.145699	+	0.0465114i
$459$		0			0
$460$	3.77852	+	3.12483i	0.176174	+	0.145696i
$461$	6.26259	−	23.3723i	0.291678	−	1.08856i	−0.652142	−	0.758097i	$-0.726129\pi$
$461$	6.26259	−	23.3723i	0.291678	−	1.08856i	0.943820	−	0.330460i	$-0.107204\pi$
$462$		0			0
$463$	12.7547	−	12.7547i	0.592763	−	0.592763i	−0.345614	−	0.938377i	$-0.612329\pi$
$463$	12.7547	−	12.7547i	0.592763	−	0.592763i	0.938377	+	0.345614i	$0.112329\pi$
$464$	−20.9316	+	18.0796i	−0.971727	+	0.839323i
$465$		0			0
$466$	−9.87350	+	19.1334i	−0.457381	+	0.886336i
$467$		−	18.1587i		−	0.840286i	−0.907458	−	0.420143i	$-0.861980\pi$
$467$		−	18.1587i		−	0.840286i	0.907458	−	0.420143i	$-0.138020\pi$
$468$		0			0
$469$			10.7712i			0.497367i
$470$	3.82634	+	1.97453i	0.176496	+	0.0910782i
$471$		0			0
$472$	39.1417	+	4.72699i	1.80164	+	0.217577i
$473$	−9.59686	+	9.59686i	−0.441264	+	0.441264i
$474$		0			0
$475$	7.42117	−	27.6962i	0.340507	−	1.27079i
$476$	−2.86864	−	2.37236i	−0.131484	−	0.108737i
$477$		0			0
$478$	12.2410	+	38.3455i	0.559892	+	1.75388i
$479$	−4.24253	−	15.8334i	−0.193846	−	0.723444i	−0.992562	−	0.121736i	$-0.961154\pi$
$479$	−4.24253	−	15.8334i	−0.193846	−	0.723444i	0.798716	−	0.601708i	$-0.205513\pi$
$480$		0			0
$481$	−11.3348	+	6.69263i	−0.516822	+	0.305158i
$482$	3.55957	−	3.91256i	0.162134	−	0.178212i
$483$		0			0
$484$	−16.0116	−	7.32754i	−0.727800	−	0.333070i
$485$	−0.411007	−	0.711885i	−0.0186629	−	0.0323251i
$486$		0			0
$487$	−9.33917	+	34.8542i	−0.423198	+	1.57940i	0.344629	+	0.938739i	$0.388005\pi$
$487$	−9.33917	+	34.8542i	−0.423198	+	1.57940i	−0.767827	+	0.640658i	$0.778662\pi$
$488$	−24.6472	−	31.4180i	−1.11573	−	1.42222i
$489$		0			0
$490$	−1.05002	+	4.81769i	−0.0474349	+	0.217641i
$491$	12.9846	+	7.49664i	0.585985	+	0.338319i	0.763508	−	0.645798i	$-0.223475\pi$
$491$	12.9846	+	7.49664i	0.585985	+	0.338319i	−0.177523	+	0.984117i	$0.556808\pi$
$492$		0			0
$493$	−8.68730			−0.391256
$494$	−14.7029	+	29.1883i	−0.661516	+	1.31324i
$495$		0			0
$496$	8.40210	−	4.06510i	0.377266	−	0.182528i
$497$	2.80433	−	4.85724i	0.125791	−	0.217877i
$498$		0			0
$499$	−30.5157	+	30.5157i	−1.36607	+	1.36607i	−0.500105	+	0.865965i	$0.666705\pi$
$499$	−30.5157	+	30.5157i	−1.36607	+	1.36607i	−0.865965	+	0.500105i	$0.833295\pi$
$500$	−13.5555	−	2.29048i	−0.606221	−	0.102433i
$501$		0			0
$502$	−31.7082	+	1.49790i	−1.41521	+	0.0668546i
$503$	−30.7732	+	17.7669i	−1.37211	+	0.792187i	−0.991193	−	0.132424i	$-0.957724\pi$
$503$	−30.7732	+	17.7669i	−1.37211	+	0.792187i	−0.380914	+	0.924610i	$0.624391\pi$
$504$		0			0
$505$	−8.02797	+	2.15109i	−0.357240	+	0.0957222i
$506$	4.76485	−	5.23736i	0.211823	−	0.232829i
$507$		0			0
$508$	37.4599	−	3.54714i	1.66201	−	0.157379i
$509$	−17.3479	+	4.64835i	−0.768931	+	0.206034i	−0.621899	−	0.783097i	$-0.713639\pi$
$509$	−17.3479	+	4.64835i	−0.768931	+	0.206034i	−0.147032	+	0.989132i	$0.546972\pi$
$510$		0			0
$511$	−4.63141	−	8.02185i	−0.204882	−	0.354866i
$512$	−9.32657	−	20.6159i	−0.412180	−	0.911102i
$513$		0			0
$514$	−22.7719	−	35.4646i	−1.00443	−	1.56428i
$515$	1.27702	+	1.27702i	0.0562724	+	0.0562724i
$516$		0			0
$517$	3.10887	−	5.38472i	0.136728	−	0.236820i
$518$	−3.50761	+	6.79722i	−0.154115	+	0.298653i
$519$		0			0
$520$	6.89284	+	2.69105i	0.302271	+	0.118010i
$521$	33.0188			1.44658			0.723289	−	0.690545i	$-0.242629\pi$
$521$	33.0188			1.44658			0.723289	+	0.690545i	$0.242629\pi$
$522$		0			0
$523$	0.905353	−	1.56812i	0.0395883	−	0.0685690i	−0.845552	−	0.533893i	$-0.820729\pi$
$523$	0.905353	−	1.56812i	0.0395883	−	0.0685690i	0.885141	+	0.465324i	$0.154062\pi$
$524$	1.62357	+	2.28380i	0.0709261	+	0.0997684i
$525$		0			0
$526$	−1.86738	−	2.90823i	−0.0814217	−	0.126805i
$527$	2.83176	+	0.758768i	0.123353	+	0.0330524i
$528$		0			0
$529$	5.79177	+	10.0316i	0.251816	+	0.436158i
$530$	−0.501776	+	0.160182i	−0.0217957	+	0.00695786i
$531$		0			0
$532$	1.79029	+	18.9066i	0.0776190	+	0.819703i
$533$	6.03462	−	3.56315i	0.261389	−	0.154337i
$534$		0			0
$535$	−7.19106	+	1.92684i	−0.310897	+	0.0833045i
$536$	−18.9135	+	8.07274i	−0.816940	+	0.348689i
$537$		0			0
$538$	37.4541	−	1.76934i	1.61476	−	0.0762815i
$539$	6.87768	+	1.84287i	0.296243	+	0.0793780i
$540$		0			0
$541$	−27.7884	+	27.7884i	−1.19472	+	1.19472i	−0.218990	+	0.975727i	$0.570276\pi$
$541$	−27.7884	+	27.7884i	−1.19472	+	1.19472i	−0.975727	+	0.218990i	$0.929724\pi$
$542$	2.00165	−	9.18399i	0.0859783	−	0.394486i
$543$		0			0
$544$	2.01574	−	6.81517i	0.0864241	−	0.292198i
$545$			7.39896i			0.316937i
$546$		0			0
$547$	6.37762			0.272687			0.136344	−	0.990662i	$-0.456465\pi$
$547$	6.37762			0.272687			0.136344	+	0.990662i	$0.456465\pi$
$548$	31.4249	−	11.6926i	1.34240	−	0.499484i
$549$		0			0
$550$	−1.99632	+	9.15950i	−0.0851232	+	0.390562i
$551$	31.3388	+	31.3388i	1.33508	+	1.33508i
$552$		0			0
$553$	1.24578	−	4.64933i	0.0529761	−	0.197710i
$554$	0.117270	+	2.48242i	0.00498231	+	0.105468i
$555$		0			0
$556$	12.6104	−	27.5553i	0.534799	−	1.16860i
$557$	1.53541	+	5.73023i	0.0650574	+	0.242798i	0.990795	−	0.135368i	$-0.0432217\pi$
$557$	1.53541	+	5.73023i	0.0650574	+	0.242798i	−0.925738	+	0.378166i	$0.876555\pi$
$558$		0			0
$559$	23.5786	+	23.1224i	0.997269	+	0.977972i
$560$	4.22331	−	0.807061i	0.178468	−	0.0341046i
$561$		0			0
$562$	−10.5569	−	33.0698i	−0.445315	−	1.39497i
$563$	−5.39506	+	3.11484i	−0.227375	+	0.131275i	−0.609360	−	0.792893i	$-0.708574\pi$
$563$	−5.39506	+	3.11484i	−0.227375	+	0.131275i	0.381986	+	0.924168i	$0.375240\pi$
$564$		0			0
$565$	0.890693	−	3.32411i	0.0374717	−	0.139846i
$566$	−3.05488	−	4.75761i	−0.128406	−	0.199977i
$567$		0			0
$568$	10.6308	+	1.28384i	0.446058	+	0.0538687i
$569$	1.68213	+	0.971181i	0.0705187	+	0.0407140i	0.534845	−	0.844950i	$-0.320370\pi$
$569$	1.68213	+	0.971181i	0.0705187	+	0.0407140i	−0.464326	+	0.885664i	$0.653703\pi$
$570$		0			0
$571$			31.5350i			1.31970i	0.751398	+	0.659850i	$0.229380\pi$
$571$			31.5350i			1.31970i	−0.751398	+	0.659850i	$0.770620\pi$
$572$	4.35137	−	9.75913i	0.181940	−	0.408050i
$573$		0			0
$574$	1.86744	−	3.61883i	0.0779456	−	0.151047i
$575$	13.0902	+	7.55764i	0.545900	+	0.315175i
$576$		0			0
$577$	17.6927	−	17.6927i	0.736558	−	0.736558i	−0.235352	−	0.971910i	$-0.575624\pi$
$577$	17.6927	−	17.6927i	0.736558	−	0.736558i	0.971910	+	0.235352i	$0.0756242\pi$
$578$	−18.3519	+	11.7838i	−0.763338	+	0.490142i
$579$		0			0
$580$	6.39488	−	7.73263i	0.265533	−	0.321080i
$581$	5.26050	−	3.03715i	0.218242	−	0.126002i
$582$		0			0
$583$	0.196861	+	0.734696i	0.00815316	+	0.0304280i
$584$	10.6147	−	14.1446i	0.439240	−	0.585310i
$585$		0			0
$586$	−21.9977	−	20.0131i	−0.908716	−	0.826733i
$587$	−7.64218	−	28.5210i	−0.315427	−	1.17719i	−0.923592	−	0.383377i	$-0.874761\pi$
$587$	−7.64218	−	28.5210i	−0.315427	−	1.17719i	0.608165	−	0.793810i	$-0.291906\pi$
$588$		0			0
$589$	−7.47818	−	12.9526i	−0.308133	−	0.533702i
$590$	−14.2875	+	0.674944i	−0.588207	+	0.0277870i
$591$		0			0
$592$	−14.5643	−	1.06479i	−0.598591	−	0.0437624i
$593$	20.5469	+	20.5469i	0.843759	+	0.843759i	0.989346	−	0.145586i	$-0.0465069\pi$
$593$	20.5469	+	20.5469i	0.843759	+	0.843759i	−0.145586	+	0.989346i	$0.546507\pi$
$594$		0			0
$595$	1.16957	+	0.675250i	0.0479476	+	0.0276825i
$596$	−14.5858	+	5.42709i	−0.597456	+	0.222302i
$597$		0			0
$598$	−12.8565	−	11.4690i	−0.525741	−	0.469004i
$599$			28.2451i			1.15407i	0.816721	+	0.577033i	$0.195789\pi$
$599$			28.2451i			1.15407i	−0.816721	+	0.577033i	$0.804211\pi$
$600$		0			0
$601$	−2.74994	+	4.76304i	−0.112172	+	0.194288i	−0.916646	−	0.399700i	$-0.869114\pi$
$601$	−2.74994	+	4.76304i	−0.112172	+	0.194288i	0.804473	+	0.593989i	$0.202448\pi$
$602$	18.7496	+	4.08648i	0.764177	+	0.166553i
$603$		0			0
$604$	19.4126	+	3.28016i	0.789889	+	0.133468i
$605$	6.17059	+	1.65341i	0.250870	+	0.0672205i
$606$		0			0
$607$	−1.25794	+	0.726274i	−0.0510584	+	0.0294786i	−0.525312	−	0.850910i	$-0.676051\pi$
$607$	−1.25794	+	0.726274i	−0.0510584	+	0.0294786i	0.474254	+	0.880388i	$0.342718\pi$
$608$	−31.8569	+	17.3136i	−1.29197	+	0.702161i
$609$		0			0
$610$	10.7158	+	9.74908i	0.433872	+	0.394729i
$611$	−13.1757	−	7.43632i	−0.533031	−	0.300841i
$612$		0			0
$613$	30.9474	−	8.29232i	1.24995	−	0.334924i	0.427634	−	0.903952i	$-0.359347\pi$
$613$	30.9474	−	8.29232i	1.24995	−	0.334924i	0.822318	+	0.569028i	$0.192681\pi$
$614$	−1.05363	−	3.30053i	−0.0425210	−	0.133199i
$615$		0			0
$616$	−0.876356	−	6.14687i	−0.0353094	−	0.247665i
$617$	4.26824	+	1.14367i	0.171833	+	0.0460425i	0.343710	−	0.939076i	$-0.388316\pi$
$617$	4.26824	+	1.14367i	0.171833	+	0.0460425i	−0.171877	+	0.985118i	$0.554983\pi$
$618$		0			0
$619$	−8.69550	−	8.69550i	−0.349502	−	0.349502i	0.510422	−	0.859924i	$-0.329489\pi$
$619$	−8.69550	−	8.69550i	−0.349502	−	0.349502i	−0.859924	+	0.510422i	$0.829489\pi$
$620$	−2.75990	+	1.96203i	−0.110840	+	0.0787970i
$621$		0			0
$622$	2.86614	+	1.47903i	0.114922	+	0.0593038i
$623$	3.14803			0.126123
$624$		0			0
$625$	−17.3801			−0.695204
$626$	40.5383	+	20.9192i	1.62024	+	0.836099i
$627$		0			0
$628$	−17.3089	+	12.3050i	−0.690700	+	0.491024i
$629$	−3.24329	−	3.24329i	−0.129319	−	0.129319i
$630$		0			0
$631$	−9.04870	−	2.42459i	−0.360223	−	0.0965215i	0.0741682	−	0.997246i	$-0.476370\pi$
$631$	−9.04870	−	2.42459i	−0.360223	−	0.0965215i	−0.434391	+	0.900724i	$0.643037\pi$
$632$	9.09761	−	1.29704i	0.361884	−	0.0515935i
$633$		0			0
$634$	10.9346	+	34.2531i	0.434270	+	1.36037i
$635$	−13.1858	+	3.53312i	−0.523261	+	0.140207i
$636$		0			0
$637$	4.32047	−	16.7782i	0.171183	−	0.664775i
$638$	−10.7181	−	9.75114i	−0.424334	−	0.386051i
$639$		0			0
$640$	4.58242	+	6.81100i	0.181136	+	0.269228i
$641$	31.6965	−	18.3000i	1.25194	−	0.722805i	0.280442	−	0.959871i	$-0.409519\pi$
$641$	31.6965	−	18.3000i	1.25194	−	0.722805i	0.971494	+	0.237066i	$0.0761856\pi$
$642$		0			0
$643$	−13.8446	−	3.70965i	−0.545977	−	0.146294i	−0.0247210	−	0.999694i	$-0.507870\pi$
$643$	−13.8446	−	3.70965i	−0.545977	−	0.146294i	−0.521256	+	0.853400i	$0.674536\pi$
$644$	−9.87137	−	1.66797i	−0.388987	−	0.0657272i
$645$		0			0
$646$	−11.1270	−	2.42512i	−0.437784	−	0.0954152i
$647$	−16.5697	+	28.6996i	−0.651422	+	1.12830i	0.331356	+	0.943506i	$0.392494\pi$
$647$	−16.5697	+	28.6996i	−0.651422	+	1.12830i	−0.982778	+	0.184790i	$0.940839\pi$
$648$		0			0
$649$			20.6549i			0.810774i
$650$	22.3338	+	4.63958i	0.876003	+	0.181979i
$651$		0			0
$652$	21.7259	−	8.08381i	0.850853	−	0.316586i
$653$	35.8657	+	20.7071i	1.40353	+	0.810330i	0.994753	−	0.102303i	$-0.0326210\pi$
$653$	35.8657	+	20.7071i	1.40353	+	0.810330i	0.408780	+	0.912633i	$0.365954\pi$
$654$		0			0
$655$	−0.718828	−	0.718828i	−0.0280869	−	0.0280869i
$656$	7.75403	+	0.566890i	0.302744	+	0.0221333i
$657$		0			0
$658$	−8.78161	+	0.414845i	−0.342343	+	0.0161723i
$659$	−14.1419	−	24.4945i	−0.550889	−	0.954168i	−0.998211	−	0.0597950i	$-0.980955\pi$
$659$	−14.1419	−	24.4945i	−0.550889	−	0.954168i	0.447321	−	0.894373i	$-0.352378\pi$
$660$		0			0
$661$	−6.42654	−	23.9842i	−0.249963	−	0.932876i	−0.970823	−	0.239796i	$-0.922920\pi$
$661$	−6.42654	−	23.9842i	−0.249963	−	0.932876i	0.720860	−	0.693081i	$-0.243747\pi$
$662$	30.4299	+	27.6846i	1.18269	+	1.07599i
$663$		0			0
$664$	9.27567	+	6.96084i	0.359966	+	0.270133i
$665$	−1.78322	−	6.65505i	−0.0691502	−	0.258072i
$666$		0			0
$667$	−20.2334	+	11.6817i	−0.783440	+	0.452319i
$668$	11.4673	−	13.8662i	0.443684	−	0.536500i
$669$		0			0
$670$	6.27781	−	4.03100i	0.242533	−	0.155731i
$671$	14.7927	−	14.7927i	0.571064	−	0.571064i
$672$		0			0
$673$	19.3181	+	11.1533i	0.744658	+	0.429929i	0.823761	−	0.566938i	$-0.191872\pi$
$673$	19.3181	+	11.1533i	0.744658	+	0.429929i	−0.0791022	+	0.996867i	$0.525205\pi$
$674$	−9.03890	+	17.5160i	−0.348165	+	0.674693i
$675$		0			0
$676$	−23.8488	−	10.3555i	−0.917260	−	0.398288i
$677$		−	7.36423i		−	0.283030i	−0.989936	−	0.141515i	$-0.954803\pi$
$677$		−	7.36423i		−	0.283030i	0.989936	−	0.141515i	$-0.0451974\pi$
$678$		0			0
$679$	1.45351	+	0.839184i	0.0557805	+	0.0322049i
$680$	−0.309134	+	2.55977i	−0.0118547	+	0.0981627i
$681$		0			0
$682$	2.64205	+	4.11468i	0.101169	+	0.157559i
$683$	−1.34151	+	5.00660i	−0.0513316	+	0.191572i	−0.986831	−	0.161757i	$-0.948284\pi$
$683$	−1.34151	+	5.00660i	−0.0513316	+	0.191572i	0.935499	+	0.353329i	$0.114951\pi$
$684$		0			0
$685$	−10.5346	+	6.08214i	−0.402506	+	0.232387i
$686$	−7.52169	−	23.5620i	−0.287179	−	0.899600i
$687$		0			0
$688$	6.87677	+	35.9858i	0.262174	+	1.37195i
$689$	1.78294	−	0.496455i	0.0679245	−	0.0189134i
$690$		0			0
$691$	6.75090	+	25.1947i	0.256816	+	0.958451i	0.967071	+	0.254506i	$0.0819130\pi$
$691$	6.75090	+	25.1947i	0.256816	+	0.958451i	−0.710255	+	0.703945i	$0.751420\pi$
$692$	−11.6076	+	25.3641i	−0.441256	+	0.964200i
$693$		0			0
$694$	1.92860	+	40.8254i	0.0732086	+	1.54971i
$695$	−2.84544	+	10.6193i	−0.107934	+	0.402814i
$696$		0			0
$697$	1.72672	+	1.72672i	0.0654044	+	0.0654044i
$698$	5.91213	−	27.1260i	0.223777	−	1.02674i
$699$		0			0
$700$	12.4228	−	4.62229i	0.469537	−	0.174706i
$701$	2.13901			0.0807892			0.0403946	−	0.999184i	$-0.487138\pi$
$701$	2.13901			0.0807892			0.0403946	+	0.999184i	$0.487138\pi$
$702$		0			0
$703$			23.3999i			0.882545i
$704$	10.1367	−	6.14576i	0.382042	−	0.231627i
$705$		0			0
$706$	−5.62413	+	25.8047i	−0.211667	+	0.971171i
$707$	11.9993	−	11.9993i	0.451279	−	0.451279i
$708$		0			0
$709$	−31.8967	−	8.54671i	−1.19791	−	0.320978i	−0.395901	−	0.918293i	$-0.629567\pi$
$709$	−31.8967	−	8.54671i	−1.19791	−	0.320978i	−0.802007	+	0.597315i	$0.796234\pi$
$710$	−3.88045	+	0.183313i	−0.145631	+	0.00687962i
$711$		0			0
$712$	2.35937	+	5.52774i	0.0884212	+	0.207161i
$713$	7.61569	−	2.04062i	0.285210	−	0.0764218i
$714$		0			0
$715$	−0.966691	+	3.75406i	−0.0361522	+	0.140394i
$716$	1.74948	+	18.4755i	0.0653810	+	0.690462i
$717$		0			0
$718$	−31.2167	+	9.96532i	−1.16500	+	0.371902i
$719$	−24.1212	−	41.7791i	−0.899568	−	1.55810i	−0.828047	−	0.560659i	$-0.810548\pi$
$719$	−24.1212	−	41.7791i	−0.899568	−	1.55810i	−0.0715216	−	0.997439i	$-0.522785\pi$
$720$		0			0
$721$	−3.56176	−	0.954371i	−0.132647	−	0.0355426i
$722$	16.8732	+	26.2780i	0.627954	+	0.977964i
$723$		0			0
$724$	24.0883	+	33.8839i	0.895234	+	1.25928i
$725$	15.4665	−	26.7888i	0.574412	−	0.994910i
$726$		0			0
$727$	35.9735			1.33418			0.667092	−	0.744976i	$-0.267539\pi$
$727$	35.9735			1.33418			0.667092	+	0.744976i	$0.267539\pi$
$728$	−14.9354	+	2.27841i	−0.553541	+	0.0844436i
$729$		0			0
$730$	−2.94214	+	5.70143i	−0.108894	+	0.211020i
$731$	−5.75364	+	9.96560i	−0.212806	+	0.368591i
$732$		0			0
$733$	7.99326	+	7.99326i	0.295238	+	0.295238i	0.839145	−	0.543907i	$-0.183056\pi$
$733$	7.99326	+	7.99326i	0.295238	+	0.295238i	−0.543907	+	0.839145i	$0.683056\pi$
$734$	22.4985	+	35.0387i	0.830433	+	1.29330i
$735$		0			0
$736$	−4.46951	−	18.5836i	−0.164748	−	0.685001i
$737$	−5.38670	−	9.33004i	−0.198422	−	0.343677i
$738$		0			0
$739$	10.6104	−	2.84304i	0.390308	−	0.104583i	−0.0583274	−	0.998298i	$-0.518577\pi$
$739$	10.6104	−	2.84304i	0.390308	−	0.104583i	0.448636	+	0.893715i	$0.351910\pi$
$740$	5.27433	−	0.499435i	0.193888	−	0.0183596i
$741$		0			0
$742$	0.723726	−	0.795494i	0.0265688	−	0.0292035i
$743$	−9.10445	+	2.43953i	−0.334010	+	0.0894977i	−0.421926	−	0.906630i	$-0.638646\pi$
$743$	−9.10445	+	2.43953i	−0.334010	+	0.0894977i	0.0879163	+	0.996128i	$0.471979\pi$
$744$		0			0
$745$	4.88959	−	2.82301i	0.179141	−	0.103427i
$746$	−33.7095	+	1.59244i	−1.23419	+	0.0583035i
$747$		0			0
$748$	3.67125	+	0.620332i	0.134234	+	0.0226816i
$749$	10.7484	−	10.7484i	0.392736	−	0.392736i
$750$		0			0
$751$	11.9625	−	20.7197i	0.436519	−	0.756073i	−0.560899	−	0.827884i	$-0.689544\pi$
$751$	11.9625	−	20.7197i	0.436519	−	0.756073i	0.997418	+	0.0718109i	$0.0228778\pi$
$752$	−7.31005	−	15.1090i	−0.266570	−	0.550970i
$753$		0			0
$754$	−23.4711	+	26.3104i	−0.854767	+	0.958170i
$755$	−7.14257			−0.259945
$756$		0			0
$757$	4.03960	+	2.33226i	0.146822	+	0.0847676i	0.571611	−	0.820525i	$-0.306319\pi$
$757$	4.03960	+	2.33226i	0.146822	+	0.0847676i	−0.424789	+	0.905292i	$0.639652\pi$
$758$	−3.77069	+	17.3007i	−0.136958	+	0.628390i
$759$		0			0
$760$	10.3494	−	8.11902i	0.375411	−	0.294508i
$761$	5.39526	−	20.1354i	0.195578	−	0.729907i	−0.796538	−	0.604588i	$-0.793338\pi$
$761$	5.39526	−	20.1354i	0.195578	−	0.729907i	0.992116	−	0.125319i	$-0.0399955\pi$
$762$		0			0
$763$	−7.55350	−	13.0831i	−0.273455	−	0.473638i
$764$	47.3792	+	21.6826i	1.71412	+	0.784449i
$765$		0			0
$766$	32.1535	−	35.3420i	1.16175	−	1.27696i
$767$	50.2562	−	0.490983i	1.81464	−	0.0177284i
$768$		0			0
$769$	−10.2054	−	38.0871i	−0.368016	−	1.37346i	−0.863285	−	0.504716i	$-0.831597\pi$
$769$	−10.2054	−	38.0871i	−0.368016	−	1.37346i	0.495269	−	0.868740i	$-0.335070\pi$
$770$	0.685034	+	2.14589i	0.0246869	+	0.0773326i
$771$		0			0
$772$	−23.1626	−	19.1555i	−0.833641	−	0.689420i
$773$	12.6898	−	47.3590i	0.456421	−	1.70339i	−0.227456	−	0.973788i	$-0.573041\pi$
$773$	12.6898	−	47.3590i	0.456421	−	1.70339i	0.683877	−	0.729597i	$-0.260293\pi$
$774$		0			0
$775$	−7.38134	+	7.38134i	−0.265146	+	0.265146i
$776$	−0.384184	+	3.18122i	−0.0137914	+	0.114199i
$777$		0			0
$778$	−37.1303	−	19.1606i	−1.33119	−	0.686940i
$779$		−	12.4581i		−	0.446357i
$780$		0			0
$781$			5.60981i			0.200735i
$782$	2.75300	−	5.33490i	0.0984471	−	0.190776i
$783$		0			0
$784$	14.5461	−	12.5641i	0.519502	−	0.448717i
$785$	5.44798	−	5.44798i	0.194447	−	0.194447i
$786$		0			0
$787$	4.46886	−	16.6780i	0.159298	−	0.594507i	−0.839401	−	0.543512i	$-0.817094\pi$
$787$	4.46886	−	16.6780i	0.159298	−	0.594507i	0.998699	−	0.0509947i	$-0.0162392\pi$
$788$	−30.7608	−	25.4392i	−1.09581	−	0.906232i
$789$		0			0
$790$	−3.17601	+	1.01388i	−0.112997	+	0.0360721i
$791$	1.81859	+	6.78708i	0.0646617	+	0.241321i
$792$		0			0
$793$	−36.3442	−	35.6409i	−1.29062	−	1.26565i
$794$	−30.3783	−	27.6376i	−1.07809	−	0.980823i
$795$		0			0
$796$	9.37128	−	20.4774i	0.332156	−	0.725803i
$797$	7.88369	+	13.6550i	0.279255	+	0.483683i	0.971200	−	0.238267i	$-0.0765793\pi$
$797$	7.88369	+	13.6550i	0.279255	+	0.483683i	−0.691945	+	0.721950i	$0.743246\pi$
$798$		0			0
$799$	1.36445	−	5.09220i	0.0482708	−	0.180149i
$800$	17.4270	+	18.3493i	0.616138	+	0.648747i
$801$		0			0
$802$	7.64102	+	1.66536i	0.269814	+	0.0588060i
$803$	8.02350	+	4.63237i	0.283143	+	0.163473i
$804$		0			0
$805$	3.63201			0.128012
$806$	9.94878	−	6.52628i	0.350431	−	0.229878i
$807$		0			0
$808$	30.0631	+	12.0768i	1.05762	+	0.424860i
$809$	−16.1331	+	27.9433i	−0.567210	+	0.982436i	0.429631	+	0.903005i	$0.358644\pi$
$809$	−16.1331	+	27.9433i	−0.567210	+	0.982436i	−0.996840	+	0.0794311i	$0.974690\pi$
$810$		0			0
$811$	−2.82597	+	2.82597i	−0.0992332	+	0.0992332i	−0.754980	−	0.655747i	$-0.772354\pi$
$811$	−2.82597	+	2.82597i	−0.0992332	+	0.0992332i	0.655747	+	0.754980i	$0.272354\pi$
$812$	−3.41346	+	20.2015i	−0.119789	+	0.708934i
$813$		0			0
$814$	−0.361006	−	7.64194i	−0.0126533	−	0.267850i
$815$	−7.28319	+	4.20495i	−0.255119	+	0.147293i
$816$		0			0
$817$	56.7061	−	15.1944i	1.98390	−	0.531583i
$818$	−19.3186	−	17.5757i	−0.675460	−	0.614521i
$819$		0			0
$820$	−2.80804	+	0.265898i	−0.0980612	+	0.00928557i
$821$	−25.7200	+	6.89166i	−0.897635	+	0.240521i	−0.678000	−	0.735062i	$-0.737153\pi$
$821$	−25.7200	+	6.89166i	−0.897635	+	0.240521i	−0.219635	+	0.975582i	$0.570487\pi$
$822$		0			0
$823$	−1.80298	−	3.12285i	−0.0628478	−	0.108856i	0.832889	−	0.553439i	$-0.186685\pi$
$823$	−1.80298	−	3.12285i	−0.0628478	−	0.108856i	−0.895737	+	0.444584i	$0.853352\pi$
$824$	−0.993639	−	6.96951i	−0.0346151	−	0.242794i
$825$		0			0
$826$	24.5745	−	15.7794i	0.855057	−	0.549035i
$827$	−18.5758	−	18.5758i	−0.645943	−	0.645943i	0.306067	−	0.952010i	$-0.400987\pi$
$827$	−18.5758	−	18.5758i	−0.645943	−	0.645943i	−0.952010	+	0.306067i	$0.900987\pi$
$828$		0			0
$829$	0.283646	−	0.491289i	0.00985143	−	0.0170632i	−0.861058	−	0.508507i	$-0.830197\pi$
$829$	0.283646	−	0.491289i	0.00985143	−	0.0170632i	0.870909	+	0.491444i	$0.163531\pi$
$830$	−3.73884	−	1.92938i	−0.129777	−	0.0669696i
$831$		0			0
$832$	−15.1944	−	24.5179i	−0.526772	−	0.850006i
$833$	6.03708			0.209172
$834$		0			0
$835$	−3.26397	+	5.65336i	−0.112954	+	0.195643i
$836$	−11.0060	−	15.4816i	−0.380650	−	0.535442i
$837$		0			0
$838$	−33.6572	+	21.6114i	−1.16267	+	0.746554i
$839$	−32.7243	−	8.76844i	−1.12977	−	0.302720i	−0.354937	−	0.934890i	$-0.615498\pi$
$839$	−32.7243	−	8.76844i	−1.12977	−	0.302720i	−0.774830	+	0.632170i	$0.782164\pi$
$840$		0			0
$841$	9.40638	+	16.2923i	0.324358	+	0.561805i
$842$	11.9768	+	37.5177i	0.412747	+	1.29294i
$843$		0			0
$844$	2.27696	−	0.215609i	0.0783764	−	0.00742158i
$845$	9.15713	+	2.26286i	0.315015	+	0.0778446i
$846$		0			0
$847$	−12.5990	+	3.37588i	−0.432905	+	0.115997i
$848$	1.93925	+	0.674613i	0.0665942	+	0.0231663i
$849$		0			0
$850$	0.375064	+	7.93952i	0.0128646	+	0.272323i
$851$	−11.9151	−	3.19264i	−0.408445	−	0.109442i
$852$		0			0
$853$	15.4913	−	15.4913i	0.530411	−	0.530411i	−0.390283	−	0.920695i	$-0.627623\pi$
$853$	15.4913	−	15.4913i	0.530411	−	0.530411i	0.920695	+	0.390283i	$0.127623\pi$
$854$	−28.9008	−	6.29893i	−0.988963	−	0.215545i
$855$		0			0
$856$	26.9290	+	10.8178i	0.920416	+	0.369745i
$857$			17.3171i			0.591540i	0.955259	+	0.295770i	$0.0955762\pi$
$857$			17.3171i			0.591540i	−0.955259	+	0.295770i	$0.904424\pi$
$858$		0			0
$859$	−22.9629			−0.783484			−0.391742	−	0.920075i	$-0.628127\pi$
$859$	−22.9629			−0.783484			−0.391742	+	0.920075i	$0.628127\pi$
$860$	−4.63510	−	12.4572i	−0.158056	−	0.424788i
$861$		0			0
$862$	−44.0391	−	9.59833i	−1.49998	−	0.326920i
$863$	18.9344	+	18.9344i	0.644536	+	0.644536i	0.951667	−	0.307131i	$-0.0993691\pi$
$863$	18.9344	+	18.9344i	0.644536	+	0.644536i	−0.307131	+	0.951667i	$0.599369\pi$
$864$		0			0
$865$	2.61917	−	9.77489i	0.0890546	−	0.332356i
$866$	21.4827	−	1.01485i	0.730013	−	0.0344859i
$867$		0			0
$868$	2.87711	−	6.28686i	0.0976556	−	0.213390i
$869$	1.24604	+	4.65029i	0.0422690	+	0.157750i
$870$		0			0
$871$	−22.5732	+	13.3284i	−0.764865	+	0.451615i
$872$	17.3118	−	23.0689i	0.586253	−	0.781212i
$873$		0			0
$874$	−29.1766	+	9.31404i	−0.986912	+	0.315052i
$875$	−8.81910	+	5.09171i	−0.298140	+	0.172131i
$876$		0			0
$877$	11.6288	−	43.3992i	0.392676	−	1.46549i	−0.433027	−	0.901381i	$-0.642554\pi$
$877$	11.6288	−	43.3992i	0.392676	−	1.46549i	0.825703	−	0.564106i	$-0.190779\pi$
$878$	3.93017	−	2.52358i	0.132637	−	0.0851666i
$879$		0			0
$880$	−3.25464	+	2.81117i	−0.109714	+	0.0947645i
$881$	−2.13057	−	1.23009i	−0.0717808	−	0.0414427i	0.463680	−	0.886003i	$-0.346529\pi$
$881$	−2.13057	−	1.23009i	−0.0717808	−	0.0414427i	−0.535461	+	0.844560i	$0.679862\pi$
$882$		0			0
$883$		−	39.7470i		−	1.33759i	−0.743446	−	0.668796i	$-0.766810\pi$
$883$		−	39.7470i		−	1.33759i	0.743446	−	0.668796i	$-0.233190\pi$
$884$	1.42209	−	8.94741i	0.0478299	−	0.300934i
$885$		0			0
$886$	15.2269	+	7.85763i	0.511558	+	0.263982i
$887$	−17.1497	−	9.90141i	−0.575832	−	0.332457i	0.183643	−	0.982993i	$-0.441211\pi$
$887$	−17.1497	−	9.90141i	−0.575832	−	0.332457i	−0.759475	+	0.650536i	$0.774544\pi$
$888$		0			0
$889$	19.7085	−	19.7085i	0.661003	−	0.661003i
$890$	−1.17812	−	1.83478i	−0.0394905	−	0.0615019i
$891$		0			0
$892$	−22.6295	−	18.7146i	−0.757692	−	0.626610i
$893$	−23.2919	+	13.4476i	−0.779435	+	0.450007i
$894$		0			0
$895$	−1.74256	−	6.50333i	−0.0582474	−	0.217382i
$896$	−15.0560	−	7.36526i	−0.502986	−	0.246056i
$897$		0			0
$898$	−9.05616	+	9.95422i	−0.302208	+	0.332177i
$899$	−4.17607	−	15.5853i	−0.139280	−	0.519799i
$900$		0			0
$901$	0.322450	+	0.558500i	0.0107424	+	0.0186063i
$902$	0.192199	+	4.06855i	0.00639953	+	0.135468i
$903$		0			0
$904$	−10.5547	+	8.28008i	−0.351044	+	0.275391i
$905$	−10.6650	−	10.6650i	−0.354515	−	0.354515i
$906$		0			0
$907$	−16.4874	−	9.51900i	−0.547455	−	0.316073i	0.200640	−	0.979665i	$-0.435698\pi$
$907$	−16.4874	−	9.51900i	−0.547455	−	0.316073i	−0.748095	+	0.663592i	$0.769031\pi$
$908$	6.24928	+	16.7955i	0.207390	+	0.557377i
$909$		0			0
$910$	5.20497	−	1.71779i	0.172543	−	0.0569443i
$911$		−	1.28948i		−	0.0427225i	−0.999772	−	0.0213612i	$-0.993200\pi$
$911$		−	1.28948i		−	0.0427225i	0.999772	−	0.0213612i	$-0.00680001\pi$
$912$		0			0
$913$	−3.03778	+	5.26159i	−0.100536	+	0.174133i
$914$	3.65161	−	16.7543i	0.120784	−	0.554184i
$915$		0			0
$916$	−4.56418	−	0.771212i	−0.150805	−	0.0254816i
$917$	2.00489	+	0.537210i	0.0662074	+	0.0177402i
$918$		0			0
$919$	23.2515	−	13.4243i	0.766997	−	0.442826i	−0.0648055	−	0.997898i	$-0.520643\pi$
$919$	23.2515	−	13.4243i	0.766997	−	0.442826i	0.831802	+	0.555072i	$0.187309\pi$
$920$	2.72211	+	6.37759i	0.0897452	+	0.210263i
$921$		0			0
$922$	23.0281	−	25.3116i	0.758389	−	0.833595i
$923$	13.6494	−	0.133350i	0.449277	−	0.00438926i
$924$		0			0
$925$	15.7755	−	4.22703i	0.518695	−	0.138984i
$926$	24.3013	−	7.75770i	0.798589	−	0.254934i
$927$		0			0
$928$	−38.0309	+	9.14672i	−1.24842	+	0.300256i
$929$	−37.8024	−	10.1291i	−1.24026	−	0.332326i	−0.421692	−	0.906739i	$-0.638564\pi$
$929$	−37.8024	−	10.1291i	−1.24026	−	0.332326i	−0.818566	+	0.574413i	$0.805230\pi$
$930$		0			0
$931$	−21.7784	−	21.7784i	−0.713757	−	0.713757i
$932$	−24.8170	+	17.6426i	−0.812907	+	0.577902i
$933$		0			0
$934$	11.7764	−	22.8209i	0.385336	−	0.746724i
$935$	−1.35078			−0.0441752
$936$		0			0
$937$	46.1571			1.50789			0.753943	−	0.656939i	$-0.228149\pi$
$937$	46.1571			1.50789			0.753943	+	0.656939i	$0.228149\pi$
$938$	−6.98540	+	13.5367i	−0.228081	+	0.441988i
$939$		0			0
$940$	3.52821	+	4.96297i	0.115077	+	0.161874i
$941$	−35.7367	−	35.7367i	−1.16498	−	1.16498i	−0.983370	−	0.181611i	$-0.941869\pi$
$941$	−35.7367	−	35.7367i	−1.16498	−	1.16498i	−0.181611	−	0.983370i	$-0.558131\pi$
$942$		0			0
$943$	6.34359	+	1.69976i	0.206576	+	0.0553518i
$944$	46.1256	+	31.3250i	1.50126	+	1.01954i
$945$		0			0
$946$	−18.2846	+	5.83701i	−0.594485	+	0.189777i
$947$	−0.723796	+	0.193941i	−0.0235202	+	0.00630222i	−0.270560	−	0.962703i	$-0.587209\pi$
$947$	−0.723796	+	0.193941i	−0.0235202	+	0.00630222i	0.247040	+	0.969005i	$0.420542\pi$
$948$		0			0
$949$	11.0805	−	19.6324i	0.359687	−	0.637295i
$950$	27.2883	−	29.9943i	0.885348	−	0.973143i
$951$		0			0
$952$	−2.06662	−	4.84184i	−0.0669794	−	0.156925i
$953$	41.5062	−	23.9636i	1.34452	−	0.776257i	0.357050	−	0.934085i	$-0.383783\pi$
$953$	41.5062	−	23.9636i	1.34452	−	0.776257i	0.987467	+	0.157828i	$0.0504492\pi$
$954$		0			0
$955$	−18.2591	−	4.89251i	−0.590851	−	0.158318i
$956$	−9.48418	+	56.1293i	−0.306740	+	1.81535i
$957$		0			0
$958$	4.93656	−	22.6499i	0.159493	−	0.731786i
$959$	12.4184	−	21.5092i	0.401010	−	0.694569i
$960$		0			0
$961$		−	25.5550i		−	0.824354i
$962$	−18.5853	+	1.06003i	−0.599215	+	0.0341769i
$963$		0			0
$964$	7.01088	−	2.60862i	0.225805	−	0.0840179i
$965$	9.44359	+	5.45226i	0.304000	+	0.175514i
$966$		0			0
$967$	8.44481	+	8.44481i	0.271567	+	0.271567i	0.829731	−	0.558164i	$-0.188494\pi$
$967$	8.44481	+	8.44481i	0.271567	+	0.271567i	−0.558164	+	0.829731i	$0.688494\pi$
$968$	−15.3704	−	19.5928i	−0.494025	−	0.629737i
$969$		0			0
$970$	−0.0548557	−	1.16121i	−0.00176131	−	0.0372842i
$971$	−24.1539	−	41.8358i	−0.775136	−	1.34257i	−0.934718	−	0.355390i	$-0.884348\pi$
$971$	−24.1539	−	41.8358i	−0.775136	−	1.34257i	0.159582	−	0.987185i	$-0.448985\pi$
$972$		0			0
$973$	−5.80974	−	21.6822i	−0.186252	−	0.695101i
$974$	−34.3409	+	37.7463i	−1.10035	+	1.20947i
$975$		0			0
$976$	−10.5999	−	55.4688i	−0.339295	−	1.77551i
$977$	−8.21436	−	30.6564i	−0.262801	−	0.980786i	−0.963583	−	0.267410i	$-0.913832\pi$
$977$	−8.21436	−	30.6564i	−0.262801	−	0.980786i	0.700782	−	0.713376i	$-0.252835\pi$
$978$		0			0
$979$	−2.72683	+	1.57434i	−0.0871500	+	0.0503161i
$980$	−4.44400	+	5.37365i	−0.141958	+	0.171655i
$981$		0			0
$982$	11.4565	+	17.8422i	0.365593	+	0.569368i
$983$	−18.1345	+	18.1345i	−0.578400	+	0.578400i	−0.934462	−	0.356062i	$-0.884119\pi$
$983$	−18.1345	+	18.1345i	−0.578400	+	0.578400i	0.356062	+	0.934462i	$0.384119\pi$
$984$		0			0
$985$	12.5414	+	7.24080i	0.399603	+	0.230711i
$986$	−10.9177	−	5.63394i	−0.347692	−	0.179421i
$987$		0			0
$988$	−37.4073	+	27.1471i	−1.19008	+	0.863664i
$989$			30.9475i			0.984074i
$990$		0			0
$991$	15.3411	+	8.85718i	0.487326	+	0.281358i	0.723464	−	0.690362i	$-0.242549\pi$
$991$	15.3411	+	8.85718i	0.487326	+	0.281358i	−0.236139	+	0.971719i	$0.575882\pi$
$992$	13.1956	+	0.340182i	0.418962	+	0.0108008i
$993$		0			0
$994$	6.67438	−	4.28564i	0.211698	−	0.135932i
$995$	−2.11456	+	7.89164i	−0.0670360	+	0.250182i
$996$		0			0
$997$	4.27051	−	2.46558i	0.135249	−	0.0780858i	−0.430849	−	0.902424i	$-0.641786\pi$
$997$	4.27051	−	2.46558i	0.135249	−	0.0780858i	0.566098	+	0.824338i	$0.308453\pi$
$998$	−58.1407	+	18.5603i	−1.84041	+	0.587515i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.ed.e.19.12		56
3.2	odd	2		312.2.bt.d.19.3	✓	56
8.3	odd	2	inner	936.2.ed.e.19.5		56
13.11	odd	12	inner	936.2.ed.e.739.5		56
24.11	even	2		312.2.bt.d.19.10	yes	56
39.11	even	12		312.2.bt.d.115.10	yes	56
104.11	even	12	inner	936.2.ed.e.739.12		56
312.11	odd	12		312.2.bt.d.115.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.d.19.3	✓	56	3.2	odd	2
312.2.bt.d.19.10	yes	56	24.11	even	2
312.2.bt.d.115.3	yes	56	312.11	odd	12
312.2.bt.d.115.10	yes	56	39.11	even	12
936.2.ed.e.19.5		56	8.3	odd	2	inner
936.2.ed.e.19.12		56	1.1	even	1	trivial
936.2.ed.e.739.5		56	13.11	odd	12	inner
936.2.ed.e.739.12		56	104.11	even	12	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.ed (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25675 + 0.648526i) q^{2} +(1.15883 + 1.63007i) q^{4} +(-0.513065 - 0.513065i) q^{5} +(1.43100 + 0.383434i) q^{7} +(0.399211 + 2.80011i) q^{8} +(-0.312057 - 0.977529i) q^{10} +(-1.43129 + 0.383513i) q^{11} +(0.967164 + 3.47341i) q^{13} +(1.54973 + 1.40992i) q^{14} +(-1.31424 + 3.77793i) q^{16} +(-1.08804 + 0.628178i) q^{17} +(6.19113 + 1.65891i) q^{19} +(0.241777 - 1.43088i) q^{20} +(-2.04749 - 0.446251i) q^{22} +(-1.68941 + 2.92615i) q^{23} -4.47353i q^{25} +(-1.03712 + 4.99243i) q^{26} +(1.03325 + 2.77695i) q^{28} +(5.98829 + 3.45734i) q^{29} +(-1.65000 - 1.65000i) q^{31} +(-4.10176 + 3.89559i) q^{32} +(-1.77478 + 0.0838407i) q^{34} +(-0.537467 - 0.930920i) q^{35} +(0.944898 + 3.52641i) q^{37} +(6.70484 + 6.09994i) q^{38} +(1.23182 - 1.64146i) q^{40} +(-0.503062 - 1.87745i) q^{41} +(7.93214 - 4.57963i) q^{43} +(-2.28377 - 1.88867i) q^{44} +(-4.02085 + 2.58180i) q^{46} +(-2.96711 + 2.96711i) q^{47} +(-4.16145 - 2.40261i) q^{49} +(2.90120 - 5.62210i) q^{50} +(-4.54112 + 5.60163i) q^{52} -0.513310i q^{53} +(0.931112 + 0.537578i) q^{55} +(-0.502390 + 4.16002i) q^{56} +(5.28359 + 8.22856i) q^{58} +(3.60773 - 13.4642i) q^{59} +(-12.2267 + 7.05906i) q^{61} +(-1.00357 - 3.14371i) q^{62} +(-7.68126 + 2.23567i) q^{64} +(1.28587 - 2.27830i) q^{65} +(1.88176 + 7.02284i) q^{67} +(-2.28482 - 1.04562i) q^{68} +(-0.0717338 - 1.51849i) q^{70} +(0.979852 - 3.65686i) q^{71} +(-4.42114 - 4.42114i) q^{73} +(-1.09947 + 5.04459i) q^{74} +(4.47032 + 12.0143i) q^{76} -2.19522 q^{77} -3.24902i q^{79} +(2.61261 - 1.26403i) q^{80} +(0.585356 - 2.68573i) q^{82} +(2.89926 - 2.89926i) q^{83} +(0.880529 + 0.235937i) q^{85} +(12.9387 - 0.611226i) q^{86} +(-1.64527 - 3.85467i) q^{88} +(2.05252 - 0.549972i) q^{89} +(0.0521823 + 5.34128i) q^{91} +(-6.72756 + 0.637043i) q^{92} +(-5.65316 + 1.80466i) q^{94} +(-2.32532 - 4.02758i) q^{95} +(1.09430 + 0.293217i) q^{97} +(-3.67173 - 5.71829i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{8} + 28 q^{14} + 12 q^{16} - 8 q^{19} + 4 q^{20} + 10 q^{22} - 34 q^{26} - 14 q^{28} + 30 q^{32} + 56 q^{34} - 28 q^{40} - 40 q^{41} + 44 q^{44} - 18 q^{46} + 24 q^{49} + 72 q^{50} + 32 q^{52}+ \cdots - 4 q^{98}+O(q^{100}) \) 56 * q + 12 * q^8 + 28 * q^14 + 12 * q^16 - 8 * q^19 + 4 * q^20 + 10 * q^22 - 34 * q^26 - 14 * q^28 + 30 * q^32 + 56 * q^34 - 28 * q^40 - 40 * q^41 + 44 * q^44 - 18 * q^46 + 24 * q^49 + 72 * q^50 + 32 * q^52 + 54 * q^56 - 16 * q^58 - 32 * q^59 - 48 * q^65 - 24 * q^67 + 26 * q^68 + 64 * q^70 + 44 * q^73 + 6 * q^74 + 6 * q^76 + 4 * q^80 - 30 * q^82 - 40 * q^83 + 28 * q^86 + 126 * q^88 + 68 * q^89 - 72 * q^91 - 52 * q^92 + 34 * q^94 - 4 * q^97 - 4 * q^98

Introduction

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