LMFDB - Embedded newform 666.2.k.a.175.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.1
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(-1.70988 - 0.276261i) q^{3} -1.00000 q^{4} -0.372969i q^{5} +(-0.276261 + 1.70988i) q^{6} +(0.0210491 - 0.0364581i) q^{7} +1.00000i q^{8} +(2.84736 + 0.944746i) q^{9} -0.372969 q^{10} +(1.29042 + 2.23507i) q^{11} +(1.70988 + 0.276261i) q^{12} +2.23210i q^{13} +(-0.0364581 - 0.0210491i) q^{14} +(-0.103037 + 0.637732i) q^{15} +1.00000 q^{16} +(-2.25134 - 1.29981i) q^{17} +(0.944746 - 2.84736i) q^{18} +(5.14372 - 2.96973i) q^{19} +0.372969i q^{20} +(-0.0460634 + 0.0565239i) q^{21} +(2.23507 - 1.29042i) q^{22} +(3.66709 + 2.11720i) q^{23} +(0.276261 - 1.70988i) q^{24} +4.86089 q^{25} +2.23210 q^{26} +(-4.60764 - 2.40201i) q^{27} +(-0.0210491 + 0.0364581i) q^{28} +(-0.672857 + 0.388474i) q^{29} +(0.637732 + 0.103037i) q^{30} +(-8.09859 - 4.67573i) q^{31} -1.00000i q^{32} +(-1.58899 - 4.17819i) q^{33} +(-1.29981 + 2.25134i) q^{34} +(-0.0135978 - 0.00785067i) q^{35} +(-2.84736 - 0.944746i) q^{36} +(5.51271 - 2.57099i) q^{37} +(-2.96973 - 5.14372i) q^{38} +(0.616644 - 3.81662i) q^{39} +0.372969 q^{40} +7.23366 q^{41} +(0.0565239 + 0.0460634i) q^{42} +(9.57847 - 5.53013i) q^{43} +(-1.29042 - 2.23507i) q^{44} +(0.352361 - 1.06198i) q^{45} +(2.11720 - 3.66709i) q^{46} +(-5.02395 - 8.70173i) q^{47} +(-1.70988 - 0.276261i) q^{48} +(3.49911 + 6.06064i) q^{49} -4.86089i q^{50} +(3.49042 + 2.84447i) q^{51} -2.23210i q^{52} +(3.61144 - 6.25519i) q^{53} +(-2.40201 + 4.60764i) q^{54} +(0.833612 - 0.481286i) q^{55} +(0.0364581 + 0.0210491i) q^{56} +(-9.61555 + 3.65686i) q^{57} +(0.388474 + 0.672857i) q^{58} +(-10.8565 + 6.26801i) q^{59} +(0.103037 - 0.637732i) q^{60} +(8.09882 + 4.67586i) q^{61} +(-4.67573 + 8.09859i) q^{62} +(0.0943781 - 0.0839234i) q^{63} -1.00000 q^{64} +0.832506 q^{65} +(-4.17819 + 1.58899i) q^{66} +2.32184 q^{67} +(2.25134 + 1.29981i) q^{68} +(-5.68537 - 4.63322i) q^{69} +(-0.00785067 + 0.0135978i) q^{70} +(-0.342015 - 0.592387i) q^{71} +(-0.944746 + 2.84736i) q^{72} +13.1748 q^{73} +(-2.57099 - 5.51271i) q^{74} +(-8.31153 - 1.34288i) q^{75} +(-5.14372 + 2.96973i) q^{76} +0.108649 q^{77} +(-3.81662 - 0.616644i) q^{78} +(-3.39917 - 1.96251i) q^{79} -0.372969i q^{80} +(7.21491 + 5.38006i) q^{81} -7.23366i q^{82} -8.36842 q^{83} +(0.0460634 - 0.0565239i) q^{84} +(-0.484789 + 0.839680i) q^{85} +(-5.53013 - 9.57847i) q^{86} +(1.25782 - 0.478359i) q^{87} +(-2.23507 + 1.29042i) q^{88} +(5.63029 + 3.25065i) q^{89} +(-1.06198 - 0.352361i) q^{90} +(0.0813784 + 0.0469838i) q^{91} +(-3.66709 - 2.11720i) q^{92} +(12.5559 + 10.2322i) q^{93} +(-8.70173 + 5.02395i) q^{94} +(-1.10762 - 1.91845i) q^{95} +(-0.276261 + 1.70988i) q^{96} +(-5.13338 + 2.96376i) q^{97} +(6.06064 - 3.49911i) q^{98} +(1.56271 + 7.58316i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.70988	−	0.276261i	−0.987198	−	0.159500i
$3$	−1.70988	−	0.276261i	−0.987198	−	0.159500i
$4$	−1.00000			−0.500000
$5$		−	0.372969i		−	0.166797i	−0.996516	−	0.0833985i	$-0.973423\pi$
$5$		−	0.372969i		−	0.166797i	0.996516	−	0.0833985i	$-0.0265774\pi$
$6$	−0.276261	+	1.70988i	−0.112783	+	0.698054i
$7$	0.0210491	−	0.0364581i	0.00795582	−	0.0137799i	−0.862020	−	0.506874i	$-0.830801\pi$
$7$	0.0210491	−	0.0364581i	0.00795582	−	0.0137799i	0.869976	+	0.493094i	$0.164134\pi$
$8$			1.00000i			0.353553i
$9$	2.84736	+	0.944746i	0.949120	+	0.314915i
$10$	−0.372969			−0.117943
$11$	1.29042	+	2.23507i	0.389076	+	0.673899i	0.992325	−	0.123653i	$-0.0394611\pi$
$11$	1.29042	+	2.23507i	0.389076	+	0.673899i	−0.603250	+	0.797552i	$0.706128\pi$
$12$	1.70988	+	0.276261i	0.493599	+	0.0797498i
$13$			2.23210i			0.619074i	0.950887	+	0.309537i	$0.100174\pi$
$13$			2.23210i			0.619074i	−0.950887	+	0.309537i	$0.899826\pi$
$14$	−0.0364581	−	0.0210491i	−0.00974385	−	0.00562561i
$15$	−0.103037	+	0.637732i	−0.0266040	+	0.164662i
$16$	1.00000			0.250000
$17$	−2.25134	−	1.29981i	−0.546030	−	0.315250i	0.201489	−	0.979491i	$-0.435422\pi$
$17$	−2.25134	−	1.29981i	−0.546030	−	0.315250i	−0.747519	+	0.664240i	$0.768755\pi$
$18$	0.944746	−	2.84736i	0.222679	−	0.671129i
$19$	5.14372	−	2.96973i	1.18005	−	0.681302i	0.224024	−	0.974584i	$-0.428081\pi$
$19$	5.14372	−	2.96973i	1.18005	−	0.681302i	0.956026	+	0.293281i	$0.0947472\pi$
$20$			0.372969i			0.0833985i
$21$	−0.0460634	+	0.0565239i	−0.0100519	+	0.0123345i
$22$	2.23507	−	1.29042i	0.476518	−	0.275118i
$23$	3.66709	+	2.11720i	0.764641	+	0.441466i	0.830960	−	0.556333i	$-0.187792\pi$
$23$	3.66709	+	2.11720i	0.764641	+	0.441466i	−0.0663185	+	0.997799i	$0.521125\pi$
$24$	0.276261	−	1.70988i	0.0563916	−	0.349027i
$25$	4.86089			0.972179
$26$	2.23210			0.437751
$27$	−4.60764	−	2.40201i	−0.886740	−	0.462268i
$28$	−0.0210491	+	0.0364581i	−0.00397791	+	0.00688994i
$29$	−0.672857	+	0.388474i	−0.124946	+	0.0721379i	−0.561171	−	0.827700i	$-0.689649\pi$
$29$	−0.672857	+	0.388474i	−0.124946	+	0.0721379i	0.436224	+	0.899838i	$0.356315\pi$
$30$	0.637732	+	0.103037i	0.116433	+	0.0188119i
$31$	−8.09859	−	4.67573i	−1.45455	−	0.839785i	−0.455816	−	0.890074i	$-0.650652\pi$
$31$	−8.09859	−	4.67573i	−1.45455	−	0.839785i	−0.998735	+	0.0502891i	$0.983986\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.58899	−	4.17819i	−0.276608	−	0.727329i
$34$	−1.29981	+	2.25134i	−0.222916	+	0.386101i
$35$	−0.0135978	−	0.00785067i	−0.00229844	−	0.00132701i
$36$	−2.84736	−	0.944746i	−0.474560	−	0.157458i
$37$	5.51271	−	2.57099i	0.906284	−	0.422669i
$37$	5.51271	−	2.57099i	0.906284	−	0.422669i
$38$	−2.96973	−	5.14372i	−0.481754	−	0.834422i
$39$	0.616644	−	3.81662i	0.0987420	−	0.611149i
$40$	0.372969			0.0589716
$41$	7.23366			1.12971			0.564854	−	0.825191i	$-0.308932\pi$
$41$	7.23366			1.12971			0.564854	+	0.825191i	$0.308932\pi$
$42$	0.0565239	+	0.0460634i	0.00872183	+	0.00710773i
$43$	9.57847	−	5.53013i	1.46070	−	0.843337i	0.461659	−	0.887057i	$-0.347254\pi$
$43$	9.57847	−	5.53013i	1.46070	−	0.843337i	0.999044	+	0.0437202i	$0.0139210\pi$
$44$	−1.29042	−	2.23507i	−0.194538	−	0.336949i
$45$	0.352361	−	1.06198i	0.0525269	−	0.158310i
$46$	2.11720	−	3.66709i	0.312163	−	0.540683i
$47$	−5.02395	−	8.70173i	−0.732818	−	1.26928i	−0.955674	−	0.294427i	$-0.904871\pi$
$47$	−5.02395	−	8.70173i	−0.732818	−	1.26928i	0.222856	−	0.974851i	$-0.428462\pi$
$48$	−1.70988	−	0.276261i	−0.246800	−	0.0398749i
$49$	3.49911	+	6.06064i	0.499873	+	0.865806i
$50$		−	4.86089i		−	0.687434i
$51$	3.49042	+	2.84447i	0.488757	+	0.398306i
$52$		−	2.23210i		−	0.309537i
$53$	3.61144	−	6.25519i	0.496069	−	0.859217i	−0.503921	−	0.863750i	$-0.668110\pi$
$53$	3.61144	−	6.25519i	0.496069	−	0.859217i	0.999990	+	0.00453324i	$0.00144298\pi$
$54$	−2.40201	+	4.60764i	−0.326873	+	0.627020i
$55$	0.833612	−	0.481286i	0.112404	−	0.0648966i
$56$	0.0364581	+	0.0210491i	0.00487192	+	0.00281281i
$57$	−9.61555	+	3.65686i	−1.27361	+	0.484363i
$58$	0.388474	+	0.672857i	0.0510092	+	0.0883505i
$59$	−10.8565	+	6.26801i	−1.41340	+	0.816025i	−0.995707	−	0.0925642i	$-0.970494\pi$
$59$	−10.8565	+	6.26801i	−1.41340	+	0.816025i	−0.417690	+	0.908589i	$0.637160\pi$
$60$	0.103037	−	0.637732i	0.0133020	−	0.0823308i
$61$	8.09882	+	4.67586i	1.03695	+	0.598682i	0.918967	−	0.394334i	$-0.129025\pi$
$61$	8.09882	+	4.67586i	1.03695	+	0.598682i	0.117980	+	0.993016i	$0.462358\pi$
$62$	−4.67573	+	8.09859i	−0.593818	+	1.02852i
$63$	0.0943781	−	0.0839234i	0.0118905	−	0.0105734i
$64$	−1.00000			−0.125000
$65$	0.832506			0.103260
$66$	−4.17819	+	1.58899i	−0.514299	+	0.195592i
$67$	2.32184			0.283658			0.141829	−	0.989891i	$-0.454702\pi$
$67$	2.32184			0.283658			0.141829	+	0.989891i	$0.454702\pi$
$68$	2.25134	+	1.29981i	0.273015	+	0.157625i
$69$	−5.68537	−	4.63322i	−0.684439	−	0.557774i
$70$	−0.00785067	+	0.0135978i	−0.000938335	+	0.00162524i
$71$	−0.342015	−	0.592387i	−0.0405897	−	0.0703034i	0.845017	−	0.534740i	$-0.179590\pi$
$71$	−0.342015	−	0.592387i	−0.0405897	−	0.0703034i	−0.885607	+	0.464436i	$0.846257\pi$
$72$	−0.944746	+	2.84736i	−0.111339	+	0.335565i
$73$	13.1748			1.54199			0.770995	−	0.636841i	$-0.219759\pi$
$73$	13.1748			1.54199			0.770995	+	0.636841i	$0.219759\pi$
$74$	−2.57099	−	5.51271i	−0.298872	−	0.640840i
$75$	−8.31153	−	1.34288i	−0.959733	−	0.155062i
$76$	−5.14372	+	2.96973i	−0.590025	+	0.340651i
$77$	0.108649			0.0123817
$78$	−3.81662	−	0.616644i	−0.432147	−	0.0698212i
$79$	−3.39917	−	1.96251i	−0.382436	−	0.220800i	0.296442	−	0.955051i	$-0.404200\pi$
$79$	−3.39917	−	1.96251i	−0.382436	−	0.220800i	−0.678878	+	0.734251i	$0.737533\pi$
$80$		−	0.372969i		−	0.0416992i
$81$	7.21491	+	5.38006i	0.801657	+	0.597785i
$82$		−	7.23366i		−	0.798825i
$83$	−8.36842			−0.918554			−0.459277	−	0.888293i	$-0.651891\pi$
$83$	−8.36842			−0.918554			−0.459277	+	0.888293i	$0.651891\pi$
$84$	0.0460634	−	0.0565239i	0.00502593	−	0.00616726i
$85$	−0.484789	+	0.839680i	−0.0525828	+	0.0910761i
$86$	−5.53013	−	9.57847i	−0.596329	−	1.03287i
$87$	1.25782	−	0.478359i	0.134853	−	0.0512855i
$88$	−2.23507	+	1.29042i	−0.238259	+	0.137559i
$89$	5.63029	+	3.25065i	0.596809	+	0.344568i	0.767785	−	0.640707i	$-0.221359\pi$
$89$	5.63029	+	3.25065i	0.596809	+	0.344568i	−0.170976	+	0.985275i	$0.554692\pi$
$90$	−1.06198	−	0.352361i	−0.111942	−	0.0371421i
$91$	0.0813784	+	0.0469838i	0.00853077	+	0.00492524i
$92$	−3.66709	−	2.11720i	−0.382321	−	0.220733i
$93$	12.5559	+	10.2322i	1.30198	+	1.06103i
$94$	−8.70173	+	5.02395i	−0.897515	+	0.518181i
$95$	−1.10762	−	1.91845i	−0.113639	−	0.196829i
$96$	−0.276261	+	1.70988i	−0.0281958	+	0.174514i
$97$	−5.13338	+	2.96376i	−0.521216	+	0.300924i	−0.737432	−	0.675421i	$-0.763962\pi$
$97$	−5.13338	+	2.96376i	−0.521216	+	0.300924i	0.216216	+	0.976346i	$0.430628\pi$
$98$	6.06064	−	3.49911i	0.612217	−	0.353464i
$99$	1.56271	+	7.58316i	0.157058	+	0.762137i
$100$	−4.86089			−0.486089
$101$	4.82354	+	8.35461i	0.479960	+	0.831315i	0.999736	−	0.0229877i	$-0.00731785\pi$
$101$	4.82354	+	8.35461i	0.479960	+	0.831315i	−0.519776	+	0.854303i	$0.673985\pi$
$102$	2.84447	−	3.49042i	0.281645	−	0.345603i
$103$	0.515555	+	0.297656i	0.0507991	+	0.0293289i	0.525184	−	0.850988i	$-0.323996\pi$
$103$	0.515555	+	0.297656i	0.0507991	+	0.0293289i	−0.474385	+	0.880317i	$0.657330\pi$
$104$	−2.23210			−0.218876
$105$	0.0210817	+	0.0171802i	0.00205736	+	0.00167662i
$106$	−6.25519	−	3.61144i	−0.607558	−	0.350774i
$107$	4.79286	+	8.30148i	0.463343	+	0.802534i	0.999125	−	0.0418223i	$-0.0133163\pi$
$107$	4.79286	+	8.30148i	0.463343	+	0.802534i	−0.535782	+	0.844357i	$0.679983\pi$
$108$	4.60764	+	2.40201i	0.443370	+	0.231134i
$109$	8.01087	+	4.62508i	0.767302	+	0.443002i	0.831911	−	0.554909i	$-0.187247\pi$
$109$	8.01087	+	4.62508i	0.767302	+	0.443002i	−0.0646094	+	0.997911i	$0.520580\pi$
$110$	−0.481286	−	0.833612i	−0.0458888	−	0.0794818i
$111$	−10.1363	+	2.87313i	−0.962097	+	0.272706i
$112$	0.0210491	−	0.0364581i	0.00198895	−	0.00344497i
$113$	−13.3019	+	7.67987i	−1.25134	+	0.722462i	−0.971376	−	0.237549i	$-0.923656\pi$
$113$	−13.3019	+	7.67987i	−1.25134	+	0.722462i	−0.279965	+	0.960010i	$0.590323\pi$
$114$	3.65686	+	9.61555i	0.342496	+	0.900579i
$115$	0.789649	−	1.36771i	0.0736351	−	0.127540i
$116$	0.672857	−	0.388474i	0.0624732	−	0.0360689i
$117$	−2.10877	+	6.35560i	−0.194956	+	0.587575i
$118$	6.26801	+	10.8565i	0.577017	+	0.999423i
$119$	−0.0947774	+	0.0547197i	−0.00868823	+	0.00501615i
$120$	−0.637732	−	0.103037i	−0.0582167	−	0.00940594i
$121$	2.16964	−	3.75793i	0.197240	−	0.341630i
$122$	4.67586	−	8.09882i	0.423332	−	0.733233i
$123$	−12.3687	−	1.99838i	−1.11525	−	0.180188i
$124$	8.09859	+	4.67573i	0.727275	+	0.419893i
$125$		−	3.67781i		−	0.328953i
$126$	−0.0839234	−	0.0943781i	−0.00747649	−	0.00840787i
$127$	−1.27625	+	2.21054i	−0.113249	+	0.196153i	−0.917079	−	0.398707i	$-0.869459\pi$
$127$	−1.27625	+	2.21054i	−0.113249	+	0.196153i	0.803829	+	0.594860i	$0.202792\pi$
$128$			1.00000i			0.0883883i
$129$	−17.9058	+	6.80969i	−1.57651	+	0.599559i
$130$		−	0.832506i		−	0.0730156i
$131$	9.82049	−	5.66986i	0.858020	−	0.495378i	−0.00532877	−	0.999986i	$-0.501696\pi$
$131$	9.82049	−	5.66986i	0.858020	−	0.495378i	0.863349	+	0.504608i	$0.168363\pi$
$132$	1.58899	+	4.17819i	0.138304	+	0.363665i
$133$		−	0.250041i		−	0.0216813i
$134$		−	2.32184i		−	0.200576i
$135$	−0.895877	+	1.71851i	−0.0771048	+	0.147906i
$136$	1.29981	−	2.25134i	0.111458	−	0.193051i
$137$	−7.60904	−	13.1792i	−0.650084	−	1.12598i	−0.983102	−	0.183058i	$-0.941400\pi$
$137$	−7.60904	−	13.1792i	−0.650084	−	1.12598i	0.333018	−	0.942921i	$-0.391933\pi$
$138$	−4.63322	+	5.68537i	−0.394406	+	0.483971i
$139$	8.10261	+	14.0341i	0.687254	+	1.19036i	0.972723	+	0.231971i	$0.0745175\pi$
$139$	8.10261	+	14.0341i	0.687254	+	1.19036i	−0.285468	+	0.958388i	$0.592149\pi$
$140$	0.0135978	+	0.00785067i	0.00114922	+	0.000663503i
$141$	6.18638	+	16.2668i	0.520987	+	1.36991i
$142$	−0.592387	+	0.342015i	−0.0497120	+	0.0287013i
$143$	−4.98891	+	2.88035i	−0.417193	+	0.240867i
$144$	2.84736	+	0.944746i	0.237280	+	0.0787288i
$145$	0.144889	+	0.250955i	0.0120324	+	0.0208407i
$146$		−	13.1748i		−	1.09035i
$147$	−4.30873	−	11.3296i	−0.355378	−	0.934452i
$148$	−5.51271	+	2.57099i	−0.453142	+	0.211334i
$149$	0.177156	−	0.306844i	0.0145132	−	0.0251376i	−0.858678	−	0.512516i	$-0.828713\pi$
$149$	0.177156	−	0.306844i	0.0145132	−	0.0251376i	0.873191	+	0.487379i	$0.162047\pi$
$150$	−1.34288	+	8.31153i	−0.109645	+	0.678634i
$151$	−3.44680	+	5.97003i	−0.280496	+	0.485834i	−0.971507	−	0.237010i	$-0.923832\pi$
$151$	−3.44680	+	5.97003i	−0.280496	+	0.485834i	0.691011	+	0.722845i	$0.257166\pi$
$152$	2.96973	+	5.14372i	0.240877	+	0.417211i
$153$	−5.18238	−	5.82797i	−0.418970	−	0.471163i
$154$		−	0.108649i		−	0.00875516i
$155$	−1.74390	+	3.02053i	−0.140074	+	0.242615i
$156$	−0.616644	+	3.81662i	−0.0493710	+	0.305574i
$157$	−5.77978	−	10.0109i	−0.461276	−	0.798954i	0.537749	−	0.843105i	$-0.319275\pi$
$157$	−5.77978	−	10.0109i	−0.461276	−	0.798954i	−0.999025	+	0.0441513i	$0.985942\pi$
$158$	−1.96251	+	3.39917i	−0.156129	+	0.270423i
$159$	−7.90318	+	9.69791i	−0.626763	+	0.769094i
$160$	−0.372969			−0.0294858
$161$	0.154378	−	0.0891302i	0.0121667	−	0.00702444i
$162$	5.38006	−	7.21491i	0.422698	−	0.566857i
$163$	12.6667	+	7.31312i	0.992132	+	0.572808i	0.905911	−	0.423468i	$-0.139187\pi$
$163$	12.6667	+	7.31312i	0.992132	+	0.572808i	0.0862213	+	0.996276i	$0.472521\pi$
$164$	−7.23366			−0.564854
$165$	−1.55834	+	0.592646i	−0.121316	+	0.0461374i
$166$			8.36842i			0.649515i
$167$		−	11.6626i		−	0.902478i	−0.892403	−	0.451239i	$-0.850982\pi$
$167$		−	11.6626i		−	0.902478i	0.892403	−	0.451239i	$-0.149018\pi$
$168$	−0.0565239	−	0.0460634i	−0.00436091	−	0.00355387i
$169$	8.01771			0.616747
$170$	0.839680	+	0.484789i	0.0644005	+	0.0371816i
$171$	17.4517	−	3.59638i	1.33456	−	0.275022i
$172$	−9.57847	+	5.53013i	−0.730351	+	0.421669i
$173$	−0.0584707			−0.00444544			−0.00222272	−	0.999998i	$-0.500708\pi$
$173$	−0.0584707			−0.00444544			−0.00222272	+	0.999998i	$0.500708\pi$
$174$	−0.478359	−	1.25782i	−0.0362643	−	0.0953554i
$175$	0.102318	−	0.177219i	0.00773448	−	0.0133965i
$176$	1.29042	+	2.23507i	0.0972689	+	0.168475i
$177$	20.2949	−	7.71829i	1.52546	−	0.580142i
$178$	3.25065	−	5.63029i	0.243646	−	0.422008i
$179$			8.49336i			0.634823i	0.948288	+	0.317412i	$0.102814\pi$
$179$			8.49336i			0.634823i	−0.948288	+	0.317412i	$0.897186\pi$
$180$	−0.352361	+	1.06198i	−0.0262634	+	0.0791551i
$181$	8.04344	+	13.9316i	0.597864	+	1.03553i	0.993136	+	0.116967i	$0.0373171\pi$
$181$	8.04344	+	13.9316i	0.597864	+	1.03553i	−0.395272	+	0.918564i	$0.629350\pi$
$182$	0.0469838	−	0.0813784i	0.00348267	−	0.00603216i
$183$	−12.5562	−	10.2325i	−0.928183	−	0.756410i
$184$	−2.11720	+	3.66709i	−0.156082	+	0.270341i
$185$	−0.958902	−	2.05607i	−0.0704999	−	0.151165i
$186$	10.2322	−	12.5559i	0.750265	−	0.920642i
$187$		−	6.70920i		−	0.490625i
$188$	5.02395	+	8.70173i	0.366409	+	0.634639i
$189$	−0.184560	+	0.117426i	−0.0134247	+	0.00854146i
$190$	−1.91845	+	1.10762i	−0.139179	+	0.0803550i
$191$	−7.11315	+	4.10678i	−0.514689	+	0.297156i	−0.734759	−	0.678328i	$-0.762705\pi$
$191$	−7.11315	+	4.10678i	−0.514689	+	0.297156i	0.220070	+	0.975484i	$0.429372\pi$
$192$	1.70988	+	0.276261i	0.123400	+	0.0199374i
$193$	−16.6788	−	9.62948i	−1.20056	−	0.693145i	−0.239883	−	0.970802i	$-0.577109\pi$
$193$	−16.6788	−	9.62948i	−1.20056	−	0.693145i	−0.960680	+	0.277656i	$0.910442\pi$
$194$	2.96376	+	5.13338i	0.212785	+	0.368555i
$195$	−1.42348	−	0.229989i	−0.101938	−	0.0164699i
$196$	−3.49911	−	6.06064i	−0.249937	−	0.432903i
$197$	−0.245783	+	0.425708i	−0.0175113	+	0.0303304i	−0.874648	−	0.484758i	$-0.838908\pi$
$197$	−0.245783	+	0.425708i	−0.0175113	+	0.0303304i	0.857137	+	0.515089i	$0.172241\pi$
$198$	7.58316	−	1.56271i	0.538912	−	0.111057i
$199$			10.8937i			0.772236i	0.922449	+	0.386118i	$0.126184\pi$
$199$			10.8937i			0.772236i	−0.922449	+	0.386118i	$0.873816\pi$
$200$			4.86089i			0.343717i
$201$	−3.97006	−	0.641435i	−0.280027	−	0.0452433i
$202$	8.35461	−	4.82354i	0.587828	−	0.339383i
$203$			0.0327082i			0.00229566i
$204$	−3.49042	−	2.84447i	−0.244379	−	0.199153i
$205$		−	2.69793i		−	0.188432i
$206$	0.297656	−	0.515555i	0.0207387	−	0.0359204i
$207$	8.44131	+	9.49288i	0.586712	+	0.659801i
$208$			2.23210i			0.154769i
$209$	13.2751	+	7.66438i	0.918258	+	0.530156i
$210$	0.0171802	−	0.0210817i	0.00118555	−	0.00145477i
$211$	6.38957	−	11.0671i	0.439876	−	0.761888i	−0.557803	−	0.829973i	$-0.688356\pi$
$211$	6.38957	−	11.0671i	0.439876	−	0.761888i	0.997680	+	0.0680853i	$0.0216890\pi$
$212$	−3.61144	+	6.25519i	−0.248034	+	0.429608i
$213$	0.421150	+	1.10739i	0.0288567	+	0.0758774i
$214$	8.30148	−	4.79286i	0.567477	−	0.327633i
$215$	−2.06257	−	3.57247i	−0.140666	−	0.243641i
$216$	2.40201	−	4.60764i	0.163436	−	0.313510i
$217$	−0.340937	+	0.196840i	−0.0231443	+	0.0133624i
$218$	4.62508	−	8.01087i	0.313250	−	0.542564i
$219$	−22.5272	−	3.63968i	−1.52225	−	0.245947i
$220$	−0.833612	+	0.481286i	−0.0562021	+	0.0324483i
$221$	2.90131	−	5.02522i	0.195163	−	0.338033i
$222$	2.87313	+	10.1363i	0.192832	+	0.680306i
$223$	−14.1726	−	24.5477i	−0.949067	−	1.64383i	−0.747395	−	0.664380i	$-0.768696\pi$
$223$	−14.1726	−	24.5477i	−0.949067	−	1.64383i	−0.201673	−	0.979453i	$-0.564638\pi$
$224$	−0.0364581	−	0.0210491i	−0.00243596	−	0.00140640i
$225$	13.8407	+	4.59231i	0.922714	+	0.306154i
$226$	7.67987	+	13.3019i	0.510858	+	0.884831i
$227$	−0.708998	−	0.409340i	−0.0470579	−	0.0271689i	0.476286	−	0.879290i	$-0.341983\pi$
$227$	−0.708998	−	0.409340i	−0.0470579	−	0.0271689i	−0.523344	+	0.852121i	$0.675316\pi$
$228$	9.61555	−	3.65686i	0.636805	−	0.242181i
$229$	−17.3120			−1.14401			−0.572004	−	0.820251i	$-0.693834\pi$
$229$	−17.3120			−1.14401			−0.572004	+	0.820251i	$0.693834\pi$
$230$	−1.36771	−	0.789649i	−0.0901842	−	0.0520679i
$231$	−0.185776	−	0.0300154i	−0.0122232	−	0.00197487i
$232$	−0.388474	−	0.672857i	−0.0255046	−	0.0441752i
$233$	−9.20929			−0.603320			−0.301660	−	0.953416i	$-0.597541\pi$
$233$	−9.20929			−0.603320			−0.301660	+	0.953416i	$0.597541\pi$
$234$	6.35560	+	2.10877i	0.415479	+	0.137855i
$235$	−3.24548	+	1.87378i	−0.211712	+	0.122232i
$236$	10.8565	−	6.26801i	0.706699	−	0.408013i
$237$	5.26999	+	4.29471i	0.342323	+	0.278971i
$238$	0.0547197	+	0.0947774i	0.00354695	+	0.00614350i
$239$	−2.00849	+	1.15960i	−0.129918	+	0.0750084i	−0.563551	−	0.826082i	$-0.690565\pi$
$239$	−2.00849	+	1.15960i	−0.129918	+	0.0750084i	0.433632	+	0.901090i	$0.357232\pi$
$240$	−0.103037	+	0.637732i	−0.00665101	+	0.0411654i
$241$	−5.75406	−	3.32211i	−0.370652	−	0.213996i	0.303091	−	0.952961i	$-0.401981\pi$
$241$	−5.75406	−	3.32211i	−0.370652	−	0.213996i	−0.673743	+	0.738966i	$0.735315\pi$
$242$	−3.75793	−	2.16964i	−0.241569	−	0.139470i
$243$	−10.8503	−	11.1924i	−0.696048	−	0.717996i
$244$	−8.09882	−	4.67586i	−0.518474	−	0.299341i
$245$	2.26043	−	1.30506i	0.144414	−	0.0833773i
$246$	−1.99838	+	12.3687i	−0.127412	+	0.788598i
$247$	6.62874	+	11.4813i	0.421777	+	0.730539i
$248$	4.67573	−	8.09859i	0.296909	−	0.514261i
$249$	14.3090	+	2.31187i	0.906794	+	0.146509i
$250$	−3.67781			−0.232605
$251$		−	26.2916i		−	1.65951i	−0.558128	−	0.829755i	$-0.688480\pi$
$251$		−	26.2916i		−	1.65951i	0.558128	−	0.829755i	$-0.311520\pi$
$252$	−0.0943781	+	0.0839234i	−0.00594526	+	0.00528668i
$253$			10.9283i			0.687054i
$254$	2.21054	+	1.27625i	0.138701	+	0.0800792i
$255$	1.06090	−	1.30182i	0.0664362	−	0.0815232i
$256$	1.00000			0.0625000
$257$	−6.35277	+	3.66777i	−0.396275	+	0.228789i	−0.684875	−	0.728660i	$-0.740143\pi$
$257$	−6.35277	+	3.66777i	−0.396275	+	0.228789i	0.288600	+	0.957450i	$0.406810\pi$
$258$	6.80969	+	17.9058i	0.423953	+	1.11476i
$259$	0.0223041	−	0.255100i	0.00138591	−	0.0158512i
$260$	−0.832506			−0.0516298
$261$	−2.28288	+	0.470447i	−0.141306	+	0.0291199i
$262$	−5.66986	−	9.82049i	−0.350285	−	0.606712i
$263$	−10.2772	+	17.8006i	−0.633719	+	1.09763i	0.353066	+	0.935598i	$0.385139\pi$
$263$	−10.2772	+	17.8006i	−0.633719	+	1.09763i	−0.986785	+	0.162035i	$0.948194\pi$
$264$	4.17819	−	1.58899i	0.257150	−	0.0977958i
$265$	−2.33299	−	1.34695i	−0.143315	−	0.0827428i
$266$	−0.250041			−0.0153310
$267$	−8.72907	−	7.11364i	−0.534210	−	0.435347i
$268$	−2.32184			−0.141829
$269$	25.4958			1.55450			0.777252	−	0.629189i	$-0.216613\pi$
$269$	25.4958			1.55450			0.777252	+	0.629189i	$0.216613\pi$
$270$	1.71851	+	0.895877i	0.104585	+	0.0545214i
$271$	10.5407	−	18.2571i	0.640303	−	1.10904i	−0.345062	−	0.938580i	$-0.612142\pi$
$271$	10.5407	−	18.2571i	0.640303	−	1.10904i	0.985365	−	0.170457i	$-0.0545245\pi$
$272$	−2.25134	−	1.29981i	−0.136507	−	0.0788126i
$273$	−0.126167	−	0.102818i	−0.00763598	−	0.00622284i
$274$	−13.1792	+	7.60904i	−0.796187	+	0.459679i
$275$	6.27259	+	10.8644i	0.378251	+	0.655150i
$276$	5.68537	+	4.63322i	0.342219	+	0.278887i
$277$	−14.3138	−	8.26407i	−0.860032	−	0.496540i	0.00399116	−	0.999992i	$-0.498730\pi$
$277$	−14.3138	−	8.26407i	−0.860032	−	0.496540i	−0.864023	+	0.503452i	$0.832063\pi$
$278$	14.0341	−	8.10261i	0.841711	−	0.485962i
$279$	−18.6422	−	20.9646i	−1.11608	−	1.25512i
$280$	0.00785067	−	0.0135978i	0.000469168	−	0.000812622i
$281$			2.09286i			0.124849i	0.998050	+	0.0624247i	$0.0198833\pi$
$281$			2.09286i			0.124849i	−0.998050	+	0.0624247i	$0.980117\pi$
$282$	16.2668	−	6.18638i	0.968675	−	0.368394i
$283$		−	9.75704i		−	0.579996i	−0.957027	−	0.289998i	$-0.906345\pi$
$283$		−	9.75704i		−	0.579996i	0.957027	−	0.289998i	$-0.0936546\pi$
$284$	0.342015	+	0.592387i	0.0202948	+	0.0351517i
$285$	1.36390	+	3.58630i	0.0807902	+	0.212434i
$286$	2.88035	+	4.98891i	0.170318	+	0.295000i
$287$	0.152262	−	0.263726i	0.00898776	−	0.0155673i
$288$	0.944746	−	2.84736i	0.0556697	−	0.167782i
$289$	−5.12098	−	8.86981i	−0.301234	−	0.521753i
$290$	0.250955	−	0.144889i	0.0147366	−	0.00850817i
$291$	9.59622	−	3.64951i	0.562541	−	0.213938i
$292$	−13.1748			−0.770995
$293$	−1.38135			−0.0806992			−0.0403496	−	0.999186i	$-0.512847\pi$
$293$	−1.38135			−0.0806992			−0.0403496	+	0.999186i	$0.512847\pi$
$294$	−11.3296	+	4.30873i	−0.660757	+	0.251290i
$295$	2.33777	+	4.04914i	0.136110	+	0.235750i
$296$	2.57099	+	5.51271i	0.149436	+	0.320420i
$297$	−0.577110	−	13.3980i	−0.0334873	−	0.777430i
$298$	−0.306844	−	0.177156i	−0.0177750	−	0.0102624i
$299$	−4.72580	+	8.18532i	−0.273300	+	0.473370i
$300$	8.31153	+	1.34288i	0.479866	+	0.0775310i
$301$		−	0.465618i		−	0.0268378i
$302$	5.97003	+	3.44680i	0.343537	+	0.198341i
$303$	−5.93960	−	15.6179i	−0.341221	−	0.897226i
$304$	5.14372	−	2.96973i	0.295013	−	0.170326i
$305$	1.74395	−	3.02061i	0.0998583	−	0.172960i
$306$	−5.82797	+	5.18238i	−0.333163	+	0.296257i
$307$	−22.3771			−1.27713			−0.638564	−	0.769569i	$-0.720471\pi$
$307$	−22.3771			−1.27713			−0.638564	+	0.769569i	$0.720471\pi$
$308$	−0.108649			−0.00619083
$309$	−0.799304	−	0.651382i	−0.0454708	−	0.0370558i
$310$	3.02053	+	1.74390i	0.171554	+	0.0990470i
$311$	−24.5656	+	14.1829i	−1.39299	+	0.804241i	−0.993645	−	0.112561i	$-0.964095\pi$
$311$	−24.5656	+	14.1829i	−1.39299	+	0.804241i	−0.399342	+	0.916802i	$0.630761\pi$
$312$	3.81662	+	0.616644i	0.216074	+	0.0349106i
$313$			13.8093i			0.780548i	0.920699	+	0.390274i	$0.127620\pi$
$313$			13.8093i			0.780548i	−0.920699	+	0.390274i	$0.872380\pi$
$314$	−10.0109	+	5.77978i	−0.564946	+	0.326172i
$315$	−0.0313008	−	0.0352001i	−0.00176360	−	0.00198330i
$316$	3.39917	+	1.96251i	0.191218	+	0.110400i
$317$	7.32076			0.411175			0.205587	−	0.978639i	$-0.434090\pi$
$317$	7.32076			0.411175			0.205587	+	0.978639i	$0.434090\pi$
$318$	9.69791	+	7.90318i	0.543832	+	0.443188i
$319$	−1.73653	−	1.00259i	−0.0972273	−	0.0561342i
$320$			0.372969i			0.0208496i
$321$	−5.90183	−	15.5186i	−0.329408	−	0.866163i
$322$	−0.0891302	−	0.154378i	−0.00496703	−	0.00860315i
$323$	−15.4403			−0.859123
$324$	−7.21491	−	5.38006i	−0.400828	−	0.298892i
$325$			10.8500i			0.601851i
$326$	7.31312	−	12.6667i	0.405036	−	0.701543i
$327$	−12.4199	−	10.1214i	−0.686820	−	0.559715i
$328$			7.23366i			0.399412i
$329$	−0.422999			−0.0233207
$330$	0.592646	+	1.55834i	0.0326241	+	0.0857835i
$331$			13.2880i			0.730376i	0.930934	+	0.365188i	$0.118995\pi$
$331$			13.2880i			0.730376i	−0.930934	+	0.365188i	$0.881005\pi$
$332$	8.36842			0.459277
$333$	18.1256	−	2.11243i	0.993277	−	0.115761i
$334$	−11.6626			−0.638148
$335$		−	0.865975i		−	0.0473133i
$336$	−0.0460634	+	0.0565239i	−0.00251296	+	0.00308363i
$337$	−9.96243			−0.542688			−0.271344	−	0.962482i	$-0.587468\pi$
$337$	−9.96243			−0.542688			−0.271344	+	0.962482i	$0.587468\pi$
$338$		−	8.01771i		−	0.436106i
$339$	24.8663	−	9.45683i	1.35055	−	0.513625i
$340$	0.484789	−	0.839680i	0.0262914	−	0.0455380i
$341$		−	24.1346i		−	1.30696i
$342$	−3.59638	−	17.4517i	−0.194470	−	0.943678i
$343$	0.589301			0.0318193
$344$	5.53013	+	9.57847i	0.298165	+	0.516436i
$345$	−1.72805	+	2.12047i	−0.0930350	+	0.114162i
$346$			0.0584707i			0.00314340i
$347$	18.1956	+	10.5053i	0.976793	+	0.563952i	0.901300	−	0.433195i	$-0.142614\pi$
$347$	18.1956	+	10.5053i	0.976793	+	0.563952i	0.0754928	+	0.997146i	$0.475947\pi$
$348$	−1.25782	+	0.478359i	−0.0674264	+	0.0256427i
$349$	−30.7742			−1.64730			−0.823652	−	0.567095i	$-0.808067\pi$
$349$	−30.7742			−1.64730			−0.823652	+	0.567095i	$0.808067\pi$
$350$	−0.177219	−	0.102318i	−0.00947276	−	0.00546910i
$351$	5.36154	−	10.2847i	0.286178	−	0.548958i
$352$	2.23507	−	1.29042i	0.119130	−	0.0687795i
$353$			0.288111i			0.0153346i	0.999971	+	0.00766729i	$0.00244060\pi$
$353$			0.288111i			0.0153346i	−0.999971	+	0.00766729i	$0.997559\pi$
$354$	−7.71829	−	20.2949i	−0.410223	−	1.07866i
$355$	−0.220942	+	0.127561i	−0.0117264	+	0.00677024i
$356$	−5.63029	−	3.25065i	−0.298405	−	0.172284i
$357$	0.177175	−	0.0673807i	0.00937707	−	0.00356617i
$358$	8.49336			0.448888
$359$	−6.45640			−0.340756			−0.170378	−	0.985379i	$-0.554499\pi$
$359$	−6.45640			−0.340756			−0.170378	+	0.985379i	$0.554499\pi$
$360$	1.06198	+	0.352361i	0.0559711	+	0.0185711i
$361$	8.13857	−	14.0964i	0.428346	−	0.741917i
$362$	13.9316	−	8.04344i	0.732231	−	0.422754i
$363$	−4.74799	+	5.82621i	−0.249205	+	0.305797i
$364$	−0.0813784	−	0.0469838i	−0.00426538	−	0.00246262i
$365$		−	4.91378i		−	0.257199i
$366$	−10.2325	+	12.5562i	−0.534863	+	0.656325i
$367$	18.2746	−	31.6525i	0.953924	−	1.65225i	0.217113	−	0.976146i	$-0.430336\pi$
$367$	18.2746	−	31.6525i	0.953924	−	1.65225i	0.736811	−	0.676099i	$-0.236331\pi$
$368$	3.66709	+	2.11720i	0.191160	+	0.110366i
$369$	20.5968	+	6.83397i	1.07223	+	0.355762i
$370$	−2.05607	+	0.958902i	−0.106890	+	0.0498509i
$371$	−0.152035	−	0.263333i	−0.00789327	−	0.0136715i
$372$	−12.5559	−	10.2322i	−0.650992	−	0.530517i
$373$	2.94276			0.152370			0.0761851	−	0.997094i	$-0.475726\pi$
$373$	2.94276			0.152370			0.0761851	+	0.997094i	$0.475726\pi$
$374$	−6.70920			−0.346924
$375$	−1.01604	+	6.28860i	−0.0524679	+	0.324742i
$376$	8.70173	−	5.02395i	0.448758	−	0.259090i
$377$	−0.867115	−	1.50189i	−0.0446587	−	0.0773511i
$378$	0.117426	+	0.184560i	0.00603972	+	0.00949273i
$379$	−1.75610	+	3.04166i	−0.0902049	+	0.156239i	−0.907597	−	0.419842i	$-0.862086\pi$
$379$	−1.75610	+	3.04166i	−0.0902049	+	0.156239i	0.817392	+	0.576081i	$0.195419\pi$
$380$	1.10762	+	1.91845i	0.0568196	+	0.0984144i
$381$	2.79292	−	3.42716i	0.143086	−	0.175579i
$382$	4.10678	+	7.11315i	0.210121	+	0.363940i
$383$			17.2557i			0.881725i	0.897575	+	0.440863i	$0.145327\pi$
$383$			17.2557i			0.881725i	−0.897575	+	0.440863i	$0.854673\pi$
$384$	0.276261	−	1.70988i	0.0140979	−	0.0872568i
$385$		−	0.0405226i		−	0.00206522i
$386$	−9.62948	+	16.6788i	−0.490128	+	0.848926i
$387$	32.4979	−	6.69706i	1.65196	−	0.340430i
$388$	5.13338	−	2.96376i	0.260608	−	0.150462i
$389$	16.2892	+	9.40455i	0.825893	+	0.476830i	0.852444	−	0.522818i	$-0.175119\pi$
$389$	16.2892	+	9.40455i	0.825893	+	0.476830i	−0.0265513	+	0.999647i	$0.508453\pi$
$390$	−0.229989	+	1.42348i	−0.0116460	+	0.0720808i
$391$	−5.50391	−	9.53305i	−0.278345	−	0.482107i
$392$	−6.06064	+	3.49911i	−0.306109	+	0.176732i
$393$	−18.3582	+	6.98174i	−0.926048	+	0.352182i
$394$	0.425708	+	0.245783i	0.0214469	+	0.0123824i
$395$	−0.731956	+	1.26778i	−0.0368287	+	0.0637891i
$396$	−1.56271	−	7.58316i	−0.0785292	−	0.381068i
$397$	7.41696			0.372246			0.186123	−	0.982526i	$-0.440408\pi$
$397$	7.41696			0.372246			0.186123	+	0.982526i	$0.440408\pi$
$398$	10.8937			0.546053
$399$	−0.0690766	+	0.427539i	−0.00345815	+	0.0214037i
$400$	4.86089			0.243045
$401$	−17.6319	−	10.1798i	−0.880496	−	0.508354i	−0.00967393	−	0.999953i	$-0.503079\pi$
$401$	−17.6319	−	10.1798i	−0.880496	−	0.508354i	−0.870822	+	0.491599i	$0.836413\pi$
$402$	−0.641435	+	3.97006i	−0.0319919	+	0.198009i
$403$	10.4367	−	18.0769i	0.519889	−	0.900474i
$404$	−4.82354	−	8.35461i	−0.239980	−	0.415658i
$405$	2.00660	−	2.69094i	0.0997086	−	0.133714i
$406$	0.0327082			0.00162328
$407$	12.8601	+	9.00364i	0.637449	+	0.446294i
$408$	−2.84447	+	3.49042i	−0.140822	+	0.172802i
$409$	−6.60183	+	3.81157i	−0.326439	+	0.188470i	−0.654259	−	0.756270i	$-0.727019\pi$
$409$	−6.60183	+	3.81157i	−0.326439	+	0.188470i	0.327820	+	0.944740i	$0.393686\pi$
$410$	−2.69793			−0.133241
$411$	9.36961	+	24.6370i	0.462169	+	1.21525i
$412$	−0.515555	−	0.297656i	−0.0253996	−	0.0146644i
$413$			0.527744i			0.0259686i
$414$	9.49288	−	8.44131i	0.466550	−	0.414868i
$415$			3.12116i			0.153212i
$416$	2.23210			0.109438
$417$	−9.97738	−	26.2351i	−0.488594	−	1.28474i
$418$	7.66438	−	13.2751i	0.374877	−	0.649306i
$419$	17.2784	+	29.9271i	0.844106	+	1.46203i	0.886395	+	0.462929i	$0.153202\pi$
$419$	17.2784	+	29.9271i	0.844106	+	1.46203i	−0.0422892	+	0.999105i	$0.513465\pi$
$420$	−0.0210817	−	0.0171802i	−0.00102868	−	0.000838309i
$421$	16.1271	−	9.31096i	0.785985	−	0.453789i	−0.0525623	−	0.998618i	$-0.516739\pi$
$421$	16.1271	−	9.31096i	0.785985	−	0.453789i	0.838547	+	0.544829i	$0.183405\pi$
$422$	−11.0671	−	6.38957i	−0.538736	−	0.311039i
$423$	−6.08406	−	29.5233i	−0.295817	−	1.43547i
$424$	6.25519	+	3.61144i	0.303779	+	0.175387i
$425$	−10.9435	−	6.31824i	−0.530838	−	0.306480i
$426$	1.10739	−	0.421150i	0.0536534	−	0.0204048i
$427$	0.340946	−	0.196845i	0.0164995	−	0.00952601i
$428$	−4.79286	−	8.30148i	−0.231672	−	0.401267i
$429$	9.32615	−	3.54680i	0.450271	−	0.171241i
$430$	−3.57247	+	2.06257i	−0.172280	+	0.0994659i
$431$	18.6073	−	10.7429i	0.896281	−	0.517468i	0.0202895	−	0.999794i	$-0.493541\pi$
$431$	18.6073	−	10.7429i	0.896281	−	0.517468i	0.875992	+	0.482326i	$0.160208\pi$
$432$	−4.60764	−	2.40201i	−0.221685	−	0.115567i
$433$	−30.8001			−1.48016			−0.740080	−	0.672519i	$-0.765212\pi$
$433$	−30.8001			−1.48016			−0.740080	+	0.672519i	$0.765212\pi$
$434$	0.196840	+	0.340937i	0.00944861	+	0.0163655i
$435$	−0.178413	−	0.469129i	−0.00855426	−	0.0224930i
$436$	−8.01087	−	4.62508i	−0.383651	−	0.221501i
$437$	25.1500			1.20309
$438$	−3.63968	+	22.5272i	−0.173911	+	1.07639i
$439$	−25.6425	−	14.8047i	−1.22385	−	0.706590i	−0.258114	−	0.966115i	$-0.583101\pi$
$439$	−25.6425	−	14.8047i	−1.22385	−	0.706590i	−0.965737	+	0.259524i	$0.916434\pi$
$440$	0.481286	+	0.833612i	0.0229444	+	0.0397409i
$441$	4.23747	+	20.5626i	0.201784	+	0.979172i
$442$	−5.02522	−	2.90131i	−0.239025	−	0.138001i
$443$	0.902430	+	1.56305i	0.0428758	+	0.0742630i	0.886667	−	0.462409i	$-0.153015\pi$
$443$	0.902430	+	1.56305i	0.0428758	+	0.0742630i	−0.843791	+	0.536672i	$0.819681\pi$
$444$	10.1363	−	2.87313i	0.481049	−	0.136353i
$445$	1.21239	−	2.09992i	0.0574729	−	0.0995459i
$446$	−24.5477	+	14.1726i	−1.16237	+	0.671092i
$447$	−0.387685	+	0.475724i	−0.0183368	+	0.0225010i
$448$	−0.0210491	+	0.0364581i	−0.000994477	+	0.00172249i
$449$	−32.7760	+	18.9232i	−1.54679	+	0.893042i	−0.548410	+	0.836210i	$0.684767\pi$
$449$	−32.7760	+	18.9232i	−1.54679	+	0.893042i	−0.998384	+	0.0568322i	$0.981900\pi$
$450$	4.59231	−	13.8407i	0.216484	−	0.652457i
$451$	9.33445	+	16.1677i	0.439542	+	0.761309i
$452$	13.3019	−	7.67987i	0.625670	−	0.361231i
$453$	7.54289	−	9.25580i	0.354396	−	0.434875i
$454$	−0.409340	+	0.708998i	−0.0192113	+	0.0332749i
$455$	0.0175235	−	0.0303516i	0.000821515	−	0.00142291i
$456$	−3.65686	−	9.61555i	−0.171248	−	0.450289i
$457$	12.9779	+	7.49278i	0.607079	+	0.350497i	0.771821	−	0.635839i	$-0.219346\pi$
$457$	12.9779	+	7.49278i	0.607079	+	0.350497i	−0.164742	+	0.986337i	$0.552679\pi$
$458$			17.3120i			0.808936i
$459$	7.25119	+	11.3968i	0.338456	+	0.531957i
$460$	−0.789649	+	1.36771i	−0.0368176	+	0.0637699i
$461$			17.8177i			0.829852i	0.909855	+	0.414926i	$0.136193\pi$
$461$			17.8177i			0.829852i	−0.909855	+	0.414926i	$0.863807\pi$
$462$	−0.0300154	+	0.185776i	−0.00139644	+	0.00864308i
$463$			23.2712i			1.08150i	0.841182	+	0.540752i	$0.181860\pi$
$463$			23.2712i			1.08150i	−0.841182	+	0.540752i	$0.818140\pi$
$464$	−0.672857	+	0.388474i	−0.0312366	+	0.0180345i
$465$	3.81631	−	4.68296i	0.176977	−	0.217167i
$466$			9.20929i			0.426612i
$467$		−	17.6430i		−	0.816422i	−0.912888	−	0.408211i	$-0.866153\pi$
$467$		−	17.6430i		−	0.816422i	0.912888	−	0.408211i	$-0.133847\pi$
$468$	2.10877	−	6.35560i	0.0974779	−	0.293788i
$469$	0.0488727	−	0.0846500i	0.00225673	−	0.00390877i
$470$	1.87378	+	3.24548i	0.0864309	+	0.149703i
$471$	7.11709	+	18.7141i	0.327938	+	0.862299i
$472$	−6.26801	−	10.8565i	−0.288508	−	0.499711i
$473$	24.7205	+	14.2724i	1.13665	+	0.656244i
$474$	4.29471	−	5.26999i	0.197262	−	0.242059i
$475$	25.0031	−	14.4355i	1.14722	−	0.662348i
$476$	0.0947774	−	0.0547197i	0.00434411	−	0.00250808i
$477$	16.1926	−	14.3989i	0.741409	−	0.659280i
$478$	1.15960	+	2.00849i	0.0530389	+	0.0918661i
$479$			1.87253i			0.0855583i	0.999085	+	0.0427791i	$0.0136212\pi$
$479$			1.87253i			0.0855583i	−0.999085	+	0.0427791i	$0.986379\pi$
$480$	0.637732	+	0.103037i	0.0291083	+	0.00470297i
$481$	5.73872	+	12.3049i	0.261663	+	0.561057i
$482$	−3.32211	+	5.75406i	−0.151318	+	0.262090i
$483$	−0.288591	+	0.109753i	−0.0131313	+	0.00499394i
$484$	−2.16964	+	3.75793i	−0.0986201	+	0.170815i
$485$	1.10539	+	1.91459i	0.0501932	+	0.0869372i
$486$	−11.1924	+	10.8503i	−0.507700	+	0.492180i
$487$		−	5.36851i		−	0.243270i	−0.992575	−	0.121635i	$-0.961186\pi$
$487$		−	5.36851i		−	0.243270i	0.992575	−	0.121635i	$-0.0388138\pi$
$488$	−4.67586	+	8.09882i	−0.211666	+	0.366616i
$489$	−19.6382	−	16.0039i	−0.888068	−	0.723719i
$490$	−1.30506	−	2.26043i	−0.0589567	−	0.102116i
$491$	19.2176	−	33.2859i	0.867279	−	1.50217i	0.00251360	−	0.999997i	$-0.499200\pi$
$491$	19.2176	−	33.2859i	0.867279	−	1.50217i	0.864766	−	0.502175i	$-0.167467\pi$
$492$	12.3687	+	1.99838i	0.557623	+	0.0900940i
$493$	2.01977			0.0909660
$494$	11.4813	−	6.62874i	0.516569	−	0.298241i
$495$	2.82829	−	0.582843i	0.127122	−	0.0261969i
$496$	−8.09859	−	4.67573i	−0.363638	−	0.209946i
$497$	−0.0287964			−0.00129170
$498$	2.31187	−	14.3090i	0.103597	−	0.641200i
$499$			3.32725i			0.148948i	0.997223	+	0.0744740i	$0.0237278\pi$
$499$			3.32725i			0.148948i	−0.997223	+	0.0744740i	$0.976272\pi$
$500$			3.67781i			0.164477i
$501$	−3.22192	+	19.9416i	−0.143945	+	0.890925i
$502$	−26.2916			−1.17345
$503$	10.6045	+	6.12250i	0.472830	+	0.272989i	0.717424	−	0.696637i	$-0.245321\pi$
$503$	10.6045	+	6.12250i	0.472830	+	0.272989i	−0.244594	+	0.969626i	$0.578655\pi$
$504$	0.0839234	+	0.0943781i	0.00373824	+	0.00420393i
$505$	3.11601	−	1.79903i	0.138661	−	0.0800558i
$506$	10.9283			0.485821
$507$	−13.7093	−	2.21498i	−0.608852	−	0.0983709i
$508$	1.27625	−	2.21054i	0.0566246	−	0.0980766i
$509$	0.866989	+	1.50167i	0.0384286	+	0.0665603i	0.884600	−	0.466351i	$-0.154431\pi$
$509$	0.866989	+	1.50167i	0.0384286	+	0.0665603i	−0.846171	+	0.532911i	$0.821098\pi$
$510$	−1.30182	−	1.06090i	−0.0576456	−	0.0469775i
$511$	0.277317	−	0.480328i	0.0122678	−	0.0212484i
$512$		−	1.00000i		−	0.0441942i
$513$	−30.8337	+	1.32814i	−1.36134	+	0.0586390i
$514$	3.66777	+	6.35277i	0.161779	+	0.280209i
$515$	0.111016	−	0.192286i	0.00489197	−	0.00847313i
$516$	17.9058	−	6.80969i	0.788257	−	0.299780i
$517$	12.9660	−	22.4577i	0.570243	−	0.987691i
$518$	−0.255100	−	0.0223041i	−0.0112085	−	0.000979984i
$519$	0.0999777	+	0.0161532i	0.00438853	+	0.000709046i
$520$			0.832506i			0.0365078i
$521$	3.37632	+	5.84796i	0.147919	+	0.256204i	0.930458	−	0.366398i	$-0.119409\pi$
$521$	3.37632	+	5.84796i	0.147919	+	0.256204i	−0.782539	+	0.622602i	$0.786076\pi$
$522$	0.470447	+	2.28288i	0.0205909	+	0.0999188i
$523$	−24.4520	+	14.1174i	−1.06921	+	0.617309i	−0.927966	−	0.372666i	$-0.878444\pi$
$523$	−24.4520	+	14.1174i	−1.06921	+	0.617309i	−0.141245	+	0.989975i	$0.545110\pi$
$524$	−9.82049	+	5.66986i	−0.429010	+	0.247689i
$525$	−0.223909	+	0.274757i	−0.00977220	+	0.0119914i
$526$	17.8006	+	10.2772i	0.776144	+	0.448107i
$527$	12.1551	+	21.0533i	0.529485	+	0.917095i
$528$	−1.58899	−	4.17819i	−0.0691520	−	0.181832i
$529$	−2.53497	−	4.39069i	−0.110216	−	0.190900i
$530$	−1.34695	+	2.33299i	−0.0585080	+	0.101339i
$531$	−36.8341	+	7.59063i	−1.59846	+	0.329405i
$532$			0.250041i			0.0108406i
$533$			16.1463i			0.699373i
$534$	−7.11364	+	8.72907i	−0.307837	+	0.377744i
$535$	3.09620	−	1.78759i	0.133860	−	0.0772842i
$536$			2.32184i			0.100288i
$537$	2.34639	−	14.5226i	0.101254	−	0.626696i
$538$		−	25.4958i		−	1.09920i
$539$	−9.03064	+	15.6415i	−0.388977	+	0.673728i
$540$	0.895877	−	1.71851i	0.0385524	−	0.0739528i
$541$			13.9031i			0.597741i	0.954294	+	0.298870i	$0.0966098\pi$
$541$			13.9031i			0.597741i	−0.954294	+	0.298870i	$0.903390\pi$
$542$	−18.2571	−	10.5407i	−0.784208	−	0.452763i
$543$	−9.90452	−	26.0435i	−0.425044	−	1.11763i
$544$	−1.29981	+	2.25134i	−0.0557289	+	0.0965253i
$545$	1.72501	−	2.98781i	0.0738913	−	0.127984i
$546$	−0.102818	+	0.126167i	−0.00440021	+	0.00539946i
$547$	−6.72089	+	3.88031i	−0.287365	+	0.165910i	−0.636753	−	0.771068i	$-0.719723\pi$
$547$	−6.72089	+	3.88031i	−0.287365	+	0.165910i	0.349388	+	0.936978i	$0.386389\pi$
$548$	7.60904	+	13.1792i	0.325042	+	0.562989i
$549$	18.6428	+	20.9652i	0.795653	+	0.894771i
$550$	10.8644	−	6.27259i	0.463261	−	0.267464i
$551$	−2.30733	+	3.99641i	−0.0982954	+	0.170253i
$552$	4.63322	−	5.68537i	0.197203	−	0.241986i
$553$	−0.143099	+	0.0826182i	−0.00608518	+	0.00351328i
$554$	−8.26407	+	14.3138i	−0.351106	+	0.608134i
$555$	1.07159	+	3.78054i	0.0454865	+	0.160475i
$556$	−8.10261	−	14.0341i	−0.343627	−	0.595180i
$557$	−19.0159	−	10.9788i	−0.805730	−	0.465189i	0.0397407	−	0.999210i	$-0.487347\pi$
$557$	−19.0159	−	10.9788i	−0.805730	−	0.465189i	−0.845471	+	0.534021i	$0.820680\pi$
$558$	−20.9646	+	18.6422i	−0.887502	+	0.789189i
$559$	12.3438	+	21.3801i	0.522088	+	0.904283i
$560$	−0.0135978	−	0.00785067i	−0.000574611	−	0.000331752i
$561$	−1.85349	+	11.4719i	−0.0782545	+	0.484344i
$562$	2.09286			0.0882819
$563$	−9.39056	−	5.42164i	−0.395765	−	0.228495i	0.288890	−	0.957362i	$-0.406714\pi$
$563$	−9.39056	−	5.42164i	−0.395765	−	0.228495i	−0.684655	+	0.728867i	$0.740047\pi$
$564$	−6.18638	−	16.2668i	−0.260494	−	0.684957i
$565$	2.86436	+	4.96121i	0.120504	+	0.208720i
$566$	−9.75704			−0.410119
$567$	0.348015	−	0.149797i	0.0146152	−	0.00629087i
$568$	0.592387	−	0.342015i	0.0248560	−	0.0143506i
$569$	7.21399	−	4.16500i	0.302426	−	0.174606i	−0.341106	−	0.940025i	$-0.610802\pi$
$569$	7.21399	−	4.16500i	0.302426	−	0.174606i	0.643532	+	0.765419i	$0.277468\pi$
$570$	3.58630	−	1.36390i	0.150214	−	0.0571273i
$571$	6.63685	+	11.4954i	0.277744	+	0.481066i	0.970824	−	0.239795i	$-0.0770801\pi$
$571$	6.63685	+	11.4954i	0.277744	+	0.481066i	−0.693080	+	0.720861i	$0.743747\pi$
$572$	4.98891	−	2.88035i	0.208597	−	0.120433i
$573$	13.2972	−	5.05700i	0.555497	−	0.211259i
$574$	−0.263726	−	0.152262i	−0.0110077	−	0.00635530i
$575$	17.8253	+	10.2915i	0.743368	+	0.429184i
$576$	−2.84736	−	0.944746i	−0.118640	−	0.0393644i
$577$	24.9225	+	14.3890i	1.03754	+	0.599022i	0.919134	−	0.393944i	$-0.128890\pi$
$577$	24.9225	+	14.3890i	1.03754	+	0.599022i	0.118402	+	0.992966i	$0.462223\pi$
$578$	−8.86981	+	5.12098i	−0.368935	+	0.213005i
$579$	25.8584	+	21.0729i	1.07464	+	0.875761i
$580$	−0.144889	−	0.250955i	−0.00601619	−	0.0104203i
$581$	−0.176148	+	0.305097i	−0.00730785	+	0.0126576i
$582$	−3.64951	−	9.59622i	−0.151277	−	0.397776i
$583$	18.6411			0.772033
$584$			13.1748i			0.545176i
$585$	2.37044	+	0.786506i	0.0980058	+	0.0325180i
$586$			1.38135i			0.0570630i
$587$	−21.2120	−	12.2468i	−0.875514	−	0.505478i	−0.00633710	−	0.999980i	$-0.502017\pi$
$587$	−21.2120	−	12.2468i	−0.875514	−	0.505478i	−0.869177	+	0.494502i	$0.835351\pi$
$588$	4.30873	+	11.3296i	0.177689	+	0.467226i
$589$	−55.5425			−2.28859
$590$	4.04914	−	2.33777i	0.166701	−	0.0962446i
$591$	0.537865	−	0.660008i	0.0221248	−	0.0271491i
$592$	5.51271	−	2.57099i	0.226571	−	0.105667i
$593$	−33.7386			−1.38548			−0.692740	−	0.721188i	$-0.743597\pi$
$593$	−33.7386			−1.38548			−0.692740	+	0.721188i	$0.743597\pi$
$594$	−13.3980	+	0.577110i	−0.549726	+	0.0236791i
$595$	0.0204088	+	0.0353490i	0.000836678	+	0.00144917i
$596$	−0.177156	+	0.306844i	−0.00725660	+	0.0125688i
$597$	3.00951	−	18.6269i	0.123171	−	0.762349i
$598$	8.18532	+	4.72580i	0.334723	+	0.193252i
$599$	−19.7504			−0.806979			−0.403489	−	0.914984i	$-0.632203\pi$
$599$	−19.7504			−0.806979			−0.403489	+	0.914984i	$0.632203\pi$
$600$	1.34288	−	8.31153i	0.0548227	−	0.339317i
$601$	−13.7029			−0.558952			−0.279476	−	0.960153i	$-0.590161\pi$
$601$	−13.7029			−0.558952			−0.279476	+	0.960153i	$0.590161\pi$
$602$	−0.465618			−0.0189772
$603$	6.61111	+	2.19355i	0.269225	+	0.0893282i
$604$	3.44680	−	5.97003i	0.140248	−	0.242917i
$605$	−1.40159	−	0.809210i	−0.0569828	−	0.0328991i
$606$	−15.6179	+	5.93960i	−0.634435	+	0.241280i
$607$	−9.37497	+	5.41264i	−0.380518	+	0.219692i	−0.678044	−	0.735021i	$-0.737172\pi$
$607$	−9.37497	+	5.41264i	−0.380518	+	0.219692i	0.297525	+	0.954714i	$0.403839\pi$
$608$	−2.96973	−	5.14372i	−0.120438	−	0.208605i
$609$	0.00903600	−	0.0559270i	0.000366157	−	0.00226627i
$610$	−3.02061	−	1.74395i	−0.122301	−	0.0706105i
$611$	19.4232	−	11.2140i	0.785777	−	0.453669i
$612$	5.18238	+	5.82797i	0.209485	+	0.235582i
$613$	10.2622	−	17.7747i	0.414487	−	0.717913i	−0.580887	−	0.813984i	$-0.697294\pi$
$613$	10.2622	−	17.7747i	0.414487	−	0.717913i	0.995375	+	0.0960708i	$0.0306275\pi$
$614$			22.3771i			0.903065i
$615$	−0.745335	+	4.61314i	−0.0300548	+	0.186020i
$616$			0.108649i			0.00437758i
$617$	7.71528	+	13.3633i	0.310605	+	0.537984i	0.978494	−	0.206277i	$-0.0661349\pi$
$617$	7.71528	+	13.3633i	0.310605	+	0.537984i	−0.667888	+	0.744262i	$0.732802\pi$
$618$	−0.651382	+	0.799304i	−0.0262024	+	0.0321527i
$619$	−6.19852	−	10.7361i	−0.249139	−	0.431522i	0.714148	−	0.699995i	$-0.246814\pi$
$619$	−6.19852	−	10.7361i	−0.249139	−	0.431522i	−0.963287	+	0.268473i	$0.913481\pi$
$620$	1.74390	−	3.02053i	0.0700368	−	0.121307i
$621$	−11.8111	−	18.5637i	−0.473963	−	0.744935i
$622$	14.1829	+	24.5656i	0.568684	+	0.984990i
$623$	0.237025	−	0.136847i	0.00949621	−	0.00548264i
$624$	0.616644	−	3.81662i	0.0246855	−	0.152787i
$625$	22.9328			0.917310
$626$	13.8093			0.551931
$627$	−20.5814	−	16.7725i	−0.821943	−	0.669831i
$628$	5.77978	+	10.0109i	0.230638	+	0.399477i
$629$	−15.7528	−	1.37730i	−0.628105	−	0.0549167i
$630$	−0.0352001	+	0.0313008i	−0.00140241	+	0.00124706i
$631$	−31.5489	−	18.2148i	−1.25594	−	0.725118i	−0.283658	−	0.958925i	$-0.591548\pi$
$631$	−31.5489	−	18.2148i	−1.25594	−	0.725118i	−0.972283	+	0.233808i	$0.924881\pi$
$632$	1.96251	−	3.39917i	0.0780644	−	0.135212i
$633$	−13.9828	+	17.1581i	−0.555766	+	0.681974i
$634$		−	7.32076i		−	0.290744i
$635$	0.824462	+	0.476003i	0.0327178	+	0.0188896i
$636$	7.90318	−	9.69791i	0.313381	−	0.384547i
$637$	−13.5280	+	7.81038i	−0.535998	+	0.309459i
$638$	−1.00259	+	1.73653i	−0.0396929	+	0.0687501i
$639$	−0.414184	−	2.00986i	−0.0163849	−	0.0795087i
$640$	0.372969			0.0147429
$641$	48.4888			1.91519			0.957596	−	0.288115i	$-0.0930284\pi$
$641$	48.4888			1.91519			0.957596	+	0.288115i	$0.0930284\pi$
$642$	−15.5186	+	5.90183i	−0.612470	+	0.232927i
$643$	18.1536	+	10.4810i	0.715907	+	0.413329i	0.813244	−	0.581922i	$-0.197699\pi$
$643$	18.1536	+	10.4810i	0.715907	+	0.413329i	−0.0973375	+	0.995251i	$0.531033\pi$
$644$	−0.154378	+	0.0891302i	−0.00608335	+	0.00351222i
$645$	2.53980	+	6.67830i	0.100005	+	0.262958i
$646$			15.4403i			0.607492i
$647$	−33.9152	+	19.5810i	−1.33334	+	0.769807i	−0.985811	−	0.167861i	$-0.946314\pi$
$647$	−33.9152	+	19.5810i	−1.33334	+	0.769807i	−0.347534	+	0.937667i	$0.612981\pi$
$648$	−5.38006	+	7.21491i	−0.211349	+	0.283428i
$649$	−28.0189	−	16.1767i	−1.09984	−	0.634991i
$650$	10.8500			0.425573
$651$	0.637339	−	0.242384i	0.0249793	−	0.00949979i
$652$	−12.6667	−	7.31312i	−0.496066	−	0.286404i
$653$		−	39.0374i		−	1.52765i	−0.645423	−	0.763825i	$-0.723319\pi$
$653$		−	39.0374i		−	1.52765i	0.645423	−	0.763825i	$-0.276681\pi$
$654$	−10.1214	+	12.4199i	−0.395778	+	0.485655i
$655$	−2.11468	−	3.66274i	−0.0826275	−	0.143115i
$656$	7.23366			0.282427
$657$	37.5133	+	12.4468i	1.46353	+	0.485596i
$658$			0.422999i			0.0164902i
$659$	−23.2367	+	40.2472i	−0.905174	+	1.56781i	−0.0844908	+	0.996424i	$0.526926\pi$
$659$	−23.2367	+	40.2472i	−0.905174	+	1.56781i	−0.820683	+	0.571383i	$0.806407\pi$
$660$	1.55834	−	0.592646i	0.0606581	−	0.0230687i
$661$			40.3144i			1.56805i	0.620730	+	0.784024i	$0.286836\pi$
$661$			40.3144i			1.56805i	−0.620730	+	0.784024i	$0.713164\pi$
$662$	13.2880			0.516454
$663$	−6.34916	+	7.79099i	−0.246581	+	0.302577i
$664$		−	8.36842i		−	0.324758i
$665$	−0.0932575			−0.00361637
$666$	−2.11243	−	18.1256i	−0.0818551	−	0.702353i
$667$	−3.28990			−0.127386
$668$			11.6626i			0.451239i
$669$	17.4518	+	45.8888i	0.674727	+	1.77416i
$670$	−0.865975			−0.0334555
$671$			24.1352i			0.931730i
$672$	0.0565239	+	0.0460634i	0.00218046	+	0.00177693i
$673$	−23.0883	+	39.9902i	−0.889990	+	1.54151i	−0.0501056	+	0.998744i	$0.515956\pi$
$673$	−23.0883	+	39.9902i	−0.889990	+	1.54151i	−0.839885	+	0.542765i	$0.817378\pi$
$674$			9.96243i			0.383738i
$675$	−22.3972	−	11.6759i	−0.862070	−	0.449407i
$676$	−8.01771			−0.308374
$677$	21.2133	+	36.7426i	0.815294	+	1.41213i	0.909116	+	0.416542i	$0.136758\pi$
$677$	21.2133	+	36.7426i	0.815294	+	1.41213i	−0.0938220	+	0.995589i	$0.529908\pi$
$678$	−9.45683	−	24.8663i	−0.363187	−	0.954985i
$679$			0.249538i			0.00957639i
$680$	−0.839680	−	0.484789i	−0.0322003	−	0.0185908i
$681$	1.09921	+	0.895790i	0.0421220	+	0.0343268i
$682$	−24.1346			−0.924160
$683$	44.0035	+	25.4054i	1.68375	+	0.972112i	0.959132	+	0.282960i	$0.0913163\pi$
$683$	44.0035	+	25.4054i	1.68375	+	0.972112i	0.724616	+	0.689153i	$0.242017\pi$
$684$	−17.4517	+	3.59638i	−0.667281	+	0.137511i
$685$	−4.91545	+	2.83794i	−0.187810	+	0.108432i
$686$		−	0.589301i		−	0.0224996i
$687$	29.6014	+	4.78263i	1.12936	+	0.182469i
$688$	9.57847	−	5.53013i	0.365176	−	0.210834i
$689$	13.9622	+	8.06110i	0.531919	+	0.307103i
$690$	2.12047	+	1.72805i	0.0807249	+	0.0657857i
$691$	−4.33821			−0.165033			−0.0825166	−	0.996590i	$-0.526296\pi$
$691$	−4.33821			−0.165033			−0.0825166	+	0.996590i	$0.526296\pi$
$692$	0.0584707			0.00222272
$693$	0.309362	+	0.102645i	0.0117517	+	0.00389917i
$694$	10.5053	−	18.1956i	0.398774	−	0.690697i
$695$	5.23430	−	3.02202i	0.198548	−	0.114632i
$696$	0.478359	+	1.25782i	0.0181321	+	0.0476777i
$697$	−16.2854	−	9.40239i	−0.616854	−	0.356141i
$698$			30.7742i			1.16482i
$699$	15.7467	+	2.54417i	0.595597	+	0.0962293i
$700$	−0.102318	+	0.177219i	−0.00386724	+	0.00669826i
$701$	−39.9218	−	23.0488i	−1.50782	−	0.870542i	−0.999959	−	0.00910594i	$-0.997101\pi$
$701$	−39.9218	−	23.0488i	−1.50782	−	0.870542i	−0.507865	−	0.861437i	$-0.669565\pi$
$702$	−10.2847	−	5.36154i	−0.388172	−	0.202358i
$703$	20.7207	−	29.5957i	0.781496	−	1.11622i
$704$	−1.29042	−	2.23507i	−0.0486345	−	0.0842374i
$705$	6.06702	−	2.30733i	0.228497	−	0.0868991i
$706$	0.288111			0.0108432
$707$	0.406125			0.0152739
$708$	−20.2949	+	7.71829i	−0.762729	+	0.290071i
$709$	−39.1822	+	22.6218i	−1.47152	+	0.849581i	−0.999488	−	0.0320017i	$-0.989812\pi$
$709$	−39.1822	+	22.6218i	−1.47152	+	0.849581i	−0.472030	+	0.881583i	$0.656478\pi$
$710$	0.127561	+	0.220942i	0.00478728	+	0.00829181i
$711$	−7.82457	−	8.79932i	−0.293444	−	0.330000i
$712$	−3.25065	+	5.63029i	−0.121823	+	0.211004i
$713$	−19.7989	−	34.2926i	−0.741473	−	1.28427i
$714$	−0.0673807	−	0.177175i	−0.00252166	−	0.00663059i
$715$	1.07428	+	1.86071i	0.0401758	+	0.0695866i
$716$		−	8.49336i		−	0.317412i
$717$	3.75462	−	1.42791i	0.140219	−	0.0533262i
$718$			6.45640i			0.240951i
$719$	−1.96437	+	3.40238i	−0.0732585	+	0.126887i	−0.900328	−	0.435213i	$-0.856673\pi$
$719$	−1.96437	+	3.40238i	−0.0732585	+	0.126887i	0.827069	+	0.562100i	$0.190006\pi$
$720$	0.352361	−	1.06198i	0.0131317	−	0.0395776i
$721$	0.0217039	−	0.0125308i	0.000808297	−	0.000466671i
$722$	−14.0964	−	8.13857i	−0.524614	−	0.302886i
$723$	8.92097	+	7.27002i	0.331774	+	0.270375i
$724$	−8.04344	−	13.9316i	−0.298932	−	0.517765i
$725$	−3.27069	+	1.88833i	−0.121470	+	0.0701309i
$726$	5.82621	+	4.74799i	0.216231	+	0.176215i
$727$	36.6043	+	21.1335i	1.35758	+	0.783798i	0.989297	−	0.145916i	$-0.0466129\pi$
$727$	36.6043	+	21.1335i	1.35758	+	0.783798i	0.368282	+	0.929714i	$0.379946\pi$
$728$	−0.0469838	+	0.0813784i	−0.00174134	+	0.00301608i
$729$	15.4607	+	22.1352i	0.572617	+	0.819823i
$730$	−4.91378			−0.181867
$731$	−28.7525			−1.06345
$732$	12.5562	+	10.2325i	0.464092	+	0.378205i
$733$	−4.09527			−0.151262			−0.0756312	−	0.997136i	$-0.524097\pi$
$733$	−4.09527			−0.151262			−0.0756312	+	0.997136i	$0.524097\pi$
$734$	−31.6525	−	18.2746i	−1.16831	−	0.674526i
$735$	−4.22560	+	1.60703i	−0.155864	+	0.0592760i
$736$	2.11720	−	3.66709i	0.0780409	−	0.135171i
$737$	2.99615	+	5.18948i	0.110364	+	0.191157i
$738$	6.83397	−	20.5968i	0.251562	−	0.758180i
$739$	43.9364			1.61623			0.808114	−	0.589027i	$-0.200489\pi$
$739$	43.9364			1.61623			0.808114	+	0.589027i	$0.200489\pi$
$740$	0.958902	+	2.05607i	0.0352499	+	0.0755827i
$741$	−8.16249	−	21.4629i	−0.299857	−	0.788459i
$742$	−0.263333	+	0.152035i	−0.00966724	+	0.00558139i
$743$	−17.8855			−0.656156			−0.328078	−	0.944651i	$-0.606401\pi$
$743$	−17.8855			−0.656156			−0.328078	+	0.944651i	$0.606401\pi$
$744$	−10.2322	+	12.5559i	−0.375132	+	0.460321i
$745$	−0.114443	−	0.0660738i	−0.00419288	−	0.00242076i
$746$		−	2.94276i		−	0.107742i
$747$	−23.8279	−	7.90603i	−0.871817	−	0.289267i
$748$			6.70920i			0.245313i
$749$	0.403542			0.0147451
$750$	6.28860	+	1.01604i	0.229627	+	0.0371004i
$751$	8.35475	−	14.4709i	0.304869	−	0.528049i	−0.672363	−	0.740222i	$-0.734721\pi$
$751$	8.35475	−	14.4709i	0.304869	−	0.528049i	0.977232	+	0.212173i	$0.0680539\pi$
$752$	−5.02395	−	8.70173i	−0.183205	−	0.317320i
$753$	−7.26335	+	44.9554i	−0.264691	+	1.63827i
$754$	−1.50189	+	0.867115i	−0.0546955	+	0.0315785i
$755$	2.22664	+	1.28555i	0.0810356	+	0.0467859i
$756$	0.184560	−	0.117426i	0.00671237	−	0.00427073i
$757$	7.69103	+	4.44042i	0.279535	+	0.161390i	0.633213	−	0.773978i	$-0.281736\pi$
$757$	7.69103	+	4.44042i	0.279535	+	0.161390i	−0.353678	+	0.935367i	$0.615069\pi$
$758$	3.04166	+	1.75610i	0.110478	+	0.0637845i
$759$	3.01906	−	18.6860i	0.109585	−	0.678259i
$760$	1.91845	−	1.10762i	0.0695895	−	0.0401775i
$761$	−14.0530	−	24.3406i	−0.509423	−	0.882346i	−0.999940	−	0.0109147i	$-0.996526\pi$
$761$	−14.0530	−	24.3406i	−0.509423	−	0.882346i	0.490518	−	0.871431i	$-0.336808\pi$
$762$	−3.42716	−	2.79292i	−0.124153	−	0.101177i
$763$	0.337243	−	0.194708i	0.0122090	−	0.00704889i
$764$	7.11315	−	4.10678i	0.257345	−	0.148578i
$765$	−2.17365	+	1.93287i	−0.0785886	+	0.0698830i
$766$	17.2557			0.623474
$767$	−13.9908	−	24.2329i	−0.505180	−	0.874998i
$768$	−1.70988	−	0.276261i	−0.0616999	−	0.00996872i
$769$	8.59532	+	4.96251i	0.309955	+	0.178953i	0.646906	−	0.762569i	$-0.276062\pi$
$769$	8.59532	+	4.96251i	0.309955	+	0.178953i	−0.336951	+	0.941522i	$0.609396\pi$
$770$	−0.0405226			−0.00146033
$771$	11.8757	−	4.51642i	0.427694	−	0.162655i
$772$	16.6788	+	9.62948i	0.600282	+	0.346573i
$773$	−18.3764	−	31.8289i	−0.660954	−	1.14481i	−0.980365	−	0.197190i	$-0.936818\pi$
$773$	−18.3764	−	31.8289i	−0.660954	−	1.14481i	0.319411	−	0.947616i	$-0.396515\pi$
$774$	−6.69706	−	32.4979i	−0.240721	−	1.16811i
$775$	−39.3664	−	22.7282i	−1.41408	−	0.816421i
$776$	−2.96376	−	5.13338i	−0.106393	−	0.184278i
$777$	−0.108612	+	0.430029i	−0.00389642	+	0.0154272i
$778$	9.40455	−	16.2892i	0.337169	−	0.583995i
$779$	37.2079	−	21.4820i	1.33311	−	0.769673i
$780$	1.42348	+	0.229989i	0.0509689	+	0.00823493i
$781$	0.882684	−	1.52885i	0.0315849	−	0.0547067i
$782$	−9.53305	+	5.50391i	−0.340901	+	0.196819i
$783$	4.03340	−	0.173736i	0.144142	−	0.00620883i
$784$	3.49911	+	6.06064i	0.124968	+	0.216452i
$785$	−3.73374	+	2.15568i	−0.133263	+	0.0769395i
$786$	6.98174	+	18.3582i	0.249031	+	0.654815i
$787$	−1.31315	+	2.27445i	−0.0468088	+	0.0810752i	−0.888481	−	0.458914i	$-0.848238\pi$
$787$	−1.31315	+	2.27445i	−0.0468088	+	0.0810752i	0.841672	+	0.539990i	$0.181572\pi$
$788$	0.245783	−	0.425708i	0.00875565	−	0.0151652i
$789$	22.4904	−	27.5977i	0.800678	−	0.982503i
$790$	1.26778	+	0.731956i	0.0451057	+	0.0260418i
$791$			0.646618i			0.0229911i
$792$	−7.58316	+	1.56271i	−0.269456	+	0.0555285i
$793$	−10.4370	+	18.0774i	−0.370628	+	0.641947i
$794$		−	7.41696i		−	0.263218i
$795$	3.61702	+	2.94764i	0.128283	+	0.104542i
$796$		−	10.8937i		−	0.386118i
$797$	25.5748	−	14.7656i	0.905905	−	0.523024i	0.0267936	−	0.999641i	$-0.491470\pi$
$797$	25.5748	−	14.7656i	0.905905	−	0.523024i	0.879111	+	0.476617i	$0.158137\pi$
$798$	0.427539	+	0.0690766i	0.0151347	+	0.00244528i
$799$			26.1207i			0.924085i
$800$		−	4.86089i		−	0.171859i
$801$	12.9604	+	14.5749i	0.457934	+	0.514980i
$802$	−10.1798	+	17.6319i	−0.359461	+	0.622605i
$803$	17.0010	+	29.4465i	0.599951	+	1.03915i
$804$	3.97006	+	0.641435i	0.140013	+	0.0226217i
$805$	−0.0332428	−	0.0575783i	−0.00117166	−	0.00202937i
$806$	−18.0769	−	10.4367i	−0.636732	−	0.367617i
$807$	−43.5946	−	7.04349i	−1.53460	−	0.247943i
$808$	−8.35461	+	4.82354i	−0.293914	+	0.169691i
$809$	10.2145	−	5.89735i	0.359123	−	0.207340i	−0.309573	−	0.950876i	$-0.600186\pi$
$809$	10.2145	−	5.89735i	0.359123	−	0.207340i	0.668696	+	0.743536i	$0.266853\pi$
$810$	−2.69094	−	2.00660i	−0.0945500	−	0.0705046i
$811$	11.7556	+	20.3614i	0.412797	+	0.714985i	0.995194	−	0.0979192i	$-0.0312187\pi$
$811$	11.7556	+	20.3614i	0.412797	+	0.714985i	−0.582398	+	0.812904i	$0.697885\pi$
$812$		−	0.0327082i		−	0.00114783i
$813$	−23.0670	+	28.3053i	−0.808997	+	0.992711i
$814$	9.00364	−	12.8601i	0.315577	−	0.450745i
$815$	2.72757	−	4.72429i	0.0955426	−	0.165485i
$816$	3.49042	+	2.84447i	0.122189	+	0.0995765i
$817$	32.8460	−	56.8909i	1.14914	−	1.99036i
$818$	3.81157	+	6.60183i	0.133268	+	0.230828i
$819$	0.187326	+	0.210662i	0.00654569	+	0.00736111i
$820$			2.69793i			0.0942159i
$821$	16.9663	−	29.3865i	0.592127	−	1.02559i	−0.401818	−	0.915719i	$-0.631622\pi$
$821$	16.9663	−	29.3865i	0.592127	−	1.02559i	0.993945	−	0.109875i	$-0.0350450\pi$
$822$	24.6370	−	9.36961i	0.859313	−	0.326803i
$823$	−9.93334	−	17.2051i	−0.346255	−	0.599731i	0.639326	−	0.768936i	$-0.279213\pi$
$823$	−9.93334	−	17.2051i	−0.346255	−	0.599731i	−0.985581	+	0.169205i	$0.945880\pi$
$824$	−0.297656	+	0.515555i	−0.0103693	+	0.0179602i
$825$	−7.72393	−	20.3097i	−0.268913	−	0.707094i
$826$	0.527744			0.0183626
$827$	−15.8162	+	9.13148i	−0.549982	+	0.317533i	−0.749115	−	0.662440i	$-0.769521\pi$
$827$	−15.8162	+	9.13148i	−0.549982	+	0.317533i	0.199132	+	0.979973i	$0.436188\pi$
$828$	−8.44131	−	9.49288i	−0.293356	−	0.329901i
$829$	−39.8474	−	23.0059i	−1.38396	−	0.799028i	−0.391331	−	0.920250i	$-0.627985\pi$
$829$	−39.8474	−	23.0059i	−1.38396	−	0.799028i	−0.992625	+	0.121223i	$0.961319\pi$
$830$	3.12116			0.108337
$831$	22.1918	+	18.0849i	0.769824	+	0.627358i
$832$		−	2.23210i		−	0.0773843i
$833$		−	18.1927i		−	0.630341i
$834$	−26.2351	+	9.97738i	−0.908446	+	0.345488i
$835$	−4.34979			−0.150531
$836$	−13.2751	−	7.66438i	−0.459129	−	0.265078i
$837$	26.0842	+	40.9970i	0.901603	+	1.41706i
$838$	29.9271	−	17.2784i	1.03381	−	0.596873i
$839$	−12.2387			−0.422525			−0.211263	−	0.977429i	$-0.567758\pi$
$839$	−12.2387			−0.422525			−0.211263	+	0.977429i	$0.567758\pi$
$840$	−0.0171802	+	0.0210817i	−0.000592774	+	0.000727387i
$841$	−14.1982	+	24.5920i	−0.489592	+	0.847999i
$842$	−9.31096	−	16.1271i	−0.320877	−	0.555775i
$843$	0.578175	−	3.57853i	0.0199134	−	0.123251i
$844$	−6.38957	+	11.0671i	−0.219938	+	0.380944i
$845$		−	2.99036i		−	0.102872i
$846$	−29.5233	+	6.08406i	−1.01503	+	0.209174i
$847$	−0.0913381	−	0.158202i	−0.00313842	−	0.00543589i
$848$	3.61144	−	6.25519i	0.124017	−	0.214804i
$849$	−2.69549	+	16.6833i	−0.0925091	+	0.572571i
$850$	−6.31824	+	10.9435i	−0.216714	+	0.375359i
$851$	25.6589	+	2.24342i	0.879576	+	0.0769035i
$852$	−0.421150	−	1.10739i	−0.0144284	−	0.0379387i
$853$		−	17.9609i		−	0.614970i	−0.951553	−	0.307485i	$-0.900513\pi$
$853$		−	17.9609i		−	0.614970i	0.951553	−	0.307485i	$-0.0994874\pi$
$854$	−0.196845	−	0.340946i	−0.00673591	−	0.0116669i
$855$	−1.34134	−	6.50893i	−0.0458728	−	0.222601i
$856$	−8.30148	+	4.79286i	−0.283739	+	0.163817i
$857$	44.5684	−	25.7316i	1.52243	−	0.878975i	0.522780	−	0.852468i	$-0.324895\pi$
$857$	44.5684	−	25.7316i	1.52243	−	0.878975i	0.999649	−	0.0265070i	$-0.00843842\pi$
$858$	−3.54680	−	9.32615i	−0.121086	−	0.318389i
$859$	−6.87771	−	3.97085i	−0.234664	−	0.135484i	0.378058	−	0.925782i	$-0.376592\pi$
$859$	−6.87771	−	3.97085i	−0.234664	−	0.135484i	−0.612722	+	0.790299i	$0.709925\pi$
$860$	2.06257	+	3.57247i	0.0703330	+	0.121820i
$861$	−0.333207	+	0.408875i	−0.0113557	+	0.0139344i
$862$	−10.7429	−	18.6073i	−0.365905	−	0.633767i
$863$	12.2981	−	21.3010i	0.418634	−	0.725095i	−0.577169	−	0.816625i	$-0.695842\pi$
$863$	12.2981	−	21.3010i	0.418634	−	0.725095i	0.995802	+	0.0915301i	$0.0291758\pi$
$864$	−2.40201	+	4.60764i	−0.0817182	+	0.156755i
$865$			0.0218078i			0.000741486i
$866$			30.8001i			1.04663i
$867$	6.30587	+	16.5810i	0.214159	+	0.563121i
$868$	0.340937	−	0.196840i	0.0115721	−	0.00668118i
$869$		−	10.1298i		−	0.343631i
$870$	−0.469129	+	0.178413i	−0.0159050	+	0.00604877i
$871$			5.18259i			0.175605i
$872$	−4.62508	+	8.01087i	−0.156625	+	0.271282i
$873$	−17.4166	+	3.58915i	−0.589462	+	0.121474i
$874$		−	25.1500i		−	0.850711i
$875$	−0.134086	−	0.0774147i	−0.00453294	−	0.00261709i
$876$	22.5272	+	3.63968i	0.761125	+	0.122973i
$877$	−6.30917	+	10.9278i	−0.213046	+	0.369006i	−0.952666	−	0.304018i	$-0.901672\pi$
$877$	−6.30917	+	10.9278i	−0.213046	+	0.369006i	0.739621	+	0.673024i	$0.235005\pi$
$878$	−14.8047	+	25.6425i	−0.499635	+	0.865393i
$879$	2.36194	+	0.381613i	0.0796661	+	0.0128715i
$880$	0.833612	−	0.481286i	0.0281011	−	0.0162242i
$881$	−6.02320	−	10.4325i	−0.202927	−	0.351480i	0.746543	−	0.665337i	$-0.231712\pi$
$881$	−6.02320	−	10.4325i	−0.202927	−	0.351480i	−0.949470	+	0.313857i	$0.898379\pi$
$882$	20.5626	−	4.23747i	0.692379	−	0.142683i
$883$	−10.3476	+	5.97418i	−0.348224	+	0.201047i	−0.663903	−	0.747819i	$-0.731101\pi$
$883$	−10.3476	+	5.97418i	−0.348224	+	0.201047i	0.315679	+	0.948866i	$0.397768\pi$
$884$	−2.90131	+	5.02522i	−0.0975817	+	0.169016i
$885$	−2.87868	−	7.56937i	−0.0967659	−	0.254442i
$886$	1.56305	−	0.902430i	0.0525119	−	0.0303177i
$887$	20.6333	−	35.7380i	0.692800	−	1.19996i	−0.278117	−	0.960547i	$-0.589710\pi$
$887$	20.6333	−	35.7380i	0.692800	−	1.19996i	0.970917	−	0.239417i	$-0.0769563\pi$
$888$	−2.87313	−	10.1363i	−0.0964161	−	0.340153i
$889$	0.0537280	+	0.0930596i	0.00180198	+	0.00312112i
$890$	−2.09992	−	1.21239i	−0.0703896	−	0.0406394i
$891$	−2.71456	+	23.0684i	−0.0909412	+	0.772819i
$892$	14.1726	+	24.5477i	0.474534	+	0.821917i
$893$	−51.6836	−	29.8395i	−1.72952	−	0.998542i
$894$	0.475724	+	0.387685i	0.0159106	+	0.0129661i
$895$	3.16776			0.105887
$896$	0.0364581	+	0.0210491i	0.00121798	+	0.000703202i
$897$	10.3418	−	12.6903i	0.345303	−	0.423718i
$898$	18.9232	+	32.7760i	0.631476	+	1.09375i
$899$	7.26560			0.242321
$900$	−13.8407	−	4.59231i	−0.461357	−	0.153077i
$901$	−16.2611	+	9.38837i	−0.541737	+	0.312772i
$902$	16.1677	−	9.33445i	0.538327	−	0.310803i
$903$	−0.128632	+	0.796149i	−0.00428061	+	0.0264942i
$904$	−7.67987	−	13.3019i	−0.255429	−	0.442416i
$905$	5.19607	−	2.99995i	0.172723	−	0.0997219i
$906$	−9.25580	−	7.54289i	−0.307503	−	0.250596i
$907$	−19.3749	−	11.1861i	−0.643332	−	0.371428i	0.142565	−	0.989785i	$-0.454465\pi$
$907$	−19.3749	−	11.1861i	−0.643332	−	0.371428i	−0.785897	+	0.618358i	$0.787798\pi$
$908$	0.708998	+	0.409340i	0.0235289	+	0.0135844i
$909$	5.84136	+	28.3456i	0.193746	+	0.940164i
$910$	−0.0303516	−	0.0175235i	−0.00100615	−	0.000580899i
$911$	−42.7829	+	24.7007i	−1.41746	+	0.818371i	−0.996075	−	0.0885116i	$-0.971789\pi$
$911$	−42.7829	+	24.7007i	−1.41746	+	0.818371i	−0.421384	+	0.906882i	$0.638456\pi$
$912$	−9.61555	+	3.65686i	−0.318403	+	0.121091i
$913$	−10.7988	−	18.7040i	−0.357387	−	0.619012i
$914$	7.49278	−	12.9779i	0.247839	−	0.429270i
$915$	−3.81642	+	4.68309i	−0.126167	+	0.154818i
$916$	17.3120			0.572004
$917$		−	0.477382i		−	0.0157646i
$918$	11.3968	−	7.25119i	0.376151	−	0.239325i
$919$		−	23.9475i		−	0.789956i	−0.918691	−	0.394978i	$-0.870752\pi$
$919$		−	23.9475i		−	0.789956i	0.918691	−	0.394978i	$-0.129248\pi$
$920$	1.36771	+	0.789649i	0.0450921	+	0.0260339i
$921$	38.2621	+	6.18192i	1.26078	+	0.203701i
$922$	17.8177			0.586794
$923$	1.32227	−	0.763413i	0.0435230	−	0.0251280i
$924$	0.185776	+	0.0300154i	0.00611158	+	0.000987435i
$925$	26.7967	−	12.4973i	0.881070	−	0.410910i
$926$	23.2712			0.764739
$927$	1.18676	+	1.33460i	0.0389783	+	0.0438340i
$928$	0.388474	+	0.672857i	0.0127523	+	0.0220876i
$929$	5.88326	−	10.1901i	0.193024	−	0.334327i	−0.753227	−	0.657760i	$-0.771504\pi$
$929$	5.88326	−	10.1901i	0.193024	−	0.334327i	0.946251	+	0.323434i	$0.104837\pi$
$930$	−4.68296	−	3.81631i	−0.153560	−	0.125142i
$931$	35.9969	+	20.7828i	1.17975	+	0.681130i
$932$	9.20929			0.301660
$933$	45.9223	−	17.4646i	1.50343	−	0.571765i
$934$	−17.6430			−0.577297
$935$	−2.50232			−0.0818347
$936$	−6.35560	−	2.10877i	−0.207739	−	0.0689273i
$937$	−3.04601	+	5.27585i	−0.0995090	+	0.172355i	−0.911482	−	0.411341i	$-0.865061\pi$
$937$	−3.04601	+	5.27585i	−0.0995090	+	0.172355i	0.811973	+	0.583696i	$0.198394\pi$
$938$	−0.0846500	−	0.0488727i	−0.00276392	−	0.00159575i
$939$	3.81497	−	23.6122i	0.124497	−	0.770555i
$940$	3.24548	−	1.87378i	0.105856	−	0.0611159i
$941$	4.01840	+	6.96008i	0.130996	+	0.226892i	0.924061	−	0.382245i	$-0.124849\pi$
$941$	4.01840	+	6.96008i	0.130996	+	0.226892i	−0.793065	+	0.609137i	$0.791516\pi$
$942$	18.7141	−	7.11709i	0.609738	−	0.231887i
$943$	26.5265	+	15.3151i	0.863822	+	0.498728i
$944$	−10.8565	+	6.26801i	−0.353349	+	0.204006i
$945$	0.0437962	+	0.0688351i	0.00142469	+	0.00223921i
$946$	14.2724	−	24.7205i	0.464035	−	0.803731i
$947$		−	20.8482i		−	0.677476i	−0.940881	−	0.338738i	$-0.890000\pi$
$947$		−	20.8482i		−	0.677476i	0.940881	−	0.338738i	$-0.110000\pi$
$948$	−5.26999	−	4.29471i	−0.171161	−	0.139486i
$949$			29.4074i			0.954606i
$950$	−14.4355	−	25.0031i	−0.468351	−	0.811207i
$951$	−12.5176	−	2.02244i	−0.405911	−	0.0655822i
$952$	−0.0547197	−	0.0947774i	−0.00177348	−	0.00307175i
$953$	20.3122	−	35.1818i	0.657978	−	1.13965i	−0.323161	−	0.946344i	$-0.604745\pi$
$953$	20.3122	−	35.1818i	0.657978	−	1.13965i	0.981138	−	0.193307i	$-0.0619212\pi$
$954$	−14.3989	−	16.1926i	−0.466181	−	0.524256i
$955$	1.53170	+	2.65299i	0.0495647	+	0.0858486i
$956$	2.00849	−	1.15960i	0.0649591	−	0.0375042i
$957$	2.69228	+	2.19404i	0.0870292	+	0.0709233i
$958$	1.87253			0.0604988
$959$	−0.640655			−0.0206878
$960$	0.103037	−	0.637732i	0.00332550	−	0.0205827i
$961$	28.2248	+	48.8868i	0.910478	+	1.57699i
$962$	12.3049	−	5.73872i	0.396727	−	0.185024i
$963$	5.80421	+	28.1653i	0.187038	+	0.907615i
$964$	5.75406	+	3.32211i	0.185326	+	0.106998i
$965$	−3.59150	+	6.22066i	−0.115615	+	0.200250i
$966$	0.109753	+	0.288591i	0.00353125	+	0.00928525i
$967$			0.593848i			0.0190969i	0.999954	+	0.00954843i	$0.00303941\pi$
$967$			0.593848i			0.0190969i	−0.999954	+	0.00954843i	$0.996961\pi$
$968$	3.75793	+	2.16964i	0.120784	+	0.0697349i
$969$	26.4011	+	4.26557i	0.848125	+	0.137030i
$970$	1.91459	−	1.10539i	0.0614739	−	0.0354920i
$971$	3.85800	−	6.68226i	0.123809	−	0.214444i	−0.797458	−	0.603375i	$-0.793822\pi$
$971$	3.85800	−	6.68226i	0.123809	−	0.214444i	0.921267	+	0.388931i	$0.127156\pi$
$972$	10.8503	+	11.1924i	0.348024	+	0.358998i
$973$	0.682211			0.0218707
$974$	−5.36851			−0.172018
$975$	2.99744	−	18.5522i	0.0959949	−	0.594146i
$976$	8.09882	+	4.67586i	0.259237	+	0.149670i
$977$	26.0268	−	15.0266i	0.832671	−	0.480743i	−0.0220950	−	0.999756i	$-0.507034\pi$
$977$	26.0268	−	15.0266i	0.832671	−	0.480743i	0.854766	+	0.519013i	$0.173700\pi$
$978$	−16.0039	+	19.6382i	−0.511747	+	0.627959i
$979$			16.7788i			0.536252i
$980$	−2.26043	+	1.30506i	−0.0722069	+	0.0416887i
$981$	18.4403	+	20.7375i	0.588753	+	0.662097i
$982$	−33.2859	−	19.2176i	−1.06220	−	0.613259i
$983$	13.5572			0.432408			0.216204	−	0.976348i	$-0.430632\pi$
$983$	13.5572			0.432408			0.216204	+	0.976348i	$0.430632\pi$
$984$	1.99838	−	12.3687i	0.0637061	−	0.394299i
$985$	0.158776	+	0.0916694i	0.00505902	+	0.00292083i
$986$		−	2.01977i		−	0.0643226i
$987$	0.723276	+	0.116858i	0.0230221	+	0.00371964i
$988$	−6.62874	−	11.4813i	−0.210888	−	0.365269i
$989$	46.8335			1.48922
$990$	−0.582843	−	2.82829i	−0.0185240	−	0.0898889i
$991$		−	16.5362i		−	0.525288i	−0.964893	−	0.262644i	$-0.915405\pi$
$991$		−	16.5362i		−	0.525288i	0.964893	−	0.262644i	$-0.0845945\pi$
$992$	−4.67573	+	8.09859i	−0.148454	+	0.257131i
$993$	3.67097	−	22.7209i	0.116495	−	0.721026i
$994$			0.0287964i			0.000913368i
$995$	4.06302			0.128806
$996$	−14.3090	−	2.31187i	−0.453397	−	0.0732544i
$997$		−	20.2725i		−	0.642037i	−0.947073	−	0.321019i	$-0.895975\pi$
$997$		−	20.2725i		−	0.642037i	0.947073	−	0.321019i	$-0.104025\pi$
$998$	3.32725			0.105322
$999$	−31.5761	−	1.39540i	−0.999025	−	0.0441486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.1	✓	76
3.2	odd	2		1998.2.k.a.1063.32		76
9.2	odd	6		1998.2.t.a.397.33		76
9.7	even	3		666.2.t.a.619.13	yes	76
37.11	even	6		666.2.t.a.85.13	yes	76
111.11	odd	6		1998.2.t.a.307.33		76
333.11	odd	6		1998.2.k.a.1639.7		76
333.196	even	6	inner	666.2.k.a.529.20	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.1	✓	76	1.1	even	1	trivial
666.2.k.a.529.20	yes	76	333.196	even	6	inner
666.2.t.a.85.13	yes	76	37.11	even	6
666.2.t.a.619.13	yes	76	9.7	even	3
1998.2.k.a.1063.32		76	3.2	odd	2
1998.2.k.a.1639.7		76	333.11	odd	6
1998.2.t.a.307.33		76	111.11	odd	6
1998.2.t.a.397.33		76	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.70988 - 0.276261i) q^{3} -1.00000 q^{4} -0.372969i q^{5} +(-0.276261 + 1.70988i) q^{6} +(0.0210491 - 0.0364581i) q^{7} +1.00000i q^{8} +(2.84736 + 0.944746i) q^{9} -0.372969 q^{10} +(1.29042 + 2.23507i) q^{11} +(1.70988 + 0.276261i) q^{12} +2.23210i q^{13} +(-0.0364581 - 0.0210491i) q^{14} +(-0.103037 + 0.637732i) q^{15} +1.00000 q^{16} +(-2.25134 - 1.29981i) q^{17} +(0.944746 - 2.84736i) q^{18} +(5.14372 - 2.96973i) q^{19} +0.372969i q^{20} +(-0.0460634 + 0.0565239i) q^{21} +(2.23507 - 1.29042i) q^{22} +(3.66709 + 2.11720i) q^{23} +(0.276261 - 1.70988i) q^{24} +4.86089 q^{25} +2.23210 q^{26} +(-4.60764 - 2.40201i) q^{27} +(-0.0210491 + 0.0364581i) q^{28} +(-0.672857 + 0.388474i) q^{29} +(0.637732 + 0.103037i) q^{30} +(-8.09859 - 4.67573i) q^{31} -1.00000i q^{32} +(-1.58899 - 4.17819i) q^{33} +(-1.29981 + 2.25134i) q^{34} +(-0.0135978 - 0.00785067i) q^{35} +(-2.84736 - 0.944746i) q^{36} +(5.51271 - 2.57099i) q^{37} +(-2.96973 - 5.14372i) q^{38} +(0.616644 - 3.81662i) q^{39} +0.372969 q^{40} +7.23366 q^{41} +(0.0565239 + 0.0460634i) q^{42} +(9.57847 - 5.53013i) q^{43} +(-1.29042 - 2.23507i) q^{44} +(0.352361 - 1.06198i) q^{45} +(2.11720 - 3.66709i) q^{46} +(-5.02395 - 8.70173i) q^{47} +(-1.70988 - 0.276261i) q^{48} +(3.49911 + 6.06064i) q^{49} -4.86089i q^{50} +(3.49042 + 2.84447i) q^{51} -2.23210i q^{52} +(3.61144 - 6.25519i) q^{53} +(-2.40201 + 4.60764i) q^{54} +(0.833612 - 0.481286i) q^{55} +(0.0364581 + 0.0210491i) q^{56} +(-9.61555 + 3.65686i) q^{57} +(0.388474 + 0.672857i) q^{58} +(-10.8565 + 6.26801i) q^{59} +(0.103037 - 0.637732i) q^{60} +(8.09882 + 4.67586i) q^{61} +(-4.67573 + 8.09859i) q^{62} +(0.0943781 - 0.0839234i) q^{63} -1.00000 q^{64} +0.832506 q^{65} +(-4.17819 + 1.58899i) q^{66} +2.32184 q^{67} +(2.25134 + 1.29981i) q^{68} +(-5.68537 - 4.63322i) q^{69} +(-0.00785067 + 0.0135978i) q^{70} +(-0.342015 - 0.592387i) q^{71} +(-0.944746 + 2.84736i) q^{72} +13.1748 q^{73} +(-2.57099 - 5.51271i) q^{74} +(-8.31153 - 1.34288i) q^{75} +(-5.14372 + 2.96973i) q^{76} +0.108649 q^{77} +(-3.81662 - 0.616644i) q^{78} +(-3.39917 - 1.96251i) q^{79} -0.372969i q^{80} +(7.21491 + 5.38006i) q^{81} -7.23366i q^{82} -8.36842 q^{83} +(0.0460634 - 0.0565239i) q^{84} +(-0.484789 + 0.839680i) q^{85} +(-5.53013 - 9.57847i) q^{86} +(1.25782 - 0.478359i) q^{87} +(-2.23507 + 1.29042i) q^{88} +(5.63029 + 3.25065i) q^{89} +(-1.06198 - 0.352361i) q^{90} +(0.0813784 + 0.0469838i) q^{91} +(-3.66709 - 2.11720i) q^{92} +(12.5559 + 10.2322i) q^{93} +(-8.70173 + 5.02395i) q^{94} +(-1.10762 - 1.91845i) q^{95} +(-0.276261 + 1.70988i) q^{96} +(-5.13338 + 2.96376i) q^{97} +(6.06064 - 3.49911i) q^{98} +(1.56271 + 7.58316i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

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