LMFDB - Embedded newform 420.2.bn.a.269.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [420,2,Mod(89,420)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("420.89"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(420, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bn (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.16
Character	$\chi$	$=$	420.269
Dual form			420.2.bn.a.89.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73102 - 0.0597684i) q^{3} +(-2.14829 + 0.620379i) q^{5} +(2.58416 + 0.567546i) q^{7} +(2.99286 - 0.206921i) q^{9} +(-0.793196 - 0.457952i) q^{11} +4.31153 q^{13} +(-3.68164 + 1.20229i) q^{15} +(0.465109 + 0.268531i) q^{17} +(-1.12887 + 0.651755i) q^{19} +(4.50715 + 0.827982i) q^{21} +(3.99480 + 6.91920i) q^{23} +(4.23026 - 2.66550i) q^{25} +(5.16832 - 0.537062i) q^{27} -3.46154i q^{29} +(-5.56113 - 3.21072i) q^{31} +(-1.40041 - 0.745316i) q^{33} +(-5.90361 + 0.383907i) q^{35} +(-4.36775 + 2.52172i) q^{37} +(7.46334 - 0.257693i) q^{39} -9.89809 q^{41} -8.22096i q^{43} +(-6.30114 + 2.30123i) q^{45} +(-3.75969 + 2.17066i) q^{47} +(6.35578 + 2.93326i) q^{49} +(0.821162 + 0.437033i) q^{51} +(0.984927 - 1.70594i) q^{53} +(1.98812 + 0.491730i) q^{55} +(-1.91514 + 1.19567i) q^{57} +(7.15363 - 12.3904i) q^{59} +(-8.38395 + 4.84048i) q^{61} +(7.85146 + 1.16387i) q^{63} +(-9.26240 + 2.67478i) q^{65} +(-10.4850 - 6.05349i) q^{67} +(7.32863 + 11.7385i) q^{69} -0.943900i q^{71} +(-5.11210 + 8.85442i) q^{73} +(7.16335 - 4.86687i) q^{75} +(-1.78984 - 1.63360i) q^{77} +(5.71817 + 9.90416i) q^{79} +(8.91437 - 1.23857i) q^{81} -9.35240i q^{83} +(-1.16578 - 0.288337i) q^{85} +(-0.206891 - 5.99199i) q^{87} +(-0.874507 - 1.51469i) q^{89} +(11.1417 + 2.44699i) q^{91} +(-9.81833 - 5.22544i) q^{93} +(2.02080 - 2.10048i) q^{95} -10.7844 q^{97} +(-2.46868 - 1.20646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{15} + 12 q^{19} - 8 q^{21} + 6 q^{25} - 12 q^{31} + 24 q^{39} + 33 q^{45} - 44 q^{49} - 10 q^{51} - 24 q^{61} + 21 q^{75} - 28 q^{79} - 20 q^{81} - 4 q^{85} + 16 q^{91} - 28 q^{99}+O(q^{100}) $ 32 * q + 2 * q^15 + 12 * q^19 - 8 * q^21 + 6 * q^25 - 12 * q^31 + 24 * q^39 + 33 * q^45 - 44 * q^49 - 10 * q^51 - 24 * q^61 + 21 * q^75 - 28 * q^79 - 20 * q^81 - 4 * q^85 + 16 * q^91 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.73102	−	0.0597684i	0.999404	−	0.0345073i
$3$	1.73102	−	0.0597684i	0.999404	−	0.0345073i
$4$		0			0
$5$	−2.14829	+	0.620379i	−0.960742	+	0.277442i
$5$	−2.14829	+	0.620379i	−0.960742	+	0.277442i
$6$		0			0
$7$	2.58416	+	0.567546i	0.976721	+	0.214512i
$7$	2.58416	+	0.567546i	0.976721	+	0.214512i
$8$		0			0
$9$	2.99286	−	0.206921i	0.997618	−	0.0689735i
$10$		0			0
$11$	−0.793196	−	0.457952i	−0.239158	−	0.138078i	0.375632	−	0.926769i	$-0.377426\pi$
$11$	−0.793196	−	0.457952i	−0.239158	−	0.138078i	−0.614790	+	0.788691i	$0.710759\pi$
$12$		0			0
$13$	4.31153			1.19580			0.597902	−	0.801569i	$-0.296001\pi$
$13$	4.31153			1.19580			0.597902	+	0.801569i	$0.296001\pi$
$14$		0			0
$15$	−3.68164	+	1.20229i	−0.950597	+	0.310429i
$16$		0			0
$17$	0.465109	+	0.268531i	0.112805	+	0.0651283i	0.555341	−	0.831623i	$-0.312588\pi$
$17$	0.465109	+	0.268531i	0.112805	+	0.0651283i	−0.442536	+	0.896751i	$0.645921\pi$
$18$		0			0
$19$	−1.12887	+	0.651755i	−0.258981	+	0.149523i	−0.623870	−	0.781528i	$-0.714440\pi$
$19$	−1.12887	+	0.651755i	−0.258981	+	0.149523i	0.364889	+	0.931051i	$0.381107\pi$
$20$		0			0
$21$	4.50715	+	0.827982i	0.983542	+	0.180681i
$22$		0			0
$23$	3.99480	+	6.91920i	0.832974	+	1.44275i	0.895669	+	0.444721i	$0.146697\pi$
$23$	3.99480	+	6.91920i	0.832974	+	1.44275i	−0.0626950	+	0.998033i	$0.519970\pi$
$24$		0			0
$25$	4.23026	−	2.66550i	0.846052	−	0.533100i
$26$		0			0
$27$	5.16832	−	0.537062i	0.994644	−	0.103358i
$28$		0			0
$29$		−	3.46154i		−	0.642791i	−0.946945	−	0.321396i	$-0.895848\pi$
$29$		−	3.46154i		−	0.642791i	0.946945	−	0.321396i	$-0.104152\pi$
$30$		0			0
$31$	−5.56113	−	3.21072i	−0.998809	−	0.576663i	−0.0909133	−	0.995859i	$-0.528979\pi$
$31$	−5.56113	−	3.21072i	−0.998809	−	0.576663i	−0.907896	+	0.419196i	$0.862312\pi$
$32$		0			0
$33$	−1.40041	−	0.745316i	−0.243780	−	0.129743i
$34$		0			0
$35$	−5.90361	+	0.383907i	−0.997892	+	0.0648921i
$36$		0			0
$37$	−4.36775	+	2.52172i	−0.718054	+	0.414569i	−0.814036	−	0.580814i	$-0.802734\pi$
$37$	−4.36775	+	2.52172i	−0.718054	+	0.414569i	0.0959820	+	0.995383i	$0.469401\pi$
$38$		0			0
$39$	7.46334	−	0.257693i	1.19509	−	0.0412640i
$40$		0			0
$41$	−9.89809			−1.54582			−0.772911	−	0.634515i	$-0.781200\pi$
$41$	−9.89809			−1.54582			−0.772911	+	0.634515i	$0.781200\pi$
$42$		0			0
$43$		−	8.22096i		−	1.25369i	−0.779146	−	0.626843i	$-0.784347\pi$
$43$		−	8.22096i		−	1.25369i	0.779146	−	0.626843i	$-0.215653\pi$
$44$		0			0
$45$	−6.30114	+	2.30123i	−0.939318	+	0.343047i
$46$		0			0
$47$	−3.75969	+	2.17066i	−0.548407	+	0.316623i	−0.748479	−	0.663158i	$-0.769216\pi$
$47$	−3.75969	+	2.17066i	−0.548407	+	0.316623i	0.200072	+	0.979781i	$0.435882\pi$
$48$		0			0
$49$	6.35578	+	2.93326i	0.907969	+	0.419038i
$50$		0			0
$51$	0.821162	+	0.437033i	0.114986	+	0.0611969i
$52$		0			0
$53$	0.984927	−	1.70594i	0.135290	−	0.234329i	−0.790418	−	0.612568i	$-0.790137\pi$
$53$	0.984927	−	1.70594i	0.135290	−	0.234329i	0.925708	+	0.378238i	$0.123470\pi$
$54$		0			0
$55$	1.98812	+	0.491730i	0.268077	+	0.0663048i
$56$		0			0
$57$	−1.91514	+	1.19567i	−0.253667	+	0.158370i
$58$		0			0
$59$	7.15363	−	12.3904i	0.931323	−	1.61310i	0.150260	−	0.988647i	$-0.451989\pi$
$59$	7.15363	−	12.3904i	0.931323	−	1.61310i	0.781063	−	0.624452i	$-0.214678\pi$
$60$		0			0
$61$	−8.38395	+	4.84048i	−1.07345	+	0.619759i	−0.929123	−	0.369770i	$-0.879436\pi$
$61$	−8.38395	+	4.84048i	−1.07345	+	0.619759i	−0.144331	+	0.989529i	$0.546103\pi$
$62$		0			0
$63$	7.85146	+	1.16387i	0.989191	+	0.146634i
$64$		0			0
$65$	−9.26240	+	2.67478i	−1.14886	+	0.331766i
$66$		0			0
$67$	−10.4850	−	6.05349i	−1.28094	−	0.739551i	−0.303920	−	0.952697i	$-0.598296\pi$
$67$	−10.4850	−	6.05349i	−1.28094	−	0.739551i	−0.977020	+	0.213146i	$0.931629\pi$
$68$		0			0
$69$	7.32863	+	11.7385i	0.882264	+	1.41315i
$70$		0			0
$71$		−	0.943900i		−	0.112020i	−0.998430	−	0.0560102i	$-0.982162\pi$
$71$		−	0.943900i		−	0.112020i	0.998430	−	0.0560102i	$-0.0178379\pi$
$72$		0			0
$73$	−5.11210	+	8.85442i	−0.598326	+	1.03633i	0.394742	+	0.918792i	$0.370834\pi$
$73$	−5.11210	+	8.85442i	−0.598326	+	1.03633i	−0.993068	+	0.117540i	$0.962499\pi$
$74$		0			0
$75$	7.16335	−	4.86687i	0.827152	−	0.561978i
$76$		0			0
$77$	−1.78984	−	1.63360i	−0.203971	−	0.186166i
$78$		0			0
$79$	5.71817	+	9.90416i	0.643345	+	1.11431i	0.984681	+	0.174364i	$0.0557870\pi$
$79$	5.71817	+	9.90416i	0.643345	+	1.11431i	−0.341337	+	0.939941i	$0.610880\pi$
$80$		0			0
$81$	8.91437	−	1.23857i	0.990485	−	0.137618i
$82$		0			0
$83$		−	9.35240i		−	1.02656i	−0.858222	−	0.513279i	$-0.828430\pi$
$83$		−	9.35240i		−	1.02656i	0.858222	−	0.513279i	$-0.171570\pi$
$84$		0			0
$85$	−1.16578	−	0.288337i	−0.126446	−	0.0312746i
$86$		0			0
$87$	−0.206891	−	5.99199i	−0.0221810	−	0.642408i
$88$		0			0
$89$	−0.874507	−	1.51469i	−0.0926976	−	0.160557i	0.815948	−	0.578126i	$-0.196216\pi$
$89$	−0.874507	−	1.51469i	−0.0926976	−	0.160557i	−0.908645	+	0.417569i	$0.862882\pi$
$90$		0			0
$91$	11.1417	+	2.44699i	1.16797	+	0.256515i
$92$		0			0
$93$	−9.81833	−	5.22544i	−1.01811	−	0.541853i
$94$		0			0
$95$	2.02080	−	2.10048i	0.207330	−	0.215505i
$96$		0			0
$97$	−10.7844			−1.09499			−0.547494	−	0.836809i	$-0.684418\pi$
$97$	−10.7844			−1.09499			−0.547494	+	0.836809i	$0.684418\pi$
$98$		0			0
$99$	−2.46868	−	1.20646i	−0.248112	−	0.121253i
$100$		0			0
$101$	−4.92480	+	8.53000i	−0.490036	+	0.848767i	−0.999934	−	0.0114677i	$-0.996350\pi$
$101$	−4.92480	+	8.53000i	−0.490036	+	0.848767i	0.509898	+	0.860235i	$0.329683\pi$
$102$		0			0
$103$	1.22897	+	2.12863i	0.121094	+	0.209741i	0.920199	−	0.391450i	$-0.128026\pi$
$103$	1.22897	+	2.12863i	0.121094	+	0.209741i	−0.799106	+	0.601191i	$0.794693\pi$
$104$		0			0
$105$	−10.1963	+	1.01740i	−0.995059	+	0.0992881i
$106$		0			0
$107$	0.749815	+	1.29872i	0.0724873	+	0.125552i	0.899991	−	0.435909i	$-0.143573\pi$
$107$	0.749815	+	1.29872i	0.0724873	+	0.125552i	−0.827504	+	0.561461i	$0.810240\pi$
$108$		0			0
$109$	1.93226	−	3.34677i	0.185077	−	0.320563i	−0.758525	−	0.651643i	$-0.774080\pi$
$109$	1.93226	−	3.34677i	0.185077	−	0.320563i	0.943602	+	0.331081i	$0.107413\pi$
$110$		0			0
$111$	−7.40994	+	4.62620i	−0.703321	+	0.439100i
$112$		0			0
$113$	−10.1791			−0.957567			−0.478783	−	0.877933i	$-0.658922\pi$
$113$	−10.1791			−0.957567			−0.478783	+	0.877933i	$0.658922\pi$
$114$		0			0
$115$	−12.8745	−	12.3861i	−1.20055	−	1.15501i
$116$		0			0
$117$	12.9038	−	0.892144i	1.19296	−	0.0824788i
$118$		0			0
$119$	1.04951	+	0.957898i	0.0962087	+	0.0878104i
$120$		0			0
$121$	−5.08056	−	8.79979i	−0.461869	−	0.799981i
$122$		0			0
$123$	−17.1338	+	0.591593i	−1.54490	+	0.0533421i
$124$		0			0
$125$	−7.43419	+	8.35062i	−0.664934	+	0.746902i
$126$		0			0
$127$			9.73798i			0.864106i	0.901848	+	0.432053i	$0.142211\pi$
$127$			9.73798i			0.864106i	−0.901848	+	0.432053i	$0.857789\pi$
$128$		0			0
$129$	−0.491354	−	14.2306i	−0.0432613	−	1.25294i
$130$		0			0
$131$	−8.80008	−	15.2422i	−0.768867	−	1.33172i	−0.938178	−	0.346154i	$-0.887488\pi$
$131$	−8.80008	−	15.2422i	−0.768867	−	1.33172i	0.169311	−	0.985563i	$-0.445846\pi$
$132$		0			0
$133$	−3.28709	+	1.04355i	−0.285027	+	0.0904874i
$134$		0			0
$135$	−10.7699	+	4.36008i	−0.926921	+	0.375256i
$136$		0			0
$137$	5.20973	−	9.02351i	0.445097	−	0.770931i	−0.552962	−	0.833207i	$-0.686503\pi$
$137$	5.20973	−	9.02351i	0.445097	−	0.770931i	0.998059	+	0.0622758i	$0.0198358\pi$
$138$		0			0
$139$			7.09182i			0.601520i	0.953700	+	0.300760i	$0.0972403\pi$
$139$			7.09182i			0.601520i	−0.953700	+	0.300760i	$0.902760\pi$
$140$		0			0
$141$	−6.37836	+	3.98216i	−0.537155	+	0.335359i
$142$		0			0
$143$	−3.41989	−	1.97447i	−0.285986	−	0.165114i
$144$		0			0
$145$	2.14746	+	7.43637i	0.178337	+	0.617557i
$146$		0			0
$147$	11.1773	+	4.69766i	0.921888	+	0.387456i
$148$		0			0
$149$	5.42586	−	3.13262i	0.444504	−	0.256634i	−0.261003	−	0.965338i	$-0.584053\pi$
$149$	5.42586	−	3.13262i	0.444504	−	0.256634i	0.705506	+	0.708704i	$0.250720\pi$
$150$		0			0
$151$	8.85578	−	15.3387i	0.720673	−	1.24824i	−0.240057	−	0.970759i	$-0.577166\pi$
$151$	8.85578	−	15.3387i	0.720673	−	1.24824i	0.960730	−	0.277484i	$-0.0895006\pi$
$152$		0			0
$153$	1.44757	+	0.707433i	0.117029	+	0.0571926i
$154$		0			0
$155$	13.9388	+	3.44754i	1.11959	+	0.276913i
$156$		0			0
$157$	−0.386973	+	0.670256i	−0.0308838	+	0.0534923i	−0.881054	−	0.473015i	$-0.843166\pi$
$157$	−0.386973	+	0.670256i	−0.0308838	+	0.0534923i	0.850170	+	0.526508i	$0.176499\pi$
$158$		0			0
$159$	1.60297	−	3.01189i	0.127123	−	0.238858i
$160$		0			0
$161$	6.39625	+	20.1476i	0.504095	+	1.58785i
$162$		0			0
$163$	5.96435	−	3.44352i	0.467164	−	0.269717i	−0.247888	−	0.968789i	$-0.579736\pi$
$163$	5.96435	−	3.44352i	0.467164	−	0.269717i	0.715052	+	0.699072i	$0.246403\pi$
$164$		0			0
$165$	3.47086	+	0.732367i	0.270206	+	0.0570147i
$166$		0			0
$167$			9.49709i			0.734907i	0.930042	+	0.367453i	$0.119770\pi$
$167$			9.49709i			0.734907i	−0.930042	+	0.367453i	$0.880230\pi$
$168$		0			0
$169$	5.58930			0.429946
$170$		0			0
$171$	−3.24369	+	2.18419i	−0.248051	+	0.167029i
$172$		0			0
$173$	−10.3489	+	5.97492i	−0.786809	+	0.454264i	−0.838838	−	0.544381i	$-0.816765\pi$
$173$	−10.3489	+	5.97492i	−0.786809	+	0.454264i	0.0520289	+	0.998646i	$0.483431\pi$
$174$		0			0
$175$	12.4445	−	4.48722i	0.940714	−	0.339202i
$176$		0			0
$177$	11.6425	−	21.8757i	0.875105	−	1.64428i
$178$		0			0
$179$	16.2343	+	9.37286i	1.21341	+	0.700561i	0.963500	−	0.267709i	$-0.0862667\pi$
$179$	16.2343	+	9.37286i	1.21341	+	0.700561i	0.249907	+	0.968270i	$0.419600\pi$
$180$		0			0
$181$			16.1024i			1.19688i	0.801167	+	0.598441i	$0.204213\pi$
$181$			16.1024i			1.19688i	−0.801167	+	0.598441i	$0.795787\pi$
$182$		0			0
$183$	−14.2235	+	8.88005i	−1.05143	+	0.656432i
$184$		0			0
$185$	7.81876	−	8.12704i	0.574846	−	0.597512i
$186$		0			0
$187$	−0.245948	−	0.425995i	−0.0179855	−	0.0311519i
$188$		0			0
$189$	13.6606	+	1.54541i	0.993662	+	0.112412i
$190$		0			0
$191$	14.9979	−	8.65904i	1.08521	−	0.626546i	0.152912	−	0.988240i	$-0.451135\pi$
$191$	14.9979	−	8.65904i	1.08521	−	0.626546i	0.932297	+	0.361694i	$0.117801\pi$
$192$		0			0
$193$	13.1033	+	7.56517i	0.943193	+	0.544553i	0.890960	−	0.454082i	$-0.150033\pi$
$193$	13.1033	+	7.56517i	0.943193	+	0.544553i	0.0522332	+	0.998635i	$0.483366\pi$
$194$		0			0
$195$	−15.8735	+	5.18370i	−1.13673	+	0.371212i
$196$		0			0
$197$	18.6287			1.32724			0.663619	−	0.748071i	$-0.269020\pi$
$197$	18.6287			1.32724			0.663619	+	0.748071i	$0.269020\pi$
$198$		0			0
$199$	−8.70283	−	5.02458i	−0.616927	−	0.356183i	0.158745	−	0.987320i	$-0.449255\pi$
$199$	−8.70283	−	5.02458i	−0.616927	−	0.356183i	−0.775672	+	0.631137i	$0.782589\pi$
$200$		0			0
$201$	−18.5115	−	9.85204i	−1.30570	−	0.694909i
$202$		0			0
$203$	1.96458	−	8.94517i	0.137887	−	0.627828i
$204$		0			0
$205$	21.2639	−	6.14056i	1.48514	−	0.428875i
$206$		0			0
$207$	13.3876	+	19.8816i	0.930502	+	1.38186i
$208$		0			0
$209$	1.19389			0.0825830
$210$		0			0
$211$	−1.68592			−0.116064			−0.0580319	−	0.998315i	$-0.518483\pi$
$211$	−1.68592			−0.116064			−0.0580319	+	0.998315i	$0.518483\pi$
$212$		0			0
$213$	−0.0564154	−	1.63391i	−0.00386552	−	0.111954i
$214$		0			0
$215$	5.10011	+	17.6610i	0.347825	+	1.20447i
$216$		0			0
$217$	−12.5486	−	11.4532i	−0.851857	−	0.777495i
$218$		0			0
$219$	−8.31993	+	15.6327i	−0.562209	+	1.05636i
$220$		0			0
$221$	2.00533	+	1.15778i	0.134893	+	0.0778806i
$222$		0			0
$223$	14.2095			0.951541			0.475770	−	0.879570i	$-0.342169\pi$
$223$	14.2095			0.951541			0.475770	+	0.879570i	$0.342169\pi$
$224$		0			0
$225$	12.1090	−	8.85279i	0.807268	−	0.590186i
$226$		0			0
$227$	−0.590416	−	0.340877i	−0.0391873	−	0.0226248i	0.480278	−	0.877116i	$-0.340536\pi$
$227$	−0.590416	−	0.340877i	−0.0391873	−	0.0226248i	−0.519466	+	0.854491i	$0.673869\pi$
$228$		0			0
$229$	−2.56113	+	1.47867i	−0.169244	+	0.0977133i	−0.582230	−	0.813024i	$-0.697819\pi$
$229$	−2.56113	+	1.47867i	−0.169244	+	0.0977133i	0.412985	+	0.910738i	$0.364486\pi$
$230$		0			0
$231$	−3.19588	−	2.72081i	−0.210274	−	0.179016i
$232$		0			0
$233$	13.4685	+	23.3282i	0.882353	+	1.52828i	0.848717	+	0.528847i	$0.177375\pi$
$233$	13.4685	+	23.3282i	0.882353	+	1.52828i	0.0336360	+	0.999434i	$0.489291\pi$
$234$		0			0
$235$	6.73026	−	6.99563i	0.439034	−	0.456344i
$236$		0			0
$237$	10.4902	+	16.8025i	0.681413	+	1.09144i
$238$		0			0
$239$		−	17.3461i		−	1.12202i	−0.827808	−	0.561012i	$-0.810412\pi$
$239$		−	17.3461i		−	1.12202i	0.827808	−	0.561012i	$-0.189588\pi$
$240$		0			0
$241$	1.32282	+	0.763728i	0.0852101	+	0.0491961i	0.542000	−	0.840379i	$-0.317667\pi$
$241$	1.32282	+	0.763728i	0.0852101	+	0.0491961i	−0.456790	+	0.889575i	$0.651001\pi$
$242$		0			0
$243$	15.3569	−	2.67678i	0.985147	−	0.171716i
$244$		0			0
$245$	−15.4738	−	2.35849i	−0.988583	−	0.150679i
$246$		0			0
$247$	−4.86717	+	2.81006i	−0.309690	+	0.178800i
$248$		0			0
$249$	−0.558978	−	16.1892i	−0.0354238	−	1.02595i
$250$		0			0
$251$	6.56268			0.414233			0.207116	−	0.978316i	$-0.433592\pi$
$251$	6.56268			0.414233			0.207116	+	0.978316i	$0.433592\pi$
$252$		0			0
$253$		−	7.31771i		−	0.460061i
$254$		0			0
$255$	−2.03522	−	0.429441i	−0.127450	−	0.0268926i
$256$		0			0
$257$	−14.6990	+	8.48645i	−0.916896	+	0.529370i	−0.882644	−	0.470043i	$-0.844238\pi$
$257$	−14.6990	+	8.48645i	−0.916896	+	0.529370i	−0.0342527	+	0.999413i	$0.510905\pi$
$258$		0			0
$259$	−12.7182	+	4.03764i	−0.790269	+	0.250887i
$260$		0			0
$261$	−0.716263	−	10.3599i	−0.0443356	−	0.641260i
$262$		0			0
$263$	2.65984	−	4.60699i	0.164013	−	0.284079i	−0.772291	−	0.635269i	$-0.780889\pi$
$263$	2.65984	−	4.60699i	0.164013	−	0.284079i	0.936304	+	0.351190i	$0.114223\pi$
$264$		0			0
$265$	−1.05757	+	4.27588i	−0.0649662	+	0.262665i
$266$		0			0
$267$	−1.60432	−	2.56969i	−0.0981828	−	0.157263i
$268$		0			0
$269$	−3.27834	+	5.67825i	−0.199884	+	0.346209i	−0.948491	−	0.316805i	$-0.897390\pi$
$269$	−3.27834	+	5.67825i	−0.199884	+	0.346209i	0.748607	+	0.663014i	$0.230723\pi$
$270$		0			0
$271$	4.54171	−	2.62216i	0.275889	−	0.159285i	−0.355672	−	0.934611i	$-0.615748\pi$
$271$	4.54171	−	2.62216i	0.275889	−	0.159285i	0.631561	+	0.775326i	$0.282415\pi$
$272$		0			0
$273$	19.4327	+	3.56987i	1.17612	+	0.216058i
$274$		0			0
$275$	−4.57610	+	0.177008i	−0.275949	+	0.0106740i
$276$		0			0
$277$	−2.40171	−	1.38663i	−0.144305	−	0.0833145i	0.426109	−	0.904672i	$-0.359884\pi$
$277$	−2.40171	−	1.38663i	−0.144305	−	0.0833145i	−0.570414	+	0.821357i	$0.693217\pi$
$278$		0			0
$279$	−17.3080	−	8.45851i	−1.03620	−	0.506398i
$280$		0			0
$281$			22.4373i			1.33850i	0.743038	+	0.669250i	$0.233384\pi$
$281$			22.4373i			1.33850i	−0.743038	+	0.669250i	$0.766616\pi$
$282$		0			0
$283$	3.62340	−	6.27592i	0.215389	−	0.373064i	−0.738004	−	0.674796i	$-0.764231\pi$
$283$	3.62340	−	6.27592i	0.215389	−	0.373064i	0.953393	+	0.301732i	$0.0975648\pi$
$284$		0			0
$285$	3.37251	−	3.75676i	0.199770	−	0.222531i
$286$		0			0
$287$	−25.5783	−	5.61762i	−1.50984	−	0.331598i
$288$		0			0
$289$	−8.35578	−	14.4726i	−0.491517	−	0.851332i
$290$		0			0
$291$	−18.6680	+	0.644566i	−1.09434	+	0.0377851i
$292$		0			0
$293$		−	26.1686i		−	1.52879i	−0.644750	−	0.764393i	$-0.723039\pi$
$293$		−	26.1686i		−	1.52879i	0.644750	−	0.764393i	$-0.276961\pi$
$294$		0			0
$295$	−7.68127	+	31.0562i	−0.447221	+	1.80816i
$296$		0			0
$297$	−4.34544	−	1.94085i	−0.252148	−	0.112619i
$298$		0			0
$299$	17.2237	+	29.8324i	0.996073	+	1.72525i
$300$		0			0
$301$	4.66578	−	21.2443i	0.268931	−	1.22450i
$302$		0			0
$303$	−8.01510	+	15.0599i	−0.460455	+	0.865171i
$304$		0			0
$305$	15.0082	−	15.5999i	0.859366	−	0.893250i
$306$		0			0
$307$	−22.4144			−1.27926			−0.639630	−	0.768683i	$-0.720912\pi$
$307$	−22.4144			−1.27926			−0.639630	+	0.768683i	$0.720912\pi$
$308$		0			0
$309$	2.25459	+	3.61125i	0.128259	+	0.205437i
$310$		0			0
$311$	9.81378	−	16.9980i	0.556488	−	0.963866i	−0.441298	−	0.897361i	$-0.645482\pi$
$311$	9.81378	−	16.9980i	0.556488	−	0.963866i	0.997786	−	0.0665052i	$-0.0211849\pi$
$312$		0			0
$313$	−6.41664	−	11.1139i	−0.362690	−	0.628197i	0.625713	−	0.780054i	$-0.284808\pi$
$313$	−6.41664	−	11.1139i	−0.362690	−	0.628197i	−0.988403	+	0.151856i	$0.951475\pi$
$314$		0			0
$315$	−17.5892	+	2.37056i	−0.991040	+	0.133566i
$316$		0			0
$317$	7.98449	+	13.8295i	0.448454	+	0.776745i	0.998286	−	0.0585306i	$-0.0186415\pi$
$317$	7.98449	+	13.8295i	0.448454	+	0.776745i	−0.549832	+	0.835275i	$0.685308\pi$
$318$		0			0
$319$	−1.58522	+	2.74568i	−0.0887552	+	0.153728i
$320$		0			0
$321$	1.37557	+	2.20329i	0.0767766	+	0.122976i
$322$		0			0
$323$	−0.700065			−0.0389526
$324$		0			0
$325$	18.2389	−	11.4924i	1.01171	−	0.637483i
$326$		0			0
$327$	3.14475	−	5.90882i	0.173905	−	0.326758i
$328$		0			0
$329$	−10.9476	+	3.47553i	−0.603561	+	0.191612i
$330$		0			0
$331$	9.81888	+	17.0068i	0.539694	+	0.934778i	0.998920	+	0.0464584i	$0.0147935\pi$
$331$	9.81888	+	17.0068i	0.539694	+	0.934778i	−0.459226	+	0.888319i	$0.651873\pi$
$332$		0			0
$333$	−12.5503	+	8.45093i	−0.687750	+	0.463108i
$334$		0			0
$335$	26.2801	+	6.49998i	1.43584	+	0.355132i
$336$		0			0
$337$		−	0.304237i		−	0.0165729i	−0.999966	−	0.00828643i	$-0.997362\pi$
$337$		−	0.304237i		−	0.0165729i	0.999966	−	0.00828643i	$-0.00263768\pi$
$338$		0			0
$339$	−17.6202	+	0.608387i	−0.956996	+	0.0330430i
$340$		0			0
$341$	2.94071	+	5.09346i	0.159249	+	0.275827i
$342$		0			0
$343$	14.7596	+	11.1872i	0.796944	+	0.604053i
$344$		0			0
$345$	−23.0263	−	20.6711i	−1.23970	−	1.11290i
$346$		0			0
$347$	14.2235	−	24.6358i	0.763556	−	1.32252i	−0.177451	−	0.984130i	$-0.556785\pi$
$347$	14.2235	−	24.6358i	0.763556	−	1.32252i	0.941007	−	0.338388i	$-0.109882\pi$
$348$		0			0
$349$		−	13.9719i		−	0.747897i	−0.927450	−	0.373948i	$-0.878004\pi$
$349$		−	13.9719i		−	0.747897i	0.927450	−	0.373948i	$-0.121996\pi$
$350$		0			0
$351$	22.2834	−	2.31556i	1.18940	−	0.123595i
$352$		0			0
$353$	29.9676	+	17.3018i	1.59501	+	0.920881i	0.992428	+	0.122826i	$0.0391958\pi$
$353$	29.9676	+	17.3018i	1.59501	+	0.920881i	0.602585	+	0.798055i	$0.294138\pi$
$354$		0			0
$355$	0.585575	+	2.02777i	0.0310791	+	0.107623i
$356$		0			0
$357$	1.87398	+	1.59541i	0.0991815	+	0.0844382i
$358$		0			0
$359$	−19.8260	+	11.4465i	−1.04638	+	0.604126i	−0.921633	−	0.388064i	$-0.873144\pi$
$359$	−19.8260	+	11.4465i	−1.04638	+	0.604126i	−0.124743	+	0.992189i	$0.539811\pi$
$360$		0			0
$361$	−8.65043	+	14.9830i	−0.455286	+	0.788578i
$362$		0			0
$363$	−9.32050	−	14.9289i	−0.489199	−	0.783566i
$364$		0			0
$365$	5.48916	−	22.1933i	0.287316	−	1.16165i
$366$		0			0
$367$	−14.4999	+	25.1145i	−0.756887	+	1.31097i	0.187543	+	0.982256i	$0.439947\pi$
$367$	−14.4999	+	25.1145i	−0.756887	+	1.31097i	−0.944431	+	0.328711i	$0.893386\pi$
$368$		0			0
$369$	−29.6235	+	2.04812i	−1.54214	+	0.106621i
$370$		0			0
$371$	3.51341	−	3.84944i	0.182407	−	0.199853i
$372$		0			0
$373$	−20.8113	+	12.0154i	−1.07757	+	0.622136i	−0.930240	−	0.366952i	$-0.880401\pi$
$373$	−20.8113	+	12.0154i	−1.07757	+	0.622136i	−0.147331	+	0.989087i	$0.547068\pi$
$374$		0			0
$375$	−12.3696	+	14.8994i	−0.638764	+	0.769402i
$376$		0			0
$377$		−	14.9245i		−	0.768652i
$378$		0			0
$379$	−14.0820			−0.723342			−0.361671	−	0.932306i	$-0.617794\pi$
$379$	−14.0820			−0.723342			−0.361671	+	0.932306i	$0.617794\pi$
$380$		0			0
$381$	0.582023	+	16.8566i	0.0298180	+	0.863591i
$382$		0			0
$383$	−25.4637	+	14.7015i	−1.30114	+	0.751211i	−0.980599	−	0.196025i	$-0.937197\pi$
$383$	−25.4637	+	14.7015i	−1.30114	+	0.751211i	−0.320537	+	0.947236i	$0.603863\pi$
$384$		0			0
$385$	4.85853	+	2.39906i	0.247614	+	0.122267i
$386$		0			0
$387$	−1.70109	−	24.6042i	−0.0864711	−	1.25070i
$388$		0			0
$389$	−20.2730	−	11.7046i	−1.02788	−	0.593448i	−0.111504	−	0.993764i	$-0.535567\pi$
$389$	−20.2730	−	11.7046i	−1.02788	−	0.593448i	−0.916377	+	0.400316i	$0.868900\pi$
$390$		0			0
$391$			4.29091i			0.217001i
$392$		0			0
$393$	−16.1441	−	25.8586i	−0.814363	−	1.30439i
$394$		0			0
$395$	−18.4286	−	17.7295i	−0.927243	−	0.892070i
$396$		0			0
$397$	−5.96889	−	10.3384i	−0.299570	−	0.518871i	0.676467	−	0.736473i	$-0.263510\pi$
$397$	−5.96889	−	10.3384i	−0.299570	−	0.518871i	−0.976038	+	0.217602i	$0.930177\pi$
$398$		0			0
$399$	−5.62764	+	2.00287i	−0.281734	+	0.100269i
$400$		0			0
$401$	21.6844	−	12.5195i	1.08287	−	0.625193i	0.151198	−	0.988504i	$-0.451687\pi$
$401$	21.6844	−	12.5195i	1.08287	−	0.625193i	0.931668	+	0.363311i	$0.118354\pi$
$402$		0			0
$403$	−23.9770	−	13.8431i	−1.19438	−	0.689575i
$404$		0			0
$405$	−18.3822	+	8.19108i	−0.913420	+	0.407018i
$406$		0			0
$407$	4.61931			0.228971
$408$		0			0
$409$	26.1378	+	15.0906i	1.29243	+	0.746184i	0.979084	−	0.203455i	$-0.0652172\pi$
$409$	26.1378	+	15.0906i	1.29243	+	0.746184i	0.313345	+	0.949640i	$0.398551\pi$
$410$		0			0
$411$	8.47882	−	15.9313i	0.418229	−	0.785831i
$412$		0			0
$413$	25.5183	−	27.9589i	1.25567	−	1.37577i
$414$		0			0
$415$	5.80203	+	20.0916i	0.284810	+	0.986259i
$416$		0			0
$417$	0.423867	+	12.2761i	0.0207568	+	0.601162i
$418$		0			0
$419$	−9.85560			−0.481477			−0.240739	−	0.970590i	$-0.577390\pi$
$419$	−9.85560			−0.481477			−0.240739	+	0.970590i	$0.577390\pi$
$420$		0			0
$421$	−8.16112			−0.397749			−0.198874	−	0.980025i	$-0.563729\pi$
$421$	−8.16112			−0.397749			−0.198874	+	0.980025i	$0.563729\pi$
$422$		0			0
$423$	−10.8031	+	7.27443i	−0.525263	+	0.353695i
$424$		0			0
$425$	2.68330	−	0.103793i	0.130159	−	0.00503470i
$426$		0			0
$427$	−24.4127	+	7.75029i	−1.18141	+	0.375063i
$428$		0			0
$429$	−6.03791	−	3.21345i	−0.291513	−	0.155147i
$430$		0			0
$431$	−2.84702	−	1.64373i	−0.137136	−	0.0791755i	0.429862	−	0.902894i	$-0.358562\pi$
$431$	−2.84702	−	1.64373i	−0.137136	−	0.0791755i	−0.566998	+	0.823719i	$0.691895\pi$
$432$		0			0
$433$	31.9717			1.53646			0.768231	−	0.640173i	$-0.221137\pi$
$433$	31.9717			1.53646			0.768231	+	0.640173i	$0.221137\pi$
$434$		0			0
$435$	4.16176	+	12.7441i	0.199541	+	0.611035i
$436$		0			0
$437$	−9.01924	−	5.20726i	−0.431449	−	0.249097i
$438$		0			0
$439$	36.1217	−	20.8549i	1.72399	−	0.995349i	0.813827	−	0.581107i	$-0.197380\pi$
$439$	36.1217	−	20.8549i	1.72399	−	0.995349i	0.910167	−	0.414242i	$-0.135953\pi$
$440$		0			0
$441$	19.6289	+	7.46369i	0.934709	+	0.355414i
$442$		0			0
$443$	9.47885	+	16.4179i	0.450354	+	0.780036i	0.998408	−	0.0564073i	$-0.0179645\pi$
$443$	9.47885	+	16.4179i	0.450354	+	0.780036i	−0.548054	+	0.836443i	$0.684631\pi$
$444$		0			0
$445$	2.81837	+	2.71146i	0.133604	+	0.128536i
$446$		0			0
$447$	9.20503	−	5.74692i	0.435383	−	0.271820i
$448$		0			0
$449$			40.0091i			1.88815i	0.329737	+	0.944073i	$0.393040\pi$
$449$			40.0091i			1.88815i	−0.329737	+	0.944073i	$0.606960\pi$
$450$		0			0
$451$	7.85112	+	4.53285i	0.369695	+	0.213444i
$452$		0			0
$453$	14.4128	−	27.0808i	0.677171	−	1.27237i
$454$		0			0
$455$	−25.4536	+	1.65523i	−1.19328	+	0.0775982i
$456$		0			0
$457$	−9.86127	+	5.69340i	−0.461291	+	0.266326i	−0.712587	−	0.701584i	$-0.752477\pi$
$457$	−9.86127	+	5.69340i	−0.461291	+	0.266326i	0.251296	+	0.967910i	$0.419143\pi$
$458$		0			0
$459$	2.54805	+	1.13806i	0.118933	+	0.0531202i
$460$		0			0
$461$	−8.71020			−0.405674			−0.202837	−	0.979212i	$-0.565016\pi$
$461$	−8.71020			−0.405674			−0.202837	+	0.979212i	$0.565016\pi$
$462$		0			0
$463$		−	16.1154i		−	0.748944i	−0.927238	−	0.374472i	$-0.877824\pi$
$463$		−	16.1154i		−	0.748944i	0.927238	−	0.374472i	$-0.122176\pi$
$464$		0			0
$465$	24.3343	+	5.13466i	1.12848	+	0.238114i
$466$		0			0
$467$	7.88492	−	4.55236i	0.364870	−	0.210658i	−0.306345	−	0.951921i	$-0.599106\pi$
$467$	7.88492	−	4.55236i	0.364870	−	0.210658i	0.671215	+	0.741263i	$0.265773\pi$
$468$		0			0
$469$	−23.6592	−	21.5939i	−1.09248	−	0.997113i
$470$		0			0
$471$	−0.629797	+	1.18336i	−0.0290195	+	0.0545261i
$472$		0			0
$473$	−3.76481	+	6.52084i	−0.173106	+	0.299828i
$474$		0			0
$475$	−3.03817	+	5.76610i	−0.139401	+	0.264567i
$476$		0			0
$477$	2.59475	−	5.30944i	0.118805	−	0.243103i
$478$		0			0
$479$	−13.2092	+	22.8791i	−0.603546	+	1.04537i	0.388733	+	0.921350i	$0.372913\pi$
$479$	−13.2092	+	22.8791i	−0.603546	+	1.04537i	−0.992279	+	0.124022i	$0.960421\pi$
$480$		0			0
$481$	−18.8317	+	10.8725i	−0.858652	+	0.495743i
$482$		0			0
$483$	12.2762	+	34.4935i	0.558587	+	1.56951i
$484$		0			0
$485$	23.1679	−	6.69040i	1.05200	−	0.303796i
$486$		0			0
$487$	7.93392	+	4.58065i	0.359520	+	0.207569i	0.668870	−	0.743379i	$-0.266778\pi$
$487$	7.93392	+	4.58065i	0.359520	+	0.207569i	−0.309350	+	0.950948i	$0.600111\pi$
$488$		0			0
$489$	10.1186	−	6.31727i	0.457578	−	0.285677i
$490$		0			0
$491$		−	33.0800i		−	1.49288i	−0.665453	−	0.746440i	$-0.731761\pi$
$491$		−	33.0800i		−	1.49288i	0.665453	−	0.746440i	$-0.268239\pi$
$492$		0			0
$493$	0.929529	−	1.60999i	0.0418639	−	0.0725104i
$494$		0			0
$495$	6.05189	+	1.06029i	0.272012	+	0.0476567i
$496$		0			0
$497$	0.535707	−	2.43919i	0.0240297	−	0.109413i
$498$		0			0
$499$	−8.54365	−	14.7980i	−0.382466	−	0.662451i	0.608948	−	0.793210i	$-0.291592\pi$
$499$	−8.54365	−	14.7980i	−0.382466	−	0.662451i	−0.991414	+	0.130759i	$0.958259\pi$
$500$		0			0
$501$	0.567626	+	16.4396i	0.0253597	+	0.734469i
$502$		0			0
$503$		−	21.1753i		−	0.944158i	−0.881556	−	0.472079i	$-0.843504\pi$
$503$		−	21.1753i		−	0.944158i	0.881556	−	0.472079i	$-0.156496\pi$
$504$		0			0
$505$	5.28804	−	21.3801i	0.235315	−	0.951403i
$506$		0			0
$507$	9.67518	−	0.334063i	0.429690	−	0.0148363i
$508$		0			0
$509$	−15.5918	−	27.0059i	−0.691096	−	1.19701i	−0.971479	−	0.237125i	$-0.923795\pi$
$509$	−15.5918	−	27.0059i	−0.691096	−	1.19701i	0.280383	−	0.959888i	$-0.409539\pi$
$510$		0			0
$511$	−18.2358	+	19.9799i	−0.806704	+	0.883859i
$512$		0			0
$513$	−5.48434	+	3.97475i	−0.242140	+	0.175490i
$514$		0			0
$515$	−3.96073	−	3.81049i	−0.174531	−	0.167910i
$516$		0			0
$517$	3.97623			0.174874
$518$		0			0
$519$	−17.5570	+	10.9612i	−0.770665	+	0.481145i
$520$		0			0
$521$	−19.4555	+	33.6980i	−0.852363	+	1.47634i	0.0267070	+	0.999643i	$0.491498\pi$
$521$	−19.4555	+	33.6980i	−0.852363	+	1.47634i	−0.879070	+	0.476693i	$0.841835\pi$
$522$		0			0
$523$	1.88123	+	3.25839i	0.0822606	+	0.142480i	0.904221	−	0.427066i	$-0.140453\pi$
$523$	1.88123	+	3.25839i	0.0822606	+	0.142480i	−0.821960	+	0.569545i	$0.807119\pi$
$524$		0			0
$525$	21.2734	−	8.51124i	0.928449	−	0.371461i
$526$		0			0
$527$	−1.72436	−	2.98667i	−0.0751141	−	0.130101i
$528$		0			0
$529$	−20.4169	+	35.3631i	−0.887692	+	1.53753i
$530$		0			0
$531$	18.8459	−	38.5630i	0.817844	−	1.67349i
$532$		0			0
$533$	−42.6759			−1.84850
$534$		0			0
$535$	−2.41651	−	2.32485i	−0.104475	−	0.100512i
$536$		0			0
$537$	28.6620	+	15.2543i	1.23686	+	0.658272i
$538$		0			0
$539$	−3.69809	−	5.23730i	−0.159288	−	0.225586i
$540$		0			0
$541$	−13.6223	−	23.5945i	−0.585667	−	1.01440i	−0.994792	−	0.101927i	$-0.967499\pi$
$541$	−13.6223	−	23.5945i	−0.585667	−	1.01440i	0.409125	−	0.912478i	$-0.365834\pi$
$542$		0			0
$543$	0.962414	+	27.8736i	0.0413012	+	1.19617i
$544$		0			0
$545$	−2.07478	+	8.38856i	−0.0888739	+	0.359326i
$546$		0			0
$547$		−	13.4516i		−	0.575148i	−0.957758	−	0.287574i	$-0.907151\pi$
$547$		−	13.4516i		−	0.575148i	0.957758	−	0.287574i	$-0.0928487\pi$
$548$		0			0
$549$	−24.0904	+	16.2217i	−1.02815	+	0.692323i
$550$		0			0
$551$	2.25607	+	3.90763i	0.0961119	+	0.166471i
$552$		0			0
$553$	9.15561	+	28.8393i	0.389336	+	1.22637i
$554$		0			0
$555$	13.0487	−	14.5354i	0.553885	−	0.616992i
$556$		0			0
$557$	−18.8087	+	32.5776i	−0.796950	+	1.38036i	0.124644	+	0.992202i	$0.460221\pi$
$557$	−18.8087	+	32.5776i	−0.796950	+	1.38036i	−0.921594	+	0.388156i	$0.873112\pi$
$558$		0			0
$559$		−	35.4449i		−	1.49916i
$560$		0			0
$561$	−0.451203	−	0.722706i	−0.0190498	−	0.0305127i
$562$		0			0
$563$	8.81514	+	5.08942i	0.371514	+	0.214494i	0.674120	−	0.738622i	$-0.264523\pi$
$563$	8.81514	+	5.08942i	0.371514	+	0.214494i	−0.302606	+	0.953116i	$0.597857\pi$
$564$		0			0
$565$	21.8676	−	6.31488i	0.919975	−	0.265669i
$566$		0			0
$567$	23.7391	+	1.85866i	0.996949	+	0.0780564i
$568$		0			0
$569$	−0.744706	+	0.429956i	−0.0312197	+	0.0180247i	−0.515529	−	0.856872i	$-0.672404\pi$
$569$	−0.744706	+	0.429956i	−0.0312197	+	0.0180247i	0.484309	+	0.874897i	$0.339071\pi$
$570$		0			0
$571$	−1.71817	+	2.97596i	−0.0719032	+	0.124540i	−0.899735	−	0.436436i	$-0.856241\pi$
$571$	−1.71817	+	2.97596i	−0.0719032	+	0.124540i	0.827832	+	0.560976i	$0.189574\pi$
$572$		0			0
$573$	25.4441	−	15.8854i	1.06294	−	0.663620i
$574$		0			0
$575$	35.3422	+	18.6219i	1.47387	+	0.776586i
$576$		0			0
$577$	12.8498	−	22.2565i	0.534944	−	0.926550i	−0.464222	−	0.885719i	$-0.653666\pi$
$577$	12.8498	−	22.2565i	0.534944	−	0.926550i	0.999166	−	0.0408310i	$-0.0130005\pi$
$578$		0			0
$579$	23.1341	+	12.3123i	0.961422	+	0.511681i
$580$		0			0
$581$	5.30792	−	24.1681i	0.220210	−	1.00266i
$582$		0			0
$583$	−1.56248	+	0.902098i	−0.0647113	+	0.0373611i
$584$		0			0
$585$	−27.1676	+	9.92181i	−1.12324	+	0.410217i
$586$		0			0
$587$			22.5090i			0.929048i	0.885561	+	0.464524i	$0.153775\pi$
$587$			22.5090i			0.929048i	−0.885561	+	0.464524i	$0.846225\pi$
$588$		0			0
$589$	8.37041			0.344897
$590$		0			0
$591$	32.2466	−	1.11341i	1.32645	−	0.0457994i
$592$		0			0
$593$	−20.5878	+	11.8863i	−0.845438	+	0.488114i	−0.859109	−	0.511793i	$-0.828982\pi$
$593$	−20.5878	+	11.8863i	−0.845438	+	0.488114i	0.0136712	+	0.999907i	$0.495648\pi$
$594$		0			0
$595$	−2.84891	−	1.40674i	−0.116794	−	0.0576708i
$596$		0			0
$597$	−15.3651	−	8.17749i	−0.628850	−	0.334682i
$598$		0			0
$599$	−37.6990	−	21.7655i	−1.54034	−	0.889314i	−0.998817	−	0.0486270i	$-0.984515\pi$
$599$	−37.6990	−	21.7655i	−1.54034	−	0.889314i	−0.541521	−	0.840687i	$-0.682151\pi$
$600$		0			0
$601$		−	19.9347i		−	0.813153i	−0.913617	−	0.406577i	$-0.866722\pi$
$601$		−	19.9347i		−	0.813153i	0.913617	−	0.406577i	$-0.133278\pi$
$602$		0			0
$603$	−32.6325	−	15.9477i	−1.32890	−	0.649439i
$604$		0			0
$605$	16.3737	+	15.7526i	0.665685	+	0.640434i
$606$		0			0
$607$	−5.31663	−	9.20867i	−0.215795	−	0.373768i	0.737723	−	0.675103i	$-0.235901\pi$
$607$	−5.31663	−	9.20867i	−0.215795	−	0.373768i	−0.953518	+	0.301335i	$0.902568\pi$
$608$		0			0
$609$	2.86609	−	15.6017i	0.116140	−	0.632212i
$610$		0			0
$611$	−16.2100	+	9.35886i	−0.655788	+	0.378619i
$612$		0			0
$613$	−13.1068	−	7.56721i	−0.529378	−	0.305637i	0.211385	−	0.977403i	$-0.432203\pi$
$613$	−13.1068	−	7.56721i	−0.529378	−	0.305637i	−0.740763	+	0.671766i	$0.765536\pi$
$614$		0			0
$615$	36.4412	−	11.9003i	1.46945	−	0.479868i
$616$		0			0
$617$	7.39865			0.297858			0.148929	−	0.988848i	$-0.452417\pi$
$617$	7.39865			0.297858			0.148929	+	0.988848i	$0.452417\pi$
$618$		0			0
$619$	16.0456	+	9.26396i	0.644929	+	0.372350i	0.786511	−	0.617577i	$-0.211885\pi$
$619$	16.0456	+	9.26396i	0.644929	+	0.372350i	−0.141582	+	0.989927i	$0.545219\pi$
$620$		0			0
$621$	24.3625	+	33.6152i	0.977632	+	1.34893i
$622$		0			0
$623$	−1.40021	−	4.41053i	−0.0560983	−	0.176704i
$624$		0			0
$625$	10.7902	−	22.5515i	0.431609	−	0.902061i
$626$		0			0
$627$	2.06665	−	0.0713568i	0.0825339	−	0.00284972i
$628$		0			0
$629$	−2.70864			−0.108001
$630$		0			0
$631$	13.1786			0.524632			0.262316	−	0.964982i	$-0.415514\pi$
$631$	13.1786			0.524632			0.262316	+	0.964982i	$0.415514\pi$
$632$		0			0
$633$	−2.91837	+	0.100765i	−0.115995	+	0.00400505i
$634$		0			0
$635$	−6.04123	−	20.9200i	−0.239739	−	0.830183i
$636$		0			0
$637$	27.4032	+	12.6469i	1.08575	+	0.501087i
$638$		0			0
$639$	−0.195312	−	2.82496i	−0.00772643	−	0.111754i
$640$		0			0
$641$	−12.2389	−	7.06611i	−0.483406	−	0.279094i	0.238429	−	0.971160i	$-0.423368\pi$
$641$	−12.2389	−	7.06611i	−0.483406	−	0.279094i	−0.721835	+	0.692065i	$0.756701\pi$
$642$		0			0
$643$	17.9278			0.707005			0.353503	−	0.935434i	$-0.384991\pi$
$643$	17.9278			0.707005			0.353503	+	0.935434i	$0.384991\pi$
$644$		0			0
$645$	9.88396	+	30.2667i	0.389180	+	1.19175i
$646$		0			0
$647$	20.7892	+	12.0026i	0.817306	+	0.471872i	0.849487	−	0.527610i	$-0.176912\pi$
$647$	20.7892	+	12.0026i	0.817306	+	0.471872i	−0.0321804	+	0.999482i	$0.510245\pi$
$648$		0			0
$649$	−11.3485	+	6.55204i	−0.445466	+	0.257190i
$650$		0			0
$651$	−22.4065	−	19.0757i	−0.878179	−	0.747637i
$652$		0			0
$653$	14.4745	+	25.0705i	0.566430	+	0.981085i	0.996915	+	0.0784876i	$0.0250091\pi$
$653$	14.4745	+	25.0705i	0.566430	+	0.981085i	−0.430485	+	0.902598i	$0.641658\pi$
$654$		0			0
$655$	28.3610	+	27.2852i	1.10816	+	1.06612i
$656$		0			0
$657$	−13.4676	+	27.5578i	−0.525422	+	1.07513i
$658$		0			0
$659$		−	5.09127i		−	0.198328i	−0.995071	−	0.0991638i	$-0.968383\pi$
$659$		−	5.09127i		−	0.198328i	0.995071	−	0.0991638i	$-0.0316168\pi$
$660$		0			0
$661$	25.1768	+	14.5358i	0.979264	+	0.565378i	0.902048	−	0.431636i	$-0.142064\pi$
$661$	25.1768	+	14.5358i	0.979264	+	0.565378i	0.0772160	+	0.997014i	$0.475397\pi$
$662$		0			0
$663$	3.54047	+	1.88428i	0.137500	+	0.0731794i
$664$		0			0
$665$	6.41421	−	4.28109i	0.248732	−	0.166013i
$666$		0			0
$667$	23.9511	−	13.8282i	0.927389	−	0.535429i
$668$		0			0
$669$	24.5970	−	0.849281i	0.950974	−	0.0328351i
$670$		0			0
$671$	8.86682			0.342300
$672$		0			0
$673$		−	8.51862i		−	0.328369i	−0.986430	−	0.164184i	$-0.947501\pi$
$673$		−	8.51862i		−	0.328369i	0.986430	−	0.164184i	$-0.0524992\pi$
$674$		0			0
$675$	20.4318	−	16.0481i	0.786421	−	0.617691i
$676$		0			0
$677$	−16.4341	+	9.48823i	−0.631614	+	0.364662i	−0.781377	−	0.624060i	$-0.785482\pi$
$677$	−16.4341	+	9.48823i	−0.631614	+	0.364662i	0.149763	+	0.988722i	$0.452149\pi$
$678$		0			0
$679$	−27.8686	−	6.12064i	−1.06950	−	0.234889i
$680$		0			0
$681$	−1.04239	−	0.554776i	−0.0399447	−	0.0212591i
$682$		0			0
$683$	−10.4587	+	18.1149i	−0.400190	+	0.693149i	−0.993749	−	0.111642i	$-0.964389\pi$
$683$	−10.4587	+	18.1149i	−0.400190	+	0.693149i	0.593559	+	0.804791i	$0.297722\pi$
$684$		0			0
$685$	−5.59399	+	22.6171i	−0.213735	+	0.864154i
$686$		0			0
$687$	−4.34499	+	2.71268i	−0.165772	+	0.103495i
$688$		0			0
$689$	4.24654	−	7.35523i	0.161780	−	0.280212i
$690$		0			0
$691$	29.4902	−	17.0261i	1.12186	−	0.647705i	0.179984	−	0.983670i	$-0.442396\pi$
$691$	29.4902	−	17.0261i	1.12186	−	0.647705i	0.941875	+	0.335964i	$0.109062\pi$
$692$		0			0
$693$	−5.69475	−	4.51877i	−0.216326	−	0.171654i
$694$		0			0
$695$	−4.39961	−	15.2352i	−0.166887	−	0.577906i
$696$		0			0
$697$	−4.60369	−	2.65794i	−0.174377	−	0.100677i
$698$		0			0
$699$	24.7086	+	39.5766i	0.934565	+	1.49692i
$700$		0			0
$701$		−	18.9758i		−	0.716706i	−0.933586	−	0.358353i	$-0.883338\pi$
$701$		−	18.9758i		−	0.716706i	0.933586	−	0.358353i	$-0.116662\pi$
$702$		0			0
$703$	3.28709	−	5.69340i	0.123975	−	0.214731i
$704$		0			0
$705$	11.2321	−	12.5118i	0.423025	−	0.471223i
$706$		0			0
$707$	−17.5676	+	19.2479i	−0.660699	+	0.723890i
$708$		0			0
$709$	−1.53691	−	2.66200i	−0.0577197	−	0.0999735i	0.835722	−	0.549153i	$-0.185050\pi$
$709$	−1.53691	−	2.66200i	−0.0577197	−	0.0999735i	−0.893441	+	0.449180i	$0.851716\pi$
$710$		0			0
$711$	19.1630	+	28.4585i	0.718670	+	1.06728i
$712$		0			0
$713$		−	51.3048i		−	1.92138i
$714$		0			0
$715$	8.57182	+	2.12011i	0.320568	+	0.0792875i
$716$		0			0
$717$	−1.03675	−	30.0264i	−0.0387180	−	1.12136i
$718$		0			0
$719$	6.70106	+	11.6066i	0.249907	+	0.432852i	0.963500	−	0.267709i	$-0.0862665\pi$
$719$	6.70106	+	11.6066i	0.249907	+	0.432852i	−0.713593	+	0.700561i	$0.752933\pi$
$720$		0			0
$721$	1.96775	+	6.19823i	0.0732829	+	0.230834i
$722$		0			0
$723$	2.33547	+	1.24297i	0.0868569	+	0.0462264i
$724$		0			0
$725$	−9.22673	−	14.6432i	−0.342672	−	0.543835i
$726$		0			0
$727$	−4.88627			−0.181222			−0.0906109	−	0.995886i	$-0.528882\pi$
$727$	−4.88627			−0.181222			−0.0906109	+	0.995886i	$0.528882\pi$
$728$		0			0
$729$	26.4231	−	5.55142i	0.978634	−	0.205608i
$730$		0			0
$731$	2.20758	−	3.82364i	0.0816504	−	0.141423i
$732$		0			0
$733$	18.4955	+	32.0351i	0.683145	+	1.18324i	0.974016	+	0.226480i	$0.0727217\pi$
$733$	18.4955	+	32.0351i	0.683145	+	1.18324i	−0.290871	+	0.956762i	$0.593945\pi$
$734$		0			0
$735$	−26.9264	−	3.15776i	−0.993194	−	0.116476i
$736$		0			0
$737$	5.54441	+	9.60321i	0.204231	+	0.353739i
$738$		0			0
$739$	−18.9759	+	32.8672i	−0.698040	+	1.20904i	0.271105	+	0.962550i	$0.412611\pi$
$739$	−18.9759	+	32.8672i	−0.698040	+	1.20904i	−0.969145	+	0.246491i	$0.920722\pi$
$740$		0			0
$741$	−8.25721	+	5.15517i	−0.303336	+	0.189380i
$742$		0			0
$743$	−14.0878			−0.516830			−0.258415	−	0.966034i	$-0.583200\pi$
$743$	−14.0878			−0.516830			−0.258415	+	0.966034i	$0.583200\pi$
$744$		0			0
$745$	−9.71288	+	10.0958i	−0.355852	+	0.369883i
$746$		0			0
$747$	−1.93520	−	27.9904i	−0.0708054	−	1.02411i
$748$		0			0
$749$	1.20056	+	3.78165i	0.0438675	+	0.138178i
$750$		0			0
$751$	12.8752	+	22.3005i	0.469823	+	0.813757i	0.999405	−	0.0345016i	$-0.0109844\pi$
$751$	12.8752	+	22.3005i	0.469823	+	0.813757i	−0.529582	+	0.848259i	$0.677651\pi$
$752$		0			0
$753$	11.3601	−	0.392241i	0.413986	−	0.0142941i
$754$		0			0
$755$	−9.50897	+	38.4458i	−0.346067	+	1.39918i
$756$		0			0
$757$			40.3111i			1.46513i	0.680697	+	0.732565i	$0.261677\pi$
$757$			40.3111i			1.46513i	−0.680697	+	0.732565i	$0.738323\pi$
$758$		0			0
$759$	−0.437368	−	12.6671i	−0.0158755	−	0.459787i
$760$		0			0
$761$	9.76529	+	16.9140i	0.353991	+	0.613131i	0.986945	−	0.161059i	$-0.0514909\pi$
$761$	9.76529	+	16.9140i	0.353991	+	0.613131i	−0.632953	+	0.774190i	$0.718158\pi$
$762$		0			0
$763$	6.89272	−	7.55196i	0.249533	−	0.273399i
$764$		0			0
$765$	−3.54867	−	0.621728i	−0.128302	−	0.0224786i
$766$		0			0
$767$	30.8431	−	53.4218i	1.11368	−	1.92895i
$768$		0			0
$769$		−	47.6475i		−	1.71821i	−0.511797	−	0.859107i	$-0.671020\pi$
$769$		−	47.6475i		−	1.71821i	0.511797	−	0.859107i	$-0.328980\pi$
$770$		0			0
$771$	−24.9370	+	15.5687i	−0.898083	+	0.560695i
$772$		0			0
$773$	−18.2945	−	10.5624i	−0.658009	−	0.379901i	0.133509	−	0.991048i	$-0.457375\pi$
$773$	−18.2945	−	10.5624i	−0.658009	−	0.379901i	−0.791518	+	0.611146i	$0.790709\pi$
$774$		0			0
$775$	−32.0832	+	1.24101i	−1.15246	+	0.0445785i
$776$		0			0
$777$	−21.7741	+	7.74937i	−0.781141	+	0.278007i
$778$		0			0
$779$	11.1737	−	6.45112i	0.400338	−	0.231135i
$780$		0			0
$781$	−0.432261	+	0.748698i	−0.0154675	+	0.0267905i
$782$		0			0
$783$	−1.85906	−	17.8903i	−0.0664373	−	0.639349i
$784$		0			0
$785$	0.415515	−	1.67997i	0.0148304	−	0.0599608i
$786$		0			0
$787$	3.27330	−	5.66953i	0.116681	−	0.202097i	−0.801770	−	0.597633i	$-0.796108\pi$
$787$	3.27330	−	5.66953i	0.116681	−	0.202097i	0.918450	+	0.395536i	$0.129441\pi$
$788$		0			0
$789$	4.32889	−	8.13376i	0.154113	−	0.289569i
$790$		0			0
$791$	−26.3044	−	5.77709i	−0.935276	−	0.205410i
$792$		0			0
$793$	−36.1477	+	20.8699i	−1.28364	+	0.741110i
$794$		0			0
$795$	−1.57512	+	7.46484i	−0.0558637	+	0.264751i
$796$		0			0
$797$			6.50728i			0.230500i	0.993337	+	0.115250i	$0.0367669\pi$
$797$			6.50728i			0.230500i	−0.993337	+	0.115250i	$0.963233\pi$
$798$		0			0
$799$	−2.33156			−0.0824845
$800$		0			0
$801$	−2.93069	−	4.35230i	−0.103551	−	0.153781i
$802$		0			0
$803$	8.10980	−	4.68219i	0.286189	−	0.165231i
$804$		0			0
$805$	−26.2401	−	39.3146i	−0.924842	−	1.38566i
$806$		0			0
$807$	−5.33549	+	10.0251i	−0.187818	+	0.352900i
$808$		0			0
$809$	1.41519	+	0.817063i	0.0497556	+	0.0287264i	0.524671	−	0.851305i	$-0.324188\pi$
$809$	1.41519	+	0.817063i	0.0497556	+	0.0287264i	−0.474916	+	0.880031i	$0.657522\pi$
$810$		0			0
$811$		−	29.4411i		−	1.03382i	−0.856041	−	0.516909i	$-0.827083\pi$
$811$		−	29.4411i		−	1.03382i	0.856041	−	0.516909i	$-0.172917\pi$
$812$		0			0
$813$	7.70506	−	4.81045i	0.270228	−	0.168710i
$814$		0			0
$815$	−10.6768	+	11.0978i	−0.373993	+	0.388739i
$816$		0			0
$817$	5.35805	+	9.28042i	0.187454	+	0.324681i
$818$		0			0
$819$	33.8518	+	5.01805i	1.18288	+	0.175345i
$820$		0			0
$821$	−19.6357	+	11.3367i	−0.685292	+	0.395654i	−0.801846	−	0.597531i	$-0.796149\pi$
$821$	−19.6357	+	11.3367i	−0.685292	+	0.395654i	0.116554	+	0.993184i	$0.462815\pi$
$822$		0			0
$823$	16.6180	+	9.59438i	0.579266	+	0.334439i	0.760841	−	0.648938i	$-0.224786\pi$
$823$	16.6180	+	9.59438i	0.579266	+	0.334439i	−0.181576	+	0.983377i	$0.558120\pi$
$824$		0			0
$825$	−7.91073	+	0.579911i	−0.275416	+	0.0201899i
$826$		0			0
$827$	32.5074			1.13039			0.565196	−	0.824957i	$-0.308800\pi$
$827$	32.5074			1.13039			0.565196	+	0.824957i	$0.308800\pi$
$828$		0			0
$829$	44.7613	+	25.8429i	1.55462	+	0.897563i	0.997756	+	0.0669618i	$0.0213306\pi$
$829$	44.7613	+	25.8429i	1.55462	+	0.897563i	0.556868	+	0.830601i	$0.312003\pi$
$830$		0			0
$831$	−4.24029	−	2.25674i	−0.147094	−	0.0782853i
$832$		0			0
$833$	2.16846	+	3.07101i	0.0751327	+	0.106404i
$834$		0			0
$835$	−5.89179	−	20.4025i	−0.203894	−	0.706056i
$836$		0			0
$837$	−30.4661	−	13.6074i	−1.05306	−	0.470340i
$838$		0			0
$839$	−2.88841			−0.0997192			−0.0498596	−	0.998756i	$-0.515877\pi$
$839$	−2.88841			−0.0997192			−0.0498596	+	0.998756i	$0.515877\pi$
$840$		0			0
$841$	17.0178			0.586819
$842$		0			0
$843$	1.34104	+	38.8395i	0.0461880	+	1.33770i
$844$		0			0
$845$	−12.0074	+	3.46748i	−0.413067	+	0.119285i
$846$		0			0
$847$	−8.13470	−	25.6235i	−0.279512	−	0.880435i
$848$		0			0
$849$	5.89708	−	11.0803i	0.202387	−	0.380275i
$850$		0			0
$851$	−34.8966	−	20.1476i	−1.19624	−	0.690650i
$852$		0			0
$853$	−49.3673			−1.69031			−0.845153	−	0.534525i	$-0.820491\pi$
$853$	−49.3673			−1.69031			−0.845153	+	0.534525i	$0.820491\pi$
$854$		0			0
$855$	5.61334	−	6.70459i	0.191972	−	0.229292i
$856$		0			0
$857$	−15.1586	−	8.75185i	−0.517809	−	0.298957i	0.218228	−	0.975898i	$-0.429972\pi$
$857$	−15.1586	−	8.75185i	−0.517809	−	0.298957i	−0.736038	+	0.676940i	$0.763306\pi$
$858$		0			0
$859$	−5.23153	+	3.02042i	−0.178497	+	0.103056i	−0.586586	−	0.809887i	$-0.699529\pi$
$859$	−5.23153	+	3.02042i	−0.178497	+	0.103056i	0.408089	+	0.912942i	$0.366195\pi$
$860$		0			0
$861$	−44.6122	−	8.19544i	−1.52038	−	0.279300i
$862$		0			0
$863$	17.0085	+	29.4595i	0.578975	+	1.00281i	0.995597	+	0.0937342i	$0.0298804\pi$
$863$	17.0085	+	29.4595i	0.578975	+	1.00281i	−0.416622	+	0.909080i	$0.636786\pi$
$864$		0			0
$865$	18.5256	−	19.2560i	0.629889	−	0.654725i
$866$		0			0
$867$	−15.3290	−	24.5530i	−0.520601	−	0.833864i
$868$		0			0
$869$		−	10.4746i		−	0.355326i
$870$		0			0
$871$	−45.2062	−	26.0998i	−1.53175	−	0.884358i
$872$		0			0
$873$	−32.2761	+	2.23151i	−1.09238	+	0.0755252i
$874$		0			0
$875$	−23.9505	+	17.3601i	−0.809675	+	0.586879i
$876$		0			0
$877$	−6.27005	+	3.62002i	−0.211725	+	0.122239i	−0.602113	−	0.798411i	$-0.705674\pi$
$877$	−6.27005	+	3.62002i	−0.211725	+	0.122239i	0.390388	+	0.920650i	$0.372341\pi$
$878$		0			0
$879$	−1.56406	−	45.2984i	−0.0527543	−	1.52788i
$880$		0			0
$881$	25.9119			0.872993			0.436496	−	0.899706i	$-0.356219\pi$
$881$	25.9119			0.872993			0.436496	+	0.899706i	$0.356219\pi$
$882$		0			0
$883$		−	17.5664i		−	0.591155i	−0.955319	−	0.295577i	$-0.904488\pi$
$883$		−	17.5664i		−	0.591155i	0.955319	−	0.295577i	$-0.0955120\pi$
$884$		0			0
$885$	−11.4402	+	54.2179i	−0.384560	+	1.82252i
$886$		0			0
$887$	−12.7893	+	7.38392i	−0.429423	+	0.247928i	−0.699101	−	0.715023i	$-0.746416\pi$
$887$	−12.7893	+	7.38392i	−0.429423	+	0.247928i	0.269678	+	0.962951i	$0.413083\pi$
$888$		0			0
$889$	−5.52675	+	25.1645i	−0.185361	+	0.843990i
$890$		0			0
$891$	−7.63805	−	3.09993i	−0.255884	−	0.103851i
$892$		0			0
$893$	2.82947	−	4.90079i	0.0946847	−	0.163999i
$894$		0			0
$895$	−40.6906	−	10.0642i	−1.36014	−	0.336409i
$896$		0			0
$897$	31.5976	+	50.6110i	1.05501	+	1.68985i
$898$		0			0
$899$	−11.1140	+	19.2501i	−0.370674	+	0.642026i
$900$		0			0
$901$	0.916197	−	0.528966i	0.0305229	−	0.0176224i
$902$		0			0
$903$	6.80681	−	37.0532i	0.226517	−	1.23305i
$904$		0			0
$905$	−9.98958	−	34.5925i	−0.332065	−	1.14989i
$906$		0			0
$907$	25.3957	+	14.6622i	0.843250	+	0.486851i	0.858368	−	0.513035i	$-0.171479\pi$
$907$	25.3957	+	14.6622i	0.843250	+	0.486851i	−0.0151176	+	0.999886i	$0.504812\pi$
$908$		0			0
$909$	−12.9742	+	26.5481i	−0.430326	+	0.880545i
$910$		0			0
$911$			30.3043i			1.00403i	0.864860	+	0.502013i	$0.167407\pi$
$911$			30.3043i			1.00403i	−0.864860	+	0.502013i	$0.832593\pi$
$912$		0			0
$913$	−4.28295	+	7.41828i	−0.141745	+	0.245509i
$914$		0			0
$915$	25.0471	−	27.9008i	0.828031	−	0.922373i
$916$		0			0
$917$	−14.0902	−	44.3827i	−0.465299	−	1.46565i
$918$		0			0
$919$	3.81888	+	6.61449i	0.125973	+	0.218192i	0.922113	−	0.386921i	$-0.126461\pi$
$919$	3.81888	+	6.61449i	0.125973	+	0.218192i	−0.796140	+	0.605113i	$0.793128\pi$
$920$		0			0
$921$	−38.7998	+	1.33968i	−1.27850	+	0.0441438i
$922$		0			0
$923$		−	4.06965i		−	0.133954i
$924$		0			0
$925$	−11.7551	+	22.3098i	−0.386505	+	0.733541i
$926$		0			0
$927$	4.11858	+	6.11640i	0.135272	+	0.200889i
$928$		0			0
$929$	−8.62508	−	14.9391i	−0.282980	−	0.490135i	0.689138	−	0.724631i	$-0.257990\pi$
$929$	−8.62508	−	14.9391i	−0.282980	−	0.490135i	−0.972117	+	0.234495i	$0.924656\pi$
$930$		0			0
$931$	−9.08663	+	0.831132i	−0.297802	+	0.0272393i
$932$		0			0
$933$	15.9719	−	30.0104i	0.522896	−	0.982495i
$934$		0			0
$935$	0.792646	+	0.762578i	0.0259223	+	0.0249390i
$936$		0			0
$937$	−36.0492			−1.17768			−0.588839	−	0.808251i	$-0.700415\pi$
$937$	−36.0492			−1.17768			−0.588839	+	0.808251i	$0.700415\pi$
$938$		0			0
$939$	−11.7716	−	18.8549i	−0.384151	−	0.615308i
$940$		0			0
$941$	15.8153	−	27.3930i	0.515565	−	0.892985i	−0.484272	−	0.874918i	$-0.660915\pi$
$941$	15.8153	−	27.3930i	0.515565	−	0.892985i	0.999837	−	0.0180673i	$-0.00575131\pi$
$942$		0			0
$943$	−39.5409	−	68.4869i	−1.28763	−	2.23024i
$944$		0			0
$945$	−30.3056	+	5.15476i	−0.985841	+	0.167684i
$946$		0			0
$947$	−20.3087	−	35.1757i	−0.659944	−	1.14306i	−0.980630	−	0.195871i	$-0.937247\pi$
$947$	−20.3087	−	35.1757i	−0.659944	−	1.14306i	0.320685	−	0.947186i	$-0.396087\pi$
$948$		0			0
$949$	−22.0410	+	38.1761i	−0.715481	+	1.23925i
$950$		0			0
$951$	14.6479	+	23.4620i	0.474990	+	0.760807i
$952$		0			0
$953$	−5.31938			−0.172312			−0.0861558	−	0.996282i	$-0.527458\pi$
$953$	−5.31938			−0.172312			−0.0861558	+	0.996282i	$0.527458\pi$
$954$		0			0
$955$	−26.8479	+	27.9065i	−0.868777	+	0.903032i
$956$		0			0
$957$	−2.57994	+	4.84757i	−0.0833975	+	0.156700i
$958$		0			0
$959$	18.5840	−	20.3615i	0.600110	−	0.657506i
$960$		0			0
$961$	5.11747	+	8.86371i	0.165080	+	0.285926i
$962$		0			0
$963$	2.51282	+	3.73172i	0.0809745	+	0.120253i
$964$		0			0
$965$	−32.8428	−	8.12316i	−1.05725	−	0.261494i
$966$		0			0
$967$		−	6.75930i		−	0.217364i	−0.994077	−	0.108682i	$-0.965337\pi$
$967$		−	6.75930i		−	0.217364i	0.994077	−	0.108682i	$-0.0346631\pi$
$968$		0			0
$969$	−1.21183	+	0.0418417i	−0.0389294	+	0.00134415i
$970$		0			0
$971$	21.9851	+	38.0793i	0.705535	+	1.22202i	0.966498	+	0.256674i	$0.0826266\pi$
$971$	21.9851	+	38.0793i	0.705535	+	1.22202i	−0.260963	+	0.965349i	$0.584040\pi$
$972$		0			0
$973$	−4.02493	+	18.3264i	−0.129033	+	0.587517i
$974$		0			0
$975$	30.8850	−	20.9837i	0.989112	−	0.672015i
$976$		0			0
$977$	−4.62443	+	8.00974i	−0.147949	+	0.256254i	−0.930469	−	0.366370i	$-0.880600\pi$
$977$	−4.62443	+	8.00974i	−0.147949	+	0.256254i	0.782521	+	0.622625i	$0.213934\pi$
$978$		0			0
$979$			1.60193i			0.0511979i
$980$		0			0
$981$	5.09046	−	10.4162i	0.162526	−	0.332565i
$982$		0			0
$983$	11.3787	+	6.56947i	0.362923	+	0.209533i	0.670362	−	0.742034i	$-0.266139\pi$
$983$	11.3787	+	6.56947i	0.362923	+	0.209533i	−0.307439	+	0.951568i	$0.599472\pi$
$984$		0			0
$985$	−40.0197	+	11.5568i	−1.27513	+	0.368231i
$986$		0			0
$987$	−18.7428	+	6.67054i	−0.596589	+	0.212326i
$988$		0			0
$989$	56.8825	−	32.8411i	1.80876	−	1.04429i
$990$		0			0
$991$	3.18520	−	5.51694i	0.101181	−	0.175251i	−0.810990	−	0.585060i	$-0.801071\pi$
$991$	3.18520	−	5.51694i	0.101181	−	0.175251i	0.912172	+	0.409808i	$0.134404\pi$
$992$		0			0
$993$	18.0131	+	28.8522i	0.571630	+	0.915598i
$994$		0			0
$995$	21.8133	+	5.39518i	0.691528	+	0.171039i
$996$		0			0
$997$	11.7546	−	20.3595i	0.372271	−	0.644792i	−0.617644	−	0.786458i	$-0.711913\pi$
$997$	11.7546	−	20.3595i	0.372271	−	0.644792i	0.989915	+	0.141666i	$0.0452459\pi$
$998$		0			0
$999$	−21.2196	+	15.3788i	−0.671359	+	0.486565i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bn.a.269.16	yes	32
3.2	odd	2	inner	420.2.bn.a.269.6	yes	32
5.2	odd	4		2100.2.bi.n.101.8		32
5.3	odd	4		2100.2.bi.n.101.9		32
5.4	even	2	inner	420.2.bn.a.269.1	yes	32
7.3	odd	6		2940.2.f.a.1469.23		32
7.4	even	3		2940.2.f.a.1469.10		32
7.5	odd	6	inner	420.2.bn.a.89.11	yes	32
15.2	even	4		2100.2.bi.n.101.3		32
15.8	even	4		2100.2.bi.n.101.14		32
15.14	odd	2	inner	420.2.bn.a.269.11	yes	32
21.5	even	6	inner	420.2.bn.a.89.1	✓	32
21.11	odd	6		2940.2.f.a.1469.11		32
21.17	even	6		2940.2.f.a.1469.22		32
35.4	even	6		2940.2.f.a.1469.24		32
35.12	even	12		2100.2.bi.n.1601.3		32
35.19	odd	6	inner	420.2.bn.a.89.6	yes	32
35.24	odd	6		2940.2.f.a.1469.9		32
35.33	even	12		2100.2.bi.n.1601.14		32
105.47	odd	12		2100.2.bi.n.1601.8		32
105.59	even	6		2940.2.f.a.1469.12		32
105.68	odd	12		2100.2.bi.n.1601.9		32
105.74	odd	6		2940.2.f.a.1469.21		32
105.89	even	6	inner	420.2.bn.a.89.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bn.a.89.1	✓	32	21.5	even	6	inner
420.2.bn.a.89.6	yes	32	35.19	odd	6	inner
420.2.bn.a.89.11	yes	32	7.5	odd	6	inner
420.2.bn.a.89.16	yes	32	105.89	even	6	inner
420.2.bn.a.269.1	yes	32	5.4	even	2	inner
420.2.bn.a.269.6	yes	32	3.2	odd	2	inner
420.2.bn.a.269.11	yes	32	15.14	odd	2	inner
420.2.bn.a.269.16	yes	32	1.1	even	1	trivial
2100.2.bi.n.101.3		32	15.2	even	4
2100.2.bi.n.101.8		32	5.2	odd	4
2100.2.bi.n.101.9		32	5.3	odd	4
2100.2.bi.n.101.14		32	15.8	even	4
2100.2.bi.n.1601.3		32	35.12	even	12
2100.2.bi.n.1601.8		32	105.47	odd	12
2100.2.bi.n.1601.9		32	105.68	odd	12
2100.2.bi.n.1601.14		32	35.33	even	12
2940.2.f.a.1469.9		32	35.24	odd	6
2940.2.f.a.1469.10		32	7.4	even	3
2940.2.f.a.1469.11		32	21.11	odd	6
2940.2.f.a.1469.12		32	105.59	even	6
2940.2.f.a.1469.21		32	105.74	odd	6
2940.2.f.a.1469.22		32	21.17	even	6
2940.2.f.a.1469.23		32	7.3	odd	6
2940.2.f.a.1469.24		32	35.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73102 - 0.0597684i) q^{3} +(-2.14829 + 0.620379i) q^{5} +(2.58416 + 0.567546i) q^{7} +(2.99286 - 0.206921i) q^{9} +(-0.793196 - 0.457952i) q^{11} +4.31153 q^{13} +(-3.68164 + 1.20229i) q^{15} +(0.465109 + 0.268531i) q^{17} +(-1.12887 + 0.651755i) q^{19} +(4.50715 + 0.827982i) q^{21} +(3.99480 + 6.91920i) q^{23} +(4.23026 - 2.66550i) q^{25} +(5.16832 - 0.537062i) q^{27} -3.46154i q^{29} +(-5.56113 - 3.21072i) q^{31} +(-1.40041 - 0.745316i) q^{33} +(-5.90361 + 0.383907i) q^{35} +(-4.36775 + 2.52172i) q^{37} +(7.46334 - 0.257693i) q^{39} -9.89809 q^{41} -8.22096i q^{43} +(-6.30114 + 2.30123i) q^{45} +(-3.75969 + 2.17066i) q^{47} +(6.35578 + 2.93326i) q^{49} +(0.821162 + 0.437033i) q^{51} +(0.984927 - 1.70594i) q^{53} +(1.98812 + 0.491730i) q^{55} +(-1.91514 + 1.19567i) q^{57} +(7.15363 - 12.3904i) q^{59} +(-8.38395 + 4.84048i) q^{61} +(7.85146 + 1.16387i) q^{63} +(-9.26240 + 2.67478i) q^{65} +(-10.4850 - 6.05349i) q^{67} +(7.32863 + 11.7385i) q^{69} -0.943900i q^{71} +(-5.11210 + 8.85442i) q^{73} +(7.16335 - 4.86687i) q^{75} +(-1.78984 - 1.63360i) q^{77} +(5.71817 + 9.90416i) q^{79} +(8.91437 - 1.23857i) q^{81} -9.35240i q^{83} +(-1.16578 - 0.288337i) q^{85} +(-0.206891 - 5.99199i) q^{87} +(-0.874507 - 1.51469i) q^{89} +(11.1417 + 2.44699i) q^{91} +(-9.81833 - 5.22544i) q^{93} +(2.02080 - 2.10048i) q^{95} -10.7844 q^{97} +(-2.46868 - 1.20646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{15} + 12 q^{19} - 8 q^{21} + 6 q^{25} - 12 q^{31} + 24 q^{39} + 33 q^{45} - 44 q^{49} - 10 q^{51} - 24 q^{61} + 21 q^{75} - 28 q^{79} - 20 q^{81} - 4 q^{85} + 16 q^{91} - 28 q^{99}+O(q^{100}) \) 32 * q + 2 * q^15 + 12 * q^19 - 8 * q^21 + 6 * q^25 - 12 * q^31 + 24 * q^39 + 33 * q^45 - 44 * q^49 - 10 * q^51 - 24 * q^61 + 21 * q^75 - 28 * q^79 - 20 * q^81 - 4 * q^85 + 16 * q^91 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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