LMFDB - Embedded newform 399.2.w.c.170.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [399,2,Mod(170,399)] 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("399.170"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(399, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.w (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0] 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:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.8
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} + 7x^{4} + 36x^{2} + 81 $ x^8 + 4x^6 + 7x^4 + 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			170.3
Root			$0.178197 + 1.72286i$ of defining polynomial
Character	$\chi$	$=$	399.170
Dual form			399.2.w.c.284.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.178197 + 1.72286i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(-2.93649 + 0.614017i) q^{9} +(-3.87298 + 2.23607i) q^{11} +(-2.80588 + 2.03151i) q^{12} +4.24264i q^{13} +(1.58114 - 3.53553i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.93649 - 1.11803i) q^{17} +(3.17423 + 2.98735i) q^{19} -4.47214i q^{20} +(2.62769 - 3.75437i) q^{21} +(-1.93649 - 1.11803i) q^{23} +(-1.58114 - 4.94975i) q^{27} +(1.00000 - 5.19615i) q^{28} -9.48683 q^{29} +(-4.54259 - 6.27415i) q^{33} +(1.93649 + 5.59017i) q^{35} +(-4.00000 - 4.47214i) q^{36} +(7.34847 + 4.24264i) q^{37} +(-7.30948 + 0.756026i) q^{39} +9.48683 q^{41} +5.00000 q^{43} +(-7.74597 - 4.47214i) q^{44} +(6.37298 + 2.09406i) q^{45} +(3.87298 + 2.23607i) q^{47} +(-6.32456 - 2.82843i) q^{48} +(1.00000 + 6.92820i) q^{49} +(2.27129 + 3.13707i) q^{51} +(-7.34847 + 4.24264i) q^{52} +(4.74342 + 8.21584i) q^{53} +10.0000 q^{55} +(-4.58114 + 6.00110i) q^{57} +(7.70486 - 0.796921i) q^{60} +(2.00000 - 3.46410i) q^{61} +(6.93649 + 3.85812i) q^{63} -8.00000 q^{64} +(4.74342 - 8.21584i) q^{65} +(-11.0227 + 6.36396i) q^{67} +(3.87298 + 2.23607i) q^{68} +(1.58114 - 3.53553i) q^{69} +(-4.00000 - 6.92820i) q^{73} +(-2.00000 + 8.48528i) q^{76} +(11.6190 + 2.23607i) q^{77} +(-11.0227 - 6.36396i) q^{79} +(7.74597 - 4.47214i) q^{80} +(8.24597 - 3.60611i) q^{81} +15.6525i q^{83} +(9.13044 + 0.796921i) q^{84} -5.00000 q^{85} +(-1.69052 - 16.3445i) q^{87} +(-4.74342 + 8.21584i) q^{89} +(7.34847 - 8.48528i) q^{91} -4.47214i q^{92} +(-2.80692 - 9.33387i) q^{95} +8.48528i q^{97} +(10.0000 - 8.94427i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 16 q^{7} - 8 q^{9} - 16 q^{16} - 4 q^{19} + 8 q^{28} - 32 q^{36} - 12 q^{39} + 40 q^{43} + 20 q^{45} + 8 q^{49} + 80 q^{55} - 24 q^{57} + 16 q^{61} + 40 q^{63} - 64 q^{64} - 32 q^{73} - 16 q^{76}+ \cdots + 80 q^{99}+O(q^{100}) $ 8 * q + 8 * q^4 - 16 * q^7 - 8 * q^9 - 16 * q^16 - 4 * q^19 + 8 * q^28 - 32 * q^36 - 12 * q^39 + 40 * q^43 + 20 * q^45 + 8 * q^49 + 80 * q^55 - 24 * q^57 + 16 * q^61 + 40 * q^63 - 64 * q^64 - 32 * q^73 - 16 * q^76 + 4 * q^81 - 40 * q^85 - 60 * q^87 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

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		−0.866025	−	0.500000i	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$	0.178197	+	1.72286i	0.102882	+	0.994694i
$3$	0.178197	+	1.72286i	0.102882	+	0.994694i
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	−1.93649	−	1.11803i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$5$	−1.93649	−	1.11803i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$		0			0
$9$	−2.93649	+	0.614017i	−0.978831	+	0.204672i
$10$		0			0
$11$	−3.87298	+	2.23607i	−1.16775	+	0.674200i	−0.953149	−	0.302502i	$-0.902178\pi$
$11$	−3.87298	+	2.23607i	−1.16775	+	0.674200i	−0.214600	+	0.976702i	$0.568845\pi$
$12$	−2.80588	+	2.03151i	−0.809989	+	0.586445i
$13$			4.24264i			1.17670i	0.808608	+	0.588348i	$0.200222\pi$
$13$			4.24264i			1.17670i	−0.808608	+	0.588348i	$0.799778\pi$
$14$		0			0
$15$	1.58114	−	3.53553i	0.408248	−	0.912871i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	1.93649	−	1.11803i	0.469668	−	0.271163i	−0.246433	−	0.969160i	$-0.579258\pi$
$17$	1.93649	−	1.11803i	0.469668	−	0.271163i	0.716101	+	0.697997i	$0.245925\pi$
$18$		0			0
$19$	3.17423	+	2.98735i	0.728219	+	0.685344i
$19$	3.17423	+	2.98735i	0.728219	+	0.685344i
$20$		−	4.47214i		−	1.00000i
$21$	2.62769	−	3.75437i	0.573408	−	0.819270i
$22$		0			0
$23$	−1.93649	−	1.11803i	−0.403786	−	0.233126i	0.284330	−	0.958726i	$-0.408229\pi$
$23$	−1.93649	−	1.11803i	−0.403786	−	0.233126i	−0.688116	+	0.725600i	$0.741562\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.58114	−	4.94975i	−0.304290	−	0.952579i
$28$	1.00000	−	5.19615i	0.188982	−	0.981981i
$29$	−9.48683			−1.76166			−0.880830	−	0.473432i	$-0.843015\pi$
$29$	−9.48683			−1.76166			−0.880830	+	0.473432i	$0.843015\pi$
$30$		0			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$		0			0
$33$	−4.54259	−	6.27415i	−0.790763	−	1.09219i
$34$		0			0
$35$	1.93649	+	5.59017i	0.327327	+	0.944911i
$36$	−4.00000	−	4.47214i	−0.666667	−	0.745356i
$37$	7.34847	+	4.24264i	1.20808	+	0.697486i	0.962340	−	0.271850i	$-0.0876353\pi$
$37$	7.34847	+	4.24264i	1.20808	+	0.697486i	0.245741	+	0.969335i	$0.420969\pi$
$38$		0			0
$39$	−7.30948	+	0.756026i	−1.17045	+	0.121061i
$40$		0			0
$41$	9.48683			1.48159			0.740797	−	0.671729i	$-0.234448\pi$
$41$	9.48683			1.48159			0.740797	+	0.671729i	$0.234448\pi$
$42$		0			0
$43$	5.00000			0.762493			0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000			0.762493			0.381246	+	0.924473i	$0.375495\pi$
$44$	−7.74597	−	4.47214i	−1.16775	−	0.674200i
$45$	6.37298	+	2.09406i	0.950028	+	0.312164i
$46$		0			0
$47$	3.87298	+	2.23607i	0.564933	+	0.326164i	0.755123	−	0.655583i	$-0.227577\pi$
$47$	3.87298	+	2.23607i	0.564933	+	0.326164i	−0.190190	+	0.981747i	$0.560910\pi$
$48$	−6.32456	−	2.82843i	−0.912871	−	0.408248i
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$	2.27129	+	3.13707i	0.318045	+	0.439278i
$52$	−7.34847	+	4.24264i	−1.01905	+	0.588348i
$53$	4.74342	+	8.21584i	0.651558	+	1.12853i	0.982745	+	0.184967i	$0.0592178\pi$
$53$	4.74342	+	8.21584i	0.651558	+	1.12853i	−0.331186	+	0.943565i	$0.607449\pi$
$54$		0			0
$55$	10.0000			1.34840
$56$		0			0
$57$	−4.58114	+	6.00110i	−0.606787	+	0.794865i
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	7.70486	−	0.796921i	0.994694	−	0.102882i
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$		0			0
$63$	6.93649	+	3.85812i	0.873916	+	0.486077i
$64$	−8.00000			−1.00000
$65$	4.74342	−	8.21584i	0.588348	−	1.01905i
$66$		0			0
$67$	−11.0227	+	6.36396i	−1.34664	+	0.777482i	−0.987772	−	0.155908i	$-0.950170\pi$
$67$	−11.0227	+	6.36396i	−1.34664	+	0.777482i	−0.358866	+	0.933389i	$0.616836\pi$
$68$	3.87298	+	2.23607i	0.469668	+	0.271163i
$69$	1.58114	−	3.53553i	0.190347	−	0.425628i
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−4.00000	−	6.92820i	−0.468165	−	0.810885i	0.531174	−	0.847263i	$-0.321751\pi$
$73$	−4.00000	−	6.92820i	−0.468165	−	0.810885i	−0.999338	+	0.0363782i	$0.988418\pi$
$74$		0			0
$75$		0			0
$76$	−2.00000	+	8.48528i	−0.229416	+	0.973329i
$77$	11.6190	+	2.23607i	1.32410	+	0.254824i
$78$		0			0
$79$	−11.0227	−	6.36396i	−1.24015	−	0.716002i	−0.271026	−	0.962572i	$-0.587363\pi$
$79$	−11.0227	−	6.36396i	−1.24015	−	0.716002i	−0.969125	+	0.246570i	$0.920696\pi$
$80$	7.74597	−	4.47214i	0.866025	−	0.500000i
$81$	8.24597	−	3.60611i	0.916219	−	0.400679i
$82$		0			0
$83$			15.6525i			1.71808i	0.511906	+	0.859041i	$0.328939\pi$
$83$			15.6525i			1.71808i	−0.511906	+	0.859041i	$0.671061\pi$
$84$	9.13044	+	0.796921i	0.996213	+	0.0869512i
$85$	−5.00000			−0.542326
$86$		0			0
$87$	−1.69052	−	16.3445i	−0.181243	−	1.75231i
$88$		0			0
$89$	−4.74342	+	8.21584i	−0.502801	+	0.870877i	0.497194	+	0.867640i	$0.334364\pi$
$89$	−4.74342	+	8.21584i	−0.502801	+	0.870877i	−0.999995	+	0.00323751i	$0.998969\pi$
$90$		0			0
$91$	7.34847	−	8.48528i	0.770329	−	0.889499i
$92$		−	4.47214i		−	0.466252i
$93$		0			0
$94$		0			0
$95$	−2.80692	−	9.33387i	−0.287984	−	0.957635i
$96$		0			0
$97$			8.48528i			0.861550i	0.902459	+	0.430775i	$0.141760\pi$
$97$			8.48528i			0.861550i	−0.902459	+	0.430775i	$0.858240\pi$
$98$		0			0
$99$	10.0000	−	8.94427i	1.00504	−	0.898933i
$100$		0			0
$101$	13.5554	−	7.82624i	1.34882	−	0.778740i	0.360735	−	0.932668i	$-0.382526\pi$
$101$	13.5554	−	7.82624i	1.34882	−	0.778740i	0.988082	+	0.153929i	$0.0491926\pi$
$102$		0			0
$103$	3.67423	+	2.12132i	0.362033	+	0.209020i	0.669972	−	0.742386i	$-0.266306\pi$
$103$	3.67423	+	2.12132i	0.362033	+	0.209020i	−0.307939	+	0.951406i	$0.599639\pi$
$104$		0			0
$105$	−9.28600	+	4.33246i	−0.906221	+	0.422804i
$106$		0			0
$107$	−4.74342	+	8.21584i	−0.458563	+	0.794255i	−0.998885	−	0.0472033i	$-0.984969\pi$
$107$	−4.74342	+	8.21584i	−0.458563	+	0.794255i	0.540322	+	0.841458i	$0.318302\pi$
$108$	6.99208	−	7.68836i	0.672813	−	0.739813i
$109$	7.34847	−	4.24264i	0.703856	−	0.406371i	−0.104926	−	0.994480i	$-0.533461\pi$
$109$	7.34847	−	4.24264i	0.703856	−	0.406371i	0.808782	+	0.588109i	$0.200127\pi$
$110$		0			0
$111$	−6.00000	+	13.4164i	−0.569495	+	1.27343i
$112$	10.0000	−	3.46410i	0.944911	−	0.327327i
$113$	9.48683			0.892446			0.446223	−	0.894922i	$-0.352769\pi$
$113$	9.48683			0.892446			0.446223	+	0.894922i	$0.352769\pi$
$114$		0			0
$115$	2.50000	+	4.33013i	0.233126	+	0.403786i
$116$	−9.48683	−	16.4317i	−0.880830	−	1.52564i
$117$	−2.60505	−	12.4585i	−0.240837	−	1.15179i
$118$		0			0
$119$	−5.80948	−	1.11803i	−0.532554	−	0.102490i
$120$		0			0
$121$	4.50000	−	7.79423i	0.409091	−	0.708566i
$122$		0			0
$123$	1.69052	+	16.3445i	0.152430	+	1.47373i
$124$		0			0
$125$			11.1803i			1.00000i
$126$		0			0
$127$		−	12.7279i		−	1.12942i	−0.825289	−	0.564710i	$-0.808988\pi$
$127$		−	12.7279i		−	1.12942i	0.825289	−	0.564710i	$-0.191012\pi$
$128$		0			0
$129$	0.890985	+	8.61430i	0.0784468	+	0.758447i
$130$		0			0
$131$	−13.5554	−	7.82624i	−1.18434	−	0.683782i	−0.227329	−	0.973818i	$-0.572999\pi$
$131$	−13.5554	−	7.82624i	−1.18434	−	0.683782i	−0.957016	+	0.290036i	$0.906333\pi$
$132$	6.32456	−	14.1421i	0.550482	−	1.23091i
$133$	−1.17423	−	11.4726i	−0.101819	−	0.994803i
$134$		0			0
$135$	−2.47212	+	11.3529i	−0.212767	+	0.977103i
$136$		0			0
$137$	−3.87298	+	2.23607i	−0.330891	+	0.191040i	−0.656237	−	0.754555i	$-0.727853\pi$
$137$	−3.87298	+	2.23607i	−0.330891	+	0.191040i	0.325345	+	0.945595i	$0.394519\pi$
$138$		0			0
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$	−7.74597	+	8.94427i	−0.654654	+	0.755929i
$141$	−3.16228	+	7.07107i	−0.266312	+	0.595491i
$142$		0			0
$143$	−9.48683	−	16.4317i	−0.793329	−	1.37409i
$144$	3.74597	−	11.4003i	0.312164	−	0.950028i
$145$	18.3712	+	10.6066i	1.52564	+	0.880830i
$146$		0			0
$147$	−11.7581	+	2.95744i	−0.969794	+	0.243926i
$148$			16.9706i			1.39497i
$149$	−1.93649	−	1.11803i	−0.158644	−	0.0915929i	0.418576	−	0.908182i	$-0.362529\pi$
$149$	−1.93649	−	1.11803i	−0.158644	−	0.0915929i	−0.577220	+	0.816589i	$0.695863\pi$
$150$		0			0
$151$	3.67423	−	2.12132i	0.299005	−	0.172631i	−0.342991	−	0.939339i	$-0.611440\pi$
$151$	3.67423	−	2.12132i	0.299005	−	0.172631i	0.641996	+	0.766708i	$0.278107\pi$
$152$		0			0
$153$	−5.00000	+	4.47214i	−0.404226	+	0.361551i
$154$		0			0
$155$		0			0
$156$	−8.61895	−	11.9044i	−0.690068	−	0.953111i
$157$	−5.50000	−	9.52628i	−0.438948	−	0.760280i	0.558661	−	0.829396i	$-0.311315\pi$
$157$	−5.50000	−	9.52628i	−0.438948	−	0.760280i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$		0			0
$159$	−13.3095	+	9.63628i	−1.05551	+	0.764207i
$160$		0			0
$161$	1.93649	+	5.59017i	0.152617	+	0.440567i
$162$		0			0
$163$	−8.50000	+	14.7224i	−0.665771	+	1.15315i	0.313304	+	0.949653i	$0.398564\pi$
$163$	−8.50000	+	14.7224i	−0.665771	+	1.15315i	−0.979076	+	0.203497i	$0.934769\pi$
$164$	9.48683	+	16.4317i	0.740797	+	1.28310i
$165$	1.78197	+	17.2286i	0.138726	+	1.34124i
$166$		0			0
$167$	9.48683			0.734113			0.367057	−	0.930199i	$-0.380366\pi$
$167$	9.48683			0.734113			0.367057	+	0.930199i	$0.380366\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$		0			0
$171$	−11.1554	−	6.82328i	−0.853074	−	0.521789i
$172$	5.00000	+	8.66025i	0.381246	+	0.660338i
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$		0			0
$175$		0			0
$176$		−	17.8885i		−	1.34840i
$177$		0			0
$178$		0			0
$179$	4.74342	+	8.21584i	0.354540	+	0.614081i	0.987039	−	0.160480i	$-0.0513043\pi$
$179$	4.74342	+	8.21584i	0.354540	+	0.614081i	−0.632499	+	0.774561i	$0.717971\pi$
$180$	2.74597	+	13.1324i	0.204672	+	0.978831i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	6.32456	+	2.82843i	0.467525	+	0.209083i
$184$		0			0
$185$	−9.48683	−	16.4317i	−0.697486	−	1.20808i
$186$		0			0
$187$	−5.00000	+	8.66025i	−0.365636	+	0.633300i
$188$			8.94427i			0.652328i
$189$	−5.41094	+	12.6381i	−0.393588	+	0.919287i
$190$		0			0
$191$	−13.5554	−	7.82624i	−0.980837	−	0.566287i	−0.0783145	−	0.996929i	$-0.524954\pi$
$191$	−13.5554	−	7.82624i	−0.980837	−	0.566287i	−0.902523	+	0.430642i	$0.858287\pi$
$192$	−1.42558	−	13.7829i	−0.102882	−	0.994694i
$193$	11.0227	−	6.36396i	0.793432	−	0.458088i	−0.0477376	−	0.998860i	$-0.515201\pi$
$193$	11.0227	−	6.36396i	0.793432	−	0.458088i	0.841169	+	0.540772i	$0.181868\pi$
$194$		0			0
$195$	15.0000	+	6.70820i	1.07417	+	0.480384i
$196$	−11.0000	+	8.66025i	−0.785714	+	0.618590i
$197$		−	11.1803i		−	0.796566i	−0.917263	−	0.398283i	$-0.869606\pi$
$197$		−	11.1803i		−	0.796566i	0.917263	−	0.398283i	$-0.130394\pi$
$198$		0			0
$199$	−8.50000	−	14.7224i	−0.602549	−	1.04365i	−0.992434	−	0.122782i	$-0.960818\pi$
$199$	−8.50000	−	14.7224i	−0.602549	−	1.04365i	0.389885	−	0.920864i	$-0.372515\pi$
$200$		0			0
$201$	−12.9284	−	17.8565i	−0.911901	−	1.25950i
$202$		0			0
$203$	18.9737	+	16.4317i	1.33169	+	1.15328i
$204$	−3.16228	+	7.07107i	−0.221404	+	0.495074i
$205$	−18.3712	−	10.6066i	−1.28310	−	0.740797i
$206$		0			0
$207$	6.37298	+	2.09406i	0.442953	+	0.145547i
$208$	−14.6969	−	8.48528i	−1.01905	−	0.588348i
$209$	−18.9737	−	4.47214i	−1.31244	−	0.309344i
$210$		0			0
$211$			4.24264i			0.292075i	0.989279	+	0.146038i	$0.0466521\pi$
$211$			4.24264i			0.292075i	−0.989279	+	0.146038i	$0.953348\pi$
$212$	−9.48683	+	16.4317i	−0.651558	+	1.12853i
$213$		0			0
$214$		0			0
$215$	−9.68246	−	5.59017i	−0.660338	−	0.381246i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	11.2235	−	8.12602i	0.758416	−	0.549106i
$220$	10.0000	+	17.3205i	0.674200	+	1.16775i
$221$	4.74342	+	8.21584i	0.319077	+	0.552657i
$222$		0			0
$223$		−	4.24264i		−	0.284108i	−0.989859	−	0.142054i	$-0.954629\pi$
$223$		−	4.24264i		−	0.284108i	0.989859	−	0.142054i	$-0.0453707\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.48683	+	16.4317i	0.629663	+	1.09061i	0.987619	+	0.156870i	$0.0501404\pi$
$227$	9.48683	+	16.4317i	0.629663	+	1.09061i	−0.357956	+	0.933738i	$0.616526\pi$
$228$	−14.9753	−	1.93367i	−0.991766	−	0.128060i
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$		0			0
$231$	−1.78197	+	20.4163i	−0.117245	+	1.34329i
$232$		0			0
$233$	−1.93649	−	1.11803i	−0.126864	−	0.0732448i	0.435225	−	0.900322i	$-0.356669\pi$
$233$	−1.93649	−	1.11803i	−0.126864	−	0.0732448i	−0.562089	+	0.827077i	$0.690002\pi$
$234$		0			0
$235$	−5.00000	−	8.66025i	−0.326164	−	0.564933i
$236$		0			0
$237$	9.00000	−	20.1246i	0.584613	−	1.30723i
$238$		0			0
$239$			15.6525i			1.01247i	0.862394	+	0.506237i	$0.168964\pi$
$239$			15.6525i			1.01247i	−0.862394	+	0.506237i	$0.831036\pi$
$240$	9.08517	+	12.5483i	0.586445	+	0.809989i
$241$	14.6969	−	8.48528i	0.946713	−	0.546585i	0.0546547	−	0.998505i	$-0.482594\pi$
$241$	14.6969	−	8.48528i	0.946713	−	0.546585i	0.892058	+	0.451920i	$0.149261\pi$
$242$		0			0
$243$	7.68223	+	13.5640i	0.492815	+	0.870134i
$244$	8.00000			0.512148
$245$	5.80948	−	14.5344i	0.371154	−	0.928571i
$246$		0			0
$247$	−12.6742	+	13.4671i	−0.806442	+	0.856893i
$248$		0			0
$249$	−26.9670	+	2.78922i	−1.70897	+	0.176760i
$250$		0			0
$251$		−	11.1803i		−	0.705697i	−0.935681	−	0.352848i	$-0.885213\pi$
$251$		−	11.1803i		−	0.705697i	0.935681	−	0.352848i	$-0.114787\pi$
$252$	0.254033	+	15.8725i	0.0160026	+	0.999872i
$253$	10.0000			0.628695
$254$		0			0
$255$	−0.890985	−	8.61430i	−0.0557956	−	0.539448i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	4.74342	−	8.21584i	0.295886	−	0.512490i	−0.679304	−	0.733857i	$-0.737718\pi$
$257$	4.74342	−	8.21584i	0.295886	−	0.512490i	0.975191	+	0.221367i	$0.0710518\pi$
$258$		0			0
$259$	−7.34847	−	21.2132i	−0.456612	−	1.31812i
$260$	18.9737			1.17670
$261$	27.8580	−	5.82508i	1.72437	−	0.360563i
$262$		0			0
$263$	−9.68246	+	5.59017i	−0.597046	+	0.344705i	−0.767879	−	0.640595i	$-0.778688\pi$
$263$	−9.68246	+	5.59017i	−0.597046	+	0.344705i	0.170833	+	0.985300i	$0.445354\pi$
$264$		0			0
$265$		−	21.2132i		−	1.30312i
$266$		0			0
$267$	−15.0000	−	6.70820i	−0.917985	−	0.410535i
$268$	−22.0454	−	12.7279i	−1.34664	−	0.777482i
$269$	−9.48683	−	16.4317i	−0.578422	−	1.00186i	−0.995661	−	0.0930598i	$-0.970335\pi$
$269$	−9.48683	−	16.4317i	−0.578422	−	1.00186i	0.417238	−	0.908797i	$-0.362998\pi$
$270$		0			0
$271$	−8.50000	+	14.7224i	−0.516338	+	0.894324i	0.483482	+	0.875354i	$0.339372\pi$
$271$	−8.50000	+	14.7224i	−0.516338	+	0.894324i	−0.999820	+	0.0189696i	$0.993961\pi$
$272$			8.94427i			0.542326i
$273$	15.9284	+	11.1483i	0.964032	+	0.674728i
$274$		0			0
$275$		0			0
$276$	7.70486	−	0.796921i	0.463778	−	0.0479690i
$277$	2.00000	+	3.46410i	0.120168	+	0.208138i	0.919834	−	0.392308i	$-0.128323\pi$
$277$	2.00000	+	3.46410i	0.120168	+	0.208138i	−0.799666	+	0.600446i	$0.794990\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.48683			−0.565937			−0.282969	−	0.959129i	$-0.591319\pi$
$281$	−9.48683			−0.565937			−0.282969	+	0.959129i	$0.591319\pi$
$282$		0			0
$283$	3.50000	+	6.06218i	0.208053	+	0.360359i	0.951101	−	0.308879i	$-0.0999539\pi$
$283$	3.50000	+	6.06218i	0.208053	+	0.360359i	−0.743048	+	0.669238i	$0.766621\pi$
$284$		0			0
$285$	15.5808	−	6.49921i	0.922925	−	0.384980i
$286$		0			0
$287$	−18.9737	−	16.4317i	−1.11998	−	0.969931i
$288$		0			0
$289$	−6.00000	+	10.3923i	−0.352941	+	0.611312i
$290$		0			0
$291$	−14.6190	+	1.51205i	−0.856978	+	0.0886380i
$292$	8.00000	−	13.8564i	0.468165	−	0.810885i
$293$	−18.9737			−1.10845			−0.554227	−	0.832366i	$-0.686986\pi$
$293$	−18.9737			−1.10845			−0.554227	+	0.832366i	$0.686986\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	17.1917	+	15.6348i	0.997563	+	0.907221i
$298$		0			0
$299$	4.74342	−	8.21584i	0.274319	−	0.475134i
$300$		0			0
$301$	−10.0000	−	8.66025i	−0.576390	−	0.499169i
$302$		0			0
$303$	15.8990	+	21.9595i	0.913377	+	1.26154i
$304$	−16.6969	+	5.02118i	−0.957635	+	0.287984i
$305$	−7.74597	+	4.47214i	−0.443533	+	0.256074i
$306$		0			0
$307$			25.4558i			1.45284i	0.687250	+	0.726421i	$0.258818\pi$
$307$			25.4558i			1.45284i	−0.687250	+	0.726421i	$0.741182\pi$
$308$	7.74597	+	22.3607i	0.441367	+	1.27412i
$309$	−3.00000	+	6.70820i	−0.170664	+	0.381616i
$310$		0			0
$311$	13.5554	−	7.82624i	0.768659	−	0.443785i	−0.0637373	−	0.997967i	$-0.520302\pi$
$311$	13.5554	−	7.82624i	0.768659	−	0.443785i	0.832396	+	0.554181i	$0.186969\pi$
$312$		0			0
$313$	−2.50000	+	4.33013i	−0.141308	+	0.244753i	−0.927990	−	0.372606i	$-0.878464\pi$
$313$	−2.50000	+	4.33013i	−0.141308	+	0.244753i	0.786681	+	0.617359i	$0.211798\pi$
$314$		0			0
$315$	−9.11895	−	15.2264i	−0.513795	−	0.857913i
$316$		−	25.4558i		−	1.43200i
$317$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$317$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$318$		0			0
$319$	36.7423	−	21.2132i	2.05718	−	1.18771i
$320$	15.4919	+	8.94427i	0.866025	+	0.500000i
$321$	−15.0000	−	6.70820i	−0.837218	−	0.374415i
$322$		0			0
$323$	9.48683	+	2.23607i	0.527862	+	0.124418i
$324$	14.4919	+	10.6763i	0.805107	+	0.593129i
$325$		0			0
$326$		0			0
$327$	8.61895	+	11.9044i	0.476629	+	0.658312i
$328$		0			0
$329$	−3.87298	−	11.1803i	−0.213524	−	0.616392i
$330$		0			0
$331$	−22.0454	−	12.7279i	−1.21173	−	0.699590i	−0.248590	−	0.968609i	$-0.579967\pi$
$331$	−22.0454	−	12.7279i	−1.21173	−	0.699590i	−0.963135	+	0.269019i	$0.913301\pi$
$332$	−27.1109	+	15.6525i	−1.48790	+	0.859041i
$333$	−24.1838	−	7.94640i	−1.32526	−	0.435460i
$334$		0			0
$335$	28.4605			1.55496
$336$	7.75013	+	16.6113i	0.422804	+	0.906221i
$337$			16.9706i			0.924445i	0.886764	+	0.462223i	$0.152948\pi$
$337$			16.9706i			0.924445i	−0.886764	+	0.462223i	$0.847052\pi$
$338$		0			0
$339$	1.69052	+	16.3445i	0.0918167	+	0.887710i
$340$	−5.00000	−	8.66025i	−0.271163	−	0.469668i
$341$		0			0
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$	−7.01471	+	5.07877i	−0.377659	+	0.273432i
$346$		0			0
$347$	1.93649	−	1.11803i	0.103956	−	0.0600192i	−0.447120	−	0.894474i	$-0.647550\pi$
$347$	1.93649	−	1.11803i	0.103956	−	0.0600192i	0.551077	+	0.834455i	$0.314217\pi$
$348$	26.6190	−	19.2726i	1.42693	−	1.03312i
$349$	−1.00000			−0.0535288			−0.0267644	−	0.999642i	$-0.508520\pi$
$349$	−1.00000			−0.0535288			−0.0267644	+	0.999642i	$0.508520\pi$
$350$		0			0
$351$	21.0000	−	6.70820i	1.12090	−	0.358057i
$352$		0			0
$353$	7.74597	−	4.47214i	0.412276	−	0.238028i	−0.279491	−	0.960148i	$-0.590166\pi$
$353$	7.74597	−	4.47214i	0.412276	−	0.238028i	0.691767	+	0.722121i	$0.256832\pi$
$354$		0			0
$355$		0			0
$356$	−18.9737			−1.00560
$357$	0.890985	−	10.2081i	0.0471559	−	0.540272i
$358$		0			0
$359$	27.1109	+	15.6525i	1.43086	+	0.826106i	0.997186	−	0.0749650i	$-0.0238845\pi$
$359$	27.1109	+	15.6525i	1.43086	+	0.826106i	0.433672	+	0.901071i	$0.357218\pi$
$360$		0			0
$361$	1.15153	+	18.9651i	0.0606069	+	0.998162i
$362$		0			0
$363$	14.2302	+	6.36396i	0.746894	+	0.334021i
$364$	22.0454	+	4.24264i	1.15549	+	0.222375i
$365$			17.8885i			0.936329i
$366$		0			0
$367$	5.00000	+	8.66025i	0.260998	+	0.452062i	0.966507	−	0.256639i	$-0.0826151\pi$
$367$	5.00000	+	8.66025i	0.260998	+	0.452062i	−0.705509	+	0.708700i	$0.749282\pi$
$368$	7.74597	−	4.47214i	0.403786	−	0.233126i
$369$	−27.8580	+	5.82508i	−1.45023	+	0.303241i
$370$		0			0
$371$	4.74342	−	24.6475i	0.246266	−	1.27964i
$372$		0			0
$373$	3.67423	+	2.12132i	0.190245	+	0.109838i	0.592097	−	0.805867i	$-0.298300\pi$
$373$	3.67423	+	2.12132i	0.190245	+	0.109838i	−0.401852	+	0.915704i	$0.631634\pi$
$374$		0			0
$375$	−19.2622	+	1.99230i	−0.994694	+	0.102882i
$376$		0			0
$377$		−	40.2492i		−	2.07294i
$378$		0			0
$379$			12.7279i			0.653789i	0.945061	+	0.326895i	$0.106002\pi$
$379$			12.7279i			0.653789i	−0.945061	+	0.326895i	$0.893998\pi$
$380$	13.3598	−	14.1956i	0.685344	−	0.728219i
$381$	21.9284	−	2.26808i	1.12343	−	0.116197i
$382$		0			0
$383$	4.74342	−	8.21584i	0.242377	−	0.419810i	−0.719014	−	0.694996i	$-0.755406\pi$
$383$	4.74342	−	8.21584i	0.242377	−	0.419810i	0.961391	+	0.275186i	$0.0887395\pi$
$384$		0			0
$385$	−20.0000	−	17.3205i	−1.01929	−	0.882735i
$386$		0			0
$387$	−14.6825	+	3.07008i	−0.746351	+	0.156061i
$388$	−14.6969	+	8.48528i	−0.746124	+	0.430775i
$389$	25.1744	−	14.5344i	1.27639	−	0.736925i	0.300209	−	0.953873i	$-0.402944\pi$
$389$	25.1744	−	14.5344i	1.27639	−	0.736925i	0.976183	+	0.216948i	$0.0696102\pi$
$390$		0			0
$391$	−5.00000			−0.252861
$392$		0			0
$393$	11.0680	−	24.7487i	0.558305	−	1.24841i
$394$		0			0
$395$	14.2302	+	24.6475i	0.716002	+	1.24015i
$396$	25.4919	+	8.37624i	1.28102	+	0.420922i
$397$	12.5000	−	21.6506i	0.627357	−	1.08661i	−0.360723	−	0.932673i	$-0.617470\pi$
$397$	12.5000	−	21.6506i	0.627357	−	1.08661i	0.988080	−	0.153941i	$-0.0491966\pi$
$398$		0			0
$399$	19.5565	−	4.06743i	0.979049	−	0.203626i
$400$		0			0
$401$	−9.48683	+	16.4317i	−0.473750	+	0.820559i	−0.999548	−	0.0300503i	$-0.990433\pi$
$401$	−9.48683	+	16.4317i	−0.473750	+	0.820559i	0.525799	+	0.850609i	$0.323767\pi$
$402$		0			0
$403$		0			0
$404$	27.1109	+	15.6525i	1.34882	+	0.778740i
$405$	−20.0000	−	2.23607i	−0.993808	−	0.111111i
$406$		0			0
$407$	−37.9473			−1.88098
$408$		0			0
$409$	11.0227	−	6.36396i	0.545038	−	0.314678i	−0.202080	−	0.979369i	$-0.564770\pi$
$409$	11.0227	−	6.36396i	0.545038	−	0.314678i	0.747118	+	0.664691i	$0.231437\pi$
$410$		0			0
$411$	−4.54259	−	6.27415i	−0.224069	−	0.309481i
$412$			8.48528i			0.418040i
$413$		0			0
$414$		0			0
$415$	17.5000	−	30.3109i	0.859041	−	1.48790i
$416$		0			0
$417$	0.356394	+	3.44572i	0.0174527	+	0.168738i
$418$		0			0
$419$			2.23607i			0.109239i	0.998507	+	0.0546195i	$0.0173946\pi$
$419$			2.23607i			0.109239i	−0.998507	+	0.0546195i	$0.982605\pi$
$420$	−16.7900	−	11.7514i	−0.819270	−	0.573408i
$421$		−	4.24264i		−	0.206774i	−0.994641	−	0.103387i	$-0.967032\pi$
$421$		−	4.24264i		−	0.206774i	0.994641	−	0.103387i	$-0.0329680\pi$
$422$		0			0
$423$	−12.7460	−	4.18812i	−0.619730	−	0.203633i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−10.0000	+	3.46410i	−0.483934	+	0.167640i
$428$	−18.9737			−0.917127
$429$	26.6190	−	19.2726i	1.28518	−	0.930488i
$430$		0			0
$431$	18.9737	+	32.8634i	0.913929	+	1.58297i	0.808461	+	0.588549i	$0.200301\pi$
$431$	18.9737	+	32.8634i	0.913929	+	1.58297i	0.105468	+	0.994423i	$0.466366\pi$
$432$	20.3087	+	4.42227i	0.977103	+	0.212767i
$433$			12.7279i			0.611665i	0.952085	+	0.305832i	$0.0989347\pi$
$433$			12.7279i			0.611665i	−0.952085	+	0.305832i	$0.901065\pi$
$434$		0			0
$435$	−15.0000	+	33.5410i	−0.719195	+	1.60817i
$436$	14.6969	+	8.48528i	0.703856	+	0.406371i
$437$	−2.80692	−	9.33387i	−0.134273	−	0.446500i
$438$		0			0
$439$	−11.0227	−	6.36396i	−0.526085	−	0.303735i	0.213336	−	0.976979i	$-0.431567\pi$
$439$	−11.0227	−	6.36396i	−0.526085	−	0.303735i	−0.739421	+	0.673244i	$0.764901\pi$
$440$		0			0
$441$	−7.19052	−	19.7306i	−0.342406	−	0.939552i
$442$		0			0
$443$	9.68246	+	5.59017i	0.460027	+	0.265597i	0.712056	−	0.702123i	$-0.247764\pi$
$443$	9.68246	+	5.59017i	0.460027	+	0.265597i	−0.252028	+	0.967720i	$0.581098\pi$
$444$	−29.2379	+	3.02410i	−1.38757	+	0.143518i
$445$	18.3712	−	10.6066i	0.870877	−	0.502801i
$446$		0			0
$447$	1.58114	−	3.53553i	0.0747853	−	0.167225i
$448$	16.0000	+	13.8564i	0.755929	+	0.654654i
$449$	28.4605			1.34313			0.671567	−	0.740944i	$-0.265622\pi$
$449$	28.4605			1.34313			0.671567	+	0.740944i	$0.265622\pi$
$450$		0			0
$451$	−36.7423	+	21.2132i	−1.73013	+	0.998891i
$452$	9.48683	+	16.4317i	0.446223	+	0.772881i
$453$	4.30948	+	5.95218i	0.202477	+	0.279658i
$454$		0			0
$455$	−23.7171	+	8.21584i	−1.11187	+	0.385164i
$456$		0			0
$457$	2.00000	−	3.46410i	0.0935561	−	0.162044i	−0.815449	−	0.578829i	$-0.803510\pi$
$457$	2.00000	−	3.46410i	0.0935561	−	0.162044i	0.909005	+	0.416785i	$0.136843\pi$
$458$		0			0
$459$	−8.59585	−	7.81738i	−0.401220	−	0.364884i
$460$	−5.00000	+	8.66025i	−0.233126	+	0.403786i
$461$		−	4.47214i		−	0.208288i	−0.994562	−	0.104144i	$-0.966790\pi$
$461$		−	4.47214i		−	0.208288i	0.994562	−	0.104144i	$-0.0332103\pi$
$462$		0			0
$463$	38.0000			1.76601			0.883005	−	0.469364i	$-0.155517\pi$
$463$	38.0000			1.76601			0.883005	+	0.469364i	$0.155517\pi$
$464$	18.9737	−	32.8634i	0.880830	−	1.52564i
$465$		0			0
$466$		0			0
$467$	−7.74597	−	4.47214i	−0.358441	−	0.206946i	0.309956	−	0.950751i	$-0.399686\pi$
$467$	−7.74597	−	4.47214i	−0.358441	−	0.206946i	−0.668397	+	0.743805i	$0.733019\pi$
$468$	18.9737	−	16.9706i	0.877058	−	0.784465i
$469$	33.0681	+	6.36396i	1.52694	+	0.293860i
$470$		0			0
$471$	15.4324	−	11.1733i	0.711086	−	0.514838i
$472$		0			0
$473$	−19.3649	+	11.1803i	−0.890400	+	0.514073i
$474$		0			0
$475$		0			0
$476$	−3.87298	−	11.1803i	−0.177518	−	0.512450i
$477$	−18.9737	−	21.2132i	−0.868744	−	0.971286i
$478$		0			0
$479$	−21.3014	+	12.2984i	−0.973286	+	0.561927i	−0.900236	−	0.435401i	$-0.856607\pi$
$479$	−21.3014	+	12.2984i	−0.973286	+	0.561927i	−0.0730497	+	0.997328i	$0.523273\pi$
$480$		0			0
$481$	−18.0000	+	31.1769i	−0.820729	+	1.42154i
$482$		0			0
$483$	−9.28600	+	4.33246i	−0.422528	+	0.197134i
$484$	18.0000			0.818182
$485$	9.48683	−	16.4317i	0.430775	−	0.746124i
$486$		0			0
$487$	−3.67423	+	2.12132i	−0.166495	+	0.0961262i	−0.580932	−	0.813952i	$-0.697312\pi$
$487$	−3.67423	+	2.12132i	−0.166495	+	0.0961262i	0.414437	+	0.910078i	$0.363979\pi$
$488$		0			0
$489$	−26.8794	−	12.0208i	−1.21553	−	0.543600i
$490$		0			0
$491$			2.23607i			0.100912i	0.998726	+	0.0504562i	$0.0160675\pi$
$491$			2.23607i			0.100912i	−0.998726	+	0.0504562i	$0.983932\pi$
$492$	−26.6190	+	19.2726i	−1.20007	+	0.868874i
$493$	−18.3712	+	10.6066i	−0.827396	+	0.477697i
$494$		0			0
$495$	−29.3649	+	6.14017i	−1.31985	+	0.275980i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	3.50000	−	6.06218i	0.156682	−	0.271380i	−0.776989	−	0.629515i	$-0.783254\pi$
$499$	3.50000	−	6.06218i	0.156682	−	0.271380i	0.933670	+	0.358134i	$0.116587\pi$
$500$	−19.3649	+	11.1803i	−0.866025	+	0.500000i
$501$	1.69052	+	16.3445i	0.0755271	+	0.730218i
$502$		0			0
$503$			29.0689i			1.29612i	0.761590	+	0.648059i	$0.224419\pi$
$503$			29.0689i			1.29612i	−0.761590	+	0.648059i	$0.775581\pi$
$504$		0			0
$505$	−35.0000			−1.55748
$506$		0			0
$507$	−0.890985	−	8.61430i	−0.0395700	−	0.382574i
$508$	22.0454	−	12.7279i	0.978107	−	0.564710i
$509$	−9.48683	+	16.4317i	−0.420496	+	0.728321i	−0.995988	−	0.0894865i	$-0.971477\pi$
$509$	−9.48683	+	16.4317i	−0.420496	+	0.728321i	0.575492	+	0.817808i	$0.304811\pi$
$510$		0			0
$511$	−4.00000	+	20.7846i	−0.176950	+	0.919457i
$512$		0			0
$513$	9.76770	−	20.4351i	0.431255	−	0.902230i
$514$		0			0
$515$	−4.74342	−	8.21584i	−0.209020	−	0.362033i
$516$	−14.0294	+	10.1575i	−0.617611	+	0.447160i
$517$	−20.0000			−0.879599
$518$		0			0
$519$		0			0
$520$		0			0
$521$	4.74342	+	8.21584i	0.207813	+	0.359942i	0.951025	−	0.309113i	$-0.100032\pi$
$521$	4.74342	+	8.21584i	0.207813	+	0.359942i	−0.743212	+	0.669056i	$0.766699\pi$
$522$		0			0
$523$	7.34847	+	4.24264i	0.321326	+	0.185518i	0.651984	−	0.758233i	$-0.273937\pi$
$523$	7.34847	+	4.24264i	0.321326	+	0.185518i	−0.330657	+	0.943751i	$0.607270\pi$
$524$		−	31.3050i		−	1.36756i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	30.8195	−	3.18768i	1.34124	−	0.138726i
$529$	−9.00000	−	15.5885i	−0.391304	−	0.677759i
$530$		0			0
$531$		0			0
$532$	18.6969	−	13.5065i	0.810615	−	0.585579i
$533$			40.2492i			1.74339i
$534$		0			0
$535$	18.3712	−	10.6066i	0.794255	−	0.458563i
$536$		0			0
$537$	−13.3095	+	9.63628i	−0.574346	+	0.415836i
$538$		0			0
$539$	−19.3649	−	24.5967i	−0.834106	−	1.05946i
$540$	−22.1359	+	7.07107i	−0.952579	+	0.304290i
$541$	0.500000	−	0.866025i	0.0214967	−	0.0372333i	−0.855077	−	0.518501i	$-0.826490\pi$
$541$	0.500000	−	0.866025i	0.0214967	−	0.0372333i	0.876574	+	0.481268i	$0.159824\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−18.9737			−0.812743
$546$		0			0
$547$		−	4.24264i		−	0.181402i	−0.995878	−	0.0907011i	$-0.971089\pi$
$547$		−	4.24264i		−	0.181402i	0.995878	−	0.0907011i	$-0.0289108\pi$
$548$	−7.74597	−	4.47214i	−0.330891	−	0.191040i
$549$	−3.74597	+	11.4003i	−0.159874	+	0.486555i
$550$		0			0
$551$	−30.1134	−	28.3405i	−1.28288	−	1.20734i
$552$		0			0
$553$	11.0227	+	31.8198i	0.468733	+	1.35312i
$554$		0			0
$555$	26.6190	−	19.2726i	1.12991	−	0.818075i
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	25.1744	−	14.5344i	1.06667	−	0.615844i	0.139403	−	0.990236i	$-0.455482\pi$
$557$	25.1744	−	14.5344i	1.06667	−	0.615844i	0.927271	+	0.374392i	$0.122148\pi$
$558$		0			0
$559$			21.2132i			0.897223i
$560$	−23.2379	−	4.47214i	−0.981981	−	0.188982i
$561$	−15.8114	−	7.07107i	−0.667557	−	0.298541i
$562$		0			0
$563$	14.2302	+	24.6475i	0.599734	+	1.03877i	0.992860	+	0.119285i	$0.0380601\pi$
$563$	14.2302	+	24.6475i	0.599734	+	1.03877i	−0.393127	+	0.919484i	$0.628607\pi$
$564$	−15.4097	+	1.59384i	−0.648867	+	0.0671129i
$565$	−18.3712	−	10.6066i	−0.772881	−	0.446223i
$566$		0			0
$567$	−22.7379	−	7.07021i	−0.954902	−	0.296921i
$568$		0			0
$569$	−14.2302	+	24.6475i	−0.596563	+	1.03328i	0.396761	+	0.917922i	$0.370134\pi$
$569$	−14.2302	+	24.6475i	−0.596563	+	1.03328i	−0.993324	+	0.115356i	$0.963199\pi$
$570$		0			0
$571$	−14.5000	−	25.1147i	−0.606806	−	1.05102i	−0.991763	−	0.128085i	$-0.959117\pi$
$571$	−14.5000	−	25.1147i	−0.606806	−	1.05102i	0.384957	−	0.922934i	$-0.374216\pi$
$572$	18.9737	−	32.8634i	0.793329	−	1.37409i
$573$	11.0680	−	24.7487i	0.462371	−	1.03389i
$574$		0			0
$575$		0			0
$576$	23.4919	−	4.91213i	0.978831	−	0.204672i
$577$	5.00000	+	8.66025i	0.208153	+	0.360531i	0.951133	−	0.308783i	$-0.0999216\pi$
$577$	5.00000	+	8.66025i	0.208153	+	0.360531i	−0.742980	+	0.669314i	$0.766588\pi$
$578$		0			0
$579$	12.9284	+	17.8565i	0.537287	+	0.742092i
$580$			42.4264i			1.76166i
$581$	27.1109	−	31.3050i	1.12475	−	1.29875i
$582$		0			0
$583$	−36.7423	−	21.2132i	−1.52171	−	0.878561i
$584$		0			0
$585$	−8.88434	+	27.0383i	−0.367322	+	1.11790i
$586$		0			0
$587$		−	11.1803i		−	0.461462i	−0.973018	−	0.230731i	$-0.925888\pi$
$587$		−	11.1803i		−	0.461462i	0.973018	−	0.230731i	$-0.0741117\pi$
$588$	−16.8806	−	17.4082i	−0.696143	−	0.717903i
$589$		0			0
$590$		0			0
$591$	19.2622	−	1.99230i	0.792339	−	0.0819524i
$592$	−29.3939	+	16.9706i	−1.20808	+	0.697486i
$593$	9.68246	+	5.59017i	0.397611	+	0.229561i	0.685453	−	0.728117i	$-0.259604\pi$
$593$	9.68246	+	5.59017i	0.397611	+	0.229561i	−0.287842	+	0.957678i	$0.592938\pi$
$594$		0			0
$595$	10.0000	+	8.66025i	0.409960	+	0.355036i
$596$		−	4.47214i		−	0.183186i
$597$	23.8500	−	17.2678i	0.976116	−	0.706724i
$598$		0			0
$599$	−14.2302	−	24.6475i	−0.581432	−	1.00707i	−0.995310	−	0.0967377i	$-0.969159\pi$
$599$	−14.2302	−	24.6475i	−0.581432	−	1.00707i	0.413878	−	0.910333i	$-0.364174\pi$
$600$		0			0
$601$		−	4.24264i		−	0.173061i	−0.996249	−	0.0865305i	$-0.972422\pi$
$601$		−	4.24264i		−	0.173061i	0.996249	−	0.0865305i	$-0.0275780\pi$
$602$		0			0
$603$	28.4605	−	25.4558i	1.15900	−	1.03664i
$604$	7.34847	+	4.24264i	0.299005	+	0.172631i
$605$	−17.4284	+	10.0623i	−0.708566	+	0.409091i
$606$		0			0
$607$	25.7196	+	14.8492i	1.04393	+	0.602712i	0.920943	−	0.389696i	$-0.127420\pi$
$607$	25.7196	+	14.8492i	1.04393	+	0.602712i	0.122985	+	0.992409i	$0.460753\pi$
$608$		0			0
$609$	−24.9284	+	35.6170i	−1.01015	+	1.44328i
$610$		0			0
$611$	−9.48683	+	16.4317i	−0.383796	+	0.664754i
$612$	−12.7460	−	4.18812i	−0.515225	−	0.169295i
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	0.999984	+	0.00563283i	$0.00179300\pi$
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	−0.495114	+	0.868828i	$0.664874\pi$
$614$		0			0
$615$	15.0000	−	33.5410i	0.604858	−	1.35250i
$616$		0			0
$617$		−	38.0132i		−	1.53035i	−0.643821	−	0.765176i	$-0.722652\pi$
$617$		−	38.0132i		−	1.53035i	0.643821	−	0.765176i	$-0.277348\pi$
$618$		0			0
$619$	15.5000	+	26.8468i	0.622998	+	1.07906i	0.988924	+	0.148420i	$0.0474187\pi$
$619$	15.5000	+	26.8468i	0.622998	+	1.07906i	−0.365927	+	0.930644i	$0.619248\pi$
$620$		0			0
$621$	−2.47212	+	11.3529i	−0.0992029	+	0.455577i
$622$		0			0
$623$	23.7171	−	8.21584i	0.950205	−	0.329161i
$624$	12.0000	−	26.8328i	0.480384	−	1.07417i
$625$	12.5000	−	21.6506i	0.500000	−	0.866025i
$626$		0			0
$627$	4.32381	−	33.4859i	0.172676	−	1.33730i
$628$	11.0000	−	19.0526i	0.438948	−	0.760280i
$629$	18.9737			0.756530
$630$		0			0
$631$	−19.0000			−0.756378			−0.378189	−	0.925728i	$-0.623453\pi$
$631$	−19.0000			−0.756378			−0.378189	+	0.925728i	$0.623453\pi$
$632$		0			0
$633$	−7.30948	+	0.756026i	−0.290526	+	0.0300493i
$634$		0			0
$635$	−14.2302	+	24.6475i	−0.564710	+	0.978107i
$636$	−30.0000	−	13.4164i	−1.18958	−	0.531995i
$637$	−29.3939	+	4.24264i	−1.16463	+	0.168100i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−18.9737	−	32.8634i	−0.749415	−	1.29802i	−0.948104	−	0.317962i	$-0.897002\pi$
$641$	−18.9737	−	32.8634i	−0.749415	−	1.29802i	0.198689	−	0.980063i	$-0.436332\pi$
$642$		0			0
$643$	23.0000			0.907031			0.453516	−	0.891248i	$-0.350170\pi$
$643$	23.0000			0.907031			0.453516	+	0.891248i	$0.350170\pi$
$644$	−7.74597	+	8.94427i	−0.305234	+	0.352454i
$645$	7.90569	−	17.6777i	0.311286	−	0.696058i
$646$		0			0
$647$	−9.68246	+	5.59017i	−0.380657	+	0.219772i	−0.678104	−	0.734966i	$-0.737198\pi$
$647$	−9.68246	+	5.59017i	−0.380657	+	0.219772i	0.297447	+	0.954738i	$0.403865\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−34.0000			−1.33154
$653$	21.3014	+	12.2984i	0.833589	+	0.481273i	0.855080	−	0.518496i	$-0.173508\pi$
$653$	21.3014	+	12.2984i	0.833589	+	0.481273i	−0.0214912	+	0.999769i	$0.506841\pi$
$654$		0			0
$655$	17.5000	+	30.3109i	0.683782	+	1.18434i
$656$	−18.9737	+	32.8634i	−0.740797	+	1.28310i
$657$	16.0000	+	17.8885i	0.624219	+	0.697899i
$658$		0			0
$659$	18.9737			0.739109			0.369555	−	0.929209i	$-0.379510\pi$
$659$	18.9737			0.739109			0.369555	+	0.929209i	$0.379510\pi$
$660$	−28.0588	+	20.3151i	−1.09219	+	0.790763i
$661$	−22.0454	+	12.7279i	−0.857467	+	0.495059i	−0.863163	−	0.504925i	$-0.831520\pi$
$661$	−22.0454	+	12.7279i	−0.857467	+	0.495059i	0.00569625	+	0.999984i	$0.498187\pi$
$662$		0			0
$663$	−13.3095	+	9.63628i	−0.516897	+	0.374242i
$664$		0			0
$665$	−10.5529	+	23.5295i	−0.409224	+	0.912434i
$666$		0			0
$667$	18.3712	+	10.6066i	0.711335	+	0.410689i
$668$	9.48683	+	16.4317i	0.367057	+	0.635761i
$669$	7.30948	−	0.756026i	0.282601	−	0.0292296i
$670$		0			0
$671$			17.8885i			0.690580i
$672$		0			0
$673$			46.6690i			1.79896i	0.436962	+	0.899480i	$0.356054\pi$
$673$			46.6690i			1.79896i	−0.436962	+	0.899480i	$0.643946\pi$
$674$		0			0
$675$		0			0
$676$	−5.00000	−	8.66025i	−0.192308	−	0.333087i
$677$	−14.2302	+	24.6475i	−0.546913	+	0.947281i	0.451571	+	0.892235i	$0.350864\pi$
$677$	−14.2302	+	24.6475i	−0.546913	+	0.947281i	−0.998484	+	0.0550457i	$0.982470\pi$
$678$		0			0
$679$	14.6969	−	16.9706i	0.564017	−	0.651270i
$680$		0			0
$681$	−26.6190	+	19.2726i	−1.02004	+	0.738526i
$682$		0			0
$683$	−9.48683	−	16.4317i	−0.363004	−	0.628741i	0.625450	−	0.780264i	$-0.284915\pi$
$683$	−9.48683	−	16.4317i	−0.363004	−	0.628741i	−0.988454	+	0.151524i	$0.951582\pi$
$684$	0.662878	−	26.1450i	0.0253458	−	0.999679i
$685$	10.0000			0.382080
$686$		0			0
$687$	20.5548	+	9.19239i	0.784215	+	0.350711i
$688$	−10.0000	+	17.3205i	−0.381246	+	0.660338i
$689$	−34.8569	+	20.1246i	−1.32794	+	0.766687i
$690$		0			0
$691$	9.50000	−	16.4545i	0.361397	−	0.625958i	−0.626794	−	0.779185i	$-0.715633\pi$
$691$	9.50000	−	16.4545i	0.361397	−	0.625958i	0.988191	+	0.153227i	$0.0489666\pi$
$692$		0			0
$693$	−35.4919	+	0.568036i	−1.34823	+	0.0215779i
$694$		0			0
$695$	−3.87298	−	2.23607i	−0.146911	−	0.0848189i
$696$		0			0
$697$	18.3712	−	10.6066i	0.695858	−	0.401754i
$698$		0			0
$699$	1.58114	−	3.53553i	0.0598042	−	0.133726i
$700$		0			0
$701$			29.0689i			1.09792i	0.835850	+	0.548958i	$0.184975\pi$
$701$			29.0689i			1.09792i	−0.835850	+	0.548958i	$0.815025\pi$
$702$		0			0
$703$	10.6515	+	35.4196i	0.401730	+	1.33587i
$704$	30.9839	−	17.8885i	1.16775	−	0.674200i
$705$	14.0294	−	10.1575i	0.528378	−	0.382555i
$706$		0			0
$707$	−40.6663	−	7.82624i	−1.52941	−	0.294336i
$708$		0			0
$709$	−11.5000	+	19.9186i	−0.431892	+	0.748058i	−0.997036	−	0.0769337i	$-0.975487\pi$
$709$	−11.5000	+	19.9186i	−0.431892	+	0.748058i	0.565145	+	0.824992i	$0.308820\pi$
$710$		0			0
$711$	36.2757	+	11.9196i	1.36044	+	0.447020i
$712$		0			0
$713$		0			0
$714$		0			0
$715$			42.4264i			1.58666i
$716$	−9.48683	+	16.4317i	−0.354540	+	0.614081i
$717$	−26.9670	+	2.78922i	−1.00710	+	0.104165i
$718$		0			0
$719$	−1.93649	−	1.11803i	−0.0722190	−	0.0416956i	0.463456	−	0.886120i	$-0.346609\pi$
$719$	−1.93649	−	1.11803i	−0.0722190	−	0.0416956i	−0.535675	+	0.844424i	$0.679943\pi$
$720$	−20.0000	+	17.8885i	−0.745356	+	0.666667i
$721$	−3.67423	−	10.6066i	−0.136836	−	0.395010i
$722$		0			0
$723$	17.2379	+	23.8087i	0.641084	+	0.885456i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−49.0000			−1.81731			−0.908655	−	0.417548i	$-0.862889\pi$
$727$	−49.0000			−1.81731			−0.908655	+	0.417548i	$0.862889\pi$
$728$		0			0
$729$	−22.0000	+	15.6525i	−0.814815	+	0.579721i
$730$		0			0
$731$	9.68246	−	5.59017i	0.358119	−	0.206760i
$732$	1.42558	+	13.7829i	0.0526908	+	0.509430i
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$		0			0
$735$	26.0760	+	7.41892i	0.961829	+	0.273651i
$736$		0			0
$737$	28.4605	−	49.2950i	1.04836	−	1.81581i
$738$		0			0
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	−0.867581	−	0.497296i	$-0.834326\pi$
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	0.00311943	−	0.999995i	$-0.499007\pi$
$740$	18.9737	−	32.8634i	0.697486	−	1.20808i
$741$	−25.4605	−	19.4361i	−0.935315	−	0.714004i
$742$		0			0
$743$	−18.9737			−0.696076			−0.348038	−	0.937480i	$-0.613152\pi$
$743$	−18.9737			−0.696076			−0.348038	+	0.937480i	$0.613152\pi$
$744$		0			0
$745$	2.50000	+	4.33013i	0.0915929	+	0.158644i
$746$		0			0
$747$	−9.61088	−	45.9634i	−0.351644	−	1.68171i
$748$	−20.0000			−0.731272
$749$	23.7171	−	8.21584i	0.866603	−	0.300200i
$750$		0			0
$751$	−40.4166	−	23.3345i	−1.47482	−	0.851489i	−0.475225	−	0.879864i	$-0.657633\pi$
$751$	−40.4166	−	23.3345i	−1.47482	−	0.851489i	−0.999597	+	0.0283756i	$0.990967\pi$
$752$	−15.4919	+	8.94427i	−0.564933	+	0.326164i
$753$	19.2622	−	1.99230i	0.701952	−	0.0726036i
$754$		0			0
$755$	−9.48683			−0.345261
$756$	−27.3008	+	3.26609i	−0.992920	+	0.118787i
$757$	44.0000			1.59921			0.799604	−	0.600528i	$-0.205043\pi$
$757$	44.0000			1.59921			0.799604	+	0.600528i	$0.205043\pi$
$758$		0			0
$759$	1.78197	+	17.2286i	0.0646814	+	0.625358i
$760$		0			0
$761$	−1.93649	−	1.11803i	−0.0701978	−	0.0405287i	0.464490	−	0.885578i	$-0.346238\pi$
$761$	−1.93649	−	1.11803i	−0.0701978	−	0.0405287i	−0.534688	+	0.845050i	$0.679571\pi$
$762$		0			0
$763$	−22.0454	−	4.24264i	−0.798097	−	0.153594i
$764$		−	31.3050i		−	1.13257i
$765$	14.6825	−	3.07008i	0.530845	−	0.110999i
$766$		0			0
$767$		0			0
$768$	22.4471	−	16.2520i	0.809989	−	0.586445i
$769$	29.0000			1.04577			0.522883	−	0.852404i	$-0.324856\pi$
$769$	29.0000			1.04577			0.522883	+	0.852404i	$0.324856\pi$
$770$		0			0
$771$	15.0000	+	6.70820i	0.540212	+	0.241590i
$772$	22.0454	+	12.7279i	0.793432	+	0.458088i
$773$	−23.7171	−	41.0792i	−0.853044	−	1.47752i	−0.878448	−	0.477839i	$-0.841420\pi$
$773$	−23.7171	−	41.0792i	−0.853044	−	1.47752i	0.0254035	−	0.999677i	$-0.491913\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	35.2379	−	16.4405i	1.26415	−	0.589800i
$778$		0			0
$779$	30.1134	+	28.3405i	1.07893	+	1.01540i
$780$	3.38105	+	32.6890i	0.121061	+	1.17045i
$781$		0			0
$782$		0			0
$783$	15.0000	+	46.9574i	0.536056	+	1.67812i
$784$	−26.0000	−	10.3923i	−0.928571	−	0.371154i
$785$			24.5967i			0.877896i
$786$		0			0
$787$	44.0908	−	25.4558i	1.57167	−	0.907403i	0.575703	−	0.817659i	$-0.304728\pi$
$787$	44.0908	−	25.4558i	1.57167	−	0.907403i	0.995965	−	0.0897439i	$-0.0286049\pi$
$788$	19.3649	−	11.1803i	0.689847	−	0.398283i
$789$	−11.3565	−	15.6854i	−0.404301	−	0.558414i
$790$		0			0
$791$	−18.9737	−	16.4317i	−0.674626	−	0.584243i
$792$		0			0
$793$	14.6969	+	8.48528i	0.521904	+	0.301321i
$794$		0			0
$795$	36.5474	−	3.78013i	1.29620	−	0.134067i
$796$	17.0000	−	29.4449i	0.602549	−	1.04365i
$797$	37.9473			1.34416			0.672082	−	0.740477i	$-0.265400\pi$
$797$	37.9473			1.34416			0.672082	+	0.740477i	$0.265400\pi$
$798$		0			0
$799$	10.0000			0.353775
$800$		0			0
$801$	8.88434	−	27.0383i	0.313913	−	0.955351i
$802$		0			0
$803$	30.9839	+	17.8885i	1.09340	+	0.631273i
$804$	18.0000	−	40.2492i	0.634811	−	1.41948i
$805$	2.50000	−	12.9904i	0.0881134	−	0.457851i
$806$		0			0
$807$	26.6190	−	19.2726i	0.937031	−	0.678426i
$808$		0			0
$809$	−44.5393	+	25.7148i	−1.56592	+	0.904084i	−0.569282	+	0.822143i	$0.692779\pi$
$809$	−44.5393	+	25.7148i	−1.56592	+	0.904084i	−0.996637	+	0.0819409i	$0.973888\pi$
$810$		0			0
$811$			25.4558i			0.893876i	0.894565	+	0.446938i	$0.147485\pi$
$811$			25.4558i			0.893876i	−0.894565	+	0.446938i	$0.852515\pi$
$812$	−9.48683	+	49.2950i	−0.332923	+	1.72992i
$813$	−26.8794	−	12.0208i	−0.942700	−	0.421588i
$814$		0			0
$815$	32.9204	−	19.0066i	1.15315	−	0.665771i
$816$	−15.4097	+	1.59384i	−0.539448	+	0.0557956i
$817$	15.8712	+	14.9367i	0.555262	+	0.522570i
$818$		0			0
$819$	−16.3686	+	29.4290i	−0.571966	+	1.02833i
$820$		−	42.4264i		−	1.48159i
$821$	38.7298	+	22.3607i	1.35168	+	0.780393i	0.988485	−	0.151320i	$-0.0483523\pi$
$821$	38.7298	+	22.3607i	1.35168	+	0.780393i	0.363196	+	0.931713i	$0.381686\pi$
$822$		0			0
$823$	−1.00000	−	1.73205i	−0.0348578	−	0.0603755i	0.848070	−	0.529884i	$-0.177765\pi$
$823$	−1.00000	−	1.73205i	−0.0348578	−	0.0603755i	−0.882928	+	0.469508i	$0.844431\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$	2.74597	+	13.1324i	0.0954289	+	0.456382i
$829$	29.3939	−	16.9706i	1.02089	−	0.589412i	0.106529	−	0.994310i	$-0.466026\pi$
$829$	29.3939	−	16.9706i	1.02089	−	0.589412i	0.914362	+	0.404898i	$0.132693\pi$
$830$		0			0
$831$	−5.61177	+	4.06301i	−0.194670	+	0.140944i
$832$		−	33.9411i		−	1.17670i
$833$	9.68246	+	12.2984i	0.335477	+	0.426113i
$834$		0			0
$835$	−18.3712	−	10.6066i	−0.635761	−	0.367057i
$836$	−11.2277	−	37.3355i	−0.388318	−	1.29127i
$837$		0			0
$838$		0			0
$839$	−9.48683			−0.327522			−0.163761	−	0.986500i	$-0.552363\pi$
$839$	−9.48683			−0.327522			−0.163761	+	0.986500i	$0.552363\pi$
$840$		0			0
$841$	61.0000			2.10345
$842$		0			0
$843$	−1.69052	−	16.3445i	−0.0582248	−	0.562934i
$844$	−7.34847	+	4.24264i	−0.252945	+	0.146038i
$845$	9.68246	+	5.59017i	0.333087	+	0.192308i
$846$		0			0
$847$	−22.5000	+	7.79423i	−0.773109	+	0.267813i
$848$	−37.9473			−1.30312
$849$	−9.82059	+	7.11027i	−0.337042	+	0.244024i
$850$		0			0
$851$	−9.48683	−	16.4317i	−0.325204	−	0.563271i
$852$		0			0
$853$	5.00000			0.171197			0.0855984	−	0.996330i	$-0.472720\pi$
$853$	5.00000			0.171197			0.0855984	+	0.996330i	$0.472720\pi$
$854$		0			0
$855$	13.9737	+	25.6853i	0.477889	+	0.878420i
$856$		0			0
$857$	−4.74342	−	8.21584i	−0.162032	−	0.280648i	0.773565	−	0.633717i	$-0.218471\pi$
$857$	−4.74342	−	8.21584i	−0.162032	−	0.280648i	−0.935597	+	0.353069i	$0.885138\pi$
$858$		0			0
$859$	−14.5000	+	25.1147i	−0.494734	+	0.856904i	−0.999982	−	0.00607046i	$-0.998068\pi$
$859$	−14.5000	+	25.1147i	−0.494734	+	0.856904i	0.505248	+	0.862974i	$0.331401\pi$
$860$		−	22.3607i		−	0.762493i
$861$	24.9284	−	35.6170i	0.849558	−	1.21383i
$862$		0			0
$863$	9.48683	−	16.4317i	0.322936	−	0.559341i	−0.658157	−	0.752881i	$-0.728664\pi$
$863$	9.48683	−	16.4317i	0.322936	−	0.559341i	0.981092	+	0.193540i	$0.0619970\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−18.9737	−	8.48528i	−0.644379	−	0.288175i
$868$		0			0
$869$	56.9210			1.93091
$870$		0			0
$871$	−27.0000	−	46.7654i	−0.914860	−	1.58458i
$872$		0			0
$873$	−5.21011	−	24.9170i	−0.176335	−	0.843311i
$874$		0			0
$875$	19.3649	−	22.3607i	0.654654	−	0.755929i
$876$	25.2982	+	11.3137i	0.854748	+	0.382255i
$877$	−7.34847	−	4.24264i	−0.248140	−	0.143264i	0.370772	−	0.928724i	$-0.379093\pi$
$877$	−7.34847	−	4.24264i	−0.248140	−	0.143264i	−0.618912	+	0.785460i	$0.712426\pi$
$878$		0			0
$879$	−3.38105	−	32.6890i	−0.114040	−	1.10257i
$880$	−20.0000	+	34.6410i	−0.674200	+	1.16775i
$881$		−	38.0132i		−	1.28070i	−0.768085	−	0.640348i	$-0.778790\pi$
$881$		−	38.0132i		−	1.28070i	0.768085	−	0.640348i	$-0.221210\pi$
$882$		0			0
$883$	−7.00000			−0.235569			−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000			−0.235569			−0.117784	+	0.993039i	$0.537579\pi$
$884$	−9.48683	+	16.4317i	−0.319077	+	0.552657i
$885$		0			0
$886$		0			0
$887$	18.9737	−	32.8634i	0.637073	−	1.10344i	−0.348998	−	0.937123i	$-0.613478\pi$
$887$	18.9737	−	32.8634i	0.637073	−	1.10344i	0.986072	−	0.166320i	$-0.0531885\pi$
$888$		0			0
$889$	−22.0454	+	25.4558i	−0.739379	+	0.853762i
$890$		0			0
$891$	−23.8730	+	32.4049i	−0.799775	+	1.08561i
$892$	7.34847	−	4.24264i	0.246045	−	0.142054i
$893$	5.61385	+	18.6677i	0.187860	+	0.624692i
$894$		0			0
$895$		−	21.2132i		−	0.709079i
$896$		0			0
$897$	15.0000	+	6.70820i	0.500835	+	0.223980i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	18.3712	+	10.6066i	0.612033	+	0.353357i
$902$		0			0
$903$	13.1384	−	18.7718i	0.437220	−	0.624687i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−29.3939	+	16.9706i	−0.976008	+	0.563498i	−0.901062	−	0.433689i	$-0.857212\pi$
$907$	−29.3939	+	16.9706i	−0.976008	+	0.563498i	−0.0749452	+	0.997188i	$0.523878\pi$
$908$	−18.9737	+	32.8634i	−0.629663	+	1.09061i
$909$	−35.0000	+	31.3050i	−1.16088	+	1.03832i
$910$		0			0
$911$	18.9737			0.628626			0.314313	−	0.949319i	$-0.398226\pi$
$911$	18.9737			0.628626			0.314313	+	0.949319i	$0.398226\pi$
$912$	−11.6261	−	27.8717i	−0.384980	−	0.922925i
$913$	−35.0000	−	60.6218i	−1.15833	−	2.00629i
$914$		0			0
$915$	−9.08517	−	12.5483i	−0.300346	−	0.414834i
$916$	26.0000			0.859064
$917$	13.5554	+	39.1312i	0.447640	+	1.29223i
$918$		0			0
$919$	9.50000	−	16.4545i	0.313376	−	0.542783i	−0.665715	−	0.746206i	$-0.731873\pi$
$919$	9.50000	−	16.4545i	0.313376	−	0.542783i	0.979091	+	0.203423i	$0.0652066\pi$
$920$		0			0
$921$	−43.8569	+	4.53615i	−1.44513	+	0.149471i
$922$		0			0
$923$		0			0
$924$	−37.1440	+	17.3298i	−1.22195	+	0.570109i
$925$		0			0
$926$		0			0
$927$	−12.0919	−	3.97320i	−0.397150	−	0.130497i
$928$		0			0
$929$	−13.5554	−	7.82624i	−0.444740	−	0.256771i	0.260866	−	0.965375i	$-0.415992\pi$
$929$	−13.5554	−	7.82624i	−0.444740	−	0.256771i	−0.705606	+	0.708604i	$0.749325\pi$
$930$		0			0
$931$	−17.5227	+	24.9791i	−0.574283	+	0.818657i
$932$		−	4.47214i		−	0.146490i
$933$	15.8990	+	21.9595i	0.520512	+	0.718922i
$934$		0			0
$935$	19.3649	−	11.1803i	0.633300	−	0.365636i
$936$		0			0
$937$	35.0000			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$938$		0			0
$939$	−7.90569	−	3.53553i	−0.257993	−	0.115378i
$940$	10.0000	−	17.3205i	0.326164	−	0.564933i
$941$	28.4605	+	49.2950i	0.927786	+	1.60697i	0.787019	+	0.616929i	$0.211624\pi$
$941$	28.4605	+	49.2950i	0.927786	+	1.60697i	0.140767	+	0.990043i	$0.455043\pi$
$942$		0			0
$943$	−18.3712	−	10.6066i	−0.598248	−	0.345398i
$944$		0			0
$945$	24.6081	−	18.4240i	0.800500	−	0.599332i
$946$		0			0
$947$	27.1109	+	15.6525i	0.880985	+	0.508637i	0.870983	−	0.491313i	$-0.163483\pi$
$947$	27.1109	+	15.6525i	0.880985	+	0.508637i	0.0100022	+	0.999950i	$0.496816\pi$
$948$	43.8569	−	4.53615i	1.42440	−	0.147327i
$949$	29.3939	−	16.9706i	0.954166	−	0.550888i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	56.9210			1.84385			0.921926	−	0.387366i	$-0.126615\pi$
$953$	56.9210			1.84385			0.921926	+	0.387366i	$0.126615\pi$
$954$		0			0
$955$	17.5000	+	30.3109i	0.566287	+	0.980837i
$956$	−27.1109	+	15.6525i	−0.876829	+	0.506237i
$957$	43.0948	+	59.5218i	1.39306	+	1.92407i
$958$		0			0
$959$	11.6190	+	2.23607i	0.375195	+	0.0722064i
$960$	−12.6491	+	28.2843i	−0.408248	+	0.912871i
$961$	−15.5000	+	26.8468i	−0.500000	+	0.866025i
$962$		0			0
$963$	8.88434	−	27.0383i	0.286294	−	0.871296i
$964$	29.3939	+	16.9706i	0.946713	+	0.546585i
$965$	−28.4605			−0.916176
$966$		0			0
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$		0			0
$969$	−2.16191	+	16.7429i	−0.0694504	+	0.537861i
$970$		0			0
$971$	−18.9737	+	32.8634i	−0.608894	+	1.05464i	0.382529	+	0.923943i	$0.375053\pi$
$971$	−18.9737	+	32.8634i	−0.608894	+	1.05464i	−0.991423	+	0.130692i	$0.958280\pi$
$972$	−15.8114	+	26.8701i	−0.507151	+	0.861858i
$973$	−4.00000	−	3.46410i	−0.128234	−	0.111054i
$974$		0			0
$975$		0			0
$976$	8.00000	+	13.8564i	0.256074	+	0.443533i
$977$	14.2302	+	24.6475i	0.455266	+	0.788544i	0.998703	−	0.0509058i	$-0.0162108\pi$
$977$	14.2302	+	24.6475i	0.455266	+	0.788544i	−0.543437	+	0.839450i	$0.682877\pi$
$978$		0			0
$979$		−	42.4264i		−	1.35595i
$980$	30.9839	−	4.47214i	0.989743	−	0.142857i
$981$	−18.9737	+	16.9706i	−0.605783	+	0.541828i
$982$		0			0
$983$	−4.74342	−	8.21584i	−0.151291	−	0.262045i	0.780411	−	0.625267i	$-0.215010\pi$
$983$	−4.74342	−	8.21584i	−0.151291	−	0.262045i	−0.931702	+	0.363222i	$0.881677\pi$
$984$		0			0
$985$	−12.5000	+	21.6506i	−0.398283	+	0.689847i
$986$		0			0
$987$	18.5720	−	8.66491i	0.591153	−	0.275807i
$988$	−36.0000	−	8.48528i	−1.14531	−	0.269953i
$989$	−9.68246	−	5.59017i	−0.307884	−	0.177757i
$990$		0			0
$991$	−36.7423	+	21.2132i	−1.16716	+	0.673860i	−0.953009	−	0.302941i	$-0.902031\pi$
$991$	−36.7423	+	21.2132i	−1.16716	+	0.673860i	−0.214150	+	0.976801i	$0.568698\pi$
$992$		0			0
$993$	18.0000	−	40.2492i	0.571213	−	1.27727i
$994$		0			0
$995$			38.0132i			1.20510i
$996$	−31.7981	−	43.9190i	−1.00756	−	1.39163i
$997$	0.500000	+	0.866025i	0.0158352	+	0.0274273i	0.873834	−	0.486224i	$-0.161626\pi$
$997$	0.500000	+	0.866025i	0.0158352	+	0.0274273i	−0.857999	+	0.513651i	$0.828293\pi$
$998$		0			0
$999$	9.38105	−	43.0813i	0.296803	−	1.36303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.w.c.170.3	yes	8
3.2	odd	2	inner	399.2.w.c.170.1	✓	8
7.4	even	3	inner	399.2.w.c.284.4	yes	8
19.18	odd	2	inner	399.2.w.c.170.2	yes	8
21.11	odd	6	inner	399.2.w.c.284.2	yes	8
57.56	even	2	inner	399.2.w.c.170.4	yes	8
133.18	odd	6	inner	399.2.w.c.284.1	yes	8
399.284	even	6	inner	399.2.w.c.284.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.w.c.170.1	✓	8	3.2	odd	2	inner
399.2.w.c.170.2	yes	8	19.18	odd	2	inner
399.2.w.c.170.3	yes	8	1.1	even	1	trivial
399.2.w.c.170.4	yes	8	57.56	even	2	inner
399.2.w.c.284.1	yes	8	133.18	odd	6	inner
399.2.w.c.284.2	yes	8	21.11	odd	6	inner
399.2.w.c.284.3	yes	8	399.284	even	6	inner
399.2.w.c.284.4	yes	8	7.4	even	3	inner

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:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.178197 + 1.72286i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(-2.93649 + 0.614017i) q^{9} +(-3.87298 + 2.23607i) q^{11} +(-2.80588 + 2.03151i) q^{12} +4.24264i q^{13} +(1.58114 - 3.53553i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.93649 - 1.11803i) q^{17} +(3.17423 + 2.98735i) q^{19} -4.47214i q^{20} +(2.62769 - 3.75437i) q^{21} +(-1.93649 - 1.11803i) q^{23} +(-1.58114 - 4.94975i) q^{27} +(1.00000 - 5.19615i) q^{28} -9.48683 q^{29} +(-4.54259 - 6.27415i) q^{33} +(1.93649 + 5.59017i) q^{35} +(-4.00000 - 4.47214i) q^{36} +(7.34847 + 4.24264i) q^{37} +(-7.30948 + 0.756026i) q^{39} +9.48683 q^{41} +5.00000 q^{43} +(-7.74597 - 4.47214i) q^{44} +(6.37298 + 2.09406i) q^{45} +(3.87298 + 2.23607i) q^{47} +(-6.32456 - 2.82843i) q^{48} +(1.00000 + 6.92820i) q^{49} +(2.27129 + 3.13707i) q^{51} +(-7.34847 + 4.24264i) q^{52} +(4.74342 + 8.21584i) q^{53} +10.0000 q^{55} +(-4.58114 + 6.00110i) q^{57} +(7.70486 - 0.796921i) q^{60} +(2.00000 - 3.46410i) q^{61} +(6.93649 + 3.85812i) q^{63} -8.00000 q^{64} +(4.74342 - 8.21584i) q^{65} +(-11.0227 + 6.36396i) q^{67} +(3.87298 + 2.23607i) q^{68} +(1.58114 - 3.53553i) q^{69} +(-4.00000 - 6.92820i) q^{73} +(-2.00000 + 8.48528i) q^{76} +(11.6190 + 2.23607i) q^{77} +(-11.0227 - 6.36396i) q^{79} +(7.74597 - 4.47214i) q^{80} +(8.24597 - 3.60611i) q^{81} +15.6525i q^{83} +(9.13044 + 0.796921i) q^{84} -5.00000 q^{85} +(-1.69052 - 16.3445i) q^{87} +(-4.74342 + 8.21584i) q^{89} +(7.34847 - 8.48528i) q^{91} -4.47214i q^{92} +(-2.80692 - 9.33387i) q^{95} +8.48528i q^{97} +(10.0000 - 8.94427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 16 q^{7} - 8 q^{9} - 16 q^{16} - 4 q^{19} + 8 q^{28} - 32 q^{36} - 12 q^{39} + 40 q^{43} + 20 q^{45} + 8 q^{49} + 80 q^{55} - 24 q^{57} + 16 q^{61} + 40 q^{63} - 64 q^{64} - 32 q^{73} - 16 q^{76}+ \cdots + 80 q^{99}+O(q^{100}) \) 8 * q + 8 * q^4 - 16 * q^7 - 8 * q^9 - 16 * q^16 - 4 * q^19 + 8 * q^28 - 32 * q^36 - 12 * q^39 + 40 * q^43 + 20 * q^45 + 8 * q^49 + 80 * q^55 - 24 * q^57 + 16 * q^61 + 40 * q^63 - 64 * q^64 - 32 * q^73 - 16 * q^76 + 4 * q^81 - 40 * q^85 - 60 * q^87 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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