LMFDB - Embedded newform 171.2.x.a.110.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(14,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 7]))

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

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

chi := DirichletCharacter("171.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (of order $18$, 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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			110.2
Character	$\chi$	$=$	171.110
Dual form			171.2.x.a.14.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86688 + 1.56649i) q^{2} +(-1.40345 - 1.01505i) q^{3} +(0.684023 - 3.87929i) q^{4} +(0.0603078 - 0.165694i) q^{5} +(4.21014 - 0.303523i) q^{6} +(0.340059 + 0.588999i) q^{7} +(2.36286 + 4.09260i) q^{8} +(0.939343 + 2.84915i) q^{9} +O(q^{10})$	\(q+(-1.86688 + 1.56649i) q^{2} +(-1.40345 - 1.01505i) q^{3} +(0.684023 - 3.87929i) q^{4} +(0.0603078 - 0.165694i) q^{5} +(4.21014 - 0.303523i) q^{6} +(0.340059 + 0.588999i) q^{7} +(2.36286 + 4.09260i) q^{8} +(0.939343 + 2.84915i) q^{9} +(0.146972 + 0.403802i) q^{10} +5.07127i q^{11} +(-4.89766 + 4.75006i) q^{12} +(-0.848831 - 2.33215i) q^{13} +(-1.55751 - 0.566888i) q^{14} +(-0.252827 + 0.171328i) q^{15} +(-3.41905 - 1.24443i) q^{16} +(-1.07653 + 2.95775i) q^{17} +(-6.21681 - 3.84753i) q^{18} +(-0.122437 + 4.35718i) q^{19} +(-0.601523 - 0.347290i) q^{20} +(0.120609 - 1.17181i) q^{21} +(-7.94412 - 9.46744i) q^{22} +(-0.413419 - 0.0728969i) q^{23} +(0.838036 - 8.14218i) q^{24} +(3.80640 + 3.19395i) q^{25} +(5.23796 + 3.02414i) q^{26} +(1.57371 - 4.95212i) q^{27} +(2.51750 - 0.916297i) q^{28} +(0.0433231 - 0.245698i) q^{29} +(0.203612 - 0.715901i) q^{30} +9.69968i q^{31} +(-0.549104 + 0.199857i) q^{32} +(5.14760 - 7.11728i) q^{33} +(-2.62355 - 7.20814i) q^{34} +(0.118102 - 0.0208246i) q^{35} +(11.6952 - 1.69510i) q^{36} +5.05202i q^{37} +(-6.59692 - 8.32611i) q^{38} +(-1.17595 + 4.13466i) q^{39} +(0.820619 - 0.144697i) q^{40} +(8.91555 - 7.48103i) q^{41} +(1.61047 + 2.37655i) q^{42} +(0.329703 + 1.86984i) q^{43} +(19.6729 + 3.46887i) q^{44} +(0.528737 + 0.0161819i) q^{45} +(0.885995 - 0.511529i) q^{46} +(0.352276 + 0.0621158i) q^{47} +(3.53531 + 5.21702i) q^{48} +(3.26872 - 5.66159i) q^{49} -12.1094 q^{50} +(4.51313 - 3.05832i) q^{51} +(-9.62768 + 1.69762i) q^{52} +(-4.97407 - 4.17374i) q^{53} +(4.81954 + 11.7102i) q^{54} +(0.840281 + 0.305837i) q^{55} +(-1.60702 + 2.78345i) q^{56} +(4.59459 - 5.99080i) q^{57} +(0.304005 + 0.526553i) q^{58} +(-0.574271 - 3.25685i) q^{59} +(0.491691 + 1.09798i) q^{60} +(-7.26652 + 2.64480i) q^{61} +(-15.1945 - 18.1081i) q^{62} +(-1.35871 + 1.52215i) q^{63} +(4.35051 - 7.53531i) q^{64} -0.437614 q^{65} +(1.53925 + 21.3508i) q^{66} +(-4.89332 + 5.83164i) q^{67} +(10.7376 + 6.19936i) q^{68} +(0.506219 + 0.521949i) q^{69} +(-0.187860 + 0.223883i) q^{70} +(-10.2100 + 8.56721i) q^{71} +(-9.44087 + 10.5765i) q^{72} +(-2.55026 - 14.4632i) q^{73} +(-7.91396 - 9.43149i) q^{74} +(-2.10007 - 8.34625i) q^{75} +(16.8190 + 3.45538i) q^{76} +(-2.98698 + 1.72453i) q^{77} +(-4.28156 - 9.56101i) q^{78} +(2.04479 - 5.61802i) q^{79} +(-0.412391 + 0.491469i) q^{80} +(-7.23527 + 5.35265i) q^{81} +(-4.92522 + 27.9323i) q^{82} +(-0.844295 + 0.487454i) q^{83} +(-4.46328 - 1.26942i) q^{84} +(0.425160 + 0.356751i) q^{85} +(-3.54460 - 2.97428i) q^{86} +(-0.310198 + 0.300849i) q^{87} +(-20.7547 + 11.9827i) q^{88} +(-1.48229 + 8.40648i) q^{89} +(-1.01243 + 0.798054i) q^{90} +(1.08498 - 1.29303i) q^{91} +(-0.565576 + 1.55391i) q^{92} +(9.84567 - 13.6130i) q^{93} +(-0.754960 + 0.435876i) q^{94} +(0.714576 + 0.283059i) q^{95} +(0.973505 + 0.276878i) q^{96} +(8.73912 + 10.4149i) q^{97} +(2.76656 + 15.6899i) q^{98} +(-14.4488 + 4.76367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−1.86688	+	1.56649i	−1.32008	+	1.10768i	−0.333792	+	0.942647i	$0.608328\pi$
$2$	−1.86688	+	1.56649i	−1.32008	+	1.10768i	−0.986288	+	0.165032i	$0.947227\pi$
$3$	−1.40345	−	1.01505i	−0.810282	−	0.586040i
$3$	−1.40345	−	1.01505i	−0.810282	−	0.586040i
$4$	0.684023	−	3.87929i	0.342011	−	1.93964i
$5$	0.0603078	−	0.165694i	0.0269705	−	0.0741007i	−0.925477	−	0.378805i	$-0.876335\pi$
$5$	0.0603078	−	0.165694i	0.0269705	−	0.0741007i	0.952447	+	0.304704i	$0.0985575\pi$
$6$	4.21014	−	0.303523i	1.71878	−	0.123913i
$7$	0.340059	+	0.588999i	0.128530	+	0.222621i	0.923107	−	0.384542i	$-0.125641\pi$
$7$	0.340059	+	0.588999i	0.128530	+	0.222621i	−0.794577	+	0.607163i	$0.792307\pi$
$8$	2.36286	+	4.09260i	0.835398	+	1.44695i
$9$	0.939343	+	2.84915i	0.313114	+	0.949715i
$10$	0.146972	+	0.403802i	0.0464766	+	0.127694i
$11$			5.07127i			1.52905i	0.644596	+	0.764523i	$0.277026\pi$
$11$			5.07127i			1.52905i	−0.644596	+	0.764523i	$0.722974\pi$
$12$	−4.89766	+	4.75006i	−1.41383	+	1.37123i
$13$	−0.848831	−	2.33215i	−0.235423	−	0.646821i	−0.999997	−	0.00228466i	$-0.999273\pi$
$13$	−0.848831	−	2.33215i	−0.235423	−	0.646821i	0.764574	−	0.644536i	$-0.222949\pi$
$14$	−1.55751	−	0.566888i	−0.416263	−	0.151507i
$15$	−0.252827	+	0.171328i	−0.0652797	+	0.0442367i
$16$	−3.41905	−	1.24443i	−0.854764	−	0.311109i
$17$	−1.07653	+	2.95775i	−0.261098	+	0.717361i	0.737996	+	0.674805i	$0.235772\pi$
$17$	−1.07653	+	2.95775i	−0.261098	+	0.717361i	−0.999094	+	0.0425558i	$0.986450\pi$
$18$	−6.21681	−	3.84753i	−1.46532	−	0.906871i
$19$	−0.122437	+	4.35718i	−0.0280891	+	0.999605i
$19$	−0.122437	+	4.35718i	−0.0280891	+	0.999605i
$20$	−0.601523	−	0.347290i	−0.134505	−	0.0776563i
$21$	0.120609	−	1.17181i	0.0263190	−	0.255710i
$22$	−7.94412	−	9.46744i	−1.69369	−	2.01846i
$23$	−0.413419	−	0.0728969i	−0.0862038	−	0.0152001i	0.130380	−	0.991464i	$-0.458380\pi$
$23$	−0.413419	−	0.0728969i	−0.0862038	−	0.0152001i	−0.216584	+	0.976264i	$0.569491\pi$
$24$	0.838036	−	8.14218i	0.171063	−	1.66202i
$25$	3.80640	+	3.19395i	0.761281	+	0.638791i
$26$	5.23796	+	3.02414i	1.02725	+	0.593082i
$27$	1.57371	−	4.95212i	0.302860	−	0.953035i
$28$	2.51750	−	0.916297i	0.475764	−	0.173164i
$29$	0.0433231	−	0.245698i	0.00804490	−	0.0456249i	−0.980521	−	0.196414i	$-0.937070\pi$
$29$	0.0433231	−	0.245698i	0.00804490	−	0.0456249i	0.988566	+	0.150789i	$0.0481814\pi$
$30$	0.203612	−	0.715901i	0.0371743	−	0.130705i
$31$			9.69968i			1.74211i	0.491181	+	0.871057i	$0.336565\pi$
$31$			9.69968i			1.74211i	−0.491181	+	0.871057i	$0.663435\pi$
$32$	−0.549104	+	0.199857i	−0.0970687	+	0.0353301i
$33$	5.14760	−	7.11728i	0.896083	−	1.23896i
$34$	−2.62355	−	7.20814i	−0.449935	−	1.23619i
$35$	0.118102	−	0.0208246i	0.0199629	−	0.00352000i
$36$	11.6952	−	1.69510i	1.94920	−	0.282516i
$37$			5.05202i			0.830547i	0.909697	+	0.415273i	$0.136314\pi$
$37$			5.05202i			0.830547i	−0.909697	+	0.415273i	$0.863686\pi$
$38$	−6.59692	−	8.32611i	−1.07016	−	1.35067i
$39$	−1.17595	+	4.13466i	−0.188303	+	0.662075i
$40$	0.820619	−	0.144697i	0.129751	−	0.0228786i
$41$	8.91555	−	7.48103i	1.39237	−	1.16834i	0.428007	−	0.903776i	$-0.359216\pi$
$41$	8.91555	−	7.48103i	1.39237	−	1.16834i	0.964368	−	0.264565i	$-0.0852285\pi$
$42$	1.61047	+	2.37655i	0.248501	+	0.366710i
$43$	0.329703	+	1.86984i	0.0502792	+	0.285147i	0.999572	−	0.0292450i	$-0.00931031\pi$
$43$	0.329703	+	1.86984i	0.0502792	+	0.285147i	−0.949293	+	0.314393i	$0.898199\pi$
$44$	19.6729	+	3.46887i	2.96580	+	0.522951i
$45$	0.528737	+	0.0161819i	0.0788194	+	0.00241226i
$46$	0.885995	−	0.511529i	0.130633	−	0.0754209i
$47$	0.352276	+	0.0621158i	0.0513848	+	0.00906052i	0.199281	−	0.979942i	$-0.436139\pi$
$47$	0.352276	+	0.0621158i	0.0513848	+	0.00906052i	−0.147897	+	0.989003i	$0.547250\pi$
$48$	3.53531	+	5.21702i	0.510278	+	0.753011i
$49$	3.26872	−	5.66159i	0.466960	−	0.808798i
$50$	−12.1094			−1.71253
$51$	4.51313	−	3.05832i	0.631965	−	0.428251i
$52$	−9.62768	+	1.69762i	−1.33512	+	0.235417i
$53$	−4.97407	−	4.17374i	−0.683241	−	0.573308i	0.233710	−	0.972306i	$-0.424913\pi$
$53$	−4.97407	−	4.17374i	−0.683241	−	0.573308i	−0.916951	+	0.398999i	$0.869358\pi$
$54$	4.81954	+	11.7102i	0.655857	+	1.59355i
$55$	0.840281	+	0.305837i	0.113303	+	0.0412391i
$56$	−1.60702	+	2.78345i	−0.214748	+	0.371954i
$57$	4.59459	−	5.99080i	0.608569	−	0.793501i
$58$	0.304005	+	0.526553i	0.0399178	+	0.0691397i
$59$	−0.574271	−	3.25685i	−0.0747637	−	0.424006i	−0.999100	−	0.0424263i	$-0.986491\pi$
$59$	−0.574271	−	3.25685i	−0.0747637	−	0.424006i	0.924336	−	0.381580i	$-0.124620\pi$
$60$	0.491691	+	1.09798i	0.0634771	+	0.141749i
$61$	−7.26652	+	2.64480i	−0.930382	+	0.338632i	−0.762361	−	0.647152i	$-0.775960\pi$
$61$	−7.26652	+	2.64480i	−0.930382	+	0.338632i	−0.168021	+	0.985783i	$0.553738\pi$
$62$	−15.1945	−	18.1081i	−1.92970	−	2.29973i
$63$	−1.35871	+	1.52215i	−0.171182	+	0.191773i
$64$	4.35051	−	7.53531i	0.543814	−	0.941914i
$65$	−0.437614			−0.0542794
$66$	1.53925	+	21.3508i	0.189468	+	2.62810i
$67$	−4.89332	+	5.83164i	−0.597815	+	0.712448i	−0.977088	−	0.212837i	$-0.931730\pi$
$67$	−4.89332	+	5.83164i	−0.597815	+	0.712448i	0.379273	+	0.925285i	$0.376174\pi$
$68$	10.7376	+	6.19936i	1.30213	+	0.751782i
$69$	0.506219	+	0.521949i	0.0609416	+	0.0628352i
$70$	−0.187860	+	0.223883i	−0.0224536	+	0.0267591i
$71$	−10.2100	+	8.56721i	−1.21170	+	1.01674i	−0.212488	+	0.977164i	$0.568157\pi$
$71$	−10.2100	+	8.56721i	−1.21170	+	1.01674i	−0.999217	+	0.0395775i	$0.987399\pi$
$72$	−9.44087	+	10.5765i	−1.11262	+	1.24645i
$73$	−2.55026	−	14.4632i	−0.298485	−	1.69279i	−0.652689	−	0.757626i	$-0.726359\pi$
$73$	−2.55026	−	14.4632i	−0.298485	−	1.69279i	0.354204	−	0.935168i	$-0.384752\pi$
$74$	−7.91396	−	9.43149i	−0.919979	−	1.09639i
$75$	−2.10007	−	8.34625i	−0.242496	−	0.963742i
$76$	16.8190	+	3.45538i	1.92927	+	0.396359i
$77$	−2.98698	+	1.72453i	−0.340398	+	0.196529i
$78$	−4.28156	−	9.56101i	−0.484791	−	1.08257i
$79$	2.04479	−	5.61802i	0.230057	−	0.632077i	−0.769924	−	0.638135i	$-0.779706\pi$
$79$	2.04479	−	5.61802i	0.230057	−	0.632077i	0.999982	+	0.00605797i	$0.00192832\pi$
$80$	−0.412391	+	0.491469i	−0.0461067	+	0.0549479i
$81$	−7.23527	+	5.35265i	−0.803919	+	0.594739i
$82$	−4.92522	+	27.9323i	−0.543900	+	3.08461i
$83$	−0.844295	+	0.487454i	−0.0926734	+	0.0535050i	−0.545621	−	0.838032i	$-0.683706\pi$
$83$	−0.844295	+	0.487454i	−0.0926734	+	0.0535050i	0.452947	+	0.891537i	$0.350373\pi$
$84$	−4.46328	−	1.26942i	−0.486984	−	0.138505i
$85$	0.425160	+	0.356751i	0.0461150	+	0.0386951i
$86$	−3.54460	−	2.97428i	−0.382224	−	0.320724i
$87$	−0.310198	+	0.300849i	−0.0332567	+	0.0322544i
$88$	−20.7547	+	11.9827i	−2.21246	+	1.27736i
$89$	−1.48229	+	8.40648i	−0.157122	+	0.891085i	0.799698	+	0.600403i	$0.204993\pi$
$89$	−1.48229	+	8.40648i	−0.157122	+	0.891085i	−0.956820	+	0.290682i	$0.906118\pi$
$90$	−1.01243	+	0.798054i	−0.106720	+	0.0841223i
$91$	1.08498	−	1.29303i	0.113737	−	0.135546i
$92$	−0.565576	+	1.55391i	−0.0589654	+	0.162006i
$93$	9.84567	−	13.6130i	1.02095	−	1.41160i
$94$	−0.754960	+	0.435876i	−0.0778682	+	0.0449572i
$95$	0.714576	+	0.283059i	0.0733139	+	0.0290412i
$96$	0.973505	+	0.276878i	0.0993579	+	0.0282588i
$97$	8.73912	+	10.4149i	0.887323	+	1.05747i	0.997975	+	0.0636112i	$0.0202617\pi$
$97$	8.73912	+	10.4149i	0.887323	+	1.05747i	−0.110652	+	0.993859i	$0.535294\pi$
$98$	2.76656	+	15.6899i	0.279464	+	1.58492i
$99$	−14.4488	+	4.76367i	−1.45216	+	0.478766i
$100$	14.9939	−	12.5814i	1.49939	−	1.25814i
$101$	10.1706	−	12.1208i	1.01201	−	1.20607i	0.0335929	−	0.999436i	$-0.489305\pi$
$101$	10.1706	−	12.1208i	1.01201	−	1.20607i	0.978419	−	0.206633i	$-0.0662505\pi$
$102$	−3.63461	+	12.7793i	−0.359880	+	1.26534i
$103$	4.22161	+	2.43735i	0.415968	+	0.240159i	0.693351	−	0.720600i	$-0.256134\pi$
$103$	4.22161	+	2.43735i	0.415968	+	0.240159i	−0.277383	+	0.960759i	$0.589467\pi$
$104$	7.53886	−	8.98446i	0.739246	−	0.880999i
$105$	−0.186888	−	0.0906533i	−0.0182384	−	0.00884686i
$106$	15.8241			1.53697
$107$	4.81520	−	8.34017i	0.465503	−	0.806274i	−0.533721	−	0.845660i	$-0.679207\pi$
$107$	4.81520	−	8.34017i	0.465503	−	0.806274i	0.999224	+	0.0393861i	$0.0125402\pi$
$108$	−18.1342	−	9.49222i	−1.74497	−	0.913389i
$109$	−3.66067	−	4.36262i	−0.350629	−	0.417863i	0.561687	−	0.827350i	$-0.310152\pi$
$109$	−3.66067	−	4.36262i	−0.350629	−	0.417863i	−0.912316	+	0.409486i	$0.865708\pi$
$110$	−2.04779	+	0.745336i	−0.195249	+	0.0710650i
$111$	5.12806	−	7.09026i	0.486734	−	0.672977i
$112$	−0.429709	−	2.43700i	−0.0406037	−	0.230275i
$113$	7.66584	+	13.2776i	0.721142	+	1.24905i	0.960542	+	0.278134i	$0.0897158\pi$
$113$	7.66584	+	13.2776i	0.721142	+	1.24905i	−0.239401	+	0.970921i	$0.576951\pi$
$114$	0.807025	+	18.3815i	0.0755848	+	1.72158i
$115$	−0.0370110	+	0.0641049i	−0.00345129	+	0.00597781i
$116$	−0.923498	−	0.336126i	−0.0857446	−	0.0312085i
$117$	5.84728	−	4.60913i	0.540581	−	0.426114i
$118$	6.17394	+	5.18055i	0.568357	+	0.476908i
$119$	−2.10820	+	0.371733i	−0.193258	+	0.0340767i
$120$	−1.29857	−	0.629894i	−0.118543	−	0.0575012i
$121$	−14.7178			−1.33798
$122$	9.42263	−	16.3205i	0.853085	−	1.47759i
$123$	−20.1062	+	1.44952i	−1.81291	+	0.130699i
$124$	37.6278	+	6.63480i	3.37908	+	0.595823i
$125$	1.52230	−	0.878900i	0.136159	−	0.0786112i
$126$	0.152109	−	4.97008i	0.0135509	−	0.442770i
$127$	−15.7611	−	2.77910i	−1.39857	−	0.246606i	−0.577014	−	0.816734i	$-0.695782\pi$
$127$	−15.7611	−	2.77910i	−1.39857	−	0.246606i	−0.821556	+	0.570128i	$0.806893\pi$
$128$	3.47922	+	19.7316i	0.307522	+	1.74404i
$129$	1.43526	−	2.95889i	0.126367	−	0.260516i
$130$	0.816971	−	0.685520i	0.0716531	−	0.0601241i
$131$	3.52417	−	0.621407i	0.307908	−	0.0542925i	−0.0175590	−	0.999846i	$-0.505590\pi$
$131$	3.52417	−	0.621407i	0.307908	−	0.0542925i	0.325467	+	0.945553i	$0.394478\pi$
$132$	−24.0889	−	24.8374i	−2.09667	−	2.16182i
$133$	−2.60801	+	1.40958i	−0.226143	+	0.122226i
$134$		−	18.5523i		−	1.60267i
$135$	−0.725630	−	0.559405i	−0.0624523	−	0.0481460i
$136$	−14.6486	+	2.58294i	−1.25611	+	0.221485i
$137$	3.43710	+	9.44335i	0.293651	+	0.806800i	0.995525	+	0.0944987i	$0.0301248\pi$
$137$	3.43710	+	9.44335i	0.293651	+	0.806800i	−0.701874	+	0.712301i	$0.747653\pi$
$138$	−1.76268	−	0.181424i	−0.150049	−	0.0154438i
$139$	−7.18300	+	2.61440i	−0.609254	+	0.221750i	−0.628177	−	0.778071i	$-0.716198\pi$
$139$	−7.18300	+	2.61440i	−0.609254	+	0.221750i	0.0189230	+	0.999821i	$0.493976\pi$
$140$		−	0.472396i		−	0.0399247i
$141$	−0.431351	−	0.444755i	−0.0363263	−	0.0374551i
$142$	5.64032	−	31.9878i	0.473325	−	2.68436i
$143$	11.8269	−	4.30466i	0.989019	−	0.359974i
$144$	0.333910	−	10.9103i	0.0278258	−	0.909195i
$145$	−0.0380980	−	0.0219959i	−0.00316387	−	0.00182666i
$146$	27.4176	+	23.0061i	2.26910	+	1.90400i
$147$	−10.3343	+	4.62784i	−0.852358	+	0.381698i
$148$	19.5982	+	3.45570i	1.61096	+	0.284056i
$149$	−4.59930	−	5.48124i	−0.376790	−	0.449040i	0.544009	−	0.839080i	$-0.316906\pi$
$149$	−4.59930	−	5.48124i	−0.376790	−	0.449040i	−0.920798	+	0.390039i	$0.872461\pi$
$150$	16.9949	+	12.2917i	1.38763	+	1.00361i
$151$	15.1021	+	8.71921i	1.22899	+	0.709560i	0.966819	−	0.255461i	$-0.0822273\pi$
$151$	15.1021	+	8.71921i	1.22899	+	0.709560i	0.262174	+	0.965021i	$0.415561\pi$
$152$	−18.1215	+	9.79432i	−1.46985	+	0.794424i
$153$	−9.43831	−	0.288859i	−0.763042	−	0.0233528i
$154$	2.87484	−	7.89857i	0.231662	−	0.636485i
$155$	1.60718	+	0.584966i	0.129092	+	0.0469856i
$156$	15.2351	+	7.39006i	1.21979	+	0.591678i
$157$	7.70027	+	2.80267i	0.614548	+	0.223677i	0.630492	−	0.776196i	$-0.282853\pi$
$157$	7.70027	+	2.80267i	0.614548	+	0.223677i	−0.0159440	+	0.999873i	$0.505075\pi$
$158$	4.98323	+	13.6913i	0.396444	+	1.08922i
$159$	2.74430	+	10.9066i	0.217637	+	0.864948i
$160$			0.103036i			0.00814573i
$161$	−0.0976506	−	0.268293i	−0.00769595	−	0.0211444i
$162$	5.12245	−	21.3267i	0.402458	−	1.67559i
$163$	0.902969	+	1.56399i	0.0707260	+	0.122501i	0.899220	−	0.437497i	$-0.144135\pi$
$163$	0.902969	+	1.56399i	0.0707260	+	0.122501i	−0.828494	+	0.559998i	$0.810802\pi$
$164$	−22.9226	−	39.7031i	−1.78996	−	3.10029i
$165$	−0.868852	−	1.28216i	−0.0676400	−	0.0998157i
$166$	0.812600	−	2.23260i	0.0630700	−	0.173283i
$167$	2.52373	−	14.3128i	0.195292	−	1.10756i	−0.716710	−	0.697371i	$-0.754353\pi$
$167$	2.52373	−	14.3128i	0.195292	−	1.10756i	0.912002	−	0.410185i	$-0.134536\pi$
$168$	5.08072	−	2.27522i	0.391986	−	0.175537i
$169$	5.24019	−	4.39704i	0.403092	−	0.338234i
$170$	−1.35257			−0.103737
$171$	−12.5293	+	3.74404i	−0.958136	+	0.286314i
$172$	7.47916			0.570280
$173$	−14.6287	+	12.2749i	−1.11220	+	0.933246i	−0.998184	−	0.0602325i	$-0.980816\pi$
$173$	−14.6287	+	12.2749i	−1.11220	+	0.933246i	−0.114015	+	0.993479i	$0.536371\pi$
$174$	0.107822	−	1.04757i	0.00817393	−	0.0794161i
$175$	−0.586834	+	3.32810i	−0.0443605	+	0.251581i
$176$	6.31087	−	17.3390i	0.475700	−	1.30697i
$177$	−2.49991	+	5.15374i	−0.187905	+	0.387379i
$178$	−10.4015	−	18.0158i	−0.779622	−	1.35034i
$179$	3.53331	+	6.11987i	0.264092	+	0.457420i	0.967325	−	0.253539i	$-0.0815945\pi$
$179$	3.53331	+	6.11987i	0.264092	+	0.457420i	−0.703233	+	0.710959i	$0.748261\pi$
$180$	0.424442	−	2.04005i	0.0316361	−	0.152057i
$181$	−8.71420	−	23.9421i	−0.647721	−	1.77960i	−0.625985	−	0.779835i	$-0.715303\pi$
$181$	−8.71420	−	23.9421i	−0.647721	−	1.77960i	−0.0217366	−	0.999764i	$-0.506920\pi$
$182$			4.11354i			0.304916i
$183$	12.8828	+	3.66405i	0.952324	+	0.270854i
$184$	−0.678514	−	1.86420i	−0.0500207	−	0.137431i
$185$	0.837091	+	0.304676i	0.0615441	+	0.0224002i
$186$	2.94407	+	40.8370i	0.215870	+	2.99431i
$187$	−14.9996	−	5.45940i	−1.09688	−	0.399231i
$188$	0.481930	−	1.32409i	0.0351484	−	0.0965693i
$189$	3.45195	−	0.757098i	0.251092	−	0.0550708i
$190$	−1.77743	+	0.590943i	−0.128949	+	0.0428715i
$191$	−7.39281	−	4.26824i	−0.534925	−	0.308839i	0.208095	−	0.978109i	$-0.433274\pi$
$191$	−7.39281	−	4.26824i	−0.534925	−	0.308839i	−0.743020	+	0.669270i	$0.766607\pi$
$192$	−13.7545	+	6.15944i	−0.992642	+	0.444519i
$193$	5.77319	+	6.88022i	0.415563	+	0.495249i	0.932700	−	0.360654i	$-0.117446\pi$
$193$	5.77319	+	6.88022i	0.415563	+	0.495249i	−0.517136	+	0.855903i	$0.673002\pi$
$194$	−32.6297	−	5.75350i	−2.34268	−	0.413077i
$195$	0.614170	+	0.444201i	0.0439816	+	0.0318099i
$196$	−19.7270	−	16.5530i	−1.40907	−	1.18235i
$197$	7.27273	+	4.19891i	0.518161	+	0.299160i	0.736182	−	0.676784i	$-0.236627\pi$
$197$	7.27273	+	4.19891i	0.518161	+	0.299160i	−0.218021	+	0.975944i	$0.569960\pi$
$198$	19.5119	−	31.5271i	1.38665	−	2.24054i
$199$	5.96674	−	2.17172i	0.422971	−	0.153949i	−0.121760	−	0.992560i	$-0.538854\pi$
$199$	5.96674	−	2.17172i	0.422971	−	0.153949i	0.544731	+	0.838611i	$0.316632\pi$
$200$	−4.07755	+	23.1249i	−0.288326	+	1.63518i
$201$	12.7869	−	3.21744i	0.901921	−	0.226940i
$202$			38.5603i			2.71309i
$203$	0.159448	−	0.0580344i	0.0111911	−	0.00407322i
$204$	−8.77702	−	19.5997i	−0.614514	−	1.37225i
$205$	−0.701887	−	1.92842i	−0.0490219	−	0.134687i
$206$	−11.6993	+	2.06290i	−0.815130	+	0.143729i
$207$	−0.180648	−	1.24637i	−0.0125559	−	0.0866285i
$208$			9.03005i			0.626121i
$209$	−22.0965	−	0.620913i	−1.52844	−	0.0429495i
$210$	0.490905	−	0.123521i	0.0338757	−	0.00852376i
$211$	−13.6964	+	2.41505i	−0.942902	+	0.166259i	−0.623908	−	0.781498i	$-0.714456\pi$
$211$	−13.6964	+	2.41505i	−0.942902	+	0.166259i	−0.318994	+	0.947757i	$0.603345\pi$
$212$	−19.5935	+	16.4409i	−1.34569	+	1.12917i
$213$	23.0254	−	1.65998i	1.57767	−	0.113740i
$214$	4.07545	+	23.1130i	0.278592	+	1.57997i
$215$	0.329705	+	0.0581359i	0.0224857	+	0.00396483i
$216$	23.9855	−	5.26061i	1.63200	−	0.357939i
$217$	−5.71311	+	3.29846i	−0.387831	+	0.223914i
$218$	13.6680	+	2.41004i	0.925716	+	0.163229i
$219$	−11.1018	+	22.8871i	−0.750188	+	1.54657i
$220$	1.76120	−	3.05049i	0.118740	−	0.205664i
$221$	7.81171			0.525472
$222$	1.53340	+	21.2697i	0.102915	+	1.42753i
$223$	3.23131	−	0.569767i	0.216385	−	0.0381544i	−0.0644048	−	0.997924i	$-0.520515\pi$
$223$	3.23131	−	0.569767i	0.216385	−	0.0381544i	0.280789	+	0.959769i	$0.409404\pi$
$224$	−0.304443	−	0.255458i	−0.0203415	−	0.0170685i
$225$	−5.52452	+	13.8452i	−0.368301	+	0.923015i
$226$	−35.1105	−	12.7792i	−2.33552	−	0.850059i
$227$	6.29847	−	10.9093i	0.418044	−	0.724074i	−0.577698	−	0.816250i	$-0.696049\pi$
$227$	6.29847	−	10.9093i	0.418044	−	0.724074i	0.995743	+	0.0921763i	$0.0293823\pi$
$228$	−20.0972	−	21.9216i	−1.33097	−	1.45179i
$229$	−2.16119	−	3.74330i	−0.142816	−	0.247364i	0.785740	−	0.618557i	$-0.212282\pi$
$229$	−2.16119	−	3.74330i	−0.142816	−	0.247364i	−0.928556	+	0.371193i	$0.878949\pi$
$230$	−0.0313251	−	0.177653i	−0.00206552	−	0.0117141i
$231$	5.94256	+	0.611640i	0.390992	+	0.0402429i
$232$	1.10791	−	0.403246i	0.0727377	−	0.0264744i
$233$	9.49430	+	11.3149i	0.621992	+	0.741262i	0.981412	−	0.191915i	$-0.0614697\pi$
$233$	9.49430	+	11.3149i	0.621992	+	0.741262i	−0.359419	+	0.933176i	$0.617025\pi$
$234$	−3.69597	+	17.7644i	−0.241613	+	1.16130i
$235$	0.0315372	−	0.0546241i	0.00205726	−	0.00356328i
$236$	−13.0271			−0.847991
$237$	−8.57235	+	5.80905i	−0.556834	+	0.377338i
$238$	3.35343	−	3.99646i	0.217371	−	0.259052i
$239$	12.4236	+	7.17276i	0.803615	+	0.463967i	0.844734	−	0.535187i	$-0.179759\pi$
$239$	12.4236	+	7.17276i	0.803615	+	0.463967i	−0.0411186	+	0.999154i	$0.513092\pi$
$240$	1.07764	−	0.271154i	0.0695611	−	0.0175029i
$241$	5.11028	−	6.09020i	0.329182	−	0.392304i	−0.575914	−	0.817510i	$-0.695354\pi$
$241$	5.11028	−	6.09020i	0.329182	−	0.392304i	0.905097	+	0.425206i	$0.139798\pi$
$242$	27.4763	−	23.0554i	1.76625	−	1.48206i
$243$	15.5876	−	0.168010i	0.999942	−	0.0107779i
$244$	5.28946	+	29.9980i	0.338623	+	1.92043i
$245$	−0.740964	−	0.883046i	−0.0473384	−	0.0564157i
$246$	35.2650	−	34.2022i	2.24842	−	2.18066i
$247$	10.2655	−	3.41297i	0.653178	−	0.217162i
$248$	−39.6969	+	22.9190i	−2.52075	+	1.45536i
$249$	1.67972	+	0.172885i	0.106448	+	0.0109562i
$250$	−1.46515	+	4.02547i	−0.0926643	+	0.254593i
$251$	15.0671	−	17.9562i	0.951025	−	1.13339i	−0.0399312	−	0.999202i	$-0.512714\pi$
$251$	15.0671	−	17.9562i	0.951025	−	1.13339i	0.990956	−	0.134185i	$-0.0428417\pi$
$252$	4.97546	+	6.31202i	0.313425	+	0.397620i
$253$	0.369680	−	2.09656i	0.0232416	−	0.131810i
$254$	33.7774	−	19.5014i	2.11938	−	1.22363i
$255$	−0.234569	−	0.932241i	−0.0146893	−	0.0583792i
$256$	−24.0740	−	20.2005i	−1.50462	−	1.26253i
$257$	4.06877	+	3.41410i	0.253803	+	0.212966i	0.760808	−	0.648977i	$-0.224803\pi$
$257$	4.06877	+	3.41410i	0.253803	+	0.212966i	−0.507005	+	0.861943i	$0.669247\pi$
$258$	1.95563	+	7.77220i	0.121752	+	0.483876i
$259$	−2.97564	+	1.71798i	−0.184897	+	0.106750i
$260$	−0.299338	+	1.69763i	−0.0185642	+	0.105283i
$261$	0.740724	−	0.107360i	0.0458497	−	0.00664545i
$262$	−5.60576	+	6.68068i	−0.346325	+	0.412734i
$263$	8.50820	−	23.3761i	0.524638	−	1.44143i	−0.340666	−	0.940184i	$-0.610653\pi$
$263$	8.50820	−	23.3761i	0.524638	−	1.44143i	0.865304	−	0.501247i	$-0.167125\pi$
$264$	41.2912	+	4.24991i	2.54130	+	0.261564i
$265$	−0.991540	+	0.572466i	−0.0609098	+	0.0351663i
$266$	2.66073	−	6.71695i	0.163140	−	0.411843i
$267$	10.6133	−	10.2935i	0.649525	−	0.629950i
$268$	19.2754	+	22.9716i	1.17743	+	1.40321i
$269$	3.82949	+	21.7181i	0.233488	+	1.32418i	0.845774	+	0.533541i	$0.179139\pi$
$269$	3.82949	+	21.7181i	0.233488	+	1.32418i	−0.612286	+	0.790636i	$0.709750\pi$
$270$	2.23097	−	0.0923555i	0.135772	−	0.00562057i
$271$	0.263153	−	0.220812i	0.0159854	−	0.0134133i	−0.634760	−	0.772709i	$-0.718901\pi$
$271$	0.263153	−	0.220812i	0.0159854	−	0.0134133i	0.650745	+	0.759296i	$0.274457\pi$
$272$	7.36146	−	8.77305i	0.446354	−	0.531944i
$273$	−2.83520	+	0.713391i	−0.171594	+	0.0431764i
$274$	−21.2096	−	12.2454i	−1.28132	−	0.739770i
$275$	−16.1974	+	19.3033i	−0.976741	+	1.16403i
$276$	2.37105	−	1.60674i	0.142721	−	0.0967145i
$277$	−25.1866			−1.51332			−0.756659	−	0.653809i	$-0.773170\pi$
$277$	−25.1866			−1.51332			−0.756659	+	0.653809i	$0.773170\pi$
$278$	9.31432	−	16.1329i	0.558636	−	0.967586i
$279$	−27.6358	+	9.11133i	−1.65451	+	0.545481i
$280$	0.364285	+	0.434138i	0.0217702	+	0.0259447i
$281$	8.78018	−	3.19573i	0.523782	−	0.190641i	−0.0665779	−	0.997781i	$-0.521208\pi$
$281$	8.78018	−	3.19573i	0.523782	−	0.190641i	0.590360	+	0.807140i	$0.298986\pi$
$282$	1.50199	+	0.154592i	0.0894419	+	0.00920584i
$283$	1.39729	+	7.92443i	0.0830604	+	0.471059i	0.997758	+	0.0669205i	$0.0213174\pi$
$283$	1.39729	+	7.92443i	0.0830604	+	0.471059i	−0.914698	+	0.404138i	$0.867571\pi$
$284$	26.2508	+	45.4677i	1.55770	+	2.69801i
$285$	−0.715552	−	1.12259i	−0.0423856	−	0.0664965i
$286$	−15.3362	+	26.5631i	−0.906850	+	1.57071i
$287$	7.43813	+	2.70726i	0.439059	+	0.159804i
$288$	−1.08522	−	1.37674i	−0.0639472	−	0.0811253i
$289$	5.43337	+	4.55914i	0.319610	+	0.268185i
$290$	0.105581	−	0.0186167i	0.00619991	−	0.00109321i
$291$	−1.69328	−	23.4874i	−0.0992621	−	1.37686i
$292$	−57.8515			−3.38550
$293$	12.4915	−	21.6360i	0.729764	−	1.26399i	−0.227219	−	0.973844i	$-0.572963\pi$
$293$	12.4915	−	21.6360i	0.729764	−	1.26399i	0.956983	−	0.290144i	$-0.0937032\pi$
$294$	12.0433	−	24.8282i	0.702382	−	1.44801i
$295$	−0.574275	−	0.101260i	−0.0334356	−	0.00589560i
$296$	−20.6759	+	11.9372i	−1.20176	+	0.693837i
$297$	25.1135	+	7.98071i	1.45724	+	0.463087i
$298$	17.1727	+	3.02800i	0.994785	+	0.175408i
$299$	0.180917	+	1.02603i	0.0104627	+	0.0593369i
$300$	−33.8140	+	2.43776i	−1.95225	+	0.140744i
$301$	−0.989214	+	0.830050i	−0.0570174	+	0.0478433i
$302$	−41.8524	+	7.37970i	−2.40833	+	0.424654i
$303$	−26.5772	+	6.68732i	−1.52682	+	0.384176i
$304$	5.84084	−	14.7451i	0.334995	−	0.845688i
$305$			1.36352i			0.0780751i
$306$	18.0726	−	14.2458i	1.03314	−	0.814378i
$307$	16.5638	−	2.92064i	0.945343	−	0.166690i	0.320332	−	0.947305i	$-0.396205\pi$
$307$	16.5638	−	2.92064i	0.945343	−	0.166690i	0.625011	+	0.780616i	$0.285094\pi$
$308$	4.64679	+	12.7670i	0.264776	+	0.727465i
$309$	−3.45079	−	7.70584i	−0.196308	−	0.438370i
$310$	−3.91676	+	1.42558i	−0.222457	+	0.0809676i
$311$		−	11.1764i		−	0.633753i	−0.948467	−	0.316877i	$-0.897366\pi$
$311$		−	11.1764i		−	0.633753i	0.948467	−	0.316877i	$-0.102634\pi$
$312$	−19.7001	+	4.95691i	−1.11530	+	0.280630i
$313$	1.68577	−	9.56048i	0.0952854	−	0.540390i	−0.899374	−	0.437180i	$-0.855977\pi$
$313$	1.68577	−	9.56048i	0.0952854	−	0.540390i	0.994660	−	0.103211i	$-0.0329115\pi$
$314$	−18.7658	+	6.83019i	−1.05902	+	0.385450i
$315$	0.170271	+	0.316929i	0.00959366	+	0.0178569i
$316$	−20.3952	−	11.7752i	−1.14732	−	0.662406i
$317$	−11.5630	−	9.70254i	−0.649445	−	0.544949i	0.257457	−	0.966290i	$-0.417115\pi$
$317$	−11.5630	−	9.70254i	−0.649445	−	0.544949i	−0.906903	+	0.421341i	$0.861560\pi$
$318$	−22.2084	−	16.0623i	−1.24538	−	0.900728i
$319$	1.24600	+	0.219704i	0.0697626	+	0.0123010i
$320$	−0.986188	−	1.17529i	−0.0551296	−	0.0657009i
$321$	−15.2236	+	6.81733i	−0.849697	+	0.380506i
$322$	0.602581	+	0.347900i	0.0335805	+	0.0193877i
$323$	−12.7557	−	5.05279i	−0.709744	−	0.281145i
$324$	15.8154	+	31.7290i	0.878632	+	1.76272i
$325$	4.21777	−	11.5882i	0.233960	−	0.642799i
$326$	−4.13571	−	1.50528i	−0.229056	−	0.0833695i
$327$	0.709289	+	9.83849i	0.0392238	+	0.544070i
$328$	51.6830	+	18.8111i	2.85372	+	1.03867i
$329$	0.0832085	+	0.228614i	0.00458744	+	0.0126039i
$330$	3.63053	+	1.03257i	0.199854	+	0.0568413i
$331$		−	13.2009i		−	0.725585i	−0.931870	−	0.362793i	$-0.881823\pi$
$331$		−	13.2009i		−	0.725585i	0.931870	−	0.362793i	$-0.118177\pi$
$332$	1.31346	+	3.60869i	0.0720853	+	0.198053i
$333$	−14.3939	+	4.74558i	−0.788783	+	0.260056i
$334$	17.7094	+	30.6736i	0.969016	+	1.67838i
$335$	0.671163	+	1.16249i	0.0366696	+	0.0635135i
$336$	−1.87061	+	3.85639i	−0.102050	+	0.210383i
$337$	7.18695	−	19.7460i	0.391498	−	1.07563i	−0.574820	−	0.818280i	$-0.694928\pi$
$337$	7.18695	−	19.7460i	0.391498	−	1.07563i	0.966318	−	0.257352i	$-0.0828499\pi$
$338$	−2.89484	+	16.4175i	−0.157459	+	0.892992i
$339$	2.71884	−	26.4157i	0.147667	−	1.43470i
$340$	1.67476	−	1.40529i	0.0908265	−	0.0762125i
$341$	−49.1898			−2.66377
$342$	17.5255	−	26.6167i	0.947672	−	1.43926i
$343$	9.20705			0.497134
$344$	−6.87345	+	5.76751i	−0.370591	+	0.310963i
$345$	0.117013	−	0.0524000i	0.00629976	−	0.00282112i
$346$	8.08134	−	45.8316i	0.434456	−	2.46392i
$347$	−3.04230	+	8.35865i	−0.163319	+	0.448716i	−0.994176	−	0.107771i	$-0.965629\pi$
$347$	−3.04230	+	8.35865i	−0.163319	+	0.448716i	0.830857	+	0.556487i	$0.187851\pi$
$348$	0.954898	+	1.40913i	0.0511879	+	0.0755374i
$349$	3.92052	+	6.79054i	0.209861	+	0.363489i	0.951670	−	0.307121i	$-0.0993657\pi$
$349$	3.92052	+	6.79054i	0.209861	+	0.363489i	−0.741810	+	0.670610i	$0.766032\pi$
$350$	−4.11791	−	7.13242i	−0.220111	−	0.381244i
$351$	−12.8849	+	0.533395i	−0.687743	+	0.0284705i
$352$	−1.01353	−	2.78466i	−0.0540214	−	0.148423i
$353$			0.171537i			0.00913001i	0.999990	+	0.00456501i	$0.00145309\pi$
$353$			0.171537i			0.00913001i	−0.999990	+	0.00456501i	$0.998547\pi$
$354$	−3.40629	−	13.5375i	−0.181042	−	0.719510i
$355$	0.803795	+	2.20841i	0.0426610	+	0.117210i
$356$	31.5972	+	11.5004i	1.67465	+	0.609522i
$357$	3.33608	+	1.61822i	0.176564	+	0.0856454i
$358$	−16.1830	−	5.89012i	−0.855297	−	0.311303i
$359$	−4.87953	+	13.4064i	−0.257532	+	0.707563i	0.741786	+	0.670636i	$0.233979\pi$
$359$	−4.87953	+	13.4064i	−0.257532	+	0.707563i	−0.999318	+	0.0369264i	$0.988243\pi$
$360$	1.18311	+	2.20214i	0.0623552	+	0.116063i
$361$	−18.9700	−	1.06696i	−0.998422	−	0.0561559i
$362$	53.7734	+	31.0461i	2.82627	+	1.63175i
$363$	20.6557	+	14.9393i	1.08414	+	0.784112i
$364$	−4.27387	−	5.09341i	−0.224012	−	0.266967i
$365$	−2.55028	−	0.449683i	−0.133488	−	0.0235375i
$366$	−29.7903	+	13.3405i	−1.55716	+	0.697320i
$367$	−3.46143	−	2.90449i	−0.180685	−	0.151613i	0.547959	−	0.836505i	$-0.315405\pi$
$367$	−3.46143	−	2.90449i	−0.180685	−	0.151613i	−0.728645	+	0.684892i	$0.759849\pi$
$368$	1.32279	+	0.763711i	0.0689550	+	0.0398112i
$369$	29.6893	+	18.3744i	1.54556	+	0.956535i
$370$	−2.04002	+	0.742506i	−0.106055	+	0.0386010i
$371$	0.766854	−	4.34904i	0.0398131	−	0.225791i
$372$	−46.0741	−	47.5058i	−2.38883	−	2.46306i
$373$		−	6.81791i		−	0.353018i	−0.984299	−	0.176509i	$-0.943519\pi$
$373$		−	6.81791i		−	0.353018i	0.984299	−	0.176509i	$-0.0564805\pi$
$374$	36.5545	−	13.3047i	1.89019	−	0.687972i
$375$	−3.02860	−	0.311719i	−0.156396	−	0.0160971i
$376$	0.578165	+	1.58850i	0.0298166	+	0.0819204i
$377$	−0.609777	+	0.107520i	−0.0314051	+	0.00553757i
$378$	−5.25836	+	6.82086i	−0.270461	+	0.350827i
$379$			2.43440i			0.125047i	0.998044	+	0.0625233i	$0.0199148\pi$
$379$			2.43440i			0.125047i	−0.998044	+	0.0625233i	$0.980085\pi$
$380$	1.58685	−	2.57842i	0.0814038	−	0.132270i
$381$	19.2990	+	19.8986i	0.988715	+	1.01944i
$382$	20.4876	−	3.61252i	1.04824	−	0.184833i
$383$	−6.13769	+	5.15013i	−0.313621	+	0.263159i	−0.785987	−	0.618243i	$-0.787845\pi$
$383$	−6.13769	+	5.15013i	−0.313621	+	0.263159i	0.472366	+	0.881403i	$0.343400\pi$
$384$	15.1457	−	31.2239i	0.772900	−	1.59339i
$385$	0.105607	+	0.598928i	0.00538224	+	0.0305242i
$386$	−21.5557	−	3.80084i	−1.09715	−	0.193458i
$387$	−5.01774	+	2.69579i	−0.255066	+	0.137035i
$388$	46.3800	−	26.7775i	2.35459	−	1.35942i
$389$	36.2433	+	6.39067i	1.83761	+	0.324020i	0.981306	−	0.192454i	$-0.0616445\pi$
$389$	36.2433	+	6.39067i	1.83761	+	0.324020i	0.856303	+	0.516474i	$0.172756\pi$
$390$	−1.84242	+	0.132826i	−0.0932944	+	0.00672590i
$391$	0.660671	−	1.14432i	0.0334116	−	0.0578705i
$392$	30.8941			1.56039
$393$	−5.57676	−	2.70510i	−0.281310	−	0.136454i
$394$	−20.1549	+	3.55385i	−1.01539	+	0.179040i
$395$	−0.807558	−	0.677621i	−0.0406326	−	0.0340948i
$396$	8.59631	+	59.3095i	0.431981	+	2.98041i
$397$	16.0394	+	5.83787i	0.804996	+	0.292995i	0.711555	−	0.702630i	$-0.247991\pi$
$397$	16.0394	+	5.83787i	0.804996	+	0.292995i	0.0934407	+	0.995625i	$0.470213\pi$
$398$	−7.73719	+	13.4012i	−0.387830	+	0.671741i
$399$	5.09101	+	0.668987i	0.254869	+	0.0334912i
$400$	−9.03964	−	15.6571i	−0.451982	−	0.782856i
$401$	2.03940	+	11.5660i	0.101843	+	0.577579i	0.992434	+	0.122775i	$0.0391794\pi$
$401$	2.03940	+	11.5660i	0.101843	+	0.577579i	−0.890592	+	0.454804i	$0.849709\pi$
$402$	−18.8315	+	26.0372i	−0.939231	+	1.29862i
$403$	22.6211	−	8.23340i	1.12684	−	0.410135i
$404$	−40.0633	−	47.7455i	−1.99322	−	2.37543i
$405$	0.450561	+	1.52165i	0.0223885	+	0.0756114i
$406$	−0.206759	+	0.358118i	−0.0102613	+	0.0177731i
$407$	−25.6202			−1.26994
$408$	23.1804	+	11.2440i	1.14760	+	0.556663i
$409$	5.19289	−	6.18865i	0.256772	−	0.306009i	−0.622223	−	0.782840i	$-0.713770\pi$
$409$	5.19289	−	6.18865i	0.256772	−	0.306009i	0.878995	+	0.476831i	$0.158215\pi$
$410$	4.33119	+	2.50062i	0.213902	+	0.123497i
$411$	4.76169	−	16.7421i	0.234877	−	0.825827i
$412$	12.3428	−	14.7096i	0.608088	−	0.724691i
$413$	1.72300	−	1.44577i	0.0847832	−	0.0711416i
$414$	2.28967	+	2.04383i	0.112531	+	0.100449i
$415$	0.0298508	+	0.169292i	0.00146532	+	0.00831022i
$416$	0.932193	+	1.11094i	0.0457045	+	0.0544685i
$417$	12.7347	+	3.62193i	0.623622	+	0.177367i
$418$	42.2240	−	33.4548i	2.06524	−	1.63633i
$419$	4.08004	−	2.35561i	0.199323	−	0.115079i	−0.397017	−	0.917811i	$-0.629954\pi$
$419$	4.08004	−	2.35561i	0.199323	−	0.115079i	0.596340	+	0.802732i	$0.296621\pi$
$420$	−0.479506	+	0.662984i	−0.0233975	+	0.0323503i
$421$	10.7149	−	29.4388i	0.522211	−	1.43476i	−0.345844	−	0.938292i	$-0.612407\pi$
$421$	10.7149	−	29.4388i	0.522211	−	1.43476i	0.868054	−	0.496469i	$-0.165371\pi$
$422$	21.7864	−	25.9640i	1.06054	−	1.26391i
$423$	0.153931	+	1.06203i	0.00748439	+	0.0516379i
$424$	5.32840	−	30.2188i	0.258770	−	1.46756i
$425$	−13.5447	+	7.82001i	−0.657012	+	0.379326i
$426$	−40.3852	+	39.1681i	−1.95667	+	1.89770i
$427$	−4.02883	−	3.38059i	−0.194969	−	0.163598i
$428$	−29.0602	−	24.3844i	−1.40468	−	1.17866i
$429$	−20.9680	−	5.96359i	−1.01234	−	0.287925i
$430$	−0.706588	+	0.407949i	−0.0340747	+	0.0196730i
$431$	6.11308	−	34.6690i	0.294457	−	1.66995i	−0.374946	−	0.927047i	$-0.622339\pi$
$431$	6.11308	−	34.6690i	0.294457	−	1.66995i	0.669402	−	0.742900i	$-0.266550\pi$
$432$	−11.5432	+	14.9732i	−0.555371	+	0.720397i
$433$	−19.7644	+	23.5543i	−0.949816	+	1.13195i	0.0413267	+	0.999146i	$0.486842\pi$
$433$	−19.7644	+	23.5543i	−0.949816	+	1.13195i	−0.991143	+	0.132801i	$0.957603\pi$
$434$	5.49863	−	15.1074i	0.263943	−	0.725177i
$435$	0.0311417	+	0.0695415i	0.00149313	+	0.00333426i
$436$	−19.4278	+	11.2167i	−0.930424	+	0.537181i
$437$	0.368243	−	1.79242i	0.0176154	−	0.0857429i
$438$	−15.1269	−	60.1182i	−0.722790	−	2.87256i
$439$	18.0716	+	21.5369i	0.862510	+	1.02790i	0.999304	+	0.0373002i	$0.0118758\pi$
$439$	18.0716	+	21.5369i	0.862510	+	1.02790i	−0.136794	+	0.990600i	$0.543680\pi$
$440$	0.733799	+	4.16158i	0.0349825	+	0.198396i
$441$	19.2011	+	3.99489i	0.914340	+	0.190233i
$442$	−14.5835	+	12.2370i	−0.693666	+	0.582055i
$443$	−9.02653	+	10.7574i	−0.428863	+	0.511099i	−0.936594	−	0.350417i	$-0.886040\pi$
$443$	−9.02653	+	10.7574i	−0.428863	+	0.511099i	0.507731	+	0.861516i	$0.330484\pi$
$444$	−23.9974	−	24.7431i	−1.13887	−	1.17426i
$445$	1.30351	+	0.752583i	0.0617924	+	0.0356758i
$446$	−5.13992	+	6.12552i	−0.243382	+	0.290052i
$447$	0.891158	+	12.3612i	0.0421503	+	0.584663i
$448$	5.91773			0.279586
$449$	−12.7630	+	22.1062i	−0.602325	+	1.04326i	0.390143	+	0.920754i	$0.372425\pi$
$449$	−12.7630	+	22.1062i	−0.602325	+	1.04326i	−0.992468	+	0.122503i	$0.960908\pi$
$450$	−11.3749	−	34.5014i	−0.536217	−	1.62641i
$451$	37.9384	+	45.2132i	1.78645	+	2.12901i
$452$	56.7513	−	20.6558i	2.66936	−	0.971567i
$453$	−12.3446	−	27.5664i	−0.580001	−	1.29518i
$454$	5.33086	+	30.2328i	0.250189	+	1.41889i
$455$	−0.148815	−	0.257755i	−0.00697654	−	0.0120837i
$456$	35.3743	+	4.64838i	1.65655	+	0.217680i
$457$	−6.57163	+	11.3824i	−0.307408	+	0.532446i	−0.977795	−	0.209566i	$-0.932795\pi$
$457$	−6.57163	+	11.3824i	−0.307408	+	0.532446i	0.670386	+	0.742012i	$0.266128\pi$
$458$	9.89853	+	3.60277i	0.462528	+	0.168346i
$459$	12.9530	+	9.98576i	0.604594	+	0.466096i
$460$	0.223365	+	0.187425i	0.0104144	+	0.00873875i
$461$	−3.13578	+	0.552922i	−0.146048	+	0.0257522i	−0.246194	−	0.969221i	$-0.579180\pi$
$461$	−3.13578	+	0.552922i	−0.146048	+	0.0257522i	0.100146	+	0.994973i	$0.468069\pi$
$462$	−12.0522	+	8.16713i	−0.560717	+	0.379969i
$463$	3.17519			0.147564			0.0737818	−	0.997274i	$-0.476493\pi$
$463$	3.17519			0.147564			0.0737818	+	0.997274i	$0.476493\pi$
$464$	−0.453879	+	0.786141i	−0.0210708	+	0.0364957i
$465$	−1.66183	−	2.45234i	−0.0770655	−	0.113725i
$466$	−35.4494	−	6.25068i	−1.64216	−	0.289557i
$467$	14.5792	−	8.41731i	0.674645	−	0.389507i	−0.123189	−	0.992383i	$-0.539312\pi$
$467$	14.5792	−	8.41731i	0.674645	−	0.389507i	0.797834	+	0.602877i	$0.205979\pi$
$468$	−13.8805	−	25.8360i	−0.641624	−	1.19427i
$469$	−5.09885	−	0.899064i	−0.235443	−	0.0415149i
$470$	0.0266923	+	0.151379i	0.00123122	+	0.00698261i
$471$	−7.96209	−	11.7496i	−0.366874	−	0.541391i
$472$	11.9721	−	10.0458i	0.551059	−	0.462393i
$473$	−9.48246	+	1.67201i	−0.436004	+	0.0768792i
$474$	6.90367	−	24.2733i	0.317096	−	1.11491i
$475$	−14.3827	+	16.1941i	−0.659922	+	0.743038i
$476$			8.43258i			0.386507i
$477$	7.21924	−	18.0924i	0.330546	−	0.828396i
$478$	−34.4294	+	6.07083i	−1.57476	+	0.277673i
$479$	3.80159	+	10.4448i	0.173699	+	0.477235i	0.995741	−	0.0921921i	$-0.0293874\pi$
$479$	3.80159	+	10.4448i	0.173699	+	0.477235i	−0.822042	+	0.569427i	$0.807165\pi$
$480$	0.104587	−	0.144606i	0.00477373	−	0.00660034i
$481$	11.7820	−	4.28831i	0.537215	−	0.195530i
$482$			19.3749i			0.882501i
$483$	−0.135283	+	0.475656i	−0.00615560	+	0.0216431i
$484$	−10.0673	+	57.0946i	−0.457606	+	2.59521i
$485$	2.25272	−	0.819924i	0.102291	−	0.0372308i
$486$	−28.8368	+	24.7315i	−1.30807	+	1.12184i
$487$	28.5991	+	16.5117i	1.29595	+	0.748216i	0.979702	−	0.200461i	$-0.0642439\pi$
$487$	28.5991	+	16.5117i	1.29595	+	0.748216i	0.316247	+	0.948677i	$0.397577\pi$
$488$	−27.9939	−	23.4896i	−1.26722	−	1.06333i
$489$	0.320256	−	3.11154i	0.0144825	−	0.140709i
$490$	2.76657	+	0.487822i	0.124981	+	0.0220375i
$491$	−4.21825	−	5.02711i	−0.190367	−	0.226870i	0.662416	−	0.749136i	$-0.269531\pi$
$491$	−4.21825	−	5.02711i	−0.190367	−	0.226870i	−0.852783	+	0.522266i	$0.825087\pi$
$492$	−8.12997	+	78.9890i	−0.366527	+	3.56110i
$493$	0.680075	+	0.392641i	0.0306290	+	0.0176837i
$494$	−13.8180	+	22.4524i	−0.621702	+	1.01018i
$495$	−0.0820631	+	2.68137i	−0.00368846	+	0.120519i
$496$	12.0706	−	33.1638i	0.541987	−	1.48910i
$497$	−8.51809	−	3.10033i	−0.382088	−	0.139069i
$498$	−3.40665	+	2.30851i	−0.152655	+	0.103447i
$499$	−9.81287	−	3.57159i	−0.439285	−	0.159887i	0.112904	−	0.993606i	$-0.463985\pi$
$499$	−9.81287	−	3.57159i	−0.439285	−	0.159887i	−0.552188	+	0.833719i	$0.686207\pi$
$500$	−2.36822	−	6.50662i	−0.105910	−	0.290985i
$501$	−18.0701	+	17.5256i	−0.807314	+	0.782984i
$502$			57.1245i			2.54959i
$503$	6.21077	+	17.0640i	0.276925	+	0.760844i	0.997707	+	0.0676826i	$0.0215605\pi$
$503$	6.21077	+	17.0640i	0.276925	+	0.760844i	−0.720782	+	0.693161i	$0.756217\pi$
$504$	−9.44000	−	1.96404i	−0.420491	−	0.0874851i
$505$	−1.39499	−	2.41619i	−0.0620761	−	0.107519i
$506$	2.59410	+	4.49312i	0.115322	+	0.199744i
$507$	−11.8176	+	0.851967i	−0.524837	+	0.0378372i
$508$	−21.5619	+	59.2408i	−0.956653	+	2.62838i
$509$	1.45182	−	8.23367i	0.0643507	−	0.364951i	−0.935579	−	0.353117i	$-0.885122\pi$
$509$	1.45182	−	8.23367i	0.0643507	−	0.364951i	0.999930	−	0.0118342i	$-0.00376705\pi$
$510$	1.89826	+	1.37293i	0.0840565	+	0.0607942i
$511$	7.65160	−	6.42045i	0.338487	−	0.284024i
$512$	36.5150			1.61375
$513$	21.3846	+	7.46325i	0.944152	+	0.329511i
$514$	−12.9441			−0.570938
$515$	0.658450	−	0.552506i	0.0290148	−	0.0243463i
$516$	−10.4966	−	7.59172i	−0.462088	−	0.334207i
$517$	−0.315006	+	1.78649i	−0.0138540	+	0.0785697i
$518$	2.86393	−	7.86858i	0.125834	−	0.345726i
$519$	32.9903	−	2.37838i	1.44812	−	0.104399i
$520$	−1.03402	−	1.79098i	−0.0453449	−	0.0785396i
$521$	0.915257	+	1.58527i	0.0400982	+	0.0694520i	0.885378	−	0.464872i	$-0.153900\pi$
$521$	0.915257	+	1.58527i	0.0400982	+	0.0694520i	−0.845280	+	0.534324i	$0.820566\pi$
$522$	−1.21466	+	1.36077i	−0.0531642	+	0.0595592i
$523$	7.02772	+	19.3085i	0.307301	+	0.844302i	0.993180	+	0.116587i	$0.0371954\pi$
$523$	7.02772	+	19.3085i	0.307301	+	0.844302i	−0.685880	+	0.727715i	$0.740582\pi$
$524$		−	14.0963i		−	0.615801i
$525$	4.20179	−	4.07516i	0.183381	−	0.177854i
$526$	20.7348	+	56.9683i	0.904078	+	2.48394i
$527$	−28.6893	−	10.4420i	−1.24972	−	0.454863i
$528$	−26.4569	+	17.9285i	−1.15139	+	0.780239i
$529$	−21.4473	−	7.80619i	−0.932493	−	0.339400i
$530$	0.954318	−	2.62197i	0.0414529	−	0.113891i
$531$	8.73981	−	4.69548i	0.379276	−	0.203767i
$532$	3.68423	+	11.0814i	0.159732	+	0.480440i
$533$	−25.0147	−	14.4422i	−1.08350	−	0.625562i
$534$	−3.68908	+	35.8423i	−0.159642	+	1.55105i
$535$	−1.09152	−	1.30083i	−0.0471907	−	0.0562397i
$536$	−35.4288	−	6.24705i	−1.53029	−	0.269831i
$537$	1.25316	−	12.1754i	0.0540778	−	0.525408i
$538$	−41.1705	−	34.5461i	−1.77499	−	1.48939i
$539$	28.7115	+	16.5766i	1.23669	+	0.714004i
$540$	−2.66644	+	2.43228i	−0.114745	+	0.104669i
$541$	−18.9614	+	6.90139i	−0.815214	+	0.296714i	−0.715776	−	0.698330i	$-0.753927\pi$
$541$	−18.9614	+	6.90139i	−0.815214	+	0.296714i	−0.0994383	+	0.995044i	$0.531705\pi$
$542$	−0.145374	+	0.824456i	−0.00624434	+	0.0354134i
$543$	−12.0725	+	42.4468i	−0.518079	+	1.82157i
$544$		−	1.83927i		−	0.0788579i
$545$	−0.943628	+	0.343453i	−0.0404206	+	0.0147119i
$546$	4.17545	−	5.77314i	0.178693	−	0.247068i
$547$	10.3522	+	28.4423i	0.442627	+	1.21611i	0.937758	+	0.347289i	$0.112898\pi$
$547$	10.3522	+	28.4423i	0.442627	+	1.21611i	−0.495132	+	0.868818i	$0.664880\pi$
$548$	38.9845	−	6.87402i	1.66534	−	0.293644i
$549$	−14.3612	−	18.2190i	−0.612920	−	0.777568i
$550$		−	61.4101i		−	2.61853i
$551$	1.06524	+	0.218849i	0.0453809	+	0.00932329i
$552$	−0.940000	+	3.30504i	−0.0400090	+	0.140672i
$553$	4.00436	−	0.706077i	0.170283	−	0.0300255i
$554$	47.0203	−	39.4547i	1.99770	−	1.67627i
$555$	−0.865553	−	1.27729i	−0.0367407	−	0.0542178i
$556$	5.22866	+	29.6532i	0.221744	+	1.25758i
$557$	−32.1147	−	5.66269i	−1.36074	−	0.239936i	−0.554828	−	0.831965i	$-0.687216\pi$
$557$	−32.1147	−	5.66269i	−1.36074	−	0.239936i	−0.805917	+	0.592029i	$0.798327\pi$
$558$	37.3198	−	60.3011i	1.57987	−	2.55275i
$559$	4.08087	−	2.35609i	0.172602	−	0.0996520i
$560$	−0.429712	−	0.0757698i	−0.0181587	−	0.00320186i
$561$	15.5096	+	22.8873i	0.654816	+	0.966304i
$562$	−11.3854	+	19.7201i	−0.480265	+	0.831844i
$563$	9.73673			0.410354			0.205177	−	0.978725i	$-0.434223\pi$
$563$	9.73673			0.410354			0.205177	+	0.978725i	$0.434223\pi$
$564$	−2.02039	+	1.36911i	−0.0850736	+	0.0576501i
$565$	2.66234	−	0.469442i	0.112005	−	0.0197496i
$566$	−15.0222	−	12.6051i	−0.631428	−	0.529831i
$567$	−5.61313	−	2.44135i	−0.235729	−	0.102527i
$568$	−59.1870	−	21.5423i	−2.48343	−	0.903895i
$569$	−0.953311	+	1.65118i	−0.0399649	+	0.0692212i	−0.885316	−	0.464990i	$-0.846058\pi$
$569$	−0.953311	+	1.65118i	−0.0399649	+	0.0692212i	0.845351	+	0.534211i	$0.179391\pi$
$570$	3.09438	+	0.974827i	0.129609	+	0.0408310i
$571$	−22.4448	−	38.8755i	−0.939286	−	1.62689i	−0.766807	−	0.641877i	$-0.778156\pi$
$571$	−22.4448	−	38.8755i	−0.939286	−	1.62689i	−0.172478	−	0.985013i	$-0.555177\pi$
$572$	−8.60909	−	48.8246i	−0.359964	−	2.04146i
$573$	6.04295	+	13.4943i	0.252448	+	0.563734i
$574$	−18.1270	+	6.59768i	−0.756605	+	0.275382i
$575$	−1.34081	−	1.59792i	−0.0559157	−	0.0666377i
$576$	25.5558	+	5.31701i	1.06483	+	0.221542i
$577$	4.60536	−	7.97671i	0.191724	−	0.332075i	−0.754098	−	0.656762i	$-0.771926\pi$
$577$	4.60536	−	7.97671i	0.191724	−	0.332075i	0.945822	+	0.324687i	$0.105259\pi$
$578$	−17.2853			−0.718974
$579$	−1.11861	−	15.5161i	−0.0464878	−	0.644828i
$580$	−0.111388	+	0.132747i	−0.00462514	+	0.00551203i
$581$	−0.574220	−	0.331526i	−0.0238227	−	0.0137540i
$582$	39.9540	+	41.1955i	1.65615	+	1.70761i
$583$	21.1662	−	25.2249i	0.876614	−	1.04471i
$584$	53.1663	−	44.6118i	2.20004	−	1.84605i
$585$	−0.411070	−	1.24683i	−0.0169956	−	0.0515500i
$586$	10.5725	+	59.9596i	0.436746	+	2.47691i
$587$	−11.3944	−	13.5794i	−0.470299	−	0.560480i	0.477795	−	0.878471i	$-0.341436\pi$
$587$	−11.3944	−	13.5794i	−0.470299	−	0.560480i	−0.948094	+	0.317991i	$0.896992\pi$
$588$	10.8838	+	43.2552i	0.448841	+	1.78381i
$589$	−42.2633	−	1.18760i	−1.74143	−	0.0489344i
$590$	1.23072	−	0.710558i	0.0506681	−	0.0292532i
$591$	−5.94480	−	13.2752i	−0.244536	−	0.546067i
$592$	6.28691	−	17.2731i	0.258390	−	0.709921i
$593$	−14.9759	+	17.8476i	−0.614988	+	0.732914i	−0.980200	−	0.198010i	$-0.936552\pi$
$593$	−14.9759	+	17.8476i	−0.614988	+	0.732914i	0.365212	+	0.930924i	$0.380996\pi$
$594$	−59.3856	+	24.4412i	−2.43662	+	1.00284i
$595$	−0.0655469	+	0.371735i	−0.00268716	+	0.0152397i
$596$	−24.4093	+	14.0927i	−0.999844	+	0.577260i
$597$	−10.5784	−	3.00865i	−0.432946	−	0.123136i
$598$	−1.94502	−	1.63207i	−0.0795378	−	0.0667401i
$599$	−10.1981	−	8.55723i	−0.416683	−	0.349639i	0.410216	−	0.911988i	$-0.365453\pi$
$599$	−10.1981	−	8.55723i	−0.416683	−	0.349639i	−0.826900	+	0.562349i	$0.809898\pi$
$600$	29.1956	−	28.3158i	1.19191	−	1.15599i
$601$	3.88142	−	2.24094i	0.158327	−	0.0914099i	−0.418743	−	0.908105i	$-0.637529\pi$
$601$	3.88142	−	2.24094i	0.158327	−	0.0914099i	0.577070	+	0.816695i	$0.304196\pi$
$602$	0.546472	−	3.09920i	0.0222725	−	0.126314i
$603$	−21.2117	−	8.46389i	−0.863807	−	0.344676i
$604$	44.1545	−	52.6213i	1.79662	−	2.14113i
$605$	−0.887599	+	2.43866i	−0.0360860	+	0.0991456i
$606$	39.1406	−	54.1174i	1.58998	−	2.19837i
$607$	11.4577	−	6.61510i	0.465053	−	0.268499i	−0.249113	−	0.968474i	$-0.580139\pi$
$607$	11.4577	−	6.61510i	0.465053	−	0.268499i	0.714167	+	0.699976i	$0.246806\pi$
$608$	−0.803584	−	2.41701i	−0.0325896	−	0.0980228i
$609$	−0.282685	−	0.0803997i	−0.0114550	−	0.00325796i
$610$	−2.13595	−	2.54553i	−0.0864821	−	0.103065i
$611$	−0.154160	−	0.874286i	−0.00623665	−	0.0353698i
$612$	−7.57658	+	36.4163i	−0.306265	+	1.47204i
$613$	10.4469	−	8.76601i	0.421948	−	0.354056i	−0.406956	−	0.913448i	$-0.633410\pi$
$613$	10.4469	−	8.76601i	0.421948	−	0.354056i	0.828903	+	0.559392i	$0.188965\pi$
$614$	−26.3473	+	31.3995i	−1.06329	+	1.26718i
$615$	−0.972380	+	3.41889i	−0.0392102	+	0.137863i
$616$	−14.1156	−	8.14966i	−0.568735	−	0.328359i
$617$	6.47210	−	7.71315i	0.260557	−	0.310520i	−0.619867	−	0.784707i	$-0.712814\pi$
$617$	6.47210	−	7.71315i	0.260557	−	0.310520i	0.880424	+	0.474187i	$0.157258\pi$
$618$	18.5133	+	8.98021i	0.744716	+	0.361237i
$619$	−17.2670			−0.694018			−0.347009	−	0.937862i	$-0.612803\pi$
$619$	−17.2670			−0.694018			−0.347009	+	0.937862i	$0.612803\pi$
$620$	3.36860	−	5.83459i	0.135286	−	0.234323i
$621$	−1.01159	+	1.93258i	−0.0405939	+	0.0775518i
$622$	17.5077	+	20.8649i	0.701995	+	0.836605i
$623$	−5.45548	+	1.98563i	−0.218569	+	0.0795526i
$624$	9.16596	−	12.6732i	0.366932	−	0.507335i
$625$	4.26039	+	24.1619i	0.170415	+	0.966474i
$626$	11.8293	+	20.4890i	0.472795	+	0.818904i
$627$	30.3810	+	23.3004i	1.21330	+	0.930530i
$628$	16.1395	−	27.9544i	0.644036	−	1.11550i
$629$	−14.9426	−	5.43867i	−0.595802	−	0.216854i
$630$	−0.814341	−	0.324938i	−0.0324441	−	0.0129458i
$631$	−18.9204	−	15.8761i	−0.753208	−	0.632017i	0.183141	−	0.983087i	$-0.441373\pi$
$631$	−18.9204	−	15.8761i	−0.753208	−	0.632017i	−0.936349	+	0.351070i	$0.885818\pi$
$632$	27.8239	−	4.90610i	1.10677	−	0.195154i
$633$	21.6737	+	10.5132i	0.861451	+	0.417862i
$634$	36.7857			1.46095
$635$	−1.41100	+	2.44392i	−0.0559937	+	0.0969840i
$636$	44.1869	−	3.18558i	1.75212	−	0.126316i
$637$	−15.9782	−	2.81739i	−0.633081	−	0.111629i
$638$	−2.67029	+	1.54169i	−0.105718	+	0.0610363i
$639$	−33.9999	−	21.0423i	−1.34502	−	0.832419i
$640$	3.47924	+	0.613484i	0.137529	+	0.0242501i
$641$	−1.43513	−	8.13903i	−0.0566842	−	0.321472i	0.943260	−	0.332056i	$-0.107742\pi$
$641$	−1.43513	−	8.13903i	−0.0566842	−	0.321472i	−0.999944	+	0.0105835i	$0.996631\pi$
$642$	17.7412	−	36.5748i	0.700190	−	1.44349i
$643$	17.9288	−	15.0440i	0.707041	−	0.593278i	−0.216726	−	0.976232i	$-0.569538\pi$
$643$	17.9288	−	15.0440i	0.707041	−	0.593278i	0.923767	+	0.382954i	$0.125093\pi$
$644$	−1.10758	+	0.195296i	−0.0436447	+	0.00769575i
$645$	−0.403713	−	0.416258i	−0.0158962	−	0.0163901i
$646$	31.7284	−	10.5487i	1.24834	−	0.415034i
$647$		−	38.0849i		−	1.49727i	−0.662982	−	0.748635i	$-0.730709\pi$
$647$		−	38.0849i		−	1.49727i	0.662982	−	0.748635i	$-0.269291\pi$
$648$	−39.0022	−	16.9635i	−1.53215	−	0.666388i
$649$	16.5164	−	2.91229i	0.648325	−	0.114317i
$650$	10.2788	+	28.2409i	0.403169	+	1.10770i
$651$	11.3662	+	1.16987i	0.445475	+	0.0458507i
$652$	6.68481	−	2.43307i	0.261797	−	0.0952864i
$653$			25.0470i			0.980164i	0.871676	+	0.490082i	$0.163033\pi$
$653$			25.0470i			0.980164i	−0.871676	+	0.490082i	$0.836967\pi$
$654$	−16.7361	−	17.2561i	−0.654433	−	0.674768i
$655$	0.109571	−	0.621411i	0.00428131	−	0.0242805i
$656$	−39.7924	+	14.4832i	−1.55363	+	0.565476i
$657$	38.8123	−	20.8520i	1.51421	−	0.813514i
$658$	−0.513462	−	0.296447i	−0.0200168	−	0.0115567i
$659$	−20.1652	−	16.9206i	−0.785525	−	0.659134i	0.159108	−	0.987261i	$-0.449138\pi$
$659$	−20.1652	−	16.9206i	−0.785525	−	0.659134i	−0.944634	+	0.328127i	$0.893583\pi$
$660$	−5.56816	+	2.49350i	−0.216740	+	0.0970594i
$661$	32.1080	+	5.66150i	1.24886	+	0.220207i	0.758707	−	0.651432i	$-0.225831\pi$
$661$	32.1080	+	5.66150i	1.24886	+	0.220207i	0.490148	+	0.871639i	$0.336943\pi$
$662$	20.6791	+	24.6444i	0.803716	+	0.957831i
$663$	−10.9633	−	7.92928i	−0.425781	−	0.307948i
$664$	−3.98990	−	2.30357i	−0.154838	−	0.0893959i
$665$	0.0762763	+	0.517141i	0.00295787	+	0.0200539i
$666$	19.4378	−	31.4074i	0.753198	−	1.21701i
$667$	−0.0358212	+	0.0984180i	−0.00138700	+	0.00381076i
$668$	−53.7971	−	19.5805i	−2.08147	−	0.757594i
$669$	−5.11333	−	2.48031i	−0.197693	−	0.0958942i
$670$	−3.07401	−	1.11885i	−0.118759	−	0.0432249i
$671$	−13.4125	−	36.8505i	−0.517783	−	1.42260i
$672$	0.167968	+	0.667549i	0.00647950	+	0.0257513i
$673$			35.9564i			1.38602i	0.720930	+	0.693008i	$0.243715\pi$
$673$			35.9564i			1.38602i	−0.720930	+	0.693008i	$0.756285\pi$
$674$	17.5148	+	48.1216i	0.674646	+	1.85357i
$675$	21.8070	−	13.8234i	0.839351	−	0.532063i
$676$	−13.4730	−	23.3359i	−0.518191	−	0.897534i
$677$	15.4187	+	26.7060i	0.592590	+	1.02640i	0.993882	+	0.110446i	$0.0352280\pi$
$677$	15.4187	+	26.7060i	0.592590	+	1.02640i	−0.401292	+	0.915950i	$0.631439\pi$
$678$	36.3043	+	53.5739i	1.39426	+	2.05749i
$679$	−3.16254	+	8.68901i	−0.121367	+	0.333453i
$680$	−0.455445	+	2.58296i	−0.0174655	+	0.0990520i
$681$	−19.9131	+	8.91735i	−0.763070	+	0.341714i
$682$	91.8312	−	77.0555i	3.51640	−	2.95061i
$683$	23.5676			0.901789			0.450895	−	0.892577i	$-0.351105\pi$
$683$	23.5676			0.901789			0.450895	+	0.892577i	$0.351105\pi$
$684$	5.95392	+	51.1656i	0.227654	+	1.95636i
$685$	1.77199			0.0677044
$686$	−17.1884	+	14.4228i	−0.656257	+	0.550665i
$687$	−0.766510	+	7.44725i	−0.0292442	+	0.284130i
$688$	1.19962	−	6.80337i	0.0457350	−	0.259376i
$689$	−5.51162	+	15.1431i	−0.209976	+	0.576905i
$690$	−0.136364	+	0.281124i	−0.00519129	+	0.0107022i
$691$	−11.1790	−	19.3626i	−0.425269	−	0.736587i	0.571177	−	0.820827i	$-0.306487\pi$
$691$	−11.1790	−	19.3626i	−0.425269	−	0.736587i	−0.996445	+	0.0842402i	$0.973154\pi$
$692$	37.6116	+	65.1453i	1.42978	+	2.47645i
$693$	−7.71924	−	6.89041i	−0.293230	−	0.261745i
$694$	−7.41418	−	20.3703i	−0.281439	−	0.773246i
$695$			1.34785i			0.0511269i
$696$	−1.96421	−	0.558648i	−0.0744531	−	0.0211755i
$697$	12.5292	+	34.4236i	0.474576	+	1.30389i
$698$	−17.9565	−	6.53562i	−0.679662	−	0.247377i
$699$	−1.83961	−	25.5170i	−0.0695804	−	0.965143i
$700$	12.5092	+	4.55299i	0.472805	+	0.172087i
$701$	−11.7795	+	32.3639i	−0.444906	+	1.22237i	0.491323	+	0.870977i	$0.336513\pi$
$701$	−11.7795	+	32.3639i	−0.444906	+	1.22237i	−0.936229	+	0.351391i	$0.885709\pi$
$702$	23.2189	−	21.1799i	0.876340	−	0.799382i
$703$	−22.0126	−	0.618556i	−0.830219	−	0.0233293i
$704$	38.2136	+	22.0627i	1.44023	+	0.831518i
$705$	−0.0997072	+	0.0446503i	−0.00375519	+	0.00168163i
$706$	−0.268712	−	0.320239i	−0.0101131	−	0.0120523i
$707$	10.5978	+	1.86867i	0.398570	+	0.0702786i
$708$	18.2828	+	13.2231i	0.687112	+	0.496956i
$709$	19.0902	+	16.0186i	0.716948	+	0.601591i	0.926539	−	0.376198i	$-0.122769\pi$
$709$	19.0902	+	16.0186i	0.716948	+	0.601591i	−0.209591	+	0.977789i	$0.567213\pi$
$710$	−4.96005	−	2.86368i	−0.186147	−	0.107472i
$711$	17.9273	+	0.548664i	0.672328	+	0.0205765i
$712$	−37.9068	+	13.7969i	−1.42062	+	0.517062i
$713$	0.707077	−	4.01003i	0.0264803	−	0.150177i
$714$	−8.76299	+	2.20493i	−0.327947	+	0.0825175i
$715$		−	2.21926i		−	0.0829957i
$716$	26.1576	−	9.52058i	0.977555	−	0.355801i
$717$	−10.1552	−	22.6772i	−0.379252	−	0.846895i
$718$	−11.8916	−	32.6718i	−0.443790	−	1.21930i
$719$	3.48510	−	0.614518i	0.129972	−	0.0229177i	−0.108283	−	0.994120i	$-0.534535\pi$
$719$	3.48510	−	0.614518i	0.129972	−	0.0229177i	0.238256	+	0.971202i	$0.423424\pi$
$720$	−1.78764	−	0.713305i	−0.0666215	−	0.0265833i
$721$			3.31537i			0.123471i
$722$	37.0861	−	27.7245i	1.38020	−	1.03180i
$723$	−13.3539	+	3.36009i	−0.496636	+	0.124963i
$724$	−98.8388	+	17.4279i	−3.67331	+	0.647704i
$725$	0.949652	−	0.796853i	0.0352692	−	0.0295944i
$726$	−61.9641	+	4.46719i	−2.29970	+	0.165793i
$727$	−2.17554	−	12.3381i	−0.0806863	−	0.457595i	−0.998204	−	0.0599007i	$-0.980922\pi$
$727$	−2.17554	−	12.3381i	−0.0806863	−	0.457595i	0.917518	−	0.397694i	$-0.130190\pi$
$728$	7.85550	+	1.38514i	0.291144	+	0.0513366i
$729$	−22.0469	−	15.5864i	−0.816551	−	0.577273i
$730$	5.46547	−	3.15549i	0.202286	−	0.116790i
$731$	−5.88545	−	1.03776i	−0.217681	−	0.0383831i
$732$	23.0260	−	47.4698i	0.851066	−	1.75453i
$733$	19.4345	−	33.6615i	0.717829	−	1.24332i	−0.244029	−	0.969768i	$-0.578469\pi$
$733$	19.4345	−	33.6615i	0.717829	−	1.24332i	0.961858	−	0.273549i	$-0.0881975\pi$
$734$	11.0119			0.406458
$735$	0.143569	+	1.99143i	0.00529560	+	0.0734549i
$736$	0.241579	−	0.0425969i	0.00890472	−	0.00157014i
$737$	−29.5738	−	24.8154i	−1.08937	−	0.914086i
$738$	−84.2097	+	12.2053i	−3.09980	+	0.449285i
$739$	−26.3214	−	9.58021i	−0.968249	−	0.352414i	−0.190988	−	0.981592i	$-0.561169\pi$
$739$	−26.3214	−	9.58021i	−0.968249	−	0.352414i	−0.777261	+	0.629179i	$0.783391\pi$
$740$	1.75451	−	3.03891i	0.0644972	−	0.111712i
$741$	−17.8715	−	5.63008i	−0.656524	−	0.206826i
$742$	5.38113	+	9.32040i	0.197548	+	0.342162i
$743$	−3.32856	−	18.8772i	−0.122113	−	0.692536i	−0.982981	−	0.183708i	$-0.941190\pi$
$743$	−3.32856	−	18.8772i	−0.122113	−	0.692536i	0.860868	−	0.508828i	$-0.169921\pi$
$744$	78.9766	+	8.12868i	2.89542	+	0.298012i
$745$	−1.18558	+	0.431517i	−0.0434364	+	0.0158096i
$746$	10.6802	+	12.7282i	0.391031	+	0.466012i
$747$	−2.18191	−	1.94763i	−0.0798319	−	0.0712602i
$748$	−31.4386	+	54.4533i	−1.14951	+	1.99101i
$749$	6.54980			0.239325
$750$	6.14232	−	4.16234i	0.224286	−	0.151987i
$751$	11.0746	−	13.1982i	0.404118	−	0.481609i	−0.525153	−	0.851008i	$-0.675992\pi$
$751$	11.0746	−	13.1982i	0.404118	−	0.481609i	0.929271	+	0.369399i	$0.120436\pi$
$752$	−1.12715	−	0.650762i	−0.0411030	−	0.0237309i
$753$	−39.3724	+	9.90683i	−1.43481	+	0.361025i
$754$	0.969948	−	1.15594i	0.0353234	−	0.0420968i
$755$	2.35550	−	1.97650i	0.0857254	−	0.0719321i
$756$	−0.575790	−	13.9090i	−0.0209413	−	0.505864i
$757$	1.00826	+	5.71811i	0.0366457	+	0.207828i	0.997633	−	0.0687647i	$-0.0219058\pi$
$757$	1.00826	+	5.71811i	0.0366457	+	0.207828i	−0.960987	+	0.276593i	$0.910795\pi$
$758$	−3.81347	−	4.54471i	−0.138511	−	0.165071i
$759$	−2.64694	+	2.56717i	−0.0960780	+	0.0931825i
$760$	0.529997	+	3.59330i	0.0192250	+	0.130343i
$761$	−12.8353	+	7.41048i	−0.465280	+	0.268630i	−0.714262	−	0.699878i	$-0.753237\pi$
$761$	−12.8353	+	7.41048i	−0.465280	+	0.268630i	0.248982	+	0.968508i	$0.419904\pi$
$762$	−67.1999	−	6.91656i	−2.43439	−	0.250561i
$763$	1.32474	−	3.63968i	0.0479587	−	0.131765i
$764$	−21.6146	+	25.7592i	−0.781988	+	0.931936i
$765$	−0.617066	+	1.54645i	−0.0223101	+	0.0559121i
$766$	3.39065	−	19.2293i	0.122509	−	0.694783i
$767$	−7.10800	+	4.10380i	−0.256655	+	0.148180i
$768$	13.2821	+	52.7867i	0.479277	+	1.90477i
$769$	−28.2272	−	23.6854i	−1.01790	−	0.854118i	−0.0285362	−	0.999593i	$-0.509085\pi$
$769$	−28.2272	−	23.6854i	−1.01790	−	0.854118i	−0.989362	+	0.145475i	$0.953529\pi$
$770$	−1.13537	−	0.952691i	−0.0409160	−	0.0343326i
$771$	−2.24483	−	8.92154i	−0.0808455	−	0.321301i
$772$	30.6393	−	17.6896i	1.10273	−	0.636664i
$773$	−5.60834	+	31.8065i	−0.201718	+	1.14400i	0.700803	+	0.713354i	$0.252825\pi$
$773$	−5.60834	+	31.8065i	−0.201718	+	1.14400i	−0.902521	+	0.430645i	$0.858286\pi$
$774$	5.14455	−	12.8930i	0.184917	−	0.463428i
$775$	−30.9803	+	36.9209i	−1.11285	+	1.32624i
$776$	−21.9746	+	60.3746i	−0.788840	+	2.16732i
$777$	5.92000	+	0.609318i	0.212379	+	0.0218591i
$778$	−77.6727	+	44.8444i	−2.78470	+	1.60775i
$779$	31.5046	+	39.7626i	1.12877	+	1.42464i
$780$	2.14329	−	2.07870i	0.0767420	−	0.0744293i
$781$	−43.4467	−	51.7777i	−1.55464	−	1.85275i
$782$	0.559174	+	3.17123i	0.0199960	+	0.113403i
$783$	−1.14855	−	0.601198i	−0.0410457	−	0.0214851i
$784$	−18.2214	+	15.2896i	−0.650765	+	0.546056i
$785$	0.928772	−	1.10687i	0.0331493	−	0.0395058i
$786$	14.6486	−	3.68587i	0.522500	−	0.131471i
$787$	4.58873	+	2.64930i	0.163570	+	0.0944374i	0.579551	−	0.814936i	$-0.303228\pi$
$787$	4.58873	+	2.64930i	0.163570	+	0.0944374i	−0.415980	+	0.909374i	$0.636561\pi$
$788$	21.2635	−	25.3408i	0.757481	−	0.902730i
$789$	−35.6687	+	24.1709i	−1.26984	+	0.860507i
$790$	2.56910			0.0914045
$791$	−5.21368	+	9.03035i	−0.185377	+	0.321082i
$792$	−53.6363	−	47.8772i	−1.90588	−	1.70124i
$793$	12.3361	+	14.7016i	0.438068	+	0.522069i
$794$	−39.0886	+	14.2271i	−1.38720	+	0.504901i
$795$	1.97266	+	0.203037i	0.0699630	+	0.00720097i
$796$	−4.34332	−	24.6322i	−0.153945	−	0.873065i
$797$	−22.0106	−	38.1235i	−0.779655	−	1.35040i	−0.932141	−	0.362096i	$-0.882061\pi$
$797$	−22.0106	−	38.1235i	−0.779655	−	1.35040i	0.152486	−	0.988306i	$-0.451272\pi$
$798$	−10.5522	+	6.72613i	−0.373546	+	0.238102i
$799$	−0.562961	+	0.975077i	−0.0199161	+	0.0344957i
$800$	−2.72845	−	0.993073i	−0.0964651	−	0.0351104i
$801$	−25.3437	+	3.67331i	−0.895474	+	0.129790i
$802$	−21.9254	−	18.3976i	−0.774213	−	0.649642i
$803$	73.3471	−	12.9331i	2.58836	−	0.456398i
$804$	−3.73479	−	51.8050i	−0.131716	−	1.82702i
$805$	−0.0503437			−0.00177438
$806$	−29.3332	+	50.8065i	−1.03322	+	1.78958i
$807$	16.6705	−	34.3674i	0.586829	−	1.20979i
$808$	73.6374	+	12.9843i	2.59055	+	0.456785i
$809$	27.7834	−	16.0408i	0.976812	−	0.563963i	0.0755062	−	0.997145i	$-0.475943\pi$
$809$	27.7834	−	16.0408i	0.976812	−	0.563963i	0.901306	+	0.433182i	$0.142609\pi$
$810$	−3.22480	−	2.13493i	−0.113308	−	0.0750138i
$811$	−38.0489	−	6.70906i	−1.33608	−	0.235587i	−0.540453	−	0.841374i	$-0.681747\pi$
$811$	−38.0489	−	6.70906i	−1.33608	−	0.235587i	−0.795626	+	0.605788i	$0.792858\pi$
$812$	−0.116066	−	0.658242i	−0.00407311	−	0.0230998i
$813$	−0.593457	+	0.0427843i	−0.0208134	+	0.00150051i
$814$	47.8297	−	40.1339i	1.67643	−	1.40669i
$815$	0.313600	−	0.0552961i	0.0109849	−	0.00193694i
$816$	−19.2365	+	4.84027i	−0.673413	+	0.169443i
$817$	−8.18758	+	1.20764i	−0.286447	+	0.0422498i
$818$			19.6881i			0.688378i
$819$	4.70319	+	1.87667i	0.164343	+	0.0655761i
$820$	−7.96100	+	1.40374i	−0.278010	+	0.0490207i
$821$	−6.60547	−	18.1484i	−0.230532	−	0.633383i	0.769453	−	0.638703i	$-0.220529\pi$
$821$	−6.60547	−	18.1484i	−0.230532	−	0.633383i	−0.999986	+	0.00532019i	$0.998307\pi$
$822$	17.3369	+	38.7146i	0.604695	+	1.35033i
$823$	17.2703	−	6.28588i	0.602005	−	0.219112i	−0.0229964	−	0.999736i	$-0.507321\pi$
$823$	17.2703	−	6.28588i	0.602005	−	0.219112i	0.625001	+	0.780624i	$0.285098\pi$
$824$			23.0365i			0.802513i
$825$	42.3261	−	10.6500i	1.47361	−	0.370787i
$826$	−0.951837	+	5.39814i	−0.0331186	+	0.187825i
$827$	35.4168	−	12.8906i	1.23156	−	0.448252i	0.357429	−	0.933940i	$-0.383653\pi$
$827$	35.4168	−	12.8906i	1.23156	−	0.448252i	0.874132	+	0.485689i	$0.161431\pi$
$828$	−4.95858	−	0.151757i	−0.172323	−	0.00527391i
$829$	−11.4754	−	6.62535i	−0.398559	−	0.230108i	0.287303	−	0.957840i	$-0.407241\pi$
$829$	−11.4754	−	6.62535i	−0.398559	−	0.230108i	−0.685862	+	0.727732i	$0.740575\pi$
$830$	−0.320923	−	0.269286i	−0.0111394	−	0.00934706i
$831$	35.3482	+	25.5657i	1.22622	+	0.886865i
$832$	−21.2663	−	3.74982i	−0.737276	−	0.130002i
$833$	13.2267	+	15.7630i	0.458278	+	0.546154i
$834$	−29.4479	+	13.1872i	−1.01970	+	0.456634i
$835$	−2.21935	−	1.28134i	−0.0768036	−	0.0443426i
$836$	−17.5232	+	85.2937i	−0.606052	+	2.94994i
$837$	48.0340	+	15.2645i	1.66030	+	0.527617i
$838$	−3.92687	+	10.7890i	−0.135652	+	0.372700i
$839$	36.8382	+	13.4080i	1.27180	+	0.462896i	0.887711	−	0.460402i	$-0.152295\pi$
$839$	36.8382	+	13.4080i	1.27180	+	0.462896i	0.384085	+	0.923298i	$0.374517\pi$
$840$	−0.0705836	−	0.979059i	−0.00243537	−	0.0337808i
$841$	27.1926	+	9.89730i	0.937676	+	0.341286i
$842$	26.1125	+	71.7434i	0.899895	+	2.47244i
$843$	−15.5664	−	4.42729i	−0.536134	−	0.152484i
$844$			54.7844i			1.88576i
$845$	−0.412540	−	1.13345i	−0.0141918	−	0.0389917i
$846$	−1.95104	−	1.74155i	−0.0670782	−	0.0598759i
$847$	−5.00493	−	8.66879i	−0.171971	−	0.297863i
$848$	11.8127	+	20.4602i	0.405649	+	0.702605i
$849$	6.08268	−	12.5399i	0.208757	−	0.430367i
$850$	13.0362	−	35.8166i	0.447137	−	1.22850i
$851$	0.368277	−	2.08860i	0.0126244	−	0.0715963i
$852$	9.31037	−	90.4575i	0.318968	−	3.09902i
$853$	26.3930	−	22.1464i	0.903681	−	0.758278i	−0.0672256	−	0.997738i	$-0.521415\pi$
$853$	26.3930	−	22.1464i	0.903681	−	0.758278i	0.970906	+	0.239460i	$0.0769703\pi$
$854$	12.8170			0.438589
$855$	−0.135245	+	2.30182i	−0.00462527	+	0.0787206i
$856$	45.5106			1.55552
$857$	11.9299	−	10.0104i	0.407519	−	0.341949i	−0.415872	−	0.909423i	$-0.636524\pi$
$857$	11.9299	−	10.0104i	0.407519	−	0.341949i	0.823391	+	0.567474i	$0.192079\pi$
$858$	48.4865	−	21.7130i	1.65530	−	0.741268i
$859$	−8.85977	+	50.2462i	−0.302291	+	1.71438i	0.333697	+	0.942680i	$0.391704\pi$
$859$	−8.85977	+	50.2462i	−0.302291	+	1.71438i	−0.635988	+	0.771699i	$0.719407\pi$
$860$	0.451051	−	1.23925i	0.0153807	−	0.0422582i
$861$	−7.69104	−	11.3496i	−0.262110	−	0.386793i
$862$	42.8964	+	74.2988i	1.46106	+	2.53063i
$863$	−21.0067	−	36.3847i	−0.715076	−	1.23855i	−0.962930	−	0.269751i	$-0.913059\pi$
$863$	−21.0067	−	36.3847i	−0.715076	−	1.23855i	0.247854	−	0.968798i	$-0.420275\pi$
$864$	0.125588	+	3.03374i	0.00427259	+	0.103210i
$865$	1.15166	+	3.16417i	0.0391577	+	0.107585i
$866$		−	74.9337i		−	2.54635i
$867$	−2.99771	−	11.9137i	−0.101807	−	0.404610i
$868$	8.88779	+	24.4190i	0.301671	+	0.828835i
$869$	28.4905	+	10.3697i	0.966476	+	0.351768i
$870$	−0.167074	−	0.0810421i	−0.00566434	−	0.00274758i
$871$	17.7538	+	6.46187i	0.601566	+	0.218952i
$872$	9.20478	−	25.2899i	0.311713	−	0.856425i
$873$	−21.4645	+	34.6822i	−0.726462	+	1.17381i
$874$	2.12035	+	3.92307i	0.0717218	+	0.132700i
$875$	1.03534	+	0.597755i	0.0350010	+	0.0202078i
$876$	81.1916	+	58.7222i	2.74321	+	1.98404i
$877$	−6.10512	−	7.27579i	−0.206155	−	0.245686i	0.653053	−	0.757312i	$-0.273488\pi$
$877$	−6.10512	−	7.27579i	−0.206155	−	0.245686i	−0.859208	+	0.511626i	$0.829043\pi$
$878$	−67.4748	−	11.8976i	−2.27717	−	0.401526i
$879$	−39.4929	+	17.6855i	−1.33206	+	0.596516i
$880$	−2.49237	−	2.09135i	−0.0840179	−	0.0704994i
$881$	12.3480	+	7.12911i	0.416014	+	0.240186i	0.693371	−	0.720581i	$-0.256125\pi$
$881$	12.3480	+	7.12911i	0.416014	+	0.240186i	−0.277356	+	0.960767i	$0.589458\pi$
$882$	−42.1041	+	22.6205i	−1.41772	+	0.761673i
$883$	48.1856	−	17.5381i	1.62157	−	0.590205i	0.637893	−	0.770125i	$-0.279806\pi$
$883$	48.1856	−	17.5381i	1.62157	−	0.590205i	0.983681	+	0.179920i	$0.0575840\pi$
$884$	5.34339	−	30.3038i	0.179718	−	1.01923i
$885$	0.703182	+	0.725032i	0.0236372	+	0.0243717i
$886$		−	34.2227i		−	1.14973i
$887$	−42.9886	+	15.6466i	−1.44342	+	0.525360i	−0.940744	−	0.339118i	$-0.889872\pi$
$887$	−42.9886	+	15.6466i	−1.44342	+	0.525360i	−0.502671	+	0.864478i	$0.667649\pi$
$888$	41.1344	+	4.23377i	1.38038	+	0.142076i
$889$	−3.72281	−	10.2283i	−0.124859	−	0.343047i
$890$	−3.61241	+	0.636965i	−0.121088	+	0.0213511i
$891$	−27.1448	−	36.6920i	−0.909384	−	1.22923i
$892$		−	12.9249i		−	0.432758i
$893$	−0.313782	+	1.52733i	−0.0105003	+	0.0511100i
$894$	−21.0274	−	21.6808i	−0.703261	−	0.725114i
$895$	1.22711	−	0.216373i	0.0410179	−	0.00723256i
$896$	−10.4388	+	8.75917i	−0.348735	+	0.292623i
$897$	0.787566	−	1.62362i	0.0262960	−	0.0542112i
$898$	−10.8023	−	61.2628i	−0.360477	−	2.04437i
$899$	2.38319	+	0.420221i	0.0794838	+	0.0140151i
$900$	49.9307	+	30.9016i	1.66436	+	1.03005i
$901$	17.6997	−	10.2189i	0.589661	−	0.340441i
$902$	−141.652	−	24.9771i	−4.71651	−	0.831648i
$903$	2.23086	−	0.160830i	0.0742382	−	0.00535208i
$904$	−36.2266	+	62.7464i	−1.20488	+	2.08691i
$905$	−4.49260			−0.149339
$906$	66.2285	+	32.1253i	2.20029	+	1.06729i
$907$	−26.1818	+	4.61655i	−0.869351	+	0.153290i	−0.590493	−	0.807043i	$-0.701067\pi$
$907$	−26.1818	+	4.61655i	−0.869351	+	0.153290i	−0.278857	+	0.960333i	$0.589956\pi$
$908$	−38.0119	−	31.8958i	−1.26147	−	1.05850i
$909$	44.0877	+	17.5919i	1.46230	+	0.583486i
$910$	0.681590	+	0.248078i	0.0225945	+	0.00822372i
$911$	−2.51245	+	4.35169i	−0.0832412	+	0.144178i	−0.904640	−	0.426176i	$-0.859861\pi$
$911$	−2.51245	+	4.35169i	−0.0832412	+	0.144178i	0.821399	+	0.570354i	$0.193194\pi$
$912$	−23.1643	+	14.7652i	−0.767048	+	0.488925i
$913$	−2.47201	−	4.28165i	−0.0818117	−	0.141702i
$914$	−5.56205	−	31.5440i	−0.183976	−	1.04338i
$915$	1.38404	−	1.91364i	0.0457551	−	0.0632628i
$916$	−15.9996	+	5.82339i	−0.528642	+	0.192410i
$917$	1.56443	+	1.86442i	0.0516622	+	0.0615686i
$918$	−39.8243	+	1.64861i	−1.31440	+	0.0544121i
$919$	26.2111	−	45.3990i	0.864625	−	1.49757i	−0.00279410	−	0.999996i	$-0.500889\pi$
$919$	26.2111	−	45.3990i	0.864625	−	1.49757i	0.867419	−	0.497578i	$-0.165777\pi$
$920$	−0.349807			−0.0115328
$921$	−26.2110	−	12.7141i	−0.863682	−	0.418943i
$922$	4.98796	−	5.94442i	0.164270	−	0.195769i
$923$	28.6466	+	16.5391i	0.942913	+	0.544391i
$924$	6.43757	−	22.6345i	0.211781	−	0.744621i
$925$	−16.1359	+	19.2300i	−0.530545	+	0.632279i
$926$	−5.92769	+	4.97392i	−0.194796	+	0.163453i
$927$	−2.97882	+	14.3175i	−0.0978373	+	0.470248i
$928$	0.0253156	+	0.143572i	0.000831026	+	0.00471298i
$929$	7.27587	+	8.67105i	0.238714	+	0.284488i	0.872079	−	0.489365i	$-0.162771\pi$
$929$	7.27587	+	8.67105i	0.238714	+	0.284488i	−0.633365	+	0.773853i	$0.718327\pi$
$930$	6.94401	+	1.97497i	0.227703	+	0.0647619i
$931$	24.2683	+	14.9356i	0.795363	+	0.489494i
$932$	50.3879	−	29.0915i	1.65051	−	0.952923i
$933$	−11.3446	+	15.6855i	−0.371405	+	0.513519i
$934$	−14.0319	+	38.5523i	−0.459138	+	1.26147i
$935$	−1.80918	+	2.15610i	−0.0591666	+	0.0705120i
$936$	32.6796	+	13.0398i	1.06817	+	0.426220i
$937$	−6.37744	+	36.1683i	−0.208342	+	1.18157i	0.683752	+	0.729715i	$0.260347\pi$
$937$	−6.37744	+	36.1683i	−0.208342	+	1.18157i	−0.892093	+	0.451851i	$0.850764\pi$
$938$	10.9273	−	6.30888i	0.356789	−	0.205992i
$939$	−12.0703	+	11.7065i	−0.393898	+	0.382028i
$940$	−0.190330	−	0.159706i	−0.00620789	−	0.00520904i
$941$	42.1364	+	35.3566i	1.37361	+	1.15259i	0.971511	+	0.236994i	$0.0761623\pi$
$941$	42.1364	+	35.3566i	1.37361	+	1.15259i	0.402095	+	0.915598i	$0.368282\pi$
$942$	33.2699	+	9.46241i	1.08399	+	0.308302i
$943$	−4.23120	+	2.44289i	−0.137787	+	0.0795513i
$944$	−2.08948	+	11.8500i	−0.0680066	+	0.385685i
$945$	0.0827324	−	0.617627i	0.00269129	−	0.0200914i
$946$	15.0834	−	17.9757i	0.490403	−	0.584439i
$947$	−18.4440	+	50.6744i	−0.599348	+	1.64670i	0.153228	+	0.988191i	$0.451033\pi$
$947$	−18.4440	+	50.6744i	−0.599348	+	1.64670i	−0.752576	+	0.658505i	$0.771189\pi$
$948$	16.6713	+	37.2281i	0.541458	+	1.20911i
$949$	−31.5656	+	18.2244i	−1.02466	+	0.591590i
$950$	1.48264	−	52.7628i	0.0481033	−	1.71185i
$951$	6.37957	+	25.3541i	0.206872	+	0.822163i
$952$	−6.50274	−	7.74966i	−0.210755	−	0.251168i
$953$	−4.48205	−	25.4190i	−0.145188	−	0.823401i	−0.967216	−	0.253954i	$-0.918269\pi$
$953$	−4.48205	−	25.4190i	−0.145188	−	0.823401i	0.822028	−	0.569447i	$-0.192842\pi$
$954$	14.8643	+	45.0852i	0.481249	+	1.45969i
$955$	−1.15307	+	0.967538i	−0.0373124	+	0.0313088i
$956$	36.3232	−	43.2883i	1.17478	−	1.40004i
$957$	−1.52569	−	1.57310i	−0.0493185	−	0.0508510i
$958$	−23.4588	−	13.5440i	−0.757920	−	0.437585i
$959$	−4.39331	+	5.23575i	−0.141867	+	0.169071i
$960$	0.191083	+	2.65050i	0.00616718	+	0.0855444i
$961$	−63.0839			−2.03496
$962$	−15.2780	+	26.4623i	−0.492582	+	0.853177i
$963$	28.2855	+	5.88492i	0.911487	+	0.189639i
$964$	−20.1301	−	23.9901i	−0.648346	−	0.772668i
$965$	1.48818	−	0.541654i	0.0479063	−	0.0174365i
$966$	−0.492555	−	1.09991i	−0.0158477	−	0.0353890i
$967$	−2.59974	−	14.7439i	−0.0836020	−	0.474130i	−0.997650	−	0.0685233i	$-0.978171\pi$
$967$	−2.59974	−	14.7439i	−0.0836020	−	0.474130i	0.914048	−	0.405607i	$-0.132940\pi$
$968$	−34.7762	−	60.2341i	−1.11775	−	1.93600i
$969$	12.7731	+	20.0390i	0.410331	+	0.643745i
$970$	−2.92115	+	5.05957i	−0.0937923	+	0.162453i
$971$	12.9364	+	4.70848i	0.415150	+	0.151102i	0.541146	−	0.840928i	$-0.317990\pi$
$971$	12.9364	+	4.70848i	0.415150	+	0.151102i	−0.125996	+	0.992031i	$0.540213\pi$
$972$	10.0105	−	60.5835i	0.321086	−	1.94322i
$973$	−3.98252	−	3.34173i	−0.127674	−	0.107131i
$974$	−79.2564	+	13.9750i	−2.53954	+	0.447789i
$975$	−17.6821	+	11.9822i	−0.566279	+	0.383739i
$976$	28.1359			0.900608
$977$	10.5020	−	18.1901i	0.335990	−	0.581952i	−0.647684	−	0.761909i	$-0.724262\pi$
$977$	10.5020	−	18.1901i	0.335990	−	0.581952i	0.983674	+	0.179957i	$0.0575958\pi$
$978$	4.27633	+	6.31053i	0.136742	+	0.201789i
$979$	−42.6316	−	7.51709i	−1.36251	−	0.240247i
$980$	−3.93242	+	2.27039i	−0.125617	+	0.0725248i
$981$	8.99111	−	14.5278i	0.287064	−	0.463837i
$982$	15.7499	+	2.77713i	0.502599	+	0.0886218i
$983$	4.12942	+	23.4191i	0.131708	+	0.746953i	0.977096	+	0.212800i	$0.0682583\pi$
$983$	4.12942	+	23.4191i	0.131708	+	0.746953i	−0.845388	+	0.534153i	$0.820631\pi$
$984$	−53.4403	−	78.8613i	−1.70362	−	2.51401i
$985$	1.13434	−	0.951823i	0.0361430	−	0.0303276i
$986$	−1.88469	+	0.332321i	−0.0600206	+	0.0105833i
$987$	0.115275	−	0.405309i	0.00366926	−	0.0129011i
$988$	−6.21804	−	42.1574i	−0.197822	−	1.34120i
$989$		−	0.797061i		−	0.0253451i
$990$	−4.04715	−	5.13434i	−0.128627	−	0.163180i
$991$	27.8616	−	4.91275i	0.885052	−	0.156059i	0.287397	−	0.957812i	$-0.407210\pi$
$991$	27.8616	−	4.91275i	0.885052	−	0.156059i	0.597655	+	0.801753i	$0.296099\pi$
$992$	−1.93855	−	5.32613i	−0.0615491	−	0.169105i
$993$	−13.3996	+	18.5268i	−0.425222	+	0.587929i
$994$	20.7589	−	7.55561i	0.658431	−	0.239649i
$995$		−	1.11963i		−	0.0354946i
$996$	1.81964	−	6.39784i	0.0576574	−	0.202723i
$997$	−7.96636	+	45.1795i	−0.252297	+	1.43085i	0.550620	+	0.834756i	$0.314391\pi$
$997$	−7.96636	+	45.1795i	−0.252297	+	1.43085i	−0.802917	+	0.596091i	$0.796720\pi$
$998$	23.9143	−	8.70409i	0.756994	−	0.275523i
$999$	25.0182	+	7.95040i	0.791540	+	0.251540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.110.2	yes	108
3.2	odd	2		513.2.bo.a.224.17		108
9.4	even	3		513.2.cd.a.395.2		108
9.5	odd	6		171.2.bd.a.167.17	yes	108
19.14	odd	18		171.2.bd.a.128.17	yes	108
57.14	even	18		513.2.cd.a.413.2		108
171.14	even	18	inner	171.2.x.a.14.2	✓	108
171.166	odd	18		513.2.bo.a.71.17		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.2	✓	108	171.14	even	18	inner
171.2.x.a.110.2	yes	108	1.1	even	1	trivial
171.2.bd.a.128.17	yes	108	19.14	odd	18
171.2.bd.a.167.17	yes	108	9.5	odd	6
513.2.bo.a.71.17		108	171.166	odd	18
513.2.bo.a.224.17		108	3.2	odd	2
513.2.cd.a.395.2		108	9.4	even	3
513.2.cd.a.413.2		108	57.14	even	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86688 + 1.56649i) q^{2} +(-1.40345 - 1.01505i) q^{3} +(0.684023 - 3.87929i) q^{4} +(0.0603078 - 0.165694i) q^{5} +(4.21014 - 0.303523i) q^{6} +(0.340059 + 0.588999i) q^{7} +(2.36286 + 4.09260i) q^{8} +(0.939343 + 2.84915i) q^{9} +O(q^{10})\)	\(q+(-1.86688 + 1.56649i) q^{2} +(-1.40345 - 1.01505i) q^{3} +(0.684023 - 3.87929i) q^{4} +(0.0603078 - 0.165694i) q^{5} +(4.21014 - 0.303523i) q^{6} +(0.340059 + 0.588999i) q^{7} +(2.36286 + 4.09260i) q^{8} +(0.939343 + 2.84915i) q^{9} +(0.146972 + 0.403802i) q^{10} +5.07127i q^{11} +(-4.89766 + 4.75006i) q^{12} +(-0.848831 - 2.33215i) q^{13} +(-1.55751 - 0.566888i) q^{14} +(-0.252827 + 0.171328i) q^{15} +(-3.41905 - 1.24443i) q^{16} +(-1.07653 + 2.95775i) q^{17} +(-6.21681 - 3.84753i) q^{18} +(-0.122437 + 4.35718i) q^{19} +(-0.601523 - 0.347290i) q^{20} +(0.120609 - 1.17181i) q^{21} +(-7.94412 - 9.46744i) q^{22} +(-0.413419 - 0.0728969i) q^{23} +(0.838036 - 8.14218i) q^{24} +(3.80640 + 3.19395i) q^{25} +(5.23796 + 3.02414i) q^{26} +(1.57371 - 4.95212i) q^{27} +(2.51750 - 0.916297i) q^{28} +(0.0433231 - 0.245698i) q^{29} +(0.203612 - 0.715901i) q^{30} +9.69968i q^{31} +(-0.549104 + 0.199857i) q^{32} +(5.14760 - 7.11728i) q^{33} +(-2.62355 - 7.20814i) q^{34} +(0.118102 - 0.0208246i) q^{35} +(11.6952 - 1.69510i) q^{36} +5.05202i q^{37} +(-6.59692 - 8.32611i) q^{38} +(-1.17595 + 4.13466i) q^{39} +(0.820619 - 0.144697i) q^{40} +(8.91555 - 7.48103i) q^{41} +(1.61047 + 2.37655i) q^{42} +(0.329703 + 1.86984i) q^{43} +(19.6729 + 3.46887i) q^{44} +(0.528737 + 0.0161819i) q^{45} +(0.885995 - 0.511529i) q^{46} +(0.352276 + 0.0621158i) q^{47} +(3.53531 + 5.21702i) q^{48} +(3.26872 - 5.66159i) q^{49} -12.1094 q^{50} +(4.51313 - 3.05832i) q^{51} +(-9.62768 + 1.69762i) q^{52} +(-4.97407 - 4.17374i) q^{53} +(4.81954 + 11.7102i) q^{54} +(0.840281 + 0.305837i) q^{55} +(-1.60702 + 2.78345i) q^{56} +(4.59459 - 5.99080i) q^{57} +(0.304005 + 0.526553i) q^{58} +(-0.574271 - 3.25685i) q^{59} +(0.491691 + 1.09798i) q^{60} +(-7.26652 + 2.64480i) q^{61} +(-15.1945 - 18.1081i) q^{62} +(-1.35871 + 1.52215i) q^{63} +(4.35051 - 7.53531i) q^{64} -0.437614 q^{65} +(1.53925 + 21.3508i) q^{66} +(-4.89332 + 5.83164i) q^{67} +(10.7376 + 6.19936i) q^{68} +(0.506219 + 0.521949i) q^{69} +(-0.187860 + 0.223883i) q^{70} +(-10.2100 + 8.56721i) q^{71} +(-9.44087 + 10.5765i) q^{72} +(-2.55026 - 14.4632i) q^{73} +(-7.91396 - 9.43149i) q^{74} +(-2.10007 - 8.34625i) q^{75} +(16.8190 + 3.45538i) q^{76} +(-2.98698 + 1.72453i) q^{77} +(-4.28156 - 9.56101i) q^{78} +(2.04479 - 5.61802i) q^{79} +(-0.412391 + 0.491469i) q^{80} +(-7.23527 + 5.35265i) q^{81} +(-4.92522 + 27.9323i) q^{82} +(-0.844295 + 0.487454i) q^{83} +(-4.46328 - 1.26942i) q^{84} +(0.425160 + 0.356751i) q^{85} +(-3.54460 - 2.97428i) q^{86} +(-0.310198 + 0.300849i) q^{87} +(-20.7547 + 11.9827i) q^{88} +(-1.48229 + 8.40648i) q^{89} +(-1.01243 + 0.798054i) q^{90} +(1.08498 - 1.29303i) q^{91} +(-0.565576 + 1.55391i) q^{92} +(9.84567 - 13.6130i) q^{93} +(-0.754960 + 0.435876i) q^{94} +(0.714576 + 0.283059i) q^{95} +(0.973505 + 0.276878i) q^{96} +(8.73912 + 10.4149i) q^{97} +(2.76656 + 15.6899i) q^{98} +(-14.4488 + 4.76367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

L-functions

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