LMFDB - Embedded newform 525.2.bf.g.32.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(32,525)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("525.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bf (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.18
Character	$\chi$	$=$	525.32
Dual form			525.2.bf.g.443.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.14072 + 0.573605i) q^{2} +(1.69002 + 0.379239i) q^{3} +(2.52162 + 1.45586i) q^{4} +(3.40034 + 1.78125i) q^{6} +(0.453654 - 2.60657i) q^{7} +(1.42877 + 1.42877i) q^{8} +(2.71236 + 1.28185i) q^{9} +O(q^{10})$	\(q+(2.14072 + 0.573605i) q^{2} +(1.69002 + 0.379239i) q^{3} +(2.52162 + 1.45586i) q^{4} +(3.40034 + 1.78125i) q^{6} +(0.453654 - 2.60657i) q^{7} +(1.42877 + 1.42877i) q^{8} +(2.71236 + 1.28185i) q^{9} +(-1.48001 - 0.854482i) q^{11} +(3.70948 + 3.41673i) q^{12} +(-2.36139 + 2.36139i) q^{13} +(2.46629 - 5.31972i) q^{14} +(-0.672671 - 1.16510i) q^{16} +(-0.743563 - 2.77501i) q^{17} +(5.07113 + 4.29990i) q^{18} +(-5.48004 + 3.16390i) q^{19} +(1.75520 - 4.23312i) q^{21} +(-2.67815 - 2.67815i) q^{22} +(-2.31249 + 8.63034i) q^{23} +(1.87280 + 2.95649i) q^{24} +(-6.40958 + 3.70057i) q^{26} +(4.09782 + 3.19498i) q^{27} +(4.93874 - 5.91232i) q^{28} +0.382334 q^{29} +(0.780575 - 1.35200i) q^{31} +(-1.81762 - 6.78347i) q^{32} +(-2.17719 - 2.00537i) q^{33} -6.36705i q^{34} +(4.97335 + 7.18113i) q^{36} +(0.864327 - 3.22571i) q^{37} +(-13.5461 + 3.62966i) q^{38} +(-4.88633 + 3.09527i) q^{39} +10.2040i q^{41} +(6.18553 - 8.05514i) q^{42} +(5.71902 - 5.71902i) q^{43} +(-2.48801 - 4.30936i) q^{44} +(-9.90082 + 17.1487i) q^{46} +(2.80718 + 0.752183i) q^{47} +(-0.694978 - 2.22415i) q^{48} +(-6.58840 - 2.36496i) q^{49} +(-0.204245 - 4.97183i) q^{51} +(-9.39236 + 2.51668i) q^{52} +(7.08863 - 1.89939i) q^{53} +(6.93963 + 9.19009i) q^{54} +(4.37234 - 3.07601i) q^{56} +(-10.4613 + 3.26882i) q^{57} +(0.818471 + 0.219309i) q^{58} +(-3.86036 + 6.68634i) q^{59} +(-3.20053 - 5.54348i) q^{61} +(2.44651 - 2.44651i) q^{62} +(4.57169 - 6.48842i) q^{63} -12.8734i q^{64} +(-3.51048 - 5.54179i) q^{66} +(12.5466 - 3.36186i) q^{67} +(2.16504 - 8.08006i) q^{68} +(-7.18113 + 13.7085i) q^{69} -5.92487i q^{71} +(2.04386 + 5.70678i) q^{72} +(-4.23299 - 15.7977i) q^{73} +(3.70057 - 6.40958i) q^{74} -18.4248 q^{76} +(-2.89868 + 3.47010i) q^{77} +(-12.2357 + 3.82329i) q^{78} +(5.61994 - 3.24467i) q^{79} +(5.71374 + 6.95364i) q^{81} +(-5.85309 + 21.8440i) q^{82} +(0.826081 + 0.826081i) q^{83} +(10.5888 - 8.11899i) q^{84} +(15.5233 - 8.96238i) q^{86} +(0.646153 + 0.144996i) q^{87} +(-0.893728 - 3.33544i) q^{88} +(0.430623 + 0.745860i) q^{89} +(5.08386 + 7.22637i) q^{91} +(-18.3958 + 18.3958i) q^{92} +(1.83192 - 1.98888i) q^{93} +(5.57795 + 3.22043i) q^{94} +(-0.499272 - 12.1535i) q^{96} +(2.59782 + 2.59782i) q^{97} +(-12.7474 - 8.84186i) q^{98} +(-2.91899 - 4.21480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{6}+O(q^{10}) $ 80 * q + 16 * q^6	$ 80 q + 16 q^{6} + 72 q^{16} + 44 q^{21} + 72 q^{31} - 240 q^{36} - 92 q^{51} - 24 q^{61} - 216 q^{66} - 208 q^{76} - 20 q^{81} - 40 q^{91} - 156 q^{96}+O(q^{100}) $ 80 * q + 16 * q^6 + 72 * q^16 + 44 * q^21 + 72 * q^31 - 240 * q^36 - 92 * q^51 - 24 * q^61 - 216 * q^66 - 208 * q^76 - 20 * q^81 - 40 * q^91 - 156 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.14072	+	0.573605i	1.51372	+	0.405600i	0.917669	−	0.397347i	$-0.130069\pi$
$2$	2.14072	+	0.573605i	1.51372	+	0.405600i	0.596051	+	0.802947i	$0.296736\pi$
$3$	1.69002	+	0.379239i	0.975735	+	0.218954i
$3$	1.69002	+	0.379239i	0.975735	+	0.218954i
$4$	2.52162	+	1.45586i	1.26081	+	0.727929i
$5$		0			0
$5$		0			0
$6$	3.40034	+	1.78125i	1.38818	+	0.727193i
$7$	0.453654	−	2.60657i	0.171465	−	0.985190i
$7$	0.453654	−	2.60657i	0.171465	−	0.985190i
$8$	1.42877	+	1.42877i	0.505145	+	0.505145i
$9$	2.71236	+	1.28185i	0.904119	+	0.427282i
$10$		0			0
$11$	−1.48001	−	0.854482i	−0.446239	−	0.257636i	0.260002	−	0.965608i	$-0.416277\pi$
$11$	−1.48001	−	0.854482i	−0.446239	−	0.257636i	−0.706240	+	0.707972i	$0.749610\pi$
$12$	3.70948	+	3.41673i	1.07083	+	0.986325i
$13$	−2.36139	+	2.36139i	−0.654931	+	0.654931i	−0.954176	−	0.299245i	$-0.903265\pi$
$13$	−2.36139	+	2.36139i	−0.654931	+	0.654931i	0.299245	+	0.954176i	$0.403265\pi$
$14$	2.46629	−	5.31972i	0.659143	−	1.42176i
$15$		0			0
$16$	−0.672671	−	1.16510i	−0.168168	−	0.291275i
$17$	−0.743563	−	2.77501i	−0.180341	−	0.673040i	−0.995580	−	0.0939161i	$-0.970061\pi$
$17$	−0.743563	−	2.77501i	−0.180341	−	0.673040i	0.815240	−	0.579124i	$-0.196605\pi$
$18$	5.07113	+	4.29990i	1.19528	+	1.01350i
$19$	−5.48004	+	3.16390i	−1.25721	+	0.725849i	−0.972531	−	0.232774i	$-0.925220\pi$
$19$	−5.48004	+	3.16390i	−1.25721	+	0.725849i	−0.284677	+	0.958623i	$0.591886\pi$
$20$		0			0
$21$	1.75520	−	4.23312i	0.383016	−	0.923742i
$22$	−2.67815	−	2.67815i	−0.570983	−	0.570983i
$23$	−2.31249	+	8.63034i	−0.482188	+	1.79955i	0.110213	+	0.993908i	$0.464847\pi$
$23$	−2.31249	+	8.63034i	−0.482188	+	1.79955i	−0.592401	+	0.805643i	$0.701820\pi$
$24$	1.87280	+	2.95649i	0.382285	+	0.603491i
$25$		0			0
$26$	−6.40958	+	3.70057i	−1.25702	+	0.725742i
$27$	4.09782	+	3.19498i	0.788625	+	0.614874i
$28$	4.93874	−	5.91232i	0.933334	−	1.11732i
$29$	0.382334			0.0709976			0.0354988	−	0.999370i	$-0.488698\pi$
$29$	0.382334			0.0709976			0.0354988	+	0.999370i	$0.488698\pi$
$30$		0			0
$31$	0.780575	−	1.35200i	0.140195	−	0.242826i	−0.787375	−	0.616475i	$-0.788560\pi$
$31$	0.780575	−	1.35200i	0.140195	−	0.242826i	0.927570	+	0.373649i	$0.121894\pi$
$32$	−1.81762	−	6.78347i	−0.321314	−	1.19916i
$33$	−2.17719	−	2.00537i	−0.379001	−	0.349090i
$34$		−	6.36705i		−	1.09194i
$35$		0			0
$36$	4.97335	+	7.18113i	0.828891	+	1.19686i
$37$	0.864327	−	3.22571i	0.142095	−	0.530304i	−0.857773	−	0.514029i	$-0.828152\pi$
$37$	0.864327	−	3.22571i	0.142095	−	0.530304i	0.999868	−	0.0162754i	$-0.00518085\pi$
$38$	−13.5461	+	3.62966i	−2.19746	+	0.588809i
$39$	−4.88633	+	3.09527i	−0.782439	+	0.495639i
$40$		0			0
$41$			10.2040i			1.59360i	0.604241	+	0.796802i	$0.293477\pi$
$41$			10.2040i			1.59360i	−0.604241	+	0.796802i	$0.706523\pi$
$42$	6.18553	−	8.05514i	0.954448	−	1.24293i
$43$	5.71902	−	5.71902i	0.872143	−	0.872143i	−0.120563	−	0.992706i	$-0.538470\pi$
$43$	5.71902	−	5.71902i	0.872143	−	0.872143i	0.992706	+	0.120563i	$0.0384699\pi$
$44$	−2.48801	−	4.30936i	−0.375082	−	0.649660i
$45$		0			0
$46$	−9.90082	+	17.1487i	−1.45980	+	2.52844i
$47$	2.80718	+	0.752183i	0.409470	+	0.109717i	0.457673	−	0.889120i	$-0.348683\pi$
$47$	2.80718	+	0.752183i	0.409470	+	0.109717i	−0.0482034	+	0.998838i	$0.515350\pi$
$48$	−0.694978	−	2.22415i	−0.100311	−	0.321028i
$49$	−6.58840	−	2.36496i	−0.941199	−	0.337852i
$50$		0			0
$51$	−0.204245	−	4.97183i	−0.0286000	−	0.696195i
$52$	−9.39236	+	2.51668i	−1.30249	+	0.349000i
$53$	7.08863	−	1.89939i	0.973698	−	0.260902i	0.263310	−	0.964711i	$-0.415186\pi$
$53$	7.08863	−	1.89939i	0.973698	−	0.260902i	0.710389	+	0.703810i	$0.248519\pi$
$54$	6.93963	+	9.19009i	0.944365	+	1.25061i
$55$		0			0
$56$	4.37234	−	3.07601i	0.584279	−	0.411049i
$57$	−10.4613	+	3.26882i	−1.38563	+	0.432966i
$58$	0.818471	+	0.219309i	0.107470	+	0.0287966i
$59$	−3.86036	+	6.68634i	−0.502576	+	0.870487i	0.497419	+	0.867510i	$0.334281\pi$
$59$	−3.86036	+	6.68634i	−0.502576	+	0.870487i	−0.999996	+	0.00297725i	$0.999052\pi$
$60$		0			0
$61$	−3.20053	−	5.54348i	−0.409786	−	0.709770i	0.585079	−	0.810976i	$-0.301063\pi$
$61$	−3.20053	−	5.54348i	−0.409786	−	0.709770i	−0.994866	+	0.101206i	$0.967730\pi$
$62$	2.44651	−	2.44651i	0.310707	−	0.310707i
$63$	4.57169	−	6.48842i	0.575979	−	0.817465i
$64$		−	12.8734i		−	1.60918i
$65$		0			0
$66$	−3.51048	−	5.54179i	−0.432110	−	0.682148i
$67$	12.5466	−	3.36186i	1.53282	−	0.410717i	0.608880	−	0.793262i	$-0.291619\pi$
$67$	12.5466	−	3.36186i	1.53282	−	0.410717i	0.923937	+	0.382545i	$0.124952\pi$
$68$	2.16504	−	8.08006i	0.262550	−	0.979851i
$69$	−7.18113	+	13.7085i	−0.864507	+	1.65031i
$70$		0			0
$71$		−	5.92487i		−	0.703153i	−0.936159	−	0.351576i	$-0.885646\pi$
$71$		−	5.92487i		−	0.703153i	0.936159	−	0.351576i	$-0.114354\pi$
$72$	2.04386	+	5.70678i	0.240872	+	0.672550i
$73$	−4.23299	−	15.7977i	−0.495434	−	1.84898i	−0.527586	−	0.849502i	$-0.676903\pi$
$73$	−4.23299	−	15.7977i	−0.495434	−	1.84898i	0.0321523	−	0.999483i	$-0.489764\pi$
$74$	3.70057	−	6.40958i	0.430183	−	0.745098i
$75$		0			0
$76$	−18.4248			−2.11347
$77$	−2.89868	+	3.47010i	−0.330335	+	0.395455i
$78$	−12.2357	+	3.82329i	−1.38542	+	0.432902i
$79$	5.61994	−	3.24467i	0.632293	−	0.365054i	−0.149347	−	0.988785i	$-0.547717\pi$
$79$	5.61994	−	3.24467i	0.632293	−	0.365054i	0.781639	+	0.623731i	$0.214384\pi$
$80$		0			0
$81$	5.71374	+	6.95364i	0.634861	+	0.772627i
$82$	−5.85309	+	21.8440i	−0.646366	+	2.41227i
$83$	0.826081	+	0.826081i	0.0906742	+	0.0906742i	0.750989	−	0.660315i	$-0.229577\pi$
$83$	0.826081	+	0.826081i	0.0906742	+	0.0906742i	−0.660315	+	0.750989i	$0.729577\pi$
$84$	10.5888	−	8.11899i	1.15533	−	0.885855i
$85$		0			0
$86$	15.5233	−	8.96238i	1.67392	−	0.966439i
$87$	0.646153	+	0.144996i	0.0692749	+	0.0155452i
$88$	−0.893728	−	3.33544i	−0.0952718	−	0.355559i
$89$	0.430623	+	0.745860i	0.0456459	+	0.0790610i	0.887946	−	0.459948i	$-0.152132\pi$
$89$	0.430623	+	0.745860i	0.0456459	+	0.0790610i	−0.842300	+	0.539009i	$0.818799\pi$
$90$		0			0
$91$	5.08386	+	7.22637i	0.532933	+	0.757529i
$92$	−18.3958	+	18.3958i	−1.91789	+	1.91789i
$93$	1.83192	−	1.98888i	0.189961	−	0.206237i
$94$	5.57795	+	3.22043i	0.575321	+	0.332162i
$95$		0			0
$96$	−0.499272	−	12.1535i	−0.0509567	−	1.24041i
$97$	2.59782	+	2.59782i	0.263769	+	0.263769i	0.826583	−	0.562814i	$-0.190281\pi$
$97$	2.59782	+	2.59782i	0.263769	+	0.263769i	−0.562814	+	0.826583i	$0.690281\pi$
$98$	−12.7474	−	8.84186i	−1.28768	−	0.893163i
$99$	−2.91899	−	4.21480i	−0.293370	−	0.423603i
$100$		0			0
$101$	−5.34871	−	3.08808i	−0.532216	−	0.307275i	0.209702	−	0.977765i	$-0.432751\pi$
$101$	−5.34871	−	3.08808i	−0.532216	−	0.307275i	−0.741919	+	0.670490i	$0.766084\pi$
$102$	2.41463	−	10.7605i	0.239084	−	1.06544i
$103$	4.87140	+	1.30529i	0.479993	+	0.128614i	0.490699	−	0.871329i	$-0.336741\pi$
$103$	4.87140	+	1.30529i	0.479993	+	0.128614i	−0.0107064	+	0.999943i	$0.503408\pi$
$104$	−6.74774			−0.661670
$105$		0			0
$106$	16.2643			1.57973
$107$	7.38559	+	1.97896i	0.713992	+	0.191314i	0.597489	−	0.801877i	$-0.296165\pi$
$107$	7.38559	+	1.97896i	0.713992	+	0.191314i	0.116502	+	0.993190i	$0.462832\pi$
$108$	5.68170	+	14.0224i	0.546722	+	1.34930i
$109$	0.824463	+	0.476004i	0.0789692	+	0.0455929i	0.538965	−	0.842328i	$-0.318816\pi$
$109$	0.824463	+	0.476004i	0.0789692	+	0.0455929i	−0.459995	+	0.887921i	$0.652149\pi$
$110$		0			0
$111$	2.68405	−	5.12374i	0.254759	−	0.486324i
$112$	−3.34207	+	1.22481i	−0.315796	+	0.115734i
$113$	9.70524	+	9.70524i	0.912992	+	0.912992i	0.996507	−	0.0835145i	$-0.0266145\pi$
$113$	9.70524	+	9.70524i	0.912992	+	0.912992i	−0.0835145	+	0.996507i	$0.526614\pi$
$114$	−24.2697	+	0.997009i	−2.27307	+	0.0933784i
$115$		0			0
$116$	0.964101	+	0.556624i	0.0895145	+	0.0516812i
$117$	−9.43185	+	3.37799i	−0.871975	+	0.312295i
$118$	−12.0993	+	12.0993i	−1.11383	+	1.11383i
$119$	−7.57059	+	0.679250i	−0.693994	+	0.0622668i
$120$		0			0
$121$	−4.03972	−	6.99700i	−0.367247	−	0.636091i
$122$	−3.67168	−	13.7029i	−0.332418	−	1.24060i
$123$	−3.86977	+	17.2451i	−0.348926	+	1.55494i
$124$	3.93663	−	2.27281i	0.353520	−	0.204105i
$125$		0			0
$126$	13.5085	−	11.2676i	1.20343	−	1.00380i
$127$	1.21697	+	1.21697i	0.107988	+	0.107988i	0.759036	−	0.651048i	$-0.225670\pi$
$127$	1.21697	+	1.21697i	0.107988	+	0.107988i	−0.651048	+	0.759036i	$0.725670\pi$
$128$	3.74902	−	13.9915i	0.331369	−	1.23669i
$129$	11.8342	−	7.49640i	1.04194	−	0.660022i
$130$		0			0
$131$	−14.6679	+	8.46851i	−1.28154	+	0.739897i	−0.977130	−	0.212644i	$-0.931793\pi$
$131$	−14.6679	+	8.46851i	−1.28154	+	0.739897i	−0.304410	+	0.952541i	$0.598459\pi$
$132$	−2.57052	−	8.22647i	−0.223735	−	0.716022i
$133$	5.76089	+	15.7194i	0.499532	+	1.36305i
$134$	28.7873			2.48684
$135$		0			0
$136$	2.90247	−	5.02723i	0.248885	−	0.431081i
$137$	1.50520	+	5.61748i	0.128598	+	0.479934i	0.999942	−	0.0107379i	$-0.00341803\pi$
$137$	1.50520	+	5.61748i	0.128598	+	0.479934i	−0.871344	+	0.490672i	$0.836751\pi$
$138$	−23.2361	+	25.2269i	−1.97799	+	2.14746i
$139$			8.81465i			0.747649i	0.927499	+	0.373824i	$0.121954\pi$
$139$			8.81465i			0.747649i	−0.927499	+	0.373824i	$0.878046\pi$
$140$		0			0
$141$	4.45895	+	2.33580i	0.375511	+	0.196710i
$142$	3.39853	−	12.6835i	0.285199	−	1.06438i
$143$	5.51263	−	1.47711i	0.460989	−	0.123522i
$144$	−0.331044	−	4.02243i	−0.0275870	−	0.335202i
$145$		0			0
$146$		−	36.2466i		−	2.99979i
$147$	−10.2377	−	6.49542i	−0.844387	−	0.535733i
$148$	6.87569	−	6.87569i	0.565178	−	0.565178i
$149$	−2.82690	−	4.89634i	−0.231589	−	0.401123i	0.726687	−	0.686969i	$-0.241059\pi$
$149$	−2.82690	−	4.89634i	−0.231589	−	0.401123i	−0.958276	+	0.285845i	$0.907726\pi$
$150$		0			0
$151$	4.94810	−	8.57035i	0.402670	−	0.697445i	−0.591377	−	0.806395i	$-0.701415\pi$
$151$	4.94810	−	8.57035i	0.402670	−	0.697445i	0.994047	+	0.108950i	$0.0347488\pi$
$152$	−12.3502	−	3.30922i	−1.00173	−	0.268413i
$153$	1.54033	−	8.47996i	0.124529	−	0.685564i
$154$	−8.19573	+	5.76582i	−0.660431	+	0.464623i
$155$		0			0
$156$	−16.8277	+	0.691290i	−1.34730	+	0.0553475i
$157$	−7.73847	+	2.07352i	−0.617597	+	0.165485i	−0.554035	−	0.832493i	$-0.686913\pi$
$157$	−7.73847	+	2.07352i	−0.617597	+	0.165485i	−0.0635619	+	0.997978i	$0.520246\pi$
$158$	13.8919	−	3.72232i	1.10518	−	0.296132i
$159$	12.7003	−	0.521732i	1.00720	−	0.0413760i
$160$		0			0
$161$	21.4465	+	9.94287i	1.69022	+	0.783608i
$162$	8.24290	+	18.1632i	0.647623	+	1.42704i
$163$	−20.5294	−	5.50084i	−1.60799	−	0.430859i	−0.660545	−	0.750786i	$-0.729675\pi$
$163$	−20.5294	−	5.50084i	−1.60799	−	0.430859i	−0.947442	+	0.319927i	$0.896342\pi$
$164$	−14.8556	+	25.7307i	−1.16003	+	2.00923i
$165$		0			0
$166$	1.29457	+	2.24225i	0.100478	+	0.174033i
$167$	8.33709	−	8.33709i	0.645143	−	0.645143i	−0.306672	−	0.951815i	$-0.599215\pi$
$167$	8.33709	−	8.33709i	0.645143	−	0.645143i	0.951815	+	0.306672i	$0.0992155\pi$
$168$	8.55590	−	3.54037i	0.660102	−	0.273145i
$169$			1.84771i			0.142131i
$170$		0			0
$171$	−18.9195	+	1.55707i	−1.44681	+	0.119072i
$172$	22.7473	−	6.09512i	1.73446	−	0.464748i
$173$	4.31457	−	16.1022i	0.328031	−	1.22423i	−0.583200	−	0.812329i	$-0.698199\pi$
$173$	4.31457	−	16.1022i	0.328031	−	1.22423i	0.911230	−	0.411898i	$-0.135134\pi$
$174$	1.30006	+	0.681033i	0.0985576	+	0.0516290i
$175$		0			0
$176$			2.29914i			0.173304i
$177$	−9.05982	+	9.83607i	−0.680978	+	0.739324i
$178$	0.494014	+	1.84369i	0.0370279	+	0.138190i
$179$	−8.87741	+	15.3761i	−0.663529	+	1.14927i	0.316153	+	0.948708i	$0.397609\pi$
$179$	−8.87741	+	15.3761i	−0.663529	+	1.14927i	−0.979682	+	0.200558i	$0.935725\pi$
$180$		0			0
$181$	−10.3769			−0.771305			−0.385653	−	0.922644i	$-0.626024\pi$
$181$	−10.3769			−0.771305			−0.385653	+	0.922644i	$0.626024\pi$
$182$	6.73806	+	18.3858i	0.499458	+	1.36284i
$183$	−3.30667	−	10.5824i	−0.244436	−	0.782272i
$184$	−15.6348	+	9.02673i	−1.15261	+	0.665460i
$185$		0			0
$186$	5.06246	−	3.20684i	0.371198	−	0.235137i
$187$	−1.27072	+	4.74240i	−0.0929245	+	0.346799i
$188$	5.98358	+	5.98358i	0.436398	+	0.436398i
$189$	10.1869	−	9.23182i	0.740990	−	0.671516i
$190$		0			0
$191$	−11.5911	+	6.69211i	−0.838700	+	0.484224i	−0.856822	−	0.515612i	$-0.827565\pi$
$191$	−11.5911	+	6.69211i	−0.838700	+	0.484224i	0.0181220	+	0.999836i	$0.494231\pi$
$192$	4.88211	−	21.7564i	0.352336	−	1.57013i
$193$	2.04347	+	7.62633i	0.147092	+	0.548955i	0.999653	+	0.0263279i	$0.00838139\pi$
$193$	2.04347	+	7.62633i	0.147092	+	0.548955i	−0.852561	+	0.522627i	$0.824952\pi$
$194$	4.07110	+	7.05135i	0.292288	+	0.506257i
$195$		0			0
$196$	−13.1704	−	15.5553i	−0.940742	−	1.11109i
$197$	6.12629	−	6.12629i	0.436480	−	0.436480i	−0.454345	−	0.890826i	$-0.650127\pi$
$197$	6.12629	−	6.12629i	0.436480	−	0.436480i	0.890826	+	0.454345i	$0.150127\pi$
$198$	−3.83112	−	10.6971i	−0.272266	−	0.760207i
$199$	−4.74722	−	2.74081i	−0.336522	−	0.194291i	0.322211	−	0.946668i	$-0.395574\pi$
$199$	−4.74722	−	2.74081i	−0.336522	−	0.194291i	−0.658733	+	0.752377i	$0.728907\pi$
$200$		0			0
$201$	22.4791	−	0.923449i	1.58555	−	0.0651351i
$202$	−9.67876	−	9.67876i	−0.680995	−	0.680995i
$203$	0.173447	−	0.996579i	0.0121736	−	0.0699462i
$204$	6.72325	−	12.8344i	0.470721	−	0.898588i
$205$		0			0
$206$	9.67959	+	5.58851i	0.674409	+	0.389370i
$207$	−17.3351	+	20.4443i	−1.20487	+	1.42098i
$208$	4.33969	+	1.16282i	0.300903	+	0.0806268i
$209$	10.8140			0.748020
$210$		0			0
$211$	−6.13476			−0.422334			−0.211167	−	0.977450i	$-0.567726\pi$
$211$	−6.13476			−0.422334			−0.211167	+	0.977450i	$0.567726\pi$
$212$	20.6401	+	5.53049i	1.41757	+	0.379836i
$213$	2.24694	−	10.0132i	0.153958	−	0.686091i
$214$	14.6754	+	8.47282i	1.00319	+	0.579190i
$215$		0			0
$216$	1.28994	+	10.4197i	0.0877696	+	0.708971i
$217$	−3.16996	−	2.64796i	−0.215191	−	0.179755i
$218$	1.49191	+	1.49191i	0.101045	+	0.101045i
$219$	−1.16273	−	28.3038i	−0.0785702	−	1.91260i
$220$		0			0
$221$	8.30872	+	4.79704i	0.558905	+	0.322684i
$222$	8.68481	−	9.42893i	0.582886	−	0.632828i
$223$	5.63870	−	5.63870i	0.377595	−	0.377595i	−0.492639	−	0.870234i	$-0.663968\pi$
$223$	5.63870	−	5.63870i	0.377595	−	0.377595i	0.870234	+	0.492639i	$0.163968\pi$
$224$	−18.5061	+	1.66041i	−1.23649	+	0.110941i
$225$		0			0
$226$	15.2093	+	26.3432i	1.01170	+	1.75232i
$227$	4.79798	+	17.9063i	0.318453	+	1.18848i	0.920731	+	0.390197i	$0.127593\pi$
$227$	4.79798	+	17.9063i	0.318453	+	1.18848i	−0.602278	+	0.798286i	$0.705740\pi$
$228$	−31.1383	−	6.98740i	−2.06218	−	0.462752i
$229$	−2.22555	+	1.28492i	−0.147068	+	0.0849099i	−0.571728	−	0.820443i	$-0.693727\pi$
$229$	−2.22555	+	1.28492i	−0.147068	+	0.0849099i	0.424660	+	0.905353i	$0.360394\pi$
$230$		0			0
$231$	−6.21483	+	4.76526i	−0.408906	+	0.313531i
$232$	0.546266	+	0.546266i	0.0358641	+	0.0358641i
$233$	0.210541	−	0.785749i	0.0137930	−	0.0514761i	−0.958686	−	0.284465i	$-0.908184\pi$
$233$	0.210541	−	0.785749i	0.0137930	−	0.0514761i	0.972479	+	0.232989i	$0.0748506\pi$
$234$	−22.1286	+	1.82118i	−1.44659	+	0.119054i
$235$		0			0
$236$	−19.4687	+	11.2403i	−1.26731	+	0.731680i
$237$	10.7283	−	3.35227i	0.696880	−	0.217754i
$238$	−16.5961	−	2.88844i	−1.07577	−	0.187230i
$239$	17.4594			1.12935			0.564677	−	0.825312i	$-0.309001\pi$
$239$	17.4594			1.12935			0.564677	+	0.825312i	$0.309001\pi$
$240$		0			0
$241$	−2.39134	+	4.14192i	−0.154040	+	0.266804i	−0.932709	−	0.360630i	$-0.882562\pi$
$241$	−2.39134	+	4.14192i	−0.154040	+	0.266804i	0.778669	+	0.627434i	$0.215895\pi$
$242$	−4.63441	−	17.2958i	−0.297911	−	1.11182i
$243$	7.01927	+	13.9187i	0.450286	+	0.892884i
$244$		−	18.6381i		−	1.19318i
$245$		0			0
$246$	−18.1760	+	34.6972i	−1.15886	+	2.21221i
$247$	5.46930	−	20.4117i	0.348003	−	1.29877i
$248$	3.04695	−	0.816427i	0.193481	−	0.0518431i
$249$	1.08281	+	1.70938i	0.0686205	+	0.108327i
$250$		0			0
$251$			13.1757i			0.831640i	0.909447	+	0.415820i	$0.136505\pi$
$251$			13.1757i			0.831640i	−0.909447	+	0.415820i	$0.863495\pi$
$252$	20.9743	−	9.70561i	1.32126	−	0.611396i
$253$	10.7970	−	10.7970i	0.678801	−	0.678801i
$254$	1.90713	+	3.30325i	0.119664	+	0.207264i
$255$		0			0
$256$	3.17777	−	5.50407i	0.198611	−	0.344004i
$257$	−2.34506	−	0.628358i	−0.146281	−	0.0391959i	0.184936	−	0.982751i	$-0.440792\pi$
$257$	−2.34506	−	0.628358i	−0.146281	−	0.0391959i	−0.331216	+	0.943555i	$0.607459\pi$
$258$	29.6336	−	9.25959i	1.84491	−	0.576477i
$259$	−8.01594	−	3.71629i	−0.498086	−	0.230919i
$260$		0			0
$261$	1.03703	+	0.490093i	0.0641903	+	0.0303360i
$262$	−36.2575	+	9.71516i	−2.23999	+	0.600205i
$263$	−25.3967	+	6.80504i	−1.56603	+	0.419617i	−0.934566	−	0.355789i	$-0.884212\pi$
$263$	−25.3967	+	6.80504i	−1.56603	+	0.419617i	−0.631464	+	0.775405i	$0.717546\pi$
$264$	−0.245493	−	5.97591i	−0.0151090	−	0.367792i
$265$		0			0
$266$	3.31572	+	36.9554i	0.203300	+	2.26588i
$267$	0.444903	+	1.42383i	0.0272276	+	0.0871370i
$268$	36.5323	+	9.78880i	2.23156	+	0.597946i
$269$	3.55031	−	6.14932i	0.216466	−	0.374931i	−0.737259	−	0.675610i	$-0.763880\pi$
$269$	3.55031	−	6.14932i	0.216466	−	0.374931i	0.953725	+	0.300680i	$0.0972135\pi$
$270$		0			0
$271$	10.3579	+	17.9405i	0.629199	+	1.08981i	0.987713	+	0.156281i	$0.0499504\pi$
$271$	10.3579	+	17.9405i	0.629199	+	1.08981i	−0.358513	+	0.933525i	$0.616716\pi$
$272$	−2.73300	+	2.73300i	−0.165712	+	0.165712i
$273$	5.85132	+	14.1407i	0.354138	+	0.855836i
$274$			12.8889i			0.778645i
$275$		0			0
$276$	−38.0657	+	24.1129i	−2.29129	+	1.45143i
$277$	−26.7643	+	7.17149i	−1.60811	+	0.430893i	−0.947480	−	0.319815i	$-0.896379\pi$
$277$	−26.7643	+	7.17149i	−1.60811	+	0.430893i	−0.660634	+	0.750708i	$0.729712\pi$
$278$	−5.05613	+	18.8697i	−0.303246	+	1.13173i
$279$	3.85025	−	2.66652i	0.230508	−	0.159640i
$280$		0			0
$281$		−	19.3192i		−	1.15249i	−0.817278	−	0.576244i	$-0.804518\pi$
$281$		−	19.3192i		−	1.15249i	0.817278	−	0.576244i	$-0.195482\pi$
$282$	8.20555	+	7.55798i	0.488633	+	0.450071i
$283$	2.20080	+	8.21349i	0.130824	+	0.488242i	0.999980	−	0.00629604i	$-0.00200410\pi$
$283$	2.20080	+	8.21349i	0.130824	+	0.488242i	−0.869156	+	0.494538i	$0.835337\pi$
$284$	8.62577	−	14.9403i	0.511845	−	0.886542i
$285$		0			0
$286$	12.6483			0.747909
$287$	26.5975	+	4.62911i	1.57000	+	0.273248i
$288$	3.76531	−	20.7291i	0.221873	−	1.22147i
$289$	7.57461	−	4.37320i	0.445565	−	0.257247i
$290$		0			0
$291$	3.40519	+	5.37558i	0.199616	+	0.315122i
$292$	12.3253	−	45.9985i	0.721281	−	2.69186i
$293$	2.64242	+	2.64242i	0.154372	+	0.154372i	0.780067	−	0.625695i	$-0.215185\pi$
$293$	2.64242	+	2.64242i	0.154372	+	0.154372i	−0.625695	+	0.780067i	$0.715185\pi$
$294$	−18.1902	−	19.7773i	−1.06087	−	1.15343i
$295$		0			0
$296$	5.84371	−	3.37387i	0.339659	−	0.196102i
$297$	−3.33474	−	8.23010i	−0.193502	−	0.477559i
$298$	−3.24305	−	12.1032i	−0.187865	−	0.701121i
$299$	−14.9189	−	25.8403i	−0.862782	−	1.49438i
$300$		0			0
$301$	−12.3126	−	17.5015i	−0.709684	−	1.00877i
$302$	15.5085	−	15.5085i	0.892414	−	0.892414i
$303$	−7.86832	−	7.24736i	−0.452023	−	0.416350i
$304$	7.37253	+	4.25653i	0.422844	+	0.244129i
$305$		0			0
$306$	8.16157	−	17.2697i	0.466566	−	0.987243i
$307$	16.3600	+	16.3600i	0.933714	+	0.933714i	0.997936	−	0.0642218i	$-0.0204565\pi$
$307$	16.3600	+	16.3600i	0.933714	+	0.933714i	−0.0642218	+	0.997936i	$0.520457\pi$
$308$	−12.3613	+	4.53021i	−0.704353	+	0.258133i
$309$	7.73776	+	4.05339i	0.440186	+	0.230589i
$310$		0			0
$311$	5.58346	+	3.22361i	0.316609	+	0.182794i	0.649880	−	0.760037i	$-0.274819\pi$
$311$	5.58346	+	3.22361i	0.316609	+	0.182794i	−0.333271	+	0.942831i	$0.608152\pi$
$312$	−11.4038	−	2.55901i	−0.645615	−	0.144875i
$313$	−8.16253	−	2.18714i	−0.461374	−	0.123625i	0.0206427	−	0.999787i	$-0.493429\pi$
$313$	−8.16253	−	2.18714i	−0.461374	−	0.123625i	−0.482016	+	0.876162i	$0.660095\pi$
$314$	−17.7553			−1.00199
$315$		0			0
$316$	18.8951			1.06293
$317$	−19.1336	−	5.12685i	−1.07465	−	0.287952i	−0.322249	−	0.946655i	$-0.604439\pi$
$317$	−19.1336	−	5.12685i	−1.07465	−	0.287952i	−0.752403	+	0.658703i	$0.771106\pi$
$318$	27.4870	+	6.16805i	1.54140	+	0.345887i
$319$	−0.565857	−	0.326698i	−0.0316819	−	0.0182916i
$320$		0			0
$321$	11.7313	+	6.14540i	0.654778	+	0.343003i
$322$	40.2078	+	33.5867i	2.24069	+	1.87172i
$323$	12.8546	+	12.8546i	0.715251	+	0.715251i
$324$	4.28438	+	25.8528i	0.238021	+	1.43627i
$325$		0			0
$326$	−40.7925	−	23.5515i	−2.25929	−	1.30440i
$327$	1.21284	+	1.11713i	0.0670703	+	0.0617772i
$328$	−14.5792	+	14.5792i	−0.805001	+	0.805001i
$329$	3.23411	−	6.97589i	0.178302	−	0.384593i
$330$		0			0
$331$	6.54487	+	11.3360i	0.359739	+	0.623085i	0.987917	−	0.154984i	$-0.0495325\pi$
$331$	6.54487	+	11.3360i	0.359739	+	0.623085i	−0.628178	+	0.778069i	$0.716199\pi$
$332$	0.880406	+	3.28572i	0.0483185	+	0.180327i
$333$	6.47923	−	7.64135i	0.355060	−	0.418743i
$334$	22.6296	−	13.0652i	1.23824	−	0.714896i
$335$		0			0
$336$	−6.11268	+	0.802512i	−0.333474	+	0.0437806i
$337$	10.0263	+	10.0263i	0.546168	+	0.546168i	0.925330	−	0.379163i	$-0.123788\pi$
$337$	10.0263	+	10.0263i	0.546168	+	0.546168i	−0.379163	+	0.925330i	$0.623788\pi$
$338$	−1.05985	+	3.95543i	−0.0576485	+	0.215147i
$339$	12.7215	+	20.0827i	0.690936	+	1.09074i
$340$		0			0
$341$	−2.31051	+	1.33398i	−0.125121	+	0.0722388i
$342$	−41.3945	−	7.51905i	−2.23836	−	0.406584i
$343$	−9.15329	+	16.1002i	−0.494231	+	0.869331i
$344$	16.3423			0.881118
$345$		0			0
$346$	18.4726	−	31.9955i	0.993092	−	1.72009i
$347$	−0.303201	−	1.13156i	−0.0162767	−	0.0607455i	0.957310	−	0.289064i	$-0.0933440\pi$
$347$	−0.303201	−	1.13156i	−0.0162767	−	0.0607455i	−0.973587	+	0.228318i	$0.926677\pi$
$348$	1.41826	+	1.30633i	0.0760267	+	0.0700267i
$349$			5.25811i			0.281460i	0.990048	+	0.140730i	$0.0449450\pi$
$349$			5.25811i			0.281460i	−0.990048	+	0.140730i	$0.955055\pi$
$350$		0			0
$351$	−17.2211	+	2.13195i	−0.919195	+	0.113795i
$352$	−3.10626	+	11.5927i	−0.165564	+	0.617893i
$353$	−24.6784	+	6.61257i	−1.31350	+	0.351952i	−0.846539	−	0.532326i	$-0.821318\pi$
$353$	−24.6784	+	6.61257i	−1.31350	+	0.351952i	−0.466962	+	0.884278i	$0.654651\pi$
$354$	−25.0366	+	15.8595i	−1.33068	+	0.842925i
$355$		0			0
$356$			2.50770i			0.132908i
$357$	−13.0521	−	1.72311i	−0.690788	−	0.0911968i
$358$	−27.8239	+	27.8239i	−1.47054	+	1.47054i
$359$	2.45953	+	4.26002i	0.129809	+	0.224835i	0.923602	−	0.383352i	$-0.125230\pi$
$359$	2.45953	+	4.26002i	0.129809	+	0.224835i	−0.793794	+	0.608187i	$0.791897\pi$
$360$		0			0
$361$	10.5206	−	18.2222i	0.553715	−	0.959062i
$362$	−22.2140	−	5.95221i	−1.16754	−	0.312841i
$363$	−4.17368	−	13.3571i	−0.219062	−	0.701066i
$364$	2.29900	+	25.6235i	0.120500	+	1.34304i
$365$		0			0
$366$	−1.00855	−	24.5507i	−0.0527178	−	1.28328i
$367$	26.2450	−	7.03232i	1.36998	−	0.367084i	0.502506	−	0.864574i	$-0.332411\pi$
$367$	26.2450	−	7.03232i	1.36998	−	0.367084i	0.867470	+	0.497490i	$0.165745\pi$
$368$	11.6108	−	3.11109i	0.605253	−	0.162177i
$369$	−13.0800	+	27.6770i	−0.680918	+	1.44081i
$370$		0			0
$371$	−1.73511	−	19.3387i	−0.0900824	−	1.00401i
$372$	7.51493	−	2.34818i	0.389631	−	0.121748i
$373$	−1.18585	−	0.317748i	−0.0614010	−	0.0164524i	0.227988	−	0.973664i	$-0.426785\pi$
$373$	−1.18585	−	0.317748i	−0.0614010	−	0.0164524i	−0.289389	+	0.957212i	$0.593452\pi$
$374$	−5.44053	+	9.42328i	−0.281323	+	0.487266i
$375$		0			0
$376$	2.93612	+	5.08550i	0.151419	+	0.262265i
$377$	−0.902838	+	0.902838i	−0.0464985	+	0.0464985i
$378$	27.1028	−	13.9195i	1.39402	−	0.715942i
$379$			3.68867i			0.189474i	0.995502	+	0.0947372i	$0.0302011\pi$
$379$			3.68867i			0.189474i	−0.995502	+	0.0947372i	$0.969799\pi$
$380$		0			0
$381$	1.59518	+	2.51822i	0.0817236	+	0.129012i
$382$	−28.6519	+	7.67725i	−1.46596	+	0.392802i
$383$	6.67215	−	24.9008i	0.340931	−	1.27237i	−0.556363	−	0.830939i	$-0.687804\pi$
$383$	6.67215	−	24.9008i	0.340931	−	1.27237i	0.897294	−	0.441433i	$-0.145530\pi$
$384$	11.6421	−	22.2242i	0.594106	−	1.13412i
$385$		0			0
$386$			17.4980i			0.890625i
$387$	22.8429	−	8.18112i	1.16117	−	0.415870i
$388$	2.76866	+	10.3328i	0.140558	+	0.524568i
$389$	−5.79887	+	10.0439i	−0.294014	+	0.509248i	−0.974755	−	0.223277i	$-0.928325\pi$
$389$	−5.79887	+	10.0439i	−0.294014	+	0.509248i	0.680741	+	0.732524i	$0.261658\pi$
$390$		0			0
$391$	25.6688			1.29813
$392$	−6.03430	−	12.7923i	−0.304778	−	0.646107i
$393$	−28.0007	+	8.74934i	−1.41245	+	0.441346i
$394$	16.6288	−	9.60062i	0.837745	−	0.483672i
$395$		0			0
$396$	−1.22443	−	14.8778i	−0.0615302	−	0.747636i
$397$	7.43927	−	27.7637i	0.373366	−	1.39342i	−0.482351	−	0.875978i	$-0.660217\pi$
$397$	7.43927	−	27.7637i	0.373366	−	1.39342i	0.855717	−	0.517444i	$-0.173117\pi$
$398$	−8.59034	−	8.59034i	−0.430595	−	0.430595i
$399$	3.77461	+	28.7509i	0.188967	+	1.43935i
$400$		0			0
$401$	10.2246	−	5.90315i	0.510590	−	0.294789i	−0.222486	−	0.974936i	$-0.571417\pi$
$401$	10.2246	−	5.90315i	0.510590	−	0.294789i	0.733076	+	0.680147i	$0.238084\pi$
$402$	48.6512	+	10.9173i	2.42650	+	0.544503i
$403$	1.34934	+	5.03582i	0.0672157	+	0.250852i
$404$	−8.99161	−	15.5739i	−0.447349	−	0.774831i
$405$		0			0
$406$	0.942946	−	2.03391i	0.0467976	−	0.100941i
$407$	−4.03553	+	4.03553i	−0.200034	+	0.200034i
$408$	6.81176	−	7.39540i	0.337232	−	0.366127i
$409$	0.546811	+	0.315702i	0.0270381	+	0.0156104i	0.513458	−	0.858115i	$-0.328364\pi$
$409$	0.546811	+	0.315702i	0.0270381	+	0.0156104i	−0.486420	+	0.873725i	$0.661698\pi$
$410$		0			0
$411$	0.413454	+	10.0645i	0.0203942	+	0.496446i
$412$	10.3835	+	10.3835i	0.511558	+	0.511558i
$413$	15.6771	+	13.0956i	0.771421	+	0.644391i
$414$	−48.8365	+	33.8221i	−2.40018	+	1.66227i
$415$		0			0
$416$	20.3105	+	11.7263i	0.995804	+	0.574928i
$417$	−3.34286	+	14.8970i	−0.163701	+	0.729507i
$418$	23.1498	+	6.20296i	1.13229	+	0.303397i
$419$	35.8106			1.74946			0.874732	−	0.484607i	$-0.161037\pi$
$419$	35.8106			1.74946			0.874732	+	0.484607i	$0.161037\pi$
$420$		0			0
$421$	13.8462			0.674822			0.337411	−	0.941357i	$-0.390449\pi$
$421$	13.8462			0.674822			0.337411	+	0.941357i	$0.390449\pi$
$422$	−13.1328	−	3.51893i	−0.639295	−	0.171299i
$423$	6.64990	+	5.63856i	0.323329	+	0.274156i
$424$	12.8418	+	7.41421i	0.623652	+	0.360066i
$425$		0			0
$426$	10.5537	−	20.1466i	0.511327	−	0.976104i
$427$	−15.9014	+	5.82758i	−0.769523	+	0.282016i
$428$	15.7426	+	15.7426i	0.760945	+	0.760945i
$429$	9.87665	−	0.405737i	0.476849	−	0.0195892i
$430$		0			0
$431$	−27.9526	−	16.1384i	−1.34643	−	0.777362i	−0.358688	−	0.933458i	$-0.616776\pi$
$431$	−27.9526	−	16.1384i	−1.34643	−	0.777362i	−0.987742	+	0.156096i	$0.950109\pi$
$432$	0.965988	−	6.92354i	0.0464761	−	0.333109i
$433$	6.59937	−	6.59937i	0.317145	−	0.317145i	−0.530524	−	0.847670i	$-0.678005\pi$
$433$	6.59937	−	6.59937i	0.317145	−	0.317145i	0.847670	+	0.530524i	$0.178005\pi$
$434$	−5.26712	−	7.48685i	−0.252830	−	0.359380i
$435$		0			0
$436$	1.38599	+	2.40060i	0.0663768	+	0.114968i
$437$	−14.6330	−	54.6112i	−0.699992	−	2.61241i
$438$	13.7461	−	61.2576i	0.656816	−	2.92700i
$439$	−2.47419	+	1.42848i	−0.118087	+	0.0681774i	−0.557880	−	0.829922i	$-0.688385\pi$
$439$	−2.47419	+	1.42848i	−0.118087	+	0.0681774i	0.439793	+	0.898099i	$0.355052\pi$
$440$		0			0
$441$	−14.8386	−	14.8599i	−0.706598	−	0.707615i
$442$	15.0351	+	15.0351i	0.715145	+	0.715145i
$443$	−9.37788	+	34.9987i	−0.445556	+	1.66284i	0.268907	+	0.963166i	$0.413338\pi$
$443$	−9.37788	+	34.9987i	−0.445556	+	1.66284i	−0.714463	+	0.699673i	$0.753329\pi$
$444$	14.2276	−	9.01254i	0.675212	−	0.427716i
$445$		0			0
$446$	15.3053	−	8.83650i	0.724726	−	0.418421i
$447$	−2.92065	−	9.34699i	−0.138142	−	0.442097i
$448$	−33.5555	−	5.84009i	−1.58535	−	0.275918i
$449$	4.07133			0.192138			0.0960690	−	0.995375i	$-0.469373\pi$
$449$	4.07133			0.192138			0.0960690	+	0.995375i	$0.469373\pi$
$450$		0			0
$451$	8.71918	−	15.1021i	0.410570	−	0.711128i
$452$	10.3435	+	38.6024i	0.486516	+	1.81570i
$453$	11.6126	−	12.6076i	0.545608	−	0.592356i
$454$			41.0846i			1.92819i
$455$		0			0
$456$	−19.6171	−	10.2763i	−0.918655	−	0.481233i
$457$	2.62075	−	9.78077i	0.122593	−	0.457525i	−0.877149	−	0.480218i	$-0.840557\pi$
$457$	2.62075	−	9.78077i	0.122593	−	0.457525i	0.999742	+	0.0226933i	$0.00722412\pi$
$458$	−5.50131	+	1.47407i	−0.257059	+	0.0688789i
$459$	5.81913	−	13.7472i	0.271614	−	0.641663i
$460$		0			0
$461$		−	14.4769i		−	0.674257i	−0.941459	−	0.337129i	$-0.890544\pi$
$461$		−	14.4769i		−	0.674257i	0.941459	−	0.337129i	$-0.109456\pi$
$462$	−16.0376	+	6.63623i	−0.746137	+	0.308746i
$463$	−18.1704	+	18.1704i	−0.844452	+	0.844452i	−0.989434	−	0.144982i	$-0.953687\pi$
$463$	−18.1704	+	18.1704i	−0.844452	+	0.844452i	0.144982	+	0.989434i	$0.453687\pi$
$464$	−0.257185	−	0.445457i	−0.0119395	−	0.0206798i
$465$		0			0
$466$	0.901419	−	1.56130i	0.0417574	−	0.0723260i
$467$	−16.0274	−	4.29453i	−0.741659	−	0.198727i	−0.131844	−	0.991271i	$-0.542090\pi$
$467$	−16.0274	−	4.29453i	−0.741659	−	0.198727i	−0.609815	+	0.792544i	$0.708756\pi$
$468$	−28.7014	−	5.21344i	−1.32672	−	0.240991i
$469$	−3.07109	−	34.2288i	−0.141810	−	1.58054i
$470$		0			0
$471$	−13.8646	+	0.569561i	−0.638845	+	0.0262440i
$472$	−15.0688	+	4.03767i	−0.693596	+	0.185849i
$473$	−13.3510	+	3.57739i	−0.613880	+	0.164489i
$474$	24.8893	−	1.02246i	1.14320	−	0.0469632i
$475$		0			0
$476$	−20.0790	−	9.30889i	−0.920321	−	0.426672i
$477$	21.6616	+	3.93470i	0.991817	+	0.180158i
$478$	37.3757	+	10.0148i	1.70952	+	0.458066i
$479$	8.40526	−	14.5583i	0.384046	−	0.665188i	−0.607590	−	0.794251i	$-0.707864\pi$
$479$	8.40526	−	14.5583i	0.384046	−	0.665188i	0.991636	+	0.129063i	$0.0411970\pi$
$480$		0			0
$481$	5.57615	+	9.65817i	0.254250	+	0.440375i
$482$	−7.49501	+	7.49501i	−0.341388	+	0.341388i
$483$	32.4744	+	24.9370i	1.47764	+	1.13467i
$484$		−	23.5250i		−	1.06932i
$485$		0			0
$486$	7.04248	+	33.8223i	0.319453	+	1.53421i
$487$	−4.25512	+	1.14016i	−0.192818	+	0.0516654i	−0.353936	−	0.935270i	$-0.615157\pi$
$487$	−4.25512	+	1.14016i	−0.192818	+	0.0516654i	0.161118	+	0.986935i	$0.448490\pi$
$488$	3.34753	−	12.4932i	0.151536	−	0.565539i
$489$	−32.6090	−	17.0821i	−1.47463	−	0.772479i
$490$		0			0
$491$		−	5.57629i		−	0.251654i	−0.992052	−	0.125827i	$-0.959842\pi$
$491$		−	5.57629i		−	0.251654i	0.992052	−	0.125827i	$-0.0401585\pi$
$492$	−34.8645	+	37.8517i	−1.57181	+	1.70649i
$493$	−0.284289	−	1.06098i	−0.0128037	−	0.0477842i
$494$	23.4165	−	40.5586i	1.05356	−	1.82482i
$495$		0			0
$496$	−2.10028			−0.0943054
$497$	−15.4436	−	2.68784i	−0.692739	−	0.120566i
$498$	1.33750	+	4.28041i	0.0599346	+	0.191810i
$499$	−25.7467	+	14.8649i	−1.15258	+	0.665444i	−0.949515	−	0.313721i	$-0.898424\pi$
$499$	−25.7467	+	14.8649i	−1.15258	+	0.665444i	−0.203067	+	0.979165i	$0.565091\pi$
$500$		0			0
$501$	17.2516	−	10.9281i	0.770746	−	0.488232i
$502$	−7.55762	+	28.2054i	−0.337313	+	1.25887i
$503$	−28.9208	−	28.9208i	−1.28951	−	1.28951i	−0.935081	−	0.354434i	$-0.884674\pi$
$503$	−28.9208	−	28.9208i	−1.28951	−	1.28951i	−0.354434	−	0.935081i	$-0.615326\pi$
$504$	15.8023	−	2.73857i	0.703891	−	0.121985i
$505$		0			0
$506$	29.3066	−	16.9201i	1.30284	−	0.752192i
$507$	−0.700723	+	3.12267i	−0.0311202	+	0.138683i
$508$	1.29700	+	4.84046i	0.0575449	+	0.214761i
$509$	−14.8892	−	25.7888i	−0.659951	−	1.14307i	−0.980628	−	0.195880i	$-0.937244\pi$
$509$	−14.8892	−	25.7888i	−0.659951	−	1.14307i	0.320677	−	0.947189i	$-0.396090\pi$
$510$		0			0
$511$	−43.0982	+	3.86687i	−1.90655	+	0.171060i
$512$	−10.5251	+	10.5251i	−0.465149	+	0.465149i
$513$	−32.5648	−	4.54352i	−1.43777	−	0.200601i
$514$	−4.65970	−	2.69028i	−0.205531	−	0.118663i
$515$		0			0
$516$	40.7549	−	1.67423i	1.79414	−	0.0737038i
$517$	−3.51193	−	3.51193i	−0.154454	−	0.154454i
$518$	−15.0282	−	12.5535i	−0.660302	−	0.551570i
$519$	13.3983	−	25.5768i	0.588120	−	1.12270i
$520$		0			0
$521$	12.6774	+	7.31932i	0.555409	+	0.320665i	0.751301	−	0.659960i	$-0.229427\pi$
$521$	12.6774	+	7.31932i	0.555409	+	0.320665i	−0.195892	+	0.980625i	$0.562760\pi$
$522$	1.93886	+	1.64400i	0.0848618	+	0.0719558i
$523$	−4.69348	−	1.25761i	−0.205231	−	0.0549916i	0.154739	−	0.987955i	$-0.450546\pi$
$523$	−4.69348	−	1.25761i	−0.205231	−	0.0549916i	−0.359970	+	0.932964i	$0.617213\pi$
$524$	−49.3158			−2.15437
$525$		0			0
$526$	−58.2708			−2.54073
$527$	−4.33221	−	1.16081i	−0.188714	−	0.0505658i
$528$	−0.871924	+	3.88560i	−0.0379456	+	0.169099i
$529$	−49.2166	−	28.4152i	−2.13985	−	1.23545i
$530$		0			0
$531$	−19.0415	+	13.1873i	−0.826332	+	0.572282i
$532$	−8.35848	+	48.0254i	−0.362386	+	2.08217i
$533$	−24.0957	−	24.0957i	−1.04370	−	1.04370i
$534$	0.135698	+	3.30322i	0.00587221	+	0.142944i
$535$		0			0
$536$	22.7296	+	13.1229i	0.981767	+	0.566823i
$537$	−20.8343	+	22.6194i	−0.899065	+	0.976097i
$538$	11.1275	−	11.1275i	0.479741	−	0.479741i
$539$	7.73005	+	9.12983i	0.332957	+	0.393250i
$540$		0			0
$541$	−13.9369	−	24.1395i	−0.599195	−	1.03784i	−0.992940	−	0.118616i	$-0.962154\pi$
$541$	−13.9369	−	24.1395i	−0.599195	−	1.03784i	0.393745	−	0.919220i	$-0.371179\pi$
$542$	11.8827	+	44.3469i	0.510406	+	1.90486i
$543$	−17.5371	−	3.93531i	−0.752590	−	0.168880i
$544$	−17.4727	+	10.0879i	−0.749136	+	0.432514i
$545$		0			0
$546$	4.41487	+	33.6277i	0.188939	+	1.43913i
$547$	−19.9877	−	19.9877i	−0.854612	−	0.854612i	0.136085	−	0.990697i	$-0.456548\pi$
$547$	−19.9877	−	19.9877i	−0.854612	−	0.854612i	−0.990697	+	0.136085i	$0.956548\pi$
$548$	−4.38272	+	16.3565i	−0.187220	+	0.698716i
$549$	−1.57509	−	19.1385i	−0.0672233	−	0.816811i
$550$		0			0
$551$	−2.09521	+	1.20967i	−0.0892588	+	0.0515336i
$552$	−29.8464	+	9.32608i	−1.27035	+	0.396944i
$553$	−5.90795	−	16.1207i	−0.251232	−	0.685523i
$554$	−61.4086			−2.60900
$555$		0			0
$556$	−12.8329	+	22.2272i	−0.544235	+	0.942643i
$557$	−2.98236	−	11.1303i	−0.126367	−	0.471607i	0.873518	−	0.486792i	$-0.161833\pi$
$557$	−2.98236	−	11.1303i	−0.126367	−	0.471607i	−0.999885	+	0.0151851i	$0.995166\pi$
$558$	9.77184	−	3.49975i	0.413675	−	0.148156i
$559$			27.0096i			1.14239i
$560$		0			0
$561$	−3.94606	+	7.53286i	−0.166603	+	0.318038i
$562$	11.0816	−	41.3571i	0.467449	−	1.74454i
$563$	−19.7907	+	5.30291i	−0.834079	+	0.223491i	−0.650493	−	0.759513i	$-0.725437\pi$
$563$	−19.7907	+	5.30291i	−0.834079	+	0.223491i	−0.183587	+	0.983004i	$0.558771\pi$
$564$	7.84318	+	12.3816i	0.330258	+	0.521359i
$565$		0			0
$566$			18.8452i			0.792123i
$567$	20.7172	−	11.7387i	0.870041	−	0.492980i
$568$	8.46525	−	8.46525i	0.355194	−	0.355194i
$569$	8.69408	+	15.0586i	0.364475	+	0.631289i	0.988692	−	0.149962i	$-0.0479151\pi$
$569$	8.69408	+	15.0586i	0.364475	+	0.631289i	−0.624217	+	0.781251i	$0.714582\pi$
$570$		0			0
$571$	−7.08776	+	12.2764i	−0.296613	+	0.513750i	−0.975359	−	0.220624i	$-0.929191\pi$
$571$	−7.08776	+	12.2764i	−0.296613	+	0.513750i	0.678745	+	0.734374i	$0.262524\pi$
$572$	16.0512	+	4.30091i	0.671135	+	0.179830i
$573$	−22.1271	+	6.91403i	−0.924372	+	0.288838i
$574$	54.2827	+	25.1661i	2.26571	+	1.05041i
$575$		0			0
$576$	16.5018	−	34.9173i	0.687573	−	1.45489i
$577$	5.23184	−	1.40187i	0.217805	−	0.0583605i	−0.148267	−	0.988947i	$-0.547369\pi$
$577$	5.23184	−	1.40187i	0.217805	−	0.0583605i	0.366071	+	0.930587i	$0.380703\pi$
$578$	18.7236	−	5.01698i	0.778800	−	0.208679i
$579$	0.561307	+	13.6636i	0.0233271	+	0.567841i
$580$		0			0
$581$	2.52799	−	1.77848i	0.104879	−	0.0737838i
$582$	4.20610	+	13.4609i	0.174348	+	0.557970i
$583$	−12.1142	−	3.24600i	−0.501720	−	0.134435i
$584$	16.5233	−	28.6192i	0.683740	−	1.18427i
$585$		0			0
$586$	4.14099	+	7.17240i	0.171063	+	0.296289i
$587$	−22.3599	+	22.3599i	−0.922893	+	0.922893i	−0.997233	−	0.0743398i	$-0.976315\pi$
$587$	−22.3599	+	22.3599i	−0.922893	+	0.922893i	0.0743398	+	0.997233i	$0.476315\pi$
$588$	−16.3591	−	31.2835i	−0.674637	−	1.29011i
$589$			9.87866i			0.407043i
$590$		0			0
$591$	12.6769	−	8.03025i	0.521458	−	0.330320i
$592$	−4.33969	+	1.16282i	−0.178360	+	0.0477914i
$593$	10.0873	−	37.6462i	0.414235	−	1.54595i	−0.372128	−	0.928181i	$-0.621372\pi$
$593$	10.0873	−	37.6462i	0.414235	−	1.54595i	0.786363	−	0.617764i	$-0.211961\pi$
$594$	−2.41794	−	19.5312i	−0.0992091	−	0.801375i
$595$		0			0
$596$		−	16.4623i		−	0.674321i
$597$	−6.98349	−	6.43236i	−0.285815	−	0.263259i
$598$	−17.1151	−	63.8744i	−0.699888	−	2.61202i
$599$	−8.22678	+	14.2492i	−0.336137	+	0.582207i	−0.983703	−	0.179803i	$-0.942454\pi$
$599$	−8.22678	+	14.2492i	−0.336137	+	0.582207i	0.647565	+	0.762010i	$0.275787\pi$
$600$		0			0
$601$	−21.2977			−0.868752			−0.434376	−	0.900732i	$-0.643031\pi$
$601$	−21.2977			−0.868752			−0.434376	+	0.900732i	$0.643031\pi$
$602$	−16.3188	−	44.5284i	−0.665107	−	1.81484i
$603$	38.3404	+	6.96429i	1.56134	+	0.283608i
$604$	24.9544	−	14.4074i	1.01538	−	0.586231i
$605$		0			0
$606$	−12.6868	−	20.0279i	−0.515365	−	0.813578i
$607$	7.46766	−	27.8697i	0.303103	−	1.13120i	−0.631463	−	0.775406i	$-0.717545\pi$
$607$	7.46766	−	27.8697i	0.303103	−	1.13120i	0.934566	−	0.355790i	$-0.115788\pi$
$608$	31.4229	+	31.4229i	1.27437	+	1.27437i
$609$	0.671072	−	1.61846i	0.0271932	−	0.0655835i
$610$		0			0
$611$	−8.40504	+	4.85265i	−0.340032	+	0.196317i
$612$	16.2298	−	19.1407i	0.656049	−	0.773718i
$613$	6.74902	+	25.1877i	0.272590	+	1.01732i	0.957439	+	0.288636i	$0.0932016\pi$
$613$	6.74902	+	25.1877i	0.272590	+	1.01732i	−0.684849	+	0.728685i	$0.740132\pi$
$614$	25.6380	+	44.4064i	1.03467	+	1.79210i
$615$		0			0
$616$	−9.09950	+	0.816427i	−0.366629	+	0.0328948i
$617$	14.0996	−	14.0996i	0.567629	−	0.567629i	−0.363835	−	0.931463i	$-0.618533\pi$
$617$	14.0996	−	14.0996i	0.567629	−	0.567629i	0.931463	+	0.363835i	$0.118533\pi$
$618$	14.2393	+	13.1156i	0.572790	+	0.527587i
$619$	−20.7434	−	11.9762i	−0.833750	−	0.481365i	0.0213852	−	0.999771i	$-0.493192\pi$
$619$	−20.7434	−	11.9762i	−0.833750	−	0.481365i	−0.855135	+	0.518406i	$0.826526\pi$
$620$		0			0
$621$	−37.0500	+	27.9772i	−1.48676	+	1.12269i
$622$	10.1036	+	10.1036i	0.405116	+	0.405116i
$623$	2.13949	−	0.784084i	0.0857168	−	0.0314137i
$624$	6.89319	+	3.61096i	0.275948	+	0.144554i
$625$		0			0
$626$	−16.2192	−	9.36414i	−0.648248	−	0.374266i
$627$	18.2759	+	4.10109i	0.729870	+	0.163782i
$628$	−22.5322	−	6.03749i	−0.899134	−	0.240922i
$629$	−9.59409			−0.382541
$630$		0			0
$631$	−1.86220			−0.0741332			−0.0370666	−	0.999313i	$-0.511801\pi$
$631$	−1.86220			−0.0741332			−0.0370666	+	0.999313i	$0.511801\pi$
$632$	12.6655	+	3.39370i	0.503805	+	0.134994i
$633$	−10.3679	−	2.32654i	−0.412086	−	0.0924716i
$634$	−38.0190	−	21.9503i	−1.50993	−	0.871758i
$635$		0			0
$636$	32.7848	+	17.1742i	1.30000	+	0.681001i
$637$	21.1423	−	9.97316i	0.837690	−	0.395151i
$638$	−1.02395	−	1.02395i	−0.0405385	−	0.0405385i
$639$	7.59477	−	16.0704i	0.300444	−	0.635733i
$640$		0			0
$641$	26.4970	+	15.2981i	1.04657	+	0.604237i	0.921687	−	0.387934i	$-0.126811\pi$
$641$	26.4970	+	15.2981i	1.04657	+	0.604237i	0.124883	+	0.992171i	$0.460145\pi$
$642$	21.5885	+	19.8847i	0.852029	+	0.784788i
$643$	11.3733	−	11.3733i	0.448521	−	0.448521i	−0.446342	−	0.894863i	$-0.647273\pi$
$643$	11.3733	−	11.3733i	0.448521	−	0.448521i	0.894863	+	0.446342i	$0.147273\pi$
$644$	39.6045	+	56.2952i	1.56064	+	2.21834i
$645$		0			0
$646$	20.1447	+	34.8917i	0.792584	+	1.37280i
$647$	11.1350	+	41.5564i	0.437762	+	1.63375i	0.734369	+	0.678751i	$0.237478\pi$
$647$	11.1350	+	41.5564i	0.437762	+	1.63375i	−0.296606	+	0.955000i	$0.595855\pi$
$648$	−1.77152	+	18.0987i	−0.0695919	+	0.710985i
$649$	11.4267	−	6.59722i	0.448538	−	0.258964i
$650$		0			0
$651$	−4.35309	−	5.67729i	−0.170611	−	0.222510i
$652$	−43.7589	−	43.7589i	−1.71373	−	1.71373i
$653$	9.44244	−	35.2397i	0.369511	−	1.37904i	−0.491690	−	0.870770i	$-0.663621\pi$
$653$	9.44244	−	35.2397i	0.369511	−	1.37904i	0.861201	−	0.508265i	$-0.169713\pi$
$654$	1.95557	+	3.08715i	0.0764688	+	0.120717i
$655$		0			0
$656$	11.8887	−	6.86396i	0.464177	−	0.267993i
$657$	8.76888	−	48.2751i	0.342106	−	1.88339i
$658$	10.9247	−	13.0783i	0.425890	−	0.509847i
$659$	−24.1200			−0.939581			−0.469791	−	0.882778i	$-0.655671\pi$
$659$	−24.1200			−0.939581			−0.469791	+	0.882778i	$0.655671\pi$
$660$		0			0
$661$	13.4049	−	23.2180i	0.521391	−	0.903076i	−0.478299	−	0.878197i	$-0.658747\pi$
$661$	13.4049	−	23.2180i	0.521391	−	0.903076i	0.999690	−	0.0248793i	$-0.00792015\pi$
$662$	7.50834	+	28.0215i	0.291820	+	1.08909i
$663$	12.2227	+	11.2581i	0.474691	+	0.437229i
$664$			2.36055i			0.0916072i
$665$		0			0
$666$	18.2533	−	12.6415i	0.707303	−	0.489848i
$667$	−0.884145	+	3.29967i	−0.0342342	+	0.127764i
$668$	33.1606	−	8.88535i	1.28302	−	0.343785i
$669$	11.6679	−	7.39111i	0.451109	−	0.285757i
$670$		0			0
$671$			10.9392i			0.422303i
$672$	−31.9055	−	4.21211i	−1.23078	−	0.162486i
$673$	32.9918	−	32.9918i	1.27174	−	1.27174i	0.326567	−	0.945174i	$-0.394108\pi$
$673$	32.9918	−	32.9918i	1.27174	−	1.27174i	0.945174	−	0.326567i	$-0.105892\pi$
$674$	15.7124	+	27.2147i	0.605219	+	1.04827i
$675$		0			0
$676$	−2.69000	+	4.65922i	−0.103462	+	0.179201i
$677$	22.0362	+	5.90457i	0.846918	+	0.226931i	0.656081	−	0.754691i	$-0.272213\pi$
$677$	22.0362	+	5.90457i	0.846918	+	0.226931i	0.190837	+	0.981622i	$0.438880\pi$
$678$	15.7136	+	50.2886i	0.603478	+	1.93132i
$679$	7.94992	−	5.59289i	0.305090	−	0.214635i
$680$		0			0
$681$	1.31793	+	32.0816i	0.0505031	+	1.22937i
$682$	−5.71134	+	1.53035i	−0.218699	+	0.0586001i
$683$	14.0422	−	3.76258i	0.537308	−	0.143971i	0.0200472	−	0.999799i	$-0.493618\pi$
$683$	14.0422	−	3.76258i	0.537308	−	0.143971i	0.517261	+	0.855828i	$0.326952\pi$
$684$	−49.9746	−	23.6177i	−1.91082	−	0.903046i
$685$		0			0
$686$	−28.8298	+	29.2157i	−1.10073	+	1.11546i
$687$	−4.24851	+	1.32753i	−0.162091	+	0.0506484i
$688$	−10.5103	−	2.81621i	−0.400700	−	0.107367i
$689$	−12.2538	+	21.2242i	−0.466832	+	0.808577i
$690$		0			0
$691$	−5.38460	−	9.32640i	−0.204840	−	0.354793i	0.745242	−	0.666794i	$-0.232334\pi$
$691$	−5.38460	−	9.32640i	−0.204840	−	0.354793i	−0.950082	+	0.312001i	$0.899001\pi$
$692$	34.3222	−	34.3222i	1.30473	−	1.30473i
$693$	−12.3104	+	5.69649i	−0.467633	+	0.216392i
$694$		−	2.59628i		−	0.0985534i
$695$		0			0
$696$	0.716037	+	1.13037i	0.0271413	+	0.0428465i
$697$	28.3164	−	7.58735i	1.07256	−	0.287391i
$698$	−3.01608	+	11.2562i	−0.114160	+	0.426052i
$699$	0.653806	−	1.24809i	0.0247292	−	0.0472071i
$700$		0			0
$701$		−	15.6058i		−	0.589425i	−0.955586	−	0.294712i	$-0.904776\pi$
$701$		−	15.6058i		−	0.589425i	0.955586	−	0.294712i	$-0.0952238\pi$
$702$	−38.0885	−	5.31420i	−1.43756	−	0.200572i
$703$	5.46930	+	20.4117i	0.206278	+	0.769842i
$704$	−11.0001	+	19.0528i	−0.414583	+	0.718078i
$705$		0			0
$706$	−56.6227			−2.13102
$707$	−10.4758	+	12.5409i	−0.393981	+	0.471647i
$708$	−37.1653	+	11.6130i	−1.39676	+	0.436444i
$709$	4.98148	−	2.87606i	0.187084	−	0.108013i	−0.403533	−	0.914965i	$-0.632218\pi$
$709$	4.98148	−	2.87606i	0.187084	−	0.108013i	0.590617	+	0.806952i	$0.298885\pi$
$710$		0			0
$711$	19.4024	−	1.59682i	0.727649	−	0.0598852i
$712$	−0.450401	+	1.68092i	−0.0168795	+	0.0629951i
$713$	9.86311	+	9.86311i	0.369376	+	0.369376i
$714$	−26.9525	−	11.1754i	−1.00867	−	0.418230i
$715$		0			0
$716$	−44.7709	+	25.8485i	−1.67317	+	0.966004i
$717$	29.5068	+	6.62128i	1.10195	+	0.247276i
$718$	2.82159	+	10.5303i	0.105301	+	0.392988i
$719$	20.2675	+	35.1043i	0.755850	+	1.30917i	0.944951	+	0.327212i	$0.106109\pi$
$719$	20.2675	+	35.1043i	0.755850	+	1.30917i	−0.189101	+	0.981958i	$0.560557\pi$
$720$		0			0
$721$	5.61225	−	12.1055i	0.209011	−	0.450832i
$722$	32.9740	−	32.9740i	1.22716	−	1.22716i
$723$	−5.61219	+	6.09305i	−0.208720	+	0.226603i
$724$	−26.1665	−	15.1072i	−0.972469	−	0.561456i
$725$		0			0
$726$	−1.27300	−	30.9879i	−0.0472453	−	1.15007i
$727$	11.1039	+	11.1039i	0.411820	+	0.411820i	0.882372	−	0.470552i	$-0.155945\pi$
$727$	11.1039	+	11.1039i	0.411820	+	0.411820i	−0.470552	+	0.882372i	$0.655945\pi$
$728$	−3.06114	+	17.5884i	−0.113453	+	0.651871i
$729$	6.58421	+	26.1849i	0.243860	+	0.969810i
$730$		0			0
$731$	−20.1228	−	11.6179i	−0.744270	−	0.429704i
$732$	7.06829	−	31.4988i	0.261251	−	1.16423i
$733$	−18.7384	−	5.02095i	−0.692120	−	0.185453i	−0.104422	−	0.994533i	$-0.533299\pi$
$733$	−18.7384	−	5.02095i	−0.692120	−	0.185453i	−0.587698	+	0.809080i	$0.699966\pi$
$734$	60.2170			2.22265
$735$		0			0
$736$	62.7469			2.31288
$737$	−21.4418	−	5.74531i	−0.789818	−	0.211631i
$738$	−43.8763	+	51.7460i	−1.61511	+	1.90480i
$739$	28.0225	+	16.1788i	1.03082	+	0.595146i	0.917220	−	0.398380i	$-0.130428\pi$
$739$	28.0225	+	16.1788i	1.03082	+	0.595146i	0.113603	+	0.993526i	$0.463761\pi$
$740$		0			0
$741$	16.9842	−	32.4221i	0.623928	−	1.19105i
$742$	7.37837	−	42.3940i	0.270868	−	1.55633i
$743$	3.87363	+	3.87363i	0.142110	+	0.142110i	0.774582	−	0.632473i	$-0.217960\pi$
$743$	3.87363	+	3.87363i	0.142110	+	0.142110i	−0.632473	+	0.774582i	$0.717960\pi$
$744$	5.45903	−	0.224259i	0.200138	−	0.00822173i
$745$		0			0
$746$	−2.35632	−	1.36042i	−0.0862709	−	0.0498085i
$747$	1.18172	+	3.29953i	0.0432368	+	0.120724i
$748$	−10.1085	+	10.1085i	−0.369605	+	0.369605i
$749$	8.50881	−	18.3533i	0.310905	−	0.670614i
$750$		0			0
$751$	18.1770	+	31.4835i	0.663288	+	1.14885i	0.979746	+	0.200242i	$0.0641730\pi$
$751$	18.1770	+	31.4835i	0.663288	+	1.14885i	−0.316458	+	0.948606i	$0.602494\pi$
$752$	−1.01194	−	3.77662i	−0.0369018	−	0.137719i
$753$	−4.99672	+	22.2672i	−0.182091	+	0.811460i
$754$	−2.45060	+	1.41485i	−0.0892455	+	0.0515259i
$755$		0			0
$756$	39.1278	−	8.44844i	1.42306	−	0.307267i
$757$	5.12602	+	5.12602i	0.186308	+	0.186308i	0.794098	−	0.607790i	$-0.207944\pi$
$757$	5.12602	+	5.12602i	0.186308	+	0.186308i	−0.607790	+	0.794098i	$0.707944\pi$
$758$	−2.11584	+	7.89643i	−0.0768508	+	0.286811i
$759$	22.3418	−	14.1525i	0.810956	−	0.513704i
$760$		0			0
$761$	10.4338	−	6.02395i	0.378224	−	0.218368i	−0.298821	−	0.954309i	$-0.596593\pi$
$761$	10.4338	−	6.02395i	0.378224	−	0.218368i	0.677045	+	0.735941i	$0.263260\pi$
$762$	1.97037	+	6.30582i	0.0713791	+	0.228436i
$763$	1.61476	−	1.93308i	0.0584581	−	0.0699821i
$764$	−38.9710			−1.40992
$765$		0			0
$766$	28.5665	−	49.4785i	1.03215	−	1.78773i
$767$	−6.67323	−	24.9048i	−0.240956	−	0.899262i
$768$	7.45787	−	8.09686i	0.269113	−	0.292170i
$769$			7.03355i			0.253636i	0.991926	+	0.126818i	$0.0404765\pi$
$769$			7.03355i			0.253636i	−0.991926	+	0.126818i	$0.959524\pi$
$770$		0			0
$771$	−3.72491	−	1.95128i	−0.134149	−	0.0702736i
$772$	−5.95000	+	22.2057i	−0.214145	+	0.799201i
$773$	39.0264	−	10.4571i	1.40368	−	0.376115i	0.524016	−	0.851709i	$-0.324433\pi$
$773$	39.0264	−	10.4571i	1.40368	−	0.376115i	0.879665	+	0.475593i	$0.157767\pi$
$774$	53.5931	−	4.41069i	1.92636	−	0.158539i
$775$		0			0
$776$			7.42337i			0.266483i
$777$	−12.1378	−	9.32057i	−0.435440	−	0.334373i
$778$	−18.1750	+	18.1750i	−0.651606	+	0.651606i
$779$	−32.2846	−	55.9186i	−1.15672	−	2.00349i
$780$		0			0
$781$	−5.06270	+	8.76885i	−0.181158	+	0.313774i
$782$	54.9498	+	14.7238i	1.96500	+	0.526521i
$783$	1.56673	+	1.22155i	0.0559905	+	0.0436546i
$784$	1.67640	+	9.26698i	0.0598716	+	0.330964i
$785$		0			0
$786$	−64.9603	+	2.66860i	−2.31706	+	0.0951857i
$787$	−46.4227	+	12.4389i	−1.65479	+	0.443400i	−0.960948	−	0.276728i	$-0.910750\pi$
$787$	−46.4227	+	12.4389i	−1.65479	+	0.443400i	−0.693841	+	0.720128i	$0.744083\pi$
$788$	24.3672	−	6.52917i	0.868045	−	0.232592i
$789$	−45.5018	+	1.86923i	−1.61991	+	0.0665464i
$790$		0			0
$791$	29.7002	−	20.8945i	1.05602	−	0.742924i
$792$	1.85141	−	10.1925i	0.0657870	−	0.362175i
$793$	20.6480	+	5.53262i	0.733232	+	0.196469i
$794$	31.8508	−	55.1673i	1.13034	−	1.95781i
$795$		0			0
$796$	−7.98046	−	13.8226i	−0.282860	−	0.489928i
$797$	−30.8216	+	30.8216i	−1.09176	+	1.09176i	−0.0964167	+	0.995341i	$0.530738\pi$
$797$	−30.8216	+	30.8216i	−1.09176	+	1.09176i	−0.995341	+	0.0964167i	$0.969262\pi$
$798$	−8.41128	+	63.7129i	−0.297756	+	2.25541i
$799$		−	8.34927i		−	0.295376i
$800$		0			0
$801$	0.211924	+	2.57503i	0.00748797	+	0.0909842i
$802$	25.2740	−	6.77215i	0.892456	−	0.239133i
$803$	−7.23403	+	26.9978i	−0.255283	+	0.952731i
$804$	58.0281	+	30.3978i	2.04649	+	1.07205i
$805$		0			0
$806$			11.5543i			0.406983i
$807$	8.33217	−	9.04608i	0.293306	−	0.318437i
$808$	−3.22991	−	12.0542i	−0.113628	−	0.424065i
$809$	−19.0846	+	33.0555i	−0.670979	+	1.16217i	0.306648	+	0.951823i	$0.400793\pi$
$809$	−19.0846	+	33.0555i	−0.670979	+	1.16217i	−0.977627	+	0.210347i	$0.932541\pi$
$810$		0			0
$811$	31.3640			1.10134			0.550669	−	0.834724i	$-0.314373\pi$
$811$	31.3640			1.10134			0.550669	+	0.834724i	$0.314373\pi$
$812$	1.88825	−	2.26048i	0.0662645	−	0.0793273i
$813$	10.7014	+	34.2479i	0.375315	+	1.20113i
$814$	−10.9537	+	6.32415i	−0.383928	+	0.221661i
$815$		0			0
$816$	−5.65529	+	3.58237i	−0.197975	+	0.125408i
$817$	−13.2461	+	49.4349i	−0.463421	+	1.72951i
$818$	0.989484	+	0.989484i	0.0345965	+	0.0345965i
$819$	4.52615	+	26.1172i	0.158157	+	0.912609i
$820$		0			0
$821$	−23.9871	+	13.8489i	−0.837155	+	0.483332i	−0.856296	−	0.516485i	$-0.827240\pi$
$821$	−23.9871	+	13.8489i	−0.837155	+	0.483332i	0.0191413	+	0.999817i	$0.493907\pi$
$822$	−4.88796	+	21.7825i	−0.170487	+	0.759751i
$823$	4.17345	+	15.5755i	0.145477	+	0.542928i	0.999734	+	0.0230765i	$0.00734613\pi$
$823$	4.17345	+	15.5755i	0.145477	+	0.542928i	−0.854257	+	0.519852i	$0.825987\pi$
$824$	5.09514	+	8.82504i	0.177498	+	0.307435i
$825$		0			0
$826$	26.0487	+	37.0265i	0.906350	+	1.28832i
$827$	7.45257	−	7.45257i	0.259151	−	0.259151i	−0.565558	−	0.824709i	$-0.691339\pi$
$827$	7.45257	−	7.45257i	0.259151	−	0.259151i	0.824709	+	0.565558i	$0.191339\pi$
$828$	−73.4765	+	26.3154i	−2.55348	+	0.914522i
$829$	23.9775	+	13.8434i	0.832773	+	0.480802i	0.854801	−	0.518956i	$-0.173679\pi$
$829$	23.9775	+	13.8434i	0.832773	+	0.480802i	−0.0220284	+	0.999757i	$0.507012\pi$
$830$		0			0
$831$	−47.9521	+	1.96989i	−1.66344	+	0.0683347i
$832$	30.3992	+	30.3992i	1.05390	+	1.05390i
$833$	−1.66392	+	20.0414i	−0.0576513	+	0.694393i
$834$	−15.7011	+	29.9728i	−0.543685	+	1.03787i
$835$		0			0
$836$	27.2688	+	15.7437i	0.943111	+	0.544506i
$837$	7.51825	−	3.04631i	0.259869	−	0.105296i
$838$	76.6606	+	20.5412i	2.64820	+	0.709583i
$839$	30.4470			1.05115			0.525574	−	0.850748i	$-0.323851\pi$
$839$	30.4470			1.05115			0.525574	+	0.850748i	$0.323851\pi$
$840$		0			0
$841$	−28.8538			−0.994959
$842$	29.6409	+	7.94224i	1.02149	+	0.273708i
$843$	7.32660	−	32.6499i	0.252342	−	1.12452i
$844$	−15.4695	−	8.93134i	−0.532483	−	0.307429i
$845$		0			0
$846$	11.0013	+	15.8850i	0.378232	+	0.546138i
$847$	−20.0708	+	7.35559i	−0.689641	+	0.252741i
$848$	−6.98130	−	6.98130i	−0.239739	−	0.239739i
$849$	0.604524	+	14.7156i	0.0207472	+	0.505039i
$850$		0			0
$851$	25.8403	+	14.9189i	0.885793	+	0.511413i
$852$	20.2437	−	21.9782i	0.693537	−	0.752960i
$853$	19.1062	−	19.1062i	0.654184	−	0.654184i	−0.299813	−	0.953998i	$-0.596924\pi$
$853$	19.1062	−	19.1062i	0.654184	−	0.654184i	0.953998	+	0.299813i	$0.0969244\pi$
$854$	−37.3832	+	3.35411i	−1.27923	+	0.114775i
$855$		0			0
$856$	7.72481	+	13.3798i	0.264028	+	0.457311i
$857$	−4.48559	−	16.7405i	−0.153225	−	0.571843i	−0.999251	−	0.0387013i	$-0.987678\pi$
$857$	−4.48559	−	16.7405i	−0.153225	−	0.571843i	0.846026	−	0.533142i	$-0.178989\pi$
$858$	21.3759	+	4.79673i	0.729761	+	0.163758i
$859$	6.29120	−	3.63222i	0.214653	−	0.123930i	−0.388819	−	0.921314i	$-0.627117\pi$
$859$	6.29120	−	3.63222i	0.214653	−	0.123930i	0.603472	+	0.797384i	$0.293784\pi$
$860$		0			0
$861$	43.1949	+	17.9101i	1.47208	+	0.610375i
$862$	−50.5817	−	50.5817i	−1.72282	−	1.72282i
$863$	12.4168	−	46.3400i	0.422672	−	1.57743i	−0.346284	−	0.938130i	$-0.612557\pi$
$863$	12.4168	−	46.3400i	0.422672	−	1.57743i	0.768955	−	0.639302i	$-0.220777\pi$
$864$	14.2247	−	33.6047i	0.483936	−	1.14325i
$865$		0			0
$866$	17.9129	−	10.3420i	0.608703	−	0.351435i
$867$	14.4598	−	4.51823i	0.491079	−	0.153447i
$868$	−4.13837	−	11.2922i	−0.140466	−	0.383281i
$869$	−11.0901			−0.376205
$870$		0			0
$871$	−21.6888	+	37.5661i	−0.734898	+	1.27288i
$872$	0.497866	+	1.85806i	0.0168599	+	0.0629219i
$873$	3.71621	+	10.3762i	0.125775	+	0.351182i
$874$		−	125.301i		−	4.23837i
$875$		0			0
$876$	38.2744	−	73.0643i	1.29317	−	2.46861i
$877$	−15.1013	+	56.3587i	−0.509934	+	1.90310i	−0.0889356	+	0.996037i	$0.528347\pi$
$877$	−15.1013	+	56.3587i	−0.509934	+	1.90310i	−0.420998	+	0.907061i	$0.638320\pi$
$878$	−6.11594	+	1.63876i	−0.206403	+	0.0553055i
$879$	3.46365	+	5.46787i	0.116826	+	0.184427i
$880$		0			0
$881$		−	0.214145i		−	0.00721472i	−0.999993	−	0.00360736i	$-0.998852\pi$
$881$		−	0.214145i		−	0.00721472i	0.999993	−	0.00360736i	$-0.00114826\pi$
$882$	−23.2415	−	40.3224i	−0.782582	−	1.35773i
$883$	−4.91078	+	4.91078i	−0.165261	+	0.165261i	−0.784893	−	0.619632i	$-0.787282\pi$
$883$	−4.91078	+	4.91078i	−0.165261	+	0.165261i	0.619632	+	0.784893i	$0.287282\pi$
$884$	13.9676	+	24.1926i	0.469782	+	0.813686i
$885$		0			0
$886$	−40.1509	+	69.5433i	−1.34889	+	2.33635i
$887$	42.1903	+	11.3049i	1.41661	+	0.379580i	0.884280	−	0.466957i	$-0.154650\pi$
$887$	42.1903	+	11.3049i	1.41661	+	0.379580i	0.532331	+	0.846536i	$0.321316\pi$
$888$	11.1555	−	3.48575i	0.374355	−	0.116974i
$889$	3.72419	−	2.62002i	0.124905	−	0.0878728i
$890$		0			0
$891$	−2.51462	−	15.1737i	−0.0842429	−	0.508339i
$892$	22.4278	−	6.00951i	0.750938	−	0.201213i
$893$	−17.7633	+	4.75967i	−0.594427	+	0.159276i
$894$	−0.890812	−	21.6846i	−0.0297932	−	0.725242i
$895$		0			0
$896$	−34.7691	−	16.1194i	−1.16155	−	0.538511i
$897$	−15.4136	−	49.3285i	−0.514646	−	1.64703i
$898$	8.71559	+	2.33534i	0.290843	+	0.0779312i
$899$	0.298440	−	0.516914i	0.00995354	−	0.0172400i
$900$		0			0
$901$	−10.5417	−	18.2587i	−0.351194	−	0.608287i
$902$	27.3280	−	27.3280i	0.909921	−	0.909921i
$903$	−14.1713	−	34.2473i	−0.471590	−	1.13968i
$904$			27.7330i			0.922387i
$905$		0			0
$906$	32.0911	−	20.3283i	1.06616	−	0.675362i
$907$	13.4565	−	3.60565i	0.446815	−	0.119724i	−0.0283939	−	0.999597i	$-0.509039\pi$
$907$	13.4565	−	3.60565i	0.446815	−	0.119724i	0.475209	+	0.879873i	$0.342373\pi$
$908$	−13.9704	+	52.1381i	−0.463622	+	1.73026i
$909$	−10.5492	−	15.2322i	−0.349894	−	0.505220i
$910$		0			0
$911$			2.00995i			0.0665927i	0.999446	+	0.0332963i	$0.0106005\pi$
$911$			2.00995i			0.0665927i	−0.999446	+	0.0332963i	$0.989399\pi$
$912$	10.8455	+	9.98959i	0.359130	+	0.330788i
$913$	−0.516734	−	1.92848i	−0.0171014	−	0.0638233i
$914$	11.2206	−	19.4346i	0.371144	−	0.642841i
$915$		0			0
$916$	−7.48264			−0.247233
$917$	15.4196	+	42.0746i	0.509200	+	1.38943i
$918$	20.3426	−	26.0910i	0.671405	−	0.861131i
$919$	30.4194	−	17.5627i	1.00344	−	0.579339i	0.0941788	−	0.995555i	$-0.469977\pi$
$919$	30.4194	−	17.5627i	1.00344	−	0.579339i	0.909266	+	0.416216i	$0.136644\pi$
$920$		0			0
$921$	21.4444	+	33.8531i	0.706617	+	1.11550i
$922$	8.30403	−	30.9911i	0.273479	−	1.02064i
$923$	13.9909	+	13.9909i	0.460516	+	0.460516i
$924$	−22.6090	+	2.96825i	−0.743781	+	0.0976484i
$925$		0			0
$926$	−49.3205	+	28.4752i	−1.62077	+	0.935754i
$927$	11.5398	+	9.78478i	0.379016	+	0.321374i
$928$	−0.694939	−	2.59355i	−0.0228125	−	0.0851374i
$929$	−19.8199	−	34.3290i	−0.650268	−	1.12630i	−0.983058	−	0.183296i	$-0.941323\pi$
$929$	−19.8199	−	34.3290i	−0.650268	−	1.12630i	0.332789	−	0.943001i	$-0.392010\pi$
$930$		0			0
$931$	43.5872	−	7.88496i	1.42851	−	0.258419i
$932$	1.67484	−	1.67484i	0.0548613	−	0.0548613i
$933$	8.21366	+	7.56544i	0.268903	+	0.247682i
$934$	−31.8468	−	18.3868i	−1.04206	−	0.601634i
$935$		0			0
$936$	−18.3023	−	8.64956i	−0.598228	−	0.282720i
$937$	0.653785	+	0.653785i	0.0213582	+	0.0213582i	0.717705	−	0.696347i	$-0.245193\pi$
$937$	0.653785	+	0.653785i	0.0213582	+	0.0213582i	−0.696347	+	0.717705i	$0.745193\pi$
$938$	13.0595	−	75.0360i	0.426407	−	2.45001i
$939$	−12.9654	−	6.79188i	−0.423111	−	0.221645i
$940$		0			0
$941$	−38.9192	−	22.4700i	−1.26873	−	0.732502i	−0.293983	−	0.955811i	$-0.594981\pi$
$941$	−38.9192	−	22.4700i	−1.26873	−	0.732502i	−0.974748	+	0.223309i	$0.928314\pi$
$942$	−30.0069	−	6.73350i	−0.977676	−	0.219389i
$943$	−88.0644	−	23.5968i	−2.86777	−	0.768417i
$944$	10.3870			0.338068
$945$		0			0
$946$	−30.6328			−0.995958
$947$	−21.7745	−	5.83445i	−0.707576	−	0.189594i	−0.112954	−	0.993600i	$-0.536031\pi$
$947$	−21.7745	−	5.83445i	−0.707576	−	0.189594i	−0.594621	+	0.804006i	$0.702698\pi$
$948$	31.9332	+	7.16577i	1.03714	+	0.232734i
$949$	47.3003	+	27.3088i	1.53543	+	0.886482i
$950$		0			0
$951$	−30.3920	−	15.9207i	−0.985528	−	0.516264i
$952$	−11.7871	−	9.84611i	−0.382022	−	0.319114i
$953$	2.82580	+	2.82580i	0.0915365	+	0.0915365i	0.751392	−	0.659856i	$-0.229383\pi$
$953$	2.82580	+	2.82580i	0.0915365	+	0.0915365i	−0.659856	+	0.751392i	$0.729383\pi$
$954$	44.1145	+	20.8483i	1.42826	+	0.674989i
$955$		0			0
$956$	44.0259	+	25.4184i	1.42390	+	0.822089i
$957$	−0.832415	−	0.766722i	−0.0269081	−	0.0247846i
$958$	26.3441	−	26.3441i	0.851139	−	0.851139i
$959$	15.3252	−	1.37501i	0.494876	−	0.0444014i
$960$		0			0
$961$	14.2814	+	24.7361i	0.460690	+	0.797939i
$962$	6.39701	+	23.8740i	0.206248	+	0.769727i
$963$	17.4956	+	14.8348i	0.563788	+	0.478046i
$964$	−12.0601	+	6.96289i	−0.388429	+	0.224260i
$965$		0			0
$966$	55.2146	+	72.0107i	1.77650	+	2.31691i
$967$	3.58319	+	3.58319i	0.115228	+	0.115228i	0.762370	−	0.647142i	$-0.224036\pi$
$967$	3.58319	+	3.58319i	0.115228	+	0.115228i	−0.647142	+	0.762370i	$0.724036\pi$
$968$	4.22526	−	15.7689i	0.135805	−	0.506831i
$969$	16.8497	+	26.5996i	0.541289	+	0.854503i
$970$		0			0
$971$	13.7968	−	7.96560i	0.442761	−	0.255628i	−0.262007	−	0.965066i	$-0.584384\pi$
$971$	13.7968	−	7.96560i	0.442761	−	0.255628i	0.704768	+	0.709438i	$0.251051\pi$
$972$	−2.56371	+	45.3167i	−0.0822309	+	1.45353i
$973$	22.9760	+	3.99880i	0.736576	+	0.128196i
$974$	−9.76304			−0.312828
$975$		0			0
$976$	−4.30581	+	7.45788i	−0.137826	+	0.238721i
$977$	2.89979	+	10.8222i	0.0927726	+	0.346232i	0.996672	−	0.0815124i	$-0.0259750\pi$
$977$	2.89979	+	10.8222i	0.0927726	+	0.346232i	−0.903900	+	0.427744i	$0.859308\pi$
$978$	−60.0085	−	55.2727i	−1.91886	−	1.76743i
$979$		−	1.47184i		−	0.0470401i
$980$		0			0
$981$	1.62607	+	2.34792i	0.0519165	+	0.0749635i
$982$	3.19859	−	11.9373i	0.102071	−	0.380934i
$983$	51.6385	−	13.8365i	1.64701	−	0.441316i	0.688239	−	0.725484i	$-0.258384\pi$
$983$	51.6385	−	13.8365i	1.64701	−	0.441316i	0.958775	+	0.284168i	$0.0917173\pi$
$984$	−30.1682	+	19.1102i	−0.961726	+	0.609210i
$985$		0			0
$986$		−	2.43434i		−	0.0775251i
$987$	8.11124	−	10.5629i	0.258184	−	0.336221i
$988$	43.5080	−	43.5080i	1.38417	−	1.38417i
$989$	36.1319	+	62.5823i	1.14893	+	1.99000i
$990$		0			0
$991$	−13.9802	+	24.2144i	−0.444096	+	0.769196i	−0.997989	−	0.0633917i	$-0.979808\pi$
$991$	−13.9802	+	24.2144i	−0.444096	+	0.769196i	0.553893	+	0.832588i	$0.313142\pi$
$992$	−10.5900	−	2.83758i	−0.336233	−	0.0900934i
$993$	6.76191	+	21.6402i	0.214583	+	0.686733i
$994$	−31.5187	−	14.6124i	−0.999711	−	0.463478i
$995$		0			0
$996$	0.241833	+	5.88682i	0.00766277	+	0.186531i
$997$	−20.4010	+	5.46642i	−0.646105	+	0.173123i	−0.566967	−	0.823740i	$-0.691883\pi$
$997$	−20.4010	+	5.46642i	−0.646105	+	0.173123i	−0.0791380	+	0.996864i	$0.525217\pi$
$998$	−63.6432	+	17.0531i	−2.01459	+	0.539808i
$999$	13.8479	−	10.4569i	0.438130	−	0.330841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bf.g.32.18	yes	80
3.2	odd	2	inner	525.2.bf.g.32.4	yes	80
5.2	odd	4	inner	525.2.bf.g.368.4	yes	80
5.3	odd	4	inner	525.2.bf.g.368.17	yes	80
5.4	even	2	inner	525.2.bf.g.32.3	✓	80
7.2	even	3	inner	525.2.bf.g.107.3	yes	80
15.2	even	4	inner	525.2.bf.g.368.18	yes	80
15.8	even	4	inner	525.2.bf.g.368.3	yes	80
15.14	odd	2	inner	525.2.bf.g.32.17	yes	80
21.2	odd	6	inner	525.2.bf.g.107.17	yes	80
35.2	odd	12	inner	525.2.bf.g.443.17	yes	80
35.9	even	6	inner	525.2.bf.g.107.18	yes	80
35.23	odd	12	inner	525.2.bf.g.443.4	yes	80
105.2	even	12	inner	525.2.bf.g.443.3	yes	80
105.23	even	12	inner	525.2.bf.g.443.18	yes	80
105.44	odd	6	inner	525.2.bf.g.107.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bf.g.32.3	✓	80	5.4	even	2	inner
525.2.bf.g.32.4	yes	80	3.2	odd	2	inner
525.2.bf.g.32.17	yes	80	15.14	odd	2	inner
525.2.bf.g.32.18	yes	80	1.1	even	1	trivial
525.2.bf.g.107.3	yes	80	7.2	even	3	inner
525.2.bf.g.107.4	yes	80	105.44	odd	6	inner
525.2.bf.g.107.17	yes	80	21.2	odd	6	inner
525.2.bf.g.107.18	yes	80	35.9	even	6	inner
525.2.bf.g.368.3	yes	80	15.8	even	4	inner
525.2.bf.g.368.4	yes	80	5.2	odd	4	inner
525.2.bf.g.368.17	yes	80	5.3	odd	4	inner
525.2.bf.g.368.18	yes	80	15.2	even	4	inner
525.2.bf.g.443.3	yes	80	105.2	even	12	inner
525.2.bf.g.443.4	yes	80	35.23	odd	12	inner
525.2.bf.g.443.17	yes	80	35.2	odd	12	inner
525.2.bf.g.443.18	yes	80	105.23	even	12	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.14072 + 0.573605i) q^{2} +(1.69002 + 0.379239i) q^{3} +(2.52162 + 1.45586i) q^{4} +(3.40034 + 1.78125i) q^{6} +(0.453654 - 2.60657i) q^{7} +(1.42877 + 1.42877i) q^{8} +(2.71236 + 1.28185i) q^{9} +O(q^{10})\)	\(q+(2.14072 + 0.573605i) q^{2} +(1.69002 + 0.379239i) q^{3} +(2.52162 + 1.45586i) q^{4} +(3.40034 + 1.78125i) q^{6} +(0.453654 - 2.60657i) q^{7} +(1.42877 + 1.42877i) q^{8} +(2.71236 + 1.28185i) q^{9} +(-1.48001 - 0.854482i) q^{11} +(3.70948 + 3.41673i) q^{12} +(-2.36139 + 2.36139i) q^{13} +(2.46629 - 5.31972i) q^{14} +(-0.672671 - 1.16510i) q^{16} +(-0.743563 - 2.77501i) q^{17} +(5.07113 + 4.29990i) q^{18} +(-5.48004 + 3.16390i) q^{19} +(1.75520 - 4.23312i) q^{21} +(-2.67815 - 2.67815i) q^{22} +(-2.31249 + 8.63034i) q^{23} +(1.87280 + 2.95649i) q^{24} +(-6.40958 + 3.70057i) q^{26} +(4.09782 + 3.19498i) q^{27} +(4.93874 - 5.91232i) q^{28} +0.382334 q^{29} +(0.780575 - 1.35200i) q^{31} +(-1.81762 - 6.78347i) q^{32} +(-2.17719 - 2.00537i) q^{33} -6.36705i q^{34} +(4.97335 + 7.18113i) q^{36} +(0.864327 - 3.22571i) q^{37} +(-13.5461 + 3.62966i) q^{38} +(-4.88633 + 3.09527i) q^{39} +10.2040i q^{41} +(6.18553 - 8.05514i) q^{42} +(5.71902 - 5.71902i) q^{43} +(-2.48801 - 4.30936i) q^{44} +(-9.90082 + 17.1487i) q^{46} +(2.80718 + 0.752183i) q^{47} +(-0.694978 - 2.22415i) q^{48} +(-6.58840 - 2.36496i) q^{49} +(-0.204245 - 4.97183i) q^{51} +(-9.39236 + 2.51668i) q^{52} +(7.08863 - 1.89939i) q^{53} +(6.93963 + 9.19009i) q^{54} +(4.37234 - 3.07601i) q^{56} +(-10.4613 + 3.26882i) q^{57} +(0.818471 + 0.219309i) q^{58} +(-3.86036 + 6.68634i) q^{59} +(-3.20053 - 5.54348i) q^{61} +(2.44651 - 2.44651i) q^{62} +(4.57169 - 6.48842i) q^{63} -12.8734i q^{64} +(-3.51048 - 5.54179i) q^{66} +(12.5466 - 3.36186i) q^{67} +(2.16504 - 8.08006i) q^{68} +(-7.18113 + 13.7085i) q^{69} -5.92487i q^{71} +(2.04386 + 5.70678i) q^{72} +(-4.23299 - 15.7977i) q^{73} +(3.70057 - 6.40958i) q^{74} -18.4248 q^{76} +(-2.89868 + 3.47010i) q^{77} +(-12.2357 + 3.82329i) q^{78} +(5.61994 - 3.24467i) q^{79} +(5.71374 + 6.95364i) q^{81} +(-5.85309 + 21.8440i) q^{82} +(0.826081 + 0.826081i) q^{83} +(10.5888 - 8.11899i) q^{84} +(15.5233 - 8.96238i) q^{86} +(0.646153 + 0.144996i) q^{87} +(-0.893728 - 3.33544i) q^{88} +(0.430623 + 0.745860i) q^{89} +(5.08386 + 7.22637i) q^{91} +(-18.3958 + 18.3958i) q^{92} +(1.83192 - 1.98888i) q^{93} +(5.57795 + 3.22043i) q^{94} +(-0.499272 - 12.1535i) q^{96} +(2.59782 + 2.59782i) q^{97} +(-12.7474 - 8.84186i) q^{98} +(-2.91899 - 4.21480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{6}+O(q^{10}) \) 80 * q + 16 * q^6	\( 80 q + 16 q^{6} + 72 q^{16} + 44 q^{21} + 72 q^{31} - 240 q^{36} - 92 q^{51} - 24 q^{61} - 216 q^{66} - 208 q^{76} - 20 q^{81} - 40 q^{91} - 156 q^{96}+O(q^{100}) \) 80 * q + 16 * q^6 + 72 * q^16 + 44 * q^21 + 72 * q^31 - 240 * q^36 - 92 * q^51 - 24 * q^61 - 216 * q^66 - 208 * q^76 - 20 * q^81 - 40 * q^91 - 156 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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