LMFDB - Embedded newform 756.2.o.a.179.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("756.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			179.16
Character	$\chi$	$=$	756.179
Dual form			756.2.o.a.359.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.608644 - 1.27654i) q^{2} +(-1.25910 + 1.55392i) q^{4} -3.13896i q^{5} +(-0.228884 + 2.63583i) q^{7} +(2.74998 + 0.661514i) q^{8} +O(q^{10})$	\(q+(-0.608644 - 1.27654i) q^{2} +(-1.25910 + 1.55392i) q^{4} -3.13896i q^{5} +(-0.228884 + 2.63583i) q^{7} +(2.74998 + 0.661514i) q^{8} +(-4.00700 + 1.91051i) q^{10} -3.69232 q^{11} +(0.398951 - 0.691003i) q^{13} +(3.50405 - 1.31210i) q^{14} +(-0.829311 - 3.91309i) q^{16} +(-2.63178 - 1.51946i) q^{17} +(-3.92177 + 2.26423i) q^{19} +(4.87768 + 3.95228i) q^{20} +(2.24731 + 4.71340i) q^{22} -2.21235 q^{23} -4.85305 q^{25} +(-1.12491 - 0.0887014i) q^{26} +(-3.80767 - 3.67446i) q^{28} +(-8.16616 + 4.71474i) q^{29} +(1.87502 - 1.08254i) q^{31} +(-4.49045 + 3.44033i) q^{32} +(-0.337832 + 4.28438i) q^{34} +(8.27376 + 0.718458i) q^{35} +(-2.94414 - 5.09940i) q^{37} +(5.27734 + 3.62818i) q^{38} +(2.07647 - 8.63207i) q^{40} +(9.25469 + 5.34320i) q^{41} +(4.01769 - 2.31962i) q^{43} +(4.64902 - 5.73756i) q^{44} +(1.34654 + 2.82416i) q^{46} +(-5.30030 + 9.18039i) q^{47} +(-6.89522 - 1.20660i) q^{49} +(2.95378 + 6.19511i) q^{50} +(0.571440 + 1.48998i) q^{52} +(-6.12081 - 3.53385i) q^{53} +11.5900i q^{55} +(-2.37307 + 7.09708i) q^{56} +(10.9888 + 7.55483i) q^{58} +(0.254704 + 0.441160i) q^{59} +(-4.78075 + 8.28050i) q^{61} +(-2.52312 - 1.73465i) q^{62} +(7.12480 + 3.63830i) q^{64} +(-2.16903 - 1.25229i) q^{65} +(-6.45716 + 3.72804i) q^{67} +(5.67480 - 2.17641i) q^{68} +(-4.11864 - 10.9991i) q^{70} -2.15661 q^{71} +(1.27196 - 2.20310i) q^{73} +(-4.71765 + 6.86203i) q^{74} +(1.41949 - 8.94500i) q^{76} +(0.845115 - 9.73235i) q^{77} +(9.00359 + 5.19822i) q^{79} +(-12.2830 + 2.60317i) q^{80} +(1.18799 - 15.0661i) q^{82} +(-0.812599 - 1.40746i) q^{83} +(-4.76952 + 8.26105i) q^{85} +(-5.40643 - 3.71692i) q^{86} +(-10.1538 - 2.44253i) q^{88} +(-1.73558 + 1.00204i) q^{89} +(1.73006 + 1.20973i) q^{91} +(2.78558 - 3.43781i) q^{92} +(14.9451 + 1.17845i) q^{94} +(7.10733 + 12.3103i) q^{95} +(-1.88309 - 3.26161i) q^{97} +(2.65647 + 9.53641i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 3 q^{2} + q^{4}+O(q^{10}) $ 88 * q + 3 * q^2 + q^4	$ 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) $ 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.608644	−	1.27654i	−0.430376	−	0.902650i
$2$	−0.608644	−	1.27654i	−0.430376	−	0.902650i
$3$		0			0
$3$		0			0
$4$	−1.25910	+	1.55392i	−0.629552	+	0.776958i
$5$		−	3.13896i		−	1.40378i	−0.712283	−	0.701892i	$-0.752339\pi$
$5$		−	3.13896i		−	1.40378i	0.712283	−	0.701892i	$-0.247661\pi$
$6$		0			0
$7$	−0.228884	+	2.63583i	−0.0865101	+	0.996251i
$7$	−0.228884	+	2.63583i	−0.0865101	+	0.996251i
$8$	2.74998	+	0.661514i	0.972265	+	0.233881i
$9$		0			0
$10$	−4.00700	+	1.91051i	−1.26713	+	0.604156i
$11$	−3.69232			−1.11328			−0.556639	−	0.830755i	$-0.687909\pi$
$11$	−3.69232			−1.11328			−0.556639	+	0.830755i	$0.687909\pi$
$12$		0			0
$13$	0.398951	−	0.691003i	0.110649	−	0.191650i	−0.805383	−	0.592755i	$-0.798040\pi$
$13$	0.398951	−	0.691003i	0.110649	−	0.191650i	0.916032	+	0.401105i	$0.131374\pi$
$14$	3.50405	−	1.31210i	0.936497	−	0.350675i
$15$		0			0
$16$	−0.829311	−	3.91309i	−0.207328	−	0.978272i
$17$	−2.63178	−	1.51946i	−0.638301	−	0.368523i	0.145659	−	0.989335i	$-0.453470\pi$
$17$	−2.63178	−	1.51946i	−0.638301	−	0.368523i	−0.783960	+	0.620812i	$0.786803\pi$
$18$		0			0
$19$	−3.92177	+	2.26423i	−0.899715	+	0.519451i	−0.877108	−	0.480294i	$-0.840530\pi$
$19$	−3.92177	+	2.26423i	−0.899715	+	0.519451i	−0.0226074	+	0.999744i	$0.507197\pi$
$20$	4.87768	+	3.95228i	1.09068	+	0.883756i
$21$		0			0
$22$	2.24731	+	4.71340i	0.479129	+	1.00490i
$23$	−2.21235			−0.461308			−0.230654	−	0.973036i	$-0.574086\pi$
$23$	−2.21235			−0.461308			−0.230654	+	0.973036i	$0.574086\pi$
$24$		0			0
$25$	−4.85305			−0.970610
$26$	−1.12491	−	0.0887014i	−0.220613	−	0.0173958i
$27$		0			0
$28$	−3.80767	−	3.67446i	−0.719583	−	0.694407i
$29$	−8.16616	+	4.71474i	−1.51642	+	0.875505i	−0.516604	+	0.856224i	$0.672804\pi$
$29$	−8.16616	+	4.71474i	−1.51642	+	0.875505i	−0.999814	+	0.0192805i	$0.993862\pi$
$30$		0			0
$31$	1.87502	−	1.08254i	0.336763	−	0.194430i	−0.322077	−	0.946714i	$-0.604381\pi$
$31$	1.87502	−	1.08254i	0.336763	−	0.194430i	0.658840	+	0.752283i	$0.271048\pi$
$32$	−4.49045	+	3.44033i	−0.793807	+	0.608169i
$33$		0			0
$34$	−0.337832	+	4.28438i	−0.0579377	+	0.734766i
$35$	8.27376	+	0.718458i	1.39852	+	0.121441i
$36$		0			0
$37$	−2.94414	−	5.09940i	−0.484013	−	0.838336i	0.515818	−	0.856698i	$-0.327488\pi$
$37$	−2.94414	−	5.09940i	−0.484013	−	0.838336i	−0.999831	+	0.0183623i	$0.994155\pi$
$38$	5.27734	+	3.62818i	0.856098	+	0.588568i
$39$		0			0
$40$	2.07647	−	8.63207i	0.328318	−	1.36485i
$41$	9.25469	+	5.34320i	1.44534	+	0.834467i	0.998199	−	0.0599959i	$-0.0191088\pi$
$41$	9.25469	+	5.34320i	1.44534	+	0.834467i	0.447141	+	0.894463i	$0.352442\pi$
$42$		0			0
$43$	4.01769	−	2.31962i	0.612693	−	0.353738i	−0.161326	−	0.986901i	$-0.551577\pi$
$43$	4.01769	−	2.31962i	0.612693	−	0.353738i	0.774019	+	0.633163i	$0.218244\pi$
$44$	4.64902	−	5.73756i	0.700867	−	0.864970i
$45$		0			0
$46$	1.34654	+	2.82416i	0.198536	+	0.416399i
$47$	−5.30030	+	9.18039i	−0.773128	+	1.33910i	0.162712	+	0.986674i	$0.447976\pi$
$47$	−5.30030	+	9.18039i	−0.773128	+	1.33910i	−0.935840	+	0.352424i	$0.885358\pi$
$48$		0			0
$49$	−6.89522	−	1.20660i	−0.985032	−	0.172371i
$50$	2.95378	+	6.19511i	0.417728	+	0.876121i
$51$		0			0
$52$	0.571440	+	1.48998i	0.0792445	+	0.206623i
$53$	−6.12081	−	3.53385i	−0.840758	−	0.485412i	0.0167637	−	0.999859i	$-0.494664\pi$
$53$	−6.12081	−	3.53385i	−0.840758	−	0.485412i	−0.857522	+	0.514447i	$0.827997\pi$
$54$		0			0
$55$			11.5900i			1.56280i
$56$	−2.37307	+	7.09708i	−0.317115	+	0.948387i
$57$		0			0
$58$	10.9888	+	7.55483i	1.44290	+	0.991998i
$59$	0.254704	+	0.441160i	0.0331596	+	0.0574341i	0.882129	−	0.471008i	$-0.156110\pi$
$59$	0.254704	+	0.441160i	0.0331596	+	0.0574341i	−0.848969	+	0.528442i	$0.822776\pi$
$60$		0			0
$61$	−4.78075	+	8.28050i	−0.612112	+	1.06021i	0.378772	+	0.925490i	$0.376347\pi$
$61$	−4.78075	+	8.28050i	−0.612112	+	1.06021i	−0.990884	+	0.134719i	$0.956987\pi$
$62$	−2.52312	−	1.73465i	−0.320437	−	0.220301i
$63$		0			0
$64$	7.12480	+	3.63830i	0.890600	+	0.454788i
$65$	−2.16903	−	1.25229i	−0.269035	−	0.155327i
$66$		0			0
$67$	−6.45716	+	3.72804i	−0.788868	+	0.455453i	−0.839564	−	0.543261i	$-0.817189\pi$
$67$	−6.45716	+	3.72804i	−0.788868	+	0.455453i	0.0506962	+	0.998714i	$0.483856\pi$
$68$	5.67480	−	2.17641i	0.688171	−	0.263929i
$69$		0			0
$70$	−4.11864	−	10.9991i	−0.492272	−	1.31464i
$71$	−2.15661			−0.255942			−0.127971	−	0.991778i	$-0.540847\pi$
$71$	−2.15661			−0.255942			−0.127971	+	0.991778i	$0.540847\pi$
$72$		0			0
$73$	1.27196	−	2.20310i	0.148871	−	0.257853i	−0.781939	−	0.623355i	$-0.785769\pi$
$73$	1.27196	−	2.20310i	0.148871	−	0.257853i	0.930811	+	0.365502i	$0.119103\pi$
$74$	−4.71765	+	6.86203i	−0.548416	+	0.797695i
$75$		0			0
$76$	1.41949	−	8.94500i	0.162826	−	1.02606i
$77$	0.845115	−	9.73235i	0.0963098	−	1.10910i
$78$		0			0
$79$	9.00359	+	5.19822i	1.01298	+	0.584846i	0.912064	−	0.410049i	$-0.134488\pi$
$79$	9.00359	+	5.19822i	1.01298	+	0.584846i	0.100919	+	0.994895i	$0.467822\pi$
$80$	−12.2830	+	2.60317i	−1.37328	+	0.291044i
$81$		0			0
$82$	1.18799	−	15.0661i	0.131191	−	1.66377i
$83$	−0.812599	−	1.40746i	−0.0891943	−	0.154489i	0.817976	−	0.575252i	$-0.195096\pi$
$83$	−0.812599	−	1.40746i	−0.0891943	−	0.154489i	−0.907171	+	0.420763i	$0.861763\pi$
$84$		0			0
$85$	−4.76952	+	8.26105i	−0.517327	+	0.896037i
$86$	−5.40643	−	3.71692i	−0.582990	−	0.400806i
$87$		0			0
$88$	−10.1538	−	2.44253i	−1.08240	−	0.260374i
$89$	−1.73558	+	1.00204i	−0.183971	+	0.106216i	−0.589157	−	0.808019i	$-0.700540\pi$
$89$	−1.73558	+	1.00204i	−0.183971	+	0.106216i	0.405186	+	0.914234i	$0.367207\pi$
$90$		0			0
$91$	1.73006	+	1.20973i	0.181359	+	0.126814i
$92$	2.78558	−	3.43781i	0.290417	−	0.358417i
$93$		0			0
$94$	14.9451	+	1.17845i	1.54147	+	0.121548i
$95$	7.10733	+	12.3103i	0.729197	+	1.26301i
$96$		0			0
$97$	−1.88309	−	3.26161i	−0.191199	−	0.331167i	0.754449	−	0.656359i	$-0.227904\pi$
$97$	−1.88309	−	3.26161i	−0.191199	−	0.331167i	−0.945648	+	0.325192i	$0.894571\pi$
$98$	2.65647	+	9.53641i	0.268343	+	0.963323i
$99$		0			0
$100$	6.11050	−	7.54124i	0.611050	−	0.754124i
$101$		−	17.1439i		−	1.70589i	−0.522004	−	0.852943i	$-0.674815\pi$
$101$		−	17.1439i		−	1.70589i	0.522004	−	0.852943i	$-0.325185\pi$
$102$		0			0
$103$			3.21669i			0.316950i	0.987363	+	0.158475i	$0.0506577\pi$
$103$			3.21669i			0.316950i	−0.987363	+	0.158475i	$0.949342\pi$
$104$	1.55422	−	1.63634i	0.152403	−	0.160456i
$105$		0			0
$106$	−0.785705	+	9.96432i	−0.0763144	+	0.967820i
$107$	−1.77960	−	3.08236i	−0.172041	−	0.297983i	0.767092	−	0.641537i	$-0.221703\pi$
$107$	−1.77960	−	3.08236i	−0.172041	−	0.297983i	−0.939133	+	0.343553i	$0.888369\pi$
$108$		0			0
$109$	2.56961	−	4.45070i	0.246124	−	0.426300i	−0.716323	−	0.697769i	$-0.754176\pi$
$109$	2.56961	−	4.45070i	0.246124	−	0.426300i	0.962447	+	0.271469i	$0.0875095\pi$
$110$	14.7952	−	7.05422i	1.41066	−	0.672593i
$111$		0			0
$112$	10.5041	−	1.29028i	0.992540	−	0.121920i
$113$	7.11141	+	4.10577i	0.668985	+	0.386239i	0.795692	−	0.605701i	$-0.207107\pi$
$113$	7.11141	+	4.10577i	0.668985	+	0.386239i	−0.126707	+	0.991940i	$0.540441\pi$
$114$		0			0
$115$			6.94448i			0.647576i
$116$	2.95575	−	18.6259i	0.274434	−	1.72937i
$117$		0			0
$118$	0.408134	−	0.593649i	0.0375718	−	0.0546498i
$119$	4.60742	−	6.58916i	0.422361	−	0.604027i
$120$		0			0
$121$	2.63326			0.239388
$122$	13.4802	+	1.06294i	1.22044	+	0.0962336i
$123$		0			0
$124$	−0.678664	+	4.27665i	−0.0609458	+	0.384055i
$125$		−	0.461263i		−	0.0412566i
$126$		0			0
$127$		−	16.6020i		−	1.47319i	−0.676333	−	0.736596i	$-0.736432\pi$
$127$		−	16.6020i		−	1.47319i	0.676333	−	0.736596i	$-0.263568\pi$
$128$	0.307972	−	11.3095i	0.0272211	−	0.999629i
$129$		0			0
$130$	−0.278430	+	3.53105i	−0.0244199	+	0.309694i
$131$	−11.4911			−1.00398			−0.501990	−	0.864874i	$-0.667398\pi$
$131$	−11.4911			−1.00398			−0.501990	+	0.864874i	$0.667398\pi$
$132$		0			0
$133$	−5.07051	−	10.8554i	−0.439669	−	0.941280i
$134$	8.68910	+	5.97377i	0.750624	+	0.516055i
$135$		0			0
$136$	−6.23221	−	5.91945i	−0.534408	−	0.507589i
$137$			13.9244i			1.18964i	0.803859	+	0.594819i	$0.202776\pi$
$137$			13.9244i			1.18964i	−0.803859	+	0.594819i	$0.797224\pi$
$138$		0			0
$139$	−13.1223	−	7.57615i	−1.11302	−	0.642601i	−0.173408	−	0.984850i	$-0.555478\pi$
$139$	−13.1223	−	7.57615i	−1.11302	−	0.642601i	−0.939609	+	0.342249i	$0.888811\pi$
$140$	−11.5340	+	11.9521i	−0.974797	+	1.01014i
$141$		0			0
$142$	1.31261	+	2.75300i	0.110152	+	0.231026i
$143$	−1.47306	+	2.55141i	−0.123183	+	0.213360i
$144$		0			0
$145$	14.7994	+	25.6332i	1.22902	+	2.12872i
$146$	−3.58651	−	0.282803i	−0.296822	−	0.0234049i
$147$		0			0
$148$	11.6310	+	1.84573i	0.956064	+	0.151718i
$149$		−	18.1088i		−	1.48353i	−0.670658	−	0.741766i	$-0.733988\pi$
$149$		−	18.1088i		−	1.48353i	0.670658	−	0.741766i	$-0.266012\pi$
$150$		0			0
$151$		−	19.7445i		−	1.60679i	−0.595449	−	0.803393i	$-0.703026\pi$
$151$		−	19.7445i		−	1.60679i	0.595449	−	0.803393i	$-0.296974\pi$
$152$	−12.2826	+	3.63229i	−0.996251	+	0.294618i
$153$		0			0
$154$	−12.9381	+	4.84472i	−1.04258	+	0.390398i
$155$	−3.39805	−	5.88560i	−0.272938	−	0.472743i
$156$		0			0
$157$	2.81051	+	4.86795i	0.224303	+	0.388504i	0.956110	−	0.293007i	$-0.0946561\pi$
$157$	2.81051	+	4.86795i	0.224303	+	0.388504i	−0.731807	+	0.681512i	$0.761323\pi$
$158$	1.15576	−	14.6573i	0.0919469	−	1.16607i
$159$		0			0
$160$	10.7990	+	14.0953i	0.853739	+	1.11433i
$161$	0.506373	−	5.83139i	0.0399078	−	0.459578i
$162$		0			0
$163$	−3.24708	+	1.87470i	−0.254331	+	0.146838i	−0.621746	−	0.783219i	$-0.713576\pi$
$163$	−3.24708	+	1.87470i	−0.254331	+	0.146838i	0.367415	+	0.930057i	$0.380243\pi$
$164$	−19.9555	+	7.65337i	−1.55826	+	0.597628i
$165$		0			0
$166$	−1.30210	+	1.89396i	−0.101062	+	0.147000i
$167$	0.739116	−	1.28019i	0.0571945	−	0.0990638i	−0.836011	−	0.548713i	$-0.815118\pi$
$167$	0.739116	−	1.28019i	0.0571945	−	0.0990638i	0.893205	+	0.449650i	$0.148451\pi$
$168$		0			0
$169$	6.18168	+	10.7070i	0.475514	+	0.823614i
$170$	13.4485	+	1.06044i	1.03145	+	0.0813320i
$171$		0			0
$172$	−1.45421	+	9.16380i	−0.110882	+	0.698733i
$173$	5.98628	+	3.45618i	0.455129	+	0.262769i	0.709994	−	0.704208i	$-0.248698\pi$
$173$	5.98628	+	3.45618i	0.455129	+	0.262769i	−0.254865	+	0.966977i	$0.582031\pi$
$174$		0			0
$175$	1.11079	−	12.7918i	0.0839676	−	0.966972i
$176$	3.06209	+	14.4484i	0.230813	+	1.08909i
$177$		0			0
$178$	2.33549	+	1.60565i	0.175052	+	0.120348i
$179$	−1.52346	+	2.63872i	−0.113869	+	0.197227i	−0.917327	−	0.398134i	$-0.869658\pi$
$179$	−1.52346	+	2.63872i	−0.113869	+	0.197227i	0.803458	+	0.595361i	$0.202991\pi$
$180$		0			0
$181$	−2.27649			−0.169210			−0.0846049	−	0.996415i	$-0.526963\pi$
$181$	−2.27649			−0.169210			−0.0846049	+	0.996415i	$0.526963\pi$
$182$	0.491277	−	2.94478i	0.0364158	−	0.218281i
$183$		0			0
$184$	−6.08393	−	1.46350i	−0.448513	−	0.107891i
$185$	−16.0068	+	9.24153i	−1.17684	+	0.679451i
$186$		0			0
$187$	9.71740	+	5.61034i	0.710606	+	0.410269i
$188$	−7.59192	−	19.7953i	−0.553698	−	1.44372i
$189$		0			0
$190$	11.3887	−	16.5654i	0.826223	−	1.20178i
$191$	4.32021	−	7.48282i	0.312599	−	0.541438i	−0.666325	−	0.745661i	$-0.732134\pi$
$191$	4.32021	−	7.48282i	0.312599	−	0.541438i	0.978924	+	0.204224i	$0.0654670\pi$
$192$		0			0
$193$	−11.4781	−	19.8807i	−0.826215	−	1.43105i	−0.900987	−	0.433846i	$-0.857156\pi$
$193$	−11.4781	−	19.8807i	−0.826215	−	1.43105i	0.0747719	−	0.997201i	$-0.476177\pi$
$194$	−3.01744	+	4.38901i	−0.216640	+	0.315112i
$195$		0			0
$196$	10.5568	−	9.19536i	0.754055	−	0.656812i
$197$		−	6.30658i		−	0.449325i	−0.974437	−	0.224663i	$-0.927872\pi$
$197$		−	6.30658i		−	0.449325i	0.974437	−	0.224663i	$-0.0721280\pi$
$198$		0			0
$199$	−11.1317	−	6.42691i	−0.789108	−	0.455592i	0.0505404	−	0.998722i	$-0.483906\pi$
$199$	−11.1317	−	6.42691i	−0.789108	−	0.455592i	−0.839648	+	0.543130i	$0.817239\pi$
$200$	−13.3458	−	3.21036i	−0.943691	−	0.227007i
$201$		0			0
$202$	−21.8849	+	10.4346i	−1.53982	+	0.734173i
$203$	−10.5582	−	22.6038i	−0.741037	−	1.58647i
$204$		0			0
$205$	16.7721	−	29.0501i	1.17141	−	2.02895i
$206$	4.10623	−	1.95782i	0.286094	−	0.136408i
$207$		0			0
$208$	−3.03481	−	0.988073i	−0.210426	−	0.0685105i
$209$	14.4804	−	8.36029i	1.00163	−	0.578293i
$210$		0			0
$211$	−12.3528	−	7.13189i	−0.850402	−	0.490980i	0.0103847	−	0.999946i	$-0.496694\pi$
$211$	−12.3528	−	7.13189i	−0.850402	−	0.490980i	−0.860786	+	0.508966i	$0.830028\pi$
$212$	13.1981	−	5.06174i	0.906446	−	0.347642i
$213$		0			0
$214$	−2.85161	+	4.14780i	−0.194932	+	0.283537i
$215$	−7.28118	−	12.6114i	−0.496572	−	0.860088i
$216$		0			0
$217$	2.42424	+	5.19001i	0.164568	+	0.352321i
$218$	−7.24547	−	0.571319i	−0.490725	−	0.0386946i
$219$		0			0
$220$	−18.0100	−	14.5931i	−1.21423	−	0.983866i
$221$	−2.09991	+	1.21238i	−0.141255	+	0.0815536i
$222$		0			0
$223$	3.96034	−	2.28651i	0.265204	−	0.153116i	−0.361502	−	0.932371i	$-0.617736\pi$
$223$	3.96034	−	2.28651i	0.265204	−	0.153116i	0.626706	+	0.779256i	$0.284403\pi$
$224$	−8.04033	−	12.6235i	−0.537217	−	0.843444i
$225$		0			0
$226$	0.912864	−	11.5769i	0.0607228	−	0.770087i
$227$	6.44214			0.427580			0.213790	−	0.976880i	$-0.431419\pi$
$227$	6.44214			0.427580			0.213790	+	0.976880i	$0.431419\pi$
$228$		0			0
$229$	−6.59977			−0.436125			−0.218063	−	0.975935i	$-0.569974\pi$
$229$	−6.59977			−0.436125			−0.218063	+	0.975935i	$0.569974\pi$
$230$	8.86491	−	4.22672i	0.584535	−	0.278702i
$231$		0			0
$232$	−25.5757	+	7.56341i	−1.67912	+	0.496562i
$233$	−4.20962	+	2.43043i	−0.275781	+	0.159222i	−0.631512	−	0.775366i	$-0.717565\pi$
$233$	−4.20962	+	2.43043i	−0.275781	+	0.159222i	0.355731	+	0.934589i	$0.384232\pi$
$234$		0			0
$235$	28.8169	+	16.6374i	1.87980	+	1.08531i
$236$	−1.00622	−	0.159678i	−0.0654996	−	0.0103942i
$237$		0			0
$238$	−11.2156	−	1.87110i	−0.726999	−	0.121285i
$239$	7.00661	−	12.1358i	0.453220	−	0.785000i	−0.545364	−	0.838199i	$-0.683608\pi$
$239$	7.00661	−	12.1358i	0.453220	−	0.785000i	0.998584	+	0.0531992i	$0.0169418\pi$
$240$		0			0
$241$	−4.19457			−0.270196			−0.135098	−	0.990832i	$-0.543135\pi$
$241$	−4.19457			−0.270196			−0.135098	+	0.990832i	$0.543135\pi$
$242$	−1.60272	−	3.36146i	−0.103027	−	0.216083i
$243$		0			0
$244$	−6.84774	−	17.8549i	−0.438382	−	1.14304i
$245$	−3.78747	+	21.6438i	−0.241972	+	1.38277i
$246$		0			0
$247$			3.61327i			0.229907i
$248$	5.87238	−	1.73662i	0.372896	−	0.110275i
$249$		0			0
$250$	−0.588820	+	0.280745i	−0.0372403	+	0.0177559i
$251$	−4.07143			−0.256986			−0.128493	−	0.991710i	$-0.541014\pi$
$251$	−4.07143			−0.256986			−0.128493	+	0.991710i	$0.541014\pi$
$252$		0			0
$253$	8.16873			0.513564
$254$	−21.1931	+	10.1047i	−1.32978	+	0.634027i
$255$		0			0
$256$	−14.6245	+	6.49033i	−0.914030	+	0.405646i
$257$			26.4169i			1.64784i	0.566705	+	0.823920i	$0.308218\pi$
$257$			26.4169i			1.64784i	−0.566705	+	0.823920i	$0.691782\pi$
$258$		0			0
$259$	14.1150	−	6.59309i	0.877065	−	0.409674i
$260$	4.67699	−	1.79373i	0.290055	−	0.111242i
$261$		0			0
$262$	6.99397	+	14.6688i	0.432089	+	0.906241i
$263$	−2.73869			−0.168875			−0.0844373	−	0.996429i	$-0.526909\pi$
$263$	−2.73869			−0.168875			−0.0844373	+	0.996429i	$0.526909\pi$
$264$		0			0
$265$	−11.0926	+	19.2130i	−0.681414	+	1.18024i
$266$	−10.7712	+	13.0798i	−0.660423	+	0.801972i
$267$		0			0
$268$	2.33717	−	14.7279i	0.142766	−	0.899648i
$269$	11.0850	+	6.39993i	0.675865	+	0.390211i	0.798295	−	0.602266i	$-0.205735\pi$
$269$	11.0850	+	6.39993i	0.675865	+	0.390211i	−0.122430	+	0.992477i	$0.539069\pi$
$270$		0			0
$271$	−19.3102	+	11.1488i	−1.17301	+	0.677240i	−0.954388	−	0.298569i	$-0.903491\pi$
$271$	−19.3102	+	11.1488i	−1.17301	+	0.677240i	−0.218626	+	0.975809i	$0.570157\pi$
$272$	−3.76321	+	11.5585i	−0.228178	+	0.700837i
$273$		0			0
$274$	17.7750	−	8.47498i	1.07383	−	0.511992i
$275$	17.9190			1.08056
$276$		0			0
$277$	18.0351			1.08362			0.541811	−	0.840500i	$-0.317739\pi$
$277$	18.0351			1.08362			0.541811	+	0.840500i	$0.317739\pi$
$278$	−1.68446	+	21.3623i	−0.101027	+	1.28123i
$279$		0			0
$280$	22.2774	+	7.44896i	1.33133	+	0.445160i
$281$	−6.29086	+	3.63203i	−0.375281	+	0.216669i	−0.675763	−	0.737119i	$-0.736186\pi$
$281$	−6.29086	+	3.63203i	−0.375281	+	0.216669i	0.300482	+	0.953788i	$0.402853\pi$
$282$		0			0
$283$	8.65772	−	4.99854i	0.514648	−	0.297132i	−0.220094	−	0.975479i	$-0.570636\pi$
$283$	8.65772	−	4.99854i	0.514648	−	0.297132i	0.734742	+	0.678346i	$0.237303\pi$
$284$	2.71540	−	3.35119i	0.161129	−	0.198857i
$285$		0			0
$286$	4.15354	+	0.327514i	0.245604	+	0.0193663i
$287$	−16.2020	+	23.1708i	−0.956375	+	1.36773i
$288$		0			0
$289$	−3.88248	−	6.72465i	−0.228381	−	0.395568i
$290$	23.7143	−	34.4935i	1.39255	−	2.02553i
$291$		0			0
$292$	1.82190	+	4.75045i	0.106619	+	0.277999i
$293$	20.0527	+	11.5774i	1.17149	+	0.676361i	0.954031	−	0.299708i	$-0.0968893\pi$
$293$	20.0527	+	11.5774i	1.17149	+	0.676361i	0.217460	+	0.976069i	$0.430223\pi$
$294$		0			0
$295$	1.38478	−	0.799505i	0.0806252	−	0.0465490i
$296$	−4.72300	−	15.9708i	−0.274519	−	0.928286i
$297$		0			0
$298$	−23.1166	+	11.0218i	−1.33911	+	0.638477i
$299$	−0.882621	+	1.52874i	−0.0510433	+	0.0884096i
$300$		0			0
$301$	5.19453	+	11.1209i	0.299408	+	0.640998i
$302$	−25.2047	+	12.0174i	−1.45037	+	0.691523i
$303$		0			0
$304$	12.1125	+	13.4685i	0.694700	+	0.772469i
$305$	25.9921	+	15.0066i	1.48831	+	0.859273i
$306$		0			0
$307$			28.4146i			1.62171i	0.585250	+	0.810853i	$0.300996\pi$
$307$			28.4146i			1.62171i	−0.585250	+	0.810853i	$0.699004\pi$
$308$	14.0592	+	13.5673i	0.801095	+	0.773068i
$309$		0			0
$310$	−5.44499	+	7.91998i	−0.309255	+	0.449825i
$311$	2.29962	+	3.98306i	0.130400	+	0.225859i	0.923831	−	0.382801i	$-0.125041\pi$
$311$	2.29962	+	3.98306i	0.130400	+	0.225859i	−0.793431	+	0.608660i	$0.791707\pi$
$312$		0			0
$313$	10.6751	−	18.4899i	0.603395	−	1.04511i	−0.388908	−	0.921277i	$-0.627148\pi$
$313$	10.6751	−	18.4899i	0.603395	−	1.04511i	0.992303	−	0.123834i	$-0.0395191\pi$
$314$	4.50352	−	6.55057i	0.254149	−	0.369670i
$315$		0			0
$316$	−19.4141	+	7.44571i	−1.09213	+	0.418854i
$317$	1.84862	+	1.06730i	0.103829	+	0.0599457i	0.551015	−	0.834495i	$-0.314241\pi$
$317$	1.84862	+	1.06730i	0.103829	+	0.0599457i	−0.447186	+	0.894441i	$0.647574\pi$
$318$		0			0
$319$	30.1521	−	17.4083i	1.68820	−	0.974680i
$320$	11.4205	−	22.3644i	0.638424	−	1.25021i
$321$		0			0
$322$	−7.75220	+	2.90284i	−0.432013	+	0.161769i
$323$	13.7617			0.765719
$324$		0			0
$325$	−1.93613	+	3.35348i	−0.107397	+	0.186017i
$326$	4.36945	+	3.00400i	0.242001	+	0.166376i
$327$		0			0
$328$	21.9156	+	20.8158i	1.21009	+	1.14936i
$329$	−22.9848	−	16.0719i	−1.26719	−	0.886075i
$330$		0			0
$331$	−25.1216	−	14.5039i	−1.38081	−	0.797209i	−0.388551	−	0.921427i	$-0.627024\pi$
$331$	−25.1216	−	14.5039i	−1.38081	−	0.797209i	−0.992255	+	0.124218i	$0.960358\pi$
$332$	3.21023	+	0.509432i	0.176184	+	0.0279587i
$333$		0			0
$334$	−2.08407	−	0.164332i	−0.114035	−	0.00899187i
$335$	11.7022	+	20.2687i	0.639358	+	1.10740i
$336$		0			0
$337$	6.37475	−	11.0414i	0.347255	−	0.601463i	−0.638506	−	0.769617i	$-0.720447\pi$
$337$	6.37475	−	11.0414i	0.347255	−	0.601463i	0.985761	+	0.168154i	$0.0537807\pi$
$338$	9.90543	−	14.4079i	0.538785	−	0.783686i
$339$		0			0
$340$	−6.83166	−	17.8130i	−0.370499	−	0.966044i
$341$	−6.92317	+	3.99709i	−0.374911	+	0.216455i
$342$		0			0
$343$	4.75860	−	17.8985i	0.256940	−	0.966427i
$344$	12.5830	−	3.72114i	0.678432	−	0.200630i
$345$		0			0
$346$	0.768436	−	9.74531i	0.0413114	−	0.523911i
$347$	15.7693	+	27.3133i	0.846542	+	1.46625i	0.884276	+	0.466965i	$0.154653\pi$
$347$	15.7693	+	27.3133i	0.846542	+	1.46625i	−0.0377338	+	0.999288i	$0.512014\pi$
$348$		0			0
$349$	4.19035	+	7.25790i	0.224304	+	0.388507i	0.956111	−	0.293006i	$-0.0946557\pi$
$349$	4.19035	+	7.25790i	0.224304	+	0.388507i	−0.731806	+	0.681513i	$0.761322\pi$
$350$	−17.0053	+	6.36771i	−0.908974	+	0.340368i
$351$		0			0
$352$	16.5802	−	12.7028i	0.883728	−	0.677061i
$353$			11.4208i			0.607866i	0.952693	+	0.303933i	$0.0982999\pi$
$353$			11.4208i			0.607866i	−0.952693	+	0.303933i	$0.901700\pi$
$354$		0			0
$355$			6.76951i			0.359288i
$356$	0.628193	−	3.95861i	0.0332942	−	0.209806i
$357$		0			0
$358$	4.29567	+	0.338722i	0.227033	+	0.0179020i
$359$	1.41558	+	2.45186i	0.0747117	+	0.129404i	0.900961	−	0.433900i	$-0.142863\pi$
$359$	1.41558	+	2.45186i	0.0747117	+	0.129404i	−0.826249	+	0.563305i	$0.809530\pi$
$360$		0			0
$361$	0.753506	−	1.30511i	0.0396582	−	0.0686900i
$362$	1.38557	+	2.90602i	0.0728239	+	0.152737i
$363$		0			0
$364$	−4.05814	+	1.16519i	−0.212704	+	0.0610724i
$365$	−6.91543	−	3.99262i	−0.361970	−	0.208983i
$366$		0			0
$367$			27.8085i			1.45159i	0.687909	+	0.725797i	$0.258529\pi$
$367$			27.8085i			1.45159i	−0.687909	+	0.725797i	$0.741471\pi$
$368$	1.83473	+	8.65713i	0.0956419	+	0.451284i
$369$		0			0
$370$	21.5396	+	14.8085i	1.11979	+	0.769857i
$371$	10.7156	−	15.3246i	0.556326	−	0.795613i
$372$		0			0
$373$	31.3191			1.62164			0.810821	−	0.585295i	$-0.199021\pi$
$373$	31.3191			1.62164			0.810821	+	0.585295i	$0.199021\pi$
$374$	1.24738	−	15.8193i	0.0645007	−	0.817999i
$375$		0			0
$376$	−20.6487	+	21.7397i	−1.06487	+	1.12114i
$377$			7.52380i			0.387495i
$378$		0			0
$379$			26.7198i			1.37250i	0.727364	+	0.686252i	$0.240745\pi$
$379$			26.7198i			1.37250i	−0.727364	+	0.686252i	$0.759255\pi$
$380$	−28.0780	−	4.45571i	−1.44037	−	0.228573i
$381$		0			0
$382$	−12.1816	−	0.960540i	−0.623264	−	0.0491455i
$383$	−7.44276			−0.380307			−0.190154	−	0.981754i	$-0.560899\pi$
$383$	−7.44276			−0.380307			−0.190154	+	0.981754i	$0.560899\pi$
$384$		0			0
$385$	−30.5494	−	2.65278i	−1.55694	−	0.135198i
$386$	−18.3924	+	26.7526i	−0.936150	+	1.36167i
$387$		0			0
$388$	7.43929	+	1.18054i	0.377673	+	0.0599330i
$389$		−	30.7200i		−	1.55757i	−0.627292	−	0.778784i	$-0.715837\pi$
$389$		−	30.7200i		−	1.55757i	0.627292	−	0.778784i	$-0.284163\pi$
$390$		0			0
$391$	5.82243	+	3.36158i	0.294453	+	0.170003i
$392$	−18.1636	−	7.87942i	−0.917398	−	0.397971i
$393$		0			0
$394$	−8.05059	+	3.83846i	−0.405583	+	0.193379i
$395$	16.3170	−	28.2619i	0.820997	−	1.42201i
$396$		0			0
$397$	−2.16714	−	3.75359i	−0.108765	−	0.188387i	0.806505	−	0.591227i	$-0.201356\pi$
$397$	−2.16714	−	3.75359i	−0.108765	−	0.188387i	−0.915270	+	0.402840i	$0.868023\pi$
$398$	−1.42894	+	18.1218i	−0.0716262	+	0.908364i
$399$		0			0
$400$	4.02469	+	18.9904i	0.201235	+	0.949521i
$401$			13.2140i			0.659878i	0.944002	+	0.329939i	$0.107028\pi$
$401$			13.2140i			0.659878i	−0.944002	+	0.329939i	$0.892972\pi$
$402$		0			0
$403$		−	1.72752i		−	0.0860541i
$404$	26.6403	+	21.5860i	1.32540	+	1.07394i
$405$		0			0
$406$	−22.4284	+	27.2355i	−1.11310	+	1.35168i
$407$	10.8707	+	18.8286i	0.538841	+	0.933301i
$408$		0			0
$409$	11.9930	+	20.7724i	0.593014	+	1.02713i	0.993824	+	0.110969i	$0.0353953\pi$
$409$	11.9930	+	20.7724i	0.593014	+	1.02713i	−0.400810	+	0.916161i	$0.631271\pi$
$410$	−47.2918	−	3.72905i	−2.33557	−	0.184164i
$411$		0			0
$412$	−4.99846	−	4.05015i	−0.246257	−	0.199536i
$413$	−1.22112	+	0.570382i	−0.0600875	+	0.0280667i
$414$		0			0
$415$	−4.41796	+	2.55071i	−0.216869	+	0.125210i
$416$	0.585806	+	4.47544i	0.0287215	+	0.219426i
$417$		0			0
$418$	−19.4857	−	13.3964i	−0.953075	−	0.655240i
$419$	−9.47883	+	16.4178i	−0.463071	+	0.802063i	−0.999112	−	0.0421291i	$-0.986586\pi$
$419$	−9.47883	+	16.4178i	−0.463071	+	0.802063i	0.536041	+	0.844192i	$0.319919\pi$
$420$		0			0
$421$	−6.69978	−	11.6044i	−0.326527	−	0.565562i	0.655293	−	0.755375i	$-0.272545\pi$
$421$	−6.69978	−	11.6044i	−0.326527	−	0.565562i	−0.981820	+	0.189813i	$0.939212\pi$
$422$	−1.58568	+	20.1096i	−0.0771897	+	0.978921i
$423$		0			0
$424$	−14.4944	−	13.7670i	−0.703912	−	0.668586i
$425$	12.7722	+	7.37402i	0.619542	+	0.357693i
$426$		0			0
$427$	−20.7318	−	14.4965i	−1.00328	−	0.701536i
$428$	7.03044	+	1.11566i	0.339829	+	0.0539276i
$429$		0			0
$430$	−11.6673	+	16.9705i	−0.562645	+	0.818392i
$431$	8.82760	−	15.2899i	0.425211	−	0.736486i	−0.571229	−	0.820790i	$-0.693533\pi$
$431$	8.82760	−	15.2899i	0.425211	−	0.736486i	0.996440	+	0.0843040i	$0.0268667\pi$
$432$		0			0
$433$	22.5556			1.08395			0.541976	−	0.840394i	$-0.317676\pi$
$433$	22.5556			1.08395			0.541976	+	0.840394i	$0.317676\pi$
$434$	5.14975	−	6.25350i	0.247196	−	0.300178i
$435$		0			0
$436$	3.68060	+	9.59686i	0.176269	+	0.459606i
$437$	8.67634	−	5.00929i	0.415045	−	0.239627i
$438$		0			0
$439$	−29.0213	−	16.7555i	−1.38511	−	0.799694i	−0.392352	−	0.919815i	$-0.628338\pi$
$439$	−29.0213	−	16.7555i	−1.38511	−	0.799694i	−0.992759	+	0.120121i	$0.961672\pi$
$440$	−7.66698	+	31.8724i	−0.365509	+	1.51946i
$441$		0			0
$442$	2.82575	+	1.94270i	0.134407	+	0.0924049i
$443$	−1.49171	+	2.58372i	−0.0708733	+	0.122756i	−0.899284	−	0.437365i	$-0.855912\pi$
$443$	−1.49171	+	2.58372i	−0.0708733	+	0.122756i	0.828411	+	0.560121i	$0.189245\pi$
$444$		0			0
$445$	3.14535	+	5.44790i	0.149104	+	0.258255i
$446$	−5.32926	−	3.66387i	−0.252348	−	0.173489i
$447$		0			0
$448$	−11.2207	+	17.9470i	−0.530129	+	0.847917i
$449$		−	39.5688i		−	1.86737i	−0.358099	−	0.933684i	$-0.616575\pi$
$449$		−	39.5688i		−	1.86737i	0.358099	−	0.933684i	$-0.383425\pi$
$450$		0			0
$451$	−34.1713	−	19.7288i	−1.60906	−	0.928994i
$452$	−15.3340	+	5.88094i	−0.721252	+	0.276616i
$453$		0			0
$454$	−3.92097	−	8.22364i	−0.184020	−	0.385955i
$455$	3.79728	−	5.43057i	0.178019	−	0.254589i
$456$		0			0
$457$	−14.6044	+	25.2956i	−0.683165	+	1.18328i	0.290844	+	0.956770i	$0.406064\pi$
$457$	−14.6044	+	25.2956i	−0.683165	+	1.18328i	−0.974010	+	0.226507i	$0.927269\pi$
$458$	4.01691	+	8.42487i	0.187698	+	0.393668i
$459$		0			0
$460$	−10.7911	−	8.74383i	−0.503140	−	0.407683i
$461$	1.80514	−	1.04220i	0.0840737	−	0.0485400i	−0.457374	−	0.889275i	$-0.651210\pi$
$461$	1.80514	−	1.04220i	0.0840737	−	0.0485400i	0.541447	+	0.840735i	$0.317877\pi$
$462$		0			0
$463$	−17.8405	−	10.3002i	−0.829118	−	0.478692i	0.0244325	−	0.999701i	$-0.492222\pi$
$463$	−17.8405	−	10.3002i	−0.829118	−	0.478692i	−0.853551	+	0.521010i	$0.825555\pi$
$464$	25.2215	+	28.0449i	1.17088	+	1.30195i
$465$		0			0
$466$	5.66469	+	3.89448i	0.262412	+	0.180408i
$467$	7.00189	+	12.1276i	0.324009	+	0.561199i	0.981311	−	0.192427i	$-0.0616360\pi$
$467$	7.00189	+	12.1276i	0.324009	+	0.561199i	−0.657303	+	0.753627i	$0.728303\pi$
$468$		0			0
$469$	−8.34855	−	17.8733i	−0.385500	−	0.825311i
$470$	3.69911	−	46.9121i	0.170627	−	2.16389i
$471$		0			0
$472$	0.408597	+	1.38167i	0.0188072	+	0.0635966i
$473$	−14.8346	+	8.56478i	−0.682097	+	0.393809i
$474$		0			0
$475$	19.0325	−	10.9884i	0.873273	−	0.504184i
$476$	4.43778	+	15.4560i	0.203405	+	0.708424i
$477$		0			0
$478$	−19.7564	−	1.55783i	−0.903635	−	0.0712533i
$479$	−37.5412			−1.71530			−0.857650	−	0.514234i	$-0.828076\pi$
$479$	−37.5412			−1.71530			−0.857650	+	0.514234i	$0.828076\pi$
$480$		0			0
$481$	−4.69827			−0.214223
$482$	2.55300	+	5.35453i	0.116286	+	0.243892i
$483$		0			0
$484$	−3.31555	+	4.09187i	−0.150707	+	0.185994i
$485$	−10.2381	+	5.91095i	−0.464887	+	0.268402i
$486$		0			0
$487$	−0.414665	−	0.239407i	−0.0187903	−	0.0108486i	0.490575	−	0.871399i	$-0.336787\pi$
$487$	−0.414665	−	0.239407i	−0.0187903	−	0.0108486i	−0.509366	+	0.860550i	$0.670120\pi$
$488$	−18.6246	+	19.6087i	−0.843098	+	0.887643i
$489$		0			0
$490$	29.9344	−	8.33853i	1.35230	−	0.376696i
$491$	−1.44107	+	2.49601i	−0.0650346	+	0.112643i	−0.896709	−	0.442620i	$-0.854049\pi$
$491$	−1.44107	+	2.49601i	−0.0650346	+	0.112643i	0.831675	+	0.555263i	$0.187382\pi$
$492$		0			0
$493$	28.6554			1.29058
$494$	4.61248	−	2.19920i	0.207526	−	0.0989466i
$495$		0			0
$496$	−5.79105	−	6.43934i	−0.260026	−	0.289135i
$497$	0.493614	−	5.68446i	0.0221416	−	0.254983i
$498$		0			0
$499$			17.4015i			0.778997i	0.921027	+	0.389498i	$0.127352\pi$
$499$			17.4015i			0.778997i	−0.921027	+	0.389498i	$0.872648\pi$
$500$	0.716764	+	0.580778i	0.0320547	+	0.0259732i
$501$		0			0
$502$	2.47805	+	5.19734i	0.110601	+	0.231969i
$503$	−22.3882			−0.998240			−0.499120	−	0.866533i	$-0.666343\pi$
$503$	−22.3882			−0.998240			−0.499120	+	0.866533i	$0.666343\pi$
$504$		0			0
$505$	−53.8141			−2.39470
$506$	−4.97185	−	10.4277i	−0.221026	−	0.463568i
$507$		0			0
$508$	25.7982	+	20.9037i	1.14461	+	0.927451i
$509$		−	11.3657i		−	0.503774i	−0.967757	−	0.251887i	$-0.918949\pi$
$509$		−	11.3657i		−	0.503774i	0.967757	−	0.251887i	$-0.0810512\pi$
$510$		0			0
$511$	5.51586	+	3.85692i	0.244007	+	0.170620i
$512$	17.1863	+	14.7184i	0.759533	+	0.650469i
$513$		0			0
$514$	33.7222	−	16.0785i	1.48742	−	0.709192i
$515$	10.0970			0.444929
$516$		0			0
$517$	19.5704	−	33.8970i	0.860707	−	1.49079i
$518$	−17.0074	−	14.0055i	−0.747261	−	0.615368i
$519$		0			0
$520$	−5.13639	−	4.87862i	−0.225245	−	0.213942i
$521$	21.0799	+	12.1705i	0.923529	+	0.533200i	0.884759	−	0.466049i	$-0.154323\pi$
$521$	21.0799	+	12.1705i	0.923529	+	0.533200i	0.0387695	+	0.999248i	$0.487656\pi$
$522$		0			0
$523$	36.0137	−	20.7925i	1.57477	−	0.909194i	0.579199	−	0.815186i	$-0.303366\pi$
$523$	36.0137	−	20.7925i	1.57477	−	0.909194i	0.995571	−	0.0940077i	$-0.0299678\pi$
$524$	14.4685	−	17.8562i	0.632057	−	0.780050i
$525$		0			0
$526$	1.66689	+	3.49604i	0.0726797	+	0.152435i
$527$	−6.57952			−0.286608
$528$		0			0
$529$	−18.1055			−0.787195
$530$	31.2776	+	2.46629i	1.35861	+	0.107129i
$531$		0			0
$532$	23.2526	+	5.78890i	1.00813	+	0.250981i
$533$	7.38434	−	4.26335i	0.319851	−	0.184666i
$534$		0			0
$535$	−9.67541	+	5.58610i	−0.418304	+	0.241508i
$536$	−20.2232	+	5.98055i	−0.873510	+	0.258320i
$537$		0			0
$538$	1.42294	−	18.0457i	0.0613473	−	0.778007i
$539$	25.4594	+	4.45516i	1.09661	+	0.191897i
$540$		0			0
$541$	9.99498	+	17.3118i	0.429718	+	0.744293i	0.996848	−	0.0793350i	$-0.0252797\pi$
$541$	9.99498	+	17.3118i	0.429718	+	0.744293i	−0.567130	+	0.823628i	$0.691946\pi$
$542$	25.9849	+	17.8646i	1.11615	+	0.767352i
$543$		0			0
$544$	17.0453	−	2.23112i	0.730813	−	0.0956587i
$545$	−13.9706	−	8.06590i	−0.598433	−	0.345505i
$546$		0			0
$547$	−10.5952	+	6.11715i	−0.453019	+	0.261551i	−0.709104	−	0.705104i	$-0.750900\pi$
$547$	−10.5952	+	6.11715i	−0.453019	+	0.261551i	0.256085	+	0.966654i	$0.417567\pi$
$548$	−21.6373	−	17.5322i	−0.924299	−	0.748940i
$549$		0			0
$550$	−10.9063	−	22.8744i	−0.465047	−	0.975366i
$551$	21.3505	−	36.9802i	0.909563	−	1.57541i
$552$		0			0
$553$	−15.7624	+	22.5422i	−0.670286	+	0.958590i
$554$	−10.9769	−	23.0225i	−0.466365	−	0.978131i
$555$		0			0
$556$	28.2950	−	10.8518i	1.19998	−	0.460217i
$557$	6.58200	+	3.80012i	0.278888	+	0.161016i	0.632920	−	0.774217i	$-0.281856\pi$
$557$	6.58200	+	3.80012i	0.278888	+	0.161016i	−0.354032	+	0.935233i	$0.615190\pi$
$558$		0			0
$559$		−	3.70165i		−	0.156563i
$560$	−4.05014	−	32.9718i	−0.171150	−	1.39331i
$561$		0			0
$562$	8.46533	+	5.81992i	0.357088	+	0.245498i
$563$	−8.50399	−	14.7293i	−0.358401	−	0.620768i	0.629293	−	0.777168i	$-0.283344\pi$
$563$	−8.50399	−	14.7293i	−0.358401	−	0.620768i	−0.987694	+	0.156400i	$0.950011\pi$
$564$		0			0
$565$	12.8878	−	22.3224i	0.542196	−	0.939111i
$566$	−11.6503	−	8.00959i	−0.489699	−	0.336668i
$567$		0			0
$568$	−5.93064	−	1.42663i	−0.248844	−	0.0598600i
$569$	3.82577	+	2.20881i	0.160385	+	0.0925982i	0.578044	−	0.816005i	$-0.303816\pi$
$569$	3.82577	+	2.20881i	0.160385	+	0.0925982i	−0.417659	+	0.908604i	$0.637149\pi$
$570$		0			0
$571$	−0.790053	+	0.456137i	−0.0330627	+	0.0190887i	−0.516440	−	0.856323i	$-0.672743\pi$
$571$	−0.790053	+	0.456137i	−0.0330627	+	0.0190887i	0.483378	+	0.875412i	$0.339410\pi$
$572$	−2.10994	−	5.50150i	−0.0882212	−	0.230029i
$573$		0			0
$574$	39.4398	+	6.57973i	1.64618	+	0.274632i
$575$	10.7367			0.447750
$576$		0			0
$577$	4.46070	−	7.72616i	0.185701	−	0.321644i	−0.758111	−	0.652125i	$-0.773878\pi$
$577$	4.46070	−	7.72616i	0.185701	−	0.321644i	0.943813	+	0.330481i	$0.107211\pi$
$578$	−6.22123	+	9.04906i	−0.258769	+	0.376391i
$579$		0			0
$580$	−58.4658	−	9.27797i	−2.42766	−	0.385247i
$581$	3.89583	−	1.81973i	0.161626	−	0.0754951i
$582$		0			0
$583$	22.6000	+	13.0481i	0.935997	+	0.540398i
$584$	4.95524	−	5.21706i	0.205049	−	0.215883i
$585$		0			0
$586$	2.57409	−	32.6446i	0.106335	−	1.34854i
$587$	6.93517	+	12.0121i	0.286245	+	0.495791i	0.972910	−	0.231183i	$-0.0742596\pi$
$587$	6.93517	+	12.0121i	0.286245	+	0.495791i	−0.686665	+	0.726974i	$0.740926\pi$
$588$		0			0
$589$	−4.90225	+	8.49095i	−0.201994	+	0.349864i
$590$	−1.86344	−	1.28112i	−0.0767166	−	0.0527427i
$591$		0			0
$592$	−17.5128	+	15.7497i	−0.719771	+	0.647307i
$593$	−14.8781	+	8.58990i	−0.610972	+	0.352745i	−0.773346	−	0.633984i	$-0.781418\pi$
$593$	−14.8781	+	8.58990i	−0.610972	+	0.352745i	0.162374	+	0.986729i	$0.448085\pi$
$594$		0			0
$595$	−20.6831	−	14.4625i	−0.847924	−	0.592904i
$596$	28.1396	+	22.8009i	1.15264	+	0.933961i
$597$		0			0
$598$	2.48870	+	0.196239i	0.101771	+	0.00802481i
$599$	5.21355	+	9.03013i	0.213020	+	0.368961i	0.952658	−	0.304043i	$-0.0983368\pi$
$599$	5.21355	+	9.03013i	0.213020	+	0.368961i	−0.739638	+	0.673004i	$0.765003\pi$
$600$		0			0
$601$	13.3792	+	23.1735i	0.545750	+	0.945267i	0.998559	+	0.0536595i	$0.0170885\pi$
$601$	13.3792	+	23.1735i	0.545750	+	0.945267i	−0.452809	+	0.891607i	$0.649578\pi$
$602$	11.0346	−	13.3997i	0.449738	−	0.546131i
$603$		0			0
$604$	30.6813	+	24.8604i	1.24841	+	1.01156i
$605$		−	8.26570i		−	0.336048i
$606$		0			0
$607$			30.0884i			1.22125i	0.791919	+	0.610626i	$0.209082\pi$
$607$			30.0884i			1.22125i	−0.791919	+	0.610626i	$0.790918\pi$
$608$	9.82081	−	23.6596i	0.398286	−	0.959523i
$609$		0			0
$610$	3.33651	−	42.3136i	0.135091	−	1.71323i
$611$	4.22912	+	7.32505i	0.171092	+	0.296340i
$612$		0			0
$613$	3.42095	−	5.92526i	0.138171	−	0.239319i	−0.788633	−	0.614864i	$-0.789211\pi$
$613$	3.42095	−	5.92526i	0.138171	−	0.239319i	0.926804	+	0.375545i	$0.122544\pi$
$614$	36.2723	−	17.2944i	1.46383	−	0.697944i
$615$		0			0
$616$	8.76214	−	26.2047i	0.353037	−	1.05582i
$617$	−3.69878	−	2.13549i	−0.148907	−	0.0859716i	0.423695	−	0.905805i	$-0.360733\pi$
$617$	−3.69878	−	2.13549i	−0.148907	−	0.0859716i	−0.572602	+	0.819833i	$0.694066\pi$
$618$		0			0
$619$		−	22.4099i		−	0.900730i	−0.892845	−	0.450365i	$-0.851294\pi$
$619$		−	22.4099i		−	0.900730i	0.892845	−	0.450365i	$-0.148706\pi$
$620$	13.4242	+	2.13030i	0.539130	+	0.0855547i
$621$		0			0
$622$	3.68488	−	5.35983i	0.147750	−	0.214909i
$623$	−2.24395	−	4.80404i	−0.0899020	−	0.192470i
$624$		0			0
$625$	−25.7131			−1.02853
$626$	−30.1004	−	2.37348i	−1.20306	−	0.0948632i
$627$		0			0
$628$	−11.1031	−	1.76196i	−0.443062	−	0.0703097i
$629$			17.8940i			0.713481i
$630$		0			0
$631$		−	5.90962i		−	0.235258i	−0.993058	−	0.117629i	$-0.962471\pi$
$631$		−	5.90962i		−	0.235258i	0.993058	−	0.117629i	$-0.0375294\pi$
$632$	21.3210	+	20.2510i	0.848104	+	0.805542i
$633$		0			0
$634$	0.237300	−	3.00945i	0.00942440	−	0.119520i
$635$	−52.1130			−2.06804
$636$		0			0
$637$	−3.58462	+	4.28325i	−0.142028	+	0.169709i
$638$	−40.5743	−	27.8949i	−1.60635	−	1.10437i
$639$		0			0
$640$	−35.5001	−	0.966710i	−1.40326	−	0.0382126i
$641$		−	7.47286i		−	0.295160i	−0.989050	−	0.147580i	$-0.952852\pi$
$641$		−	7.47286i		−	0.295160i	0.989050	−	0.147580i	$-0.0471484\pi$
$642$		0			0
$643$	15.9307	+	9.19760i	0.628246	+	0.362718i	0.780073	−	0.625689i	$-0.215182\pi$
$643$	15.9307	+	9.19760i	0.628246	+	0.362718i	−0.151826	+	0.988407i	$0.548515\pi$
$644$	8.42392	+	8.12919i	0.331949	+	0.320335i
$645$		0			0
$646$	−8.37595	−	17.5673i	−0.329547	−	0.691176i
$647$	−1.76191	+	3.05173i	−0.0692680	+	0.119976i	−0.898579	−	0.438811i	$-0.855400\pi$
$647$	−1.76191	+	3.05173i	−0.0692680	+	0.119976i	0.829311	+	0.558787i	$0.188733\pi$
$648$		0			0
$649$	−0.940449	−	1.62891i	−0.0369159	−	0.0639402i
$650$	5.45926	+	0.430473i	0.214130	+	0.0168845i
$651$		0			0
$652$	1.17528	−	7.40613i	0.0460276	−	0.290047i
$653$			7.29974i			0.285661i	0.989747	+	0.142830i	$0.0456204\pi$
$653$			7.29974i			0.285661i	−0.989747	+	0.142830i	$0.954380\pi$
$654$		0			0
$655$			36.0700i			1.40937i
$656$	13.2334	−	40.6456i	0.516677	−	1.58694i
$657$		0			0
$658$	−6.52690	+	39.1231i	−0.254445	+	1.52518i
$659$	−21.3105	−	36.9109i	−0.830139	−	1.43784i	−0.897927	−	0.440144i	$-0.854927\pi$
$659$	−21.3105	−	36.9109i	−0.830139	−	1.43784i	0.0677880	−	0.997700i	$-0.478406\pi$
$660$		0			0
$661$	−7.45877	−	12.9190i	−0.290113	−	0.502490i	0.683723	−	0.729741i	$-0.260359\pi$
$661$	−7.45877	−	12.9190i	−0.290113	−	0.502490i	−0.973836	+	0.227251i	$0.927026\pi$
$662$	−3.22476	+	40.8964i	−0.125334	+	1.58948i
$663$		0			0
$664$	−1.30358	−	4.40804i	−0.0505885	−	0.171065i
$665$	−34.0745	+	15.9161i	−1.32135	+	0.617200i
$666$		0			0
$667$	18.0664	−	10.4307i	0.699535	−	0.403877i
$668$	1.05868	+	2.76041i	0.0409615	+	0.106804i
$669$		0			0
$670$	18.7514	−	27.2747i	0.724430	−	1.05371i
$671$	17.6521	−	30.5743i	0.681451	−	1.18031i
$672$		0			0
$673$	9.11649	+	15.7902i	0.351415	+	0.608668i	0.986498	−	0.163776i	$-0.0523673\pi$
$673$	9.11649	+	15.7902i	0.351415	+	0.608668i	−0.635083	+	0.772444i	$0.719034\pi$
$674$	−17.9747	−	1.41734i	−0.692360	−	0.0545939i
$675$		0			0
$676$	−24.4211	−	3.87540i	−0.939274	−	0.149054i
$677$	−20.9888	−	12.1179i	−0.806665	−	0.465728i	0.0391315	−	0.999234i	$-0.487541\pi$
$677$	−20.9888	−	12.1179i	−0.806665	−	0.465728i	−0.845796	+	0.533506i	$0.820874\pi$
$678$		0			0
$679$	9.02808	−	4.21699i	0.346466	−	0.161833i
$680$	−18.5809	+	19.5626i	−0.712545	+	0.750193i
$681$		0			0
$682$	9.31620	+	6.40489i	0.356736	+	0.245256i
$683$	−17.8152	+	30.8568i	−0.681678	+	1.18070i	0.292790	+	0.956177i	$0.405416\pi$
$683$	−17.8152	+	30.8568i	−0.681678	+	1.18070i	−0.974468	+	0.224524i	$0.927917\pi$
$684$		0			0
$685$	43.7080			1.67000
$686$	−25.7444	+	4.81926i	−0.982926	+	0.184000i
$687$		0			0
$688$	−12.4088	−	13.7979i	−0.473080	−	0.526040i
$689$	−4.88381	+	2.81967i	−0.186058	+	0.107421i
$690$		0			0
$691$	−8.46952	−	4.88988i	−0.322196	−	0.186020i	0.330175	−	0.943920i	$-0.392892\pi$
$691$	−8.46952	−	4.88988i	−0.322196	−	0.186020i	−0.652371	+	0.757900i	$0.726226\pi$
$692$	−12.9080	+	4.95049i	−0.490688	+	0.188189i
$693$		0			0
$694$	25.2686	−	36.7542i	0.959181	−	1.39517i
$695$	−23.7812	+	41.1903i	−0.902073	+	1.56244i
$696$		0			0
$697$	−16.2376	−	28.1243i	−0.615041	−	1.06528i
$698$	6.71456	−	9.76663i	0.254150	−	0.369672i
$699$		0			0
$700$	18.4788	+	17.8323i	0.698434	+	0.673998i
$701$			13.9885i			0.528337i	0.964476	+	0.264169i	$0.0850976\pi$
$701$			13.9885i			0.528337i	−0.964476	+	0.264169i	$0.914902\pi$
$702$		0			0
$703$	23.0925	+	13.3324i	0.870949	+	0.502842i
$704$	−26.3071	−	13.4338i	−0.991485	−	0.506305i
$705$		0			0
$706$	14.5791	−	6.95118i	0.548690	−	0.261611i
$707$	45.1886	+	3.92398i	1.69949	+	0.147576i
$708$		0			0
$709$	−19.2682	+	33.3735i	−0.723633	+	1.25337i	0.235901	+	0.971777i	$0.424196\pi$
$709$	−19.2682	+	33.3735i	−0.723633	+	1.25337i	−0.959534	+	0.281593i	$0.909137\pi$
$710$	8.64154	−	4.12022i	0.324311	−	0.154629i
$711$		0			0
$712$	−5.43567	+	1.60747i	−0.203710	+	0.0602425i
$713$	−4.14820	+	2.39496i	−0.155351	+	0.0896921i
$714$		0			0
$715$	8.00876	+	4.62386i	0.299511	+	0.172923i
$716$	−2.18214	−	5.68976i	−0.0815506	−	0.212636i
$717$		0			0
$718$	2.26831	−	3.29936i	0.0846527	−	0.123131i
$719$	−11.8394	−	20.5064i	−0.441534	−	0.764760i	0.556269	−	0.831002i	$-0.312232\pi$
$719$	−11.8394	−	20.5064i	−0.441534	−	0.764760i	−0.997804	+	0.0662424i	$0.978899\pi$
$720$		0			0
$721$	−8.47865	−	0.736249i	−0.315761	−	0.0274193i
$722$	−2.12464	−	0.167532i	−0.0790710	−	0.00623489i
$723$		0			0
$724$	2.86633	−	3.53747i	0.106526	−	0.131469i
$725$	39.6308	−	22.8809i	1.47185	−	0.849774i
$726$		0			0
$727$	−23.5627	+	13.6039i	−0.873892	+	0.504542i	−0.868640	−	0.495444i	$-0.835005\pi$
$727$	−23.5627	+	13.6039i	−0.873892	+	0.504542i	−0.00525253	+	0.999986i	$0.501672\pi$
$728$	3.95737	+	4.47119i	0.146670	+	0.165713i
$729$		0			0
$730$	−0.887706	+	11.2579i	−0.0328555	+	0.416674i
$731$	−14.0983			−0.521443
$732$		0			0
$733$	11.5480			0.426535			0.213267	−	0.976994i	$-0.431589\pi$
$733$	11.5480			0.426535			0.213267	+	0.976994i	$0.431589\pi$
$734$	35.4987	−	16.9255i	1.31028	−	0.624732i
$735$		0			0
$736$	9.93447	−	7.61122i	0.366189	−	0.280553i
$737$	23.8419	−	13.7651i	0.878229	−	0.507046i
$738$		0			0
$739$	8.71192	+	5.02983i	0.320473	+	0.185025i	0.651603	−	0.758560i	$-0.274097\pi$
$739$	8.71192	+	5.02983i	0.320473	+	0.185025i	−0.331130	+	0.943585i	$0.607430\pi$
$740$	5.79367	−	36.5093i	0.212980	−	1.34211i
$741$		0			0
$742$	−26.0844	−	4.35166i	−0.957590	−	0.159754i
$743$	22.8644	−	39.6022i	0.838812	−	1.45286i	−0.0520771	−	0.998643i	$-0.516584\pi$
$743$	22.8644	−	39.6022i	0.838812	−	1.45286i	0.890889	−	0.454221i	$-0.150082\pi$
$744$		0			0
$745$	−56.8428			−2.08256
$746$	−19.0622	−	39.9800i	−0.697916	−	1.46377i
$747$		0			0
$748$	−20.9532	+	8.03601i	−0.766126	+	0.293826i
$749$	8.53192	−	3.98523i	0.311749	−	0.145617i
$750$		0			0
$751$		−	7.41704i		−	0.270652i	−0.990801	−	0.135326i	$-0.956792\pi$
$751$		−	7.41704i		−	0.270652i	0.990801	−	0.135326i	$-0.0432081\pi$
$752$	40.3193	+	13.1271i	1.47029	+	0.478697i
$753$		0			0
$754$	9.60442	−	4.57932i	0.349772	−	0.166769i
$755$	−61.9772			−2.25558
$756$		0			0
$757$	−30.6722			−1.11480			−0.557401	−	0.830244i	$-0.688201\pi$
$757$	−30.6722			−1.11480			−0.557401	+	0.830244i	$0.688201\pi$
$758$	34.1089	−	16.2628i	1.23889	−	0.590693i
$759$		0			0
$760$	11.4016	+	38.5546i	0.413580	+	1.39852i
$761$			5.64185i			0.204517i	0.994758	+	0.102258i	$0.0326069\pi$
$761$			5.64185i			0.204517i	−0.994758	+	0.102258i	$0.967393\pi$
$762$		0			0
$763$	11.1432	+	7.79176i	0.403409	+	0.282081i
$764$	6.18808	+	16.1349i	0.223877	+	0.583740i
$765$		0			0
$766$	4.52999	+	9.50098i	0.163675	+	0.343284i
$767$	0.406458			0.0146763
$768$		0			0
$769$	−3.33932	+	5.78387i	−0.120419	+	0.208572i	−0.919933	−	0.392076i	$-0.871757\pi$
$769$	−3.33932	+	5.78387i	−0.120419	+	0.208572i	0.799514	+	0.600647i	$0.205090\pi$
$770$	15.2074	+	40.6121i	0.548035	+	1.46356i
$771$		0			0
$772$	45.3452	+	7.19584i	1.63201	+	0.258984i
$773$	−11.7948	−	6.80973i	−0.424230	−	0.244929i	0.272656	−	0.962112i	$-0.412098\pi$
$773$	−11.7948	−	6.80973i	−0.424230	−	0.244929i	−0.696885	+	0.717183i	$0.745431\pi$
$774$		0			0
$775$	−9.09955	+	5.25363i	−0.326866	+	0.188716i
$776$	−3.02087	−	10.2151i	−0.108443	−	0.366700i
$777$		0			0
$778$	−39.2153	+	18.6976i	−1.40594	+	0.670341i
$779$	−48.3930			−1.73386
$780$		0			0
$781$	7.96290			0.284935
$782$	0.747403	−	9.47857i	0.0267271	−	0.338953i
$783$		0			0
$784$	0.996755	+	27.9823i	0.0355984	+	0.999366i
$785$	15.2803	−	8.82207i	0.545376	−	0.314873i
$786$		0			0
$787$	16.2793	−	9.39883i	0.580293	−	0.335032i	−0.180957	−	0.983491i	$-0.557919\pi$
$787$	16.2793	−	9.39883i	0.580293	−	0.335032i	0.761250	+	0.648459i	$0.224586\pi$
$788$	9.79989	+	7.94064i	0.349107	+	0.282874i
$789$		0			0
$790$	−46.0086	−	3.62787i	−1.63691	−	0.129074i
$791$	−12.4498	+	17.8047i	−0.442665	+	0.633064i
$792$		0			0
$793$	3.81457	+	6.60703i	0.135459	+	0.234622i
$794$	−3.47259	+	5.05104i	−0.123238	+	0.179255i
$795$		0			0
$796$	24.0029	−	9.20564i	0.850761	−	0.326285i
$797$	−26.5106	−	15.3059i	−0.939054	−	0.542163i	−0.0493904	−	0.998780i	$-0.515728\pi$
$797$	−26.5106	−	15.3059i	−0.939054	−	0.542163i	−0.889664	+	0.456616i	$0.849061\pi$
$798$		0			0
$799$	27.8985	−	16.1072i	0.986977	−	0.569832i
$800$	21.7924	−	16.6961i	0.770478	−	0.590296i
$801$		0			0
$802$	16.8682	−	8.04265i	0.595638	−	0.283996i
$803$	−4.69648	+	8.13455i	−0.165735	+	0.287062i
$804$		0			0
$805$	−18.3045	−	1.58948i	−0.645149	−	0.0560219i
$806$	−2.20525	+	1.05145i	−0.0776767	+	0.0370357i
$807$		0			0
$808$	11.3410	−	47.1455i	0.398974	−	1.65857i
$809$	−0.871099	−	0.502929i	−0.0306262	−	0.0176821i	0.484609	−	0.874731i	$-0.338962\pi$
$809$	−0.871099	−	0.502929i	−0.0306262	−	0.0176821i	−0.515235	+	0.857049i	$0.672295\pi$
$810$		0			0
$811$		−	37.9915i		−	1.33406i	−0.745030	−	0.667031i	$-0.767565\pi$
$811$		−	37.9915i		−	1.33406i	0.745030	−	0.667031i	$-0.232435\pi$
$812$	48.4182	+	12.0540i	1.69914	+	0.423013i
$813$		0			0
$814$	17.4191	−	25.3368i	0.610539	−	0.888056i
$815$	5.88461	+	10.1924i	0.206129	+	0.357026i
$816$		0			0
$817$	−10.5043	+	18.1940i	−0.367499	+	0.636527i
$818$	19.2174	−	27.9525i	0.671919	−	0.977336i
$819$		0			0
$820$	24.0236	+	62.6395i	0.838940	+	2.18747i
$821$	−45.9915	−	26.5532i	−1.60512	−	0.926714i	−0.990442	−	0.137933i	$-0.955954\pi$
$821$	−45.9915	−	26.5532i	−1.60512	−	0.926714i	−0.614674	−	0.788781i	$-0.710712\pi$
$822$		0			0
$823$	−4.12542	+	2.38181i	−0.143803	+	0.0830247i	−0.570175	−	0.821523i	$-0.693125\pi$
$823$	−4.12542	+	2.38181i	−0.143803	+	0.0830247i	0.426372	+	0.904548i	$0.359791\pi$
$824$	−2.12789	+	8.84583i	−0.0741284	+	0.308159i
$825$		0			0
$826$	1.47134	+	1.21165i	0.0511946	+	0.0421587i
$827$	−2.02105			−0.0702787			−0.0351393	−	0.999382i	$-0.511188\pi$
$827$	−2.02105			−0.0702787			−0.0351393	+	0.999382i	$0.511188\pi$
$828$		0			0
$829$	−1.51810	+	2.62943i	−0.0527259	+	0.0913240i	−0.891184	−	0.453643i	$-0.850124\pi$
$829$	−1.51810	+	2.62943i	−0.0527259	+	0.0913240i	0.838458	+	0.544967i	$0.183458\pi$
$830$	5.94505	+	4.08723i	0.206356	+	0.141870i
$831$		0			0
$832$	5.35653	−	3.47175i	0.185704	−	0.120361i
$833$	16.3134	+	13.6525i	0.565224	+	0.473032i
$834$		0			0
$835$	−4.01845	−	2.32005i	−0.139064	−	0.0802887i
$836$	−5.24120	+	33.0279i	−0.181271	+	1.14229i
$837$		0			0
$838$	26.7272	+	2.10749i	0.923277	+	0.0728021i
$839$	14.7757	+	25.5923i	0.510114	+	0.883543i	0.999931	+	0.0117180i	$0.00373004\pi$
$839$	14.7757	+	25.5923i	0.510114	+	0.883543i	−0.489818	+	0.871825i	$0.662937\pi$
$840$		0			0
$841$	29.9575	−	51.8879i	1.03302	−	1.78924i
$842$	−10.7356	+	15.6155i	−0.369974	+	0.538144i
$843$		0			0
$844$	26.6358	−	10.2154i	0.916843	−	0.351629i
$845$	33.6087	−	19.4040i	1.15618	−	0.667518i
$846$		0			0
$847$	−0.602712	+	6.94084i	−0.0207094	+	0.238490i
$848$	−8.75221	+	26.8819i	−0.300552	+	0.923129i
$849$		0			0
$850$	1.63951	−	20.7923i	0.0562349	−	0.713171i
$851$	6.51348	+	11.2817i	0.223279	+	0.386731i
$852$		0			0
$853$	−10.4280	−	18.0618i	−0.357048	−	0.618426i	0.630418	−	0.776256i	$-0.282884\pi$
$853$	−10.4280	−	18.0618i	−0.357048	−	0.618426i	−0.987466	+	0.157830i	$0.949550\pi$
$854$	−5.88711	+	35.2881i	−0.201453	+	1.20754i
$855$		0			0
$856$	−2.85485	−	9.65368i	−0.0975767	−	0.329956i
$857$			22.0586i			0.753507i	0.926313	+	0.376754i	$0.122960\pi$
$857$			22.0586i			0.753507i	−0.926313	+	0.376754i	$0.877040\pi$
$858$		0			0
$859$			54.0357i			1.84367i	0.387579	+	0.921836i	$0.373311\pi$
$859$			54.0357i			1.84367i	−0.387579	+	0.921836i	$0.626689\pi$
$860$	28.7648	+	4.56469i	0.980871	+	0.155655i
$861$		0			0
$862$	−24.8910	−	1.96270i	−0.847790	−	0.0668498i
$863$	−14.8916	−	25.7931i	−0.506917	−	0.878007i	−0.999968	−	0.00800595i	$-0.997452\pi$
$863$	−14.8916	−	25.7931i	−0.506917	−	0.878007i	0.493051	−	0.870001i	$-0.335882\pi$
$864$		0			0
$865$	10.8488	−	18.7907i	0.368871	−	0.638903i
$866$	−13.7283	−	28.7931i	−0.466508	−	0.978429i
$867$		0			0
$868$	−11.1172	−	2.76770i	−0.377342	−	0.0939419i
$869$	−33.2442	−	19.1935i	−1.12773	−	0.651096i
$870$		0			0
$871$			5.94923i			0.201582i
$872$	10.0106	−	10.5395i	0.339001	−	0.356913i
$873$		0			0
$874$	−11.6754	−	8.02681i	−0.394925	−	0.271511i
$875$	1.21581	+	0.105576i	0.0411019	+	0.00356911i
$876$		0			0
$877$	10.8706			0.367073			0.183536	−	0.983013i	$-0.441245\pi$
$877$	10.8706			0.367073			0.183536	+	0.983013i	$0.441245\pi$
$878$	−3.72535	+	47.2449i	−0.125724	+	1.59444i
$879$		0			0
$880$	45.3529	−	9.61176i	1.52884	−	0.324012i
$881$		−	40.5406i		−	1.36585i	−0.730490	−	0.682923i	$-0.760708\pi$
$881$		−	40.5406i		−	1.36585i	0.730490	−	0.682923i	$-0.239292\pi$
$882$		0			0
$883$		−	18.8427i		−	0.634106i	−0.948408	−	0.317053i	$-0.897307\pi$
$883$		−	18.8427i		−	0.634106i	0.948408	−	0.317053i	$-0.102693\pi$
$884$	0.760062	−	4.78959i	0.0255637	−	0.161091i
$885$		0			0
$886$	4.20614	+	0.331662i	0.141308	+	0.0111424i
$887$	2.11941			0.0711629			0.0355814	−	0.999367i	$-0.488672\pi$
$887$	2.11941			0.0711629			0.0355814	+	0.999367i	$0.488672\pi$
$888$		0			0
$889$	43.7602	+	3.79994i	1.46767	+	0.127446i
$890$	5.04006	−	7.33099i	0.168943	−	0.245735i
$891$		0			0
$892$	−1.43345	+	9.03299i	−0.0479954	+	0.302447i
$893$		−	48.0045i		−	1.60641i
$894$		0			0
$895$	8.28282	+	4.78209i	0.276864	+	0.159848i
$896$	29.7395	+	3.40033i	0.993527	+	0.113597i
$897$		0			0
$898$	−50.5111	+	24.0833i	−1.68558	+	0.803671i
$899$	−10.2078	+	17.6804i	−0.340449	+	0.589675i
$900$		0			0
$901$	10.7391	+	18.6007i	0.357771	+	0.619678i
$902$	−4.38644	+	55.6289i	−0.146052	+	1.85224i
$903$		0			0
$904$	16.8402	+	15.9951i	0.560097	+	0.531989i
$905$			7.14579i			0.237534i
$906$		0			0
$907$			18.9717i			0.629945i	0.949101	+	0.314972i	$0.101995\pi$
$907$			18.9717i			0.629945i	−0.949101	+	0.314972i	$0.898005\pi$
$908$	−8.11133	+	10.0105i	−0.269184	+	0.332212i
$909$		0			0
$910$	−9.24353	−	1.54210i	−0.306420	−	0.0511200i
$911$	7.63448	+	13.2233i	0.252942	+	0.438108i	0.964334	−	0.264687i	$-0.0852686\pi$
$911$	7.63448	+	13.2233i	0.252942	+	0.438108i	−0.711393	+	0.702795i	$0.751935\pi$
$912$		0			0
$913$	3.00038	+	5.19681i	0.0992980	+	0.171989i
$914$	41.1797	+	3.24709i	1.36210	+	0.107404i
$915$		0			0
$916$	8.30980	−	10.2555i	0.274564	−	0.338851i
$917$	2.63012	−	30.2885i	0.0868543	−	1.00022i
$918$		0			0
$919$	11.7046	−	6.75766i	0.386099	−	0.222914i	−0.294369	−	0.955692i	$-0.595110\pi$
$919$	11.7046	−	6.75766i	0.386099	−	0.222914i	0.680469	+	0.732777i	$0.261776\pi$
$920$	−4.59388	+	19.0972i	−0.151456	+	0.629616i
$921$		0			0
$922$	−2.42909	−	1.67000i	−0.0799980	−	0.0549986i
$923$	−0.860382	+	1.49022i	−0.0283198	+	0.0490513i
$924$		0			0
$925$	14.2881	+	24.7476i	0.469789	+	0.813698i
$926$	−2.29011	+	29.0433i	−0.0752578	+	0.954421i
$927$		0			0
$928$	20.4495	−	49.2656i	0.671289	−	1.61722i
$929$	3.33429	+	1.92505i	0.109394	+	0.0631589i	0.553699	−	0.832717i	$-0.313216\pi$
$929$	3.33429	+	1.92505i	0.109394	+	0.0631589i	−0.444305	+	0.895876i	$0.646549\pi$
$930$		0			0
$931$	29.7735	−	10.8804i	0.975787	−	0.356590i
$932$	1.52367	−	9.60156i	0.0499096	−	0.314509i
$933$		0			0
$934$	11.2197	−	16.3196i	0.367121	−	0.533993i
$935$	17.6106	−	30.5025i	0.575929	−	0.997538i
$936$		0			0
$937$	−54.7523			−1.78868			−0.894340	−	0.447389i	$-0.852354\pi$
$937$	−54.7523			−1.78868			−0.894340	+	0.447389i	$0.852354\pi$
$938$	−17.7346	+	21.5357i	−0.579057	+	0.703166i
$939$		0			0
$940$	−62.1366	+	23.8307i	−2.02667	+	0.777273i
$941$	−0.470342	+	0.271552i	−0.0153327	+	0.00885234i	−0.507647	−	0.861565i	$-0.669484\pi$
$941$	−0.470342	+	0.271552i	−0.0153327	+	0.00885234i	0.492314	+	0.870418i	$0.336151\pi$
$942$		0			0
$943$	−20.4746	−	11.8210i	−0.666746	−	0.384946i
$944$	1.51507	−	1.36254i	0.0493113	−	0.0443468i
$945$		0			0
$946$	19.9623	+	13.7241i	0.649030	+	0.446209i
$947$	18.9232	−	32.7759i	0.614921	−	1.06507i	−0.375477	−	0.926832i	$-0.622521\pi$
$947$	18.9232	−	32.7759i	0.614921	−	1.06507i	0.990398	−	0.138243i	$-0.0441455\pi$
$948$		0			0
$949$	−1.01490	−	1.75786i	−0.0329450	−	0.0570624i
$950$	−25.6112	−	17.6077i	−0.830938	−	0.571270i
$951$		0			0
$952$	17.0291	−	15.0722i	0.551917	−	0.488493i
$953$			55.2382i			1.78934i	0.446726	+	0.894671i	$0.352590\pi$
$953$			55.2382i			1.78934i	−0.446726	+	0.894671i	$0.647410\pi$
$954$		0			0
$955$	−23.4883	−	13.5609i	−0.760062	−	0.438822i
$956$	10.0360	+	26.1679i	0.324587	+	0.846332i
$957$		0			0
$958$	22.8492	+	47.9228i	0.738225	+	1.54832i
$959$	−36.7023	−	3.18707i	−1.18518	−	0.102916i
$960$		0			0
$961$	−13.1562	+	22.7872i	−0.424394	+	0.735072i
$962$	2.85957	+	5.99753i	0.0921964	+	0.193368i
$963$		0			0
$964$	5.28140	−	6.51801i	0.170102	−	0.209931i
$965$	−62.4048	+	36.0294i	−2.00888	+	1.15983i
$966$		0			0
$967$	−13.0909	−	7.55803i	−0.420975	−	0.243050i	0.274519	−	0.961582i	$-0.411481\pi$
$967$	−13.0909	−	7.55803i	−0.420975	−	0.243050i	−0.695494	+	0.718532i	$0.744815\pi$
$968$	7.24142	+	1.74194i	0.232748	+	0.0559881i
$969$		0			0
$970$	13.7769	+	9.47163i	0.442350	+	0.304116i
$971$	24.1097	+	41.7592i	0.773716	+	1.34012i	0.935513	+	0.353292i	$0.114938\pi$
$971$	24.1097	+	41.7592i	0.773716	+	1.34012i	−0.161797	+	0.986824i	$0.551729\pi$
$972$		0			0
$973$	22.9730	−	32.8541i	0.736479	−	1.05325i
$974$	−0.0532289	+	0.675049i	−0.00170556	+	0.0216300i
$975$		0			0
$976$	36.3670	+	11.8404i	1.16408	+	0.379001i
$977$	32.6814	−	18.8686i	1.04557	−	0.603660i	0.124164	−	0.992262i	$-0.460375\pi$
$977$	32.6814	−	18.8686i	1.04557	−	0.603660i	0.921406	+	0.388602i	$0.127042\pi$
$978$		0			0
$979$	6.40831	−	3.69984i	0.204811	−	0.118247i
$980$	−28.8639	−	33.1372i	−0.922022	−	1.05853i
$981$		0			0
$982$	4.06335	+	0.320403i	0.129667	+	0.0102245i
$983$	38.1254			1.21601			0.608006	−	0.793933i	$-0.291970\pi$
$983$	38.1254			1.21601			0.608006	+	0.793933i	$0.291970\pi$
$984$		0			0
$985$	−19.7961			−0.630755
$986$	−17.4410	−	36.5798i	−0.555433	−	1.16494i
$987$		0			0
$988$	−5.61472	−	4.54949i	−0.178628	−	0.144739i
$989$	−8.88856	+	5.13181i	−0.282640	+	0.163182i
$990$		0			0
$991$	32.4040	+	18.7085i	1.02935	+	0.594294i	0.916798	−	0.399352i	$-0.130765\pi$
$991$	32.4040	+	18.7085i	1.02935	+	0.594294i	0.112550	+	0.993646i	$0.464098\pi$
$992$	−4.69538	+	11.3118i	−0.149078	+	0.359149i
$993$		0			0
$994$	−7.55687	+	2.82970i	−0.239689	+	0.0897525i
$995$	−20.1738	+	34.9421i	−0.639553	+	1.10774i
$996$		0			0
$997$	−4.66793			−0.147835			−0.0739174	−	0.997264i	$-0.523550\pi$
$997$	−4.66793			−0.147835			−0.0739174	+	0.997264i	$0.523550\pi$
$998$	22.2137	−	10.5913i	0.703161	−	0.335262i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.o.a.179.16		88
3.2	odd	2		252.2.o.a.95.29	✓	88
4.3	odd	2	inner	756.2.o.a.179.3		88
7.2	even	3		756.2.bb.a.611.14		88
9.2	odd	6		756.2.bb.a.683.31		88
9.7	even	3		252.2.bb.a.11.14	yes	88
12.11	even	2		252.2.o.a.95.42	yes	88
21.2	odd	6		252.2.bb.a.23.31	yes	88
28.23	odd	6		756.2.bb.a.611.31		88
36.7	odd	6		252.2.bb.a.11.31	yes	88
36.11	even	6		756.2.bb.a.683.14		88
63.2	odd	6	inner	756.2.o.a.359.3		88
63.16	even	3		252.2.o.a.191.42	yes	88
84.23	even	6		252.2.bb.a.23.14	yes	88
252.79	odd	6		252.2.o.a.191.29	yes	88
252.191	even	6	inner	756.2.o.a.359.16		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.29	✓	88	3.2	odd	2
252.2.o.a.95.42	yes	88	12.11	even	2
252.2.o.a.191.29	yes	88	252.79	odd	6
252.2.o.a.191.42	yes	88	63.16	even	3
252.2.bb.a.11.14	yes	88	9.7	even	3
252.2.bb.a.11.31	yes	88	36.7	odd	6
252.2.bb.a.23.14	yes	88	84.23	even	6
252.2.bb.a.23.31	yes	88	21.2	odd	6
756.2.o.a.179.3		88	4.3	odd	2	inner
756.2.o.a.179.16		88	1.1	even	1	trivial
756.2.o.a.359.3		88	63.2	odd	6	inner
756.2.o.a.359.16		88	252.191	even	6	inner
756.2.bb.a.611.14		88	7.2	even	3
756.2.bb.a.611.31		88	28.23	odd	6
756.2.bb.a.683.14		88	36.11	even	6
756.2.bb.a.683.31		88	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.608644 - 1.27654i) q^{2} +(-1.25910 + 1.55392i) q^{4} -3.13896i q^{5} +(-0.228884 + 2.63583i) q^{7} +(2.74998 + 0.661514i) q^{8} +O(q^{10})\)	\(q+(-0.608644 - 1.27654i) q^{2} +(-1.25910 + 1.55392i) q^{4} -3.13896i q^{5} +(-0.228884 + 2.63583i) q^{7} +(2.74998 + 0.661514i) q^{8} +(-4.00700 + 1.91051i) q^{10} -3.69232 q^{11} +(0.398951 - 0.691003i) q^{13} +(3.50405 - 1.31210i) q^{14} +(-0.829311 - 3.91309i) q^{16} +(-2.63178 - 1.51946i) q^{17} +(-3.92177 + 2.26423i) q^{19} +(4.87768 + 3.95228i) q^{20} +(2.24731 + 4.71340i) q^{22} -2.21235 q^{23} -4.85305 q^{25} +(-1.12491 - 0.0887014i) q^{26} +(-3.80767 - 3.67446i) q^{28} +(-8.16616 + 4.71474i) q^{29} +(1.87502 - 1.08254i) q^{31} +(-4.49045 + 3.44033i) q^{32} +(-0.337832 + 4.28438i) q^{34} +(8.27376 + 0.718458i) q^{35} +(-2.94414 - 5.09940i) q^{37} +(5.27734 + 3.62818i) q^{38} +(2.07647 - 8.63207i) q^{40} +(9.25469 + 5.34320i) q^{41} +(4.01769 - 2.31962i) q^{43} +(4.64902 - 5.73756i) q^{44} +(1.34654 + 2.82416i) q^{46} +(-5.30030 + 9.18039i) q^{47} +(-6.89522 - 1.20660i) q^{49} +(2.95378 + 6.19511i) q^{50} +(0.571440 + 1.48998i) q^{52} +(-6.12081 - 3.53385i) q^{53} +11.5900i q^{55} +(-2.37307 + 7.09708i) q^{56} +(10.9888 + 7.55483i) q^{58} +(0.254704 + 0.441160i) q^{59} +(-4.78075 + 8.28050i) q^{61} +(-2.52312 - 1.73465i) q^{62} +(7.12480 + 3.63830i) q^{64} +(-2.16903 - 1.25229i) q^{65} +(-6.45716 + 3.72804i) q^{67} +(5.67480 - 2.17641i) q^{68} +(-4.11864 - 10.9991i) q^{70} -2.15661 q^{71} +(1.27196 - 2.20310i) q^{73} +(-4.71765 + 6.86203i) q^{74} +(1.41949 - 8.94500i) q^{76} +(0.845115 - 9.73235i) q^{77} +(9.00359 + 5.19822i) q^{79} +(-12.2830 + 2.60317i) q^{80} +(1.18799 - 15.0661i) q^{82} +(-0.812599 - 1.40746i) q^{83} +(-4.76952 + 8.26105i) q^{85} +(-5.40643 - 3.71692i) q^{86} +(-10.1538 - 2.44253i) q^{88} +(-1.73558 + 1.00204i) q^{89} +(1.73006 + 1.20973i) q^{91} +(2.78558 - 3.43781i) q^{92} +(14.9451 + 1.17845i) q^{94} +(7.10733 + 12.3103i) q^{95} +(-1.88309 - 3.26161i) q^{97} +(2.65647 + 9.53641i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 3 q^{2} + q^{4}+O(q^{10}) \) 88 * q + 3 * q^2 + q^4	\( 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) \) 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

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