LMFDB - Embedded newform 432.2.be.b.335.5

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			335.5
Character	$\chi$	$=$	432.335
Dual form			432.2.be.b.383.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15860 + 1.28750i) q^{3} +(-0.152066 + 0.417798i) q^{5} +(2.02729 + 0.357466i) q^{7} +(-0.315297 + 2.98339i) q^{9} +O(q^{10})$	\(q+(1.15860 + 1.28750i) q^{3} +(-0.152066 + 0.417798i) q^{5} +(2.02729 + 0.357466i) q^{7} +(-0.315297 + 2.98339i) q^{9} +(1.69871 - 0.618279i) q^{11} +(-1.30897 + 1.09836i) q^{13} +(-0.714097 + 0.288276i) q^{15} +(-1.80110 + 1.03987i) q^{17} +(2.98630 + 1.72414i) q^{19} +(1.88858 + 3.02429i) q^{21} +(-1.25099 - 7.09471i) q^{23} +(3.67879 + 3.08687i) q^{25} +(-4.20640 + 3.05060i) q^{27} +(-5.04980 + 6.01812i) q^{29} +(4.88540 - 0.861427i) q^{31} +(2.76415 + 1.47074i) q^{33} +(-0.457630 + 0.792639i) q^{35} +(-3.34776 - 5.79849i) q^{37} +(-2.93071 - 0.412742i) q^{39} +(0.844832 + 1.00683i) q^{41} +(0.952433 + 2.61679i) q^{43} +(-1.19851 - 0.585402i) q^{45} +(1.10583 - 6.27146i) q^{47} +(-2.59573 - 0.944769i) q^{49} +(-3.42558 - 1.11413i) q^{51} -4.42366i q^{53} +0.803736i q^{55} +(1.24010 + 5.84245i) q^{57} +(-1.57194 - 0.572141i) q^{59} +(0.506551 - 2.87280i) q^{61} +(-1.70566 + 5.93547i) q^{63} +(-0.259842 - 0.713910i) q^{65} +(6.09081 + 7.25875i) q^{67} +(7.68502 - 9.83056i) q^{69} +(-4.39265 - 7.60829i) q^{71} +(7.57844 - 13.1262i) q^{73} +(0.287904 + 8.31288i) q^{75} +(3.66478 - 0.646200i) q^{77} +(7.55750 - 9.00668i) q^{79} +(-8.80118 - 1.88131i) q^{81} +(3.93218 + 3.29949i) q^{83} +(-0.160568 - 0.910626i) q^{85} +(-13.5990 + 0.470981i) q^{87} +(-14.5334 - 8.39084i) q^{89} +(-3.04629 + 1.75878i) q^{91} +(6.76930 + 5.29188i) q^{93} +(-1.17446 + 0.985488i) q^{95} +(11.3511 - 4.13145i) q^{97} +(1.30897 + 5.26284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{18}\right)$

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
$3$	1.15860	+	1.28750i	0.668917	+	0.743337i
$3$	1.15860	+	1.28750i	0.668917	+	0.743337i
$4$		0			0
$5$	−0.152066	+	0.417798i	−0.0680060	+	0.186845i	−0.969040	−	0.246903i	$-0.920587\pi$
$5$	−0.152066	+	0.417798i	−0.0680060	+	0.186845i	0.901034	+	0.433748i	$0.142809\pi$
$6$		0			0
$7$	2.02729	+	0.357466i	0.766243	+	0.135109i	0.543090	−	0.839674i	$-0.317254\pi$
$7$	2.02729	+	0.357466i	0.766243	+	0.135109i	0.223153	+	0.974784i	$0.428365\pi$
$8$		0			0
$9$	−0.315297	+	2.98339i	−0.105099	+	0.994462i
$10$		0			0
$11$	1.69871	−	0.618279i	0.512180	−	0.186418i	−0.0729845	−	0.997333i	$-0.523252\pi$
$11$	1.69871	−	0.618279i	0.512180	−	0.186418i	0.585164	+	0.810915i	$0.301030\pi$
$12$		0			0
$13$	−1.30897	+	1.09836i	−0.363044	+	0.304630i	−0.806003	−	0.591912i	$-0.798373\pi$
$13$	−1.30897	+	1.09836i	−0.363044	+	0.304630i	0.442959	+	0.896542i	$0.353929\pi$
$14$		0			0
$15$	−0.714097	+	0.288276i	−0.184379	+	0.0744325i
$16$		0			0
$17$	−1.80110	+	1.03987i	−0.436832	+	0.252205i	−0.702253	−	0.711928i	$-0.747822\pi$
$17$	−1.80110	+	1.03987i	−0.436832	+	0.252205i	0.265421	+	0.964133i	$0.414489\pi$
$18$		0			0
$19$	2.98630	+	1.72414i	0.685105	+	0.395545i	0.801776	−	0.597625i	$-0.203889\pi$
$19$	2.98630	+	1.72414i	0.685105	+	0.395545i	−0.116671	+	0.993171i	$0.537222\pi$
$20$		0			0
$21$	1.88858	+	3.02429i	0.412122	+	0.659954i
$22$		0			0
$23$	−1.25099	−	7.09471i	−0.260849	−	1.47935i	−0.780600	−	0.625031i	$-0.785086\pi$
$23$	−1.25099	−	7.09471i	−0.260849	−	1.47935i	0.519751	−	0.854318i	$-0.326025\pi$
$24$		0			0
$25$	3.67879	+	3.08687i	0.735758	+	0.617374i
$26$		0			0
$27$	−4.20640	+	3.05060i	−0.809523	+	0.587089i
$28$		0			0
$29$	−5.04980	+	6.01812i	−0.937724	+	1.11754i	0.0551631	+	0.998477i	$0.482432\pi$
$29$	−5.04980	+	6.01812i	−0.937724	+	1.11754i	−0.992887	+	0.119059i	$0.962012\pi$
$30$		0			0
$31$	4.88540	−	0.861427i	0.877443	−	0.154717i	0.283256	−	0.959044i	$-0.408585\pi$
$31$	4.88540	−	0.861427i	0.877443	−	0.154717i	0.594186	+	0.804327i	$0.297474\pi$
$32$		0			0
$33$	2.76415	+	1.47074i	0.481177	+	0.256024i
$34$		0			0
$35$	−0.457630	+	0.792639i	−0.0773536	+	0.133980i
$36$		0			0
$37$	−3.34776	−	5.79849i	−0.550368	−	0.953266i	−0.998248	−	0.0591718i	$-0.981154\pi$
$37$	−3.34776	−	5.79849i	−0.550368	−	0.953266i	0.447880	−	0.894094i	$-0.352179\pi$
$38$		0			0
$39$	−2.93071	−	0.412742i	−0.469289	−	0.0660916i
$40$		0			0
$41$	0.844832	+	1.00683i	0.131941	+	0.157241i	0.827970	−	0.560773i	$-0.189496\pi$
$41$	0.844832	+	1.00683i	0.131941	+	0.157241i	−0.696029	+	0.718014i	$0.745052\pi$
$42$		0			0
$43$	0.952433	+	2.61679i	0.145245	+	0.399056i	0.990887	−	0.134693i	$-0.0430048\pi$
$43$	0.952433	+	2.61679i	0.145245	+	0.399056i	−0.845643	+	0.533749i	$0.820783\pi$
$44$		0			0
$45$	−1.19851	−	0.585402i	−0.178663	−	0.0872666i
$46$		0			0
$47$	1.10583	−	6.27146i	0.161302	−	0.914787i	−0.791495	−	0.611176i	$-0.790697\pi$
$47$	1.10583	−	6.27146i	0.161302	−	0.914787i	0.952796	−	0.303611i	$-0.0981922\pi$
$48$		0			0
$49$	−2.59573	−	0.944769i	−0.370819	−	0.134967i
$50$		0			0
$51$	−3.42558	−	1.11413i	−0.479678	−	0.156009i
$52$		0			0
$53$		−	4.42366i		−	0.607637i	−0.952730	−	0.303818i	$-0.901738\pi$
$53$		−	4.42366i		−	0.607637i	0.952730	−	0.303818i	$-0.0982616\pi$
$54$		0			0
$55$			0.803736i			0.108376i
$56$		0			0
$57$	1.24010	+	5.84245i	0.164255	+	0.773851i
$58$		0			0
$59$	−1.57194	−	0.572141i	−0.204650	−	0.0744864i	0.237662	−	0.971348i	$-0.423619\pi$
$59$	−1.57194	−	0.572141i	−0.204650	−	0.0744864i	−0.442311	+	0.896862i	$0.645841\pi$
$60$		0			0
$61$	0.506551	−	2.87280i	0.0648573	−	0.367824i	−0.935054	−	0.354505i	$-0.884649\pi$
$61$	0.506551	−	2.87280i	0.0648573	−	0.367824i	0.999911	−	0.0133186i	$-0.00423957\pi$
$62$		0			0
$63$	−1.70566	+	5.93547i	−0.214893	+	0.747799i
$64$		0			0
$65$	−0.259842	−	0.713910i	−0.0322294	−	0.0885496i
$66$		0			0
$67$	6.09081	+	7.25875i	0.744111	+	0.886797i	0.996733	−	0.0807679i	$-0.0257373\pi$
$67$	6.09081	+	7.25875i	0.744111	+	0.886797i	−0.252622	+	0.967565i	$0.581293\pi$
$68$		0			0
$69$	7.68502	−	9.83056i	0.925168	−	1.18346i
$70$		0			0
$71$	−4.39265	−	7.60829i	−0.521311	−	0.902937i	−0.999693	−	0.0247854i	$-0.992110\pi$
$71$	−4.39265	−	7.60829i	−0.521311	−	0.902937i	0.478382	−	0.878152i	$-0.341224\pi$
$72$		0			0
$73$	7.57844	−	13.1262i	0.886990	−	1.53631i	0.0435738	−	0.999050i	$-0.486126\pi$
$73$	7.57844	−	13.1262i	0.886990	−	1.53631i	0.843416	−	0.537261i	$-0.180541\pi$
$74$		0			0
$75$	0.287904	+	8.31288i	0.0332443	+	0.959889i
$76$		0			0
$77$	3.66478	−	0.646200i	0.417641	−	0.0736413i
$78$		0			0
$79$	7.55750	−	9.00668i	0.850286	−	1.01333i	−0.149413	−	0.988775i	$-0.547738\pi$
$79$	7.55750	−	9.00668i	0.850286	−	1.01333i	0.999698	−	0.0245560i	$-0.00781720\pi$
$80$		0			0
$81$	−8.80118	−	1.88131i	−0.977908	−	0.209034i
$82$		0			0
$83$	3.93218	+	3.29949i	0.431613	+	0.362166i	0.832560	−	0.553935i	$-0.186874\pi$
$83$	3.93218	+	3.29949i	0.431613	+	0.362166i	−0.400947	+	0.916101i	$0.631319\pi$
$84$		0			0
$85$	−0.160568	−	0.910626i	−0.0174160	−	0.0987713i
$86$		0			0
$87$	−13.5990	+	0.470981i	−1.45797	+	0.0504945i
$88$		0			0
$89$	−14.5334	−	8.39084i	−1.54053	−	0.889428i	−0.998805	−	0.0488745i	$-0.984437\pi$
$89$	−14.5334	−	8.39084i	−1.54053	−	0.889428i	−0.541729	−	0.840553i	$-0.682230\pi$
$90$		0			0
$91$	−3.04629	+	1.75878i	−0.319338	+	0.184370i
$92$		0			0
$93$	6.76930	+	5.29188i	0.701944	+	0.548743i
$94$		0			0
$95$	−1.17446	+	0.985488i	−0.120497	+	0.101109i
$96$		0			0
$97$	11.3511	−	4.13145i	1.15253	−	0.419486i	0.306105	−	0.951998i	$-0.400974\pi$
$97$	11.3511	−	4.13145i	1.15253	−	0.419486i	0.846422	+	0.532512i	$0.178752\pi$
$98$		0			0
$99$	1.30897	+	5.26284i	0.131556	+	0.528935i
$100$		0			0
$101$	−0.692830	−	0.122165i	−0.0689392	−	0.0121558i	0.139072	−	0.990282i	$-0.455588\pi$
$101$	−0.692830	−	0.122165i	−0.0689392	−	0.0121558i	−0.208011	+	0.978126i	$0.566699\pi$
$102$		0			0
$103$	−2.85950	+	7.85641i	−0.281755	+	0.774115i	0.715398	+	0.698717i	$0.246245\pi$
$103$	−2.85950	+	7.85641i	−0.281755	+	0.774115i	−0.997153	+	0.0753988i	$0.975977\pi$
$104$		0			0
$105$	−1.55073	+	0.329153i	−0.151336	+	0.0321220i
$106$		0			0
$107$	−8.50879			−0.822576			−0.411288	−	0.911505i	$-0.634921\pi$
$107$	−8.50879			−0.822576			−0.411288	+	0.911505i	$0.634921\pi$
$108$		0			0
$109$	−6.36306			−0.609470			−0.304735	−	0.952437i	$-0.598568\pi$
$109$	−6.36306			−0.609470			−0.304735	+	0.952437i	$0.598568\pi$
$110$		0			0
$111$	3.58683	−	11.0284i	0.340447	−	1.04676i
$112$		0			0
$113$	6.85202	−	18.8258i	0.644584	−	1.77098i	0.00776102	−	0.999970i	$-0.497530\pi$
$113$	6.85202	−	18.8258i	0.644584	−	1.77098i	0.636823	−	0.771010i	$-0.280248\pi$
$114$		0			0
$115$	3.15439	+	0.556204i	0.294148	+	0.0518663i
$116$		0			0
$117$	−2.86411	−	4.25148i	−0.264787	−	0.393050i
$118$		0			0
$119$	−4.02307	+	1.46428i	−0.368795	+	0.134230i
$120$		0			0
$121$	−5.92315	+	4.97011i	−0.538468	+	0.451829i
$122$		0			0
$123$	−0.317471	+	2.25423i	−0.0286254	+	0.203257i
$124$		0			0
$125$	−3.77433	+	2.17911i	−0.337587	+	0.194906i
$126$		0			0
$127$	−11.1837	−	6.45690i	−0.992391	−	0.572957i	−0.0864027	−	0.996260i	$-0.527537\pi$
$127$	−11.1837	−	6.45690i	−0.992391	−	0.572957i	−0.905988	+	0.423303i	$0.860871\pi$
$128$		0			0
$129$	−2.26562	+	4.25806i	−0.199477	+	0.374901i
$130$		0			0
$131$	−3.53455	−	20.0454i	−0.308815	−	1.75138i	−0.604979	−	0.796241i	$-0.706819\pi$
$131$	−3.53455	−	20.0454i	−0.308815	−	1.75138i	0.296164	−	0.955137i	$-0.404293\pi$
$132$		0			0
$133$	5.43778	+	4.56284i	0.471515	+	0.395648i
$134$		0			0
$135$	−0.634885	−	2.22132i	−0.0546422	−	0.191181i
$136$		0			0
$137$	−10.0866	+	12.0208i	−0.861759	+	1.02700i	0.137574	+	0.990491i	$0.456069\pi$
$137$	−10.0866	+	12.0208i	−0.861759	+	1.02700i	−0.999333	+	0.0365127i	$0.988375\pi$
$138$		0			0
$139$	−0.978203	+	0.172484i	−0.0829701	+	0.0146299i	−0.214979	−	0.976619i	$-0.568968\pi$
$139$	−0.978203	+	0.172484i	−0.0829701	+	0.0146299i	0.132009	+	0.991249i	$0.457857\pi$
$140$		0			0
$141$	9.35570	−	5.84236i	0.787892	−	0.492015i
$142$		0			0
$143$	−1.54447	+	2.67510i	−0.129155	+	0.223703i
$144$		0			0
$145$	−1.74645	−	3.02495i	−0.145035	−	0.251208i
$146$		0			0
$147$	−1.79102	−	4.43661i	−0.147721	−	0.365925i
$148$		0			0
$149$	14.0031	+	16.6882i	1.14718	+	1.36715i	0.919345	+	0.393452i	$0.128719\pi$
$149$	14.0031	+	16.6882i	1.14718	+	1.36715i	0.227832	+	0.973701i	$0.426836\pi$
$150$		0			0
$151$	−3.78962	−	10.4119i	−0.308395	−	0.847308i	−0.992970	−	0.118366i	$-0.962234\pi$
$151$	−3.78962	−	10.4119i	−0.308395	−	0.847308i	0.684575	−	0.728942i	$-0.259988\pi$
$152$		0			0
$153$	−2.53444	−	5.70125i	−0.204898	−	0.460919i
$154$		0			0
$155$	−0.383000	+	2.17210i	−0.0307633	+	0.174467i
$156$		0			0
$157$	−12.6388	−	4.60016i	−1.00869	−	0.367133i	−0.215760	−	0.976446i	$-0.569223\pi$
$157$	−12.6388	−	4.60016i	−1.00869	−	0.367133i	−0.792930	+	0.609313i	$0.791445\pi$
$158$		0			0
$159$	5.69545	−	5.12525i	0.451679	−	0.406459i
$160$		0			0
$161$		−	14.8302i		−	1.16878i
$162$		0			0
$163$		−	1.23966i		−	0.0970978i	−0.998821	−	0.0485489i	$-0.984540\pi$
$163$		−	1.23966i		−	0.0970978i	0.998821	−	0.0485489i	$-0.0154597\pi$
$164$		0			0
$165$	−1.03481	+	0.931207i	−0.0805597	+	0.0724944i
$166$		0			0
$167$	17.7939	+	6.47644i	1.37693	+	0.501162i	0.921247	−	0.388979i	$-0.127172\pi$
$167$	17.7939	+	6.47644i	1.37693	+	0.501162i	0.455685	+	0.890141i	$0.349394\pi$
$168$		0			0
$169$	−1.75041	+	9.92705i	−0.134647	+	0.763619i
$170$		0			0
$171$	−6.08536	+	8.36567i	−0.465359	+	0.639739i
$172$		0			0
$173$	7.56075	+	20.7730i	0.574833	+	1.57934i	0.796772	+	0.604280i	$0.206539\pi$
$173$	7.56075	+	20.7730i	0.574833	+	1.57934i	−0.221939	+	0.975061i	$0.571238\pi$
$174$		0			0
$175$	6.35452	+	7.57302i	0.480357	+	0.572467i
$176$		0			0
$177$	−1.08462	−	2.68675i	−0.0815252	−	0.201949i
$178$		0			0
$179$	10.1858	+	17.6423i	0.761322	+	1.31865i	0.942169	+	0.335137i	$0.108783\pi$
$179$	10.1858	+	17.6423i	0.761322	+	1.31865i	−0.180848	+	0.983511i	$0.557884\pi$
$180$		0			0
$181$	1.72626	−	2.98996i	0.128312	−	0.222242i	−0.794711	−	0.606988i	$-0.792378\pi$
$181$	1.72626	−	2.98996i	0.128312	−	0.222242i	0.923023	+	0.384746i	$0.125711\pi$
$182$		0			0
$183$	4.28561	−	2.67623i	0.316801	−	0.197833i
$184$		0			0
$185$	2.93168	−	0.516934i	0.215541	−	0.0380057i
$186$		0			0
$187$	−2.41662	+	2.88002i	−0.176721	+	0.210608i
$188$		0			0
$189$	−9.61808	+	4.68081i	−0.699612	+	0.340479i
$190$		0			0
$191$	5.95082	+	4.99333i	0.430586	+	0.361305i	0.832173	−	0.554516i	$-0.187097\pi$
$191$	5.95082	+	4.99333i	0.430586	+	0.361305i	−0.401586	+	0.915821i	$0.631541\pi$
$192$		0			0
$193$	2.57608	+	14.6097i	0.185430	+	1.05163i	0.925402	+	0.378988i	$0.123728\pi$
$193$	2.57608	+	14.6097i	0.185430	+	1.05163i	−0.739971	+	0.672638i	$0.765161\pi$
$194$		0			0
$195$	0.618104	−	1.16168i	0.0442634	−	0.0831897i
$196$		0			0
$197$	−2.87202	−	1.65816i	−0.204623	−	0.118139i	0.394187	−	0.919030i	$-0.371026\pi$
$197$	−2.87202	−	1.65816i	−0.204623	−	0.118139i	−0.598810	+	0.800891i	$0.704360\pi$
$198$		0			0
$199$	−13.0069	+	7.50956i	−0.922037	+	0.532338i	−0.884284	−	0.466949i	$-0.845353\pi$
$199$	−13.0069	+	7.50956i	−0.922037	+	0.532338i	−0.0377528	+	0.999287i	$0.512020\pi$
$200$		0			0
$201$	−2.28881	+	16.2519i	−0.161440	+	1.14632i
$202$		0			0
$203$	−12.3887	+	10.3953i	−0.869514	+	0.729609i
$204$		0			0
$205$	−0.549123	+	0.199864i	−0.0383524	+	0.0139591i
$206$		0			0
$207$	21.5607	−	1.49524i	1.49857	−	0.103926i
$208$		0			0
$209$	6.13886	+	1.08245i	0.424634	+	0.0748743i
$210$		0			0
$211$	2.44987	−	6.73095i	0.168656	−	0.463378i	−0.826355	−	0.563150i	$-0.809589\pi$
$211$	2.44987	−	6.73095i	0.168656	−	0.463378i	0.995010	+	0.0997724i	$0.0318115\pi$
$212$		0			0
$213$	4.70633	−	14.4705i	0.322473	−	0.991500i
$214$		0			0
$215$	−1.23812			−0.0844392
$216$		0			0
$217$	10.2120			0.693238
$218$		0			0
$219$	25.6804	−	5.45083i	1.73532	−	0.368333i
$220$		0			0
$221$	1.21545	−	3.33942i	0.0817600	−	0.224634i
$222$		0			0
$223$	6.45788	+	1.13870i	0.432452	+	0.0762529i	0.385637	−	0.922651i	$-0.373982\pi$
$223$	6.45788	+	1.13870i	0.432452	+	0.0762529i	0.0468150	+	0.998904i	$0.485093\pi$
$224$		0			0
$225$	−10.3692	+	10.0020i	−0.691283	+	0.666798i
$226$		0			0
$227$	21.7532	−	7.91750i	1.44381	−	0.525503i	0.502953	−	0.864314i	$-0.332247\pi$
$227$	21.7532	−	7.91750i	1.44381	−	0.525503i	0.940855	+	0.338810i	$0.110025\pi$
$228$		0			0
$229$	−21.1402	+	17.7388i	−1.39699	+	1.17221i	−0.434568	+	0.900639i	$0.643099\pi$
$229$	−21.1402	+	17.7388i	−1.39699	+	1.17221i	−0.962418	+	0.271571i	$0.912457\pi$
$230$		0			0
$231$	5.07799	+	3.96971i	0.334107	+	0.261188i
$232$		0			0
$233$	4.01328	−	2.31707i	0.262919	−	0.151796i	−0.362747	−	0.931888i	$-0.618161\pi$
$233$	4.01328	−	2.31707i	0.262919	−	0.151796i	0.625665	+	0.780092i	$0.284828\pi$
$234$		0			0
$235$	2.45205	+	1.41569i	0.159954	+	0.0923494i
$236$		0			0
$237$	20.3522	−	0.704868i	1.32202	−	0.0457861i
$238$		0			0
$239$	−0.764983	−	4.33844i	−0.0494826	−	0.280630i	0.950019	−	0.312192i	$-0.101063\pi$
$239$	−0.764983	−	4.33844i	−0.0494826	−	0.280630i	−0.999502	+	0.0315616i	$0.989952\pi$
$240$		0			0
$241$	16.8708	+	14.1563i	1.08675	+	0.911888i	0.996463	−	0.0840284i	$-0.0267786\pi$
$241$	16.8708	+	14.1563i	1.08675	+	0.911888i	0.0902822	+	0.995916i	$0.471223\pi$
$242$		0			0
$243$	−7.77485	−	13.5112i	−0.498757	−	0.866742i
$244$		0			0
$245$	0.789445	−	0.940824i	0.0504358	−	0.0601071i
$246$		0			0
$247$	−5.80272	+	1.02318i	−0.369218	+	0.0651031i
$248$		0			0
$249$	0.307735	+	8.88546i	0.0195019	+	0.563093i
$250$		0			0
$251$	−8.70574	+	15.0788i	−0.549502	+	0.951765i	0.448807	+	0.893629i	$0.351849\pi$
$251$	−8.70574	+	15.0788i	−0.549502	+	0.951765i	−0.998309	+	0.0581360i	$0.981484\pi$
$252$		0			0
$253$	−6.51157	−	11.2784i	−0.409379	−	0.709065i
$254$		0			0
$255$	0.986395	−	1.26178i	0.0617704	−	0.0790158i
$256$		0			0
$257$	6.95312	+	8.28640i	0.433724	+	0.516892i	0.937993	−	0.346655i	$-0.112683\pi$
$257$	6.95312	+	8.28640i	0.433724	+	0.516892i	−0.504269	+	0.863547i	$0.668238\pi$
$258$		0			0
$259$	−4.71411	−	12.9519i	−0.292921	−	0.804793i
$260$		0			0
$261$	−16.3622	−	16.9630i	−1.01279	−	1.04998i
$262$		0			0
$263$	−4.28066	+	24.2768i	−0.263957	+	1.49697i	0.508032	+	0.861338i	$0.330373\pi$
$263$	−4.28066	+	24.2768i	−0.263957	+	1.49697i	−0.771989	+	0.635636i	$0.780738\pi$
$264$		0			0
$265$	1.84820	+	0.672689i	0.113534	+	0.0413229i
$266$		0			0
$267$	−6.03516	−	28.4333i	−0.369346	−	1.74009i
$268$		0			0
$269$			7.81109i			0.476251i	0.971234	+	0.238125i	$0.0765329\pi$
$269$			7.81109i			0.476251i	−0.971234	+	0.238125i	$0.923467\pi$
$270$		0			0
$271$		−	7.90855i		−	0.480410i	−0.970722	−	0.240205i	$-0.922785\pi$
$271$		−	7.90855i		−	0.480410i	0.970722	−	0.240205i	$-0.0772147\pi$
$272$		0			0
$273$	−5.79385	−	1.88438i	−0.350660	−	0.114048i
$274$		0			0
$275$	8.15774	+	2.96917i	0.491930	+	0.179048i
$276$		0			0
$277$	−2.45699	+	13.9343i	−0.147626	+	0.837229i	0.817595	+	0.575794i	$0.195307\pi$
$277$	−2.45699	+	13.9343i	−0.147626	+	0.837229i	−0.965221	+	0.261435i	$0.915804\pi$
$278$		0			0
$279$	1.02962	+	14.8466i	0.0616415	+	0.888844i
$280$		0			0
$281$	−2.27518	−	6.25100i	−0.135726	−	0.372903i	0.853146	−	0.521672i	$-0.174691\pi$
$281$	−2.27518	−	6.25100i	−0.135726	−	0.372903i	−0.988872	+	0.148768i	$0.952469\pi$
$282$		0			0
$283$	−15.9306	−	18.9853i	−0.946973	−	1.12856i	−0.991572	−	0.129553i	$-0.958646\pi$
$283$	−15.9306	−	18.9853i	−0.946973	−	1.12856i	0.0445995	−	0.999005i	$-0.485799\pi$
$284$		0			0
$285$	−2.62954	−	0.370327i	−0.155760	−	0.0219363i
$286$		0			0
$287$	1.35281	+	2.34314i	0.0798539	+	0.138311i
$288$		0			0
$289$	−6.33735	+	10.9766i	−0.372785	+	0.645683i
$290$		0			0
$291$	18.4706	+	9.82778i	1.08276	+	0.576115i
$292$		0			0
$293$	9.99675	−	1.76270i	0.584016	−	0.102978i	0.126169	−	0.992009i	$-0.459732\pi$
$293$	9.99675	−	1.76270i	0.584016	−	0.102978i	0.457847	+	0.889031i	$0.348621\pi$
$294$		0			0
$295$	0.478078	−	0.569752i	0.0278348	−	0.0331722i
$296$		0			0
$297$	−5.25932	+	7.78281i	−0.305177	+	0.451604i
$298$		0			0
$299$	9.43005	+	7.91275i	0.545354	+	0.457606i
$300$		0			0
$301$	0.995444	+	5.64545i	0.0573765	+	0.325398i
$302$		0			0
$303$	−0.645426	−	1.03356i	−0.0370787	−	0.0593763i
$304$		0			0
$305$	1.12322	+	0.648491i	0.0643153	+	0.0371325i
$306$		0			0
$307$	−0.726000	+	0.419157i	−0.0414350	+	0.0239225i	−0.520574	−	0.853816i	$-0.674282\pi$
$307$	−0.726000	+	0.419157i	−0.0414350	+	0.0239225i	0.479139	+	0.877739i	$0.340949\pi$
$308$		0			0
$309$	−13.4281	+	5.42083i	−0.763899	+	0.308380i
$310$		0			0
$311$	−17.2626	+	14.4851i	−0.978873	+	0.821372i	−0.983919	−	0.178615i	$-0.942838\pi$
$311$	−17.2626	+	14.4851i	−0.978873	+	0.821372i	0.00504590	+	0.999987i	$0.498394\pi$
$312$		0			0
$313$	12.1717	−	4.43014i	0.687985	−	0.250406i	0.0257128	−	0.999669i	$-0.491814\pi$
$313$	12.1717	−	4.43014i	0.687985	−	0.250406i	0.662272	+	0.749263i	$0.269592\pi$
$314$		0			0
$315$	−2.22046	−	1.61520i	−0.125109	−	0.0910064i
$316$		0			0
$317$	−11.9257	−	2.10282i	−0.669812	−	0.118106i	−0.171607	−	0.985165i	$-0.554896\pi$
$317$	−11.9257	−	2.10282i	−0.669812	−	0.118106i	−0.498205	+	0.867059i	$0.666007\pi$
$318$		0			0
$319$	−4.85726	+	13.3452i	−0.271954	+	0.747188i
$320$		0			0
$321$	−9.85827	−	10.9550i	−0.550235	−	0.611451i
$322$		0			0
$323$	−7.17152			−0.399034
$324$		0			0
$325$	−8.20594			−0.455183
$326$		0			0
$327$	−7.37223	−	8.19242i	−0.407685	−	0.453042i
$328$		0			0
$329$	4.48367	−	12.3188i	0.247192	−	0.679156i
$330$		0			0
$331$	−32.9907	−	5.81715i	−1.81333	−	0.319739i	−0.838877	−	0.544321i	$-0.816787\pi$
$331$	−32.9907	−	5.81715i	−1.81333	−	0.319739i	−0.974455	+	0.224582i	$0.927898\pi$
$332$		0			0
$333$	18.3547	−	8.15941i	1.00583	−	0.447133i
$334$		0			0
$335$	−3.95890	+	1.44092i	−0.216298	+	0.0787259i
$336$		0			0
$337$	3.87860	−	3.25454i	0.211281	−	0.177286i	−0.531006	−	0.847368i	$-0.678186\pi$
$337$	3.87860	−	3.25454i	0.211281	−	0.177286i	0.742287	+	0.670082i	$0.233741\pi$
$338$		0			0
$339$	32.1769	−	12.9896i	1.74761	−	0.705496i
$340$		0			0
$341$	7.76626	−	4.48385i	0.420566	−	0.242814i
$342$		0			0
$343$	−17.4039	−	10.0482i	−0.939725	−	0.542550i
$344$		0			0
$345$	2.93856	+	4.70568i	0.158207	+	0.253345i
$346$		0			0
$347$	−5.38369	−	30.5324i	−0.289011	−	1.63906i	−0.690594	−	0.723242i	$-0.742651\pi$
$347$	−5.38369	−	30.5324i	−0.289011	−	1.63906i	0.401583	−	0.915823i	$-0.368460\pi$
$348$		0			0
$349$	−9.97730	−	8.37195i	−0.534073	−	0.448140i	0.335432	−	0.942064i	$-0.391118\pi$
$349$	−9.97730	−	8.37195i	−0.534073	−	0.448140i	−0.869505	+	0.493924i	$0.835562\pi$
$350$		0			0
$351$	2.15541	−	8.61330i	0.115047	−	0.459744i
$352$		0			0
$353$	7.93813	−	9.46029i	0.422504	−	0.503521i	−0.512240	−	0.858842i	$-0.671184\pi$
$353$	7.93813	−	9.46029i	0.422504	−	0.503521i	0.934744	+	0.355322i	$0.115629\pi$
$354$		0			0
$355$	3.84670	−	0.678277i	0.204162	−	0.0359992i
$356$		0			0
$357$	−6.54638	−	3.48318i	−0.346471	−	0.184350i
$358$		0			0
$359$	−4.14726	+	7.18327i	−0.218884	+	0.379119i	−0.954467	−	0.298316i	$-0.903575\pi$
$359$	−4.14726	+	7.18327i	−0.218884	+	0.379119i	0.735583	+	0.677435i	$0.236908\pi$
$360$		0			0
$361$	−3.55466	−	6.15686i	−0.187088	−	0.324045i
$362$		0			0
$363$	−13.2616	−	1.86767i	−0.696052	−	0.0980273i
$364$		0			0
$365$	4.33170	+	5.16232i	0.226731	+	0.270208i
$366$		0			0
$367$	1.95537	+	5.37235i	0.102070	+	0.280434i	0.980207	−	0.197974i	$-0.0634362\pi$
$367$	1.95537	+	5.37235i	0.102070	+	0.280434i	−0.878138	+	0.478408i	$0.841214\pi$
$368$		0			0
$369$	−3.27014	+	2.20301i	−0.170237	+	0.114684i
$370$		0			0
$371$	1.58131	−	8.96804i	0.0820974	−	0.465597i
$372$		0			0
$373$	−5.03339	−	1.83200i	−0.260619	−	0.0948575i	0.208406	−	0.978042i	$-0.433172\pi$
$373$	−5.03339	−	1.83200i	−0.260619	−	0.0948575i	−0.469025	+	0.883185i	$0.655395\pi$
$374$		0			0
$375$	−7.17854	−	2.33473i	−0.370698	−	0.120565i
$376$		0			0
$377$		−	13.4241i		−	0.691374i
$378$		0			0
$379$			1.49353i			0.0767173i	0.999264	+	0.0383586i	$0.0122129\pi$
$379$			1.49353i			0.0767173i	−0.999264	+	0.0383586i	$0.987787\pi$
$380$		0			0
$381$	−4.64416	−	21.8799i	−0.237927	−	1.12094i
$382$		0			0
$383$	29.5136	+	10.7421i	1.50808	+	0.548895i	0.958137	−	0.286309i	$-0.0924285\pi$
$383$	29.5136	+	10.7421i	1.50808	+	0.548895i	0.549940	+	0.835204i	$0.314651\pi$
$384$		0			0
$385$	−0.287308	+	1.62940i	−0.0146426	+	0.0830421i
$386$		0			0
$387$	−8.10719	+	2.01641i	−0.412111	+	0.102500i
$388$		0			0
$389$	8.55268	+	23.4983i	0.433638	+	1.19141i	0.943563	+	0.331193i	$0.107451\pi$
$389$	8.55268	+	23.4983i	0.433638	+	1.19141i	−0.509925	+	0.860219i	$0.670327\pi$
$390$		0			0
$391$	9.63072	+	11.4774i	0.487046	+	0.580439i
$392$		0			0
$393$	21.7133	−	27.7754i	1.09529	−	1.40108i
$394$		0			0
$395$	2.61373	+	4.52712i	0.131511	+	0.227784i
$396$		0			0
$397$	9.51975	−	16.4887i	0.477783	−	0.827544i	−0.521893	−	0.853011i	$-0.674774\pi$
$397$	9.51975	−	16.4887i	0.477783	−	0.827544i	0.999676	+	0.0254673i	$0.00810736\pi$
$398$		0			0
$399$	0.425563	+	12.2876i	0.0213048	+	0.615150i
$400$		0			0
$401$	−11.7900	+	2.07890i	−0.588765	+	0.103815i	−0.460091	−	0.887872i	$-0.652183\pi$
$401$	−11.7900	+	2.07890i	−0.588765	+	0.103815i	−0.128674	+	0.991687i	$0.541072\pi$
$402$		0			0
$403$	−5.44870	+	6.49351i	−0.271419	+	0.323465i
$404$		0			0
$405$	2.12437	−	3.39103i	0.105561	−	0.168502i
$406$		0			0
$407$	−9.27195	−	7.78009i	−0.459593	−	0.385645i
$408$		0			0
$409$	−2.47539	−	14.0386i	−0.122400	−	0.694166i	−0.982818	−	0.184577i	$-0.940909\pi$
$409$	−2.47539	−	14.0386i	−0.122400	−	0.694166i	0.860418	−	0.509589i	$-0.170203\pi$
$410$		0			0
$411$	−27.1631	+	0.940752i	−1.33986	+	0.0464039i
$412$		0			0
$413$	−2.98226	−	1.72181i	−0.146748	−	0.0847247i
$414$		0			0
$415$	−1.97647	+	1.14112i	−0.0970213	+	0.0560152i
$416$		0			0
$417$	−1.35542	−	1.05959i	−0.0663751	−	0.0518886i
$418$		0			0
$419$	−23.1313	+	19.4094i	−1.13004	+	0.948213i	−0.999068	−	0.0431738i	$-0.986253\pi$
$419$	−23.1313	+	19.4094i	−1.13004	+	0.948213i	−0.130968	+	0.991387i	$0.541809\pi$
$420$		0			0
$421$	−6.98780	+	2.54335i	−0.340564	+	0.123955i	−0.506640	−	0.862158i	$-0.669113\pi$
$421$	−6.98780	+	2.54335i	−0.340564	+	0.123955i	0.166076	+	0.986113i	$0.446890\pi$
$422$		0			0
$423$	18.3615	+	5.27649i	0.892768	+	0.256552i
$424$		0			0
$425$	−9.83582	−	1.73432i	−0.477107	−	0.0841269i
$426$		0			0
$427$	2.05385	−	5.64291i	0.0993929	−	0.273080i
$428$		0			0
$429$	−5.23361	+	1.11087i	−0.252681	+	0.0536332i
$430$		0			0
$431$	17.9406			0.864166			0.432083	−	0.901834i	$-0.357779\pi$
$431$	17.9406			0.864166			0.432083	+	0.901834i	$0.357779\pi$
$432$		0			0
$433$	0.557812			0.0268067			0.0134034	−	0.999910i	$-0.495733\pi$
$433$	0.557812			0.0268067			0.0134034	+	0.999910i	$0.495733\pi$
$434$		0			0
$435$	1.87117	−	5.75325i	0.0897158	−	0.275847i
$436$		0			0
$437$	8.49646	−	23.3438i	0.406441	−	1.11669i
$438$		0			0
$439$	10.2642	+	1.80986i	0.489885	+	0.0863800i	0.413134	−	0.910670i	$-0.364434\pi$
$439$	10.2642	+	1.80986i	0.489885	+	0.0863800i	0.0767514	+	0.997050i	$0.475545\pi$
$440$		0			0
$441$	3.63704	−	7.44619i	0.173192	−	0.354580i
$442$		0			0
$443$	−1.69720	+	0.617731i	−0.0806365	+	0.0293493i	−0.382023	−	0.924153i	$-0.624773\pi$
$443$	−1.69720	+	0.617731i	−0.0806365	+	0.0293493i	0.301387	+	0.953502i	$0.402550\pi$
$444$		0			0
$445$	5.71571	−	4.79605i	0.270951	−	0.227355i
$446$		0			0
$447$	−5.26208	+	37.3639i	−0.248888	+	1.76725i
$448$		0			0
$449$	−1.84433	+	1.06482i	−0.0870392	+	0.0502521i	−0.542888	−	0.839805i	$-0.682669\pi$
$449$	−1.84433	+	1.06482i	−0.0870392	+	0.0502521i	0.455849	+	0.890057i	$0.349336\pi$
$450$		0			0
$451$	2.05763	+	1.18797i	0.0968898	+	0.0559394i
$452$		0			0
$453$	9.01464	−	16.9423i	0.423545	−	0.796021i
$454$		0			0
$455$	−0.271576	−	1.54019i	−0.0127317	−	0.0722050i
$456$		0			0
$457$	−6.28416	−	5.27304i	−0.293961	−	0.246662i	0.483865	−	0.875143i	$-0.339233\pi$
$457$	−6.28416	−	5.27304i	−0.293961	−	0.246662i	−0.777825	+	0.628481i	$0.783677\pi$
$458$		0			0
$459$	4.40394	−	9.86855i	0.205559	−	0.460625i
$460$		0			0
$461$	15.2984	−	18.2319i	0.712517	−	0.849145i	−0.281364	−	0.959601i	$-0.590787\pi$
$461$	15.2984	−	18.2319i	0.712517	−	0.849145i	0.993881	+	0.110456i	$0.0352311\pi$
$462$		0			0
$463$	−12.2115	+	2.15322i	−0.567518	+	0.100069i	−0.450043	−	0.893007i	$-0.648591\pi$
$463$	−12.2115	+	2.15322i	−0.567518	+	0.100069i	−0.117476	+	0.993076i	$0.537480\pi$
$464$		0			0
$465$	−3.24032	+	2.02348i	−0.150266	+	0.0938368i
$466$		0			0
$467$	3.88410	−	6.72745i	0.179735	−	0.311309i	−0.762055	−	0.647512i	$-0.775809\pi$
$467$	3.88410	−	6.72745i	0.179735	−	0.311309i	0.941790	+	0.336203i	$0.109143\pi$
$468$		0			0
$469$	9.75308	+	16.8928i	0.450355	+	0.780038i
$470$		0			0
$471$	−8.72065	−	21.6022i	−0.401827	−	0.995378i
$472$		0			0
$473$	3.23581	+	3.85629i	0.148783	+	0.177312i
$474$		0			0
$475$	5.66378	+	15.5611i	0.259872	+	0.713992i
$476$		0			0
$477$	13.1975	+	1.39477i	0.604271	+	0.0638621i
$478$		0			0
$479$	−1.35373	+	7.67736i	−0.0618533	+	0.350788i	0.938136	+	0.346266i	$0.112550\pi$
$479$	−1.35373	+	7.67736i	−0.0618533	+	0.350788i	−0.999990	+	0.00452178i	$0.998561\pi$
$480$		0			0
$481$	10.7510	+	3.91303i	0.490201	+	0.178419i
$482$		0			0
$483$	19.0938	−	17.1823i	0.868800	−	0.781820i
$484$		0			0
$485$			5.37071i			0.243871i
$486$		0			0
$487$			21.1590i			0.958808i	0.877594	+	0.479404i	$0.159147\pi$
$487$			21.1590i			0.958808i	−0.877594	+	0.479404i	$0.840853\pi$
$488$		0			0
$489$	1.59606	−	1.43627i	0.0721764	−	0.0649504i
$490$		0			0
$491$	6.05980	+	2.20559i	0.273475	+	0.0995367i	0.475117	−	0.879922i	$-0.342406\pi$
$491$	6.05980	+	2.20559i	0.273475	+	0.0995367i	−0.201642	+	0.979459i	$0.564628\pi$
$492$		0			0
$493$	2.83717	−	16.0904i	0.127780	−	0.724674i
$494$		0			0
$495$	−2.39785	−	0.253416i	−0.107776	−	0.0113902i
$496$		0			0
$497$	−6.18546	−	16.9944i	−0.277456	−	0.762304i
$498$		0			0
$499$	−15.2390	−	18.1611i	−0.682190	−	0.813002i	0.308198	−	0.951322i	$-0.400274\pi$
$499$	−15.2390	−	18.1611i	−0.682190	−	0.813002i	−0.990388	+	0.138320i	$0.955830\pi$
$500$		0			0
$501$	12.2776	+	30.4132i	0.548521	+	1.35876i
$502$		0			0
$503$	−18.4480	−	31.9529i	−0.822556	−	1.42471i	−0.903773	−	0.428012i	$-0.859214\pi$
$503$	−18.4480	−	31.9529i	−0.822556	−	1.42471i	0.0812173	−	0.996696i	$-0.474119\pi$
$504$		0			0
$505$	0.156396	−	0.270886i	0.00695954	−	0.0120543i
$506$		0			0
$507$	−14.8091	+	9.24783i	−0.657694	+	0.410710i
$508$		0			0
$509$	−34.4663	+	6.07734i	−1.52769	+	0.269373i	−0.873451	−	0.486912i	$-0.838123\pi$
$509$	−34.4663	+	6.07734i	−1.52769	+	0.269373i	−0.654242	+	0.756285i	$0.727012\pi$
$510$		0			0
$511$	20.0559	−	23.9017i	0.887220	−	1.05735i
$512$		0			0
$513$	−17.8213	+	1.85758i	−0.786828	+	0.0820143i
$514$		0			0
$515$	−2.84756	−	2.38939i	−0.125479	−	0.105289i
$516$		0			0
$517$	−1.99904	−	11.3371i	−0.0879175	−	0.498605i
$518$		0			0
$519$	−17.9853	+	33.8020i	−0.789466	+	1.48374i
$520$		0			0
$521$	12.5914	+	7.26968i	0.551641	+	0.318490i	0.749784	−	0.661683i	$-0.230157\pi$
$521$	12.5914	+	7.26968i	0.551641	+	0.318490i	−0.198142	+	0.980173i	$0.563491\pi$
$522$		0			0
$523$	19.8454	−	11.4578i	0.867780	−	0.501013i	0.00117013	−	0.999999i	$-0.499628\pi$
$523$	19.8454	−	11.4578i	0.867780	−	0.501013i	0.866610	+	0.498986i	$0.166294\pi$
$524$		0			0
$525$	−2.38790	+	16.9555i	−0.104217	+	0.740000i
$526$		0			0
$527$	−7.90333	+	6.63168i	−0.344275	+	0.288881i
$528$		0			0
$529$	−27.1570	+	9.88433i	−1.18074	+	0.429753i
$530$		0			0
$531$	2.20255	−	4.50932i	0.0955823	−	0.195688i
$532$		0			0
$533$	−2.21173	−	0.389987i	−0.0958005	−	0.0168922i
$534$		0			0
$535$	1.29390	−	3.55496i	0.0559401	−	0.153694i
$536$		0			0
$537$	−10.9132	+	33.5545i	−0.470938	+	1.44798i
$538$		0			0
$539$	−4.99352			−0.215086
$540$		0			0
$541$	−3.02688			−0.130136			−0.0650678	−	0.997881i	$-0.520726\pi$
$541$	−3.02688			−0.130136			−0.0650678	+	0.997881i	$0.520726\pi$
$542$		0			0
$543$	5.84961	−	1.24162i	0.251031	−	0.0532829i
$544$		0			0
$545$	0.967605	−	2.65847i	0.0414476	−	0.113876i
$546$		0			0
$547$	26.1687	+	4.61425i	1.11889	+	0.197291i	0.702355	−	0.711827i	$-0.252132\pi$
$547$	26.1687	+	4.61425i	1.11889	+	0.197291i	0.416539	+	0.909118i	$0.363243\pi$
$548$		0			0
$549$	8.41094	+	2.41702i	0.358970	+	0.103156i
$550$		0			0
$551$	−25.4563	+	9.26534i	−1.08448	+	0.394717i
$552$		0			0
$553$	18.5408	−	15.5576i	0.788436	−	0.661576i
$554$		0			0
$555$	4.06219	+	3.17561i	0.172430	+	0.134797i
$556$		0			0
$557$	−17.1848	+	9.92166i	−0.728144	+	0.420394i	−0.817743	−	0.575584i	$-0.804775\pi$
$557$	−17.1848	+	9.92166i	−0.728144	+	0.420394i	0.0895989	+	0.995978i	$0.471441\pi$
$558$		0			0
$559$	−4.12088	−	2.37919i	−0.174295	−	0.100629i
$560$		0			0
$561$	−6.50790	+	0.225392i	−0.274764	+	0.00951604i
$562$		0			0
$563$	−5.64850	−	32.0343i	−0.238056	−	1.35008i	−0.836081	−	0.548606i	$-0.815159\pi$
$563$	−5.64850	−	32.0343i	−0.238056	−	1.35008i	0.598025	−	0.801477i	$-0.295952\pi$
$564$		0			0
$565$	6.82341	+	5.72552i	0.287063	+	0.240875i
$566$		0			0
$567$	−17.1700	−	6.96007i	−0.721073	−	0.292295i
$568$		0			0
$569$	−18.3999	+	21.9281i	−0.771363	+	0.919275i	−0.998509	−	0.0545857i	$-0.982616\pi$
$569$	−18.3999	+	21.9281i	−0.771363	+	0.919275i	0.227146	+	0.973861i	$0.427061\pi$
$570$		0			0
$571$	12.8329	−	2.26279i	0.537042	−	0.0946949i	0.101452	−	0.994840i	$-0.467651\pi$
$571$	12.8329	−	2.26279i	0.537042	−	0.0946949i	0.435589	+	0.900145i	$0.356540\pi$
$572$		0			0
$573$	0.465715	+	13.4469i	0.0194555	+	0.561754i
$574$		0			0
$575$	17.2983	−	29.9616i	0.721390	−	1.24948i
$576$		0			0
$577$	10.7869	+	18.6834i	0.449063	+	0.777799i	0.998325	−	0.0578505i	$-0.0184247\pi$
$577$	10.7869	+	18.6834i	0.449063	+	0.777799i	−0.549263	+	0.835650i	$0.685091\pi$
$578$		0			0
$579$	−15.8253	+	20.2434i	−0.657675	+	0.841288i
$580$		0			0
$581$	6.79221	+	8.09464i	0.281788	+	0.335822i
$582$		0			0
$583$	−2.73506	−	7.51451i	−0.113274	−	0.311219i
$584$		0			0
$585$	2.21180	−	0.550115i	0.0914465	−	0.0227444i
$586$		0			0
$587$	4.10449	−	23.2777i	0.169410	−	0.960773i	−0.774990	−	0.631974i	$-0.782245\pi$
$587$	4.10449	−	23.2777i	0.169410	−	0.960773i	0.944400	−	0.328799i	$-0.106644\pi$
$588$		0			0
$589$	16.0745	+	5.85064i	0.662338	+	0.241071i
$590$		0			0
$591$	−1.19264	−	5.61886i	−0.0490587	−	0.231129i
$592$		0			0
$593$			12.4183i			0.509957i	0.966947	+	0.254979i	$0.0820684\pi$
$593$			12.4183i			0.509957i	−0.966947	+	0.254979i	$0.917932\pi$
$594$		0			0
$595$		−	1.90350i		−	0.0780359i
$596$		0			0
$597$	−24.7384	−	8.04583i	−1.01247	−	0.329294i
$598$		0			0
$599$	37.2167	+	13.5458i	1.52063	+	0.553465i	0.961306	−	0.275482i	$-0.0888373\pi$
$599$	37.2167	+	13.5458i	1.52063	+	0.553465i	0.559327	+	0.828947i	$0.311060\pi$
$600$		0			0
$601$	7.53152	−	42.7134i	0.307217	−	1.74231i	−0.305664	−	0.952139i	$-0.598879\pi$
$601$	7.53152	−	42.7134i	0.307217	−	1.74231i	0.612881	−	0.790175i	$-0.290010\pi$
$602$		0			0
$603$	−23.5761	+	15.8826i	−0.960091	+	0.646789i
$604$		0			0
$605$	−1.17579	−	3.23047i	−0.0478028	−	0.131337i
$606$		0			0
$607$	27.4679	+	32.7350i	1.11489	+	1.32867i	0.938865	+	0.344286i	$0.111879\pi$
$607$	27.4679	+	32.7350i	1.11489	+	1.32867i	0.176023	+	0.984386i	$0.443677\pi$
$608$		0			0
$609$	−27.7374	−	3.90636i	−1.12398	−	0.158294i
$610$		0			0
$611$	5.44082	+	9.42378i	0.220112	+	0.381245i
$612$		0			0
$613$	−17.9539	+	31.0971i	−0.725152	+	1.25600i	0.233760	+	0.972294i	$0.424897\pi$
$613$	−17.9539	+	31.0971i	−0.725152	+	1.25600i	−0.958911	+	0.283705i	$0.908436\pi$
$614$		0			0
$615$	−0.893538	−	0.475431i	−0.0360309	−	0.0191712i
$616$		0			0
$617$	−42.3464	+	7.46681i	−1.70480	+	0.300602i	−0.939367	−	0.342913i	$-0.888587\pi$
$617$	−42.3464	+	7.46681i	−1.70480	+	0.300602i	−0.765434	+	0.643515i	$0.777475\pi$
$618$		0			0
$619$	−19.3912	+	23.1095i	−0.779398	+	0.928850i	−0.998906	−	0.0467604i	$-0.985110\pi$
$619$	−19.3912	+	23.1095i	−0.779398	+	0.928850i	0.219508	+	0.975611i	$0.429555\pi$
$620$		0			0
$621$	26.9053	+	26.0269i	1.07967	+	1.04442i
$622$		0			0
$623$	−26.4639	−	22.2058i	−1.06025	−	0.889658i
$624$		0			0
$625$	3.83309	+	21.7385i	0.153324	+	0.869541i
$626$		0			0
$627$	5.71883	+	9.15788i	0.228388	+	0.365730i
$628$		0			0
$629$	12.0593	+	6.96245i	0.480837	+	0.277611i
$630$		0			0
$631$	3.64386	−	2.10378i	0.145060	−	0.0837503i	−0.425714	−	0.904858i	$-0.639977\pi$
$631$	3.64386	−	2.10378i	0.145060	−	0.0837503i	0.570773	+	0.821108i	$0.306644\pi$
$632$		0			0
$633$	11.5045	−	4.64428i	0.457263	−	0.184593i
$634$		0			0
$635$	4.39834	−	3.69064i	0.174543	−	0.146459i
$636$		0			0
$637$	4.43544	−	1.61437i	0.175739	−	0.0639636i
$638$		0			0
$639$	24.0834	−	10.7061i	0.952726	−	0.423526i
$640$		0			0
$641$	25.5760	+	4.50975i	1.01019	+	0.178124i	0.654166	−	0.756351i	$-0.273020\pi$
$641$	25.5760	+	4.50975i	1.01019	+	0.178124i	0.356027	+	0.934476i	$0.384131\pi$
$642$		0			0
$643$	4.56003	−	12.5286i	0.179830	−	0.494079i	−0.816724	−	0.577029i	$-0.804212\pi$
$643$	4.56003	−	12.5286i	0.179830	−	0.494079i	0.996554	+	0.0829500i	$0.0264342\pi$
$644$		0			0
$645$	−1.43449	−	1.59408i	−0.0564828	−	0.0627668i
$646$		0			0
$647$	12.6602			0.497722			0.248861	−	0.968539i	$-0.419944\pi$
$647$	12.6602			0.497722			0.248861	+	0.968539i	$0.419944\pi$
$648$		0			0
$649$	−3.02401			−0.118703
$650$		0			0
$651$	11.8317	+	13.1480i	0.463719	+	0.515309i
$652$		0			0
$653$	−3.46261	+	9.51344i	−0.135502	+	0.372290i	−0.988822	−	0.149098i	$-0.952363\pi$
$653$	−3.46261	+	9.51344i	−0.135502	+	0.372290i	0.853320	+	0.521387i	$0.174585\pi$
$654$		0			0
$655$	8.91243	+	1.57150i	0.348238	+	0.0614037i
$656$		0			0
$657$	36.7712	+	26.7481i	1.43458	+	1.04354i
$658$		0			0
$659$	15.3038	−	5.57012i	0.596151	−	0.216981i	−0.0262816	−	0.999655i	$-0.508367\pi$
$659$	15.3038	−	5.57012i	0.596151	−	0.216981i	0.622433	+	0.782673i	$0.286144\pi$
$660$		0			0
$661$	17.2086	−	14.4397i	0.669338	−	0.561641i	−0.243532	−	0.969893i	$-0.578306\pi$
$661$	17.2086	−	14.4397i	0.669338	−	0.561641i	0.912869	+	0.408252i	$0.133861\pi$
$662$		0			0
$663$	5.70771	−	2.30416i	0.221669	−	0.0894862i
$664$		0			0
$665$	−2.73324	+	1.57804i	−0.105991	+	0.0611937i
$666$		0			0
$667$	49.0140	+	28.2983i	1.89783	+	1.09571i
$668$		0			0
$669$	6.01603	+	9.63380i	0.232593	+	0.372464i
$670$		0			0
$671$	−0.915707	−	5.19323i	−0.0353505	−	0.200482i
$672$		0			0
$673$	−24.5581	−	20.6067i	−0.946645	−	0.794330i	0.0320843	−	0.999485i	$-0.489785\pi$
$673$	−24.5581	−	20.6067i	−0.946645	−	0.794330i	−0.978729	+	0.205156i	$0.934230\pi$
$674$		0			0
$675$	−24.8913	−	1.76210i	−0.958066	−	0.0678233i
$676$		0			0
$677$	12.9188	−	15.3960i	0.496510	−	0.591718i	−0.458350	−	0.888772i	$-0.651560\pi$
$677$	12.9188	−	15.3960i	0.496510	−	0.591718i	0.954861	+	0.297053i	$0.0960040\pi$
$678$		0			0
$679$	24.4888	−	4.31803i	0.939792	−	0.165711i
$680$		0			0
$681$	35.3970	+	18.8339i	1.35641	+	0.721717i
$682$		0			0
$683$	1.52883	−	2.64801i	0.0584991	−	0.101323i	−0.835293	−	0.549805i	$-0.814702\pi$
$683$	1.52883	−	2.64801i	0.0584991	−	0.101323i	0.893792	+	0.448482i	$0.148035\pi$
$684$		0			0
$685$	−3.48842	−	6.04212i	−0.133286	−	0.230858i
$686$		0			0
$687$	−47.3317	−	6.66588i	−1.80582	−	0.254319i
$688$		0			0
$689$	4.85877	+	5.79046i	0.185104	+	0.220599i
$690$		0			0
$691$	9.23503	+	25.3730i	0.351317	+	0.965236i	0.981948	+	0.189153i	$0.0605742\pi$
$691$	9.23503	+	25.3730i	0.351317	+	0.965236i	−0.630630	+	0.776083i	$0.717204\pi$
$692$		0			0
$693$	0.772367	+	11.1372i	0.0293398	+	0.423067i
$694$		0			0
$695$	0.0766882	−	0.434920i	0.00290895	−	0.0164975i
$696$		0			0
$697$	−2.56860	−	0.934895i	−0.0972927	−	0.0354117i
$698$		0			0
$699$	7.63300	+	2.48253i	0.288707	+	0.0938981i
$700$		0			0
$701$			23.3660i			0.882522i	0.897379	+	0.441261i	$0.145469\pi$
$701$			23.3660i			0.882522i	−0.897379	+	0.441261i	$0.854531\pi$
$702$		0			0
$703$		−	23.0881i		−	0.870783i
$704$		0			0
$705$	1.01824	+	4.79722i	0.0383492	+	0.180674i
$706$		0			0
$707$	−1.36090	−	0.495326i	−0.0511818	−	0.0186287i
$708$		0			0
$709$	−3.79023	+	21.4955i	−0.142345	+	0.807280i	0.827115	+	0.562032i	$0.189980\pi$
$709$	−3.79023	+	21.4955i	−0.142345	+	0.807280i	−0.969460	+	0.245248i	$0.921131\pi$
$710$		0			0
$711$	24.4875	+	25.3867i	0.918355	+	0.952077i
$712$		0			0
$713$	−12.2231	−	33.5828i	−0.457760	−	1.25769i
$714$		0			0
$715$	−0.882791	−	1.05207i	−0.0330145	−	0.0393452i
$716$		0			0
$717$	4.69941	−	6.01142i	0.175503	−	0.224501i
$718$		0			0
$719$	−4.24194	−	7.34726i	−0.158198	−	0.274006i	0.776021	−	0.630707i	$-0.217235\pi$
$719$	−4.24194	−	7.34726i	−0.158198	−	0.274006i	−0.934219	+	0.356701i	$0.883902\pi$
$720$		0			0
$721$	−8.60543	+	14.9050i	−0.320483	+	0.555093i
$722$		0			0
$723$	1.32032	+	38.1226i	0.0491032	+	1.41780i
$724$		0			0
$725$	−37.1543	+	6.55131i	−1.37988	+	0.243309i
$726$		0			0
$727$	−9.20122	+	10.9656i	−0.341254	+	0.406691i	−0.909190	−	0.416382i	$-0.863298\pi$
$727$	−9.20122	+	10.9656i	−0.341254	+	0.406691i	0.567935	+	0.823073i	$0.307742\pi$
$728$		0			0
$729$	8.38765	−	25.6641i	0.310654	−	0.950523i
$730$		0			0
$731$	−4.43654	−	3.72270i	−0.164091	−	0.137689i
$732$		0			0
$733$	−4.79357	−	27.1857i	−0.177054	−	1.00413i	−0.935746	−	0.352675i	$-0.885272\pi$
$733$	−4.79357	−	27.1857i	−0.177054	−	1.00413i	0.758691	−	0.651450i	$-0.225839\pi$
$734$		0			0
$735$	2.12596	−	0.0736294i	0.0784172	−	0.00271586i
$736$		0			0
$737$	14.8344	+	8.56467i	0.546434	+	0.315484i
$738$		0			0
$739$	38.3598	−	22.1470i	1.41109	−	0.814692i	0.415598	−	0.909549i	$-0.363572\pi$
$739$	38.3598	−	22.1470i	1.41109	−	0.814692i	0.995491	+	0.0948563i	$0.0302392\pi$
$740$		0			0
$741$	−8.04036	−	6.28554i	−0.295370	−	0.230905i
$742$		0			0
$743$	−9.83752	+	8.25466i	−0.360903	+	0.302834i	−0.805151	−	0.593070i	$-0.797916\pi$
$743$	−9.83752	+	8.25466i	−0.360903	+	0.302834i	0.444247	+	0.895904i	$0.353471\pi$
$744$		0			0
$745$	−9.10170	+	3.31275i	−0.333460	+	0.121370i
$746$		0			0
$747$	−11.0835	+	10.6909i	−0.405523	+	0.391159i
$748$		0			0
$749$	−17.2498	−	3.04160i	−0.630293	−	0.111138i
$750$		0			0
$751$	−2.94509	+	8.09156i	−0.107468	+	0.295265i	−0.981757	−	0.190140i	$-0.939106\pi$
$751$	−2.94509	+	8.09156i	−0.107468	+	0.295265i	0.874289	+	0.485405i	$0.161328\pi$
$752$		0			0
$753$	−29.5004	+	6.26165i	−1.07505	+	0.228187i
$754$		0			0
$755$	4.92634			0.179288
$756$		0			0
$757$	41.0240			1.49104			0.745522	−	0.666481i	$-0.232200\pi$
$757$	41.0240			1.49104			0.745522	+	0.666481i	$0.232200\pi$
$758$		0			0
$759$	6.97657	−	21.4507i	0.253234	−	0.778612i
$760$		0			0
$761$	−13.0186	+	35.7684i	−0.471925	+	1.29660i	0.444278	+	0.895889i	$0.353460\pi$
$761$	−13.0186	+	35.7684i	−0.471925	+	1.29660i	−0.916203	+	0.400714i	$0.868762\pi$
$762$		0			0
$763$	−12.8998	−	2.27457i	−0.467002	−	0.0823451i
$764$		0			0
$765$	2.76738	−	0.191918i	0.100055	−	0.00693881i
$766$		0			0
$767$	2.68605	−	0.977642i	0.0969876	−	0.0353006i
$768$		0			0
$769$	3.98313	−	3.34224i	0.143635	−	0.120524i	−0.568139	−	0.822933i	$-0.692336\pi$
$769$	3.98313	−	3.34224i	0.143635	−	0.120524i	0.711774	+	0.702408i	$0.247892\pi$
$770$		0			0
$771$	−2.61285	+	18.5527i	−0.0940993	+	0.668160i
$772$		0			0
$773$	11.0302	−	6.36828i	0.396728	−	0.229051i	−0.288343	−	0.957527i	$-0.593104\pi$
$773$	11.0302	−	6.36828i	0.396728	−	0.229051i	0.685071	+	0.728476i	$0.259771\pi$
$774$		0			0
$775$	20.6315	+	11.9116i	0.741104	+	0.427877i
$776$		0			0
$777$	11.2138	−	21.0755i	0.402292	−	0.756079i
$778$		0			0
$779$	0.787003	+	4.46332i	0.0281973	+	0.159915i
$780$		0			0
$781$	−12.1659	−	10.2084i	−0.435329	−	0.365284i
$782$		0			0
$783$	2.88261	−	40.7195i	0.103016	−	1.45520i
$784$		0			0
$785$	3.84388	−	4.58096i	0.137194	−	0.163501i
$786$		0			0
$787$	−24.8893	+	4.38866i	−0.887209	+	0.156439i	−0.598638	−	0.801020i	$-0.704291\pi$
$787$	−24.8893	+	4.38866i	−0.887209	+	0.156439i	−0.288571	+	0.957458i	$0.593180\pi$
$788$		0			0
$789$	−36.2159	+	22.6158i	−1.28932	+	0.805143i
$790$		0			0
$791$	20.6206	−	35.7159i	0.733184	−	1.26991i
$792$		0			0
$793$	2.49230	+	4.31679i	0.0885042	+	0.153294i
$794$		0			0
$795$	1.27523	+	3.15892i	0.0452279	+	0.112035i
$796$		0			0
$797$	−14.9904	−	17.8649i	−0.530988	−	0.632807i	0.432154	−	0.901800i	$-0.357754\pi$
$797$	−14.9904	−	17.8649i	−0.530988	−	0.632807i	−0.963142	+	0.268993i	$0.913309\pi$
$798$		0			0
$799$	4.52978	+	12.4455i	0.160252	+	0.440289i
$800$		0			0
$801$	29.6155	−	40.7130i	1.04641	−	1.43852i
$802$		0			0
$803$	4.75787	−	26.9832i	0.167902	−	0.952218i
$804$		0			0
$805$	6.19603	+	2.25517i	0.218381	+	0.0794843i
$806$		0			0
$807$	−10.0568	+	9.04992i	−0.354015	+	0.318572i
$808$		0			0
$809$			49.8079i			1.75115i	0.483081	+	0.875576i	$0.339518\pi$
$809$			49.8079i			1.75115i	−0.483081	+	0.875576i	$0.660482\pi$
$810$		0			0
$811$			43.3099i			1.52082i	0.649445	+	0.760408i	$0.275001\pi$
$811$			43.3099i			1.52082i	−0.649445	+	0.760408i	$0.724999\pi$
$812$		0			0
$813$	10.1822	−	9.16284i	0.357107	−	0.321355i
$814$		0			0
$815$	0.517928	+	0.188510i	0.0181422	+	0.00660323i
$816$		0			0
$817$	−1.66746	+	9.45665i	−0.0583371	+	0.330846i
$818$		0			0
$819$	−4.28662	−	9.64280i	−0.149787	−	0.336947i
$820$		0			0
$821$	−14.6377	−	40.2168i	−0.510860	−	1.40358i	−0.880342	−	0.474339i	$-0.842687\pi$
$821$	−14.6377	−	40.2168i	−0.510860	−	1.40358i	0.369482	−	0.929238i	$-0.379535\pi$
$822$		0			0
$823$	−29.2869	−	34.9028i	−1.02088	−	1.21663i	−0.976029	−	0.217640i	$-0.930164\pi$
$823$	−29.2869	−	34.9028i	−1.02088	−	1.21663i	−0.0448480	−	0.998994i	$-0.514280\pi$
$824$		0			0
$825$	5.62874	+	13.9431i	0.195968	+	0.485438i
$826$		0			0
$827$	−5.17389	−	8.96144i	−0.179914	−	0.311620i	0.761937	−	0.647651i	$-0.224249\pi$
$827$	−5.17389	−	8.96144i	−0.179914	−	0.311620i	−0.941851	+	0.336031i	$0.890915\pi$
$828$		0			0
$829$	−3.62683	+	6.28186i	−0.125965	+	0.218178i	−0.922110	−	0.386928i	$-0.873536\pi$
$829$	−3.62683	+	6.28186i	−0.125965	+	0.218178i	0.796145	+	0.605106i	$0.206869\pi$
$830$		0			0
$831$	−20.7870	+	12.9809i	−0.721093	+	0.450301i
$832$		0			0
$833$	5.65762	−	0.997591i	0.196025	−	0.0345645i
$834$		0			0
$835$	−5.41169	+	6.44940i	−0.187279	+	0.223191i
$836$		0			0
$837$	−17.9221	+	18.5269i	−0.619477	+	0.640384i
$838$		0			0
$839$	−2.82885	−	2.37368i	−0.0976627	−	0.0819487i	0.592649	−	0.805461i	$-0.298082\pi$
$839$	−2.82885	−	2.37368i	−0.0976627	−	0.0819487i	−0.690312	+	0.723512i	$0.742527\pi$
$840$		0			0
$841$	−5.68145	−	32.2211i	−0.195912	−	1.11107i
$842$		0			0
$843$	5.41212	−	10.1717i	0.186403	−	0.350331i
$844$		0			0
$845$	−3.88133	−	2.24088i	−0.133522	−	0.0770888i
$846$		0			0
$847$	−13.7846	+	7.95853i	−0.473644	+	0.273458i
$848$		0			0
$849$	5.98639	−	42.5069i	0.205452	−	1.45883i
$850$		0			0
$851$	−36.9506	+	31.0052i	−1.26665	+	1.06284i
$852$		0			0
$853$	3.95082	−	1.43798i	0.135273	−	0.0492355i	−0.273496	−	0.961873i	$-0.588180\pi$
$853$	3.95082	−	1.43798i	0.135273	−	0.0492355i	0.408770	+	0.912638i	$0.365958\pi$
$854$		0			0
$855$	−2.56979	−	3.81458i	−0.0878848	−	0.130456i
$856$		0			0
$857$	25.2638	+	4.45468i	0.862994	+	0.152169i	0.587589	−	0.809159i	$-0.300077\pi$
$857$	25.2638	+	4.45468i	0.862994	+	0.152169i	0.275404	+	0.961328i	$0.411188\pi$
$858$		0			0
$859$	13.5141	−	37.1296i	0.461094	−	1.26684i	−0.463570	−	0.886060i	$-0.653432\pi$
$859$	13.5141	−	37.1296i	0.461094	−	1.26684i	0.924664	−	0.380785i	$-0.124346\pi$
$860$		0			0
$861$	−1.44942	+	4.45650i	−0.0493960	+	0.151877i
$862$		0			0
$863$	−11.3206			−0.385358			−0.192679	−	0.981262i	$-0.561718\pi$
$863$	−11.3206			−0.385358			−0.192679	+	0.981262i	$0.561718\pi$
$864$		0			0
$865$	−9.82865			−0.334184
$866$		0			0
$867$	−21.4748	+	4.55817i	−0.729323	+	0.154804i
$868$		0			0
$869$	7.26935	−	19.9724i	0.246596	−	0.677516i
$870$		0			0
$871$	−15.9454	−	2.81161i	−0.540290	−	0.0952678i
$872$		0			0
$873$	8.74676	+	35.1673i	0.296033	+	1.19023i
$874$		0			0
$875$	−8.43062	+	3.06849i	−0.285007	+	0.103734i
$876$		0			0
$877$	29.0374	−	24.3652i	0.980522	−	0.822756i	−0.00364595	−	0.999993i	$-0.501161\pi$
$877$	29.0374	−	24.3652i	0.980522	−	0.822756i	0.984168	+	0.177238i	$0.0567161\pi$
$878$		0			0
$879$	13.8517	+	10.8285i	0.467206	+	0.365237i
$880$		0			0
$881$	14.8709	−	8.58569i	0.501012	−	0.289259i	−0.228119	−	0.973633i	$-0.573258\pi$
$881$	14.8709	−	8.58569i	0.501012	−	0.289259i	0.729131	+	0.684374i	$0.239924\pi$
$882$		0			0
$883$	10.2770	+	5.93340i	0.345847	+	0.199675i	0.662855	−	0.748748i	$-0.269345\pi$
$883$	10.2770	+	5.93340i	0.345847	+	0.199675i	−0.317008	+	0.948423i	$0.602678\pi$
$884$		0			0
$885$	1.28745	−	0.0445891i	0.0432773	−	0.00149885i
$886$		0			0
$887$	−5.71307	−	32.4005i	−0.191826	−	1.08790i	−0.916866	−	0.399194i	$-0.869290\pi$
$887$	−5.71307	−	32.4005i	−0.191826	−	1.08790i	0.725040	−	0.688707i	$-0.241821\pi$
$888$		0			0
$889$	−20.3644	−	17.0878i	−0.683001	−	0.573106i
$890$		0			0
$891$	−16.1138	+	2.24579i	−0.539832	+	0.0752368i
$892$		0			0
$893$	14.1152	−	16.8219i	0.472348	−	0.562923i
$894$		0			0
$895$	−8.91983	+	1.57281i	−0.298157	+	0.0525732i
$896$		0			0
$897$	0.738001	+	21.3089i	0.0246411	+	0.711482i
$898$		0			0
$899$	−19.4861	+	33.7509i	−0.649898	+	1.12566i
$900$		0			0
$901$	4.60002	+	7.96747i	0.153249	+	0.265435i
$902$		0			0
$903$	−6.11517	+	7.82244i	−0.203500	+	0.260314i
$904$		0			0
$905$	0.986696	+	1.17590i	0.0327989	+	0.0390882i
$906$		0			0
$907$	3.01330	+	8.27899i	0.100055	+	0.274899i	0.979613	−	0.200892i	$-0.0643840\pi$
$907$	3.01330	+	8.27899i	0.100055	+	0.274899i	−0.879558	+	0.475791i	$0.842162\pi$
$908$		0			0
$909$	0.582912	−	2.02846i	0.0193340	−	0.0672798i
$910$		0			0
$911$	4.53802	−	25.7364i	0.150351	−	0.852685i	−0.812562	−	0.582875i	$-0.801928\pi$
$911$	4.53802	−	25.7364i	0.150351	−	0.852685i	0.962913	−	0.269811i	$-0.0869611\pi$
$912$		0			0
$913$	8.71963	+	3.17369i	0.288578	+	0.105034i
$914$		0			0
$915$	0.466430	+	2.19748i	0.0154197	+	0.0726465i
$916$		0			0
$917$		−	41.9014i		−	1.38371i
$918$		0			0
$919$		−	49.1881i		−	1.62257i	−0.584653	−	0.811283i	$-0.698769\pi$
$919$		−	49.1881i		−	1.62257i	0.584653	−	0.811283i	$-0.301231\pi$
$920$		0			0
$921$	−1.38081	−	0.449089i	−0.0454991	−	0.0147980i
$922$		0			0
$923$	14.1065	+	5.13434i	0.464321	+	0.168999i
$924$		0			0
$925$	5.58349	−	31.6655i	0.183584	−	1.04116i
$926$		0			0
$927$	−22.5371	−	11.0081i	−0.740216	−	0.361553i
$928$		0			0
$929$	−5.06551	−	13.9174i	−0.166194	−	0.456614i	0.828439	−	0.560079i	$-0.189229\pi$
$929$	−5.06551	−	13.9174i	−0.166194	−	0.456614i	−0.994633	+	0.103465i	$0.967007\pi$
$930$		0			0
$931$	−6.12272	−	7.29678i	−0.200664	−	0.239142i
$932$		0			0
$933$	−38.6499	−	5.44320i	−1.26534	−	0.178202i
$934$		0			0
$935$	−0.835779	−	1.44761i	−0.0273329	−	0.0473420i
$936$		0			0
$937$	2.38562	−	4.13202i	0.0779348	−	0.134987i	−0.824424	−	0.565973i	$-0.808501\pi$
$937$	2.38562	−	4.13202i	0.0779348	−	0.134987i	0.902359	+	0.430986i	$0.141834\pi$
$938$		0			0
$939$	19.8059	+	10.5383i	0.646341	+	0.343904i
$940$		0			0
$941$	−35.8707	+	6.32497i	−1.16935	+	0.206188i	−0.724408	−	0.689371i	$-0.757887\pi$
$941$	−35.8707	+	6.32497i	−1.16935	+	0.206188i	−0.444942	+	0.895559i	$0.646776\pi$
$942$		0			0
$943$	6.08630	−	7.25337i	0.198197	−	0.236202i
$944$		0			0
$945$	−0.493049	−	4.73021i	−0.0160389	−	0.153874i
$946$		0			0
$947$	9.68625	+	8.12773i	0.314761	+	0.264116i	0.786456	−	0.617646i	$-0.211913\pi$
$947$	9.68625	+	8.12773i	0.314761	+	0.264116i	−0.471696	+	0.881761i	$0.656358\pi$
$948$		0			0
$949$	4.49736	+	25.5058i	0.145990	+	0.827952i
$950$		0			0
$951$	−11.1097	−	17.7906i	−0.360256	−	0.576899i
$952$		0			0
$953$	−5.21139	−	3.00880i	−0.168814	−	0.0974645i	0.413213	−	0.910635i	$-0.364407\pi$
$953$	−5.21139	−	3.00880i	−0.168814	−	0.0974645i	−0.582026	+	0.813170i	$0.697740\pi$
$954$		0			0
$955$	−2.99112	+	1.72693i	−0.0967905	+	0.0558820i
$956$		0			0
$957$	−22.8095	+	9.20803i	−0.737327	+	0.297653i
$958$		0			0
$959$	−24.7455	+	20.7640i	−0.799074	+	0.670503i
$960$		0			0
$961$	−6.00544	+	2.18580i	−0.193724	+	0.0705097i
$962$		0			0
$963$	2.68280	−	25.3850i	0.0864520	−	0.818020i
$964$		0			0
$965$	−6.49562	−	1.14535i	−0.209101	−	0.0368702i
$966$		0			0
$967$	−4.01247	+	11.0242i	−0.129032	+	0.354513i	−0.987339	−	0.158623i	$-0.949294\pi$
$967$	−4.01247	+	11.0242i	−0.129032	+	0.354513i	0.858307	+	0.513137i	$0.171517\pi$
$968$		0			0
$969$	−8.30892	−	9.23331i	−0.266921	−	0.296617i
$970$		0			0
$971$	11.5643			0.371116			0.185558	−	0.982633i	$-0.440591\pi$
$971$	11.5643			0.371116			0.185558	+	0.982633i	$0.440591\pi$
$972$		0			0
$973$	−2.04476			−0.0655519
$974$		0			0
$975$	−9.50739	−	10.5651i	−0.304480	−	0.338355i
$976$		0			0
$977$	2.97224	−	8.16617i	0.0950905	−	0.261259i	−0.883023	−	0.469329i	$-0.844496\pi$
$977$	2.97224	−	8.16617i	0.0950905	−	0.261259i	0.978114	+	0.208070i	$0.0667181\pi$
$978$		0			0
$979$	−29.8758	−	5.26791i	−0.954835	−	0.168363i
$980$		0			0
$981$	2.00626	−	18.9835i	0.0640548	−	0.606095i
$982$		0			0
$983$	−49.4924	+	18.0138i	−1.57856	+	0.574550i	−0.974891	−	0.222683i	$-0.928518\pi$
$983$	−49.4924	+	18.0138i	−1.57856	+	0.574550i	−0.603672	+	0.797233i	$0.706296\pi$
$984$		0			0
$985$	1.12951	−	0.947775i	0.0359893	−	0.0301986i
$986$		0			0
$987$	21.0551	−	8.49981i	0.670193	−	0.270552i
$988$		0			0
$989$	17.3739	−	10.0308i	0.552457	−	0.318961i
$990$		0			0
$991$	−28.2548	−	16.3129i	−0.897543	−	0.518197i	−0.0211406	−	0.999777i	$-0.506730\pi$
$991$	−28.2548	−	16.3129i	−0.897543	−	0.518197i	−0.876402	+	0.481580i	$0.840063\pi$
$992$		0			0
$993$	−30.7334	−	49.2152i	−0.975295	−	1.56180i
$994$		0			0
$995$	−1.15957	−	6.57622i	−0.0367607	−	0.208480i
$996$		0			0
$997$	−25.8627	−	21.7014i	−0.819081	−	0.687291i	0.133676	−	0.991025i	$-0.457322\pi$
$997$	−25.8627	−	21.7014i	−0.819081	−	0.687291i	−0.952757	+	0.303735i	$0.901766\pi$
$998$		0			0
$999$	31.7709	+	14.1781i	1.00519	+	0.448575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.b.335.5	✓	36
4.3	odd	2		432.2.be.c.335.2	yes	36
27.5	odd	18		432.2.be.c.383.2	yes	36
108.59	even	18	inner	432.2.be.b.383.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.335.5	✓	36	1.1	even	1	trivial
432.2.be.b.383.5	yes	36	108.59	even	18	inner
432.2.be.c.335.2	yes	36	4.3	odd	2
432.2.be.c.383.2	yes	36	27.5	odd	18

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)

\(f(q)\)	\(=\)	\(q+(1.15860 + 1.28750i) q^{3} +(-0.152066 + 0.417798i) q^{5} +(2.02729 + 0.357466i) q^{7} +(-0.315297 + 2.98339i) q^{9} +O(q^{10})\)	\(q+(1.15860 + 1.28750i) q^{3} +(-0.152066 + 0.417798i) q^{5} +(2.02729 + 0.357466i) q^{7} +(-0.315297 + 2.98339i) q^{9} +(1.69871 - 0.618279i) q^{11} +(-1.30897 + 1.09836i) q^{13} +(-0.714097 + 0.288276i) q^{15} +(-1.80110 + 1.03987i) q^{17} +(2.98630 + 1.72414i) q^{19} +(1.88858 + 3.02429i) q^{21} +(-1.25099 - 7.09471i) q^{23} +(3.67879 + 3.08687i) q^{25} +(-4.20640 + 3.05060i) q^{27} +(-5.04980 + 6.01812i) q^{29} +(4.88540 - 0.861427i) q^{31} +(2.76415 + 1.47074i) q^{33} +(-0.457630 + 0.792639i) q^{35} +(-3.34776 - 5.79849i) q^{37} +(-2.93071 - 0.412742i) q^{39} +(0.844832 + 1.00683i) q^{41} +(0.952433 + 2.61679i) q^{43} +(-1.19851 - 0.585402i) q^{45} +(1.10583 - 6.27146i) q^{47} +(-2.59573 - 0.944769i) q^{49} +(-3.42558 - 1.11413i) q^{51} -4.42366i q^{53} +0.803736i q^{55} +(1.24010 + 5.84245i) q^{57} +(-1.57194 - 0.572141i) q^{59} +(0.506551 - 2.87280i) q^{61} +(-1.70566 + 5.93547i) q^{63} +(-0.259842 - 0.713910i) q^{65} +(6.09081 + 7.25875i) q^{67} +(7.68502 - 9.83056i) q^{69} +(-4.39265 - 7.60829i) q^{71} +(7.57844 - 13.1262i) q^{73} +(0.287904 + 8.31288i) q^{75} +(3.66478 - 0.646200i) q^{77} +(7.55750 - 9.00668i) q^{79} +(-8.80118 - 1.88131i) q^{81} +(3.93218 + 3.29949i) q^{83} +(-0.160568 - 0.910626i) q^{85} +(-13.5990 + 0.470981i) q^{87} +(-14.5334 - 8.39084i) q^{89} +(-3.04629 + 1.75878i) q^{91} +(6.76930 + 5.29188i) q^{93} +(-1.17446 + 0.985488i) q^{95} +(11.3511 - 4.13145i) q^{97} +(1.30897 + 5.26284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more