LMFDB - Embedded newform 728.2.c.a.365.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(365,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.365"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [34] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			365.1
Character	$\chi$	$=$	728.365
Dual form			728.2.c.a.365.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41239 - 0.0717634i) q^{2} +1.60179i q^{3} +(1.98970 + 0.202716i) q^{4} -2.04118i q^{5} +(0.114950 - 2.26236i) q^{6} -1.00000 q^{7} +(-2.79569 - 0.429102i) q^{8} +0.434268 q^{9} +(-0.146482 + 2.88295i) q^{10} -3.30009i q^{11} +(-0.324709 + 3.18708i) q^{12} +1.00000i q^{13} +(1.41239 + 0.0717634i) q^{14} +3.26954 q^{15} +(3.91781 + 0.806688i) q^{16} -4.91083 q^{17} +(-0.613356 - 0.0311646i) q^{18} -4.94776i q^{19} +(0.413780 - 4.06134i) q^{20} -1.60179i q^{21} +(-0.236826 + 4.66102i) q^{22} -9.20320 q^{23} +(0.687332 - 4.47811i) q^{24} +0.833579 q^{25} +(0.0717634 - 1.41239i) q^{26} +5.50098i q^{27} +(-1.98970 - 0.202716i) q^{28} -7.07766i q^{29} +(-4.61788 - 0.234634i) q^{30} -7.44816 q^{31} +(-5.47559 - 1.42052i) q^{32} +5.28605 q^{33} +(6.93601 + 0.352418i) q^{34} +2.04118i q^{35} +(0.864063 + 0.0880331i) q^{36} -4.63185i q^{37} +(-0.355068 + 6.98818i) q^{38} -1.60179 q^{39} +(-0.875875 + 5.70651i) q^{40} +4.33522 q^{41} +(-0.114950 + 2.26236i) q^{42} +7.48166i q^{43} +(0.668981 - 6.56619i) q^{44} -0.886420i q^{45} +(12.9985 + 0.660453i) q^{46} +0.246211 q^{47} +(-1.29215 + 6.27551i) q^{48} +1.00000 q^{49} +(-1.17734 - 0.0598204i) q^{50} -7.86611i q^{51} +(-0.202716 + 1.98970i) q^{52} -9.84928i q^{53} +(0.394769 - 7.76953i) q^{54} -6.73608 q^{55} +(2.79569 + 0.429102i) q^{56} +7.92528 q^{57} +(-0.507917 + 9.99642i) q^{58} +4.04217i q^{59} +(6.50541 + 0.662789i) q^{60} -10.6561i q^{61} +(10.5197 + 0.534506i) q^{62} -0.434268 q^{63} +(7.63174 + 2.39927i) q^{64} +2.04118 q^{65} +(-7.46597 - 0.379345i) q^{66} -10.2757i q^{67} +(-9.77107 - 0.995503i) q^{68} -14.7416i q^{69} +(0.146482 - 2.88295i) q^{70} +11.1847 q^{71} +(-1.21408 - 0.186345i) q^{72} +5.93073 q^{73} +(-0.332397 + 6.54198i) q^{74} +1.33522i q^{75} +(1.00299 - 9.84456i) q^{76} +3.30009i q^{77} +(2.26236 + 0.114950i) q^{78} -6.84608 q^{79} +(1.64660 - 7.99697i) q^{80} -7.50861 q^{81} +(-6.12303 - 0.311110i) q^{82} -8.53099i q^{83} +(0.324709 - 3.18708i) q^{84} +10.0239i q^{85} +(0.536910 - 10.5670i) q^{86} +11.3369 q^{87} +(-1.41607 + 9.22602i) q^{88} -14.4730 q^{89} +(-0.0636125 + 1.25197i) q^{90} -1.00000i q^{91} +(-18.3116 - 1.86564i) q^{92} -11.9304i q^{93} +(-0.347747 - 0.0176690i) q^{94} -10.0993 q^{95} +(2.27537 - 8.77075i) q^{96} -3.61044 q^{97} +(-1.41239 - 0.0717634i) q^{98} -1.43312i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 2 q^{2} - 2 q^{4} - 6 q^{6} - 34 q^{7} + 8 q^{8} - 26 q^{9} - 4 q^{12} - 2 q^{14} - 8 q^{15} - 6 q^{16} - 20 q^{17} + 14 q^{18} - 4 q^{20} - 10 q^{22} - 20 q^{23} + 10 q^{24} - 22 q^{25} + 2 q^{28}+ \cdots + 2 q^{98}+O(q^{100}) $ 34 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 - 34 * q^7 + 8 * q^8 - 26 * q^9 - 4 * q^12 - 2 * q^14 - 8 * q^15 - 6 * q^16 - 20 * q^17 + 14 * q^18 - 4 * q^20 - 10 * q^22 - 20 * q^23 + 10 * q^24 - 22 * q^25 + 2 * q^28 - 60 * q^30 + 16 * q^31 + 12 * q^32 - 8 * q^33 + 28 * q^34 - 4 * q^36 - 28 * q^38 + 8 * q^39 + 64 * q^40 + 8 * q^41 + 6 * q^42 + 24 * q^44 + 16 * q^46 + 24 * q^48 + 34 * q^49 + 10 * q^50 - 4 * q^52 - 18 * q^54 - 32 * q^55 - 8 * q^56 + 8 * q^57 + 44 * q^58 - 24 * q^60 + 60 * q^62 + 26 * q^63 - 2 * q^64 - 20 * q^65 + 24 * q^66 + 12 * q^68 + 64 * q^71 - 92 * q^72 - 22 * q^74 + 4 * q^76 + 20 * q^79 - 56 * q^80 - 6 * q^81 - 20 * q^82 + 4 * q^84 - 12 * q^86 - 56 * q^87 - 34 * q^88 - 4 * q^90 - 54 * q^92 + 12 * q^94 + 42 * q^96 + 2 * q^98

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 $

$2$	−1.41239	−	0.0717634i	−0.998712	−	0.0507444i
$2$	−1.41239	−	0.0717634i	−0.998712	−	0.0507444i
$3$			1.60179i			0.924794i	0.886673	+	0.462397i	$0.153011\pi$
$3$			1.60179i			0.924794i	−0.886673	+	0.462397i	$0.846989\pi$
$4$	1.98970	+	0.202716i	0.994850	+	0.101358i
$5$		−	2.04118i		−	0.912844i	−0.889763	−	0.456422i	$-0.849131\pi$
$5$		−	2.04118i		−	0.912844i	0.889763	−	0.456422i	$-0.150869\pi$
$6$	0.114950	−	2.26236i	0.0469281	−	0.923603i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−2.79569	−	0.429102i	−0.988425	−	0.151711i
$9$	0.434268			0.144756
$10$	−0.146482	+	2.88295i	−0.0463217	+	0.911668i
$11$		−	3.30009i		−	0.995014i	−0.867460	−	0.497507i	$-0.834249\pi$
$11$		−	3.30009i		−	0.995014i	0.867460	−	0.497507i	$-0.165751\pi$
$12$	−0.324709	+	3.18708i	−0.0937353	+	0.920031i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	1.41239	+	0.0717634i	0.377478	+	0.0191796i
$15$	3.26954			0.844193
$16$	3.91781	+	0.806688i	0.979453	+	0.201672i
$17$	−4.91083			−1.19105			−0.595525	−	0.803337i	$-0.703056\pi$
$17$	−4.91083			−1.19105			−0.595525	+	0.803337i	$0.703056\pi$
$18$	−0.613356	−	0.0311646i	−0.144570	−	0.00734556i
$19$		−	4.94776i		−	1.13509i	−0.823341	−	0.567547i	$-0.807892\pi$
$19$		−	4.94776i		−	1.13509i	0.823341	−	0.567547i	$-0.192108\pi$
$20$	0.413780	−	4.06134i	0.0925241	−	0.908143i
$21$		−	1.60179i		−	0.349539i
$22$	−0.236826	+	4.66102i	−0.0504914	+	0.993732i
$23$	−9.20320			−1.91900			−0.959500	−	0.281709i	$-0.909099\pi$
$23$	−9.20320			−1.91900			−0.959500	+	0.281709i	$0.909099\pi$
$24$	0.687332	−	4.47811i	0.140301	−	0.914090i
$25$	0.833579			0.166716
$26$	0.0717634	−	1.41239i	0.0140740	−	0.276993i
$27$			5.50098i			1.05866i
$28$	−1.98970	−	0.202716i	−0.376018	−	0.0383097i
$29$		−	7.07766i		−	1.31429i	−0.753765	−	0.657144i	$-0.771764\pi$
$29$		−	7.07766i		−	1.31429i	0.753765	−	0.657144i	$-0.228236\pi$
$30$	−4.61788	−	0.234634i	−0.843105	−	0.0428380i
$31$	−7.44816			−1.33773			−0.668865	−	0.743384i	$-0.733220\pi$
$31$	−7.44816			−1.33773			−0.668865	+	0.743384i	$0.733220\pi$
$32$	−5.47559	−	1.42052i	−0.967958	−	0.251114i
$33$	5.28605			0.920183
$34$	6.93601	+	0.352418i	1.18952	+	0.0604391i
$35$			2.04118i			0.345023i
$36$	0.864063	+	0.0880331i	0.144011	+	0.0146722i
$37$		−	4.63185i		−	0.761471i	−0.924684	−	0.380735i	$-0.875671\pi$
$37$		−	4.63185i		−	0.761471i	0.924684	−	0.380735i	$-0.124329\pi$
$38$	−0.355068	+	6.98818i	−0.0575997	+	1.13363i
$39$	−1.60179			−0.256492
$40$	−0.875875	+	5.70651i	−0.138488	+	0.902278i
$41$	4.33522			0.677047			0.338524	−	0.940958i	$-0.390072\pi$
$41$	4.33522			0.677047			0.338524	+	0.940958i	$0.390072\pi$
$42$	−0.114950	+	2.26236i	−0.0177372	+	0.349089i
$43$			7.48166i			1.14094i	0.821318	+	0.570471i	$0.193239\pi$
$43$			7.48166i			1.14094i	−0.821318	+	0.570471i	$0.806761\pi$
$44$	0.668981	−	6.56619i	0.100853	−	0.989890i
$45$		−	0.886420i		−	0.132140i
$46$	12.9985	+	0.660453i	1.91653	+	0.0973785i
$47$	0.246211			0.0359136			0.0179568	−	0.999839i	$-0.494284\pi$
$47$	0.246211			0.0359136			0.0179568	+	0.999839i	$0.494284\pi$
$48$	−1.29215	+	6.27551i	−0.186505	+	0.905792i
$49$	1.00000			0.142857
$50$	−1.17734	−	0.0598204i	−0.166501	−	0.00845989i
$51$		−	7.86611i		−	1.10148i
$52$	−0.202716	+	1.98970i	−0.0281117	+	0.275922i
$53$		−	9.84928i		−	1.35290i	−0.736487	−	0.676451i	$-0.763517\pi$
$53$		−	9.84928i		−	1.35290i	0.736487	−	0.676451i	$-0.236483\pi$
$54$	0.394769	−	7.76953i	0.0537212	−	1.05730i
$55$	−6.73608			−0.908293
$56$	2.79569	+	0.429102i	0.373590	+	0.0573412i
$57$	7.92528			1.04973
$58$	−0.507917	+	9.99642i	−0.0666927	+	1.31259i
$59$			4.04217i			0.526246i	0.964762	+	0.263123i	$0.0847525\pi$
$59$			4.04217i			0.526246i	−0.964762	+	0.263123i	$0.915248\pi$
$60$	6.50541	+	0.662789i	0.839845	+	0.0855657i
$61$		−	10.6561i		−	1.36438i	−0.731175	−	0.682190i	$-0.761028\pi$
$61$		−	10.6561i		−	1.36438i	0.731175	−	0.682190i	$-0.238972\pi$
$62$	10.5197	+	0.534506i	1.33601	+	0.0678823i
$63$	−0.434268			−0.0547126
$64$	7.63174	+	2.39927i	0.953968	+	0.299909i
$65$	2.04118			0.253177
$66$	−7.46597	−	0.379345i	−0.918997	−	0.0466941i
$67$		−	10.2757i		−	1.25538i	−0.778464	−	0.627689i	$-0.784001\pi$
$67$		−	10.2757i		−	1.25538i	0.778464	−	0.627689i	$-0.215999\pi$
$68$	−9.77107	−	0.995503i	−1.18492	−	0.120722i
$69$		−	14.7416i		−	1.77468i
$70$	0.146482	−	2.88295i	0.0175080	−	0.344578i
$71$	11.1847			1.32738			0.663691	−	0.748007i	$-0.268989\pi$
$71$	11.1847			1.32738			0.663691	+	0.748007i	$0.268989\pi$
$72$	−1.21408	−	0.186345i	−0.143080	−	0.0219610i
$73$	5.93073			0.694140			0.347070	−	0.937839i	$-0.387177\pi$
$73$	5.93073			0.694140			0.347070	+	0.937839i	$0.387177\pi$
$74$	−0.332397	+	6.54198i	−0.0386404	+	0.760490i
$75$			1.33522i			0.154178i
$76$	1.00299	−	9.84456i	0.115051	−	1.12925i
$77$			3.30009i			0.376080i
$78$	2.26236	+	0.114950i	0.256161	+	0.0130155i
$79$	−6.84608			−0.770245			−0.385122	−	0.922866i	$-0.625841\pi$
$79$	−6.84608			−0.770245			−0.385122	+	0.922866i	$0.625841\pi$
$80$	1.64660	−	7.99697i	0.184095	−	0.894088i
$81$	−7.50861			−0.834290
$82$	−6.12303	−	0.311110i	−0.676175	−	0.0343564i
$83$		−	8.53099i		−	0.936398i	−0.883623	−	0.468199i	$-0.844903\pi$
$83$		−	8.53099i		−	0.936398i	0.883623	−	0.468199i	$-0.155097\pi$
$84$	0.324709	−	3.18708i	0.0354286	−	0.347739i
$85$			10.0239i			1.08724i
$86$	0.536910	−	10.5670i	0.0578964	−	1.13947i
$87$	11.3369			1.21545
$88$	−1.41607	+	9.22602i	−0.150954	+	0.983497i
$89$	−14.4730			−1.53413			−0.767066	−	0.641568i	$-0.778284\pi$
$89$	−14.4730			−1.53413			−0.767066	+	0.641568i	$0.778284\pi$
$90$	−0.0636125	+	1.25197i	−0.00670535	+	0.131969i
$91$		−	1.00000i		−	0.104828i
$92$	−18.3116	−	1.86564i	−1.90912	−	0.194506i
$93$		−	11.9304i		−	1.23712i
$94$	−0.347747	−	0.0176690i	−0.0358674	−	0.00182242i
$95$	−10.0993			−1.03616
$96$	2.27537	−	8.77075i	0.232229	−	0.895161i
$97$	−3.61044			−0.366584			−0.183292	−	0.983058i	$-0.558675\pi$
$97$	−3.61044			−0.366584			−0.183292	+	0.983058i	$0.558675\pi$
$98$	−1.41239	−	0.0717634i	−0.142673	−	0.00724920i
$99$		−	1.43312i		−	0.144034i
$100$	1.65857	+	0.168980i	0.165857	+	0.0168980i
$101$			6.51050i			0.647819i	0.946088	+	0.323909i	$0.104997\pi$
$101$			6.51050i			0.647819i	−0.946088	+	0.323909i	$0.895003\pi$
$102$	−0.564499	+	11.1100i	−0.0558937	+	1.10006i
$103$	18.3047			1.80362			0.901809	−	0.432134i	$-0.142239\pi$
$103$	18.3047			1.80362			0.901809	+	0.432134i	$0.142239\pi$
$104$	0.429102	−	2.79569i	0.0420769	−	0.274140i
$105$	−3.26954			−0.319075
$106$	−0.706818	+	13.9110i	−0.0686522	+	1.35116i
$107$		−	16.0316i		−	1.54983i	−0.632064	−	0.774916i	$-0.717792\pi$
$107$		−	16.0316i		−	1.54983i	0.632064	−	0.774916i	$-0.282208\pi$
$108$	−1.11514	+	10.9453i	−0.107304	+	1.05321i
$109$			10.7704i			1.03162i	0.856703	+	0.515810i	$0.172509\pi$
$109$			10.7704i			1.03162i	−0.856703	+	0.515810i	$0.827491\pi$
$110$	9.51398	+	0.483404i	0.907122	+	0.0460908i
$111$	7.41925			0.704204
$112$	−3.91781	−	0.806688i	−0.370198	−	0.0762249i
$113$	5.36213			0.504426			0.252213	−	0.967672i	$-0.418842\pi$
$113$	5.36213			0.504426			0.252213	+	0.967672i	$0.418842\pi$
$114$	−11.1936	−	0.568745i	−1.04838	−	0.0532679i
$115$			18.7854i			1.75175i
$116$	1.43475	−	14.0824i	0.133214	−	1.30752i
$117$			0.434268i			0.0401481i
$118$	0.290080	−	5.70913i	0.0267040	−	0.525568i
$119$	4.91083			0.450175
$120$	−9.14063	−	1.40297i	−0.834421	−	0.128073i
$121$	0.109419			0.00994719
$122$	−0.764721	+	15.0507i	−0.0692346	+	1.36262i
$123$			6.94411i			0.626129i
$124$	−14.8196	−	1.50986i	−1.33084	−	0.135590i
$125$		−	11.9074i		−	1.06503i
$126$	0.613356	+	0.0311646i	0.0546421	+	0.00277636i
$127$	−18.4402			−1.63630			−0.818152	−	0.575002i	$-0.805001\pi$
$127$	−18.4402			−1.63630			−0.818152	+	0.575002i	$0.805001\pi$
$128$	−10.6068	−	3.93639i	−0.937520	−	0.347931i
$129$	−11.9841			−1.05514
$130$	−2.88295	−	0.146482i	−0.252851	−	0.0128473i
$131$			9.95924i			0.870143i	0.900396	+	0.435072i	$0.143277\pi$
$131$			9.95924i			0.870143i	−0.900396	+	0.435072i	$0.856723\pi$
$132$	10.5177	+	1.07157i	0.915444	+	0.0932679i
$133$			4.94776i			0.429025i
$134$	−0.737421	+	14.5133i	−0.0637034	+	1.25376i
$135$	11.2285			0.966395
$136$	13.7291	+	2.10725i	1.17726	+	0.180695i
$137$	11.7779			1.00626			0.503128	−	0.864212i	$-0.332182\pi$
$137$	11.7779			1.00626			0.503128	+	0.864212i	$0.332182\pi$
$138$	−1.05791	+	20.8209i	−0.0900550	+	1.77239i
$139$			6.87146i			0.582829i	0.956597	+	0.291415i	$0.0941259\pi$
$139$			6.87146i			0.582829i	−0.956597	+	0.291415i	$0.905874\pi$
$140$	−0.413780	+	4.06134i	−0.0349708	+	0.343246i
$141$			0.394379i			0.0332127i
$142$	−15.7972	−	0.802654i	−1.32567	−	0.0673572i
$143$	3.30009			0.275967
$144$	1.70138	+	0.350319i	0.141782	+	0.0291932i
$145$	−14.4468			−1.19974
$146$	−8.37652	−	0.425610i	−0.693245	−	0.0352237i
$147$			1.60179i			0.132113i
$148$	0.938950	−	9.21599i	0.0771812	−	0.757549i
$149$		−	15.7608i		−	1.29118i	−0.763686	−	0.645588i	$-0.776612\pi$
$149$		−	15.7608i		−	1.29118i	0.763686	−	0.645588i	$-0.223388\pi$
$150$	0.0958198	−	1.88585i	0.00782365	−	0.153979i
$151$	−3.89237			−0.316757			−0.158378	−	0.987378i	$-0.550627\pi$
$151$	−3.89237			−0.316757			−0.158378	+	0.987378i	$0.550627\pi$
$152$	−2.12310	+	13.8324i	−0.172206	+	1.12196i
$153$	−2.13261			−0.172412
$154$	0.236826	−	4.66102i	0.0190839	−	0.375595i
$155$			15.2031i			1.22114i
$156$	−3.18708	−	0.324709i	−0.255171	−	0.0259975i
$157$			10.5821i			0.844545i	0.906469	+	0.422273i	$0.138768\pi$
$157$			10.5821i			0.844545i	−0.906469	+	0.422273i	$0.861232\pi$
$158$	9.66935	+	0.491298i	0.769252	+	0.0390856i
$159$	15.7765			1.25116
$160$	−2.89953	+	11.1767i	−0.229228	+	0.883594i
$161$	9.20320			0.725314
$162$	10.6051	+	0.538843i	0.833215	+	0.0423355i
$163$			18.4249i			1.44315i	0.692338	+	0.721573i	$0.256581\pi$
$163$			18.4249i			1.44315i	−0.692338	+	0.721573i	$0.743419\pi$
$164$	8.62578	+	0.878818i	0.673561	+	0.0686242i
$165$		−	10.7898i		−	0.839984i
$166$	−0.612213	+	12.0491i	−0.0475169	+	0.935192i
$167$	−13.1609			−1.01842			−0.509212	−	0.860641i	$-0.670063\pi$
$167$	−13.1609			−1.01842			−0.509212	+	0.860641i	$0.670063\pi$
$168$	−0.687332	+	4.47811i	−0.0530288	+	0.345493i
$169$	−1.00000			−0.0769231
$170$	0.719348	−	14.1577i	0.0551715	−	1.08584i
$171$		−	2.14866i		−	0.164312i
$172$	−1.51665	+	14.8863i	−0.115644	+	1.13507i
$173$		−	7.42763i		−	0.564713i	−0.959310	−	0.282356i	$-0.908884\pi$
$173$		−	7.42763i		−	0.564713i	0.959310	−	0.282356i	$-0.0911160\pi$
$174$	−16.0122	−	0.813576i	−1.21388	−	0.0616770i
$175$	−0.833579			−0.0630126
$176$	2.66214	−	12.9291i	0.200667	−	0.974570i
$177$	−6.47471			−0.486669
$178$	20.4415	+	1.03863i	1.53216	+	0.0778486i
$179$			18.5579i			1.38708i	0.720419	+	0.693540i	$0.243950\pi$
$179$			18.5579i			1.38708i	−0.720419	+	0.693540i	$0.756050\pi$
$180$	0.179692	−	1.76371i	0.0133934	−	0.131459i
$181$			18.9137i			1.40584i	0.711267	+	0.702922i	$0.248122\pi$
$181$			18.9137i			1.40584i	−0.711267	+	0.702922i	$0.751878\pi$
$182$	−0.0717634	+	1.41239i	−0.00531946	+	0.104693i
$183$	17.0689			1.26177
$184$	25.7293	+	3.94911i	1.89679	+	0.291132i
$185$	−9.45444			−0.695104
$186$	−0.856166	+	16.8504i	−0.0627771	+	1.23553i
$187$			16.2062i			1.18511i
$188$	0.489887	+	0.0499110i	0.0357287	+	0.00364013i
$189$		−	5.50098i		−	0.400137i
$190$	14.2641	+	0.724759i	1.03483	+	0.0525795i
$191$	17.3720			1.25699			0.628496	−	0.777813i	$-0.283671\pi$
$191$	17.3720			1.25699			0.628496	+	0.777813i	$0.283671\pi$
$192$	−3.84313	+	12.2245i	−0.277354	+	0.882224i
$193$	10.9562			0.788647			0.394324	−	0.918972i	$-0.370979\pi$
$193$	10.9562			0.788647			0.394324	+	0.918972i	$0.370979\pi$
$194$	5.09935	+	0.259097i	0.366112	+	0.0186021i
$195$			3.26954i			0.234137i
$196$	1.98970	+	0.202716i	0.142121	+	0.0144797i
$197$			4.36246i			0.310812i	0.987851	+	0.155406i	$0.0496687\pi$
$197$			4.36246i			0.310812i	−0.987851	+	0.155406i	$0.950331\pi$
$198$	−0.102846	+	2.02413i	−0.00730893	+	0.143849i
$199$	10.1073			0.716484			0.358242	−	0.933629i	$-0.383376\pi$
$199$	10.1073			0.716484			0.358242	+	0.933629i	$0.383376\pi$
$200$	−2.33043	−	0.357690i	−0.164786	−	0.0252925i
$201$	16.4595			1.16097
$202$	0.467216	−	9.19538i	0.0328732	−	0.646984i
$203$			7.07766i			0.496754i
$204$	1.59459	−	15.6512i	0.111643	−	1.09580i
$205$		−	8.84897i		−	0.618039i
$206$	−25.8534	−	1.31361i	−1.80129	−	0.0915235i
$207$	−3.99665			−0.277787
$208$	−0.806688	+	3.91781i	−0.0559338	+	0.271651i
$209$	−16.3281			−1.12944
$210$	4.61788	+	0.234634i	0.318664	+	0.0161913i
$211$		−	24.7203i		−	1.70181i	−0.525317	−	0.850906i	$-0.676053\pi$
$211$		−	24.7203i		−	1.70181i	0.525317	−	0.850906i	$-0.323947\pi$
$212$	1.99661	−	19.5971i	0.137128	−	1.34594i
$213$			17.9156i			1.22756i
$214$	−1.15048	+	22.6429i	−0.0786453	+	1.54784i
$215$	15.2714			1.04150
$216$	2.36048	−	15.3790i	0.160610	−	1.04641i
$217$	7.44816			0.505614
$218$	0.772923	−	15.2121i	0.0523489	−	1.03029i
$219$			9.49979i			0.641936i
$220$	−13.4028	−	1.36551i	−0.903615	−	0.0920628i
$221$		−	4.91083i		−	0.330338i
$222$	−10.4789	−	0.532430i	−0.703297	−	0.0357344i
$223$	−9.86265			−0.660452			−0.330226	−	0.943902i	$-0.607125\pi$
$223$	−9.86265			−0.660452			−0.330226	+	0.943902i	$0.607125\pi$
$224$	5.47559	+	1.42052i	0.365854	+	0.0949122i
$225$	0.361997			0.0241331
$226$	−7.57342	−	0.384804i	−0.503776	−	0.0255968i
$227$			3.27410i			0.217310i	0.994080	+	0.108655i	$0.0346543\pi$
$227$			3.27410i			0.217310i	−0.994080	+	0.108655i	$0.965346\pi$
$228$	15.7689	+	1.60658i	1.04432	+	0.106398i
$229$		−	0.592074i		−	0.0391254i	−0.999809	−	0.0195627i	$-0.993773\pi$
$229$		−	0.592074i		−	0.0391254i	0.999809	−	0.0195627i	$-0.00622739\pi$
$230$	1.34810	−	26.5323i	0.0888914	−	1.74949i
$231$	−5.28605			−0.347796
$232$	−3.03704	+	19.7869i	−0.199391	+	1.29907i
$233$	15.3194			1.00361			0.501804	−	0.864981i	$-0.332670\pi$
$233$	15.3194			1.00361			0.501804	+	0.864981i	$0.332670\pi$
$234$	0.0311646	−	0.613356i	0.00203729	−	0.0400964i
$235$		−	0.502562i		−	0.0327835i
$236$	−0.819413	+	8.04271i	−0.0533392	+	0.523536i
$237$		−	10.9660i		−	0.712318i
$238$	−6.93601	−	0.352418i	−0.449595	−	0.0228438i
$239$	−8.41048			−0.544028			−0.272014	−	0.962293i	$-0.587690\pi$
$239$	−8.41048			−0.544028			−0.272014	+	0.962293i	$0.587690\pi$
$240$	12.8095	+	2.63750i	0.826847	+	0.170250i
$241$	−21.7077			−1.39831			−0.699157	−	0.714968i	$-0.746441\pi$
$241$	−21.7077			−1.39831			−0.699157	+	0.714968i	$0.746441\pi$
$242$	−0.154543	−	0.00785228i	−0.00993437	−	0.000504764i
$243$			4.47572i			0.287117i
$244$	2.16017	−	21.2025i	0.138291	−	1.35735i
$245$		−	2.04118i		−	0.130406i
$246$	0.498333	−	9.80780i	0.0317726	−	0.625323i
$247$	4.94776			0.314819
$248$	20.8227	+	3.19602i	1.32225	+	0.202948i
$249$	13.6649			0.865975
$250$	−0.854515	+	16.8179i	−0.0540443	+	1.06366i
$251$			14.6293i			0.923394i	0.887038	+	0.461697i	$0.152759\pi$
$251$			14.6293i			0.923394i	−0.887038	+	0.461697i	$0.847241\pi$
$252$	−0.864063	−	0.0880331i	−0.0544309	−	0.00554556i
$253$			30.3714i			1.90943i
$254$	26.0448	+	1.32333i	1.63420	+	0.0830333i
$255$	−16.0562			−1.00548
$256$	14.6985	+	6.32091i	0.918657	+	0.395057i
$257$	−16.6321			−1.03748			−0.518740	−	0.854932i	$-0.673599\pi$
$257$	−16.6321			−1.03748			−0.518740	+	0.854932i	$0.673599\pi$
$258$	16.9262	+	0.860016i	1.05378	+	0.0535423i
$259$			4.63185i			0.287809i
$260$	4.06134	+	0.413780i	0.251874	+	0.0256616i
$261$		−	3.07360i		−	0.190251i
$262$	0.714709	−	14.0663i	0.0441549	−	0.869022i
$263$	−15.6456			−0.964750			−0.482375	−	0.875965i	$-0.660226\pi$
$263$	−15.6456			−0.964750			−0.482375	+	0.875965i	$0.660226\pi$
$264$	−14.7781	−	2.26825i	−0.909532	−	0.139601i
$265$	−20.1042			−1.23499
$266$	0.355068	−	6.98818i	0.0217706	−	0.428473i
$267$		−	23.1827i		−	1.41876i
$268$	2.08305	−	20.4456i	0.127243	−	1.24891i
$269$			11.9287i			0.727305i	0.931535	+	0.363652i	$0.118470\pi$
$269$			11.9287i			0.727305i	−0.931535	+	0.363652i	$0.881530\pi$
$270$	−15.8590	−	0.805795i	−0.965150	−	0.0490391i
$271$	−5.99184			−0.363978			−0.181989	−	0.983301i	$-0.558254\pi$
$271$	−5.99184			−0.363978			−0.181989	+	0.983301i	$0.558254\pi$
$272$	−19.2397	−	3.96151i	−1.16658	−	0.240202i
$273$	1.60179			0.0969448
$274$	−16.6351	−	0.845225i	−1.00496	−	0.0510619i
$275$		−	2.75088i		−	0.165884i
$276$	2.98836	−	29.3313i	0.179878	−	1.76554i
$277$		−	12.9046i		−	0.775363i	−0.921793	−	0.387682i	$-0.873276\pi$
$277$		−	12.9046i		−	0.775363i	0.921793	−	0.387682i	$-0.126724\pi$
$278$	0.493119	−	9.70519i	0.0295753	−	0.582078i
$279$	−3.23450			−0.193644
$280$	0.875875	−	5.70651i	0.0523436	−	0.341029i
$281$	−17.9330			−1.06979			−0.534896	−	0.844918i	$-0.679649\pi$
$281$	−17.9330			−1.06979			−0.534896	+	0.844918i	$0.679649\pi$
$282$	0.0283020	−	0.557018i	0.00168536	−	0.0331699i
$283$		−	12.8586i		−	0.764364i	−0.924087	−	0.382182i	$-0.875173\pi$
$283$		−	12.8586i		−	0.764364i	0.924087	−	0.382182i	$-0.124827\pi$
$284$	22.2542	+	2.26732i	1.32055	+	0.134541i
$285$		−	16.1769i		−	0.958239i
$286$	−4.66102	−	0.236826i	−0.275612	−	0.0140038i
$287$	−4.33522			−0.255900
$288$	−2.37788	−	0.616884i	−0.140118	−	0.0363503i
$289$	7.11620			0.418600
$290$	20.4045	+	1.03675i	1.19819	+	0.0608801i
$291$		−	5.78316i		−	0.339015i
$292$	11.8004	+	1.20225i	0.690565	+	0.0703566i
$293$			26.7615i			1.56342i	0.623641	+	0.781711i	$0.285653\pi$
$293$			26.7615i			1.56342i	−0.623641	+	0.781711i	$0.714347\pi$
$294$	0.114950	−	2.26236i	0.00670402	−	0.131943i
$295$	8.25080			0.480380
$296$	−1.98754	+	12.9492i	−0.115523	+	0.752657i
$297$	18.1537			1.05338
$298$	−1.13105	+	22.2604i	−0.0655199	+	1.28951i
$299$		−	9.20320i		−	0.532235i
$300$	−0.270670	+	2.65668i	−0.0156271	+	0.153384i
$301$		−	7.48166i		−	0.431236i
$302$	5.49756	+	0.279330i	0.316349	+	0.0160736i
$303$	−10.4285			−0.599099
$304$	3.99130	−	19.3844i	0.228917	−	1.11177i
$305$	−21.7511			−1.24547
$306$	3.01209	+	0.153044i	0.172190	+	0.00874892i
$307$			10.2784i			0.586622i	0.956017	+	0.293311i	$0.0947571\pi$
$307$			10.2784i			0.586622i	−0.956017	+	0.293311i	$0.905243\pi$
$308$	−0.668981	+	6.56619i	−0.0381187	+	0.374143i
$309$			29.3203i			1.66798i
$310$	1.09102	−	21.4727i	0.0619659	−	1.21957i
$311$	−4.51151			−0.255824			−0.127912	−	0.991786i	$-0.540828\pi$
$311$	−4.51151			−0.255824			−0.127912	+	0.991786i	$0.540828\pi$
$312$	4.47811	+	0.687332i	0.253523	+	0.0389125i
$313$	−2.90958			−0.164459			−0.0822296	−	0.996613i	$-0.526204\pi$
$313$	−2.90958			−0.164459			−0.0822296	+	0.996613i	$0.526204\pi$
$314$	0.759409	−	14.9461i	0.0428559	−	0.843457i
$315$			0.886420i			0.0499441i
$316$	−13.6217	−	1.38781i	−0.766278	−	0.0780705i
$317$		−	8.78517i		−	0.493424i	−0.969089	−	0.246712i	$-0.920650\pi$
$317$		−	8.78517i		−	0.493424i	0.969089	−	0.246712i	$-0.0793502\pi$
$318$	−22.2826	−	1.13217i	−1.24954	−	0.0634892i
$319$	−23.3569			−1.30773
$320$	4.89735	−	15.5778i	0.273770	−	0.870824i
$321$	25.6793			1.43328
$322$	−12.9985	−	0.660453i	−0.724379	−	0.0368056i
$323$			24.2976i			1.35195i
$324$	−14.9399	−	1.52212i	−0.829993	−	0.0845620i
$325$			0.833579i			0.0462386i
$326$	1.32223	−	26.0231i	0.0732316	−	1.44129i
$327$	−17.2520			−0.954036
$328$	−12.1199	−	1.86025i	−0.669210	−	0.102715i
$329$	−0.246211			−0.0135741
$330$	−0.774312	+	15.2394i	−0.0426245	+	0.838901i
$331$		−	11.5276i		−	0.633614i	−0.948490	−	0.316807i	$-0.897389\pi$
$331$		−	11.5276i		−	0.633614i	0.948490	−	0.316807i	$-0.102611\pi$
$332$	1.72937	−	16.9741i	0.0949115	−	0.931575i
$333$		−	2.01146i		−	0.110227i
$334$	18.5884	+	0.944474i	1.01711	+	0.0516793i
$335$	−20.9746			−1.14597
$336$	1.29215	−	6.27551i	0.0704923	−	0.342357i
$337$	17.7814			0.968615			0.484307	−	0.874898i	$-0.339072\pi$
$337$	17.7814			0.968615			0.484307	+	0.874898i	$0.339072\pi$
$338$	1.41239	+	0.0717634i	0.0768240	+	0.00390341i
$339$			8.58900i			0.466490i
$340$	−2.03200	+	19.9445i	−0.110201	+	1.08164i
$341$			24.5796i			1.33106i
$342$	−0.154195	+	3.03474i	−0.00833790	+	0.164100i
$343$	−1.00000			−0.0539949
$344$	3.21040	−	20.9164i	0.173093	−	1.12774i
$345$	−30.0903			−1.62001
$346$	−0.533032	+	10.4907i	−0.0286560	+	0.563985i
$347$		−	14.2957i		−	0.767435i	−0.923451	−	0.383717i	$-0.874644\pi$
$347$		−	14.2957i		−	0.767435i	0.923451	−	0.383717i	$-0.125356\pi$
$348$	22.5571	+	2.29818i	1.20919	+	0.123195i
$349$		−	27.0196i		−	1.44632i	−0.690678	−	0.723162i	$-0.742688\pi$
$349$		−	27.0196i		−	1.44632i	0.690678	−	0.723162i	$-0.257312\pi$
$350$	1.17734	+	0.0598204i	0.0629314	+	0.00319754i
$351$	−5.50098			−0.293620
$352$	−4.68783	+	18.0699i	−0.249862	+	0.963131i
$353$	21.9915			1.17049			0.585244	−	0.810857i	$-0.300999\pi$
$353$	21.9915			1.17049			0.585244	+	0.810857i	$0.300999\pi$
$354$	9.14482	+	0.464647i	0.486042	+	0.0246957i
$355$		−	22.8300i		−	1.21169i
$356$	−28.7969	−	2.93390i	−1.52623	−	0.155497i
$357$			7.86611i			0.416319i
$358$	1.33177	−	26.2110i	0.0703865	−	1.38529i
$359$	3.86395			0.203931			0.101966	−	0.994788i	$-0.467487\pi$
$359$	3.86395			0.203931			0.101966	+	0.994788i	$0.467487\pi$
$360$	−0.380365	+	2.47815i	−0.0200470	+	0.130610i
$361$	−5.48036			−0.288440
$362$	1.35731	−	26.7136i	0.0713387	−	1.40403i
$363$			0.175266i			0.00919910i
$364$	0.202716	−	1.98970i	0.0106252	−	0.104289i
$365$		−	12.1057i		−	0.633641i
$366$	−24.1080	−	1.22492i	−1.26014	−	0.0640278i
$367$	29.1363			1.52090			0.760450	−	0.649396i	$-0.224978\pi$
$367$	29.1363			1.52090			0.760450	+	0.649396i	$0.224978\pi$
$368$	−36.0564	−	7.42411i	−1.87957	−	0.387009i
$369$	1.88265			0.0980067
$370$	13.3534	+	0.678483i	0.694209	+	0.0352726i
$371$			9.84928i			0.511349i
$372$	2.41848	−	23.7379i	0.125392	−	1.23075i
$373$		−	16.0903i		−	0.833123i	−0.909107	−	0.416562i	$-0.863235\pi$
$373$		−	16.0903i		−	0.833123i	0.909107	−	0.416562i	$-0.136765\pi$
$374$	1.16301	−	22.8894i	0.0601378	−	1.18358i
$375$	19.0731			0.984933
$376$	−0.688330	−	0.105650i	−0.0354979	−	0.00544847i
$377$	7.07766			0.364518
$378$	−0.394769	+	7.76953i	−0.0203047	+	0.399622i
$379$		−	23.9974i		−	1.23266i	−0.787487	−	0.616331i	$-0.788618\pi$
$379$		−	23.9974i		−	1.23266i	0.787487	−	0.616331i	$-0.211382\pi$
$380$	−20.0945	−	2.04729i	−1.03083	−	0.105024i
$381$		−	29.5374i		−	1.51324i
$382$	−24.5360	−	1.24667i	−1.25537	−	0.0637853i
$383$	18.3411			0.937186			0.468593	−	0.883414i	$-0.344761\pi$
$383$	18.3411			0.937186			0.468593	+	0.883414i	$0.344761\pi$
$384$	6.30527	−	16.9899i	0.321765	−	0.867013i
$385$	6.73608			0.343302
$386$	−15.4745	−	0.786257i	−0.787631	−	0.0400194i
$387$			3.24905i			0.165158i
$388$	−7.18368	−	0.731893i	−0.364696	−	0.0371563i
$389$		−	0.628023i		−	0.0318420i	−0.999873	−	0.0159210i	$-0.994932\pi$
$389$		−	0.628023i		−	0.0318420i	0.999873	−	0.0159210i	$-0.00506803\pi$
$390$	0.234634	−	4.61788i	0.0118811	−	0.233835i
$391$	45.1953			2.28562
$392$	−2.79569	−	0.429102i	−0.141204	−	0.0216729i
$393$	−15.9526			−0.804703
$394$	0.313065	−	6.16150i	0.0157720	−	0.310412i
$395$			13.9741i			0.703113i
$396$	0.290517	−	2.85148i	0.0145990	−	0.143292i
$397$		−	5.60043i		−	0.281078i	−0.990075	−	0.140539i	$-0.955117\pi$
$397$		−	5.60043i		−	0.281078i	0.990075	−	0.140539i	$-0.0448835\pi$
$398$	−14.2754	−	0.725331i	−0.715561	−	0.0363576i
$399$	−7.92528			−0.396760
$400$	3.26580	+	0.672438i	0.163290	+	0.0336219i
$401$	16.1431			0.806147			0.403073	−	0.915168i	$-0.367942\pi$
$401$	16.1431			0.806147			0.403073	+	0.915168i	$0.367942\pi$
$402$	−23.2473	−	1.18119i	−1.15947	−	0.0589126i
$403$		−	7.44816i		−	0.371019i
$404$	−1.31978	+	12.9539i	−0.0656617	+	0.644483i
$405$			15.3264i			0.761576i
$406$	0.507917	−	9.99642i	0.0252075	−	0.496114i
$407$	−15.2855			−0.757674
$408$	−3.37537	+	21.9912i	−0.167105	+	1.08873i
$409$	35.6500			1.76278			0.881390	−	0.472389i	$-0.156608\pi$
$409$	35.6500			1.76278			0.881390	+	0.472389i	$0.156608\pi$
$410$	−0.635032	+	12.4982i	−0.0313620	+	0.617242i
$411$			18.8658i			0.930580i
$412$	36.4209	+	3.71066i	1.79433	+	0.182811i
$413$		−	4.04217i		−	0.198902i
$414$	5.64484	+	0.286814i	0.277429	+	0.0140961i
$415$	−17.4133			−0.854785
$416$	1.42052	−	5.47559i	0.0696465	−	0.268463i
$417$	−11.0066			−0.538997
$418$	23.0616	+	1.17176i	1.12798	+	0.0573125i
$419$			31.0570i			1.51724i	0.651536	+	0.758618i	$0.274125\pi$
$419$			31.0570i			1.51724i	−0.651536	+	0.758618i	$0.725875\pi$
$420$	−6.50541	−	0.662789i	−0.317432	−	0.0323408i
$421$			1.20004i			0.0584864i	0.999572	+	0.0292432i	$0.00930972\pi$
$421$			1.20004i			0.0584864i	−0.999572	+	0.0292432i	$0.990690\pi$
$422$	−1.77401	+	34.9147i	−0.0863575	+	1.69962i
$423$	0.106922			0.00519871
$424$	−4.22635	+	27.5355i	−0.205250	+	1.33724i
$425$	−4.09356			−0.198567
$426$	1.28568	−	25.3038i	0.0622915	−	1.22597i
$427$			10.6561i			0.515687i
$428$	3.24986	−	31.8981i	0.157088	−	1.54185i
$429$			5.28605i			0.255213i
$430$	−21.5692	−	1.09593i	−1.04016	−	0.0528504i
$431$	22.6281			1.08996			0.544978	−	0.838450i	$-0.316538\pi$
$431$	22.6281			1.08996			0.544978	+	0.838450i	$0.316538\pi$
$432$	−4.43757	+	21.5518i	−0.213503	+	1.03691i
$433$	−7.81312			−0.375475			−0.187737	−	0.982219i	$-0.560115\pi$
$433$	−7.81312			−0.375475			−0.187737	+	0.982219i	$0.560115\pi$
$434$	−10.5197	−	0.534506i	−0.504963	−	0.0256571i
$435$		−	23.1407i		−	1.10951i
$436$	−2.18334	+	21.4299i	−0.104563	+	1.02631i
$437$			45.5352i			2.17825i
$438$	0.681737	−	13.4174i	0.0325747	−	0.641109i
$439$	−6.45379			−0.308023			−0.154011	−	0.988069i	$-0.549219\pi$
$439$	−6.45379			−0.308023			−0.154011	+	0.988069i	$0.549219\pi$
$440$	18.8320	+	2.89047i	0.897779	+	0.137798i
$441$	0.434268			0.0206794
$442$	−0.352418	+	6.93601i	−0.0167628	+	0.329912i
$443$		−	6.15949i		−	0.292646i	−0.989237	−	0.146323i	$-0.953256\pi$
$443$		−	6.15949i		−	0.292646i	0.989237	−	0.146323i	$-0.0467439\pi$
$444$	14.7621	+	1.50400i	0.700577	+	0.0713767i
$445$			29.5420i			1.40042i
$446$	13.9299	+	0.707777i	0.659601	+	0.0335142i
$447$	25.2455			1.19407
$448$	−7.63174	−	2.39927i	−0.360566	−	0.113355i
$449$	−3.77506			−0.178156			−0.0890781	−	0.996025i	$-0.528392\pi$
$449$	−3.77506			−0.178156			−0.0890781	+	0.996025i	$0.528392\pi$
$450$	−0.511281	−	0.0259781i	−0.0241020	−	0.00122462i
$451$		−	14.3066i		−	0.673672i
$452$	10.6690	+	1.08699i	0.501829	+	0.0511277i
$453$		−	6.23477i		−	0.292935i
$454$	0.234961	−	4.62431i	0.0110273	−	0.217030i
$455$	−2.04118			−0.0956921
$456$	−22.1566	−	3.40075i	−1.03758	−	0.159255i
$457$	16.8871			0.789945			0.394972	−	0.918693i	$-0.370754\pi$
$457$	16.8871			0.789945			0.394972	+	0.918693i	$0.370754\pi$
$458$	−0.0424893	+	0.836241i	−0.00198539	+	0.0390750i
$459$		−	27.0143i		−	1.26092i
$460$	−3.80810	+	37.3773i	−0.177554	+	1.74273i
$461$		−	22.1909i		−	1.03353i	−0.856127	−	0.516766i	$-0.827136\pi$
$461$		−	22.1909i		−	1.03353i	0.856127	−	0.516766i	$-0.172864\pi$
$462$	7.46597	+	0.379345i	0.347348	+	0.0176487i
$463$	−0.870232			−0.0404431			−0.0202216	−	0.999796i	$-0.506437\pi$
$463$	−0.870232			−0.0404431			−0.0202216	+	0.999796i	$0.506437\pi$
$464$	5.70946	−	27.7289i	0.265055	−	1.28728i
$465$	−24.3521			−1.12930
$466$	−21.6370	−	1.09937i	−1.00231	−	0.0509275i
$467$		−	8.29553i		−	0.383871i	−0.981408	−	0.191936i	$-0.938523\pi$
$467$		−	8.29553i		−	0.383871i	0.981408	−	0.191936i	$-0.0614765\pi$
$468$	−0.0880331	+	0.864063i	−0.00406933	+	0.0399413i
$469$			10.2757i			0.474489i
$470$	−0.0360656	+	0.709815i	−0.00166358	+	0.0327413i
$471$	−16.9503			−0.781030
$472$	1.73450	−	11.3006i	0.0798370	−	0.520154i
$473$	24.6901			1.13525
$474$	−0.786957	+	15.4883i	−0.0361461	+	0.711400i
$475$		−	4.12435i		−	0.189238i
$476$	9.77107	+	0.995503i	0.447856	+	0.0456288i
$477$		−	4.27723i		−	0.195841i
$478$	11.8789	+	0.603564i	0.543328	+	0.0276064i
$479$	14.4135			0.658572			0.329286	−	0.944230i	$-0.393192\pi$
$479$	14.4135			0.658572			0.329286	+	0.944230i	$0.393192\pi$
$480$	−17.9027	−	4.64444i	−0.817143	−	0.211989i
$481$	4.63185			0.211194
$482$	30.6597	+	1.55782i	1.39651	+	0.0709566i
$483$			14.7416i			0.670766i
$484$	0.217711	+	0.0221810i	0.00989596	+	0.00100823i
$485$			7.36955i			0.334634i
$486$	0.321193	−	6.32146i	0.0145696	−	0.286747i
$487$	−13.8036			−0.625503			−0.312751	−	0.949835i	$-0.601251\pi$
$487$	−13.8036			−0.625503			−0.312751	+	0.949835i	$0.601251\pi$
$488$	−4.57257	+	29.7913i	−0.206991	+	1.34859i
$489$	−29.5128			−1.33461
$490$	−0.146482	+	2.88295i	−0.00661739	+	0.130238i
$491$		−	25.7469i		−	1.16194i	−0.813925	−	0.580970i	$-0.802673\pi$
$491$		−	25.7469i		−	1.16194i	0.813925	−	0.580970i	$-0.197327\pi$
$492$	−1.40768	+	13.8167i	−0.0634632	+	0.622905i
$493$			34.7571i			1.56538i
$494$	−6.98818	−	0.355068i	−0.314413	−	0.0159753i
$495$	−2.92526			−0.131481
$496$	−29.1805	−	6.00835i	−1.31024	−	0.269783i
$497$	−11.1847			−0.501703
$498$	−19.3001	−	0.980637i	−0.864860	−	0.0439434i
$499$		−	12.7680i		−	0.571575i	−0.958293	−	0.285788i	$-0.907745\pi$
$499$		−	12.7680i		−	0.571575i	0.958293	−	0.285788i	$-0.0922552\pi$
$500$	2.41382	−	23.6921i	0.107949	−	1.05954i
$501$		−	21.0811i		−	0.941832i
$502$	1.04985	−	20.6623i	0.0468571	−	0.922204i
$503$	11.8527			0.528486			0.264243	−	0.964456i	$-0.414878\pi$
$503$	11.8527			0.528486			0.264243	+	0.964456i	$0.414878\pi$
$504$	1.21408	+	0.186345i	0.0540793	+	0.00830048i
$505$	13.2891			0.591358
$506$	2.17955	−	42.8963i	0.0968929	−	1.90697i
$507$		−	1.60179i		−	0.0711380i
$508$	−36.6905	−	3.73813i	−1.62788	−	0.165853i
$509$			20.3465i			0.901841i	0.892564	+	0.450920i	$0.148904\pi$
$509$			20.3465i			0.901841i	−0.892564	+	0.450920i	$0.851096\pi$
$510$	22.6776	+	1.15224i	1.00418	+	0.0510223i
$511$	−5.93073			−0.262360
$512$	−20.3064	−	9.98241i	−0.897426	−	0.441164i
$513$	27.2175			1.20168
$514$	23.4910	+	1.19357i	1.03614	+	0.0526462i
$515$		−	37.3633i		−	1.64642i
$516$	−23.8447	−	2.42936i	−1.04970	−	0.106947i
$517$		−	0.812519i		−	0.0357346i
$518$	0.332397	−	6.54198i	0.0146047	−	0.287438i
$519$	11.8975			0.522243
$520$	−5.70651	−	0.875875i	−0.250247	−	0.0384097i
$521$	38.3974			1.68222			0.841111	−	0.540863i	$-0.181902\pi$
$521$	38.3974			1.68222			0.841111	+	0.540863i	$0.181902\pi$
$522$	−0.220572	+	4.34113i	−0.00965417	+	0.190006i
$523$			23.6884i			1.03582i	0.855435	+	0.517911i	$0.173290\pi$
$523$			23.6884i			1.03582i	−0.855435	+	0.517911i	$0.826710\pi$
$524$	−2.01890	+	19.8159i	−0.0881960	+	0.865662i
$525$		−	1.33522i		−	0.0582737i
$526$	22.0977	+	1.12278i	0.963507	+	0.0489556i
$527$	36.5766			1.59330
$528$	20.7097	+	4.26419i	0.901276	+	0.185575i
$529$	61.6989			2.68256
$530$	28.3950	+	1.44274i	1.23340	+	0.0626688i
$531$			1.75539i			0.0761772i
$532$	−1.00299	+	9.84456i	−0.0434852	+	0.426816i
$533$			4.33522i			0.187779i
$534$	−1.66367	+	32.7430i	−0.0719939	+	1.41693i
$535$	−32.7234			−1.41476
$536$	−4.40933	+	28.7277i	−0.190454	+	1.24085i
$537$	−29.7258			−1.28276
$538$	0.856043	−	16.8480i	0.0369067	−	0.726368i
$539$		−	3.30009i		−	0.142145i
$540$	22.3413	+	2.27620i	0.961418	+	0.0979519i
$541$		−	3.94405i		−	0.169568i	−0.996399	−	0.0847839i	$-0.972980\pi$
$541$		−	3.94405i		−	0.169568i	0.996399	−	0.0847839i	$-0.0270200\pi$
$542$	8.46282	+	0.429995i	0.363509	+	0.0184699i
$543$	−30.2958			−1.30012
$544$	26.8897	+	6.97590i	1.15289	+	0.299089i
$545$	21.9844			0.941708
$546$	−2.26236	−	0.114950i	−0.0968199	−	0.00491940i
$547$		−	18.7051i		−	0.799771i	−0.916565	−	0.399886i	$-0.869050\pi$
$547$		−	18.7051i		−	0.799771i	0.916565	−	0.399886i	$-0.130950\pi$
$548$	23.4346	+	2.38758i	1.00107	+	0.101992i
$549$		−	4.62762i		−	0.197502i
$550$	−0.197413	+	3.88532i	−0.00841771	+	0.165671i
$551$	−35.0186			−1.49184
$552$	−6.32565	+	41.2129i	−0.269238	+	1.75414i
$553$	6.84608			0.291125
$554$	−0.926079	+	18.2264i	−0.0393453	+	0.774364i
$555$		−	15.1440i		−	0.642828i
$556$	−1.39295	+	13.6721i	−0.0590744	+	0.579828i
$557$		−	17.9717i		−	0.761487i	−0.924681	−	0.380744i	$-0.875668\pi$
$557$		−	17.9717i		−	0.761487i	0.924681	−	0.380744i	$-0.124332\pi$
$558$	4.56838	+	0.232119i	0.193395	+	0.00982637i
$559$	−7.48166			−0.316441
$560$	−1.64660	+	7.99697i	−0.0695814	+	0.337933i
$561$	−25.9589			−1.09598
$562$	25.3284	+	1.28693i	1.06841	+	0.0542860i
$563$		−	3.54863i		−	0.149557i	−0.997200	−	0.0747784i	$-0.976175\pi$
$563$		−	3.54863i		−	0.149557i	0.997200	−	0.0747784i	$-0.0238249\pi$
$564$	−0.0799470	+	0.784696i	−0.00336637	+	0.0330417i
$565$		−	10.9451i		−	0.460463i
$566$	−0.922776	+	18.1614i	−0.0387872	+	0.763379i
$567$	7.50861			0.315332
$568$	−31.2690	−	4.79939i	−1.31202	−	0.201378i
$569$	−26.3743			−1.10567			−0.552835	−	0.833291i	$-0.686454\pi$
$569$	−26.3743			−1.10567			−0.552835	+	0.833291i	$0.686454\pi$
$570$	−1.16091	+	22.8482i	−0.0486252	+	0.957004i
$571$		−	28.8831i		−	1.20872i	−0.796711	−	0.604361i	$-0.793429\pi$
$571$		−	28.8831i		−	1.20872i	0.796711	−	0.604361i	$-0.206571\pi$
$572$	6.56619	+	0.668981i	0.274546	+	0.0279715i
$573$			27.8263i			1.16246i
$574$	6.12303	+	0.311110i	0.255570	+	0.0129855i
$575$	−7.67159			−0.319927
$576$	3.31422	+	1.04193i	0.138093	+	0.0434136i
$577$	−2.90293			−0.120851			−0.0604253	−	0.998173i	$-0.519246\pi$
$577$	−2.90293			−0.120851			−0.0604253	+	0.998173i	$0.519246\pi$
$578$	−10.0509	−	0.510683i	−0.418061	−	0.0212416i
$579$			17.5496i			0.729336i
$580$	−28.7448	−	2.92859i	−1.19356	−	0.121603i
$581$			8.53099i			0.353925i
$582$	−0.415019	+	8.16809i	−0.0172031	+	0.338578i
$583$	−32.5035			−1.34616
$584$	−16.5805	−	2.54489i	−0.686105	−	0.105308i
$585$	0.886420			0.0366489
$586$	1.92050	−	37.7977i	0.0793349	−	1.56141i
$587$			37.8683i			1.56299i	0.623909	+	0.781497i	$0.285544\pi$
$587$			37.8683i			1.56299i	−0.623909	+	0.781497i	$0.714456\pi$
$588$	−0.324709	+	3.18708i	−0.0133908	+	0.131433i
$589$			36.8517i			1.51845i
$590$	−11.6534	−	0.592106i	−0.479761	−	0.0243766i
$591$	−6.98775			−0.287438
$592$	3.73646	−	18.1467i	0.153567	−	0.745825i
$593$	−6.49295			−0.266634			−0.133317	−	0.991073i	$-0.542563\pi$
$593$	−6.49295			−0.266634			−0.133317	+	0.991073i	$0.542563\pi$
$594$	−25.6401	−	1.30277i	−1.05203	−	0.0534534i
$595$		−	10.0239i		−	0.410939i
$596$	3.19497	−	31.3593i	0.130871	−	1.28453i
$597$			16.1897i			0.662600i
$598$	−0.660453	+	12.9985i	−0.0270079	+	0.531549i
$599$	25.2803			1.03293			0.516463	−	0.856310i	$-0.327248\pi$
$599$	25.2803			1.03293			0.516463	+	0.856310i	$0.327248\pi$
$600$	0.572945	−	3.73285i	0.0233904	−	0.152393i
$601$	−16.8805			−0.688571			−0.344285	−	0.938865i	$-0.611879\pi$
$601$	−16.8805			−0.688571			−0.344285	+	0.938865i	$0.611879\pi$
$602$	−0.536910	+	10.5670i	−0.0218828	+	0.430680i
$603$		−	4.46242i		−	0.181724i
$604$	−7.74466	−	0.789047i	−0.315126	−	0.0321059i
$605$		−	0.223344i		−	0.00908023i
$606$	14.7291	+	0.748381i	0.598327	+	0.0304009i
$607$	−7.10773			−0.288494			−0.144247	−	0.989542i	$-0.546076\pi$
$607$	−7.10773			−0.288494			−0.144247	+	0.989542i	$0.546076\pi$
$608$	−7.02837	+	27.0919i	−0.285038	+	1.09872i
$609$	−11.3369			−0.459395
$610$	30.7211	+	1.56093i	1.24386	+	0.0632004i
$611$			0.246211i			0.00996065i
$612$	−4.24326	−	0.432315i	−0.171524	−	0.0174753i
$613$			44.5259i			1.79838i	0.437554	+	0.899192i	$0.355845\pi$
$613$			44.5259i			1.79838i	−0.437554	+	0.899192i	$0.644155\pi$
$614$	0.737616	−	14.5172i	0.0297678	−	0.585866i
$615$	14.1742			0.571558
$616$	1.41607	−	9.22602i	0.0570553	−	0.371727i
$617$	−38.8785			−1.56519			−0.782596	−	0.622530i	$-0.786105\pi$
$617$	−38.8785			−1.56519			−0.782596	+	0.622530i	$0.786105\pi$
$618$	2.10413	−	41.4118i	0.0846404	−	1.66583i
$619$		−	12.3262i		−	0.495431i	−0.968833	−	0.247716i	$-0.920320\pi$
$619$		−	12.3262i		−	0.495431i	0.968833	−	0.247716i	$-0.0796798\pi$
$620$	−3.08190	+	30.2495i	−0.123772	+	1.21485i
$621$		−	50.6266i		−	2.03157i
$622$	6.37202	+	0.323761i	0.255495	+	0.0129816i
$623$	14.4730			0.579847
$624$	−6.27551	−	1.29215i	−0.251222	−	0.0517272i
$625$	−20.1373			−0.805490
$626$	4.10947	+	0.208801i	0.164247	+	0.00834538i
$627$		−	26.1541i		−	1.04449i
$628$	−2.14517	+	21.0552i	−0.0856014	+	0.840196i
$629$			22.7462i			0.906950i
$630$	0.0636125	−	1.25197i	0.00253438	−	0.0498797i
$631$	20.7693			0.826815			0.413407	−	0.910546i	$-0.364339\pi$
$631$	20.7693			0.826815			0.413407	+	0.910546i	$0.364339\pi$
$632$	19.1395	+	2.93767i	0.761329	+	0.116854i
$633$	39.5967			1.57383
$634$	−0.630454	+	12.4081i	−0.0250385	+	0.492789i
$635$			37.6398i			1.49369i
$636$	31.3905	+	3.19815i	1.24471	+	0.126815i
$637$			1.00000i			0.0396214i
$638$	32.9891	+	1.67617i	1.30605	+	0.0663602i
$639$	4.85717			0.192147
$640$	−8.03489	+	21.6505i	−0.317607	+	0.855810i
$641$	−19.0642			−0.752989			−0.376495	−	0.926419i	$-0.622871\pi$
$641$	−19.0642			−0.752989			−0.376495	+	0.926419i	$0.622871\pi$
$642$	−36.2692	−	1.84283i	−1.43143	−	0.0727307i
$643$		−	34.7530i		−	1.37052i	−0.728297	−	0.685262i	$-0.759688\pi$
$643$		−	34.7530i		−	1.37052i	0.728297	−	0.685262i	$-0.240312\pi$
$644$	18.3116	+	1.86564i	0.721578	+	0.0735164i
$645$			24.4616i			0.963176i
$646$	1.74368	−	34.3177i	0.0686041	−	1.35021i
$647$	−15.8459			−0.622967			−0.311483	−	0.950252i	$-0.600826\pi$
$647$	−15.8459			−0.622967			−0.311483	+	0.950252i	$0.600826\pi$
$648$	20.9917	+	3.22196i	0.824633	+	0.126571i
$649$	13.3395			0.523622
$650$	0.0598204	−	1.17734i	0.00234635	−	0.0461791i
$651$			11.9304i			0.467589i
$652$	−3.73501	+	36.6599i	−0.146274	+	1.43571i
$653$		−	7.69423i		−	0.301098i	−0.988603	−	0.150549i	$-0.951896\pi$
$653$		−	7.69423i		−	0.301098i	0.988603	−	0.150549i	$-0.0481042\pi$
$654$	24.3665	+	1.23806i	0.952807	+	0.0484120i
$655$	20.3286			0.794305
$656$	16.9846	+	3.49717i	0.663136	+	0.136542i
$657$	2.57553			0.100481
$658$	0.347747	+	0.0176690i	0.0135566	+	0.000688808i
$659$			40.5243i			1.57860i	0.614006	+	0.789301i	$0.289557\pi$
$659$			40.5243i			1.57860i	−0.614006	+	0.789301i	$0.710443\pi$
$660$	2.18726	−	21.4684i	0.0851391	−	0.835658i
$661$		−	22.9742i		−	0.893594i	−0.894635	−	0.446797i	$-0.852565\pi$
$661$		−	22.9742i		−	0.893594i	0.894635	−	0.446797i	$-0.147435\pi$
$662$	−0.827259	+	16.2815i	−0.0321523	+	0.632797i
$663$	7.86611			0.305494
$664$	−3.66067	+	23.8500i	−0.142061	+	0.925559i
$665$	10.0993			0.391633
$666$	−0.144349	+	2.84097i	−0.00559343	+	0.110085i
$667$			65.1371i			2.52212i
$668$	−26.1863	−	2.66793i	−1.01318	−	0.103225i
$669$		−	15.7979i		−	0.610782i
$670$	29.6244	+	1.50521i	1.14449	+	0.0581513i
$671$	−35.1662			−1.35758
$672$	−2.27537	+	8.77075i	−0.0877742	+	0.338339i
$673$	23.7759			0.916494			0.458247	−	0.888825i	$-0.348477\pi$
$673$	23.7759			0.916494			0.458247	+	0.888825i	$0.348477\pi$
$674$	−25.1143	−	1.27605i	−0.967367	−	0.0491518i
$675$			4.58550i			0.176496i
$676$	−1.98970	−	0.202716i	−0.0765269	−	0.00779677i
$677$		−	28.8401i		−	1.10842i	−0.832378	−	0.554208i	$-0.813021\pi$
$677$		−	28.8401i		−	1.10842i	0.832378	−	0.554208i	$-0.186979\pi$
$678$	0.616376	−	12.1310i	0.0236718	−	0.465889i
$679$	3.61044			0.138556
$680$	4.30127	−	28.0237i	0.164946	−	1.07466i
$681$	−5.24442			−0.200967
$682$	1.76392	−	34.7160i	0.0675438	−	1.32934i
$683$		−	14.1254i		−	0.540492i	−0.962791	−	0.270246i	$-0.912895\pi$
$683$		−	14.1254i		−	0.540492i	0.962791	−	0.270246i	$-0.0871050\pi$
$684$	0.435567	−	4.27518i	0.0166543	−	0.163466i
$685$		−	24.0409i		−	0.918555i
$686$	1.41239	+	0.0717634i	0.0539254	+	0.00273994i
$687$	0.948379			0.0361829
$688$	−6.03537	+	29.3117i	−0.230096	+	1.11750i
$689$	9.84928			0.375228
$690$	42.4992	+	2.15938i	1.61792	+	0.0822062i
$691$		−	21.5228i		−	0.818766i	−0.912363	−	0.409383i	$-0.865744\pi$
$691$		−	21.5228i		−	0.818766i	0.912363	−	0.409383i	$-0.134256\pi$
$692$	1.50570	−	14.7788i	0.0572382	−	0.561804i
$693$			1.43312i			0.0544398i
$694$	−1.02591	+	20.1912i	−0.0389430	+	0.766446i
$695$	14.0259			0.532032
$696$	−31.6945	−	4.86470i	−1.20138	−	0.184396i
$697$	−21.2895			−0.806397
$698$	−1.93902	+	38.1622i	−0.0733929	+	1.44446i
$699$			24.5385i			0.928131i
$700$	−1.65857	−	0.168980i	−0.0626881	−	0.00638684i
$701$			28.0267i			1.05855i	0.848449	+	0.529277i	$0.177537\pi$
$701$			28.0267i			1.05855i	−0.848449	+	0.529277i	$0.822463\pi$
$702$	7.76953	+	0.394769i	0.293242	+	0.0148996i
$703$	−22.9173			−0.864342
$704$	7.91781	−	25.1854i	0.298414	−	0.949211i
$705$	0.804999			0.0303180
$706$	−31.0606	−	1.57818i	−1.16898	−	0.0593957i
$707$		−	6.51050i		−	0.244853i
$708$	−12.8827	−	1.31253i	−0.484163	−	0.0493278i
$709$			28.2833i			1.06220i	0.847308	+	0.531101i	$0.178222\pi$
$709$			28.2833i			1.06220i	−0.847308	+	0.531101i	$0.821778\pi$
$710$	−1.63836	+	32.2450i	−0.0614866	+	1.21013i
$711$	−2.97303			−0.111498
$712$	40.4619	+	6.21038i	1.51637	+	0.232744i
$713$	68.5469			2.56710
$714$	0.564499	−	11.1100i	0.0211258	−	0.415782i
$715$		−	6.73608i		−	0.251915i
$716$	−3.76197	+	36.9246i	−0.140592	+	1.37994i
$717$		−	13.4718i		−	0.503114i
$718$	−5.45740	−	0.277290i	−0.203669	−	0.0103484i
$719$	13.6899			0.510545			0.255273	−	0.966869i	$-0.417835\pi$
$719$	13.6899			0.510545			0.255273	+	0.966869i	$0.417835\pi$
$720$	0.715064	−	3.47283i	0.0266489	−	0.129425i
$721$	−18.3047			−0.681704
$722$	7.74041	+	0.393289i	0.288068	+	0.0146367i
$723$		−	34.7712i		−	1.29315i
$724$	−3.83411	+	37.6326i	−0.142494	+	1.39860i
$725$		−	5.89978i		−	0.219112i
$726$	0.0125777	−	0.247545i	0.000466803	−	0.00918725i
$727$	13.1391			0.487303			0.243651	−	0.969863i	$-0.421655\pi$
$727$	13.1391			0.487303			0.243651	+	0.969863i	$0.421655\pi$
$728$	−0.429102	+	2.79569i	−0.0159036	+	0.103615i
$729$	−29.6950			−1.09981
$730$	−0.868746	+	17.0980i	−0.0321537	+	0.632825i
$731$		−	36.7411i		−	1.35892i
$732$	33.9620	+	3.46014i	1.25527	+	0.127891i
$733$			4.10881i			0.151762i	0.997117	+	0.0758812i	$0.0241770\pi$
$733$			4.10881i			0.151762i	−0.997117	+	0.0758812i	$0.975823\pi$
$734$	−41.1518	−	2.09092i	−1.51894	−	0.0771772i
$735$	3.26954			0.120599
$736$	50.3930	+	13.0733i	1.85751	+	0.481888i
$737$	−33.9108			−1.24912
$738$	−2.65903	−	0.135105i	−0.0978804	−	0.00497329i
$739$			5.60947i			0.206348i	0.994663	+	0.103174i	$0.0328998\pi$
$739$			5.60947i			0.206348i	−0.994663	+	0.103174i	$0.967100\pi$
$740$	−18.8115	−	1.91657i	−0.691524	−	0.0704544i
$741$			7.92528i			0.291142i
$742$	0.706818	−	13.9110i	0.0259481	−	0.510690i
$743$	−15.2173			−0.558268			−0.279134	−	0.960252i	$-0.590047\pi$
$743$	−15.2173			−0.558268			−0.279134	+	0.960252i	$0.590047\pi$
$744$	−5.11936	+	33.3537i	−0.187685	+	1.22280i
$745$	−32.1707			−1.17864
$746$	−1.15469	+	22.7258i	−0.0422763	+	0.832050i
$747$		−	3.70474i		−	0.135549i
$748$	−3.28525	+	32.2454i	−0.120121	+	1.17901i
$749$			16.0316i			0.585782i
$750$	−26.9387	−	1.36875i	−0.983664	−	0.0499798i
$751$	−30.0338			−1.09595			−0.547974	−	0.836495i	$-0.684601\pi$
$751$	−30.0338			−1.09595			−0.547974	+	0.836495i	$0.684601\pi$
$752$	0.964610	+	0.198616i	0.0351757	+	0.00724278i
$753$	−23.4331			−0.853949
$754$	−9.99642	−	0.507917i	−0.364048	−	0.0184972i
$755$			7.94504i			0.289150i
$756$	1.11514	−	10.9453i	0.0405571	−	0.398076i
$757$		−	24.4007i		−	0.886858i	−0.896310	−	0.443429i	$-0.853762\pi$
$757$		−	24.4007i		−	0.886858i	0.896310	−	0.443429i	$-0.146238\pi$
$758$	−1.72213	+	33.8937i	−0.0625507	+	1.23107i
$759$	−48.6486			−1.76583
$760$	28.2344	+	4.33362i	1.02417	+	0.157197i
$761$	−50.2706			−1.82231			−0.911153	−	0.412068i	$-0.864807\pi$
$761$	−50.2706			−1.82231			−0.911153	+	0.412068i	$0.864807\pi$
$762$	−2.11970	+	41.7183i	−0.0767887	+	1.51130i
$763$		−	10.7704i		−	0.389916i
$764$	34.5650	+	3.52158i	1.25052	+	0.127406i
$765$			4.35305i			0.157385i
$766$	−25.9048	−	1.31622i	−0.935979	−	0.0475569i
$767$	−4.04217			−0.145954
$768$	−10.1248	+	23.5439i	−0.365346	+	0.849568i
$769$	−20.7181			−0.747115			−0.373557	−	0.927607i	$-0.621862\pi$
$769$	−20.7181			−0.747115			−0.373557	+	0.927607i	$0.621862\pi$
$770$	−9.51398	−	0.483404i	−0.342860	−	0.0174207i
$771$		−	26.6411i		−	0.959454i
$772$	21.7996	+	2.22101i	0.784586	+	0.0799357i
$773$			46.0405i			1.65596i	0.560756	+	0.827981i	$0.310511\pi$
$773$			46.0405i			1.65596i	−0.560756	+	0.827981i	$0.689489\pi$
$774$	0.233163	−	4.58893i	0.00838086	−	0.164946i
$775$	−6.20863			−0.223021
$776$	10.0937	+	1.54925i	0.362341	+	0.0556147i
$777$	−7.41925			−0.266164
$778$	−0.0450691	+	0.887015i	−0.00161580	+	0.0318010i
$779$		−	21.4496i		−	0.768513i
$780$	−0.662789	+	6.50541i	−0.0237317	+	0.232931i
$781$		−	36.9106i		−	1.32076i
$782$	−63.8335	−	3.24337i	−2.28268	−	0.115983i
$783$	38.9340			1.39139
$784$	3.91781	+	0.806688i	0.139922	+	0.0288103i
$785$	21.6000			0.770938
$786$	22.5313	+	1.14481i	0.803666	+	0.0408342i
$787$		−	42.3137i		−	1.50832i	−0.656691	−	0.754160i	$-0.728044\pi$
$787$		−	42.3137i		−	1.50832i	0.656691	−	0.754160i	$-0.271956\pi$
$788$	−0.884341	+	8.67999i	−0.0315033	+	0.309212i
$789$		−	25.0610i		−	0.892195i
$790$	1.00283	−	19.7369i	0.0356791	−	0.702207i
$791$	−5.36213			−0.190655
$792$	−0.614956	+	4.00656i	−0.0218515	+	0.142367i
$793$	10.6561			0.378411
$794$	−0.401906	+	7.91000i	−0.0142631	+	0.280715i
$795$		−	32.2027i		−	1.14211i
$796$	20.1104	+	2.04890i	0.712794	+	0.0726214i
$797$			17.9127i			0.634502i	0.948342	+	0.317251i	$0.102760\pi$
$797$			17.9127i			0.634502i	−0.948342	+	0.317251i	$0.897240\pi$
$798$	11.1936	+	0.568745i	0.396249	+	0.0201334i
$799$	−1.20910			−0.0427749
$800$	−4.56434	−	1.18411i	−0.161374	−	0.0418647i
$801$	−6.28515			−0.222075
$802$	−22.8003	−	1.15848i	−0.805108	−	0.0409074i
$803$		−	19.5719i		−	0.690679i
$804$	32.7496	+	3.33661i	1.15499	+	0.117673i
$805$		−	18.7854i		−	0.662098i
$806$	−0.534506	+	10.5197i	−0.0188272	+	0.370541i
$807$	−19.1073			−0.672607
$808$	2.79367	−	18.2013i	0.0982809	−	0.640320i
$809$	−4.46270			−0.156900			−0.0784500	−	0.996918i	$-0.524997\pi$
$809$	−4.46270			−0.156900			−0.0784500	+	0.996918i	$0.524997\pi$
$810$	1.09988	−	21.6469i	0.0386457	−	0.760595i
$811$		−	30.1488i		−	1.05867i	−0.848413	−	0.529334i	$-0.822442\pi$
$811$		−	30.1488i		−	1.05867i	0.848413	−	0.529334i	$-0.177558\pi$
$812$	−1.43475	+	14.0824i	−0.0503500	+	0.494196i
$813$		−	9.59767i		−	0.336605i
$814$	21.5891	+	1.09694i	0.756698	+	0.0384477i
$815$	37.6085			1.31737
$816$	6.34550	−	30.8179i	0.222137	−	1.07884i
$817$	37.0175			1.29508
$818$	−50.3518	−	2.55837i	−1.76051	−	0.0894512i
$819$		−	0.434268i		−	0.0151746i
$820$	1.79383	−	17.6068i	0.0626432	−	0.614856i
$821$			16.5840i			0.578786i	0.957210	+	0.289393i	$0.0934535\pi$
$821$			16.5840i			0.578786i	−0.957210	+	0.289393i	$0.906547\pi$
$822$	1.35387	−	26.6459i	0.0472217	−	0.929381i
$823$	33.0671			1.15265			0.576324	−	0.817221i	$-0.304487\pi$
$823$	33.0671			1.15265			0.576324	+	0.817221i	$0.304487\pi$
$824$	−51.1743	−	7.85460i	−1.78274	−	0.273628i
$825$	4.40634			0.153409
$826$	−0.290080	+	5.70913i	−0.0100932	+	0.198646i
$827$		−	24.9129i		−	0.866308i	−0.901320	−	0.433154i	$-0.857401\pi$
$827$		−	24.9129i		−	0.866308i	0.901320	−	0.433154i	$-0.142599\pi$
$828$	−7.95214	−	0.810186i	−0.276356	−	0.0281559i
$829$			42.3263i			1.47005i	0.678038	+	0.735027i	$0.262831\pi$
$829$			42.3263i			1.47005i	−0.678038	+	0.735027i	$0.737169\pi$
$830$	24.5944	+	1.24964i	0.853684	+	0.0433756i
$831$	20.6705			0.717051
$832$	−2.39927	+	7.63174i	−0.0831798	+	0.264583i
$833$	−4.91083			−0.170150
$834$	15.5457	+	0.789873i	0.538303	+	0.0273511i
$835$			26.8639i			0.929662i
$836$	−32.4879	−	3.30996i	−1.12362	−	0.114477i
$837$		−	40.9722i		−	1.41621i
$838$	2.22876	−	43.8647i	0.0769912	−	1.51528i
$839$	−22.8739			−0.789695			−0.394847	−	0.918747i	$-0.629203\pi$
$839$	−22.8739			−0.789695			−0.394847	+	0.918747i	$0.629203\pi$
$840$	9.14063	+	1.40297i	0.315382	+	0.0484070i
$841$	−21.0932			−0.727352
$842$	0.0861190	−	1.69493i	0.00296786	−	0.0584110i
$843$		−	28.7249i		−	0.989338i
$844$	5.01119	−	49.1859i	0.172492	−	1.69305i
$845$			2.04118i			0.0702188i
$846$	−0.151015	−	0.00767307i	−0.00519201	−	0.000263806i
$847$	−0.109419			−0.00375968
$848$	7.94530	−	38.5876i	0.272843	−	1.32510i
$849$	20.5968			0.706879
$850$	5.78171	+	0.293768i	0.198311	+	0.0100762i
$851$			42.6278i			1.46126i
$852$	−3.63178	+	35.6466i	−0.124423	+	1.22123i
$853$			8.85133i			0.303064i	0.988452	+	0.151532i	$0.0484206\pi$
$853$			8.85133i			0.303064i	−0.988452	+	0.151532i	$0.951579\pi$
$854$	0.764721	−	15.0507i	0.0261682	−	0.515023i
$855$	−4.38579			−0.149991
$856$	−6.87919	+	44.8193i	−0.235126	+	1.53189i
$857$	−8.20832			−0.280391			−0.140195	−	0.990124i	$-0.544773\pi$
$857$	−8.20832			−0.280391			−0.140195	+	0.990124i	$0.544773\pi$
$858$	0.379345	−	7.46597i	0.0129506	−	0.254884i
$859$		−	21.9662i		−	0.749476i	−0.927131	−	0.374738i	$-0.877733\pi$
$859$		−	21.9662i		−	0.749476i	0.927131	−	0.374738i	$-0.122267\pi$
$860$	30.3856	+	3.09576i	1.03614	+	0.105565i
$861$		−	6.94411i		−	0.236655i
$862$	−31.9597	−	1.62387i	−1.08855	−	0.0553092i
$863$	−33.8494			−1.15225			−0.576123	−	0.817363i	$-0.695435\pi$
$863$	−33.8494			−1.15225			−0.576123	+	0.817363i	$0.695435\pi$
$864$	7.81422	−	30.1211i	0.265845	−	1.02474i
$865$	−15.1611			−0.515495
$866$	11.0352	+	0.560696i	0.374991	+	0.0190532i
$867$			11.3987i			0.387119i
$868$	14.8196	+	1.50986i	0.503010	+	0.0512481i
$869$			22.5927i			0.766404i
$870$	−1.66066	+	32.6837i	−0.0563015	+	1.10808i
$871$	10.2757			0.348179
$872$	4.62162	−	30.1108i	0.156508	−	1.01968i
$873$	−1.56790			−0.0530653
$874$	3.26776	−	64.3136i	0.110534	−	2.17544i
$875$			11.9074i			0.402543i
$876$	−1.92576	+	18.9017i	−0.0650654	+	0.638630i
$877$		−	26.3189i		−	0.888728i	−0.895846	−	0.444364i	$-0.853430\pi$
$877$		−	26.3189i		−	0.888728i	0.895846	−	0.444364i	$-0.146570\pi$
$878$	9.11528	+	0.463146i	0.307626	+	0.0156304i
$879$	−42.8663			−1.44584
$880$	−26.3907	−	5.43392i	−0.889630	−	0.183177i
$881$	36.5036			1.22984			0.614919	−	0.788590i	$-0.289188\pi$
$881$	36.5036			1.22984			0.614919	+	0.788590i	$0.289188\pi$
$882$	−0.613356	−	0.0311646i	−0.0206528	−	0.00104937i
$883$		−	35.3164i		−	1.18849i	−0.804283	−	0.594246i	$-0.797451\pi$
$883$		−	35.3164i		−	1.18849i	0.804283	−	0.594246i	$-0.202549\pi$
$884$	0.995503	−	9.77107i	0.0334824	−	0.328637i
$885$			13.2161i			0.444253i
$886$	−0.442026	+	8.69961i	−0.0148502	+	0.292269i
$887$	23.3302			0.783351			0.391676	−	0.920103i	$-0.371896\pi$
$887$	23.3302			0.783351			0.391676	+	0.920103i	$0.371896\pi$
$888$	−20.7419	−	3.18361i	−0.696053	−	0.106835i
$889$	18.4402			0.618465
$890$	2.12003	−	41.7248i	0.0710636	−	1.39862i
$891$			24.7791i			0.830130i
$892$	−19.6237	−	1.99932i	−0.657051	−	0.0669421i
$893$		−	1.21820i		−	0.0407654i
$894$	−35.6565	−	1.81170i	−1.19253	−	0.0605924i
$895$	37.8799			1.26619
$896$	10.6068	+	3.93639i	0.354349	+	0.131506i
$897$	14.7416			0.492207
$898$	5.33186	+	0.270911i	0.177927	+	0.00904043i
$899$			52.7155i			1.75816i
$900$	0.720264	+	0.0733825i	0.0240088	+	0.00244608i
$901$			48.3681i			1.61137i
$902$	−1.02669	+	20.2065i	−0.0341851	+	0.672804i
$903$	11.9841			0.398804
$904$	−14.9908	−	2.30090i	−0.498588	−	0.0765268i
$905$	38.6063			1.28332
$906$	−0.447428	+	8.80593i	−0.0148648	+	0.292557i
$907$		−	30.1817i		−	1.00217i	−0.865399	−	0.501083i	$-0.832935\pi$
$907$		−	30.1817i		−	1.00217i	0.865399	−	0.501083i	$-0.167065\pi$
$908$	−0.663713	+	6.51448i	−0.0220261	+	0.216191i
$909$			2.82730i			0.0937757i
$910$	2.88295	+	0.146482i	0.0955688	+	0.00485584i
$911$	7.93273			0.262823			0.131412	−	0.991328i	$-0.458049\pi$
$911$	7.93273			0.262823			0.131412	+	0.991328i	$0.458049\pi$
$912$	31.0498	+	6.39323i	1.02816	+	0.211701i
$913$	−28.1530			−0.931729
$914$	−23.8512	−	1.21188i	−0.788927	−	0.0400853i
$915$		−	34.8407i		−	1.15180i
$916$	0.120023	−	1.17805i	0.00396567	−	0.0389239i
$917$		−	9.95924i		−	0.328883i
$918$	−1.93864	+	38.1548i	−0.0639847	+	1.25930i
$919$	29.3071			0.966750			0.483375	−	0.875413i	$-0.339411\pi$
$919$	29.3071			0.966750			0.483375	+	0.875413i	$0.339411\pi$
$920$	8.06085	−	52.5181i	0.265758	−	1.73147i
$921$	−16.4639			−0.542504
$922$	−1.59249	+	31.3422i	−0.0524459	+	1.03220i
$923$			11.1847i			0.368150i
$924$	−10.5177	−	1.07157i	−0.346005	−	0.0352520i
$925$		−	3.86101i		−	0.126949i
$926$	1.22911	+	0.0624508i	0.0403910	+	0.00205226i
$927$	7.94916			0.261085
$928$	−10.0539	+	38.7544i	−0.330036	+	1.27217i
$929$	2.37267			0.0778447			0.0389224	−	0.999242i	$-0.487607\pi$
$929$	2.37267			0.0778447			0.0389224	+	0.999242i	$0.487607\pi$
$930$	34.3947	+	1.74759i	1.12785	+	0.0573057i
$931$		−	4.94776i		−	0.162156i
$932$	30.4810	+	3.10549i	0.998439	+	0.101724i
$933$		−	7.22649i		−	0.236585i
$934$	−0.595316	+	11.7165i	−0.0194793	+	0.383377i
$935$	33.0797			1.08182
$936$	0.186345	−	1.21408i	0.00609089	−	0.0396834i
$937$	32.6751			1.06745			0.533725	−	0.845658i	$-0.320792\pi$
$937$	32.6751			1.06745			0.533725	+	0.845658i	$0.320792\pi$
$938$	0.737421	−	14.5133i	0.0240776	−	0.473877i
$939$		−	4.66054i		−	0.152091i
$940$	0.101877	−	0.999948i	0.00332288	−	0.0326147i
$941$		−	38.3641i		−	1.25063i	−0.780371	−	0.625316i	$-0.784970\pi$
$941$		−	38.3641i		−	1.25063i	0.780371	−	0.625316i	$-0.215030\pi$
$942$	23.9405	+	1.21641i	0.780024	+	0.0396329i
$943$	−39.8979			−1.29925
$944$	−3.26077	+	15.8365i	−0.106129	+	0.515433i
$945$	−11.2285			−0.365263
$946$	−34.8721	−	1.77185i	−1.13379	−	0.0576078i
$947$			9.22751i			0.299854i	0.988697	+	0.149927i	$0.0479039\pi$
$947$			9.22751i			0.299854i	−0.988697	+	0.149927i	$0.952096\pi$
$948$	2.22298	−	21.8190i	0.0721991	−	0.708649i
$949$			5.93073i			0.192520i
$950$	−0.295977	+	5.82520i	−0.00960277	+	0.188994i
$951$	14.0720			0.456316
$952$	−13.7291	−	2.10725i	−0.444964	−	0.0682962i
$953$	20.3151			0.658072			0.329036	−	0.944317i	$-0.393276\pi$
$953$	20.3151			0.658072			0.329036	+	0.944317i	$0.393276\pi$
$954$	−0.306948	+	6.04112i	−0.00993782	+	0.195588i
$955$		−	35.4593i		−	1.14744i
$956$	−16.7343	−	1.70494i	−0.541227	−	0.0551417i
$957$		−	37.4128i		−	1.20939i
$958$	−20.3576	−	1.03436i	−0.657723	−	0.0334188i
$959$	−11.7779			−0.380329
$960$	24.9523	+	7.84452i	0.805333	+	0.253181i
$961$	24.4751			0.789521
$962$	−6.54198	−	0.332397i	−0.210922	−	0.0107169i
$963$		−	6.96201i		−	0.224348i
$964$	−43.1918	−	4.40050i	−1.39111	−	0.141730i
$965$		−	22.3637i		−	0.719912i
$966$	1.05791	−	20.8209i	0.0340376	−	0.669902i
$967$	13.9577			0.448851			0.224425	−	0.974491i	$-0.427950\pi$
$967$	13.9577			0.448851			0.224425	+	0.974491i	$0.427950\pi$
$968$	−0.305901	−	0.0469519i	−0.00983205	−	0.00150909i
$969$	−38.9197			−1.25028
$970$	0.528864	−	10.4087i	0.0169808	−	0.334203i
$971$			11.4952i			0.368898i	0.982842	+	0.184449i	$0.0590501\pi$
$971$			11.4952i			0.368898i	−0.982842	+	0.184449i	$0.940950\pi$
$972$	−0.907300	+	8.90533i	−0.0291017	+	0.285639i
$973$		−	6.87146i		−	0.220289i
$974$	19.4962	+	0.990597i	0.624697	+	0.0317408i
$975$	−1.33522			−0.0427612
$976$	8.59619	−	41.7488i	0.275157	−	1.33635i
$977$	−7.39204			−0.236492			−0.118246	−	0.992984i	$-0.537727\pi$
$977$	−7.39204			−0.236492			−0.118246	+	0.992984i	$0.537727\pi$
$978$	41.6836	+	2.11794i	1.33289	+	0.0677241i
$979$			47.7621i			1.52648i
$980$	0.413780	−	4.06134i	0.0132177	−	0.129735i
$981$			4.67725i			0.149333i
$982$	−1.84768	+	36.3647i	−0.0589619	+	1.16044i
$983$	−34.2578			−1.09265			−0.546327	−	0.837572i	$-0.683974\pi$
$983$	−34.2578			−1.09265			−0.546327	+	0.837572i	$0.683974\pi$
$984$	2.97973	−	19.4136i	0.0949904	−	0.618882i
$985$	8.90457			0.283723
$986$	2.49429	−	49.0907i	0.0794344	−	1.56337i
$987$		−	0.394379i		−	0.0125532i
$988$	9.84456	+	1.00299i	0.313197	+	0.0319094i
$989$		−	68.8552i		−	2.18947i
$990$	4.13162	+	0.209927i	0.131311	+	0.00667191i
$991$	50.9734			1.61922			0.809612	−	0.586966i	$-0.199678\pi$
$991$	50.9734			1.61922			0.809612	+	0.586966i	$0.199678\pi$
$992$	40.7831	+	10.5802i	1.29487	+	0.335923i
$993$	18.4648			0.585962
$994$	15.7972	+	0.802654i	0.501057	+	0.0254586i
$995$		−	20.6307i		−	0.654038i
$996$	27.1890	+	2.77009i	0.861515	+	0.0877735i
$997$		−	7.97874i		−	0.252689i	−0.991986	−	0.126345i	$-0.959675\pi$
$997$		−	7.97874i		−	0.252689i	0.991986	−	0.126345i	$-0.0403245\pi$
$998$	−0.916277	+	18.0334i	−0.0290042	+	0.570839i
$999$	25.4797			0.806141

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.c.a.365.1	✓	34
4.3	odd	2		2912.2.c.a.1457.9		34
8.3	odd	2		2912.2.c.a.1457.26		34
8.5	even	2	inner	728.2.c.a.365.2	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.c.a.365.1	✓	34	1.1	even	1	trivial
728.2.c.a.365.2	yes	34	8.5	even	2	inner
2912.2.c.a.1457.9		34	4.3	odd	2
2912.2.c.a.1457.26		34	8.3	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.41239 - 0.0717634i) q^{2} +1.60179i q^{3} +(1.98970 + 0.202716i) q^{4} -2.04118i q^{5} +(0.114950 - 2.26236i) q^{6} -1.00000 q^{7} +(-2.79569 - 0.429102i) q^{8} +0.434268 q^{9} +(-0.146482 + 2.88295i) q^{10} -3.30009i q^{11} +(-0.324709 + 3.18708i) q^{12} +1.00000i q^{13} +(1.41239 + 0.0717634i) q^{14} +3.26954 q^{15} +(3.91781 + 0.806688i) q^{16} -4.91083 q^{17} +(-0.613356 - 0.0311646i) q^{18} -4.94776i q^{19} +(0.413780 - 4.06134i) q^{20} -1.60179i q^{21} +(-0.236826 + 4.66102i) q^{22} -9.20320 q^{23} +(0.687332 - 4.47811i) q^{24} +0.833579 q^{25} +(0.0717634 - 1.41239i) q^{26} +5.50098i q^{27} +(-1.98970 - 0.202716i) q^{28} -7.07766i q^{29} +(-4.61788 - 0.234634i) q^{30} -7.44816 q^{31} +(-5.47559 - 1.42052i) q^{32} +5.28605 q^{33} +(6.93601 + 0.352418i) q^{34} +2.04118i q^{35} +(0.864063 + 0.0880331i) q^{36} -4.63185i q^{37} +(-0.355068 + 6.98818i) q^{38} -1.60179 q^{39} +(-0.875875 + 5.70651i) q^{40} +4.33522 q^{41} +(-0.114950 + 2.26236i) q^{42} +7.48166i q^{43} +(0.668981 - 6.56619i) q^{44} -0.886420i q^{45} +(12.9985 + 0.660453i) q^{46} +0.246211 q^{47} +(-1.29215 + 6.27551i) q^{48} +1.00000 q^{49} +(-1.17734 - 0.0598204i) q^{50} -7.86611i q^{51} +(-0.202716 + 1.98970i) q^{52} -9.84928i q^{53} +(0.394769 - 7.76953i) q^{54} -6.73608 q^{55} +(2.79569 + 0.429102i) q^{56} +7.92528 q^{57} +(-0.507917 + 9.99642i) q^{58} +4.04217i q^{59} +(6.50541 + 0.662789i) q^{60} -10.6561i q^{61} +(10.5197 + 0.534506i) q^{62} -0.434268 q^{63} +(7.63174 + 2.39927i) q^{64} +2.04118 q^{65} +(-7.46597 - 0.379345i) q^{66} -10.2757i q^{67} +(-9.77107 - 0.995503i) q^{68} -14.7416i q^{69} +(0.146482 - 2.88295i) q^{70} +11.1847 q^{71} +(-1.21408 - 0.186345i) q^{72} +5.93073 q^{73} +(-0.332397 + 6.54198i) q^{74} +1.33522i q^{75} +(1.00299 - 9.84456i) q^{76} +3.30009i q^{77} +(2.26236 + 0.114950i) q^{78} -6.84608 q^{79} +(1.64660 - 7.99697i) q^{80} -7.50861 q^{81} +(-6.12303 - 0.311110i) q^{82} -8.53099i q^{83} +(0.324709 - 3.18708i) q^{84} +10.0239i q^{85} +(0.536910 - 10.5670i) q^{86} +11.3369 q^{87} +(-1.41607 + 9.22602i) q^{88} -14.4730 q^{89} +(-0.0636125 + 1.25197i) q^{90} -1.00000i q^{91} +(-18.3116 - 1.86564i) q^{92} -11.9304i q^{93} +(-0.347747 - 0.0176690i) q^{94} -10.0993 q^{95} +(2.27537 - 8.77075i) q^{96} -3.61044 q^{97} +(-1.41239 - 0.0717634i) q^{98} -1.43312i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 2 q^{2} - 2 q^{4} - 6 q^{6} - 34 q^{7} + 8 q^{8} - 26 q^{9} - 4 q^{12} - 2 q^{14} - 8 q^{15} - 6 q^{16} - 20 q^{17} + 14 q^{18} - 4 q^{20} - 10 q^{22} - 20 q^{23} + 10 q^{24} - 22 q^{25} + 2 q^{28}+ \cdots + 2 q^{98}+O(q^{100}) \) 34 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 - 34 * q^7 + 8 * q^8 - 26 * q^9 - 4 * q^12 - 2 * q^14 - 8 * q^15 - 6 * q^16 - 20 * q^17 + 14 * q^18 - 4 * q^20 - 10 * q^22 - 20 * q^23 + 10 * q^24 - 22 * q^25 + 2 * q^28 - 60 * q^30 + 16 * q^31 + 12 * q^32 - 8 * q^33 + 28 * q^34 - 4 * q^36 - 28 * q^38 + 8 * q^39 + 64 * q^40 + 8 * q^41 + 6 * q^42 + 24 * q^44 + 16 * q^46 + 24 * q^48 + 34 * q^49 + 10 * q^50 - 4 * q^52 - 18 * q^54 - 32 * q^55 - 8 * q^56 + 8 * q^57 + 44 * q^58 - 24 * q^60 + 60 * q^62 + 26 * q^63 - 2 * q^64 - 20 * q^65 + 24 * q^66 + 12 * q^68 + 64 * q^71 - 92 * q^72 - 22 * q^74 + 4 * q^76 + 20 * q^79 - 56 * q^80 - 6 * q^81 - 20 * q^82 + 4 * q^84 - 12 * q^86 - 56 * q^87 - 34 * q^88 - 4 * q^90 - 54 * q^92 + 12 * q^94 + 42 * q^96 + 2 * q^98

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