LMFDB - Embedded newform 1690.2.e.o.191.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(191,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.191"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,-1,-3,-6,-1,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.3
Root			$-0.623490 + 1.07992i$ of defining polynomial
Character	$\chi$	$=$	1690.191
Dual form			1690.2.e.o.991.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.623490 - 1.07992i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.623490 + 1.07992i) q^{6} +(-0.0990311 - 0.171527i) q^{7} +1.00000 q^{8} +(0.722521 + 1.25144i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.554958 + 0.961216i) q^{11} -1.24698 q^{12} +0.198062 q^{14} +(-0.623490 + 1.07992i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.24698 - 5.62393i) q^{17} -1.44504 q^{18} +(0.246980 + 0.427781i) q^{19} +(0.500000 + 0.866025i) q^{20} -0.246980 q^{21} +(-0.554958 - 0.961216i) q^{22} +(3.38135 - 5.85668i) q^{23} +(0.623490 - 1.07992i) q^{24} +1.00000 q^{25} +5.54288 q^{27} +(-0.0990311 + 0.171527i) q^{28} +(0.178448 - 0.309081i) q^{29} +(-0.623490 - 1.07992i) q^{30} +6.27413 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.692021 + 1.19862i) q^{33} +6.49396 q^{34} +(0.0990311 + 0.171527i) q^{35} +(0.722521 - 1.25144i) q^{36} +(-1.10992 + 1.92243i) q^{37} -0.493959 q^{38} -1.00000 q^{40} +(-4.48307 + 7.76491i) q^{41} +(0.123490 - 0.213891i) q^{42} +(-2.82640 - 4.89546i) q^{43} +1.10992 q^{44} +(-0.722521 - 1.25144i) q^{45} +(3.38135 + 5.85668i) q^{46} -1.43296 q^{47} +(0.623490 + 1.07992i) q^{48} +(3.48039 - 6.02820i) q^{49} +(-0.500000 + 0.866025i) q^{50} -8.09783 q^{51} +9.92154 q^{53} +(-2.77144 + 4.80027i) q^{54} +(0.554958 - 0.961216i) q^{55} +(-0.0990311 - 0.171527i) q^{56} +0.615957 q^{57} +(0.178448 + 0.309081i) q^{58} +(-2.30798 - 3.99754i) q^{59} +1.24698 q^{60} +(-2.75182 - 4.76630i) q^{61} +(-3.13706 + 5.43355i) q^{62} +(0.143104 - 0.247864i) q^{63} +1.00000 q^{64} -1.38404 q^{66} +(1.93631 - 3.35379i) q^{67} +(-3.24698 + 5.62393i) q^{68} +(-4.21648 - 7.30316i) q^{69} -0.198062 q^{70} +(-6.80194 - 11.7813i) q^{71} +(0.722521 + 1.25144i) q^{72} +0.591794 q^{73} +(-1.10992 - 1.92243i) q^{74} +(0.623490 - 1.07992i) q^{75} +(0.246980 - 0.427781i) q^{76} +0.219833 q^{77} +2.93362 q^{79} +(0.500000 - 0.866025i) q^{80} +(1.28836 - 2.23151i) q^{81} +(-4.48307 - 7.76491i) q^{82} +15.6625 q^{83} +(0.123490 + 0.213891i) q^{84} +(3.24698 + 5.62393i) q^{85} +5.65279 q^{86} +(-0.222521 - 0.385418i) q^{87} +(-0.554958 + 0.961216i) q^{88} +(8.54019 - 14.7920i) q^{89} +1.44504 q^{90} -6.76271 q^{92} +(3.91185 - 6.77553i) q^{93} +(0.716480 - 1.24098i) q^{94} +(-0.246980 - 0.427781i) q^{95} -1.24698 q^{96} +(-6.78986 - 11.7604i) q^{97} +(3.48039 + 6.02820i) q^{98} -1.60388 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - q^{3} - 3 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} + 6 q^{8} + 4 q^{9} + 3 q^{10} - 4 q^{11} + 2 q^{12} + 10 q^{14} + q^{15} - 3 q^{16} - 10 q^{17} - 8 q^{18} - 8 q^{19} + 3 q^{20} + 8 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - q^3 - 3 * q^4 - 6 * q^5 - q^6 - 5 * q^7 + 6 * q^8 + 4 * q^9 + 3 * q^10 - 4 * q^11 + 2 * q^12 + 10 * q^14 + q^15 - 3 * q^16 - 10 * q^17 - 8 * q^18 - 8 * q^19 + 3 * q^20 + 8 * q^21 - 4 * q^22 + 3 * q^23 - q^24 + 6 * q^25 - 4 * q^27 - 5 * q^28 - 3 * q^29 + q^30 + 16 * q^31 - 3 * q^32 - 6 * q^33 + 20 * q^34 + 5 * q^35 + 4 * q^36 - 8 * q^37 + 16 * q^38 - 6 * q^40 - 11 * q^41 - 4 * q^42 + q^43 + 8 * q^44 - 4 * q^45 + 3 * q^46 + 30 * q^47 - q^48 + 8 * q^49 - 3 * q^50 - 12 * q^51 + 8 * q^53 + 2 * q^54 + 4 * q^55 - 5 * q^56 + 24 * q^57 - 3 * q^58 - 24 * q^59 - 2 * q^60 + 15 * q^61 - 8 * q^62 + 9 * q^63 + 6 * q^64 + 12 * q^66 - 5 * q^67 - 10 * q^68 - 6 * q^69 - 10 * q^70 - 32 * q^71 + 4 * q^72 - 52 * q^73 - 8 * q^74 - q^75 - 8 * q^76 + 4 * q^77 + 4 * q^79 + 3 * q^80 + 5 * q^81 - 11 * q^82 + 14 * q^83 - 4 * q^84 + 10 * q^85 - 2 * q^86 - q^87 - 4 * q^88 + 17 * q^89 + 8 * q^90 - 6 * q^92 + 16 * q^93 - 15 * q^94 + 8 * q^95 + 2 * q^96 + 6 * q^97 + 8 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.623490	−	1.07992i	0.359972	−	0.623490i	−0.627984	−	0.778226i	$-0.716120\pi$
$3$	0.623490	−	1.07992i	0.359972	−	0.623490i	0.987956	+	0.154737i	$0.0494529\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.623490	+	1.07992i	0.254539	+	0.440874i
$7$	−0.0990311	−	0.171527i	−0.0374302	−	0.0648311i	0.846703	−	0.532065i	$-0.178584\pi$
$7$	−0.0990311	−	0.171527i	−0.0374302	−	0.0648311i	−0.884134	+	0.467234i	$0.845251\pi$
$8$	1.00000			0.353553
$9$	0.722521	+	1.25144i	0.240840	+	0.417148i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−0.554958	+	0.961216i	−0.167326	+	0.289817i	−0.937479	−	0.348042i	$-0.886847\pi$
$11$	−0.554958	+	0.961216i	−0.167326	+	0.289817i	0.770153	+	0.637860i	$0.220180\pi$
$12$	−1.24698			−0.359972
$13$		0			0
$13$		0			0
$14$	0.198062			0.0529344
$15$	−0.623490	+	1.07992i	−0.160984	+	0.278833i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.24698	−	5.62393i	−0.787508	−	1.36400i	−0.927489	−	0.373850i	$-0.878037\pi$
$17$	−3.24698	−	5.62393i	−0.787508	−	1.36400i	0.139981	−	0.990154i	$-0.455296\pi$
$18$	−1.44504			−0.340600
$19$	0.246980	+	0.427781i	0.0566610	+	0.0981397i	0.892965	−	0.450127i	$-0.148621\pi$
$19$	0.246980	+	0.427781i	0.0566610	+	0.0981397i	−0.836304	+	0.548267i	$0.815288\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−0.246980			−0.0538954
$22$	−0.554958	−	0.961216i	−0.118317	−	0.204932i
$23$	3.38135	−	5.85668i	0.705061	−	1.22120i	−0.261608	−	0.965174i	$-0.584253\pi$
$23$	3.38135	−	5.85668i	0.705061	−	1.22120i	0.966669	−	0.256028i	$-0.0824138\pi$
$24$	0.623490	−	1.07992i	0.127269	−	0.220437i
$25$	1.00000			0.200000
$26$		0			0
$27$	5.54288			1.06673
$28$	−0.0990311	+	0.171527i	−0.0187151	+	0.0324155i
$29$	0.178448	−	0.309081i	0.0331369	−	0.0573949i	−0.848981	−	0.528423i	$-0.822784\pi$
$29$	0.178448	−	0.309081i	0.0331369	−	0.0573949i	0.882118	+	0.471028i	$0.156117\pi$
$30$	−0.623490	−	1.07992i	−0.113833	−	0.197165i
$31$	6.27413			1.12687			0.563433	−	0.826162i	$-0.309480\pi$
$31$	6.27413			1.12687			0.563433	+	0.826162i	$0.309480\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.692021	+	1.19862i	0.120465	+	0.208652i
$34$	6.49396			1.11370
$35$	0.0990311	+	0.171527i	0.0167393	+	0.0289933i
$36$	0.722521	−	1.25144i	0.120420	−	0.208574i
$37$	−1.10992	+	1.92243i	−0.182469	+	0.316046i	−0.942721	−	0.333583i	$-0.891742\pi$
$37$	−1.10992	+	1.92243i	−0.182469	+	0.316046i	0.760252	+	0.649629i	$0.225076\pi$
$38$	−0.493959			−0.0801308
$39$		0			0
$40$	−1.00000			−0.158114
$41$	−4.48307	+	7.76491i	−0.700139	+	1.21268i	0.268279	+	0.963341i	$0.413545\pi$
$41$	−4.48307	+	7.76491i	−0.700139	+	1.21268i	−0.968417	+	0.249334i	$0.919788\pi$
$42$	0.123490	−	0.213891i	0.0190549	−	0.0330040i
$43$	−2.82640	−	4.89546i	−0.431021	−	0.746551i	0.565940	−	0.824446i	$-0.308513\pi$
$43$	−2.82640	−	4.89546i	−0.431021	−	0.746551i	−0.996962	+	0.0778954i	$0.975180\pi$
$44$	1.10992			0.167326
$45$	−0.722521	−	1.25144i	−0.107707	−	0.186554i
$46$	3.38135	+	5.85668i	0.498554	+	0.863520i
$47$	−1.43296			−0.209019			−0.104509	−	0.994524i	$-0.533327\pi$
$47$	−1.43296			−0.209019			−0.104509	+	0.994524i	$0.533327\pi$
$48$	0.623490	+	1.07992i	0.0899930	+	0.155872i
$49$	3.48039	−	6.02820i	0.497198	−	0.861172i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−8.09783			−1.13392
$52$		0			0
$53$	9.92154			1.36283			0.681414	−	0.731898i	$-0.261365\pi$
$53$	9.92154			1.36283			0.681414	+	0.731898i	$0.261365\pi$
$54$	−2.77144	+	4.80027i	−0.377145	+	0.653234i
$55$	0.554958	−	0.961216i	0.0748305	−	0.129610i
$56$	−0.0990311	−	0.171527i	−0.0132336	−	0.0229213i
$57$	0.615957			0.0815855
$58$	0.178448	+	0.309081i	0.0234314	+	0.0405843i
$59$	−2.30798	−	3.99754i	−0.300473	−	0.520435i	0.675770	−	0.737113i	$-0.263811\pi$
$59$	−2.30798	−	3.99754i	−0.300473	−	0.520435i	−0.976243	+	0.216678i	$0.930478\pi$
$60$	1.24698			0.160984
$61$	−2.75182	−	4.76630i	−0.352335	−	0.610262i	0.634323	−	0.773068i	$-0.281279\pi$
$61$	−2.75182	−	4.76630i	−0.352335	−	0.610262i	−0.986658	+	0.162806i	$0.947946\pi$
$62$	−3.13706	+	5.43355i	−0.398407	+	0.690062i
$63$	0.143104	−	0.247864i	0.0180294	−	0.0312279i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.38404			−0.170364
$67$	1.93631	−	3.35379i	0.236558	−	0.409731i	−0.723166	−	0.690674i	$-0.757314\pi$
$67$	1.93631	−	3.35379i	0.236558	−	0.409731i	0.959724	+	0.280943i	$0.0906473\pi$
$68$	−3.24698	+	5.62393i	−0.393754	+	0.682002i
$69$	−4.21648	−	7.30316i	−0.507605	−	0.879197i
$70$	−0.198062			−0.0236730
$71$	−6.80194	−	11.7813i	−0.807241	−	1.39818i	−0.914767	−	0.403981i	$-0.867626\pi$
$71$	−6.80194	−	11.7813i	−0.807241	−	1.39818i	0.107526	−	0.994202i	$-0.465707\pi$
$72$	0.722521	+	1.25144i	0.0851499	+	0.147484i
$73$	0.591794			0.0692642			0.0346321	−	0.999400i	$-0.488974\pi$
$73$	0.591794			0.0692642			0.0346321	+	0.999400i	$0.488974\pi$
$74$	−1.10992	−	1.92243i	−0.129025	−	0.223478i
$75$	0.623490	−	1.07992i	0.0719944	−	0.124698i
$76$	0.246980	−	0.427781i	0.0283305	−	0.0490699i
$77$	0.219833			0.0250522
$78$		0			0
$79$	2.93362			0.330059			0.165029	−	0.986289i	$-0.447228\pi$
$79$	2.93362			0.330059			0.165029	+	0.986289i	$0.447228\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	1.28836	−	2.23151i	0.143152	−	0.247946i
$82$	−4.48307	−	7.76491i	−0.495073	−	0.857491i
$83$	15.6625			1.71918			0.859590	−	0.510984i	$-0.170719\pi$
$83$	15.6625			1.71918			0.859590	+	0.510984i	$0.170719\pi$
$84$	0.123490	+	0.213891i	0.0134738	+	0.0233374i
$85$	3.24698	+	5.62393i	0.352184	+	0.610001i
$86$	5.65279			0.609556
$87$	−0.222521	−	0.385418i	−0.0238567	−	0.0413211i
$88$	−0.554958	+	0.961216i	−0.0591587	+	0.102466i
$89$	8.54019	−	14.7920i	0.905258	−	1.56795i	0.0846878	−	0.996408i	$-0.473011\pi$
$89$	8.54019	−	14.7920i	0.905258	−	1.56795i	0.820570	−	0.571546i	$-0.193656\pi$
$90$	1.44504			0.152321
$91$		0			0
$92$	−6.76271			−0.705061
$93$	3.91185	−	6.77553i	0.405640	−	0.702590i
$94$	0.716480	−	1.24098i	0.0738993	−	0.127997i
$95$	−0.246980	−	0.427781i	−0.0253396	−	0.0438894i
$96$	−1.24698			−0.127269
$97$	−6.78986	−	11.7604i	−0.689405	−	1.19409i	−0.972030	−	0.234855i	$-0.924539\pi$
$97$	−6.78986	−	11.7604i	−0.689405	−	1.19409i	0.282625	−	0.959230i	$-0.408795\pi$
$98$	3.48039	+	6.02820i	0.351572	+	0.608941i
$99$	−1.60388			−0.161196
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	2.77748	−	4.81073i	0.276369	−	0.478686i	−0.694110	−	0.719869i	$-0.744202\pi$
$101$	2.77748	−	4.81073i	0.276369	−	0.478686i	0.970480	+	0.241183i	$0.0775353\pi$
$102$	4.04892	−	7.01293i	0.400903	−	0.694384i
$103$	−4.39373			−0.432927			−0.216464	−	0.976291i	$-0.569452\pi$
$103$	−4.39373			−0.432927			−0.216464	+	0.976291i	$0.569452\pi$
$104$		0			0
$105$	0.246980			0.0241027
$106$	−4.96077	+	8.59231i	−0.481833	+	0.834559i
$107$	8.98792	−	15.5675i	0.868895	−	1.50497i	0.00576774	−	0.999983i	$-0.498164\pi$
$107$	8.98792	−	15.5675i	0.868895	−	1.50497i	0.863127	−	0.504987i	$-0.168503\pi$
$108$	−2.77144	−	4.80027i	−0.266682	−	0.461906i
$109$	6.73556			0.645150			0.322575	−	0.946544i	$-0.395452\pi$
$109$	6.73556			0.645150			0.322575	+	0.946544i	$0.395452\pi$
$110$	0.554958	+	0.961216i	0.0529132	+	0.0916483i
$111$	1.38404	+	2.39723i	0.131368	+	0.227535i
$112$	0.198062			0.0187151
$113$	−1.13706	−	1.96945i	−0.106966	−	0.185270i	0.807574	−	0.589767i	$-0.200780\pi$
$113$	−1.13706	−	1.96945i	−0.106966	−	0.185270i	−0.914540	+	0.404496i	$0.867447\pi$
$114$	−0.307979	+	0.533434i	−0.0288448	+	0.0499607i
$115$	−3.38135	+	5.85668i	−0.315313	+	0.546138i
$116$	−0.356896			−0.0331369
$117$		0			0
$118$	4.61596			0.424933
$119$	−0.643104	+	1.11389i	−0.0589533	+	0.102110i
$120$	−0.623490	+	1.07992i	−0.0569166	+	0.0985824i
$121$	4.88404	+	8.45941i	0.444004	+	0.769037i
$122$	5.50365			0.498277
$123$	5.59030	+	9.68269i	0.504061	+	0.873058i
$124$	−3.13706	−	5.43355i	−0.281717	−	0.487947i
$125$	−1.00000			−0.0894427
$126$	0.143104	+	0.247864i	0.0127487	+	0.0220814i
$127$	−6.88889	+	11.9319i	−0.611290	+	1.05879i	0.379733	+	0.925096i	$0.376016\pi$
$127$	−6.88889	+	11.9319i	−0.611290	+	1.05879i	−0.991023	+	0.133689i	$0.957318\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−7.04892			−0.620623
$130$		0			0
$131$	−19.3056			−1.68674			−0.843368	−	0.537336i	$-0.819431\pi$
$131$	−19.3056			−1.68674			−0.843368	+	0.537336i	$0.819431\pi$
$132$	0.692021	−	1.19862i	0.0602327	−	0.104326i
$133$	0.0489173	−	0.0847273i	0.00424167	−	0.00734679i
$134$	1.93631	+	3.35379i	0.167272	+	0.289723i
$135$	−5.54288			−0.477055
$136$	−3.24698	−	5.62393i	−0.278426	−	0.482248i
$137$	−9.76809	−	16.9188i	−0.834544	−	1.44547i	−0.894401	−	0.447265i	$-0.852398\pi$
$137$	−9.76809	−	16.9188i	−0.834544	−	1.44547i	0.0598573	−	0.998207i	$-0.480935\pi$
$138$	8.43296			0.717861
$139$	9.20775	+	15.9483i	0.780991	+	1.35272i	0.931365	+	0.364087i	$0.118619\pi$
$139$	9.20775	+	15.9483i	0.780991	+	1.35272i	−0.150374	+	0.988629i	$0.548048\pi$
$140$	0.0990311	−	0.171527i	0.00836966	−	0.0144967i
$141$	−0.893436	+	1.54748i	−0.0752409	+	0.130321i
$142$	13.6039			1.14161
$143$		0			0
$144$	−1.44504			−0.120420
$145$	−0.178448	+	0.309081i	−0.0148193	+	0.0256678i
$146$	−0.295897	+	0.512509i	−0.0244886	+	0.0424155i
$147$	−4.33997	−	7.51705i	−0.357955	−	0.619996i
$148$	2.21983			0.182469
$149$	−8.63318	−	14.9531i	−0.707258	−	1.22501i	−0.965871	−	0.259025i	$-0.916599\pi$
$149$	−8.63318	−	14.9531i	−0.707258	−	1.22501i	0.258613	−	0.965981i	$-0.416735\pi$
$150$	0.623490	+	1.07992i	0.0509077	+	0.0881748i
$151$	3.97584			0.323549			0.161775	−	0.986828i	$-0.448278\pi$
$151$	3.97584			0.323549			0.161775	+	0.986828i	$0.448278\pi$
$152$	0.246980	+	0.427781i	0.0200327	+	0.0346976i
$153$	4.69202	−	8.12682i	0.379327	−	0.657014i
$154$	−0.109916	+	0.190381i	−0.00885730	+	0.0153413i
$155$	−6.27413			−0.503950
$156$		0			0
$157$	17.4034			1.38894			0.694472	−	0.719520i	$-0.255638\pi$
$157$	17.4034			1.38894			0.694472	+	0.719520i	$0.255638\pi$
$158$	−1.46681	+	2.54059i	−0.116693	+	0.202119i
$159$	6.18598	−	10.7144i	0.490580	−	0.849710i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−1.33944			−0.105562
$162$	1.28836	+	2.23151i	0.101223	+	0.175324i
$163$	4.58426	+	7.94017i	0.359067	+	0.621922i	0.987805	−	0.155695i	$-0.0497616\pi$
$163$	4.58426	+	7.94017i	0.359067	+	0.621922i	−0.628738	+	0.777617i	$0.716428\pi$
$164$	8.96615			0.700139
$165$	−0.692021	−	1.19862i	−0.0538738	−	0.0933122i
$166$	−7.83124	+	13.5641i	−0.607822	+	1.05278i
$167$	−3.68114	+	6.37592i	−0.284855	+	0.493383i	−0.972574	−	0.232594i	$-0.925279\pi$
$167$	−3.68114	+	6.37592i	−0.284855	+	0.493383i	0.687719	+	0.725977i	$0.258612\pi$
$168$	−0.246980			−0.0190549
$169$		0			0
$170$	−6.49396			−0.498064
$171$	−0.356896	+	0.618162i	−0.0272925	+	0.0472720i
$172$	−2.82640	+	4.89546i	−0.215511	+	0.373275i
$173$	4.29590	+	7.44071i	0.326611	+	0.565707i	0.981837	−	0.189726i	$-0.0607600\pi$
$173$	4.29590	+	7.44071i	0.326611	+	0.565707i	−0.655226	+	0.755433i	$0.727427\pi$
$174$	0.445042			0.0337385
$175$	−0.0990311	−	0.171527i	−0.00748605	−	0.0129662i
$176$	−0.554958	−	0.961216i	−0.0418315	−	0.0724544i
$177$	−5.75600			−0.432648
$178$	8.54019	+	14.7920i	0.640114	+	1.10871i
$179$	0.329749	−	0.571142i	0.0246466	−	0.0426891i	−0.853439	−	0.521193i	$-0.825487\pi$
$179$	0.329749	−	0.571142i	0.0246466	−	0.0426891i	0.878086	+	0.478504i	$0.158821\pi$
$180$	−0.722521	+	1.25144i	−0.0538535	+	0.0932771i
$181$	−20.4101			−1.51707			−0.758536	−	0.651631i	$-0.774085\pi$
$181$	−20.4101			−1.51707			−0.758536	+	0.651631i	$0.774085\pi$
$182$		0			0
$183$	−6.86294			−0.507323
$184$	3.38135	−	5.85668i	0.249277	−	0.431760i
$185$	1.10992	−	1.92243i	0.0816027	−	0.141340i
$186$	3.91185	+	6.77553i	0.286831	+	0.496806i
$187$	7.20775			0.527083
$188$	0.716480	+	1.24098i	0.0522547	+	0.0905078i
$189$	−0.548917	−	0.950753i	−0.0399279	−	0.0691571i
$190$	0.493959			0.0358356
$191$	−6.36658	−	11.0272i	−0.460670	−	0.797904i	0.538325	−	0.842738i	$-0.319057\pi$
$191$	−6.36658	−	11.0272i	−0.460670	−	0.797904i	−0.998994	+	0.0448339i	$0.985724\pi$
$192$	0.623490	−	1.07992i	0.0449965	−	0.0779362i
$193$	−4.34481	+	7.52544i	−0.312747	+	0.541693i	−0.978956	−	0.204072i	$-0.934582\pi$
$193$	−4.34481	+	7.52544i	−0.312747	+	0.541693i	0.666209	+	0.745765i	$0.267916\pi$
$194$	13.5797			0.974967
$195$		0			0
$196$	−6.96077			−0.497198
$197$	−2.64310	+	4.57799i	−0.188313	+	0.326168i	−0.944688	−	0.327970i	$-0.893635\pi$
$197$	−2.64310	+	4.57799i	−0.188313	+	0.326168i	0.756375	+	0.654139i	$0.226969\pi$
$198$	0.801938	−	1.38900i	0.0569912	−	0.0987117i
$199$	5.47219	+	9.47811i	0.387913	+	0.671885i	0.992169	−	0.124905i	$-0.0398627\pi$
$199$	5.47219	+	9.47811i	0.387913	+	0.671885i	−0.604255	+	0.796791i	$0.706529\pi$
$200$	1.00000			0.0707107
$201$	−2.41454	−	4.18211i	−0.170309	−	0.294983i
$202$	2.77748	+	4.81073i	0.195423	+	0.338482i
$203$	−0.0706876			−0.00496130
$204$	4.04892	+	7.01293i	0.283481	+	0.491003i
$205$	4.48307	−	7.76491i	0.313111	−	0.542325i
$206$	2.19687	−	3.80508i	0.153063	−	0.265113i
$207$	9.77240			0.679229
$208$		0			0
$209$	−0.548253			−0.0379235
$210$	−0.123490	+	0.213891i	−0.00852161	+	0.0147599i
$211$	−1.65279	+	2.86272i	−0.113783	+	0.197078i	−0.917293	−	0.398214i	$-0.869630\pi$
$211$	−1.65279	+	2.86272i	−0.113783	+	0.197078i	0.803510	+	0.595292i	$0.202964\pi$
$212$	−4.96077	−	8.59231i	−0.340707	−	0.590122i
$213$	−16.9638			−1.16234
$214$	8.98792	+	15.5675i	0.614401	+	1.06417i
$215$	2.82640	+	4.89546i	0.192759	+	0.333868i
$216$	5.54288			0.377145
$217$	−0.621334	−	1.07618i	−0.0421789	−	0.0730560i
$218$	−3.36778	+	5.83317i	−0.228095	+	0.395072i
$219$	0.368977	−	0.639088i	0.0249332	−	0.0431855i
$220$	−1.10992			−0.0748305
$221$		0			0
$222$	−2.76809			−0.185782
$223$	8.31551	−	14.4029i	0.556848	−	0.964489i	−0.440909	−	0.897552i	$-0.645344\pi$
$223$	8.31551	−	14.4029i	0.556848	−	0.964489i	0.997757	−	0.0669371i	$-0.0213227\pi$
$224$	−0.0990311	+	0.171527i	−0.00661680	+	0.0114606i
$225$	0.722521	+	1.25144i	0.0481681	+	0.0834295i
$226$	2.27413			0.151273
$227$	5.43080	+	9.40643i	0.360455	+	0.624327i	0.988036	−	0.154225i	$-0.0492881\pi$
$227$	5.43080	+	9.40643i	0.360455	+	0.624327i	−0.627581	+	0.778552i	$0.715955\pi$
$228$	−0.307979	−	0.533434i	−0.0203964	−	0.0353276i
$229$	−23.3991			−1.54626			−0.773128	−	0.634250i	$-0.781309\pi$
$229$	−23.3991			−1.54626			−0.773128	+	0.634250i	$0.781309\pi$
$230$	−3.38135	−	5.85668i	−0.222960	−	0.386178i
$231$	0.137063	−	0.237401i	0.00901811	−	0.0156198i
$232$	0.178448	−	0.309081i	0.0117157	−	0.0202922i
$233$	14.3913			0.942808			0.471404	−	0.881917i	$-0.343747\pi$
$233$	14.3913			0.942808			0.471404	+	0.881917i	$0.343747\pi$
$234$		0			0
$235$	1.43296			0.0934760
$236$	−2.30798	+	3.99754i	−0.150237	+	0.260217i
$237$	1.82908	−	3.16807i	0.118812	−	0.205788i
$238$	−0.643104	−	1.11389i	−0.0416862	−	0.0722027i
$239$	3.56033			0.230299			0.115149	−	0.993348i	$-0.463265\pi$
$239$	3.56033			0.230299			0.115149	+	0.993348i	$0.463265\pi$
$240$	−0.623490	−	1.07992i	−0.0402461	−	0.0697083i
$241$	14.5945	+	25.2784i	0.940113	+	1.62832i	0.765252	+	0.643731i	$0.222614\pi$
$241$	14.5945	+	25.2784i	0.940113	+	1.62832i	0.174861	+	0.984593i	$0.444052\pi$
$242$	−9.76809			−0.627916
$243$	6.70775	+	11.6182i	0.430302	+	0.745306i
$244$	−2.75182	+	4.76630i	−0.176167	+	0.305131i
$245$	−3.48039	+	6.02820i	−0.222354	+	0.385128i
$246$	−11.1806			−0.712849
$247$		0			0
$248$	6.27413			0.398407
$249$	9.76540	−	16.9142i	0.618857	−	1.07189i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	14.6799	+	25.4264i	0.926590	+	1.60490i	0.788985	+	0.614413i	$0.210607\pi$
$251$	14.6799	+	25.4264i	0.926590	+	1.60490i	0.137605	+	0.990487i	$0.456060\pi$
$252$	−0.286208			−0.0180294
$253$	3.75302	+	6.50042i	0.235950	+	0.408678i
$254$	−6.88889	−	11.9319i	−0.432247	−	0.748674i
$255$	8.09783			0.507106
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.7681	+	18.6509i	−0.671695	+	1.16341i	0.305729	+	0.952119i	$0.401100\pi$
$257$	−10.7681	+	18.6509i	−0.671695	+	1.16341i	−0.977423	+	0.211291i	$0.932233\pi$
$258$	3.52446	−	6.10454i	0.219423	−	0.380052i
$259$	0.439665			0.0273195
$260$		0			0
$261$	0.515729			0.0319229
$262$	9.65279	−	16.7191i	0.596352	−	1.03291i
$263$	3.28501	−	5.68981i	0.202563	−	0.350849i	−0.746791	−	0.665059i	$-0.768406\pi$
$263$	3.28501	−	5.68981i	0.202563	−	0.350849i	0.949353	+	0.314210i	$0.101740\pi$
$264$	0.692021	+	1.19862i	0.0425910	+	0.0737697i
$265$	−9.92154			−0.609476
$266$	0.0489173	+	0.0847273i	0.00299931	+	0.00519497i
$267$	−10.6494	−	18.4454i	−0.651735	−	1.12884i
$268$	−3.87263			−0.236558
$269$	−3.68449	−	6.38172i	−0.224647	−	0.389100i	0.731566	−	0.681770i	$-0.238790\pi$
$269$	−3.68449	−	6.38172i	−0.224647	−	0.389100i	−0.956214	+	0.292670i	$0.905456\pi$
$270$	2.77144	−	4.80027i	0.168664	−	0.292135i
$271$	−7.78986	+	13.4924i	−0.473200	+	0.819607i	−0.999529	−	0.0306742i	$-0.990235\pi$
$271$	−7.78986	+	13.4924i	−0.473200	+	0.819607i	0.526329	+	0.850281i	$0.323568\pi$
$272$	6.49396			0.393754
$273$		0			0
$274$	19.5362			1.18022
$275$	−0.554958	+	0.961216i	−0.0334652	+	0.0579635i
$276$	−4.21648	+	7.30316i	−0.253802	+	0.439598i
$277$	6.99761	+	12.1202i	0.420445	+	0.728233i	0.995983	−	0.0895425i	$-0.0285405\pi$
$277$	6.99761	+	12.1202i	0.420445	+	0.728233i	−0.575538	+	0.817775i	$0.695207\pi$
$278$	−18.4155			−1.10449
$279$	4.53319	+	7.85171i	0.271395	+	0.470070i
$280$	0.0990311	+	0.171527i	0.00591824	+	0.0102507i
$281$	13.3341			0.795443			0.397722	−	0.917506i	$-0.369801\pi$
$281$	13.3341			0.795443			0.397722	+	0.917506i	$0.369801\pi$
$282$	−0.893436	−	1.54748i	−0.0532033	−	0.0921509i
$283$	10.3644	−	17.9517i	0.616101	−	1.06712i	−0.374089	−	0.927393i	$-0.622045\pi$
$283$	10.3644	−	17.9517i	0.616101	−	1.06712i	0.990190	−	0.139726i	$-0.0446222\pi$
$284$	−6.80194	+	11.7813i	−0.403621	+	0.699092i
$285$	−0.615957			−0.0364861
$286$		0			0
$287$	1.77586			0.104825
$288$	0.722521	−	1.25144i	0.0425750	−	0.0737420i
$289$	−12.5858	+	21.7992i	−0.740338	+	1.28230i
$290$	−0.178448	−	0.309081i	−0.0104788	−	0.0181499i
$291$	−16.9336			−0.992667
$292$	−0.295897	−	0.512509i	−0.0173161	−	0.0299923i
$293$	−8.19567	−	14.1953i	−0.478796	−	0.829299i	0.520908	−	0.853613i	$-0.325593\pi$
$293$	−8.19567	−	14.1953i	−0.478796	−	0.829299i	−0.999704	+	0.0243135i	$0.992260\pi$
$294$	8.67994			0.506224
$295$	2.30798	+	3.99754i	0.134376	+	0.232746i
$296$	−1.10992	+	1.92243i	−0.0645126	+	0.111739i
$297$	−3.07606	+	5.32790i	−0.178491	+	0.309156i
$298$	17.2664			1.00021
$299$		0			0
$300$	−1.24698			−0.0719944
$301$	−0.559802	+	0.969606i	−0.0322665	+	0.0558872i
$302$	−1.98792	+	3.44318i	−0.114392	+	0.198132i
$303$	−3.46346	−	5.99889i	−0.198971	−	0.344627i
$304$	−0.493959			−0.0283305
$305$	2.75182	+	4.76630i	0.157569	+	0.272917i
$306$	4.69202	+	8.12682i	0.268225	+	0.464579i
$307$	−6.94869			−0.396583			−0.198291	−	0.980143i	$-0.563539\pi$
$307$	−6.94869			−0.396583			−0.198291	+	0.980143i	$0.563539\pi$
$308$	−0.109916	−	0.190381i	−0.00626306	−	0.0108479i
$309$	−2.73945	+	4.74486i	−0.155842	+	0.269926i
$310$	3.13706	−	5.43355i	0.178173	−	0.308605i
$311$	−24.3612			−1.38140			−0.690699	−	0.723143i	$-0.742697\pi$
$311$	−24.3612			−1.38140			−0.690699	+	0.723143i	$0.742697\pi$
$312$		0			0
$313$	2.89008			0.163357			0.0816786	−	0.996659i	$-0.473972\pi$
$313$	2.89008			0.163357			0.0816786	+	0.996659i	$0.473972\pi$
$314$	−8.70171	+	15.0718i	−0.491066	+	0.850551i
$315$	−0.143104	+	0.247864i	−0.00806300	+	0.0139655i
$316$	−1.46681	−	2.54059i	−0.0825146	−	0.142920i
$317$	5.01208			0.281507			0.140753	−	0.990045i	$-0.455048\pi$
$317$	5.01208			0.281507			0.140753	+	0.990045i	$0.455048\pi$
$318$	6.18598	+	10.7144i	0.346893	+	0.600836i
$319$	0.198062	+	0.343054i	0.0110894	+	0.0192073i
$320$	−1.00000			−0.0559017
$321$	−11.2078	−	19.4124i	−0.625556	−	1.08349i
$322$	0.669719	−	1.15999i	0.0373220	−	0.0646435i
$323$	1.60388	−	2.77799i	0.0892420	−	0.154572i
$324$	−2.57673			−0.143152
$325$		0			0
$326$	−9.16852			−0.507797
$327$	4.19955	−	7.27384i	0.232236	−	0.402244i
$328$	−4.48307	+	7.76491i	−0.247536	+	0.428746i
$329$	0.141908	+	0.245791i	0.00782362	+	0.0135509i
$330$	1.38404			0.0761891
$331$	12.0097	+	20.8014i	0.660112	+	1.14335i	0.980586	+	0.196090i	$0.0628246\pi$
$331$	12.0097	+	20.8014i	0.660112	+	1.14335i	−0.320474	+	0.947257i	$0.603842\pi$
$332$	−7.83124	−	13.5641i	−0.429795	−	0.744427i
$333$	−3.20775			−0.175784
$334$	−3.68114	−	6.37592i	−0.201423	−	0.348875i
$335$	−1.93631	+	3.35379i	−0.105792	+	0.183237i
$336$	0.123490	−	0.213891i	0.00673692	−	0.0116687i
$337$	28.5133			1.55322			0.776610	−	0.629981i	$-0.216938\pi$
$337$	28.5133			1.55322			0.776610	+	0.629981i	$0.216938\pi$
$338$		0			0
$339$	−2.83579			−0.154019
$340$	3.24698	−	5.62393i	0.176092	−	0.305001i
$341$	−3.48188	+	6.03079i	−0.188554	+	0.326586i
$342$	−0.356896	−	0.618162i	−0.0192987	−	0.0334264i
$343$	−2.76510			−0.149301
$344$	−2.82640	−	4.89546i	−0.152389	−	0.263946i
$345$	4.21648	+	7.30316i	0.227008	+	0.393189i
$346$	−8.59179			−0.461898
$347$	12.5993	+	21.8227i	0.676367	+	1.17150i	0.976067	+	0.217469i	$0.0697801\pi$
$347$	12.5993	+	21.8227i	0.676367	+	1.17150i	−0.299700	+	0.954034i	$0.596887\pi$
$348$	−0.222521	+	0.385418i	−0.0119284	+	0.0206606i
$349$	8.20775	−	14.2162i	0.439351	−	0.760978i	−0.558289	−	0.829647i	$-0.688542\pi$
$349$	8.20775	−	14.2162i	0.439351	−	0.760978i	0.997640	+	0.0686688i	$0.0218752\pi$
$350$	0.198062			0.0105869
$351$		0			0
$352$	1.10992			0.0591587
$353$	0.554958	−	0.961216i	0.0295374	−	0.0511603i	−0.850879	−	0.525362i	$-0.823930\pi$
$353$	0.554958	−	0.961216i	0.0295374	−	0.0511603i	0.880416	+	0.474202i	$0.157263\pi$
$354$	2.87800	−	4.98485i	0.152964	−	0.264942i
$355$	6.80194	+	11.7813i	0.361009	+	0.625287i
$356$	−17.0804			−0.905258
$357$	0.801938	+	1.38900i	0.0424430	+	0.0735135i
$358$	0.329749	+	0.571142i	0.0174278	+	0.0301858i
$359$	−36.7633			−1.94029			−0.970146	−	0.242520i	$-0.922026\pi$
$359$	−36.7633			−1.94029			−0.970146	+	0.242520i	$0.922026\pi$
$360$	−0.722521	−	1.25144i	−0.0380802	−	0.0659568i
$361$	9.37800	−	16.2432i	0.493579	−	0.854904i
$362$	10.2051	−	17.6757i	0.536366	−	0.929013i
$363$	12.1806			0.639316
$364$		0			0
$365$	−0.591794			−0.0309759
$366$	3.43147	−	5.94348i	0.179366	−	0.310671i
$367$	−3.54743	+	6.14432i	−0.185174	+	0.320731i	−0.943635	−	0.330987i	$-0.892618\pi$
$367$	−3.54743	+	6.14432i	−0.185174	+	0.320731i	0.758461	+	0.651718i	$0.225952\pi$
$368$	3.38135	+	5.85668i	0.176265	+	0.305300i
$369$	−12.9565			−0.674486
$370$	1.10992	+	1.92243i	0.0577018	+	0.0999424i
$371$	−0.982542	−	1.70181i	−0.0510110	−	0.0883537i
$372$	−7.82371			−0.405640
$373$	−13.4450	−	23.2875i	−0.696158	−	1.20578i	−0.969789	−	0.243946i	$-0.921558\pi$
$373$	−13.4450	−	23.2875i	−0.696158	−	1.20578i	0.273631	−	0.961835i	$-0.411775\pi$
$374$	−3.60388	+	6.24210i	−0.186352	+	0.322771i
$375$	−0.623490	+	1.07992i	−0.0321969	+	0.0557666i
$376$	−1.43296			−0.0738993
$377$		0			0
$378$	1.09783			0.0564665
$379$	4.23490	−	7.33506i	0.217532	−	0.376777i	−0.736521	−	0.676415i	$-0.763533\pi$
$379$	4.23490	−	7.33506i	0.217532	−	0.376777i	0.954053	+	0.299638i	$0.0968660\pi$
$380$	−0.246980	+	0.427781i	−0.0126698	+	0.0219447i
$381$	8.59030	+	14.8788i	0.440094	+	0.762266i
$382$	12.7332			0.651486
$383$	−2.39828	−	4.15394i	−0.122546	−	0.212257i	0.798225	−	0.602360i	$-0.205773\pi$
$383$	−2.39828	−	4.15394i	−0.122546	−	0.212257i	−0.920771	+	0.390103i	$0.872439\pi$
$384$	0.623490	+	1.07992i	0.0318173	+	0.0551092i
$385$	−0.219833			−0.0112037
$386$	−4.34481	−	7.52544i	−0.221145	−	0.383035i
$387$	4.08426	−	7.07415i	0.207615	−	0.359599i
$388$	−6.78986	+	11.7604i	−0.344703	+	0.597043i
$389$	29.2131			1.48116			0.740582	−	0.671966i	$-0.234550\pi$
$389$	29.2131			1.48116			0.740582	+	0.671966i	$0.234550\pi$
$390$		0			0
$391$	−43.9168			−2.22097
$392$	3.48039	−	6.02820i	0.175786	−	0.304470i
$393$	−12.0368	+	20.8484i	−0.607178	+	1.05166i
$394$	−2.64310	−	4.57799i	−0.133158	−	0.230636i
$395$	−2.93362			−0.147607
$396$	0.801938	+	1.38900i	0.0402989	+	0.0697997i
$397$	−11.3056	−	19.5818i	−0.567411	−	0.982785i	−0.996821	−	0.0796751i	$-0.974612\pi$
$397$	−11.3056	−	19.5818i	−0.567411	−	0.982785i	0.429410	−	0.903110i	$-0.358722\pi$
$398$	−10.9444			−0.548592
$399$	−0.0609989	−	0.105653i	−0.00305377	−	0.00528928i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	5.29470	−	9.17069i	0.264405	−	0.457962i	−0.703003	−	0.711187i	$-0.748158\pi$
$401$	5.29470	−	9.17069i	0.264405	−	0.457962i	0.967407	+	0.253225i	$0.0814912\pi$
$402$	4.82908			0.240853
$403$		0			0
$404$	−5.55496			−0.276369
$405$	−1.28836	+	2.23151i	−0.0640193	+	0.110885i
$406$	0.0353438	−	0.0612173i	0.00175408	−	0.00303816i
$407$	−1.23191	−	2.13374i	−0.0610637	−	0.105765i
$408$	−8.09783			−0.400903
$409$	5.85636	+	10.1435i	0.289579	+	0.501565i	0.973709	−	0.227795i	$-0.0731515\pi$
$409$	5.85636	+	10.1435i	0.289579	+	0.501565i	−0.684131	+	0.729359i	$0.739818\pi$
$410$	4.48307	+	7.76491i	0.221403	+	0.383482i
$411$	−24.3612			−1.20165
$412$	2.19687	+	3.80508i	0.108232	+	0.187463i
$413$	−0.457123	+	0.791761i	−0.0224936	+	0.0389600i
$414$	−4.88620	+	8.46314i	−0.240144	+	0.415941i
$415$	−15.6625			−0.768841
$416$		0			0
$417$	22.9638			1.12454
$418$	0.274127	−	0.474801i	0.0134080	−	0.0232233i
$419$	−10.6625	+	18.4680i	−0.520896	+	0.902219i	0.478808	+	0.877919i	$0.341069\pi$
$419$	−10.6625	+	18.4680i	−0.520896	+	0.902219i	−0.999705	+	0.0242995i	$0.992264\pi$
$420$	−0.123490	−	0.213891i	−0.00602569	−	0.0104368i
$421$	−22.1457			−1.07931			−0.539657	−	0.841885i	$-0.681446\pi$
$421$	−22.1457			−1.07931			−0.539657	+	0.841885i	$0.681446\pi$
$422$	−1.65279	−	2.86272i	−0.0804567	−	0.139355i
$423$	−1.03534	−	1.79327i	−0.0503401	−	0.0871917i
$424$	9.92154			0.481833
$425$	−3.24698	−	5.62393i	−0.157502	−	0.272801i
$426$	8.48188	−	14.6910i	0.410948	−	0.711783i
$427$	−0.545032	+	0.944024i	−0.0263760	+	0.0456845i
$428$	−17.9758			−0.868895
$429$		0			0
$430$	−5.65279			−0.272602
$431$	−18.4034	+	31.8757i	−0.886462	+	1.53540i	−0.0424323	+	0.999099i	$0.513511\pi$
$431$	−18.4034	+	31.8757i	−0.886462	+	1.53540i	−0.844029	+	0.536297i	$0.819823\pi$
$432$	−2.77144	+	4.80027i	−0.133341	+	0.230953i
$433$	−1.04354	−	1.80747i	−0.0501494	−	0.0868612i	0.839861	−	0.542801i	$-0.182636\pi$
$433$	−1.04354	−	1.80747i	−0.0501494	−	0.0868612i	−0.890010	+	0.455940i	$0.849303\pi$
$434$	1.24267			0.0596500
$435$	0.222521	+	0.385418i	0.0106691	+	0.0184794i
$436$	−3.36778	−	5.83317i	−0.161287	−	0.279358i
$437$	3.34050			0.159798
$438$	0.368977	+	0.639088i	0.0176304	+	0.0305368i
$439$	−4.97823	+	8.62255i	−0.237598	+	0.411532i	−0.960025	−	0.279916i	$-0.909693\pi$
$439$	−4.97823	+	8.62255i	−0.237598	+	0.411532i	0.722427	+	0.691448i	$0.243027\pi$
$440$	0.554958	−	0.961216i	0.0264566	−	0.0458242i
$441$	10.0586			0.478981
$442$		0			0
$443$	−15.3884			−0.731123			−0.365561	−	0.930787i	$-0.619123\pi$
$443$	−15.3884			−0.731123			−0.365561	+	0.930787i	$0.619123\pi$
$444$	1.38404	−	2.39723i	0.0656838	−	0.113768i
$445$	−8.54019	+	14.7920i	−0.404844	+	0.701210i
$446$	8.31551	+	14.4029i	0.393751	+	0.681997i
$447$	−21.5308			−1.01837
$448$	−0.0990311	−	0.171527i	−0.00467878	−	0.00810389i
$449$	−4.09030	−	7.08461i	−0.193033	−	0.334343i	0.753221	−	0.657768i	$-0.228499\pi$
$449$	−4.09030	−	7.08461i	−0.193033	−	0.334343i	−0.946254	+	0.323424i	$0.895166\pi$
$450$	−1.44504			−0.0681199
$451$	−4.97584	−	8.61840i	−0.234303	−	0.405825i
$452$	−1.13706	+	1.96945i	−0.0534830	+	0.0926352i
$453$	2.47889	−	4.29357i	0.116469	−	0.201730i
$454$	−10.8616			−0.509761
$455$		0			0
$456$	0.615957			0.0288448
$457$	−8.03684	+	13.9202i	−0.375947	+	0.651160i	−0.990468	−	0.137741i	$-0.956016\pi$
$457$	−8.03684	+	13.9202i	−0.375947	+	0.651160i	0.614521	+	0.788900i	$0.289349\pi$
$458$	11.6996	−	20.2642i	0.546684	−	0.946885i
$459$	−17.9976	−	31.1728i	−0.840056	−	1.45502i
$460$	6.76271			0.315313
$461$	−13.7654	−	23.8424i	−0.641118	−	1.11045i	−0.985183	−	0.171504i	$-0.945137\pi$
$461$	−13.7654	−	23.8424i	−0.641118	−	1.11045i	0.344065	−	0.938946i	$-0.388196\pi$
$462$	0.137063	+	0.237401i	0.00637676	+	0.0110449i
$463$	−10.6595			−0.495389			−0.247694	−	0.968838i	$-0.579673\pi$
$463$	−10.6595			−0.495389			−0.247694	+	0.968838i	$0.579673\pi$
$464$	0.178448	+	0.309081i	0.00828424	+	0.0143487i
$465$	−3.91185	+	6.77553i	−0.181408	+	0.314208i
$466$	−7.19567	+	12.4633i	−0.333333	+	0.577350i
$467$	−10.7976			−0.499655			−0.249827	−	0.968290i	$-0.580374\pi$
$467$	−10.7976			−0.499655			−0.249827	+	0.968290i	$0.580374\pi$
$468$		0			0
$469$	−0.767021			−0.0354177
$470$	−0.716480	+	1.24098i	−0.0330488	+	0.0572421i
$471$	10.8509	−	18.7942i	0.499981	−	0.865993i
$472$	−2.30798	−	3.99754i	−0.106233	−	0.184002i
$473$	6.27413			0.288485
$474$	1.82908	+	3.16807i	0.0840126	+	0.145514i
$475$	0.246980	+	0.427781i	0.0113322	+	0.0196279i
$476$	1.28621			0.0589533
$477$	7.16852	+	12.4162i	0.328224	+	0.568501i
$478$	−1.78017	+	3.08334i	−0.0814230	+	0.141029i
$479$	−4.54288	+	7.86849i	−0.207569	+	0.359521i	−0.950948	−	0.309350i	$-0.899889\pi$
$479$	−4.54288	+	7.86849i	−0.207569	+	0.359521i	0.743379	+	0.668870i	$0.233222\pi$
$480$	1.24698			0.0569166
$481$		0			0
$482$	−29.1890			−1.32952
$483$	−0.835126	+	1.44648i	−0.0379995	+	0.0658171i
$484$	4.88404	−	8.45941i	0.222002	−	0.384519i
$485$	6.78986	+	11.7604i	0.308311	+	0.534011i
$486$	−13.4155			−0.608540
$487$	20.4236	+	35.3747i	0.925480	+	1.60298i	0.790787	+	0.612091i	$0.209672\pi$
$487$	20.4236	+	35.3747i	0.925480	+	1.60298i	0.134693	+	0.990887i	$0.456995\pi$
$488$	−2.75182	−	4.76630i	−0.124569	−	0.215760i
$489$	11.4330			0.517016
$490$	−3.48039	−	6.02820i	−0.157228	−	0.272327i
$491$	−14.5472	+	25.1965i	−0.656505	+	1.13710i	0.325009	+	0.945711i	$0.394633\pi$
$491$	−14.5472	+	25.1965i	−0.656505	+	1.13710i	−0.981514	+	0.191390i	$0.938701\pi$
$492$	5.59030	−	9.68269i	0.252030	−	0.436529i
$493$	−2.31767			−0.104382
$494$		0			0
$495$	1.60388			0.0720888
$496$	−3.13706	+	5.43355i	−0.140858	+	0.243974i
$497$	−1.34721	+	2.33343i	−0.0604305	+	0.104669i
$498$	9.76540	+	16.9142i	0.437598	+	0.757942i
$499$	16.2150			0.725885			0.362943	−	0.931812i	$-0.381772\pi$
$499$	16.2150			0.725885			0.362943	+	0.931812i	$0.381772\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	4.59030	+	7.95064i	0.205080	+	0.355208i
$502$	−29.3599			−1.31040
$503$	0.747512	+	1.29473i	0.0333299	+	0.0577291i	0.882209	−	0.470858i	$-0.156055\pi$
$503$	0.747512	+	1.29473i	0.0333299	+	0.0577291i	−0.848879	+	0.528587i	$0.822722\pi$
$504$	0.143104	−	0.247864i	0.00637436	−	0.0110407i
$505$	−2.77748	+	4.81073i	−0.123596	+	0.214075i
$506$	−7.50604			−0.333684
$507$		0			0
$508$	13.7778			0.611290
$509$	2.31551	−	4.01058i	0.102633	−	0.177766i	−0.810136	−	0.586243i	$-0.800607\pi$
$509$	2.31551	−	4.01058i	0.102633	−	0.177766i	0.912769	+	0.408477i	$0.133940\pi$
$510$	−4.04892	+	7.01293i	−0.179289	+	0.310538i
$511$	−0.0586060	−	0.101509i	−0.00259258	−	0.00449048i
$512$	1.00000			0.0441942
$513$	1.36898	+	2.37114i	0.0604418	+	0.104688i
$514$	−10.7681	−	18.6509i	−0.474960	−	0.822655i
$515$	4.39373			0.193611
$516$	3.52446	+	6.10454i	0.155156	+	0.268737i
$517$	0.795233	−	1.37738i	0.0349743	−	0.0605773i
$518$	−0.219833	+	0.380761i	−0.00965889	+	0.0167297i
$519$	10.7138			0.470283
$520$		0			0
$521$	−9.23729			−0.404693			−0.202347	−	0.979314i	$-0.564857\pi$
$521$	−9.23729			−0.404693			−0.202347	+	0.979314i	$0.564857\pi$
$522$	−0.257865	+	0.446635i	−0.0112864	+	0.0195487i
$523$	1.44235	−	2.49823i	0.0630697	−	0.109240i	−0.832766	−	0.553625i	$-0.813244\pi$
$523$	1.44235	−	2.49823i	0.0630697	−	0.109240i	0.895836	+	0.444385i	$0.146578\pi$
$524$	9.65279	+	16.7191i	0.421684	+	0.730378i
$525$	−0.246980			−0.0107791
$526$	3.28501	+	5.68981i	0.143233	+	0.248087i
$527$	−20.3720	−	35.2853i	−0.887417	−	1.53705i
$528$	−1.38404			−0.0602327
$529$	−11.3671	−	19.6884i	−0.494222	−	0.856018i
$530$	4.96077	−	8.59231i	0.215482	−	0.373226i
$531$	3.33513	−	5.77661i	0.144732	−	0.250683i
$532$	−0.0978347			−0.00424167
$533$		0			0
$534$	21.2989			0.921693
$535$	−8.98792	+	15.5675i	−0.388582	+	0.673043i
$536$	1.93631	−	3.35379i	0.0836360	−	0.144862i
$537$	−0.411190	−	0.712202i	−0.0177442	−	0.0307338i
$538$	7.36898			0.317699
$539$	3.86294	+	6.69080i	0.166388	+	0.288193i
$540$	2.77144	+	4.80027i	0.119264	+	0.206571i
$541$	28.2301			1.21371			0.606854	−	0.794814i	$-0.292431\pi$
$541$	28.2301			1.21371			0.606854	+	0.794814i	$0.292431\pi$
$542$	−7.78986	−	13.4924i	−0.334603	−	0.579549i
$543$	−12.7255	+	22.0412i	−0.546104	+	0.945879i
$544$	−3.24698	+	5.62393i	−0.139213	+	0.241124i
$545$	−6.73556			−0.288520
$546$		0			0
$547$	37.8756			1.61944			0.809722	−	0.586814i	$-0.199618\pi$
$547$	37.8756			1.61944			0.809722	+	0.586814i	$0.199618\pi$
$548$	−9.76809	+	16.9188i	−0.417272	+	0.722736i
$549$	3.97650	−	6.88750i	0.169713	−	0.293951i
$550$	−0.554958	−	0.961216i	−0.0236635	−	0.0409864i
$551$	0.176292			0.00751029
$552$	−4.21648	−	7.30316i	−0.179465	−	0.310843i
$553$	−0.290520	−	0.503196i	−0.0123542	−	0.0213981i
$554$	−13.9952			−0.594600
$555$	−1.38404	−	2.39723i	−0.0587494	−	0.101757i
$556$	9.20775	−	15.9483i	0.390496	−	0.676358i
$557$	20.6015	−	35.6828i	0.872913	−	1.51193i	0.0139432	−	0.999903i	$-0.495562\pi$
$557$	20.6015	−	35.6828i	0.872913	−	1.51193i	0.858970	−	0.512027i	$-0.171105\pi$
$558$	−9.06638			−0.383810
$559$		0			0
$560$	−0.198062			−0.00836966
$561$	4.49396	−	7.78377i	0.189735	−	0.328631i
$562$	−6.66703	+	11.5476i	−0.281232	+	0.487108i
$563$	−4.00418	−	6.93544i	−0.168756	−	0.292294i	0.769227	−	0.638976i	$-0.220642\pi$
$563$	−4.00418	−	6.93544i	−0.168756	−	0.292294i	−0.937983	+	0.346682i	$0.887308\pi$
$564$	1.78687			0.0752409
$565$	1.13706	+	1.96945i	0.0478366	+	0.0828554i
$566$	10.3644	+	17.9517i	0.435649	+	0.754567i
$567$	−0.510353			−0.0214328
$568$	−6.80194	−	11.7813i	−0.285403	−	0.494332i
$569$	−21.5688	+	37.3583i	−0.904212	+	1.56614i	−0.0822411	+	0.996612i	$0.526208\pi$
$569$	−21.5688	+	37.3583i	−0.904212	+	1.56614i	−0.821971	+	0.569529i	$0.807126\pi$
$570$	0.307979	−	0.533434i	0.0128998	−	0.0223431i
$571$	−8.98792			−0.376133			−0.188066	−	0.982156i	$-0.560222\pi$
$571$	−8.98792			−0.376133			−0.188066	+	0.982156i	$0.560222\pi$
$572$		0			0
$573$	−15.8780			−0.663313
$574$	−0.887928	+	1.53794i	−0.0370614	+	0.0641922i
$575$	3.38135	−	5.85668i	0.141012	−	0.244240i
$576$	0.722521	+	1.25144i	0.0301050	+	0.0521435i
$577$	1.03624			0.0431394			0.0215697	−	0.999767i	$-0.493134\pi$
$577$	1.03624			0.0431394			0.0215697	+	0.999767i	$0.493134\pi$
$578$	−12.5858	−	21.7992i	−0.523498	−	0.906726i
$579$	5.41789	+	9.38407i	0.225160	+	0.389989i
$580$	0.356896			0.0148193
$581$	−1.55107	−	2.68654i	−0.0643494	−	0.111456i
$582$	8.46681	−	14.6649i	0.350961	−	0.607882i
$583$	−5.50604	+	9.53674i	−0.228037	+	0.394972i
$584$	0.591794			0.0244886
$585$		0			0
$586$	16.3913			0.677120
$587$	−1.85205	+	3.20785i	−0.0764423	+	0.132402i	−0.901713	−	0.432336i	$-0.857689\pi$
$587$	−1.85205	+	3.20785i	−0.0764423	+	0.132402i	0.825270	+	0.564738i	$0.191023\pi$
$588$	−4.33997	+	7.51705i	−0.178977	+	0.309998i
$589$	1.54958	+	2.68395i	0.0638494	+	0.110590i
$590$	−4.61596			−0.190036
$591$	3.29590	+	5.70866i	0.135575	+	0.234823i
$592$	−1.10992	−	1.92243i	−0.0456173	−	0.0790114i
$593$	−12.2064			−0.501258			−0.250629	−	0.968083i	$-0.580637\pi$
$593$	−12.2064			−0.501258			−0.250629	+	0.968083i	$0.580637\pi$
$594$	−3.07606	−	5.32790i	−0.126212	−	0.218606i
$595$	0.643104	−	1.11389i	0.0263647	−	0.0456650i
$596$	−8.63318	+	14.9531i	−0.353629	+	0.612503i
$597$	13.6474			0.558552
$598$		0			0
$599$	−31.5013			−1.28711			−0.643553	−	0.765401i	$-0.722540\pi$
$599$	−31.5013			−1.28711			−0.643553	+	0.765401i	$0.722540\pi$
$600$	0.623490	−	1.07992i	0.0254539	−	0.0440874i
$601$	−9.84535	+	17.0526i	−0.401600	+	0.695592i	−0.993919	−	0.110112i	$-0.964879\pi$
$601$	−9.84535	+	17.0526i	−0.401600	+	0.695592i	0.592319	+	0.805703i	$0.298212\pi$
$602$	−0.559802	−	0.969606i	−0.0228158	−	0.0395182i
$603$	5.59611			0.227891
$604$	−1.98792	−	3.44318i	−0.0808873	−	0.140101i
$605$	−4.88404	−	8.45941i	−0.198565	−	0.343924i
$606$	6.92692			0.281387
$607$	15.5281	+	26.8955i	0.630266	+	1.09165i	0.987497	+	0.157637i	$0.0503877\pi$
$607$	15.5281	+	26.8955i	0.630266	+	1.09165i	−0.357231	+	0.934016i	$0.616279\pi$
$608$	0.246980	−	0.427781i	0.0100163	−	0.0173488i
$609$	−0.0440730	+	0.0763367i	−0.00178593	+	0.00309332i
$610$	−5.50365			−0.222836
$611$		0			0
$612$	−9.38404			−0.379327
$613$	9.18598	−	15.9106i	0.371018	−	0.642622i	−0.618704	−	0.785624i	$-0.712342\pi$
$613$	9.18598	−	15.9106i	0.371018	−	0.642622i	0.989722	+	0.143002i	$0.0456754\pi$
$614$	3.47434	−	6.01774i	0.140213	−	0.242856i
$615$	−5.59030	−	9.68269i	−0.225423	−	0.390444i
$616$	0.219833			0.00885730
$617$	−4.63773	−	8.03278i	−0.186708	−	0.323388i	0.757443	−	0.652901i	$-0.226448\pi$
$617$	−4.63773	−	8.03278i	−0.186708	−	0.323388i	−0.944151	+	0.329514i	$0.893115\pi$
$618$	−2.73945	−	4.74486i	−0.110197	−	0.190866i
$619$	14.9095			0.599262			0.299631	−	0.954055i	$-0.403136\pi$
$619$	14.9095			0.599262			0.299631	+	0.954055i	$0.403136\pi$
$620$	3.13706	+	5.43355i	0.125987	+	0.218217i
$621$	18.7424	−	32.4628i	0.752108	−	1.30269i
$622$	12.1806	−	21.0974i	0.488398	−	0.845930i
$623$	−3.38298			−0.135536
$624$		0			0
$625$	1.00000			0.0400000
$626$	−1.44504	+	2.50289i	−0.0577555	+	0.100035i
$627$	−0.341830	+	0.592068i	−0.0136514	+	0.0236449i
$628$	−8.70171	−	15.0718i	−0.347236	−	0.601430i
$629$	14.4155			0.574784
$630$	−0.143104	−	0.247864i	−0.00570141	−	0.00987512i
$631$	15.0411	+	26.0520i	0.598779	+	1.03712i	0.993002	+	0.118100i	$0.0376804\pi$
$631$	15.0411	+	26.0520i	0.598779	+	1.03712i	−0.394223	+	0.919015i	$0.628986\pi$
$632$	2.93362			0.116693
$633$	2.06100	+	3.56975i	0.0819174	+	0.141885i
$634$	−2.50604	+	4.34059i	−0.0995276	+	0.172387i
$635$	6.88889	−	11.9319i	0.273377	−	0.473503i
$636$	−12.3720			−0.490580
$637$		0			0
$638$	−0.396125			−0.0156827
$639$	9.82908	−	17.0245i	0.388833	−	0.673478i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−6.08934	−	10.5471i	−0.240515	−	0.416583i	0.720346	−	0.693614i	$-0.243983\pi$
$641$	−6.08934	−	10.5471i	−0.240515	−	0.416583i	−0.960861	+	0.277031i	$0.910650\pi$
$642$	22.4155			0.884669
$643$	−1.68233	−	2.91389i	−0.0663447	−	0.114912i	0.830945	−	0.556355i	$-0.187800\pi$
$643$	−1.68233	−	2.91389i	−0.0663447	−	0.114912i	−0.897290	+	0.441442i	$0.854467\pi$
$644$	0.669719	+	1.15999i	0.0263906	+	0.0457099i
$645$	7.04892			0.277551
$646$	1.60388	+	2.77799i	0.0631036	+	0.109299i
$647$	−14.1957	+	24.5876i	−0.558089	+	0.966639i	0.439567	+	0.898210i	$0.355132\pi$
$647$	−14.1957	+	24.5876i	−0.558089	+	0.966639i	−0.997656	+	0.0684291i	$0.978201\pi$
$648$	1.28836	−	2.23151i	0.0506117	−	0.0876621i
$649$	5.12333			0.201108
$650$		0			0
$651$	−1.54958			−0.0607329
$652$	4.58426	−	7.94017i	0.179534	−	0.310961i
$653$	12.8412	−	22.2416i	0.502514	−	0.870379i	−0.497482	−	0.867474i	$-0.665742\pi$
$653$	12.8412	−	22.2416i	0.502514	−	0.870379i	0.999996	−	0.00290498i	$-0.000924684\pi$
$654$	4.19955	+	7.27384i	0.164216	+	0.284430i
$655$	19.3056			0.754332
$656$	−4.48307	−	7.76491i	−0.175035	−	0.303169i
$657$	0.427583	+	0.740596i	0.0166816	+	0.0288934i
$658$	−0.283815			−0.0110643
$659$	2.63102	+	4.55706i	0.102490	+	0.177518i	0.912710	−	0.408608i	$-0.133986\pi$
$659$	2.63102	+	4.55706i	0.102490	+	0.177518i	−0.810220	+	0.586126i	$0.800652\pi$
$660$	−0.692021	+	1.19862i	−0.0269369	+	0.0466561i
$661$	−16.4738	+	28.5335i	−0.640757	+	1.10982i	0.344507	+	0.938784i	$0.388046\pi$
$661$	−16.4738	+	28.5335i	−0.640757	+	1.10982i	−0.985264	+	0.171040i	$0.945287\pi$
$662$	−24.0194			−0.933540
$663$		0			0
$664$	15.6625			0.607822
$665$	−0.0489173	+	0.0847273i	−0.00189693	+	0.00328558i
$666$	1.60388	−	2.77799i	0.0621489	−	0.107645i
$667$	−1.20679	−	2.09022i	−0.0467272	−	0.0809338i
$668$	7.36227			0.284855
$669$	−10.3693	−	17.9601i	−0.400899	−	0.694378i
$670$	−1.93631	−	3.35379i	−0.0748063	−	0.129568i
$671$	6.10859			0.235819
$672$	0.123490	+	0.213891i	0.00476372	+	0.00825101i
$673$	−10.0828	+	17.4639i	−0.388662	+	0.673183i	−0.992270	−	0.124099i	$-0.960396\pi$
$673$	−10.0828	+	17.4639i	−0.388662	+	0.673183i	0.603608	+	0.797281i	$0.293729\pi$
$674$	−14.2567	+	24.6933i	−0.549146	+	0.951149i
$675$	5.54288			0.213345
$676$		0			0
$677$	46.4590			1.78557			0.892783	−	0.450487i	$-0.148750\pi$
$677$	46.4590			1.78557			0.892783	+	0.450487i	$0.148750\pi$
$678$	1.41789	−	2.45587i	0.0544539	−	0.0943170i
$679$	−1.34481	+	2.32929i	−0.0516092	+	0.0893898i
$680$	3.24698	+	5.62393i	0.124516	+	0.215668i
$681$	13.5442			0.519015
$682$	−3.48188	−	6.03079i	−0.133328	−	0.230931i
$683$	−13.5456	−	23.4616i	−0.518307	−	0.897733i	−0.999774	−	0.0212693i	$-0.993229\pi$
$683$	−13.5456	−	23.4616i	−0.518307	−	0.897733i	0.481467	−	0.876464i	$-0.340104\pi$
$684$	0.713792			0.0272925
$685$	9.76809	+	16.9188i	0.373219	+	0.646435i
$686$	1.38255	−	2.39465i	0.0527860	−	0.0914281i
$687$	−14.5891	+	25.2691i	−0.556609	+	0.964075i
$688$	5.65279			0.215511
$689$		0			0
$690$	−8.43296			−0.321037
$691$	−1.73556	+	3.00608i	−0.0660239	+	0.114357i	−0.897148	−	0.441731i	$-0.854365\pi$
$691$	−1.73556	+	3.00608i	−0.0660239	+	0.114357i	0.831124	+	0.556087i	$0.187698\pi$
$692$	4.29590	−	7.44071i	0.163305	−	0.282853i
$693$	0.158834	+	0.275108i	0.00603359	+	0.0104505i
$694$	−25.1987			−0.956528
$695$	−9.20775	−	15.9483i	−0.349270	−	0.604953i
$696$	−0.222521	−	0.385418i	−0.00843463	−	0.0146092i
$697$	58.2258			2.20546
$698$	8.20775	+	14.2162i	0.310668	+	0.538093i
$699$	8.97285	−	15.5414i	0.339384	−	0.587831i
$700$	−0.0990311	+	0.171527i	−0.00374302	+	0.00648311i
$701$	8.07606			0.305029			0.152514	−	0.988301i	$-0.451263\pi$
$701$	8.07606			0.305029			0.152514	+	0.988301i	$0.451263\pi$
$702$		0			0
$703$	−1.09651			−0.0413555
$704$	−0.554958	+	0.961216i	−0.0209158	+	0.0362272i
$705$	0.893436	−	1.54748i	0.0336488	−	0.0582813i
$706$	0.554958	+	0.961216i	0.0208861	+	0.0361758i
$707$	−1.10023			−0.0413783
$708$	2.87800	+	4.98485i	0.108162	+	0.187342i
$709$	10.2579	+	17.7671i	0.385242	+	0.667259i	0.991803	−	0.127778i	$-0.0407846\pi$
$709$	10.2579	+	17.7671i	0.385242	+	0.667259i	−0.606561	+	0.795037i	$0.707451\pi$
$710$	−13.6039			−0.510544
$711$	2.11960	+	3.67126i	0.0794914	+	0.137683i
$712$	8.54019	−	14.7920i	0.320057	−	0.554355i
$713$	21.2150	−	36.7455i	0.794510	−	1.37613i
$714$	−1.60388			−0.0600235
$715$		0			0
$716$	−0.659498			−0.0246466
$717$	2.21983	−	3.84486i	0.0829012	−	0.143589i
$718$	18.3817	−	31.8380i	0.685997	−	1.18818i
$719$	−26.2325	−	45.4360i	−0.978307	−	1.69448i	−0.668558	−	0.743660i	$-0.733088\pi$
$719$	−26.2325	−	45.4360i	−0.978307	−	1.69448i	−0.309749	−	0.950818i	$-0.600245\pi$
$720$	1.44504			0.0538535
$721$	0.435116	+	0.753643i	0.0162046	+	0.0280671i
$722$	9.37800	+	16.2432i	0.349013	+	0.604508i
$723$	36.3980			1.35366
$724$	10.2051	+	17.6757i	0.379268	+	0.656912i
$725$	0.178448	−	0.309081i	0.00662739	−	0.0114790i
$726$	−6.09030	+	10.5487i	−0.226032	+	0.391499i
$727$	4.11397			0.152579			0.0762893	−	0.997086i	$-0.475693\pi$
$727$	4.11397			0.152579			0.0762893	+	0.997086i	$0.475693\pi$
$728$		0			0
$729$	24.4590			0.905890
$730$	0.295897	−	0.512509i	0.0109516	−	0.0189688i
$731$	−18.3545	+	31.7909i	−0.678866	+	1.17583i
$732$	3.43147	+	5.94348i	0.126831	+	0.219677i
$733$	−20.9336			−0.773201			−0.386601	−	0.922247i	$-0.626351\pi$
$733$	−20.9336			−0.773201			−0.386601	+	0.922247i	$0.626351\pi$
$734$	−3.54743	−	6.14432i	−0.130938	−	0.226791i
$735$	4.33997	+	7.51705i	0.160082	+	0.277271i
$736$	−6.76271			−0.249277
$737$	2.14914	+	3.72243i	0.0791648	+	0.137117i
$738$	6.47823	−	11.2206i	0.238467	−	0.413037i
$739$	12.9148	−	22.3692i	0.475080	−	0.822863i	−0.524513	−	0.851403i	$-0.675752\pi$
$739$	12.9148	−	22.3692i	0.475080	−	0.822863i	0.999593	+	0.0285400i	$0.00908579\pi$
$740$	−2.21983			−0.0816027
$741$		0			0
$742$	1.96508			0.0721405
$743$	−26.0206	+	45.0690i	−0.954602	+	1.65342i	−0.219327	+	0.975652i	$0.570386\pi$
$743$	−26.0206	+	45.0690i	−0.954602	+	1.65342i	−0.735276	+	0.677768i	$0.762947\pi$
$744$	3.91185	−	6.77553i	0.143416	−	0.248403i
$745$	8.63318	+	14.9531i	0.316295	+	0.547839i
$746$	26.8901			0.984516
$747$	11.3165	+	19.6007i	0.414048	+	0.717152i
$748$	−3.60388	−	6.24210i	−0.131771	−	0.228234i
$749$	−3.56033			−0.130092
$750$	−0.623490	−	1.07992i	−0.0227666	−	0.0394330i
$751$	−3.94869	+	6.83933i	−0.144090	+	0.249571i	−0.929033	−	0.369997i	$-0.879359\pi$
$751$	−3.94869	+	6.83933i	−0.144090	+	0.249571i	0.784943	+	0.619568i	$0.212692\pi$
$752$	0.716480	−	1.24098i	0.0261273	−	0.0452539i
$753$	36.6112			1.33419
$754$		0			0
$755$	−3.97584			−0.144696
$756$	−0.548917	+	0.950753i	−0.0199639	+	0.0345785i
$757$	8.06829	−	13.9747i	0.293247	−	0.507919i	−0.681328	−	0.731978i	$-0.738597\pi$
$757$	8.06829	−	13.9747i	0.293247	−	0.507919i	0.974576	+	0.224059i	$0.0719308\pi$
$758$	4.23490	+	7.33506i	0.153818	+	0.266421i
$759$	9.35988			0.339742
$760$	−0.246980	−	0.427781i	−0.00895889	−	0.0155173i
$761$	16.2032	+	28.0648i	0.587366	+	1.01735i	0.994576	+	0.104013i	$0.0331683\pi$
$761$	16.2032	+	28.0648i	0.587366	+	1.01735i	−0.407210	+	0.913334i	$0.633498\pi$
$762$	−17.1806			−0.622388
$763$	−0.667030	−	1.15533i	−0.0241481	−	0.0418258i
$764$	−6.36658	+	11.0272i	−0.230335	+	0.398952i
$765$	−4.69202	+	8.12682i	−0.169640	+	0.293826i
$766$	4.79656			0.173307
$767$		0			0
$768$	−1.24698			−0.0449965
$769$	2.72468	−	4.71928i	0.0982544	−	0.170182i	−0.812708	−	0.582671i	$-0.802007\pi$
$769$	2.72468	−	4.71928i	0.0982544	−	0.170182i	0.910962	+	0.412490i	$0.135341\pi$
$770$	0.109916	−	0.190381i	0.00396111	−	0.00686084i
$771$	13.4276	+	23.2573i	0.483583	+	0.837590i
$772$	8.68963			0.312747
$773$	−17.5308	−	30.3642i	−0.630539	−	1.09213i	−0.987442	−	0.157984i	$-0.949501\pi$
$773$	−17.5308	−	30.3642i	−0.630539	−	1.09213i	0.356903	−	0.934142i	$-0.383833\pi$
$774$	4.08426	+	7.07415i	0.146806	+	0.254275i
$775$	6.27413			0.225373
$776$	−6.78986	−	11.7604i	−0.243742	−	0.422173i
$777$	0.274127	−	0.474801i	0.00983424	−	0.0170334i
$778$	−14.6066	+	25.2993i	−0.523671	+	0.907024i
$779$	−4.42891			−0.158682
$780$		0			0
$781$	15.0992			0.540291
$782$	21.9584	−	38.0330i	0.785230	−	1.36006i
$783$	0.989115	−	1.71320i	0.0353481	−	0.0612247i
$784$	3.48039	+	6.02820i	0.124299	+	0.215293i
$785$	−17.4034			−0.621155
$786$	−12.0368	−	20.8484i	−0.429340	−	0.743638i
$787$	20.1172	+	34.8440i	0.717101	+	1.24206i	0.962144	+	0.272543i	$0.0878648\pi$
$787$	20.1172	+	34.8440i	0.717101	+	1.24206i	−0.245042	+	0.969512i	$0.578802\pi$
$788$	5.28621			0.188313
$789$	−4.09634	−	7.09507i	−0.145834	−	0.252591i
$790$	1.46681	−	2.54059i	0.0521868	−	0.0903902i
$791$	−0.225209	+	0.390074i	−0.00800752	+	0.0138694i
$792$	−1.60388			−0.0569912
$793$		0			0
$794$	22.6112			0.802440
$795$	−6.18598	+	10.7144i	−0.219394	+	0.380002i
$796$	5.47219	−	9.47811i	0.193957	−	0.335943i
$797$	1.36658	+	2.36699i	0.0484069	+	0.0838432i	0.889214	−	0.457492i	$-0.151252\pi$
$797$	1.36658	+	2.36699i	0.0484069	+	0.0838432i	−0.840807	+	0.541335i	$0.817919\pi$
$798$	0.121998			0.00431868
$799$	4.65279	+	8.05887i	0.164604	+	0.285102i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	24.6819			0.872091
$802$	5.29470	+	9.17069i	0.186962	+	0.323828i
$803$	−0.328421	+	0.568842i	−0.0115897	+	0.0200740i
$804$	−2.41454	+	4.18211i	−0.0851543	+	0.147492i
$805$	1.33944			0.0472090
$806$		0			0
$807$	−9.18896			−0.323467
$808$	2.77748	−	4.81073i	0.0977114	−	0.169241i
$809$	18.2391	−	31.5910i	0.641252	−	1.11068i	−0.343902	−	0.939006i	$-0.611749\pi$
$809$	18.2391	−	31.5910i	0.641252	−	1.11068i	0.985154	−	0.171675i	$-0.0549179\pi$
$810$	−1.28836	−	2.23151i	−0.0452685	−	0.0784073i
$811$	−3.51679			−0.123491			−0.0617457	−	0.998092i	$-0.519667\pi$
$811$	−3.51679			−0.123491			−0.0617457	+	0.998092i	$0.519667\pi$
$812$	0.0353438	+	0.0612173i	0.00124032	+	0.00214830i
$813$	9.71379	+	16.8248i	0.340678	+	0.590071i
$814$	2.46383			0.0863571
$815$	−4.58426	−	7.94017i	−0.160580	−	0.278132i
$816$	4.04892	−	7.01293i	0.141740	−	0.245502i
$817$	1.39612	−	2.41816i	0.0488442	−	0.0846007i
$818$	−11.7127			−0.409526
$819$		0			0
$820$	−8.96615			−0.313111
$821$	14.6990	−	25.4595i	0.512999	−	0.888541i	−0.486887	−	0.873465i	$-0.661868\pi$
$821$	14.6990	−	25.4595i	0.512999	−	0.888541i	0.999886	−	0.0150760i	$-0.00479903\pi$
$822$	12.1806	−	21.0974i	0.424847	−	0.735857i
$823$	−26.8659	−	46.5331i	−0.936487	−	1.62204i	−0.771960	−	0.635671i	$-0.780724\pi$
$823$	−26.8659	−	46.5331i	−0.936487	−	1.62204i	−0.164527	−	0.986373i	$-0.552610\pi$
$824$	−4.39373			−0.153063
$825$	0.692021	+	1.19862i	0.0240931	+	0.0417305i
$826$	−0.457123	−	0.791761i	−0.0159054	−	0.0275489i
$827$	47.3099			1.64513			0.822563	−	0.568674i	$-0.192543\pi$
$827$	47.3099			1.64513			0.822563	+	0.568674i	$0.192543\pi$
$828$	−4.88620	−	8.46314i	−0.169807	−	0.294115i
$829$	24.6875	−	42.7600i	0.857431	−	1.48511i	−0.0169396	−	0.999857i	$-0.505392\pi$
$829$	24.6875	−	42.7600i	0.857431	−	1.48511i	0.874371	−	0.485258i	$-0.161274\pi$
$830$	7.83124	−	13.5641i	0.271826	−	0.470817i
$831$	17.4517			0.605394
$832$		0			0
$833$	−45.2030			−1.56619
$834$	−11.4819	+	19.8872i	−0.397585	+	0.688637i
$835$	3.68114	−	6.37592i	0.127391	−	0.220648i
$836$	0.274127	+	0.474801i	0.00948087	+	0.0164213i
$837$	34.7767			1.20206
$838$	−10.6625	−	18.4680i	−0.368329	−	0.637965i
$839$	5.31096	+	9.19886i	0.183355	+	0.317580i	0.943021	−	0.332734i	$-0.107971\pi$
$839$	5.31096	+	9.19886i	0.183355	+	0.317580i	−0.759666	+	0.650313i	$0.774638\pi$
$840$	0.246980			0.00852161
$841$	14.4363	+	25.0044i	0.497804	+	0.862222i
$842$	11.0728	−	19.1787i	0.381595	−	0.660943i
$843$	8.31365	−	14.3997i	0.286337	−	0.495951i
$844$	3.30559			0.113783
$845$		0			0
$846$	2.07069			0.0711917
$847$	0.967345	−	1.67549i	0.0332384	−	0.0575705i
$848$	−4.96077	+	8.59231i	−0.170354	+	0.295061i
$849$	−12.9242	−	22.3854i	−0.443558	−	0.768266i
$850$	6.49396			0.222741
$851$	7.50604	+	13.0008i	0.257304	+	0.445663i
$852$	8.48188	+	14.6910i	0.290584	+	0.503307i
$853$	−11.4625			−0.392469			−0.196234	−	0.980557i	$-0.562871\pi$
$853$	−11.4625			−0.392469			−0.196234	+	0.980557i	$0.562871\pi$
$854$	−0.545032	−	0.944024i	−0.0186506	−	0.0323038i
$855$	0.356896	−	0.618162i	0.0122056	−	0.0211407i
$856$	8.98792	−	15.5675i	0.307201	−	0.532087i
$857$	−19.4819			−0.665488			−0.332744	−	0.943017i	$-0.607975\pi$
$857$	−19.4819			−0.665488			−0.332744	+	0.943017i	$0.607975\pi$
$858$		0			0
$859$	−23.1448			−0.789692			−0.394846	−	0.918747i	$-0.629202\pi$
$859$	−23.1448			−0.789692			−0.394846	+	0.918747i	$0.629202\pi$
$860$	2.82640	−	4.89546i	0.0963793	−	0.166934i
$861$	1.10723	−	1.91777i	0.0377342	−	0.0653576i
$862$	−18.4034	−	31.8757i	−0.626823	−	1.08569i
$863$	38.9681			1.32649			0.663244	−	0.748403i	$-0.269179\pi$
$863$	38.9681			1.32649			0.663244	+	0.748403i	$0.269179\pi$
$864$	−2.77144	−	4.80027i	−0.0942862	−	0.163309i
$865$	−4.29590	−	7.44071i	−0.146065	−	0.252992i
$866$	2.08708			0.0709219
$867$	15.6942	+	27.1831i	0.533002	+	0.923187i
$868$	−0.621334	+	1.07618i	−0.0210894	+	0.0365280i
$869$	−1.62804	+	2.81985i	−0.0552274	+	0.0956567i
$870$	−0.445042			−0.0150883
$871$		0			0
$872$	6.73556			0.228095
$873$	9.81163	−	16.9942i	0.332073	−	0.575168i
$874$	−1.67025	+	2.89296i	−0.0564971	+	0.0978558i
$875$	0.0990311	+	0.171527i	0.00334786	+	0.00579867i
$876$	−0.737955			−0.0249332
$877$	−14.1032	−	24.4275i	−0.476232	−	0.824857i	0.523398	−	0.852089i	$-0.324664\pi$
$877$	−14.1032	−	24.4275i	−0.476232	−	0.824857i	−0.999629	+	0.0272313i	$0.991331\pi$
$878$	−4.97823	−	8.62255i	−0.168007	−	0.290997i
$879$	−20.4397			−0.689413
$880$	0.554958	+	0.961216i	0.0187076	+	0.0324026i
$881$	10.6474	−	18.4419i	0.358721	−	0.621322i	−0.629027	−	0.777384i	$-0.716546\pi$
$881$	10.6474	−	18.4419i	0.358721	−	0.621322i	0.987747	+	0.156061i	$0.0498798\pi$
$882$	−5.02930	+	8.71101i	−0.169345	+	0.293315i
$883$	−46.8068			−1.57518			−0.787588	−	0.616202i	$-0.788670\pi$
$883$	−46.8068			−1.57518			−0.787588	+	0.616202i	$0.788670\pi$
$884$		0			0
$885$	5.75600			0.193486
$886$	7.69418	−	13.3267i	0.258491	−	0.447719i
$887$	−0.812823	+	1.40785i	−0.0272919	+	0.0472710i	−0.879349	−	0.476178i	$-0.842022\pi$
$887$	−0.812823	+	1.40785i	−0.0272919	+	0.0472710i	0.852057	+	0.523449i	$0.175355\pi$
$888$	1.38404	+	2.39723i	0.0464454	+	0.0804459i
$889$	2.72886			0.0915229
$890$	−8.54019	−	14.7920i	−0.286268	−	0.495830i
$891$	1.42998	+	2.47679i	0.0479060	+	0.0829756i
$892$	−16.6310			−0.556848
$893$	−0.353912	−	0.612994i	−0.0118432	−	0.0205130i
$894$	10.7654	−	18.6462i	0.360049	−	0.623623i
$895$	−0.329749	+	0.571142i	−0.0110223	+	0.0190912i
$896$	0.198062			0.00661680
$897$		0			0
$898$	8.18060			0.272990
$899$	1.11960	−	1.93921i	0.0373409	−	0.0646764i
$900$	0.722521	−	1.25144i	0.0240840	−	0.0417148i
$901$	−32.2150	−	55.7981i	−1.07324	−	1.85890i
$902$	9.95167			0.331354
$903$	0.698062	+	1.20908i	0.0232301	+	0.0402356i
$904$	−1.13706	−	1.96945i	−0.0378182	−	0.0655030i
$905$	20.4101			0.678456
$906$	2.47889	+	4.29357i	0.0823557	+	0.142644i
$907$	14.4221	−	24.9798i	0.478877	−	0.829440i	−0.520829	−	0.853661i	$-0.674377\pi$
$907$	14.4221	−	24.9798i	0.478877	−	0.829440i	0.999707	+	0.0242212i	$0.00771060\pi$
$908$	5.43080	−	9.40643i	0.180228	−	0.312163i
$909$	8.02715			0.266244
$910$		0			0
$911$	11.5254			0.381854			0.190927	−	0.981604i	$-0.438851\pi$
$911$	11.5254			0.381854			0.190927	+	0.981604i	$0.438851\pi$
$912$	−0.307979	+	0.533434i	−0.0101982	+	0.0176638i
$913$	−8.69202	+	15.0550i	−0.287664	+	0.498249i
$914$	−8.03684	−	13.9202i	−0.265835	−	0.460440i
$915$	6.86294			0.226882
$916$	11.6996	+	20.2642i	0.386564	+	0.669549i
$917$	1.91185	+	3.31143i	0.0631350	+	0.109353i
$918$	35.9952			1.18802
$919$	−4.14138	−	7.17307i	−0.136611	−	0.236618i	0.789600	−	0.613621i	$-0.210288\pi$
$919$	−4.14138	−	7.17307i	−0.136611	−	0.236618i	−0.926212	+	0.377003i	$0.876954\pi$
$920$	−3.38135	+	5.85668i	−0.111480	+	0.193089i
$921$	−4.33244	+	7.50400i	−0.142759	+	0.247265i
$922$	27.5308			0.906678
$923$		0			0
$924$	−0.274127			−0.00901811
$925$	−1.10992	+	1.92243i	−0.0364938	+	0.0632092i
$926$	5.32975	−	9.23140i	0.175146	−	0.303362i
$927$	−3.17456	−	5.49850i	−0.104266	−	0.180595i
$928$	−0.356896			−0.0117157
$929$	−12.6923	−	21.9837i	−0.416421	−	0.721263i	0.579155	−	0.815217i	$-0.303383\pi$
$929$	−12.6923	−	21.9837i	−0.416421	−	0.721263i	−0.995577	+	0.0939543i	$0.970049\pi$
$930$	−3.91185	−	6.77553i	−0.128275	−	0.222178i
$931$	3.43834			0.112687
$932$	−7.19567	−	12.4633i	−0.235702	−	0.408248i
$933$	−15.1890	+	26.3081i	−0.497264	+	0.861287i
$934$	5.39881	−	9.35102i	0.176655	−	0.305975i
$935$	−7.20775			−0.235719
$936$		0			0
$937$	−21.4819			−0.701782			−0.350891	−	0.936416i	$-0.614121\pi$
$937$	−21.4819			−0.701782			−0.350891	+	0.936416i	$0.614121\pi$
$938$	0.383510	−	0.664260i	0.0125221	−	0.0216888i
$939$	1.80194	−	3.12105i	0.0588040	−	0.101852i
$940$	−0.716480	−	1.24098i	−0.0233690	−	0.0404763i
$941$	12.1148			0.394932			0.197466	−	0.980310i	$-0.436729\pi$
$941$	12.1148			0.394932			0.197466	+	0.980310i	$0.436729\pi$
$942$	10.8509	+	18.7942i	0.353540	+	0.612349i
$943$	30.3177	+	52.5118i	0.987281	+	1.71002i
$944$	4.61596			0.150237
$945$	0.548917	+	0.950753i	0.0178563	+	0.0309280i
$946$	−3.13706	+	5.43355i	−0.101995	+	0.176660i
$947$	11.7277	−	20.3129i	0.381098	−	0.660081i	−0.610122	−	0.792308i	$-0.708879\pi$
$947$	11.7277	−	20.3129i	0.381098	−	0.660081i	0.991219	+	0.132227i	$0.0422128\pi$
$948$	−3.65817			−0.118812
$949$		0			0
$950$	−0.493959			−0.0160262
$951$	3.12498	−	5.41263i	0.101334	−	0.175516i
$952$	−0.643104	+	1.11389i	−0.0208431	+	0.0361014i
$953$	21.2543	+	36.8135i	0.688494	+	1.19251i	0.972325	+	0.233632i	$0.0750610\pi$
$953$	21.2543	+	36.8135i	0.688494	+	1.19251i	−0.283832	+	0.958874i	$0.591606\pi$
$954$	−14.3370			−0.464179
$955$	6.36658	+	11.0272i	0.206018	+	0.356833i
$956$	−1.78017	−	3.08334i	−0.0575747	−	0.0997224i
$957$	0.493959			0.0159674
$958$	−4.54288	−	7.86849i	−0.146774	−	0.254219i
$959$	−1.93469	+	3.35098i	−0.0624744	+	0.108209i
$960$	−0.623490	+	1.07992i	−0.0201230	+	0.0348541i
$961$	8.36467			0.269828
$962$		0			0
$963$	25.9758			0.837060
$964$	14.5945	−	25.2784i	0.470057	−	0.814162i
$965$	4.34481	−	7.52544i	0.139865	−	0.242252i
$966$	−0.835126	−	1.44648i	−0.0268697	−	0.0465397i
$967$	−24.7827			−0.796957			−0.398479	−	0.917178i	$-0.630462\pi$
$967$	−24.7827			−0.796957			−0.398479	+	0.917178i	$0.630462\pi$
$968$	4.88404	+	8.45941i	0.156979	+	0.271896i
$969$	−2.00000	−	3.46410i	−0.0642493	−	0.111283i
$970$	−13.5797			−0.436018
$971$	23.0562	+	39.9345i	0.739909	+	1.28156i	0.952536	+	0.304427i	$0.0984648\pi$
$971$	23.0562	+	39.9345i	0.739909	+	1.28156i	−0.212627	+	0.977134i	$0.568202\pi$
$972$	6.70775	−	11.6182i	0.215151	−	0.372653i
$973$	1.82371	−	3.15875i	0.0584654	−	0.101265i
$974$	−40.8471			−1.30883
$975$		0			0
$976$	5.50365			0.176167
$977$	−7.19136	+	12.4558i	−0.230072	+	0.398496i	−0.957829	−	0.287339i	$-0.907229\pi$
$977$	−7.19136	+	12.4558i	−0.230072	+	0.398496i	0.727757	+	0.685835i	$0.240563\pi$
$978$	−5.71648	+	9.90123i	−0.182793	+	0.316607i
$979$	9.47889	+	16.4179i	0.302947	+	0.524719i
$980$	6.96077			0.222354
$981$	4.86658	+	8.42917i	0.155378	+	0.269123i
$982$	−14.5472	−	25.1965i	−0.464219	−	0.804052i
$983$	−9.73615			−0.310535			−0.155268	−	0.987872i	$-0.549624\pi$
$983$	−9.73615			−0.310535			−0.155268	+	0.987872i	$0.549624\pi$
$984$	5.59030	+	9.68269i	0.178212	+	0.308673i
$985$	2.64310	−	4.57799i	0.0842163	−	0.145867i
$986$	1.15883	−	2.00716i	0.0369048	−	0.0639210i
$987$	0.353912			0.0112651
$988$		0			0
$989$	−38.2282			−1.21559
$990$	−0.801938	+	1.38900i	−0.0254873	+	0.0441452i
$991$	12.8974	−	22.3389i	0.409699	−	0.709619i	−0.585157	−	0.810920i	$-0.698967\pi$
$991$	12.8974	−	22.3389i	0.409699	−	0.709619i	0.994856	+	0.101301i	$0.0323005\pi$
$992$	−3.13706	−	5.43355i	−0.0996019	−	0.172515i
$993$	29.9517			0.950488
$994$	−1.34721	−	2.33343i	−0.0427308	−	0.0740119i
$995$	−5.47219	−	9.47811i	−0.173480	−	0.300476i
$996$	−19.5308			−0.618857
$997$	−14.9487	−	25.8919i	−0.473430	−	0.820004i	0.526108	−	0.850418i	$-0.323651\pi$
$997$	−14.9487	−	25.8919i	−0.473430	−	0.820004i	−0.999537	+	0.0304136i	$0.990318\pi$
$998$	−8.10752	+	14.0426i	−0.256639	+	0.444512i
$999$	−6.15213	+	10.6558i	−0.194645	+	0.337135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.e.o.191.3		6
13.2	odd	12		1690.2.l.l.361.3		12
13.3	even	3	inner	1690.2.e.o.991.3		6
13.4	even	6		1690.2.a.q.1.1	✓	3
13.5	odd	4		1690.2.l.l.1161.6		12
13.6	odd	12		1690.2.d.j.1351.1		6
13.7	odd	12		1690.2.d.j.1351.4		6
13.8	odd	4		1690.2.l.l.1161.3		12
13.9	even	3		1690.2.a.s.1.1	yes	3
13.10	even	6		1690.2.e.q.991.3		6
13.11	odd	12		1690.2.l.l.361.6		12
13.12	even	2		1690.2.e.q.191.3		6
65.4	even	6		8450.2.a.bz.1.3		3
65.9	even	6		8450.2.a.bo.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.a.q.1.1	✓	3	13.4	even	6
1690.2.a.s.1.1	yes	3	13.9	even	3
1690.2.d.j.1351.1		6	13.6	odd	12
1690.2.d.j.1351.4		6	13.7	odd	12
1690.2.e.o.191.3		6	1.1	even	1	trivial
1690.2.e.o.991.3		6	13.3	even	3	inner
1690.2.e.q.191.3		6	13.12	even	2
1690.2.e.q.991.3		6	13.10	even	6
1690.2.l.l.361.3		12	13.2	odd	12
1690.2.l.l.361.6		12	13.11	odd	12
1690.2.l.l.1161.3		12	13.8	odd	4
1690.2.l.l.1161.6		12	13.5	odd	4
8450.2.a.bo.1.3		3	65.9	even	6
8450.2.a.bz.1.3		3	65.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.623490 - 1.07992i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.623490 + 1.07992i) q^{6} +(-0.0990311 - 0.171527i) q^{7} +1.00000 q^{8} +(0.722521 + 1.25144i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.554958 + 0.961216i) q^{11} -1.24698 q^{12} +0.198062 q^{14} +(-0.623490 + 1.07992i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.24698 - 5.62393i) q^{17} -1.44504 q^{18} +(0.246980 + 0.427781i) q^{19} +(0.500000 + 0.866025i) q^{20} -0.246980 q^{21} +(-0.554958 - 0.961216i) q^{22} +(3.38135 - 5.85668i) q^{23} +(0.623490 - 1.07992i) q^{24} +1.00000 q^{25} +5.54288 q^{27} +(-0.0990311 + 0.171527i) q^{28} +(0.178448 - 0.309081i) q^{29} +(-0.623490 - 1.07992i) q^{30} +6.27413 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.692021 + 1.19862i) q^{33} +6.49396 q^{34} +(0.0990311 + 0.171527i) q^{35} +(0.722521 - 1.25144i) q^{36} +(-1.10992 + 1.92243i) q^{37} -0.493959 q^{38} -1.00000 q^{40} +(-4.48307 + 7.76491i) q^{41} +(0.123490 - 0.213891i) q^{42} +(-2.82640 - 4.89546i) q^{43} +1.10992 q^{44} +(-0.722521 - 1.25144i) q^{45} +(3.38135 + 5.85668i) q^{46} -1.43296 q^{47} +(0.623490 + 1.07992i) q^{48} +(3.48039 - 6.02820i) q^{49} +(-0.500000 + 0.866025i) q^{50} -8.09783 q^{51} +9.92154 q^{53} +(-2.77144 + 4.80027i) q^{54} +(0.554958 - 0.961216i) q^{55} +(-0.0990311 - 0.171527i) q^{56} +0.615957 q^{57} +(0.178448 + 0.309081i) q^{58} +(-2.30798 - 3.99754i) q^{59} +1.24698 q^{60} +(-2.75182 - 4.76630i) q^{61} +(-3.13706 + 5.43355i) q^{62} +(0.143104 - 0.247864i) q^{63} +1.00000 q^{64} -1.38404 q^{66} +(1.93631 - 3.35379i) q^{67} +(-3.24698 + 5.62393i) q^{68} +(-4.21648 - 7.30316i) q^{69} -0.198062 q^{70} +(-6.80194 - 11.7813i) q^{71} +(0.722521 + 1.25144i) q^{72} +0.591794 q^{73} +(-1.10992 - 1.92243i) q^{74} +(0.623490 - 1.07992i) q^{75} +(0.246980 - 0.427781i) q^{76} +0.219833 q^{77} +2.93362 q^{79} +(0.500000 - 0.866025i) q^{80} +(1.28836 - 2.23151i) q^{81} +(-4.48307 - 7.76491i) q^{82} +15.6625 q^{83} +(0.123490 + 0.213891i) q^{84} +(3.24698 + 5.62393i) q^{85} +5.65279 q^{86} +(-0.222521 - 0.385418i) q^{87} +(-0.554958 + 0.961216i) q^{88} +(8.54019 - 14.7920i) q^{89} +1.44504 q^{90} -6.76271 q^{92} +(3.91185 - 6.77553i) q^{93} +(0.716480 - 1.24098i) q^{94} +(-0.246980 - 0.427781i) q^{95} -1.24698 q^{96} +(-6.78986 - 11.7604i) q^{97} +(3.48039 + 6.02820i) q^{98} -1.60388 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - q^{3} - 3 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} + 6 q^{8} + 4 q^{9} + 3 q^{10} - 4 q^{11} + 2 q^{12} + 10 q^{14} + q^{15} - 3 q^{16} - 10 q^{17} - 8 q^{18} - 8 q^{19} + 3 q^{20} + 8 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - q^3 - 3 * q^4 - 6 * q^5 - q^6 - 5 * q^7 + 6 * q^8 + 4 * q^9 + 3 * q^10 - 4 * q^11 + 2 * q^12 + 10 * q^14 + q^15 - 3 * q^16 - 10 * q^17 - 8 * q^18 - 8 * q^19 + 3 * q^20 + 8 * q^21 - 4 * q^22 + 3 * q^23 - q^24 + 6 * q^25 - 4 * q^27 - 5 * q^28 - 3 * q^29 + q^30 + 16 * q^31 - 3 * q^32 - 6 * q^33 + 20 * q^34 + 5 * q^35 + 4 * q^36 - 8 * q^37 + 16 * q^38 - 6 * q^40 - 11 * q^41 - 4 * q^42 + q^43 + 8 * q^44 - 4 * q^45 + 3 * q^46 + 30 * q^47 - q^48 + 8 * q^49 - 3 * q^50 - 12 * q^51 + 8 * q^53 + 2 * q^54 + 4 * q^55 - 5 * q^56 + 24 * q^57 - 3 * q^58 - 24 * q^59 - 2 * q^60 + 15 * q^61 - 8 * q^62 + 9 * q^63 + 6 * q^64 + 12 * q^66 - 5 * q^67 - 10 * q^68 - 6 * q^69 - 10 * q^70 - 32 * q^71 + 4 * q^72 - 52 * q^73 - 8 * q^74 - q^75 - 8 * q^76 + 4 * q^77 + 4 * q^79 + 3 * q^80 + 5 * q^81 - 11 * q^82 + 14 * q^83 - 4 * q^84 + 10 * q^85 - 2 * q^86 - q^87 - 4 * q^88 + 17 * q^89 + 8 * q^90 - 6 * q^92 + 16 * q^93 - 15 * q^94 + 8 * q^95 + 2 * q^96 + 6 * q^97 + 8 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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