LMFDB - Embedded newform 432.2.be.b.239.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			239.5
Character	$\chi$	$=$	432.239
Dual form			432.2.be.b.47.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36628 + 1.06456i) q^{3} +(1.83017 + 0.322709i) q^{5} +(-0.441545 - 0.526213i) q^{7} +(0.733433 + 2.90896i) q^{9} +O(q^{10})$	\(q+(1.36628 + 1.06456i) q^{3} +(1.83017 + 0.322709i) q^{5} +(-0.441545 - 0.526213i) q^{7} +(0.733433 + 2.90896i) q^{9} +(-0.0632128 - 0.358498i) q^{11} +(2.50997 - 0.913554i) q^{13} +(2.15698 + 2.38923i) q^{15} +(2.50099 + 1.44395i) q^{17} +(-2.50751 + 1.44771i) q^{19} +(-0.0430893 - 1.18900i) q^{21} +(-1.39029 - 1.16659i) q^{23} +(-1.45308 - 0.528877i) q^{25} +(-2.09469 + 4.75524i) q^{27} +(2.03639 - 5.59492i) q^{29} +(-2.94453 + 3.50915i) q^{31} +(0.295275 - 0.557101i) q^{33} +(-0.638290 - 1.10555i) q^{35} +(1.77265 - 3.07032i) q^{37} +(4.40185 + 1.42384i) q^{39} +(3.29740 + 9.05952i) q^{41} +(-11.8245 + 2.08497i) q^{43} +(0.403559 + 5.56059i) q^{45} +(7.61569 - 6.39032i) q^{47} +(1.13360 - 6.42896i) q^{49} +(1.87989 + 4.63529i) q^{51} -1.01980i q^{53} -0.676511i q^{55} +(-4.96713 - 0.691413i) q^{57} +(0.864840 - 4.90475i) q^{59} +(-9.61210 + 8.06551i) q^{61} +(1.20689 - 1.67038i) q^{63} +(4.88848 - 0.861972i) q^{65} +(1.71306 + 4.70659i) q^{67} +(-0.657619 - 3.07394i) q^{69} +(8.29859 - 14.3736i) q^{71} +(-6.84801 - 11.8611i) q^{73} +(-1.42229 - 2.26948i) q^{75} +(-0.160735 + 0.191556i) q^{77} +(2.52383 - 6.93417i) q^{79} +(-7.92415 + 4.26706i) q^{81} +(3.65593 + 1.33065i) q^{83} +(4.11127 + 3.44977i) q^{85} +(8.73839 - 5.47637i) q^{87} +(-12.1121 + 6.99291i) q^{89} +(-1.58899 - 0.917403i) q^{91} +(-7.75874 + 1.65986i) q^{93} +(-5.05636 + 1.84037i) q^{95} +(-0.204961 - 1.16239i) q^{97} +(0.996494 - 0.446818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q + 3 * q^5 + 6 * q^9	$ 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{18}\right)$

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			0
$2$		0			0
$3$	1.36628	+	1.06456i	0.788821	+	0.614623i
$3$	1.36628	+	1.06456i	0.788821	+	0.614623i
$4$		0			0
$5$	1.83017	+	0.322709i	0.818477	+	0.144320i	0.567184	−	0.823591i	$-0.308033\pi$
$5$	1.83017	+	0.322709i	0.818477	+	0.144320i	0.251294	+	0.967911i	$0.419144\pi$
$6$		0			0
$7$	−0.441545	−	0.526213i	−0.166888	−	0.198890i	0.676118	−	0.736793i	$-0.263661\pi$
$7$	−0.441545	−	0.526213i	−0.166888	−	0.198890i	−0.843006	+	0.537903i	$0.819216\pi$
$8$		0			0
$9$	0.733433	+	2.90896i	0.244478	+	0.969655i
$10$		0			0
$11$	−0.0632128	−	0.358498i	−0.0190594	−	0.108091i	0.973794	−	0.227432i	$-0.0730330\pi$
$11$	−0.0632128	−	0.358498i	−0.0190594	−	0.108091i	−0.992853	+	0.119341i	$0.961922\pi$
$12$		0			0
$13$	2.50997	−	0.913554i	0.696140	−	0.253374i	0.0303782	−	0.999538i	$-0.490329\pi$
$13$	2.50997	−	0.913554i	0.696140	−	0.253374i	0.665762	+	0.746164i	$0.268107\pi$
$14$		0			0
$15$	2.15698	+	2.38923i	0.556930	+	0.616897i
$16$		0			0
$17$	2.50099	+	1.44395i	0.606580	+	0.350209i	0.771626	−	0.636077i	$-0.219444\pi$
$17$	2.50099	+	1.44395i	0.606580	+	0.350209i	−0.165046	+	0.986286i	$0.552777\pi$
$18$		0			0
$19$	−2.50751	+	1.44771i	−0.575262	+	0.332128i	−0.759248	−	0.650801i	$-0.774433\pi$
$19$	−2.50751	+	1.44771i	−0.575262	+	0.332128i	0.183986	+	0.982929i	$0.441100\pi$
$20$		0			0
$21$	−0.0430893	−	1.18900i	−0.00940286	−	0.259462i
$22$		0			0
$23$	−1.39029	−	1.16659i	−0.289896	−	0.243252i	0.486228	−	0.873832i	$-0.338372\pi$
$23$	−1.39029	−	1.16659i	−0.289896	−	0.243252i	−0.776124	+	0.630580i	$0.782817\pi$
$24$		0			0
$25$	−1.45308	−	0.528877i	−0.290616	−	0.105775i
$26$		0			0
$27$	−2.09469	+	4.75524i	−0.403123	+	0.915146i
$28$		0			0
$29$	2.03639	−	5.59492i	0.378147	−	1.03895i	−0.593976	−	0.804482i	$-0.702443\pi$
$29$	2.03639	−	5.59492i	0.378147	−	1.03895i	0.972124	−	0.234469i	$-0.0753350\pi$
$30$		0			0
$31$	−2.94453	+	3.50915i	−0.528853	+	0.630262i	−0.962650	−	0.270748i	$-0.912729\pi$
$31$	−2.94453	+	3.50915i	−0.528853	+	0.630262i	0.433797	+	0.901011i	$0.357173\pi$
$32$		0			0
$33$	0.295275	−	0.557101i	0.0514008	−	0.0969788i
$34$		0			0
$35$	−0.638290	−	1.10555i	−0.107891	−	0.186872i
$36$		0			0
$37$	1.77265	−	3.07032i	0.291422	−	0.504757i	−0.682725	−	0.730676i	$-0.739205\pi$
$37$	1.77265	−	3.07032i	0.291422	−	0.504757i	0.974146	+	0.225919i	$0.0725384\pi$
$38$		0			0
$39$	4.40185	+	1.42384i	0.704860	+	0.227997i
$40$		0			0
$41$	3.29740	+	9.05952i	0.514967	+	1.41486i	0.876002	+	0.482308i	$0.160201\pi$
$41$	3.29740	+	9.05952i	0.514967	+	1.41486i	−0.361035	+	0.932552i	$0.617577\pi$
$42$		0			0
$43$	−11.8245	+	2.08497i	−1.80322	+	0.317956i	−0.971463	−	0.237190i	$-0.923774\pi$
$43$	−11.8245	+	2.08497i	−1.80322	+	0.317956i	−0.831753	+	0.555146i	$0.812662\pi$
$44$		0			0
$45$	0.403559	+	5.56059i	0.0601591	+	0.828923i
$46$		0			0
$47$	7.61569	−	6.39032i	1.11086	−	0.932124i	0.112755	−	0.993623i	$-0.464033\pi$
$47$	7.61569	−	6.39032i	1.11086	−	0.932124i	0.998107	+	0.0614989i	$0.0195881\pi$
$48$		0			0
$49$	1.13360	−	6.42896i	0.161943	−	0.918423i
$50$		0			0
$51$	1.87989	+	4.63529i	0.263237	+	0.649070i
$52$		0			0
$53$		−	1.01980i		−	0.140081i	−0.997544	−	0.0700403i	$-0.977687\pi$
$53$		−	1.01980i		−	0.140081i	0.997544	−	0.0700403i	$-0.0223128\pi$
$54$		0			0
$55$		−	0.676511i		−	0.0912207i
$56$		0			0
$57$	−4.96713	−	0.691413i	−0.657913	−	0.0915799i
$58$		0			0
$59$	0.864840	−	4.90475i	0.112593	−	0.638544i	−0.875321	−	0.483541i	$-0.839350\pi$
$59$	0.864840	−	4.90475i	0.112593	−	0.638544i	0.987914	−	0.155003i	$-0.0495387\pi$
$60$		0			0
$61$	−9.61210	+	8.06551i	−1.23070	+	1.03268i	−0.232510	+	0.972594i	$0.574694\pi$
$61$	−9.61210	+	8.06551i	−1.23070	+	1.03268i	−0.998193	+	0.0600881i	$0.980862\pi$
$62$		0			0
$63$	1.20689	−	1.67038i	0.152054	−	0.210448i
$64$		0			0
$65$	4.88848	−	0.861972i	0.606342	−	0.106914i
$66$		0			0
$67$	1.71306	+	4.70659i	0.209283	+	0.575001i	0.999273	−	0.0381187i	$-0.0121365\pi$
$67$	1.71306	+	4.70659i	0.209283	+	0.575001i	−0.789990	+	0.613120i	$0.789914\pi$
$68$		0			0
$69$	−0.657619	−	3.07394i	−0.0791681	−	0.370059i
$70$		0			0
$71$	8.29859	−	14.3736i	0.984862	−	1.70583i	0.342312	−	0.939586i	$-0.388790\pi$
$71$	8.29859	−	14.3736i	0.984862	−	1.70583i	0.642549	−	0.766244i	$-0.277877\pi$
$72$		0			0
$73$	−6.84801	−	11.8611i	−0.801499	−	1.38824i	−0.918629	−	0.395120i	$-0.870703\pi$
$73$	−6.84801	−	11.8611i	−0.801499	−	1.38824i	0.117131	−	0.993117i	$-0.462630\pi$
$74$		0			0
$75$	−1.42229	−	2.26948i	−0.164232	−	0.262057i
$76$		0			0
$77$	−0.160735	+	0.191556i	−0.0183174	+	0.0218299i
$78$		0			0
$79$	2.52383	−	6.93417i	0.283953	−	0.780155i	−0.712928	−	0.701237i	$-0.752631\pi$
$79$	2.52383	−	6.93417i	0.283953	−	0.780155i	0.996881	−	0.0789179i	$-0.0251465\pi$
$80$		0			0
$81$	−7.92415	+	4.26706i	−0.880461	+	0.474118i
$82$		0			0
$83$	3.65593	+	1.33065i	0.401291	+	0.146058i	0.534778	−	0.844993i	$-0.320395\pi$
$83$	3.65593	+	1.33065i	0.401291	+	0.146058i	−0.133487	+	0.991051i	$0.542617\pi$
$84$		0			0
$85$	4.11127	+	3.44977i	0.445930	+	0.374180i
$86$		0			0
$87$	8.73839	−	5.47637i	0.936854	−	0.587129i
$88$		0			0
$89$	−12.1121	+	6.99291i	−1.28388	+	0.741247i	−0.977555	−	0.210680i	$-0.932432\pi$
$89$	−12.1121	+	6.99291i	−1.28388	+	0.741247i	−0.306323	+	0.951928i	$0.599099\pi$
$90$		0			0
$91$	−1.58899	−	0.917403i	−0.166571	−	0.0961700i
$92$		0			0
$93$	−7.75874	+	1.65986i	−0.804544	+	0.172119i
$94$		0			0
$95$	−5.05636	+	1.84037i	−0.518772	+	0.188818i
$96$		0			0
$97$	−0.204961	−	1.16239i	−0.0208106	−	0.118023i	0.972633	−	0.232348i	$-0.0746407\pi$
$97$	−0.204961	−	1.16239i	−0.0208106	−	0.118023i	−0.993443	+	0.114325i	$0.963530\pi$
$98$		0			0
$99$	0.996494	−	0.446818i	0.100151	−	0.0449069i
$100$		0			0
$101$	−4.52719	−	5.39529i	−0.450472	−	0.536851i	0.492240	−	0.870460i	$-0.336178\pi$
$101$	−4.52719	−	5.39529i	−0.450472	−	0.536851i	−0.942712	+	0.333608i	$0.891734\pi$
$102$		0			0
$103$	−9.09521	−	1.60373i	−0.896178	−	0.158020i	−0.293457	−	0.955972i	$-0.594806\pi$
$103$	−9.09521	−	1.60373i	−0.896178	−	0.158020i	−0.602721	+	0.797952i	$0.705917\pi$
$104$		0			0
$105$	0.304841	−	2.18999i	0.0297494	−	0.213721i
$106$		0			0
$107$	−11.7246			−1.13346			−0.566730	−	0.823904i	$-0.691792\pi$
$107$	−11.7246			−1.13346			−0.566730	+	0.823904i	$0.691792\pi$
$108$		0			0
$109$	−12.7988			−1.22590			−0.612951	−	0.790121i	$-0.710018\pi$
$109$	−12.7988			−1.22590			−0.612951	+	0.790121i	$0.710018\pi$
$110$		0			0
$111$	5.69046	−	2.30782i	0.540115	−	0.219049i
$112$		0			0
$113$	11.2080	+	1.97627i	1.05436	+	0.185912i	0.673851	−	0.738867i	$-0.264639\pi$
$113$	11.2080	+	1.97627i	1.05436	+	0.185912i	0.380506	+	0.924779i	$0.375750\pi$
$114$		0			0
$115$	−2.16800	−	2.58372i	−0.202167	−	0.240934i
$116$		0			0
$117$	4.49839	+	6.63138i	0.415876	+	0.613071i
$118$		0			0
$119$	−0.344477	−	1.95362i	−0.0315781	−	0.179088i
$120$		0			0
$121$	10.2121	−	3.71690i	0.928372	−	0.337900i
$122$		0			0
$123$	−5.13923	+	15.8881i	−0.463388	+	1.43258i
$124$		0			0
$125$	−10.5358	−	6.08287i	−0.942354	−	0.544068i
$126$		0			0
$127$	10.3478	−	5.97431i	0.918220	−	0.530135i	0.0351532	−	0.999382i	$-0.488808\pi$
$127$	10.3478	−	5.97431i	0.918220	−	0.530135i	0.883067	+	0.469247i	$0.155475\pi$
$128$		0			0
$129$	−18.3751	−	9.73919i	−1.61784	−	0.857488i
$130$		0			0
$131$	0.871001	+	0.730857i	0.0760998	+	0.0638553i	0.680044	−	0.733171i	$-0.261961\pi$
$131$	0.871001	+	0.730857i	0.0760998	+	0.0638553i	−0.603944	+	0.797027i	$0.706405\pi$
$132$		0			0
$133$	1.86898	+	0.680255i	0.162062	+	0.0589856i
$134$		0			0
$135$	−5.36819	+	8.02692i	−0.462021	+	0.690848i
$136$		0			0
$137$	2.75201	−	7.56110i	0.235120	−	0.645988i	−0.764878	−	0.644175i	$-0.777201\pi$
$137$	2.75201	−	7.56110i	0.235120	−	0.645988i	0.999998	−	0.00181278i	$-0.000577027\pi$
$138$		0			0
$139$	−3.48845	+	4.15737i	−0.295886	+	0.352623i	−0.893422	−	0.449219i	$-0.851702\pi$
$139$	−3.48845	+	4.15737i	−0.295886	+	0.352623i	0.597535	+	0.801843i	$0.296147\pi$
$140$		0			0
$141$	17.2080	−	0.623615i	1.44918	−	0.0525179i
$142$		0			0
$143$	−0.486169	−	0.842069i	−0.0406555	−	0.0704174i
$144$		0			0
$145$	5.53246	−	9.58251i	0.459446	−	0.795784i
$146$		0			0
$147$	8.39281	−	7.57697i	0.692228	−	0.624938i
$148$		0			0
$149$	0.679944	+	1.86813i	0.0557032	+	0.153043i	0.964423	−	0.264363i	$-0.0851616\pi$
$149$	0.679944	+	1.86813i	0.0557032	+	0.153043i	−0.908720	+	0.417406i	$0.862939\pi$
$150$		0			0
$151$	−2.82458	+	0.498049i	−0.229861	+	0.0405307i	−0.287392	−	0.957813i	$-0.592788\pi$
$151$	−2.82458	+	0.498049i	−0.229861	+	0.0405307i	0.0575312	+	0.998344i	$0.481677\pi$
$152$		0			0
$153$	−2.36609	+	8.33434i	−0.191287	+	0.673792i
$154$		0			0
$155$	−6.52142	+	5.47212i	−0.523813	+	0.439532i
$156$		0			0
$157$	−2.10204	+	11.9213i	−0.167761	+	0.951421i	0.778411	+	0.627756i	$0.216026\pi$
$157$	−2.10204	+	11.9213i	−0.167761	+	0.951421i	−0.946172	+	0.323665i	$0.895085\pi$
$158$		0			0
$159$	1.08564	−	1.39333i	0.0860968	−	0.110499i
$160$		0			0
$161$			1.24669i			0.0982532i
$162$		0			0
$163$		−	3.69079i		−	0.289085i	−0.989499	−	0.144543i	$-0.953829\pi$
$163$		−	3.69079i		−	0.289085i	0.989499	−	0.144543i	$-0.0461710\pi$
$164$		0			0
$165$	0.720185	−	0.924302i	0.0560663	−	0.0719568i
$166$		0			0
$167$	−3.60391	+	20.4388i	−0.278879	+	1.58160i	0.447487	+	0.894291i	$0.352319\pi$
$167$	−3.60391	+	20.4388i	−0.278879	+	1.58160i	−0.726365	+	0.687309i	$0.758792\pi$
$168$		0			0
$169$	−4.49321	+	3.77025i	−0.345632	+	0.290020i
$170$		0			0
$171$	−6.05043	−	6.23246i	−0.462688	−	0.476608i
$172$		0			0
$173$	6.14247	−	1.08308i	0.467003	−	0.0823452i	0.0648051	−	0.997898i	$-0.479357\pi$
$173$	6.14247	−	1.08308i	0.467003	−	0.0823452i	0.402198	+	0.915553i	$0.368246\pi$
$174$		0			0
$175$	0.363298	+	0.998152i	0.0274627	+	0.0754532i
$176$		0			0
$177$	6.40300	−	5.78058i	0.481279	−	0.434495i
$178$		0			0
$179$	6.76734	−	11.7214i	0.505815	−	0.876097i	−0.494163	−	0.869369i	$-0.664525\pi$
$179$	6.76734	−	11.7214i	0.505815	−	0.876097i	0.999977	−	0.00672715i	$-0.00214133\pi$
$180$		0			0
$181$	−3.39270	−	5.87633i	−0.252177	−	0.436784i	0.711948	−	0.702232i	$-0.247813\pi$
$181$	−3.39270	−	5.87633i	−0.252177	−	0.436784i	−0.964125	+	0.265449i	$0.914480\pi$
$182$		0			0
$183$	−21.7190	+	0.787093i	−1.60551	+	0.0581836i
$184$		0			0
$185$	4.23507	−	5.04715i	0.311368	−	0.371074i
$186$		0			0
$187$	0.359557	−	0.987876i	0.0262934	−	0.0722406i
$188$		0			0
$189$	3.42717	−	0.997400i	0.249290	−	0.0725502i
$190$		0			0
$191$	15.3682	+	5.59358i	1.11201	+	0.404737i	0.831729	−	0.555181i	$-0.187351\pi$
$191$	15.3682	+	5.59358i	1.11201	+	0.404737i	0.280278	+	0.959919i	$0.409573\pi$
$192$		0			0
$193$	14.5207	+	12.1843i	1.04522	+	0.877046i	0.992583	−	0.121568i	$-0.0387922\pi$
$193$	14.5207	+	12.1843i	1.04522	+	0.877046i	0.0526393	+	0.998614i	$0.483237\pi$
$194$		0			0
$195$	7.59665	+	4.02638i	0.544007	+	0.288335i
$196$		0			0
$197$	−20.4041	+	11.7803i	−1.45373	+	0.839312i	−0.998691	−	0.0511593i	$-0.983708\pi$
$197$	−20.4041	+	11.7803i	−1.45373	+	0.839312i	−0.455040	+	0.890471i	$0.650375\pi$
$198$		0			0
$199$	10.8690	+	6.27522i	0.770482	+	0.444838i	0.833047	−	0.553203i	$-0.186594\pi$
$199$	10.8690	+	6.27522i	0.770482	+	0.444838i	−0.0625642	+	0.998041i	$0.519928\pi$
$200$		0			0
$201$	−2.66992	+	8.25416i	−0.188322	+	0.582203i
$202$		0			0
$203$	−3.84328	+	1.39884i	−0.269745	+	0.0981792i
$204$		0			0
$205$	3.11121	+	17.6446i	0.217297	+	1.23235i
$206$		0			0
$207$	2.37389	−	4.89993i	0.164997	−	0.340569i
$208$		0			0
$209$	0.677508	+	0.807423i	0.0468642	+	0.0558506i
$210$		0			0
$211$	19.5778	+	3.45209i	1.34779	+	0.237652i	0.800520	−	0.599305i	$-0.204556\pi$
$211$	19.5778	+	3.45209i	1.34779	+	0.237652i	0.547269	+	0.836957i	$0.315668\pi$
$212$		0			0
$213$	26.6397	−	10.8040i	1.82532	−	0.740277i
$214$		0			0
$215$	−22.3137			−1.52178
$216$		0			0
$217$	3.14670			0.213612
$218$		0			0
$219$	3.27054	−	23.4957i	0.221003	−	1.58769i
$220$		0			0
$221$	7.59654	+	1.33948i	0.510999	+	0.0901029i
$222$		0			0
$223$	5.80196	+	6.91450i	0.388528	+	0.463029i	0.924486	−	0.381215i	$-0.124494\pi$
$223$	5.80196	+	6.91450i	0.388528	+	0.463029i	−0.535959	+	0.844244i	$0.680050\pi$
$224$		0			0
$225$	0.472750	−	4.61485i	0.0315167	−	0.307657i
$226$		0			0
$227$	2.31547	+	13.1317i	0.153683	+	0.871579i	0.959980	+	0.280068i	$0.0903571\pi$
$227$	2.31547	+	13.1317i	0.153683	+	0.871579i	−0.806297	+	0.591511i	$0.798532\pi$
$228$		0			0
$229$	8.54248	−	3.10921i	0.564503	−	0.205462i	−0.0439755	−	0.999033i	$-0.514002\pi$
$229$	8.54248	−	3.10921i	0.564503	−	0.205462i	0.608479	+	0.793570i	$0.291780\pi$
$230$		0			0
$231$	−0.423531	+	0.0906077i	−0.0278663	+	0.00596155i
$232$		0			0
$233$	6.17144	+	3.56308i	0.404304	+	0.233425i	0.688340	−	0.725389i	$-0.258340\pi$
$233$	6.17144	+	3.56308i	0.404304	+	0.233425i	−0.284035	+	0.958814i	$0.591673\pi$
$234$		0			0
$235$	16.0002	−	9.23773i	1.04374	−	0.602603i
$236$		0			0
$237$	10.8301	−	6.78724i	0.703490	−	0.440879i
$238$		0			0
$239$	6.43186	+	5.39697i	0.416042	+	0.349101i	0.826655	−	0.562709i	$-0.190241\pi$
$239$	6.43186	+	5.39697i	0.416042	+	0.349101i	−0.410613	+	0.911810i	$0.634685\pi$
$240$		0			0
$241$	7.89267	+	2.87270i	0.508412	+	0.185047i	0.583474	−	0.812132i	$-0.301693\pi$
$241$	7.89267	+	2.87270i	0.508412	+	0.185047i	−0.0750618	+	0.997179i	$0.523915\pi$
$242$		0			0
$243$	−15.3691	−	2.60573i	−0.985930	−	0.167158i
$244$		0			0
$245$	4.14936	−	11.4003i	0.265093	−	0.728337i
$246$		0			0
$247$	−4.97121	+	5.92446i	−0.316311	+	0.376964i
$248$		0			0
$249$	3.57847	+	5.70999i	0.226776	+	0.361856i
$250$		0			0
$251$	15.6479	+	27.1030i	0.987688	+	1.71073i	0.629322	+	0.777145i	$0.283333\pi$
$251$	15.6479	+	27.1030i	0.987688	+	1.71073i	0.358366	+	0.933581i	$0.383334\pi$
$252$		0			0
$253$	−0.330337	+	0.572160i	−0.0207681	+	0.0359714i
$254$		0			0
$255$	1.94466	+	9.09003i	0.121780	+	0.569240i
$256$		0			0
$257$	7.17068	+	19.7013i	0.447295	+	1.22893i	0.934600	+	0.355700i	$0.115758\pi$
$257$	7.17068	+	19.7013i	0.447295	+	1.22893i	−0.487305	+	0.873232i	$0.662020\pi$
$258$		0			0
$259$	−2.39834	+	0.422893i	−0.149026	+	0.0262773i
$260$		0			0
$261$	17.7690	+	1.82027i	1.09987	+	0.112672i
$262$		0			0
$263$	−5.60982	+	4.70720i	−0.345916	+	0.290258i	−0.799148	−	0.601135i	$-0.794716\pi$
$263$	−5.60982	+	4.70720i	−0.345916	+	0.290258i	0.453231	+	0.891393i	$0.350271\pi$
$264$		0			0
$265$	0.329099	−	1.86641i	0.0202164	−	0.114653i
$266$		0			0
$267$	−23.9928	−	3.33975i	−1.46834	−	0.204389i
$268$		0			0
$269$		−	18.3626i		−	1.11959i	−0.828632	−	0.559793i	$-0.810880\pi$
$269$		−	18.3626i		−	1.11959i	0.828632	−	0.559793i	$-0.189120\pi$
$270$		0			0
$271$			1.08071i			0.0656483i	0.999461	+	0.0328241i	$0.0104501\pi$
$271$			1.08071i			0.0656483i	−0.999461	+	0.0328241i	$0.989550\pi$
$272$		0			0
$273$	−1.19437	−	2.94500i	−0.0722867	−	0.178239i
$274$		0			0
$275$	−0.0977481	+	0.554357i	−0.00589443	+	0.0334290i
$276$		0			0
$277$	−10.6528	+	8.93879i	−0.640067	+	0.537080i	−0.904039	−	0.427450i	$-0.859412\pi$
$277$	−10.6528	+	8.93879i	−0.640067	+	0.537080i	0.263972	+	0.964530i	$0.414967\pi$
$278$		0			0
$279$	−12.3676	−	5.99180i	−0.740430	−	0.358720i
$280$		0			0
$281$	5.52866	−	0.974852i	0.329812	−	0.0581548i	−0.00629033	−	0.999980i	$-0.502002\pi$
$281$	5.52866	−	0.974852i	0.329812	−	0.0581548i	0.336102	+	0.941825i	$0.390891\pi$
$282$		0			0
$283$	5.59448	+	15.3707i	0.332558	+	0.913694i	0.987444	+	0.157967i	$0.0504941\pi$
$283$	5.59448	+	15.3707i	0.332558	+	0.913694i	−0.654887	+	0.755727i	$0.727284\pi$
$284$		0			0
$285$	−8.86757	−	2.86834i	−0.525270	−	0.169906i
$286$		0			0
$287$	3.31129	−	5.73532i	0.195459	−	0.338545i
$288$		0			0
$289$	−4.33002	−	7.49982i	−0.254707	−	0.441166i
$290$		0			0
$291$	0.957398	−	1.80634i	0.0561237	−	0.105890i
$292$		0			0
$293$	−7.32574	+	8.73048i	−0.427975	+	0.510040i	−0.936337	−	0.351103i	$-0.885807\pi$
$293$	−7.32574	+	8.73048i	−0.427975	+	0.510040i	0.508362	+	0.861143i	$0.330251\pi$
$294$		0			0
$295$	3.16561	−	8.69744i	0.184309	−	0.506385i
$296$		0			0
$297$	1.83715	+	0.450349i	0.106602	+	0.0261319i
$298$		0			0
$299$	−4.55534	−	1.65801i	−0.263442	−	0.0958850i
$300$		0			0
$301$	6.31818	+	5.30159i	0.364174	+	0.305578i
$302$		0			0
$303$	−0.441797	−	12.1909i	−0.0253806	−	0.700350i
$304$		0			0
$305$	−20.1946	+	11.6593i	−1.15634	+	0.667612i
$306$		0			0
$307$	6.20934	+	3.58496i	0.354386	+	0.204605i	0.666615	−	0.745402i	$-0.267742\pi$
$307$	6.20934	+	3.58496i	0.354386	+	0.204605i	−0.312230	+	0.950007i	$0.601076\pi$
$308$		0			0
$309$	−10.7193	−	11.8735i	−0.609801	−	0.675461i
$310$		0			0
$311$	−20.1437	+	7.33171i	−1.14224	+	0.415743i	−0.842723	−	0.538347i	$-0.819049\pi$
$311$	−20.1437	+	7.33171i	−1.14224	+	0.415743i	−0.299521	+	0.954090i	$0.596827\pi$
$312$		0			0
$313$	1.26646	+	7.18245i	0.0715845	+	0.405976i	0.999453	+	0.0330687i	$0.0105280\pi$
$313$	1.26646	+	7.18245i	0.0715845	+	0.405976i	−0.927869	+	0.372907i	$0.878361\pi$
$314$		0			0
$315$	2.74786	−	2.66761i	0.154825	−	0.150303i
$316$		0			0
$317$	−14.9507	−	17.8176i	−0.839717	−	1.00074i	−0.999907	−	0.0136497i	$-0.995655\pi$
$317$	−14.9507	−	17.8176i	−0.839717	−	1.00074i	0.160190	−	0.987086i	$-0.448789\pi$
$318$		0			0
$319$	−2.13449	−	0.376368i	−0.119509	−	0.0210726i
$320$		0			0
$321$	−16.0191	−	12.4815i	−0.894097	−	0.696650i
$322$		0			0
$323$	−8.36169			−0.465257
$324$		0			0
$325$	−4.13034			−0.229110
$326$		0			0
$327$	−17.4867	−	13.6251i	−0.967018	−	0.753467i
$328$		0			0
$329$	−6.72534	−	1.18586i	−0.370780	−	0.0653785i
$330$		0			0
$331$	−7.44461	−	8.87214i	−0.409193	−	0.487657i	0.521607	−	0.853186i	$-0.325333\pi$
$331$	−7.44461	−	8.87214i	−0.409193	−	0.487657i	−0.930800	+	0.365529i	$0.880888\pi$
$332$		0			0
$333$	10.2316	+	2.90470i	0.560686	+	0.159177i
$334$		0			0
$335$	1.61633	+	9.16668i	0.0883097	+	0.500829i
$336$		0			0
$337$	9.71533	−	3.53609i	0.529228	−	0.192623i	−0.0635658	−	0.997978i	$-0.520247\pi$
$337$	9.71533	−	3.53609i	0.529228	−	0.192623i	0.592793	+	0.805355i	$0.298025\pi$
$338$		0			0
$339$	13.2094	+	14.6317i	0.717434	+	0.794683i
$340$		0			0
$341$	1.44415	+	0.833783i	0.0782053	+	0.0451519i
$342$		0			0
$343$	−8.04778	+	4.64639i	−0.434540	+	0.250882i
$344$		0			0
$345$	−0.211570	−	5.83805i	−0.0113905	−	0.314310i
$346$		0			0
$347$	−9.93967	−	8.34038i	−0.533590	−	0.447735i	0.335749	−	0.941951i	$-0.391011\pi$
$347$	−9.93967	−	8.34038i	−0.533590	−	0.447735i	−0.869339	+	0.494217i	$0.835455\pi$
$348$		0			0
$349$	−18.4970	−	6.73235i	−0.990121	−	0.360375i	−0.204354	−	0.978897i	$-0.565509\pi$
$349$	−18.4970	−	6.73235i	−0.990121	−	0.360375i	−0.785767	+	0.618522i	$0.787732\pi$
$350$		0			0
$351$	−0.913437	+	13.8491i	−0.0487557	+	0.739211i
$352$		0			0
$353$	−1.12185	+	3.08225i	−0.0597099	+	0.164052i	−0.965961	−	0.258689i	$-0.916710\pi$
$353$	−1.12185	+	3.08225i	−0.0597099	+	0.164052i	0.906251	+	0.422740i	$0.138932\pi$
$354$		0			0
$355$	19.8263	−	23.6281i	1.05227	−	1.25405i
$356$		0			0
$357$	1.60910	−	3.03591i	0.0851624	−	0.160677i
$358$		0			0
$359$	4.91834	+	8.51881i	0.259580	+	0.449606i	0.966129	−	0.258058i	$-0.0830825\pi$
$359$	4.91834	+	8.51881i	0.259580	+	0.449606i	−0.706549	+	0.707664i	$0.749749\pi$
$360$		0			0
$361$	−5.30826	+	9.19417i	−0.279382	+	0.483904i
$362$		0			0
$363$	17.9094	+	5.79305i	0.940001	+	0.304056i
$364$		0			0
$365$	−8.70535	−	23.9177i	−0.455659	−	1.25191i
$366$		0			0
$367$	28.4143	−	5.01021i	1.48321	−	0.261531i	0.627352	−	0.778735i	$-0.284139\pi$
$367$	28.4143	−	5.01021i	1.48321	−	0.261531i	0.855862	+	0.517205i	$0.173027\pi$
$368$		0			0
$369$	−23.9354	+	16.2366i	−1.24603	+	0.845242i
$370$		0			0
$371$	−0.536634	+	0.450289i	−0.0278606	+	0.0233778i
$372$		0			0
$373$	0.186692	−	1.05878i	0.00966652	−	0.0548216i	−0.979593	−	0.200992i	$-0.935584\pi$
$373$	0.186692	−	1.05878i	0.00966652	−	0.0548216i	0.989259	+	0.146170i	$0.0466947\pi$
$374$		0			0
$375$	−7.91932	−	19.5269i	−0.408952	−	1.00836i
$376$		0			0
$377$		−	15.9034i		−	0.819068i
$378$		0			0
$379$		−	26.9955i		−	1.38667i	−0.720617	−	0.693333i	$-0.756142\pi$
$379$		−	26.9955i		−	1.38667i	0.720617	−	0.693333i	$-0.243858\pi$
$380$		0			0
$381$	20.4980	+	2.85327i	1.05014	+	0.146178i
$382$		0			0
$383$	−3.42477	+	19.4229i	−0.174998	+	0.992461i	0.763149	+	0.646223i	$0.223652\pi$
$383$	−3.42477	+	19.4229i	−0.174998	+	0.992461i	−0.938147	+	0.346239i	$0.887459\pi$
$384$		0			0
$385$	−0.355989	+	0.298710i	−0.0181429	+	0.0152237i
$386$		0			0
$387$	−14.7376	−	32.8678i	−0.749153	−	1.67076i
$388$		0			0
$389$	−20.2544	+	3.57139i	−1.02694	+	0.181077i	−0.661646	−	0.749817i	$-0.730142\pi$
$389$	−20.2544	+	3.57139i	−1.02694	+	0.181077i	−0.365291	+	0.930893i	$0.619031\pi$
$390$		0			0
$391$	−1.79261	−	4.92515i	−0.0906561	−	0.249076i
$392$		0			0
$393$	0.411991	+	1.92579i	0.0207822	+	0.0971430i
$394$		0			0
$395$	6.85676	−	11.8763i	0.345001	−	0.597559i
$396$		0			0
$397$	11.5650	+	20.0311i	0.580430	+	1.00533i	0.995428	+	0.0955122i	$0.0304489\pi$
$397$	11.5650	+	20.0311i	0.580430	+	1.00533i	−0.414998	+	0.909822i	$0.636218\pi$
$398$		0			0
$399$	1.82938	+	2.91906i	0.0915837	+	0.146136i
$400$		0			0
$401$	−9.33843	+	11.1291i	−0.466339	+	0.555761i	−0.947037	−	0.321125i	$-0.895939\pi$
$401$	−9.33843	+	11.1291i	−0.466339	+	0.555761i	0.480698	+	0.876886i	$0.340383\pi$
$402$		0			0
$403$	−4.18488	+	11.4979i	−0.208463	+	0.572749i
$404$		0			0
$405$	−15.8796	+	5.25226i	−0.789062	+	0.260987i
$406$		0			0
$407$	−1.21275	−	0.441407i	−0.0601140	−	0.0218797i
$408$		0			0
$409$	−15.2899	−	12.8298i	−0.756038	−	0.634392i	0.181054	−	0.983473i	$-0.442049\pi$
$409$	−15.2899	−	12.8298i	−0.756038	−	0.634392i	−0.937092	+	0.349082i	$0.886494\pi$
$410$		0			0
$411$	11.8092	−	7.40088i	0.582507	−	0.365059i
$412$		0			0
$413$	−2.96281	+	1.71058i	−0.145790	+	0.0841721i
$414$		0			0
$415$	6.26157	+	3.61512i	0.307368	+	0.177459i
$416$		0			0
$417$	−9.19195	+	1.96647i	−0.450132	+	0.0962984i
$418$		0			0
$419$	24.7184	−	8.99676i	1.20757	−	0.439520i	0.341711	−	0.939805i	$-0.388994\pi$
$419$	24.7184	−	8.99676i	1.20757	−	0.439520i	0.865861	+	0.500285i	$0.166771\pi$
$420$		0			0
$421$	1.54271	+	8.74913i	0.0751870	+	0.426407i	0.999046	+	0.0436734i	$0.0139061\pi$
$421$	1.54271	+	8.74913i	0.0751870	+	0.426407i	−0.923859	+	0.382733i	$0.874983\pi$
$422$		0			0
$423$	24.1748	+	17.4669i	1.17542	+	0.849269i
$424$		0			0
$425$	−2.87047	−	3.42089i	−0.139238	−	0.165938i
$426$		0			0
$427$	8.48835	+	1.49673i	0.410780	+	0.0724316i
$428$		0			0
$429$	0.232190	−	1.66806i	0.0112102	−	0.0805345i
$430$		0			0
$431$	−35.6692			−1.71812			−0.859062	−	0.511872i	$-0.828952\pi$
$431$	−35.6692			−1.71812			−0.859062	+	0.511872i	$0.828952\pi$
$432$		0			0
$433$	20.3661			0.978735			0.489367	−	0.872078i	$-0.337228\pi$
$433$	20.3661			0.978735			0.489367	+	0.872078i	$0.337228\pi$
$434$		0			0
$435$	17.7600	−	7.20274i	0.851528	−	0.345345i
$436$		0			0
$437$	5.17506	+	0.912503i	0.247557	+	0.0436510i
$438$		0			0
$439$	−21.4995	−	25.6222i	−1.02612	−	1.22288i	−0.974541	−	0.224209i	$-0.928020\pi$
$439$	−21.4995	−	25.6222i	−1.02612	−	1.22288i	−0.0515759	−	0.998669i	$-0.516424\pi$
$440$		0			0
$441$	19.5330	−	1.41761i	0.930145	−	0.0675052i
$442$		0			0
$443$	−2.76559	−	15.6845i	−0.131397	−	0.745191i	−0.977301	−	0.211855i	$-0.932049\pi$
$443$	−2.76559	−	15.6845i	−0.131397	−	0.745191i	0.845904	−	0.533336i	$-0.179062\pi$
$444$		0			0
$445$	−24.4239	+	8.88956i	−1.15780	+	0.421405i
$446$		0			0
$447$	−1.05974	+	3.27623i	−0.0501240	+	0.154960i
$448$		0			0
$449$	21.6096	+	12.4763i	1.01982	+	0.588795i	0.914052	−	0.405596i	$-0.132936\pi$
$449$	21.6096	+	12.4763i	1.01982	+	0.588795i	0.105770	+	0.994391i	$0.466269\pi$
$450$		0			0
$451$	3.03938	−	1.75479i	0.143119	−	0.0826297i
$452$		0			0
$453$	−4.38936	−	2.32645i	−0.206230	−	0.109306i
$454$		0			0
$455$	−2.61207	−	2.19178i	−0.122456	−	0.102752i
$456$		0			0
$457$	−16.1920	−	5.89341i	−0.757431	−	0.275682i	−0.0657017	−	0.997839i	$-0.520929\pi$
$457$	−16.1920	−	5.89341i	−0.757431	−	0.275682i	−0.691729	+	0.722157i	$0.743151\pi$
$458$		0			0
$459$	−12.1051	+	8.86819i	−0.565019	+	0.413932i
$460$		0			0
$461$	2.09999	−	5.76968i	0.0978065	−	0.268721i	−0.881134	−	0.472866i	$-0.843219\pi$
$461$	2.09999	−	5.76968i	0.0978065	−	0.268721i	0.978941	+	0.204145i	$0.0654415\pi$
$462$		0			0
$463$	−3.43905	+	4.09850i	−0.159826	+	0.190474i	−0.840014	−	0.542564i	$-0.817454\pi$
$463$	−3.43905	+	4.09850i	−0.159826	+	0.190474i	0.680188	+	0.733038i	$0.261898\pi$
$464$		0			0
$465$	−14.7355	+	0.534011i	−0.683341	+	0.0247642i
$466$		0			0
$467$	16.2724	+	28.1846i	0.752995	+	1.30423i	0.946365	+	0.323100i	$0.104725\pi$
$467$	16.2724	+	28.1846i	0.752995	+	1.30423i	−0.193370	+	0.981126i	$0.561942\pi$
$468$		0			0
$469$	1.72028	−	2.97960i	0.0794349	−	0.137585i
$470$		0			0
$471$	−15.5629	+	14.0500i	−0.717098	+	0.647391i
$472$		0			0
$473$	1.49492	+	4.10725i	0.0687363	+	0.188852i
$474$		0			0
$475$	4.40927	−	0.777474i	0.202311	−	0.0356729i
$476$		0			0
$477$	2.96657	−	0.747957i	0.135830	−	0.0342466i
$478$		0			0
$479$	31.7640	−	26.6531i	1.45133	−	1.21781i	0.519732	−	0.854330i	$-0.326032\pi$
$479$	31.7640	−	26.6531i	1.45133	−	1.21781i	0.931601	−	0.363483i	$-0.118413\pi$
$480$		0			0
$481$	1.64439	−	9.32581i	0.0749778	−	0.425220i
$482$		0			0
$483$	−1.32718	+	1.70333i	−0.0603887	+	0.0775042i
$484$		0			0
$485$		−	2.19352i		−	0.0996024i
$486$		0			0
$487$			40.8059i			1.84909i	0.381072	+	0.924545i	$0.375555\pi$
$487$			40.8059i			1.84909i	−0.381072	+	0.924545i	$0.624445\pi$
$488$		0			0
$489$	3.92906	−	5.04265i	0.177678	−	0.228036i
$490$		0			0
$491$	4.86890	−	27.6129i	0.219730	−	1.24615i	−0.652777	−	0.757550i	$-0.726396\pi$
$491$	4.86890	−	27.6129i	0.219730	−	1.24615i	0.872507	−	0.488602i	$-0.162493\pi$
$492$		0			0
$493$	13.1718	−	11.0524i	0.593227	−	0.497776i
$494$		0			0
$495$	1.96795	−	0.496175i	0.0884526	−	0.0223014i
$496$		0			0
$497$	−11.2278	+	1.97976i	−0.503634	+	0.0888043i
$498$		0			0
$499$	−3.37784	−	9.28054i	−0.151213	−	0.415454i	0.840839	−	0.541286i	$-0.182062\pi$
$499$	−3.37784	−	9.28054i	−0.151213	−	0.415454i	−0.992052	+	0.125832i	$0.959840\pi$
$500$		0			0
$501$	−26.6822	+	24.0885i	−1.19207	+	1.07619i
$502$		0			0
$503$	12.4724	−	21.6029i	0.556117	−	0.963224i	−0.441698	−	0.897164i	$-0.645624\pi$
$503$	12.4724	−	21.6029i	0.556117	−	0.963224i	0.997816	−	0.0660600i	$-0.0210429\pi$
$504$		0			0
$505$	−6.54442	−	11.3353i	−0.291223	−	0.504413i
$506$		0			0
$507$	−10.1526	+	0.367930i	−0.450894	+	0.0163403i
$508$		0			0
$509$	−4.22498	+	5.03513i	−0.187269	+	0.223178i	−0.851508	−	0.524342i	$-0.824311\pi$
$509$	−4.22498	+	5.03513i	−0.187269	+	0.223178i	0.664239	+	0.747520i	$0.268756\pi$
$510$		0			0
$511$	−3.21776	+	8.84072i	−0.142345	+	0.391091i
$512$		0			0
$513$	−1.63176	−	14.9563i	−0.0720440	−	0.660337i
$514$		0			0
$515$	−16.1283	−	5.87020i	−0.710696	−	0.258672i
$516$		0			0
$517$	−2.77232	−	2.32625i	−0.121927	−	0.102309i
$518$		0			0
$519$	9.54532	+	5.05922i	0.418993	+	0.222075i
$520$		0			0
$521$	17.2065	−	9.93418i	0.753831	−	0.435224i	−0.0732458	−	0.997314i	$-0.523336\pi$
$521$	17.2065	−	9.93418i	0.753831	−	0.435224i	0.827076	+	0.562090i	$0.190002\pi$
$522$		0			0
$523$	−25.5708	−	14.7633i	−1.11813	−	0.645554i	−0.177209	−	0.984173i	$-0.556707\pi$
$523$	−25.5708	−	14.7633i	−1.11813	−	0.645554i	−0.940923	+	0.338620i	$0.890040\pi$
$524$		0			0
$525$	−0.566225	+	1.75051i	−0.0247121	+	0.0763983i
$526$		0			0
$527$	−12.4313	+	4.52462i	−0.541515	+	0.197095i
$528$		0			0
$529$	−3.42194	−	19.4068i	−0.148780	−	0.843773i
$530$		0			0
$531$	14.9021	−	1.08152i	0.646694	−	0.0469338i
$532$		0			0
$533$	16.5527	+	19.7268i	0.716978	+	0.854461i
$534$		0			0
$535$	−21.4580	−	3.78363i	−0.927711	−	0.163580i
$536$		0			0
$537$	21.7241	−	8.81043i	0.937466	−	0.380198i
$538$		0			0
$539$	−2.37642			−0.102360
$540$		0			0
$541$	−13.0123			−0.559444			−0.279722	−	0.960081i	$-0.590242\pi$
$541$	−13.0123			−0.559444			−0.279722	+	0.960081i	$0.590242\pi$
$542$		0			0
$543$	1.62032	−	11.6404i	0.0695346	−	0.499538i
$544$		0			0
$545$	−23.4240	−	4.13028i	−1.00337	−	0.176922i
$546$		0			0
$547$	13.8628	+	16.5211i	0.592732	+	0.706391i	0.976129	−	0.217193i	$-0.0696902\pi$
$547$	13.8628	+	16.5211i	0.592732	+	0.706391i	−0.383396	+	0.923584i	$0.625246\pi$
$548$		0			0
$549$	−30.5121	−	22.0457i	−1.30222	−	0.940889i
$550$		0			0
$551$	2.99358	+	16.9774i	0.127531	+	0.723263i
$552$		0			0
$553$	−4.76324	+	1.73368i	−0.202553	+	0.0737234i
$554$		0			0
$555$	11.1593	−	2.38735i	0.473685	−	0.101337i
$556$		0			0
$557$	26.8521	+	15.5031i	1.13776	+	0.656886i	0.945875	−	0.324531i	$-0.105207\pi$
$557$	26.8521	+	15.5031i	1.13776	+	0.656886i	0.191885	+	0.981417i	$0.438540\pi$
$558$		0			0
$559$	−27.7743	+	16.0355i	−1.17473	+	0.678230i
$560$		0			0
$561$	1.54291	−	0.966944i	0.0651416	−	0.0408244i
$562$		0			0
$563$	8.12175	+	6.81496i	0.342291	+	0.287216i	0.797686	−	0.603073i	$-0.206057\pi$
$563$	8.12175	+	6.81496i	0.342291	+	0.287216i	−0.455395	+	0.890290i	$0.650502\pi$
$564$		0			0
$565$	19.8747	+	7.23382i	0.836137	+	0.304329i
$566$		0			0
$567$	5.74425	+	2.28569i	0.241236	+	0.0959901i
$568$		0			0
$569$	−3.42133	+	9.40004i	−0.143430	+	0.394070i	−0.990518	−	0.137382i	$-0.956131\pi$
$569$	−3.42133	+	9.40004i	−0.143430	+	0.394070i	0.847088	+	0.531452i	$0.178353\pi$
$570$		0			0
$571$	−18.8465	+	22.4604i	−0.788702	+	0.939938i	−0.999291	−	0.0376364i	$-0.988017\pi$
$571$	−18.8465	+	22.4604i	−0.788702	+	0.939938i	0.210590	+	0.977575i	$0.432462\pi$
$572$		0			0
$573$	15.0426	+	24.0028i	0.628414	+	1.00273i
$574$		0			0
$575$	1.40322	+	2.43045i	0.0585182	+	0.101357i
$576$		0			0
$577$	−3.08995	+	5.35195i	−0.128636	+	0.222805i	−0.923148	−	0.384444i	$-0.874393\pi$
$577$	−3.08995	+	5.35195i	−0.128636	+	0.222805i	0.794512	+	0.607248i	$0.207727\pi$
$578$		0			0
$579$	6.86841	+	32.1053i	0.285441	+	1.33425i
$580$		0			0
$581$	−0.914054	−	2.51134i	−0.0379213	−	0.104188i
$582$		0			0
$583$	−0.365597	+	0.0644646i	−0.0151415	+	0.00266985i
$584$		0			0
$585$	6.09282	+	13.5882i	0.251907	+	0.561804i
$586$		0			0
$587$	−21.4842	+	18.0274i	−0.886749	+	0.744071i	−0.967555	−	0.252659i	$-0.918695\pi$
$587$	−21.4842	+	18.0274i	−0.886749	+	0.744071i	0.0808061	+	0.996730i	$0.474251\pi$
$588$		0			0
$589$	2.30320	−	13.0621i	0.0949015	−	0.538213i
$590$		0			0
$591$	−40.4185	−	5.62616i	−1.66259	−	0.231429i
$592$		0			0
$593$		−	3.19379i		−	0.131153i	−0.997848	−	0.0655767i	$-0.979111\pi$
$593$		−	3.19379i		−	0.131153i	0.997848	−	0.0655767i	$-0.0208887\pi$
$594$		0			0
$595$		−	3.68663i		−	0.151137i
$596$		0			0
$597$	8.16974	+	20.1444i	0.334365	+	0.824454i
$598$		0			0
$599$	4.65896	−	26.4223i	0.190360	−	1.07958i	−0.728513	−	0.685032i	$-0.759788\pi$
$599$	4.65896	−	26.4223i	0.190360	−	1.07958i	0.918873	−	0.394553i	$-0.129101\pi$
$600$		0			0
$601$	16.5609	−	13.8962i	0.675532	−	0.566839i	−0.239165	−	0.970979i	$-0.576874\pi$
$601$	16.5609	−	13.8962i	0.675532	−	0.566839i	0.914697	+	0.404140i	$0.132429\pi$
$602$		0			0
$603$	−12.4349	+	8.43519i	−0.506388	+	0.343507i
$604$		0			0
$605$	19.8894	−	3.50703i	0.808617	−	0.142581i
$606$		0			0
$607$	−6.00813	−	16.5072i	−0.243862	−	0.670007i	−0.999881	−	0.0154559i	$-0.995080\pi$
$607$	−6.00813	−	16.5072i	−0.243862	−	0.670007i	0.756018	−	0.654551i	$-0.227142\pi$
$608$		0			0
$609$	−6.74013	−	2.18019i	−0.273124	−	0.0883457i
$610$		0			0
$611$	13.2772	−	22.9968i	0.537139	−	0.930353i
$612$		0			0
$613$	13.8232	+	23.9424i	0.558313	+	0.967026i	0.997638	+	0.0686979i	$0.0218844\pi$
$613$	13.8232	+	23.9424i	0.558313	+	0.967026i	−0.439325	+	0.898328i	$0.644782\pi$
$614$		0			0
$615$	−14.5329	+	27.4195i	−0.586023	+	1.10566i
$616$		0			0
$617$	30.7467	−	36.6425i	1.23782	−	1.47517i	0.412046	−	0.911163i	$-0.364814\pi$
$617$	30.7467	−	36.6425i	1.23782	−	1.47517i	0.825769	−	0.564008i	$-0.190741\pi$
$618$		0			0
$619$	−14.6524	+	40.2571i	−0.588929	+	1.61807i	0.183538	+	0.983013i	$0.441245\pi$
$619$	−14.6524	+	40.2571i	−0.588929	+	1.61807i	−0.772467	+	0.635055i	$0.780977\pi$
$620$		0			0
$621$	8.45966	−	4.16752i	0.339474	−	0.167237i
$622$		0			0
$623$	9.02779	+	3.28585i	0.361691	+	0.131645i
$624$		0			0
$625$	−11.3966	−	9.56287i	−0.455863	−	0.382515i
$626$		0			0
$627$	0.0661163	+	1.82441i	0.00264043	+	0.0728599i
$628$		0			0
$629$	8.86676	−	5.11923i	0.353541	−	0.204117i
$630$		0			0
$631$	6.97385	+	4.02635i	0.277625	+	0.160287i	0.632348	−	0.774685i	$-0.282091\pi$
$631$	6.97385	+	4.02635i	0.277625	+	0.160287i	−0.354723	+	0.934971i	$0.615425\pi$
$632$		0			0
$633$	23.0737	+	25.5582i	0.917099	+	1.01585i
$634$		0			0
$635$	20.8662	−	7.59469i	0.828051	−	0.301386i
$636$		0			0
$637$	−3.02790	−	17.1721i	−0.119970	−	0.680383i
$638$		0			0
$639$	47.8987	+	13.5983i	1.89484	+	0.537939i
$640$		0			0
$641$	29.9247	+	35.6629i	1.18195	+	1.40860i	0.892286	+	0.451471i	$0.149101\pi$
$641$	29.9247	+	35.6629i	1.18195	+	1.40860i	0.289668	+	0.957127i	$0.406455\pi$
$642$		0			0
$643$	7.30455	+	1.28799i	0.288063	+	0.0507933i	0.315813	−	0.948822i	$-0.397723\pi$
$643$	7.30455	+	1.28799i	0.288063	+	0.0507933i	−0.0277494	+	0.999615i	$0.508834\pi$
$644$		0			0
$645$	−30.4867	−	23.7542i	−1.20041	−	0.935320i
$646$		0			0
$647$	−13.4394			−0.528359			−0.264180	−	0.964474i	$-0.585101\pi$
$647$	−13.4394			−0.528359			−0.264180	+	0.964474i	$0.585101\pi$
$648$		0			0
$649$	−1.81301			−0.0711669
$650$		0			0
$651$	4.29927	+	3.34985i	0.168502	+	0.131291i
$652$		0			0
$653$	20.6649	+	3.64379i	0.808681	+	0.142592i	0.562678	−	0.826676i	$-0.309771\pi$
$653$	20.6649	+	3.64379i	0.808681	+	0.142592i	0.246004	+	0.969269i	$0.420882\pi$
$654$		0			0
$655$	1.35823	+	1.61867i	0.0530704	+	0.0632468i
$656$		0			0
$657$	29.4810	−	28.6199i	1.15016	−	1.11657i
$658$		0			0
$659$	−6.93840	−	39.3496i	−0.270282	−	1.53284i	−0.753561	−	0.657378i	$-0.771666\pi$
$659$	−6.93840	−	39.3496i	−0.270282	−	1.53284i	0.483279	−	0.875466i	$-0.339446\pi$
$660$		0			0
$661$	8.62964	−	3.14093i	0.335654	−	0.122168i	−0.168694	−	0.985668i	$-0.553955\pi$
$661$	8.62964	−	3.14093i	0.335654	−	0.122168i	0.504348	+	0.863500i	$0.331733\pi$
$662$		0			0
$663$	8.95304	+	9.91706i	0.347707	+	0.385147i
$664$		0			0
$665$	3.20104	+	1.84812i	0.124131	+	0.0716670i
$666$		0			0
$667$	−9.35817	+	5.40294i	−0.362350	+	0.209203i
$668$		0			0
$669$	0.566198	+	15.6237i	0.0218905	+	0.604045i
$670$		0			0
$671$	3.49907	+	2.93607i	0.135080	+	0.113346i
$672$		0			0
$673$	9.36707	+	3.40934i	0.361074	+	0.131420i	0.516186	−	0.856477i	$-0.327351\pi$
$673$	9.36707	+	3.40934i	0.361074	+	0.131420i	−0.155112	+	0.987897i	$0.549574\pi$
$674$		0			0
$675$	5.55868	−	5.80190i	0.213954	−	0.223315i
$676$		0			0
$677$	−13.1036	+	36.0019i	−0.503613	+	1.38366i	0.384111	+	0.923287i	$0.374508\pi$
$677$	−13.1036	+	36.0019i	−0.503613	+	1.38366i	−0.887723	+	0.460377i	$0.847714\pi$
$678$		0			0
$679$	−0.521166	+	0.621101i	−0.0200005	+	0.0238357i
$680$		0			0
$681$	−10.8158	+	20.4065i	−0.414464	+	0.781977i
$682$		0			0
$683$	20.9774	+	36.3339i	0.802677	+	1.39028i	0.917848	+	0.396932i	$0.129925\pi$
$683$	20.9774	+	36.3339i	0.802677	+	1.39028i	−0.115171	+	0.993346i	$0.536742\pi$
$684$		0			0
$685$	7.47669	−	12.9500i	0.285669	−	0.494794i
$686$		0			0
$687$	14.9813	+	4.84592i	0.571574	+	0.184883i
$688$		0			0
$689$	−0.931645	−	2.55967i	−0.0354928	−	0.0975158i
$690$		0			0
$691$	−21.7535	+	3.83573i	−0.827542	+	0.145918i	−0.571349	−	0.820707i	$-0.693580\pi$
$691$	−21.7535	+	3.83573i	−0.827542	+	0.145918i	−0.256194	+	0.966625i	$0.582469\pi$
$692$		0			0
$693$	−0.675119	−	0.327078i	−0.0256456	−	0.0124247i
$694$		0			0
$695$	−7.72607	+	6.48295i	−0.293067	+	0.245912i
$696$		0			0
$697$	−4.83472	+	27.4191i	−0.183128	+	1.03857i
$698$		0			0
$699$	4.63879	+	11.4380i	0.175455	+	0.432625i
$700$		0			0
$701$		−	27.1898i		−	1.02695i	−0.858106	−	0.513473i	$-0.828359\pi$
$701$		−	27.1898i		−	1.02695i	0.858106	−	0.513473i	$-0.171641\pi$
$702$		0			0
$703$			10.2651i			0.387157i
$704$		0			0
$705$	31.6949	+	4.41185i	1.19370	+	0.166160i
$706$		0			0
$707$	−0.840115	+	4.76453i	−0.0315958	+	0.179189i
$708$		0			0
$709$	34.1540	−	28.6586i	1.28268	−	1.07630i	0.289810	−	0.957084i	$-0.406408\pi$
$709$	34.1540	−	28.6586i	1.28268	−	1.07630i	0.992869	−	0.119211i	$-0.0380366\pi$
$710$		0			0
$711$	22.0223	+	2.25599i	0.825902	+	0.0846063i
$712$		0			0
$713$	8.18751	−	1.44368i	0.306625	−	0.0540662i
$714$		0			0
$715$	−0.618029	−	1.69802i	−0.0231130	−	0.0635024i
$716$		0			0
$717$	3.04232	+	14.2208i	0.113618	+	0.531087i
$718$		0			0
$719$	21.5033	−	37.2448i	0.801937	−	1.38900i	−0.116403	−	0.993202i	$-0.537136\pi$
$719$	21.5033	−	37.2448i	0.801937	−	1.38900i	0.918340	−	0.395793i	$-0.129530\pi$
$720$		0			0
$721$	3.17204	+	5.49414i	0.118133	+	0.204612i
$722$		0			0
$723$	7.72544	+	12.3271i	0.287312	+	0.458450i
$724$		0			0
$725$	−5.91806	+	7.05286i	−0.219791	+	0.261937i
$726$		0			0
$727$	9.94324	−	27.3188i	0.368775	−	1.01320i	−0.607054	−	0.794661i	$-0.707649\pi$
$727$	9.94324	−	27.3188i	0.368775	−	1.01320i	0.975828	−	0.218539i	$-0.0701291\pi$
$728$		0			0
$729$	−18.2246	−	19.9215i	−0.674984	−	0.737833i
$730$		0			0
$731$	−32.5835	−	11.8594i	−1.20515	−	0.438637i
$732$		0			0
$733$	−12.0928	−	10.1471i	−0.446658	−	0.374791i	0.391536	−	0.920163i	$-0.371944\pi$
$733$	−12.0928	−	10.1471i	−0.446658	−	0.374791i	−0.838194	+	0.545372i	$0.816388\pi$
$734$		0			0
$735$	17.8054	−	11.1587i	0.656763	−	0.411595i
$736$		0			0
$737$	1.57901	−	0.911643i	0.0581637	−	0.0335808i
$738$		0			0
$739$	−40.2356	−	23.2300i	−1.48009	−	0.854531i	−0.480345	−	0.877080i	$-0.659489\pi$
$739$	−40.2356	−	23.2300i	−1.48009	−	0.854531i	−0.999746	+	0.0225487i	$0.992822\pi$
$740$		0			0
$741$	−13.0990	+	2.80232i	−0.481203	+	0.102946i
$742$		0			0
$743$	39.2909	−	14.3007i	1.44144	−	0.524643i	0.501257	−	0.865299i	$-0.332871\pi$
$743$	39.2909	−	14.3007i	1.44144	−	0.524643i	0.940188	+	0.340656i	$0.110649\pi$
$744$		0			0
$745$	0.641552	+	3.63842i	0.0235047	+	0.133302i
$746$		0			0
$747$	−1.18944	+	11.6109i	−0.0435192	+	0.424821i
$748$		0			0
$749$	5.17694	+	6.16964i	0.189161	+	0.225434i
$750$		0			0
$751$	−31.0407	−	5.47331i	−1.13269	−	0.199724i	−0.424284	−	0.905529i	$-0.639474\pi$
$751$	−31.0407	−	5.47331i	−1.13269	−	0.199724i	−0.708406	+	0.705805i	$0.750585\pi$
$752$		0			0
$753$	−7.47329	+	53.6884i	−0.272342	+	1.95651i
$754$		0			0
$755$	−5.33018			−0.193985
$756$		0			0
$757$	11.5123			0.418421			0.209210	−	0.977871i	$-0.432911\pi$
$757$	11.5123			0.418421			0.209210	+	0.977871i	$0.432911\pi$
$758$		0			0
$759$	−1.06043	+	0.430067i	−0.0384911	+	0.0156104i
$760$		0			0
$761$	−27.5836	−	4.86373i	−0.999903	−	0.176310i	−0.350344	−	0.936621i	$-0.613935\pi$
$761$	−27.5836	−	4.86373i	−0.999903	−	0.176310i	−0.649559	+	0.760311i	$0.725047\pi$
$762$		0			0
$763$	5.65125	+	6.73489i	0.204589	+	0.243820i
$764$		0			0
$765$	−7.01991	+	14.4897i	−0.253805	+	0.523877i
$766$		0			0
$767$	−2.31003	−	13.1009i	−0.0834105	−	0.473044i
$768$		0			0
$769$	−25.9996	+	9.46309i	−0.937571	+	0.341248i	−0.765206	−	0.643785i	$-0.777363\pi$
$769$	−25.9996	+	9.46309i	−0.937571	+	0.341248i	−0.172365	+	0.985033i	$0.555141\pi$
$770$		0			0
$771$	−11.1760	+	34.5510i	−0.402494	+	1.24432i
$772$		0			0
$773$	37.0220	+	21.3747i	1.33159	+	0.768793i	0.985543	−	0.169425i	$-0.0541911\pi$
$773$	37.0220	+	21.3747i	1.33159	+	0.768793i	0.346045	+	0.938218i	$0.387524\pi$
$774$		0			0
$775$	6.13454	−	3.54178i	0.220359	−	0.127224i
$776$		0			0
$777$	−3.72700	−	1.97539i	−0.133705	−	0.0708666i
$778$		0			0
$779$	−21.3838	−	17.9432i	−0.766156	−	0.642881i
$780$		0			0
$781$	−5.67747	−	2.06643i	−0.203156	−	0.0739427i
$782$		0			0
$783$	22.3396	+	21.4031i	0.798352	+	0.764885i
$784$		0			0
$785$	−7.69419	+	21.1396i	−0.274617	+	0.754505i
$786$		0			0
$787$	12.9543	−	15.4383i	0.461769	−	0.550315i	−0.484037	−	0.875048i	$-0.660830\pi$
$787$	12.9543	−	15.4383i	0.461769	−	0.550315i	0.945806	+	0.324733i	$0.105274\pi$
$788$		0			0
$789$	−12.6757	+	0.459364i	−0.451266	+	0.0163538i
$790$		0			0
$791$	−3.90889	−	6.77039i	−0.138984	−	0.240727i
$792$		0			0
$793$	−16.7578	+	29.0253i	−0.595086	+	1.03072i
$794$		0			0
$795$	2.43655	−	2.19969i	0.0864154	−	0.0780151i
$796$		0			0
$797$	−17.2695	−	47.4474i	−0.611716	−	1.68067i	−0.726400	−	0.687273i	$-0.758808\pi$
$797$	−17.2695	−	47.4474i	−0.611716	−	1.68067i	0.114684	−	0.993402i	$-0.463414\pi$
$798$		0			0
$799$	28.2741	−	4.98548i	1.00027	−	0.176374i
$800$		0			0
$801$	−29.2255	−	30.1048i	−1.03263	−	1.06370i
$802$		0			0
$803$	−3.81929	+	3.20477i	−0.134780	+	0.113094i
$804$		0			0
$805$	−0.402319	+	2.28166i	−0.0141799	+	0.0804180i
$806$		0			0
$807$	19.5480	−	25.0884i	0.688124	−	0.883154i
$808$		0			0
$809$		−	9.20124i		−	0.323498i	−0.986832	−	0.161749i	$-0.948286\pi$
$809$		−	9.20124i		−	0.323498i	0.986832	−	0.161749i	$-0.0517135\pi$
$810$		0			0
$811$		−	11.4571i		−	0.402312i	−0.979559	−	0.201156i	$-0.935530\pi$
$811$		−	11.4571i		−	0.402312i	0.979559	−	0.201156i	$-0.0644697\pi$
$812$		0			0
$813$	−1.15048	+	1.47655i	−0.0403489	+	0.0517847i
$814$		0			0
$815$	1.19105	−	6.75478i	0.0417206	−	0.236610i
$816$		0			0
$817$	26.6316	−	22.3465i	0.931721	−	0.781807i
$818$		0			0
$819$	1.50328	−	5.29517i	0.0525288	−	0.185028i
$820$		0			0
$821$	6.64372	−	1.17147i	0.231867	−	0.0408845i	−0.0565070	−	0.998402i	$-0.517996\pi$
$821$	6.64372	−	1.17147i	0.231867	−	0.0408845i	0.288374	+	0.957518i	$0.406885\pi$
$822$		0			0
$823$	−5.31714	−	14.6087i	−0.185344	−	0.509228i	0.811869	−	0.583840i	$-0.198450\pi$
$823$	−5.31714	−	14.6087i	−0.185344	−	0.509228i	−0.997213	+	0.0746118i	$0.976228\pi$
$824$		0			0
$825$	−0.723696	+	0.653347i	−0.0251959	+	0.0227466i
$826$		0			0
$827$	−18.0772	+	31.3106i	−0.628606	+	1.08878i	0.359226	+	0.933251i	$0.383041\pi$
$827$	−18.0772	+	31.3106i	−0.628606	+	1.08878i	−0.987832	+	0.155527i	$0.950292\pi$
$828$		0			0
$829$	−7.04448	−	12.2014i	−0.244665	−	0.423772i	0.717373	−	0.696690i	$-0.245345\pi$
$829$	−7.04448	−	12.2014i	−0.244665	−	0.423772i	−0.962037	+	0.272918i	$0.912011\pi$
$830$		0			0
$831$	−24.0706	+	0.872315i	−0.835000	+	0.0302603i
$832$		0			0
$833$	12.1182	−	14.4419i	0.419871	−	0.500383i
$834$		0			0
$835$	−13.1915	+	36.2434i	−0.456512	+	1.25426i
$836$		0			0
$837$	−10.5190	−	21.3525i	−0.363589	−	0.738051i
$838$		0			0
$839$	15.6165	+	5.68395i	0.539142	+	0.196232i	0.597216	−	0.802081i	$-0.296274\pi$
$839$	15.6165	+	5.68395i	0.539142	+	0.196232i	−0.0580737	+	0.998312i	$0.518496\pi$
$840$		0			0
$841$	−4.94101	−	4.14600i	−0.170380	−	0.142965i
$842$		0			0
$843$	8.59147	+	4.55366i	0.295906	+	0.156836i
$844$		0			0
$845$	−9.44004	+	5.45021i	−0.324747	+	0.187493i
$846$		0			0
$847$	−6.46498	−	3.73256i	−0.222139	−	0.128252i
$848$		0			0
$849$	−8.71940	+	26.9563i	−0.299249	+	0.925139i
$850$		0			0
$851$	−6.04631	+	2.20068i	−0.207265	+	0.0754382i
$852$		0			0
$853$	−8.76180	−	49.6906i	−0.299998	−	1.70138i	−0.646161	−	0.763201i	$-0.723627\pi$
$853$	−8.76180	−	49.6906i	−0.299998	−	1.70138i	0.346163	−	0.938174i	$-0.387484\pi$
$854$		0			0
$855$	−9.06206	−	13.3590i	−0.309916	−	0.456868i
$856$		0			0
$857$	−25.4251	−	30.3005i	−0.868506	−	1.03504i	−0.999049	−	0.0436021i	$-0.986117\pi$
$857$	−25.4251	−	30.3005i	−0.868506	−	1.03504i	0.130543	−	0.991443i	$-0.458328\pi$
$858$		0			0
$859$	−18.3052	−	3.22771i	−0.624567	−	0.110128i	−0.147597	−	0.989048i	$-0.547154\pi$
$859$	−18.3052	−	3.22771i	−0.624567	−	0.110128i	−0.476970	+	0.878920i	$0.658265\pi$
$860$		0			0
$861$	10.6297	−	4.31099i	0.362260	−	0.146918i
$862$		0			0
$863$	−35.2494			−1.19990			−0.599952	−	0.800036i	$-0.704813\pi$
$863$	−35.2494			−1.19990			−0.599952	+	0.800036i	$0.704813\pi$
$864$		0			0
$865$	11.5913			0.394115
$866$		0			0
$867$	2.06798	−	14.8564i	0.0702321	−	0.504550i
$868$		0			0
$869$	−2.64542	−	0.466459i	−0.0897398	−	0.0158235i
$870$		0			0
$871$	8.59944	+	10.2484i	0.291381	+	0.347254i
$872$		0			0
$873$	3.23103	−	1.44876i	0.109354	−	0.0490331i
$874$		0			0
$875$	1.45116	+	8.22996i	0.0490583	+	0.278223i
$876$		0			0
$877$	−41.9724	+	15.2767i	−1.41731	+	0.515858i	−0.933266	−	0.359187i	$-0.883054\pi$
$877$	−41.9724	+	15.2767i	−1.41731	+	0.515858i	−0.484042	+	0.875045i	$0.660832\pi$
$878$		0			0
$879$	−19.3031	+	4.12959i	−0.651078	+	0.139288i
$880$		0			0
$881$	2.33653	+	1.34900i	0.0787198	+	0.0454489i	0.538843	−	0.842406i	$-0.318862\pi$
$881$	2.33653	+	1.34900i	0.0787198	+	0.0454489i	−0.460123	+	0.887855i	$0.652195\pi$
$882$		0			0
$883$	−17.3880	+	10.0389i	−0.585151	+	0.337837i	−0.763178	−	0.646188i	$-0.776362\pi$
$883$	−17.3880	+	10.0389i	−0.585151	+	0.337837i	0.178027	+	0.984026i	$0.443029\pi$
$884$		0			0
$885$	13.5840	−	8.51315i	0.456622	−	0.286166i
$886$		0			0
$887$	17.5348	+	14.7135i	0.588762	+	0.494030i	0.887811	−	0.460208i	$-0.152225\pi$
$887$	17.5348	+	14.7135i	0.588762	+	0.494030i	−0.299049	+	0.954238i	$0.596669\pi$
$888$		0			0
$889$	−7.71279	−	2.80723i	−0.258679	−	0.0941513i
$890$		0			0
$891$	2.03064	+	2.57106i	0.0680289	+	0.0861336i
$892$		0			0
$893$	−9.84507	+	27.0491i	−0.329453	+	0.905164i
$894$		0			0
$895$	16.1680	−	19.2682i	0.540436	−	0.644066i
$896$		0			0
$897$	−4.45881	−	7.11472i	−0.148875	−	0.237553i
$898$		0			0
$899$	13.6372	+	23.6204i	0.454828	+	0.787784i
$900$		0			0
$901$	1.47254	−	2.55052i	0.0490575	−	0.0849701i
$902$		0			0
$903$	2.98855	+	13.9695i	0.0994528	+	0.464876i
$904$		0			0
$905$	−4.31288	−	11.8495i	−0.143365	−	0.393892i
$906$		0			0
$907$	−2.29373	+	0.404447i	−0.0761621	+	0.0134294i	−0.211599	−	0.977356i	$-0.567867\pi$
$907$	−2.29373	+	0.404447i	−0.0761621	+	0.0134294i	0.135437	+	0.990786i	$0.456756\pi$
$908$		0			0
$909$	12.3743	−	17.1265i	0.410430	−	0.568050i
$910$		0			0
$911$	1.41352	−	1.18609i	0.0468320	−	0.0392968i	−0.619071	−	0.785335i	$-0.712491\pi$
$911$	1.41352	−	1.18609i	0.0468320	−	0.0392968i	0.665903	+	0.746038i	$0.268046\pi$
$912$		0			0
$913$	0.245933	−	1.39476i	0.00813920	−	0.0461597i
$914$		0			0
$915$	−40.0035	−	5.56839i	−1.32247	−	0.184085i
$916$		0			0
$917$		−	0.781039i		−	0.0257922i
$918$		0			0
$919$			7.95591i			0.262441i	0.991353	+	0.131221i	$0.0418896\pi$
$919$			7.95591i			0.262441i	−0.991353	+	0.131221i	$0.958110\pi$
$920$		0			0
$921$	4.66728	+	11.5083i	0.153792	+	0.379210i
$922$		0			0
$923$	7.69816	−	43.6585i	0.253388	−	1.43704i
$924$		0			0
$925$	−4.19962	+	3.52390i	−0.138083	+	0.115865i
$926$		0			0
$927$	−2.00553	−	27.6339i	−0.0658702	−	0.907616i
$928$		0			0
$929$	−33.5766	+	5.92047i	−1.10161	+	0.194244i	−0.694755	−	0.719247i	$-0.744487\pi$
$929$	−33.5766	+	5.92047i	−1.10161	+	0.194244i	−0.406859	+	0.913491i	$0.633376\pi$
$930$		0			0
$931$	6.46477	+	17.7618i	0.211874	+	0.582120i
$932$		0			0
$933$	−35.3269	−	11.4270i	−1.15655	−	0.374103i
$934$		0			0
$935$	0.976848	−	1.69195i	0.0319463	−	0.0553327i
$936$		0			0
$937$	25.5356	+	44.2290i	0.834213	+	1.44490i	0.894670	+	0.446728i	$0.147411\pi$
$937$	25.5356	+	44.2290i	0.834213	+	1.44490i	−0.0604570	+	0.998171i	$0.519256\pi$
$938$		0			0
$939$	−5.91580	+	11.1614i	−0.193055	+	0.364240i
$940$		0			0
$941$	−19.1713	+	22.8475i	−0.624968	+	0.744808i	−0.981916	−	0.189317i	$-0.939373\pi$
$941$	−19.1713	+	22.8475i	−0.624968	+	0.744808i	0.356948	+	0.934124i	$0.383817\pi$
$942$		0			0
$943$	5.98444	−	16.4421i	0.194880	−	0.535429i
$944$		0			0
$945$	6.59417	−	0.719436i	0.214508	−	0.0234032i
$946$		0			0
$947$	−39.9500	−	14.5406i	−1.29820	−	0.472507i	−0.401791	−	0.915731i	$-0.631612\pi$
$947$	−39.9500	−	14.5406i	−1.29820	−	0.472507i	−0.896411	+	0.443225i	$0.853834\pi$
$948$		0			0
$949$	−28.0240	−	23.5150i	−0.909699	−	0.763328i
$950$		0			0
$951$	−1.45901	−	40.2597i	−0.0473115	−	1.30551i
$952$		0			0
$953$	20.2227	−	11.6756i	0.655078	−	0.378209i	−0.135321	−	0.990802i	$-0.543207\pi$
$953$	20.2227	−	11.6756i	0.655078	−	0.378209i	0.790399	+	0.612592i	$0.209873\pi$
$954$		0			0
$955$	26.3214	+	15.1967i	0.851741	+	0.491753i
$956$		0			0
$957$	−2.51564	−	2.78651i	−0.0813192	−	0.0900752i
$958$		0			0
$959$	−5.19389	+	1.89042i	−0.167719	+	0.0610448i
$960$		0			0
$961$	1.73919	+	9.86344i	0.0561029	+	0.318175i
$962$		0			0
$963$	−8.59920	−	34.1064i	−0.277105	−	1.09906i
$964$		0			0
$965$	22.6434	+	26.9853i	0.728916	+	0.868688i
$966$		0			0
$967$	33.8501	+	5.96869i	1.08855	+	0.191940i	0.688992	−	0.724769i	$-0.258053\pi$
$967$	33.8501	+	5.96869i	1.08855	+	0.191940i	0.399555	+	0.916709i	$0.369165\pi$
$968$		0			0
$969$	−11.4244	−	8.90151i	−0.367005	−	0.285958i
$970$		0			0
$971$	46.5628			1.49427			0.747136	−	0.664672i	$-0.231429\pi$
$971$	46.5628			1.49427			0.747136	+	0.664672i	$0.231429\pi$
$972$		0			0
$973$	3.72797			0.119513
$974$		0			0
$975$	−5.64319	−	4.39699i	−0.180727	−	0.140816i
$976$		0			0
$977$	−53.9905	−	9.51998i	−1.72731	−	0.304571i	−0.780212	−	0.625516i	$-0.784889\pi$
$977$	−53.9905	−	9.51998i	−1.72731	−	0.304571i	−0.947098	+	0.320944i	$0.896000\pi$
$978$		0			0
$979$	3.27258	+	3.90011i	0.104592	+	0.124648i
$980$		0			0
$981$	−9.38705	−	37.2312i	−0.299706	−	1.18870i
$982$		0			0
$983$	−5.28596	−	29.9782i	−0.168596	−	0.956156i	−0.945279	−	0.326264i	$-0.894210\pi$
$983$	−5.28596	−	29.9782i	−0.168596	−	0.956156i	0.776683	−	0.629892i	$-0.216901\pi$
$984$		0			0
$985$	−41.1446	+	14.9754i	−1.31097	+	0.477156i
$986$		0			0
$987$	−7.92627	−	8.77973i	−0.252296	−	0.279462i
$988$		0			0
$989$	18.8718	+	10.8956i	0.600088	+	0.346461i
$990$		0			0
$991$	−25.9511	+	14.9829i	−0.824364	+	0.475946i	−0.851919	−	0.523674i	$-0.824561\pi$
$991$	−25.9511	+	14.9829i	−0.824364	+	0.475946i	0.0275554	+	0.999620i	$0.491228\pi$
$992$		0			0
$993$	−0.726501	−	20.0470i	−0.0230548	−	0.636173i
$994$		0			0
$995$	17.8670	+	14.9922i	0.566423	+	0.475286i
$996$		0			0
$997$	18.0596	+	6.57315i	0.571953	+	0.208174i	0.611773	−	0.791033i	$-0.290456\pi$
$997$	18.0596	+	6.57315i	0.571953	+	0.208174i	−0.0398208	+	0.999207i	$0.512679\pi$
$998$		0			0
$999$	10.8869	+	14.8607i	0.344447	+	0.470172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.b.239.5	yes	36
4.3	odd	2		432.2.be.c.239.2	yes	36
27.20	odd	18		432.2.be.c.47.2	yes	36
108.47	even	18	inner	432.2.be.b.47.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.47.5	✓	36	108.47	even	18	inner
432.2.be.b.239.5	yes	36	1.1	even	1	trivial
432.2.be.c.47.2	yes	36	27.20	odd	18
432.2.be.c.239.2	yes	36	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36628 + 1.06456i) q^{3} +(1.83017 + 0.322709i) q^{5} +(-0.441545 - 0.526213i) q^{7} +(0.733433 + 2.90896i) q^{9} +O(q^{10})\)	\(q+(1.36628 + 1.06456i) q^{3} +(1.83017 + 0.322709i) q^{5} +(-0.441545 - 0.526213i) q^{7} +(0.733433 + 2.90896i) q^{9} +(-0.0632128 - 0.358498i) q^{11} +(2.50997 - 0.913554i) q^{13} +(2.15698 + 2.38923i) q^{15} +(2.50099 + 1.44395i) q^{17} +(-2.50751 + 1.44771i) q^{19} +(-0.0430893 - 1.18900i) q^{21} +(-1.39029 - 1.16659i) q^{23} +(-1.45308 - 0.528877i) q^{25} +(-2.09469 + 4.75524i) q^{27} +(2.03639 - 5.59492i) q^{29} +(-2.94453 + 3.50915i) q^{31} +(0.295275 - 0.557101i) q^{33} +(-0.638290 - 1.10555i) q^{35} +(1.77265 - 3.07032i) q^{37} +(4.40185 + 1.42384i) q^{39} +(3.29740 + 9.05952i) q^{41} +(-11.8245 + 2.08497i) q^{43} +(0.403559 + 5.56059i) q^{45} +(7.61569 - 6.39032i) q^{47} +(1.13360 - 6.42896i) q^{49} +(1.87989 + 4.63529i) q^{51} -1.01980i q^{53} -0.676511i q^{55} +(-4.96713 - 0.691413i) q^{57} +(0.864840 - 4.90475i) q^{59} +(-9.61210 + 8.06551i) q^{61} +(1.20689 - 1.67038i) q^{63} +(4.88848 - 0.861972i) q^{65} +(1.71306 + 4.70659i) q^{67} +(-0.657619 - 3.07394i) q^{69} +(8.29859 - 14.3736i) q^{71} +(-6.84801 - 11.8611i) q^{73} +(-1.42229 - 2.26948i) q^{75} +(-0.160735 + 0.191556i) q^{77} +(2.52383 - 6.93417i) q^{79} +(-7.92415 + 4.26706i) q^{81} +(3.65593 + 1.33065i) q^{83} +(4.11127 + 3.44977i) q^{85} +(8.73839 - 5.47637i) q^{87} +(-12.1121 + 6.99291i) q^{89} +(-1.58899 - 0.917403i) q^{91} +(-7.75874 + 1.65986i) q^{93} +(-5.05636 + 1.84037i) q^{95} +(-0.204961 - 1.16239i) q^{97} +(0.996494 - 0.446818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q + 3 * q^5 + 6 * q^9	\( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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