LMFDB - Embedded newform 351.2.ba.a.89.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(71,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.71"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.ba (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.8
Character	$\chi$	$=$	351.89
Dual form			351.2.ba.a.71.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.662754 - 0.662754i) q^{2} +1.12151i q^{4} +(-0.101414 - 0.0271738i) q^{5} +(-0.353095 - 0.0946115i) q^{7} +(2.06880 + 2.06880i) q^{8} +(-0.0852221 + 0.0492030i) q^{10} +(2.25143 + 2.25143i) q^{11} +(3.51083 + 0.821016i) q^{13} +(-0.296719 + 0.171311i) q^{14} +0.499177 q^{16} +(0.713952 - 1.23660i) q^{17} +(2.92701 - 0.784289i) q^{19} +(0.0304758 - 0.113737i) q^{20} +2.98429 q^{22} +(-1.83687 + 3.18155i) q^{23} +(-4.32058 - 2.49449i) q^{25} +(2.87095 - 1.78269i) q^{26} +(0.106108 - 0.396001i) q^{28} +5.17142i q^{29} +(1.46476 - 5.46656i) q^{31} +(-3.80676 + 3.80676i) q^{32} +(-0.346388 - 1.29274i) q^{34} +(0.0332378 + 0.0191899i) q^{35} +(-4.32627 - 1.15922i) q^{37} +(1.42009 - 2.45967i) q^{38} +(-0.153588 - 0.266022i) q^{40} +(-1.76108 - 6.57243i) q^{41} +(1.94536 - 1.12315i) q^{43} +(-2.52501 + 2.52501i) q^{44} +(0.891194 + 3.32598i) q^{46} +(4.42009 - 1.18436i) q^{47} +(-5.94645 - 3.43319i) q^{49} +(-4.51671 + 1.21025i) q^{50} +(-0.920781 + 3.93745i) q^{52} -13.0901i q^{53} +(-0.167147 - 0.289507i) q^{55} +(-0.534750 - 0.926214i) q^{56} +(3.42738 + 3.42738i) q^{58} +(-2.44633 - 2.44633i) q^{59} +(3.12378 + 5.41055i) q^{61} +(-2.65221 - 4.59376i) q^{62} +6.04425i q^{64} +(-0.333737 - 0.178665i) q^{65} +(-14.8055 + 3.96713i) q^{67} +(1.38687 + 0.800708i) q^{68} +(0.0347467 - 0.00931034i) q^{70} +(-1.56835 - 5.85317i) q^{71} +(-4.13084 + 4.13084i) q^{73} +(-3.63553 + 2.09897i) q^{74} +(0.879591 + 3.28268i) q^{76} +(-0.581958 - 1.00798i) q^{77} +(8.15587 - 14.1264i) q^{79} +(-0.0506235 - 0.0135645i) q^{80} +(-5.52307 - 3.18874i) q^{82} +(4.29512 + 16.0296i) q^{83} +(-0.106008 + 0.106008i) q^{85} +(0.544920 - 2.03367i) q^{86} +9.31551i q^{88} +(-0.630472 + 2.35295i) q^{89} +(-1.16198 - 0.622062i) q^{91} +(-3.56816 - 2.06008i) q^{92} +(2.14449 - 3.71437i) q^{94} -0.318151 q^{95} +(-3.20249 + 11.9519i) q^{97} +(-6.21639 + 1.66568i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 30 q^{8} - 12 q^{10} + 6 q^{11} - 2 q^{13} + 12 q^{14} - 28 q^{16} - 4 q^{19} + 18 q^{20} - 4 q^{22} + 6 q^{23} + 48 q^{26} - 18 q^{31} - 54 q^{32} + 6 q^{34} - 6 q^{35}+ \cdots - 36 q^{98}+O(q^{100}) $ 48 * q + 6 * q^2 + 6 * q^5 - 4 * q^7 - 30 * q^8 - 12 * q^10 + 6 * q^11 - 2 * q^13 + 12 * q^14 - 28 * q^16 - 4 * q^19 + 18 * q^20 - 4 * q^22 + 6 * q^23 + 48 * q^26 - 18 * q^31 - 54 * q^32 + 6 * q^34 - 6 * q^35 - 6 * q^37 - 36 * q^38 - 12 * q^40 - 18 * q^41 - 30 * q^43 - 12 * q^44 - 12 * q^46 + 36 * q^47 - 6 * q^49 + 60 * q^50 + 56 * q^52 - 4 * q^55 + 6 * q^56 + 50 * q^58 + 6 * q^59 + 2 * q^61 - 18 * q^62 - 72 * q^65 + 26 * q^67 - 42 * q^68 - 16 * q^70 + 48 * q^71 - 22 * q^73 - 30 * q^74 + 6 * q^76 - 72 * q^77 + 8 * q^79 + 54 * q^80 - 12 * q^82 - 54 * q^83 - 24 * q^85 + 54 * q^86 - 16 * q^91 - 120 * q^92 + 26 * q^94 + 12 * q^95 - 24 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.662754	−	0.662754i	0.468638	−	0.468638i	−0.432835	−	0.901473i	$-0.642487\pi$
$2$	0.662754	−	0.662754i	0.468638	−	0.468638i	0.901473	+	0.432835i	$0.142487\pi$
$3$		0			0
$3$		0			0
$4$			1.12151i			0.560757i
$5$	−0.101414	−	0.0271738i	−0.0453537	−	0.0121525i	0.236071	−	0.971736i	$-0.424140\pi$
$5$	−0.101414	−	0.0271738i	−0.0453537	−	0.0121525i	−0.281425	+	0.959583i	$0.590807\pi$
$6$		0			0
$7$	−0.353095	−	0.0946115i	−0.133457	−	0.0357598i	0.191472	−	0.981498i	$-0.438674\pi$
$7$	−0.353095	−	0.0946115i	−0.133457	−	0.0357598i	−0.324929	+	0.945738i	$0.605341\pi$
$8$	2.06880	+	2.06880i	0.731430	+	0.731430i
$9$		0			0
$10$	−0.0852221	+	0.0492030i	−0.0269496	+	0.0155594i
$11$	2.25143	+	2.25143i	0.678833	+	0.678833i	0.959736	−	0.280903i	$-0.0906341\pi$
$11$	2.25143	+	2.25143i	0.678833	+	0.678833i	−0.280903	+	0.959736i	$0.590634\pi$
$12$		0			0
$13$	3.51083	+	0.821016i	0.973729	+	0.227709i
$13$	3.51083	+	0.821016i	0.973729	+	0.227709i
$14$	−0.296719	+	0.171311i	−0.0793016	+	0.0457848i
$15$		0			0
$16$	0.499177			0.124794
$17$	0.713952	−	1.23660i	0.173159	−	0.299920i	−0.766364	−	0.642407i	$-0.777936\pi$
$17$	0.713952	−	1.23660i	0.173159	−	0.299920i	0.939523	+	0.342487i	$0.111269\pi$
$18$		0			0
$19$	2.92701	−	0.784289i	0.671501	−	0.179928i	0.0930701	−	0.995660i	$-0.470332\pi$
$19$	2.92701	−	0.784289i	0.671501	−	0.179928i	0.578431	+	0.815731i	$0.303665\pi$
$20$	0.0304758	−	0.113737i	0.00681460	−	0.0254324i
$21$		0			0
$22$	2.98429			0.636253
$23$	−1.83687	+	3.18155i	−0.383014	+	0.663400i	−0.991492	−	0.130171i	$-0.958447\pi$
$23$	−1.83687	+	3.18155i	−0.383014	+	0.663400i	0.608477	+	0.793571i	$0.291781\pi$
$24$		0			0
$25$	−4.32058	−	2.49449i	−0.864116	−	0.498898i
$26$	2.87095	−	1.78269i	0.563039	−	0.349613i
$27$		0			0
$28$	0.106108	−	0.396001i	0.0200526	−	0.0748372i
$29$			5.17142i			0.960309i	0.877184	+	0.480155i	$0.159419\pi$
$29$			5.17142i			0.960309i	−0.877184	+	0.480155i	$0.840581\pi$
$30$		0			0
$31$	1.46476	−	5.46656i	0.263079	−	0.981823i	−0.700337	−	0.713812i	$-0.746967\pi$
$31$	1.46476	−	5.46656i	0.263079	−	0.981823i	0.963416	−	0.268011i	$-0.0863663\pi$
$32$	−3.80676	+	3.80676i	−0.672947	+	0.672947i
$33$		0			0
$34$	−0.346388	−	1.29274i	−0.0594050	−	0.221703i
$35$	0.0332378	+	0.0191899i	0.00561822	+	0.00324368i
$36$		0			0
$37$	−4.32627	−	1.15922i	−0.711234	−	0.190575i	−0.114977	−	0.993368i	$-0.536679\pi$
$37$	−4.32627	−	1.15922i	−0.711234	−	0.190575i	−0.596257	+	0.802793i	$0.703346\pi$
$38$	1.42009	−	2.45967i	0.230370	−	0.399012i
$39$		0			0
$40$	−0.153588	−	0.266022i	−0.0242844	−	0.0420618i
$41$	−1.76108	−	6.57243i	−0.275034	−	1.02644i	−0.955818	−	0.293958i	$-0.905028\pi$
$41$	−1.76108	−	6.57243i	−0.275034	−	1.02644i	0.680784	−	0.732484i	$-0.261639\pi$
$42$		0			0
$43$	1.94536	−	1.12315i	0.296665	−	0.171279i	−0.344279	−	0.938867i	$-0.611877\pi$
$43$	1.94536	−	1.12315i	0.296665	−	0.171279i	0.640944	+	0.767588i	$0.278543\pi$
$44$	−2.52501	+	2.52501i	−0.380660	+	0.380660i
$45$		0			0
$46$	0.891194	+	3.32598i	0.131399	+	0.490389i
$47$	4.42009	−	1.18436i	0.644736	−	0.172756i	0.0783882	−	0.996923i	$-0.475023\pi$
$47$	4.42009	−	1.18436i	0.644736	−	0.172756i	0.566348	+	0.824166i	$0.308356\pi$
$48$		0			0
$49$	−5.94645	−	3.43319i	−0.849493	−	0.490455i
$50$	−4.51671	+	1.21025i	−0.638760	+	0.171155i
$51$		0			0
$52$	−0.920781	+	3.93745i	−0.127689	+	0.546026i
$53$		−	13.0901i		−	1.79807i	−0.437881	−	0.899033i	$-0.644271\pi$
$53$		−	13.0901i		−	1.79807i	0.437881	−	0.899033i	$-0.355729\pi$
$54$		0			0
$55$	−0.167147	−	0.289507i	−0.0225381	−	0.0390371i
$56$	−0.534750	−	0.926214i	−0.0714589	−	0.123771i
$57$		0			0
$58$	3.42738	+	3.42738i	0.450037	+	0.450037i
$59$	−2.44633	−	2.44633i	−0.318485	−	0.318485i	0.529700	−	0.848185i	$-0.322304\pi$
$59$	−2.44633	−	2.44633i	−0.318485	−	0.318485i	−0.848185	+	0.529700i	$0.822304\pi$
$60$		0			0
$61$	3.12378	+	5.41055i	0.399959	+	0.692750i	0.993720	−	0.111892i	$-0.0356909\pi$
$61$	3.12378	+	5.41055i	0.399959	+	0.692750i	−0.593761	+	0.804641i	$0.702358\pi$
$62$	−2.65221	−	4.59376i	−0.336831	−	0.583408i
$63$		0			0
$64$			6.04425i			0.755531i
$65$	−0.333737	−	0.178665i	−0.0413950	−	0.0221607i
$66$		0			0
$67$	−14.8055	+	3.96713i	−1.80878	+	0.484662i	−0.995292	−	0.0969186i	$-0.969101\pi$
$67$	−14.8055	+	3.96713i	−1.80878	+	0.484662i	−0.813489	+	0.581580i	$0.802435\pi$
$68$	1.38687	+	0.800708i	0.168182	+	0.0971001i
$69$		0			0
$70$	0.0347467	−	0.00931034i	0.00415302	−	0.00111280i
$71$	−1.56835	−	5.85317i	−0.186129	−	0.694643i	−0.994386	−	0.105813i	$-0.966255\pi$
$71$	−1.56835	−	5.85317i	−0.186129	−	0.694643i	0.808257	−	0.588830i	$-0.200411\pi$
$72$		0			0
$73$	−4.13084	+	4.13084i	−0.483478	+	0.483478i	−0.906241	−	0.422763i	$-0.861060\pi$
$73$	−4.13084	+	4.13084i	−0.483478	+	0.483478i	0.422763	+	0.906241i	$0.361060\pi$
$74$	−3.63553	+	2.09897i	−0.422622	+	0.244001i
$75$		0			0
$76$	0.879591	+	3.28268i	0.100896	+	0.376549i
$77$	−0.581958	−	1.00798i	−0.0663203	−	0.114870i
$78$		0			0
$79$	8.15587	−	14.1264i	0.917607	−	1.58934i	0.114569	−	0.993415i	$-0.463451\pi$
$79$	8.15587	−	14.1264i	0.917607	−	1.58934i	0.803039	−	0.595927i	$-0.203215\pi$
$80$	−0.0506235	−	0.0135645i	−0.00565988	−	0.00151656i
$81$		0			0
$82$	−5.52307	−	3.18874i	−0.609921	−	0.352138i
$83$	4.29512	+	16.0296i	0.471450	+	1.75948i	0.634565	+	0.772870i	$0.281179\pi$
$83$	4.29512	+	16.0296i	0.471450	+	1.75948i	−0.163114	+	0.986607i	$0.552154\pi$
$84$		0			0
$85$	−0.106008	+	0.106008i	−0.0114982	+	0.0114982i
$86$	0.544920	−	2.03367i	0.0587603	−	0.219296i
$87$		0			0
$88$			9.31551i			0.993037i
$89$	−0.630472	+	2.35295i	−0.0668298	+	0.249412i	−0.991257	−	0.131947i	$-0.957877\pi$
$89$	−0.630472	+	2.35295i	−0.0668298	+	0.249412i	0.924427	+	0.381359i	$0.124544\pi$
$90$		0			0
$91$	−1.16198	−	0.622062i	−0.121809	−	0.0652098i
$92$	−3.56816	−	2.06008i	−0.372006	−	0.214778i
$93$		0			0
$94$	2.14449	−	3.71437i	0.221187	−	0.383108i
$95$	−0.318151			−0.0326416
$96$		0			0
$97$	−3.20249	+	11.9519i	−0.325164	+	1.21353i	0.588983	+	0.808145i	$0.299529\pi$
$97$	−3.20249	+	11.9519i	−0.325164	+	1.21353i	−0.914147	+	0.405383i	$0.867138\pi$
$98$	−6.21639	+	1.66568i	−0.627951	+	0.168259i
$99$		0			0
$100$	2.79760	−	4.84559i	0.279760	−	0.484559i
$101$	−3.80275			−0.378388			−0.189194	−	0.981940i	$-0.560587\pi$
$101$	−3.80275			−0.378388			−0.189194	+	0.981940i	$0.560587\pi$
$102$		0			0
$103$	−5.80875	+	3.35368i	−0.572353	+	0.330448i	−0.758089	−	0.652152i	$-0.773867\pi$
$103$	−5.80875	+	3.35368i	−0.572353	+	0.330448i	0.185736	+	0.982600i	$0.440533\pi$
$104$	5.56468	+	8.96171i	0.545662	+	0.878768i
$105$		0			0
$106$	−8.67553	−	8.67553i	−0.842642	−	0.842642i
$107$	10.4912	−	6.05707i	1.01422	−	0.585559i	0.101795	−	0.994805i	$-0.467542\pi$
$107$	10.4912	−	6.05707i	1.01422	−	0.585559i	0.912424	+	0.409246i	$0.134208\pi$
$108$		0			0
$109$	−0.643264	−	0.643264i	−0.0616135	−	0.0616135i	0.675629	−	0.737242i	$-0.263872\pi$
$109$	−0.643264	−	0.643264i	−0.0616135	−	0.0616135i	−0.737242	+	0.675629i	$0.763872\pi$
$110$	−0.302649	−	0.0810946i	−0.0288565	−	0.00773206i
$111$		0			0
$112$	−0.176257	−	0.0472279i	−0.0166547	−	0.00446262i
$113$		−	3.07587i		−	0.289354i	−0.989479	−	0.144677i	$-0.953786\pi$
$113$		−	3.07587i		−	0.289354i	0.989479	−	0.144677i	$-0.0462143\pi$
$114$		0			0
$115$	0.272739	−	0.272739i	0.0254331	−	0.0254331i
$116$	−5.79983			−0.538500
$117$		0			0
$118$	−3.24263			−0.298508
$119$	−0.369090	+	0.369090i	−0.0338344	+	0.0338344i
$120$		0			0
$121$		−	0.862100i		−	0.0783727i
$122$	5.65616	+	1.51556i	0.512085	+	0.137213i
$123$		0			0
$124$	6.13082	+	1.64275i	0.550564	+	0.147523i
$125$	0.741584	+	0.741584i	0.0663293	+	0.0663293i
$126$		0			0
$127$	11.1811	−	6.45543i	0.992165	−	0.572827i	0.0862440	−	0.996274i	$-0.472514\pi$
$127$	11.1811	−	6.45543i	0.992165	−	0.572827i	0.905921	+	0.423448i	$0.139180\pi$
$128$	−3.60767	−	3.60767i	−0.318876	−	0.318876i
$129$		0			0
$130$	−0.339597	+	0.102775i	−0.0297846	+	0.00901393i
$131$	13.4537	−	7.76749i	1.17545	−	0.678649i	0.220495	−	0.975388i	$-0.429233\pi$
$131$	13.4537	−	7.76749i	1.17545	−	0.678649i	0.954958	+	0.296739i	$0.0958993\pi$
$132$		0			0
$133$	−1.10771			−0.0960510
$134$	−7.18319	+	12.4416i	−0.620533	+	1.07479i
$135$		0			0
$136$	4.03530	−	1.08125i	0.346024	−	0.0927168i
$137$	4.77136	−	17.8070i	0.407645	−	1.52135i	−0.391480	−	0.920187i	$-0.628037\pi$
$137$	4.77136	−	17.8070i	0.407645	−	1.52135i	0.799125	−	0.601165i	$-0.205297\pi$
$138$		0			0
$139$	9.08265			0.770381			0.385190	−	0.922837i	$-0.374136\pi$
$139$	9.08265			0.770381			0.385190	+	0.922837i	$0.374136\pi$
$140$	−0.0215217	+	0.0372767i	−0.00181892	+	0.00315046i
$141$		0			0
$142$	−4.91864	−	2.83978i	−0.412763	−	0.238309i
$143$	6.05594	+	9.75286i	0.506423	+	0.815575i
$144$		0			0
$145$	0.140527	−	0.524455i	0.0116702	−	0.0435536i
$146$			5.47546i			0.453152i
$147$		0			0
$148$	1.30008	−	4.85197i	0.106866	−	0.398830i
$149$	−8.51487	+	8.51487i	−0.697565	+	0.697565i	−0.963885	−	0.266319i	$-0.914192\pi$
$149$	−8.51487	+	8.51487i	−0.697565	+	0.697565i	0.266319	+	0.963885i	$0.414192\pi$
$150$		0			0
$151$	−0.0109208	−	0.0407571i	−0.000888724	−	0.00331676i	0.965480	−	0.260477i	$-0.0838798\pi$
$151$	−0.0109208	−	0.0407571i	−0.000888724	−	0.00331676i	−0.966369	+	0.257160i	$0.917213\pi$
$152$	7.67791	+	4.43284i	0.622761	+	0.359551i
$153$		0			0
$154$	−1.05374	−	0.282348i	−0.0849127	−	0.0227523i
$155$	−0.297094	+	0.514583i	−0.0238632	+	0.0413323i
$156$		0			0
$157$	−6.95508	−	12.0466i	−0.555076	−	0.961420i	−0.997898	−	0.0648102i	$-0.979356\pi$
$157$	−6.95508	−	12.0466i	−0.555076	−	0.961420i	0.442822	−	0.896610i	$-0.353978\pi$
$158$	−3.95698	−	14.7677i	−0.314801	−	1.17485i
$159$		0			0
$160$	0.489503	−	0.282615i	0.0386986	−	0.0223427i
$161$	0.949602	−	0.949602i	0.0748391	−	0.0748391i
$162$		0			0
$163$	0.208136	+	0.776776i	0.0163025	+	0.0608418i	0.973598	−	0.228270i	$-0.0733068\pi$
$163$	0.208136	+	0.776776i	0.0163025	+	0.0608418i	−0.957295	+	0.289112i	$0.906640\pi$
$164$	7.37108	−	1.97507i	0.575584	−	0.154227i
$165$		0			0
$166$	13.4703	+	7.77707i	1.04550	+	0.603618i
$167$	−14.9871	+	4.01578i	−1.15974	+	0.310750i	−0.786860	−	0.617131i	$-0.788295\pi$
$167$	−14.9871	+	4.01578i	−1.15974	+	0.310750i	−0.372875	+	0.927881i	$0.621628\pi$
$168$		0			0
$169$	11.6519	+	5.76490i	0.896297	+	0.443454i
$170$			0.140514i			0.0107770i
$171$		0			0
$172$	1.25963	+	2.18175i	0.0960462	+	0.166357i
$173$	−7.66869	−	13.2826i	−0.583039	−	1.00985i	−0.995117	−	0.0987051i	$-0.968530\pi$
$173$	−7.66869	−	13.2826i	−0.583039	−	1.00985i	0.412077	−	0.911149i	$-0.364803\pi$
$174$		0			0
$175$	1.28957	+	1.28957i	0.0974822	+	0.0974822i
$176$	1.12386	+	1.12386i	0.0847144	+	0.0847144i
$177$		0			0
$178$	1.14158	+	1.97728i	0.0855651	+	0.148203i
$179$	9.33636	+	16.1710i	0.697832	+	1.20868i	0.969217	+	0.246209i	$0.0791851\pi$
$179$	9.33636	+	16.1710i	0.697832	+	1.20868i	−0.271385	+	0.962471i	$0.587482\pi$
$180$		0			0
$181$		−	14.2199i		−	1.05695i	−0.848947	−	0.528477i	$-0.822763\pi$
$181$		−	14.2199i		−	1.05695i	0.848947	−	0.528477i	$-0.177237\pi$
$182$	−1.18238	+	0.357832i	−0.0876439	+	0.0265243i
$183$		0			0
$184$	−10.3821	+	2.78188i	−0.765378	+	0.205083i
$185$	0.407244	+	0.235122i	0.0299412	+	0.0172865i
$186$		0			0
$187$	4.39154	−	1.17671i	0.321141	−	0.0860495i
$188$	1.32827	+	4.95719i	0.0968744	+	0.361540i
$189$		0			0
$190$	−0.210856	+	0.210856i	−0.0152971	+	0.0152971i
$191$	−6.35291	+	3.66785i	−0.459680	+	0.265397i	−0.711910	−	0.702271i	$-0.752170\pi$
$191$	−6.35291	+	3.66785i	−0.459680	+	0.265397i	0.252229	+	0.967667i	$0.418836\pi$
$192$		0			0
$193$	5.53999	+	20.6755i	0.398777	+	1.48826i	0.815250	+	0.579109i	$0.196599\pi$
$193$	5.53999	+	20.6755i	0.398777	+	1.48826i	−0.416473	+	0.909148i	$0.636734\pi$
$194$	5.79868	+	10.0436i	0.416321	+	0.721090i
$195$		0			0
$196$	3.85037	−	6.66903i	0.275026	−	0.476359i
$197$	−3.74628	−	1.00381i	−0.266911	−	0.0715186i	0.122881	−	0.992421i	$-0.460787\pi$
$197$	−3.74628	−	1.00381i	−0.266911	−	0.0715186i	−0.389792	+	0.920903i	$0.627453\pi$
$198$		0			0
$199$	8.87017	+	5.12119i	0.628790	+	0.363032i	0.780283	−	0.625426i	$-0.215075\pi$
$199$	8.87017	+	5.12119i	0.628790	+	0.363032i	−0.151494	+	0.988458i	$0.548408\pi$
$200$	−3.77781	−	14.0990i	−0.267132	−	0.996949i
$201$		0			0
$202$	−2.52029	+	2.52029i	−0.177327	+	0.177327i
$203$	0.489276	−	1.82600i	0.0343405	−	0.128160i
$204$		0			0
$205$			0.714392i			0.0498953i
$206$	−1.62710	+	6.07244i	−0.113366	+	0.423087i
$207$		0			0
$208$	1.75253	+	0.409832i	0.121516	+	0.0284168i
$209$	8.35573	+	4.82418i	0.577978	+	0.333696i
$210$		0			0
$211$	9.03550	−	15.6500i	0.622030	−	1.07739i	−0.367078	−	0.930190i	$-0.619642\pi$
$211$	9.03550	−	15.6500i	0.622030	−	1.07739i	0.989107	−	0.147197i	$-0.0470250\pi$
$212$	14.6808			1.00828
$213$		0			0
$214$	2.93871	−	10.9674i	0.200886	−	0.749717i
$215$	−0.227807	+	0.0610407i	−0.0155363	+	0.00416294i
$216$		0			0
$217$	−1.03440	+	1.79163i	−0.0702196	+	0.121624i
$218$	−0.852651			−0.0577488
$219$		0			0
$220$	0.324686	−	0.187458i	0.0218903	−	0.0126384i
$221$	3.52183	−	3.75533i	0.236904	−	0.252611i
$222$		0			0
$223$	2.26872	+	2.26872i	0.151925	+	0.151925i	0.778977	−	0.627052i	$-0.215739\pi$
$223$	2.26872	+	2.26872i	0.151925	+	0.151925i	−0.627052	+	0.778977i	$0.715739\pi$
$224$	1.70431	−	0.983985i	0.113874	−	0.0657453i
$225$		0			0
$226$	−2.03855	−	2.03855i	−0.135602	−	0.135602i
$227$	3.66821	+	0.982895i	0.243468	+	0.0652370i	0.378489	−	0.925606i	$-0.376444\pi$
$227$	3.66821	+	0.982895i	0.243468	+	0.0652370i	−0.135021	+	0.990843i	$0.543110\pi$
$228$		0			0
$229$	16.9464	+	4.54078i	1.11985	+	0.300063i	0.770823	−	0.637050i	$-0.219845\pi$
$229$	16.9464	+	4.54078i	1.11985	+	0.300063i	0.349027	+	0.937113i	$0.386512\pi$
$230$		−	0.361518i		−	0.0238378i
$231$		0			0
$232$	−10.6986	+	10.6986i	−0.702399	+	0.702399i
$233$	−14.4728			−0.948143			−0.474072	−	0.880486i	$-0.657216\pi$
$233$	−14.4728			−0.948143			−0.474072	+	0.880486i	$0.657216\pi$
$234$		0			0
$235$	−0.480442			−0.0313406
$236$	2.74359	−	2.74359i	0.178593	−	0.178593i
$237$		0			0
$238$			0.489231i			0.0317122i
$239$	19.7813	+	5.30038i	1.27955	+	0.342853i	0.833681	−	0.552247i	$-0.186229\pi$
$239$	19.7813	+	5.30038i	1.27955	+	0.342853i	0.445865	+	0.895100i	$0.352896\pi$
$240$		0			0
$241$	−23.3290	−	6.25098i	−1.50275	−	0.402661i	−0.588732	−	0.808329i	$-0.700372\pi$
$241$	−23.3290	−	6.25098i	−1.50275	−	0.402661i	−0.914021	+	0.405667i	$0.867039\pi$
$242$	−0.571360	−	0.571360i	−0.0367284	−	0.0367284i
$243$		0			0
$244$	−6.06801	+	3.50337i	−0.388464	+	0.224280i
$245$	0.509761	+	0.509761i	0.0325674	+	0.0325674i
$246$		0			0
$247$	10.9201	−	0.350386i	0.694831	−	0.0222945i
$248$	14.3395	−	8.27891i	0.910558	−	0.525711i
$249$		0			0
$250$	0.982975			0.0621688
$251$	−3.92544	+	6.79906i	−0.247772	+	0.429153i	−0.962907	−	0.269833i	$-0.913032\pi$
$251$	−3.92544	+	6.79906i	−0.247772	+	0.429153i	0.715136	+	0.698986i	$0.246365\pi$
$252$		0			0
$253$	−11.2986	+	3.02746i	−0.710340	+	0.190335i
$254$	3.13198	−	11.6887i	0.196518	−	0.733414i
$255$		0			0
$256$	−16.8705			−1.05441
$257$	−13.1768	+	22.8229i	−0.821947	+	1.42365i	0.0822831	+	0.996609i	$0.473779\pi$
$257$	−13.1768	+	22.8229i	−0.821947	+	1.42365i	−0.904230	+	0.427045i	$0.859554\pi$
$258$		0			0
$259$	1.41791	+	0.818630i	0.0881046	+	0.0508672i
$260$	0.200376	−	0.374291i	0.0124268	−	0.0232126i
$261$		0			0
$262$	3.76855	−	14.0644i	0.232822	−	0.868903i
$263$			21.1195i			1.30229i	0.758955	+	0.651143i	$0.225710\pi$
$263$			21.1195i			1.30229i	−0.758955	+	0.651143i	$0.774290\pi$
$264$		0			0
$265$	−0.355708	+	1.32752i	−0.0218510	+	0.0815490i
$266$	−0.734142	+	0.734142i	−0.0450131	+	0.0450131i
$267$		0			0
$268$	−4.44919	−	16.6046i	−0.271777	−	1.01429i
$269$	3.78449	+	2.18498i	0.230744	+	0.133220i	0.610915	−	0.791696i	$-0.290802\pi$
$269$	3.78449	+	2.18498i	0.230744	+	0.133220i	−0.380171	+	0.924916i	$0.624135\pi$
$270$		0			0
$271$	13.6523	+	3.65813i	0.829320	+	0.222216i	0.648417	−	0.761285i	$-0.275431\pi$
$271$	13.6523	+	3.65813i	0.829320	+	0.222216i	0.180903	+	0.983501i	$0.442098\pi$
$272$	0.356389	−	0.617283i	0.0216092	−	0.0374283i
$273$		0			0
$274$	−8.63940	−	14.9639i	−0.521925	−	0.904001i
$275$	−4.11132	−	15.3437i	−0.247922	−	0.925258i
$276$		0			0
$277$	−21.2996	+	12.2973i	−1.27977	+	0.738874i	−0.976805	−	0.214129i	$-0.931309\pi$
$277$	−21.2996	+	12.2973i	−1.27977	+	0.738874i	−0.302961	+	0.953003i	$0.597975\pi$
$278$	6.01957	−	6.01957i	0.361030	−	0.361030i
$279$		0			0
$280$	0.0290624	+	0.108462i	0.00173681	+	0.00648186i
$281$	−20.3630	+	5.45626i	−1.21476	+	0.325493i	−0.808627	−	0.588322i	$-0.799789\pi$
$281$	−20.3630	+	5.45626i	−1.21476	+	0.325493i	−0.406131	+	0.913815i	$0.633122\pi$
$282$		0			0
$283$	3.49027	+	2.01511i	0.207475	+	0.119786i	0.600137	−	0.799897i	$-0.295113\pi$
$283$	3.49027	+	2.01511i	0.207475	+	0.119786i	−0.392662	+	0.919683i	$0.628446\pi$
$284$	6.56441	−	1.75893i	0.389526	−	0.104373i
$285$		0			0
$286$	10.4773	+	2.45015i	0.619538	+	0.144881i
$287$			2.48731i			0.146821i
$288$		0			0
$289$	7.48054	+	12.9567i	0.440032	+	0.762158i
$290$	−0.254450	−	0.440720i	−0.0149418	−	0.0258799i
$291$		0			0
$292$	−4.63279	−	4.63279i	−0.271114	−	0.271114i
$293$	8.16540	+	8.16540i	0.477028	+	0.477028i	0.904180	−	0.427152i	$-0.140483\pi$
$293$	8.16540	+	8.16540i	0.477028	+	0.477028i	−0.427152	+	0.904180i	$0.640483\pi$
$294$		0			0
$295$	0.181616	+	0.314568i	0.0105741	+	0.0183149i
$296$	−6.55198	−	11.3484i	−0.380826	−	0.659610i
$297$		0			0
$298$			11.2865i			0.653811i
$299$	−9.06105	+	9.66180i	−0.524014	+	0.558756i
$300$		0			0
$301$	−0.793160	+	0.212527i	−0.0457170	+	0.0122498i
$302$	−0.0342497	−	0.0197741i	−0.00197085	−	0.00113787i
$303$		0			0
$304$	1.46109	−	0.391499i	0.0837995	−	0.0224540i
$305$	−0.169770	−	0.633591i	−0.00972101	−	0.0362793i
$306$		0			0
$307$	−17.9190	+	17.9190i	−1.02269	+	1.02269i	−0.0229527	+	0.999737i	$0.507307\pi$
$307$	−17.9190	+	17.9190i	−1.02269	+	1.02269i	−0.999737	+	0.0229527i	$0.992693\pi$
$308$	1.13047	−	0.652675i	0.0644143	−	0.0371896i
$309$		0			0
$310$	0.144141	+	0.537942i	0.00818667	+	0.0305531i
$311$	−11.1301	−	19.2779i	−0.631129	−	1.09315i	−0.987321	−	0.158735i	$-0.949258\pi$
$311$	−11.1301	−	19.2779i	−0.631129	−	1.09315i	0.356192	−	0.934413i	$-0.384075\pi$
$312$		0			0
$313$	4.30058	−	7.44883i	0.243083	−	0.421033i	−0.718508	−	0.695519i	$-0.755175\pi$
$313$	4.30058	−	7.44883i	0.243083	−	0.421033i	0.961591	+	0.274486i	$0.0885078\pi$
$314$	−12.5934	−	3.37439i	−0.710687	−	0.190428i
$315$		0			0
$316$	15.8429	+	9.14693i	0.891235	+	0.514555i
$317$	−8.15039	−	30.4177i	−0.457771	−	1.70843i	−0.679810	−	0.733388i	$-0.737938\pi$
$317$	−8.15039	−	30.4177i	−0.457771	−	1.70843i	0.222039	−	0.975038i	$-0.428729\pi$
$318$		0			0
$319$	−11.6431	+	11.6431i	−0.651889	+	0.651889i
$320$	0.164245	−	0.612971i	0.00918158	−	0.0342661i
$321$		0			0
$322$		−	1.25870i		−	0.0701449i
$323$	1.11989	−	4.17948i	0.0623123	−	0.232553i
$324$		0			0
$325$	−13.1208	−	12.3050i	−0.727812	−	0.682558i
$326$	0.652755	+	0.376868i	0.0361527	+	0.0208728i
$327$		0			0
$328$	9.95371	−	17.2403i	0.549602	−	0.951938i
$329$	−1.67276			−0.0922225
$330$		0			0
$331$	−4.04974	+	15.1138i	−0.222594	+	0.830732i	0.760760	+	0.649033i	$0.224826\pi$
$331$	−4.04974	+	15.1138i	−0.222594	+	0.830732i	−0.983354	+	0.181699i	$0.941840\pi$
$332$	−17.9774	+	4.81704i	−0.986639	+	0.264369i
$333$		0			0
$334$	−7.27128	+	12.5942i	−0.397867	+	0.689125i
$335$	1.60929			0.0879248
$336$		0			0
$337$	5.42515	−	3.13221i	0.295527	−	0.170622i	−0.344905	−	0.938638i	$-0.612089\pi$
$337$	5.42515	−	3.13221i	0.295527	−	0.170622i	0.640432	+	0.768015i	$0.278756\pi$
$338$	11.5430	−	3.90161i	0.627858	−	0.212220i
$339$		0			0
$340$	−0.118889	−	0.118889i	−0.00644768	−	0.00644768i
$341$	15.6054	−	9.00978i	0.845080	−	0.487907i
$342$		0			0
$343$	3.58423	+	3.58423i	0.193530	+	0.193530i
$344$	6.34813	+	1.70098i	0.342268	+	0.0917105i
$345$		0			0
$346$	−13.8855	−	3.72061i	−0.746490	−	0.200021i
$347$		−	18.2400i		−	0.979176i	−0.871954	−	0.489588i	$-0.837147\pi$
$347$		−	18.2400i		−	0.979176i	0.871954	−	0.489588i	$-0.162853\pi$
$348$		0			0
$349$	5.66873	−	5.66873i	0.303440	−	0.303440i	−0.538918	−	0.842358i	$-0.681167\pi$
$349$	5.66873	−	5.66873i	0.303440	−	0.303440i	0.842358	+	0.538918i	$0.181167\pi$
$350$	1.70933			0.0913677
$351$		0			0
$352$	−17.1413			−0.913636
$353$	−12.2134	+	12.2134i	−0.650052	+	0.650052i	−0.953005	−	0.302954i	$-0.902027\pi$
$353$	−12.2134	+	12.2134i	−0.650052	+	0.650052i	0.302954	+	0.953005i	$0.402027\pi$
$354$		0			0
$355$			0.636211i			0.0337666i
$356$	−2.63887	−	0.707083i	−0.139860	−	0.0374753i
$357$		0			0
$358$	16.9051	+	4.52972i	0.893464	+	0.239403i
$359$	−21.8853	−	21.8853i	−1.15506	−	1.15506i	−0.985523	−	0.169540i	$-0.945772\pi$
$359$	−21.8853	−	21.8853i	−1.15506	−	1.15506i	−0.169540	−	0.985523i	$-0.554228\pi$
$360$		0			0
$361$	−8.50223	+	4.90877i	−0.447486	+	0.258356i
$362$	−9.42428	−	9.42428i	−0.495329	−	0.495329i
$363$		0			0
$364$	0.697651	−	1.30318i	0.0365669	−	0.0683050i
$365$	0.531175	−	0.306674i	0.0278030	−	0.0160521i
$366$		0			0
$367$	−1.31076			−0.0684213			−0.0342106	−	0.999415i	$-0.510892\pi$
$367$	−1.31076			−0.0684213			−0.0342106	+	0.999415i	$0.510892\pi$
$368$	−0.916924	+	1.58816i	−0.0477980	+	0.0827885i
$369$		0			0
$370$	0.425731	−	0.114074i	0.0221327	−	0.00593044i
$371$	−1.23848	+	4.62206i	−0.0642985	+	0.239965i
$372$		0			0
$373$	−28.8214			−1.49231			−0.746157	−	0.665770i	$-0.768103\pi$
$373$	−28.8214			−1.49231			−0.746157	+	0.665770i	$0.768103\pi$
$374$	2.13064	−	3.69038i	0.110173	−	0.190825i
$375$		0			0
$376$	11.5945	+	6.69406i	0.597938	+	0.345220i
$377$	−4.24582	+	18.1560i	−0.218671	+	0.935081i
$378$		0			0
$379$	−4.45400	+	16.6226i	−0.228787	+	0.853843i	0.752065	+	0.659088i	$0.229058\pi$
$379$	−4.45400	+	16.6226i	−0.228787	+	0.853843i	−0.980852	+	0.194755i	$0.937609\pi$
$380$		−	0.356811i		−	0.0183040i
$381$		0			0
$382$	−1.77953	+	6.64130i	−0.0910487	+	0.339798i
$383$	−22.6717	+	22.6717i	−1.15847	+	1.15847i	−0.173666	+	0.984805i	$0.555561\pi$
$383$	−22.6717	+	22.6717i	−1.15847	+	1.15847i	−0.984805	+	0.173666i	$0.944439\pi$
$384$		0			0
$385$	0.0316280	+	0.118037i	0.00161191	+	0.00601575i
$386$	17.3744	+	10.0311i	0.884336	+	0.510571i
$387$		0			0
$388$	−13.4042	−	3.59164i	−0.680495	−	0.182338i
$389$	8.01814	−	13.8878i	0.406536	−	0.704141i	−0.587963	−	0.808888i	$-0.700070\pi$
$389$	8.01814	−	13.8878i	0.406536	−	0.704141i	0.994499	+	0.104747i	$0.0334033\pi$
$390$		0			0
$391$	2.62288	+	4.54295i	0.132645	+	0.229747i
$392$	−5.19944	−	19.4046i	−0.262611	−	0.980078i
$393$		0			0
$394$	−3.14814	+	1.81758i	−0.158601	+	0.0915684i
$395$	−1.21099	+	1.21099i	−0.0609314	+	0.0609314i
$396$		0			0
$397$	−7.81599	−	29.1697i	−0.392273	−	1.46398i	−0.826375	−	0.563120i	$-0.809601\pi$
$397$	−7.81599	−	29.1697i	−0.392273	−	1.46398i	0.434102	−	0.900864i	$-0.357066\pi$
$398$	9.27283	−	2.48465i	0.464805	−	0.124544i
$399$		0			0
$400$	−2.15673	−	1.24519i	−0.107837	−	0.0622596i
$401$	−10.9633	+	2.93761i	−0.547482	+	0.146697i	−0.521949	−	0.852977i	$-0.674795\pi$
$401$	−10.9633	+	2.93761i	−0.547482	+	0.146697i	−0.0255329	+	0.999674i	$0.508128\pi$
$402$		0			0
$403$	9.63066	−	17.9896i	0.479737	−	0.896124i
$404$		−	4.26484i		−	0.212184i
$405$		0			0
$406$	−0.885922	−	1.53446i	−0.0439676	−	0.0761541i
$407$	−7.13040	−	12.3502i	−0.353441	−	0.612177i
$408$		0			0
$409$	8.33215	+	8.33215i	0.411998	+	0.411998i	0.882434	−	0.470436i	$-0.155903\pi$
$409$	8.33215	+	8.33215i	0.411998	+	0.411998i	−0.470436	+	0.882434i	$0.655903\pi$
$410$	0.473466	+	0.473466i	0.0233828	+	0.0233828i
$411$		0			0
$412$	−3.76120	−	6.51459i	−0.185301	−	0.320951i
$413$	0.632336	+	1.09524i	0.0311152	+	0.0538931i
$414$		0			0
$415$		−	1.74234i		−	0.0855281i
$416$	−16.4903	+	10.2395i	−0.808504	+	0.502032i
$417$		0			0
$418$	8.73504	−	2.34055i	0.427245	−	0.114480i
$419$	2.49796	+	1.44220i	0.122033	+	0.0704561i	0.559774	−	0.828645i	$-0.310888\pi$
$419$	2.49796	+	1.44220i	0.122033	+	0.0704561i	−0.437741	+	0.899101i	$0.644221\pi$
$420$		0			0
$421$	2.42199	−	0.648970i	0.118040	−	0.0316288i	−0.199315	−	0.979935i	$-0.563872\pi$
$421$	2.42199	−	0.648970i	0.118040	−	0.0316288i	0.317356	+	0.948307i	$0.397205\pi$
$422$	−4.38375	−	16.3604i	−0.213398	−	0.796411i
$423$		0			0
$424$	27.0808	−	27.0808i	1.31516	−	1.31516i
$425$	−6.16938	+	3.56189i	−0.299259	+	0.172777i
$426$		0			0
$427$	−0.591092	−	2.20598i	−0.0286049	−	0.106755i
$428$	6.79309	+	11.7660i	0.328357	+	0.568730i
$429$		0			0
$430$	−0.110525	+	0.191435i	−0.00532999	+	0.00923182i
$431$	14.9429	+	4.00393i	0.719773	+	0.192863i	0.600071	−	0.799947i	$-0.295139\pi$
$431$	14.9429	+	4.00393i	0.719773	+	0.192863i	0.119703	+	0.992810i	$0.461806\pi$
$432$		0			0
$433$	4.53654	+	2.61917i	0.218012	+	0.125869i	0.605029	−	0.796203i	$-0.293161\pi$
$433$	4.53654	+	2.61917i	0.218012	+	0.125869i	−0.387017	+	0.922072i	$0.626495\pi$
$434$	0.501859	+	1.87296i	0.0240900	+	0.0899051i
$435$		0			0
$436$	0.721429	−	0.721429i	0.0345502	−	0.0345502i
$437$	−2.88127	+	10.7531i	−0.137830	+	0.514389i
$438$		0			0
$439$			15.7759i			0.752941i	0.926429	+	0.376470i	$0.122862\pi$
$439$			15.7759i			0.752941i	−0.926429	+	0.376470i	$0.877138\pi$
$440$	0.253138	−	0.944723i	0.0120679	−	0.0450379i
$441$		0			0
$442$	−0.154751	−	4.82297i	−0.00736076	−	0.229405i
$443$	22.7538	+	13.1369i	1.08107	+	0.624155i	0.931184	−	0.364549i	$-0.118777\pi$
$443$	22.7538	+	13.1369i	1.08107	+	0.624155i	0.149884	+	0.988704i	$0.452110\pi$
$444$		0			0
$445$	0.127877	−	0.221490i	0.00606196	−	0.0104996i
$446$	3.00721			0.142395
$447$		0			0
$448$	0.571855	−	2.13419i	0.0270176	−	0.100831i
$449$	−12.2297	+	3.27694i	−0.577156	+	0.154648i	−0.535576	−	0.844487i	$-0.679906\pi$
$449$	−12.2297	+	3.27694i	−0.577156	+	0.154648i	−0.0415795	+	0.999135i	$0.513239\pi$
$450$		0			0
$451$	10.8324	−	18.7623i	0.510080	−	0.883484i
$452$	3.44964			0.162257
$453$		0			0
$454$	3.08254	−	1.77971i	0.144671	−	0.0835258i
$455$	0.100937	+	0.0946612i	0.00473201	+	0.00443778i
$456$		0			0
$457$	−9.27033	−	9.27033i	−0.433648	−	0.433648i	0.456219	−	0.889867i	$-0.349203\pi$
$457$	−9.27033	−	9.27033i	−0.433648	−	0.433648i	−0.889867	+	0.456219i	$0.849203\pi$
$458$	14.2407	−	8.22188i	0.665425	−	0.384183i
$459$		0			0
$460$	0.305881	+	0.305881i	0.0142618	+	0.0142618i
$461$	32.3624	+	8.67148i	1.50727	+	0.403871i	0.915527	−	0.402257i	$-0.131774\pi$
$461$	32.3624	+	8.67148i	1.50727	+	0.403871i	0.591741	+	0.806128i	$0.298441\pi$
$462$		0			0
$463$	14.9116	+	3.99555i	0.693000	+	0.185689i	0.588093	−	0.808793i	$-0.299879\pi$
$463$	14.9116	+	3.99555i	0.693000	+	0.185689i	0.104907	+	0.994482i	$0.466545\pi$
$464$			2.58146i			0.119841i
$465$		0			0
$466$	−9.59189	+	9.59189i	−0.444336	+	0.444336i
$467$	20.9252			0.968302			0.484151	−	0.874985i	$-0.339129\pi$
$467$	20.9252			0.968302			0.484151	+	0.874985i	$0.339129\pi$
$468$		0			0
$469$	5.60309			0.258727
$470$	−0.318415	+	0.318415i	−0.0146874	+	0.0146874i
$471$		0			0
$472$		−	10.1219i		−	0.465899i
$473$	6.90855	+	1.85114i	0.317656	+	0.0851156i
$474$		0			0
$475$	−14.6028	−	3.91280i	−0.670021	−	0.179531i
$476$	−0.413939	−	0.413939i	−0.0189729	−	0.0189729i
$477$		0			0
$478$	16.6230	−	9.59729i	0.760318	−	0.438970i
$479$	16.0406	+	16.0406i	0.732914	+	0.732914i	0.971196	−	0.238282i	$-0.0765844\pi$
$479$	16.0406	+	16.0406i	0.732914	+	0.732914i	−0.238282	+	0.971196i	$0.576584\pi$
$480$		0			0
$481$	−14.2371	−	7.62176i	−0.649154	−	0.347523i
$482$	−19.6042	+	11.3185i	−0.892949	+	0.515544i
$483$		0			0
$484$	0.966857			0.0439481
$485$	0.649556	−	1.12506i	0.0294948	−	0.0510865i
$486$		0			0
$487$	6.17114	−	1.65355i	0.279641	−	0.0749295i	−0.116273	−	0.993217i	$-0.537095\pi$
$487$	6.17114	−	1.65355i	0.279641	−	0.0749295i	0.395914	+	0.918288i	$0.370428\pi$
$488$	−4.73085	+	17.6558i	−0.214156	+	0.799240i
$489$		0			0
$490$	0.675692			0.0305247
$491$	6.90407	−	11.9582i	0.311576	−	0.539666i	−0.667128	−	0.744943i	$-0.732476\pi$
$491$	6.90407	−	11.9582i	0.311576	−	0.539666i	0.978704	+	0.205278i	$0.0658098\pi$
$492$		0			0
$493$	6.39499	+	3.69215i	0.288016	+	0.166286i
$494$	7.00514	−	7.46958i	0.315176	−	0.336072i
$495$		0			0
$496$	0.731175	−	2.72878i	0.0328307	−	0.122526i
$497$			2.21511i			0.0993612i
$498$		0			0
$499$	−1.01763	+	3.79783i	−0.0455552	+	0.170014i	−0.984956	−	0.172808i	$-0.944716\pi$
$499$	−1.01763	+	3.79783i	−0.0455552	+	0.170014i	0.939400	+	0.342822i	$0.111383\pi$
$500$	−0.831697	+	0.831697i	−0.0371946	+	0.0371946i
$501$		0			0
$502$	1.90450	+	7.10771i	0.0850022	+	0.317232i
$503$	9.04338	+	5.22120i	0.403224	+	0.232802i	0.687874	−	0.725830i	$-0.258544\pi$
$503$	9.04338	+	5.22120i	0.403224	+	0.232802i	−0.284650	+	0.958632i	$0.591877\pi$
$504$		0			0
$505$	0.385652	+	0.103335i	0.0171613	+	0.00459835i
$506$	−5.48176	+	9.49469i	−0.243694	+	0.422090i
$507$		0			0
$508$	7.23985	+	12.5398i	0.321217	+	0.556363i
$509$	8.12088	+	30.3075i	0.359952	+	1.34336i	0.874137	+	0.485679i	$0.161428\pi$
$509$	8.12088	+	30.3075i	0.359952	+	1.34336i	−0.514186	+	0.857679i	$0.671906\pi$
$510$		0			0
$511$	1.84940	−	1.06775i	0.0818128	−	0.0472346i
$512$	−3.96564	+	3.96564i	−0.175258	+	0.175258i
$513$		0			0
$514$	6.39299	+	23.8590i	0.281983	+	1.05237i
$515$	0.680221	−	0.182265i	0.0299741	−	0.00803154i
$516$		0			0
$517$	12.6180	+	7.28502i	0.554940	+	0.320395i
$518$	1.48227	−	0.397174i	0.0651274	−	0.0174508i
$519$		0			0
$520$	−0.320813	−	1.06006i	−0.0140686	−	0.0464865i
$521$			22.8205i			0.999785i	0.866087	+	0.499893i	$0.166627\pi$
$521$			22.8205i			0.999785i	−0.866087	+	0.499893i	$0.833373\pi$
$522$		0			0
$523$	−1.54860	−	2.68225i	−0.0677156	−	0.117287i	0.830180	−	0.557496i	$-0.188238\pi$
$523$	−1.54860	−	2.68225i	−0.0677156	−	0.117287i	−0.897895	+	0.440209i	$0.854904\pi$
$524$	8.71135	+	15.0885i	0.380557	+	0.659144i
$525$		0			0
$526$	13.9970	+	13.9970i	0.610300	+	0.610300i
$527$	−5.71419	−	5.71419i	−0.248914	−	0.248914i
$528$		0			0
$529$	4.75181	+	8.23037i	0.206600	+	0.357842i
$530$	0.644073	+	1.11557i	0.0279767	+	0.0484571i
$531$		0			0
$532$		−	1.24232i		−	0.0538613i
$533$	−0.786773	−	24.5206i	−0.0340789	−	1.06210i
$534$		0			0
$535$	−1.22854	+	0.329187i	−0.0531146	+	0.0142320i
$536$	−38.8368	−	22.4224i	−1.67749	−	0.968501i
$537$		0			0
$538$	3.95629	−	1.06008i	0.170568	−	0.0457035i
$539$	−5.65845	−	21.1176i	−0.243727	−	0.909601i
$540$		0			0
$541$	−5.55366	+	5.55366i	−0.238771	+	0.238771i	−0.816341	−	0.577570i	$-0.804001\pi$
$541$	−5.55366	+	5.55366i	−0.238771	+	0.238771i	0.577570	+	0.816341i	$0.304001\pi$
$542$	11.4726	−	6.62369i	0.492789	−	0.284512i
$543$		0			0
$544$	1.98960	+	7.42529i	0.0853034	+	0.318357i
$545$	0.0477560	+	0.0827159i	0.00204564	+	0.00354316i
$546$		0			0
$547$	−8.77561	+	15.1998i	−0.375218	+	0.649897i	−0.990360	−	0.138520i	$-0.955766\pi$
$547$	−8.77561	+	15.1998i	−0.375218	+	0.649897i	0.615142	+	0.788417i	$0.289099\pi$
$548$	19.9708	+	5.35115i	0.853109	+	0.228590i
$549$		0			0
$550$	−12.8939	−	7.44428i	−0.549797	−	0.317425i
$551$	4.05589	+	15.1368i	0.172787	+	0.644849i
$552$		0			0
$553$	−4.21632	+	4.21632i	−0.179296	+	0.179296i
$554$	−5.96628	+	22.2665i	−0.253483	+	0.946011i
$555$		0			0
$556$			10.1863i			0.431996i
$557$	4.44615	−	16.5933i	0.188390	−	0.703079i	−0.805490	−	0.592609i	$-0.798098\pi$
$557$	4.44615	−	16.5933i	0.188390	−	0.703079i	0.993879	−	0.110470i	$-0.0352356\pi$
$558$		0			0
$559$	7.75196	−	2.34603i	0.327873	−	0.0992266i
$560$	0.0165916	+	0.00957914i	0.000701121	+	0.000404793i
$561$		0			0
$562$	−9.87953	+	17.1119i	−0.416743	+	0.721820i
$563$	−9.32207			−0.392879			−0.196439	−	0.980516i	$-0.562938\pi$
$563$	−9.32207			−0.392879			−0.196439	+	0.980516i	$0.562938\pi$
$564$		0			0
$565$	−0.0835832	+	0.311937i	−0.00351637	+	0.0131233i
$566$	3.64871	−	0.977668i	0.153367	−	0.0410945i
$567$		0			0
$568$	8.86441	−	15.3536i	0.371942	−	0.644223i
$569$	26.0138			1.09056			0.545278	−	0.838255i	$-0.316424\pi$
$569$	26.0138			1.09056			0.545278	+	0.838255i	$0.316424\pi$
$570$		0			0
$571$	−2.90676	+	1.67822i	−0.121644	+	0.0702313i	−0.559587	−	0.828771i	$-0.689040\pi$
$571$	−2.90676	+	1.67822i	−0.121644	+	0.0702313i	0.437943	+	0.899003i	$0.355707\pi$
$572$	−10.9380	+	6.79182i	−0.457340	+	0.283980i
$573$		0			0
$574$	1.64848	+	1.64848i	0.0688060	+	0.0688060i
$575$	15.8727	−	9.16411i	0.661937	−	0.382170i
$576$		0			0
$577$	19.0194	+	19.0194i	0.791788	+	0.791788i	0.981785	−	0.189997i	$-0.0608478\pi$
$577$	19.0194	+	19.0194i	0.791788	+	0.791788i	−0.189997	+	0.981785i	$0.560848\pi$
$578$	13.5449	+	3.62933i	0.563392	+	0.150960i
$579$		0			0
$580$	0.588184	+	0.157603i	0.0244230	+	0.00654412i
$581$		−	6.06634i		−	0.251674i
$582$		0			0
$583$	29.4715	−	29.4715i	1.22059	−	1.22059i
$584$	−17.0917			−0.707260
$585$		0			0
$586$	10.8233			0.447107
$587$	7.56353	−	7.56353i	0.312180	−	0.312180i	−0.533573	−	0.845754i	$-0.679151\pi$
$587$	7.56353	−	7.56353i	0.312180	−	0.312180i	0.845754	+	0.533573i	$0.179151\pi$
$588$		0			0
$589$		−	17.1494i		−	0.706630i
$590$	0.328848	+	0.0881146i	0.0135385	+	0.00362762i
$591$		0			0
$592$	−2.15957	−	0.578656i	−0.0887580	−	0.0237826i
$593$	−11.0116	−	11.0116i	−0.452191	−	0.452191i	0.443890	−	0.896081i	$-0.353598\pi$
$593$	−11.0116	−	11.0116i	−0.452191	−	0.452191i	−0.896081	+	0.443890i	$0.853598\pi$
$594$		0			0
$595$	0.0474604	−	0.0274013i	0.00194569	−	0.00112334i
$596$	−9.54955	−	9.54955i	−0.391165	−	0.391165i
$597$		0			0
$598$	0.398147	+	12.4086i	0.0162814	+	0.507427i
$599$	18.9127	−	10.9193i	0.772752	−	0.446149i	−0.0611031	−	0.998131i	$-0.519462\pi$
$599$	18.9127	−	10.9193i	0.772752	−	0.446149i	0.833856	+	0.551983i	$0.186129\pi$
$600$		0			0
$601$	12.2925			0.501420			0.250710	−	0.968062i	$-0.419336\pi$
$601$	12.2925			0.501420			0.250710	+	0.968062i	$0.419336\pi$
$602$	−0.384817	+	0.666523i	−0.0156840	+	0.0271655i
$603$		0			0
$604$	0.0457096	−	0.0122479i	0.00185990	−	0.000498358i
$605$	−0.0234265	+	0.0874290i	−0.000952424	+	0.00355449i
$606$		0			0
$607$	25.1603			1.02123			0.510613	−	0.859811i	$-0.329418\pi$
$607$	25.1603			1.02123			0.510613	+	0.859811i	$0.329418\pi$
$608$	−8.15681	+	14.1280i	−0.330802	+	0.572966i
$609$		0			0
$610$	−0.532430	−	0.307399i	−0.0215575	−	0.0124462i
$611$	16.4905	−	0.529120i	0.667136	−	0.0214059i
$612$		0			0
$613$	−0.567750	+	2.11887i	−0.0229312	+	0.0855804i	−0.976443	−	0.215775i	$-0.930772\pi$
$613$	−0.567750	+	2.11887i	−0.0229312	+	0.0855804i	0.953512	+	0.301355i	$0.0974390\pi$
$614$			23.7517i			0.958542i
$615$		0			0
$616$	0.881355	−	3.28926i	0.0355108	−	0.132528i
$617$	−7.90933	+	7.90933i	−0.318417	+	0.318417i	−0.848159	−	0.529742i	$-0.822289\pi$
$617$	−7.90933	+	7.90933i	−0.318417	+	0.318417i	0.529742	+	0.848159i	$0.322289\pi$
$618$		0			0
$619$	−2.85556	−	10.6571i	−0.114775	−	0.428345i	0.884495	−	0.466549i	$-0.154503\pi$
$619$	−2.85556	−	10.6571i	−0.114775	−	0.428345i	−0.999270	+	0.0382041i	$0.987836\pi$
$620$	−0.577112	−	0.333196i	−0.0231774	−	0.0133815i
$621$		0			0
$622$	−20.1530	−	5.39998i	−0.808061	−	0.216519i
$623$	0.445233	−	0.771166i	0.0178379	−	0.0308961i
$624$		0			0
$625$	12.4174	+	21.5075i	0.496695	+	0.860302i
$626$	−2.08651	−	7.78697i	−0.0833938	−	0.311230i
$627$		0			0
$628$	13.5104	−	7.80023i	0.539123	−	0.311263i
$629$	−4.52224	+	4.52224i	−0.180314	+	0.180314i
$630$		0			0
$631$	−0.654527	−	2.44273i	−0.0260563	−	0.0972435i	0.951673	−	0.307113i	$-0.0993629\pi$
$631$	−0.654527	−	2.44273i	−0.0260563	−	0.0972435i	−0.977729	+	0.209869i	$0.932696\pi$
$632$	46.0974	−	12.3518i	1.83366	−	0.491327i
$633$		0			0
$634$	−25.5611	−	14.7577i	−1.01516	−	0.586104i
$635$	−1.30934	+	0.350837i	−0.0519596	+	0.0139225i
$636$		0			0
$637$	−18.0583	−	16.9355i	−0.715495	−	0.671008i
$638$			15.4330i			0.611000i
$639$		0			0
$640$	0.267834	+	0.463903i	0.0105871	+	0.0183374i
$641$	−8.99758	−	15.5843i	−0.355383	−	0.615541i	0.631801	−	0.775131i	$-0.282316\pi$
$641$	−8.99758	−	15.5843i	−0.355383	−	0.615541i	−0.987183	+	0.159590i	$0.948983\pi$
$642$		0			0
$643$	−25.2949	−	25.2949i	−0.997532	−	0.997532i	0.00246501	−	0.999997i	$-0.499215\pi$
$643$	−25.2949	−	25.2949i	−0.997532	−	0.997532i	−0.999997	+	0.00246501i	$0.999215\pi$
$644$	1.06499	+	1.06499i	0.0419666	+	0.0419666i
$645$		0			0
$646$	−2.02776	−	3.51218i	−0.0797811	−	0.138185i
$647$	−10.1566	−	17.5918i	−0.399298	−	0.691605i	0.594341	−	0.804213i	$-0.297413\pi$
$647$	−10.1566	−	17.5918i	−0.399298	−	0.691605i	−0.993639	+	0.112608i	$0.964079\pi$
$648$		0			0
$649$		−	11.0155i		−	0.432396i
$650$	−16.8511	+	0.540687i	−0.660953	+	0.0212075i
$651$		0			0
$652$	−0.871165	+	0.233428i	−0.0341175	+	0.00914175i
$653$	−25.3293	−	14.6239i	−0.991213	−	0.572277i	−0.0855762	−	0.996332i	$-0.527273\pi$
$653$	−25.3293	−	14.6239i	−0.991213	−	0.572277i	−0.905637	+	0.424055i	$0.860606\pi$
$654$		0			0
$655$	−1.57546	+	0.422144i	−0.0615585	+	0.0164945i
$656$	−0.879090	−	3.28081i	−0.0343227	−	0.128094i
$657$		0			0
$658$	−1.10863	+	1.10863i	−0.0432189	+	0.0432189i
$659$	−36.4402	+	21.0388i	−1.41951	+	0.819554i	−0.996256	−	0.0864566i	$-0.972446\pi$
$659$	−36.4402	+	21.0388i	−1.41951	+	0.819554i	−0.423254	+	0.906011i	$0.639112\pi$
$660$		0			0
$661$	−4.83701	−	18.0520i	−0.188138	−	0.702141i	−0.993937	−	0.109951i	$-0.964930\pi$
$661$	−4.83701	−	18.0520i	−0.188138	−	0.702141i	0.805799	−	0.592189i	$-0.201736\pi$
$662$	7.33278	+	12.7007i	0.284997	+	0.493628i
$663$		0			0
$664$	−24.2762	+	42.0477i	−0.942101	+	1.63177i
$665$	0.112338	+	0.0301008i	0.00435627	+	0.00116726i
$666$		0			0
$667$	−16.4532	−	9.49924i	−0.637069	−	0.367812i
$668$	−4.50375	−	16.8082i	−0.174255	−	0.650330i
$669$		0			0
$670$	1.06656	−	1.06656i	0.0412049	−	0.0412049i
$671$	−5.14850	+	19.2145i	−0.198756	+	0.741767i
$672$		0			0
$673$		−	6.01382i		−	0.231816i	−0.993260	−	0.115908i	$-0.963022\pi$
$673$		−	6.01382i		−	0.231816i	0.993260	−	0.115908i	$-0.0369777\pi$
$674$	1.51965	−	5.67142i	0.0585349	−	0.218455i
$675$		0			0
$676$	−6.46542	+	13.0677i	−0.248670	+	0.502605i
$677$	−23.1275	−	13.3527i	−0.888863	−	0.513185i	−0.0152925	−	0.999883i	$-0.504868\pi$
$677$	−23.1275	−	13.3527i	−0.888863	−	0.513185i	−0.873570	+	0.486698i	$0.838201\pi$
$678$		0			0
$679$	2.26157	−	3.91715i	0.0867911	−	0.150327i
$680$	−0.438617			−0.0168202
$681$		0			0
$682$	4.37127	−	16.3138i	0.167385	−	0.624688i
$683$	−29.2534	+	7.83841i	−1.11935	+	0.299929i	−0.770620	−	0.637295i	$-0.780053\pi$
$683$	−29.2534	+	7.83841i	−1.11935	+	0.299929i	−0.348729	+	0.937224i	$0.613387\pi$
$684$		0			0
$685$	−0.967766	+	1.67622i	−0.0369764	+	0.0640451i
$686$	4.75092			0.181391
$687$		0			0
$688$	0.971079	−	0.560653i	0.0370220	−	0.0213747i
$689$	10.7472	−	45.9572i	0.409436	−	1.75083i
$690$		0			0
$691$	30.2032	+	30.2032i	1.14898	+	1.14898i	0.986753	+	0.162231i	$0.0518689\pi$
$691$	30.2032	+	30.2032i	1.14898	+	1.14898i	0.162231	+	0.986753i	$0.448131\pi$
$692$	14.8966	−	8.60054i	0.566283	−	0.326944i
$693$		0			0
$694$	−12.0886	−	12.0886i	−0.458879	−	0.458879i
$695$	−0.921108	−	0.246810i	−0.0349396	−	0.00936205i
$696$		0			0
$697$	−9.38480	−	2.51465i	−0.355475	−	0.0952492i
$698$		−	7.51395i		−	0.284407i
$699$		0			0
$700$	−1.44627	+	1.44627i	−0.0546638	+	0.0546638i
$701$	23.1973			0.876151			0.438075	−	0.898938i	$-0.355660\pi$
$701$	23.1973			0.876151			0.438075	+	0.898938i	$0.355660\pi$
$702$		0			0
$703$	−13.5722			−0.511884
$704$	−13.6082	+	13.6082i	−0.512879	+	0.512879i
$705$		0			0
$706$			16.1889i			0.609278i
$707$	1.34273	+	0.359784i	0.0504986	+	0.0135311i
$708$		0			0
$709$	8.81969	+	2.36323i	0.331230	+	0.0887529i	0.420602	−	0.907245i	$-0.361819\pi$
$709$	8.81969	+	2.36323i	0.331230	+	0.0887529i	−0.0893711	+	0.995998i	$0.528486\pi$
$710$	0.421651	+	0.421651i	0.0158243	+	0.0158243i
$711$		0			0
$712$	−6.17209	+	3.56346i	−0.231309	+	0.133546i
$713$	14.7016	+	14.7016i	0.550578	+	0.550578i
$714$		0			0
$715$	−0.349134	−	1.15364i	−0.0130569	−	0.0431437i
$716$	−18.1361	+	10.4709i	−0.677776	+	0.391314i
$717$		0			0
$718$	−29.0092			−1.08261
$719$	7.26683	−	12.5865i	0.271007	−	0.469398i	−0.698113	−	0.715988i	$-0.745977\pi$
$719$	7.26683	−	12.5865i	0.271007	−	0.469398i	0.969120	+	0.246590i	$0.0793100\pi$
$720$		0			0
$721$	2.36834	−	0.634594i	0.0882015	−	0.0236335i
$722$	−2.38158	+	8.88819i	−0.0886334	+	0.330784i
$723$		0			0
$724$	15.9478			0.592695
$725$	12.9001	−	22.3436i	0.479096	−	0.829819i
$726$		0			0
$727$	−23.7883	−	13.7342i	−0.882259	−	0.509372i	−0.0108564	−	0.999941i	$-0.503456\pi$
$727$	−23.7883	−	13.7342i	−0.882259	−	0.509372i	−0.871403	+	0.490569i	$0.836789\pi$
$728$	−1.11698	−	3.69082i	−0.0413980	−	0.136791i
$729$		0			0
$730$	0.148789	−	0.555288i	0.00550693	−	0.0205521i
$731$		−	3.20751i		−	0.118634i
$732$		0			0
$733$	9.56277	−	35.6888i	0.353209	−	1.31819i	−0.529514	−	0.848301i	$-0.677626\pi$
$733$	9.56277	−	35.6888i	0.353209	−	1.31819i	0.882723	−	0.469893i	$-0.155708\pi$
$734$	−0.868713	+	0.868713i	−0.0320648	+	0.0320648i
$735$		0			0
$736$	−5.11889	−	19.1039i	−0.188685	−	0.704181i
$737$	−42.2653	−	24.4019i	−1.55686	−	0.898856i
$738$		0			0
$739$	−6.91898	−	1.85394i	−0.254519	−	0.0681981i	0.129304	−	0.991605i	$-0.458726\pi$
$739$	−6.91898	−	1.85394i	−0.254519	−	0.0681981i	−0.383822	+	0.923407i	$0.625393\pi$
$740$	−0.263693	+	0.456730i	−0.00969355	+	0.0167897i
$741$		0			0
$742$	2.24248	+	3.88409i	0.0823241	+	0.142589i
$743$	4.09506	+	15.2830i	0.150233	+	0.560678i	0.999467	+	0.0326604i	$0.0103980\pi$
$743$	4.09506	+	15.2830i	0.150233	+	0.560678i	−0.849233	+	0.528018i	$0.822935\pi$
$744$		0			0
$745$	1.09491	−	0.632146i	0.0401144	−	0.0231600i
$746$	−19.1015	+	19.1015i	−0.699355	+	0.699355i
$747$		0			0
$748$	1.31970	+	4.92518i	0.0482529	+	0.180082i
$749$	−4.27745	+	1.14614i	−0.156294	+	0.0418790i
$750$		0			0
$751$	−32.7770	−	18.9238i	−1.19605	−	0.690539i	−0.236377	−	0.971661i	$-0.575960\pi$
$751$	−32.7770	−	18.9238i	−1.19605	−	0.690539i	−0.959672	+	0.281123i	$0.909293\pi$
$752$	2.20641	−	0.591204i	0.0804593	−	0.0215590i
$753$		0			0
$754$	9.21902	+	14.8469i	0.335737	+	0.540692i
$755$			0.00443010i			0.000161228i
$756$		0			0
$757$	8.84072	+	15.3126i	0.321322	+	0.556545i	0.980761	−	0.195212i	$-0.0625396\pi$
$757$	8.84072	+	15.3126i	0.321322	+	0.556545i	−0.659439	+	0.751758i	$0.729206\pi$
$758$	8.06476	+	13.9686i	0.292925	+	0.507361i
$759$		0			0
$760$	−0.658190	−	0.658190i	−0.0238751	−	0.0238751i
$761$	33.1394	+	33.1394i	1.20130	+	1.20130i	0.973771	+	0.227530i	$0.0730651\pi$
$761$	33.1394	+	33.1394i	1.20130	+	1.20130i	0.227530	+	0.973771i	$0.426935\pi$
$762$		0			0
$763$	0.166273	+	0.287993i	0.00601949	+	0.0104261i
$764$	−4.11355	−	7.12488i	−0.148823	−	0.257769i
$765$		0			0
$766$			30.0516i			1.08581i
$767$	−6.58017	−	10.5971i	−0.237596	−	0.382640i
$768$		0			0
$769$	18.4717	−	4.94948i	0.666107	−	0.178483i	0.0901064	−	0.995932i	$-0.471279\pi$
$769$	18.4717	−	4.94948i	0.666107	−	0.178483i	0.576001	+	0.817449i	$0.304613\pi$
$770$	0.0991914	+	0.0572682i	0.00357461	+	0.00206380i
$771$		0			0
$772$	−23.1879	+	6.21318i	−0.834551	+	0.223617i
$773$	−5.12420	−	19.1238i	−0.184305	−	0.687834i	−0.994778	−	0.102059i	$-0.967457\pi$
$773$	−5.12420	−	19.1238i	−0.184305	−	0.687834i	0.810474	−	0.585775i	$-0.199210\pi$
$774$		0			0
$775$	−19.9649	+	19.9649i	−0.717160	+	0.717160i
$776$	−31.3513	+	18.1007i	−1.12545	+	0.649776i
$777$		0			0
$778$	−3.89016	−	14.5183i	−0.139469	−	0.520505i
$779$	−10.3094	−	17.8563i	−0.369371	−	0.639770i
$780$		0			0
$781$	9.64697	−	16.7090i	0.345196	−	0.597897i
$782$	4.74918	+	1.27254i	0.169830	+	0.0455059i
$783$		0			0
$784$	−2.96833	−	1.71377i	−0.106012	−	0.0612060i
$785$	0.377992	+	1.41069i	0.0134911	+	0.0503495i
$786$		0			0
$787$	4.56589	−	4.56589i	0.162757	−	0.162757i	−0.621030	−	0.783787i	$-0.713286\pi$
$787$	4.56589	−	4.56589i	0.162757	−	0.162757i	0.783787	+	0.621030i	$0.213286\pi$
$788$	1.12579	−	4.20150i	0.0401046	−	0.149672i
$789$		0			0
$790$			1.60517i			0.0571095i
$791$	−0.291013	+	1.08608i	−0.0103472	+	0.0386164i
$792$		0			0
$793$	6.52492	+	21.5602i	0.231707	+	0.765625i
$794$	−24.5124	−	14.1522i	−0.869913	−	0.502244i
$795$		0			0
$796$	−5.74349	+	9.94802i	−0.203573	+	0.352598i
$797$	49.4625			1.75205			0.876026	−	0.482263i	$-0.160185\pi$
$797$	49.4625			1.75205			0.876026	+	0.482263i	$0.160185\pi$
$798$		0			0
$799$	1.69115	−	6.31146i	0.0598286	−	0.223283i
$800$	25.9433	−	6.95150i	0.917235	−	0.245772i
$801$		0			0
$802$	−5.31907	+	9.21290i	−0.187823	+	0.325319i
$803$	−18.6006			−0.656401
$804$		0			0
$805$	−0.122107	+	0.0704986i	−0.00430371	+	0.00248475i
$806$	−5.53990	−	18.3054i	−0.195135	−	0.644781i
$807$		0			0
$808$	−7.86711	−	7.86711i	−0.276764	−	0.276764i
$809$	−42.4000	+	24.4797i	−1.49071	+	0.860659i	−0.999943	−	0.0106348i	$-0.996615\pi$
$809$	−42.4000	+	24.4797i	−1.49071	+	0.860659i	−0.490762	+	0.871294i	$0.663281\pi$
$810$		0			0
$811$	2.24360	+	2.24360i	0.0787834	+	0.0787834i	0.745400	−	0.666617i	$-0.232258\pi$
$811$	2.24360	+	2.24360i	0.0787834	+	0.0787834i	−0.666617	+	0.745400i	$0.732258\pi$
$812$	2.04789	+	0.548731i	0.0718669	+	0.0192567i
$813$		0			0
$814$	−12.9109	−	3.45945i	−0.452525	−	0.121254i
$815$		−	0.0844318i		−	0.00295752i
$816$		0			0
$817$	4.81320	−	4.81320i	0.168393	−	0.168393i
$818$	11.0443			0.386156
$819$		0			0
$820$	−0.801201			−0.0279791
$821$	−8.81907	+	8.81907i	−0.307788	+	0.307788i	−0.844051	−	0.536263i	$-0.819835\pi$
$821$	−8.81907	+	8.81907i	−0.307788	+	0.307788i	0.536263	+	0.844051i	$0.319835\pi$
$822$		0			0
$823$			12.4797i			0.435016i	0.976059	+	0.217508i	$0.0697928\pi$
$823$			12.4797i			0.435016i	−0.976059	+	0.217508i	$0.930207\pi$
$824$	−18.9552	−	5.07903i	−0.660336	−	0.176936i
$825$		0			0
$826$	1.14496	+	0.306790i	0.0398381	+	0.0106746i
$827$	9.01542	+	9.01542i	0.313497	+	0.313497i	0.846263	−	0.532766i	$-0.178847\pi$
$827$	9.01542	+	9.01542i	0.313497	+	0.313497i	−0.532766	+	0.846263i	$0.678847\pi$
$828$		0			0
$829$	−12.1868	+	7.03605i	−0.423265	+	0.244372i	−0.696473	−	0.717583i	$-0.745249\pi$
$829$	−12.1868	+	7.03605i	−0.423265	+	0.244372i	0.273208	+	0.961955i	$0.411915\pi$
$830$	−1.15474	−	1.15474i	−0.0400817	−	0.0400817i
$831$		0			0
$832$	−4.96242	+	21.2203i	−0.172041	+	0.735682i
$833$	−8.49097	+	4.90226i	−0.294195	+	0.169853i
$834$		0			0
$835$	1.62902			0.0563747
$836$	−5.41039	+	9.37107i	−0.187122	+	0.324105i
$837$		0			0
$838$	2.61136	−	0.699711i	0.0902079	−	0.0241711i
$839$	13.5515	−	50.5750i	0.467851	−	1.74604i	−0.179410	−	0.983774i	$-0.557419\pi$
$839$	13.5515	−	50.5750i	0.467851	−	1.74604i	0.647260	−	0.762269i	$-0.275915\pi$
$840$		0			0
$841$	2.25637			0.0778057
$842$	1.17507	−	2.03529i	0.0404957	−	0.0701407i
$843$		0			0
$844$	17.5516	+	10.1334i	0.604152	+	0.348808i
$845$	−1.02501	−	0.901267i	−0.0352614	−	0.0310045i
$846$		0			0
$847$	−0.0815646	+	0.304403i	−0.00280259	+	0.0104594i
$848$		−	6.53429i		−	0.224388i
$849$		0			0
$850$	−1.72812	+	6.44944i	−0.0592741	+	0.221214i
$851$	11.6349	−	11.6349i	0.398840	−	0.398840i
$852$		0			0
$853$	3.77435	+	14.0861i	0.129231	+	0.482297i	0.999955	−	0.00947475i	$-0.00301595\pi$
$853$	3.77435	+	14.0861i	0.129231	+	0.482297i	−0.870724	+	0.491772i	$0.836349\pi$
$854$	−1.85377	−	1.07028i	−0.0634348	−	0.0366241i
$855$		0			0
$856$	34.2349	+	9.17322i	1.17013	+	0.313534i
$857$	6.89566	−	11.9436i	0.235551	−	0.407986i	−0.723882	−	0.689924i	$-0.757644\pi$
$857$	6.89566	−	11.9436i	0.235551	−	0.407986i	0.959433	+	0.281938i	$0.0909772\pi$
$858$		0			0
$859$	14.9164	+	25.8359i	0.508940	+	0.881510i	0.999946	+	0.0103542i	$0.00329591\pi$
$859$	14.9164	+	25.8359i	0.508940	+	0.881510i	−0.491006	+	0.871156i	$0.663371\pi$
$860$	−0.0684581	−	0.255489i	−0.00233440	−	0.00871210i
$861$		0			0
$862$	12.5571	−	7.24983i	0.427696	−	0.246930i
$863$	−33.0412	+	33.0412i	−1.12473	+	1.12473i	−0.133714	+	0.991020i	$0.542690\pi$
$863$	−33.0412	+	33.0412i	−1.12473	+	1.12473i	−0.991020	+	0.133714i	$0.957310\pi$
$864$		0			0
$865$	0.416775	+	1.55542i	0.0141708	+	0.0528860i
$866$	4.74247	−	1.27074i	0.161156	−	0.0431816i
$867$		0			0
$868$	−2.00934	−	1.16009i	−0.0682015	−	0.0393761i
$869$	50.1670	−	13.4422i	1.70180	−	0.455996i
$870$		0			0
$871$	−55.2367	+	1.77234i	−1.87163	+	0.0600534i
$872$		−	2.66156i		−	0.0901319i
$873$		0			0
$874$	5.21706	+	9.03621i	0.176470	+	0.305654i
$875$	−0.191687	−	0.332012i	−0.00648021	−	0.0112241i
$876$		0			0
$877$	−7.18363	−	7.18363i	−0.242574	−	0.242574i	0.575340	−	0.817914i	$-0.304870\pi$
$877$	−7.18363	−	7.18363i	−0.242574	−	0.242574i	−0.817914	+	0.575340i	$0.804870\pi$
$878$	10.4555	+	10.4555i	0.352856	+	0.352856i
$879$		0			0
$880$	−0.0834359	−	0.144515i	−0.00281262	−	0.00487160i
$881$	2.67563	+	4.63432i	0.0901441	+	0.156134i	0.907572	−	0.419897i	$-0.137934\pi$
$881$	2.67563	+	4.63432i	0.0901441	+	0.156134i	−0.817428	+	0.576031i	$0.804601\pi$
$882$		0			0
$883$			11.6579i			0.392321i	0.980572	+	0.196161i	$0.0628474\pi$
$883$			11.6579i			0.392321i	−0.980572	+	0.196161i	$0.937153\pi$
$884$	4.21166	+	3.94979i	0.141653	+	0.132846i
$885$		0			0
$886$	23.7868	−	6.37364i	0.799132	−	0.214127i
$887$	−8.35407	−	4.82322i	−0.280502	−	0.161948i	0.353149	−	0.935567i	$-0.385111\pi$
$887$	−8.35407	−	4.82322i	−0.280502	−	0.161948i	−0.633651	+	0.773619i	$0.718444\pi$
$888$		0			0
$889$	−4.55876	+	1.22152i	−0.152896	+	0.0409683i
$890$	−0.0620422	−	0.231545i	−0.00207966	−	0.00776139i
$891$		0			0
$892$	−2.54440	+	2.54440i	−0.0851929	+	0.0851929i
$893$	12.0087	−	6.93325i	0.401857	−	0.232012i
$894$		0			0
$895$	−0.507409	−	1.89367i	−0.0169608	−	0.0632986i
$896$	0.932524	+	1.61518i	0.0311534	+	0.0539593i
$897$		0			0
$898$	−5.93349	+	10.2771i	−0.198003	+	0.342951i
$899$	28.2699	+	7.57490i	0.942854	+	0.252637i
$900$		0			0
$901$	−16.1873	−	9.34572i	−0.539276	−	0.311351i
$902$	−5.25557	−	19.6141i	−0.174991	−	0.653077i
$903$		0			0
$904$	6.36336	−	6.36336i	0.211642	−	0.211642i
$905$	−0.386408	+	1.44209i	−0.0128446	+	0.0479368i
$906$		0			0
$907$		−	43.6107i		−	1.44807i	−0.689764	−	0.724035i	$-0.742286\pi$
$907$		−	43.6107i		−	1.44807i	0.689764	−	0.724035i	$-0.257714\pi$
$908$	−1.10233	+	4.11396i	−0.0365821	+	0.136526i
$909$		0			0
$910$	0.129634	−	0.00415946i	0.00429731	−	0.000137885i
$911$	−15.2019	−	8.77681i	−0.503661	−	0.290789i	0.226563	−	0.973996i	$-0.427251\pi$
$911$	−15.2019	−	8.77681i	−0.503661	−	0.290789i	−0.730224	+	0.683208i	$0.760584\pi$
$912$		0			0
$913$	−26.4194	+	45.7597i	−0.874354	+	1.51443i
$914$	−12.2879			−0.406448
$915$		0			0
$916$	−5.09255	+	19.0056i	−0.168262	+	0.627964i
$917$	−5.48532	+	1.46979i	−0.181141	+	0.0485367i
$918$		0			0
$919$	−2.44511	+	4.23505i	−0.0806566	+	0.139701i	−0.903532	−	0.428520i	$-0.859035\pi$
$919$	−2.44511	+	4.23505i	−0.0806566	+	0.139701i	0.822876	+	0.568222i	$0.192368\pi$
$920$	1.12848			0.0372050
$921$		0			0
$922$	27.1954	−	15.7013i	0.895632	−	0.517094i
$923$	−0.700671	−	21.8371i	−0.0230629	−	0.718777i
$924$		0			0
$925$	15.8003	+	15.8003i	0.519512	+	0.519512i
$926$	12.5308	−	7.23465i	0.411787	−	0.237745i
$927$		0			0
$928$	−19.6864	−	19.6864i	−0.646237	−	0.646237i
$929$	31.5303	+	8.44852i	1.03448	+	0.277187i	0.735822	−	0.677175i	$-0.236796\pi$
$929$	31.5303	+	8.44852i	1.03448	+	0.277187i	0.298653	+	0.954362i	$0.403463\pi$
$930$		0			0
$931$	−20.0979	−	5.38522i	−0.658682	−	0.176493i
$932$		−	16.2314i		−	0.531678i
$933$		0			0
$934$	13.8682	−	13.8682i	0.453783	−	0.453783i
$935$	−0.477339			−0.0156107
$936$		0			0
$937$	35.2389			1.15121			0.575603	−	0.817729i	$-0.304767\pi$
$937$	35.2389			1.15121			0.575603	+	0.817729i	$0.304767\pi$
$938$	3.71347	−	3.71347i	0.121249	−	0.121249i
$939$		0			0
$940$		−	0.538823i		−	0.0175745i
$941$	23.6245	+	6.33017i	0.770137	+	0.206358i	0.622432	−	0.782674i	$-0.286145\pi$
$941$	23.6245	+	6.33017i	0.770137	+	0.206358i	0.147705	+	0.989031i	$0.452811\pi$
$942$		0			0
$943$	24.1454	+	6.46975i	0.786283	+	0.210684i
$944$	−1.22115	−	1.22115i	−0.0397451	−	0.0397451i
$945$		0			0
$946$	5.80552	−	3.35182i	0.188754	−	0.108977i
$947$	−2.70978	−	2.70978i	−0.0880561	−	0.0880561i	0.661707	−	0.749763i	$-0.269832\pi$
$947$	−2.70978	−	2.70978i	−0.0880561	−	0.0880561i	−0.749763	+	0.661707i	$0.769832\pi$
$948$		0			0
$949$	−17.8942	+	11.1112i	−0.580869	+	0.360684i
$950$	−12.2713	+	7.08482i	−0.398132	+	0.229862i
$951$		0			0
$952$	−1.52714			−0.0494950
$953$	−12.0041	+	20.7918i	−0.388852	+	0.673512i	−0.992295	−	0.123894i	$-0.960462\pi$
$953$	−12.0041	+	20.7918i	−0.388852	+	0.673512i	0.603443	+	0.797406i	$0.293795\pi$
$954$		0			0
$955$	0.743943	−	0.199339i	0.0240734	−	0.00645046i
$956$	−5.94446	+	22.1850i	−0.192257	+	0.717515i
$957$		0			0
$958$	21.2619			0.686942
$959$	−3.36949	+	5.83613i	−0.108806	+	0.188458i
$960$		0			0
$961$	−0.890953	−	0.514392i	−0.0287404	−	0.0165933i
$962$	−14.4870	+	4.38431i	−0.467080	+	0.141356i
$963$		0			0
$964$	7.01057	−	26.1638i	0.225795	−	0.842679i
$965$		−	2.24733i		−	0.0723441i
$966$		0			0
$967$	−2.77473	+	10.3554i	−0.0892294	+	0.333009i	−0.996081	−	0.0884405i	$-0.971812\pi$
$967$	−2.77473	+	10.3554i	−0.0892294	+	0.333009i	0.906852	+	0.421449i	$0.138478\pi$
$968$	1.78351	−	1.78351i	0.0573241	−	0.0573241i
$969$		0			0
$970$	−0.315145	−	1.17614i	−0.0101187	−	0.0377634i
$971$	46.2535	+	26.7045i	1.48435	+	0.856988i	0.999842	−	0.0178003i	$-0.00566631\pi$
$971$	46.2535	+	26.7045i	1.48435	+	0.856988i	0.484505	+	0.874788i	$0.339000\pi$
$972$		0			0
$973$	−3.20704	−	0.859324i	−0.102813	−	0.0275487i
$974$	2.99405	−	5.18584i	0.0959355	−	0.166165i
$975$		0			0
$976$	1.55932	+	2.70082i	0.0499126	+	0.0864512i
$977$	9.64944	+	36.0122i	0.308713	+	1.15213i	0.929702	+	0.368313i	$0.120064\pi$
$977$	9.64944	+	36.0122i	0.308713	+	1.15213i	−0.620989	+	0.783819i	$0.713269\pi$
$978$		0			0
$979$	−6.71698	+	3.87805i	−0.214676	+	0.123943i
$980$	−0.571704	+	0.571704i	−0.0182624	+	0.0182624i
$981$		0			0
$982$	−3.34964	−	12.5010i	−0.106891	−	0.398924i
$983$	−15.8187	+	4.23860i	−0.504537	+	0.135190i	−0.502105	−	0.864807i	$-0.667441\pi$
$983$	−15.8187	+	4.23860i	−0.504537	+	0.135190i	−0.00243220	+	0.999997i	$0.500774\pi$
$984$		0			0
$985$	0.352648	+	0.203601i	0.0112363	+	0.00648727i
$986$	6.68529	−	1.79132i	0.212903	−	0.0570472i
$987$		0			0
$988$	0.392963	+	12.2471i	0.0125018	+	0.389632i
$989$			8.25236i			0.262410i
$990$		0			0
$991$	−25.9576	−	44.9599i	−0.824571	−	1.42820i	−0.902247	−	0.431220i	$-0.858083\pi$
$991$	−25.9576	−	44.9599i	−0.824571	−	1.42820i	0.0776754	−	0.996979i	$-0.475250\pi$
$992$	15.2339	+	26.3859i	0.483676	+	0.837752i
$993$		0			0
$994$	1.46807	+	1.46807i	0.0465644	+	0.0465644i
$995$	−0.760397	−	0.760397i	−0.0241062	−	0.0241062i
$996$		0			0
$997$	−0.731834	−	1.26757i	−0.0231774	−	0.0401445i	0.854204	−	0.519938i	$-0.174045\pi$
$997$	−0.731834	−	1.26757i	−0.0231774	−	0.0401445i	−0.877381	+	0.479793i	$0.840712\pi$
$998$	1.84259	+	3.19146i	0.0583262	+	0.101024i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.ba.a.89.8		48
3.2	odd	2		117.2.x.a.11.5	✓	48
9.4	even	3		117.2.bc.a.50.8	yes	48
9.5	odd	6		351.2.bf.a.206.5		48
13.6	odd	12		351.2.bf.a.305.5		48
39.32	even	12		117.2.bc.a.110.8	yes	48
117.32	even	12	inner	351.2.ba.a.71.8		48
117.58	odd	12		117.2.x.a.32.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.5	✓	48	3.2	odd	2
117.2.x.a.32.5	yes	48	117.58	odd	12
117.2.bc.a.50.8	yes	48	9.4	even	3
117.2.bc.a.110.8	yes	48	39.32	even	12
351.2.ba.a.71.8		48	117.32	even	12	inner
351.2.ba.a.89.8		48	1.1	even	1	trivial
351.2.bf.a.206.5		48	9.5	odd	6
351.2.bf.a.305.5		48	13.6	odd	12

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.ba (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.662754 - 0.662754i) q^{2} +1.12151i q^{4} +(-0.101414 - 0.0271738i) q^{5} +(-0.353095 - 0.0946115i) q^{7} +(2.06880 + 2.06880i) q^{8} +(-0.0852221 + 0.0492030i) q^{10} +(2.25143 + 2.25143i) q^{11} +(3.51083 + 0.821016i) q^{13} +(-0.296719 + 0.171311i) q^{14} +0.499177 q^{16} +(0.713952 - 1.23660i) q^{17} +(2.92701 - 0.784289i) q^{19} +(0.0304758 - 0.113737i) q^{20} +2.98429 q^{22} +(-1.83687 + 3.18155i) q^{23} +(-4.32058 - 2.49449i) q^{25} +(2.87095 - 1.78269i) q^{26} +(0.106108 - 0.396001i) q^{28} +5.17142i q^{29} +(1.46476 - 5.46656i) q^{31} +(-3.80676 + 3.80676i) q^{32} +(-0.346388 - 1.29274i) q^{34} +(0.0332378 + 0.0191899i) q^{35} +(-4.32627 - 1.15922i) q^{37} +(1.42009 - 2.45967i) q^{38} +(-0.153588 - 0.266022i) q^{40} +(-1.76108 - 6.57243i) q^{41} +(1.94536 - 1.12315i) q^{43} +(-2.52501 + 2.52501i) q^{44} +(0.891194 + 3.32598i) q^{46} +(4.42009 - 1.18436i) q^{47} +(-5.94645 - 3.43319i) q^{49} +(-4.51671 + 1.21025i) q^{50} +(-0.920781 + 3.93745i) q^{52} -13.0901i q^{53} +(-0.167147 - 0.289507i) q^{55} +(-0.534750 - 0.926214i) q^{56} +(3.42738 + 3.42738i) q^{58} +(-2.44633 - 2.44633i) q^{59} +(3.12378 + 5.41055i) q^{61} +(-2.65221 - 4.59376i) q^{62} +6.04425i q^{64} +(-0.333737 - 0.178665i) q^{65} +(-14.8055 + 3.96713i) q^{67} +(1.38687 + 0.800708i) q^{68} +(0.0347467 - 0.00931034i) q^{70} +(-1.56835 - 5.85317i) q^{71} +(-4.13084 + 4.13084i) q^{73} +(-3.63553 + 2.09897i) q^{74} +(0.879591 + 3.28268i) q^{76} +(-0.581958 - 1.00798i) q^{77} +(8.15587 - 14.1264i) q^{79} +(-0.0506235 - 0.0135645i) q^{80} +(-5.52307 - 3.18874i) q^{82} +(4.29512 + 16.0296i) q^{83} +(-0.106008 + 0.106008i) q^{85} +(0.544920 - 2.03367i) q^{86} +9.31551i q^{88} +(-0.630472 + 2.35295i) q^{89} +(-1.16198 - 0.622062i) q^{91} +(-3.56816 - 2.06008i) q^{92} +(2.14449 - 3.71437i) q^{94} -0.318151 q^{95} +(-3.20249 + 11.9519i) q^{97} +(-6.21639 + 1.66568i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 30 q^{8} - 12 q^{10} + 6 q^{11} - 2 q^{13} + 12 q^{14} - 28 q^{16} - 4 q^{19} + 18 q^{20} - 4 q^{22} + 6 q^{23} + 48 q^{26} - 18 q^{31} - 54 q^{32} + 6 q^{34} - 6 q^{35}+ \cdots - 36 q^{98}+O(q^{100}) \) 48 * q + 6 * q^2 + 6 * q^5 - 4 * q^7 - 30 * q^8 - 12 * q^10 + 6 * q^11 - 2 * q^13 + 12 * q^14 - 28 * q^16 - 4 * q^19 + 18 * q^20 - 4 * q^22 + 6 * q^23 + 48 * q^26 - 18 * q^31 - 54 * q^32 + 6 * q^34 - 6 * q^35 - 6 * q^37 - 36 * q^38 - 12 * q^40 - 18 * q^41 - 30 * q^43 - 12 * q^44 - 12 * q^46 + 36 * q^47 - 6 * q^49 + 60 * q^50 + 56 * q^52 - 4 * q^55 + 6 * q^56 + 50 * q^58 + 6 * q^59 + 2 * q^61 - 18 * q^62 - 72 * q^65 + 26 * q^67 - 42 * q^68 - 16 * q^70 + 48 * q^71 - 22 * q^73 - 30 * q^74 + 6 * q^76 - 72 * q^77 + 8 * q^79 + 54 * q^80 - 12 * q^82 - 54 * q^83 - 24 * q^85 + 54 * q^86 - 16 * q^91 - 120 * q^92 + 26 * q^94 + 12 * q^95 - 24 * q^97 - 36 * q^98

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