LMFDB - Embedded newform 420.2.bn.a.269.11

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)

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")

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);

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			269.11
Character	$\chi$	$=$	420.269
Dual form			420.2.bn.a.89.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.813749 + 1.52899i) q^{3} +(-1.61141 + 1.55028i) q^{5} +(-2.58416 - 0.567546i) q^{7} +(-1.67563 + 2.48843i) q^{9} +(0.793196 + 0.457952i) q^{11} -4.31153 q^{13} +(-3.68164 - 1.20229i) q^{15} +(0.465109 + 0.268531i) q^{17} +(-1.12887 + 0.651755i) q^{19} +(-1.23509 - 4.41300i) q^{21} +(3.99480 + 6.91920i) q^{23} +(0.193261 - 4.99626i) q^{25} +(-5.16832 - 0.537062i) q^{27} +3.46154i q^{29} +(-5.56113 - 3.21072i) q^{31} +(-0.0547421 + 1.58545i) q^{33} +(5.04399 - 3.09163i) q^{35} +(4.36775 - 2.52172i) q^{37} +(-3.50850 - 6.59229i) q^{39} +9.89809 q^{41} +8.22096i q^{43} +(-1.15765 - 6.60756i) q^{45} +(-3.75969 + 2.17066i) q^{47} +(6.35578 + 2.93326i) q^{49} +(-0.0320993 + 0.929664i) q^{51} +(0.984927 - 1.70594i) q^{53} +(-1.98812 + 0.491730i) q^{55} +(-1.91514 - 1.19567i) q^{57} +(-7.15363 + 12.3904i) q^{59} +(-8.38395 + 4.84048i) q^{61} +(5.74239 - 5.47951i) q^{63} +(6.94763 - 6.68408i) q^{65} +(10.4850 + 6.05349i) q^{67} +(-7.32863 + 11.7385i) q^{69} +0.943900i q^{71} +(5.11210 - 8.85442i) q^{73} +(7.79651 - 3.77021i) q^{75} +(-1.78984 - 1.63360i) q^{77} +(5.71817 + 9.90416i) q^{79} +(-3.38455 - 8.33935i) q^{81} -9.35240i q^{83} +(-1.16578 + 0.288337i) q^{85} +(-5.29266 + 2.81682i) q^{87} +(0.874507 + 1.51469i) q^{89} +(11.1417 + 2.44699i) q^{91} +(0.383799 - 11.1156i) q^{93} +(0.808669 - 2.80031i) q^{95} +10.7844 q^{97} +(-2.46868 + 1.20646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.813749	+	1.52899i	0.469818	+	0.882763i
$3$	0.813749	+	1.52899i	0.469818	+	0.882763i
$4$		0			0
$5$	−1.61141	+	1.55028i	−0.720643	+	0.693307i
$5$	−1.61141	+	1.55028i	−0.720643	+	0.693307i
$6$		0			0
$7$	−2.58416	−	0.567546i	−0.976721	−	0.214512i
$7$	−2.58416	−	0.567546i	−0.976721	−	0.214512i
$8$		0			0
$9$	−1.67563	+	2.48843i	−0.558542	+	0.829476i
$10$		0			0
$11$	0.793196	+	0.457952i	0.239158	+	0.138078i	0.614790	−	0.788691i	$-0.289241\pi$
$11$	0.793196	+	0.457952i	0.239158	+	0.138078i	−0.375632	+	0.926769i	$0.622574\pi$
$12$		0			0
$13$	−4.31153			−1.19580			−0.597902	−	0.801569i	$-0.703999\pi$
$13$	−4.31153			−1.19580			−0.597902	+	0.801569i	$0.703999\pi$
$14$		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
$21$	−1.23509	−	4.41300i	−0.269518	−	0.962995i
$22$		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
$25$	0.193261	−	4.99626i	0.0386521	−	0.999253i
$26$		0			0
$27$	−5.16832	−	0.537062i	−0.994644	−	0.103358i
$28$		0			0
$29$			3.46154i			0.642791i	0.946945	+	0.321396i	$0.104152\pi$
$29$			3.46154i			0.642791i	−0.946945	+	0.321396i	$0.895848\pi$
$30$		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
$33$	−0.0547421	+	1.58545i	−0.00952938	+	0.275991i
$34$		0			0
$35$	5.04399	−	3.09163i	0.852590	−	0.522580i
$36$		0			0
$37$	4.36775	−	2.52172i	0.718054	−	0.414569i	−0.0959820	−	0.995383i	$-0.530599\pi$
$37$	4.36775	−	2.52172i	0.718054	−	0.414569i	0.814036	+	0.580814i	$0.197266\pi$
$38$		0			0
$39$	−3.50850	−	6.59229i	−0.561810	−	1.05561i
$40$		0			0
$41$	9.89809			1.54582			0.772911	−	0.634515i	$-0.218800\pi$
$41$	9.89809			1.54582			0.772911	+	0.634515i	$0.218800\pi$
$42$		0			0
$43$			8.22096i			1.25369i	0.779146	+	0.626843i	$0.215653\pi$
$43$			8.22096i			1.25369i	−0.779146	+	0.626843i	$0.784347\pi$
$44$		0			0
$45$	−1.15765	−	6.60756i	−0.172572	−	0.984997i
$46$		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
$51$	−0.0320993	+	0.929664i	−0.00449480	+	0.130179i
$52$		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	$0.548011\pi$
$59$	−7.15363	+	12.3904i	−0.931323	+	1.61310i	−0.781063	+	0.624452i	$0.785322\pi$
$60$		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
$63$	5.74239	−	5.47951i	0.723473	−	0.690353i
$64$		0			0
$65$	6.94763	−	6.68408i	0.861747	−	0.829058i
$66$		0			0
$67$	10.4850	+	6.05349i	1.28094	+	0.739551i	0.977020	−	0.213146i	$-0.0683710\pi$
$67$	10.4850	+	6.05349i	1.28094	+	0.739551i	0.303920	+	0.952697i	$0.401704\pi$
$68$		0			0
$69$	−7.32863	+	11.7385i	−0.882264	+	1.41315i
$70$		0			0
$71$			0.943900i			0.112020i	0.998430	+	0.0560102i	$0.0178379\pi$
$71$			0.943900i			0.112020i	−0.998430	+	0.0560102i	$0.982162\pi$
$72$		0			0
$73$	5.11210	−	8.85442i	0.598326	−	1.03633i	−0.394742	−	0.918792i	$-0.629166\pi$
$73$	5.11210	−	8.85442i	0.598326	−	1.03633i	0.993068	−	0.117540i	$-0.0375007\pi$
$74$		0			0
$75$	7.79651	−	3.77021i	0.900263	−	0.435346i
$76$		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
$81$	−3.38455	−	8.33935i	−0.376062	−	0.926595i
$82$		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
$87$	−5.29266	+	2.81682i	−0.567433	+	0.301995i
$88$		0			0
$89$	0.874507	+	1.51469i	0.0926976	+	0.160557i	0.908645	−	0.417569i	$-0.137118\pi$
$89$	0.874507	+	1.51469i	0.0926976	+	0.160557i	−0.815948	+	0.578126i	$0.803784\pi$
$90$		0			0
$91$	11.1417	+	2.44699i	1.16797	+	0.256515i
$92$		0			0
$93$	0.383799	−	11.1156i	0.0397981	−	1.15264i
$94$		0			0
$95$	0.808669	−	2.80031i	0.0829677	−	0.287306i
$96$		0			0
$97$	10.7844			1.09499			0.547494	−	0.836809i	$-0.315582\pi$
$97$	10.7844			1.09499			0.547494	+	0.836809i	$0.315582\pi$
$98$		0			0
$99$	−2.46868	+	1.20646i	−0.248112	+	0.121253i
$100$		0			0
$101$	4.92480	−	8.53000i	0.490036	−	0.848767i	−0.509898	−	0.860235i	$-0.670317\pi$
$101$	4.92480	−	8.53000i	0.490036	−	0.848767i	0.999934	+	0.0114677i	$0.00365037\pi$
$102$		0			0
$103$	−1.22897	−	2.12863i	−0.121094	−	0.209741i	0.799106	−	0.601191i	$-0.205307\pi$
$103$	−1.22897	−	2.12863i	−0.121094	−	0.209741i	−0.920199	+	0.391450i	$0.871974\pi$
$104$		0			0
$105$	8.83161	+	5.19641i	0.861877	+	0.507117i
$106$		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
$115$	−17.1640	−	4.95658i	−1.60055	−	0.462204i
$116$		0			0
$117$	7.22451	−	10.7289i	0.667907	−	0.991891i
$118$		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
$123$	8.05456	+	15.1341i	0.726255	+	1.36459i
$124$		0			0
$125$	7.43419	+	8.35062i	0.664934	+	0.746902i
$126$		0			0
$127$		−	9.73798i		−	0.864106i	−0.901848	−	0.432053i	$-0.857789\pi$
$127$		−	9.73798i		−	0.864106i	0.901848	−	0.432053i	$-0.142211\pi$
$128$		0			0
$129$	−12.5698	+	6.68980i	−1.10671	+	0.589004i
$130$		0			0
$131$	8.80008	+	15.2422i	0.768867	+	1.33172i	0.938178	+	0.346154i	$0.112512\pi$
$131$	8.80008	+	15.2422i	0.768867	+	1.33172i	−0.169311	+	0.985563i	$0.554154\pi$
$132$		0			0
$133$	3.28709	−	1.04355i	0.285027	−	0.0904874i
$134$		0			0
$135$	9.16086	−	7.14693i	0.788442	−	0.615109i
$136$		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
$145$	−5.36635	−	5.57794i	−0.445651	−	0.463223i
$146$		0			0
$147$	0.687078	+	12.1049i	0.0566692	+	0.998393i
$148$		0			0
$149$	−5.42586	+	3.13262i	−0.444504	+	0.256634i	−0.705506	−	0.708704i	$-0.749280\pi$
$149$	−5.42586	+	3.13262i	−0.444504	+	0.256634i	0.261003	+	0.965338i	$0.415947\pi$
$150$		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	−0.850170	−	0.526508i	$-0.823501\pi$
$157$	0.386973	−	0.670256i	0.0308838	−	0.0534923i	0.881054	+	0.473015i	$0.156834\pi$
$158$		0			0
$159$	3.40985	+	0.117735i	0.270419	+	0.00933699i
$160$		0			0
$161$	−6.39625	−	20.1476i	−0.504095	−	1.58785i
$162$		0			0
$163$	−5.96435	+	3.44352i	−0.467164	+	0.269717i	−0.715052	−	0.699072i	$-0.753597\pi$
$163$	−5.96435	+	3.44352i	−0.467164	+	0.269717i	0.247888	+	0.968789i	$0.420264\pi$
$164$		0			0
$165$	−2.36968	−	2.63967i	−0.184479	−	0.205498i
$166$		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
$171$	0.269723	−	3.90121i	0.0206262	−	0.298333i
$172$		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
$175$	−3.33503	+	12.8015i	−0.252104	+	0.967700i
$176$		0			0
$177$	−24.7661	−	0.855122i	−1.86154	−	0.0642749i
$178$		0			0
$179$	−16.2343	−	9.37286i	−1.21341	−	0.700561i	−0.249907	−	0.968270i	$-0.580400\pi$
$179$	−16.2343	−	9.37286i	−1.21341	−	0.700561i	−0.963500	+	0.267709i	$0.913733\pi$
$180$		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
$185$	−3.12885	+	10.8348i	−0.230037	+	0.796587i
$186$		0			0
$187$	0.245948	+	0.425995i	0.0179855	+	0.0311519i
$188$		0			0
$189$	13.0510	+	4.32112i	0.949319	+	0.314315i
$190$		0			0
$191$	−14.9979	+	8.65904i	−1.08521	+	0.626546i	−0.932297	−	0.361694i	$-0.882199\pi$
$191$	−14.9979	+	8.65904i	−1.08521	+	0.626546i	−0.152912	+	0.988240i	$0.548865\pi$
$192$		0			0
$193$	−13.1033	−	7.56517i	−0.943193	−	0.544553i	−0.0522332	−	0.998635i	$-0.516634\pi$
$193$	−13.1033	−	7.56517i	−0.943193	−	0.544553i	−0.890960	+	0.454082i	$0.849967\pi$
$194$		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
$201$	−0.723615	+	20.9574i	−0.0510398	+	1.47822i
$202$		0			0
$203$	1.96458	−	8.94517i	0.137887	−	0.627828i
$204$		0			0
$205$	−15.9498	+	15.3448i	−1.11399	+	1.07173i
$206$		0			0
$207$	−23.9117	−	1.65321i	−1.66198	−	0.114906i
$208$		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
$213$	−1.44321	+	0.768097i	−0.0988874	+	0.0526292i
$214$		0			0
$215$	−12.7448	−	13.2473i	−0.869188	−	0.903459i
$216$		0			0
$217$	12.5486	+	11.4532i	0.851857	+	0.777495i
$218$		0			0
$219$	17.6983	+	0.611084i	1.19594	+	0.0412933i
$220$		0			0
$221$	−2.00533	−	1.15778i	−0.134893	−	0.0778806i
$222$		0			0
$223$	−14.2095			−0.951541			−0.475770	−	0.879570i	$-0.657831\pi$
$223$	−14.2095			−0.951541			−0.475770	+	0.879570i	$0.657831\pi$
$224$		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
$231$	1.04128	−	4.06598i	0.0685110	−	0.267522i
$232$		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
$235$	2.69326	−	9.32639i	0.175689	−	0.608387i
$236$		0			0
$237$	−10.4902	+	16.8025i	−0.681413	+	1.09144i
$238$		0			0
$239$			17.3461i			1.12202i	0.827808	+	0.561012i	$0.189588\pi$
$239$			17.3461i			1.12202i	−0.827808	+	0.561012i	$0.810412\pi$
$240$		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
$243$	9.99662	−	11.9611i	0.641283	−	0.767304i
$244$		0			0
$245$	−14.7891	+	5.12657i	−0.944843	+	0.327524i
$246$		0			0
$247$	4.86717	−	2.81006i	0.309690	−	0.178800i
$248$		0			0
$249$	14.2997	−	7.61050i	0.906208	−	0.482296i
$250$		0			0
$251$	−6.56268			−0.414233			−0.207116	−	0.978316i	$-0.566408\pi$
$251$	−6.56268			−0.414233			−0.207116	+	0.978316i	$0.566408\pi$
$252$		0			0
$253$			7.31771i			0.460061i
$254$		0			0
$255$	−1.38951	−	1.54783i	−0.0870148	−	0.0969288i
$256$		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
$261$	−8.61379	−	5.80024i	−0.533180	−	0.359026i
$262$		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	−0.748607	−	0.663014i	$-0.769277\pi$
$269$	3.27834	−	5.67825i	0.199884	−	0.346209i	0.948491	+	0.316805i	$0.102610\pi$
$270$		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
$273$	5.32511	+	19.0268i	0.322290	+	1.15155i
$274$		0			0
$275$	2.44134	−	3.87451i	0.147218	−	0.233642i
$276$		0			0
$277$	2.40171	+	1.38663i	0.144305	+	0.0833145i	0.570414	−	0.821357i	$-0.306783\pi$
$277$	2.40171	+	1.38663i	0.144305	+	0.0833145i	−0.426109	+	0.904672i	$0.640116\pi$
$278$		0			0
$279$	17.3080	−	8.45851i	1.03620	−	0.506398i
$280$		0			0
$281$		−	22.4373i		−	1.33850i	−0.743038	−	0.669250i	$-0.766616\pi$
$281$		−	22.4373i		−	1.33850i	0.743038	−	0.669250i	$-0.233384\pi$
$282$		0			0
$283$	−3.62340	+	6.27592i	−0.215389	+	0.373064i	−0.953393	−	0.301732i	$-0.902435\pi$
$283$	−3.62340	+	6.27592i	−0.215389	+	0.373064i	0.738004	+	0.674796i	$0.235769\pi$
$284$		0			0
$285$	4.93970	−	1.04230i	0.292603	−	0.0617406i
$286$		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
$291$	8.77578	+	16.4892i	0.514445	+	0.966616i
$292$		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
$297$	−3.85355	−	2.79284i	−0.223605	−	0.162057i
$298$		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
$303$	17.0498	+	0.588695i	0.979488	+	0.0338196i
$304$		0			0
$305$	6.00585	−	20.7974i	0.343894	−	1.19086i
$306$		0			0
$307$	22.4144			1.27926			0.639630	−	0.768683i	$-0.279088\pi$
$307$	22.4144			1.27926			0.639630	+	0.768683i	$0.279088\pi$
$308$		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	$0.354518\pi$
$311$	−9.81378	+	16.9980i	−0.556488	+	0.963866i	−0.997786	+	0.0665052i	$0.978815\pi$
$312$		0			0
$313$	6.41664	+	11.1139i	0.362690	+	0.628197i	0.988403	−	0.151856i	$-0.0485251\pi$
$313$	6.41664	+	11.1139i	0.362690	+	0.628197i	−0.625713	+	0.780054i	$0.715192\pi$
$314$		0			0
$315$	−0.758547	+	17.7320i	−0.0427393	+	0.999086i
$316$		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
$325$	−0.833250	+	21.5415i	−0.0462204	+	1.19491i
$326$		0			0
$327$	6.68956	+	0.230976i	0.369934	+	0.0127730i
$328$		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
$333$	−1.04359	+	15.0943i	−0.0571885	+	0.827163i
$334$		0			0
$335$	−26.2801	+	6.49998i	−1.43584	+	0.355132i
$336$		0			0
$337$			0.304237i			0.0165729i	0.999966	+	0.00828643i	$0.00263768\pi$
$337$			0.304237i			0.0165729i	−0.999966	+	0.00828643i	$0.997362\pi$
$338$		0			0
$339$	−8.28321	−	15.5637i	−0.449882	−	0.845305i
$340$		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
$345$	−6.38858	−	30.2769i	−0.343950	−	1.63006i
$346$		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
$355$	−1.46331	−	1.52101i	−0.0776644	−	0.0807266i
$356$		0			0
$357$	0.610577	−	2.38418i	0.0323152	−	0.126184i
$358$		0			0
$359$	19.8260	−	11.4465i	1.04638	−	0.604126i	0.124743	−	0.992189i	$-0.460189\pi$
$359$	19.8260	−	11.4465i	1.04638	−	0.604126i	0.921633	+	0.388064i	$0.126856\pi$
$360$		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	$-0.560053\pi$
$367$	14.4999	−	25.1145i	0.756887	−	1.31097i	0.944431	−	0.328711i	$-0.106614\pi$
$368$		0			0
$369$	−16.5855	+	24.6307i	−0.863406	+	1.28222i
$370$		0			0
$371$	−3.51341	+	3.84944i	−0.182407	+	0.199853i
$372$		0			0
$373$	20.8113	−	12.0154i	1.07757	−	0.622136i	0.147331	−	0.989087i	$-0.452932\pi$
$373$	20.8113	−	12.0154i	1.07757	−	0.622136i	0.930240	+	0.366952i	$0.119599\pi$
$374$		0			0
$375$	−6.71846	+	18.1621i	−0.346940	+	0.937887i
$376$		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
$381$	14.8893	−	7.92427i	0.762801	−	0.405972i
$382$		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
$385$	5.41669	−	0.142362i	0.276060	−	0.00725542i
$386$		0			0
$387$	−20.4573	−	13.7753i	−1.03990	−	0.700236i
$388$		0			0
$389$	20.2730	+	11.7046i	1.02788	+	0.593448i	0.916377	−	0.400316i	$-0.131100\pi$
$389$	20.2730	+	11.7046i	1.02788	+	0.593448i	0.111504	+	0.993764i	$0.464433\pi$
$390$		0			0
$391$			4.29091i			0.217001i
$392$		0			0
$393$	−16.1441	+	25.8586i	−0.814363	+	1.30439i
$394$		0			0
$395$	−24.5685	−	7.09486i	−1.23618	−	0.356981i
$396$		0			0
$397$	5.96889	+	10.3384i	0.299570	+	0.518871i	0.976038	−	0.217602i	$-0.0698234\pi$
$397$	5.96889	+	10.3384i	0.299570	+	0.518871i	−0.676467	+	0.736473i	$0.736490\pi$
$398$		0			0
$399$	4.27045	+	4.17674i	0.213790	+	0.209099i
$400$		0			0
$401$	−21.6844	+	12.5195i	−1.08287	+	0.625193i	−0.931668	−	0.363311i	$-0.881646\pi$
$401$	−21.6844	+	12.5195i	−1.08287	+	0.625193i	−0.151198	+	0.988504i	$0.548313\pi$
$402$		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
$411$	18.0363	+	0.622754i	0.889664	+	0.0307182i
$412$		0			0
$413$	25.5183	−	27.9589i	1.25567	−	1.37577i
$414$		0			0
$415$	14.4988	+	15.0705i	0.711720	+	0.739782i
$416$		0			0
$417$	−10.8433	+	5.77096i	−0.531000	+	0.282605i
$418$		0			0
$419$	9.85560			0.481477			0.240739	−	0.970590i	$-0.422610\pi$
$419$	9.85560			0.481477			0.240739	+	0.970590i	$0.422610\pi$
$420$		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
$423$	0.898308	−	12.9929i	0.0436772	−	0.631738i
$424$		0			0
$425$	1.43154	−	2.27191i	0.0694398	−	0.110204i
$426$		0			0
$427$	24.4127	−	7.75029i	1.18141	−	0.375063i
$428$		0			0
$429$	0.236022	−	6.83571i	0.0113953	−	0.330031i
$430$		0			0
$431$	2.84702	+	1.64373i	0.137136	+	0.0791755i	0.566998	−	0.823719i	$-0.308105\pi$
$431$	2.84702	+	1.64373i	0.137136	+	0.0791755i	−0.429862	+	0.902894i	$0.641438\pi$
$432$		0			0
$433$	−31.9717			−1.53646			−0.768231	−	0.640173i	$-0.778863\pi$
$433$	−31.9717			−1.53646			−0.768231	+	0.640173i	$0.778863\pi$
$434$		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
$441$	−17.9491	+	10.9009i	−0.854720	+	0.519089i
$442$		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
$445$	−3.75738	−	1.08505i	−0.178117	−	0.0514364i
$446$		0			0
$447$	−9.20503	−	5.74692i	−0.435383	−	0.271820i
$448$		0			0
$449$		−	40.0091i		−	1.88815i	−0.329737	−	0.944073i	$-0.606960\pi$
$449$		−	40.0091i		−	1.88815i	0.329737	−	0.944073i	$-0.393040\pi$
$450$		0			0
$451$	7.85112	+	4.53285i	0.369695	+	0.213444i
$452$		0			0
$453$	30.6591	+	1.05859i	1.44049	+	0.0497370i
$454$		0			0
$455$	−21.7473	+	13.3296i	−1.01953	+	0.624904i
$456$		0			0
$457$	9.86127	−	5.69340i	0.461291	−	0.266326i	−0.251296	−	0.967910i	$-0.580857\pi$
$457$	9.86127	−	5.69340i	0.461291	−	0.266326i	0.712587	+	0.701584i	$0.247523\pi$
$458$		0			0
$459$	−2.25962	−	1.63765i	−0.105470	−	0.0764388i
$460$		0			0
$461$	8.71020			0.405674			0.202837	−	0.979212i	$-0.434984\pi$
$461$	8.71020			0.405674			0.202837	+	0.979212i	$0.434984\pi$
$462$		0			0
$463$			16.1154i			0.748944i	0.927238	+	0.374472i	$0.122176\pi$
$463$			16.1154i			0.748944i	−0.927238	+	0.374472i	$0.877824\pi$
$464$		0			0
$465$	16.6139	+	18.5068i	0.770451	+	0.858233i
$466$		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
$471$	1.33971	+	0.0462575i	0.0617308	+	0.00213143i
$472$		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	$-0.627087\pi$
$479$	13.2092	−	22.8791i	0.603546	−	1.04537i	0.992279	−	0.124022i	$-0.0395794\pi$
$480$		0			0
$481$	−18.8317	+	10.8725i	−0.858652	+	0.495743i
$482$		0			0
$483$	25.6005	−	26.1749i	1.16486	−	1.19100i
$484$		0			0
$485$	−17.3780	+	16.7188i	−0.789096	+	0.759163i
$486$		0			0
$487$	−7.93392	−	4.58065i	−0.359520	−	0.207569i	0.309350	−	0.950948i	$-0.399889\pi$
$487$	−7.93392	−	4.58065i	−0.359520	−	0.207569i	−0.668870	+	0.743379i	$0.733222\pi$
$488$		0			0
$489$	−10.1186	−	6.31727i	−0.457578	−	0.285677i
$490$		0			0
$491$			33.0800i			1.49288i	0.665453	+	0.746440i	$0.268239\pi$
$491$			33.0800i			1.49288i	−0.665453	+	0.746440i	$0.731761\pi$
$492$		0			0
$493$	−0.929529	+	1.60999i	−0.0418639	+	0.0725104i
$494$		0			0
$495$	2.10770	−	5.77124i	0.0947342	−	0.259398i
$496$		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
$501$	−14.5210	+	7.72824i	−0.648749	+	0.345272i
$502$		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
$507$	4.54828	+	8.54599i	0.201996	+	0.379541i
$508$		0			0
$509$	15.5918	+	27.0059i	0.691096	+	1.19701i	0.971479	+	0.237125i	$0.0762052\pi$
$509$	15.5918	+	27.0059i	0.691096	+	1.19701i	−0.280383	+	0.959888i	$0.590461\pi$
$510$		0			0
$511$	−18.2358	+	19.9799i	−0.806704	+	0.883859i
$512$		0			0
$513$	6.18441	−	2.76220i	0.273048	−	0.121954i
$514$		0			0
$515$	5.28035	+	1.52485i	0.232680	+	0.0671929i
$516$		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	$-0.508502\pi$
$521$	19.4555	−	33.6980i	0.852363	−	1.47634i	0.879070	−	0.476693i	$-0.158165\pi$
$522$		0			0
$523$	−1.88123	−	3.25839i	−0.0822606	−	0.142480i	0.821960	−	0.569545i	$-0.192881\pi$
$523$	−1.88123	−	3.25839i	−0.0822606	−	0.142480i	−0.904221	+	0.427066i	$0.859547\pi$
$524$		0			0
$525$	−22.2872	+	5.31795i	−0.972693	+	0.232094i
$526$		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
$535$	−3.22163	−	0.930338i	−0.139283	−	0.0402220i
$536$		0			0
$537$	1.12040	−	32.4492i	0.0483489	−	1.40029i
$538$		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
$543$	−24.6204	+	13.1033i	−1.05656	+	0.562316i
$544$		0			0
$545$	2.07478	+	8.38856i	0.0888739	+	0.359326i
$546$		0			0
$547$			13.4516i			0.575148i	0.957758	+	0.287574i	$0.0928487\pi$
$547$			13.4516i			0.575148i	−0.957758	+	0.287574i	$0.907151\pi$
$548$		0			0
$549$	2.00319	−	28.9737i	0.0854939	−	1.23657i
$550$		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
$555$	−19.1123	+	4.03280i	−0.811274	+	0.171183i
$556$		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
$565$	16.4026	−	15.7804i	0.690063	−	0.663887i
$566$		0			0
$567$	4.01327	+	23.4711i	0.168541	+	0.985695i
$568$		0			0
$569$	0.744706	−	0.429956i	0.0312197	−	0.0180247i	−0.484309	−	0.874897i	$-0.660929\pi$
$569$	0.744706	−	0.429956i	0.0312197	−	0.0180247i	0.515529	+	0.856872i	$0.327596\pi$
$570$		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	$0.346334\pi$
$577$	−12.8498	+	22.2565i	−0.534944	+	0.926550i	−0.999166	+	0.0408310i	$0.986999\pi$
$578$		0			0
$579$	0.904316	−	26.1909i	0.0375821	−	1.08846i
$580$		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
$585$	4.99123	+	28.4887i	0.206362	+	1.17786i
$586$		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
$591$	15.1591	+	28.4831i	0.623560	+	1.17164i
$592$		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
$595$	3.17620	−	0.0834771i	0.130212	−	0.00342223i
$596$		0			0
$597$	0.600622	−	17.3953i	0.0245818	−	0.711942i
$598$		0			0
$599$	37.6990	+	21.7655i	1.54034	+	0.889314i	0.998817	+	0.0486270i	$0.0154846\pi$
$599$	37.6990	+	21.7655i	1.54034	+	0.889314i	0.541521	+	0.840687i	$0.317849\pi$
$600$		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
$605$	21.8290	+	6.30374i	0.887474	+	0.256284i
$606$		0			0
$607$	5.31663	+	9.20867i	0.215795	+	0.373768i	0.953518	−	0.301335i	$-0.0974323\pi$
$607$	5.31663	+	9.20867i	0.215795	+	0.373768i	−0.737723	+	0.675103i	$0.764099\pi$
$608$		0			0
$609$	15.2758	−	4.27529i	0.619005	−	0.173244i
$610$		0			0
$611$	16.2100	−	9.35886i	0.655788	−	0.378619i
$612$		0			0
$613$	13.1068	+	7.56721i	0.529378	+	0.305637i	0.740763	−	0.671766i	$-0.234464\pi$
$613$	13.1068	+	7.56721i	0.529378	+	0.305637i	−0.211385	+	0.977403i	$0.567797\pi$
$614$		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
$621$	−16.9304	−	37.9061i	−0.679394	−	1.52112i
$622$		0			0
$623$	−1.40021	−	4.41053i	−0.0560983	−	0.176704i
$624$		0			0
$625$	−24.9253	−	1.93116i	−0.997012	−	0.0772465i
$626$		0			0
$627$	−0.971526	−	1.82545i	−0.0387990	−	0.0729013i
$628$		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
$633$	−1.37192	−	2.57776i	−0.0545288	−	0.102457i
$634$		0			0
$635$	15.0966	+	15.6918i	0.599090	+	0.622712i
$636$		0			0
$637$	−27.4032	−	12.6469i	−1.08575	−	0.501087i
$638$		0			0
$639$	−2.34883	−	1.58162i	−0.0929182	−	0.0625681i
$640$		0			0
$641$	12.2389	+	7.06611i	0.483406	+	0.279094i	0.721835	−	0.692065i	$-0.243299\pi$
$641$	12.2389	+	7.06611i	0.483406	+	0.279094i	−0.238429	+	0.971160i	$0.576632\pi$
$642$		0			0
$643$	−17.9278			−0.707005			−0.353503	−	0.935434i	$-0.615009\pi$
$643$	−17.9278			−0.707005			−0.353503	+	0.935434i	$0.615009\pi$
$644$		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
$651$	−7.30044	+	28.5068i	−0.286127	+	1.11727i
$652$		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
$655$	−37.8102	−	10.9188i	−1.47737	−	0.426632i
$656$		0			0
$657$	13.4676	+	27.5578i	0.525422	+	1.07513i
$658$		0			0
$659$			5.09127i			0.198328i	0.995071	+	0.0991638i	$0.0316168\pi$
$659$			5.09127i			0.198328i	−0.995071	+	0.0991638i	$0.968383\pi$
$660$		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
$663$	0.138397	−	4.00827i	0.00537490	−	0.155669i
$664$		0			0
$665$	−3.67904	+	6.77750i	−0.142667	+	0.262820i
$666$		0			0
$667$	−23.9511	+	13.8282i	−0.927389	+	0.535429i
$668$		0			0
$669$	−11.5630	−	21.7262i	−0.447051	−	0.839985i
$670$		0			0
$671$	−8.86682			−0.342300
$672$		0			0
$673$			8.51862i			0.328369i	0.986430	+	0.164184i	$0.0524992\pi$
$673$			8.51862i			0.328369i	−0.986430	+	0.164184i	$0.947501\pi$
$674$		0			0
$675$	−3.68214	+	25.7185i	−0.141725	+	0.989906i
$676$		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
$681$	0.0407473	−	1.18013i	0.00156144	−	0.0452226i
$682$		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
$693$	7.06419	−	1.71659i	0.268346	−	0.0652077i
$694$		0			0
$695$	−10.9943	−	11.4278i	−0.417038	−	0.433481i
$696$		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	$0.116662\pi$
$701$			18.9758i			0.716706i	−0.933586	+	0.358353i	$0.883338\pi$
$702$		0			0
$703$	−3.28709	+	5.69340i	−0.123975	+	0.214731i
$704$		0			0
$705$	16.4516	−	3.47137i	0.619603	−	0.130739i
$706$		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
$711$	−34.2273	−	2.36641i	−1.28362	−	0.0887475i
$712$		0			0
$713$		−	51.3048i		−	1.92138i
$714$		0			0
$715$	8.57182	−	2.12011i	0.320568	−	0.0792875i
$716$		0			0
$717$	−26.5220	+	14.1153i	−0.990482	+	0.527147i
$718$		0			0
$719$	−6.70106	−	11.6066i	−0.249907	−	0.432852i	0.713593	−	0.700561i	$-0.247067\pi$
$719$	−6.70106	−	11.6066i	−0.249907	−	0.432852i	−0.963500	+	0.267709i	$0.913733\pi$
$720$		0			0
$721$	1.96775	+	6.19823i	0.0732829	+	0.230834i
$722$		0			0
$723$	−0.0912936	+	2.64406i	−0.00339525	+	0.0983335i
$724$		0			0
$725$	17.2948	+	0.668979i	0.642311	+	0.0248453i
$726$		0			0
$727$	4.88627			0.181222			0.0906109	−	0.995886i	$-0.471118\pi$
$727$	4.88627			0.181222			0.0906109	+	0.995886i	$0.471118\pi$
$728$		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	$-0.927278\pi$
$733$	−18.4955	−	32.0351i	−0.683145	−	1.18324i	0.290871	−	0.956762i	$-0.406055\pi$
$734$		0			0
$735$	−19.8731	−	18.4407i	−0.733031	−	0.680196i
$736$		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
$745$	3.88682	−	13.4595i	0.142402	−	0.493119i
$746$		0			0
$747$	23.2728	+	15.6711i	0.851506	+	0.573376i
$748$		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
$753$	−5.34037	−	10.0343i	−0.194614	−	0.365669i
$754$		0			0
$755$	9.50897	+	38.4458i	0.346067	+	1.39918i
$756$		0			0
$757$		−	40.3111i		−	1.46513i	−0.680697	−	0.732565i	$-0.738323\pi$
$757$		−	40.3111i		−	1.46513i	0.680697	−	0.732565i	$-0.261677\pi$
$758$		0			0
$759$	−11.1887	+	5.95478i	−0.406125	+	0.216145i
$760$		0			0
$761$	−9.76529	−	16.9140i	−0.353991	−	0.613131i	0.632953	−	0.774190i	$-0.281842\pi$
$761$	−9.76529	−	16.9140i	−0.353991	−	0.613131i	−0.986945	+	0.161059i	$0.948509\pi$
$762$		0			0
$763$	−6.89272	+	7.55196i	−0.249533	+	0.273399i
$764$		0			0
$765$	1.23590	−	3.38410i	0.0446841	−	0.122352i
$766$		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
$775$	−17.1164	+	27.1644i	−0.614838	+	0.975773i
$776$		0			0
$777$	−16.5229	−	16.1603i	−0.592756	−	0.579749i
$778$		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	−0.918450	−	0.395536i	$-0.870559\pi$
$787$	−3.27330	+	5.66953i	−0.116681	+	0.202097i	0.801770	+	0.597633i	$0.203892\pi$
$788$		0			0
$789$	9.20848	+	0.317949i	0.327831	+	0.0113193i
$790$		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
$795$	−5.67718	+	5.09651i	−0.201349	+	0.180755i
$796$		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
$801$	−5.23455	−	0.361907i	−0.184954	−	0.0127874i
$802$		0			0
$803$	8.10980	−	4.68219i	0.286189	−	0.165231i
$804$		0			0
$805$	41.5414	+	22.5499i	1.46414	+	0.794781i
$806$		0			0
$807$	11.3497	+	0.391882i	0.399530	+	0.0137949i
$808$		0			0
$809$	−1.41519	−	0.817063i	−0.0497556	−	0.0287264i	0.474916	−	0.880031i	$-0.342478\pi$
$809$	−1.41519	−	0.817063i	−0.0497556	−	0.0287264i	−0.524671	+	0.851305i	$0.675812\pi$
$810$		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
$815$	4.27257	−	14.7953i	0.149662	−	0.518257i
$816$		0			0
$817$	−5.35805	−	9.28042i	−0.187454	−	0.324681i
$818$		0			0
$819$	−24.7585	+	23.6251i	−0.865131	+	0.825526i
$820$		0			0
$821$	19.6357	−	11.3367i	0.685292	−	0.395654i	−0.116554	−	0.993184i	$-0.537185\pi$
$821$	19.6357	−	11.3367i	0.685292	−	0.395654i	0.801846	+	0.597531i	$0.203851\pi$
$822$		0			0
$823$	−16.6180	−	9.59438i	−0.579266	−	0.334439i	0.181576	−	0.983377i	$-0.441880\pi$
$823$	−16.6180	−	9.59438i	−0.579266	−	0.334439i	−0.760841	+	0.648938i	$0.775214\pi$
$824$		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
$831$	−0.165753	+	4.80057i	−0.00574992	+	0.166530i
$832$		0			0
$833$	2.16846	+	3.07101i	0.0751327	+	0.106404i
$834$		0			0
$835$	−14.7232	−	15.3037i	−0.509516	−	0.529605i
$836$		0			0
$837$	27.0174	+	19.5807i	0.933857	+	0.676809i
$838$		0			0
$839$	2.88841			0.0997192			0.0498596	−	0.998756i	$-0.484123\pi$
$839$	2.88841			0.0997192			0.0498596	+	0.998756i	$0.484123\pi$
$840$		0			0
$841$	17.0178			0.586819
$842$		0			0
$843$	34.3065	−	18.2584i	1.18158	−	0.628851i
$844$		0			0
$845$	−9.00663	+	8.66498i	−0.309838	+	0.298084i
$846$		0			0
$847$	8.13470	+	25.6235i	0.279512	+	0.880435i
$848$		0			0
$849$	−12.5444	−	0.433130i	−0.430521	−	0.0148650i
$850$		0			0
$851$	34.8966	+	20.1476i	1.19624	+	0.690650i
$852$		0			0
$853$	49.3673			1.69031			0.845153	−	0.534525i	$-0.179509\pi$
$853$	49.3673			1.69031			0.845153	+	0.534525i	$0.179509\pi$
$854$		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
$861$	−12.2250	−	43.6803i	−0.416626	−	1.48862i
$862$		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
$865$	7.41342	−	25.6716i	0.252064	−	0.872862i
$866$		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
$873$	−18.0706	+	26.8362i	−0.611597	+	0.908267i
$874$		0			0
$875$	−14.4718	−	25.7986i	−0.489236	−	0.872152i
$876$		0			0
$877$	6.27005	−	3.62002i	0.211725	−	0.122239i	−0.390388	−	0.920650i	$-0.627659\pi$
$877$	6.27005	−	3.62002i	0.211725	−	0.122239i	0.602113	+	0.798411i	$0.294326\pi$
$878$		0			0
$879$	40.0116	−	21.2947i	1.34956	−	0.718252i
$880$		0			0
$881$	−25.9119			−0.872993			−0.436496	−	0.899706i	$-0.643781\pi$
$881$	−25.9119			−0.872993			−0.436496	+	0.899706i	$0.643781\pi$
$882$		0			0
$883$			17.5664i			0.591155i	0.955319	+	0.295577i	$0.0955120\pi$
$883$			17.5664i			0.591155i	−0.955319	+	0.295577i	$0.904488\pi$
$884$		0			0
$885$	41.2340	−	37.0165i	1.38607	−	1.24430i
$886$		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
$891$	1.13441	−	8.16471i	0.0380041	−	0.273528i
$892$		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
$903$	36.2791	−	10.1536i	1.20729	−	0.337890i
$904$		0			0
$905$	−24.9632	−	25.9475i	−0.829806	−	0.862524i
$906$		0			0
$907$	−25.3957	−	14.6622i	−0.843250	−	0.486851i	0.0151176	−	0.999886i	$-0.495188\pi$
$907$	−25.3957	−	14.6622i	−0.843250	−	0.486851i	−0.858368	+	0.513035i	$0.828521\pi$
$908$		0			0
$909$	12.9742	+	26.5481i	0.430326	+	0.880545i
$910$		0			0
$911$		−	30.3043i		−	1.00403i	−0.864860	−	0.502013i	$-0.832593\pi$
$911$		−	30.3043i		−	1.00403i	0.864860	−	0.502013i	$-0.167407\pi$
$912$		0			0
$913$	4.28295	−	7.41828i	0.141745	−	0.245509i
$914$		0			0
$915$	36.6864	−	7.74100i	1.21281	−	0.255909i
$916$		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
$921$	18.2397	+	34.2715i	0.601019	+	1.12928i
$922$		0			0
$923$		−	4.06965i		−	0.133954i
$924$		0			0
$925$	−11.7551	−	22.3098i	−0.386505	−	0.733541i
$926$		0			0
$927$	7.35624	+	0.508597i	0.241611	+	0.0167045i
$928$		0			0
$929$	8.62508	+	14.9391i	0.282980	+	0.490135i	0.972117	−	0.234495i	$-0.0753438\pi$
$929$	8.62508	+	14.9391i	0.282980	+	0.490135i	−0.689138	+	0.724631i	$0.742010\pi$
$930$		0			0
$931$	−9.08663	+	0.831132i	−0.297802	+	0.0272393i
$932$		0			0
$933$	−33.9757	−	1.17311i	−1.11231	−	0.0384058i
$934$		0			0
$935$	−1.05673	−	0.305162i	−0.0345589	−	0.00997987i
$936$		0			0
$937$	36.0492			1.17768			0.588839	−	0.808251i	$-0.299585\pi$
$937$	36.0492			1.17768			0.588839	+	0.808251i	$0.299585\pi$
$938$		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	$0.339085\pi$
$941$	−15.8153	+	27.3930i	−0.515565	+	0.892985i	−0.999837	+	0.0180673i	$0.994249\pi$
$942$		0			0
$943$	39.5409	+	68.4869i	1.28763	+	2.23024i
$944$		0			0
$945$	−27.7294	+	13.2696i	−0.902036	+	0.431660i
$946$		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
$955$	10.7438	−	37.2042i	0.347660	−	1.20390i
$956$		0			0
$957$	−5.48808	−	0.189492i	−0.177405	−	0.00612540i
$958$		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
$963$	−4.48817	−	0.310304i	−0.144629	−	0.00999941i
$964$		0			0
$965$	32.8428	−	8.12316i	1.05725	−	0.261494i
$966$		0			0
$967$			6.75930i			0.217364i	0.994077	+	0.108682i	$0.0346631\pi$
$967$			6.75930i			0.217364i	−0.994077	+	0.108682i	$0.965337\pi$
$968$		0			0
$969$	−0.569677	−	1.07039i	−0.0183007	−	0.0343860i
$970$		0			0
$971$	−21.9851	−	38.0793i	−0.705535	−	1.22202i	−0.966498	−	0.256674i	$-0.917373\pi$
$971$	−21.9851	−	38.0793i	−0.705535	−	1.22202i	0.260963	−	0.965349i	$-0.415960\pi$
$972$		0			0
$973$	4.02493	−	18.3264i	0.129033	−	0.587517i
$974$		0			0
$975$	−33.6149	+	16.2554i	−1.07654	+	0.520589i
$976$		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
$985$	−30.0184	+	28.8797i	−0.956465	+	0.920183i
$986$		0			0
$987$	14.2227	+	13.9106i	0.452712	+	0.442778i
$988$		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	−0.989915	−	0.141666i	$-0.954754\pi$
$997$	−11.7546	+	20.3595i	−0.372271	+	0.644792i	0.617644	+	0.786458i	$0.288087\pi$
$998$		0			0
$999$	−23.9283	+	10.6873i	−0.757057	+	0.338132i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.813749 + 1.52899i) q^{3} +(-1.61141 + 1.55028i) q^{5} +(-2.58416 - 0.567546i) q^{7} +(-1.67563 + 2.48843i) q^{9} +(0.793196 + 0.457952i) q^{11} -4.31153 q^{13} +(-3.68164 - 1.20229i) q^{15} +(0.465109 + 0.268531i) q^{17} +(-1.12887 + 0.651755i) q^{19} +(-1.23509 - 4.41300i) q^{21} +(3.99480 + 6.91920i) q^{23} +(0.193261 - 4.99626i) q^{25} +(-5.16832 - 0.537062i) q^{27} +3.46154i q^{29} +(-5.56113 - 3.21072i) q^{31} +(-0.0547421 + 1.58545i) q^{33} +(5.04399 - 3.09163i) q^{35} +(4.36775 - 2.52172i) q^{37} +(-3.50850 - 6.59229i) q^{39} +9.89809 q^{41} +8.22096i q^{43} +(-1.15765 - 6.60756i) q^{45} +(-3.75969 + 2.17066i) q^{47} +(6.35578 + 2.93326i) q^{49} +(-0.0320993 + 0.929664i) q^{51} +(0.984927 - 1.70594i) q^{53} +(-1.98812 + 0.491730i) q^{55} +(-1.91514 - 1.19567i) q^{57} +(-7.15363 + 12.3904i) q^{59} +(-8.38395 + 4.84048i) q^{61} +(5.74239 - 5.47951i) q^{63} +(6.94763 - 6.68408i) q^{65} +(10.4850 + 6.05349i) q^{67} +(-7.32863 + 11.7385i) q^{69} +0.943900i q^{71} +(5.11210 - 8.85442i) q^{73} +(7.79651 - 3.77021i) q^{75} +(-1.78984 - 1.63360i) q^{77} +(5.71817 + 9.90416i) q^{79} +(-3.38455 - 8.33935i) q^{81} -9.35240i q^{83} +(-1.16578 + 0.288337i) q^{85} +(-5.29266 + 2.81682i) q^{87} +(0.874507 + 1.51469i) q^{89} +(11.1417 + 2.44699i) q^{91} +(0.383799 - 11.1156i) q^{93} +(0.808669 - 2.80031i) q^{95} +10.7844 q^{97} +(-2.46868 + 1.20646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{15} + 12 q^{19} - 8 q^{21} + 6 q^{25} - 12 q^{31} + 24 q^{39} + 33 q^{45} - 44 q^{49} - 10 q^{51} - 24 q^{61} + 21 q^{75} - 28 q^{79} - 20 q^{81} - 4 q^{85} + 16 q^{91} - 28 q^{99}+O(q^{100}) \) 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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