LMFDB - Embedded newform 189.2.u.a.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			67.3
Character	$\chi$	$=$	189.67
Dual form			189.2.u.a.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65649 + 1.38996i) q^{2} +(1.69272 - 0.367032i) q^{3} +(0.464676 - 2.63531i) q^{4} +(-0.583375 + 3.30848i) q^{5} +(-2.29381 + 2.96080i) q^{6} +(-2.62399 - 0.338628i) q^{7} +(0.730849 + 1.26587i) q^{8} +(2.73057 - 1.24256i) q^{9} +O(q^{10})$	\(q+(-1.65649 + 1.38996i) q^{2} +(1.69272 - 0.367032i) q^{3} +(0.464676 - 2.63531i) q^{4} +(-0.583375 + 3.30848i) q^{5} +(-2.29381 + 2.96080i) q^{6} +(-2.62399 - 0.338628i) q^{7} +(0.730849 + 1.26587i) q^{8} +(2.73057 - 1.24256i) q^{9} +(-3.63231 - 6.29135i) q^{10} +(0.801854 + 4.54754i) q^{11} +(-0.180679 - 4.63138i) q^{12} +(-0.768974 + 4.36107i) q^{13} +(4.81730 - 3.08631i) q^{14} +(0.226832 + 5.81444i) q^{15} +(2.05901 + 0.749418i) q^{16} +(-1.47618 - 2.55683i) q^{17} +(-2.79606 + 5.85369i) q^{18} +(0.419551 - 0.726683i) q^{19} +(8.44779 + 3.07474i) q^{20} +(-4.56596 + 0.389888i) q^{21} +(-7.64917 - 6.41842i) q^{22} +(-1.89877 - 1.59326i) q^{23} +(1.70173 + 1.87451i) q^{24} +(-5.90727 - 2.15007i) q^{25} +(-4.78792 - 8.29293i) q^{26} +(4.16603 - 3.10551i) q^{27} +(-2.11170 + 6.75767i) q^{28} +(0.980067 + 5.55823i) q^{29} +(-8.45760 - 9.31629i) q^{30} +(0.519624 - 2.94694i) q^{31} +(-7.19949 + 2.62040i) q^{32} +(3.02640 + 7.40338i) q^{33} +(5.99918 + 2.18352i) q^{34} +(2.65112 - 8.48388i) q^{35} +(-2.00570 - 7.77329i) q^{36} +7.87320 q^{37} +(0.315079 + 1.78690i) q^{38} +(0.298998 + 7.66429i) q^{39} +(-4.61446 + 1.67953i) q^{40} +(-0.459534 + 2.60615i) q^{41} +(7.02155 - 6.99236i) q^{42} +(6.80164 - 5.70725i) q^{43} +12.3568 q^{44} +(2.51805 + 9.75894i) q^{45} +5.35987 q^{46} +(-0.237244 - 1.34548i) q^{47} +(3.76038 + 0.512829i) q^{48} +(6.77066 + 1.77711i) q^{49} +(12.7739 - 4.64931i) q^{50} +(-3.43720 - 3.78617i) q^{51} +(11.1354 + 4.05297i) q^{52} +(5.27760 - 9.14106i) q^{53} +(-2.58444 + 10.9349i) q^{54} -15.5132 q^{55} +(-1.48908 - 3.56911i) q^{56} +(0.443464 - 1.38406i) q^{57} +(-9.34921 - 7.84492i) q^{58} +(7.59585 - 2.76466i) q^{59} +(15.4282 + 2.10406i) q^{60} +(1.28719 + 7.30000i) q^{61} +(3.23538 + 5.60384i) q^{62} +(-7.58577 + 2.33582i) q^{63} +(6.09249 - 10.5525i) q^{64} +(-13.9799 - 5.08828i) q^{65} +(-15.3036 - 8.05706i) q^{66} +(1.59861 + 1.34139i) q^{67} +(-7.42397 + 2.70210i) q^{68} +(-3.79886 - 2.00002i) q^{69} +(7.40072 + 17.7384i) q^{70} +(-2.56447 + 4.44179i) q^{71} +(3.56856 + 2.54842i) q^{72} -2.61768 q^{73} +(-13.0419 + 10.9435i) q^{74} +(-10.7885 - 1.47130i) q^{75} +(-1.72008 - 1.44332i) q^{76} +(-0.564133 - 12.2042i) q^{77} +(-11.1484 - 12.2802i) q^{78} +(6.89183 - 5.78293i) q^{79} +(-3.68061 + 6.37500i) q^{80} +(5.91208 - 6.78582i) q^{81} +(-2.86123 - 4.95580i) q^{82} +(-1.36872 - 7.76242i) q^{83} +(-1.09422 + 12.2139i) q^{84} +(9.32038 - 3.39234i) q^{85} +(-3.33400 + 18.9080i) q^{86} +(3.69903 + 9.04880i) q^{87} +(-5.17055 + 4.33861i) q^{88} +(4.68139 - 8.10841i) q^{89} +(-17.7357 - 12.6656i) q^{90} +(3.49456 - 11.1830i) q^{91} +(-5.08104 + 4.26350i) q^{92} +(-0.202044 - 5.17905i) q^{93} +(2.26316 + 1.89901i) q^{94} +(2.15946 + 1.81200i) q^{95} +(-11.2249 + 7.07804i) q^{96} +(-8.71278 + 7.31089i) q^{97} +(-13.6857 + 6.46719i) q^{98} +(7.84012 + 11.4210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.65649	+	1.38996i	−1.17132	+	0.982852i	−0.999997	−	0.00236379i	$-0.999248\pi$
$2$	−1.65649	+	1.38996i	−1.17132	+	0.982852i	−0.171320	+	0.985215i	$0.554803\pi$
$3$	1.69272	−	0.367032i	0.977290	−	0.211906i
$3$	1.69272	−	0.367032i	0.977290	−	0.211906i
$4$	0.464676	−	2.63531i	0.232338	−	1.31765i
$5$	−0.583375	+	3.30848i	−0.260893	+	1.47960i	0.519587	+	0.854418i	$0.326086\pi$
$5$	−0.583375	+	3.30848i	−0.260893	+	1.47960i	−0.780480	+	0.625181i	$0.785025\pi$
$6$	−2.29381	+	2.96080i	−0.936444	+	1.20874i
$7$	−2.62399	−	0.338628i	−0.991776	−	0.127989i
$7$	−2.62399	−	0.338628i	−0.991776	−	0.127989i
$8$	0.730849	+	1.26587i	0.258394	+	0.447552i
$9$	2.73057	−	1.24256i	0.910192	−	0.414188i
$10$	−3.63231	−	6.29135i	−1.14864	−	1.98950i
$11$	0.801854	+	4.54754i	0.241768	+	1.37113i	0.827880	+	0.560905i	$0.189547\pi$
$11$	0.801854	+	4.54754i	0.241768	+	1.37113i	−0.586112	+	0.810230i	$0.699342\pi$
$12$	−0.180679	−	4.63138i	−0.0521575	−	1.33696i
$13$	−0.768974	+	4.36107i	−0.213275	+	1.20954i	0.670600	+	0.741820i	$0.266037\pi$
$13$	−0.768974	+	4.36107i	−0.213275	+	1.20954i	−0.883875	+	0.467724i	$0.845074\pi$
$14$	4.81730	−	3.08631i	1.28748	−	0.824852i
$15$	0.226832	+	5.81444i	0.0585678	+	1.50128i
$16$	2.05901	+	0.749418i	0.514752	+	0.187354i
$17$	−1.47618	−	2.55683i	−0.358027	−	0.620121i	0.629604	−	0.776916i	$-0.283217\pi$
$17$	−1.47618	−	2.55683i	−0.358027	−	0.620121i	−0.987631	+	0.156795i	$0.949884\pi$
$18$	−2.79606	+	5.85369i	−0.659038	+	1.37973i
$19$	0.419551	−	0.726683i	0.0962515	−	0.166713i	−0.813879	−	0.581035i	$-0.802648\pi$
$19$	0.419551	−	0.726683i	0.0962515	−	0.166713i	0.910130	+	0.414322i	$0.135981\pi$
$20$	8.44779	+	3.07474i	1.88898	+	0.687534i
$21$	−4.56596	+	0.389888i	−0.996374	+	0.0850806i
$22$	−7.64917	−	6.41842i	−1.63081	−	1.36841i
$23$	−1.89877	−	1.59326i	−0.395921	−	0.332217i	0.422994	−	0.906133i	$-0.360979\pi$
$23$	−1.89877	−	1.59326i	−0.395921	−	0.332217i	−0.818914	+	0.573916i	$0.805424\pi$
$24$	1.70173	+	1.87451i	0.347365	+	0.382633i
$25$	−5.90727	−	2.15007i	−1.18145	−	0.430014i
$26$	−4.78792	−	8.29293i	−0.938989	−	1.62638i
$27$	4.16603	−	3.10551i	0.801752	−	0.597657i
$28$	−2.11170	+	6.75767i	−0.399073	+	1.27708i
$29$	0.980067	+	5.55823i	0.181994	+	1.03214i	0.929757	+	0.368173i	$0.120017\pi$
$29$	0.980067	+	5.55823i	0.181994	+	1.03214i	−0.747764	+	0.663965i	$0.768872\pi$
$30$	−8.45760	−	9.31629i	−1.54414	−	1.70091i
$31$	0.519624	−	2.94694i	0.0933273	−	0.529285i	−0.901920	−	0.431904i	$-0.857842\pi$
$31$	0.519624	−	2.94694i	0.0933273	−	0.529285i	0.995247	−	0.0973819i	$-0.0310468\pi$
$32$	−7.19949	+	2.62040i	−1.27270	+	0.463226i
$33$	3.02640	+	7.40338i	0.526829	+	1.28876i
$34$	5.99918	+	2.18352i	1.02885	+	0.374471i
$35$	2.65112	−	8.48388i	0.448120	−	1.43404i
$36$	−2.00570	−	7.77329i	−0.334284	−	1.29555i
$37$	7.87320			1.29435			0.647173	−	0.762343i	$-0.275951\pi$
$37$	7.87320			1.29435			0.647173	+	0.762343i	$0.275951\pi$
$38$	0.315079	+	1.78690i	0.0511126	+	0.289874i
$39$	0.298998	+	7.66429i	0.0478780	+	1.22727i
$40$	−4.61446	+	1.67953i	−0.729610	+	0.265556i
$41$	−0.459534	+	2.60615i	−0.0717671	+	0.407012i	0.927668	+	0.373406i	$0.121810\pi$
$41$	−0.459534	+	2.60615i	−0.0717671	+	0.407012i	−0.999435	+	0.0336057i	$0.989301\pi$
$42$	7.02155	−	6.99236i	1.08345	−	1.07894i
$43$	6.80164	−	5.70725i	1.03724	−	0.870348i	0.0455457	−	0.998962i	$-0.485497\pi$
$43$	6.80164	−	5.70725i	1.03724	−	0.870348i	0.991695	+	0.128614i	$0.0410529\pi$
$44$	12.3568			1.86285
$45$	2.51805	+	9.75894i	0.375369	+	1.45478i
$46$	5.35987			0.790269
$47$	−0.237244	−	1.34548i	−0.0346056	−	0.196258i	0.962604	−	0.270913i	$-0.0873256\pi$
$47$	−0.237244	−	1.34548i	−0.0346056	−	0.196258i	−0.997209	+	0.0746549i	$0.976214\pi$
$48$	3.76038	+	0.512829i	0.542764	+	0.0740205i
$49$	6.77066	+	1.77711i	0.967237	+	0.253874i
$50$	12.7739	−	4.64931i	1.80650	−	0.657511i
$51$	−3.43720	−	3.78617i	−0.481304	−	0.530170i
$52$	11.1354	+	4.05297i	1.54421	+	0.562046i
$53$	5.27760	−	9.14106i	0.724934	−	1.25562i	−0.234068	−	0.972220i	$-0.575204\pi$
$53$	5.27760	−	9.14106i	0.724934	−	1.25562i	0.959001	−	0.283402i	$-0.0914629\pi$
$54$	−2.58444	+	10.9349i	−0.351698	+	1.48805i
$55$	−15.5132			−2.09180
$56$	−1.48908	−	3.56911i	−0.198987	−	0.476943i
$57$	0.443464	−	1.38406i	0.0587382	−	0.183323i
$58$	−9.34921	−	7.84492i	−1.22761	−	1.03009i
$59$	7.59585	−	2.76466i	0.988895	−	0.359928i	0.203603	−	0.979054i	$-0.434735\pi$
$59$	7.59585	−	2.76466i	0.988895	−	0.359928i	0.785292	+	0.619125i	$0.212513\pi$
$60$	15.4282	+	2.10406i	1.99178	+	0.271633i
$61$	1.28719	+	7.30000i	0.164807	+	0.934670i	0.949263	+	0.314484i	$0.101832\pi$
$61$	1.28719	+	7.30000i	0.164807	+	0.934670i	−0.784455	+	0.620185i	$0.787057\pi$
$62$	3.23538	+	5.60384i	0.410893	+	0.711688i
$63$	−7.58577	+	2.33582i	−0.955717	+	0.294286i
$64$	6.09249	−	10.5525i	0.761561	−	1.31906i
$65$	−13.9799	−	5.08828i	−1.73400	−	0.631123i
$66$	−15.3036	−	8.05706i	−1.88375	−	0.991756i
$67$	1.59861	+	1.34139i	0.195301	+	0.163877i	0.735194	−	0.677856i	$-0.237091\pi$
$67$	1.59861	+	1.34139i	0.195301	+	0.163877i	−0.539893	+	0.841734i	$0.681535\pi$
$68$	−7.42397	+	2.70210i	−0.900289	+	0.327678i
$69$	−3.79886	−	2.00002i	−0.457328	−	0.240774i
$70$	7.40072	+	17.7384i	0.884556	+	2.12015i
$71$	−2.56447	+	4.44179i	−0.304347	+	0.527144i	−0.977116	−	0.212709i	$-0.931771\pi$
$71$	−2.56447	+	4.44179i	−0.304347	+	0.527144i	0.672769	+	0.739853i	$0.265105\pi$
$72$	3.56856	+	2.54842i	0.420559	+	0.300334i
$73$	−2.61768			−0.306376			−0.153188	−	0.988197i	$-0.548954\pi$
$73$	−2.61768			−0.306376			−0.153188	+	0.988197i	$0.548954\pi$
$74$	−13.0419	+	10.9435i	−1.51609	+	1.27215i
$75$	−10.7885	−	1.47130i	−1.24575	−	0.169891i
$76$	−1.72008	−	1.44332i	−0.197307	−	0.165560i
$77$	−0.564133	−	12.2042i	−0.0642889	−	1.39080i
$78$	−11.1484	−	12.2802i	−1.26230	−	1.39046i
$79$	6.89183	−	5.78293i	0.775391	−	0.650630i	−0.166692	−	0.986009i	$-0.553309\pi$
$79$	6.89183	−	5.78293i	0.775391	−	0.650630i	0.942083	+	0.335379i	$0.108864\pi$
$80$	−3.68061	+	6.37500i	−0.411505	+	0.712747i
$81$	5.91208	−	6.78582i	0.656897	−	0.753980i
$82$	−2.86123	−	4.95580i	−0.315970	−	0.547276i
$83$	−1.36872	−	7.76242i	−0.150237	−	0.852036i	−0.963012	−	0.269459i	$-0.913155\pi$
$83$	−1.36872	−	7.76242i	−0.150237	−	0.852036i	0.812775	−	0.582578i	$-0.197956\pi$
$84$	−1.09422	+	12.2139i	−0.119389	+	1.33264i
$85$	9.32038	−	3.39234i	1.01094	−	0.367951i
$86$	−3.33400	+	18.9080i	−0.359514	+	2.03891i
$87$	3.69903	+	9.04880i	0.396577	+	0.970133i
$88$	−5.17055	+	4.33861i	−0.551182	+	0.462497i
$89$	4.68139	−	8.10841i	0.496227	−	0.859490i	−0.503764	−	0.863841i	$-0.668052\pi$
$89$	4.68139	−	8.10841i	0.496227	−	0.859490i	0.999991	+	0.00435144i	$0.00138511\pi$
$90$	−17.7357	−	12.6656i	−1.86951	−	1.33507i
$91$	3.49456	−	11.1830i	0.366330	−	1.17230i
$92$	−5.08104	+	4.26350i	−0.529735	+	0.444500i
$93$	−0.202044	−	5.17905i	−0.0209510	−	0.537042i
$94$	2.26316	+	1.89901i	0.233427	+	0.195868i
$95$	2.15946	+	1.81200i	0.221556	+	0.185908i
$96$	−11.2249	+	7.07804i	−1.14564	+	0.722399i
$97$	−8.71278	+	7.31089i	−0.884649	+	0.742308i	−0.967130	−	0.254284i	$-0.918160\pi$
$97$	−8.71278	+	7.31089i	−0.884649	+	0.742308i	0.0824809	+	0.996593i	$0.473716\pi$
$98$	−13.6857	+	6.46719i	−1.38246	+	0.653285i
$99$	7.84012	+	11.4210i	0.787962	+	1.14786i
$100$	−8.41106	+	14.5684i	−0.841106	+	1.45684i
$101$	−7.13788	+	5.98939i	−0.710246	+	0.595967i	−0.924668	−	0.380774i	$-0.875658\pi$
$101$	−7.13788	+	5.98939i	−0.710246	+	0.595967i	0.214422	+	0.976741i	$0.431213\pi$
$102$	10.9563	+	1.49419i	1.08484	+	0.147947i
$103$	−1.16238	+	6.59218i	−0.114533	+	0.649547i	0.872448	+	0.488707i	$0.162531\pi$
$103$	−1.16238	+	6.59218i	−0.114533	+	0.649547i	−0.986981	+	0.160840i	$0.948580\pi$
$104$	−6.08254	+	2.21386i	−0.596442	+	0.217087i
$105$	1.37373	−	15.3339i	0.134062	−	1.49643i
$106$	3.96344	+	22.4778i	0.384963	+	2.18323i
$107$	3.06775	+	5.31350i	0.296571	+	0.513676i	0.975349	−	0.220667i	$-0.0708236\pi$
$107$	3.06775	+	5.31350i	0.296571	+	0.513676i	−0.678778	+	0.734343i	$0.737490\pi$
$108$	−6.24814	−	12.4218i	−0.601227	−	1.19529i
$109$	−7.83322	+	13.5675i	−0.750286	+	1.29953i	0.197398	+	0.980324i	$0.436751\pi$
$109$	−7.83322	+	13.5675i	−0.750286	+	1.29953i	−0.947684	+	0.319210i	$0.896582\pi$
$110$	25.6976	−	21.5628i	2.45017	−	2.05593i
$111$	13.3271	−	2.88972i	1.26495	−	0.274280i
$112$	−5.14905	−	2.66370i	−0.486539	−	0.251696i
$113$	−7.99538	−	6.70892i	−0.752142	−	0.631122i	0.183926	−	0.982940i	$-0.441119\pi$
$113$	−7.99538	−	6.70892i	−0.752142	−	0.631122i	−0.936069	+	0.351818i	$0.885564\pi$
$114$	1.18919	+	2.90908i	0.111378	+	0.272460i
$115$	6.37896	−	5.35258i	0.594841	−	0.499131i
$116$	15.1031			1.40229
$117$	3.31916	+	12.8637i	0.306857	+	1.18925i
$118$	−8.73969	+	15.1376i	−0.804553	+	1.39353i
$119$	3.00768	+	7.20897i	0.275714	+	0.660845i
$120$	−7.19453	+	4.53662i	−0.656768	+	0.414135i
$121$	−9.70051	+	3.53070i	−0.881865	+	0.320973i
$122$	−12.2789	−	10.3033i	−1.11168	−	0.932813i
$123$	0.178679	+	4.58013i	0.0161110	+	0.412976i
$124$	−7.52463	−	2.73874i	−0.675732	−	0.245946i
$125$	2.16082	−	3.74265i	0.193270	−	0.334753i
$126$	9.31906	−	14.4132i	0.830208	−	1.28403i
$127$	0.0905653	+	0.156864i	0.00803637	+	0.0139194i	0.870016	−	0.493024i	$-0.164109\pi$
$127$	0.0905653	+	0.156864i	0.00803637	+	0.0139194i	−0.861979	+	0.506944i	$0.830775\pi$
$128$	1.91459	+	10.8582i	0.169228	+	0.959738i
$129$	9.41850	−	12.1572i	0.829253	−	1.07038i
$130$	30.2302	−	11.0029i	2.65136	−	0.965016i
$131$	−10.6507	−	8.93697i	−0.930553	−	0.780827i	0.0453635	−	0.998971i	$-0.485555\pi$
$131$	−10.6507	−	8.93697i	−0.930553	−	0.780827i	−0.975917	+	0.218144i	$0.930000\pi$
$132$	20.9165	−	4.53533i	1.82055	−	0.394750i
$133$	−1.34697	+	1.76474i	−0.116797	+	0.153022i
$134$	−4.51257			−0.389827
$135$	7.84419	+	15.5949i	0.675120	+	1.34220i
$136$	2.15774	−	3.73731i	0.185024	−	0.320471i
$137$	−0.154017	−	0.0560576i	−0.0131585	−	0.00478932i	0.335432	−	0.942064i	$-0.391118\pi$
$137$	−0.154017	−	0.0560576i	−0.0131585	−	0.00478932i	−0.348591	+	0.937275i	$0.613340\pi$
$138$	9.07273	−	1.96724i	0.772322	−	0.167463i
$139$	1.63872	−	0.596444i	0.138994	−	0.0505897i	−0.271586	−	0.962414i	$-0.587548\pi$
$139$	1.63872	−	0.596444i	0.138994	−	0.0505897i	0.410581	+	0.911824i	$0.365326\pi$
$140$	−21.1257	−	10.9288i	−1.78545	−	0.923649i
$141$	−0.895421	−	2.19044i	−0.0754081	−	0.184468i
$142$	−1.92590	−	10.9223i	−0.161618	−	0.916580i
$143$	−20.4487			−1.71001
$144$	6.55348	−	0.512106i	0.546123	−	0.0426755i
$145$	−18.9611			−1.57463
$146$	4.33617	−	3.63848i	0.358864	−	0.301123i
$147$	12.1131	+	0.523099i	0.999069	+	0.0431445i
$148$	3.65849	−	20.7483i	0.300726	−	1.70550i
$149$	9.95059	−	3.62172i	0.815184	−	0.296703i	0.0994208	−	0.995045i	$-0.468301\pi$
$149$	9.95059	−	3.62172i	0.815184	−	0.296703i	0.715764	+	0.698343i	$0.246079\pi$
$150$	19.9161	−	12.5584i	1.62614	−	1.02539i
$151$	−4.15012	−	23.5365i	−0.337732	−	1.91538i	−0.398388	−	0.917217i	$-0.630430\pi$
$151$	−4.15012	−	23.5365i	−0.337732	−	1.91538i	0.0606561	−	0.998159i	$-0.480681\pi$
$152$	1.22651			0.0994833
$153$	−7.20785	−	5.14735i	−0.582720	−	0.416139i
$154$	17.8979	+	19.4321i	1.44225	+	1.56588i
$155$	9.44675	+	3.43834i	0.758782	+	0.276174i
$156$	20.3367	+	2.77346i	1.62824	+	0.222054i
$157$	−18.4308	+	6.70827i	−1.47094	+	0.535379i	−0.948356	−	0.317209i	$-0.897254\pi$
$157$	−18.4308	+	6.70827i	−1.47094	+	0.535379i	−0.522585	+	0.852587i	$0.675032\pi$
$158$	−3.37821	+	19.1588i	−0.268756	+	1.52419i
$159$	5.57841	−	17.4103i	0.442396	−	1.38072i
$160$	−4.46955	−	25.3481i	−0.353349	−	2.00394i
$161$	4.44283	+	4.82367i	0.350144	+	0.380158i
$162$	−0.361275	+	19.4582i	−0.0283845	+	1.52878i
$163$	3.91324	+	6.77793i	0.306509	+	0.530889i	0.977596	−	0.210490i	$-0.0675058\pi$
$163$	3.91324	+	6.77793i	0.306509	+	0.530889i	−0.671087	+	0.741378i	$0.734173\pi$
$164$	6.65446	+	2.42203i	0.519626	+	0.189129i
$165$	−26.2595	+	5.69386i	−2.04430	+	0.443266i
$166$	13.0568	+	10.9559i	1.01340	+	0.850344i
$167$	12.9718	+	10.8846i	1.00379	+	0.842279i	0.987505	−	0.157589i	$-0.0503721\pi$
$167$	12.9718	+	10.8846i	1.00379	+	0.842279i	0.0162837	+	0.999867i	$0.494817\pi$
$168$	−3.83057	−	5.49495i	−0.295535	−	0.423945i
$169$	−6.21161	−	2.26084i	−0.477816	−	0.173911i
$170$	−10.7239	+	18.5744i	−0.822487	+	1.42459i
$171$	0.242665	−	2.50558i	0.0185571	−	0.191607i
$172$	−11.8798	−	20.5764i	−0.905827	−	1.56894i
$173$	−6.70217	−	2.43939i	−0.509557	−	0.185463i	0.0744307	−	0.997226i	$-0.476286\pi$
$173$	−6.70217	−	2.43939i	−0.509557	−	0.185463i	−0.583987	+	0.811763i	$0.698508\pi$
$174$	−18.7049	−	9.84776i	−1.41801	−	0.746556i
$175$	14.7726	+	7.64213i	1.11670	+	0.577691i
$176$	−1.75698	+	9.96434i	−0.132438	+	0.751091i
$177$	11.8429	−	7.46771i	0.890166	−	0.561307i
$178$	3.51569	+	19.9385i	0.263512	+	1.49445i
$179$	−2.27166	−	3.93463i	−0.169792	−	0.294088i	0.768555	−	0.639784i	$-0.220976\pi$
$179$	−2.27166	−	3.93463i	−0.169792	−	0.294088i	−0.938347	+	0.345696i	$0.887643\pi$
$180$	26.8879	−	2.10109i	2.00410	−	0.156606i
$181$	4.52457	+	7.83678i	0.336308	+	0.582503i	0.983735	−	0.179624i	$-0.0574882\pi$
$181$	4.52457	+	7.83678i	0.336308	+	0.582503i	−0.647427	+	0.762128i	$0.724155\pi$
$182$	9.75525	+	23.3819i	0.723107	+	1.73318i
$183$	4.85818	+	11.8844i	0.359127	+	0.878520i
$184$	0.629139	−	3.56802i	0.0463807	−	0.263038i
$185$	−4.59303	+	26.0484i	−0.337686	+	1.91511i
$186$	7.53336	+	8.29822i	0.552373	+	0.608455i
$187$	10.4436	−	8.76320i	0.763710	−	0.640829i
$188$	−3.65599			−0.266641
$189$	−11.9832	+	6.73811i	−0.871652	+	0.490125i
$190$	−6.09575			−0.442232
$191$	2.52135	−	2.11566i	0.182438	−	0.153084i	−0.546995	−	0.837136i	$-0.684228\pi$
$191$	2.52135	−	2.11566i	0.182438	−	0.153084i	0.729433	+	0.684052i	$0.239784\pi$
$192$	6.43975	−	20.0985i	0.464749	−	1.45049i
$193$	1.96099	−	11.1213i	0.141155	−	0.800532i	−0.829219	−	0.558924i	$-0.811214\pi$
$193$	1.96099	−	11.1213i	0.141155	−	0.800532i	0.970374	−	0.241607i	$-0.0776746\pi$
$194$	4.27079	−	24.2209i	0.306625	−	1.73896i
$195$	−25.5316	−	3.48192i	−1.82836	−	0.249346i
$196$	7.82941	−	17.0170i	0.559243	−	1.21550i
$197$	−8.04334	−	13.9315i	−0.573064	−	0.992576i	−0.996249	−	0.0865328i	$-0.972421\pi$
$197$	−8.04334	−	13.9315i	−0.573064	−	0.992576i	0.423185	−	0.906043i	$-0.360912\pi$
$198$	−28.8619	−	8.02139i	−2.05113	−	0.570055i
$199$	2.53907	+	4.39781i	0.179990	+	0.311752i	0.941877	−	0.335958i	$-0.109060\pi$
$199$	2.53907	+	4.39781i	0.179990	+	0.311752i	−0.761887	+	0.647710i	$0.775727\pi$
$200$	−1.59562	−	9.04920i	−0.112827	−	0.639875i
$201$	3.19833	+	1.68386i	0.225593	+	0.118770i
$202$	3.49881	−	19.8428i	0.246176	−	1.39613i
$203$	−0.689512	−	14.9166i	−0.0483942	−	1.04694i
$204$	−11.5749	+	7.29873i	−0.810406	+	0.511013i
$205$	−8.35431	−	3.04072i	−0.583490	−	0.212373i
$206$	−7.23741	−	12.5356i	−0.504254	−	0.873394i
$207$	−7.16446	−	1.99117i	−0.497964	−	0.138396i
$208$	−4.85159	+	8.40320i	−0.336397	+	0.582657i
$209$	3.64104	+	1.32523i	0.251856	+	0.0916680i
$210$	19.0379	+	27.3098i	1.31374	+	1.88456i
$211$	2.49358	+	2.09236i	0.171665	+	0.144044i	0.724572	−	0.689199i	$-0.242037\pi$
$211$	2.49358	+	2.09236i	0.171665	+	0.144044i	−0.552907	+	0.833243i	$0.686482\pi$
$212$	−21.6372	−	18.1557i	−1.48605	−	1.24694i
$213$	−2.71064	+	8.45993i	−0.185730	+	0.579665i
$214$	−12.4673	−	4.53772i	−0.852246	−	0.310192i
$215$	14.9144	+	25.8326i	1.01716	+	1.76177i
$216$	6.97591	+	3.00398i	0.474650	+	0.204395i
$217$	−2.36141	+	7.55678i	−0.160303	+	0.512987i
$218$	−5.88269	−	33.3624i	−0.398426	−	2.25959i
$219$	−4.43099	+	0.960773i	−0.299419	+	0.0649230i
$220$	−7.20863	+	40.8821i	−0.486005	+	2.75627i
$221$	12.2856	−	4.47161i	0.826422	−	0.300793i
$222$	−18.0596	+	23.3110i	−1.21208	+	1.56453i
$223$	−15.2986	−	5.56824i	−1.02447	−	0.372877i	−0.225498	−	0.974244i	$-0.572401\pi$
$223$	−15.2986	−	5.56824i	−1.02447	−	0.372877i	−0.798973	+	0.601367i	$0.794623\pi$
$224$	19.7787	−	4.43796i	1.32152	−	0.296523i
$225$	−18.8018	+	1.46923i	−1.25346	+	0.0979484i
$226$	22.5694			1.50130
$227$	2.25156	+	12.7692i	0.149441	+	0.847522i	0.963693	+	0.267011i	$0.0860361\pi$
$227$	2.25156	+	12.7692i	0.149441	+	0.847522i	−0.814252	+	0.580511i	$0.802853\pi$
$228$	−3.44135	−	1.81180i	−0.227909	−	0.119990i
$229$	3.14525	−	1.14478i	0.207844	−	0.0756490i	−0.236000	−	0.971753i	$-0.575837\pi$
$229$	3.14525	−	1.14478i	0.207844	−	0.0756490i	0.443844	+	0.896104i	$0.353614\pi$
$230$	−3.12681	+	17.7330i	−0.206176	+	1.16928i
$231$	−5.43426	−	20.4512i	−0.357548	−	1.34559i
$232$	−6.31971	+	5.30287i	−0.414909	+	0.348150i
$233$	9.62140			0.630319			0.315159	−	0.949039i	$-0.397942\pi$
$233$	9.62140			0.630319			0.315159	+	0.949039i	$0.397942\pi$
$234$	−23.3783	−	16.6952i	−1.52828	−	1.09140i
$235$	4.58990			0.299412
$236$	−3.75613	−	21.3021i	−0.244503	−	1.38665i
$237$	9.54338	−	12.3184i	0.619909	−	0.800165i
$238$	−15.0024	−	7.76103i	−0.972461	−	0.503073i
$239$	22.0937	−	8.04146i	1.42913	−	0.520159i	0.492444	−	0.870344i	$-0.336103\pi$
$239$	22.0937	−	8.04146i	1.42913	−	0.520159i	0.936681	+	0.350185i	$0.113881\pi$
$240$	−3.89040	+	12.1420i	−0.251124	+	0.783761i
$241$	−14.3129	−	5.20949i	−0.921978	−	0.335572i	−0.162953	−	0.986634i	$-0.552102\pi$
$241$	−14.3129	−	5.20949i	−0.921978	−	0.335572i	−0.759025	+	0.651061i	$0.774324\pi$
$242$	11.1613	−	19.3319i	0.717475	−	1.24270i
$243$	7.51685	−	13.6564i	0.482206	−	0.876058i
$244$	19.8359			1.26986
$245$	−9.82939	+	21.3639i	−0.627977	+	1.36489i
$246$	−6.66219	−	7.33859i	−0.424766	−	0.467891i
$247$	2.84649	+	2.38849i	0.181118	+	0.151976i
$248$	4.11020	−	1.49599i	0.260998	−	0.0949955i
$249$	−5.16592	−	12.6372i	−0.327377	−	0.800851i
$250$	1.62276	+	9.20313i	0.102632	+	0.582057i
$251$	14.5049	+	25.1232i	0.915540	+	1.58576i	0.806109	+	0.591767i	$0.201570\pi$
$251$	14.5049	+	25.1232i	0.915540	+	1.58576i	0.109431	+	0.993994i	$0.465097\pi$
$252$	2.63069	+	21.0762i	0.165718	+	1.32768i
$253$	5.72286	−	9.91229i	0.359793	−	0.623180i
$254$	−0.368055	−	0.133961i	−0.0230938	−	0.00840547i
$255$	14.5317	−	9.16315i	0.910008	−	0.573819i
$256$	0.404487	+	0.339405i	0.0252805	+	0.0212128i
$257$	−16.8872	+	6.14642i	−1.05339	+	0.383403i	−0.809942	−	0.586510i	$-0.800501\pi$
$257$	−16.8872	+	6.14642i	−1.05339	+	0.383403i	−0.243450	+	0.969913i	$0.578279\pi$
$258$	1.29635	+	33.2296i	0.0807072	+	2.06879i
$259$	−20.6592	−	2.66609i	−1.28370	−	0.165663i
$260$	−19.9053	+	34.4770i	−1.23448	+	2.13817i
$261$	9.58260	+	13.9594i	0.593148	+	0.864064i
$262$	30.0648			1.85741
$263$	16.7545	−	14.0587i	1.03312	−	0.866895i	0.0419054	−	0.999122i	$-0.486657\pi$
$263$	16.7545	−	14.0587i	1.03312	−	0.866895i	0.991219	+	0.132227i	$0.0422127\pi$
$264$	−7.15986	+	9.24178i	−0.440659	+	0.568793i
$265$	27.1642	+	22.7935i	1.66869	+	1.40019i
$266$	−0.221670	−	4.79552i	−0.0135914	−	0.294032i
$267$	4.94822	−	15.4435i	0.302826	−	0.945125i
$268$	4.27782	−	3.58952i	0.261310	−	0.219265i
$269$	7.08887	−	12.2783i	0.432216	−	0.748621i	−0.564848	−	0.825195i	$-0.691065\pi$
$269$	7.08887	−	12.2783i	0.432216	−	0.748621i	0.997064	+	0.0765747i	$0.0243984\pi$
$270$	−34.6702	−	14.9297i	−2.10996	−	0.908594i
$271$	−8.14156	−	14.1016i	−0.494565	−	0.856611i	0.505416	−	0.862876i	$-0.331339\pi$
$271$	−8.14156	−	14.1016i	−0.494565	−	0.856611i	−0.999980	+	0.00626473i	$0.998006\pi$
$272$	−1.12334	−	6.37081i	−0.0681128	−	0.386287i
$273$	1.81078	−	20.2123i	0.109593	−	1.22330i
$274$	0.333046	−	0.121219i	0.0201200	−	0.00732309i
$275$	5.04076	−	28.5876i	0.303969	−	1.72390i
$276$	−7.03591	+	9.08179i	−0.423512	+	0.546660i
$277$	−21.9703	+	18.4352i	−1.32007	+	1.10767i	−0.333774	+	0.942653i	$0.608322\pi$
$277$	−21.9703	+	18.4352i	−1.32007	+	1.10767i	−0.986291	+	0.165013i	$0.947233\pi$
$278$	−1.88549	+	3.26576i	−0.113084	+	0.195867i
$279$	−2.24288	−	8.69250i	−0.134278	−	0.520406i
$280$	12.6770	−	2.84448i	0.757598	−	0.169990i
$281$	−0.494621	+	0.415036i	−0.0295066	+	0.0247590i	−0.657422	−	0.753523i	$-0.728353\pi$
$281$	−0.494621	+	0.415036i	−0.0295066	+	0.0247590i	0.627915	+	0.778282i	$0.283909\pi$
$282$	4.52788	+	2.38384i	0.269631	+	0.141956i
$283$	8.60777	+	7.22277i	0.511679	+	0.429349i	0.861719	−	0.507385i	$-0.169388\pi$
$283$	8.60777	+	7.22277i	0.511679	+	0.429349i	−0.350041	+	0.936734i	$0.613832\pi$
$284$	10.5138	+	8.82216i	0.623882	+	0.523499i
$285$	4.32042	+	2.27462i	0.255920	+	0.134737i
$286$	33.8732	−	28.4230i	2.00296	−	1.68069i
$287$	2.08833	−	6.68289i	0.123270	−	0.394479i
$288$	−16.4027	+	16.1010i	−0.966540	+	0.948761i
$289$	4.14176	−	7.17374i	0.243633	−	0.421985i
$290$	31.4089	−	26.3552i	1.84439	−	1.54763i
$291$	−12.0649	+	15.5731i	−0.707259	+	0.912913i
$292$	−1.21637	+	6.89840i	−0.0711829	+	0.403698i
$293$	−12.0370	+	4.38110i	−0.703207	+	0.255947i	−0.668780	−	0.743461i	$-0.733183\pi$
$293$	−12.0370	+	4.38110i	−0.703207	+	0.255947i	−0.0344277	+	0.999407i	$0.510961\pi$
$294$	−20.7923	+	15.9702i	−1.21263	+	0.931401i
$295$	4.71561	+	26.7436i	0.274553	+	1.55707i
$296$	5.75412	+	9.96643i	0.334452	+	0.579287i
$297$	17.4630	+	16.4550i	1.01331	+	0.954816i
$298$	−11.4490	+	19.8303i	−0.663224	+	1.14874i
$299$	8.40841	−	7.05550i	0.486271	−	0.408030i
$300$	−8.89047	+	27.7473i	−0.513292	+	1.60199i
$301$	−19.7801	+	12.6726i	−1.14011	+	0.730434i
$302$	39.5895	+	33.2196i	2.27812	+	1.91157i
$303$	−9.88410	+	12.7582i	−0.567827	+	0.732938i
$304$	1.40845	−	1.18183i	0.0807800	−	0.0677825i
$305$	−24.9028			−1.42593
$306$	19.0944	−	1.49208i	1.09155	−	0.0852968i
$307$	−3.20676	+	5.55428i	−0.183020	+	0.316999i	−0.942907	−	0.333055i	$-0.891921\pi$
$307$	−3.20676	+	5.55428i	−0.183020	+	0.316999i	0.759888	+	0.650054i	$0.225254\pi$
$308$	−32.4240	−	4.18435i	−1.84753	−	0.238425i
$309$	0.451965	+	11.5853i	0.0257114	+	0.659066i
$310$	−20.4276	+	7.43505i	−1.16021	+	0.422283i
$311$	−15.1990	−	12.7535i	−0.861857	−	0.723184i	0.100510	−	0.994936i	$-0.467952\pi$
$311$	−15.1990	−	12.7535i	−0.861857	−	0.723184i	−0.962367	+	0.271752i	$0.912397\pi$
$312$	−9.48346	+	5.97993i	−0.536895	+	0.338547i
$313$	11.0474	+	4.02094i	0.624439	+	0.227277i	0.634809	−	0.772669i	$-0.281079\pi$
$313$	11.0474	+	4.02094i	0.624439	+	0.227277i	−0.0103703	+	0.999946i	$0.503301\pi$
$314$	21.2063	−	36.7304i	1.19674	−	2.07281i
$315$	−3.30269	−	26.4601i	−0.186085	−	1.49086i
$316$	−12.0373	−	20.8493i	−0.677153	−	1.17286i
$317$	0.412273	+	2.33812i	0.0231556	+	0.131322i	0.994194	−	0.107601i	$-0.0343169\pi$
$317$	0.412273	+	2.33812i	0.0231556	+	0.131322i	−0.971039	+	0.238923i	$0.923206\pi$
$318$	14.9590	+	36.5938i	0.838861	+	2.05208i
$319$	−24.4904	+	8.91378i	−1.37120	+	0.499076i
$320$	31.3586	+	26.3130i	1.75300	+	1.47094i
$321$	7.14306	+	7.86829i	0.398687	+	0.439165i
$322$	−14.0642	−	1.81500i	−0.783770	−	0.101146i
$323$	−2.47734			−0.137843
$324$	−15.1355	−	18.7333i	−0.840863	−	1.04074i
$325$	13.9191	−	24.1087i	0.772095	−	1.33731i
$326$	−15.9033	−	5.78834i	−0.880803	−	0.320586i
$327$	−8.27969	+	25.8410i	−0.457868	+	1.42901i
$328$	−3.63489	+	1.32299i	−0.200703	+	0.0730499i
$329$	0.166910	+	3.61086i	0.00920203	+	0.199073i
$330$	35.5844	−	45.9315i	1.95886	−	2.52845i
$331$	−0.922013	−	5.22900i	−0.0506784	−	0.287412i	0.948927	−	0.315495i	$-0.102171\pi$
$331$	−0.922013	−	5.22900i	−0.0506784	−	0.287412i	−0.999606	+	0.0280837i	$0.991060\pi$
$332$	−21.0924			−1.15759
$333$	21.4984	−	9.78295i	1.17810	−	0.536102i
$334$	−36.6169			−2.00359
$335$	−5.37057	+	4.50644i	−0.293425	+	0.246213i
$336$	−9.69354	−	2.61903i	−0.528826	−	0.142880i
$337$	3.26895	−	18.5391i	0.178071	−	1.00989i	−0.756468	−	0.654031i	$-0.773077\pi$
$337$	3.26895	−	18.5391i	0.178071	−	1.00989i	0.934539	−	0.355860i	$-0.115812\pi$
$338$	13.4320	−	4.88884i	0.730603	−	0.265918i
$339$	−15.9963	−	8.42174i	−0.868800	−	0.457406i
$340$	−4.60891	−	26.1384i	−0.249953	−	1.41755i
$341$	13.8180			0.748285
$342$	3.08069	+	4.48777i	0.166585	+	0.242671i
$343$	−17.1644	−	6.95587i	−0.926789	−	0.375582i
$344$	12.1956	+	4.43884i	0.657543	+	0.239326i
$345$	8.83320	−	11.4017i	0.475563	−	0.613846i
$346$	14.4928	−	5.27493i	0.779136	−	0.283582i
$347$	1.02535	−	5.81503i	0.0550435	−	0.312167i	−0.944838	−	0.327537i	$-0.893781\pi$
$347$	1.02535	−	5.81503i	0.0550435	−	0.312167i	0.999882	+	0.0153697i	$0.00489253\pi$
$348$	25.5652	−	5.54331i	1.37044	−	0.297153i
$349$	1.98947	+	11.2829i	0.106494	+	0.603958i	0.990613	+	0.136696i	$0.0436484\pi$
$349$	1.98947	+	11.2829i	0.106494	+	0.603958i	−0.884119	+	0.467262i	$0.845240\pi$
$350$	−35.0929	+	7.87415i	−1.87579	+	0.420891i
$351$	10.3398	+	20.5564i	0.551898	+	1.09722i
$352$	−17.6893	−	30.6388i	−0.942843	−	1.63305i
$353$	12.7330	+	4.63443i	0.677709	+	0.246666i	0.657863	−	0.753137i	$-0.271460\pi$
$353$	12.7330	+	4.63443i	0.677709	+	0.246666i	0.0198454	+	0.999803i	$0.493683\pi$
$354$	−9.23783	+	28.8314i	−0.490985	+	1.53237i
$355$	−13.1995	−	11.0757i	−0.700559	−	0.587839i
$356$	−19.1928	−	16.1047i	−1.01722	−	0.853547i
$357$	7.73707	+	11.0988i	0.409489	+	0.587412i
$358$	9.23197	+	3.36016i	0.487925	+	0.177590i
$359$	13.4181	−	23.2409i	0.708181	−	1.22661i	−0.257350	−	0.966318i	$-0.582849\pi$
$359$	13.4181	−	23.2409i	0.708181	−	1.22661i	0.965531	−	0.260287i	$-0.0838172\pi$
$360$	−10.5132	+	10.3198i	−0.554095	+	0.543903i
$361$	9.14795	+	15.8447i	0.481471	+	0.833933i
$362$	−18.3877	−	6.69259i	−0.966438	−	0.351755i
$363$	−15.1243	+	9.53687i	−0.793822	+	0.500556i
$364$	−27.8469	−	14.4057i	−1.45957	−	0.755065i
$365$	1.52709	−	8.66055i	0.0799315	−	0.453314i
$366$	−24.5664	−	12.9337i	−1.28411	−	0.676056i
$367$	−0.455880	−	2.58543i	−0.0237968	−	0.134958i	0.970595	−	0.240719i	$-0.0773833\pi$
$367$	−0.455880	−	2.58543i	−0.0237968	−	0.134958i	−0.994392	+	0.105761i	$0.966272\pi$
$368$	−2.71557	−	4.70350i	−0.141559	−	0.245187i
$369$	1.98351	+	7.68728i	0.103257	+	0.400184i
$370$	−28.5979	−	49.5330i	−1.48673	−	2.57510i
$371$	−16.9438	+	22.1989i	−0.879678	+	1.15251i
$372$	−13.7423	−	1.87413i	−0.712503	−	0.0971691i
$373$	−1.00291	+	5.68776i	−0.0519285	+	0.294501i	−0.999701	−	0.0244455i	$-0.992218\pi$
$373$	−1.00291	+	5.68776i	−0.0519285	+	0.294501i	0.947773	+	0.318947i	$0.103329\pi$
$374$	−5.11919	+	29.0324i	−0.264707	+	1.50123i
$375$	2.28398	−	7.12833i	0.117944	−	0.368106i
$376$	1.52981	−	1.28366i	0.0788938	−	0.0661998i
$377$	−24.9935			−1.28723
$378$	10.4844	−	27.8179i	0.539260	−	1.43080i
$379$	−2.35232			−0.120830			−0.0604152	−	0.998173i	$-0.519242\pi$
$379$	−2.35232			−0.120830			−0.0604152	+	0.998173i	$0.519242\pi$
$380$	5.77864	−	4.84886i	0.296438	−	0.248741i
$381$	0.210875	+	0.232285i	0.0108035	+	0.0119003i
$382$	−1.23590	+	7.00915i	−0.0632343	+	0.358619i
$383$	−3.69565	+	20.9591i	−0.188839	+	1.07096i	0.732084	+	0.681214i	$0.238548\pi$
$383$	−3.69565	+	20.9591i	−0.188839	+	1.07096i	−0.920923	+	0.389745i	$0.872563\pi$
$384$	7.22617	+	17.6771i	0.368759	+	0.902082i
$385$	40.7066	+	5.25322i	2.07460	+	0.267729i
$386$	12.2099	+	21.1481i	0.621466	+	1.07641i
$387$	11.4808	−	24.0355i	0.583600	−	1.22180i
$388$	15.2178	+	26.3580i	0.772568	+	1.33813i
$389$	−2.57119	−	14.5819i	−0.130364	−	0.739334i	−0.977976	−	0.208717i	$-0.933071\pi$
$389$	−2.57119	−	14.5819i	−0.130364	−	0.739334i	0.847612	−	0.530617i	$-0.178040\pi$
$390$	47.1327	−	29.7202i	2.38665	−	1.50494i
$391$	−1.27075	+	7.20676i	−0.0642644	+	0.364462i
$392$	2.69874	+	9.86957i	0.136307	+	0.498488i
$393$	−21.3087	−	11.2186i	−1.07488	−	0.565904i
$394$	32.6879	+	11.8974i	1.64679	+	0.599384i
$395$	15.1122	+	26.1751i	0.760377	+	1.31701i
$396$	33.7411	−	15.3541i	1.69555	−	0.771570i
$397$	18.9627	−	32.8444i	0.951713	−	1.64841i	0.209995	−	0.977703i	$-0.432655\pi$
$397$	18.9627	−	32.8444i	0.951713	−	1.64841i	0.741718	−	0.670712i	$-0.234011\pi$
$398$	−10.3187	−	3.75572i	−0.517232	−	0.188257i
$399$	−1.63233	+	3.48158i	−0.0817185	+	0.174297i
$400$	−10.5518	−	8.85403i	−0.527591	−	0.442701i
$401$	6.70609	+	5.62708i	0.334886	+	0.281003i	0.794687	−	0.607019i	$-0.207635\pi$
$401$	6.70609	+	5.62708i	0.334886	+	0.281003i	−0.459801	+	0.888022i	$0.652079\pi$
$402$	−7.63850	+	1.65626i	−0.380974	+	0.0826067i
$403$	12.4522	+	4.53224i	0.620289	+	0.225767i
$404$	12.4671	+	21.5936i	0.620261	+	1.07432i
$405$	19.0018	+	23.5187i	0.944208	+	1.16865i
$406$	21.8757	+	23.7509i	1.08567	+	1.17874i
$407$	6.31316	+	35.8037i	0.312931	+	1.77472i
$408$	2.28072	−	7.11816i	0.112913	−	0.352401i
$409$	5.83612	−	33.0983i	0.288578	−	1.63660i	−0.403642	−	0.914917i	$-0.632256\pi$
$409$	5.83612	−	33.0983i	0.288578	−	1.63660i	0.692219	−	0.721687i	$-0.256633\pi$
$410$	18.0653	−	6.57524i	0.892183	−	0.324728i
$411$	−0.281282	−	0.0383604i	−0.0138746	−	0.00189218i
$412$	16.8323	+	6.12646i	0.829268	+	0.301829i
$413$	−20.8676	+	4.68228i	−1.02683	+	0.230400i
$414$	14.6355	−	6.65997i	0.719296	−	0.327320i
$415$	26.4803			1.29987
$416$	−5.89153	−	33.4125i	−0.288856	−	1.63818i
$417$	2.55497	−	1.61107i	0.125117	−	0.0788945i
$418$	−7.87337	+	2.86567i	−0.385099	+	0.140165i
$419$	−0.518619	+	2.94123i	−0.0253362	+	0.143689i	−0.994852	−	0.101341i	$-0.967687\pi$
$419$	−0.518619	+	2.94123i	−0.0253362	+	0.143689i	0.969516	+	0.245030i	$0.0787977\pi$
$420$	−39.7711	−	10.7455i	−1.94063	−	0.524325i
$421$	−9.26236	+	7.77205i	−0.451420	+	0.378786i	−0.839963	−	0.542644i	$-0.817423\pi$
$421$	−9.26236	+	7.77205i	−0.451420	+	0.378786i	0.388542	+	0.921431i	$0.372979\pi$
$422$	−7.03889			−0.342648
$423$	−2.31965	−	3.37914i	−0.112785	−	0.164299i
$424$	15.4285			0.749275
$425$	3.22286	+	18.2778i	0.156332	+	0.886602i
$426$	−7.26884	−	17.7815i	−0.352176	−	0.861517i
$427$	−0.905582	−	19.5910i	−0.0438242	−	0.948076i
$428$	15.4282	−	5.61542i	0.745752	−	0.271431i
$429$	−34.6139	+	7.50535i	−1.67118	+	0.362362i
$430$	−60.6120	−	22.0610i	−2.92297	−	1.06387i
$431$	12.5494	−	21.7362i	0.604484	−	1.04700i	−0.387648	−	0.921807i	$-0.626712\pi$
$431$	12.5494	−	21.7362i	0.604484	−	1.04700i	0.992133	−	0.125190i	$-0.0399542\pi$
$432$	10.9052	−	3.27219i	0.524677	−	0.157433i
$433$	38.7840			1.86384			0.931919	−	0.362667i	$-0.118134\pi$
$433$	38.7840			1.86384			0.931919	+	0.362667i	$0.118134\pi$
$434$	−6.59198	−	15.8000i	−0.316425	−	0.758425i
$435$	−32.0957	+	6.95932i	−1.53887	+	0.333674i
$436$	32.1147	+	26.9474i	1.53802	+	1.29055i
$437$	−1.95442	+	0.711352i	−0.0934927	+	0.0340286i
$438$	6.00446	−	7.75042i	0.286904	−	0.370330i
$439$	1.32549	+	7.51721i	0.0632621	+	0.358777i	0.999963	+	0.00864550i	$0.00275198\pi$
$439$	1.32549	+	7.51721i	0.0632621	+	0.358777i	−0.936701	+	0.350131i	$0.886137\pi$
$440$	−11.3378	−	19.6377i	−0.540510	−	0.936191i
$441$	20.6960	−	3.56043i	0.985523	−	0.169544i
$442$	−14.1357	+	24.4838i	−0.672367	+	1.16457i
$443$	−5.27908	−	1.92143i	−0.250817	−	0.0912898i	0.213552	−	0.976932i	$-0.431497\pi$
$443$	−5.27908	−	1.92143i	−0.250817	−	0.0912898i	−0.464369	+	0.885642i	$0.653719\pi$
$444$	−1.42252	−	36.4638i	−0.0675098	−	1.73049i
$445$	24.0955	+	20.2186i	1.14224	+	0.958452i
$446$	33.0817	−	12.0407i	1.56646	−	0.570146i
$447$	15.5142	−	9.78273i	0.733798	−	0.462707i
$448$	−19.5600	+	25.6266i	−0.924124	+	1.21074i
$449$	−15.4853	+	26.8214i	−0.730798	+	1.26578i	0.225744	+	0.974187i	$0.427519\pi$
$449$	−15.4853	+	26.8214i	−0.730798	+	1.26578i	−0.956542	+	0.291593i	$0.905815\pi$
$450$	29.1029	−	28.5676i	1.37193	−	1.34669i
$451$	−12.2200			−0.575419
$452$	−21.3953	+	17.9528i	−1.00635	+	0.844430i
$453$	−15.6636	−	38.3174i	−0.735942	−	1.80031i
$454$	−21.4784	−	18.0225i	−1.00803	−	0.845839i
$455$	34.9602	+	18.0856i	1.63896	+	0.847866i
$456$	2.07614	−	0.450170i	0.0972241	−	0.0210811i
$457$	−2.80752	+	2.35579i	−0.131330	+	0.110199i	−0.706087	−	0.708125i	$-0.749541\pi$
$457$	−2.80752	+	2.35579i	−0.131330	+	0.110199i	0.574756	+	0.818324i	$0.305097\pi$
$458$	−3.61888	+	6.26809i	−0.169099	+	0.292889i
$459$	−14.0901	−	6.06749i	−0.657669	−	0.283206i
$460$	−11.1416	−	19.2977i	−0.519478	−	0.899762i
$461$	−2.83706	−	16.0897i	−0.132135	−	0.749374i	−0.976812	−	0.214098i	$-0.931319\pi$
$461$	−2.83706	−	16.0897i	−0.132135	−	0.749374i	0.844677	−	0.535276i	$-0.179792\pi$
$462$	37.4283	+	26.3239i	1.74132	+	1.22470i
$463$	0.873706	−	0.318003i	0.0406046	−	0.0147789i	−0.321638	−	0.946863i	$-0.604233\pi$
$463$	0.873706	−	0.318003i	0.0406046	−	0.0147789i	0.362243	+	0.932084i	$0.382011\pi$
$464$	−2.14747	+	12.1789i	−0.0996940	+	0.565393i
$465$	17.2527	+	2.35287i	0.800073	+	0.109112i
$466$	−15.9378	+	13.3734i	−0.738303	+	0.619510i
$467$	−3.02153	+	5.23345i	−0.139820	+	0.242175i	−0.927428	−	0.374001i	$-0.877986\pi$
$467$	−3.02153	+	5.23345i	−0.139820	+	0.242175i	0.787608	+	0.616176i	$0.211319\pi$
$468$	35.4422	−	2.76955i	1.63832	−	0.128022i
$469$	−3.74051	−	4.06114i	−0.172721	−	0.187526i
$470$	−7.60313	+	6.37978i	−0.350706	+	0.294277i
$471$	−28.7360	+	18.1199i	−1.32409	+	0.834921i
$472$	9.05111	+	7.59479i	0.416611	+	0.349578i
$473$	31.4079	+	26.3543i	1.44414	+	1.21177i
$474$	1.31354	+	33.6702i	0.0603328	+	1.54653i
$475$	−4.04082	+	3.39065i	−0.185405	+	0.155574i
$476$	20.3954	−	4.57633i	0.934824	−	0.209756i
$477$	3.05252	−	31.5181i	0.139765	−	1.44311i
$478$	−25.4208	+	44.0301i	−1.16272	+	2.01389i
$479$	−13.6924	+	11.4893i	−0.625622	+	0.524960i	−0.899565	−	0.436786i	$-0.856117\pi$
$479$	−13.6924	+	11.4893i	−0.625622	+	0.524960i	0.273943	+	0.961746i	$0.411672\pi$
$480$	−16.8692	−	41.2666i	−0.769972	−	1.88355i
$481$	−6.05429	+	34.3356i	−0.276052	+	1.56557i
$482$	30.9503	−	11.2650i	1.40975	−	0.513106i
$483$	9.29090	+	6.53444i	0.422751	+	0.297327i
$484$	4.79688	+	27.2045i	0.218040	+	1.23657i
$485$	−19.1051	−	33.0911i	−0.867520	−	1.50259i
$486$	6.53026	+	33.0698i	0.296219	+	1.50008i
$487$	10.5234	−	18.2271i	0.476861	−	0.825947i	−0.522788	−	0.852463i	$-0.675108\pi$
$487$	10.5234	−	18.2271i	0.476861	−	0.825947i	0.999648	+	0.0265160i	$0.00844128\pi$
$488$	−8.30010	+	6.96461i	−0.375728	+	0.315273i
$489$	9.11172	+	10.0368i	0.412046	+	0.453881i
$490$	−13.4127	−	49.0516i	−0.605924	−	2.21593i
$491$	−19.1658	−	16.0820i	−0.864942	−	0.725773i	0.0980847	−	0.995178i	$-0.468728\pi$
$491$	−19.1658	−	16.0820i	−0.864942	−	0.725773i	−0.963027	+	0.269405i	$0.913173\pi$
$492$	12.1531	+	1.65740i	0.547903	+	0.0747214i
$493$	12.7647	−	10.7108i	0.574892	−	0.482392i
$494$	−8.03510			−0.361516
$495$	−42.3600	+	19.2762i	−1.90394	+	0.866399i
$496$	3.27840	−	5.67835i	0.147204	−	0.254966i
$497$	8.23326	−	10.7868i	0.369312	−	0.483855i
$498$	26.1225	+	13.7530i	1.17058	+	0.616287i
$499$	20.7458	−	7.55087i	0.928711	−	0.338023i	0.167013	−	0.985955i	$-0.446588\pi$
$499$	20.7458	−	7.55087i	0.928711	−	0.338023i	0.761699	+	0.647931i	$0.224366\pi$
$500$	−8.85896	−	7.43355i	−0.396185	−	0.332438i
$501$	25.9526	+	13.6635i	1.15948	+	0.610441i
$502$	−58.9475	−	21.4551i	−2.63096	−	0.957590i
$503$	15.6150	−	27.0460i	0.696238	−	1.20592i	−0.273524	−	0.961865i	$-0.588189\pi$
$503$	15.6150	−	27.0460i	0.696238	−	1.20592i	0.969762	−	0.244054i	$-0.0784775\pi$
$504$	−8.50090	−	7.89545i	−0.378660	−	0.351691i
$505$	−15.6517	−	27.1096i	−0.696493	−	1.20636i
$506$	4.29783	+	24.3742i	0.191062	+	1.08357i
$507$	−11.3443	−	1.54710i	−0.503818	−	0.0687092i
$508$	0.455468	−	0.165777i	0.0202081	−	0.00735515i
$509$	−31.4621	−	26.3999i	−1.39453	−	1.17015i	−0.963465	−	0.267834i	$-0.913692\pi$
$509$	−31.4621	−	26.3999i	−1.39453	−	1.17015i	−0.431069	−	0.902319i	$-0.641864\pi$
$510$	−11.3352	+	35.3772i	−0.501929	+	1.56653i
$511$	6.86877	+	0.886420i	0.303857	+	0.0392129i
$512$	−23.1932			−1.02500
$513$	−0.508866	−	4.33030i	−0.0224670	−	0.191187i
$514$	19.4302	−	33.6540i	0.857027	−	1.48442i
$515$	−21.1320	−	7.69143i	−0.931188	−	0.338925i
$516$	−27.6614	−	30.4698i	−1.21772	−	1.34136i
$517$	5.92838	−	2.15775i	0.260730	−	0.0948979i
$518$	37.9276	−	24.2992i	1.66644	−	1.06764i
$519$	−12.2402	−	1.66928i	−0.537286	−	0.0732734i
$520$	−3.77613	−	21.4155i	−0.165594	−	0.939132i
$521$	16.8364			0.737618			0.368809	−	0.929505i	$-0.379766\pi$
$521$	16.8364			0.737618			0.368809	+	0.929505i	$0.379766\pi$
$522$	−35.2765	−	9.80415i	−1.54401	−	0.429116i
$523$	30.5435			1.33557			0.667786	−	0.744353i	$-0.267242\pi$
$523$	30.5435			1.33557			0.667786	+	0.744353i	$0.267242\pi$
$524$	−28.5008	+	23.9150i	−1.24506	+	1.04473i
$525$	27.8106	+	7.51396i	1.21376	+	0.327936i
$526$	−8.21263	+	46.5762i	−0.358088	+	2.03082i
$527$	−8.30186	+	3.02163i	−0.361635	+	0.131624i
$528$	0.683163	+	17.5117i	0.0297309	+	0.762098i
$529$	−2.92705	−	16.6001i	−0.127263	−	0.721744i
$530$	−76.6795			−3.33074
$531$	17.3058	−	16.9874i	0.751006	−	0.737192i
$532$	4.02472	+	4.36972i	0.174494	+	0.189451i
$533$	−11.0122	−	4.00812i	−0.476992	−	0.173611i
$534$	13.2691	+	32.4598i	0.574212	+	1.40467i
$535$	−19.3693	+	7.04984i	−0.837407	+	0.304791i
$536$	−0.529684	+	3.00399i	−0.0228789	+	0.129752i
$537$	−5.28941	−	5.82644i	−0.228255	−	0.251429i
$538$	5.32369	+	30.1922i	0.229521	+	1.30168i
$539$	−2.65242	+	32.2148i	−0.114248	+	1.38759i
$540$	44.7424	−	13.4253i	1.92541	−	0.577732i
$541$	2.15170	+	3.72686i	0.0925089	+	0.160230i	0.908566	−	0.417741i	$-0.137178\pi$
$541$	2.15170	+	3.72686i	0.0925089	+	0.160230i	−0.816057	+	0.577971i	$0.803845\pi$
$542$	33.0871	+	12.0427i	1.42121	+	0.517280i
$543$	10.5352	+	11.6048i	0.452107	+	0.498009i
$544$	17.3277	+	14.5396i	0.742918	+	0.623382i
$545$	−40.3182	−	33.8310i	−1.72704	−	1.44916i
$546$	25.0948	+	35.9984i	1.07396	+	1.54059i
$547$	−28.9084	−	10.5218i	−1.23603	−	0.449880i	−0.360374	−	0.932808i	$-0.617351\pi$
$547$	−28.9084	−	10.5218i	−1.23603	−	0.449880i	−0.875660	+	0.482928i	$0.839573\pi$
$548$	−0.219297	+	0.379833i	−0.00936790	+	0.0162257i
$549$	12.5855	+	18.3338i	0.537135	+	0.782467i
$550$	31.3857	+	54.3616i	1.33829	+	2.31799i
$551$	4.45026	+	1.61976i	0.189588	+	0.0690042i
$552$	−0.244626	−	6.27056i	−0.0104120	−	0.266893i
$553$	−20.0424	+	12.8406i	−0.852288	+	0.546037i
$554$	10.7693	−	61.0757i	0.457543	−	2.59486i
$555$	1.78589	+	45.7783i	0.0758070	+	1.94318i
$556$	−0.810341	−	4.59567i	−0.0343661	−	0.194900i
$557$	15.7987	+	27.3641i	0.669412	+	1.15945i	0.978069	+	0.208282i	$0.0667870\pi$
$557$	15.7987	+	27.3641i	0.669412	+	1.15945i	−0.308657	+	0.951173i	$0.599880\pi$
$558$	15.7976	+	11.2815i	0.668764	+	0.477586i
$559$	19.6594	+	34.0512i	0.831506	+	1.44021i
$560$	11.8166	−	15.4816i	0.499344	−	0.654217i
$561$	14.4616	−	18.6667i	0.610571	−	0.788111i
$562$	0.242451	−	1.37501i	0.0102272	−	0.0580012i
$563$	−0.422482	+	2.39602i	−0.0178055	+	0.100980i	−0.992415	−	0.122930i	$-0.960771\pi$
$563$	−0.422482	+	2.39602i	−0.0178055	+	0.100980i	0.974610	+	0.223910i	$0.0718821\pi$
$564$	−6.18856	+	1.34187i	−0.260585	+	0.0565028i
$565$	26.8607	−	22.5388i	1.13004	−	0.948213i
$566$	−24.2981			−1.02132
$567$	−17.8111	+	15.8039i	−0.747996	+	0.663703i
$568$	−7.49696			−0.314566
$569$	−14.2943	+	11.9944i	−0.599249	+	0.502829i	−0.891204	−	0.453603i	$-0.850139\pi$
$569$	−14.2943	+	11.9944i	−0.599249	+	0.502829i	0.291955	+	0.956432i	$0.405694\pi$
$570$	−10.3184	+	2.23734i	−0.432189	+	0.0937118i
$571$	−3.54484	+	20.1038i	−0.148347	+	0.841317i	0.816272	+	0.577668i	$0.196037\pi$
$571$	−3.54484	+	20.1038i	−0.148347	+	0.841317i	−0.964619	+	0.263649i	$0.915074\pi$
$572$	−9.50204	+	53.8887i	−0.397300	+	2.25320i
$573$	3.49141	−	4.50663i	0.145856	−	0.188267i
$574$	5.82967	+	13.9729i	0.243326	+	0.583216i
$575$	7.79093	+	13.4943i	0.324904	+	0.562751i
$576$	3.52385	−	36.3847i	0.146827	−	1.51603i
$577$	−0.0405999	−	0.0703210i	−0.00169019	−	0.00292750i	0.865179	−	0.501463i	$-0.167205\pi$
$577$	−0.0405999	−	0.0703210i	−0.00169019	−	0.00292750i	−0.866869	+	0.498536i	$0.833871\pi$
$578$	3.11043	+	17.6401i	0.129377	+	0.733733i
$579$	−0.762488	−	19.5450i	−0.0316879	−	0.812263i
$580$	−8.81075	+	49.9683i	−0.365847	+	2.07482i
$581$	0.962946	+	20.8320i	0.0399497	+	0.864258i
$582$	−1.66060	−	42.5666i	−0.0688341	−	1.76444i
$583$	45.8012	+	16.6703i	1.89689	+	0.690412i
$584$	−1.91313	−	3.31364i	−0.0791659	−	0.137119i
$585$	−44.4957	+	3.47701i	−1.83967	+	0.143757i
$586$	13.8496	−	23.9882i	0.572121	−	0.990943i
$587$	−4.39620	−	1.60009i	−0.181451	−	0.0660426i	0.249697	−	0.968324i	$-0.419669\pi$
$587$	−4.39620	−	1.60009i	−0.181451	−	0.0660426i	−0.431148	+	0.902281i	$0.641891\pi$
$588$	7.00718	−	31.6786i	0.288971	−	1.30640i
$589$	−1.92348	−	1.61399i	−0.0792556	−	0.0665034i
$590$	−44.9839	−	37.7460i	−1.85196	−	1.55398i
$591$	−18.7284	−	20.6299i	−0.770383	−	0.848599i
$592$	16.2110	+	5.90032i	0.666268	+	0.242502i
$593$	4.66656	+	8.08272i	0.191633	+	0.331918i	0.945791	−	0.324775i	$-0.105288\pi$
$593$	4.66656	+	8.08272i	0.191633	+	0.331918i	−0.754159	+	0.656692i	$0.771955\pi$
$594$	−51.7991	−	2.98468i	−2.12534	−	0.122463i
$595$	−25.6053	+	5.74533i	−1.04972	+	0.235536i
$596$	−4.92055	−	27.9058i	−0.201553	−	1.14307i
$597$	5.91207	+	6.51232i	0.241965	+	0.266531i
$598$	−4.12160	+	23.3748i	−0.168545	+	0.955865i
$599$	−22.3476	+	8.13385i	−0.913096	+	0.332340i	−0.755489	−	0.655162i	$-0.772600\pi$
$599$	−22.3476	+	8.13385i	−0.913096	+	0.332340i	−0.157608	+	0.987502i	$0.550378\pi$
$600$	−6.02228	−	14.7321i	−0.245858	−	0.601435i
$601$	−30.6186	−	11.1443i	−1.24896	−	0.454584i	−0.368910	−	0.929465i	$-0.620269\pi$
$601$	−30.6186	−	11.1443i	−1.24896	−	0.454584i	−0.880050	+	0.474881i	$0.842491\pi$
$602$	15.1512	−	48.4856i	0.617516	−	1.97612i
$603$	6.03189	+	1.67640i	0.245638	+	0.0682683i
$604$	−63.9545			−2.60227
$605$	−6.02222	−	34.1537i	−0.244838	−	1.38855i
$606$	−1.36043	−	34.8723i	−0.0552639	−	1.41659i
$607$	0.991903	−	0.361023i	0.0402601	−	0.0146535i	−0.321812	−	0.946804i	$-0.604292\pi$
$607$	0.991903	−	0.361023i	0.0402601	−	0.0146535i	0.362072	+	0.932150i	$0.382070\pi$
$608$	−1.11635	+	6.33114i	−0.0452740	+	0.256762i
$609$	−6.64203	−	24.9966i	−0.269149	−	1.01291i
$610$	41.2514	−	34.6140i	1.67022	−	1.40148i
$611$	6.05016			0.244763
$612$	−16.9142	+	16.6030i	−0.683715	+	0.671138i
$613$	−1.15378			−0.0466007			−0.0233003	−	0.999729i	$-0.507417\pi$
$613$	−1.15378			−0.0466007			−0.0233003	+	0.999729i	$0.507417\pi$
$614$	−2.40826	−	13.6579i	−0.0971893	−	0.551188i
$615$	−15.2575	−	2.08077i	−0.615242	−	0.0839049i
$616$	15.0366	−	9.63357i	0.605844	−	0.388148i
$617$	−36.6671	+	13.3457i	−1.47616	+	0.537278i	−0.949766	−	0.312962i	$-0.898679\pi$
$617$	−36.6671	+	13.3457i	−1.47616	+	0.537278i	−0.526395	+	0.850240i	$0.676457\pi$
$618$	−16.8518	−	18.5628i	−0.677880	−	0.746705i
$619$	−15.9113	−	5.79122i	−0.639527	−	0.232769i	0.00184554	−	0.999998i	$-0.499413\pi$
$619$	−15.9113	−	5.79122i	−0.639527	−	0.232769i	−0.641373	+	0.767229i	$0.721635\pi$
$620$	13.4508	−	23.2974i	0.540195	−	0.935646i
$621$	−12.8582	−	0.740894i	−0.515982	−	0.0297311i
$622$	42.9039			1.72029
$623$	−15.0297	+	19.6912i	−0.602151	+	0.788909i
$624$	−5.12812	+	16.0049i	−0.205289	+	0.640710i
$625$	−12.9563	−	10.8716i	−0.518253	−	0.434866i
$626$	−23.8890	+	8.69487i	−0.954795	+	0.347517i
$627$	6.64964	+	0.906858i	0.265561	+	0.0362164i
$628$	9.11400	+	51.6881i	0.363688	+	2.06258i
$629$	−11.6223	−	20.1304i	−0.463411	−	0.802652i
$630$	42.2494	+	39.2403i	1.68325	+	1.56337i
$631$	−19.1743	+	33.2108i	−0.763315	+	1.32210i	0.177818	+	0.984063i	$0.443096\pi$
$631$	−19.1743	+	33.2108i	−0.763315	+	1.32210i	−0.941133	+	0.338037i	$0.890237\pi$
$632$	12.3573	+	4.49769i	0.491547	+	0.178909i
$633$	4.98888	+	2.62655i	0.198290	+	0.104396i
$634$	−3.93282	−	3.30003i	−0.156192	−	0.131061i
$635$	−0.571814	+	0.208123i	−0.0226918	+	0.00825912i
$636$	−43.2893	−	22.7910i	−1.71653	−	0.903720i
$637$	−12.9566	+	28.1608i	−0.513359	+	1.11577i
$638$	28.1784	−	48.8064i	1.11559	−	1.93226i
$639$	−1.48327	+	15.3152i	−0.0586773	+	0.605858i
$640$	−37.0411			−1.46418
$641$	32.1855	−	27.0069i	1.27125	−	1.06671i	0.276864	−	0.960909i	$-0.410705\pi$
$641$	32.1855	−	27.0069i	1.27125	−	1.06671i	0.994388	−	0.105798i	$-0.0337396\pi$
$642$	−22.7691	−	3.10518i	−0.898623	−	0.122551i
$643$	−26.6672	−	22.3764i	−1.05165	−	0.882441i	−0.0583856	−	0.998294i	$-0.518595\pi$
$643$	−26.6672	−	22.3764i	−1.05165	−	0.882441i	−0.993266	+	0.115853i	$0.963040\pi$
$644$	14.7763	−	9.46679i	0.582269	−	0.373044i
$645$	34.7273	+	38.2531i	1.36739	+	1.50622i
$646$	4.10369	−	3.44340i	0.161457	−	0.135479i
$647$	8.24077	−	14.2734i	0.323978	−	0.561146i	−0.657327	−	0.753605i	$-0.728313\pi$
$647$	8.24077	−	14.2734i	0.323978	−	0.561146i	0.981305	+	0.192459i	$0.0616463\pi$
$648$	12.9108	+	2.52450i	0.507184	+	0.0991716i
$649$	18.6632	+	32.3255i	0.732593	+	1.26889i
$650$	10.4532	+	59.2829i	0.410007	+	2.32527i
$651$	−1.22361	+	13.6582i	−0.0479570	+	0.535307i
$652$	19.6803	−	7.16305i	0.770741	−	0.280527i
$653$	−5.04030	+	28.5850i	−0.197242	+	1.11862i	0.711947	+	0.702233i	$0.247814\pi$
$653$	−5.04030	+	28.5850i	−0.197242	+	1.11862i	−0.909189	+	0.416383i	$0.863297\pi$
$654$	−22.2028	−	54.3139i	−0.868198	−	2.12384i
$655$	35.7811	−	30.0239i	1.39809	−	1.17313i
$656$	−2.89928	+	5.02170i	−0.113198	+	0.196064i
$657$	−7.14777	+	3.25263i	−0.278861	+	0.126897i
$658$	−5.29545	−	5.74937i	−0.206438	−	0.224134i
$659$	7.69234	−	6.45464i	0.299651	−	0.251437i	−0.480548	−	0.876968i	$-0.659562\pi$
$659$	7.69234	−	6.45464i	0.299651	−	0.251437i	0.780199	+	0.625531i	$0.215118\pi$
$660$	2.80291	+	71.8477i	0.109103	+	2.79667i
$661$	27.8215	+	23.3450i	1.08213	+	0.908015i	0.996096	−	0.0882773i	$-0.0281362\pi$
$661$	27.8215	+	23.3450i	1.08213	+	0.908015i	0.0860341	+	0.996292i	$0.472581\pi$
$662$	8.79541	+	7.38023i	0.341843	+	0.286841i
$663$	19.1549	−	12.0784i	0.743914	−	0.469086i
$664$	8.82587	−	7.40578i	0.342510	−	0.287400i
$665$	−5.05282	−	5.48594i	−0.195940	−	0.212736i
$666$	−22.0140	+	46.0873i	−0.853023	+	1.78585i
$667$	6.99478	−	12.1153i	0.270839	−	0.469107i
$668$	34.7121	−	29.1269i	1.34305	−	1.12695i
$669$	−27.9399	−	3.81036i	−1.08022	−	0.147317i
$670$	2.63252	−	14.9298i	0.101703	−	0.576787i
$671$	−32.1649	+	11.7071i	−1.24171	+	0.451946i
$672$	31.8509	−	14.7716i	1.22868	−	0.569828i
$673$	−0.279493	−	1.58508i	−0.0107737	−	0.0611005i	0.978947	−	0.204115i	$-0.0654316\pi$
$673$	−0.279493	−	1.58508i	−0.0107737	−	0.0611005i	−0.989721	+	0.143014i	$0.954320\pi$
$674$	20.3537	+	35.2536i	0.783995	+	1.35792i
$675$	−31.2869	+	9.38786i	−1.20423	+	0.361339i
$676$	−8.84440	+	15.3190i	−0.340169	+	0.589190i
$677$	22.0017	−	18.4616i	0.845595	−	0.709539i	−0.113220	−	0.993570i	$-0.536116\pi$
$677$	22.0017	−	18.4616i	0.845595	−	0.709539i	0.958815	+	0.284031i	$0.0916720\pi$
$678$	38.2036	−	8.28371i	1.46720	−	0.318134i
$679$	25.3379	−	16.2333i	0.972380	−	0.622978i
$680$	11.1061	+	9.31908i	0.425898	+	0.357371i
$681$	8.49796	+	20.7883i	0.325642	+	0.796608i
$682$	−22.8894	+	19.2065i	−0.876479	+	0.735453i
$683$	−32.1700			−1.23095			−0.615475	−	0.788156i	$-0.711036\pi$
$683$	−32.1700			−1.23095			−0.615475	+	0.788156i	$0.711036\pi$
$684$	−6.49022	−	1.80378i	−0.248160	−	0.0689693i
$685$	0.275315	−	0.476860i	0.0105192	−	0.0182199i
$686$	38.1011	−	12.3355i	1.45471	−	0.470971i
$687$	4.90384	−	3.09219i	0.187093	−	0.117974i
$688$	18.2818	−	6.65402i	0.696985	−	0.253682i
$689$	35.8065	+	30.0452i	1.36412	+	1.14463i
$690$	1.21579	+	31.1646i	0.0462843	+	1.18642i
$691$	−29.4250	−	10.7098i	−1.11938	−	0.407421i	−0.284955	−	0.958541i	$-0.591979\pi$
$691$	−29.4250	−	10.7098i	−1.11938	−	0.407421i	−0.834426	+	0.551120i	$0.814201\pi$
$692$	−9.54289	+	16.5288i	−0.362766	+	0.628329i
$693$	−16.7049	−	32.6236i	−0.634568	−	1.23927i
$694$	6.38419	+	11.0577i	0.242341	+	0.419746i
$695$	1.01734	+	5.76961i	0.0385898	+	0.218854i
$696$	−8.75115	+	11.2958i	−0.331711	+	0.428166i
$697$	7.34182	−	2.67220i	0.278091	−	0.101217i
$698$	−18.9783	−	15.9247i	−0.718340	−	0.602759i
$699$	16.2863	−	3.53136i	0.616004	−	0.133568i
$700$	27.0038	−	35.3791i	1.02065	−	1.33720i
$701$	41.0228			1.54941			0.774705	−	0.632323i	$-0.217898\pi$
$701$	41.0228			1.54941			0.774705	+	0.632323i	$0.217898\pi$
$702$	−45.7004	−	19.6796i	−1.72485	−	0.742758i
$703$	3.30321	−	5.72132i	0.124583	−	0.215784i
$704$	52.8732	+	19.2443i	1.99273	+	0.725296i
$705$	7.76939	−	1.68464i	0.292612	−	0.0634472i
$706$	−27.5338	+	10.0215i	−1.03625	+	0.377163i
$707$	20.7579	−	13.2990i	0.780682	−	0.500161i
$708$	−14.1766	−	34.6797i	−0.532789	−	1.30334i
$709$	2.77687	+	15.7484i	0.104288	+	0.591444i	0.991502	+	0.130088i	$0.0415259\pi$
$709$	2.77687	+	15.7484i	0.104288	+	0.591444i	−0.887215	+	0.461356i	$0.847363\pi$
$710$	37.2598			1.39834
$711$	11.6330	−	24.3542i	0.436271	−	0.913355i
$712$	13.6856			0.512889
$713$	−5.68188	+	4.76766i	−0.212788	+	0.178550i
$714$	−28.2433	−	7.63087i	−1.05698	−	0.285578i
$715$	11.9293	−	67.6543i	0.446130	−	2.53013i
$716$	−11.4245	+	4.15819i	−0.426955	+	0.155399i
$717$	34.4469	−	21.7210i	1.28644	−	0.811187i
$718$	10.0769	+	57.1490i	0.376067	+	2.13278i
$719$	−19.8091			−0.738754			−0.369377	−	0.929280i	$-0.620429\pi$
$719$	−19.8091			−0.738754			−0.369377	+	0.929280i	$0.620429\pi$
$720$	−2.12884	+	21.9808i	−0.0793371	+	0.819177i
$721$	5.28237	−	16.9042i	0.196726	−	0.629546i
$722$	−37.1771	−	13.5314i	−1.38359	−	0.503585i
$723$	−26.1398	−	3.56487i	−0.972149	−	0.132579i
$724$	22.7548	−	8.28206i	0.845675	−	0.307800i
$725$	6.16108	−	34.9412i	0.228817	−	1.29768i
$726$	11.7975	−	36.8200i	0.437845	−	1.36652i
$727$	−3.88585	−	22.0377i	−0.144118	−	0.817334i	−0.968071	−	0.250676i	$-0.919347\pi$
$727$	−3.88585	−	22.0377i	−0.144118	−	0.817334i	0.823953	−	0.566658i	$-0.191764\pi$
$728$	16.7102	−	3.74944i	0.619322	−	0.138964i
$729$	7.71156	−	25.8753i	0.285613	−	0.958345i
$730$	9.50823	+	16.4687i	0.351915	+	0.609535i
$731$	−24.6329	−	8.96565i	−0.911082	−	0.331607i
$732$	33.5765	−	7.28041i	1.24102	−	0.269092i
$733$	9.35692	+	7.85139i	0.345606	+	0.289998i	0.799023	−	0.601301i	$-0.205351\pi$
$733$	9.35692	+	7.85139i	0.345606	+	0.289998i	−0.453417	+	0.891299i	$0.649795\pi$
$734$	4.34881	+	3.64908i	0.160517	+	0.134690i
$735$	−8.79712	+	39.7707i	−0.324487	+	1.46696i
$736$	17.8451	+	6.49510i	0.657781	+	0.239413i
$737$	−4.81819	+	8.34534i	−0.177480	+	0.307405i
$738$	−13.9707	−	9.97691i	−0.514268	−	0.367255i
$739$	−11.6636	−	20.2019i	−0.429051	−	0.743138i	0.567738	−	0.823209i	$-0.307819\pi$
$739$	−11.6636	−	20.2019i	−0.429051	−	0.743138i	−0.996789	+	0.0800709i	$0.974485\pi$
$740$	66.5112	+	24.2081i	2.44500	+	0.889907i
$741$	5.69496	+	2.99828i	0.209209	+	0.110145i
$742$	−2.78842	−	60.3236i	−0.102366	−	2.21455i
$743$	4.94730	−	28.0575i	0.181499	−	1.02933i	−0.748873	−	0.662714i	$-0.769405\pi$
$743$	4.94730	−	28.0575i	0.181499	−	1.02933i	0.930372	−	0.366617i	$-0.119484\pi$
$744$	6.40832	−	4.04086i	0.234941	−	0.148145i
$745$	6.17747	+	35.0342i	0.226325	+	1.28355i
$746$	−6.24447	−	10.8157i	−0.228626	−	0.395992i
$747$	−13.3827	−	19.4951i	−0.489647	−	0.713290i
$748$	−18.2409	−	31.5941i	−0.666952	−	1.15519i
$749$	−6.25046	−	14.9814i	−0.228387	−	0.547409i
$750$	6.12472	+	14.9827i	0.223643	+	0.547090i
$751$	−3.64696	+	20.6829i	−0.133079	+	0.754731i	0.843098	+	0.537759i	$0.180729\pi$
$751$	−3.64696	+	20.6829i	−0.133079	+	0.754731i	−0.976178	+	0.216972i	$0.930382\pi$
$752$	0.519838	−	2.94815i	0.0189565	−	0.107508i
$753$	33.7737	+	37.2027i	1.23078	+	1.35574i
$754$	41.4015	−	34.7400i	1.50776	−	1.26516i
$755$	80.2913			2.92210
$756$	12.1887	+	34.7105i	0.443298	+	1.26241i
$757$	51.2608			1.86310			0.931552	−	0.363608i	$-0.118455\pi$
$757$	51.2608			1.86310			0.931552	+	0.363608i	$0.118455\pi$
$758$	3.89660	−	3.26963i	0.141531	−	0.118758i
$759$	6.04905	−	18.8792i	0.219567	−	0.685270i
$760$	−0.715517	+	4.05790i	−0.0259545	+	0.147195i
$761$	−1.17021	+	6.63657i	−0.0424200	+	0.240576i	−0.998644	−	0.0520602i	$-0.983421\pi$
$761$	−1.17021	+	6.63657i	−0.0424200	+	0.240576i	0.956224	+	0.292636i	$0.0945323\pi$
$762$	−0.672181	−	0.0916700i	−0.0243505	−	0.00332085i
$763$	25.1486	−	32.9485i	0.910442	−	1.19282i
$764$	−4.40381	−	7.62762i	−0.159324	−	0.275958i
$765$	21.2348	−	20.8442i	0.767746	−	0.753624i
$766$	−23.0105	−	39.8554i	−0.831404	−	1.44003i
$767$	6.21587	+	35.2520i	0.224442	+	1.27287i
$768$	0.809255	+	0.426057i	0.0292015	+	0.0153740i
$769$	−3.96380	+	22.4798i	−0.142938	+	0.810642i	0.826061	+	0.563580i	$0.190576\pi$
$769$	−3.96380	+	22.4798i	−0.142938	+	0.810642i	−0.969000	+	0.247062i	$0.920535\pi$
$770$	−74.7319	+	47.8787i	−2.69315	+	1.72543i
$771$	−26.3292	+	16.6023i	−0.948224	+	0.597917i
$772$	−28.3969	−	10.3356i	−1.02203	−	0.371988i
$773$	−15.7670	−	27.3093i	−0.567100	−	0.982247i	−0.996851	−	0.0792989i	$-0.974732\pi$
$773$	−15.7670	−	27.3093i	−0.567100	−	0.982247i	0.429751	−	0.902948i	$-0.358601\pi$
$774$	14.3907	+	55.7725i	0.517263	+	2.00470i
$775$	−9.40568	+	16.2911i	−0.337862	+	0.585194i
$776$	−15.6223	−	5.68607i	−0.560810	−	0.204118i
$777$	−35.9487	+	3.06967i	−1.28965	+	0.110124i
$778$	24.5275	+	20.5810i	0.879353	+	0.737865i
$779$	1.70104	+	1.42735i	0.0609462	+	0.0511400i
$780$	−21.0399	+	65.6657i	−0.753348	+	2.35121i
$781$	−22.2555	−	8.10036i	−0.796366	−	0.289854i
$782$	−7.91215	−	13.7042i	−0.282938	−	0.490063i
$783$	21.3442	+	20.1121i	0.762778	+	0.718749i
$784$	12.6091	+	8.73315i	0.450323	+	0.311898i
$785$	−11.4421	−	64.8915i	−0.408387	−	2.31608i
$786$	50.8912	−	11.0348i	1.81523	−	0.393597i
$787$	3.88523	−	22.0342i	0.138493	−	0.785435i	−0.833870	−	0.551961i	$-0.813880\pi$
$787$	3.88523	−	22.0342i	0.138493	−	0.785435i	0.972363	−	0.233474i	$-0.0750092\pi$
$788$	−40.4513	+	14.7231i	−1.44102	+	0.524487i
$789$	23.2006	−	29.9468i	0.825962	−	1.06613i
$790$	−61.4157	−	22.3535i	−2.18507	−	0.795301i
$791$	18.7080	+	20.3116i	0.665179	+	0.722198i
$792$	−8.72758	+	18.2716i	−0.310121	+	0.649254i
$793$	−32.8256			−1.16567
$794$	14.2409	+	80.7640i	0.505390	+	2.86621i
$795$	54.3473	+	28.6128i	1.92750	+	1.01479i
$796$	12.7694	−	4.64769i	0.452600	−	0.164733i
$797$	−0.872685	+	4.94924i	−0.0309121	+	0.175311i	−0.996355	−	0.0853034i	$-0.972814\pi$
$797$	−0.872685	+	4.94924i	−0.0309121	+	0.175311i	0.965443	+	0.260615i	$0.0839252\pi$
$798$	−2.13533	−	8.03609i	−0.0755900	−	0.284474i
$799$	−3.08994	+	2.59277i	−0.109314	+	0.0917255i
$800$	48.1634			1.70283
$801$	2.70769	−	27.9576i	0.0956714	−	0.987832i
$802$	−18.9300			−0.668442
$803$	−2.09900	−	11.9040i	−0.0740720	−	0.420083i
$804$	5.92367	−	7.64613i	0.208912	−	0.269658i
$805$	−18.5509	+	11.8850i	−0.653832	+	0.418892i
$806$	−26.9267	+	9.80050i	−0.948451	+	0.345208i
$807$	7.49292	−	23.3855i	0.263763	−	0.823209i
$808$	−12.7985	−	4.65827i	−0.450249	−	0.163877i
$809$	−17.3627	+	30.0732i	−0.610442	+	1.05732i	0.380724	+	0.924689i	$0.375675\pi$
$809$	−17.3627	+	30.0732i	−0.610442	+	1.05732i	−0.991166	+	0.132627i	$0.957659\pi$
$810$	−64.1664	−	12.5467i	−2.25458	−	0.440846i
$811$	−41.4471			−1.45541			−0.727703	−	0.685893i	$-0.759412\pi$
$811$	−41.4471			−1.45541			−0.727703	+	0.685893i	$0.759412\pi$
$812$	−39.6303	−	5.11433i	−1.39075	−	0.179478i
$813$	−18.9571	−	20.8818i	−0.664854	−	0.732356i
$814$	−60.2235	−	50.5335i	−2.11083	−	1.77120i
$815$	−24.7076	+	8.99281i	−0.865468	+	0.315005i
$816$	−4.23979	−	10.3717i	−0.148423	−	0.363081i
$817$	−1.29373	−	7.33712i	−0.0452620	−	0.256693i
$818$	36.3379	+	62.9390i	1.27052	+	2.20061i
$819$	−4.35343	−	34.8783i	−0.152121	−	1.21875i
$820$	−11.8953	+	20.6032i	−0.415401	+	0.719496i
$821$	32.1342	+	11.6959i	1.12149	+	0.408189i	0.835196	−	0.549953i	$-0.185354\pi$
$821$	32.1342	+	11.6959i	1.12149	+	0.408189i	0.286294	+	0.958142i	$0.407576\pi$
$822$	0.519261	−	0.327427i	0.0181113	−	0.0114203i
$823$	−33.0162	−	27.7039i	−1.15087	−	0.965697i	−0.151133	−	0.988513i	$-0.548292\pi$
$823$	−33.0162	−	27.7039i	−1.15087	−	0.965697i	−0.999740	+	0.0228162i	$0.992737\pi$
$824$	−9.19436	+	3.34647i	−0.320301	+	0.116580i
$825$	−1.95999	−	50.2408i	−0.0682380	−	1.74916i
$826$	28.0589	−	36.7614i	0.976293	−	1.27909i
$827$	−22.2920	+	38.6108i	−0.775168	+	1.34263i	0.159532	+	0.987193i	$0.449001\pi$
$827$	−22.2920	+	38.6108i	−0.775168	+	1.34263i	−0.934700	+	0.355437i	$0.884332\pi$
$828$	−8.57649	+	17.9553i	−0.298054	+	0.623990i
$829$	−28.8914			−1.00344			−0.501719	−	0.865031i	$-0.667299\pi$
$829$	−28.8914			−1.00344			−0.501719	+	0.865031i	$0.667299\pi$
$830$	−43.8644	+	36.8066i	−1.52256	+	1.27758i
$831$	−30.4231	+	39.2694i	−1.05537	+	1.36224i
$832$	41.3352	+	34.6844i	1.43304	+	1.20246i
$833$	−5.45097	−	19.9347i	−0.188865	−	0.690698i
$834$	−1.99295	+	6.22003i	−0.0690103	+	0.215382i
$835$	−43.5791	+	36.5672i	−1.50812	+	1.26546i
$836$	5.18429	−	8.97945i	0.179302	−	0.310561i
$837$	−6.98699	−	13.8907i	−0.241506	−	0.480133i
$838$	−3.22911	−	5.59299i	−0.111548	−	0.193207i
$839$	−6.36419	−	36.0931i	−0.219716	−	1.24607i	−0.872532	−	0.488557i	$-0.837523\pi$
$839$	−6.36419	−	36.0931i	−0.219716	−	1.24607i	0.652816	−	0.757517i	$-0.273588\pi$
$840$	20.4146	−	9.46777i	0.704371	−	0.326669i
$841$	−2.68235	+	0.976295i	−0.0924948	+	0.0336653i
$842$	4.54019	−	25.7487i	0.156465	−	0.887358i
$843$	−0.684921	+	0.884080i	−0.0235899	+	0.0304493i
$844$	6.67272	−	5.59908i	0.229684	−	0.192728i
$845$	11.1037	−	19.2321i	0.381977	−	0.661604i
$846$	8.53936	+	2.37329i	0.293589	+	0.0815953i
$847$	26.6497	−	5.97966i	0.915693	−	0.205463i
$848$	17.7171	−	14.8664i	0.608408	−	0.510515i
$849$	17.2215	+	9.06678i	0.591040	+	0.311171i
$850$	−30.7440	−	25.7973i	−1.05451	−	0.884841i
$851$	−14.9494	−	12.5440i	−0.512459	−	0.430004i
$852$	21.0350	+	11.0745i	0.720646	+	0.379406i
$853$	−1.52194	+	1.27706i	−0.0521104	+	0.0437258i	−0.668471	−	0.743738i	$-0.733051\pi$
$853$	−1.52194	+	1.27706i	−0.0521104	+	0.0437258i	0.616360	+	0.787464i	$0.288606\pi$
$854$	28.7309	+	31.1937i	0.983150	+	1.06742i
$855$	8.14810	+	2.26455i	0.278659	+	0.0774458i
$856$	−4.48413	+	7.76674i	−0.153264	+	0.265462i
$857$	6.20506	−	5.20666i	0.211961	−	0.177856i	−0.530626	−	0.847606i	$-0.678043\pi$
$857$	6.20506	−	5.20666i	0.211961	−	0.177856i	0.742587	+	0.669750i	$0.233599\pi$
$858$	46.9055	−	60.5446i	1.60133	−	2.06696i
$859$	7.86636	−	44.6123i	0.268397	−	1.52215i	−0.490789	−	0.871279i	$-0.663291\pi$
$859$	7.86636	−	44.6123i	0.268397	−	1.52215i	0.759185	−	0.650875i	$-0.225598\pi$
$860$	75.0072	−	27.3004i	2.55772	−	0.930935i
$861$	1.08211	−	12.0787i	0.0368781	−	0.411642i
$862$	9.42453	+	53.4491i	0.321001	+	1.82048i
$863$	−22.7185	−	39.3497i	−0.773348	−	1.33948i	−0.935718	−	0.352749i	$-0.885247\pi$
$863$	−22.7185	−	39.3497i	−0.773348	−	1.33948i	0.162370	−	0.986730i	$-0.448086\pi$
$864$	−21.8556	+	33.2748i	−0.743542	+	1.13203i
$865$	11.9806	−	20.7509i	0.407351	−	0.705553i
$866$	−64.2453	+	53.9082i	−2.18314	+	1.83188i
$867$	4.37783	−	13.6633i	0.148679	−	0.464029i
$868$	18.8171	+	9.73449i	0.638696	+	0.330410i
$869$	31.8243	+	26.7038i	1.07957	+	0.905864i
$870$	43.4931	−	56.1399i	1.47455	−	1.90332i
$871$	−7.07920	+	5.94016i	−0.239870	+	0.201275i
$872$	−22.8996			−0.775478
$873$	−14.7067	+	30.7891i	−0.497745	+	1.04205i
$874$	2.24873	−	3.89492i	0.0760646	−	0.131748i
$875$	−6.93734	+	9.08897i	−0.234525	+	0.307263i
$876$	0.472959	+	12.1235i	0.0159798	+	0.409614i
$877$	−22.4907	+	8.18595i	−0.759458	+	0.276420i	−0.692580	−	0.721341i	$-0.743526\pi$
$877$	−22.4907	+	8.18595i	−0.759458	+	0.276420i	−0.0668779	+	0.997761i	$0.521304\pi$
$878$	−12.6443	−	10.6098i	−0.426724	−	0.358064i
$879$	−18.7672	+	11.8339i	−0.633001	+	0.399148i
$880$	−31.9419	−	11.6259i	−1.07676	−	0.391909i
$881$	−22.7785	+	39.4536i	−0.767429	+	1.32923i	0.171524	+	0.985180i	$0.445131\pi$
$881$	−22.7785	+	39.4536i	−0.767429	+	1.32923i	−0.938953	+	0.344045i	$0.888203\pi$
$882$	−29.3339	+	34.6644i	−0.987723	+	1.16721i
$883$	9.34145	+	16.1799i	0.314365	+	0.544496i	0.979302	−	0.202403i	$-0.0648751\pi$
$883$	9.34145	+	16.1799i	0.314365	+	0.544496i	−0.664937	+	0.746899i	$0.731542\pi$
$884$	−6.07522	−	34.4543i	−0.204332	−	1.15882i
$885$	17.7979	+	43.5385i	0.598271	+	1.46353i
$886$	11.4155	−	4.15489i	0.383510	−	0.139586i
$887$	43.0990	+	36.1643i	1.44712	+	1.21428i	0.934647	+	0.355576i	$0.115715\pi$
$887$	43.0990	+	36.1643i	1.44712	+	1.21428i	0.512474	+	0.858703i	$0.328729\pi$
$888$	13.3981	+	14.7584i	0.449611	+	0.495259i
$889$	−0.184524	−	0.442277i	−0.00618874	−	0.0148335i
$890$	−68.0171			−2.27994
$891$	35.5994	+	21.4442i	1.19262	+	0.718406i
$892$	−21.7829	+	37.7291i	−0.729346	+	1.26326i
$893$	−1.07727	−	0.392095i	−0.0360495	−	0.0131210i
$894$	−12.1016	+	37.7692i	−0.404738	+	1.26319i
$895$	14.3429	−	5.22038i	0.479430	−	0.174498i
$896$	−1.34698	−	29.1401i	−0.0449996	−	0.973504i
$897$	11.6435	−	15.0291i	0.388764	−	0.501807i
$898$	−11.6294	−	65.9535i	−0.388077	−	2.20090i
$899$	16.8890			0.563281
$900$	−4.86490	+	50.2314i	−0.162163	+	1.67438i
$901$	−31.1628			−1.03818
$902$	20.2424	−	16.9854i	0.673998	−	0.565551i
$903$	−28.8308	+	28.7110i	−0.959430	+	0.955441i
$904$	2.64919	−	15.0243i	0.0881108	−	0.499701i
$905$	−28.5674	+	10.3977i	−0.949611	+	0.345630i
$906$	79.2065	+	41.7007i	2.63146	+	1.38541i
$907$	3.82285	+	21.6804i	0.126936	+	0.719887i	0.980139	+	0.198310i	$0.0635452\pi$
$907$	3.82285	+	21.6804i	0.126936	+	0.719887i	−0.853204	+	0.521578i	$0.825344\pi$
$908$	34.6970			1.15146
$909$	−12.0483	+	25.2237i	−0.399617	+	0.836619i
$910$	−83.0496	+	18.6347i	−2.75307	+	0.617733i
$911$	−27.5675	−	10.0338i	−0.913353	−	0.332433i	−0.157762	−	0.987477i	$-0.550428\pi$
$911$	−27.5675	−	10.0338i	−0.913353	−	0.332433i	−0.755591	+	0.655044i	$0.772650\pi$
$912$	1.95033	−	2.51744i	0.0645820	−	0.0833609i
$913$	34.2024	−	12.4487i	1.13193	−	0.411990i
$914$	1.37618	−	7.80470i	0.0455200	−	0.258157i
$915$	−42.1534	+	9.14015i	−1.39355	+	0.302164i
$916$	−1.55532	−	8.82065i	−0.0513892	−	0.291442i
$917$	24.9210	+	27.0572i	0.822962	+	0.893506i
$918$	31.7737	−	9.53392i	1.04869	−	0.314666i
$919$	−17.5525	−	30.4018i	−0.579003	−	1.00286i	−0.995594	−	0.0937690i	$-0.970108\pi$
$919$	−17.5525	−	30.4018i	−0.579003	−	1.00286i	0.416591	−	0.909094i	$-0.363225\pi$
$920$	11.4377	+	4.16299i	0.377090	+	0.137250i
$921$	−3.38954	+	10.5788i	−0.111689	+	0.348583i
$922$	27.0637	+	22.7091i	0.891296	+	0.747886i
$923$	−17.3990	−	14.5995i	−0.572694	−	0.480547i
$924$	−56.4205	+	4.81776i	−1.85610	+	0.158493i
$925$	−46.5091	−	16.9279i	−1.52921	−	0.556587i
$926$	−1.00528	+	1.74119i	−0.0330354	+	0.0572190i
$927$	5.01724	+	19.4448i	0.164788	+	0.638650i
$928$	−21.6208	−	37.4483i	−0.709737	−	1.22930i
$929$	−0.262954	−	0.0957075i	−0.00862725	−	0.00314006i	0.337703	−	0.941253i	$-0.390350\pi$
$929$	−0.262954	−	0.0957075i	−0.00862725	−	0.00314006i	−0.346330	+	0.938113i	$0.612572\pi$
$930$	−31.8493	+	20.0830i	−1.04438	+	0.658549i
$931$	4.13203	−	4.17454i	0.135422	−	0.136815i
$932$	4.47083	−	25.3554i	0.146447	−	0.830542i
$933$	−30.4085	−	16.0095i	−0.995531	−	0.524127i
$934$	−2.26915	−	12.8690i	−0.0742488	−	0.421086i
$935$	22.9004	+	39.6646i	0.748923	+	1.29717i
$936$	−13.8580	+	13.6031i	−0.452962	+	0.444630i
$937$	26.7259	+	46.2907i	0.873098	+	1.51225i	0.858775	+	0.512353i	$0.171226\pi$
$937$	26.7259	+	46.2907i	0.873098	+	1.51225i	0.0143237	+	0.999897i	$0.495440\pi$
$938$	11.8410	+	1.52808i	0.386621	+	0.0498937i
$939$	20.1760	+	2.75154i	0.658419	+	0.0897932i
$940$	2.13281	−	12.0958i	0.0695647	−	0.394521i
$941$	3.30616	−	18.7502i	0.107778	−	0.611238i	−0.882297	−	0.470694i	$-0.844004\pi$
$941$	3.30616	−	18.7502i	0.107778	−	0.611238i	0.990074	−	0.140544i	$-0.0448852\pi$
$942$	22.4150	−	69.9575i	0.730320	−	2.27934i
$943$	5.02481	−	4.21632i	0.163630	−	0.137302i
$944$	17.7118			0.576470
$945$	−15.3022	−	43.5772i	−0.497781	−	1.41757i
$946$	−88.6584			−2.88253
$947$	−2.22862	+	1.87003i	−0.0724203	+	0.0607678i	−0.678279	−	0.734804i	$-0.737274\pi$
$947$	−2.22862	+	1.87003i	−0.0724203	+	0.0607678i	0.605859	+	0.795572i	$0.292830\pi$
$948$	−28.0281	−	30.8738i	−0.910312	−	1.00273i
$949$	2.01293	−	11.4159i	0.0653425	−	0.370575i
$950$	1.98071	−	11.2332i	0.0642627	−	0.364452i
$951$	1.55603	+	3.80645i	0.0504576	+	0.123433i
$952$	−6.92744	+	9.07599i	−0.224520	+	0.294155i
$953$	6.98653	+	12.1010i	0.226316	+	0.391991i	0.956713	−	0.291032i	$-0.0939985\pi$
$953$	6.98653	+	12.1010i	0.226316	+	0.391991i	−0.730398	+	0.683022i	$0.760665\pi$
$954$	38.7525	+	56.4524i	1.25466	+	1.82771i
$955$	5.52874	+	9.57605i	0.178906	+	0.309874i
$956$	−10.9253	−	61.9605i	−0.353350	−	2.00395i
$957$	−38.1837	+	24.0773i	−1.23430	+	0.778308i
$958$	6.71169	−	38.0639i	0.216845	−	1.22979i
$959$	0.385156	+	0.199249i	0.0124373	+	0.00643409i
$960$	62.7389	+	33.0308i	2.02489	+	1.06606i
$961$	20.7160	+	7.54002i	0.668259	+	0.243227i
$962$	−37.6963	−	65.2919i	−1.21538	−	2.10509i
$963$	14.9791	+	10.6970i	0.482695	+	0.344707i
$964$	−20.3795	+	35.2983i	−0.656379	+	1.13688i
$965$	35.6508	+	12.9758i	1.14764	+	0.417706i
$966$	−24.4729	+	2.08975i	−0.787404	+	0.0672365i
$967$	30.3105	+	25.4335i	0.974720	+	0.817887i	0.983284	−	0.182076i	$-0.0582817\pi$
$967$	30.3105	+	25.4335i	0.974720	+	0.817887i	−0.00856441	+	0.999963i	$0.502726\pi$
$968$	−11.5590	−	9.69916i	−0.371521	−	0.311743i
$969$	−4.19343	+	0.909262i	−0.134712	+	0.0292097i
$970$	77.6428	+	28.2597i	2.49296	+	0.907364i
$971$	−13.8858	−	24.0508i	−0.445615	−	0.771828i	0.552479	−	0.833526i	$-0.313682\pi$
$971$	−13.8858	−	24.0508i	−0.445615	−	0.771828i	−0.998095	+	0.0616980i	$0.980348\pi$
$972$	−32.4959	−	26.1550i	−1.04231	−	0.838922i
$973$	−4.50195	+	1.01015i	−0.144326	+	0.0323839i
$974$	7.90300	+	44.8201i	0.253228	+	1.43613i
$975$	14.7125	−	45.9179i	0.471177	−	1.47055i
$976$	−2.82042	+	15.9954i	−0.0902795	+	0.512001i
$977$	9.65761	−	3.51508i	0.308974	−	0.112457i	−0.182879	−	0.983135i	$-0.558542\pi$
$977$	9.65761	−	3.51508i	0.308974	−	0.112457i	0.491854	+	0.870678i	$0.336320\pi$
$978$	−29.0443	−	3.96098i	−0.928735	−	0.126658i
$979$	40.6271	+	14.7871i	1.29845	+	0.472596i
$980$	51.7330	+	35.8308i	1.65255	+	1.14457i
$981$	−4.53068	+	46.7804i	−0.144653	+	1.49358i
$982$	54.1015			1.72645
$983$	1.41371	+	8.01753i	0.0450902	+	0.255719i	0.999017	−	0.0443187i	$-0.0141117\pi$
$983$	1.41371	+	8.01753i	0.0450902	+	0.255719i	−0.953927	+	0.300038i	$0.903001\pi$
$984$	−5.66725	+	3.57357i	−0.180665	+	0.113921i
$985$	50.7843	−	18.4840i	1.61812	−	0.588949i
$986$	−6.25693	+	35.4848i	−0.199261	+	1.13007i
$987$	1.60783	+	6.05090i	0.0511779	+	0.192602i
$988$	7.61710	−	6.39151i	0.242332	−	0.203341i
$989$	−22.0079			−0.699810
$990$	43.3759	−	90.8097i	1.37858	−	2.88612i
$991$	−54.8725			−1.74308			−0.871542	−	0.490321i	$-0.836879\pi$
$991$	−54.8725			−1.74308			−0.871542	+	0.490321i	$0.836879\pi$
$992$	3.98112	+	22.5781i	0.126401	+	0.716854i
$993$	−3.47992	−	8.51280i	−0.110432	−	0.270145i
$994$	1.35494	+	29.3122i	0.0429760	+	0.929727i
$995$	−16.0313	+	5.83492i	−0.508226	+	0.184979i
$996$	−35.7034	+	7.74159i	−1.13131	+	0.245302i
$997$	−20.3347	−	7.40123i	−0.644006	−	0.234399i	−0.000690196	−	1.00000i	$-0.500220\pi$
$997$	−20.3347	−	7.40123i	−0.644006	−	0.234399i	−0.643316	+	0.765601i	$0.722442\pi$
$998$	−23.8699	+	41.3439i	−0.755589	+	1.30872i
$999$	32.8000	−	24.4503i	1.03775	−	0.773575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.67.3	✓	132
3.2	odd	2		567.2.u.a.172.20		132
7.2	even	3		189.2.w.a.121.20	yes	132
21.2	odd	6		567.2.w.a.415.3		132
27.2	odd	18		567.2.w.a.235.3		132
27.25	even	9		189.2.w.a.25.20	yes	132
189.2	odd	18		567.2.u.a.478.20		132
189.79	even	9	inner	189.2.u.a.79.3	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.3	✓	132	1.1	even	1	trivial
189.2.u.a.79.3	yes	132	189.79	even	9	inner
189.2.w.a.25.20	yes	132	27.25	even	9
189.2.w.a.121.20	yes	132	7.2	even	3
567.2.u.a.172.20		132	3.2	odd	2
567.2.u.a.478.20		132	189.2	odd	18
567.2.w.a.235.3		132	27.2	odd	18
567.2.w.a.415.3		132	21.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65649 + 1.38996i) q^{2} +(1.69272 - 0.367032i) q^{3} +(0.464676 - 2.63531i) q^{4} +(-0.583375 + 3.30848i) q^{5} +(-2.29381 + 2.96080i) q^{6} +(-2.62399 - 0.338628i) q^{7} +(0.730849 + 1.26587i) q^{8} +(2.73057 - 1.24256i) q^{9} +O(q^{10})\)	\(q+(-1.65649 + 1.38996i) q^{2} +(1.69272 - 0.367032i) q^{3} +(0.464676 - 2.63531i) q^{4} +(-0.583375 + 3.30848i) q^{5} +(-2.29381 + 2.96080i) q^{6} +(-2.62399 - 0.338628i) q^{7} +(0.730849 + 1.26587i) q^{8} +(2.73057 - 1.24256i) q^{9} +(-3.63231 - 6.29135i) q^{10} +(0.801854 + 4.54754i) q^{11} +(-0.180679 - 4.63138i) q^{12} +(-0.768974 + 4.36107i) q^{13} +(4.81730 - 3.08631i) q^{14} +(0.226832 + 5.81444i) q^{15} +(2.05901 + 0.749418i) q^{16} +(-1.47618 - 2.55683i) q^{17} +(-2.79606 + 5.85369i) q^{18} +(0.419551 - 0.726683i) q^{19} +(8.44779 + 3.07474i) q^{20} +(-4.56596 + 0.389888i) q^{21} +(-7.64917 - 6.41842i) q^{22} +(-1.89877 - 1.59326i) q^{23} +(1.70173 + 1.87451i) q^{24} +(-5.90727 - 2.15007i) q^{25} +(-4.78792 - 8.29293i) q^{26} +(4.16603 - 3.10551i) q^{27} +(-2.11170 + 6.75767i) q^{28} +(0.980067 + 5.55823i) q^{29} +(-8.45760 - 9.31629i) q^{30} +(0.519624 - 2.94694i) q^{31} +(-7.19949 + 2.62040i) q^{32} +(3.02640 + 7.40338i) q^{33} +(5.99918 + 2.18352i) q^{34} +(2.65112 - 8.48388i) q^{35} +(-2.00570 - 7.77329i) q^{36} +7.87320 q^{37} +(0.315079 + 1.78690i) q^{38} +(0.298998 + 7.66429i) q^{39} +(-4.61446 + 1.67953i) q^{40} +(-0.459534 + 2.60615i) q^{41} +(7.02155 - 6.99236i) q^{42} +(6.80164 - 5.70725i) q^{43} +12.3568 q^{44} +(2.51805 + 9.75894i) q^{45} +5.35987 q^{46} +(-0.237244 - 1.34548i) q^{47} +(3.76038 + 0.512829i) q^{48} +(6.77066 + 1.77711i) q^{49} +(12.7739 - 4.64931i) q^{50} +(-3.43720 - 3.78617i) q^{51} +(11.1354 + 4.05297i) q^{52} +(5.27760 - 9.14106i) q^{53} +(-2.58444 + 10.9349i) q^{54} -15.5132 q^{55} +(-1.48908 - 3.56911i) q^{56} +(0.443464 - 1.38406i) q^{57} +(-9.34921 - 7.84492i) q^{58} +(7.59585 - 2.76466i) q^{59} +(15.4282 + 2.10406i) q^{60} +(1.28719 + 7.30000i) q^{61} +(3.23538 + 5.60384i) q^{62} +(-7.58577 + 2.33582i) q^{63} +(6.09249 - 10.5525i) q^{64} +(-13.9799 - 5.08828i) q^{65} +(-15.3036 - 8.05706i) q^{66} +(1.59861 + 1.34139i) q^{67} +(-7.42397 + 2.70210i) q^{68} +(-3.79886 - 2.00002i) q^{69} +(7.40072 + 17.7384i) q^{70} +(-2.56447 + 4.44179i) q^{71} +(3.56856 + 2.54842i) q^{72} -2.61768 q^{73} +(-13.0419 + 10.9435i) q^{74} +(-10.7885 - 1.47130i) q^{75} +(-1.72008 - 1.44332i) q^{76} +(-0.564133 - 12.2042i) q^{77} +(-11.1484 - 12.2802i) q^{78} +(6.89183 - 5.78293i) q^{79} +(-3.68061 + 6.37500i) q^{80} +(5.91208 - 6.78582i) q^{81} +(-2.86123 - 4.95580i) q^{82} +(-1.36872 - 7.76242i) q^{83} +(-1.09422 + 12.2139i) q^{84} +(9.32038 - 3.39234i) q^{85} +(-3.33400 + 18.9080i) q^{86} +(3.69903 + 9.04880i) q^{87} +(-5.17055 + 4.33861i) q^{88} +(4.68139 - 8.10841i) q^{89} +(-17.7357 - 12.6656i) q^{90} +(3.49456 - 11.1830i) q^{91} +(-5.08104 + 4.26350i) q^{92} +(-0.202044 - 5.17905i) q^{93} +(2.26316 + 1.89901i) q^{94} +(2.15946 + 1.81200i) q^{95} +(-11.2249 + 7.07804i) q^{96} +(-8.71278 + 7.31089i) q^{97} +(-13.6857 + 6.46719i) q^{98} +(7.84012 + 11.4210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

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