LMFDB - Embedded newform 728.2.i.a.701.52

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,2,Mod(701,728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("728.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.i (of order $2$, degree $1$, 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:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			701.52
Character	$\chi$	$=$	728.701
Dual form			728.2.i.a.701.51

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.552548 + 1.30180i) q^{2} -1.24325i q^{3} +(-1.38938 + 1.43862i) q^{4} -4.24503 q^{5} +(1.61846 - 0.686953i) q^{6} -1.00000i q^{7} +(-2.64050 - 1.01380i) q^{8} +1.45434 q^{9} +(-2.34558 - 5.52619i) q^{10} +2.97219 q^{11} +(1.78855 + 1.72734i) q^{12} +(3.10071 + 1.84000i) q^{13} +(1.30180 - 0.552548i) q^{14} +5.27761i q^{15} +(-0.139235 - 3.99758i) q^{16} +3.88084 q^{17} +(0.803592 + 1.89326i) q^{18} -3.68346 q^{19} +(5.89797 - 6.10697i) q^{20} -1.24325 q^{21} +(1.64228 + 3.86921i) q^{22} +4.72588 q^{23} +(-1.26040 + 3.28278i) q^{24} +13.0203 q^{25} +(-0.682027 + 5.05320i) q^{26} -5.53784i q^{27} +(1.43862 + 1.38938i) q^{28} +7.03148i q^{29} +(-6.87041 + 2.91613i) q^{30} +2.28102i q^{31} +(5.12712 - 2.39011i) q^{32} -3.69517i q^{33} +(2.14435 + 5.05210i) q^{34} +4.24503i q^{35} +(-2.02063 + 2.09224i) q^{36} +3.24019 q^{37} +(-2.03528 - 4.79513i) q^{38} +(2.28757 - 3.85494i) q^{39} +(11.2090 + 4.30360i) q^{40} +3.82209i q^{41} +(-0.686953 - 1.61846i) q^{42} -8.00510i q^{43} +(-4.12951 + 4.27585i) q^{44} -6.17371 q^{45} +(2.61127 + 6.15217i) q^{46} -0.318216i q^{47} +(-4.96997 + 0.173103i) q^{48} -1.00000 q^{49} +(7.19431 + 16.9498i) q^{50} -4.82484i q^{51} +(-6.95512 + 1.90427i) q^{52} +2.52928i q^{53} +(7.20918 - 3.05992i) q^{54} -12.6170 q^{55} +(-1.01380 + 2.64050i) q^{56} +4.57944i q^{57} +(-9.15361 + 3.88523i) q^{58} +10.7468 q^{59} +(-7.59246 - 7.33262i) q^{60} -11.8802i q^{61} +(-2.96944 + 1.26037i) q^{62} -1.45434i q^{63} +(5.94443 + 5.35386i) q^{64} +(-13.1626 - 7.81085i) q^{65} +(4.81038 - 2.04176i) q^{66} +8.65396 q^{67} +(-5.39198 + 5.58305i) q^{68} -5.87543i q^{69} +(-5.52619 + 2.34558i) q^{70} -5.29101i q^{71} +(-3.84018 - 1.47441i) q^{72} -12.1985i q^{73} +(1.79036 + 4.21809i) q^{74} -16.1874i q^{75} +(5.11773 - 5.29908i) q^{76} -2.97219i q^{77} +(6.28237 + 0.847927i) q^{78} +2.81549 q^{79} +(0.591055 + 16.9698i) q^{80} -2.52188 q^{81} +(-4.97560 + 2.11188i) q^{82} +2.11994 q^{83} +(1.72734 - 1.78855i) q^{84} -16.4743 q^{85} +(10.4211 - 4.42320i) q^{86} +8.74186 q^{87} +(-7.84806 - 3.01320i) q^{88} +14.4314i q^{89} +(-3.41127 - 8.03696i) q^{90} +(1.84000 - 3.10071i) q^{91} +(-6.56605 + 6.79873i) q^{92} +2.83587 q^{93} +(0.414254 - 0.175829i) q^{94} +15.6364 q^{95} +(-2.97149 - 6.37427i) q^{96} -3.42799i q^{97} +(-0.552548 - 1.30180i) q^{98} +4.32258 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 84 q^{9} + 8 q^{10} - 20 q^{12} - 8 q^{16} + 8 q^{17} - 12 q^{22} - 24 q^{23} + 92 q^{25} - 40 q^{30} + 44 q^{36} + 20 q^{38} - 24 q^{39} - 28 q^{40} - 72 q^{48} - 84 q^{49} - 44 q^{52} + 32 q^{55}+ \cdots - 16 q^{95}+O(q^{100}) $ 84 * q - 84 * q^9 + 8 * q^10 - 20 * q^12 - 8 * q^16 + 8 * q^17 - 12 * q^22 - 24 * q^23 + 92 * q^25 - 40 * q^30 + 44 * q^36 + 20 * q^38 - 24 * q^39 - 28 * q^40 - 72 * q^48 - 84 * q^49 - 44 * q^52 + 32 * q^55 - 40 * q^62 + 72 * q^64 - 24 * q^65 - 60 * q^66 - 92 * q^68 + 28 * q^74 + 12 * q^78 - 40 * q^79 + 84 * q^81 + 24 * q^82 - 48 * q^87 - 108 * q^88 + 20 * q^90 + 60 * q^92 + 36 * q^94 - 16 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$	0.552548	+	1.30180i	0.390710	+	0.920514i
$2$	0.552548	+	1.30180i	0.390710	+	0.920514i
$3$		−	1.24325i		−	0.717788i	−0.933378	−	0.358894i	$-0.883154\pi$
$3$		−	1.24325i		−	0.717788i	0.933378	−	0.358894i	$-0.116846\pi$
$4$	−1.38938	+	1.43862i	−0.694691	+	0.719308i
$5$	−4.24503			−1.89843			−0.949217	−	0.314622i	$-0.898122\pi$
$5$	−4.24503			−1.89843			−0.949217	+	0.314622i	$0.898122\pi$
$6$	1.61846	−	0.686953i	0.660734	−	0.280447i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.64050	−	1.01380i	−0.933556	−	0.358432i
$9$	1.45434			0.484780
$10$	−2.34558	−	5.52619i	−0.741738	−	1.74753i
$11$	2.97219			0.896150			0.448075	−	0.893996i	$-0.352110\pi$
$11$	2.97219			0.896150			0.448075	+	0.893996i	$0.352110\pi$
$12$	1.78855	+	1.72734i	0.516311	+	0.498641i
$13$	3.10071	+	1.84000i	0.859982	+	0.510324i
$13$	3.10071	+	1.84000i	0.859982	+	0.510324i
$14$	1.30180	−	0.552548i	0.347921	−	0.147675i
$15$			5.27761i			1.36267i
$16$	−0.139235	−	3.99758i	−0.0348087	−	0.999394i
$17$	3.88084			0.941243			0.470622	−	0.882335i	$-0.344030\pi$
$17$	3.88084			0.941243			0.470622	+	0.882335i	$0.344030\pi$
$18$	0.803592	+	1.89326i	0.189408	+	0.446247i
$19$	−3.68346			−0.845043			−0.422521	−	0.906353i	$-0.638855\pi$
$19$	−3.68346			−0.845043			−0.422521	+	0.906353i	$0.638855\pi$
$20$	5.89797	−	6.10697i	1.31883	−	1.36556i
$21$	−1.24325			−0.271298
$22$	1.64228	+	3.86921i	0.350135	+	0.824919i
$23$	4.72588			0.985414			0.492707	−	0.870195i	$-0.336007\pi$
$23$	4.72588			0.985414			0.492707	+	0.870195i	$0.336007\pi$
$24$	−1.26040	+	3.28278i	−0.257278	+	0.670096i
$25$	13.0203			2.60405
$26$	−0.682027	+	5.05320i	−0.133756	+	0.991014i
$27$		−	5.53784i		−	1.06576i
$28$	1.43862	+	1.38938i	0.271873	+	0.262569i
$29$			7.03148i			1.30571i	0.757481	+	0.652857i	$0.226430\pi$
$29$			7.03148i			1.30571i	−0.757481	+	0.652857i	$0.773570\pi$
$30$	−6.87041	+	2.91613i	−1.25436	+	0.532411i
$31$			2.28102i			0.409684i	0.978795	+	0.204842i	$0.0656680\pi$
$31$			2.28102i			0.409684i	−0.978795	+	0.204842i	$0.934332\pi$
$32$	5.12712	−	2.39011i	0.906356	−	0.422515i
$33$		−	3.69517i		−	0.643246i
$34$	2.14435	+	5.05210i	0.367753	+	0.866427i
$35$			4.24503i			0.717541i
$36$	−2.02063	+	2.09224i	−0.336772	+	0.348706i
$37$	3.24019			0.532684			0.266342	−	0.963879i	$-0.414185\pi$
$37$	3.24019			0.532684			0.266342	+	0.963879i	$0.414185\pi$
$38$	−2.03528	−	4.79513i	−0.330167	−	0.777873i
$39$	2.28757	−	3.85494i	0.366305	−	0.617285i
$40$	11.2090	+	4.30360i	1.77229	+	0.680459i
$41$			3.82209i			0.596910i	0.954424	+	0.298455i	$0.0964712\pi$
$41$			3.82209i			0.596910i	−0.954424	+	0.298455i	$0.903529\pi$
$42$	−0.686953	−	1.61846i	−0.105999	−	0.249734i
$43$		−	8.00510i		−	1.22077i	−0.792106	−	0.610383i	$-0.791015\pi$
$43$		−	8.00510i		−	1.22077i	0.792106	−	0.610383i	$-0.208985\pi$
$44$	−4.12951	+	4.27585i	−0.622548	+	0.644608i
$45$	−6.17371			−0.920323
$46$	2.61127	+	6.15217i	0.385011	+	0.907087i
$47$		−	0.318216i		−	0.0464166i	−0.999731	−	0.0232083i	$-0.992612\pi$
$47$		−	0.318216i		−	0.0464166i	0.999731	−	0.0232083i	$-0.00738809\pi$
$48$	−4.96997	+	0.173103i	−0.717353	+	0.0249852i
$49$	−1.00000			−0.142857
$50$	7.19431	+	16.9498i	1.01743	+	2.39707i
$51$		−	4.82484i		−	0.675613i
$52$	−6.95512	+	1.90427i	−0.964502	+	0.264075i
$53$			2.52928i			0.347423i	0.984797	+	0.173712i	$0.0555761\pi$
$53$			2.52928i			0.347423i	−0.984797	+	0.173712i	$0.944424\pi$
$54$	7.20918	−	3.05992i	0.981045	−	0.416402i
$55$	−12.6170			−1.70128
$56$	−1.01380	+	2.64050i	−0.135474	+	0.352851i
$57$			4.57944i			0.606562i
$58$	−9.15361	+	3.88523i	−1.20193	+	0.510156i
$59$	10.7468			1.39911			0.699556	−	0.714578i	$-0.253381\pi$
$59$	10.7468			1.39911			0.699556	+	0.714578i	$0.253381\pi$
$60$	−7.59246	−	7.33262i	−0.980182	−	0.946637i
$61$		−	11.8802i		−	1.52111i	−0.649274	−	0.760555i	$-0.724927\pi$
$61$		−	11.8802i		−	1.52111i	0.649274	−	0.760555i	$-0.275073\pi$
$62$	−2.96944	+	1.26037i	−0.377120	+	0.160068i
$63$		−	1.45434i		−	0.183230i
$64$	5.94443	+	5.35386i	0.743054	+	0.669232i
$65$	−13.1626	−	7.81085i	−1.63262	−	0.968817i
$66$	4.81038	−	2.04176i	0.592117	−	0.251323i
$67$	8.65396			1.05725			0.528625	−	0.848856i	$-0.322708\pi$
$67$	8.65396			1.05725			0.528625	+	0.848856i	$0.322708\pi$
$68$	−5.39198	+	5.58305i	−0.653873	+	0.677044i
$69$		−	5.87543i		−	0.707319i
$70$	−5.52619	+	2.34558i	−0.660506	+	0.280350i
$71$		−	5.29101i		−	0.627927i	−0.949435	−	0.313964i	$-0.898343\pi$
$71$		−	5.29101i		−	0.627927i	0.949435	−	0.313964i	$-0.101657\pi$
$72$	−3.84018	−	1.47441i	−0.452569	−	0.173760i
$73$		−	12.1985i		−	1.42773i	−0.700284	−	0.713864i	$-0.746943\pi$
$73$		−	12.1985i		−	1.42773i	0.700284	−	0.713864i	$-0.253057\pi$
$74$	1.79036	+	4.21809i	0.208125	+	0.490343i
$75$		−	16.1874i		−	1.86916i
$76$	5.11773	−	5.29908i	0.587043	−	0.607846i
$77$		−	2.97219i		−	0.338713i
$78$	6.28237	+	0.847927i	0.711338	+	0.0960088i
$79$	2.81549			0.316767			0.158384	−	0.987378i	$-0.449372\pi$
$79$	2.81549			0.316767			0.158384	+	0.987378i	$0.449372\pi$
$80$	0.591055	+	16.9698i	0.0660819	+	1.89728i
$81$	−2.52188			−0.280208
$82$	−4.97560	+	2.11188i	−0.549463	+	0.233219i
$83$	2.11994			0.232693			0.116347	−	0.993209i	$-0.462882\pi$
$83$	2.11994			0.232693			0.116347	+	0.993209i	$0.462882\pi$
$84$	1.72734	−	1.78855i	0.188469	−	0.195147i
$85$	−16.4743			−1.78689
$86$	10.4211	−	4.42320i	1.12373	−	0.476966i
$87$	8.74186			0.937226
$88$	−7.84806	−	3.01320i	−0.836607	−	0.321209i
$89$			14.4314i			1.52972i	0.644194	+	0.764862i	$0.277193\pi$
$89$			14.4314i			1.52972i	−0.644194	+	0.764862i	$0.722807\pi$
$90$	−3.41127	−	8.03696i	−0.359580	−	0.847170i
$91$	1.84000	−	3.10071i	0.192884	−	0.325043i
$92$	−6.56605	+	6.79873i	−0.684559	+	0.708817i
$93$	2.83587			0.294066
$94$	0.414254	−	0.175829i	0.0427271	−	0.0181354i
$95$	15.6364			1.60426
$96$	−2.97149	−	6.37427i	−0.303277	−	0.650572i
$97$		−	3.42799i		−	0.348060i	−0.984740	−	0.174030i	$-0.944321\pi$
$97$		−	3.42799i		−	0.348060i	0.984740	−	0.174030i	$-0.0556789\pi$
$98$	−0.552548	−	1.30180i	−0.0558157	−	0.131502i
$99$	4.32258			0.434436
$100$	−18.0901	+	18.7312i	−1.80901	+	1.87312i
$101$		−	4.85023i		−	0.482616i	−0.970449	−	0.241308i	$-0.922424\pi$
$101$		−	4.85023i		−	0.482616i	0.970449	−	0.241308i	$-0.0775764\pi$
$102$	6.28100	−	2.66596i	0.621911	−	0.263969i
$103$	−10.9280			−1.07677			−0.538384	−	0.842700i	$-0.680965\pi$
$103$	−10.9280			−1.07677			−0.538384	+	0.842700i	$0.680965\pi$
$104$	−6.32202	−	8.00200i	−0.619925	−	0.784661i
$105$	5.27761			0.515042
$106$	−3.29263	+	1.39755i	−0.319808	+	0.135742i
$107$			19.3059i			1.86637i	0.359392	+	0.933187i	$0.382984\pi$
$107$			19.3059i			1.86637i	−0.359392	+	0.933187i	$0.617016\pi$
$108$	7.96683	+	7.69417i	0.766608	+	0.740372i
$109$	−5.98308			−0.573075			−0.286538	−	0.958069i	$-0.592504\pi$
$109$	−5.98308			−0.573075			−0.286538	+	0.958069i	$0.592504\pi$
$110$	−6.97152	−	16.4249i	−0.664708	−	1.56605i
$111$		−	4.02835i		−	0.382354i
$112$	−3.99758	+	0.139235i	−0.377735	+	0.0131564i
$113$	−11.8821			−1.11777			−0.558887	−	0.829244i	$-0.688772\pi$
$113$	−11.8821			−1.11777			−0.558887	+	0.829244i	$0.688772\pi$
$114$	−5.96153	+	2.53036i	−0.558348	+	0.236990i
$115$	−20.0615			−1.87074
$116$	−10.1156	−	9.76942i	−0.939211	−	0.907068i
$117$	4.50949	+	2.67598i	0.416902	+	0.247395i
$118$	5.93811	+	13.9902i	0.546647	+	1.28790i
$119$		−	3.88084i		−	0.355756i
$120$	5.35043	−	13.9355i	0.488425	−	1.27213i
$121$	−2.16606			−0.196915
$122$	15.4657	−	6.56440i	1.40020	−	0.594313i
$123$	4.75179			0.428455
$124$	−3.28152	−	3.16921i	−0.294689	−	0.284604i
$125$	−34.0462			−3.04519
$126$	1.89326	−	0.803592i	0.168665	−	0.0715897i
$127$	7.65675			0.679426			0.339713	−	0.940529i	$-0.389670\pi$
$127$	7.65675			0.679426			0.339713	+	0.940529i	$0.389670\pi$
$128$	−3.68508	+	10.6967i	−0.325719	+	0.945467i
$129$	−9.95231			−0.876252
$130$	2.89522	−	21.4510i	0.253928	−	1.88138i
$131$			2.71789i			0.237463i	0.992926	+	0.118732i	$0.0378828\pi$
$131$			2.71789i			0.237463i	−0.992926	+	0.118732i	$0.962117\pi$
$132$	5.31593	+	5.13400i	0.462692	+	0.446857i
$133$			3.68346i			0.319396i
$134$	4.78173	+	11.2658i	0.413078	+	0.973213i
$135$			23.5083i			2.02327i
$136$	−10.2474	−	3.93439i	−0.878703	−	0.337371i
$137$			23.0466i			1.96901i	0.175363	+	0.984504i	$0.443890\pi$
$137$			23.0466i			1.96901i	−0.175363	+	0.984504i	$0.556110\pi$
$138$	7.64865	−	3.24646i	0.651097	−	0.276357i
$139$			6.61294i			0.560902i	0.959868	+	0.280451i	$0.0904840\pi$
$139$			6.61294i			0.560902i	−0.959868	+	0.280451i	$0.909516\pi$
$140$	−6.10697	−	5.89797i	−0.516133	−	0.498469i
$141$	−0.395621			−0.0333173
$142$	6.88785	−	2.92354i	0.578016	−	0.245338i
$143$	9.21591	+	5.46884i	0.770673	+	0.457327i
$144$	−0.202495	−	5.81383i	−0.0168745	−	0.484486i
$145$		−	29.8488i		−	2.47881i
$146$	15.8801	−	6.74026i	1.31424	−	0.557828i
$147$			1.24325i			0.102541i
$148$	−4.50186	+	4.66139i	−0.370051	+	0.383164i
$149$	−3.51745			−0.288161			−0.144080	−	0.989566i	$-0.546022\pi$
$149$	−3.51745			−0.288161			−0.144080	+	0.989566i	$0.546022\pi$
$150$	21.0728	−	8.94430i	1.72059	−	0.730299i
$151$		−	10.1417i		−	0.825316i	−0.910886	−	0.412658i	$-0.864600\pi$
$151$		−	10.1417i		−	0.825316i	0.910886	−	0.412658i	$-0.135400\pi$
$152$	9.72614	+	3.73428i	0.788895	+	0.302890i
$153$	5.64407			0.456296
$154$	3.86921	−	1.64228i	0.311790	−	0.132339i
$155$		−	9.68301i		−	0.777758i
$156$	2.36748	+	8.64693i	0.189550	+	0.692308i
$157$			7.13358i			0.569322i	0.958628	+	0.284661i	$0.0918810\pi$
$157$			7.13358i			0.569322i	−0.958628	+	0.284661i	$0.908119\pi$
$158$	1.55569	+	3.66521i	0.123764	+	0.291589i
$159$	3.14452			0.249376
$160$	−21.7648	+	10.1461i	−1.72066	+	0.802117i
$161$		−	4.72588i		−	0.372452i
$162$	−1.39346	−	3.28298i	−0.109480	−	0.257936i
$163$	20.6173			1.61487			0.807437	−	0.589954i	$-0.200854\pi$
$163$	20.6173			1.61487			0.807437	+	0.589954i	$0.200854\pi$
$164$	−5.49852	−	5.31034i	−0.429362	−	0.414668i
$165$			15.6861i			1.22116i
$166$	1.17137	+	2.75974i	0.0909156	+	0.214197i
$167$		−	6.39044i		−	0.494507i	−0.968951	−	0.247253i	$-0.920472\pi$
$167$		−	6.39044i		−	0.494507i	0.968951	−	0.247253i	$-0.0795280\pi$
$168$	3.28278	+	1.26040i	0.253272	+	0.0972419i
$169$	6.22880	+	11.4106i	0.479139	+	0.877739i
$170$	−9.10283	−	21.4463i	−0.698155	−	1.64485i
$171$	−5.35700			−0.409660
$172$	11.5163	+	11.1221i	0.878107	+	0.848056i
$173$			3.69193i			0.280693i	0.990102	+	0.140346i	$0.0448216\pi$
$173$			3.69193i			0.280693i	−0.990102	+	0.140346i	$0.955178\pi$
$174$	4.83030	+	11.3802i	0.366184	+	0.862729i
$175$		−	13.0203i		−	0.984239i
$176$	−0.413832	−	11.8816i	−0.0311938	−	0.895607i
$177$		−	13.3609i		−	1.00427i
$178$	−18.7868	+	7.97403i	−1.40813	+	0.597679i
$179$		−	20.4497i		−	1.52848i	−0.644930	−	0.764242i	$-0.723114\pi$
$179$		−	20.4497i		−	1.52848i	0.644930	−	0.764242i	$-0.276886\pi$
$180$	8.57765	−	8.88161i	0.639340	−	0.661996i
$181$			19.6160i			1.45805i	0.684488	+	0.729024i	$0.260026\pi$
$181$			19.6160i			1.45805i	−0.684488	+	0.729024i	$0.739974\pi$
$182$	5.05320	+	0.682027i	0.374568	+	0.0505552i
$183$	−14.7701			−1.09183
$184$	−12.4787	−	4.79109i	−0.919939	−	0.353204i
$185$	−13.7547			−1.01127
$186$	1.56695	+	3.69175i	0.114895	+	0.270692i
$187$	11.5346			0.843495
$188$	0.457791	+	0.442124i	0.0333878	+	0.0322452i
$189$	−5.53784			−0.402819
$190$	8.63984	+	20.3555i	0.626800	+	1.47674i
$191$	−6.04598			−0.437472			−0.218736	−	0.975784i	$-0.570193\pi$
$191$	−6.04598			−0.437472			−0.218736	+	0.975784i	$0.570193\pi$
$192$	6.65616	−	7.39039i	0.480367	−	0.533355i
$193$		−	1.37318i		−	0.0988435i	−0.998778	−	0.0494217i	$-0.984262\pi$
$193$		−	1.37318i		−	0.0988435i	0.998778	−	0.0494217i	$-0.0157378\pi$
$194$	4.46257	−	1.89413i	0.320394	−	0.135991i
$195$	−9.71080	+	16.3643i	−0.695405	+	1.17188i
$196$	1.38938	−	1.43862i	0.0992416	−	0.102758i
$197$	15.5202			1.10577			0.552884	−	0.833258i	$-0.313527\pi$
$197$	15.5202			1.10577			0.552884	+	0.833258i	$0.313527\pi$
$198$	2.38843	+	5.62715i	0.169738	+	0.399904i
$199$	27.2936			1.93479			0.967395	−	0.253271i	$-0.0815064\pi$
$199$	27.2936			1.93479			0.967395	+	0.253271i	$0.0815064\pi$
$200$	−34.3799	−	13.1999i	−2.43103	−	0.933375i
$201$		−	10.7590i		−	0.758881i
$202$	6.31404	−	2.67998i	0.444255	−	0.188563i
$203$	7.03148			0.493513
$204$	6.94110	+	6.70355i	0.485974	+	0.469343i
$205$		−	16.2249i		−	1.13319i
$206$	−6.03824	−	14.2261i	−0.420704	−	0.991179i
$207$	6.87304			0.477709
$208$	6.92381	−	12.6515i	0.480080	−	0.877225i
$209$	−10.9479			−0.757285
$210$	2.91613	+	6.87041i	0.201232	+	0.474103i
$211$		−	6.32498i		−	0.435429i	−0.976012	−	0.217715i	$-0.930140\pi$
$211$		−	6.32498i		−	0.435429i	0.976012	−	0.217715i	$-0.0698602\pi$
$212$	−3.63866	−	3.51414i	−0.249905	−	0.241352i
$213$	−6.57803			−0.450719
$214$	−25.1325	+	10.6674i	−1.71802	+	0.729211i
$215$			33.9819i			2.31754i
$216$	−5.61425	+	14.6226i	−0.382001	+	0.994944i
$217$	2.28102			0.154846
$218$	−3.30594	−	7.78879i	−0.223906	−	0.527524i
$219$	−15.1658			−1.02481
$220$	17.5299	−	18.1511i	1.18187	−	1.22375i
$221$	12.0334	+	7.14075i	0.809452	+	0.480339i
$222$	5.24412	−	2.22586i	0.351962	−	0.149390i
$223$			9.60586i			0.643256i	0.946866	+	0.321628i	$0.104230\pi$
$223$			9.60586i			0.643256i	−0.946866	+	0.321628i	$0.895770\pi$
$224$	−2.39011	−	5.12712i	−0.159696	−	0.342570i
$225$	18.9359			1.26239
$226$	−6.56543	−	15.4682i	−0.436726	−	1.02893i
$227$	−14.4621			−0.959882			−0.479941	−	0.877301i	$-0.659342\pi$
$227$	−14.4621			−0.959882			−0.479941	+	0.877301i	$0.659342\pi$
$228$	−6.58806	−	6.36259i	−0.436305	−	0.421373i
$229$	4.33134			0.286223			0.143112	−	0.989707i	$-0.454289\pi$
$229$	4.33134			0.286223			0.143112	+	0.989707i	$0.454289\pi$
$230$	−11.0849	−	26.1161i	−0.730919	−	1.72205i
$231$	−3.69517			−0.243124
$232$	7.12850	−	18.5666i	0.468009	−	1.21896i
$233$	−24.1730			−1.58362			−0.791812	−	0.610765i	$-0.790862\pi$
$233$	−24.1730			−1.58362			−0.791812	+	0.610765i	$0.790862\pi$
$234$	−0.991899	+	7.34907i	−0.0648425	+	0.480424i
$235$			1.35084i			0.0881188i
$236$	−14.9314	+	15.4605i	−0.971951	+	1.00639i
$237$		−	3.50035i		−	0.227372i
$238$	5.05210	−	2.14435i	0.327479	−	0.138998i
$239$		−	13.4660i		−	0.871045i	−0.900178	−	0.435523i	$-0.856564\pi$
$239$		−	13.4660i		−	0.871045i	0.900178	−	0.435523i	$-0.143436\pi$
$240$	21.0977	−	0.734827i	1.36185	−	0.0474328i
$241$		−	24.4534i		−	1.57518i	−0.616200	−	0.787590i	$-0.711329\pi$
$241$		−	24.4534i		−	1.57518i	0.616200	−	0.787590i	$-0.288671\pi$
$242$	−1.19685	−	2.81978i	−0.0769365	−	0.181263i
$243$		−	13.4782i		−	0.864627i
$244$	17.0911	+	16.5062i	1.09415	+	1.05670i
$245$	4.24503			0.271205
$246$	2.62559	+	6.18590i	0.167402	+	0.394398i
$247$	−11.4213	−	6.77756i	−0.726722	−	0.431246i
$248$	2.31250	−	6.02303i	0.146844	−	0.382463i
$249$		−	2.63560i		−	0.167024i
$250$	−18.8122	−	44.3215i	−1.18979	−	2.80314i
$251$			20.9395i			1.32169i	0.750522	+	0.660846i	$0.229802\pi$
$251$			20.9395i			1.32169i	−0.750522	+	0.660846i	$0.770198\pi$
$252$	2.09224	+	2.02063i	0.131799	+	0.127288i
$253$	14.0462			0.883079
$254$	4.23072	+	9.96758i	0.265459	+	0.625421i
$255$			20.4816i			1.28261i
$256$	−15.9612	+	1.11320i	−0.997577	+	0.0695751i
$257$	1.15045			0.0717633			0.0358816	−	0.999356i	$-0.488576\pi$
$257$	1.15045			0.0717633			0.0358816	+	0.999356i	$0.488576\pi$
$258$	−5.49912	−	12.9559i	−0.342361	−	0.806602i
$259$		−	3.24019i		−	0.201336i
$260$	29.5247	−	8.08368i	1.83104	−	0.501328i
$261$			10.2262i			0.632984i
$262$	−3.53816	+	1.50177i	−0.218588	+	0.0927794i
$263$	−4.03698			−0.248931			−0.124465	−	0.992224i	$-0.539722\pi$
$263$	−4.03698			−0.248931			−0.124465	+	0.992224i	$0.539722\pi$
$264$	−3.74615	+	9.75707i	−0.230560	+	0.600506i
$265$		−	10.7369i		−	0.659560i
$266$	−4.79513	+	2.03528i	−0.294008	+	0.124791i
$267$	17.9418			1.09802
$268$	−12.0237	+	12.4497i	−0.734462	+	0.760488i
$269$		−	4.24698i		−	0.258943i	−0.991583	−	0.129472i	$-0.958672\pi$
$269$		−	4.24698i		−	0.258943i	0.991583	−	0.129472i	$-0.0413281\pi$
$270$	−30.6032	+	12.9894i	−1.86245	+	0.790513i
$271$		−	25.3475i		−	1.53975i	−0.638194	−	0.769875i	$-0.720318\pi$
$271$		−	25.3475i		−	1.53975i	0.638194	−	0.769875i	$-0.279682\pi$
$272$	−0.540348	−	15.5140i	−0.0327634	−	0.940673i
$273$	−3.85494	−	2.28757i	−0.233312	−	0.138450i
$274$	−30.0022	+	12.7344i	−1.81250	+	0.769311i
$275$	38.6987			2.33362
$276$	8.45249	+	8.16322i	0.508780	+	0.491368i
$277$		−	6.89186i		−	0.414092i	−0.978331	−	0.207046i	$-0.933615\pi$
$277$		−	6.89186i		−	0.414092i	0.978331	−	0.207046i	$-0.0663849\pi$
$278$	−8.60874	+	3.65396i	−0.516318	+	0.219150i
$279$			3.31738i			0.198607i
$280$	4.30360	−	11.2090i	0.257189	−	0.669864i
$281$		−	1.99156i		−	0.118807i	−0.998234	−	0.0594033i	$-0.981080\pi$
$281$		−	1.99156i		−	0.118807i	0.998234	−	0.0594033i	$-0.0189198\pi$
$282$	−0.218599	−	0.515020i	−0.0130174	−	0.0306690i
$283$		−	5.18039i		−	0.307942i	−0.988075	−	0.153971i	$-0.950794\pi$
$283$		−	5.18039i		−	0.307942i	0.988075	−	0.153971i	$-0.0492062\pi$
$284$	7.61173	+	7.35123i	0.451673	+	0.436216i
$285$		−	19.4398i		−	1.15152i
$286$	−2.02712	+	15.0191i	−0.119866	+	0.888098i
$287$	3.82209			0.225611
$288$	7.45658	−	3.47603i	0.439383	−	0.204827i
$289$	−1.93904			−0.114061
$290$	38.8573	−	16.4929i	2.28178	−	0.968497i
$291$	−4.26184			−0.249833
$292$	17.5490	+	16.9484i	1.02698	+	0.991830i
$293$	−8.11470			−0.474066			−0.237033	−	0.971502i	$-0.576175\pi$
$293$	−8.11470			−0.474066			−0.237033	+	0.971502i	$0.576175\pi$
$294$	−1.61846	+	0.686953i	−0.0943906	+	0.0400639i
$295$	−45.6204			−2.65612
$296$	−8.55571	−	3.28490i	−0.497290	−	0.190931i
$297$		−	16.4595i		−	0.955079i
$298$	−1.94356	−	4.57902i	−0.112587	−	0.265256i
$299$	14.6536	+	8.69562i	0.847439	+	0.502881i
$300$	23.2874	+	22.4905i	1.34450	+	1.29849i
$301$	−8.00510			−0.461406
$302$	13.2024	−	5.60375i	0.759715	−	0.322459i
$303$	−6.03003			−0.346416
$304$	0.512865	+	14.7249i	0.0294148	+	0.844530i
$305$			50.4320i			2.88773i
$306$	3.11862	+	7.34746i	0.178279	+	0.420027i
$307$	22.6768			1.29424			0.647118	−	0.762390i	$-0.275974\pi$
$307$	22.6768			1.29424			0.647118	+	0.762390i	$0.275974\pi$
$308$	4.27585	+	4.12951i	0.243639	+	0.235301i
$309$			13.5862i			0.772891i
$310$	12.6054	−	5.35032i	0.715937	−	0.303878i
$311$	1.90309			0.107914			0.0539571	−	0.998543i	$-0.482817\pi$
$311$	1.90309			0.107914			0.0539571	+	0.998543i	$0.482817\pi$
$312$	−9.94846	+	7.85983i	−0.563220	+	0.444975i
$313$	30.9361			1.74861			0.874306	−	0.485376i	$-0.161317\pi$
$313$	30.9361			1.74861			0.874306	+	0.485376i	$0.161317\pi$
$314$	−9.28652	+	3.94164i	−0.524068	+	0.222440i
$315$			6.17371i			0.347849i
$316$	−3.91179	+	4.05041i	−0.220055	+	0.227853i
$317$	10.9849			0.616975			0.308488	−	0.951228i	$-0.400177\pi$
$317$	10.9849			0.616975			0.308488	+	0.951228i	$0.400177\pi$
$318$	1.73750	+	4.09354i	0.0974339	+	0.229554i
$319$			20.8989i			1.17012i
$320$	−25.2343	−	22.7273i	−1.41064	−	1.27049i
$321$	24.0020			1.33966
$322$	6.15217	−	2.61127i	0.342847	−	0.145521i
$323$	−14.2949			−0.795390
$324$	3.50385	−	3.62801i	0.194658	−	0.201556i
$325$	40.3721	+	23.9573i	2.23944	+	1.32891i
$326$	11.3921	+	26.8397i	0.630948	+	1.48651i
$327$			7.43844i			0.411347i
$328$	3.87482	−	10.0922i	0.213951	−	0.557248i
$329$	−0.318216			−0.0175438
$330$	−20.4202	+	8.66731i	−1.12410	+	0.477120i
$331$	−21.1523			−1.16264			−0.581319	−	0.813676i	$-0.697463\pi$
$331$	−21.1523			−1.16264			−0.581319	+	0.813676i	$0.697463\pi$
$332$	−2.94540	+	3.04977i	−0.161650	+	0.167378i
$333$	4.71234			0.258235
$334$	8.31909	−	3.53102i	0.455200	−	0.193209i
$335$	−36.7363			−2.00712
$336$	0.173103	+	4.96997i	0.00944354	+	0.271134i
$337$	−22.7775			−1.24077			−0.620385	−	0.784297i	$-0.713024\pi$
$337$	−22.7775			−1.24077			−0.620385	+	0.784297i	$0.713024\pi$
$338$	−11.4127	+	14.4136i	−0.620767	+	0.783995i
$339$			14.7724i			0.802326i
$340$	22.8891	−	23.7002i	1.24134	−	1.28532i
$341$			6.77965i			0.367138i
$342$	−2.96000	−	6.97375i	−0.160058	−	0.377097i
$343$			1.00000i			0.0539949i
$344$	−8.11555	+	21.1374i	−0.437561	+	1.13965i
$345$			24.9414i			1.34280i
$346$	−4.80617	+	2.03997i	−0.258381	+	0.109669i
$347$		−	8.80009i		−	0.472414i	−0.971703	−	0.236207i	$-0.924096\pi$
$347$		−	8.80009i		−	0.472414i	0.971703	−	0.236207i	$-0.0759043\pi$
$348$	−12.1458	+	12.5762i	−0.651083	+	0.674154i
$349$	−7.29071			−0.390263			−0.195131	−	0.980777i	$-0.562513\pi$
$349$	−7.29071			−0.390263			−0.195131	+	0.980777i	$0.562513\pi$
$350$	16.9498	−	7.19431i	0.906006	−	0.384552i
$351$	10.1896	−	17.1712i	0.543882	−	0.916533i
$352$	15.2388	−	7.10386i	0.812231	−	0.378637i
$353$		−	16.0655i		−	0.855078i	−0.903997	−	0.427539i	$-0.859381\pi$
$353$		−	16.0655i		−	0.855078i	0.903997	−	0.427539i	$-0.140619\pi$
$354$	17.3933	−	7.38253i	0.924441	−	0.392377i
$355$			22.4605i			1.19208i
$356$	−20.7612	−	20.0507i	−1.10034	−	1.06269i
$357$	−4.82484			−0.255358
$358$	26.6215	−	11.2994i	1.40699	−	0.597194i
$359$			3.43324i			0.181200i	0.995887	+	0.0905999i	$0.0288784\pi$
$359$			3.43324i			0.181200i	−0.995887	+	0.0905999i	$0.971122\pi$
$360$	16.3017	+	6.25890i	0.859173	+	0.329873i
$361$	−5.43216			−0.285903
$362$	−25.5362	+	10.8388i	−1.34215	+	0.569674i
$363$			2.69295i			0.141343i
$364$	1.90427	+	6.95512i	0.0998109	+	0.364548i
$365$			51.7830i			2.71045i
$366$	−8.16117	−	19.2277i	−0.426591	−	1.00505i
$367$	−17.1507			−0.895260			−0.447630	−	0.894219i	$-0.647732\pi$
$367$	−17.1507			−0.895260			−0.447630	+	0.894219i	$0.647732\pi$
$368$	−0.658006	−	18.8921i	−0.0343010	−	0.984817i
$369$			5.55861i			0.289370i
$370$	−7.60013	−	17.9059i	−0.395112	−	0.930884i
$371$	2.52928			0.131314
$372$	−3.94011	+	4.07973i	−0.204285	+	0.211524i
$373$			9.16344i			0.474465i	0.971453	+	0.237233i	$0.0762403\pi$
$373$			9.16344i			0.474465i	−0.971453	+	0.237233i	$0.923760\pi$
$374$	6.37343	+	15.0158i	0.329562	+	0.776449i
$375$			42.3278i			2.18580i
$376$	−0.322607	+	0.840248i	−0.0166372	+	0.0433325i
$377$	−12.9379	+	21.8026i	−0.666337	+	1.12289i
$378$	−3.05992	−	7.20918i	−0.157385	−	0.370800i
$379$	−30.7837			−1.58125			−0.790627	−	0.612298i	$-0.790245\pi$
$379$	−30.7837			−1.58125			−0.790627	+	0.612298i	$0.790245\pi$
$380$	−21.7249	+	22.4947i	−1.11446	+	1.15396i
$381$		−	9.51922i		−	0.487684i
$382$	−3.34069	−	7.87068i	−0.170925	−	0.402699i
$383$			37.8476i			1.93392i	0.254921	+	0.966962i	$0.417951\pi$
$383$			37.8476i			1.93392i	−0.254921	+	0.966962i	$0.582049\pi$
$384$	13.2987	+	4.58147i	0.678645	+	0.233797i
$385$			12.6170i			0.643024i
$386$	1.78761	−	0.758746i	0.0909868	−	0.0386192i
$387$		−	11.6421i		−	0.591803i
$388$	4.93157	+	4.76279i	0.250362	+	0.241794i
$389$		−	32.2732i		−	1.63631i	−0.574994	−	0.818157i	$-0.694996\pi$
$389$		−	32.2732i		−	1.63631i	0.574994	−	0.818157i	$-0.305004\pi$
$390$	−26.6688	−	3.59947i	−1.35043	−	0.182266i
$391$	18.3404			0.927514
$392$	2.64050	+	1.01380i	0.133365	+	0.0512045i
$393$	3.37901			0.170448
$394$	8.57564	+	20.2042i	0.432035	+	1.01787i
$395$	−11.9518			−0.601362
$396$	−6.00572	+	6.21854i	−0.301799	+	0.312493i
$397$	−6.45949			−0.324192			−0.162096	−	0.986775i	$-0.551825\pi$
$397$	−6.45949			−0.324192			−0.162096	+	0.986775i	$0.551825\pi$
$398$	15.0810	+	35.5309i	0.755943	+	1.78100i
$399$	4.57944			0.229259
$400$	−1.81287	−	52.0495i	−0.0906436	−	2.60247i
$401$			2.05810i			0.102777i	0.998679	+	0.0513883i	$0.0163646\pi$
$401$			2.05810i			0.102777i	−0.998679	+	0.0513883i	$0.983635\pi$
$402$	14.0061	−	5.94486i	0.698561	−	0.296503i
$403$	−4.19708	+	7.07279i	−0.209072	+	0.352321i
$404$	6.97762	+	6.73882i	0.347150	+	0.335269i
$405$	10.7054			0.531957
$406$	3.88523	+	9.15361i	0.192821	+	0.454286i
$407$	9.63048			0.477365
$408$	−4.89142	+	12.7400i	−0.242161	+	0.630723i
$409$			25.4159i			1.25674i	0.777916	+	0.628368i	$0.216277\pi$
$409$			25.4159i			1.25674i	−0.777916	+	0.628368i	$0.783723\pi$
$410$	21.1216	−	8.96501i	1.04312	−	0.442750i
$411$	28.6526			1.41333
$412$	15.1832	−	15.7212i	0.748020	−	0.774527i
$413$		−	10.7468i		−	0.528815i
$414$	3.79768	+	8.94734i	0.186646	+	0.439738i
$415$	−8.99918			−0.441753
$416$	20.2955	+	2.02287i	0.995070	+	0.0991795i
$417$	8.22151			0.402609
$418$	−6.04926	−	14.2521i	−0.295879	−	0.697091i
$419$		−	23.1356i		−	1.13025i	−0.825006	−	0.565125i	$-0.808828\pi$
$419$		−	23.1356i		−	1.13025i	0.825006	−	0.565125i	$-0.191172\pi$
$420$	−7.33262	+	7.59246i	−0.357795	+	0.370474i
$421$	7.32172			0.356839			0.178419	−	0.983955i	$-0.442902\pi$
$421$	7.32172			0.356839			0.178419	+	0.983955i	$0.442902\pi$
$422$	8.23388	−	3.49485i	0.400819	−	0.170127i
$423$		−	0.462794i		−	0.0225018i
$424$	2.56418	−	6.67855i	0.124528	−	0.324339i
$425$	50.5296			2.45105
$426$	−3.63467	−	8.56329i	−0.176100	−	0.414893i
$427$	−11.8802			−0.574926
$428$	−27.7738	−	26.8233i	−1.34250	−	1.29655i
$429$	6.79911	−	11.4576i	0.328264	−	0.553180i
$430$	−44.2377	+	18.7766i	−2.13333	+	0.905488i
$431$		−	29.5377i		−	1.42278i	−0.702797	−	0.711390i	$-0.748066\pi$
$431$		−	29.5377i		−	1.42278i	0.702797	−	0.711390i	$-0.251934\pi$
$432$	−22.1379	+	0.771059i	−1.06511	+	0.0370976i
$433$	−27.4093			−1.31721			−0.658604	−	0.752489i	$-0.728853\pi$
$433$	−27.4093			−1.31721			−0.658604	+	0.752489i	$0.728853\pi$
$434$	1.26037	+	2.96944i	0.0604999	+	0.142538i
$435$	−37.1094			−1.77926
$436$	8.31278	−	8.60736i	0.398110	−	0.412218i
$437$	−17.4076			−0.832717
$438$	−8.37980	−	19.7428i	−0.400402	−	0.943349i
$439$	17.6695			0.843320			0.421660	−	0.906754i	$-0.361448\pi$
$439$	17.6695			0.843320			0.421660	+	0.906754i	$0.361448\pi$
$440$	33.3153	+	12.7911i	1.58824	+	0.609793i
$441$	−1.45434			−0.0692543
$442$	−2.64684	+	19.6107i	−0.125897	+	0.932785i
$443$			1.74367i			0.0828444i	0.999142	+	0.0414222i	$0.0131889\pi$
$443$			1.74367i			0.0828444i	−0.999142	+	0.0414222i	$0.986811\pi$
$444$	5.79526	+	5.59692i	0.275031	+	0.265618i
$445$		−	61.2616i		−	2.90408i
$446$	−12.5049	+	5.30770i	−0.592126	+	0.251327i
$447$			4.37305i			0.206838i
$448$	5.35386	−	5.94443i	0.252946	−	0.280848i
$449$			2.54137i			0.119935i	0.998200	+	0.0599673i	$0.0190997\pi$
$449$			2.54137i			0.119935i	−0.998200	+	0.0599673i	$0.980900\pi$
$450$	10.4630	+	24.6508i	0.493230	+	1.16205i
$451$			11.3600i			0.534921i
$452$	16.5088	−	17.0938i	0.776508	−	0.804025i
$453$	−12.6086			−0.592402
$454$	−7.99099	−	18.8268i	−0.375036	−	0.883584i
$455$	−7.81085	+	13.1626i	−0.366178	+	0.617072i
$456$	4.64263	−	12.0920i	0.217411	−	0.566259i
$457$			39.5988i			1.85235i	0.377091	+	0.926176i	$0.376924\pi$
$457$			39.5988i			1.85235i	−0.377091	+	0.926176i	$0.623076\pi$
$458$	2.39327	+	5.63855i	0.111830	+	0.263472i
$459$		−	21.4915i		−	1.00314i
$460$	27.8731	−	28.8608i	1.29959	−	1.34564i
$461$	13.1410			0.612036			0.306018	−	0.952026i	$-0.401003\pi$
$461$	13.1410			0.612036			0.306018	+	0.952026i	$0.401003\pi$
$462$	−2.04176	−	4.81038i	−0.0949911	−	0.223799i
$463$		−	26.9632i		−	1.25309i	−0.779386	−	0.626544i	$-0.784469\pi$
$463$		−	26.9632i		−	1.25309i	0.779386	−	0.626544i	$-0.215531\pi$
$464$	28.1089	−	0.979026i	1.30492	−	0.0454501i
$465$	−12.0384			−0.558266
$466$	−13.3567	−	31.4684i	−0.618738	−	1.45775i
$467$			31.2099i			1.44422i	0.691776	+	0.722112i	$0.256829\pi$
$467$			31.2099i			1.44422i	−0.691776	+	0.722112i	$0.743171\pi$
$468$	−10.1151	+	2.76946i	−0.467571	+	0.128018i
$469$		−	8.65396i		−	0.399603i
$470$	−1.75852	+	0.746401i	−0.0811146	+	0.0344289i
$471$	8.86879			0.408652
$472$	−28.3768	−	10.8951i	−1.30615	−	0.501486i
$473$		−	23.7927i		−	1.09399i
$474$	4.55676	−	1.93411i	0.209299	−	0.0888365i
$475$	−47.9595			−2.20053
$476$	5.58305	+	5.39198i	0.255899	+	0.247141i
$477$			3.67843i			0.168424i
$478$	17.5301	−	7.44062i	0.801809	−	0.340326i
$479$		−	7.12602i		−	0.325596i	−0.986659	−	0.162798i	$-0.947948\pi$
$479$		−	7.12602i		−	0.325596i	0.986659	−	0.162798i	$-0.0520519\pi$
$480$	12.6141	+	27.0590i	0.575750	+	1.23507i
$481$	10.0469	+	5.96195i	0.458099	+	0.271841i
$482$	31.8335	−	13.5117i	1.44997	−	0.615439i
$483$	−5.87543			−0.267341
$484$	3.00949	−	3.11613i	0.136795	−	0.141642i
$485$			14.5519i			0.660769i
$486$	17.5460	−	7.44735i	0.795901	−	0.337819i
$487$			1.00402i			0.0454964i	0.999741	+	0.0227482i	$0.00724160\pi$
$487$			1.00402i			0.0454964i	−0.999741	+	0.0227482i	$0.992758\pi$
$488$	−12.0442	+	31.3697i	−0.545214	+	1.42004i
$489$		−	25.6324i		−	1.15914i
$490$	2.34558	+	5.52619i	0.105963	+	0.249648i
$491$		−	9.80821i		−	0.442638i	−0.975201	−	0.221319i	$-0.928964\pi$
$491$		−	9.80821i		−	0.442638i	0.975201	−	0.221319i	$-0.0710362\pi$
$492$	−6.60206	+	6.83601i	−0.297644	+	0.308191i
$493$			27.2881i			1.22899i
$494$	2.51221	−	18.6132i	0.113030	−	0.837449i
$495$	−18.3495			−0.824748
$496$	9.11856	−	0.317597i	0.409436	−	0.0142605i
$497$	−5.29101			−0.237334
$498$	3.43103	−	1.45630i	0.153748	−	0.0652581i
$499$	2.81067			0.125823			0.0629115	−	0.998019i	$-0.479961\pi$
$499$	2.81067			0.125823			0.0629115	+	0.998019i	$0.479961\pi$
$500$	47.3032	−	48.9795i	2.11546	−	2.19043i
$501$	−7.94488			−0.354951
$502$	−27.2591	+	11.5701i	−1.21664	+	0.516398i
$503$	−1.76210			−0.0785682			−0.0392841	−	0.999228i	$-0.512508\pi$
$503$	−1.76210			−0.0785682			−0.0392841	+	0.999228i	$0.512508\pi$
$504$	−1.47441	+	3.84018i	−0.0656753	+	0.171055i
$505$			20.5894i			0.916214i
$506$	7.76122	+	18.2854i	0.345028	+	0.812887i
$507$	14.1862	−	7.74393i	0.630031	−	0.343920i
$508$	−10.6381	+	11.0151i	−0.471991	+	0.488717i
$509$	−2.58451			−0.114556			−0.0572782	−	0.998358i	$-0.518242\pi$
$509$	−2.58451			−0.114556			−0.0572782	+	0.998358i	$0.518242\pi$
$510$	−26.6630	+	11.3171i	−1.18066	+	0.501128i
$511$	−12.1985			−0.539631
$512$	−10.2685	−	20.1633i	−0.453808	−	0.891099i
$513$			20.3984i			0.900611i
$514$	0.635680	+	1.49766i	0.0280386	+	0.0660591i
$515$	46.3896			2.04417
$516$	13.8276	−	14.3176i	0.608724	−	0.630295i
$517$		−	0.945800i		−	0.0415962i
$518$	4.21809	−	1.79036i	0.185332	−	0.0786639i
$519$	4.58998			0.201478
$520$	26.8372	+	33.9687i	1.17689	+	1.48963i
$521$	−10.1321			−0.443896			−0.221948	−	0.975058i	$-0.571242\pi$
$521$	−10.1321			−0.443896			−0.221948	+	0.975058i	$0.571242\pi$
$522$	−13.3125	+	5.65045i	−0.582670	+	0.247313i
$523$			30.8439i			1.34871i	0.738408	+	0.674355i	$0.235578\pi$
$523$			30.8439i			1.34871i	−0.738408	+	0.674355i	$0.764422\pi$
$524$	−3.91000	−	3.77619i	−0.170809	−	0.164964i
$525$	−16.1874			−0.706475
$526$	−2.23063	−	5.25536i	−0.0972599	−	0.229144i
$527$			8.85230i			0.385612i
$528$	−14.7717	+	0.514495i	−0.642856	+	0.0223905i
$529$	−0.666049			−0.0289586
$530$	13.9773	−	5.93263i	0.607134	−	0.257697i
$531$	15.6295			0.678262
$532$	−5.29908	−	5.11773i	−0.229744	−	0.221882i
$533$	−7.03264	+	11.8512i	−0.304617	+	0.513332i
$534$	9.91368	+	23.3566i	0.429007	+	1.01074i
$535$		−	81.9542i		−	3.54319i
$536$	−22.8507	−	8.77336i	−0.987002	−	0.378952i
$537$	−25.4240			−1.09713
$538$	5.52873	−	2.34666i	0.238361	−	0.101172i
$539$	−2.97219			−0.128021
$540$	−33.8194	−	32.6620i	−1.45536	−	1.40555i
$541$	−39.8533			−1.71343			−0.856713	−	0.515793i	$-0.827497\pi$
$541$	−39.8533			−1.71343			−0.856713	+	0.515793i	$0.827497\pi$
$542$	32.9974	−	14.0057i	1.41736	−	0.601596i
$543$	24.3876			1.04657
$544$	19.8976	−	9.27564i	0.853101	−	0.397690i
$545$	25.3983			1.08795
$546$	0.847927	−	6.28237i	0.0362879	−	0.268861i
$547$		−	33.2749i		−	1.42273i	−0.702821	−	0.711366i	$-0.748077\pi$
$547$		−	33.2749i		−	1.42273i	0.702821	−	0.711366i	$-0.251923\pi$
$548$	−33.1553	−	32.0206i	−1.41632	−	1.36785i
$549$		−	17.2779i		−	0.737404i
$550$	21.3829	+	50.3781i	0.911770	+	2.14813i
$551$		−	25.9002i		−	1.10338i
$552$	−5.95650	+	15.5140i	−0.253525	+	0.660322i
$553$		−	2.81549i		−	0.119727i
$554$	8.97184	−	3.80808i	0.381177	−	0.161790i
$555$			17.1005i			0.725875i
$556$	−9.51348	−	9.18790i	−0.403461	−	0.389654i
$557$	24.4137			1.03444			0.517222	−	0.855852i	$-0.326966\pi$
$557$	24.4137			1.03444			0.517222	+	0.855852i	$0.326966\pi$
$558$	−4.31858	+	1.83301i	−0.182820	+	0.0775976i
$559$	14.7294	−	24.8215i	0.622986	−	1.04984i
$560$	16.9698	−	0.591055i	0.717106	−	0.0249766i
$561$		−	14.3404i		−	0.605451i
$562$	2.59262	−	1.10043i	0.109363	−	0.0464190i
$563$			11.8363i			0.498842i	0.968395	+	0.249421i	$0.0802403\pi$
$563$			11.8363i			0.498842i	−0.968395	+	0.249421i	$0.919760\pi$
$564$	0.549668	−	0.569146i	0.0231452	−	0.0239654i
$565$	50.4399			2.12202
$566$	6.74384	−	2.86241i	0.283465	−	0.120316i
$567$			2.52188i			0.105909i
$568$	−5.36401	+	13.9709i	−0.225069	+	0.586205i
$569$	−22.6270			−0.948573			−0.474286	−	0.880371i	$-0.657294\pi$
$569$	−22.6270			−0.948573			−0.474286	+	0.880371i	$0.657294\pi$
$570$	25.3069	−	10.7414i	1.05999	−	0.449910i
$571$			1.63950i			0.0686108i	0.999411	+	0.0343054i	$0.0109219\pi$
$571$			1.63950i			0.0686108i	−0.999411	+	0.0343054i	$0.989078\pi$
$572$	−20.6720	+	5.65986i	−0.864339	+	0.236651i
$573$			7.51664i			0.314012i
$574$	2.11188	+	4.97560i	0.0881484	+	0.207678i
$575$	61.5322			2.56607
$576$	8.64522	+	7.78633i	0.360218	+	0.324430i
$577$			29.5910i			1.23189i	0.787789	+	0.615945i	$0.211226\pi$
$577$			29.5910i			1.23189i	−0.787789	+	0.615945i	$0.788774\pi$
$578$	−1.07141	−	2.52425i	−0.0445649	−	0.104995i
$579$	−1.70720			−0.0709487
$580$	42.9410	+	41.4714i	1.78303	+	1.72201i
$581$		−	2.11994i		−	0.0879497i
$582$	−2.35487	−	5.54807i	−0.0976124	−	0.229975i
$583$			7.51751i			0.311344i
$584$	−12.3668	+	32.2101i	−0.511743	+	1.33286i
$585$	−19.1429	−	11.3596i	−0.791461	−	0.469663i
$586$	−4.48376	−	10.5637i	−0.185222	−	0.436384i
$587$	41.1847			1.69988			0.849938	−	0.526882i	$-0.176639\pi$
$587$	41.1847			1.69988			0.849938	+	0.526882i	$0.176639\pi$
$588$	−1.78855	−	1.72734i	−0.0737587	−	0.0712344i
$589$		−	8.40205i		−	0.346200i
$590$	−25.2074	−	59.3888i	−1.03777	−	2.44500i
$591$		−	19.2954i		−	0.793707i
$592$	−0.451147	−	12.9529i	−0.0185420	−	0.532361i
$593$			3.33933i			0.137130i	0.997647	+	0.0685650i	$0.0218421\pi$
$593$			3.33933i			0.137130i	−0.997647	+	0.0685650i	$0.978158\pi$
$594$	21.4271	−	9.09468i	0.879163	−	0.373159i
$595$			16.4743i			0.675380i
$596$	4.88708	−	5.06026i	0.200183	−	0.207276i
$597$		−	33.9326i		−	1.38877i
$598$	−3.22318	+	23.8808i	−0.131806	+	0.976560i
$599$	−27.4683			−1.12232			−0.561162	−	0.827706i	$-0.689646\pi$
$599$	−27.4683			−1.12232			−0.561162	+	0.827706i	$0.689646\pi$
$600$	−16.4107	+	42.7427i	−0.669965	+	1.74496i
$601$	−9.80041			−0.399767			−0.199884	−	0.979820i	$-0.564056\pi$
$601$	−9.80041			−0.399767			−0.199884	+	0.979820i	$0.564056\pi$
$602$	−4.42320	−	10.4211i	−0.180276	−	0.424731i
$603$	12.5858			0.512533
$604$	14.5900	+	14.0906i	0.593657	+	0.573340i
$605$	9.19499			0.373829
$606$	−3.33188	−	7.84991i	−0.135348	−	0.318881i
$607$	24.7016			1.00261			0.501304	−	0.865271i	$-0.332854\pi$
$607$	24.7016			1.00261			0.501304	+	0.865271i	$0.332854\pi$
$608$	−18.8855	+	8.80385i	−0.765909	+	0.357043i
$609$		−	8.74186i		−	0.354238i
$610$	−65.6525	+	27.8661i	−2.65819	+	1.12826i
$611$	0.585517	−	0.986695i	0.0236875	−	0.0399174i
$612$	−7.84177	+	8.11965i	−0.316985	+	0.328217i
$613$	33.1575			1.33922			0.669610	−	0.742713i	$-0.266461\pi$
$613$	33.1575			1.33922			0.669610	+	0.742713i	$0.266461\pi$
$614$	12.5300	+	29.5208i	0.505671	+	1.19136i
$615$	−20.1715			−0.813393
$616$	−3.01320	+	7.84806i	−0.121405	+	0.316208i
$617$		−	45.3381i		−	1.82524i	−0.408805	−	0.912622i	$-0.634054\pi$
$617$		−	45.3381i		−	1.82524i	0.408805	−	0.912622i	$-0.365946\pi$
$618$	−17.6865	+	7.50701i	−0.711457	+	0.301976i
$619$	−22.2066			−0.892560			−0.446280	−	0.894893i	$-0.647251\pi$
$619$	−22.2066			−0.892560			−0.446280	+	0.894893i	$0.647251\pi$
$620$	13.9301	+	13.4534i	0.559448	+	0.540301i
$621$		−	26.1712i		−	1.05021i
$622$	1.05155	+	2.47744i	0.0421632	+	0.0993364i
$623$	14.4314			0.578181
$624$	−15.7289	−	8.60800i	−0.629662	−	0.344596i
$625$	79.4259			3.17704
$626$	17.0937	+	40.2727i	0.683200	+	1.60962i
$627$			13.6110i			0.543570i
$628$	−10.2625	−	9.91127i	−0.409518	−	0.395503i
$629$	12.5747			0.501385
$630$	−8.03696	+	3.41127i	−0.320200	+	0.135908i
$631$			9.86072i			0.392549i	0.980549	+	0.196275i	$0.0628844\pi$
$631$			9.86072i			0.392549i	−0.980549	+	0.196275i	$0.937116\pi$
$632$	−7.43429	−	2.85434i	−0.295720	−	0.113539i
$633$	−7.86350			−0.312546
$634$	6.06970	+	14.3002i	0.241059	+	0.567934i
$635$	−32.5031			−1.28985
$636$	−4.36894	+	4.52375i	−0.173240	+	0.179379i
$637$	−3.10071	−	1.84000i	−0.122855	−	0.0729034i
$638$	−27.2063	+	11.5477i	−1.07711	+	0.457176i
$639$		−	7.69493i		−	0.304407i
$640$	15.6433	−	45.4079i	0.618355	−	1.79491i
$641$	−29.8909			−1.18062			−0.590311	−	0.807176i	$-0.700995\pi$
$641$	−29.8909			−1.18062			−0.590311	+	0.807176i	$0.700995\pi$
$642$	13.2622	+	31.2459i	0.523419	+	1.23318i
$643$	−34.3349			−1.35404			−0.677019	−	0.735966i	$-0.736728\pi$
$643$	−34.3349			−1.35404			−0.677019	+	0.735966i	$0.736728\pi$
$644$	6.79873	+	6.56605i	0.267908	+	0.258739i
$645$	42.2478			1.66351
$646$	−7.89862	−	18.6092i	−0.310767	−	0.732168i
$647$	−9.52056			−0.374292			−0.187146	−	0.982332i	$-0.559924\pi$
$647$	−9.52056			−0.374292			−0.187146	+	0.982332i	$0.559924\pi$
$648$	6.65900	+	2.55667i	0.261590	+	0.100436i
$649$	31.9415			1.25381
$650$	−8.88017	+	65.7940i	−0.348309	+	2.58065i
$651$		−	2.83587i		−	0.111147i
$652$	−28.6454	+	29.6604i	−1.12184	+	1.16159i
$653$		−	46.5326i		−	1.82096i	−0.413554	−	0.910480i	$-0.635713\pi$
$653$		−	46.5326i		−	1.82096i	0.413554	−	0.910480i	$-0.364287\pi$
$654$	−9.68338	+	4.11009i	−0.378650	+	0.160717i
$655$		−	11.5375i		−	0.450809i
$656$	15.2791	−	0.532167i	0.596548	−	0.0207776i
$657$		−	17.7408i		−	0.692134i
$658$	−0.175829	−	0.414254i	−0.00685455	−	0.0161493i
$659$			24.5788i			0.957456i	0.877963	+	0.478728i	$0.158902\pi$
$659$			24.5788i			0.957456i	−0.877963	+	0.478728i	$0.841098\pi$
$660$	−22.5663	−	21.7940i	−0.878391	−	0.848329i
$661$	−19.4726			−0.757395			−0.378697	−	0.925521i	$-0.623628\pi$
$661$	−19.4726			−0.757395			−0.378697	+	0.925521i	$0.623628\pi$
$662$	−11.6877	−	27.5362i	−0.454255	−	1.07022i
$663$	8.87771	−	14.9604i	0.344782	−	0.581015i
$664$	−5.59768	−	2.14919i	−0.217232	−	0.0834046i
$665$		−	15.6364i		−	0.606352i
$666$	2.60379	+	6.13454i	0.100895	+	0.237708i
$667$			33.2300i			1.28667i
$668$	9.19339	+	8.87876i	0.355703	+	0.343530i
$669$	11.9424			0.461722
$670$	−20.2986	−	47.8234i	−0.784202	−	1.84758i
$671$		−	35.3104i		−	1.36314i
$672$	−6.37427	+	2.97149i	−0.245893	+	0.114628i
$673$	−33.4160			−1.28809			−0.644046	−	0.764987i	$-0.722745\pi$
$673$	−33.4160			−1.28809			−0.644046	+	0.764987i	$0.722745\pi$
$674$	−12.5857	−	29.6518i	−0.484782	−	1.14215i
$675$		−	72.1041i		−	2.77529i
$676$	−25.0697	−	6.89284i	−0.964218	−	0.265109i
$677$			16.9070i			0.649790i	0.945750	+	0.324895i	$0.105329\pi$
$677$			16.9070i			0.649790i	−0.945750	+	0.324895i	$0.894671\pi$
$678$	−19.2307	+	8.16244i	−0.738552	+	0.313477i
$679$	−3.42799			−0.131554
$680$	43.5003	+	16.7016i	1.66816	+	0.640477i
$681$			17.9799i			0.688992i
$682$	−8.82576	+	3.74608i	−0.337956	+	0.143445i
$683$	3.07903			0.117816			0.0589080	−	0.998263i	$-0.481238\pi$
$683$	3.07903			0.117816			0.0589080	+	0.998263i	$0.481238\pi$
$684$	7.44291	−	7.70666i	0.284587	−	0.294672i
$685$		−	97.8336i		−	3.73803i
$686$	−1.30180	+	0.552548i	−0.0497031	+	0.0210964i
$687$		−	5.38492i		−	0.205448i
$688$	−32.0010	+	1.11459i	−1.22003	+	0.0424932i
$689$	−4.65388	+	7.84257i	−0.177299	+	0.298778i
$690$	−32.4688	+	13.7813i	−1.23606	+	0.524645i
$691$	−29.3592			−1.11688			−0.558439	−	0.829546i	$-0.688600\pi$
$691$	−29.3592			−1.11688			−0.558439	+	0.829546i	$0.688600\pi$
$692$	−5.31128	−	5.12951i	−0.201904	−	0.194995i
$693$		−	4.32258i		−	0.164201i
$694$	11.4560	−	4.86247i	0.434863	−	0.184577i
$695$		−	28.0721i		−	1.06484i
$696$	−23.0828	−	8.86248i	−0.874953	−	0.335931i
$697$			14.8329i			0.561837i
$698$	−4.02846	−	9.49106i	−0.152480	−	0.359242i
$699$			30.0529i			1.13671i
$700$	18.7312	+	18.0901i	0.707971	+	0.683742i
$701$			23.1700i			0.875119i	0.899190	+	0.437559i	$0.144157\pi$
$701$			23.1700i			0.875119i	−0.899190	+	0.437559i	$0.855843\pi$
$702$	27.9838	+	3.77695i	1.05618	+	0.142552i
$703$	−11.9351			−0.450141
$704$	17.6680	+	15.9127i	0.665888	+	0.599732i
$705$	1.67942			0.0632506
$706$	20.9141	−	8.87693i	0.787111	−	0.334088i
$707$	−4.85023			−0.182412
$708$	19.2212	+	18.5634i	0.722377	+	0.697655i
$709$	−1.93611			−0.0727121			−0.0363561	−	0.999339i	$-0.511575\pi$
$709$	−1.93611			−0.0727121			−0.0363561	+	0.999339i	$0.511575\pi$
$710$	−29.2391	+	12.4105i	−1.09732	+	0.465757i
$711$	4.09468			0.153562
$712$	14.6305	−	38.1060i	0.548301	−	1.42808i
$713$			10.7798i			0.403708i
$714$	−2.66596	−	6.28100i	−0.0997709	−	0.235060i
$715$	−39.1218	−	23.2154i	−1.46307	−	0.868205i
$716$	29.4193	+	28.4125i	1.09945	+	1.06182i
$717$	−16.7416			−0.625226
$718$	−4.46941	+	1.89703i	−0.166797	+	0.0707966i
$719$	−33.4382			−1.24703			−0.623517	−	0.781810i	$-0.714297\pi$
$719$	−33.4382			−1.24703			−0.623517	+	0.781810i	$0.714297\pi$
$720$	0.859595	+	24.6799i	0.0320352	+	0.919765i
$721$			10.9280i			0.406980i
$722$	−3.00153	−	7.07160i	−0.111705	−	0.263178i
$723$	−30.4015			−1.13065
$724$	−28.2200	−	27.2542i	−1.04879	−	1.01289i
$725$			91.5517i			3.40015i
$726$	−3.50568	+	1.48798i	−0.130108	+	0.0552241i
$727$	−47.6574			−1.76752			−0.883758	−	0.467943i	$-0.844995\pi$
$727$	−47.6574			−1.76752			−0.883758	+	0.467943i	$0.844995\pi$
$728$	−8.00200	+	6.32202i	−0.296574	+	0.234310i
$729$	−24.3223			−0.900828
$730$	−67.4113	+	28.6126i	−2.49500	+	1.05900i
$731$		−	31.0666i		−	1.14904i
$732$	20.5213	−	21.2485i	0.758488	−	0.785366i
$733$	−10.5296			−0.388921			−0.194460	−	0.980910i	$-0.562296\pi$
$733$	−10.5296			−0.388921			−0.194460	+	0.980910i	$0.562296\pi$
$734$	−9.47658	−	22.3268i	−0.349787	−	0.824099i
$735$		−	5.27761i		−	0.194668i
$736$	24.2302	−	11.2954i	0.893136	−	0.416353i
$737$	25.7213			0.947455
$738$	−7.23622	+	3.07140i	−0.266369	+	0.113060i
$739$	−37.2518			−1.37033			−0.685164	−	0.728388i	$-0.740270\pi$
$739$	−37.2518			−1.37033			−0.685164	+	0.728388i	$0.740270\pi$
$740$	19.1105	−	19.7877i	0.702517	−	0.727412i
$741$	−8.42617	+	14.1995i	−0.309543	+	0.521632i
$742$	1.39755	+	3.29263i	0.0513056	+	0.120876i
$743$			17.1129i			0.627810i	0.949454	+	0.313905i	$0.101637\pi$
$743$			17.1129i			0.627810i	−0.949454	+	0.313905i	$0.898363\pi$
$744$	−7.48811	−	2.87500i	−0.274527	−	0.105403i
$745$	14.9317			0.547054
$746$	−11.9290	+	5.06324i	−0.436752	+	0.185378i
$747$	3.08311			0.112805
$748$	−16.0260	+	16.5939i	−0.585969	+	0.606733i
$749$	19.3059			0.705423
$750$	−55.1025	+	23.3881i	−2.01206	+	0.854014i
$751$	0.528361			0.0192802			0.00964009	−	0.999954i	$-0.496931\pi$
$751$	0.528361			0.0192802			0.00964009	+	0.999954i	$0.496931\pi$
$752$	−1.27209	+	0.0443067i	−0.0463884	+	0.00161570i
$753$	26.0330			0.948695
$754$	−35.5315	−	4.79566i	−1.29398	−	0.174648i
$755$			43.0516i			1.56681i
$756$	7.69417	−	7.96683i	0.279834	−	0.289751i
$757$			23.8685i			0.867515i	0.901030	+	0.433758i	$0.142813\pi$
$757$			23.8685i			0.867515i	−0.901030	+	0.433758i	$0.857187\pi$
$758$	−17.0095	−	40.0744i	−0.617812	−	1.45557i
$759$		−	17.4629i		−	0.633864i
$760$	−41.2878	−	15.8521i	−1.49766	−	0.575017i
$761$			24.1900i			0.876887i	0.898759	+	0.438444i	$0.144470\pi$
$761$			24.1900i			0.876887i	−0.898759	+	0.438444i	$0.855530\pi$
$762$	12.3921	−	5.25982i	0.448920	−	0.190543i
$763$			5.98308i			0.216602i
$764$	8.40018	−	8.69785i	0.303908	−	0.314677i
$765$	−23.9592			−0.866248
$766$	−49.2702	+	20.9126i	−1.78020	+	0.755604i
$767$	33.3227	+	19.7741i	1.20321	+	0.714001i
$768$	1.38398	+	19.8437i	0.0499402	+	0.716049i
$769$		−	13.0043i		−	0.468947i	−0.972123	−	0.234474i	$-0.924663\pi$
$769$		−	13.0043i		−	0.468947i	0.972123	−	0.234474i	$-0.0753366\pi$
$770$	−16.4249	+	6.97152i	−0.591913	+	0.251236i
$771$		−	1.43030i		−	0.0515108i
$772$	1.97548	+	1.90787i	0.0710989	+	0.0686657i
$773$	3.76057			0.135258			0.0676292	−	0.997711i	$-0.478457\pi$
$773$	3.76057			0.135258			0.0676292	+	0.997711i	$0.478457\pi$
$774$	15.1558	−	6.43284i	0.544763	−	0.231224i
$775$			29.6995i			1.06684i
$776$	−3.47529	+	9.05160i	−0.124756	+	0.324933i
$777$	−4.02835			−0.144516
$778$	42.0133	−	17.8325i	1.50625	−	0.639325i
$779$		−	14.0785i		−	0.504414i
$780$	−10.0500	−	36.7065i	−0.359848	−	1.31430i
$781$		−	15.7259i		−	0.562717i
$782$	10.1340	+	23.8756i	0.362389	+	0.853790i
$783$	38.9392			1.39157
$784$	0.139235	+	3.99758i	0.00497267	+	0.142771i
$785$		−	30.2822i		−	1.08082i
$786$	1.86706	+	4.39880i	0.0665959	+	0.156900i
$787$	−19.7264			−0.703169			−0.351584	−	0.936156i	$-0.614357\pi$
$787$	−19.7264			−0.703169			−0.351584	+	0.936156i	$0.614357\pi$
$788$	−21.5635	+	22.3276i	−0.768167	+	0.795388i
$789$			5.01896i			0.178680i
$790$	−6.60396	−	15.5589i	−0.234958	−	0.553562i
$791$			11.8821i			0.422479i
$792$	−11.4138	−	4.38222i	−0.405570	−	0.155715i
$793$	21.8597	−	36.8372i	0.776259	−	1.30813i
$794$	−3.56917	−	8.40898i	−0.126665	−	0.298423i
$795$	−13.3486			−0.473425
$796$	−37.9212	+	39.2650i	−1.34408	+	1.39171i
$797$		−	13.5927i		−	0.481479i	−0.970590	−	0.240740i	$-0.922610\pi$
$797$		−	13.5927i		−	0.481479i	0.970590	−	0.240740i	$-0.0773900\pi$
$798$	2.53036	+	5.96153i	0.0895737	+	0.211036i
$799$		−	1.23495i		−	0.0436893i
$800$	66.7565	−	31.1198i	2.36020	−	1.10025i
$801$			20.9881i			0.741579i
$802$	−2.67924	+	1.13720i	−0.0946073	+	0.0401559i
$803$		−	36.2564i		−	1.27946i
$804$	15.4781	+	14.9484i	0.545870	+	0.527188i
$805$			20.0615i			0.707075i
$806$	−11.5265	−	1.55572i	−0.406003	−	0.0547979i
$807$	−5.28004			−0.185866
$808$	−4.91715	+	12.8070i	−0.172985	+	0.450549i
$809$	39.7054			1.39597			0.697983	−	0.716114i	$-0.254081\pi$
$809$	39.7054			1.39597			0.697983	+	0.716114i	$0.254081\pi$
$810$	5.91526	+	13.9364i	0.207841	+	0.489674i
$811$	1.54998			0.0544270			0.0272135	−	0.999630i	$-0.491337\pi$
$811$	1.54998			0.0544270			0.0272135	+	0.999630i	$0.491337\pi$
$812$	−9.76942	+	10.1156i	−0.342839	+	0.354988i
$813$	−31.5132			−1.10521
$814$	5.32130	+	12.5370i	0.186511	+	0.439421i
$815$	−87.5211			−3.06573
$816$	−19.2877	+	0.671785i	−0.675204	+	0.0235172i
$817$			29.4864i			1.03160i
$818$	−33.0865	+	14.0435i	−1.15684	+	0.491020i
$819$	2.67598	−	4.50949i	0.0935065	−	0.157574i
$820$	23.3414	+	22.5425i	0.815115	+	0.787219i
$821$	43.4323			1.51580			0.757900	−	0.652371i	$-0.226226\pi$
$821$	43.4323			1.51580			0.757900	+	0.652371i	$0.226226\pi$
$822$	15.8320	+	37.3001i	0.552203	+	1.30099i
$823$	56.1465			1.95714			0.978571	−	0.205908i	$-0.0660149\pi$
$823$	56.1465			1.95714			0.978571	+	0.205908i	$0.0660149\pi$
$824$	28.8553	+	11.0788i	1.00522	+	0.385947i
$825$		−	48.1121i		−	1.67505i
$826$	13.9902	−	5.93811i	0.486781	−	0.206613i
$827$	−0.504695			−0.0175500			−0.00877499	−	0.999961i	$-0.502793\pi$
$827$	−0.504695			−0.0175500			−0.00877499	+	0.999961i	$0.502793\pi$
$828$	−9.54928	+	9.88767i	−0.331860	+	0.343620i
$829$		−	8.83750i		−	0.306939i	−0.988153	−	0.153470i	$-0.950955\pi$
$829$		−	8.83750i		−	0.306939i	0.988153	−	0.153470i	$-0.0490447\pi$
$830$	−4.97248	−	11.7152i	−0.172597	−	0.406639i
$831$	−8.56827			−0.297230
$832$	8.58086	+	27.5385i	0.297488	+	0.954726i
$833$	−3.88084			−0.134463
$834$	4.54277	+	10.7028i	0.157303	+	0.370607i
$835$			27.1276i			0.938789i
$836$	15.2109	−	15.7499i	0.526079	−	0.544721i
$837$	12.6319			0.436624
$838$	30.1180	−	12.7835i	1.04041	−	0.441600i
$839$		−	3.95785i		−	0.136640i	−0.997663	−	0.0683202i	$-0.978236\pi$
$839$		−	3.95785i		−	0.136640i	0.997663	−	0.0683202i	$-0.0217639\pi$
$840$	−13.9355	−	5.35043i	−0.480821	−	0.184607i
$841$	−20.4418			−0.704888
$842$	4.04560	+	9.53144i	0.139421	+	0.328475i
$843$	−2.47600			−0.0852780
$844$	9.09922	+	8.78781i	0.313208	+	0.302489i
$845$	−26.4414	−	48.4384i	−0.909613	−	1.66633i
$846$	0.602467	−	0.255716i	0.0207132	−	0.00879169i
$847$			2.16606i			0.0744267i
$848$	10.1110	−	0.352164i	0.347213	−	0.0120933i
$849$	−6.44049			−0.221037
$850$	27.9200	+	65.7796i	0.957649	+	2.25622i
$851$	15.3128			0.524915
$852$	9.13939	−	9.46326i	0.313110	−	0.324206i
$853$	10.0094			0.342715			0.171358	−	0.985209i	$-0.445185\pi$
$853$	10.0094			0.342715			0.171358	+	0.985209i	$0.445185\pi$
$854$	−6.56440	−	15.4657i	−0.224629	−	0.529227i
$855$	22.7406			0.777712
$856$	19.5723	−	50.9772i	0.668967	−	1.74236i
$857$	16.3535			0.558624			0.279312	−	0.960200i	$-0.409894\pi$
$857$	16.3535			0.558624			0.279312	+	0.960200i	$0.409894\pi$
$858$	18.6724	+	2.52020i	0.637466	+	0.0860383i
$859$		−	46.1150i		−	1.57342i	−0.617322	−	0.786711i	$-0.711782\pi$
$859$		−	46.1150i		−	1.57342i	0.617322	−	0.786711i	$-0.288218\pi$
$860$	−48.8869	−	47.2138i	−1.66703	−	1.60998i
$861$		−	4.75179i		−	0.161941i
$862$	38.4523	−	16.3210i	1.30969	−	0.555895i
$863$			48.4827i			1.65037i	0.564864	+	0.825184i	$0.308929\pi$
$863$			48.4827i			1.65037i	−0.564864	+	0.825184i	$0.691071\pi$
$864$	−13.2360	−	28.3932i	−0.450299	−	0.965956i
$865$		−	15.6724i		−	0.532876i
$866$	−15.1450	−	35.6816i	−0.514647	−	1.21251i
$867$			2.41071i			0.0818719i
$868$	−3.16921	+	3.28152i	−0.107570	+	0.111382i
$869$	8.36818			0.283871
$870$	−20.5047	−	48.3092i	−0.695176	−	1.63783i
$871$	26.8334	+	15.9233i	0.909216	+	0.539540i
$872$	15.7983	+	6.06563i	0.534998	+	0.205408i
$873$		−	4.98547i		−	0.168732i
$874$	−9.61851	−	22.6612i	−0.325351	−	0.766527i
$875$			34.0462i			1.15097i
$876$	21.0710	−	21.8177i	0.711924	−	0.737152i
$877$	−28.3417			−0.957033			−0.478516	−	0.878079i	$-0.658825\pi$
$877$	−28.3417			−0.957033			−0.478516	+	0.878079i	$0.658825\pi$
$878$	9.76325	+	23.0022i	0.329494	+	0.776288i
$879$			10.0886i			0.340279i
$880$	1.75673	+	50.4376i	0.0592194	+	1.70025i
$881$	41.6725			1.40398			0.701991	−	0.712185i	$-0.252295\pi$
$881$	41.6725			1.40398			0.701991	+	0.712185i	$0.252295\pi$
$882$	−0.803592	−	1.89326i	−0.0270584	−	0.0637495i
$883$		−	13.9586i		−	0.469743i	−0.972026	−	0.234872i	$-0.924533\pi$
$883$		−	13.9586i		−	0.469743i	0.972026	−	0.234872i	$-0.0754670\pi$
$884$	−26.9918	+	7.39018i	−0.907831	+	0.248559i
$885$			56.7174i			1.90653i
$886$	−2.26992	+	0.963462i	−0.0762594	+	0.0323681i
$887$	−26.0576			−0.874929			−0.437465	−	0.899236i	$-0.644124\pi$
$887$	−26.0576			−0.874929			−0.437465	+	0.899236i	$0.644124\pi$
$888$	−4.08394	+	10.6368i	−0.137048	+	0.356949i
$889$		−	7.65675i		−	0.256799i
$890$	79.7506	−	33.8500i	2.67325	−	1.13465i
$891$	−7.49550			−0.251109
$892$	−13.8192	−	13.3462i	−0.462699	−	0.446864i
$893$			1.17213i			0.0392240i
$894$	−5.69285	+	2.41632i	−0.190397	+	0.0808138i
$895$			86.8096i			2.90172i
$896$	10.6967	+	3.68508i	0.357353	+	0.123110i
$897$	10.8108	−	18.2180i	0.360962	−	0.608282i
$898$	−3.30836	+	1.40423i	−0.110402	+	0.0468597i
$899$	−16.0390			−0.534930
$900$	−26.3092	+	27.2415i	−0.876973	+	0.908049i
$901$			9.81575i			0.327010i
$902$	−14.7885	+	6.27693i	−0.492402	+	0.208999i
$903$			9.95231i			0.331192i
$904$	31.3746	+	12.0461i	1.04351	+	0.400646i
$905$		−	83.2706i		−	2.76801i
$906$	−6.96684	−	16.4139i	−0.231458	−	0.545314i
$907$		−	5.70501i		−	0.189432i	−0.995504	−	0.0947159i	$-0.969806\pi$
$907$		−	5.70501i		−	0.189432i	0.995504	−	0.0947159i	$-0.0301943\pi$
$908$	20.0933	−	20.8054i	0.666821	−	0.690451i
$909$		−	7.05388i		−	0.233963i
$910$	−21.4510	−	2.89522i	−0.711093	−	0.0959757i
$911$	−37.8264			−1.25325			−0.626623	−	0.779323i	$-0.715563\pi$
$911$	−37.8264			−1.25325			−0.626623	+	0.779323i	$0.715563\pi$
$912$	18.3067	−	0.637617i	0.606194	−	0.0211136i
$913$	6.30086			0.208528
$914$	−51.5498	+	21.8802i	−1.70512	+	0.723733i
$915$	62.6993			2.07278
$916$	−6.01789	+	6.23114i	−0.198837	+	0.205883i
$917$	2.71789			0.0897527
$918$	27.9777	−	11.8751i	0.923401	−	0.391936i
$919$	15.8594			0.523152			0.261576	−	0.965183i	$-0.415758\pi$
$919$	15.8594			0.523152			0.261576	+	0.965183i	$0.415758\pi$
$920$	52.9723	+	20.3383i	1.74644	+	0.670534i
$921$		−	28.1929i		−	0.928987i
$922$	7.26101	+	17.1070i	0.239129	+	0.563388i
$923$	9.73546	−	16.4059i	0.320446	−	0.540006i
$924$	5.13400	−	5.31593i	0.168896	−	0.174881i
$925$	42.1881			1.38714
$926$	35.1008	−	14.8985i	1.15348	−	0.489594i
$927$	−15.8930			−0.521995
$928$	16.8060	+	36.0513i	0.551684	+	1.18344i
$929$			12.4095i			0.407141i	0.979060	+	0.203571i	$0.0652546\pi$
$929$			12.4095i			0.407141i	−0.979060	+	0.203571i	$0.934745\pi$
$930$	−6.65177	−	15.6716i	−0.218120	−	0.513891i
$931$	3.68346			0.120720
$932$	33.5855	−	34.7756i	1.10013	−	1.13911i
$933$		−	2.36600i		−	0.0774595i
$934$	−40.6292	+	17.2450i	−1.32943	+	0.564273i
$935$	−48.9648			−1.60132
$936$	−9.19437	−	11.6376i	−0.300527	−	0.380388i
$937$	27.8945			0.911275			0.455637	−	0.890165i	$-0.349411\pi$
$937$	27.8945			0.911275			0.455637	+	0.890165i	$0.349411\pi$
$938$	11.2658	−	4.78173i	0.367840	−	0.156129i
$939$		−	38.4612i		−	1.25513i
$940$	−1.94333	−	1.87683i	−0.0633846	−	0.0612153i
$941$	−33.5634			−1.09414			−0.547068	−	0.837088i	$-0.684256\pi$
$941$	−33.5634			−1.09414			−0.547068	+	0.837088i	$0.684256\pi$
$942$	4.90043	+	11.5454i	0.159665	+	0.376170i
$943$			18.0627i			0.588203i
$944$	−1.49632	−	42.9611i	−0.0487012	−	1.39826i
$945$	23.5083			0.764724
$946$	30.9734	−	13.1466i	1.00703	−	0.427433i
$947$	18.9092			0.614466			0.307233	−	0.951634i	$-0.400597\pi$
$947$	18.9092			0.614466			0.307233	+	0.951634i	$0.400597\pi$
$948$	5.03565	+	4.86332i	0.163550	+	0.157953i
$949$	22.4453	−	37.8241i	0.728604	−	1.22782i
$950$	−26.4999	−	62.4339i	−0.859771	−	2.02562i
$951$		−	13.6570i		−	0.442858i
$952$	−3.93439	+	10.2474i	−0.127514	+	0.332119i
$953$	−21.7892			−0.705823			−0.352911	−	0.935657i	$-0.614808\pi$
$953$	−21.7892			−0.705823			−0.352911	+	0.935657i	$0.614808\pi$
$954$	−4.78860	+	2.03251i	−0.155037	+	0.0658049i
$955$	25.6654			0.830512
$956$	19.3725	+	18.7095i	0.626550	+	0.605107i
$957$	25.9825			0.839895
$958$	9.27668	−	3.93747i	0.299716	−	0.127214i
$959$	23.0466			0.744215
$960$	−28.2556	+	31.3724i	−0.911945	+	1.01254i
$961$	25.7969			0.832159
$962$	−2.20990	+	16.3733i	−0.0712499	+	0.527897i
$963$			28.0774i			0.904781i
$964$	35.1790	+	33.9751i	1.13304	+	1.09426i
$965$			5.82918i			0.187648i
$966$	−3.24646	−	7.64865i	−0.104453	−	0.246091i
$967$			42.4630i			1.36552i	0.730643	+	0.682759i	$0.239220\pi$
$967$			42.4630i			1.36552i	−0.730643	+	0.682759i	$0.760780\pi$
$968$	5.71947	+	2.19595i	0.183831	+	0.0705804i
$969$			17.7721i			0.570922i
$970$	−18.9437	+	8.04063i	−0.608247	+	0.258169i
$971$			47.0765i			1.51076i	0.655289	+	0.755378i	$0.272547\pi$
$971$			47.0765i			1.51076i	−0.655289	+	0.755378i	$0.727453\pi$
$972$	19.3900	+	18.7264i	0.621934	+	0.600649i
$973$	6.61294			0.212001
$974$	−1.30703	+	0.554768i	−0.0418801	+	0.0177759i
$975$	29.7848	−	50.1924i	0.953876	−	1.60744i
$976$	−47.4922	+	1.65414i	−1.52019	+	0.0529478i
$977$			23.5667i			0.753967i	0.926220	+	0.376984i	$0.123039\pi$
$977$			23.5667i			0.753967i	−0.926220	+	0.376984i	$0.876961\pi$
$978$	33.3683	−	14.1631i	1.06700	−	0.452887i
$979$			42.8929i			1.37086i
$980$	−5.89797	+	6.10697i	−0.188404	+	0.195080i
$981$	−8.70143			−0.277815
$982$	12.7684	−	5.41950i	0.407455	−	0.172943i
$983$		−	33.4979i		−	1.06842i	−0.845353	−	0.534208i	$-0.820610\pi$
$983$		−	33.4979i		−	1.06842i	0.845353	−	0.534208i	$-0.179390\pi$
$984$	−12.5471	−	4.81736i	−0.399986	−	0.153572i
$985$	−65.8836			−2.09923
$986$	−35.5237	+	15.0780i	−1.13131	+	0.480181i
$987$			0.395621i			0.0125927i
$988$	25.6189	−	7.01429i	0.815045	−	0.223154i
$989$		−	37.8312i		−	1.20296i
$990$	−10.1390	−	23.8874i	−0.322237	−	0.759192i
$991$	−9.57436			−0.304140			−0.152070	−	0.988370i	$-0.548594\pi$
$991$	−9.57436			−0.304140			−0.152070	+	0.988370i	$0.548594\pi$
$992$	5.45189	+	11.6951i	0.173098	+	0.371319i
$993$			26.2976i			0.834528i
$994$	−2.92354	−	6.88785i	−0.0927289	−	0.218469i
$995$	−115.862			−3.67307
$996$	3.79162	+	3.66186i	0.120142	+	0.116030i
$997$			44.0185i			1.39408i	0.717033	+	0.697039i	$0.245500\pi$
$997$			44.0185i			1.39408i	−0.717033	+	0.697039i	$0.754500\pi$
$998$	1.55303	+	3.65894i	0.0491603	+	0.115822i
$999$		−	17.9437i		−	0.567712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.i.a.701.52	yes	84
4.3	odd	2		2912.2.i.a.337.6		84
8.3	odd	2		2912.2.i.a.337.79		84
8.5	even	2	inner	728.2.i.a.701.34	yes	84
13.12	even	2	inner	728.2.i.a.701.33	✓	84
52.51	odd	2		2912.2.i.a.337.80		84
104.51	odd	2		2912.2.i.a.337.5		84
104.77	even	2	inner	728.2.i.a.701.51	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.i.a.701.33	✓	84	13.12	even	2	inner
728.2.i.a.701.34	yes	84	8.5	even	2	inner
728.2.i.a.701.51	yes	84	104.77	even	2	inner
728.2.i.a.701.52	yes	84	1.1	even	1	trivial
2912.2.i.a.337.5		84	104.51	odd	2
2912.2.i.a.337.6		84	4.3	odd	2
2912.2.i.a.337.79		84	8.3	odd	2
2912.2.i.a.337.80		84	52.51	odd	2

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.552548 + 1.30180i) q^{2} -1.24325i q^{3} +(-1.38938 + 1.43862i) q^{4} -4.24503 q^{5} +(1.61846 - 0.686953i) q^{6} -1.00000i q^{7} +(-2.64050 - 1.01380i) q^{8} +1.45434 q^{9} +(-2.34558 - 5.52619i) q^{10} +2.97219 q^{11} +(1.78855 + 1.72734i) q^{12} +(3.10071 + 1.84000i) q^{13} +(1.30180 - 0.552548i) q^{14} +5.27761i q^{15} +(-0.139235 - 3.99758i) q^{16} +3.88084 q^{17} +(0.803592 + 1.89326i) q^{18} -3.68346 q^{19} +(5.89797 - 6.10697i) q^{20} -1.24325 q^{21} +(1.64228 + 3.86921i) q^{22} +4.72588 q^{23} +(-1.26040 + 3.28278i) q^{24} +13.0203 q^{25} +(-0.682027 + 5.05320i) q^{26} -5.53784i q^{27} +(1.43862 + 1.38938i) q^{28} +7.03148i q^{29} +(-6.87041 + 2.91613i) q^{30} +2.28102i q^{31} +(5.12712 - 2.39011i) q^{32} -3.69517i q^{33} +(2.14435 + 5.05210i) q^{34} +4.24503i q^{35} +(-2.02063 + 2.09224i) q^{36} +3.24019 q^{37} +(-2.03528 - 4.79513i) q^{38} +(2.28757 - 3.85494i) q^{39} +(11.2090 + 4.30360i) q^{40} +3.82209i q^{41} +(-0.686953 - 1.61846i) q^{42} -8.00510i q^{43} +(-4.12951 + 4.27585i) q^{44} -6.17371 q^{45} +(2.61127 + 6.15217i) q^{46} -0.318216i q^{47} +(-4.96997 + 0.173103i) q^{48} -1.00000 q^{49} +(7.19431 + 16.9498i) q^{50} -4.82484i q^{51} +(-6.95512 + 1.90427i) q^{52} +2.52928i q^{53} +(7.20918 - 3.05992i) q^{54} -12.6170 q^{55} +(-1.01380 + 2.64050i) q^{56} +4.57944i q^{57} +(-9.15361 + 3.88523i) q^{58} +10.7468 q^{59} +(-7.59246 - 7.33262i) q^{60} -11.8802i q^{61} +(-2.96944 + 1.26037i) q^{62} -1.45434i q^{63} +(5.94443 + 5.35386i) q^{64} +(-13.1626 - 7.81085i) q^{65} +(4.81038 - 2.04176i) q^{66} +8.65396 q^{67} +(-5.39198 + 5.58305i) q^{68} -5.87543i q^{69} +(-5.52619 + 2.34558i) q^{70} -5.29101i q^{71} +(-3.84018 - 1.47441i) q^{72} -12.1985i q^{73} +(1.79036 + 4.21809i) q^{74} -16.1874i q^{75} +(5.11773 - 5.29908i) q^{76} -2.97219i q^{77} +(6.28237 + 0.847927i) q^{78} +2.81549 q^{79} +(0.591055 + 16.9698i) q^{80} -2.52188 q^{81} +(-4.97560 + 2.11188i) q^{82} +2.11994 q^{83} +(1.72734 - 1.78855i) q^{84} -16.4743 q^{85} +(10.4211 - 4.42320i) q^{86} +8.74186 q^{87} +(-7.84806 - 3.01320i) q^{88} +14.4314i q^{89} +(-3.41127 - 8.03696i) q^{90} +(1.84000 - 3.10071i) q^{91} +(-6.56605 + 6.79873i) q^{92} +2.83587 q^{93} +(0.414254 - 0.175829i) q^{94} +15.6364 q^{95} +(-2.97149 - 6.37427i) q^{96} -3.42799i q^{97} +(-0.552548 - 1.30180i) q^{98} +4.32258 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 84 q^{9} + 8 q^{10} - 20 q^{12} - 8 q^{16} + 8 q^{17} - 12 q^{22} - 24 q^{23} + 92 q^{25} - 40 q^{30} + 44 q^{36} + 20 q^{38} - 24 q^{39} - 28 q^{40} - 72 q^{48} - 84 q^{49} - 44 q^{52} + 32 q^{55}+ \cdots - 16 q^{95}+O(q^{100}) \) 84 * q - 84 * q^9 + 8 * q^10 - 20 * q^12 - 8 * q^16 + 8 * q^17 - 12 * q^22 - 24 * q^23 + 92 * q^25 - 40 * q^30 + 44 * q^36 + 20 * q^38 - 24 * q^39 - 28 * q^40 - 72 * q^48 - 84 * q^49 - 44 * q^52 + 32 * q^55 - 40 * q^62 + 72 * q^64 - 24 * q^65 - 60 * q^66 - 92 * q^68 + 28 * q^74 + 12 * q^78 - 40 * q^79 + 84 * q^81 + 24 * q^82 - 48 * q^87 - 108 * q^88 + 20 * q^90 + 60 * q^92 + 36 * q^94 - 16 * q^95

Introduction

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