LMFDB - Embedded newform 460.2.w.a.3.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			3.12
Character	$\chi$	$=$	460.3
Dual form			460.2.w.a.307.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18443 + 0.772733i) q^{2} +(-1.12425 - 3.01422i) q^{3} +(0.805766 - 1.83050i) q^{4} +(1.84293 + 1.26634i) q^{5} +(3.66078 + 2.70140i) q^{6} +(-3.65616 - 0.795348i) q^{7} +(0.460113 + 2.79075i) q^{8} +(-5.55434 + 4.81286i) q^{9} +O(q^{10})$	\(q+(-1.18443 + 0.772733i) q^{2} +(-1.12425 - 3.01422i) q^{3} +(0.805766 - 1.83050i) q^{4} +(1.84293 + 1.26634i) q^{5} +(3.66078 + 2.70140i) q^{6} +(-3.65616 - 0.795348i) q^{7} +(0.460113 + 2.79075i) q^{8} +(-5.55434 + 4.81286i) q^{9} +(-3.16137 - 0.0757989i) q^{10} +(1.16386 + 0.167337i) q^{11} +(-6.42342 - 0.370822i) q^{12} +(-1.07128 - 4.92459i) q^{13} +(4.94507 - 1.88320i) q^{14} +(1.74511 - 6.97867i) q^{15} +(-2.70148 - 2.94992i) q^{16} +(-4.49365 + 2.45372i) q^{17} +(2.85969 - 9.99254i) q^{18} +(-0.196477 + 0.0576910i) q^{19} +(3.80300 - 2.35312i) q^{20} +(1.71306 + 11.9146i) q^{21} +(-1.50782 + 0.701151i) q^{22} +(-1.94882 + 4.38202i) q^{23} +(7.89466 - 4.52437i) q^{24} +(1.79278 + 4.66754i) q^{25} +(5.07425 + 5.00504i) q^{26} +(12.2808 + 6.70584i) q^{27} +(-4.40190 + 6.05174i) q^{28} +(0.349626 - 1.19072i) q^{29} +(3.32568 + 9.61428i) q^{30} +(-7.52904 + 3.43840i) q^{31} +(5.47922 + 1.40646i) q^{32} +(-0.804070 - 3.69625i) q^{33} +(3.42636 - 6.37866i) q^{34} +(-5.73086 - 6.09570i) q^{35} +(4.33446 + 14.0453i) q^{36} +(1.18764 + 0.0849418i) q^{37} +(0.188135 - 0.220156i) q^{38} +(-13.6394 + 8.76552i) q^{39} +(-2.68608 + 5.72582i) q^{40} +(-0.160371 + 0.185078i) q^{41} +(-11.2358 - 12.7883i) q^{42} +(-0.555599 - 1.48962i) q^{43} +(1.24411 - 1.99561i) q^{44} +(-16.3310 + 1.83610i) q^{45} +(-1.07789 - 6.69613i) q^{46} +(1.59397 + 1.59397i) q^{47} +(-5.85456 + 11.4593i) q^{48} +(6.36748 + 2.90793i) q^{49} +(-5.73019 - 4.14305i) q^{50} +(12.4480 + 10.7863i) q^{51} +(-9.87768 - 2.00709i) q^{52} +(1.39314 + 0.303059i) q^{53} +(-19.7277 + 1.54718i) q^{54} +(1.93300 + 1.78223i) q^{55} +(0.537373 - 10.5694i) q^{56} +(0.394782 + 0.527367i) q^{57} +(0.505998 + 1.68049i) q^{58} +(-3.38710 - 2.17676i) q^{59} +(-11.3683 - 8.81761i) q^{60} +(1.32248 + 2.89582i) q^{61} +(6.26069 - 9.89049i) q^{62} +(24.1354 - 13.1789i) q^{63} +(-7.57659 + 2.56812i) q^{64} +(4.26190 - 10.4323i) q^{65} +(3.80858 + 3.75663i) q^{66} +(-5.88517 + 7.86167i) q^{67} +(0.870705 + 10.2028i) q^{68} +(15.3993 + 0.947695i) q^{69} +(11.4982 + 2.79152i) q^{70} +(-0.414629 + 0.0596147i) q^{71} +(-15.9871 - 13.2863i) q^{72} +(-9.39263 - 5.12876i) q^{73} +(-1.47232 + 0.817122i) q^{74} +(12.0535 - 10.6513i) q^{75} +(-0.0527114 + 0.406138i) q^{76} +(-4.12215 - 1.53748i) q^{77} +(9.38157 - 20.9218i) q^{78} +(7.77924 + 4.99941i) q^{79} +(-1.24305 - 8.85747i) q^{80} +(3.26840 - 22.7322i) q^{81} +(0.0469329 - 0.343137i) q^{82} +(-6.69945 - 0.479154i) q^{83} +(23.1901 + 6.46464i) q^{84} +(-11.3887 - 1.16844i) q^{85} +(1.80915 + 1.33502i) q^{86} +(-3.98215 + 0.284809i) q^{87} +(0.0685092 + 3.32503i) q^{88} +(-15.3759 - 7.02192i) q^{89} +(17.9241 - 14.7942i) q^{90} +18.8571i q^{91} +(6.45101 + 7.09820i) q^{92} +(18.8286 + 18.8286i) q^{93} +(-3.11967 - 0.656240i) q^{94} +(-0.435150 - 0.142486i) q^{95} +(-1.92063 - 18.0968i) q^{96} +(-0.148679 - 2.07880i) q^{97} +(-9.78892 + 1.47611i) q^{98} +(-7.26983 + 4.67204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−1.18443	+	0.772733i	−0.837521	+	0.546405i
$2$	−1.18443	+	0.772733i	−0.837521	+	0.546405i
$3$	−1.12425	−	3.01422i	−0.649083	−	1.74026i	−0.672030	−	0.740523i	$-0.734578\pi$
$3$	−1.12425	−	3.01422i	−0.649083	−	1.74026i	0.0229470	−	0.999737i	$-0.492695\pi$
$4$	0.805766	−	1.83050i	0.402883	−	0.915251i
$5$	1.84293	+	1.26634i	0.824183	+	0.566323i
$5$	1.84293	+	1.26634i	0.824183	+	0.566323i
$6$	3.66078	+	2.70140i	1.49451	+	1.10284i
$7$	−3.65616	−	0.795348i	−1.38190	−	0.300613i	−0.540643	−	0.841252i	$-0.681819\pi$
$7$	−3.65616	−	0.795348i	−1.38190	−	0.300613i	−0.841255	+	0.540639i	$0.818183\pi$
$8$	0.460113	+	2.79075i	0.162675	+	0.986680i
$9$	−5.55434	+	4.81286i	−1.85145	+	1.60429i
$10$	−3.16137	−	0.0757989i	−0.999713	−	0.0239697i
$11$	1.16386	+	0.167337i	0.350916	+	0.0504541i	0.315519	−	0.948919i	$-0.397821\pi$
$11$	1.16386	+	0.167337i	0.350916	+	0.0504541i	0.0353970	+	0.999373i	$0.488730\pi$
$12$	−6.42342	−	0.370822i	−1.85428	−	0.107047i
$13$	−1.07128	−	4.92459i	−0.297119	−	1.36584i	−0.847444	−	0.530885i	$-0.821860\pi$
$13$	−1.07128	−	4.92459i	−0.297119	−	1.36584i	0.550325	−	0.834951i	$-0.314504\pi$
$14$	4.94507	−	1.88320i	1.32163	−	0.503306i
$15$	1.74511	−	6.97867i	0.450586	−	1.80188i
$16$	−2.70148	−	2.94992i	−0.675370	−	0.737479i
$17$	−4.49365	+	2.45372i	−1.08987	+	0.595114i	−0.920620	−	0.390460i	$-0.872316\pi$
$17$	−4.49365	+	2.45372i	−1.08987	+	0.595114i	−0.169249	+	0.985573i	$0.554134\pi$
$18$	2.85969	−	9.99254i	0.674035	−	2.35526i
$19$	−0.196477	+	0.0576910i	−0.0450750	+	0.0132352i	−0.304192	−	0.952611i	$-0.598387\pi$
$19$	−0.196477	+	0.0576910i	−0.0450750	+	0.0132352i	0.259117	+	0.965846i	$0.416568\pi$
$20$	3.80300	−	2.35312i	0.850378	−	0.526173i
$21$	1.71306	+	11.9146i	0.373821	+	2.59998i
$22$	−1.50782	+	0.701151i	−0.321468	+	0.149486i
$23$	−1.94882	+	4.38202i	−0.406357	+	0.913715i
$23$	−1.94882	+	4.38202i	−0.406357	+	0.913715i
$24$	7.89466	−	4.52437i	1.61149	−	0.923534i
$25$	1.79278	+	4.66754i	0.358556	+	0.933508i
$26$	5.07425	+	5.00504i	0.995143	+	0.981569i
$27$	12.2808	+	6.70584i	2.36345	+	1.29054i
$28$	−4.40190	+	6.05174i	−0.831880	+	1.14367i
$29$	0.349626	−	1.19072i	0.0649240	−	0.221111i	−0.920640	−	0.390411i	$-0.872333\pi$
$29$	0.349626	−	1.19072i	0.0649240	−	0.221111i	0.985564	+	0.169301i	$0.0541509\pi$
$30$	3.32568	+	9.61428i	0.607183	+	1.75532i
$31$	−7.52904	+	3.43840i	−1.35226	+	0.617554i	−0.954024	−	0.299730i	$-0.903103\pi$
$31$	−7.52904	+	3.43840i	−1.35226	+	0.617554i	−0.398232	+	0.917285i	$0.630376\pi$
$32$	5.47922	+	1.40646i	0.968599	+	0.248629i
$33$	−0.804070	−	3.69625i	−0.139971	−	0.643434i
$34$	3.42636	−	6.37866i	0.587616	−	1.09393i
$35$	−5.73086	−	6.09570i	−0.968693	−	1.03036i
$36$	4.33446	+	14.0453i	0.722410	+	2.34088i
$37$	1.18764	+	0.0849418i	0.195247	+	0.0139643i	0.168620	−	0.985681i	$-0.446069\pi$
$37$	1.18764	+	0.0849418i	0.195247	+	0.0139643i	0.0266268	+	0.999645i	$0.491523\pi$
$38$	0.188135	−	0.220156i	0.0305195	−	0.0357140i
$39$	−13.6394	+	8.76552i	−2.18405	+	1.40361i
$40$	−2.68608	+	5.72582i	−0.424706	+	0.905331i
$41$	−0.160371	+	0.185078i	−0.0250458	+	0.0289043i	−0.768134	−	0.640289i	$-0.778815\pi$
$41$	−0.160371	+	0.185078i	−0.0250458	+	0.0289043i	0.743088	+	0.669193i	$0.233360\pi$
$42$	−11.2358	−	12.7883i	−1.73373	−	1.97328i
$43$	−0.555599	−	1.48962i	−0.0847281	−	0.227165i	0.887676	−	0.460469i	$-0.152319\pi$
$43$	−0.555599	−	1.48962i	−0.0847281	−	0.227165i	−0.972404	+	0.233305i	$0.925046\pi$
$44$	1.24411	−	1.99561i	0.187556	−	0.300849i
$45$	−16.3310	+	1.83610i	−2.43448	+	0.273710i
$46$	−1.07789	−	6.69613i	−0.158926	−	0.987290i
$47$	1.59397	+	1.59397i	0.232505	+	0.232505i	0.813738	−	0.581233i	$-0.197429\pi$
$47$	1.59397	+	1.59397i	0.232505	+	0.232505i	−0.581233	+	0.813738i	$0.697429\pi$
$48$	−5.85456	+	11.4593i	−0.845034	+	1.65401i
$49$	6.36748	+	2.90793i	0.909641	+	0.415419i
$50$	−5.73019	−	4.14305i	−0.810372	−	0.585916i
$51$	12.4480	+	10.7863i	1.74307	+	1.51038i
$52$	−9.87768	−	2.00709i	−1.36979	−	0.278333i
$53$	1.39314	+	0.303059i	0.191362	+	0.0416283i	0.307225	−	0.951637i	$-0.400600\pi$
$53$	1.39314	+	0.303059i	0.191362	+	0.0416283i	−0.115863	+	0.993265i	$0.536963\pi$
$54$	−19.7277	+	1.54718i	−2.68460	+	0.210545i
$55$	1.93300	+	1.78223i	0.260646	+	0.240315i
$56$	0.537373	−	10.5694i	0.0718095	−	1.41239i
$57$	0.394782	+	0.527367i	0.0522902	+	0.0698515i
$58$	0.505998	+	1.68049i	0.0664408	+	0.220660i
$59$	−3.38710	−	2.17676i	−0.440963	−	0.283389i	0.301261	−	0.953542i	$-0.402592\pi$
$59$	−3.38710	−	2.17676i	−0.440963	−	0.283389i	−0.742224	+	0.670152i	$0.766229\pi$
$60$	−11.3683	−	8.81761i	−1.46764	−	1.13835i
$61$	1.32248	+	2.89582i	0.169326	+	0.370772i	0.975203	−	0.221310i	$-0.0710334\pi$
$61$	1.32248	+	2.89582i	0.169326	+	0.370772i	−0.805878	+	0.592082i	$0.798306\pi$
$62$	6.26069	−	9.89049i	0.795108	−	1.25609i
$63$	24.1354	−	13.1789i	3.04078	−	1.66039i
$64$	−7.57659	+	2.56812i	−0.947074	+	0.321016i
$65$	4.26190	−	10.4323i	0.528623	−	1.29396i
$66$	3.80858	+	3.75663i	0.468804	+	0.462409i
$67$	−5.88517	+	7.86167i	−0.718988	+	0.960456i	0.281012	+	0.959704i	$0.409330\pi$
$67$	−5.88517	+	7.86167i	−0.718988	+	0.960456i	−1.00000		0.000751253i	$0.999761\pi$
$68$	0.870705	+	10.2028i	0.105589	+	1.23727i
$69$	15.3993	+	0.947695i	1.85386	+	0.114089i
$70$	11.4982	+	2.79152i	1.37429	+	0.333651i
$71$	−0.414629	+	0.0596147i	−0.0492074	+	0.00707496i	−0.166875	−	0.985978i	$-0.553368\pi$
$71$	−0.414629	+	0.0596147i	−0.0492074	+	0.00707496i	0.117667	+	0.993053i	$0.462458\pi$
$72$	−15.9871	−	13.2863i	−1.88410	−	1.56581i
$73$	−9.39263	−	5.12876i	−1.09932	−	0.600276i	−0.176036	−	0.984384i	$-0.556327\pi$
$73$	−9.39263	−	5.12876i	−1.09932	−	0.600276i	−0.923288	+	0.384107i	$0.874509\pi$
$74$	−1.47232	+	0.817122i	−0.171154	+	0.0949885i
$75$	12.0535	−	10.6513i	1.39181	−	1.22991i
$76$	−0.0527114	+	0.406138i	−0.00604642	+	0.0465872i
$77$	−4.12215	−	1.53748i	−0.469763	−	0.175213i
$78$	9.38157	−	20.9218i	1.06225	−	2.36893i
$79$	7.77924	+	4.99941i	0.875232	+	0.562478i	0.899349	−	0.437231i	$-0.144041\pi$
$79$	7.77924	+	4.99941i	0.875232	+	0.562478i	−0.0241166	+	0.999709i	$0.507677\pi$
$80$	−1.24305	−	8.85747i	−0.138977	−	0.990296i
$81$	3.26840	−	22.7322i	0.363156	−	2.52580i
$82$	0.0469329	−	0.343137i	0.00518287	−	0.0378931i
$83$	−6.69945	−	0.479154i	−0.735360	−	0.0525940i	−0.301365	−	0.953509i	$-0.597442\pi$
$83$	−6.69945	−	0.479154i	−0.735360	−	0.0525940i	−0.433996	+	0.900915i	$0.642897\pi$
$84$	23.1901	+	6.46464i	2.53025	+	0.705350i
$85$	−11.3887	−	1.16844i	−1.23528	−	0.126735i
$86$	1.80915	+	1.33502i	0.195085	+	0.143959i
$87$	−3.98215	+	0.284809i	−0.426931	+	0.0305347i
$88$	0.0685092	+	3.32503i	0.00730310	+	0.354449i
$89$	−15.3759	−	7.02192i	−1.62984	−	0.744322i	−0.630349	−	0.776312i	$-0.717088\pi$
$89$	−15.3759	−	7.02192i	−1.62984	−	0.744322i	−0.999488	+	0.0319898i	$0.989816\pi$
$90$	17.9241	−	14.7942i	1.88937	−	1.55945i
$91$			18.8571i			1.97676i
$92$	6.45101	+	7.09820i	0.672564	+	0.740039i
$93$	18.8286	+	18.8286i	1.95243	+	1.95243i
$94$	−3.11967	−	0.656240i	−0.321770	−	0.0676860i
$95$	−0.435150	−	0.142486i	−0.0446455	−	0.0146188i
$96$	−1.92063	−	18.0968i	−0.196023	−	1.84699i
$97$	−0.148679	−	2.07880i	−0.0150961	−	0.211071i	−0.999401	−	0.0345965i	$-0.988985\pi$
$97$	−0.148679	−	2.07880i	−0.0150961	−	0.211071i	0.984305	−	0.176474i	$-0.0564692\pi$
$98$	−9.78892	+	1.47611i	−0.988830	+	0.149110i
$99$	−7.26983	+	4.67204i	−0.730645	+	0.469557i
$100$	9.98851	+	0.479257i	0.998851	+	0.0479257i
$101$	−4.55442	−	5.25608i	−0.453182	−	0.522999i	0.482476	−	0.875909i	$-0.339738\pi$
$101$	−4.55442	−	5.25608i	−0.453182	−	0.522999i	−0.935657	+	0.352910i	$0.885192\pi$
$102$	−23.0787	−	3.15662i	−2.28513	−	0.312552i
$103$	−1.74285	−	2.32817i	−0.171728	−	0.229402i	0.706418	−	0.707795i	$-0.250310\pi$
$103$	−1.74285	−	2.32817i	−0.171728	−	0.229402i	−0.878145	+	0.478394i	$0.841219\pi$
$104$	13.2504	−	5.25554i	1.29931	−	0.515348i
$105$	−11.9309	+	24.1271i	−1.16433	+	2.35457i
$106$	−1.88426	+	0.717572i	−0.183016	+	0.0696967i
$107$	5.90105	−	15.8213i	0.570476	−	1.52950i	−0.256083	−	0.966655i	$-0.582432\pi$
$107$	5.90105	−	15.8213i	0.570476	−	1.52950i	0.826559	−	0.562850i	$-0.190295\pi$
$108$	22.1706	−	17.0768i	2.13336	−	1.64321i
$109$	3.27840	−	11.1652i	0.314014	−	1.06943i	−0.639676	−	0.768644i	$-0.720932\pi$
$109$	3.27840	−	11.1652i	0.314014	−	1.06943i	0.953691	−	0.300789i	$-0.0972501\pi$
$110$	−3.66670	−	0.617234i	−0.349606	−	0.0588510i
$111$	−1.07917	−	3.67531i	−0.102430	−	0.348845i
$112$	7.53083	+	12.9340i	0.711596	+	1.22215i
$113$	−0.0473164	+	0.0632073i	−0.00445115	+	0.00594604i	−0.802761	−	0.596301i	$-0.796637\pi$
$113$	−0.0473164	+	0.0632073i	−0.00445115	+	0.00594604i	0.798310	+	0.602247i	$0.205728\pi$
$114$	−0.875107	−	0.319570i	−0.0819613	−	0.0299305i
$115$	−9.14065	+	5.60790i	−0.852370	+	0.522939i
$116$	−1.89789	−	1.59943i	−0.176215	−	0.148504i
$117$	29.6516	+	22.1969i	2.74129	+	2.05211i
$118$	5.69385	−	0.0391005i	0.524161	−	0.00359950i
$119$	18.3810	−	5.39716i	1.68499	−	0.494757i
$120$	20.2787	+	1.65919i	1.85118	+	0.151463i
$121$	−9.22786	−	2.70954i	−0.838896	−	0.246322i
$122$	−3.80408	−	2.40798i	−0.344405	−	0.218009i
$123$	0.738162	+	0.275320i	0.0665579	+	0.0248248i
$124$	0.227348	+	16.5525i	0.0204164	+	1.48646i
$125$	−2.60671	+	10.8722i	−0.233151	+	0.972441i
$126$	−18.4030	+	34.2599i	−1.63947	+	3.05211i
$127$	9.70954	−	7.26847i	0.861582	−	0.644972i	−0.0743193	−	0.997234i	$-0.523678\pi$
$127$	9.70954	−	7.26847i	0.861582	−	0.644972i	0.935901	+	0.352262i	$0.114587\pi$
$128$	6.98949	−	8.89646i	0.617790	−	0.786343i
$129$	−3.86541	+	3.34939i	−0.340330	+	0.294898i
$130$	3.01343	+	15.6496i	0.264295	+	1.37256i
$131$	−7.02002	−	10.9234i	−0.613342	−	0.954379i	−0.999490	−	0.0319423i	$-0.989831\pi$
$131$	−7.02002	−	10.9234i	−0.613342	−	0.954379i	0.386147	−	0.922437i	$-0.373806\pi$
$132$	−7.41389	−	1.50646i	−0.645296	−	0.131121i
$133$	0.764237	−	0.0546593i	0.0662677	−	0.00473956i
$134$	0.895622	−	13.8593i	0.0773700	−	1.19726i
$135$	14.1409	+	27.9101i	1.21705	+	2.40212i
$136$	−8.91530	−	11.4117i	−0.764481	−	0.978542i
$137$	10.5169	−	10.5169i	0.898523	−	0.898523i	−0.0967825	−	0.995306i	$-0.530855\pi$
$137$	10.5169	−	10.5169i	0.898523	−	0.898523i	0.995306	+	0.0967825i	$0.0308551\pi$
$138$	−18.9718	+	10.7771i	−1.61499	+	0.917407i
$139$	−10.5936			−0.898541			−0.449270	−	0.893396i	$-0.648316\pi$
$139$	−10.5936			−0.898541			−0.449270	+	0.893396i	$0.648316\pi$
$140$	−15.7759	+	5.57865i	−1.33331	+	0.471482i
$141$	3.01257	−	6.59660i	0.253704	−	0.555534i
$142$	0.445035	−	0.391007i	0.0373465	−	0.0328126i
$143$	−0.422748	−	5.91078i	−0.0353519	−	0.494285i
$144$	29.2025	+	3.38298i	2.43354	+	0.281915i
$145$	2.15219	−	1.75166i	0.178729	−	0.145468i
$146$	15.0881	−	1.18332i	1.24870	−	0.0979320i
$147$	1.60653	−	22.4622i	0.132504	−	1.85265i
$148$	1.11245	−	2.10554i	0.0914426	−	0.173074i
$149$	10.4779	+	1.50650i	0.858386	+	0.123417i	0.557433	−	0.830222i	$-0.311786\pi$
$149$	10.4779	+	1.50650i	0.858386	+	0.123417i	0.300953	+	0.953639i	$0.402695\pi$
$150$	−6.04592	+	21.9299i	−0.493647	+	1.79057i
$151$	−5.66414	+	8.81357i	−0.460941	+	0.717238i	−0.991457	−	0.130437i	$-0.958362\pi$
$151$	−5.66414	+	8.81357i	−0.460941	+	0.717238i	0.530516	+	0.847675i	$0.321998\pi$
$152$	−0.251403	−	0.521775i	−0.0203915	−	0.0423216i
$153$	13.1498	−	35.2561i	1.06310	−	2.85028i
$154$	6.07048	−	1.36428i	0.489173	−	0.109937i
$155$	−18.2297	−	3.19758i	−1.46424	−	0.256836i
$156$	5.05512	+	32.0299i	0.404734	+	2.56445i
$157$	−9.54996	+	17.4894i	−0.762170	+	1.39581i	0.151127	+	0.988514i	$0.451710\pi$
$157$	−9.54996	+	17.4894i	−0.762170	+	1.39581i	−0.913296	+	0.407296i	$0.866472\pi$
$158$	−13.0772	+	0.0898032i	−1.04037	+	0.00714436i
$159$	−0.652745	−	4.53994i	−0.0517660	−	0.360041i
$160$	8.31678	+	9.53054i	0.657499	+	0.753455i
$161$	10.6104	−	14.4714i	0.836218	−	1.14050i
$162$	13.6948	+	29.4504i	1.07596	+	2.31384i
$163$	−8.01961	−	6.00341i	−0.628145	−	0.470223i	0.237159	−	0.971471i	$-0.423784\pi$
$163$	−8.01961	−	6.00341i	−0.628145	−	0.470223i	−0.865304	+	0.501248i	$0.832875\pi$
$164$	0.209564	+	0.442689i	0.0163642	+	0.0345682i
$165$	3.19885	−	7.83015i	0.249030	−	0.609576i
$166$	8.30532	−	4.60936i	0.644618	−	0.357756i
$167$	7.96473	+	14.5863i	0.616329	+	1.12872i	0.980338	+	0.197327i	$0.0632260\pi$
$167$	7.96473	+	14.5863i	0.616329	+	1.12872i	−0.364009	+	0.931396i	$0.618592\pi$
$168$	−32.4626	+	10.2628i	−2.50454	+	0.791794i
$169$	−11.2787	+	5.15082i	−0.867595	+	0.396217i
$170$	14.3921	−	7.41649i	1.10382	−	0.568819i
$171$	0.813643	−	1.26605i	0.0622209	−	0.0968176i
$172$	−3.17443	−	0.183259i	−0.242048	−	0.0139734i
$173$	−13.9485	+	10.4417i	−1.06049	+	0.793869i	−0.979215	−	0.202823i	$-0.934988\pi$
$173$	−13.9485	+	10.4417i	−1.06049	+	0.793869i	−0.0812696	+	0.996692i	$0.525897\pi$
$174$	4.49651	−	3.41448i	0.340880	−	0.258851i
$175$	−2.84237	−	18.4911i	−0.214863	−	1.39780i
$176$	−2.65051	−	3.88534i	−0.199789	−	0.292868i
$177$	−2.75329	+	12.6567i	−0.206950	+	0.951333i
$178$	23.6378	−	3.56444i	1.77172	−	0.267166i
$179$	4.53494	−	5.23361i	0.338958	−	0.391178i	−0.560523	−	0.828139i	$-0.689400\pi$
$179$	4.53494	−	5.23361i	0.338958	−	0.391178i	0.899480	+	0.436961i	$0.143945\pi$
$180$	−9.79795	+	31.3733i	−0.730296	+	2.33843i
$181$	6.63451	−	14.5276i	0.493139	−	1.07982i	−0.485499	−	0.874237i	$-0.661362\pi$
$181$	6.63451	−	14.5276i	0.493139	−	1.07982i	0.978639	−	0.205587i	$-0.0659105\pi$
$182$	−14.5715	−	22.3350i	−1.08011	−	1.65558i
$183$	7.24184	−	7.24184i	0.535333	−	0.535333i
$184$	−13.1258	−	3.42244i	−0.967648	−	0.252306i
$185$	2.08117	+	1.66050i	0.153011	+	0.122082i
$186$	−36.8507	−	7.75173i	−2.70202	−	0.568385i
$187$	−5.64056	+	2.10382i	−0.412479	+	0.153847i
$188$	4.20214	−	1.63340i	0.306473	−	0.119128i
$189$	−39.5672	−	34.2852i	−2.87809	−	2.49388i
$190$	0.625511	−	0.167490i	0.0453793	−	0.0121510i
$191$	−7.59258	−	11.8143i	−0.549380	−	0.854852i	0.449889	−	0.893085i	$-0.351464\pi$
$191$	−7.59258	−	11.8143i	−0.549380	−	0.854852i	−0.999269	+	0.0382325i	$0.987827\pi$
$192$	16.2588	+	19.9503i	1.17338	+	1.43979i
$193$	0.936368	−	13.0921i	0.0674012	−	0.942392i	−0.845438	−	0.534073i	$-0.820661\pi$
$193$	0.936368	−	13.0921i	0.0674012	−	0.942392i	0.912839	−	0.408319i	$-0.133885\pi$
$194$	1.78246	+	2.34732i	0.127973	+	0.168527i
$195$	−36.2366	−	1.11786i	−2.59496	−	0.0800514i
$196$	10.4537	−	9.31258i	0.746692	−	0.665185i
$197$	−24.5952	+	5.35035i	−1.75233	+	0.381197i	−0.970274	−	0.242008i	$-0.922194\pi$
$197$	−24.5952	+	5.35035i	−1.75233	+	0.381197i	−0.782059	+	0.623204i	$0.785830\pi$
$198$	5.00039	−	11.1514i	0.355363	−	0.792492i
$199$	−6.49087	−	14.2130i	−0.460126	−	1.00754i	−0.987459	−	0.157876i	$-0.949535\pi$
$199$	−6.49087	−	14.2130i	−0.460126	−	1.00754i	0.527333	−	0.849659i	$-0.323192\pi$
$200$	−12.2011	+	7.15081i	−0.862746	+	0.505638i
$201$	30.3132	+	8.90075i	2.13813	+	0.627810i
$202$	9.45595	+	2.70613i	0.665319	+	0.190402i
$203$	−2.22532	+	4.07538i	−0.156187	+	0.286035i
$204$	29.7745	−	14.0949i	2.08463	−	0.986840i
$205$	−0.529924	+	0.138002i	−0.0370115	+	0.00963849i
$206$	3.86334	+	1.41081i	0.269172	+	0.0982957i
$207$	−10.2657	−	33.7186i	−0.713514	−	2.34361i
$208$	−11.6331	+	16.4639i	−0.806609	+	1.14156i
$209$	−0.238325	+	0.0342660i	−0.0164853	+	0.00237023i
$210$	−4.51251	−	37.7964i	−0.311393	−	2.60820i
$211$	−1.37114	−	4.66969i	−0.0943935	−	0.321475i	0.898737	−	0.438488i	$-0.144486\pi$
$211$	−1.37114	−	4.66969i	−0.0943935	−	0.321475i	−0.993130	+	0.117014i	$0.962668\pi$
$212$	1.67729	−	2.30595i	0.115197	−	0.158373i
$213$	0.645837	+	1.18276i	0.0442520	+	0.0810415i
$214$	5.23626	+	23.2992i	0.357943	+	1.59270i
$215$	0.862429	−	3.44884i	0.0588172	−	0.235209i
$216$	−13.0638	+	37.3582i	−0.888877	+	2.54190i
$217$	30.2621	−	6.58311i	2.05432	−	0.446891i
$218$	4.74468	+	15.7578i	0.321350	+	1.06725i
$219$	−4.89960	+	34.0774i	−0.331084	+	2.30274i
$220$	4.81992	−	2.10231i	0.324959	−	0.141737i
$221$	16.8975	+	19.5008i	1.13665	+	1.31176i
$222$	4.11823	+	3.51925i	0.276398	+	0.236196i
$223$	−1.50173	+	6.90336i	−0.100563	+	0.462283i	0.899134	+	0.437674i	$0.144198\pi$
$223$	−1.50173	+	6.90336i	−0.100563	+	0.462283i	−0.999697	+	0.0246088i	$0.992166\pi$
$224$	−18.9143	−	9.50011i	−1.26376	−	0.634753i
$225$	−32.4219	−	17.2967i	−2.16146	−	1.15311i
$226$	0.00720074	−	0.111428i	0.000478986	−	0.00741206i
$227$	4.70010	−	1.75305i	0.311957	−	0.116354i	−0.188609	−	0.982052i	$-0.560398\pi$
$227$	4.70010	−	1.75305i	0.311957	−	0.116354i	0.500566	+	0.865698i	$0.333125\pi$
$228$	1.28345	−	0.297715i	0.0849985	−	0.0197167i
$229$			6.37658i			0.421376i	0.977553	+	0.210688i	$0.0675704\pi$
$229$			6.37658i			0.421376i	−0.977553	+	0.210688i	$0.932430\pi$
$230$	6.49308	−	13.7055i	0.428141	−	0.903712i
$231$			14.1536i			0.931237i
$232$	3.48386	+	0.427855i	0.228727	+	0.0280900i
$233$	−13.2313	+	4.93504i	−0.866814	+	0.323305i	−0.743236	−	0.669030i	$-0.766710\pi$
$233$	−13.2313	+	4.93504i	−0.866814	+	0.323305i	−0.123579	+	0.992335i	$0.539437\pi$
$234$	−52.2727	−	3.37799i	−3.41717	−	0.220826i
$235$	0.919074	+	4.95609i	0.0599538	+	0.323300i
$236$	−6.71377	+	4.44614i	−0.437029	+	0.289419i
$237$	6.32355	−	29.0689i	0.410759	−	1.88823i
$238$	−17.6006	+	20.5962i	−1.14087	+	1.33505i
$239$	19.9690	+	23.0454i	1.29168	+	1.49068i	0.770835	+	0.637035i	$0.219839\pi$
$239$	19.9690	+	23.0454i	1.29168	+	1.49068i	0.520849	+	0.853649i	$0.325615\pi$
$240$	−25.3009	+	13.7048i	−1.63316	+	0.884641i
$241$	2.37695	−	16.5321i	0.153113	−	1.06492i	−0.757848	−	0.652431i	$-0.773749\pi$
$241$	2.37695	−	16.5321i	0.153113	−	1.06492i	0.910961	−	0.412493i	$-0.135342\pi$
$242$	13.0235	−	3.92140i	0.837185	−	0.252077i
$243$	−31.1765	+	6.78204i	−1.99998	+	0.435068i
$244$	6.36641	−	0.0874425i	0.407568	−	0.00559793i
$245$	8.05240	+	13.4225i	0.514449	+	0.857532i
$246$	−1.08705	+	0.244304i	−0.0693080	+	0.0155763i
$247$	0.494586	+	0.905767i	0.0314698	+	0.0576326i
$248$	−13.0599	−	19.4296i	−0.829306	−	1.23378i
$249$	6.08755	+	20.7323i	0.385783	+	1.31386i
$250$	−5.31385	−	14.8917i	−0.336077	−	0.941834i
$251$	−12.0125	+	1.72713i	−0.758220	+	0.109016i	−0.510573	−	0.859835i	$-0.670567\pi$
$251$	−12.0125	+	1.72713i	−0.758220	+	0.109016i	−0.247647	+	0.968850i	$0.579657\pi$
$252$	−4.67657	−	54.7991i	−0.294596	−	3.45202i
$253$	−3.00142	+	4.77394i	−0.188698	+	0.300135i
$254$	−5.88372	+	16.1119i	−0.369177	+	1.01095i
$255$	9.28176	+	35.6417i	0.581246	+	2.23197i
$256$	−1.40400	+	15.9383i	−0.0877502	+	0.996143i
$257$	−9.55888	+	17.5058i	−0.596266	+	1.09198i	0.389046	+	0.921218i	$0.372805\pi$
$257$	−9.55888	+	17.5058i	−0.596266	+	1.09198i	−0.985312	+	0.170762i	$0.945377\pi$
$258$	1.99013	−	6.95406i	0.123900	−	0.432941i
$259$	−4.27464	−	1.25515i	−0.265613	−	0.0779911i
$260$	−15.6622	−	16.2074i	−0.971329	−	1.00514i
$261$	3.78882	+	8.29635i	0.234522	+	0.513531i
$262$	16.7556	+	7.51340i	1.03516	+	0.464180i
$263$	15.2101	−	3.30876i	0.937896	−	0.204027i	0.282461	−	0.959279i	$-0.408849\pi$
$263$	15.2101	−	3.30876i	0.937896	−	0.204027i	0.655435	+	0.755252i	$0.272486\pi$
$264$	9.94535	−	3.94465i	0.612094	−	0.242777i
$265$	2.18368	+	2.32270i	0.134143	+	0.142682i
$266$	−0.862951	+	0.655292i	−0.0529109	+	0.0401785i
$267$	−3.87936	+	54.2406i	−0.237413	+	3.31947i
$268$	9.64873	+	17.1075i	0.589390	+	1.04501i
$269$	5.92991	+	9.22712i	0.361553	+	0.562588i	0.973608	−	0.228228i	$-0.0732931\pi$
$269$	5.92991	+	9.22712i	0.361553	+	0.562588i	−0.612055	+	0.790815i	$0.709657\pi$
$270$	−38.3160	−	22.1305i	−2.33184	−	1.34682i
$271$	−17.5170	−	15.1785i	−1.06408	−	0.922031i	−0.0669516	−	0.997756i	$-0.521327\pi$
$271$	−17.5170	−	15.1785i	−1.06408	−	0.922031i	−0.997129	+	0.0757254i	$0.975873\pi$
$272$	19.3778	+	6.62721i	1.17495	+	0.401834i
$273$	56.8395	−	21.2000i	3.44008	−	1.28308i
$274$	−4.32983	+	20.5834i	−0.261575	+	1.24349i
$275$	1.30549	+	5.73235i	0.0787238	+	0.345674i
$276$	14.1430	−	27.4249i	0.851309	−	1.65078i
$277$	8.23385	−	8.23385i	0.494724	−	0.494724i	−0.415067	−	0.909791i	$-0.636242\pi$
$277$	8.23385	−	8.23385i	0.494724	−	0.494724i	0.909791	+	0.415067i	$0.136242\pi$
$278$	12.5475	−	8.18606i	0.752547	−	0.490967i
$279$	25.2703	−	55.3343i	1.51289	−	3.31278i
$280$	14.3747	−	18.7981i	0.859055	−	1.12340i
$281$	7.28203	−	8.40391i	0.434409	−	0.501335i	−0.495763	−	0.868458i	$-0.665112\pi$
$281$	7.28203	−	8.40391i	0.434409	−	0.501335i	0.930173	+	0.367123i	$0.119657\pi$
$282$	1.52923	+	10.1412i	0.0910642	+	0.603897i
$283$	−0.585099	+	2.68966i	−0.0347805	+	0.159884i	−0.991262	−	0.131911i	$-0.957889\pi$
$283$	−0.585099	+	2.68966i	−0.0347805	+	0.159884i	0.956481	+	0.291795i	$0.0942523\pi$
$284$	−0.224970	+	0.807016i	−0.0133495	+	0.0478876i
$285$	0.0597312	+	1.47183i	0.00353817	+	0.0871836i
$286$	5.06818	+	6.67426i	0.299688	+	0.394657i
$287$	0.733544	−	0.549124i	0.0432997	−	0.0324138i
$288$	−37.2025	+	18.5588i	−2.19218	+	1.09359i
$289$	4.98124	−	7.75096i	0.293014	−	0.455939i
$290$	−1.19555	+	3.73780i	−0.0702053	+	0.219491i
$291$	−6.09882	+	2.78524i	−0.357519	+	0.163273i
$292$	−16.9565	+	13.0606i	−0.992303	+	0.764317i
$293$	−6.65766	−	12.1926i	−0.388945	−	0.712299i	0.607698	−	0.794168i	$-0.292093\pi$
$293$	−6.65766	−	12.1926i	−0.388945	−	0.712299i	−0.996643	+	0.0818690i	$0.973911\pi$
$294$	15.4545	+	27.8464i	0.901324	+	1.62404i
$295$	−3.48568	−	8.30082i	−0.202944	−	0.483292i
$296$	0.309398	+	3.35349i	0.0179834	+	0.194918i
$297$	13.1710	+	9.85969i	0.764259	+	0.572117i
$298$	−13.5746	+	6.31230i	−0.786353	+	0.365662i
$299$	23.6674	+	4.90276i	1.36872	+	0.283534i
$300$	−9.78495	−	30.6464i	−0.564934	−	1.76937i
$301$	0.846592	+	5.88818i	0.0487967	+	0.339389i
$302$	−0.101744	−	14.8160i	−0.00585469	−	0.852563i
$303$	−10.7227	+	19.6371i	−0.616002	+	1.12812i
$304$	0.700963	+	0.423741i	0.0402030	+	0.0243032i
$305$	−1.22985	+	7.01149i	−0.0704211	+	0.401477i
$306$	11.6684	+	51.9198i	0.667040	+	2.96806i
$307$	2.43460	−	6.52741i	0.138950	−	0.372539i	−0.848773	−	0.528758i	$-0.822658\pi$
$307$	2.43460	−	6.52741i	0.138950	−	0.372539i	0.987722	+	0.156219i	$0.0499306\pi$
$308$	−6.13586	+	6.30676i	−0.349623	+	0.359361i
$309$	−5.05823	+	7.87076i	−0.287753	+	0.447752i
$310$	24.0627	−	10.2994i	1.36667	−	0.584964i
$311$	17.0470	+	2.45098i	0.966644	+	0.138982i	0.607517	−	0.794306i	$-0.292166\pi$
$311$	17.0470	+	2.45098i	0.966644	+	0.138982i	0.359127	+	0.933289i	$0.383075\pi$
$312$	−30.7381	−	34.0311i	−1.74020	−	1.92663i
$313$	−0.218761	+	3.05867i	−0.0123651	+	0.172886i	0.987517	+	0.157514i	$0.0503479\pi$
$313$	−0.218761	+	3.05867i	−0.0123651	+	0.172886i	−0.999882	+	0.0153725i	$0.995107\pi$
$314$	−2.20338	−	28.0947i	−0.124344	−	1.58547i
$315$	61.1689	+	6.27573i	3.44648	+	0.353597i
$316$	15.4197	−	10.2116i	0.867425	−	0.574445i
$317$	2.51441	+	35.1561i	0.141223	+	1.97456i	0.212692	+	0.977119i	$0.431777\pi$
$317$	2.51441	+	35.1561i	0.141223	+	1.97456i	−0.0714689	+	0.997443i	$0.522769\pi$
$318$	4.28129	+	4.87286i	0.240083	+	0.273256i
$319$	0.606166	−	1.32732i	0.0339388	−	0.0743156i
$320$	−17.2152	−	4.86164i	−0.962361	−	0.271774i
$321$	−54.3232			−3.03202
$322$	−1.38483	+	25.3394i	−0.0771733	+	1.41211i
$323$	0.741343	−	0.741343i	0.0412494	−	0.0412494i
$324$	−38.9779	−	24.2997i	−2.16544	−	1.34998i
$325$	21.0652	−	13.8289i	1.16848	−	0.767092i
$326$	14.1377	+	0.913616i	0.783017	+	0.0506005i
$327$	−37.3401	+	2.67062i	−2.06491	+	0.147686i
$328$	−0.590296	−	0.362399i	−0.0325936	−	0.0200101i
$329$	−4.56005	−	7.09558i	−0.251404	−	0.391192i
$330$	2.26179	+	11.7462i	0.124507	+	0.646605i
$331$	−2.60446	+	2.25677i	−0.143154	+	0.124044i	−0.723494	−	0.690331i	$-0.757465\pi$
$331$	−2.60446	+	2.25677i	−0.143154	+	0.124044i	0.580340	+	0.814374i	$0.302920\pi$
$332$	−6.27529	+	11.8773i	−0.344401	+	0.651850i
$333$	−7.00537	+	5.24416i	−0.383892	+	0.287378i
$334$	−20.7050	−	11.1219i	−1.13293	−	0.608564i
$335$	−20.8015	+	7.03589i	−1.13651	+	0.384412i
$336$	30.5193	−	37.2405i	1.66497	−	2.03164i
$337$	19.0102	+	7.09042i	1.03555	+	0.386240i	0.809030	−	0.587767i	$-0.199993\pi$
$337$	19.0102	+	7.09042i	1.03555	+	0.386240i	0.226519	+	0.974007i	$0.427265\pi$
$338$	9.37870	−	14.8163i	0.510134	−	0.805898i
$339$	0.243716	+	0.0715614i	0.0132368	+	0.00388668i
$340$	−11.3155	+	19.9056i	−0.613668	+	1.07953i
$341$	−9.33810	+	2.74191i	−0.505687	+	0.148483i
$342$	0.0146153	+	2.12829i	0.000790304	+	0.115085i
$343$	−0.000199792	0	0.000149562i	−1.07877e−5	0	8.07560e-6i
$344$	3.90152	−	2.23593i	0.210356	−	0.120553i
$345$	27.1798	+	21.2473i	1.46331	+	1.14391i
$346$	8.45241	−	23.1460i	0.454405	−	1.24434i
$347$	14.6480	−	19.5675i	0.786348	−	1.05044i	−0.210988	−	0.977489i	$-0.567668\pi$
$347$	14.6480	−	19.5675i	0.786348	−	1.05044i	0.997336	−	0.0729488i	$-0.0232410\pi$
$348$	−2.68734	+	7.51882i	−0.144056	+	0.403051i
$349$	2.76589	+	9.41974i	0.148054	+	0.504227i	0.999806	−	0.0197195i	$-0.00627731\pi$
$349$	2.76589	+	9.41974i	0.148054	+	0.504227i	−0.851751	+	0.523947i	$0.824459\pi$
$350$	17.6553	+	19.7051i	0.943717	+	1.05328i
$351$	19.8673	−	67.6619i	1.06044	−	3.61153i
$352$	6.14168	+	2.55379i	0.327353	+	0.136118i
$353$	−7.26420	+	19.4761i	−0.386634	+	1.03661i	0.587219	+	0.809428i	$0.300223\pi$
$353$	−7.26420	+	19.4761i	−0.386634	+	1.03661i	−0.973853	+	0.227178i	$0.927050\pi$
$354$	−6.51914	−	17.1185i	−0.346488	−	0.909840i
$355$	−0.839625	−	0.415195i	−0.0445627	−	0.0220362i
$356$	−25.2430	+	22.4875i	−1.33788	+	1.19184i
$357$	−36.9330	−	49.3367i	−1.95470	−	2.61118i
$358$	−1.32716	+	9.70316i	−0.0701426	+	0.512828i
$359$	2.01641	+	2.32706i	0.106422	+	0.122818i	0.806462	−	0.591286i	$-0.201380\pi$
$359$	2.01641	+	2.32706i	0.106422	+	0.122818i	−0.700039	+	0.714104i	$0.746834\pi$
$360$	−12.6382	−	44.7309i	−0.666092	−	2.35752i
$361$	−15.9485	+	10.2495i	−0.839397	+	0.539448i
$362$	3.36778	+	22.3336i	0.177007	+	1.17383i
$363$	2.20722	+	30.8610i	0.115849	+	1.61978i
$364$	34.5180	+	15.1944i	1.80923	+	0.796405i
$365$	−10.8152	−	21.3462i	−0.566094	−	1.11731i
$366$	−2.98147	+	14.1735i	−0.155844	+	0.740861i
$367$	9.14742	+	9.14742i	0.477491	+	0.477491i	0.904328	−	0.426837i	$-0.140372\pi$
$367$	9.14742	+	9.14742i	0.477491	+	0.477491i	−0.426837	+	0.904328i	$0.640372\pi$
$368$	18.1913	−	6.08910i	0.948286	−	0.317416i
$369$		−	1.79983i		−	0.0936954i
$370$	−3.74813	−	0.358554i	−0.194856	−	0.0186403i
$371$	−4.85250	−	2.21606i	−0.251929	−	0.115052i
$372$	49.6372	−	19.2943i	2.57357	−	1.00036i
$373$	3.63185	−	0.259755i	0.188050	−	0.0134496i	0.0230035	−	0.999735i	$-0.492677\pi$
$373$	3.63185	−	0.259755i	0.188050	−	0.0134496i	0.165047	+	0.986286i	$0.447223\pi$
$374$	5.05518	−	6.85049i	0.261397	−	0.354230i
$375$	35.7018	−	4.36585i	1.84363	−	0.225451i
$376$	−3.71498	+	5.18179i	−0.191585	+	0.267231i
$377$	−6.23834	−	0.446175i	−0.321291	−	0.0229792i
$378$	73.3580	+	10.0336i	3.77313	+	0.516074i
$379$	−2.30002	+	15.9970i	−0.118144	+	0.821712i	0.841452	+	0.540332i	$0.181701\pi$
$379$	−2.30002	+	15.9970i	−0.118144	+	0.821712i	−0.959596	+	0.281380i	$0.909208\pi$
$380$	−0.611451	+	0.681733i	−0.0313668	+	0.0349722i
$381$	−32.8247	−	21.0951i	−1.68166	−	1.08074i
$382$	18.1222	+	8.12620i	0.927213	+	0.415773i
$383$	17.9278	+	6.68674i	0.916070	+	0.341676i	0.762895	−	0.646523i	$-0.223777\pi$
$383$	17.9278	+	6.68674i	0.916070	+	0.341676i	0.153175	+	0.988199i	$0.451050\pi$
$384$	−34.6738	−	11.0661i	−1.76944	−	0.564713i
$385$	−5.64987	−	8.05351i	−0.287944	−	0.410445i
$386$	9.00766	+	16.2303i	0.458478	+	0.826102i
$387$	10.2553	+	5.59983i	0.521307	+	0.284655i
$388$	−3.92506	−	1.40287i	−0.199265	−	0.0712201i
$389$	25.9973	−	3.73785i	1.31811	−	0.189516i	0.552876	−	0.833263i	$-0.313530\pi$
$389$	25.9973	−	3.73785i	1.31811	−	0.189516i	0.765238	+	0.643747i	$0.222621\pi$
$390$	43.7836	−	26.6772i	2.21707	−	1.35085i
$391$	−1.99494	−	24.4731i	−0.100889	−	1.23766i
$392$	−5.18555	+	19.1080i	−0.261910	+	0.965102i
$393$	−25.0332	+	33.4404i	−1.26276	+	1.68685i
$394$	24.9970	−	25.3426i	1.25933	−	1.27674i
$395$	8.00565	+	19.0647i	0.402808	+	0.959249i
$396$	2.69439	+	17.0720i	0.135398	+	0.857901i
$397$	−15.7713	+	8.61178i	−0.791538	+	0.432213i	−0.823528	−	0.567276i	$-0.807997\pi$
$397$	−15.7713	+	8.61178i	−0.791538	+	0.432213i	0.0319897	+	0.999488i	$0.489816\pi$
$398$	18.6709	+	11.8187i	0.935887	+	0.592417i
$399$	−1.02394	−	2.24213i	−0.0512614	−	0.112247i
$400$	8.92569	−	17.8978i	0.446284	−	0.894891i
$401$	12.4287	+	7.98744i	0.620660	+	0.398874i	0.812841	−	0.582486i	$-0.197920\pi$
$401$	12.4287	+	7.98744i	0.620660	+	0.398874i	−0.192181	+	0.981359i	$0.561556\pi$
$402$	−42.7818	+	12.8816i	−2.13376	+	0.642478i
$403$	24.9984	+	33.3940i	1.24526	+	1.66347i
$404$	−13.2911	+	4.10170i	−0.661255	+	0.204067i
$405$	34.8101	−	37.7550i	1.72973	−	1.87606i
$406$	−0.513430	−	6.54659i	−0.0254811	−	0.324902i
$407$	1.36803	+	0.297597i	0.0678108	+	0.0147513i
$408$	−24.3743	+	39.7022i	−1.20671	+	1.96555i
$409$	−20.2508	−	17.5474i	−1.00134	−	0.867662i	−0.0101240	−	0.999949i	$-0.503223\pi$
$409$	−20.2508	−	17.5474i	−1.00134	−	0.867662i	−0.991212	+	0.132287i	$0.957768\pi$
$410$	0.521021	−	0.572944i	0.0257314	−	0.0282957i
$411$	−43.5240	−	19.8767i	−2.14688	−	0.980447i
$412$	−5.66605	+	1.31432i	−0.279146	+	0.0647521i
$413$	10.6525	+	10.6525i	0.524175	+	0.524175i
$414$	38.2145	+	32.0048i	1.87814	+	1.57295i
$415$	−11.7399	−	9.36681i	−0.576287	−	0.459799i
$416$	1.05644	−	28.4896i	0.0517962	−	1.39682i
$417$	11.9099	+	31.9316i	0.583228	+	1.56369i
$418$	0.255802	−	0.224748i	0.0125117	−	0.0109928i
$419$	19.7974	−	22.8474i	0.967167	−	1.11617i	−0.0260229	−	0.999661i	$-0.508284\pi$
$419$	19.7974	−	22.8474i	0.967167	−	1.11617i	0.993190	−	0.116509i	$-0.0371702\pi$
$420$	34.5513	+	41.2803i	1.68593	+	2.01427i
$421$	−11.7320	+	7.53968i	−0.571781	+	0.367461i	−0.794354	−	0.607455i	$-0.792191\pi$
$421$	−11.7320	+	7.53968i	−0.571781	+	0.367461i	0.222573	+	0.974916i	$0.428554\pi$
$422$	5.23245	+	4.47141i	0.254712	+	0.217665i
$423$	−16.5250	−	1.18189i	−0.803475	−	0.0574657i
$424$	−0.204760	+	4.02735i	−0.00994403	+	0.195585i
$425$	−19.5089	−	16.5753i	−0.946323	−	0.804020i
$426$	−1.67891	−	0.901843i	−0.0813435	−	0.0436945i
$427$	−2.53200	−	11.6394i	−0.122532	−	0.563270i
$428$	−24.2061	−	23.5502i	−1.17005	−	1.13834i
$429$	−17.3411	+	7.91943i	−0.837237	+	0.382354i
$430$	1.64354	+	4.75135i	0.0792586	+	0.229130i
$431$	−0.220056	+	0.749441i	−0.0105997	+	0.0360993i	−0.964623	−	0.263633i	$-0.915079\pi$
$431$	−0.220056	+	0.749441i	−0.0105997	+	0.0360993i	0.954023	+	0.299732i	$0.0968974\pi$
$432$	−13.3948	−	54.3431i	−0.644456	−	2.61459i
$433$	−4.14434	−	2.26298i	−0.199164	−	0.108752i	0.376572	−	0.926387i	$-0.377103\pi$
$433$	−4.14434	−	2.26298i	−0.199164	−	0.108752i	−0.575736	+	0.817635i	$0.695284\pi$
$434$	−30.7564	+	31.1818i	−1.47636	+	1.49677i
$435$	−7.69949	−	4.51786i	−0.369162	−	0.216615i
$436$	−17.7963	−	14.9977i	−0.852290	−	0.718259i
$437$	0.130096	−	0.973397i	0.00622331	−	0.0465639i
$438$	−20.5295	−	44.1485i	−0.980939	−	2.10950i
$439$	−2.86070	−	19.8966i	−0.136534	−	0.949612i	−0.936775	−	0.349933i	$-0.886204\pi$
$439$	−2.86070	−	19.8966i	−0.136534	−	0.949612i	0.800241	−	0.599679i	$-0.204705\pi$
$440$	−4.08435	+	6.21455i	−0.194714	+	0.296267i
$441$	−49.3627	+	14.4942i	−2.35060	+	0.690199i
$442$	−35.0828	−	10.0401i	−1.66872	−	0.477558i
$443$	8.51734	−	4.65082i	0.404671	−	0.220967i	−0.264005	−	0.964521i	$-0.585043\pi$
$443$	8.51734	−	4.65082i	0.404671	−	0.220967i	0.668675	+	0.743554i	$0.266862\pi$
$444$	−7.59721	−	0.986020i	−0.360548	−	0.0467944i
$445$	−19.4445	−	32.4119i	−0.921758	−	1.53647i
$446$	−3.55575	−	9.33701i	−0.168370	−	0.442120i
$447$	−7.23886	−	33.2765i	−0.342386	−	1.57392i
$448$	29.7438	−	3.36344i	1.40526	−	0.158908i
$449$	24.3029	+	3.49424i	1.14693	+	0.164903i	0.689460	−	0.724324i	$-0.257848\pi$
$449$	24.3029	+	3.49424i	1.14693	+	0.164903i	0.457467	+	0.889227i	$0.348757\pi$
$450$	51.7674	−	4.56673i	2.44034	−	0.215278i
$451$	−0.217620	+	0.188568i	−0.0102473	+	0.00887934i
$452$	0.0775751	+	0.137543i	0.00364883	+	0.00646948i
$453$	32.9339	+	7.16434i	1.54737	+	0.336610i
$454$	−4.21232	+	5.70829i	−0.197694	+	0.267903i
$455$	−23.8795	+	34.7523i	−1.11949	+	1.62921i
$456$	−1.29011	+	1.34439i	−0.0604148	+	0.0629567i
$457$	−1.84978	−	4.95944i	−0.0865289	−	0.231993i	0.886477	−	0.462772i	$-0.153145\pi$
$457$	−1.84978	−	4.95944i	−0.0865289	−	0.231993i	−0.973006	+	0.230779i	$0.925872\pi$
$458$	−4.92739	−	7.55263i	−0.230242	−	0.352911i
$459$	−71.6400			−3.34387
$460$	2.90004	+	21.2506i	0.135215	+	0.990816i
$461$	19.9394			0.928671			0.464336	−	0.885659i	$-0.346293\pi$
$461$	19.9394			0.928671			0.464336	+	0.885659i	$0.346293\pi$
$462$	−10.9369	−	16.7640i	−0.508833	−	0.779931i
$463$	4.24076	+	11.3699i	0.197085	+	0.528405i	0.997471	−	0.0710806i	$-0.0226448\pi$
$463$	4.24076	+	11.3699i	0.197085	+	0.528405i	−0.800386	+	0.599485i	$0.795372\pi$
$464$	−4.45702	+	2.18533i	−0.206912	+	0.101452i
$465$	10.8564	+	58.5431i	0.503455	+	2.71487i
$466$	11.8582	−	16.0695i	0.549320	−	0.744406i
$467$	−13.2917	−	2.89144i	−0.615068	−	0.133800i	−0.105771	−	0.994391i	$-0.533731\pi$
$467$	−13.2917	−	2.89144i	−0.615068	−	0.133800i	−0.509297	+	0.860591i	$0.670095\pi$
$468$	64.5238	−	36.3918i	2.98261	−	1.68221i
$469$	27.7699	−	24.0627i	1.28229	−	1.11111i
$470$	−4.91832	−	5.15996i	−0.226865	−	0.238011i
$471$	63.4535	+	9.12324i	2.92378	+	0.420377i
$472$	4.51634	−	10.4541i	0.207881	−	0.481189i
$473$	−0.397369	−	1.82668i	−0.0182710	−	0.0839906i
$474$	14.9727	+	39.3166i	0.687718	+	1.80587i
$475$	−0.621516	−	0.813639i	−0.0285171	−	0.0373323i
$476$	4.93131	−	37.9954i	0.226026	−	1.74152i
$477$	−9.19655	+	5.02169i	−0.421081	+	0.229928i
$478$	−41.4599	−	11.8651i	−1.89633	−	0.542696i
$479$	−37.5986	+	11.0400i	−1.71793	+	0.504429i	−0.984507	−	0.175348i	$-0.943895\pi$
$479$	−37.5986	+	11.0400i	−1.71793	+	0.504429i	−0.733419	+	0.679776i	$0.762077\pi$
$480$	19.3770	−	35.7833i	0.884437	−	1.63327i
$481$	−0.853991	−	5.93964i	−0.0389387	−	0.270824i
$482$	9.95954	+	21.4179i	0.453645	+	0.975558i
$483$	−55.5486	−	15.7127i	−2.52755	−	0.714955i
$484$	−12.3953	+	14.7084i	−0.563424	+	0.668562i
$485$	2.35846	−	4.01937i	0.107092	−	0.182510i
$486$	31.6858	−	32.1240i	1.43730	−	1.45718i
$487$	−20.0929	−	10.9715i	−0.910495	−	0.497168i	−0.0455090	−	0.998964i	$-0.514491\pi$
$487$	−20.0929	−	10.9715i	−0.910495	−	0.497168i	−0.864986	+	0.501796i	$0.832673\pi$
$488$	−7.47302	+	5.02311i	−0.338288	+	0.227385i
$489$	−9.07957	+	30.9222i	−0.410592	+	1.39835i
$490$	−19.9096	−	9.67570i	−0.899422	−	0.437103i
$491$	−7.74527	+	3.53715i	−0.349539	+	0.159629i	−0.582445	−	0.812870i	$-0.697904\pi$
$491$	−7.74527	+	3.53715i	−0.349539	+	0.159629i	0.232906	+	0.972499i	$0.425177\pi$
$492$	1.09876	−	1.12936i	0.0495360	−	0.0509157i
$493$	1.35059	+	6.20855i	0.0608274	+	0.279619i
$494$	−1.28572	−	0.690638i	−0.0578473	−	0.0310733i
$495$	−19.3142	−	0.595820i	−0.868107	−	0.0267801i
$496$	30.4825	+	12.9213i	1.36871	+	0.580182i
$497$	1.56336	+	0.111814i	0.0701265	+	0.00501554i
$498$	−23.2308	−	19.8520i	−1.04100	−	0.889589i
$499$	25.8163	−	16.5912i	1.15570	−	0.742722i	0.184933	−	0.982751i	$-0.440793\pi$
$499$	25.8163	−	16.5912i	1.15570	−	0.742722i	0.970766	+	0.240029i	$0.0771569\pi$
$500$	17.8012	+	13.5321i	0.796095	+	0.605172i
$501$	35.0120	−	40.4060i	1.56422	−	1.80521i
$502$	12.8934	−	11.3281i	0.575458	−	0.505598i
$503$	−9.22019	−	24.7203i	−0.411108	−	1.10222i	−0.963281	−	0.268494i	$-0.913474\pi$
$503$	−9.22019	−	24.7203i	−0.411108	−	1.10222i	0.552173	−	0.833729i	$-0.313799\pi$
$504$	47.8842	+	61.2922i	2.13293	+	2.73017i
$505$	−1.73751	−	15.4540i	−0.0773180	−	0.687695i
$506$	−0.133995	−	7.97371i	−0.00595682	−	0.354475i
$507$	28.2058	+	28.2058i	1.25266	+	1.25266i
$508$	−5.48133	−	23.6300i	−0.243195	−	1.04841i
$509$	16.4986	+	7.53466i	0.731288	+	0.333968i	0.746020	−	0.665923i	$-0.231962\pi$
$509$	16.4986	+	7.53466i	0.731288	+	0.333968i	−0.0147320	+	0.999891i	$0.504690\pi$
$510$	−38.5351	−	35.0429i	−1.70636	−	1.55172i
$511$	30.2618	+	26.2220i	1.33870	+	1.15999i
$512$	−10.6531	−	19.9628i	−0.470805	−	0.882238i
$513$	−2.79977	−	0.609054i	−0.123613	−	0.0268904i
$514$	−2.20544	−	28.1209i	−0.0972778	−	1.24036i
$515$	−0.263696	−	6.49769i	−0.0116198	−	0.286322i
$516$	3.01646	+	9.77447i	0.132792	+	0.430297i
$517$	1.58843	+	2.12189i	0.0698589	+	0.0933206i
$518$	6.03293	−	1.81652i	0.265072	−	0.0798133i
$519$	47.1552	+	30.3048i	2.06988	+	1.33023i
$520$	31.0748	+	7.09387i	1.36272	+	0.311087i
$521$	−8.21695	−	17.9926i	−0.359991	−	0.788271i	−0.999805	−	0.0197408i	$-0.993716\pi$
$521$	−8.21695	−	17.9926i	−0.359991	−	0.788271i	0.639814	−	0.768530i	$-0.279011\pi$
$522$	−10.8985	−	6.89873i	−0.477013	−	0.301949i
$523$	23.4403	−	12.7993i	1.02497	−	0.559676i	0.123422	−	0.992354i	$-0.460613\pi$
$523$	23.4403	−	12.7993i	1.02497	−	0.559676i	0.901549	+	0.432678i	$0.142431\pi$
$524$	−25.6518	+	4.04849i	−1.12060	+	0.176859i
$525$	−52.5409	+	29.3561i	−2.29307	+	1.28121i
$526$	−15.4586	+	15.6724i	−0.674026	+	0.683348i
$527$	25.3960	−	33.9251i	1.10627	−	1.47780i
$528$	−8.73144	+	12.3573i	−0.379987	+	0.537782i
$529$	−15.4042	−	17.0795i	−0.669749	−	0.742588i
$530$	−4.38126	−	1.06368i	−0.190310	−	0.0462033i
$531$	29.2895	−	4.21120i	1.27106	−	0.182750i
$532$	0.515742	−	1.44298i	0.0223603	−	0.0625611i
$533$	1.08324	+	0.591492i	0.0469202	+	0.0256203i
$534$	−37.3186	−	67.2421i	−1.61494	−	2.90985i
$535$	30.9103	−	21.6849i	1.33637	−	0.937519i
$536$	−24.6478	−	12.8068i	−1.06462	−	0.553169i
$537$	−20.8736	−	7.78546i	−0.900763	−	0.335967i
$538$	−14.1537	−	6.34667i	−0.610209	−	0.273625i
$539$	6.92424	+	4.44994i	0.298248	+	0.191672i
$540$	62.4837	−	3.39588i	2.68887	−	0.146135i
$541$	−1.67877	+	11.6761i	−0.0721761	+	0.501996i	0.921381	+	0.388661i	$0.127062\pi$
$541$	−1.67877	+	11.6761i	−0.0721761	+	0.501996i	−0.993557	+	0.113335i	$0.963847\pi$
$542$	32.4767	+	4.44203i	1.39499	+	0.190802i
$543$	−51.2480	−	3.66533i	−2.19926	−	0.157294i
$544$	−28.0727	+	7.12435i	−1.20361	+	0.305454i
$545$	20.1808	−	16.4251i	0.864450	−	0.703576i
$546$	−50.9406	+	69.0318i	−2.18006	+	2.95429i
$547$	−4.97810	+	0.356040i	−0.212848	+	0.0152232i	−0.177356	−	0.984147i	$-0.556754\pi$
$547$	−4.97810	+	0.356040i	−0.212848	+	0.0152232i	−0.0354921	+	0.999370i	$0.511300\pi$
$548$	−10.7771	−	27.7255i	−0.460375	−	1.18437i
$549$	−21.2827	−	9.71947i	−0.908322	−	0.414817i
$550$	−5.97584	−	5.78080i	−0.254811	−	0.246494i
$551$			0.254119i			0.0108258i
$552$	4.44065	+	43.4117i	0.189007	+	1.84773i
$553$	−24.4658	−	24.4658i	−1.04039	−	1.04039i
$554$	−3.38988	+	16.1150i	−0.144022	+	0.684661i
$555$	2.66535	−	8.13992i	0.113138	−	0.345520i
$556$	−8.53600	+	19.3917i	−0.362007	+	0.822391i
$557$	−0.919586	−	12.8575i	−0.0389641	−	0.544789i	−0.979019	−	0.203767i	$-0.934681\pi$
$557$	−0.919586	−	12.8575i	−0.0389641	−	0.544789i	0.940055	−	0.341022i	$-0.110773\pi$
$558$	12.8276	+	85.0670i	0.543036	+	3.60117i
$559$	−6.74056	+	4.33189i	−0.285095	+	0.183220i
$560$	−2.49998	+	33.3730i	−0.105643	+	1.41027i
$561$	12.6828	+	14.6367i	0.535466	+	0.617961i
$562$	−2.13110	+	15.5809i	−0.0898950	+	0.657242i
$563$	0.774722	+	1.03491i	0.0326506	+	0.0436161i	0.816569	−	0.577247i	$-0.195873\pi$
$563$	0.774722	+	1.03491i	0.0326506	+	0.0436161i	−0.783919	+	0.620863i	$0.786782\pi$
$564$	−9.64768	−	10.8298i	−0.406240	−	0.456018i
$565$	−0.167242	+	0.0565681i	−0.00703594	+	0.00237984i
$566$	−1.38538	−	3.63785i	−0.0582317	−	0.152910i
$567$	−30.0298	+	80.5131i	−1.26113	+	3.38123i
$568$	−0.357146	−	1.12970i	−0.0149855	−	0.0474011i
$569$	−6.17450	+	21.0284i	−0.258849	+	0.881557i	0.722832	+	0.691024i	$0.242840\pi$
$569$	−6.17450	+	21.0284i	−0.258849	+	0.881557i	−0.981681	+	0.190533i	$0.938978\pi$
$570$	−1.20808	−	1.69713i	−0.0506008	−	0.0710848i
$571$	7.87517	+	26.8204i	0.329566	+	1.12240i	0.943039	+	0.332682i	$0.107954\pi$
$571$	7.87517	+	26.8204i	0.329566	+	1.12240i	−0.613474	+	0.789715i	$0.710228\pi$
$572$	−11.1603	−	3.98887i	−0.466637	−	0.166783i
$573$	−27.0749	+	36.1679i	−1.13107	+	1.51093i
$574$	−0.444507	+	1.21723i	−0.0185534	+	0.0508064i
$575$	−23.9471	−	1.24018i	−0.998662	−	0.0517191i
$576$	29.7229	−	50.7293i	1.23846	−	2.11372i
$577$	25.4062	+	19.0189i	1.05768	+	0.791766i	0.978738	−	0.205114i	$-0.0657564\pi$
$577$	25.4062	+	19.0189i	1.05768	+	0.791766i	0.0789372	+	0.996880i	$0.474847\pi$
$578$	0.0894768	+	13.0297i	0.00372175	+	0.541963i
$579$	−40.5153	+	11.8964i	−1.68376	+	0.494396i
$580$	−1.47227	−	5.35101i	−0.0611325	−	0.222189i
$581$	24.1132	+	7.08026i	1.00038	+	0.293739i
$582$	5.07140	−	8.01169i	0.210216	−	0.332095i
$583$	1.57070	+	0.585841i	0.0650518	+	0.0242631i
$584$	9.99143	−	28.5723i	0.413448	−	1.18233i
$585$	26.5371	+	78.4563i	1.09717	+	3.24377i
$586$	17.3072	+	9.29672i	0.714953	+	0.384044i
$587$	−10.2233	+	7.65309i	−0.421962	+	0.315877i	−0.789072	−	0.614301i	$-0.789438\pi$
$587$	−10.2233	+	7.65309i	−0.421962	+	0.315877i	0.367110	+	0.930178i	$0.380347\pi$
$588$	−39.8227	−	21.0401i	−1.64226	−	0.867678i
$589$	1.28092	−	1.10993i	0.0527795	−	0.0457337i
$590$	10.5429	+	7.13827i	0.434043	+	0.293878i
$591$	43.7781	+	68.1201i	1.80079	+	2.80209i
$592$	−2.95782	−	3.73291i	−0.121566	−	0.153422i
$593$	17.0159	−	1.21700i	0.698760	−	0.0499763i	0.282560	−	0.959250i	$-0.408816\pi$
$593$	17.0159	−	1.21700i	0.698760	−	0.0499763i	0.416199	+	0.909273i	$0.363362\pi$
$594$	−23.2191	−	1.50048i	−0.952691	−	0.0615653i
$595$	40.7096	+	13.3300i	1.66893	+	0.546477i
$596$	11.2004	−	17.9660i	0.458787	−	0.735917i
$597$	−35.5439	+	35.5439i	−1.45471	+	1.45471i
$598$	−31.8210	+	12.4816i	−1.30126	+	0.510410i
$599$	6.49912			0.265547			0.132773	−	0.991146i	$-0.457612\pi$
$599$	6.49912			0.265547			0.132773	+	0.991146i	$0.457612\pi$
$600$	35.2711	+	28.7374i	1.43994	+	1.17320i
$601$	−9.47272	+	20.7424i	−0.386400	+	0.846099i	0.612070	+	0.790804i	$0.290337\pi$
$601$	−9.47272	+	20.7424i	−0.386400	+	0.846099i	−0.998470	+	0.0552951i	$0.982390\pi$
$602$	−5.55272	−	6.31996i	−0.226312	−	0.257582i
$603$	−5.14889	−	71.9909i	−0.209679	−	2.93170i
$604$	11.5693	+	17.4699i	0.470748	+	0.710840i
$605$	−13.5751	−	16.6791i	−0.551906	−	0.678101i
$606$	−2.47396	−	31.5447i	−0.100498	−	1.28141i
$607$	−0.825136	+	11.5369i	−0.0334912	+	0.468269i	0.952838	+	0.303480i	$0.0981486\pi$
$607$	−0.825136	+	11.5369i	−0.0334912	+	0.468269i	−0.986329	+	0.164788i	$0.947306\pi$
$608$	−1.15768	+	0.0397650i	−0.0469503	+	0.00161268i
$609$	14.7859	+	2.12589i	0.599154	+	0.0861454i
$610$	−3.96134	−	9.25500i	−0.160390	−	0.374724i
$611$	6.14208	−	9.55726i	0.248482	−	0.386645i
$612$	−53.9407	−	52.4790i	−2.18042	−	2.12134i
$613$	2.02890	−	5.43970i	0.0819466	−	0.219707i	−0.889514	−	0.456908i	$-0.848957\pi$
$613$	2.02890	−	5.43970i	0.0819466	−	0.219707i	0.971461	+	0.237200i	$0.0762298\pi$
$614$	2.16033	+	9.61257i	0.0871837	+	0.387932i
$615$	1.01173	+	1.44216i	0.0407970	+	0.0581534i
$616$	2.39408	−	12.2113i	0.0964601	−	0.492008i
$617$	−3.64794	+	6.68071i	−0.146861	+	0.268955i	−0.940746	−	0.339112i	$-0.889873\pi$
$617$	−3.64794	+	6.68071i	−0.146861	+	0.268955i	0.793885	+	0.608068i	$0.208055\pi$
$618$	−0.0908598	−	13.2311i	−0.00365492	−	0.532231i
$619$	−3.38499	−	23.5431i	−0.136054	−	0.946277i	−0.937444	−	0.348135i	$-0.886815\pi$
$619$	−3.38499	−	23.5431i	−0.136054	−	0.946277i	0.801390	−	0.598142i	$-0.204094\pi$
$620$	−20.5420	+	30.7930i	−0.824988	+	1.23667i
$621$	−53.3183	+	40.7464i	−2.13959	+	1.63510i
$622$	−22.0849	+	10.2697i	−0.885525	+	0.411778i
$623$	50.6317	+	37.9024i	2.02852	+	1.51853i
$624$	62.7041	+	16.5552i	2.51017	+	0.662740i
$625$	−18.5719	+	16.7358i	−0.742875	+	0.669430i
$626$	−2.10443	−	3.79184i	−0.0841100	−	0.151552i
$627$	0.371222	+	0.679842i	0.0148252	+	0.0271503i
$628$	24.3194	+	31.5736i	0.970452	+	1.25993i
$629$	−5.54526	+	2.53244i	−0.221104	+	0.100975i
$630$	−77.3000	+	39.8341i	−3.07971	+	1.58703i
$631$	−22.2868	+	34.6790i	−0.887225	+	1.38055i	0.0372500	+	0.999306i	$0.488140\pi$
$631$	−22.2868	+	34.6790i	−0.887225	+	1.38055i	−0.924475	+	0.381243i	$0.875496\pi$
$632$	−10.3728	+	24.0102i	−0.412607	+	0.955075i
$633$	−12.5340	+	9.38281i	−0.498180	+	0.372933i
$634$	−30.1444	−	39.6971i	−1.19719	−	1.57657i
$635$	27.0983	−	1.09973i	1.07536	−	0.0436415i
$636$	−8.83633	−	2.46328i	−0.350383	−	0.0976754i
$637$	7.49902	−	34.4725i	0.297122	−	1.36585i
$638$	0.307700	+	2.04053i	0.0121820	+	0.0807852i
$639$	2.01607	−	2.32667i	0.0797547	−	0.0920418i
$640$	24.1471	−	7.54449i	0.954496	−	0.298222i
$641$	−10.7092	+	23.4500i	−0.422990	+	0.926219i	0.571423	+	0.820656i	$0.306392\pi$
$641$	−10.7092	+	23.4500i	−0.422990	+	0.926219i	−0.994413	+	0.105563i	$0.966336\pi$
$642$	64.3422	−	41.9773i	2.53938	−	1.65671i
$643$	6.29566	−	6.29566i	0.248277	−	0.248277i	−0.571986	−	0.820263i	$-0.693827\pi$
$643$	6.29566	−	6.29566i	0.248277	−	0.248277i	0.820263	+	0.571986i	$0.193827\pi$
$644$	−17.9404	−	31.0829i	−0.706949	−	1.22484i
$645$	−11.3651	+	1.27779i	−0.447502	+	0.0503130i
$646$	−0.305211	+	1.45093i	−0.0120084	+	0.0570861i
$647$	−0.461854	+	0.172263i	−0.0181573	+	0.00677234i	−0.358526	−	0.933520i	$-0.616721\pi$
$647$	−0.461854	+	0.172263i	−0.0181573	+	0.00677234i	0.340369	+	0.940292i	$0.389448\pi$
$648$	64.9439	−	1.33811i	2.55124	−	0.0525659i
$649$	−3.57785	−	3.10022i	−0.140443	−	0.121694i
$650$	−14.2642	+	32.6572i	−0.559488	+	1.28092i
$651$	−53.8650	−	83.8155i	−2.11113	−	3.28499i
$652$	−17.4512	+	9.84258i	−0.683441	+	0.385465i
$653$	0.481614	−	6.73385i	0.0188470	−	0.263516i	−0.979288	−	0.202472i	$-0.935102\pi$
$653$	0.481614	−	6.73385i	0.0188470	−	0.263516i	0.998135	−	0.0610439i	$-0.0194430\pi$
$654$	42.1632	−	32.0171i	1.64871	−	1.25197i
$655$	0.895256	−	29.0207i	0.0349806	−	1.13393i
$656$	0.979204	−	0.0269038i	0.0382315	−	0.00105041i
$657$	76.8539	−	16.7185i	2.99836	−	0.652252i
$658$	10.8841	+	4.88054i	0.424305	+	0.190263i
$659$	−1.88968	−	4.13781i	−0.0736113	−	0.161186i	0.869249	−	0.494374i	$-0.164603\pi$
$659$	−1.88968	−	4.13781i	−0.0736113	−	0.161186i	−0.942860	+	0.333188i	$0.891876\pi$
$660$	−11.7556	−	12.1648i	−0.457585	−	0.473513i
$661$	16.7943	+	4.93125i	0.653223	+	0.191803i	0.591519	−	0.806291i	$-0.298528\pi$
$661$	16.7943	+	4.93125i	0.653223	+	0.191803i	0.0617037	+	0.998095i	$0.480347\pi$
$662$	1.34092	−	4.68555i	0.0521164	−	0.182109i
$663$	39.7826	−	72.8564i	1.54503	−	2.82951i
$664$	−1.74531	−	18.9170i	−0.0677311	−	0.734121i
$665$	1.47765	+	0.867048i	0.0573009	+	0.0336227i
$666$	4.24507	−	11.6246i	0.164493	−	0.450446i
$667$	4.53639	+	3.85256i	0.175650	+	0.149172i
$668$	33.1180	−	2.82630i	1.28137	−	0.109353i
$669$	22.4965	−	3.23451i	0.869767	−	0.125054i
$670$	19.2011	−	24.4075i	0.741803	−	0.942946i
$671$	1.05459	+	3.59162i	0.0407122	+	0.138653i
$672$	−7.37113	+	67.6922i	−0.284347	+	2.61128i
$673$	−18.2642	−	33.4484i	−0.704033	−	1.28934i	−0.947601	−	0.319457i	$-0.896500\pi$
$673$	−18.2642	−	33.4484i	−0.704033	−	1.28934i	0.243568	−	0.969884i	$-0.421682\pi$
$674$	−27.9953	+	6.29165i	−1.07834	+	0.242345i
$675$	−9.28295	+	69.3434i	−0.357301	+	2.66903i
$676$	0.340574	+	24.7961i	0.0130990	+	0.953696i
$677$	−20.2019	+	4.39465i	−0.776422	+	0.168900i	−0.583281	−	0.812271i	$-0.698231\pi$
$677$	−20.2019	+	4.39465i	−0.776422	+	0.168900i	−0.193141	+	0.981171i	$0.561868\pi$
$678$	−0.343963	+	0.103568i	−0.0132098	+	0.00397749i
$679$	−1.10978	+	7.71868i	−0.0425894	+	0.296216i
$680$	−1.97926	−	32.3207i	−0.0759013	−	1.23944i
$681$	−10.5681	−	12.1963i	−0.404972	−	0.467362i
$682$	8.94159	−	10.4635i	0.342391	−	0.400667i
$683$	−3.47988	+	15.9967i	−0.133154	+	0.612098i	0.861405	+	0.507919i	$0.169585\pi$
$683$	−3.47988	+	15.9967i	−0.133154	+	0.612098i	−0.994559	+	0.104179i	$0.966779\pi$
$684$	−1.66191	−	2.50952i	−0.0635447	−	0.0959539i
$685$	32.7000	−	6.06399i	1.24940	−	0.231693i
$686$	0.000352212	0	2.27608e-5i	1.34475e−5	0	8.69012e-7i
$687$	19.2204	−	7.16884i	0.733304	−	0.273508i
$688$	−2.89331	+	5.66315i	−0.110306	+	0.215905i
$689$		−	7.18530i		−	0.273738i
$690$	−48.6111	−	4.16327i	−1.85059	−	0.158493i
$691$		−	7.21221i		−	0.274365i	−0.990546	−	0.137183i	$-0.956195\pi$
$691$		−	7.21221i		−	0.274365i	0.990546	−	0.137183i	$-0.0438047\pi$
$692$	7.87436	+	33.9464i	0.299338	+	1.29045i
$693$	30.2955	−	11.2997i	1.15083	−	0.429238i
$694$	−2.22918	+	34.4954i	−0.0846185	+	1.30943i
$695$	−19.5233	−	13.4151i	−0.740562	−	0.508864i
$696$	−2.62707	−	10.9821i	−0.0995789	−	0.416277i
$697$	0.266522	−	1.22518i	0.0100952	−	0.0464070i
$698$	−10.5550	−	9.01977i	−0.399511	−	0.341403i
$699$	29.7506	+	34.3340i	1.12527	+	1.29863i
$700$	−36.1384	−	9.69658i	−1.36590	−	0.366496i
$701$	5.92718	−	41.2244i	0.223866	−	1.55703i	−0.499348	−	0.866402i	$-0.666427\pi$
$701$	5.92718	−	41.2244i	0.223866	−	1.55703i	0.723214	−	0.690624i	$-0.242664\pi$
$702$	28.7531	+	95.4932i	1.08522	+	3.60416i
$703$	−0.238245	+	0.0518270i	−0.00898558	+	0.00195469i
$704$	−9.24781	+	1.72108i	−0.348540	+	0.0648658i
$705$	13.9055	−	8.34215i	0.523711	−	0.314184i
$706$	−6.44585	−	28.6814i	−0.242593	−	1.07944i
$707$	12.4713	+	22.8394i	0.469030	+	0.858964i
$708$	20.9496	+	15.2382i	0.787332	+	0.572687i
$709$	−8.08326	−	27.5291i	−0.303573	−	1.03388i	−0.960119	−	0.279590i	$-0.909801\pi$
$709$	−8.08326	−	27.5291i	−0.303573	−	1.03388i	0.656546	−	0.754286i	$-0.272017\pi$
$710$	1.31531	−	0.157036i	0.0493629	−	0.00589344i
$711$	−67.2700	+	9.67197i	−2.52282	+	0.362727i
$712$	12.5218	−	46.1411i	0.469274	−	1.72921i
$713$	−0.394405	−	39.6932i	−0.0147706	−	1.48652i
$714$	81.8689	+	29.8967i	3.06387	+	1.11886i
$715$	6.70595	−	11.4285i	0.250788	−	0.427402i
$716$	−5.92602	−	12.5183i	−0.221466	−	0.467831i
$717$	47.0139	−	86.0995i	1.75577	−	3.21544i
$718$	−4.18650	−	1.19810i	−0.156239	−	0.0447128i
$719$	−10.5462	−	3.09665i	−0.393308	−	0.115486i	0.0790976	−	0.996867i	$-0.474796\pi$
$719$	−10.5462	−	3.09665i	−0.393308	−	0.115486i	−0.472406	+	0.881381i	$0.656614\pi$
$720$	49.5341	+	43.2148i	1.84603	+	1.61052i
$721$	4.52042	+	9.89833i	0.168349	+	0.368633i
$722$	10.9699	−	24.4638i	0.408256	−	0.910449i
$723$	−52.5036	+	11.4215i	−1.95263	+	0.424768i
$724$	−21.2469	−	23.8503i	−0.789633	−	0.886390i
$725$	6.18453	−	0.502801i	0.229687	−	0.0186736i
$726$	−26.4616	−	34.8472i	−0.982083	−	1.29330i
$727$	0.271171	−	3.79147i	0.0100572	−	0.140618i	−0.989942	−	0.141471i	$-0.954817\pi$
$727$	0.271171	−	3.79147i	0.0100572	−	0.140618i	1.00000		0.000852854i	$0.000271472\pi$
$728$	−52.6255	+	8.67641i	−1.95043	+	0.321569i
$729$	18.2436	+	28.3875i	0.675688	+	1.05139i
$730$	29.3048	+	16.9259i	1.08462	+	0.626455i
$731$	6.15177	+	5.33054i	0.227531	+	0.197157i
$732$	−7.42098	−	19.0915i	−0.274287	−	0.705640i
$733$	18.3889	−	6.85871i	0.679210	−	0.253332i	0.0139046	−	0.999903i	$-0.495574\pi$
$733$	18.3889	−	6.85871i	0.679210	−	0.253332i	0.665306	+	0.746571i	$0.268301\pi$
$734$	−17.9030	−	3.76600i	−0.660813	−	0.139005i
$735$	31.4055	−	39.3619i	1.15841	−	1.45189i
$736$	−16.8411	+	21.2691i	−0.620772	+	0.783991i
$737$	−8.16505	+	8.16505i	−0.300763	+	0.300763i
$738$	1.39079	+	2.13178i	0.0511957	+	0.0784719i
$739$	−15.5110	+	33.9645i	−0.570583	+	1.24940i	0.375903	+	0.926659i	$0.377332\pi$
$739$	−15.5110	+	33.9645i	−0.570583	+	1.24940i	−0.946486	+	0.322744i	$0.895395\pi$
$740$	4.71648	−	2.47162i	0.173381	−	0.0908587i
$741$	2.17414	−	2.50910i	0.0798692	−	0.0921740i
$742$	7.45989	−	1.12491i	0.273861	−	0.0412967i
$743$	−3.73163	+	17.1540i	−0.136900	+	0.629320i	0.856647	+	0.515903i	$0.172543\pi$
$743$	−3.73163	+	17.1540i	−0.136900	+	0.629320i	−0.993547	+	0.113417i	$0.963820\pi$
$744$	−43.8826	+	61.2092i	−1.60881	+	2.24404i
$745$	17.4024	+	16.0450i	0.637574	+	0.587843i
$746$	−4.10096	+	3.11411i	−0.150147	+	0.114016i
$747$	39.5171	−	29.5822i	1.44586	−	1.08235i
$748$	−0.693926	+	12.0203i	−0.0253724	+	0.439504i
$749$	−34.1586	+	53.1519i	−1.24813	+	1.94213i
$750$	−38.9128	+	32.7590i	−1.42089	+	1.19619i
$751$	−29.2140	+	13.3416i	−1.06603	+	0.486841i	−0.869641	−	0.493684i	$-0.835650\pi$
$751$	−29.2140	+	13.3416i	−1.06603	+	0.486841i	−0.196392	+	0.980525i	$0.562923\pi$
$752$	0.395999	−	9.00818i	0.0144406	−	0.328494i
$753$	18.7109	+	34.2665i	0.681863	+	1.24874i
$754$	7.73368	−	4.29211i	0.281644	−	0.156309i
$755$	−21.5996	+	9.07009i	−0.786089	+	0.330094i
$756$	−94.6410	+	44.8020i	−3.44206	+	1.62943i
$757$	−20.3176	−	15.2096i	−0.738457	−	0.552802i	0.162501	−	0.986708i	$-0.448044\pi$
$757$	−20.3176	−	15.2096i	−0.738457	−	0.552802i	−0.900958	+	0.433906i	$0.857135\pi$
$758$	−9.63720	−	20.7247i	−0.350039	−	0.752756i
$759$	17.7640	+	3.67986i	0.644793	+	0.133571i
$760$	0.197425	−	1.27996i	0.00716136	−	0.0464289i
$761$	−6.32689	−	44.0045i	−0.229350	−	1.59516i	−0.700859	−	0.713300i	$-0.747200\pi$
$761$	−6.32689	−	44.0045i	−0.229350	−	1.59516i	0.471509	−	0.881861i	$-0.343710\pi$
$762$	55.1795	−	0.378927i	1.99894	−	0.0137271i
$763$	−20.8666	+	38.2143i	−0.755421	+	1.38345i
$764$	−27.7439	+	4.37869i	−1.00374	+	0.158415i
$765$	68.8803	−	48.3224i	2.49037	−	1.74710i
$766$	−26.4014	+	5.93344i	−0.953922	+	0.214384i
$767$	−7.09110	+	19.0120i	−0.256045	+	0.686483i
$768$	49.6199	−	13.6866i	1.79050	−	0.493871i
$769$	−14.0076	+	21.7962i	−0.505126	+	0.785992i	−0.996379	−	0.0850252i	$-0.972903\pi$
$769$	−14.0076	+	21.7962i	−0.505126	+	0.785992i	0.491252	+	0.871017i	$0.336539\pi$
$770$	12.9151	+	5.17301i	0.465428	+	0.186422i
$771$	63.5128	+	9.13176i	2.28736	+	0.328872i
$772$	−23.2107	−	12.2632i	−0.835371	−	0.441363i
$773$	1.24440	−	17.3990i	0.0447579	−	0.625798i	−0.924725	−	0.380637i	$-0.875705\pi$
$773$	1.24440	−	17.3990i	0.0447579	−	0.625798i	0.969482	−	0.245161i	$-0.0788407\pi$
$774$	−16.4739	+	1.29200i	−0.592143	+	0.0464400i
$775$	−29.5468	−	28.9778i	−1.06135	−	1.04091i
$776$	5.73302	−	1.37141i	0.205803	−	0.0492308i
$777$	1.02246	+	14.2958i	0.0366804	+	0.512859i
$778$	−27.9037	+	24.5162i	−1.00040	+	0.878948i
$779$	0.0208320	−	0.0456156i	0.000746382	−	0.00163435i
$780$	−31.2445	+	65.4304i	−1.11873	+	2.34279i
$781$	−0.492545			−0.0176246
$782$	21.2741	+	27.4452i	0.760759	+	0.981439i
$783$	12.2785	−	12.2785i	0.438797	−	0.438797i
$784$	−8.62348	−	26.6393i	−0.307981	−	0.951402i
$785$	−39.7474	+	20.1384i	−1.41865	+	0.718769i
$786$	3.80962	−	58.9520i	0.135885	−	2.10275i
$787$	−47.2476	+	3.37922i	−1.68420	+	0.120456i	−0.880332	−	0.474358i	$-0.842680\pi$
$787$	−47.2476	+	3.37922i	−1.68420	+	0.120456i	−0.803863	+	0.594814i	$0.797226\pi$
$788$	−10.0241	+	49.3327i	−0.357095	+	1.75740i
$789$	−27.0732	−	42.1268i	−0.963832	−	1.49975i
$790$	−24.2141	−	16.3946i	−0.861499	−	0.583295i
$791$	0.223268	−	0.193463i	0.00793849	−	0.00687874i
$792$	−16.3834	−	18.1386i	−0.582160	−	0.644528i
$793$	12.8440	−	9.61488i	0.456103	−	0.341434i
$794$	12.0254	−	22.3871i	0.426767	−	0.794488i
$795$	4.54613	−	9.19338i	0.161235	−	0.326056i
$796$	−31.2471	+	0.429178i	−1.10752	+	0.0152118i
$797$	33.0187	+	12.3153i	1.16958	+	0.436232i	0.857831	−	0.513932i	$-0.171812\pi$
$797$	33.0187	+	12.3153i	1.16958	+	0.436232i	0.311751	+	0.950164i	$0.399084\pi$
$798$	2.94536	+	1.86441i	0.104265	+	0.0659995i
$799$	−11.0739	−	3.25159i	−0.391767	−	0.115033i
$800$	3.25836	+	28.0960i	0.115200	+	0.993342i
$801$	119.198	−	34.9998i	4.21166	−	1.23666i
$802$	−20.8931	+	0.143476i	−0.737762	+	0.00506633i
$803$	−10.0734	−	7.54089i	−0.355484	−	0.266112i
$804$	40.7182	−	48.3164i	1.43602	−	1.70399i
$805$	37.8799	−	13.2334i	1.33509	−	0.466415i
$806$	−55.4136	−	20.2358i	−1.95186	−	0.712777i
$807$	21.1459	−	28.2476i	0.744371	−	0.994363i
$808$	12.5729	−	15.1286i	0.442312	−	0.532224i
$809$	5.88183	+	20.0317i	0.206794	+	0.704276i	0.995936	+	0.0900649i	$0.0287074\pi$
$809$	5.88183	+	20.0317i	0.206794	+	0.704276i	−0.789142	+	0.614211i	$0.789474\pi$
$810$	−12.0557	+	71.6173i	−0.423594	+	2.51637i
$811$	−10.6748	+	36.3550i	−0.374843	+	1.27660i	0.528960	+	0.848647i	$0.322582\pi$
$811$	−10.6748	+	36.3550i	−0.374843	+	1.27660i	−0.903802	+	0.427950i	$0.859236\pi$
$812$	5.66690	+	7.35726i	0.198869	+	0.258189i
$813$	−26.0581	+	69.8644i	−0.913897	+	2.45025i
$814$	−1.85030	+	0.704639i	−0.0648531	+	0.0246976i
$815$	−7.17725	−	21.2194i	−0.251408	−	0.743283i
$816$	−1.80950	−	65.8594i	−0.0633450	−	2.30554i
$817$	0.195100	+	0.260623i	0.00682569	+	0.00911806i
$818$	37.5451	+	5.13528i	1.31273	+	0.179551i
$819$	−90.7567	−	104.739i	−3.17130	−	3.65987i
$820$	−0.174382	+	1.08122i	−0.00608967	+	0.0377580i
$821$	−12.0123	+	7.71984i	−0.419232	+	0.269424i	−0.733205	−	0.680008i	$-0.761976\pi$
$821$	−12.0123	+	7.71984i	−0.419232	+	0.269424i	0.313972	+	0.949432i	$0.398340\pi$
$822$	66.9107	−	10.0898i	2.33378	−	0.351921i
$823$	−1.42188	−	19.8805i	−0.0495636	−	0.692990i	−0.960117	−	0.279599i	$-0.909799\pi$
$823$	−1.42188	−	19.8805i	−0.0495636	−	0.692990i	0.910553	−	0.413392i	$-0.135656\pi$
$824$	5.69544	−	5.93508i	0.198410	−	0.206758i
$825$	15.8109	−	10.3796i	0.550464	−	0.361371i
$826$	−20.8487	−	4.38563i	−0.725419	−	0.152596i
$827$	3.82978	+	3.82978i	0.133174	+	0.133174i	0.770552	−	0.637377i	$-0.219981\pi$
$827$	3.82978	+	3.82978i	0.133174	+	0.133174i	−0.637377	+	0.770552i	$0.719981\pi$
$828$	−69.9938	−	8.37800i	−2.43245	−	0.291156i
$829$		−	21.8450i		−	0.758709i	−0.925251	−	0.379354i	$-0.876146\pi$
$829$		−	21.8450i		−	0.758709i	0.925251	−	0.379354i	$-0.123854\pi$
$830$	21.1431	+	2.02259i	0.733888	+	0.0702053i
$831$	−34.0755	−	15.5618i	−1.18207	−	0.539831i
$832$	20.7636	+	34.5604i	0.719848	+	1.19817i
$833$	−35.7485	+	2.55678i	−1.23861	+	0.0885872i
$834$	−38.7810	−	28.6177i	−1.34288	−	0.990949i
$835$	−3.79275	+	36.9676i	−0.131253	+	1.27932i
$836$	−0.129311	+	0.463866i	−0.00447230	+	0.0160431i
$837$	−115.520	−	8.26217i	−3.99297	−	0.285583i
$838$	−5.79375	+	42.3594i	−0.200142	+	1.46328i
$839$	−6.83945	+	47.5694i	−0.236124	+	1.64228i	0.434638	+	0.900605i	$0.356876\pi$
$839$	−6.83945	+	47.5694i	−0.236124	+	1.64228i	−0.670762	+	0.741673i	$0.734033\pi$
$840$	−72.8224	−	22.1949i	−2.51261	−	0.765796i
$841$	23.1008	+	14.8460i	0.796579	+	0.511930i
$842$	8.06958	−	17.9959i	0.278096	−	0.620181i
$843$	−33.5180	−	12.5016i	−1.15442	−	0.430577i
$844$	−9.65270	−	1.25280i	−0.332260	−	0.0431230i
$845$	−27.3086	−	4.79007i	−0.939444	−	0.164783i
$846$	20.4861	−	11.3696i	0.704327	−	0.390894i
$847$	31.5835	+	17.2459i	1.08522	+	0.592576i
$848$	−2.86954	−	4.92835i	−0.0985404	−	0.169240i
$849$	8.76501	−	1.26022i	0.300814	−	0.0432506i
$850$	35.9153	+	4.55713i	1.23189	+	0.156308i
$851$	−2.68671	+	5.03873i	−0.0920993	+	0.172726i
$852$	2.68544	−	0.229176i	0.0920017	−	0.00785145i
$853$	−16.3569	+	21.8502i	−0.560049	+	0.748138i	−0.987795	−	0.155761i	$-0.950217\pi$
$853$	−16.3569	+	21.8502i	−0.560049	+	0.748138i	0.427746	+	0.903899i	$0.359308\pi$
$854$	11.9931	+	11.8295i	0.410397	+	0.404799i
$855$	3.10274	−	1.30290i	0.106111	−	0.0445583i
$856$	46.8685	+	9.18876i	1.60193	+	0.314065i
$857$	11.3581	−	6.20197i	0.387984	−	0.211855i	−0.273404	−	0.961899i	$-0.588150\pi$
$857$	11.3581	−	6.20197i	0.387984	−	0.211855i	0.661388	+	0.750044i	$0.269968\pi$
$858$	14.4198	−	22.7801i	0.492284	−	0.777700i
$859$	−10.9119	−	23.8937i	−0.372309	−	0.815242i	−0.999343	−	0.0362504i	$-0.988459\pi$
$859$	−10.9119	−	23.8937i	−0.372309	−	0.815242i	0.627034	−	0.778992i	$-0.284269\pi$
$860$	−5.61819	−	4.35764i	−0.191579	−	0.148594i
$861$	−2.47986	−	1.59371i	−0.0845135	−	0.0543135i
$862$	−0.318477	−	1.05771i	−0.0108474	−	0.0360257i
$863$	−16.7468	−	22.3712i	−0.570069	−	0.761523i	0.419158	−	0.907913i	$-0.362325\pi$
$863$	−16.7468	−	22.3712i	−0.570069	−	0.761523i	−0.989227	+	0.146390i	$0.953235\pi$
$864$	57.8580	+	54.0153i	1.96837	+	1.83764i
$865$	−38.9288	+	1.57985i	−1.32362	+	0.0537165i
$866$	6.65737	−	0.522118i	0.226227	−	0.0177423i
$867$	−28.9632	−	6.30057i	−0.983643	−	0.213978i
$868$	12.3338	−	60.6993i	0.418635	−	2.06027i
$869$	8.21733	+	7.12036i	0.278754	+	0.241542i
$870$	12.6106	−	0.598543i	0.427540	−	0.0202925i
$871$	45.0201	+	20.5600i	1.52545	+	0.696649i
$872$	32.6678	+	4.01194i	1.10627	+	0.135862i
$873$	10.8308	+	10.8308i	0.366567	+	0.366567i
$874$	0.598087	+	1.25345i	0.0202306	+	0.0423987i
$875$	18.1777	−	37.6773i	0.614520	−	1.27372i
$876$	58.4309	+	36.4272i	1.97420	+	1.23076i
$877$	−14.0625	−	37.7030i	−0.474857	−	1.27314i	−0.924926	−	0.380146i	$-0.875874\pi$
$877$	−14.0625	−	37.7030i	−0.474857	−	1.27314i	0.450070	−	0.892993i	$-0.351399\pi$
$878$	18.7631	+	21.3556i	0.633222	+	0.720717i
$879$	−29.2663	+	33.7751i	−0.987128	+	1.13921i
$880$	0.0354510	−	10.5168i	0.00119505	−	0.354523i
$881$	−41.8492	+	26.8949i	−1.40994	+	0.906111i	−0.999982	−	0.00599592i	$-0.998091\pi$
$881$	−41.8492	+	26.8949i	−1.40994	+	0.906111i	−0.409953	+	0.912106i	$0.634455\pi$
$882$	47.2667	−	55.3116i	1.59155	−	1.86244i
$883$	50.7044	+	3.62645i	1.70634	+	0.122040i	0.890126	−	0.455714i	$-0.150616\pi$
$883$	50.7044	+	3.62645i	1.70634	+	0.122040i	0.816211	+	0.577754i	$0.196071\pi$
$884$	49.3116	−	15.2179i	1.65853	−	0.511832i
$885$	−21.1017	+	19.8388i	−0.709327	+	0.666872i
$886$	−6.49438	+	12.0902i	−0.218183	+	0.406179i
$887$	−0.904293	−	4.15697i	−0.0303632	−	0.139577i	0.959470	−	0.281811i	$-0.0909352\pi$
$887$	−0.904293	−	4.15697i	−0.0303632	−	0.139577i	−0.989833	+	0.142234i	$0.954572\pi$
$888$	9.76033	−	4.70274i	0.327535	−	0.157814i
$889$	−41.2806	+	18.8522i	−1.38451	+	0.632282i
$890$	48.0765	+	23.3643i	1.61153	+	0.783175i
$891$	7.60791	−	25.9102i	0.254874	−	0.868023i
$892$	11.4266	+	8.31142i	0.382590	+	0.278287i
$893$	−0.405138	−	0.221222i	−0.0135574	−	0.00740291i
$894$	34.2878	+	33.8201i	1.14676	+	1.13111i
$895$	14.9851	−	3.90240i	0.500896	−	0.130443i
$896$	−32.6305	+	26.9678i	−1.09011	+	0.900930i
$897$	−11.8300	−	76.8506i	−0.394991	−	2.56597i
$898$	−31.4853	+	14.6410i	−1.05068	+	0.488577i
$899$	1.46181	+	10.1671i	0.0487541	+	0.339092i
$900$	−57.7862	+	45.4114i	−1.92621	+	1.51371i
$901$	−7.00389	+	2.05653i	−0.233334	+	0.0685129i
$902$	0.112043	−	0.391509i	0.00373062	−	0.0130358i
$903$	16.7965	−	9.17157i	0.558952	−	0.305211i
$904$	−0.198167	−	0.102966i	−0.00659092	−	0.00342459i
$905$	30.6237	−	18.3717i	1.01797	−	0.610697i
$906$	−44.5442	+	16.9635i	−1.47988	+	0.563573i
$907$	5.36647	+	24.6692i	0.178191	+	0.819129i	0.976267	+	0.216572i	$0.0694876\pi$
$907$	5.36647	+	24.6692i	0.178191	+	0.819129i	−0.798076	+	0.602557i	$0.794149\pi$
$908$	0.578226	−	10.0161i	0.0191891	−	0.332396i
$909$	50.5936	+	7.27426i	1.67808	+	0.241272i
$910$	1.42935	−	59.6143i	0.0473825	−	1.97619i
$911$	−5.48888	+	4.75614i	−0.181855	+	0.157578i	−0.741031	−	0.671471i	$-0.765663\pi$
$911$	−5.48888	+	4.75614i	−0.181855	+	0.157578i	0.559176	+	0.829049i	$0.311117\pi$
$912$	0.489192	−	2.58925i	0.0161988	−	0.0857385i
$913$	−7.71703	−	1.67874i	−0.255396	−	0.0555581i
$914$	6.02326	+	4.44475i	0.199232	+	0.147019i
$915$	22.5168	−	4.17560i	0.744383	−	0.138041i
$916$	11.6723	+	5.13803i	0.385665	+	0.169765i
$917$	16.9784	+	45.5209i	0.560677	+	1.50323i
$918$	84.8528	−	55.3586i	2.80056	−	1.82711i
$919$	−5.70796			−0.188288			−0.0941442	−	0.995559i	$-0.530011\pi$
$919$	−5.70796			−0.188288			−0.0941442	+	0.995559i	$0.530011\pi$
$920$	−19.8560	−	22.9290i	−0.654633	−	0.755947i
$921$	−22.4121			−0.738504
$922$	−23.6169	+	15.4079i	−0.777782	+	0.507431i
$923$	0.737761	+	1.97802i	0.0242837	+	0.0651072i
$924$	25.9082	+	11.4045i	0.852316	+	0.375180i
$925$	1.73271	+	5.69564i	0.0569712	+	0.187272i
$926$	−13.8088	−	10.1899i	−0.453785	−	0.334862i
$927$	20.8855	+	4.54337i	0.685971	+	0.149224i
$928$	3.59037	−	6.03247i	0.117860	−	0.198026i
$929$	10.7919	−	9.35127i	0.354072	−	0.306805i	−0.459604	−	0.888124i	$-0.652009\pi$
$929$	10.7919	−	9.35127i	0.354072	−	0.306805i	0.813676	+	0.581319i	$0.197463\pi$
$930$	−58.0969	−	60.9513i	−1.90507	−	1.99867i
$931$	−1.41883	−	0.203997i	−0.0465002	−	0.00668572i
$932$	−1.62778	+	28.1965i	−0.0533196	+	0.923607i
$933$	−11.7772	−	54.1388i	−0.385567	−	1.77242i
$934$	17.9775	−	6.84625i	0.588242	−	0.224016i
$935$	−13.0593	−	3.26566i	−0.427085	−	0.106798i
$936$	−48.3030	+	92.9634i	−1.57883	+	3.03860i
$937$	3.60703	−	1.96959i	0.117836	−	0.0643436i	−0.419250	−	0.907871i	$-0.637707\pi$
$937$	3.60703	−	1.96959i	0.117836	−	0.0643436i	0.537086	+	0.843527i	$0.319525\pi$
$938$	−14.2975	+	49.9594i	−0.466830	+	1.63123i
$939$	9.46545	−	2.77931i	0.308893	−	0.0906993i
$940$	9.81270	+	2.31108i	0.320055	+	0.0753792i
$941$	6.04741	+	42.0607i	0.197140	+	1.37114i	0.812531	+	0.582917i	$0.198089\pi$
$941$	6.04741	+	42.0607i	0.197140	+	1.37114i	−0.615391	+	0.788222i	$0.711002\pi$
$942$	−82.2063	+	38.2268i	−2.67843	+	1.24550i
$943$	−0.498482	−	1.06343i	−0.0162328	−	0.0346301i
$944$	2.72893	+	15.8721i	0.0888193	+	0.516593i
$945$	−29.5030	−	113.291i	−0.959732	−	3.68534i
$946$	1.88219	+	1.85652i	0.0611953	+	0.0603606i
$947$	9.66415	+	5.27702i	0.314043	+	0.171480i	0.628538	−	0.777779i	$-0.283654\pi$
$947$	9.66415	+	5.27702i	0.314043	+	0.171480i	−0.314496	+	0.949259i	$0.601835\pi$
$948$	−48.1154	−	34.9980i	−1.56271	−	1.13668i
$949$	−15.1949	+	51.7492i	−0.493248	+	1.67985i
$950$	1.36487	+	0.483435i	0.0442822	+	0.0156847i
$951$	103.141	−	47.1031i	3.34459	−	1.52742i
$952$	23.5195	+	48.8136i	0.762271	+	1.58206i
$953$	−3.76281	−	17.2973i	−0.121889	−	0.560316i	−0.997068	−	0.0765167i	$-0.975620\pi$
$953$	−3.76281	−	17.2973i	−0.121889	−	0.560316i	0.875179	−	0.483799i	$-0.160743\pi$
$954$	7.01227	−	13.0543i	0.227031	−	0.422650i
$955$	0.968274	−	31.3877i	0.0313326	−	1.01568i
$956$	58.2750	−	17.9840i	1.88475	−	0.581645i
$957$	−4.68231	−	0.334886i	−0.151358	−	0.0108253i
$958$	36.0022	−	42.1298i	1.16318	−	1.36115i
$959$	−46.8162	+	30.0870i	−1.51177	+	0.971559i
$960$	4.70010	+	57.3562i	0.151695	+	1.85116i
$961$	24.5632	−	28.3474i	0.792361	−	0.914433i
$962$	5.60125	+	6.37520i	0.180592	+	0.205545i
$963$	43.3694	+	116.278i	1.39756	+	3.74700i
$964$	−28.3467	−	17.6720i	−0.912987	−	0.569177i
$965$	18.3047	−	22.9421i	0.589250	−	0.738533i
$966$	77.9354	−	24.3135i	2.50753	−	0.782275i
$967$	−32.4799	−	32.4799i	−1.04448	−	1.04448i	−0.998963	−	0.0455206i	$-0.985505\pi$
$967$	−32.4799	−	32.4799i	−1.04448	−	1.04448i	−0.0455206	−	0.998963i	$-0.514495\pi$
$968$	3.31580	−	26.9994i	0.106574	−	0.867793i
$969$	−3.06802	−	1.40112i	−0.0985590	−	0.0450104i
$970$	0.312458	+	6.58313i	0.0100324	+	0.211372i
$971$	−11.4683	−	9.93732i	−0.368034	−	0.318904i	0.451135	−	0.892456i	$-0.351019\pi$
$971$	−11.4683	−	9.93732i	−0.368034	−	0.318904i	−0.819169	+	0.573552i	$0.805565\pi$
$972$	−12.7065	+	62.5335i	−0.407560	+	2.00576i
$973$	38.7320	+	8.42564i	1.24169	+	0.270113i
$974$	32.2767	−	2.53137i	1.03421	−	0.0811104i
$975$	−65.3659	−	47.9479i	−2.09338	−	1.53556i
$976$	4.96978	−	11.7242i	0.159079	−	0.375282i
$977$	−18.3605	−	24.5268i	−0.587405	−	0.784681i	0.404105	−	0.914713i	$-0.367583\pi$
$977$	−18.3605	−	24.5268i	−0.587405	−	0.784681i	−0.991510	+	0.130031i	$0.958492\pi$
$978$	−13.1404	−	43.6413i	−0.420185	−	1.39550i
$979$	−16.7203	−	10.7455i	−0.534382	−	0.343427i
$980$	31.0583	−	3.92455i	0.992120	−	0.125365i
$981$	35.5273	+	77.7939i	1.13430	+	2.48377i
$982$	6.44049	−	10.1745i	0.205524	−	0.324683i
$983$	11.8746	−	6.48402i	0.378741	−	0.206808i	−0.278590	−	0.960410i	$-0.589867\pi$
$983$	11.8746	−	6.48402i	0.378741	−	0.206808i	0.657331	+	0.753602i	$0.271685\pi$
$984$	−0.428712	+	2.18671i	−0.0136668	+	0.0697097i
$985$	−52.1025	−	21.2855i	−1.66012	−	0.678211i
$986$	−6.39723	−	6.30997i	−0.203729	−	0.200950i
$987$	−16.2610	+	21.7222i	−0.517594	+	0.691425i
$988$	2.05653	−	0.175505i	0.0654270	−	0.00558355i
$989$	7.61030	+	0.468348i	0.241994	+	0.0148926i
$990$	23.3368	−	14.2190i	0.741691	−	0.451909i
$991$	−12.5559	+	1.80527i	−0.398852	+	0.0573462i	−0.338822	−	0.940850i	$-0.610029\pi$
$991$	−12.5559	+	1.80527i	−0.398852	+	0.0573462i	−0.0600295	+	0.998197i	$0.519119\pi$
$992$	−46.0892	+	8.25049i	−1.46334	+	0.261953i
$993$	9.73046	+	5.31323i	0.308787	+	0.168610i
$994$	−1.93810	+	1.07563i	−0.0614729	+	0.0341168i
$995$	6.03626	−	34.4133i	0.191362	−	1.09097i
$996$	42.8557	+	5.56211i	1.35793	+	0.176242i
$997$	−5.92236	−	2.20893i	−0.187563	−	0.0699574i	0.253928	−	0.967223i	$-0.418277\pi$
$997$	−5.92236	−	2.20893i	−0.187563	−	0.0699574i	−0.441491	+	0.897266i	$0.645550\pi$
$998$	−17.7572	+	39.6003i	−0.562095	+	1.25353i
$999$	14.0156	+	9.00729i	0.443435	+	0.284978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.3.12	✓	1360
4.3	odd	2	inner	460.2.w.a.3.40	yes	1360
5.2	odd	4	inner	460.2.w.a.187.23	yes	1360
20.7	even	4	inner	460.2.w.a.187.62	yes	1360
23.8	even	11	inner	460.2.w.a.123.62	yes	1360
92.31	odd	22	inner	460.2.w.a.123.23	yes	1360
115.77	odd	44	inner	460.2.w.a.307.40	yes	1360
460.307	even	44	inner	460.2.w.a.307.12	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.3.12	✓	1360	1.1	even	1	trivial
460.2.w.a.3.40	yes	1360	4.3	odd	2	inner
460.2.w.a.123.23	yes	1360	92.31	odd	22	inner
460.2.w.a.123.62	yes	1360	23.8	even	11	inner
460.2.w.a.187.23	yes	1360	5.2	odd	4	inner
460.2.w.a.187.62	yes	1360	20.7	even	4	inner
460.2.w.a.307.12	yes	1360	460.307	even	44	inner
460.2.w.a.307.40	yes	1360	115.77	odd	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18443 + 0.772733i) q^{2} +(-1.12425 - 3.01422i) q^{3} +(0.805766 - 1.83050i) q^{4} +(1.84293 + 1.26634i) q^{5} +(3.66078 + 2.70140i) q^{6} +(-3.65616 - 0.795348i) q^{7} +(0.460113 + 2.79075i) q^{8} +(-5.55434 + 4.81286i) q^{9} +O(q^{10})\)	\(q+(-1.18443 + 0.772733i) q^{2} +(-1.12425 - 3.01422i) q^{3} +(0.805766 - 1.83050i) q^{4} +(1.84293 + 1.26634i) q^{5} +(3.66078 + 2.70140i) q^{6} +(-3.65616 - 0.795348i) q^{7} +(0.460113 + 2.79075i) q^{8} +(-5.55434 + 4.81286i) q^{9} +(-3.16137 - 0.0757989i) q^{10} +(1.16386 + 0.167337i) q^{11} +(-6.42342 - 0.370822i) q^{12} +(-1.07128 - 4.92459i) q^{13} +(4.94507 - 1.88320i) q^{14} +(1.74511 - 6.97867i) q^{15} +(-2.70148 - 2.94992i) q^{16} +(-4.49365 + 2.45372i) q^{17} +(2.85969 - 9.99254i) q^{18} +(-0.196477 + 0.0576910i) q^{19} +(3.80300 - 2.35312i) q^{20} +(1.71306 + 11.9146i) q^{21} +(-1.50782 + 0.701151i) q^{22} +(-1.94882 + 4.38202i) q^{23} +(7.89466 - 4.52437i) q^{24} +(1.79278 + 4.66754i) q^{25} +(5.07425 + 5.00504i) q^{26} +(12.2808 + 6.70584i) q^{27} +(-4.40190 + 6.05174i) q^{28} +(0.349626 - 1.19072i) q^{29} +(3.32568 + 9.61428i) q^{30} +(-7.52904 + 3.43840i) q^{31} +(5.47922 + 1.40646i) q^{32} +(-0.804070 - 3.69625i) q^{33} +(3.42636 - 6.37866i) q^{34} +(-5.73086 - 6.09570i) q^{35} +(4.33446 + 14.0453i) q^{36} +(1.18764 + 0.0849418i) q^{37} +(0.188135 - 0.220156i) q^{38} +(-13.6394 + 8.76552i) q^{39} +(-2.68608 + 5.72582i) q^{40} +(-0.160371 + 0.185078i) q^{41} +(-11.2358 - 12.7883i) q^{42} +(-0.555599 - 1.48962i) q^{43} +(1.24411 - 1.99561i) q^{44} +(-16.3310 + 1.83610i) q^{45} +(-1.07789 - 6.69613i) q^{46} +(1.59397 + 1.59397i) q^{47} +(-5.85456 + 11.4593i) q^{48} +(6.36748 + 2.90793i) q^{49} +(-5.73019 - 4.14305i) q^{50} +(12.4480 + 10.7863i) q^{51} +(-9.87768 - 2.00709i) q^{52} +(1.39314 + 0.303059i) q^{53} +(-19.7277 + 1.54718i) q^{54} +(1.93300 + 1.78223i) q^{55} +(0.537373 - 10.5694i) q^{56} +(0.394782 + 0.527367i) q^{57} +(0.505998 + 1.68049i) q^{58} +(-3.38710 - 2.17676i) q^{59} +(-11.3683 - 8.81761i) q^{60} +(1.32248 + 2.89582i) q^{61} +(6.26069 - 9.89049i) q^{62} +(24.1354 - 13.1789i) q^{63} +(-7.57659 + 2.56812i) q^{64} +(4.26190 - 10.4323i) q^{65} +(3.80858 + 3.75663i) q^{66} +(-5.88517 + 7.86167i) q^{67} +(0.870705 + 10.2028i) q^{68} +(15.3993 + 0.947695i) q^{69} +(11.4982 + 2.79152i) q^{70} +(-0.414629 + 0.0596147i) q^{71} +(-15.9871 - 13.2863i) q^{72} +(-9.39263 - 5.12876i) q^{73} +(-1.47232 + 0.817122i) q^{74} +(12.0535 - 10.6513i) q^{75} +(-0.0527114 + 0.406138i) q^{76} +(-4.12215 - 1.53748i) q^{77} +(9.38157 - 20.9218i) q^{78} +(7.77924 + 4.99941i) q^{79} +(-1.24305 - 8.85747i) q^{80} +(3.26840 - 22.7322i) q^{81} +(0.0469329 - 0.343137i) q^{82} +(-6.69945 - 0.479154i) q^{83} +(23.1901 + 6.46464i) q^{84} +(-11.3887 - 1.16844i) q^{85} +(1.80915 + 1.33502i) q^{86} +(-3.98215 + 0.284809i) q^{87} +(0.0685092 + 3.32503i) q^{88} +(-15.3759 - 7.02192i) q^{89} +(17.9241 - 14.7942i) q^{90} +18.8571i q^{91} +(6.45101 + 7.09820i) q^{92} +(18.8286 + 18.8286i) q^{93} +(-3.11967 - 0.656240i) q^{94} +(-0.435150 - 0.142486i) q^{95} +(-1.92063 - 18.0968i) q^{96} +(-0.148679 - 2.07880i) q^{97} +(-9.78892 + 1.47611i) q^{98} +(-7.26983 + 4.67204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

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