LMFDB - Embedded newform 616.2.r.f.113.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [616,2,Mod(113,616)] 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("616.113"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(616, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.r (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 21 x^{18} - 58 x^{17} + 225 x^{16} - 348 x^{15} + 1296 x^{14} - 755 x^{13} + \cdots + 10000 $ x^20 - 4x^19 + 21x^18 - 58x^17 + 225x^16 - 348x^15 + 1296x^14 - 755x^13 + 6557x^12 - 5753x^11 + 29289x^10 - 14174x^9 + 85487x^8 + 13430x^7 + 191109x^6 + 166407x^5 + 212971x^4 - 179670x^3 + 72900x^2 - 3000*x + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			113.3
Root			$0.425479 - 0.309129i$ of defining polynomial
Character	$\chi$	$=$	616.113
Dual form			616.2.r.f.169.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.162519 - 0.500181i) q^{3} +(-1.76076 - 1.27927i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(2.20328 - 1.60078i) q^{9} +(0.817183 - 3.21438i) q^{11} +(-4.14760 + 3.01341i) q^{13} +(-0.353708 + 1.08860i) q^{15} +(1.32207 + 0.960538i) q^{17} +(-1.67759 - 5.16308i) q^{19} +0.525921 q^{21} -8.91765 q^{23} +(-0.0813342 - 0.250321i) q^{25} +(-2.43519 - 1.76927i) q^{27} +(2.05779 - 6.33324i) q^{29} +(-7.29287 + 5.29858i) q^{31} +(-1.74058 + 0.113657i) q^{33} +(1.76076 - 1.27927i) q^{35} +(2.14635 - 6.60578i) q^{37} +(2.18131 + 1.58481i) q^{39} +(-0.417802 - 1.28586i) q^{41} -1.96423 q^{43} -5.92727 q^{45} +(-0.270521 - 0.832577i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(0.265582 - 0.817378i) q^{51} +(1.98977 - 1.44565i) q^{53} +(-5.55091 + 4.61435i) q^{55} +(-2.30983 + 1.67819i) q^{57} +(0.640906 - 1.97251i) q^{59} +(12.0238 + 8.73579i) q^{61} +(0.841579 + 2.59011i) q^{63} +11.1579 q^{65} -13.4064 q^{67} +(1.44928 + 4.46043i) q^{69} +(6.02676 + 4.37870i) q^{71} +(-1.10888 + 3.41278i) q^{73} +(-0.111987 + 0.0813636i) q^{75} +(2.80453 + 1.77048i) q^{77} +(10.9314 - 7.94209i) q^{79} +(2.03555 - 6.26477i) q^{81} +(-1.93890 - 1.40869i) q^{83} +(-1.09906 - 3.38255i) q^{85} -3.50219 q^{87} +14.3192 q^{89} +(-1.58424 - 4.87579i) q^{91} +(3.83547 + 2.78663i) q^{93} +(-3.65113 + 11.2370i) q^{95} +(-10.1758 + 7.39317i) q^{97} +(-3.34502 - 8.39031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{3} + 5 q^{7} - 6 q^{9} - 3 q^{11} + 2 q^{13} + 8 q^{15} + 21 q^{19} + 6 q^{21} - 6 q^{23} - 7 q^{25} + 32 q^{27} + 6 q^{29} - 18 q^{31} - 16 q^{33} + 5 q^{37} + 12 q^{39} - 12 q^{41} - 42 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) $ 20 * q - q^3 + 5 * q^7 - 6 * q^9 - 3 * q^11 + 2 * q^13 + 8 * q^15 + 21 * q^19 + 6 * q^21 - 6 * q^23 - 7 * q^25 + 32 * q^27 + 6 * q^29 - 18 * q^31 - 16 * q^33 + 5 * q^37 + 12 * q^39 - 12 * q^41 - 42 * q^43 + 18 * q^45 + 3 * q^47 - 5 * q^49 - q^51 - 38 * q^53 - 15 * q^55 - 3 * q^57 + 36 * q^59 + 23 * q^61 + 11 * q^63 - 30 * q^65 - 2 * q^67 + 43 * q^69 + 48 * q^71 + 6 * q^73 - 67 * q^75 - 17 * q^77 + 43 * q^79 + 16 * q^81 + 5 * q^83 - 16 * q^85 - 16 * q^87 - 46 * q^89 - 2 * q^91 + q^93 + 44 * q^95 + 9 * q^97 - 57 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$	$1$

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
$3$	−0.162519	−	0.500181i	−0.0938301	−	0.288779i	0.893117	−	0.449825i	$-0.148514\pi$
$3$	−0.162519	−	0.500181i	−0.0938301	−	0.288779i	−0.986947	+	0.161045i	$0.948514\pi$
$4$		0			0
$5$	−1.76076	−	1.27927i	−0.787436	−	0.572105i	0.119766	−	0.992802i	$-0.461786\pi$
$5$	−1.76076	−	1.27927i	−0.787436	−	0.572105i	−0.907201	+	0.420697i	$0.861786\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$		0			0
$9$	2.20328	−	1.60078i	0.734428	−	0.533593i
$10$		0			0
$11$	0.817183	−	3.21438i	0.246390	−	0.969171i
$11$	0.817183	−	3.21438i	0.246390	−	0.969171i
$12$		0			0
$13$	−4.14760	+	3.01341i	−1.15034	+	0.835768i	−0.988526	−	0.151054i	$-0.951733\pi$
$13$	−4.14760	+	3.01341i	−1.15034	+	0.835768i	−0.161811	+	0.986822i	$0.551733\pi$
$14$		0			0
$15$	−0.353708	+	1.08860i	−0.0913271	+	0.281076i
$16$		0			0
$17$	1.32207	+	0.960538i	0.320649	+	0.232965i	0.736452	−	0.676490i	$-0.236500\pi$
$17$	1.32207	+	0.960538i	0.320649	+	0.232965i	−0.415804	+	0.909454i	$0.636500\pi$
$18$		0			0
$19$	−1.67759	−	5.16308i	−0.384865	−	1.18449i	−0.936578	−	0.350459i	$-0.886026\pi$
$19$	−1.67759	−	5.16308i	−0.384865	−	1.18449i	0.551713	−	0.834034i	$-0.313974\pi$
$20$		0			0
$21$	0.525921			0.114765
$22$		0			0
$23$	−8.91765			−1.85946			−0.929729	−	0.368245i	$-0.879959\pi$
$23$	−8.91765			−1.85946			−0.929729	+	0.368245i	$0.879959\pi$
$24$		0			0
$25$	−0.0813342	−	0.250321i	−0.0162668	−	0.0500642i
$26$		0			0
$27$	−2.43519	−	1.76927i	−0.468652	−	0.340496i
$28$		0			0
$29$	2.05779	−	6.33324i	0.382123	−	1.17605i	−0.556423	−	0.830899i	$-0.687827\pi$
$29$	2.05779	−	6.33324i	0.382123	−	1.17605i	0.938546	−	0.345154i	$-0.112173\pi$
$30$		0			0
$31$	−7.29287	+	5.29858i	−1.30984	+	0.951653i	−0.309838	+	0.950789i	$0.600275\pi$
$31$	−7.29287	+	5.29858i	−1.30984	+	0.951653i	−1.00000		0.000863210i	$0.999725\pi$
$32$		0			0
$33$	−1.74058	+	0.113657i	−0.302995	+	0.0197851i
$34$		0			0
$35$	1.76076	−	1.27927i	0.297623	−	0.216236i
$36$		0			0
$37$	2.14635	−	6.60578i	0.352857	−	1.08598i	−0.604384	−	0.796693i	$-0.706581\pi$
$37$	2.14635	−	6.60578i	0.352857	−	1.08598i	0.957241	−	0.289290i	$-0.0934192\pi$
$38$		0			0
$39$	2.18131	+	1.58481i	0.349289	+	0.253773i
$40$		0			0
$41$	−0.417802	−	1.28586i	−0.0652497	−	0.200818i	0.913116	−	0.407699i	$-0.133669\pi$
$41$	−0.417802	−	1.28586i	−0.0652497	−	0.200818i	−0.978366	+	0.206881i	$0.933669\pi$
$42$		0			0
$43$	−1.96423			−0.299542			−0.149771	−	0.988721i	$-0.547854\pi$
$43$	−1.96423			−0.299542			−0.149771	+	0.988721i	$0.547854\pi$
$44$		0			0
$45$	−5.92727			−0.883586
$46$		0			0
$47$	−0.270521	−	0.832577i	−0.0394595	−	0.121444i	0.929386	−	0.369108i	$-0.120337\pi$
$47$	−0.270521	−	0.832577i	−0.0394595	−	0.121444i	−0.968846	+	0.247665i	$0.920337\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	0.265582	−	0.817378i	0.0371889	−	0.114456i
$52$		0			0
$53$	1.98977	−	1.44565i	0.273316	−	0.198576i	−0.442681	−	0.896679i	$-0.645973\pi$
$53$	1.98977	−	1.44565i	0.273316	−	0.198576i	0.715997	+	0.698104i	$0.245973\pi$
$54$		0			0
$55$	−5.55091	+	4.61435i	−0.748484	+	0.622199i
$56$		0			0
$57$	−2.30983	+	1.67819i	−0.305945	+	0.222282i
$58$		0			0
$59$	0.640906	−	1.97251i	0.0834388	−	0.256798i	−0.900630	−	0.434587i	$-0.856894\pi$
$59$	0.640906	−	1.97251i	0.0834388	−	0.256798i	0.984069	+	0.177789i	$0.0568943\pi$
$60$		0			0
$61$	12.0238	+	8.73579i	1.53949	+	1.11850i	0.950656	+	0.310248i	$0.100412\pi$
$61$	12.0238	+	8.73579i	1.53949	+	1.11850i	0.588832	+	0.808255i	$0.299588\pi$
$62$		0			0
$63$	0.841579	+	2.59011i	0.106029	+	0.326324i
$64$		0			0
$65$	11.1579			1.38396
$66$		0			0
$67$	−13.4064			−1.63785			−0.818927	−	0.573898i	$-0.805431\pi$
$67$	−13.4064			−1.63785			−0.818927	+	0.573898i	$0.805431\pi$
$68$		0			0
$69$	1.44928	+	4.46043i	0.174473	+	0.536973i
$70$		0			0
$71$	6.02676	+	4.37870i	0.715245	+	0.519656i	0.884861	−	0.465854i	$-0.154253\pi$
$71$	6.02676	+	4.37870i	0.715245	+	0.519656i	−0.169616	+	0.985510i	$0.554253\pi$
$72$		0			0
$73$	−1.10888	+	3.41278i	−0.129785	+	0.399436i	−0.994742	−	0.102408i	$-0.967345\pi$
$73$	−1.10888	+	3.41278i	−0.129785	+	0.399436i	0.864958	+	0.501845i	$0.167345\pi$
$74$		0			0
$75$	−0.111987	+	0.0813636i	−0.0129312	+	0.00939506i
$76$		0			0
$77$	2.80453	+	1.77048i	0.319606	+	0.201765i
$78$		0			0
$79$	10.9314	−	7.94209i	1.22987	−	0.893555i	0.232993	−	0.972478i	$-0.425148\pi$
$79$	10.9314	−	7.94209i	1.22987	−	0.893555i	0.996881	+	0.0789231i	$0.0251482\pi$
$80$		0			0
$81$	2.03555	−	6.26477i	0.226172	−	0.696085i
$82$		0			0
$83$	−1.93890	−	1.40869i	−0.212822	−	0.154624i	0.476268	−	0.879300i	$-0.341989\pi$
$83$	−1.93890	−	1.40869i	−0.212822	−	0.154624i	−0.689089	+	0.724676i	$0.741989\pi$
$84$		0			0
$85$	−1.09906	−	3.38255i	−0.119210	−	0.366890i
$86$		0			0
$87$	−3.50219			−0.375475
$88$		0			0
$89$	14.3192			1.51783			0.758914	−	0.651191i	$-0.225730\pi$
$89$	14.3192			1.51783			0.758914	+	0.651191i	$0.225730\pi$
$90$		0			0
$91$	−1.58424	−	4.87579i	−0.166074	−	0.511122i
$92$		0			0
$93$	3.83547	+	2.78663i	0.397720	+	0.288960i
$94$		0			0
$95$	−3.65113	+	11.2370i	−0.374598	+	1.15289i
$96$		0			0
$97$	−10.1758	+	7.39317i	−1.03320	+	0.750663i	−0.968946	−	0.247271i	$-0.920466\pi$
$97$	−10.1758	+	7.39317i	−1.03320	+	0.750663i	−0.0642523	+	0.997934i	$0.520466\pi$
$98$		0			0
$99$	−3.34502	−	8.39031i	−0.336187	−	0.843258i
$100$		0			0
$101$	13.3511	−	9.70014i	1.32848	−	0.965200i	0.328700	−	0.944434i	$-0.393390\pi$
$101$	13.3511	−	9.70014i	1.32848	−	0.965200i	0.999784	−	0.0207660i	$-0.00661049\pi$
$102$		0			0
$103$	5.02879	−	15.4770i	0.495501	−	1.52500i	−0.320673	−	0.947190i	$-0.603909\pi$
$103$	5.02879	−	15.4770i	0.495501	−	1.52500i	0.816174	−	0.577806i	$-0.196091\pi$
$104$		0			0
$105$	−0.926020	−	0.672793i	−0.0903703	−	0.0656579i
$106$		0			0
$107$	−0.706967	−	2.17582i	−0.0683451	−	0.210345i	0.911051	−	0.412294i	$-0.135272\pi$
$107$	−0.706967	−	2.17582i	−0.0683451	−	0.210345i	−0.979396	+	0.201949i	$0.935272\pi$
$108$		0			0
$109$	−16.2045			−1.55211			−0.776055	−	0.630665i	$-0.782782\pi$
$109$	−16.2045			−1.55211			−0.776055	+	0.630665i	$0.782782\pi$
$110$		0			0
$111$	−3.65290			−0.346718
$112$		0			0
$113$	1.72138	+	5.29785i	0.161933	+	0.498380i	0.998797	−	0.0490314i	$-0.0156134\pi$
$113$	1.72138	+	5.29785i	0.161933	+	0.498380i	−0.836864	+	0.547411i	$0.815613\pi$
$114$		0			0
$115$	15.7018	+	11.4080i	1.46420	+	1.06381i
$116$		0			0
$117$	−4.31453	+	13.2788i	−0.398879	+	1.22762i
$118$		0			0
$119$	−1.32207	+	0.960538i	−0.121194	+	0.0880524i
$120$		0			0
$121$	−9.66442	−	5.25347i	−0.878584	−	0.477588i
$122$		0			0
$123$	−0.575263	+	0.417953i	−0.0518697	+	0.0376855i
$124$		0			0
$125$	−3.53977	+	10.8943i	−0.316607	+	0.974415i
$126$		0			0
$127$	5.68733	+	4.13208i	0.504669	+	0.366663i	0.810797	−	0.585327i	$-0.199034\pi$
$127$	5.68733	+	4.13208i	0.504669	+	0.366663i	−0.306129	+	0.951990i	$0.599034\pi$
$128$		0			0
$129$	0.319223	+	0.982469i	0.0281061	+	0.0865016i
$130$		0			0
$131$	8.48279			0.741145			0.370573	−	0.928803i	$-0.379161\pi$
$131$	8.48279			0.741145			0.370573	+	0.928803i	$0.379161\pi$
$132$		0			0
$133$	5.42879			0.470736
$134$		0			0
$135$	2.02442	+	6.23051i	0.174234	+	0.536237i
$136$		0			0
$137$	10.2268	+	7.43019i	0.873732	+	0.634804i	0.931586	−	0.363521i	$-0.118426\pi$
$137$	10.2268	+	7.43019i	0.873732	+	0.634804i	−0.0578535	+	0.998325i	$0.518426\pi$
$138$		0			0
$139$	−2.24998	+	6.92472i	−0.190841	+	0.587347i	−1.00000		0.000242269i	$-0.999923\pi$
$139$	−2.24998	+	6.92472i	−0.190841	+	0.587347i	0.809159	+	0.587589i	$0.199923\pi$
$140$		0			0
$141$	−0.372474	+	0.270618i	−0.0313680	+	0.0227902i
$142$		0			0
$143$	6.29687	+	15.7944i	0.526571	+	1.32080i
$144$		0			0
$145$	−11.7252	+	8.51884i	−0.973723	+	0.707452i
$146$		0			0
$147$	−0.162519	+	0.500181i	−0.0134043	+	0.0412542i
$148$		0			0
$149$	4.37675	+	3.17989i	0.358557	+	0.260507i	0.752450	−	0.658649i	$-0.228872\pi$
$149$	4.37675	+	3.17989i	0.358557	+	0.260507i	−0.393893	+	0.919156i	$0.628872\pi$
$150$		0			0
$151$	1.86595	+	5.74280i	0.151849	+	0.467342i	0.997828	−	0.0658736i	$-0.0209834\pi$
$151$	1.86595	+	5.74280i	0.151849	+	0.467342i	−0.845979	+	0.533216i	$0.820983\pi$
$152$		0			0
$153$	4.45050			0.359801
$154$		0			0
$155$	19.6193			1.57586
$156$		0			0
$157$	−3.32454	−	10.2319i	−0.265327	−	0.816593i	−0.991618	−	0.129205i	$-0.958757\pi$
$157$	−3.32454	−	10.2319i	−0.265327	−	0.816593i	0.726291	−	0.687387i	$-0.241243\pi$
$158$		0			0
$159$	−1.04646	−	0.760299i	−0.0829898	−	0.0602956i
$160$		0			0
$161$	2.75570	−	8.48118i	0.217180	−	0.668411i
$162$		0			0
$163$	16.5785	−	12.0450i	1.29853	−	0.943436i	0.298589	−	0.954382i	$-0.403484\pi$
$163$	16.5785	−	12.0450i	1.29853	−	0.943436i	0.999940	+	0.0109454i	$0.00348410\pi$
$164$		0			0
$165$	3.21013	+	2.02654i	0.249908	+	0.157766i
$166$		0			0
$167$	−3.31917	+	2.41152i	−0.256845	+	0.186609i	−0.708755	−	0.705455i	$-0.750743\pi$
$167$	−3.31917	+	2.41152i	−0.256845	+	0.186609i	0.451910	+	0.892064i	$0.350743\pi$
$168$		0			0
$169$	4.10473	−	12.6330i	0.315748	−	0.971773i
$170$		0			0
$171$	−11.9612	−	8.69029i	−0.914692	−	0.664563i
$172$		0			0
$173$	−5.92970	−	18.2497i	−0.450826	−	1.38750i	−0.875966	−	0.482373i	$-0.839775\pi$
$173$	−5.92970	−	18.2497i	−0.450826	−	1.38750i	0.425140	−	0.905128i	$-0.360225\pi$
$174$		0			0
$175$	0.263203			0.0198963
$176$		0			0
$177$	−1.09077			−0.0819871
$178$		0			0
$179$	3.04694	+	9.37751i	0.227739	+	0.700908i	0.998002	+	0.0631818i	$0.0201248\pi$
$179$	3.04694	+	9.37751i	0.227739	+	0.700908i	−0.770263	+	0.637726i	$0.779875\pi$
$180$		0			0
$181$	−2.39615	−	1.74091i	−0.178105	−	0.129401i	0.495161	−	0.868801i	$-0.335109\pi$
$181$	−2.39615	−	1.74091i	−0.178105	−	0.129401i	−0.673266	+	0.739400i	$0.735109\pi$
$182$		0			0
$183$	2.41538	−	7.43379i	0.178550	−	0.549522i
$184$		0			0
$185$	−12.2298	+	8.88543i	−0.899149	+	0.653270i
$186$		0			0
$187$	4.16790	−	3.46469i	0.304787	−	0.253363i
$188$		0			0
$189$	2.43519	−	1.76927i	0.177134	−	0.128695i
$190$		0			0
$191$	−5.38171	+	16.5632i	−0.389407	+	1.19847i	0.543826	+	0.839198i	$0.316975\pi$
$191$	−5.38171	+	16.5632i	−0.389407	+	1.19847i	−0.933233	+	0.359273i	$0.883025\pi$
$192$		0			0
$193$	14.0398	+	10.2005i	1.01061	+	0.734249i	0.964336	−	0.264680i	$-0.0852664\pi$
$193$	14.0398	+	10.2005i	1.01061	+	0.734249i	0.0462703	+	0.998929i	$0.485266\pi$
$194$		0			0
$195$	−1.81336	−	5.58095i	−0.129857	−	0.399660i
$196$		0			0
$197$	23.6207			1.68291			0.841453	−	0.540330i	$-0.181701\pi$
$197$	23.6207			1.68291			0.841453	+	0.540330i	$0.181701\pi$
$198$		0			0
$199$	−7.11528			−0.504389			−0.252194	−	0.967677i	$-0.581152\pi$
$199$	−7.11528			−0.504389			−0.252194	+	0.967677i	$0.581152\pi$
$200$		0			0
$201$	2.17879	+	6.70562i	0.153680	+	0.472978i
$202$		0			0
$203$	5.38738	+	3.91416i	0.378120	+	0.274720i
$204$		0			0
$205$	−0.909312	+	2.79857i	−0.0635091	+	0.195461i
$206$		0			0
$207$	−19.6481	+	14.2752i	−1.36564	+	0.992193i
$208$		0			0
$209$	−17.9670	+	1.17321i	−1.24280	+	0.0811529i
$210$		0			0
$211$	8.48924	−	6.16780i	0.584424	−	0.424609i	−0.255893	−	0.966705i	$-0.582369\pi$
$211$	8.48924	−	6.16780i	0.584424	−	0.424609i	0.840316	+	0.542097i	$0.182369\pi$
$212$		0			0
$213$	1.21068	−	3.72609i	0.0829544	−	0.255307i
$214$		0			0
$215$	3.45853	+	2.51277i	0.235870	+	0.171370i
$216$		0			0
$217$	−2.78563	−	8.57328i	−0.189101	−	0.581992i
$218$		0			0
$219$	1.88722			0.127527
$220$		0			0
$221$	−8.37790			−0.563558
$222$		0			0
$223$	−3.67479	−	11.3098i	−0.246082	−	0.757362i	−0.995457	−	0.0952161i	$-0.969646\pi$
$223$	−3.67479	−	11.3098i	−0.246082	−	0.757362i	0.749375	−	0.662146i	$-0.230354\pi$
$224$		0			0
$225$	−0.579911	−	0.421330i	−0.0386607	−	0.0280887i
$226$		0			0
$227$	2.61755	−	8.05600i	0.173733	−	0.534696i	−0.825840	−	0.563904i	$-0.809299\pi$
$227$	2.61755	−	8.05600i	0.173733	−	0.534696i	0.999573	+	0.0292086i	$0.00929869\pi$
$228$		0			0
$229$	−16.5057	+	11.9921i	−1.09073	+	0.792458i	−0.979522	−	0.201339i	$-0.935471\pi$
$229$	−16.5057	+	11.9921i	−1.09073	+	0.792458i	−0.111204	+	0.993798i	$0.535471\pi$
$230$		0			0
$231$	0.429774	−	1.69051i	0.0282770	−	0.111227i
$232$		0			0
$233$	9.19786	−	6.68264i	0.602572	−	0.437794i	−0.244219	−	0.969720i	$-0.578532\pi$
$233$	9.19786	−	6.68264i	0.602572	−	0.437794i	0.846791	+	0.531926i	$0.178532\pi$
$234$		0			0
$235$	−0.588766	+	1.81204i	−0.0384069	+	0.118204i
$236$		0			0
$237$	−5.74903	−	4.17691i	−0.373440	−	0.271320i
$238$		0			0
$239$	−7.42744	−	22.8593i	−0.480441	−	1.47865i	−0.838476	−	0.544938i	$-0.816553\pi$
$239$	−7.42744	−	22.8593i	−0.480441	−	1.47865i	0.358035	−	0.933708i	$-0.383447\pi$
$240$		0			0
$241$	7.87954			0.507566			0.253783	−	0.967261i	$-0.418325\pi$
$241$	7.87954			0.507566			0.253783	+	0.967261i	$0.418325\pi$
$242$		0			0
$243$	−12.4945			−0.801523
$244$		0			0
$245$	0.672550	+	2.06990i	0.0429677	+	0.132241i
$246$		0			0
$247$	22.5164	+	16.3591i	1.43269	+	1.04091i
$248$		0			0
$249$	−0.389494	+	1.19874i	−0.0246832	+	0.0759669i
$250$		0			0
$251$	−6.73999	+	4.89689i	−0.425424	+	0.309089i	−0.779817	−	0.626008i	$-0.784688\pi$
$251$	−6.73999	+	4.89689i	−0.425424	+	0.309089i	0.354392	+	0.935097i	$0.384688\pi$
$252$		0			0
$253$	−7.28735	+	28.6647i	−0.458152	+	1.80213i
$254$		0			0
$255$	−1.51327	+	1.09946i	−0.0947647	+	0.0688506i
$256$		0			0
$257$	1.06755	−	3.28557i	0.0665918	−	0.204948i	−0.912224	−	0.409692i	$-0.865636\pi$
$257$	1.06755	−	3.28557i	0.0665918	−	0.204948i	0.978816	+	0.204744i	$0.0656361\pi$
$258$		0			0
$259$	5.61921	+	4.08259i	0.349161	+	0.253680i
$260$		0			0
$261$	−5.60421	−	17.2480i	−0.346892	−	1.06762i
$262$		0			0
$263$	−8.69569			−0.536199			−0.268100	−	0.963391i	$-0.586396\pi$
$263$	−8.69569			−0.536199			−0.268100	+	0.963391i	$0.586396\pi$
$264$		0			0
$265$	−5.35288			−0.328825
$266$		0			0
$267$	−2.32713	−	7.16217i	−0.142418	−	0.438318i
$268$		0			0
$269$	−20.7434	−	15.0710i	−1.26475	−	0.918894i	−0.265769	−	0.964037i	$-0.585626\pi$
$269$	−20.7434	−	15.0710i	−1.26475	−	0.918894i	−0.998981	+	0.0451428i	$0.985626\pi$
$270$		0			0
$271$	4.35600	−	13.4064i	0.264608	−	0.814380i	−0.727175	−	0.686452i	$-0.759167\pi$
$271$	4.35600	−	13.4064i	0.264608	−	0.814380i	0.991783	−	0.127928i	$-0.0408327\pi$
$272$		0			0
$273$	−2.18131	+	1.58481i	−0.132019	+	0.0959172i
$274$		0			0
$275$	−0.871091	+	0.0568807i	−0.0525287	+	0.00343004i
$276$		0			0
$277$	−7.10729	+	5.16375i	−0.427036	+	0.310260i	−0.780462	−	0.625203i	$-0.785016\pi$
$277$	−7.10729	+	5.16375i	−0.427036	+	0.310260i	0.353427	+	0.935462i	$0.385016\pi$
$278$		0			0
$279$	−7.58640	+	23.3485i	−0.454186	+	1.39784i
$280$		0			0
$281$	−17.4558	−	12.6824i	−1.04133	−	0.756569i	−0.0707841	−	0.997492i	$-0.522550\pi$
$281$	−17.4558	−	12.6824i	−1.04133	−	0.756569i	−0.970544	+	0.240922i	$0.922550\pi$
$282$		0			0
$283$	−0.167283	−	0.514843i	−0.00994393	−	0.0306043i	0.945961	−	0.324279i	$-0.105122\pi$
$283$	−0.167283	−	0.514843i	−0.00994393	−	0.0306043i	−0.955905	+	0.293675i	$0.905122\pi$
$284$		0			0
$285$	6.21392			0.368081
$286$		0			0
$287$	1.35204			0.0798081
$288$		0			0
$289$	−4.42806	−	13.6282i	−0.260474	−	0.801657i
$290$		0			0
$291$	5.35168	+	3.88822i	0.313721	+	0.227932i
$292$		0			0
$293$	−1.18755	+	3.65492i	−0.0693776	+	0.213522i	−0.979734	−	0.200303i	$-0.935807\pi$
$293$	−1.18755	+	3.65492i	−0.0693776	+	0.213522i	0.910356	+	0.413825i	$0.135807\pi$
$294$		0			0
$295$	−3.65184	+	2.65322i	−0.212618	+	0.154476i
$296$		0			0
$297$	−7.67709	+	6.38180i	−0.445470	+	0.370309i
$298$		0			0
$299$	36.9868	−	26.8725i	2.13900	−	1.55408i
$300$		0			0
$301$	0.606980	−	1.86809i	0.0349857	−	0.107675i
$302$		0			0
$303$	−7.02162	−	5.10151i	−0.403382	−	0.293074i
$304$		0			0
$305$	−9.99559	−	30.7633i	−0.572346	−	1.76150i
$306$		0			0
$307$	1.90905			0.108955			0.0544775	−	0.998515i	$-0.482651\pi$
$307$	1.90905			0.108955			0.0544775	+	0.998515i	$0.482651\pi$
$308$		0			0
$309$	−8.55858			−0.486880
$310$		0			0
$311$	−1.24291	−	3.82528i	−0.0704788	−	0.216911i	0.909613	−	0.415457i	$-0.136378\pi$
$311$	−1.24291	−	3.82528i	−0.0704788	−	0.216911i	−0.980092	+	0.198545i	$0.936378\pi$
$312$		0			0
$313$	−12.5924	−	9.14891i	−0.711764	−	0.517127i	0.171978	−	0.985101i	$-0.444984\pi$
$313$	−12.5924	−	9.14891i	−0.711764	−	0.517127i	−0.883742	+	0.467974i	$0.844984\pi$
$314$		0			0
$315$	1.83163	−	5.63717i	0.103201	−	0.317619i
$316$		0			0
$317$	3.65768	−	2.65746i	0.205436	−	0.149258i	−0.480310	−	0.877099i	$-0.659476\pi$
$317$	3.65768	−	2.65746i	0.205436	−	0.149258i	0.685746	+	0.727841i	$0.259476\pi$
$318$		0			0
$319$	−18.6758	−	11.7899i	−1.04565	−	0.660110i
$320$		0			0
$321$	−0.973408	+	0.707222i	−0.0543303	+	0.0394733i
$322$		0			0
$323$	2.74146	−	8.43733i	0.152539	−	0.469466i
$324$		0			0
$325$	1.09166	+	0.793138i	0.0605544	+	0.0439954i
$326$		0			0
$327$	2.63353	+	8.10518i	0.145635	+	0.448217i
$328$		0			0
$329$	0.875424			0.0482637
$330$		0			0
$331$	−24.0631			−1.32263			−0.661313	−	0.750110i	$-0.730001\pi$
$331$	−24.0631			−1.32263			−0.661313	+	0.750110i	$0.730001\pi$
$332$		0			0
$333$	−5.84538	−	17.9902i	−0.320325	−	0.985858i
$334$		0			0
$335$	23.6055	+	17.1504i	1.28970	+	0.937025i
$336$		0			0
$337$	−8.28335	+	25.4935i	−0.451223	+	1.38872i	0.424290	+	0.905526i	$0.360524\pi$
$337$	−8.28335	+	25.4935i	−0.451223	+	1.38872i	−0.875513	+	0.483195i	$0.839476\pi$
$338$		0			0
$339$	2.37013	−	1.72200i	0.128728	−	0.0935260i
$340$		0			0
$341$	11.0720	+	27.7719i	0.599583	+	1.50393i
$342$		0			0
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$		0			0
$345$	3.15425	−	9.70777i	0.169819	−	0.522649i
$346$		0			0
$347$	16.2447	+	11.8025i	0.872062	+	0.633590i	0.931140	−	0.364663i	$-0.118816\pi$
$347$	16.2447	+	11.8025i	0.872062	+	0.633590i	−0.0590772	+	0.998253i	$0.518816\pi$
$348$		0			0
$349$	−8.80285	−	27.0924i	−0.471206	−	1.45022i	−0.851007	−	0.525154i	$-0.824008\pi$
$349$	−8.80285	−	27.0924i	−0.471206	−	1.45022i	0.379802	−	0.925068i	$-0.375992\pi$
$350$		0			0
$351$	15.4317			0.823684
$352$		0			0
$353$	−6.03292			−0.321100			−0.160550	−	0.987028i	$-0.551327\pi$
$353$	−6.03292			−0.321100			−0.160550	+	0.987028i	$0.551327\pi$
$354$		0			0
$355$	−5.01015	−	15.4197i	−0.265911	−	0.818391i
$356$		0			0
$357$	0.695303	+	0.505167i	0.0367993	+	0.0267363i
$358$		0			0
$359$	0.744900	−	2.29257i	0.0393143	−	0.120997i	−0.929473	−	0.368890i	$-0.879738\pi$
$359$	0.744900	−	2.29257i	0.0393143	−	0.120997i	0.968788	+	0.247893i	$0.0797380\pi$
$360$		0			0
$361$	−8.47181	+	6.15513i	−0.445885	+	0.323954i
$362$		0			0
$363$	−1.05703	+	5.68774i	−0.0554799	+	0.298529i
$364$		0			0
$365$	6.31833	−	4.59054i	0.330717	−	0.240280i
$366$		0			0
$367$	−1.58959	+	4.89224i	−0.0829757	+	0.255373i	−0.983934	−	0.178533i	$-0.942865\pi$
$367$	−1.58959	+	4.89224i	−0.0829757	+	0.255373i	0.900958	+	0.433906i	$0.142865\pi$
$368$		0			0
$369$	−2.97892	−	2.16431i	−0.155076	−	0.112669i
$370$		0			0
$371$	0.760024	+	2.33911i	0.0394585	+	0.121441i
$372$		0			0
$373$	9.35489			0.484378			0.242189	−	0.970229i	$-0.422135\pi$
$373$	9.35489			0.484378			0.242189	+	0.970229i	$0.422135\pi$
$374$		0			0
$375$	6.02439			0.311098
$376$		0			0
$377$	10.5497	+	32.4687i	0.543338	+	1.67222i
$378$		0			0
$379$	0.462861	+	0.336288i	0.0237756	+	0.0172740i	0.599610	−	0.800293i	$-0.295323\pi$
$379$	0.462861	+	0.336288i	0.0237756	+	0.0172740i	−0.575834	+	0.817567i	$0.695323\pi$
$380$		0			0
$381$	1.14249	−	3.51623i	0.0585317	−	0.180142i
$382$		0			0
$383$	13.5191	−	9.82219i	0.690793	−	0.501890i	−0.186128	−	0.982526i	$-0.559594\pi$
$383$	13.5191	−	9.82219i	0.690793	−	0.501890i	0.876921	+	0.480635i	$0.159594\pi$
$384$		0			0
$385$	−2.67318	−	6.70514i	−0.136238	−	0.341725i
$386$		0			0
$387$	−4.32775	+	3.14429i	−0.219992	+	0.159833i
$388$		0			0
$389$	1.57969	−	4.86178i	0.0800934	−	0.246502i	−0.902990	−	0.429662i	$-0.858633\pi$
$389$	1.57969	−	4.86178i	0.0800934	−	0.246502i	0.983083	+	0.183160i	$0.0586326\pi$
$390$		0			0
$391$	−11.7897	−	8.56574i	−0.596232	−	0.433188i
$392$		0			0
$393$	−1.37861	−	4.24293i	−0.0695417	−	0.214027i
$394$		0			0
$395$	−29.4075			−1.47965
$396$		0			0
$397$	−21.8271			−1.09547			−0.547737	−	0.836651i	$-0.684510\pi$
$397$	−21.8271			−1.09547			−0.547737	+	0.836651i	$0.684510\pi$
$398$		0			0
$399$	−0.882278	−	2.71537i	−0.0441692	−	0.135939i
$400$		0			0
$401$	18.1120	+	13.1591i	0.904471	+	0.657136i	0.939610	−	0.342246i	$-0.111188\pi$
$401$	18.1120	+	13.1591i	0.904471	+	0.657136i	−0.0351397	+	0.999382i	$0.511188\pi$
$402$		0			0
$403$	14.2811	−	43.9527i	0.711393	−	2.18944i
$404$		0			0
$405$	−11.5984	+	8.42674i	−0.576330	+	0.418728i
$406$		0			0
$407$	−19.4795	−	12.2973i	−0.965563	−	0.609554i
$408$		0			0
$409$	7.61220	−	5.53058i	0.376399	−	0.273470i	−0.383460	−	0.923557i	$-0.625268\pi$
$409$	7.61220	−	5.53058i	0.376399	−	0.273470i	0.759859	+	0.650087i	$0.225268\pi$
$410$		0			0
$411$	2.05439	−	6.32278i	0.101336	−	0.311880i
$412$		0			0
$413$	1.67791	+	1.21908i	0.0825647	+	0.0599868i
$414$		0			0
$415$	1.61184	+	4.96074i	0.0791222	+	0.243513i
$416$		0			0
$417$	3.82927			0.187520
$418$		0			0
$419$	−8.07960			−0.394714			−0.197357	−	0.980332i	$-0.563236\pi$
$419$	−8.07960			−0.394714			−0.197357	+	0.980332i	$0.563236\pi$
$420$		0			0
$421$	9.79656	+	30.1507i	0.477455	+	1.46946i	0.842618	+	0.538512i	$0.181013\pi$
$421$	9.79656	+	30.1507i	0.477455	+	1.46946i	−0.365162	+	0.930944i	$0.618987\pi$
$422$		0			0
$423$	−1.92881	−	1.40136i	−0.0937817	−	0.0681364i
$424$		0			0
$425$	0.132914	−	0.409066i	0.00644726	−	0.0198426i
$426$		0			0
$427$	−12.0238	+	8.73579i	−0.581872	+	0.422755i
$428$		0			0
$429$	6.87671	−	5.71646i	0.332011	−	0.275993i
$430$		0			0
$431$	−0.237291	+	0.172402i	−0.0114299	+	0.00830431i	−0.593486	−	0.804845i	$-0.702249\pi$
$431$	−0.237291	+	0.172402i	−0.0114299	+	0.00830431i	0.582056	+	0.813149i	$0.302249\pi$
$432$		0			0
$433$	−0.693983	+	2.13586i	−0.0333507	+	0.102643i	−0.966346	−	0.257245i	$-0.917185\pi$
$433$	−0.693983	+	2.13586i	−0.0333507	+	0.102643i	0.932995	+	0.359888i	$0.117185\pi$
$434$		0			0
$435$	6.16652	+	4.48024i	0.295662	+	0.214811i
$436$		0			0
$437$	14.9601	+	46.0425i	0.715640	+	2.20251i
$438$		0			0
$439$	1.78897			0.0853829			0.0426915	−	0.999088i	$-0.486407\pi$
$439$	1.78897			0.0853829			0.0426915	+	0.999088i	$0.486407\pi$
$440$		0			0
$441$	−2.72341			−0.129686
$442$		0			0
$443$	3.67238	+	11.3024i	0.174480	+	0.536995i	0.999609	−	0.0279494i	$-0.00889773\pi$
$443$	3.67238	+	11.3024i	0.174480	+	0.536995i	−0.825129	+	0.564944i	$0.808898\pi$
$444$		0			0
$445$	−25.2126	−	18.3180i	−1.19519	−	0.868358i
$446$		0			0
$447$	0.879218	−	2.70596i	0.0415856	−	0.127987i
$448$		0			0
$449$	11.9846	−	8.70729i	0.565586	−	0.410922i	−0.267913	−	0.963443i	$-0.586334\pi$
$449$	11.9846	−	8.70729i	0.565586	−	0.410922i	0.833499	+	0.552521i	$0.186334\pi$
$450$		0			0
$451$	−4.47467	+	0.292188i	−0.210704	+	0.0137586i
$452$		0			0
$453$	2.56918	−	1.86662i	0.120711	−	0.0877015i
$454$		0			0
$455$	−3.44797	+	10.6118i	−0.161643	+	0.497487i
$456$		0			0
$457$	−21.8339	−	15.8632i	−1.02135	−	0.742051i	−0.0547877	−	0.998498i	$-0.517448\pi$
$457$	−21.8339	−	15.8632i	−1.02135	−	0.742051i	−0.966558	+	0.256447i	$0.917448\pi$
$458$		0			0
$459$	−1.52003	−	4.67819i	−0.0709492	−	0.218359i
$460$		0			0
$461$	−6.47510			−0.301575			−0.150788	−	0.988566i	$-0.548181\pi$
$461$	−6.47510			−0.301575			−0.150788	+	0.988566i	$0.548181\pi$
$462$		0			0
$463$	19.3237			0.898047			0.449024	−	0.893520i	$-0.351772\pi$
$463$	19.3237			0.898047			0.449024	+	0.893520i	$0.351772\pi$
$464$		0			0
$465$	−3.18850	−	9.81318i	−0.147863	−	0.455075i
$466$		0			0
$467$	−7.50653	−	5.45382i	−0.347361	−	0.252372i	0.400400	−	0.916340i	$-0.368871\pi$
$467$	−7.50653	−	5.45382i	−0.347361	−	0.252372i	−0.747761	+	0.663968i	$0.768871\pi$
$468$		0			0
$469$	4.14281	−	12.7503i	0.191297	−	0.588752i
$470$		0			0
$471$	−4.57749	+	3.32574i	−0.210919	+	0.153242i
$472$		0			0
$473$	−1.60513	+	6.31377i	−0.0738041	+	0.290307i
$474$		0			0
$475$	−1.15598	+	0.839871i	−0.0530401	+	0.0385359i
$476$		0			0
$477$	2.06986	−	6.37036i	0.0947722	−	0.291679i
$478$		0			0
$479$	27.8893	+	20.2628i	1.27430	+	0.925831i	0.999365	−	0.0356331i	$-0.0113448\pi$
$479$	27.8893	+	20.2628i	1.27430	+	0.925831i	0.274932	+	0.961464i	$0.411345\pi$
$480$		0			0
$481$	11.0037	+	33.8659i	0.501726	+	1.54415i
$482$		0			0
$483$	−4.68998			−0.213401
$484$		0			0
$485$	27.3750			1.24304
$486$		0			0
$487$	12.4959	+	38.4584i	0.566242	+	1.74272i	0.664231	+	0.747528i	$0.268759\pi$
$487$	12.4959	+	38.4584i	0.566242	+	1.74272i	−0.0979883	+	0.995188i	$0.531241\pi$
$488$		0			0
$489$	−8.71898	−	6.33471i	−0.394286	−	0.286466i
$490$		0			0
$491$	0.671162	−	2.06563i	0.0302891	−	0.0932204i	−0.934769	−	0.355256i	$-0.884394\pi$
$491$	0.671162	−	2.06563i	0.0302891	−	0.0932204i	0.965058	+	0.262035i	$0.0843937\pi$
$492$		0			0
$493$	8.80386	−	6.39638i	0.396506	−	0.288079i
$494$		0			0
$495$	−4.84367	+	19.0525i	−0.217707	+	0.856345i
$496$		0			0
$497$	−6.02676	+	4.37870i	−0.270337	+	0.196411i
$498$		0			0
$499$	−3.49078	+	10.7435i	−0.156269	+	0.480945i	−0.998287	−	0.0585032i	$-0.981367\pi$
$499$	−3.49078	+	10.7435i	−0.156269	+	0.480945i	0.842019	+	0.539448i	$0.181367\pi$
$500$		0			0
$501$	1.74562	+	1.26827i	0.0779887	+	0.0566621i
$502$		0			0
$503$	−5.09354	−	15.6763i	−0.227110	−	0.698971i	−0.998071	−	0.0620890i	$-0.980224\pi$
$503$	−5.09354	−	15.6763i	−0.227110	−	0.698971i	0.770961	−	0.636882i	$-0.219776\pi$
$504$		0			0
$505$	−35.9171			−1.59829
$506$		0			0
$507$	−6.98590			−0.310255
$508$		0			0
$509$	−6.91722	−	21.2890i	−0.306600	−	0.943619i	−0.979075	−	0.203499i	$-0.934769\pi$
$509$	−6.91722	−	21.2890i	−0.306600	−	0.943619i	0.672475	−	0.740120i	$-0.265231\pi$
$510$		0			0
$511$	−2.90309	−	2.10922i	−0.128425	−	0.0933063i
$512$		0			0
$513$	−5.04964	+	15.5412i	−0.222947	+	0.686160i
$514$		0			0
$515$	−28.6537	+	20.8181i	−1.26263	+	0.917357i
$516$		0			0
$517$	−2.89728	+	0.189187i	−0.127422	+	0.00832045i
$518$		0			0
$519$	−8.16447	+	5.93184i	−0.358381	+	0.260379i
$520$		0			0
$521$	10.3344	−	31.8061i	0.452759	−	1.39345i	−0.420987	−	0.907067i	$-0.638316\pi$
$521$	10.3344	−	31.8061i	0.452759	−	1.39345i	0.873746	−	0.486383i	$-0.161684\pi$
$522$		0			0
$523$	9.66045	+	7.01873i	0.422422	+	0.306908i	0.778612	−	0.627506i	$-0.215924\pi$
$523$	9.66045	+	7.01873i	0.422422	+	0.306908i	−0.356190	+	0.934414i	$0.615924\pi$
$524$		0			0
$525$	−0.0427754	−	0.131649i	−0.00186687	−	0.00574564i
$526$		0			0
$527$	−14.7312			−0.641699
$528$		0			0
$529$	56.5244			2.45758
$530$		0			0
$531$	−1.74545	−	5.37194i	−0.0757460	−	0.233122i
$532$		0			0
$533$	5.60770	+	4.07423i	0.242896	+	0.176475i
$534$		0			0
$535$	−1.53866	+	4.73550i	−0.0665219	+	0.204733i
$536$		0			0
$537$	4.19526	−	3.04804i	0.181039	−	0.131532i
$538$		0			0
$539$	−2.55048	+	2.12016i	−0.109857	+	0.0913216i
$540$		0			0
$541$	−2.83855	+	2.06233i	−0.122039	+	0.0886664i	−0.647130	−	0.762379i	$-0.724031\pi$
$541$	−2.83855	+	2.06233i	−0.122039	+	0.0886664i	0.525092	+	0.851046i	$0.324031\pi$
$542$		0			0
$543$	−0.481349	+	1.48144i	−0.0206567	+	0.0635747i
$544$		0			0
$545$	28.5322	+	20.7299i	1.22219	+	0.887970i
$546$		0			0
$547$	−4.24880	−	13.0765i	−0.181666	−	0.559109i	0.818209	−	0.574920i	$-0.194967\pi$
$547$	−4.24880	−	13.0765i	−0.181666	−	0.559109i	−0.999875	+	0.0158110i	$0.994967\pi$
$548$		0			0
$549$	40.4759			1.72747
$550$		0			0
$551$	−36.1512			−1.54009
$552$		0			0
$553$	4.17541	+	12.8506i	0.177556	+	0.546462i
$554$		0			0
$555$	6.43188	+	4.67304i	0.273018	+	0.198359i
$556$		0			0
$557$	1.20258	−	3.70117i	0.0509551	−	0.156824i	−0.922341	−	0.386377i	$-0.873726\pi$
$557$	1.20258	−	3.70117i	0.0509551	−	0.156824i	0.973296	+	0.229553i	$0.0737265\pi$
$558$		0			0
$559$	8.14683	−	5.91902i	0.344574	−	0.250348i
$560$		0			0
$561$	−2.41033	−	1.52163i	−0.101764	−	0.0642432i
$562$		0			0
$563$	21.5723	−	15.6732i	0.909165	−	0.660547i	−0.0316387	−	0.999499i	$-0.510073\pi$
$563$	21.5723	−	15.6732i	0.909165	−	0.660547i	0.940803	+	0.338953i	$0.110073\pi$
$564$		0			0
$565$	3.74643	−	11.5303i	0.157614	−	0.485085i
$566$		0			0
$567$	5.32913	+	3.87184i	0.223802	+	0.162602i
$568$		0			0
$569$	−10.4757	−	32.2407i	−0.439162	−	1.35160i	−0.888761	−	0.458372i	$-0.848433\pi$
$569$	−10.4757	−	32.2407i	−0.439162	−	1.35160i	0.449598	−	0.893231i	$-0.351567\pi$
$570$		0			0
$571$	21.5596			0.902241			0.451121	−	0.892463i	$-0.351024\pi$
$571$	21.5596			0.902241			0.451121	+	0.892463i	$0.351024\pi$
$572$		0			0
$573$	9.15922			0.382632
$574$		0			0
$575$	0.725310	+	2.23227i	0.0302475	+	0.0930923i
$576$		0			0
$577$	14.1567	+	10.2854i	0.589350	+	0.428188i	0.842083	−	0.539348i	$-0.181329\pi$
$577$	14.1567	+	10.2854i	0.589350	+	0.428188i	−0.252733	+	0.967536i	$0.581329\pi$
$578$		0			0
$579$	2.82037	−	8.68020i	0.117211	−	0.360737i
$580$		0			0
$581$	1.93890	−	1.40869i	0.0804391	−	0.0584424i
$582$		0			0
$583$	−3.02086	−	7.57723i	−0.125111	−	0.313817i
$584$		0			0
$585$	24.5839	−	17.8613i	1.01642	−	0.738473i
$586$		0			0
$587$	10.8126	−	33.2777i	0.446283	−	1.37352i	−0.434787	−	0.900534i	$-0.643176\pi$
$587$	10.8126	−	33.2777i	0.446283	−	1.37352i	0.881070	−	0.472986i	$-0.156824\pi$
$588$		0			0
$589$	39.5914	+	28.7649i	1.63134	+	1.18524i
$590$		0			0
$591$	−3.83880	−	11.8146i	−0.157907	−	0.485989i
$592$		0			0
$593$	5.55805			0.228242			0.114121	−	0.993467i	$-0.463595\pi$
$593$	5.55805			0.228242			0.114121	+	0.993467i	$0.463595\pi$
$594$		0			0
$595$	3.55663			0.145808
$596$		0			0
$597$	1.15636	+	3.55892i	0.0473268	+	0.145657i
$598$		0			0
$599$	14.7254	+	10.6986i	0.601662	+	0.437133i	0.846469	−	0.532439i	$-0.178724\pi$
$599$	14.7254	+	10.6986i	0.601662	+	0.437133i	−0.244806	+	0.969572i	$0.578724\pi$
$600$		0			0
$601$	−11.8945	+	36.6076i	−0.485188	+	1.49326i	0.346520	+	0.938043i	$0.387363\pi$
$601$	−11.8945	+	36.6076i	−0.485188	+	1.49326i	−0.831708	+	0.555213i	$0.812637\pi$
$602$		0			0
$603$	−29.5381	+	21.4607i	−1.20288	+	0.873947i
$604$		0			0
$605$	10.2961	+	21.6135i	0.418598	+	0.878712i
$606$		0			0
$607$	−3.06013	+	2.22331i	−0.124207	+	0.0902415i	−0.648154	−	0.761509i	$-0.724459\pi$
$607$	−3.06013	+	2.22331i	−0.124207	+	0.0902415i	0.523948	+	0.851751i	$0.324459\pi$
$608$		0			0
$609$	1.08224	−	3.33078i	0.0438545	−	0.134970i
$610$		0			0
$611$	3.63090	+	2.63801i	0.146891	+	0.106722i
$612$		0			0
$613$	−0.934929	−	2.87742i	−0.0377614	−	0.116218i	0.930399	−	0.366549i	$-0.119461\pi$
$613$	−0.934929	−	2.87742i	−0.0377614	−	0.116218i	−0.968160	+	0.250331i	$0.919461\pi$
$614$		0			0
$615$	1.54757			0.0624041
$616$		0			0
$617$	11.1071			0.447156			0.223578	−	0.974686i	$-0.428226\pi$
$617$	11.1071			0.447156			0.223578	+	0.974686i	$0.428226\pi$
$618$		0			0
$619$	8.04604	+	24.7632i	0.323398	+	0.995315i	0.972159	+	0.234323i	$0.0752874\pi$
$619$	8.04604	+	24.7632i	0.323398	+	0.995315i	−0.648761	+	0.760992i	$0.724713\pi$
$620$		0			0
$621$	21.7162	+	15.7777i	0.871439	+	0.633138i
$622$		0			0
$623$	−4.42487	+	13.6183i	−0.177278	+	0.545607i
$624$		0			0
$625$	19.1047	−	13.8804i	0.764188	−	0.555215i
$626$		0			0
$627$	3.50679	+	8.79607i	0.140048	+	0.351281i
$628$		0			0
$629$	9.18272	−	6.67164i	0.366139	−	0.266016i
$630$		0			0
$631$	−3.35155	+	10.3150i	−0.133423	+	0.410634i	−0.995341	−	0.0964131i	$-0.969263\pi$
$631$	−3.35155	+	10.3150i	−0.133423	+	0.410634i	0.861918	+	0.507047i	$0.169263\pi$
$632$		0			0
$633$	−4.46467	−	3.24377i	−0.177455	−	0.128928i
$634$		0			0
$635$	−4.72798	−	14.5512i	−0.187624	−	0.577447i
$636$		0			0
$637$	5.12671			0.203128
$638$		0			0
$639$	20.2880			0.802580
$640$		0			0
$641$	3.52074	+	10.8357i	0.139061	+	0.427985i	0.996200	−	0.0871006i	$-0.0277602\pi$
$641$	3.52074	+	10.8357i	0.139061	+	0.427985i	−0.857139	+	0.515086i	$0.827760\pi$
$642$		0			0
$643$	33.5046	+	24.3425i	1.32129	+	0.959976i	0.999915	+	0.0130256i	$0.00414631\pi$
$643$	33.5046	+	24.3425i	1.32129	+	0.959976i	0.321379	+	0.946951i	$0.395854\pi$
$644$		0			0
$645$	0.694764	−	2.13826i	0.0273563	−	0.0841940i
$646$		0			0
$647$	−11.0936	+	8.06000i	−0.436136	+	0.316871i	−0.784098	−	0.620638i	$-0.786874\pi$
$647$	−11.0936	+	8.06000i	−0.436136	+	0.316871i	0.347962	+	0.937509i	$0.386874\pi$
$648$		0			0
$649$	−5.81664	−	3.67201i	−0.228323	−	0.144139i
$650$		0			0
$651$	−3.83547	+	2.78663i	−0.150324	+	0.109217i
$652$		0			0
$653$	−6.22163	+	19.1482i	−0.243471	+	0.749327i	0.752413	+	0.658692i	$0.228890\pi$
$653$	−6.22163	+	19.1482i	−0.243471	+	0.749327i	−0.995884	+	0.0906355i	$0.971110\pi$
$654$		0			0
$655$	−14.9362	−	10.8518i	−0.583604	−	0.424013i
$656$		0			0
$657$	3.01993	+	9.29440i	0.117819	+	0.362609i
$658$		0			0
$659$	−28.8156			−1.12250			−0.561249	−	0.827647i	$-0.689679\pi$
$659$	−28.8156			−1.12250			−0.561249	+	0.827647i	$0.689679\pi$
$660$		0			0
$661$	−49.5634			−1.92779			−0.963896	−	0.266278i	$-0.914206\pi$
$661$	−49.5634			−1.92779			−0.963896	+	0.266278i	$0.914206\pi$
$662$		0			0
$663$	1.36156	+	4.19046i	0.0528787	+	0.162744i
$664$		0			0
$665$	−9.55879	−	6.94487i	−0.370674	−	0.269310i
$666$		0			0
$667$	−18.3507	+	56.4776i	−0.710541	+	2.18682i
$668$		0			0
$669$	−5.05974	+	3.67611i	−0.195621	+	0.142127i
$670$		0			0
$671$	37.9057	−	31.5102i	1.46334	−	1.21644i
$672$		0			0
$673$	−0.403959	+	0.293494i	−0.0155715	+	0.0113133i	−0.595544	−	0.803323i	$-0.703063\pi$
$673$	−0.403959	+	0.293494i	−0.0155715	+	0.0113133i	0.579972	+	0.814636i	$0.303063\pi$
$674$		0			0
$675$	−0.244821	+	0.753481i	−0.00942316	+	0.0290015i
$676$		0			0
$677$	5.39523	+	3.91986i	0.207355	+	0.150653i	0.686616	−	0.727020i	$-0.259095\pi$
$677$	5.39523	+	3.91986i	0.207355	+	0.150653i	−0.479261	+	0.877672i	$0.659095\pi$
$678$		0			0
$679$	−3.88682	−	11.9624i	−0.149162	−	0.459075i
$680$		0			0
$681$	−4.45486			−0.170710
$682$		0			0
$683$	−13.8925			−0.531583			−0.265792	−	0.964030i	$-0.585633\pi$
$683$	−13.8925			−0.531583			−0.265792	+	0.964030i	$0.585633\pi$
$684$		0			0
$685$	−8.50170	−	26.1655i	−0.324833	−	0.999734i
$686$		0			0
$687$	8.68068	+	6.30688i	0.331188	+	0.240622i
$688$		0			0
$689$	−3.89642	+	11.9920i	−0.148442	+	0.456857i
$690$		0			0
$691$	−6.71119	+	4.87596i	−0.255306	+	0.185490i	−0.708075	−	0.706137i	$-0.750436\pi$
$691$	−6.71119	+	4.87596i	−0.255306	+	0.185490i	0.452769	+	0.891628i	$0.350436\pi$
$692$		0			0
$693$	9.01332	−	0.588555i	0.342388	−	0.0223573i
$694$		0			0
$695$	12.8202	−	9.31444i	0.486299	−	0.353317i
$696$		0			0
$697$	0.682758	−	2.10131i	0.0258613	−	0.0795929i
$698$		0			0
$699$	−4.83735	−	3.51454i	−0.182965	−	0.132932i
$700$		0			0
$701$	0.249605	+	0.768204i	0.00942743	+	0.0290147i	0.955660	−	0.294474i	$-0.0951443\pi$
$701$	0.249605	+	0.768204i	0.00942743	+	0.0290147i	−0.946232	+	0.323488i	$0.895144\pi$
$702$		0			0
$703$	−37.7069			−1.42214
$704$		0			0
$705$	1.00203			0.0377387
$706$		0			0
$707$	5.09967	+	15.6952i	0.191793	+	0.590277i
$708$		0			0
$709$	−4.81301	−	3.49686i	−0.180756	−	0.131327i	0.493728	−	0.869617i	$-0.335634\pi$
$709$	−4.81301	−	3.49686i	−0.180756	−	0.131327i	−0.674484	+	0.738289i	$0.735634\pi$
$710$		0			0
$711$	11.3713	−	34.9974i	0.426458	−	1.31250i
$712$		0			0
$713$	65.0352	−	47.2508i	2.43559	−	1.76956i
$714$		0			0
$715$	9.11802	−	35.8656i	0.340995	−	1.34130i
$716$		0			0
$717$	−10.2267	+	7.43012i	−0.381923	+	0.277483i
$718$		0			0
$719$	−2.35485	+	7.24747i	−0.0878209	+	0.270285i	−0.985316	−	0.170739i	$-0.945385\pi$
$719$	−2.35485	+	7.24747i	−0.0878209	+	0.270285i	0.897495	+	0.441024i	$0.145385\pi$
$720$		0			0
$721$	13.1655	+	9.56532i	0.490310	+	0.356231i
$722$		0			0
$723$	−1.28057	−	3.94119i	−0.0476249	−	0.146574i
$724$		0			0
$725$	−1.75271			−0.0650941
$726$		0			0
$727$	−4.24890			−0.157583			−0.0787915	−	0.996891i	$-0.525106\pi$
$727$	−4.24890			−0.157583			−0.0787915	+	0.996891i	$0.525106\pi$
$728$		0			0
$729$	−4.07605	−	12.5448i	−0.150965	−	0.464622i
$730$		0			0
$731$	−2.59684	−	1.88672i	−0.0960477	−	0.0697827i
$732$		0			0
$733$	−8.85532	+	27.2539i	−0.327079	+	1.00665i	0.643415	+	0.765518i	$0.277517\pi$
$733$	−8.85532	+	27.2539i	−0.327079	+	1.00665i	−0.970493	+	0.241127i	$0.922483\pi$
$734$		0			0
$735$	0.926020	−	0.672793i	0.0341568	−	0.0248163i
$736$		0			0
$737$	−10.9555	+	43.0932i	−0.403551	+	1.58736i
$738$		0			0
$739$	−22.9012	+	16.6387i	−0.842433	+	0.612063i	−0.923049	−	0.384682i	$-0.874311\pi$
$739$	−22.9012	+	16.6387i	−0.842433	+	0.612063i	0.0806163	+	0.996745i	$0.474311\pi$
$740$		0			0
$741$	4.52319	−	13.9209i	0.166163	−	0.511398i
$742$		0			0
$743$	−17.6526	−	12.8253i	−0.647609	−	0.470516i	0.214847	−	0.976648i	$-0.431075\pi$
$743$	−17.6526	−	12.8253i	−0.647609	−	0.470516i	−0.862456	+	0.506132i	$0.831075\pi$
$744$		0			0
$745$	−3.63847	−	11.1981i	−0.133303	−	0.410265i
$746$		0			0
$747$	−6.52695			−0.238808
$748$		0			0
$749$	2.28779			0.0835942
$750$		0			0
$751$	−14.9835	−	46.1145i	−0.546756	−	1.68274i	−0.716779	−	0.697301i	$-0.754384\pi$
$751$	−14.9835	−	46.1145i	−0.546756	−	1.68274i	0.170023	−	0.985440i	$-0.445616\pi$
$752$		0			0
$753$	3.54470	+	2.57538i	0.129176	+	0.0938520i
$754$		0			0
$755$	4.06108	−	12.4987i	0.147798	−	0.454875i
$756$		0			0
$757$	−10.6851	+	7.76317i	−0.388356	+	0.282157i	−0.764781	−	0.644290i	$-0.777153\pi$
$757$	−10.6851	+	7.76317i	−0.388356	+	0.282157i	0.376426	+	0.926447i	$0.377153\pi$
$758$		0			0
$759$	15.5218	−	1.01355i	0.563407	−	0.0367895i
$760$		0			0
$761$	−32.1685	+	23.3718i	−1.16611	+	0.847225i	−0.990538	−	0.137242i	$-0.956176\pi$
$761$	−32.1685	+	23.3718i	−1.16611	+	0.847225i	−0.175568	+	0.984467i	$0.556176\pi$
$762$		0			0
$763$	5.00747	−	15.4114i	0.181282	−	0.557930i
$764$		0			0
$765$	−7.83626	−	5.69337i	−0.283320	−	0.205844i
$766$		0			0
$767$	3.28574	+	10.1125i	0.118641	+	0.365140i
$768$		0			0
$769$	42.5687			1.53507			0.767534	−	0.641008i	$-0.221484\pi$
$769$	42.5687			1.53507			0.767534	+	0.641008i	$0.221484\pi$
$770$		0			0
$771$	−1.81688			−0.0654332
$772$		0			0
$773$	−11.2093	−	34.4988i	−0.403172	−	1.24084i	−0.922412	−	0.386207i	$-0.873785\pi$
$773$	−11.2093	−	34.4988i	−0.403172	−	1.24084i	0.519240	−	0.854628i	$-0.326215\pi$
$774$		0			0
$775$	1.91950	+	1.39460i	0.0689507	+	0.0500956i
$776$		0			0
$777$	1.12881	−	3.47412i	0.0404958	−	0.124633i
$778$		0			0
$779$	−5.93812	+	4.31429i	−0.212755	+	0.154576i
$780$		0			0
$781$	18.9998	−	15.7941i	0.679865	−	0.565157i
$782$		0			0
$783$	−16.2163	+	11.7818i	−0.579524	+	0.421049i
$784$		0			0
$785$	−7.23559	+	22.2688i	−0.258249	+	0.794809i
$786$		0			0
$787$	2.01066	+	1.46083i	0.0716725	+	0.0520731i	0.623045	−	0.782186i	$-0.285896\pi$
$787$	2.01066	+	1.46083i	0.0716725	+	0.0520731i	−0.551372	+	0.834259i	$0.685896\pi$
$788$		0			0
$789$	1.41321	+	4.34941i	0.0503116	+	0.154843i
$790$		0			0
$791$	−5.57049			−0.198064
$792$		0			0
$793$	−76.1943			−2.70574
$794$		0			0
$795$	0.869942	+	2.67741i	0.0308537	+	0.0949578i
$796$		0			0
$797$	−45.4439	−	33.0169i	−1.60971	−	1.16952i	−0.864411	−	0.502785i	$-0.832309\pi$
$797$	−45.4439	−	33.0169i	−1.60971	−	1.16952i	−0.745295	−	0.666735i	$-0.767691\pi$
$798$		0			0
$799$	0.442076	−	1.36057i	0.0156395	−	0.0481335i
$800$		0			0
$801$	31.5492	−	22.9218i	1.11474	−	0.809902i
$802$		0			0
$803$	10.0638	+	6.35323i	0.355144	+	0.224201i
$804$		0			0
$805$	−15.7018	+	11.4080i	−0.553417	+	0.402081i
$806$		0			0
$807$	−4.16702	+	12.8248i	−0.146686	+	0.451453i
$808$		0			0
$809$	−20.6667	−	15.0152i	−0.726603	−	0.527908i	0.161884	−	0.986810i	$-0.448243\pi$
$809$	−20.6667	−	15.0152i	−0.726603	−	0.527908i	−0.888487	+	0.458902i	$0.848243\pi$
$810$		0			0
$811$	−4.98339	−	15.3373i	−0.174991	−	0.538566i	0.824642	−	0.565654i	$-0.191376\pi$
$811$	−4.98339	−	15.3373i	−0.174991	−	0.538566i	−0.999633	+	0.0270887i	$0.991376\pi$
$812$		0			0
$813$	−7.41355			−0.260004
$814$		0			0
$815$	−44.5995			−1.56225
$816$		0			0
$817$	3.29516	+	10.1415i	0.115283	+	0.354805i
$818$		0			0
$819$	−11.2956	−	8.20673i	−0.394700	−	0.286766i
$820$		0			0
$821$	−5.88368	+	18.1081i	−0.205342	+	0.631977i	0.794357	+	0.607451i	$0.207808\pi$
$821$	−5.88368	+	18.1081i	−0.205342	+	0.631977i	−0.999699	+	0.0245266i	$0.992192\pi$
$822$		0			0
$823$	29.5650	−	21.4802i	1.03057	−	0.748753i	0.0621473	−	0.998067i	$-0.480205\pi$
$823$	29.5650	−	21.4802i	1.03057	−	0.748753i	0.968423	+	0.249314i	$0.0802051\pi$
$824$		0			0
$825$	0.170019	+	0.426458i	0.00591930	+	0.0148474i
$826$		0			0
$827$	−8.52492	+	6.19372i	−0.296441	+	0.215377i	−0.726057	−	0.687635i	$-0.758649\pi$
$827$	−8.52492	+	6.19372i	−0.296441	+	0.215377i	0.429616	+	0.903012i	$0.358649\pi$
$828$		0			0
$829$	12.1919	−	37.5227i	0.423441	−	1.30322i	−0.481038	−	0.876700i	$-0.659740\pi$
$829$	12.1919	−	37.5227i	0.423441	−	1.30322i	0.904479	−	0.426518i	$-0.140260\pi$
$830$		0			0
$831$	3.73787	+	2.71572i	0.129665	+	0.0942074i
$832$		0			0
$833$	−0.504985	−	1.55418i	−0.0174967	−	0.0538493i
$834$		0			0
$835$	8.92925			0.309009
$836$		0			0
$837$	27.1341			0.937892
$838$		0			0
$839$	2.59670	+	7.99182i	0.0896480	+	0.275908i	0.985822	−	0.167795i	$-0.0536645\pi$
$839$	2.59670	+	7.99182i	0.0896480	+	0.275908i	−0.896174	+	0.443703i	$0.853665\pi$
$840$		0			0
$841$	−12.4139	−	9.01924i	−0.428066	−	0.311008i
$842$		0			0
$843$	−3.50660	+	10.7922i	−0.120774	+	0.371703i
$844$		0			0
$845$	−23.3885	+	16.9927i	−0.804588	+	0.584567i
$846$		0			0
$847$	7.98281	−	7.56800i	0.274293	−	0.260040i
$848$		0			0
$849$	−0.230328	+	0.167343i	−0.00790484	+	0.00574320i
$850$		0			0
$851$	−19.1404	+	58.9080i	−0.656123	+	2.01934i
$852$		0			0
$853$	38.2269	+	27.7735i	1.30886	+	0.950945i	1.00000		0.000161167i	$-5.13011e-5\pi$
$853$	38.2269	+	27.7735i	1.30886	+	0.950945i	0.308864	+	0.951106i	$0.400051\pi$
$854$		0			0
$855$	9.94352	+	30.6030i	0.340061	+	1.04660i
$856$		0			0
$857$	2.80919			0.0959602			0.0479801	−	0.998848i	$-0.484722\pi$
$857$	2.80919			0.0959602			0.0479801	+	0.998848i	$0.484722\pi$
$858$		0			0
$859$	26.7290			0.911980			0.455990	−	0.889985i	$-0.349285\pi$
$859$	26.7290			0.911980			0.455990	+	0.889985i	$0.349285\pi$
$860$		0			0
$861$	−0.219731	−	0.676262i	−0.00748841	−	0.0230469i
$862$		0			0
$863$	−39.5669	−	28.7471i	−1.34687	−	0.978561i	−0.999161	−	0.0409600i	$-0.986958\pi$
$863$	−39.5669	−	28.7471i	−1.34687	−	0.978561i	−0.347713	−	0.937601i	$-0.613042\pi$
$864$		0			0
$865$	−12.9055	+	39.7190i	−0.438800	+	1.35049i
$866$		0			0
$867$	−6.09690	+	4.42966i	−0.207062	+	0.150439i
$868$		0			0
$869$	−16.5960	−	41.6276i	−0.562979	−	1.41212i
$870$		0			0
$871$	55.6044	−	40.3989i	1.88408	−	1.36887i
$872$		0			0
$873$	−10.5854	+	32.5785i	−0.358261	+	1.10261i
$874$		0			0
$875$	−9.26723	−	6.73304i	−0.313290	−	0.227618i
$876$		0			0
$877$	4.48656	+	13.8082i	0.151500	+	0.466270i	0.997790	−	0.0664538i	$-0.0211685\pi$
$877$	4.48656	+	13.8082i	0.151500	+	0.466270i	−0.846289	+	0.532724i	$0.821168\pi$
$878$		0			0
$879$	2.02112			0.0681706
$880$		0			0
$881$	42.3082			1.42540			0.712700	−	0.701469i	$-0.247472\pi$
$881$	42.3082			1.42540			0.712700	+	0.701469i	$0.247472\pi$
$882$		0			0
$883$	10.8791	+	33.4824i	0.366111	+	1.12677i	0.949283	+	0.314424i	$0.101811\pi$
$883$	10.8791	+	33.4824i	0.366111	+	1.12677i	−0.583172	+	0.812349i	$0.698189\pi$
$884$		0			0
$885$	1.92058	+	1.39538i	0.0645596	+	0.0469053i
$886$		0			0
$887$	16.0130	−	49.2829i	0.537664	−	1.65476i	−0.200159	−	0.979763i	$-0.564146\pi$
$887$	16.0130	−	49.2829i	0.537664	−	1.65476i	0.737822	−	0.674995i	$-0.235854\pi$
$888$		0			0
$889$	−5.68733	+	4.13208i	−0.190747	+	0.138586i
$890$		0			0
$891$	−18.4739	−	11.6625i	−0.618899	−	0.390708i
$892$		0			0
$893$	−3.84484	+	2.79344i	−0.128663	+	0.0934790i
$894$		0			0
$895$	6.63141	−	20.4094i	0.221664	−	0.682210i
$896$		0			0
$897$	−19.4521	−	14.1328i	−0.649488	−	0.471880i
$898$		0			0
$899$	18.5499	+	57.0909i	0.618675	+	1.90409i
$900$		0			0
$901$	4.01921			0.133899
$902$		0			0
$903$	−1.03303			−0.0343770
$904$		0			0
$905$	1.99197	+	6.13064i	0.0662152	+	0.203789i
$906$		0			0
$907$	−7.35116	−	5.34093i	−0.244091	−	0.177343i	0.459013	−	0.888430i	$-0.348203\pi$
$907$	−7.35116	−	5.34093i	−0.244091	−	0.177343i	−0.703104	+	0.711087i	$0.748203\pi$
$908$		0			0
$909$	13.8885	−	42.7443i	0.460651	−	1.41774i
$910$		0			0
$911$	12.1735	−	8.84458i	0.403327	−	0.293034i	−0.367568	−	0.929997i	$-0.619809\pi$
$911$	12.1735	−	8.84458i	0.403327	−	0.293034i	0.770895	+	0.636963i	$0.219809\pi$
$912$		0			0
$913$	−6.11250	+	5.08119i	−0.202294	+	0.168163i
$914$		0			0
$915$	−13.7627	+	9.99920i	−0.454981	+	0.330563i
$916$		0			0
$917$	−2.62133	+	8.06762i	−0.0865639	+	0.266416i
$918$		0			0
$919$	−7.24093	−	5.26084i	−0.238856	−	0.173539i	0.461917	−	0.886923i	$-0.347162\pi$
$919$	−7.24093	−	5.26084i	−0.238856	−	0.173539i	−0.700774	+	0.713384i	$0.747162\pi$
$920$		0			0
$921$	−0.310255	−	0.954868i	−0.0102233	−	0.0314640i
$922$		0			0
$923$	−38.1914			−1.25708
$924$		0			0
$925$	−1.82814			−0.0601087
$926$		0			0
$927$	−13.6954	−	42.1502i	−0.449817	−	1.38440i
$928$		0			0
$929$	−13.6523	−	9.91895i	−0.447916	−	0.325430i	0.340856	−	0.940115i	$-0.389283\pi$
$929$	−13.6523	−	9.91895i	−0.447916	−	0.325430i	−0.788772	+	0.614685i	$0.789283\pi$
$930$		0			0
$931$	−1.67759	+	5.16308i	−0.0549807	+	0.169213i
$932$		0			0
$933$	−1.71133	+	1.24336i	−0.0560265	+	0.0407056i
$934$		0			0
$935$	−11.7709	+	0.768622i	−0.384951	+	0.0251366i
$936$		0			0
$937$	12.8897	−	9.36493i	0.421089	−	0.305939i	−0.356987	−	0.934109i	$-0.616196\pi$
$937$	12.8897	−	9.36493i	0.421089	−	0.305939i	0.778076	+	0.628170i	$0.216196\pi$
$938$		0			0
$939$	−2.52961	+	7.78534i	−0.0825507	+	0.254065i
$940$		0			0
$941$	−0.441300	−	0.320623i	−0.0143860	−	0.0104520i	0.580569	−	0.814211i	$-0.302830\pi$
$941$	−0.441300	−	0.320623i	−0.0143860	−	0.0104520i	−0.594955	+	0.803759i	$0.702830\pi$
$942$		0			0
$943$	3.72581	+	11.4669i	0.121329	+	0.373412i
$944$		0			0
$945$	−6.55115			−0.213109
$946$		0			0
$947$	−37.6869			−1.22466			−0.612329	−	0.790603i	$-0.709767\pi$
$947$	−37.6869			−1.22466			−0.612329	+	0.790603i	$0.709767\pi$
$948$		0			0
$949$	−5.68491	−	17.4964i	−0.184540	−	0.567956i
$950$		0			0
$951$	−1.92365	−	1.39762i	−0.0623787	−	0.0453208i
$952$		0			0
$953$	5.74668	−	17.6865i	0.186153	−	0.572920i	−0.813813	−	0.581127i	$-0.802612\pi$
$953$	5.74668	−	17.6865i	0.186153	−	0.572920i	0.999966	+	0.00820613i	$0.00261212\pi$
$954$		0			0
$955$	30.6646	−	22.2792i	0.992284	−	0.720937i
$956$		0			0
$957$	−2.86193	+	11.2574i	−0.0925131	+	0.363899i
$958$		0			0
$959$	−10.2268	+	7.43019i	−0.330240	+	0.239933i
$960$		0			0
$961$	15.5314	−	47.8009i	0.501014	−	1.54196i
$962$		0			0
$963$	−5.04066	−	3.66225i	−0.162433	−	0.118014i
$964$		0			0
$965$	−11.6715	−	35.9213i	−0.375720	−	1.15635i
$966$		0			0
$967$	−31.2311			−1.00432			−0.502162	−	0.864774i	$-0.667462\pi$
$967$	−31.2311			−1.00432			−0.502162	+	0.864774i	$0.667462\pi$
$968$		0			0
$969$	−4.66573			−0.149885
$970$		0			0
$971$	−9.13248	−	28.1069i	−0.293075	−	0.901992i	−0.983861	−	0.178933i	$-0.942735\pi$
$971$	−9.13248	−	28.1069i	−0.293075	−	0.901992i	0.690786	−	0.723059i	$-0.257265\pi$
$972$		0			0
$973$	−5.89052	−	4.27971i	−0.188841	−	0.137201i
$974$		0			0
$975$	0.219297	−	0.674927i	0.00702312	−	0.0216150i
$976$		0			0
$977$	−2.19684	+	1.59610i	−0.0702830	+	0.0510636i	−0.622372	−	0.782722i	$-0.713831\pi$
$977$	−2.19684	+	1.59610i	−0.0702830	+	0.0510636i	0.552089	+	0.833785i	$0.313831\pi$
$978$		0			0
$979$	11.7014	−	46.0272i	0.373978	−	1.47103i
$980$		0			0
$981$	−35.7031	+	25.9398i	−1.13991	+	0.828195i
$982$		0			0
$983$	11.9211	−	36.6893i	0.380223	−	1.17021i	−0.559664	−	0.828720i	$-0.689070\pi$
$983$	11.9211	−	36.6893i	0.380223	−	1.17021i	0.939887	−	0.341486i	$-0.110930\pi$
$984$		0			0
$985$	−41.5904	−	30.2172i	−1.32518	−	0.962800i
$986$		0			0
$987$	−0.142273	−	0.437870i	−0.00452858	−	0.0139376i
$988$		0			0
$989$	17.5163			0.556986
$990$		0			0
$991$	37.8923			1.20369			0.601844	−	0.798614i	$-0.294433\pi$
$991$	37.8923			1.20369			0.601844	+	0.798614i	$0.294433\pi$
$992$		0			0
$993$	3.91070	+	12.0359i	0.124102	+	0.381947i
$994$		0			0
$995$	12.5283	+	9.10234i	0.397173	+	0.288563i
$996$		0			0
$997$	−0.482514	+	1.48503i	−0.0152814	+	0.0470313i	−0.958406	−	0.285407i	$-0.907871\pi$
$997$	−0.482514	+	1.48503i	−0.0152814	+	0.0470313i	0.943125	+	0.332438i	$0.107871\pi$
$998$		0			0
$999$	−16.9142	+	12.2889i	−0.535140	+	0.388802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.r.f.113.3	✓	20
11.2	odd	10		6776.2.a.bn.1.5		10
11.4	even	5	inner	616.2.r.f.169.3	yes	20
11.9	even	5		6776.2.a.bm.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.r.f.113.3	✓	20	1.1	even	1	trivial
616.2.r.f.169.3	yes	20	11.4	even	5	inner
6776.2.a.bm.1.5		10	11.9	even	5
6776.2.a.bn.1.5		10	11.2	odd	10

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:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.r (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.162519 - 0.500181i) q^{3} +(-1.76076 - 1.27927i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(2.20328 - 1.60078i) q^{9} +(0.817183 - 3.21438i) q^{11} +(-4.14760 + 3.01341i) q^{13} +(-0.353708 + 1.08860i) q^{15} +(1.32207 + 0.960538i) q^{17} +(-1.67759 - 5.16308i) q^{19} +0.525921 q^{21} -8.91765 q^{23} +(-0.0813342 - 0.250321i) q^{25} +(-2.43519 - 1.76927i) q^{27} +(2.05779 - 6.33324i) q^{29} +(-7.29287 + 5.29858i) q^{31} +(-1.74058 + 0.113657i) q^{33} +(1.76076 - 1.27927i) q^{35} +(2.14635 - 6.60578i) q^{37} +(2.18131 + 1.58481i) q^{39} +(-0.417802 - 1.28586i) q^{41} -1.96423 q^{43} -5.92727 q^{45} +(-0.270521 - 0.832577i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(0.265582 - 0.817378i) q^{51} +(1.98977 - 1.44565i) q^{53} +(-5.55091 + 4.61435i) q^{55} +(-2.30983 + 1.67819i) q^{57} +(0.640906 - 1.97251i) q^{59} +(12.0238 + 8.73579i) q^{61} +(0.841579 + 2.59011i) q^{63} +11.1579 q^{65} -13.4064 q^{67} +(1.44928 + 4.46043i) q^{69} +(6.02676 + 4.37870i) q^{71} +(-1.10888 + 3.41278i) q^{73} +(-0.111987 + 0.0813636i) q^{75} +(2.80453 + 1.77048i) q^{77} +(10.9314 - 7.94209i) q^{79} +(2.03555 - 6.26477i) q^{81} +(-1.93890 - 1.40869i) q^{83} +(-1.09906 - 3.38255i) q^{85} -3.50219 q^{87} +14.3192 q^{89} +(-1.58424 - 4.87579i) q^{91} +(3.83547 + 2.78663i) q^{93} +(-3.65113 + 11.2370i) q^{95} +(-10.1758 + 7.39317i) q^{97} +(-3.34502 - 8.39031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{3} + 5 q^{7} - 6 q^{9} - 3 q^{11} + 2 q^{13} + 8 q^{15} + 21 q^{19} + 6 q^{21} - 6 q^{23} - 7 q^{25} + 32 q^{27} + 6 q^{29} - 18 q^{31} - 16 q^{33} + 5 q^{37} + 12 q^{39} - 12 q^{41} - 42 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) \) 20 * q - q^3 + 5 * q^7 - 6 * q^9 - 3 * q^11 + 2 * q^13 + 8 * q^15 + 21 * q^19 + 6 * q^21 - 6 * q^23 - 7 * q^25 + 32 * q^27 + 6 * q^29 - 18 * q^31 - 16 * q^33 + 5 * q^37 + 12 * q^39 - 12 * q^41 - 42 * q^43 + 18 * q^45 + 3 * q^47 - 5 * q^49 - q^51 - 38 * q^53 - 15 * q^55 - 3 * q^57 + 36 * q^59 + 23 * q^61 + 11 * q^63 - 30 * q^65 - 2 * q^67 + 43 * q^69 + 48 * q^71 + 6 * q^73 - 67 * q^75 - 17 * q^77 + 43 * q^79 + 16 * q^81 + 5 * q^83 - 16 * q^85 - 16 * q^87 - 46 * q^89 - 2 * q^91 + q^93 + 44 * q^95 + 9 * q^97 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more