LMFDB - Embedded newform 351.2.l.b.199.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(127,351)] 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("351.127"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [22] 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:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.9
Character	$\chi$	$=$	351.199
Dual form			351.2.l.b.127.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.40574i q^{2} +0.0239006 q^{4} +(2.61504 + 1.50979i) q^{5} +(-2.76663 - 1.59731i) q^{7} +2.84507i q^{8} +(-2.12237 + 3.67605i) q^{10} +0.793626i q^{11} +(1.75322 + 3.15059i) q^{13} +(2.24541 - 3.88916i) q^{14} -3.95163 q^{16} +(0.0957495 + 0.165843i) q^{17} +(6.28411 - 3.62813i) q^{19} +(0.0625010 + 0.0360850i) q^{20} -1.11563 q^{22} +(1.27250 + 2.20404i) q^{23} +(2.05894 + 3.56619i) q^{25} +(-4.42891 + 2.46456i) q^{26} +(-0.0661242 - 0.0381768i) q^{28} -8.44883 q^{29} +(-6.22662 - 3.59494i) q^{31} +0.135195i q^{32} +(-0.233132 + 0.134599i) q^{34} +(-4.82322 - 8.35407i) q^{35} +(2.25703 + 1.30310i) q^{37} +(5.10020 + 8.83381i) q^{38} +(-4.29547 + 7.43997i) q^{40} +(0.784546 - 0.452958i) q^{41} +(1.98654 - 3.44080i) q^{43} +0.0189682i q^{44} +(-3.09830 + 1.78880i) q^{46} +(6.60765 - 3.81493i) q^{47} +(1.60282 + 2.77617i) q^{49} +(-5.01313 + 2.89433i) q^{50} +(0.0419030 + 0.0753011i) q^{52} -0.0692625 q^{53} +(-1.19821 + 2.07536i) q^{55} +(4.54448 - 7.87126i) q^{56} -11.8768i q^{58} -13.5667i q^{59} +(-0.0894284 + 0.154895i) q^{61} +(5.05354 - 8.75299i) q^{62} -8.09330 q^{64} +(-0.172015 + 10.8859i) q^{65} +(9.17094 - 5.29484i) q^{67} +(0.00228847 + 0.00396375i) q^{68} +(11.7436 - 6.78019i) q^{70} +(-0.271545 + 0.156777i) q^{71} -6.55741i q^{73} +(-1.83181 + 3.17279i) q^{74} +(0.150194 - 0.0867146i) q^{76} +(1.26767 - 2.19567i) q^{77} +(-2.13465 - 3.69732i) q^{79} +(-10.3336 - 5.96613i) q^{80} +(0.636740 + 1.10287i) q^{82} +(-7.01438 + 4.04975i) q^{83} +0.578247i q^{85} +(4.83686 + 2.79256i) q^{86} -2.25792 q^{88} +(4.56933 + 2.63810i) q^{89} +(0.181987 - 11.5170i) q^{91} +(0.0304136 + 0.0526779i) q^{92} +(5.36279 + 9.28863i) q^{94} +21.9109 q^{95} +(15.2169 + 8.78548i) q^{97} +(-3.90257 + 2.25315i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 20 q^{4} + 3 q^{5} - 6 q^{7} - 7 q^{10} + 9 q^{14} + 24 q^{16} - 9 q^{17} - 6 q^{19} + 24 q^{20} + 26 q^{22} - 6 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} - 48 q^{29} - 27 q^{31} + 15 q^{34} + 27 q^{35}+ \cdots - 117 q^{98}+O(q^{100}) $ 22 * q - 20 * q^4 + 3 * q^5 - 6 * q^7 - 7 * q^10 + 9 * q^14 + 24 * q^16 - 9 * q^17 - 6 * q^19 + 24 * q^20 + 26 * q^22 - 6 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 - 48 * q^29 - 27 * q^31 + 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 - 6 * q^41 - 4 * q^43 - 15 * q^46 + 6 * q^47 + 7 * q^49 - 18 * q^50 - 22 * q^52 + 24 * q^53 - 13 * q^55 + 9 * q^56 + 3 * q^61 - 24 * q^64 + 57 * q^65 - 45 * q^67 + 69 * q^68 - 24 * q^70 - 9 * q^71 + 6 * q^74 + 18 * q^76 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 - 42 * q^83 - 45 * q^86 + 22 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 + 44 * q^94 - 6 * q^95 - 27 * q^97 - 117 * q^98

Character values

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

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			1.40574i			0.994007i	0.867749	+	0.497003i	$0.165566\pi$
$2$			1.40574i			0.994007i	−0.867749	+	0.497003i	$0.834434\pi$
$3$		0			0
$3$		0			0
$4$	0.0239006			0.0119503
$5$	2.61504	+	1.50979i	1.16948	+	0.675199i	0.953557	−	0.301211i	$-0.0973910\pi$
$5$	2.61504	+	1.50979i	1.16948	+	0.675199i	0.215922	+	0.976411i	$0.430724\pi$
$6$		0			0
$7$	−2.76663	−	1.59731i	−1.04569	−	0.603728i	−0.124249	−	0.992251i	$-0.539652\pi$
$7$	−2.76663	−	1.59731i	−1.04569	−	0.603728i	−0.921439	+	0.388523i	$0.872985\pi$
$8$			2.84507i			1.00589i
$9$		0			0
$10$	−2.12237	+	3.67605i	−0.671153	+	1.16247i
$11$			0.793626i			0.239287i	0.992817	+	0.119644i	$0.0381752\pi$
$11$			0.793626i			0.239287i	−0.992817	+	0.119644i	$0.961825\pi$
$12$		0			0
$13$	1.75322	+	3.15059i	0.486255	+	0.873817i
$13$	1.75322	+	3.15059i	0.486255	+	0.873817i
$14$	2.24541	−	3.88916i	0.600110	−	1.03942i
$15$		0			0
$16$	−3.95163			−0.987907
$17$	0.0957495	+	0.165843i	0.0232227	+	0.0402228i	0.877403	−	0.479754i	$-0.159274\pi$
$17$	0.0957495	+	0.165843i	0.0232227	+	0.0402228i	−0.854181	+	0.519977i	$0.825941\pi$
$18$		0			0
$19$	6.28411	−	3.62813i	1.44167	−	0.832350i	0.443711	−	0.896170i	$-0.353662\pi$
$19$	6.28411	−	3.62813i	1.44167	−	0.832350i	0.997961	+	0.0638195i	$0.0203282\pi$
$20$	0.0625010	+	0.0360850i	0.0139756	+	0.00806884i
$21$		0			0
$22$	−1.11563			−0.237853
$23$	1.27250	+	2.20404i	0.265335	+	0.459574i	0.967651	−	0.252291i	$-0.0811841\pi$
$23$	1.27250	+	2.20404i	0.265335	+	0.459574i	−0.702316	+	0.711865i	$0.747851\pi$
$24$		0			0
$25$	2.05894	+	3.56619i	0.411788	+	0.713238i
$26$	−4.42891	+	2.46456i	−0.868580	+	0.483340i
$27$		0			0
$28$	−0.0661242	−	0.0381768i	−0.0124963	−	0.00721474i
$29$	−8.44883			−1.56891			−0.784454	−	0.620187i	$-0.787057\pi$
$29$	−8.44883			−1.56891			−0.784454	+	0.620187i	$0.787057\pi$
$30$		0			0
$31$	−6.22662	−	3.59494i	−1.11833	−	0.645670i	−0.177358	−	0.984146i	$-0.556755\pi$
$31$	−6.22662	−	3.59494i	−1.11833	−	0.645670i	−0.940975	+	0.338476i	$0.890089\pi$
$32$			0.135195i			0.0238993i
$33$		0			0
$34$	−0.233132	+	0.134599i	−0.0399818	+	0.0230835i
$35$	−4.82322	−	8.35407i	−0.815273	−	1.41209i
$36$		0			0
$37$	2.25703	+	1.30310i	0.371054	+	0.214228i	0.673919	−	0.738806i	$-0.264610\pi$
$37$	2.25703	+	1.30310i	0.371054	+	0.214228i	−0.302865	+	0.953033i	$0.597943\pi$
$38$	5.10020	+	8.83381i	0.827362	+	1.43303i
$39$		0			0
$40$	−4.29547	+	7.43997i	−0.679173	+	1.17636i
$41$	0.784546	−	0.452958i	0.122526	−	0.0707402i	−0.437485	−	0.899226i	$-0.644131\pi$
$41$	0.784546	−	0.452958i	0.122526	−	0.0707402i	0.560010	+	0.828486i	$0.310797\pi$
$42$		0			0
$43$	1.98654	−	3.44080i	0.302945	−	0.524716i	−0.673857	−	0.738862i	$-0.735363\pi$
$43$	1.98654	−	3.44080i	0.302945	−	0.524716i	0.976802	+	0.214146i	$0.0686968\pi$
$44$			0.0189682i			0.00285956i
$45$		0			0
$46$	−3.09830	+	1.78880i	−0.456820	+	0.263745i
$47$	6.60765	−	3.81493i	0.963825	−	0.556465i	0.0664769	−	0.997788i	$-0.478824\pi$
$47$	6.60765	−	3.81493i	0.963825	−	0.556465i	0.897348	+	0.441323i	$0.145491\pi$
$48$		0			0
$49$	1.60282	+	2.77617i	0.228975	+	0.396596i
$50$	−5.01313	+	2.89433i	−0.708963	+	0.409320i
$51$		0			0
$52$	0.0419030	+	0.0753011i	0.00581090	+	0.0104424i
$53$	−0.0692625			−0.00951393			−0.00475697	−	0.999989i	$-0.501514\pi$
$53$	−0.0692625			−0.00951393			−0.00475697	+	0.999989i	$0.501514\pi$
$54$		0			0
$55$	−1.19821	+	2.07536i	−0.161567	+	0.279841i
$56$	4.54448	−	7.87126i	0.607281	−	1.05184i
$57$		0			0
$58$		−	11.8768i		−	1.55951i
$59$		−	13.5667i		−	1.76623i	−0.469155	−	0.883116i	$-0.655441\pi$
$59$		−	13.5667i		−	1.76623i	0.469155	−	0.883116i	$-0.344559\pi$
$60$		0			0
$61$	−0.0894284	+	0.154895i	−0.0114501	+	0.0198322i	−0.871694	−	0.490051i	$-0.836978\pi$
$61$	−0.0894284	+	0.154895i	−0.0114501	+	0.0198322i	0.860244	+	0.509883i	$0.170311\pi$
$62$	5.05354	−	8.75299i	0.641800	−	1.11163i
$63$		0			0
$64$	−8.09330			−1.01166
$65$	−0.172015	+	10.8859i	−0.0213359	+	1.35023i
$66$		0			0
$67$	9.17094	−	5.29484i	1.12041	−	0.646868i	0.178903	−	0.983867i	$-0.442745\pi$
$67$	9.17094	−	5.29484i	1.12041	−	0.646868i	0.941505	+	0.336998i	$0.109412\pi$
$68$	0.00228847	+	0.00396375i	0.000277518	+	0.000480675i
$69$		0			0
$70$	11.7436	−	6.78019i	1.40363	−	0.810387i
$71$	−0.271545	+	0.156777i	−0.0322265	+	0.0186060i	−0.516027	−	0.856572i	$-0.672589\pi$
$71$	−0.271545	+	0.156777i	−0.0322265	+	0.0186060i	0.483800	+	0.875178i	$0.339256\pi$
$72$		0			0
$73$		−	6.55741i		−	0.767487i	−0.923440	−	0.383743i	$-0.874635\pi$
$73$		−	6.55741i		−	0.767487i	0.923440	−	0.383743i	$-0.125365\pi$
$74$	−1.83181	+	3.17279i	−0.212944	+	0.368830i
$75$		0			0
$76$	0.150194	−	0.0867146i	0.0172284	−	0.00994685i
$77$	1.26767	−	2.19567i	0.144464	−	0.250220i
$78$		0			0
$79$	−2.13465	−	3.69732i	−0.240167	−	0.415981i	0.720595	−	0.693356i	$-0.243869\pi$
$79$	−2.13465	−	3.69732i	−0.240167	−	0.415981i	−0.960762	+	0.277376i	$0.910535\pi$
$80$	−10.3336	−	5.96613i	−1.15534	−	0.667034i
$81$		0			0
$82$	0.636740	+	1.10287i	0.0703162	+	0.121791i
$83$	−7.01438	+	4.04975i	−0.769928	+	0.444518i	−0.832849	−	0.553500i	$-0.813292\pi$
$83$	−7.01438	+	4.04975i	−0.769928	+	0.444518i	0.0629208	+	0.998019i	$0.479958\pi$
$84$		0			0
$85$			0.578247i			0.0627197i
$86$	4.83686	+	2.79256i	0.521572	+	0.301130i
$87$		0			0
$88$	−2.25792			−0.240696
$89$	4.56933	+	2.63810i	0.484348	+	0.279638i	0.722226	−	0.691657i	$-0.243119\pi$
$89$	4.56933	+	2.63810i	0.484348	+	0.279638i	−0.237879	+	0.971295i	$0.576452\pi$
$90$		0			0
$91$	0.181987	−	11.5170i	0.0190774	−	1.20731i
$92$	0.0304136	+	0.0526779i	0.00317084	+	0.00549205i
$93$		0			0
$94$	5.36279	+	9.28863i	0.553130	+	0.958049i
$95$	21.9109			2.24801
$96$		0			0
$97$	15.2169	+	8.78548i	1.54504	+	0.892030i	0.998509	+	0.0545930i	$0.0173861\pi$
$97$	15.2169	+	8.78548i	1.54504	+	0.892030i	0.546533	+	0.837437i	$0.315947\pi$
$98$	−3.90257	+	2.25315i	−0.394219	+	0.227603i
$99$		0			0
$100$	0.0492100	+	0.0852342i	0.00492100	+	0.00852342i
$101$	−1.49789			−0.149045			−0.0745227	−	0.997219i	$-0.523743\pi$
$101$	−1.49789			−0.149045			−0.0745227	+	0.997219i	$0.523743\pi$
$102$		0			0
$103$	1.62024	−	2.80634i	0.159647	−	0.276517i	−0.775094	−	0.631846i	$-0.782298\pi$
$103$	1.62024	−	2.80634i	0.159647	−	0.276517i	0.934741	+	0.355329i	$0.115631\pi$
$104$	−8.96367	+	4.98803i	−0.878960	+	0.489117i
$105$		0			0
$106$		−	0.0973649i		−	0.00945692i
$107$	2.74177	−	4.74888i	0.265057	−	0.459091i	−0.702522	−	0.711662i	$-0.747943\pi$
$107$	2.74177	−	4.74888i	0.265057	−	0.459091i	0.967578	+	0.252571i	$0.0812760\pi$
$108$		0			0
$109$		−	2.75058i		−	0.263458i	−0.991286	−	0.131729i	$-0.957947\pi$
$109$		−	2.75058i		−	0.263458i	0.991286	−	0.131729i	$-0.0420529\pi$
$110$	−2.91741	−	1.68437i	−0.278164	−	0.160598i
$111$		0			0
$112$	10.9327	+	6.31199i	1.03304	+	0.596427i
$113$	−16.5005			−1.55223			−0.776117	−	0.630589i	$-0.782813\pi$
$113$	−16.5005			−1.55223			−0.776117	+	0.630589i	$0.782813\pi$
$114$		0			0
$115$			7.68485i			0.716616i
$116$	−0.201932			−0.0187490
$117$		0			0
$118$	19.0712			1.75565
$119$		−	0.611768i		−	0.0560807i
$120$		0			0
$121$	10.3702			0.942742
$122$	−0.217741	−	0.125713i	−0.0197134	−	0.0113815i
$123$		0			0
$124$	−0.148820	−	0.0859213i	−0.0133644	−	0.00771596i
$125$		−	2.66363i		−	0.238243i
$126$		0			0
$127$	−7.71406	+	13.3611i	−0.684512	+	1.18561i	0.289078	+	0.957305i	$0.406651\pi$
$127$	−7.71406	+	13.3611i	−0.684512	+	1.18561i	−0.973590	+	0.228304i	$0.926682\pi$
$128$		−	11.1067i		−	0.981701i
$129$		0			0
$130$	−15.3027	−	0.241808i	−1.34214	−	0.0212080i
$131$	−3.53140	+	6.11657i	−0.308540	+	0.534407i	−0.978043	−	0.208402i	$-0.933174\pi$
$131$	−3.53140	+	6.11657i	−0.308540	+	0.534407i	0.669503	+	0.742809i	$0.266507\pi$
$132$		0			0
$133$	−23.1811			−2.01005
$134$	7.44316	+	12.8919i	0.642992	+	1.11369i
$135$		0			0
$136$	−0.471835	+	0.272414i	−0.0404596	+	0.0233593i
$137$	6.03791	+	3.48599i	0.515854	+	0.297828i	0.735237	−	0.677811i	$-0.237071\pi$
$137$	6.03791	+	3.48599i	0.515854	+	0.297828i	−0.219383	+	0.975639i	$0.570404\pi$
$138$		0			0
$139$	−10.9052			−0.924970			−0.462485	−	0.886627i	$-0.653042\pi$
$139$	−10.9052			−0.924970			−0.462485	+	0.886627i	$0.653042\pi$
$140$	−0.115278	−	0.199667i	−0.00974277	−	0.0168750i
$141$		0			0
$142$	−0.220387	−	0.381722i	−0.0184945	−	0.0320334i
$143$	−2.50039	+	1.39140i	−0.209093	+	0.116355i
$144$		0			0
$145$	−22.0940	−	12.7560i	−1.83481	−	1.05933i
$146$	9.21800			0.762887
$147$		0			0
$148$	0.0539445	+	0.0311448i	0.00443421	+	0.00256009i
$149$		−	14.6217i		−	1.19785i	−0.800804	−	0.598927i	$-0.795594\pi$
$149$		−	14.6217i		−	1.19785i	0.800804	−	0.598927i	$-0.204406\pi$
$150$		0			0
$151$	0.912654	−	0.526921i	0.0742707	−	0.0428802i	−0.462405	−	0.886669i	$-0.653013\pi$
$151$	0.912654	−	0.526921i	0.0742707	−	0.0428802i	0.536675	+	0.843789i	$0.319680\pi$
$152$	10.3223	+	17.8787i	0.837249	+	1.45016i
$153$		0			0
$154$	3.08653	+	1.78201i	0.248720	+	0.143599i
$155$	−10.8552	−	18.8018i	−0.871912	−	1.51020i
$156$		0			0
$157$	5.59684	−	9.69401i	0.446677	−	0.773667i	−0.551491	−	0.834181i	$-0.685941\pi$
$157$	5.59684	−	9.69401i	0.446677	−	0.773667i	0.998167	+	0.0605145i	$0.0192741\pi$
$158$	5.19746	−	3.00075i	0.413488	−	0.238727i
$159$		0			0
$160$	−0.204116	+	0.353540i	−0.0161368	+	0.0279498i
$161$		−	8.13034i		−	0.640761i
$162$		0			0
$163$	−1.69044	+	0.975977i	−0.132406	+	0.0764444i	−0.564740	−	0.825269i	$-0.691023\pi$
$163$	−1.69044	+	0.975977i	−0.132406	+	0.0764444i	0.432334	+	0.901713i	$0.357690\pi$
$164$	0.0187512	−	0.0108260i	0.00146422	−	0.000845367i
$165$		0			0
$166$	−5.69289	−	9.86038i	−0.441854	−	0.765314i
$167$	−17.2061	+	9.93395i	−1.33145	+	0.768712i	−0.985522	−	0.169549i	$-0.945769\pi$
$167$	−17.2061	+	9.93395i	−1.33145	+	0.768712i	−0.345927	+	0.938261i	$0.612435\pi$
$168$		0			0
$169$	−6.85247	+	11.0473i	−0.527113	+	0.849795i
$170$	−0.812864			−0.0623438
$171$		0			0
$172$	0.0474797	−	0.0822372i	0.00362029	−	0.00627053i
$173$	−1.68605	+	2.92032i	−0.128188	+	0.222028i	−0.922975	−	0.384861i	$-0.874249\pi$
$173$	−1.68605	+	2.92032i	−0.128188	+	0.222028i	0.794787	+	0.606889i	$0.207583\pi$
$174$		0			0
$175$		−	13.1551i		−	0.994432i
$176$		−	3.13611i		−	0.236394i
$177$		0			0
$178$	−3.70848	+	6.42327i	−0.277962	+	0.481445i
$179$	−6.46527	+	11.1982i	−0.483237	+	0.836990i	−0.999815	−	0.0192497i	$-0.993872\pi$
$179$	−6.46527	+	11.1982i	−0.483237	+	0.836990i	0.516578	+	0.856240i	$0.327206\pi$
$180$		0			0
$181$	−11.3925			−0.846798			−0.423399	−	0.905943i	$-0.639163\pi$
$181$	−11.3925			−0.846798			−0.423399	+	0.905943i	$0.639163\pi$
$182$	16.1898	+	0.255826i	1.20007	+	0.0189631i
$183$		0			0
$184$	−6.27065	+	3.62036i	−0.462279	+	0.266897i
$185$	3.93481	+	6.81529i	0.289293	+	0.501070i
$186$		0			0
$187$	−0.131617	+	0.0759893i	−0.00962481	+	0.00555688i
$188$	0.157927	−	0.0911792i	0.0115180	−	0.00664993i
$189$		0			0
$190$			30.8010i			2.23454i
$191$	1.63433	−	2.83074i	0.118256	−	0.204825i	−0.800821	−	0.598904i	$-0.795603\pi$
$191$	1.63433	−	2.83074i	0.118256	−	0.204825i	0.919077	+	0.394079i	$0.128936\pi$
$192$		0			0
$193$	−16.5094	+	9.53170i	−1.18837	+	0.686107i	−0.957936	−	0.286981i	$-0.907348\pi$
$193$	−16.5094	+	9.53170i	−1.18837	+	0.686107i	−0.230436	+	0.973088i	$0.574015\pi$
$194$	−12.3501	+	21.3910i	−0.886684	+	1.53578i
$195$		0			0
$196$	0.0383085	+	0.0663523i	0.00273632	+	0.00473945i
$197$	2.13371	+	1.23190i	0.152020	+	0.0877690i	0.574081	−	0.818799i	$-0.305360\pi$
$197$	2.13371	+	1.23190i	0.152020	+	0.0877690i	−0.422060	+	0.906568i	$0.638693\pi$
$198$		0			0
$199$	11.7617	+	20.3718i	0.833764	+	1.44412i	0.895033	+	0.446000i	$0.147152\pi$
$199$	11.7617	+	20.3718i	0.833764	+	1.44412i	−0.0612690	+	0.998121i	$0.519515\pi$
$200$	−10.1461	+	5.85784i	−0.717436	+	0.414212i
$201$		0			0
$202$		−	2.10564i		−	0.148152i
$203$	23.3748	+	13.4954i	1.64059	+	0.947194i
$204$		0			0
$205$	2.73549			0.191055
$206$	3.94498	+	2.27763i	0.274860	+	0.158690i
$207$		0			0
$208$	−6.92806	−	12.4500i	−0.480374	−	0.863250i
$209$	2.87938	+	4.98723i	0.199171	+	0.344974i
$210$		0			0
$211$	0.722675	+	1.25171i	0.0497510	+	0.0861713i	0.889828	−	0.456295i	$-0.150824\pi$
$211$	0.722675	+	1.25171i	0.0497510	+	0.0861713i	−0.840077	+	0.542466i	$0.817491\pi$
$212$	−0.00165542			−0.000113695
$213$		0			0
$214$	6.67568	+	3.85421i	0.456340	+	0.263468i
$215$	10.3898	−	5.99854i	0.708576	−	0.409097i
$216$		0			0
$217$	11.4845	+	19.8917i	0.779618	+	1.35034i
$218$	3.86660			0.261879
$219$		0			0
$220$	−0.0286380	+	0.0496024i	−0.00193077	+	0.00334419i
$221$	−0.354634	+	0.592426i	−0.0238553	+	0.0398509i
$222$		0			0
$223$		−	0.606377i		−	0.0406060i	−0.999794	−	0.0203030i	$-0.993537\pi$
$223$		−	0.606377i		−	0.0406060i	0.999794	−	0.0203030i	$-0.00646309\pi$
$224$	0.215949	−	0.374035i	0.0144287	−	0.0249912i
$225$		0			0
$226$		−	23.1953i		−	1.54293i
$227$	−19.9671	−	11.5280i	−1.32527	−	0.765143i	−0.340703	−	0.940171i	$-0.610665\pi$
$227$	−19.9671	−	11.5280i	−1.32527	−	0.765143i	−0.984563	+	0.175028i	$0.943998\pi$
$228$		0			0
$229$	−3.97688	−	2.29605i	−0.262799	−	0.151727i	0.362812	−	0.931863i	$-0.381817\pi$
$229$	−3.97688	−	2.29605i	−0.262799	−	0.151727i	−0.625611	+	0.780135i	$0.715150\pi$
$230$	−10.8029			−0.712321
$231$		0			0
$232$		−	24.0375i		−	1.57814i
$233$	7.84289			0.513804			0.256902	−	0.966437i	$-0.417298\pi$
$233$	7.84289			0.513804			0.256902	+	0.966437i	$0.417298\pi$
$234$		0			0
$235$	23.0390			1.50290
$236$		−	0.324252i		−	0.0211070i
$237$		0			0
$238$	0.859985			0.0557446
$239$	−1.19864	−	0.692034i	−0.0775334	−	0.0447639i	0.460732	−	0.887539i	$-0.347587\pi$
$239$	−1.19864	−	0.692034i	−0.0775334	−	0.0447639i	−0.538266	+	0.842775i	$0.680920\pi$
$240$		0			0
$241$	3.50441	+	2.02327i	0.225739	+	0.130330i	0.608605	−	0.793474i	$-0.291730\pi$
$241$	3.50441	+	2.02327i	0.225739	+	0.130330i	−0.382866	+	0.923804i	$0.625063\pi$
$242$			14.5777i			0.937092i
$243$		0			0
$244$	−0.00213739	+	0.00370208i	−0.000136833	+	0.000237001i
$245$			9.67972i			0.618415i
$246$		0			0
$247$	22.4482	+	13.4378i	1.42834	+	0.855024i
$248$	10.2279	−	17.7152i	0.649470	−	1.12492i
$249$		0			0
$250$	3.74437			0.236815
$251$	−3.43920	−	5.95686i	−0.217080	−	0.375994i	0.736834	−	0.676074i	$-0.236320\pi$
$251$	−3.43920	−	5.95686i	−0.217080	−	0.375994i	−0.953914	+	0.300080i	$0.902987\pi$
$252$		0			0
$253$	−1.74918	+	1.00989i	−0.109970	+	0.0634913i
$254$	−18.7823	−	10.8439i	−1.17850	−	0.680409i
$255$		0			0
$256$	−0.573533			−0.0358458
$257$	3.76772	+	6.52588i	0.235024	+	0.407073i	0.959280	−	0.282458i	$-0.0911498\pi$
$257$	3.76772	+	6.52588i	0.235024	+	0.407073i	−0.724256	+	0.689531i	$0.757817\pi$
$258$		0			0
$259$	−4.16291	−	7.21037i	−0.258671	−	0.448031i
$260$	−0.00411127	+	0.260180i	−0.000254970	+	0.0161357i
$261$		0			0
$262$	−8.59829	−	4.96422i	−0.531204	−	0.306691i
$263$	−4.51334			−0.278304			−0.139152	−	0.990271i	$-0.544438\pi$
$263$	−4.51334			−0.278304			−0.139152	+	0.990271i	$0.544438\pi$
$264$		0			0
$265$	−0.181124	−	0.104572i	−0.0111263	−	0.00642380i
$266$		−	32.5865i		−	1.99801i
$267$		0			0
$268$	0.219191	−	0.126550i	0.0133892	−	0.00773028i
$269$	7.59726	+	13.1588i	0.463213	+	0.802309i	0.999119	−	0.0419692i	$-0.0133631\pi$
$269$	7.59726	+	13.1588i	0.463213	+	0.802309i	−0.535906	+	0.844278i	$0.680030\pi$
$270$		0			0
$271$	−19.0083	−	10.9744i	−1.15467	−	0.666650i	−0.204650	−	0.978835i	$-0.565606\pi$
$271$	−19.0083	−	10.9744i	−1.15467	−	0.666650i	−0.950021	+	0.312185i	$0.898939\pi$
$272$	−0.378366	−	0.655349i	−0.0229418	−	0.0397364i
$273$		0			0
$274$	−4.90039	+	8.48773i	−0.296043	+	0.512762i
$275$	−2.83022	+	1.63403i	−0.170669	+	0.0985356i
$276$		0			0
$277$	−3.02043	+	5.23154i	−0.181480	+	0.314333i	−0.942385	−	0.334531i	$-0.891422\pi$
$277$	−3.02043	+	5.23154i	−0.181480	+	0.314333i	0.760905	+	0.648864i	$0.224756\pi$
$278$		−	15.3299i		−	0.919427i
$279$		0			0
$280$	23.7679	−	13.7224i	1.42041	−	0.820072i
$281$	6.56065	−	3.78780i	0.391376	−	0.225961i	−0.291380	−	0.956607i	$-0.594114\pi$
$281$	6.56065	−	3.78780i	0.391376	−	0.225961i	0.682756	+	0.730646i	$0.260781\pi$
$282$		0			0
$283$	14.0371	+	24.3129i	0.834416	+	1.44525i	0.894505	+	0.447058i	$0.147528\pi$
$283$	14.0371	+	24.3129i	0.834416	+	1.44525i	−0.0600886	+	0.998193i	$0.519138\pi$
$284$	−0.00649011	+	0.00374707i	−0.000385117	+	0.000222347i
$285$		0			0
$286$	−1.95594	−	3.51490i	−0.115657	−	0.207840i
$287$	−2.89406			−0.170831
$288$		0			0
$289$	8.48166	−	14.6907i	0.498921	−	0.864157i
$290$	17.9316	−	31.0584i	1.05298	−	1.82381i
$291$		0			0
$292$		−	0.156726i		−	0.00917171i
$293$			22.9365i			1.33996i	0.742377	+	0.669982i	$0.233698\pi$
$293$			22.9365i			1.33996i	−0.742377	+	0.669982i	$0.766302\pi$
$294$		0			0
$295$	20.4829	−	35.4774i	1.19256	−	2.06557i
$296$	−3.70741	+	6.42142i	−0.215489	+	0.373237i
$297$		0			0
$298$	20.5542			1.19068
$299$	−4.71306	+	7.87329i	−0.272563	+	0.455324i
$300$		0			0
$301$	−10.9921	+	6.34627i	−0.633572	+	0.365793i
$302$	0.740713	+	1.28295i	0.0426232	+	0.0738256i
$303$		0			0
$304$	−24.8324	+	14.3370i	−1.42424	+	0.822285i
$305$	−0.467717	+	0.270036i	−0.0267814	+	0.0154622i
$306$		0			0
$307$			3.31351i			0.189112i	0.995520	+	0.0945560i	$0.0301431\pi$
$307$			3.31351i			0.189112i	−0.995520	+	0.0945560i	$0.969857\pi$
$308$	0.0302981	−	0.0524779i	0.00172640	−	0.00299020i
$309$		0			0
$310$	26.4304	−	15.2596i	1.50114	−	0.866686i
$311$	−12.6695	+	21.9442i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$311$	−12.6695	+	21.9442i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$312$		0			0
$313$	−8.71624	−	15.0970i	−0.492671	−	0.853331i	0.507294	−	0.861773i	$-0.330646\pi$
$313$	−8.71624	−	15.0970i	−0.492671	−	0.853331i	−0.999964	+	0.00844245i	$0.997313\pi$
$314$	13.6272	+	7.86769i	0.769030	+	0.444000i
$315$		0			0
$316$	−0.0510194	−	0.0883682i	−0.00287007	−	0.00497110i
$317$	11.2999	−	6.52400i	0.634666	−	0.366425i	−0.147891	−	0.989004i	$-0.547248\pi$
$317$	11.2999	−	6.52400i	0.634666	−	0.366425i	0.782557	+	0.622579i	$0.213915\pi$
$318$		0			0
$319$		−	6.70521i		−	0.375420i
$320$	−21.1643	−	12.2192i	−1.18312	−	0.683074i
$321$		0			0
$322$	11.4291			0.636921
$323$	1.20340	+	0.694783i	0.0669589	+	0.0386588i
$324$		0			0
$325$	−7.62584	+	12.7392i	−0.423006	+	0.706643i
$326$	−1.37197	−	2.37632i	−0.0759862	−	0.131612i
$327$		0			0
$328$	1.28870	+	2.23209i	0.0711565	+	0.123247i
$329$	−24.3746			−1.34381
$330$		0			0
$331$	−4.11896	−	2.37808i	−0.226399	−	0.130711i	0.382511	−	0.923951i	$-0.375059\pi$
$331$	−4.11896	−	2.37808i	−0.226399	−	0.130711i	−0.608910	+	0.793240i	$0.708393\pi$
$332$	−0.167648	+	0.0967917i	−0.00920088	+	0.00531213i
$333$		0			0
$334$	−13.9645	−	24.1873i	−0.764105	−	1.32347i
$335$	31.9764			1.74706
$336$		0			0
$337$	−12.7677	+	22.1143i	−0.695500	+	1.20464i	0.274512	+	0.961584i	$0.411484\pi$
$337$	−12.7677	+	22.1143i	−0.695500	+	1.20464i	−0.970012	+	0.243057i	$0.921850\pi$
$338$	−15.5297	−	9.63277i	−0.844702	−	0.523954i
$339$		0			0
$340$			0.0138205i			0.000749520i
$341$	2.85304	−	4.94160i	0.154501	−	0.267603i
$342$		0			0
$343$			12.1215i			0.654502i
$344$	9.78932	+	5.65187i	0.527805	+	0.304728i
$345$		0			0
$346$	−4.10521	−	2.37014i	−0.220697	−	0.127420i
$347$	−5.42745			−0.291361			−0.145680	−	0.989332i	$-0.546537\pi$
$347$	−5.42745			−0.291361			−0.145680	+	0.989332i	$0.546537\pi$
$348$		0			0
$349$			26.3967i			1.41299i	0.707720	+	0.706493i	$0.249724\pi$
$349$			26.3967i			1.41299i	−0.707720	+	0.706493i	$0.750276\pi$
$350$	18.4926			0.988472
$351$		0			0
$352$	−0.107294			−0.00571881
$353$			29.8820i			1.59046i	0.606308	+	0.795230i	$0.292650\pi$
$353$			29.8820i			1.59046i	−0.606308	+	0.795230i	$0.707350\pi$
$354$		0			0
$355$	−0.946801			−0.0502510
$356$	0.109210	+	0.0630523i	0.00578811	+	0.00334176i
$357$		0			0
$358$	−15.7417	−	9.08847i	−0.831974	−	0.480341i
$359$		−	27.5815i		−	1.45570i	−0.685738	−	0.727849i	$-0.740520\pi$
$359$		−	27.5815i		−	1.45570i	0.685738	−	0.727849i	$-0.259480\pi$
$360$		0			0
$361$	16.8267	−	29.1446i	0.885614	−	1.53393i
$362$		−	16.0149i		−	0.841723i
$363$		0			0
$364$	0.00434960	−	0.275263i	0.000227981	−	0.0144277i
$365$	9.90032	−	17.1479i	0.518207	−	0.897560i
$366$		0			0
$367$	21.4395			1.11913			0.559565	−	0.828786i	$-0.310968\pi$
$367$	21.4395			1.11913			0.559565	+	0.828786i	$0.310968\pi$
$368$	−5.02845	−	8.70954i	−0.262126	−	0.454016i
$369$		0			0
$370$	−9.58051	+	5.53131i	−0.498067	+	0.287559i
$371$	0.191624	+	0.110634i	0.00994860	+	0.00574383i
$372$		0			0
$373$	−24.8449			−1.28642			−0.643211	−	0.765689i	$-0.722398\pi$
$373$	−24.8449			−1.28642			−0.643211	+	0.765689i	$0.722398\pi$
$374$	−0.106821	−	0.185019i	−0.00552358	−	0.00956712i
$375$		0			0
$376$	10.8538	+	18.7993i	0.559740	+	0.969498i
$377$	−14.8126	−	26.6188i	−0.762889	−	1.37094i
$378$		0			0
$379$	−0.763882	−	0.441027i	−0.0392380	−	0.0226540i	0.480253	−	0.877130i	$-0.340545\pi$
$379$	−0.763882	−	0.441027i	−0.0392380	−	0.0226540i	−0.519491	+	0.854476i	$0.673878\pi$
$380$	0.523684			0.0268644
$381$		0			0
$382$	3.97928	+	2.29744i	0.203598	+	0.117547i
$383$			2.86984i			0.146642i	0.997308	+	0.0733210i	$0.0233598\pi$
$383$			2.86984i			0.146642i	−0.997308	+	0.0733210i	$0.976640\pi$
$384$		0			0
$385$	6.63000	−	3.82783i	0.337896	−	0.195084i
$386$	−13.3991	−	23.2079i	−0.681995	−	1.18125i
$387$		0			0
$388$	0.363693	+	0.209979i	0.0184637	+	0.0106600i
$389$	−6.00741	−	10.4051i	−0.304588	−	0.527561i	0.672582	−	0.740023i	$-0.265185\pi$
$389$	−6.00741	−	10.4051i	−0.304588	−	0.527561i	−0.977169	+	0.212462i	$0.931852\pi$
$390$		0			0
$391$	−0.243683	+	0.422071i	−0.0123236	+	0.0213450i
$392$	−7.89842	+	4.56015i	−0.398930	+	0.230323i
$393$		0			0
$394$	−1.73172	+	2.99943i	−0.0872430	+	0.151109i
$395$		−	12.8915i		−	0.648641i
$396$		0			0
$397$	7.80521	−	4.50634i	0.391732	−	0.226167i	−0.291178	−	0.956669i	$-0.594047\pi$
$397$	7.80521	−	4.50634i	0.391732	−	0.226167i	0.682910	+	0.730502i	$0.260714\pi$
$398$	−28.6375	+	16.5339i	−1.43547	+	0.828767i
$399$		0			0
$400$	−8.13616	−	14.0922i	−0.406808	−	0.704612i
$401$	28.7872	−	16.6203i	1.43757	−	0.829979i	0.439885	−	0.898054i	$-0.355019\pi$
$401$	28.7872	−	16.6203i	1.43757	−	0.829979i	0.997680	+	0.0680755i	$0.0216859\pi$
$402$		0			0
$403$	0.409582	−	25.9202i	0.0204028	−	1.29118i
$404$	−0.0358004			−0.00178114
$405$		0			0
$406$	−18.9710	+	32.8588i	−0.941517	+	1.63076i
$407$	−1.03417	+	1.79124i	−0.0512620	+	0.0887884i
$408$		0			0
$409$		−	33.9084i		−	1.67666i	−0.545161	−	0.838332i	$-0.683531\pi$
$409$		−	33.9084i		−	1.67666i	0.545161	−	0.838332i	$-0.316469\pi$
$410$			3.84538i			0.189910i
$411$		0			0
$412$	0.0387248	−	0.0670733i	0.00190783	−	0.00330446i
$413$	−21.6703	+	37.5340i	−1.06632	+	1.84693i
$414$		0			0
$415$	−24.4571			−1.20055
$416$	−0.425945	+	0.237026i	−0.0208837	+	0.0116212i
$417$		0			0
$418$	−7.01074	+	4.04765i	−0.342906	+	0.197977i
$419$	12.6895	+	21.9788i	0.619921	+	1.07374i	0.989500	+	0.144536i	$0.0461689\pi$
$419$	12.6895	+	21.9788i	0.619921	+	1.07374i	−0.369578	+	0.929200i	$0.620498\pi$
$420$		0			0
$421$	10.2213	−	5.90124i	0.498153	−	0.287609i	−0.229797	−	0.973239i	$-0.573806\pi$
$421$	10.2213	−	5.90124i	0.498153	−	0.287609i	0.727951	+	0.685630i	$0.240473\pi$
$422$	−1.75958	+	1.01589i	−0.0856549	+	0.0494529i
$423$		0			0
$424$		−	0.197057i		−	0.00956993i
$425$	−0.394285	+	0.682921i	−0.0191256	+	0.0331265i
$426$		0			0
$427$	0.494830	−	0.285690i	0.0239465	−	0.0138255i
$428$	0.0655299	−	0.113501i	0.00316751	−	0.00548629i
$429$		0			0
$430$	8.43237	+	14.6053i	0.406645	+	0.704330i
$431$	−9.96641	−	5.75411i	−0.480065	−	0.277166i	0.240379	−	0.970679i	$-0.422728\pi$
$431$	−9.96641	−	5.75411i	−0.480065	−	0.277166i	−0.720444	+	0.693514i	$0.756062\pi$
$432$		0			0
$433$	7.00567	+	12.1342i	0.336671	+	0.583131i	0.983804	−	0.179246i	$-0.0573657\pi$
$433$	7.00567	+	12.1342i	0.336671	+	0.583131i	−0.647133	+	0.762377i	$0.724032\pi$
$434$	−27.9626	+	16.1442i	−1.34225	+	0.774946i
$435$		0			0
$436$		−	0.0657407i		−	0.00314841i
$437$	15.9931	+	9.23361i	0.765053	+	0.441703i
$438$		0			0
$439$	−34.0798			−1.62654			−0.813271	−	0.581885i	$-0.802315\pi$
$439$	−34.0798			−1.62654			−0.813271	+	0.581885i	$0.802315\pi$
$440$	−5.90455	−	3.40900i	−0.281489	−	0.162517i
$441$		0			0
$442$	−0.832796	−	0.498522i	−0.0396121	−	0.0237123i
$443$	−16.3341	−	28.2916i	−0.776058	−	1.34417i	−0.934198	−	0.356756i	$-0.883883\pi$
$443$	−16.3341	−	28.2916i	−0.776058	−	1.34417i	0.158139	−	0.987417i	$-0.449451\pi$
$444$		0			0
$445$	7.96597	+	13.7975i	0.377623	+	0.654062i
$446$	0.852407			0.0403626
$447$		0			0
$448$	22.3912	+	12.9275i	1.05788	+	0.610769i
$449$	−7.66848	+	4.42740i	−0.361898	+	0.208942i	−0.669913	−	0.742440i	$-0.733669\pi$
$449$	−7.66848	+	4.42740i	−0.361898	+	0.208942i	0.308015	+	0.951381i	$0.400335\pi$
$450$		0			0
$451$	0.359479	+	0.622636i	0.0169272	+	0.0293188i
$452$	−0.394372			−0.0185497
$453$		0			0
$454$	16.2054	−	28.0686i	0.760557	−	1.31732i
$455$	17.8641	−	29.8425i	0.837482	−	1.39904i
$456$		0			0
$457$			15.2196i			0.711945i	0.934496	+	0.355973i	$0.115850\pi$
$457$			15.2196i			0.711945i	−0.934496	+	0.355973i	$0.884150\pi$
$458$	3.22764	−	5.59044i	0.150818	−	0.261224i
$459$		0			0
$460$			0.183673i			0.00856379i
$461$	30.1473	+	17.4056i	1.40410	+	0.810658i	0.994810	−	0.101745i	$-0.0324427\pi$
$461$	30.1473	+	17.4056i	1.40410	+	0.810658i	0.409291	+	0.912404i	$0.365776\pi$
$462$		0			0
$463$	−23.7329	−	13.7022i	−1.10296	−	0.636795i	−0.165963	−	0.986132i	$-0.553073\pi$
$463$	−23.7329	−	13.7022i	−1.10296	−	0.636795i	−0.936997	+	0.349337i	$0.886407\pi$
$464$	33.3866			1.54994
$465$		0			0
$466$			11.0250i			0.510725i
$467$	9.34092			0.432246			0.216123	−	0.976366i	$-0.430659\pi$
$467$	9.34092			0.432246			0.216123	+	0.976366i	$0.430659\pi$
$468$		0			0
$469$	−33.8301			−1.56213
$470$			32.3868i			1.49389i
$471$		0			0
$472$	38.5982			1.77663
$473$	2.73070	+	1.57657i	0.125558	+	0.0724909i
$474$		0			0
$475$	25.8772	+	14.9402i	1.18733	+	0.685504i
$476$		−	0.0146216i		−	0.000670182i
$477$		0			0
$478$	0.972818	−	1.68497i	0.0444957	−	0.0770687i
$479$			11.0368i			0.504285i	0.967690	+	0.252142i	$0.0811351\pi$
$479$			11.0368i			0.504285i	−0.967690	+	0.252142i	$0.918865\pi$
$480$		0			0
$481$	−0.148466	+	9.39559i	−0.00676946	+	0.428402i
$482$	−2.84419	+	4.92628i	−0.129549	+	0.224386i
$483$		0			0
$484$	0.247853			0.0112661
$485$	26.5285	+	45.9487i	1.20460	+	2.08642i
$486$		0			0
$487$	9.99524	−	5.77075i	0.452928	−	0.261498i	−0.256138	−	0.966640i	$-0.582450\pi$
$487$	9.99524	−	5.77075i	0.452928	−	0.261498i	0.709066	+	0.705142i	$0.249117\pi$
$488$	−0.440686	−	0.254430i	−0.0199489	−	0.0115175i
$489$		0			0
$490$	−13.6071			−0.614708
$491$	−10.6222	−	18.3982i	−0.479373	−	0.830299i	0.520347	−	0.853955i	$-0.325803\pi$
$491$	−10.6222	−	18.3982i	−0.479373	−	0.830299i	−0.999720	+	0.0236560i	$0.992469\pi$
$492$		0			0
$493$	−0.808971	−	1.40118i	−0.0364342	−	0.0631059i
$494$	−18.8900	+	31.5562i	−0.849900	+	1.41978i
$495$		0			0
$496$	24.6053	+	14.2059i	1.10481	+	0.637862i
$497$	1.00169			0.0449318
$498$		0			0
$499$	11.3888	+	6.57531i	0.509832	+	0.294351i	0.732764	−	0.680482i	$-0.238230\pi$
$499$	11.3888	+	6.57531i	0.509832	+	0.294351i	−0.222933	+	0.974834i	$0.571563\pi$
$500$		−	0.0636625i		−	0.00284707i
$501$		0			0
$502$	8.37379	−	4.83461i	0.373740	−	0.215779i
$503$	3.54282	+	6.13635i	0.157967	+	0.273606i	0.934135	−	0.356919i	$-0.116173\pi$
$503$	3.54282	+	6.13635i	0.157967	+	0.273606i	−0.776169	+	0.630525i	$0.782839\pi$
$504$		0			0
$505$	−3.91703	−	2.26150i	−0.174305	−	0.100635i
$506$	−1.41964	−	2.45889i	−0.0631108	−	0.109311i
$507$		0			0
$508$	−0.184371	+	0.319340i	−0.00818013	+	0.0141684i
$509$	−7.50837	+	4.33496i	−0.332803	+	0.192144i	−0.657085	−	0.753817i	$-0.728211\pi$
$509$	−7.50837	+	4.33496i	−0.332803	+	0.192144i	0.324282	+	0.945960i	$0.394877\pi$
$510$		0			0
$511$	−10.4742	+	18.1419i	−0.463353	+	0.802551i
$512$		−	23.0196i		−	1.01733i
$513$		0			0
$514$	−9.17368	+	5.29643i	−0.404634	+	0.233615i
$515$	8.47398	−	4.89245i	0.373408	−	0.215587i
$516$		0			0
$517$	3.02763	+	5.24400i	0.133155	+	0.230631i
$518$	10.1359	−	5.85196i	0.445346	−	0.257120i
$519$		0			0
$520$	−30.9712	−	0.489396i	−1.35818	−	0.0214614i
$521$	−27.2897			−1.19558			−0.597792	−	0.801651i	$-0.703955\pi$
$521$	−27.2897			−1.19558			−0.597792	+	0.801651i	$0.703955\pi$
$522$		0			0
$523$	2.33445	−	4.04338i	0.102078	−	0.176805i	−0.810463	−	0.585790i	$-0.800784\pi$
$523$	2.33445	−	4.04338i	0.102078	−	0.176805i	0.912541	+	0.408986i	$0.134117\pi$
$524$	−0.0844027	+	0.146190i	−0.00368715	+	0.00638633i
$525$		0			0
$526$		−	6.34457i		−	0.276636i
$527$		−	1.37685i		−	0.0599767i
$528$		0			0
$529$	8.26148	−	14.3093i	0.359195	−	0.622143i
$530$	0.147001	−	0.254613i	0.00638530	−	0.0110597i
$531$		0			0
$532$	−0.554042			−0.0240208
$533$	2.80257	+	1.67765i	0.121393	+	0.0726672i
$534$		0			0
$535$	14.3396	−	8.27899i	0.619956	−	0.357932i
$536$	15.0642	+	26.0920i	0.650675	+	1.12700i
$537$		0			0
$538$	−18.4979	+	10.6798i	−0.797500	+	0.460437i
$539$	−2.20324	+	1.27204i	−0.0949004	+	0.0547908i
$540$		0			0
$541$			39.9796i			1.71886i	0.511255	+	0.859429i	$0.329181\pi$
$541$			39.9796i			1.71886i	−0.511255	+	0.859429i	$0.670819\pi$
$542$	15.4272	−	26.7207i	0.662655	−	1.14775i
$543$		0			0
$544$	−0.0224212	+	0.0129449i	−0.000961299	+	0.000555006i
$545$	4.15281	−	7.19287i	0.177887	−	0.308109i
$546$		0			0
$547$	5.31092	+	9.19878i	0.227078	+	0.393311i	0.956941	−	0.290283i	$-0.0937493\pi$
$547$	5.31092	+	9.19878i	0.227078	+	0.393311i	−0.729863	+	0.683594i	$0.760416\pi$
$548$	0.144310	+	0.0833174i	0.00616462	+	0.00355914i
$549$		0			0
$550$	−2.29702	−	3.97855i	−0.0979451	−	0.169646i
$551$	−53.0934	+	30.6535i	−2.26185	+	1.30588i
$552$		0			0
$553$			13.6388i			0.579981i
$554$	−7.35418	−	4.24594i	−0.312449	−	0.180393i
$555$		0			0
$556$	−0.260642			−0.0110537
$557$	27.4337	+	15.8389i	1.16240	+	0.671114i	0.951879	−	0.306474i	$-0.0991493\pi$
$557$	27.4337	+	15.8389i	1.16240	+	0.671114i	0.210525	+	0.977588i	$0.432483\pi$
$558$		0			0
$559$	14.3234	+	0.226333i	0.605815	+	0.00957287i
$560$	19.0596	+	33.0122i	0.805414	+	1.39502i
$561$		0			0
$562$	5.32465	+	9.22256i	0.224607	+	0.389030i
$563$	−21.2806			−0.896871			−0.448435	−	0.893815i	$-0.648019\pi$
$563$	−21.2806			−0.896871			−0.448435	+	0.893815i	$0.648019\pi$
$564$		0			0
$565$	−43.1493	−	24.9123i	−1.81530	−	1.04807i
$566$	−34.1776	+	19.7324i	−1.43659	+	0.829415i
$567$		0			0
$568$	−0.446042	−	0.772567i	−0.0187155	−	0.0324162i
$569$	3.80515			0.159520			0.0797601	−	0.996814i	$-0.474585\pi$
$569$	3.80515			0.159520			0.0797601	+	0.996814i	$0.474585\pi$
$570$		0			0
$571$	16.1472	−	27.9678i	0.675740	−	1.17042i	−0.300512	−	0.953778i	$-0.597157\pi$
$571$	16.1472	−	27.9678i	0.675740	−	1.17042i	0.976252	−	0.216638i	$-0.0695092\pi$
$572$	−0.0597609	+	0.0332553i	−0.00249873	+	0.00139047i
$573$		0			0
$574$		−	4.06830i		−	0.169807i
$575$	−5.24001	+	9.07597i	−0.218524	+	0.378494i
$576$		0			0
$577$			5.48831i			0.228481i	0.993453	+	0.114241i	$0.0364435\pi$
$577$			5.48831i			0.228481i	−0.993453	+	0.114241i	$0.963557\pi$
$578$	20.6512	+	11.9230i	0.858978	+	0.495931i
$579$		0			0
$580$	−0.528060	−	0.304876i	−0.0219265	−	0.0126593i
$581$	25.8749			1.07347
$582$		0			0
$583$		−	0.0549685i		−	0.00227656i
$584$	18.6563			0.772004
$585$		0			0
$586$	−32.2427			−1.33193
$587$		−	19.2704i		−	0.795373i	−0.917521	−	0.397687i	$-0.869813\pi$
$587$		−	19.2704i		−	0.795373i	0.917521	−	0.397687i	$-0.130187\pi$
$588$		0			0
$589$	−52.1716			−2.14969
$590$	49.8719	+	28.7935i	2.05319	+	1.18541i
$591$		0			0
$592$	−8.91894	−	5.14935i	−0.366566	−	0.211637i
$593$		−	17.9934i		−	0.738902i	−0.929250	−	0.369451i	$-0.879546\pi$
$593$		−	17.9934i		−	0.738902i	0.929250	−	0.369451i	$-0.120454\pi$
$594$		0			0
$595$	0.923642	−	1.59979i	0.0378656	−	0.0655852i
$596$		−	0.349467i		−	0.0143147i
$597$		0			0
$598$	−11.0678	−	6.62532i	−0.452595	−	0.270930i
$599$	1.96620	−	3.40556i	0.0803367	−	0.139147i	−0.823058	−	0.567958i	$-0.807734\pi$
$599$	1.96620	−	3.40556i	0.0803367	−	0.139147i	0.903395	+	0.428810i	$0.141067\pi$
$600$		0			0
$601$	24.4924			0.999066			0.499533	−	0.866295i	$-0.333505\pi$
$601$	24.4924			0.999066			0.499533	+	0.866295i	$0.333505\pi$
$602$	−8.92119	−	15.4520i	−0.363601	−	0.629775i
$603$		0			0
$604$	0.0218130	−	0.0125937i	0.000887559	−	0.000512432i
$605$	27.1183	+	15.6568i	1.10252	+	0.636538i
$606$		0			0
$607$	13.4499			0.545913			0.272956	−	0.962026i	$-0.411999\pi$
$607$	13.4499			0.545913			0.272956	+	0.962026i	$0.411999\pi$
$608$	0.490506	+	0.849580i	0.0198926	+	0.0344550i
$609$		0			0
$610$	−0.379600	−	0.657487i	−0.0153696	−	0.0266209i
$611$	23.6039	+	14.1296i	0.954913	+	0.571623i
$612$		0			0
$613$	20.2969	+	11.7184i	0.819784	+	0.473303i	0.850342	−	0.526230i	$-0.176395\pi$
$613$	20.2969	+	11.7184i	0.819784	+	0.473303i	−0.0305579	+	0.999533i	$0.509728\pi$
$614$	−4.65792			−0.187979
$615$		0			0
$616$	6.24684	+	3.60661i	0.251692	+	0.145315i
$617$		−	23.2318i		−	0.935278i	−0.883920	−	0.467639i	$-0.845105\pi$
$617$		−	23.2318i		−	0.935278i	0.883920	−	0.467639i	$-0.154895\pi$
$618$		0			0
$619$	−1.01355	+	0.585173i	−0.0407380	+	0.0235201i	−0.520231	−	0.854026i	$-0.674154\pi$
$619$	−1.01355	+	0.585173i	−0.0407380	+	0.0235201i	0.479493	+	0.877546i	$0.340821\pi$
$620$	−0.259446	−	0.449374i	−0.0104196	−	0.0180473i
$621$		0			0
$622$	−30.8478	−	17.8100i	−1.23688	−	0.714116i
$623$	−8.42775	−	14.5973i	−0.337651	−	0.584828i
$624$		0			0
$625$	14.3162	−	24.7964i	0.572649	−	0.991858i
$626$	21.2224	−	12.2527i	0.848217	−	0.489718i
$627$		0			0
$628$	0.133768	−	0.231693i	0.00533793	−	0.00924556i
$629$			0.499083i			0.0198998i
$630$		0			0
$631$	−4.36496	+	2.52011i	−0.173766	+	0.100324i	−0.584361	−	0.811494i	$-0.698655\pi$
$631$	−4.36496	+	2.52011i	−0.173766	+	0.100324i	0.410594	+	0.911818i	$0.365321\pi$
$632$	10.5191	−	6.07323i	0.418429	−	0.241580i
$633$		0			0
$634$	9.17104	+	15.8847i	0.364229	+	0.630862i
$635$	−40.3451	+	23.2932i	−1.60104	+	0.924364i
$636$		0			0
$637$	−5.93649	+	9.91708i	−0.235212	+	0.392929i
$638$	9.42577			0.373170
$639$		0			0
$640$	16.7688	−	29.0443i	0.662844	−	1.14808i
$641$	−17.3411	+	30.0357i	−0.684934	+	1.18634i	0.288524	+	0.957473i	$0.406836\pi$
$641$	−17.3411	+	30.0357i	−0.684934	+	1.18634i	−0.973458	+	0.228868i	$0.926498\pi$
$642$		0			0
$643$			38.5994i			1.52221i	0.648627	+	0.761106i	$0.275343\pi$
$643$			38.5994i			1.52221i	−0.648627	+	0.761106i	$0.724657\pi$
$644$		−	0.194320i		−	0.00765729i
$645$		0			0
$646$	−0.976683	+	1.69166i	−0.0384271	+	0.0665577i
$647$	18.4314	−	31.9241i	0.724612	−	1.25507i	−0.234521	−	0.972111i	$-0.575352\pi$
$647$	18.4314	−	31.9241i	0.724612	−	1.25507i	0.959133	−	0.282954i	$-0.0913145\pi$
$648$		0			0
$649$	10.7669			0.422637
$650$	−17.9080	−	10.7199i	−0.702408	−	0.420470i
$651$		0			0
$652$	−0.0404026	+	0.0233265i	−0.00158229	+	0.000913534i
$653$	−16.3210	−	28.2688i	−0.638690	−	1.10624i	−0.985721	−	0.168389i	$-0.946143\pi$
$653$	−16.3210	−	28.2688i	−0.638690	−	1.10624i	0.347031	−	0.937854i	$-0.387190\pi$
$654$		0			0
$655$	−18.4695	+	10.6634i	−0.721662	+	0.416652i
$656$	−3.10024	+	1.78992i	−0.121044	+	0.0698847i
$657$		0			0
$658$		−	34.2642i		−	1.33576i
$659$	4.43305	−	7.67828i	0.172687	−	0.299103i	−0.766671	−	0.642040i	$-0.778088\pi$
$659$	4.43305	−	7.67828i	0.172687	−	0.299103i	0.939358	+	0.342937i	$0.111422\pi$
$660$		0			0
$661$	16.6210	−	9.59611i	0.646480	−	0.373245i	−0.140626	−	0.990063i	$-0.544912\pi$
$661$	16.6210	−	9.59611i	0.646480	−	0.373245i	0.787106	+	0.616817i	$0.211578\pi$
$662$	3.34296	−	5.79018i	0.129928	−	0.225042i
$663$		0			0
$664$	−11.5219	−	19.9564i	−0.447135	−	0.774460i
$665$	−60.6193	−	34.9986i	−2.35071	−	1.35719i
$666$		0			0
$667$	−10.7512	−	18.6215i	−0.416286	−	0.721029i
$668$	−0.411237	+	0.237428i	−0.0159112	+	0.00918635i
$669$		0			0
$670$			44.9505i			1.73659i
$671$	−0.122928	−	0.0709727i	−0.00474559	−	0.00273987i
$672$		0			0
$673$	5.35582			0.206452			0.103226	−	0.994658i	$-0.467084\pi$
$673$	5.35582			0.206452			0.103226	+	0.994658i	$0.467084\pi$
$674$	−31.0869	−	17.9480i	−1.19742	−	0.691331i
$675$		0			0
$676$	−0.163778	+	0.264038i	−0.00629916	+	0.0101553i
$677$	−1.63177	−	2.82630i	−0.0627139	−	0.108624i	0.832964	−	0.553328i	$-0.186642\pi$
$677$	−1.63177	−	2.82630i	−0.0627139	−	0.108624i	−0.895678	+	0.444704i	$0.853309\pi$
$678$		0			0
$679$	−28.0663	−	48.6123i	−1.07709	−	1.86557i
$680$	−1.64516			−0.0630888
$681$		0			0
$682$	6.94660	+	4.01062i	0.265999	+	0.153575i
$683$	22.0781	−	12.7468i	0.844794	−	0.487742i	−0.0140968	−	0.999901i	$-0.504487\pi$
$683$	22.0781	−	12.7468i	0.844794	−	0.487742i	0.858891	+	0.512159i	$0.171154\pi$
$684$		0			0
$685$	10.5262	+	18.2320i	0.402187	+	0.696608i
$686$	−17.0397			−0.650579
$687$		0			0
$688$	−7.85008	+	13.5967i	−0.299282	+	0.518371i
$689$	−0.121432	−	0.218218i	−0.00462619	−	0.00831344i
$690$		0			0
$691$			22.1957i			0.844364i	0.906511	+	0.422182i	$0.138736\pi$
$691$			22.1957i			0.844364i	−0.906511	+	0.422182i	$0.861264\pi$
$692$	−0.0402976	+	0.0697975i	−0.00153189	+	0.00265330i
$693$		0			0
$694$		−	7.62958i		−	0.289615i
$695$	−28.5176	−	16.4646i	−1.08173	−	0.624539i
$696$		0			0
$697$	0.150240	+	0.0867410i	0.00569074	+	0.00328555i
$698$	−37.1069			−1.40452
$699$		0			0
$700$		−	0.314415i		−	0.0118838i
$701$	−35.2587			−1.33170			−0.665851	−	0.746085i	$-0.731931\pi$
$701$	−35.2587			−1.33170			−0.665851	+	0.746085i	$0.731931\pi$
$702$		0			0
$703$	18.9112			0.713250
$704$		−	6.42306i		−	0.242078i
$705$		0			0
$706$	−42.0063			−1.58093
$707$	4.14410	+	2.39260i	0.155855	+	0.0899828i
$708$		0			0
$709$	17.1633	+	9.90922i	0.644580	+	0.372149i	0.786377	−	0.617747i	$-0.211954\pi$
$709$	17.1633	+	9.90922i	0.644580	+	0.372149i	−0.141796	+	0.989896i	$0.545288\pi$
$710$		−	1.33095i		−	0.0499498i
$711$		0			0
$712$	−7.50559	+	13.0001i	−0.281284	+	0.487198i
$713$		−	18.2983i		−	0.685276i
$714$		0			0
$715$	−8.63933	−	0.136516i	−0.323093	−	0.00510540i
$716$	−0.154524	+	0.267643i	−0.00577483	+	0.0100023i
$717$		0			0
$718$	38.7724			1.44697
$719$	−12.5408	−	21.7214i	−0.467695	−	0.810071i	0.531624	−	0.846981i	$-0.321582\pi$
$719$	−12.5408	−	21.7214i	−0.467695	−	0.810071i	−0.999319	+	0.0369095i	$0.988249\pi$
$720$		0			0
$721$	−8.96521	+	5.17607i	−0.333882	+	0.192767i
$722$	40.9697	+	23.6539i	1.52474	+	0.880306i
$723$		0			0
$724$	−0.272288			−0.0101195
$725$	−17.3956	−	30.1301i	−0.646058	−	1.11900i
$726$		0			0
$727$	−5.05060	−	8.74790i	−0.187317	−	0.324442i	0.757038	−	0.653371i	$-0.226646\pi$
$727$	−5.05060	−	8.74790i	−0.187317	−	0.324442i	−0.944355	+	0.328929i	$0.893312\pi$
$728$	32.7666	+	0.517766i	1.21441	+	0.0191897i
$729$		0			0
$730$	24.1054	+	13.9173i	0.892181	+	0.515101i
$731$	0.760842			0.0281408
$732$		0			0
$733$	10.3089	+	5.95182i	0.380766	+	0.219836i	0.678152	−	0.734922i	$-0.262781\pi$
$733$	10.3089	+	5.95182i	0.380766	+	0.219836i	−0.297385	+	0.954758i	$0.596115\pi$
$734$			30.1383i			1.11242i
$735$		0			0
$736$	−0.297975	+	0.172036i	−0.0109835	+	0.00634133i
$737$	4.20213	+	7.27830i	0.154787	+	0.268100i
$738$		0			0
$739$	22.7597	+	13.1403i	0.837231	+	0.483375i	0.856322	−	0.516442i	$-0.172744\pi$
$739$	22.7597	+	13.1403i	0.837231	+	0.483375i	−0.0190912	+	0.999818i	$0.506077\pi$
$740$	0.0940444	+	0.162890i	0.00345714	+	0.00598795i
$741$		0			0
$742$	−0.155522	+	0.269373i	−0.00570940	+	0.00988898i
$743$	6.24525	−	3.60570i	0.229116	−	0.132280i	−0.381048	−	0.924555i	$-0.624437\pi$
$743$	6.24525	−	3.60570i	0.229116	−	0.132280i	0.610164	+	0.792275i	$0.291103\pi$
$744$		0			0
$745$	22.0757	−	38.2362i	0.808790	−	1.40087i
$746$		−	34.9255i		−	1.27871i
$747$		0			0
$748$	−0.00314574	+	0.00181619i	−0.000115019	+	6.64065e-5i
$749$	−15.1709	+	8.75892i	−0.554333	+	0.320044i
$750$		0			0
$751$	0.249500	+	0.432147i	0.00910439	+	0.0157693i	0.870542	−	0.492095i	$-0.163769\pi$
$751$	0.249500	+	0.432147i	0.00910439	+	0.0157693i	−0.861437	+	0.507864i	$0.830435\pi$
$752$	−26.1110	+	15.0752i	−0.952169	+	0.549735i
$753$		0			0
$754$	37.4191	−	20.8227i	1.36272	−	0.758317i
$755$	3.18216			0.115811
$756$		0			0
$757$	24.1489	−	41.8272i	0.877708	−	1.52024i	0.0238592	−	0.999715i	$-0.492405\pi$
$757$	24.1489	−	41.8272i	0.877708	−	1.52024i	0.853849	−	0.520520i	$-0.174262\pi$
$758$	0.619969	−	1.07382i	0.0225183	−	0.0390028i
$759$		0			0
$760$			62.3381i			2.26124i
$761$		−	31.6996i		−	1.14911i	−0.818467	−	0.574554i	$-0.805176\pi$
$761$		−	31.6996i		−	1.14911i	0.818467	−	0.574554i	$-0.194824\pi$
$762$		0			0
$763$	−4.39355	+	7.60985i	−0.159057	+	0.275495i
$764$	0.0390615	−	0.0676565i	0.00141320	−	0.00244773i
$765$		0			0
$766$	−4.03424			−0.145763
$767$	42.7431	−	23.7853i	1.54336	−	0.858839i
$768$		0			0
$769$	−7.69488	+	4.44264i	−0.277484	+	0.160206i	−0.632284	−	0.774737i	$-0.717882\pi$
$769$	−7.69488	+	4.44264i	−0.277484	+	0.160206i	0.354800	+	0.934942i	$0.384549\pi$
$770$	5.38093	+	9.32005i	0.193915	+	0.335871i
$771$		0			0
$772$	−0.394585	+	0.227814i	−0.0142014	+	0.00819919i
$773$	−39.3502	+	22.7188i	−1.41533	+	0.817140i	−0.995884	−	0.0906413i	$-0.971108\pi$
$773$	−39.3502	+	22.7188i	−1.41533	+	0.817140i	−0.419444	+	0.907781i	$0.637775\pi$
$774$		0			0
$775$		−	29.6071i		−	1.06352i
$776$	−24.9953	+	43.2932i	−0.897280	+	1.55414i
$777$		0			0
$778$	14.6269	−	8.44484i	0.524399	−	0.302762i
$779$	3.28678	−	5.69287i	0.117761	−	0.203968i
$780$		0			0
$781$	−0.124422	−	0.215506i	−0.00445218	−	0.00771139i
$782$	−0.593321	−	0.342554i	−0.0212171	−	0.0122497i
$783$		0			0
$784$	−6.33376	−	10.9704i	−0.226206	−	0.391800i
$785$	29.2719	−	16.9001i	1.04476	−	0.603191i
$786$		0			0
$787$			4.87839i			0.173896i	0.996213	+	0.0869478i	$0.0277113\pi$
$787$			4.87839i			0.173896i	−0.996213	+	0.0869478i	$0.972289\pi$
$788$	0.0509969	+	0.0294431i	0.00181669	+	0.00104887i
$789$		0			0
$790$	18.1220			0.644754
$791$	45.6507	+	26.3564i	1.62315	+	0.937127i
$792$		0			0
$793$	−0.644797	−	0.0101889i	−0.0228974	−	0.000361817i
$794$	6.33473	+	10.9721i	0.224811	+	0.389385i
$795$		0			0
$796$	0.281112	+	0.486900i	0.00996374	+	0.0172577i
$797$	−35.9086			−1.27195			−0.635974	−	0.771710i	$-0.719402\pi$
$797$	−35.9086			−1.27195			−0.635974	+	0.771710i	$0.719402\pi$
$798$		0			0
$799$	1.26536	+	0.730555i	0.0447652	+	0.0258452i
$800$	−0.482131	+	0.278359i	−0.0170459	+	0.00984146i
$801$		0			0
$802$	23.3638	+	40.4673i	0.825004	+	1.42895i
$803$	5.20413			0.183650
$804$		0			0
$805$	12.2751	−	21.2611i	0.432641	−	0.749356i
$806$	36.4371	+	0.575766i	1.28344	+	0.0202805i
$807$		0			0
$808$		−	4.26160i		−	0.149923i
$809$	12.1005	−	20.9587i	0.425430	−	0.736867i	−0.571030	−	0.820929i	$-0.693456\pi$
$809$	12.1005	−	20.9587i	0.425430	−	0.736867i	0.996461	+	0.0840620i	$0.0267894\pi$
$810$		0			0
$811$		−	14.3469i		−	0.503789i	−0.967755	−	0.251894i	$-0.918946\pi$
$811$		−	14.3469i		−	0.503789i	0.967755	−	0.251894i	$-0.0810536\pi$
$812$	0.558672	+	0.322549i	0.0196055	+	0.0113193i
$813$		0			0
$814$	−2.51801	−	1.45377i	−0.0882563	−	0.0509548i
$815$	−5.89408			−0.206461
$816$		0			0
$817$		−	28.8298i		−	1.00863i
$818$	47.6663			1.66661
$819$		0			0
$820$	0.0653799			0.00228317
$821$			5.00052i			0.174519i	0.996186	+	0.0872596i	$0.0278110\pi$
$821$			5.00052i			0.174519i	−0.996186	+	0.0872596i	$0.972189\pi$
$822$		0			0
$823$	4.52344			0.157677			0.0788385	−	0.996887i	$-0.474879\pi$
$823$	4.52344			0.157677			0.0788385	+	0.996887i	$0.474879\pi$
$824$	7.98425	+	4.60971i	0.278144	+	0.160587i
$825$		0			0
$826$	−52.7630	−	30.4627i	−1.83586	−	1.05993i
$827$			7.63184i			0.265385i	0.991157	+	0.132693i	$0.0423623\pi$
$827$			7.63184i			0.265385i	−0.991157	+	0.132693i	$0.957638\pi$
$828$		0			0
$829$	8.47700	−	14.6826i	0.294418	−	0.509948i	−0.680431	−	0.732812i	$-0.738207\pi$
$829$	8.47700	−	14.6826i	0.294418	−	0.509948i	0.974849	+	0.222864i	$0.0715407\pi$
$830$		−	34.3803i		−	1.19336i
$831$		0			0
$832$	−14.1893	−	25.4987i	−0.491926	−	0.884008i
$833$	−0.306939	+	0.531634i	−0.0106348	+	0.0184200i
$834$		0			0
$835$	−59.9928			−2.07614
$836$	0.0688190	+	0.119198i	0.00238015	+	0.00412255i
$837$		0			0
$838$	−30.8965	+	17.8381i	−1.06730	+	0.616206i
$839$	−19.8924	−	11.4849i	−0.686760	−	0.396501i	0.115637	−	0.993292i	$-0.463109\pi$
$839$	−19.8924	−	11.4849i	−0.686760	−	0.396501i	−0.802397	+	0.596790i	$0.796442\pi$
$840$		0			0
$841$	42.3827			1.46147
$842$	8.29560	+	14.3684i	0.285885	+	0.495168i
$843$		0			0
$844$	0.0172724	+	0.0299167i	0.000594540	+	0.00102977i
$845$	−34.5986	+	18.5434i	−1.19023	+	0.637912i
$846$		0			0
$847$	−28.6904	−	16.5644i	−0.985813	−	0.569159i
$848$	0.273700			0.00939888
$849$		0			0
$850$	−0.960008	−	0.554261i	−0.0329280	−	0.0190110i
$851$			6.63278i			0.227369i
$852$		0			0
$853$	16.0483	−	9.26548i	0.549483	−	0.317244i	−0.199430	−	0.979912i	$-0.563909\pi$
$853$	16.0483	−	9.26548i	0.549483	−	0.317244i	0.748913	+	0.662668i	$0.230576\pi$
$854$	0.401606	+	0.695602i	0.0137427	+	0.0238030i
$855$		0			0
$856$	13.5109	+	7.80053i	0.461793	+	0.266617i
$857$	−20.7985	−	36.0241i	−0.710464	−	1.23056i	−0.964683	−	0.263413i	$-0.915152\pi$
$857$	−20.7985	−	36.0241i	−0.710464	−	1.23056i	0.254219	−	0.967147i	$-0.418181\pi$
$858$		0			0
$859$	−7.48523	+	12.9648i	−0.255393	+	0.442353i	−0.965002	−	0.262242i	$-0.915538\pi$
$859$	−7.48523	+	12.9648i	−0.255393	+	0.442353i	0.709609	+	0.704595i	$0.248871\pi$
$860$	0.248322	−	0.143369i	0.00846771	−	0.00488883i
$861$		0			0
$862$	8.08877	−	14.0102i	0.275505	−	0.477188i
$863$			30.1011i			1.02465i	0.858791	+	0.512327i	$0.171216\pi$
$863$			30.1011i			1.02465i	−0.858791	+	0.512327i	$0.828784\pi$
$864$		0			0
$865$	−8.81815	+	5.09116i	−0.299826	+	0.173105i
$866$	−17.0575	+	9.84813i	−0.579636	+	0.334653i
$867$		0			0
$868$	0.274487	+	0.475425i	0.00931668	+	0.0161370i
$869$	2.93429	−	1.69411i	0.0995388	−	0.0574688i
$870$		0			0
$871$	32.7605	+	19.6109i	1.11005	+	0.664490i
$872$	7.82562			0.265009
$873$		0			0
$874$	−12.9800	+	22.4821i	−0.439056	+	0.760468i
$875$	−4.25466	+	7.36929i	−0.143834	+	0.249127i
$876$		0			0
$877$		−	4.60474i		−	0.155491i	−0.996973	−	0.0777454i	$-0.975228\pi$
$877$		−	4.60474i		−	0.155491i	0.996973	−	0.0777454i	$-0.0247721\pi$
$878$		−	47.9073i		−	1.61679i
$879$		0			0
$880$	4.73488	−	8.20105i	0.159613	−	0.276457i
$881$	23.1838	−	40.1555i	0.781082	−	1.35287i	−0.150229	−	0.988651i	$-0.548001\pi$
$881$	23.1838	−	40.1555i	0.781082	−	1.35287i	0.931312	−	0.364223i	$-0.118666\pi$
$882$		0			0
$883$	−20.7632			−0.698737			−0.349368	−	0.936985i	$-0.613604\pi$
$883$	−20.7632			−0.698737			−0.349368	+	0.936985i	$0.613604\pi$
$884$	−0.00847598	+	0.0141594i	−0.000285078	+	0.000476231i
$885$		0			0
$886$	39.7705	−	22.9615i	1.33612	−	0.771407i
$887$	19.3264	+	33.4743i	0.648916	+	1.12396i	0.983382	+	0.181548i	$0.0581109\pi$
$887$	19.3264	+	33.4743i	0.648916	+	1.12396i	−0.334466	+	0.942408i	$0.608556\pi$
$888$		0			0
$889$	42.6839	−	24.6435i	1.43157	−	0.826518i
$890$	−19.3956	+	11.1981i	−0.650142	+	0.375360i
$891$		0			0
$892$		−	0.0144928i		−	0.000485255i
$893$	27.6821	−	47.9468i	0.926347	−	1.60448i
$894$		0			0
$895$	−33.8138	+	19.5224i	−1.13027	+	0.652562i
$896$	−17.7408	+	30.7280i	−0.592680	+	1.02655i
$897$		0			0
$898$	−6.22376	−	10.7799i	−0.207690	−	0.359729i
$899$	52.6076	+	30.3730i	1.75456	+	1.01300i
$900$		0			0
$901$	−0.00663185	−	0.0114867i	−0.000220939	−	0.000382677i
$902$	−0.875264	+	0.505334i	−0.0291431	+	0.0168258i
$903$		0			0
$904$		−	46.9450i		−	1.56137i
$905$	−29.7918	−	17.2003i	−0.990312	−	0.571757i
$906$		0			0
$907$	−23.2273			−0.771250			−0.385625	−	0.922656i	$-0.626014\pi$
$907$	−23.2273			−0.771250			−0.385625	+	0.922656i	$0.626014\pi$
$908$	−0.477227	−	0.275527i	−0.0158373	−	0.00914370i
$909$		0			0
$910$	41.9507	+	25.1123i	1.39065	+	0.832463i
$911$	28.3835	+	49.1616i	0.940386	+	1.62880i	0.764737	+	0.644343i	$0.222869\pi$
$911$	28.3835	+	49.1616i	0.940386	+	1.62880i	0.175649	+	0.984453i	$0.443798\pi$
$912$		0			0
$913$	−3.21399	−	5.56679i	−0.106368	−	0.184234i
$914$	−21.3948			−0.707678
$915$		0			0
$916$	−0.0950498	−	0.0548770i	−0.00314053	−	0.00181319i
$917$	19.5401	−	11.2815i	0.645273	−	0.372548i
$918$		0			0
$919$	10.2662	+	17.7815i	0.338649	+	0.586557i	0.984179	−	0.177178i	$-0.0566967\pi$
$919$	10.2662	+	17.7815i	0.338649	+	0.586557i	−0.645530	+	0.763735i	$0.723363\pi$
$920$	−21.8640			−0.720834
$921$		0			0
$922$	−24.4677	+	42.3793i	−0.805800	+	1.39569i
$923$	−0.970018	−	0.580665i	−0.0319285	−	0.0191128i
$924$		0			0
$925$			10.7320i			0.352866i
$926$	19.2617	−	33.3622i	0.632978	−	1.09635i
$927$		0			0
$928$		−	1.14224i		−	0.0374959i
$929$	37.7777	+	21.8110i	1.23945	+	0.715595i	0.968981	−	0.247134i	$-0.0794888\pi$
$929$	37.7777	+	21.8110i	1.23945	+	0.715595i	0.270466	+	0.962729i	$0.412822\pi$
$930$		0			0
$931$	20.1446	+	11.6305i	0.660214	+	0.381175i
$932$	0.187450			0.00614013
$933$		0			0
$934$			13.1309i			0.429656i
$935$	−0.458912			−0.0150080
$936$		0			0
$937$	−50.6045			−1.65318			−0.826588	−	0.562807i	$-0.809721\pi$
$937$	−50.6045			−1.65318			−0.826588	+	0.562807i	$0.809721\pi$
$938$		−	47.5563i		−	1.55277i
$939$		0			0
$940$	0.550646			0.0179601
$941$	6.38079	+	3.68395i	0.208008	+	0.120093i	0.600385	−	0.799711i	$-0.295014\pi$
$941$	6.38079	+	3.68395i	0.208008	+	0.120093i	−0.392377	+	0.919804i	$0.628347\pi$
$942$		0			0
$943$	1.99667	+	1.15278i	0.0650207	+	0.0375397i
$944$			53.6105i			1.74487i
$945$		0			0
$946$	−2.21625	+	3.83866i	−0.0720565	+	0.124805i
$947$		−	15.5196i		−	0.504319i	−0.967686	−	0.252159i	$-0.918859\pi$
$947$		−	15.5196i		−	0.504319i	0.967686	−	0.252159i	$-0.0811407\pi$
$948$		0			0
$949$	20.6597	−	11.4966i	0.670643	−	0.373194i
$950$	−21.0020	+	36.3766i	−0.681395	+	1.18021i
$951$		0			0
$952$	1.74052			0.0564107
$953$	11.8288	+	20.4880i	0.383171	+	0.663672i	0.991514	−	0.130003i	$-0.0414986\pi$
$953$	11.8288	+	20.4880i	0.383171	+	0.663672i	−0.608343	+	0.793675i	$0.708165\pi$
$954$		0			0
$955$	8.54766	−	4.93499i	0.276596	−	0.159693i
$956$	−0.0286482	−	0.0165400i	−0.000926549	−	0.000534943i
$957$		0			0
$958$	−15.5149			−0.501263
$959$	−11.1364	−	19.2889i	−0.359615	−	0.622871i
$960$		0			0
$961$	10.3472	+	17.9218i	0.333780	+	0.578123i
$962$	−13.2077	−	0.208704i	−0.425835	−	0.00672889i
$963$		0			0
$964$	0.0837575	+	0.0483574i	0.00269765	+	0.00155749i
$965$	−57.5635			−1.85304
$966$		0			0
$967$	−12.2838	−	7.09208i	−0.395022	−	0.228066i	0.289312	−	0.957235i	$-0.406574\pi$
$967$	−12.2838	−	7.09208i	−0.395022	−	0.228066i	−0.684334	+	0.729169i	$0.739907\pi$
$968$			29.5039i			0.948290i
$969$		0			0
$970$	−64.5918	+	37.2921i	−2.07392	+	1.19738i
$971$	16.0778	+	27.8476i	0.515963	+	0.893674i	0.999828	+	0.0185312i	$0.00589901\pi$
$971$	16.0778	+	27.8476i	0.515963	+	0.893674i	−0.483866	+	0.875142i	$0.660768\pi$
$972$		0			0
$973$	30.1707	+	17.4191i	0.967230	+	0.558430i
$974$	8.11217	+	14.0507i	0.259931	+	0.450213i
$975$		0			0
$976$	0.353388	−	0.612085i	0.0113117	−	0.0195924i
$977$	45.1160	−	26.0477i	1.44339	−	0.833340i	0.445314	−	0.895375i	$-0.353092\pi$
$977$	45.1160	−	26.0477i	1.44339	−	0.833340i	0.998074	+	0.0620342i	$0.0197588\pi$
$978$		0			0
$979$	−2.09367	+	3.62634i	−0.0669138	+	0.115898i
$980$			0.231351i			0.00739025i
$981$		0			0
$982$	25.8630	−	14.9320i	0.825323	−	0.476500i
$983$	−22.2548	+	12.8488i	−0.709819	+	0.409814i	−0.810994	−	0.585055i	$-0.801073\pi$
$983$	−22.2548	+	12.8488i	−0.709819	+	0.409814i	0.101175	+	0.994869i	$0.467740\pi$
$984$		0			0
$985$	3.71981	+	6.44290i	0.118523	+	0.205288i
$986$	1.96969	−	1.13720i	0.0627277	−	0.0362159i
$987$		0			0
$988$	0.536525	+	0.321171i	0.0170691	+	0.0102178i
$989$	10.1115			0.321528
$990$		0			0
$991$	−6.04305	+	10.4669i	−0.191964	+	0.332491i	−0.945901	−	0.324455i	$-0.894819\pi$
$991$	−6.04305	+	10.4669i	−0.191964	+	0.332491i	0.753937	+	0.656947i	$0.228152\pi$
$992$	0.486018	−	0.841808i	0.0154311	−	0.0267274i
$993$		0			0
$994$			1.40811i			0.0446625i
$995$			71.0308i			2.25183i
$996$		0			0
$997$	−27.7968	+	48.1455i	−0.880335	+	1.52478i	−0.0293652	+	0.999569i	$0.509349\pi$
$997$	−27.7968	+	48.1455i	−0.880335	+	1.52478i	−0.850969	+	0.525215i	$0.823985\pi$
$998$	−9.24317	+	16.0096i	−0.292587	+	0.506776i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.l.b.199.9		22
3.2	odd	2		117.2.l.b.4.3	✓	22
9.2	odd	6		117.2.r.b.43.3	yes	22
9.7	even	3		351.2.r.b.316.9		22
13.10	even	6		351.2.r.b.10.9		22
39.23	odd	6		117.2.r.b.49.3	yes	22
117.88	even	6	inner	351.2.l.b.127.3		22
117.101	odd	6		117.2.l.b.88.9	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.3	✓	22	3.2	odd	2
117.2.l.b.88.9	yes	22	117.101	odd	6
117.2.r.b.43.3	yes	22	9.2	odd	6
117.2.r.b.49.3	yes	22	39.23	odd	6
351.2.l.b.127.3		22	117.88	even	6	inner
351.2.l.b.199.9		22	1.1	even	1	trivial
351.2.r.b.10.9		22	13.10	even	6
351.2.r.b.316.9		22	9.7	even	3

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.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.40574i q^{2} +0.0239006 q^{4} +(2.61504 + 1.50979i) q^{5} +(-2.76663 - 1.59731i) q^{7} +2.84507i q^{8} +(-2.12237 + 3.67605i) q^{10} +0.793626i q^{11} +(1.75322 + 3.15059i) q^{13} +(2.24541 - 3.88916i) q^{14} -3.95163 q^{16} +(0.0957495 + 0.165843i) q^{17} +(6.28411 - 3.62813i) q^{19} +(0.0625010 + 0.0360850i) q^{20} -1.11563 q^{22} +(1.27250 + 2.20404i) q^{23} +(2.05894 + 3.56619i) q^{25} +(-4.42891 + 2.46456i) q^{26} +(-0.0661242 - 0.0381768i) q^{28} -8.44883 q^{29} +(-6.22662 - 3.59494i) q^{31} +0.135195i q^{32} +(-0.233132 + 0.134599i) q^{34} +(-4.82322 - 8.35407i) q^{35} +(2.25703 + 1.30310i) q^{37} +(5.10020 + 8.83381i) q^{38} +(-4.29547 + 7.43997i) q^{40} +(0.784546 - 0.452958i) q^{41} +(1.98654 - 3.44080i) q^{43} +0.0189682i q^{44} +(-3.09830 + 1.78880i) q^{46} +(6.60765 - 3.81493i) q^{47} +(1.60282 + 2.77617i) q^{49} +(-5.01313 + 2.89433i) q^{50} +(0.0419030 + 0.0753011i) q^{52} -0.0692625 q^{53} +(-1.19821 + 2.07536i) q^{55} +(4.54448 - 7.87126i) q^{56} -11.8768i q^{58} -13.5667i q^{59} +(-0.0894284 + 0.154895i) q^{61} +(5.05354 - 8.75299i) q^{62} -8.09330 q^{64} +(-0.172015 + 10.8859i) q^{65} +(9.17094 - 5.29484i) q^{67} +(0.00228847 + 0.00396375i) q^{68} +(11.7436 - 6.78019i) q^{70} +(-0.271545 + 0.156777i) q^{71} -6.55741i q^{73} +(-1.83181 + 3.17279i) q^{74} +(0.150194 - 0.0867146i) q^{76} +(1.26767 - 2.19567i) q^{77} +(-2.13465 - 3.69732i) q^{79} +(-10.3336 - 5.96613i) q^{80} +(0.636740 + 1.10287i) q^{82} +(-7.01438 + 4.04975i) q^{83} +0.578247i q^{85} +(4.83686 + 2.79256i) q^{86} -2.25792 q^{88} +(4.56933 + 2.63810i) q^{89} +(0.181987 - 11.5170i) q^{91} +(0.0304136 + 0.0526779i) q^{92} +(5.36279 + 9.28863i) q^{94} +21.9109 q^{95} +(15.2169 + 8.78548i) q^{97} +(-3.90257 + 2.25315i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 20 q^{4} + 3 q^{5} - 6 q^{7} - 7 q^{10} + 9 q^{14} + 24 q^{16} - 9 q^{17} - 6 q^{19} + 24 q^{20} + 26 q^{22} - 6 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} - 48 q^{29} - 27 q^{31} + 15 q^{34} + 27 q^{35}+ \cdots - 117 q^{98}+O(q^{100}) \) 22 * q - 20 * q^4 + 3 * q^5 - 6 * q^7 - 7 * q^10 + 9 * q^14 + 24 * q^16 - 9 * q^17 - 6 * q^19 + 24 * q^20 + 26 * q^22 - 6 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 - 48 * q^29 - 27 * q^31 + 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 - 6 * q^41 - 4 * q^43 - 15 * q^46 + 6 * q^47 + 7 * q^49 - 18 * q^50 - 22 * q^52 + 24 * q^53 - 13 * q^55 + 9 * q^56 + 3 * q^61 - 24 * q^64 + 57 * q^65 - 45 * q^67 + 69 * q^68 - 24 * q^70 - 9 * q^71 + 6 * q^74 + 18 * q^76 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 - 42 * q^83 - 45 * q^86 + 22 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 + 44 * q^94 - 6 * q^95 - 27 * q^97 - 117 * q^98

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