LMFDB - Embedded newform 650.2.ba.b.73.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(73,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([11, 5]))

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

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

chi := DirichletCharacter("650.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.ba (of order $20$, degree $8$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.13
Character	$\chi$	$=$	650.73
Dual form			650.2.ba.b.187.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.932353 - 0.475057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.203489 - 2.22679i) q^{5} +(0.475057 - 0.932353i) q^{6} +1.00383i q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.11975 + 1.54121i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.932353 - 0.475057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.203489 - 2.22679i) q^{5} +(0.475057 - 0.932353i) q^{6} +1.00383i q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.11975 + 1.54121i) q^{9} +(-1.14425 - 1.92112i) q^{10} +(0.663074 - 4.18649i) q^{11} +(-0.163694 - 1.03352i) q^{12} +(3.58951 + 0.339708i) q^{13} +(0.590038 + 0.812117i) q^{14} +(-0.868129 - 2.17282i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.413553 - 0.811643i) q^{17} +1.90504i q^{18} +(-0.0794376 - 0.0404755i) q^{19} +(-2.05492 - 0.881645i) q^{20} +(0.476878 + 0.935925i) q^{21} +(-1.92432 - 3.77668i) q^{22} +(1.43905 - 9.08579i) q^{23} +(-0.739919 - 0.739919i) q^{24} +(-4.91718 - 0.906254i) q^{25} +(3.10365 - 1.83503i) q^{26} +(-0.802924 + 5.06946i) q^{27} +(0.954701 + 0.310201i) q^{28} +(-0.298702 - 0.0970542i) q^{29} +(-1.97948 - 1.24758i) q^{30} +(-3.30074 + 6.47807i) q^{31} -1.00000 q^{32} +(-1.37060 - 4.21828i) q^{33} +(-0.142501 - 0.899713i) q^{34} +(2.23532 + 0.204269i) q^{35} +(1.11975 + 1.54121i) q^{36} +(-1.30521 + 1.79646i) q^{37} +(-0.0880573 + 0.0139469i) q^{38} +(3.50807 - 1.38850i) q^{39} +(-2.18068 + 0.494586i) q^{40} +(0.577437 + 3.64579i) q^{41} +(0.935925 + 0.476878i) q^{42} +(-2.30495 + 2.30495i) q^{43} +(-3.77668 - 1.92432i) q^{44} +(3.20409 + 2.80708i) q^{45} +(-4.17628 - 8.19641i) q^{46} +(9.27602 + 3.01396i) q^{47} +(-1.03352 - 0.163694i) q^{48} +5.99232 q^{49} +(-4.51077 + 2.15707i) q^{50} -0.953199i q^{51} +(1.43230 - 3.30885i) q^{52} +(-11.8038 + 6.01434i) q^{53} +(2.33017 + 4.57323i) q^{54} +(-9.18750 - 2.32843i) q^{55} +(0.954701 - 0.310201i) q^{56} -0.0932920 q^{57} +(-0.298702 + 0.0970542i) q^{58} +(0.601119 + 3.79531i) q^{59} +(-2.33474 + 0.154201i) q^{60} +(3.46882 - 2.52025i) q^{61} +(1.13736 + 7.18099i) q^{62} +(-1.54712 - 1.12405i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(1.48688 - 7.92396i) q^{65} +(-3.58828 - 2.60704i) q^{66} +(2.74454 + 8.44683i) q^{67} +(-0.644123 - 0.644123i) q^{68} +(-2.97457 - 9.15479i) q^{69} +(1.92848 - 1.14863i) q^{70} +(6.80396 - 3.46679i) q^{71} +(1.81180 + 0.588690i) q^{72} +(2.44622 - 1.77728i) q^{73} +2.22055i q^{74} +(-5.01507 + 1.49100i) q^{75} +(-0.0630420 + 0.0630420i) q^{76} +(4.20253 + 0.665615i) q^{77} +(2.02195 - 3.18531i) q^{78} +(8.55085 + 2.77834i) q^{79} +(-1.47350 + 1.68190i) q^{80} +(-0.106392 - 0.327442i) q^{81} +(2.61010 + 2.61010i) q^{82} +(10.5726 - 3.43525i) q^{83} +(1.03748 - 0.164321i) q^{84} +(-1.72320 - 1.08606i) q^{85} +(-0.509927 + 3.21956i) q^{86} +(-0.324602 + 0.0514119i) q^{87} +(-4.18649 + 0.663074i) q^{88} +(5.56009 + 0.880631i) q^{89} +(4.24212 + 0.387654i) q^{90} +(-0.341010 + 3.60327i) q^{91} +(-8.19641 - 4.17628i) q^{92} +7.60789i q^{93} +(9.27602 - 3.01396i) q^{94} +(-0.106295 + 0.168655i) q^{95} +(-0.932353 + 0.475057i) q^{96} +(-2.13107 + 6.55876i) q^{97} +(4.84789 - 3.52220i) q^{98} +(5.70977 + 5.70977i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9}+O(q^{10}) $ 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9	$ 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9} + 6 q^{13} + 8 q^{15} - 36 q^{16} - 6 q^{17} - 20 q^{19} - 6 q^{21} + 12 q^{23} + 2 q^{25} + 14 q^{26} - 24 q^{27} + 20 q^{29} + 12 q^{30} - 6 q^{31} - 144 q^{32} - 54 q^{33} + 6 q^{34} + 40 q^{35} + 20 q^{36} - 60 q^{37} + 20 q^{39} + 52 q^{41} + 6 q^{42} - 12 q^{43} - 6 q^{45} + 28 q^{46} + 50 q^{47} - 160 q^{49} - 22 q^{50} + 6 q^{52} + 20 q^{53} - 6 q^{54} - 32 q^{55} - 28 q^{57} + 20 q^{58} - 16 q^{59} - 12 q^{60} + 12 q^{61} + 6 q^{62} - 70 q^{63} - 36 q^{64} + 44 q^{65} - 16 q^{66} - 8 q^{67} - 6 q^{68} + 26 q^{69} + 10 q^{70} + 72 q^{71} - 52 q^{73} + 32 q^{75} - 56 q^{77} - 50 q^{78} - 20 q^{79} + 124 q^{81} - 22 q^{82} + 70 q^{83} - 6 q^{84} - 18 q^{85} - 8 q^{86} + 8 q^{87} + 28 q^{89} - 14 q^{90} - 26 q^{91} + 12 q^{92} + 50 q^{94} - 46 q^{95} + 28 q^{97} - 20 q^{98} + 40 q^{99}+O(q^{100}) $ 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9 + 6 * q^13 + 8 * q^15 - 36 * q^16 - 6 * q^17 - 20 * q^19 - 6 * q^21 + 12 * q^23 + 2 * q^25 + 14 * q^26 - 24 * q^27 + 20 * q^29 + 12 * q^30 - 6 * q^31 - 144 * q^32 - 54 * q^33 + 6 * q^34 + 40 * q^35 + 20 * q^36 - 60 * q^37 + 20 * q^39 + 52 * q^41 + 6 * q^42 - 12 * q^43 - 6 * q^45 + 28 * q^46 + 50 * q^47 - 160 * q^49 - 22 * q^50 + 6 * q^52 + 20 * q^53 - 6 * q^54 - 32 * q^55 - 28 * q^57 + 20 * q^58 - 16 * q^59 - 12 * q^60 + 12 * q^61 + 6 * q^62 - 70 * q^63 - 36 * q^64 + 44 * q^65 - 16 * q^66 - 8 * q^67 - 6 * q^68 + 26 * q^69 + 10 * q^70 + 72 * q^71 - 52 * q^73 + 32 * q^75 - 56 * q^77 - 50 * q^78 - 20 * q^79 + 124 * q^81 - 22 * q^82 + 70 * q^83 - 6 * q^84 - 18 * q^85 - 8 * q^86 + 8 * q^87 + 28 * q^89 - 14 * q^90 - 26 * q^91 + 12 * q^92 + 50 * q^94 - 46 * q^95 + 28 * q^97 - 20 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.932353	−	0.475057i	0.538294	−	0.274274i	−0.163636	−	0.986521i	$-0.552322\pi$
$3$	0.932353	−	0.475057i	0.538294	−	0.274274i	0.701930	+	0.712246i	$0.252322\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.203489	−	2.22679i	0.0910030	−	0.995851i
$5$	0.203489	−	2.22679i	0.0910030	−	0.995851i
$6$	0.475057	−	0.932353i	0.193941	−	0.380631i
$7$			1.00383i			0.379413i	0.981841	+	0.189706i	$0.0607536\pi$
$7$			1.00383i			0.379413i	−0.981841	+	0.189706i	$0.939246\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−1.11975	+	1.54121i	−0.373251	+	0.513736i
$10$	−1.14425	−	1.92112i	−0.361843	−	0.607511i
$11$	0.663074	−	4.18649i	0.199924	−	1.26227i	−0.659771	−	0.751467i	$-0.729347\pi$
$11$	0.663074	−	4.18649i	0.199924	−	1.26227i	0.859696	−	0.510807i	$-0.170653\pi$
$12$	−0.163694	−	1.03352i	−0.0472543	−	0.298352i
$13$	3.58951	+	0.339708i	0.995552	+	0.0942181i
$13$	3.58951	+	0.339708i	0.995552	+	0.0942181i
$14$	0.590038	+	0.812117i	0.157694	+	0.217047i
$15$	−0.868129	−	2.17282i	−0.224150	−	0.561020i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.413553	−	0.811643i	0.100301	−	0.196852i	−0.835403	−	0.549638i	$-0.814766\pi$
$17$	0.413553	−	0.811643i	0.100301	−	0.196852i	0.935704	+	0.352786i	$0.114766\pi$
$18$			1.90504i			0.449022i
$19$	−0.0794376	−	0.0404755i	−0.0182242	−	0.00928571i	0.444855	−	0.895603i	$-0.353255\pi$
$19$	−0.0794376	−	0.0404755i	−0.0182242	−	0.00928571i	−0.463079	+	0.886317i	$0.653255\pi$
$20$	−2.05492	−	0.881645i	−0.459494	−	0.197142i
$21$	0.476878	+	0.935925i	0.104063	+	0.204236i
$22$	−1.92432	−	3.77668i	−0.410266	−	0.805192i
$23$	1.43905	−	9.08579i	0.300062	−	1.89452i	−0.129662	−	0.991558i	$-0.541389\pi$
$23$	1.43905	−	9.08579i	0.300062	−	1.89452i	0.429724	−	0.902960i	$-0.358611\pi$
$24$	−0.739919	−	0.739919i	−0.151035	−	0.151035i
$25$	−4.91718	−	0.906254i	−0.983437	−	0.181251i
$26$	3.10365	−	1.83503i	0.608676	−	0.359880i
$27$	−0.802924	+	5.06946i	−0.154523	+	0.975618i
$28$	0.954701	+	0.310201i	0.180422	+	0.0586225i
$29$	−0.298702	−	0.0970542i	−0.0554676	−	0.0180225i	0.281152	−	0.959663i	$-0.409284\pi$
$29$	−0.298702	−	0.0970542i	−0.0554676	−	0.0180225i	−0.336619	+	0.941641i	$0.609284\pi$
$30$	−1.97948	−	1.24758i	−0.361403	−	0.227775i
$31$	−3.30074	+	6.47807i	−0.592831	+	1.16350i	0.378464	+	0.925616i	$0.376452\pi$
$31$	−3.30074	+	6.47807i	−0.592831	+	1.16350i	−0.971295	+	0.237880i	$0.923548\pi$
$32$	−1.00000			−0.176777
$33$	−1.37060	−	4.21828i	−0.238591	−	0.734308i
$34$	−0.142501	−	0.899713i	−0.0244386	−	0.154300i
$35$	2.23532	+	0.204269i	0.377839	+	0.0345277i
$36$	1.11975	+	1.54121i	0.186626	+	0.256868i
$37$	−1.30521	+	1.79646i	−0.214574	+	0.295336i	−0.902713	−	0.430243i	$-0.858428\pi$
$37$	−1.30521	+	1.79646i	−0.214574	+	0.295336i	0.688139	+	0.725579i	$0.258428\pi$
$38$	−0.0880573	+	0.0139469i	−0.0142848	+	0.00226249i
$39$	3.50807	−	1.38850i	0.561741	−	0.222337i
$40$	−2.18068	+	0.494586i	−0.344796	+	0.0782010i
$41$	0.577437	+	3.64579i	0.0901805	+	0.569377i	0.990860	+	0.134893i	$0.0430692\pi$
$41$	0.577437	+	3.64579i	0.0901805	+	0.569377i	−0.900680	+	0.434484i	$0.856931\pi$
$42$	0.935925	+	0.476878i	0.144416	+	0.0735838i
$43$	−2.30495	+	2.30495i	−0.351501	+	0.351501i	−0.860668	−	0.509167i	$-0.829954\pi$
$43$	−2.30495	+	2.30495i	−0.351501	+	0.351501i	0.509167	+	0.860668i	$0.329954\pi$
$44$	−3.77668	−	1.92432i	−0.569357	−	0.290102i
$45$	3.20409	+	2.80708i	0.477638	+	0.418454i
$46$	−4.17628	−	8.19641i	−0.615759	−	1.20849i
$47$	9.27602	+	3.01396i	1.35305	+	0.439631i	0.893716	−	0.448634i	$-0.148089\pi$
$47$	9.27602	+	3.01396i	1.35305	+	0.439631i	0.459331	+	0.888265i	$0.348089\pi$
$48$	−1.03352	−	0.163694i	−0.149176	−	0.0236271i
$49$	5.99232			0.856046
$50$	−4.51077	+	2.15707i	−0.637919	+	0.305056i
$51$		−	0.953199i		−	0.133475i
$52$	1.43230	−	3.30885i	0.198625	−	0.458855i
$53$	−11.8038	+	6.01434i	−1.62138	+	0.826134i	−0.622320	+	0.782763i	$0.713810\pi$
$53$	−11.8038	+	6.01434i	−1.62138	+	0.826134i	−0.999059	+	0.0433706i	$0.986190\pi$
$54$	2.33017	+	4.57323i	0.317097	+	0.622337i
$55$	−9.18750	−	2.32843i	−1.23884	−	0.313965i
$56$	0.954701	−	0.310201i	0.127577	−	0.0414524i
$57$	−0.0932920			−0.0123568
$58$	−0.298702	+	0.0970542i	−0.0392215	+	0.0127438i
$59$	0.601119	+	3.79531i	0.0782590	+	0.494108i	0.995421	+	0.0955923i	$0.0304745\pi$
$59$	0.601119	+	3.79531i	0.0782590	+	0.494108i	−0.917162	+	0.398516i	$0.869525\pi$
$60$	−2.33474	+	0.154201i	−0.301414	+	0.0199073i
$61$	3.46882	−	2.52025i	0.444137	−	0.322684i	−0.343140	−	0.939284i	$-0.611490\pi$
$61$	3.46882	−	2.52025i	0.444137	−	0.322684i	0.787277	+	0.616600i	$0.211490\pi$
$62$	1.13736	+	7.18099i	0.144445	+	0.911987i
$63$	−1.54712	−	1.12405i	−0.194918	−	0.141616i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	1.48688	−	7.92396i	0.184425	−	0.982847i
$66$	−3.58828	−	2.60704i	−0.441687	−	0.320904i
$67$	2.74454	+	8.44683i	0.335299	+	1.03194i	0.966574	+	0.256386i	$0.0825318\pi$
$67$	2.74454	+	8.44683i	0.335299	+	1.03194i	−0.631275	+	0.775559i	$0.717468\pi$
$68$	−0.644123	−	0.644123i	−0.0781114	−	0.0781114i
$69$	−2.97457	−	9.15479i	−0.358096	−	1.10211i
$70$	1.92848	−	1.14863i	0.230497	−	0.137288i
$71$	6.80396	−	3.46679i	0.807482	−	0.411432i	−0.000966729	−	1.00000i	$-0.500308\pi$
$71$	6.80396	−	3.46679i	0.807482	−	0.411432i	0.808448	+	0.588567i	$0.200308\pi$
$72$	1.81180	+	0.588690i	0.213523	+	0.0693777i
$73$	2.44622	−	1.77728i	0.286309	−	0.208015i	−0.435356	−	0.900259i	$-0.643377\pi$
$73$	2.44622	−	1.77728i	0.286309	−	0.208015i	0.721664	+	0.692243i	$0.243377\pi$
$74$			2.22055i			0.258133i
$75$	−5.01507	+	1.49100i	−0.579091	+	0.172165i
$76$	−0.0630420	+	0.0630420i	−0.00723142	+	0.00723142i
$77$	4.20253	+	0.665615i	0.478923	+	0.0758539i
$78$	2.02195	−	3.18531i	0.228941	−	0.360665i
$79$	8.55085	+	2.77834i	0.962046	+	0.312588i	0.747601	−	0.664148i	$-0.231206\pi$
$79$	8.55085	+	2.77834i	0.962046	+	0.312588i	0.214445	+	0.976736i	$0.431206\pi$
$80$	−1.47350	+	1.68190i	−0.164742	+	0.188042i
$81$	−0.106392	−	0.327442i	−0.0118214	−	0.0363824i
$82$	2.61010	+	2.61010i	0.288237	+	0.288237i
$83$	10.5726	−	3.43525i	1.16050	−	0.377068i	0.335408	−	0.942073i	$-0.391126\pi$
$83$	10.5726	−	3.43525i	1.16050	−	0.377068i	0.825087	+	0.565005i	$0.191126\pi$
$84$	1.03748	−	0.164321i	0.113198	−	0.0179289i
$85$	−1.72320	−	1.08606i	−0.186908	−	0.117799i
$86$	−0.509927	+	3.21956i	−0.0549869	+	0.347174i
$87$	−0.324602	+	0.0514119i	−0.0348010	+	0.00551193i
$88$	−4.18649	+	0.663074i	−0.446281	+	0.0706840i
$89$	5.56009	+	0.880631i	0.589368	+	0.0933467i	0.443994	−	0.896030i	$-0.353561\pi$
$89$	5.56009	+	0.880631i	0.589368	+	0.0933467i	0.145374	+	0.989377i	$0.453561\pi$
$90$	4.24212	+	0.387654i	0.447159	+	0.0408623i
$91$	−0.341010	+	3.60327i	−0.0357475	+	0.377725i
$92$	−8.19641	−	4.17628i	−0.854535	−	0.435407i
$93$			7.60789i			0.788901i
$94$	9.27602	−	3.01396i	0.956748	−	0.310866i
$95$	−0.106295	+	0.168655i	−0.0109056	+	0.0173036i
$96$	−0.932353	+	0.475057i	−0.0951578	+	0.0484853i
$97$	−2.13107	+	6.55876i	−0.216377	+	0.665941i	0.782676	+	0.622430i	$0.213854\pi$
$97$	−2.13107	+	6.55876i	−0.216377	+	0.665941i	−0.999053	+	0.0435111i	$0.986146\pi$
$98$	4.84789	−	3.52220i	0.489711	−	0.355796i
$99$	5.70977	+	5.70977i	0.573854	+	0.573854i
$100$	−2.38139	+	4.39647i	−0.238139	+	0.439647i
$101$		−	7.40477i		−	0.736802i	−0.929667	−	0.368401i	$-0.879905\pi$
$101$		−	7.40477i		−	0.736802i	0.929667	−	0.368401i	$-0.120095\pi$
$102$	−0.560276	−	0.771154i	−0.0554756	−	0.0763556i
$103$	2.13162	+	4.18354i	0.210035	+	0.412216i	0.971858	−	0.235569i	$-0.0756954\pi$
$103$	2.13162	+	4.18354i	0.210035	+	0.412216i	−0.761823	+	0.647785i	$0.775695\pi$
$104$	−0.786139	−	3.51880i	−0.0770872	−	0.345047i
$105$	2.18115	−	0.871456i	0.212858	−	0.0850454i
$106$	−6.01434	+	11.8038i	−0.584165	+	1.14649i
$107$	−9.99181	+	9.99181i	−0.965945	+	0.965945i	−0.999439	−	0.0334944i	$-0.989336\pi$
$107$	−9.99181	+	9.99181i	−0.965945	+	0.965945i	0.0334944	+	0.999439i	$0.489336\pi$
$108$	4.57323	+	2.33017i	0.440059	+	0.224221i
$109$	−6.27765	+	0.994282i	−0.601289	+	0.0952349i	−0.449656	−	0.893202i	$-0.648453\pi$
$109$	−6.27765	+	0.994282i	−0.601289	+	0.0952349i	−0.151634	+	0.988437i	$0.548453\pi$
$110$	−8.80146	+	3.51654i	−0.839186	+	0.335288i
$111$	−0.363490	+	2.29498i	−0.0345009	+	0.217830i
$112$	0.590038	−	0.812117i	0.0557533	−	0.0767379i
$113$	−1.25588	−	7.92930i	−0.118143	−	0.745926i	−0.973635	−	0.228110i	$-0.926745\pi$
$113$	−1.25588	−	7.92930i	−0.118143	−	0.745926i	0.855492	−	0.517816i	$-0.173255\pi$
$114$	−0.0754748	+	0.0548357i	−0.00706887	+	0.00513583i
$115$	−19.9393	−	5.05331i	−1.85935	−	0.471224i
$116$	−0.184608	+	0.254091i	−0.0171404	+	0.0235918i
$117$	−4.54293	+	5.15180i	−0.419994	+	0.476284i
$118$	2.71714	+	2.71714i	0.250133	+	0.250133i
$119$	0.814753	+	0.415138i	0.0746883	+	0.0380556i
$120$	−1.79821	+	1.49708i	−0.164153	+	0.136664i
$121$	−6.62538	−	2.15272i	−0.602307	−	0.195701i
$122$	1.32497	−	4.07784i	0.119957	−	0.369190i
$123$	2.27034	+	3.12485i	0.204709	+	0.281758i
$124$	5.14102	+	5.14102i	0.461678	+	0.461678i
$125$	−3.01863	+	10.7651i	−0.269994	+	0.962862i
$126$	−1.91234			−0.170365
$127$	13.4501	+	2.13028i	1.19350	+	0.189032i	0.721404	−	0.692515i	$-0.243497\pi$
$127$	13.4501	+	2.13028i	1.19350	+	0.189032i	0.472097	+	0.881547i	$0.343497\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−1.05404	+	3.24401i	−0.0928032	+	0.285619i
$130$	−3.45467	−	7.28459i	−0.302995	−	0.638901i
$131$	−1.17550	−	3.61781i	−0.102704	−	0.316089i	0.886481	−	0.462765i	$-0.153143\pi$
$131$	−1.17550	−	3.61781i	−0.102704	−	0.316089i	−0.989185	+	0.146676i	$0.953143\pi$
$132$	−4.43536			−0.386049
$133$	0.0406306	−	0.0797420i	0.00352312	−	0.00691451i
$134$	7.18530	+	5.22043i	0.620716	+	0.450976i
$135$	11.1252	+	2.81952i	0.957508	+	0.242666i
$136$	−0.899713	−	0.142501i	−0.0771498	−	0.0122193i
$137$	−5.18345	+	7.13441i	−0.442852	+	0.609534i	−0.970843	−	0.239716i	$-0.922946\pi$
$137$	−5.18345	+	7.13441i	−0.442852	+	0.609534i	0.527991	+	0.849250i	$0.322946\pi$
$138$	−7.78753	−	5.65797i	−0.662919	−	0.481639i
$139$	−6.98966	−	9.62045i	−0.592856	−	0.815996i	0.402175	−	0.915563i	$-0.368254\pi$
$139$	−6.98966	−	9.62045i	−0.592856	−	0.815996i	−0.995031	+	0.0995669i	$0.968254\pi$
$140$	0.885024	−	2.06280i	0.0747982	−	0.174338i
$141$	10.0803	−	1.59657i	0.848916	−	0.134455i
$142$	3.46679	−	6.80396i	0.290927	−	0.570976i
$143$	3.80230	−	14.8022i	0.317964	−	1.23782i
$144$	1.81180	−	0.588690i	0.150983	−	0.0490575i
$145$	−0.276902	+	0.645397i	−0.0229954	+	0.0535973i
$146$	0.934374	−	2.87571i	0.0773293	−	0.237995i
$147$	5.58696	−	2.84670i	0.460804	−	0.234792i
$148$	1.30521	+	1.79646i	0.107287	+	0.147668i
$149$	−10.8519	+	10.8519i	−0.889024	+	0.889024i	−0.994429	−	0.105405i	$-0.966386\pi$
$149$	−10.8519	+	10.8519i	−0.889024	+	0.889024i	0.105405	+	0.994429i	$0.466386\pi$
$150$	−3.18089	+	4.15403i	−0.259719	+	0.339175i
$151$	6.53440	−	6.53440i	0.531762	−	0.531762i	−0.389334	−	0.921096i	$-0.627295\pi$
$151$	6.53440	−	6.53440i	0.531762	−	0.531762i	0.921096	+	0.389334i	$0.127295\pi$
$152$	−0.0139469	+	0.0880573i	−0.00113124	+	0.00714239i
$153$	0.787834	+	1.54621i	0.0636926	+	0.125004i
$154$	3.79116	−	1.93169i	0.305500	−	0.155660i
$155$	13.7536	+	8.66827i	1.10472	+	0.696252i
$156$	−0.236485	−	3.76544i	−0.0189339	−	0.301477i
$157$	−12.0648	+	12.0648i	−0.962873	+	0.962873i	−0.999335	−	0.0364618i	$-0.988391\pi$
$157$	−12.0648	+	12.0648i	−0.962873	+	0.962873i	0.0364618	+	0.999335i	$0.488391\pi$
$158$	8.55085	−	2.77834i	0.680269	−	0.221033i
$159$	−8.14816	+	11.2150i	−0.646191	+	0.889406i
$160$	−0.203489	+	2.22679i	−0.0160872	+	0.176043i
$161$	9.12061	+	1.44456i	0.718805	+	0.113847i
$162$	−0.278539	−	0.202370i	−0.0218841	−	0.0158997i
$163$	−15.6813	−	11.3931i	−1.22825	−	0.892379i	−0.231496	−	0.972836i	$-0.574362\pi$
$163$	−15.6813	−	11.3931i	−1.22825	−	0.892379i	−0.996758	+	0.0804570i	$0.974362\pi$
$164$	3.64579	+	0.577437i	0.284689	+	0.0450902i
$165$	−9.67212	+	2.19367i	−0.752974	+	0.170777i
$166$	6.53424	−	8.99360i	0.507155	−	0.698039i
$167$	−15.5937	+	5.06670i	−1.20668	+	0.392073i	−0.842213	−	0.539145i	$-0.818747\pi$
$167$	−15.5937	+	5.06670i	−1.20668	+	0.392073i	−0.364463	+	0.931218i	$0.618747\pi$
$168$	0.742755	−	0.742755i	0.0573048	−	0.0573048i
$169$	12.7692	+	2.43877i	0.982246	+	0.187598i
$170$	−2.03247	+	0.134237i	−0.155883	+	0.0102955i
$171$	0.151332	−	0.0771074i	0.0115726	−	0.00589655i
$172$	1.47987	+	2.90440i	0.112839	+	0.221459i
$173$	−2.59150	+	16.3621i	−0.197028	+	1.24399i	0.668723	+	0.743512i	$0.266841\pi$
$173$	−2.59150	+	16.3621i	−0.197028	+	1.24399i	−0.865751	+	0.500475i	$0.833159\pi$
$174$	−0.232389	+	0.232389i	−0.0176174	+	0.0176174i
$175$	0.909727	−	4.93603i	0.0687689	−	0.373129i
$176$	−2.99719	+	2.99719i	−0.225922	+	0.225922i
$177$	2.36345	+	3.25300i	0.177648	+	0.244511i
$178$	5.01583	−	2.55569i	0.375952	−	0.191557i
$179$	7.63715	−	23.5047i	0.570827	−	1.75683i	−0.0791393	−	0.996864i	$-0.525217\pi$
$179$	7.63715	−	23.5047i	0.570827	−	1.75683i	0.649967	−	0.759963i	$-0.274783\pi$
$180$	3.65981	−	2.17984i	0.272786	−	0.162476i
$181$	5.40634	−	1.75663i	0.401850	−	0.130569i	−0.101117	−	0.994875i	$-0.532242\pi$
$181$	5.40634	−	1.75663i	0.401850	−	0.130569i	0.502967	+	0.864305i	$0.332242\pi$
$182$	1.84206	+	3.11555i	0.136543	+	0.230940i
$183$	2.03690	−	3.99765i	0.150572	−	0.295514i
$184$	−9.08579	+	1.43905i	−0.669813	+	0.106088i
$185$	3.73475	+	3.27198i	0.274584	+	0.240561i
$186$	4.47180	+	6.15491i	0.327888	+	0.451300i
$187$	−3.12372	−	2.26951i	−0.228429	−	0.165963i
$188$	5.73289	−	7.89065i	0.418114	−	0.575485i
$189$	−5.08889	−	0.806000i	−0.370162	−	0.0586279i
$190$	0.0131381	+	0.198923i	0.000953141	+	0.0144314i
$191$	10.9674	+	7.96832i	0.793576	+	0.576567i	0.909023	−	0.416747i	$-0.136830\pi$
$191$	10.9674	+	7.96832i	0.793576	+	0.576567i	−0.115446	+	0.993314i	$0.536830\pi$
$192$	−0.475057	+	0.932353i	−0.0342843	+	0.0672867i
$193$	−0.352589			−0.0253799			−0.0126900	−	0.999919i	$-0.504039\pi$
$193$	−0.352589			−0.0253799			−0.0126900	+	0.999919i	$0.504039\pi$
$194$	2.13107	+	6.55876i	0.153002	+	0.470891i
$195$	−2.37804	−	8.09428i	−0.170295	−	0.579644i
$196$	1.85173	−	5.69904i	0.132266	−	0.407074i
$197$	−3.58585	+	11.0361i	−0.255481	+	0.786291i	0.738253	+	0.674524i	$0.235651\pi$
$197$	−3.58585	+	11.0361i	−0.255481	+	0.786291i	−0.993734	+	0.111767i	$0.964349\pi$
$198$	7.97542	+	1.26318i	0.566788	+	0.0897705i
$199$	10.8899			0.771962			0.385981	−	0.922507i	$-0.373863\pi$
$199$	10.8899			0.771962			0.385981	+	0.922507i	$0.373863\pi$
$200$	0.657595	+	4.95657i	0.0464990	+	0.350482i
$201$	6.57161	+	6.57161i	0.463526	+	0.463526i
$202$	−4.35241	−	5.99058i	−0.306235	−	0.421496i
$203$	0.0974261	−	0.299847i	0.00683797	−	0.0210451i
$204$	−0.906546	−	0.294555i	−0.0634709	−	0.0206229i
$205$	8.23592	−	0.543952i	0.575221	−	0.0379913i
$206$	4.18354	+	2.13162i	0.291481	+	0.148517i
$207$	12.3917	+	12.3917i	0.861284	+	0.861284i
$208$	−2.70430	−	2.38469i	−0.187510	−	0.165349i
$209$	−0.222123	+	0.305726i	−0.0153646	+	0.0211475i
$210$	1.25236	−	1.98707i	0.0864208	−	0.137121i
$211$	3.05582	−	2.22018i	0.210371	−	0.152844i	−0.477610	−	0.878572i	$-0.658497\pi$
$211$	3.05582	−	2.22018i	0.210371	−	0.152844i	0.687982	+	0.725728i	$0.258497\pi$
$212$	2.07240	+	13.0846i	0.142333	+	0.898656i
$213$	4.69677	−	6.46454i	0.321817	−	0.442943i
$214$	−2.21051	+	13.9566i	−0.151107	+	0.954052i
$215$	4.66360	+	5.60166i	0.318055	+	0.382030i
$216$	5.06946	−	0.802924i	0.344933	−	0.0546320i
$217$	−6.50289	−	3.31339i	−0.441445	−	0.224928i
$218$	−4.49430	+	4.49430i	−0.304392	+	0.304392i
$219$	1.43643	−	2.81915i	0.0970649	−	0.190501i
$220$	−5.05356	+	8.01830i	−0.340711	+	0.540594i
$221$	1.76017	−	2.77292i	0.118402	−	0.186526i
$222$	1.05489	+	2.07033i	0.0707994	+	0.138952i
$223$	−0.383124	−	0.527325i	−0.0256559	−	0.0353123i	0.795996	−	0.605301i	$-0.206947\pi$
$223$	−0.383124	−	0.527325i	−0.0256559	−	0.0353123i	−0.821652	+	0.569989i	$0.806947\pi$
$224$		−	1.00383i		−	0.0670714i
$225$	6.90276	−	6.56363i	0.460184	−	0.437575i
$226$	−5.67675	−	5.67675i	−0.377612	−	0.377612i
$227$	−3.51458	+	2.55349i	−0.233271	+	0.169481i	−0.698280	−	0.715825i	$-0.746051\pi$
$227$	−3.51458	+	2.55349i	−0.233271	+	0.169481i	0.465009	+	0.885306i	$0.346051\pi$
$228$	−0.0288288	+	0.0887260i	−0.00190924	+	0.00587602i
$229$	−22.6233	+	11.5272i	−1.49499	+	0.761736i	−0.994572	−	0.104047i	$-0.966821\pi$
$229$	−22.6233	+	11.5272i	−1.49499	+	0.761736i	−0.500419	+	0.865783i	$0.666821\pi$
$230$	−19.1015	+	7.63182i	−1.25952	+	0.503227i
$231$	4.23444	−	1.37585i	0.278606	−	0.0905246i
$232$			0.314074i			0.0206200i
$233$	−25.3275	−	12.9050i	−1.65926	−	0.845436i	−0.995211	−	0.0977479i	$-0.968836\pi$
$233$	−25.3275	−	12.9050i	−1.65926	−	0.845436i	−0.664050	−	0.747688i	$-0.731164\pi$
$234$	−0.647157	+	6.83816i	−0.0423060	+	0.447025i
$235$	8.59902	−	20.0424i	0.560938	−	1.30742i
$236$	3.79531	+	0.601119i	0.247054	+	0.0391295i
$237$	9.29228	−	1.47175i	0.603599	−	0.0956006i
$238$	0.903161	−	0.143047i	0.0585432	−	0.00927234i
$239$	0.544328	−	3.43675i	0.0352096	−	0.222305i	−0.963809	−	0.266593i	$-0.914102\pi$
$239$	0.544328	−	3.43675i	0.0352096	−	0.222305i	0.999019	+	0.0442883i	$0.0141020\pi$
$240$	−0.574821	+	2.26812i	−0.0371045	+	0.146407i
$241$	−20.1144	+	3.18581i	−1.29569	+	0.205216i	−0.765924	−	0.642931i	$-0.777718\pi$
$241$	−20.1144	+	3.18581i	−1.29569	+	0.205216i	−0.529761	+	0.848147i	$0.677718\pi$
$242$	−6.62538	+	2.15272i	−0.425895	+	0.138382i
$243$	−11.1427	−	11.1427i	−0.714808	−	0.714808i
$244$	−1.32497	−	4.07784i	−0.0848226	−	0.261057i
$245$	1.21937	−	13.3436i	0.0779027	−	0.852494i
$246$	3.67348	+	1.19359i	0.234213	+	0.0761003i
$247$	−0.271392	−	0.172273i	−0.0172683	−	0.0109615i
$248$	7.18099	+	1.13736i	0.455994	+	0.0722223i
$249$	8.22546	−	8.22546i	0.521268	−	0.521268i
$250$	3.88546	+	10.4835i	0.245738	+	0.663033i
$251$		−	4.83835i		−	0.305394i	−0.988273	−	0.152697i	$-0.951204\pi$
$251$		−	4.83835i		−	0.305394i	0.988273	−	0.152697i	$-0.0487958\pi$
$252$	−1.54712	+	1.12405i	−0.0974591	+	0.0708082i
$253$	−37.0833	−	12.0491i	−2.33141	−	0.757521i
$254$	12.1335	−	6.18232i	0.761322	−	0.387913i
$255$	−2.12257	−	0.193965i	−0.132921	−	0.0121466i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−16.3714	−	16.3714i	−1.02122	−	1.02122i	−0.999770	−	0.0214470i	$-0.993173\pi$
$257$	−16.3714	−	16.3714i	−1.02122	−	1.02122i	−0.0214470	−	0.999770i	$-0.506827\pi$
$258$	1.05404	+	3.24401i	0.0656217	+	0.201963i
$259$	−1.80335	−	1.31021i	−0.112054	−	0.0814123i
$260$	−7.07666	−	3.86275i	−0.438876	−	0.239558i
$261$	0.484054	−	0.351686i	0.0299622	−	0.0217688i
$262$	−3.07749	−	2.23593i	−0.190128	−	0.138136i
$263$	1.63683	+	10.3345i	0.100931	+	0.637253i	0.985348	+	0.170556i	$0.0545563\pi$
$263$	1.63683	+	10.3345i	0.100931	+	0.637253i	−0.884417	+	0.466697i	$0.845444\pi$
$264$	−3.58828	+	2.60704i	−0.220844	+	0.160452i
$265$	10.9907	+	27.5085i	0.675156	+	1.68983i
$266$	−0.0140003	−	0.0883947i	−0.000858416	−	0.00541983i
$267$	5.60231	−	1.82030i	0.342856	−	0.111401i
$268$	8.88153			0.542526
$269$	18.1623	−	5.90128i	1.10737	−	0.359808i	0.302438	−	0.953169i	$-0.402200\pi$
$269$	18.1623	−	5.90128i	1.10737	−	0.359808i	0.804936	+	0.593362i	$0.202200\pi$
$270$	10.6578	−	4.25821i	0.648612	−	0.259146i
$271$	−7.72973	−	15.1705i	−0.469548	−	0.921539i	−0.997390	−	0.0721972i	$-0.976999\pi$
$271$	−7.72973	−	15.1705i	−0.469548	−	0.921539i	0.527843	−	0.849342i	$-0.323001\pi$
$272$	−0.811643	+	0.413553i	−0.0492131	+	0.0250753i
$273$	1.39382	+	3.52151i	0.0843577	+	0.213132i
$274$			8.81861i			0.532752i
$275$	−7.05448	+	19.9848i	−0.425401	+	1.20513i
$276$	−9.62592			−0.579412
$277$	−24.1847	−	3.83048i	−1.45312	−	0.230151i	−0.620590	−	0.784135i	$-0.713107\pi$
$277$	−24.1847	−	3.83048i	−1.45312	−	0.230151i	−0.832528	+	0.553984i	$0.813107\pi$
$278$	−11.3095	−	3.67468i	−0.678300	−	0.220393i
$279$	−6.28804	−	12.3410i	−0.376455	−	0.738835i
$280$	−0.496482	−	2.18904i	−0.0296705	−	0.130820i
$281$	27.3566	+	13.9389i	1.63196	+	0.831523i	0.998323	+	0.0578897i	$0.0184372\pi$
$281$	27.3566	+	13.9389i	1.63196	+	0.831523i	0.633633	+	0.773634i	$0.281563\pi$
$282$	7.21671	−	7.21671i	0.429749	−	0.429749i
$283$	1.54190	+	0.785635i	0.0916562	+	0.0467012i	0.499218	−	0.866477i	$-0.333621\pi$
$283$	1.54190	+	0.785635i	0.0916562	+	0.0467012i	−0.407561	+	0.913178i	$0.633621\pi$
$284$	−1.19457	−	7.54225i	−0.0708850	−	0.447550i
$285$	−0.0189839	+	0.207742i	−0.00112451	+	0.0123056i
$286$	−5.62439	−	14.2102i	−0.332577	−	0.840264i
$287$	−3.65976	+	0.579650i	−0.216029	+	0.0342156i
$288$	1.11975	−	1.54121i	0.0659821	−	0.0908166i
$289$	9.50461	+	13.0820i	0.559095	+	0.769528i
$290$	0.155337	+	0.684896i	0.00912169	+	0.0402185i
$291$	1.12888	+	7.12745i	0.0661760	+	0.417819i
$292$	−0.934374	−	2.87571i	−0.0546801	−	0.168288i
$293$	1.40860			0.0822913			0.0411456	−	0.999153i	$-0.486899\pi$
$293$	1.40860			0.0822913			0.0411456	+	0.999153i	$0.486899\pi$
$294$	2.84670	−	5.58696i	0.166023	−	0.325838i
$295$	8.57369	−	0.566261i	0.499179	−	0.0329690i
$296$	2.11187	+	0.686187i	0.122750	+	0.0398838i
$297$	20.6908	+	6.72286i	1.20060	+	0.390100i
$298$	−2.40079	+	15.1580i	−0.139074	+	0.878079i
$299$	8.25200	−	32.1247i	0.477225	−	1.85782i
$300$	−0.131720	+	5.23036i	−0.00760488	+	0.301975i
$301$	−2.31378	−	2.31378i	−0.133364	−	0.133364i
$302$	1.44562	−	9.12727i	0.0831859	−	0.525215i
$303$	−3.51769	−	6.90386i	−0.202086	−	0.396616i
$304$	0.0404755	+	0.0794376i	0.00232143	+	0.00455606i
$305$	−4.90619	−	8.23717i	−0.280928	−	0.471659i
$306$	1.54621	+	0.787834i	0.0883910	+	0.0450375i
$307$		−	9.74312i		−	0.556069i	−0.960571	−	0.278035i	$-0.910317\pi$
$307$		−	9.74312i		−	0.556069i	0.960571	−	0.278035i	$-0.0896830\pi$
$308$	1.93169	−	3.79116i	0.110068	−	0.216021i
$309$	3.97484	+	2.88789i	0.226121	+	0.164286i
$310$	16.2220	−	1.07140i	0.921348	−	0.0608517i
$311$	−12.1261	−	16.6902i	−0.687611	−	0.946415i	0.312383	−	0.949956i	$-0.398873\pi$
$311$	−12.1261	−	16.6902i	−0.687611	−	0.946415i	−0.999994	+	0.00354122i	$0.998873\pi$
$312$	−2.40459	−	2.90731i	−0.136133	−	0.164594i
$313$	−4.55349	−	28.7496i	−0.257378	−	1.62502i	−0.690253	−	0.723568i	$-0.742501\pi$
$313$	−4.55349	−	28.7496i	−0.257378	−	1.62502i	0.432875	−	0.901454i	$-0.357499\pi$
$314$	−2.66911	+	16.8521i	−0.150627	+	0.951019i
$315$	−2.81783	+	3.21637i	−0.158767	+	0.181222i
$316$	5.28472	−	7.27379i	0.297289	−	0.409183i
$317$	5.40187	+	16.6253i	0.303399	+	0.933768i	0.980270	+	0.197665i	$0.0633359\pi$
$317$	5.40187	+	16.6253i	0.303399	+	0.933768i	−0.676870	+	0.736102i	$0.736664\pi$
$318$			13.8625i			0.777369i
$319$	−0.604378	+	1.18616i	−0.0338387	+	0.0664121i
$320$	1.14425	+	1.92112i	0.0639654	+	0.107394i
$321$	−4.56921	+	14.0626i	−0.255028	+	0.784896i
$322$	8.22782	−	4.19228i	0.458519	−	0.233627i
$323$	−0.0657033	+	0.0477362i	−0.00365583	+	0.00265611i
$324$	−0.344293			−0.0191274
$325$	−17.3424	−	4.92342i	−0.961985	−	0.273102i
$326$	−19.3832			−1.07353
$327$	−5.38064	+	3.90926i	−0.297550	+	0.216183i
$328$	3.28892	−	1.67579i	0.181600	−	0.0925299i
$329$	−3.02551	+	9.31156i	−0.166802	+	0.513363i
$330$	−6.53551	+	7.45985i	−0.359768	+	0.410651i
$331$	−3.68679	+	7.23572i	−0.202644	+	0.397711i	−0.969855	−	0.243684i	$-0.921644\pi$
$331$	−3.68679	+	7.23572i	−0.202644	+	0.397711i	0.767211	+	0.641395i	$0.221644\pi$
$332$		−	11.1167i		−	0.610108i
$333$	−1.30721	−	4.02319i	−0.0716349	−	0.220469i
$334$	−9.63743	+	13.2648i	−0.527337	+	0.725817i
$335$	19.3678	−	4.39268i	1.05818	−	0.239998i
$336$	0.164321	−	1.03748i	0.00896444	−	0.0565992i
$337$	−5.01825	−	31.6840i	−0.273361	−	1.72594i	−0.617113	−	0.786875i	$-0.711698\pi$
$337$	−5.01825	−	31.6840i	−0.273361	−	1.72594i	0.343751	−	0.939061i	$-0.388302\pi$
$338$	11.7640	−	5.53254i	0.639876	−	0.300930i
$339$	−4.93779	−	6.79629i	−0.268184	−	0.369124i
$340$	−1.56540	+	1.30326i	−0.0848957	+	0.0706790i
$341$	24.9317	+	18.1139i	1.35013	+	0.980925i
$342$	0.0771074	−	0.151332i	0.00416949	−	0.00818308i
$343$			13.0421i			0.704208i
$344$	2.90440	+	1.47987i	0.156595	+	0.0797891i
$345$	−20.9911	+	4.76085i	−1.13012	+	0.256315i
$346$	7.52083	+	14.7605i	0.404322	+	0.793527i
$347$	−15.0488	−	29.5349i	−0.807860	−	1.58551i	−0.810659	−	0.585518i	$-0.800891\pi$
$347$	−15.0488	−	29.5349i	−0.807860	−	1.58551i	0.00279956	−	0.999996i	$-0.499109\pi$
$348$	−0.0514119	+	0.324602i	−0.00275597	+	0.0174005i
$349$	−11.3584	−	11.3584i	−0.607999	−	0.607999i	0.334424	−	0.942423i	$-0.391458\pi$
$349$	−11.3584	−	11.3584i	−0.607999	−	0.607999i	−0.942423	+	0.334424i	$0.891458\pi$
$350$	−2.16534	−	4.52805i	−0.115742	−	0.242035i
$351$	−4.60424	+	17.9241i	−0.245756	+	0.956719i
$352$	−0.663074	+	4.18649i	−0.0353420	+	0.223140i
$353$	−21.6128	−	7.02244i	−1.15034	−	0.373767i	−0.329066	−	0.944307i	$-0.606734\pi$
$353$	−21.6128	−	7.02244i	−1.15034	−	0.373767i	−0.821270	+	0.570540i	$0.806734\pi$
$354$	3.82414	+	1.24254i	0.203251	+	0.0660401i
$355$	−6.33529	−	15.8564i	−0.336242	−	0.841573i
$356$	2.55569	−	5.01583i	0.135451	−	0.265838i
$357$	0.956851			0.0506419
$358$	−7.63715	−	23.5047i	−0.403636	−	1.24226i
$359$	3.41266	+	21.5467i	0.180113	+	1.13719i	0.897662	+	0.440684i	$0.145264\pi$
$359$	3.41266	+	21.5467i	0.180113	+	1.13719i	−0.717549	+	0.696508i	$0.754736\pi$
$360$	1.67957	−	3.91471i	0.0885211	−	0.206323i
$361$	−11.1632	−	15.3649i	−0.587539	−	0.808679i
$362$	3.34130	−	4.59891i	0.175615	−	0.241713i
$363$	−7.19985	+	1.14034i	−0.377894	+	0.0598526i
$364$	3.32153	+	1.43779i	0.174096	+	0.0753607i
$365$	−3.45986	−	5.80888i	−0.181097	−	0.304051i
$366$	−0.701869	−	4.43142i	−0.0366873	−	0.231634i
$367$	−1.90283	−	0.969543i	−0.0993272	−	0.0506097i	0.403621	−	0.914926i	$-0.367751\pi$
$367$	−1.90283	−	0.969543i	−0.0993272	−	0.0506097i	−0.502948	+	0.864316i	$0.667751\pi$
$368$	−6.50471	+	6.50471i	−0.339081	+	0.339081i
$369$	−6.26552	−	3.19244i	−0.326170	−	0.166192i
$370$	4.94469	+	0.451857i	0.257062	+	0.0234909i
$371$	−6.03739	−	11.8490i	−0.313446	−	0.615172i
$372$	7.23553	+	2.35097i	0.375145	+	0.121892i
$373$	28.7807	+	4.55841i	1.49021	+	0.236026i	0.847791	−	0.530330i	$-0.177932\pi$
$373$	28.7807	+	4.55841i	1.49021	+	0.236026i	0.642416	+	0.766356i	$0.277932\pi$
$374$	−3.86113			−0.199654
$375$	2.29962	+	11.4709i	0.118752	+	0.592355i
$376$		−	9.75338i		−	0.502992i
$377$	−1.03922	−	0.449849i	−0.0535228	−	0.0231684i
$378$	−4.59075	+	2.33910i	−0.236123	+	0.120311i
$379$	5.06870	+	9.94788i	0.260361	+	0.510988i	0.983770	−	0.179432i	$-0.0574259\pi$
$379$	5.06870	+	9.94788i	0.260361	+	0.510988i	−0.723409	+	0.690420i	$0.757426\pi$
$380$	0.127553	+	0.153210i	0.00654333	+	0.00785949i
$381$	13.5522	−	4.40338i	0.694301	−	0.225592i
$382$	13.5565			0.693611
$383$	13.6834	−	4.44600i	0.699188	−	0.227180i	0.0622114	−	0.998063i	$-0.480185\pi$
$383$	13.6834	−	4.44600i	0.699188	−	0.227180i	0.636977	+	0.770883i	$0.280185\pi$
$384$	0.163694	+	1.03352i	0.00835345	+	0.0527416i
$385$	2.33735	−	9.22270i	0.119123	−	0.470033i
$386$	−0.285251	+	0.207247i	−0.0145189	+	0.0105486i
$387$	−0.971432	−	6.13338i	−0.0493807	−	0.311777i
$388$	5.57921	+	4.05353i	0.283242	+	0.205787i
$389$	−21.7057	+	15.7701i	−1.10052	+	0.799576i	−0.981145	−	0.193273i	$-0.938090\pi$
$389$	−21.7057	+	15.7701i	−1.10052	+	0.799576i	−0.119377	+	0.992849i	$0.538090\pi$
$390$	−6.68157	−	5.15064i	−0.338334	−	0.260813i
$391$	−6.77930	−	4.92545i	−0.342844	−	0.249091i
$392$	−1.85173	−	5.69904i	−0.0935264	−	0.287845i
$393$	−2.81464	−	2.81464i	−0.141980	−	0.141980i
$394$	3.58585	+	11.0361i	0.180653	+	0.555992i
$395$	7.92678	−	18.4756i	0.398840	−	0.929608i
$396$	7.19473	−	3.66590i	0.361549	−	0.184218i
$397$	0.683206	+	0.221987i	0.0342891	+	0.0111412i	0.326111	−	0.945331i	$-0.394262\pi$
$397$	0.683206	+	0.221987i	0.0342891	+	0.0111412i	−0.291822	+	0.956473i	$0.594262\pi$
$398$	8.81008	−	6.40090i	0.441610	−	0.320848i
$399$		−	0.0936495i		−	0.00468834i
$400$	3.44540	+	3.62342i	0.172270	+	0.181171i
$401$	8.91254	−	8.91254i	0.445071	−	0.445071i	−0.448641	−	0.893712i	$-0.648092\pi$
$401$	8.91254	−	8.91254i	0.445071	−	0.445071i	0.893712	+	0.448641i	$0.148092\pi$
$402$	9.17924	+	1.45385i	0.457819	+	0.0725114i
$403$	−14.0487	+	22.1318i	−0.699816	+	1.10246i
$404$	−7.04235	−	2.28820i	−0.350370	−	0.113842i
$405$	−0.750793	+	0.170282i	−0.0373072	+	0.00846140i
$406$	−0.0974261	−	0.299847i	−0.00483518	−	0.0148811i
$407$	6.65541	+	6.65541i	0.329897	+	0.329897i
$408$	−0.906546	+	0.294555i	−0.0448807	+	0.0145826i
$409$	−14.9417	+	2.36653i	−0.738818	+	0.117017i	−0.514490	−	0.857497i	$-0.672019\pi$
$409$	−14.9417	+	2.36653i	−0.738818	+	0.117017i	−0.224328	+	0.974514i	$0.572019\pi$
$410$	6.34327	−	5.28102i	0.313272	−	0.260811i
$411$	−1.44355	+	9.11422i	−0.0712051	+	0.449571i
$412$	4.63749	−	0.734506i	0.228473	−	0.0361865i
$413$	−3.80986	+	0.603422i	−0.187471	+	0.0296925i
$414$	17.3088	+	2.74144i	0.850681	+	0.134735i
$415$	−5.49817	−	24.2420i	−0.269895	−	1.18999i
$416$	−3.58951	−	0.339708i	−0.175990	−	0.0166556i
$417$	−11.0871	−	5.64916i	−0.542937	−	0.276640i
$418$			0.377898i			0.0184836i
$419$	36.5536	−	11.8770i	1.78576	−	0.580229i	0.786462	−	0.617638i	$-0.211910\pi$
$419$	36.5536	−	11.8770i	1.78576	−	0.580229i	0.999300	+	0.0374089i	$0.0119104\pi$
$420$	−0.154792	−	2.34369i	−0.00755308	−	0.114360i
$421$	5.59548	−	2.85104i	0.272707	−	0.138951i	−0.312289	−	0.949987i	$-0.601096\pi$
$421$	5.59548	−	2.85104i	0.272707	−	0.138951i	0.584996	+	0.811036i	$0.301096\pi$
$422$	1.16722	−	3.59233i	0.0568194	−	0.174872i
$423$	−15.0320	+	10.9214i	−0.730881	+	0.531016i
$424$	9.36756	+	9.36756i	0.454929	+	0.454929i
$425$	−2.76907	+	3.61621i	−0.134320	+	0.175412i
$426$		−	7.99062i		−	0.387147i
$427$	2.52990	+	3.48211i	0.122431	+	0.168511i
$428$	6.41514	+	12.5904i	0.310087	+	0.608581i
$429$	−3.48681	−	15.6072i	−0.168345	−	0.753521i
$430$	7.06551	+	1.79064i	0.340729	+	0.0863526i
$431$	15.4792	−	30.3795i	0.745605	−	1.46333i	−0.135684	−	0.990752i	$-0.543323\pi$
$431$	15.4792	−	30.3795i	0.745605	−	1.46333i	0.881288	−	0.472579i	$-0.156677\pi$
$432$	3.62933	−	3.62933i	0.174616	−	0.174616i
$433$	−4.92168	−	2.50772i	−0.236521	−	0.120513i	0.331713	−	0.943380i	$-0.392373\pi$
$433$	−4.92168	−	2.50772i	−0.236521	−	0.120513i	−0.568234	+	0.822867i	$0.692373\pi$
$434$	−7.20851	+	1.14172i	−0.346020	+	0.0548041i
$435$	0.0484306	+	0.733282i	0.00232207	+	0.0351582i
$436$	−0.994282	+	6.27765i	−0.0476174	+	0.300645i
$437$	−0.482066	+	0.663507i	−0.0230604	+	0.0317399i
$438$	−0.494960	−	3.12505i	−0.0236501	−	0.149321i
$439$	−4.81529	+	3.49851i	−0.229821	+	0.166975i	−0.696736	−	0.717327i	$-0.745365\pi$
$439$	−4.81529	+	3.49851i	−0.229821	+	0.166975i	0.466915	+	0.884302i	$0.345365\pi$
$440$	0.624624	+	9.45735i	0.0297778	+	0.450862i
$441$	−6.70993	+	9.23542i	−0.319520	+	0.439782i
$442$	−0.205868	−	3.27794i	−0.00979213	−	0.155916i
$443$	23.0114	+	23.0114i	1.09330	+	1.09330i	0.995174	+	0.0981306i	$0.0312863\pi$
$443$	23.0114	+	23.0114i	1.09330	+	1.09330i	0.0981306	+	0.995174i	$0.468714\pi$
$444$	2.07033	+	1.05489i	0.0982537	+	0.0500628i
$445$	3.09240	−	12.2019i	0.146594	−	0.578428i
$446$	−0.619908	−	0.201420i	−0.0293535	−	0.00953753i
$447$	−4.96253	+	15.2731i	−0.234720	+	0.722393i
$448$	−0.590038	−	0.812117i	−0.0278767	−	0.0383689i
$449$	−9.84156	−	9.84156i	−0.464452	−	0.464452i	0.435660	−	0.900111i	$-0.356515\pi$
$449$	−9.84156	−	9.84156i	−0.464452	−	0.464452i	−0.900111	+	0.435660i	$0.856515\pi$
$450$	1.72645	−	9.36743i	0.0813856	−	0.441585i
$451$	15.6459			0.736739
$452$	−7.92930	−	1.25588i	−0.372963	−	0.0590715i
$453$	2.98815	−	9.19658i	0.140396	−	0.432093i
$454$	−1.34245	+	4.13163i	−0.0630042	+	0.193907i
$455$	7.95433	+	1.49258i	0.372905	+	0.0699733i
$456$	0.0288288	+	0.0887260i	0.00135003	+	0.00415498i
$457$	−15.7575			−0.737103			−0.368551	−	0.929607i	$-0.620146\pi$
$457$	−15.7575			−0.737103			−0.368551	+	0.929607i	$0.620146\pi$
$458$	−11.5272	+	22.6233i	−0.538629	+	1.05712i
$459$	3.78254	+	2.74818i	0.176554	+	0.128274i
$460$	−10.9676	+	17.4019i	−0.511366	+	0.811366i
$461$	9.67097	+	1.53173i	0.450422	+	0.0713399i	0.377525	−	0.926000i	$-0.376775\pi$
$461$	9.67097	+	1.53173i	0.450422	+	0.0713399i	0.0728976	+	0.997339i	$0.476775\pi$
$462$	2.61703	−	3.60203i	0.121755	−	0.167582i
$463$	9.66041	+	7.01870i	0.448957	+	0.326187i	0.789184	−	0.614157i	$-0.210504\pi$
$463$	9.66041	+	7.01870i	0.448957	+	0.326187i	−0.340227	+	0.940343i	$0.610504\pi$
$464$	0.184608	+	0.254091i	0.00857021	+	0.0117959i
$465$	16.9412	+	1.54812i	0.785627	+	0.0717923i
$466$	−28.0758	+	4.44677i	−1.30059	+	0.205992i
$467$	−5.29674	+	10.3954i	−0.245104	+	0.481044i	−0.980481	−	0.196615i	$-0.937005\pi$
$467$	−5.29674	+	10.3954i	−0.245104	+	0.481044i	0.735377	+	0.677658i	$0.237005\pi$
$468$	3.49581	+	5.91258i	0.161594	+	0.273309i
$469$	−8.47920	+	2.75506i	−0.391533	+	0.127217i
$470$	−4.82389	−	21.2690i	−0.222509	−	0.981068i
$471$	−5.51716	+	16.9801i	−0.254217	+	0.782400i
$472$	3.42380	−	1.74451i	0.157593	−	0.0802978i
$473$	8.12128	+	11.1780i	0.373417	+	0.513964i
$474$	6.65254	−	6.65254i	0.305561	−	0.305561i
$475$	0.353928	+	0.271016i	0.0162393	+	0.0124351i
$476$	0.646592	−	0.646592i	0.0296365	−	0.0296365i
$477$	3.94801	−	24.9267i	0.180767	−	1.14132i
$478$	−1.57970	−	3.10034i	−0.0722538	−	0.141806i
$479$	11.1034	−	5.65744i	0.507325	−	0.258495i	−0.181541	−	0.983383i	$-0.558109\pi$
$479$	11.1034	−	5.65744i	0.507325	−	0.258495i	0.688867	+	0.724888i	$0.258109\pi$
$480$	0.868129	+	2.17282i	0.0396245	+	0.0991753i
$481$	−5.29532	+	6.00503i	−0.241446	+	0.273806i
$482$	−14.4004	+	14.4004i	−0.655918	+	0.655918i
$483$	9.18987	−	2.98597i	0.418154	−	0.135866i
$484$	−4.09471	+	5.63588i	−0.186123	+	0.256177i
$485$	14.1713	+	6.08008i	0.643487	+	0.276082i
$486$	−15.5642	−	2.46513i	−0.706007	−	0.111821i
$487$	15.9547	+	11.5918i	0.722976	+	0.525273i	0.887334	−	0.461128i	$-0.152555\pi$
$487$	15.9547	+	11.5918i	0.722976	+	0.525273i	−0.164358	+	0.986401i	$0.552555\pi$
$488$	−3.46882	−	2.52025i	−0.157026	−	0.114086i
$489$	−20.0329	−	3.17290i	−0.905919	−	0.143483i
$490$	−6.85670	−	11.5120i	−0.309754	−	0.520057i
$491$	−3.34017	+	4.59735i	−0.150740	+	0.207476i	−0.877708	−	0.479195i	$-0.840929\pi$
$491$	−3.34017	+	4.59735i	−0.150740	+	0.207476i	0.726969	+	0.686671i	$0.240929\pi$
$492$	3.67348	−	1.19359i	0.165613	−	0.0538110i
$493$	−0.202302	+	0.202302i	−0.00911124	+	0.00911124i
$494$	−0.320821	+	0.0201488i	−0.0144344	+	0.000906538i
$495$	13.8763	−	11.5526i	0.623695	−	0.519250i
$496$	6.47807	−	3.30074i	0.290874	−	0.148208i
$497$	3.48008	+	6.83003i	0.156103	+	0.306369i
$498$	1.81973	−	11.4893i	0.0815442	−	0.514850i
$499$	10.5420	−	10.5420i	0.471925	−	0.471925i	−0.430612	−	0.902537i	$-0.641702\pi$
$499$	10.5420	−	10.5420i	0.471925	−	0.471925i	0.902537	+	0.430612i	$0.141702\pi$
$500$	9.30543	+	6.19749i	0.416152	+	0.277160i
$501$	−12.1318	+	12.1318i	−0.542011	+	0.542011i
$502$	−2.84391	−	3.91431i	−0.126930	−	0.174704i
$503$	−35.9819	+	18.3337i	−1.60436	+	0.817460i	−0.604574	+	0.796549i	$0.706657\pi$
$503$	−35.9819	+	18.3337i	−1.60436	+	0.817460i	−0.999781	+	0.0209110i	$0.993343\pi$
$504$	−0.590945	+	1.81874i	−0.0263228	+	0.0810133i
$505$	−16.4889	−	1.50679i	−0.733745	−	0.0670512i
$506$	−37.0833	+	12.0491i	−1.64856	+	0.535648i
$507$	13.0639	−	3.79230i	0.580190	−	0.168422i
$508$	6.18232	−	12.1335i	0.274296	−	0.538336i
$509$	15.0710	−	2.38701i	0.668010	−	0.105802i	0.186787	−	0.982400i	$-0.440193\pi$
$509$	15.0710	−	2.38701i	0.668010	−	0.105802i	0.481223	+	0.876598i	$0.340193\pi$
$510$	−1.83121	+	1.09070i	−0.0810872	+	0.0482968i
$511$	1.78410	+	2.45560i	0.0789237	+	0.108629i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	0.268971	−	0.370207i	0.0118754	−	0.0163450i
$514$	−22.8675	−	3.62186i	−1.00864	−	0.159754i
$515$	9.74962	−	3.89536i	0.429619	−	0.171650i
$516$	2.75952	+	2.00491i	0.121481	+	0.0882610i
$517$	18.7686	−	36.8354i	0.825442	−	1.62002i
$518$	−2.22906			−0.0979392
$519$	5.35674	+	16.4863i	0.235135	+	0.723670i
$520$	−7.99561	+	1.03453i	−0.350631	+	0.0453671i
$521$	0.679523	−	2.09136i	0.0297705	−	0.0916241i	−0.935067	−	0.354470i	$-0.884661\pi$
$521$	0.679523	−	2.09136i	0.0297705	−	0.0916241i	0.964838	+	0.262846i	$0.0846612\pi$
$522$	0.184892	−	0.569039i	0.00809251	−	0.0249062i
$523$	−2.41717	−	0.382843i	−0.105696	−	0.0167405i	0.103363	−	0.994644i	$-0.467040\pi$
$523$	−2.41717	−	0.382843i	−0.105696	−	0.0167405i	−0.209058	+	0.977903i	$0.567040\pi$
$524$	−3.80399			−0.166178
$525$	−1.49671	−	5.03429i	−0.0653218	−	0.219714i
$526$	7.39869	+	7.39869i	0.322598	+	0.322598i
$527$	3.89285	+	5.35805i	0.169575	+	0.233400i
$528$	−1.37060	+	4.21828i	−0.0596478	+	0.183577i
$529$	−58.6065	−	19.0424i	−2.54811	−	0.827930i
$530$	25.0608	+	15.7946i	1.08857	+	0.686075i
$531$	−6.52248	−	3.32337i	−0.283051	−	0.144222i
$532$	−0.0632836	−	0.0632836i	−0.00274369	−	0.00274369i
$533$	0.834212	+	13.2828i	0.0361337	+	0.575341i
$534$	3.46242	−	4.76561i	0.149833	−	0.206228i
$535$	20.2164	+	24.2829i	0.874033	+	1.04984i
$536$	7.18530	−	5.22043i	0.310358	−	0.225488i
$537$	−4.04558	−	25.5428i	−0.174580	−	1.10225i
$538$	11.2249	−	15.4498i	0.483940	−	0.666086i
$539$	3.97335	−	25.0868i	0.171144	−	1.08056i
$540$	6.11941	−	9.70945i	0.263337	−	0.417828i
$541$	−1.58173	+	0.250522i	−0.0680040	+	0.0107708i	−0.190344	−	0.981718i	$-0.560960\pi$
$541$	−1.58173	+	0.250522i	−0.0680040	+	0.0107708i	0.122340	+	0.992488i	$0.460960\pi$
$542$	−15.1705	−	7.72973i	−0.651627	−	0.332020i
$543$	4.20612	−	4.20612i	0.180502	−	0.180502i
$544$	−0.413553	+	0.811643i	−0.0177309	+	0.0347989i
$545$	0.936625	+	14.1813i	0.0401206	+	0.607461i
$546$	3.19752	+	2.02970i	0.136841	+	0.0868631i
$547$	13.8488	+	27.1798i	0.592132	+	1.16213i	0.971536	+	0.236894i	$0.0761293\pi$
$547$	13.8488	+	27.1798i	0.592132	+	1.16213i	−0.379403	+	0.925231i	$0.623871\pi$
$548$	5.18345	+	7.13441i	0.221426	+	0.304767i
$549$			8.16823i			0.348612i
$550$	6.03959	+	20.3146i	0.257529	+	0.866216i
$551$	0.0197999	+	0.0197999i	0.000843503	+	0.000843503i
$552$	−7.78753	+	5.65797i	−0.331459	+	0.240819i
$553$	−2.78899	+	8.58362i	−0.118600	+	0.365013i
$554$	−21.8173	+	11.1165i	−0.926930	+	0.472294i
$555$	5.03648	+	1.27642i	0.213787	+	0.0541809i
$556$	−11.3095	+	3.67468i	−0.479630	+	0.155841i
$557$			2.74442i			0.116285i	0.998308	+	0.0581425i	$0.0185178\pi$
$557$			2.74442i			0.116285i	−0.998308	+	0.0581425i	$0.981482\pi$
$558$	−12.3410	−	6.28804i	−0.522435	−	0.266194i
$559$	−9.05665	+	7.49063i	−0.383055	+	0.316820i
$560$	−1.68835	−	1.47915i	−0.0713457	−	0.0625054i
$561$	−3.99055	−	0.632041i	−0.168481	−	0.0266848i
$562$	30.3250	−	4.80301i	1.27918	−	0.202603i
$563$	9.32976	−	1.47769i	0.393202	−	0.0622771i	0.0432971	−	0.999062i	$-0.486214\pi$
$563$	9.32976	−	1.47769i	0.393202	−	0.0622771i	0.349905	+	0.936785i	$0.386214\pi$
$564$	1.59657	−	10.0803i	0.0672276	−	0.424458i
$565$	−17.9124	+	1.18305i	−0.753582	+	0.0497713i
$566$	1.70920	−	0.270711i	0.0718432	−	0.0113789i
$567$	0.328697	−	0.106800i	0.0138040	−	0.00448518i
$568$	−5.39965	−	5.39965i	−0.226564	−	0.226564i
$569$	6.85266	+	21.0903i	0.287278	+	0.884152i	0.985707	+	0.168472i	$0.0538831\pi$
$569$	6.85266	+	21.0903i	0.287278	+	0.884152i	−0.698428	+	0.715680i	$0.746117\pi$
$570$	0.106749	+	0.179225i	0.00447123	+	0.00750691i
$571$	−19.9887	−	6.49473i	−0.836502	−	0.271796i	−0.140721	−	0.990049i	$-0.544942\pi$
$571$	−19.9887	−	6.49473i	−0.836502	−	0.271796i	−0.695782	+	0.718253i	$0.744942\pi$
$572$	−12.9027	−	8.19033i	−0.539491	−	0.342455i
$573$	14.0109	+	2.21911i	0.585315	+	0.0927048i
$574$	−2.62010	+	2.62010i	−0.109361	+	0.109361i
$575$	−15.3101	+	43.3724i	−0.638475	+	1.80875i
$576$		−	1.90504i		−	0.0793766i
$577$	−0.833703	+	0.605721i	−0.0347075	+	0.0252165i	−0.605004	−	0.796223i	$-0.706828\pi$
$577$	−0.833703	+	0.605721i	−0.0347075	+	0.0252165i	0.570296	+	0.821439i	$0.306828\pi$
$578$	15.3788	+	4.99687i	0.639673	+	0.207842i
$579$	−0.328738	+	0.167500i	−0.0136619	+	0.00696107i
$580$	0.528242	+	0.462788i	0.0219341	+	0.0192162i
$581$	3.44842	+	10.6131i	0.143064	+	0.440307i
$582$	5.10269	+	5.10269i	0.211513	+	0.211513i
$583$	17.3522	+	53.4045i	0.718653	+	2.21179i
$584$	−2.44622	−	1.77728i	−0.101225	−	0.0735446i
$585$	10.5475	+	11.1645i	0.436087	+	0.461595i
$586$	1.13958	−	0.827954i	0.0470757	−	0.0342025i
$587$	−1.32824	−	0.965021i	−0.0548222	−	0.0398307i	0.560037	−	0.828468i	$-0.310787\pi$
$587$	−1.32824	−	0.965021i	−0.0548222	−	0.0398307i	−0.614859	+	0.788637i	$0.710787\pi$
$588$	−0.980905	−	6.19319i	−0.0404518	−	0.255403i
$589$	0.524406	−	0.381003i	0.0216078	−	0.0156990i
$590$	6.60342	−	5.49760i	0.271858	−	0.226333i
$591$	1.89951	+	11.9930i	0.0781355	+	0.493328i
$592$	2.11187	−	0.686187i	0.0867972	−	0.0282021i
$593$	37.7659			1.55086			0.775429	−	0.631435i	$-0.217534\pi$
$593$	37.7659			1.55086			0.775429	+	0.631435i	$0.217534\pi$
$594$	20.6908	−	6.72286i	0.848955	−	0.275842i
$595$	1.09022	−	1.72981i	0.0446945	−	0.0709152i
$596$	6.96736	+	13.6742i	0.285394	+	0.560118i
$597$	10.1532	−	5.17331i	0.415542	−	0.211729i
$598$	−12.2064	−	30.8398i	−0.499158	−	1.26113i
$599$		−	2.28508i		−	0.0933657i	−0.998910	−	0.0466829i	$-0.985135\pi$
$599$		−	2.28508i		−	0.0933657i	0.998910	−	0.0466829i	$-0.0148650\pi$
$600$	2.96776	+	4.30887i	0.121158	+	0.175909i
$601$	−17.0975			−0.697422			−0.348711	−	0.937230i	$-0.613381\pi$
$601$	−17.0975			−0.697422			−0.348711	+	0.937230i	$0.613381\pi$
$602$	−3.23189	−	0.511882i	−0.131722	−	0.0208627i
$603$	−16.0915	−	5.22846i	−0.655298	−	0.212919i
$604$	−4.19534	−	8.23383i	−0.170706	−	0.335030i
$605$	−6.14184	+	14.3153i	−0.249701	+	0.581999i
$606$	−6.90386	−	3.51769i	−0.280450	−	0.142896i
$607$	12.5285	−	12.5285i	0.508517	−	0.508517i	−0.405554	−	0.914071i	$-0.632921\pi$
$607$	12.5285	−	12.5285i	0.508517	−	0.508517i	0.914071	+	0.405554i	$0.132921\pi$
$608$	0.0794376	+	0.0404755i	0.00322162	+	0.00164150i
$609$	−0.0516089	−	0.325846i	−0.00209130	−	0.0132039i
$610$	−8.81088	−	3.78023i	−0.356742	−	0.153057i
$611$	32.2725	+	13.9698i	1.30561	+	0.565157i
$612$	1.71399	−	0.271469i	0.0692839	−	0.0109735i
$613$	−15.5899	+	21.4577i	−0.629671	+	0.866668i	−0.998012	−	0.0630228i	$-0.979926\pi$
$613$	−15.5899	+	21.4577i	−0.629671	+	0.866668i	0.368341	+	0.929691i	$0.379926\pi$
$614$	−5.72686	−	7.88235i	−0.231117	−	0.318106i
$615$	7.42037	−	4.41969i	0.299218	−	0.178219i
$616$	−0.665615	−	4.20253i	−0.0268184	−	0.169325i
$617$	6.50194	+	20.0109i	0.261758	+	0.805609i	0.992423	+	0.122872i	$0.0392104\pi$
$617$	6.50194	+	20.0109i	0.261758	+	0.805609i	−0.730664	+	0.682737i	$0.760790\pi$
$618$	4.91317			0.197637
$619$	11.9446	−	23.4426i	0.480093	−	0.942236i	−0.516221	−	0.856455i	$-0.672662\pi$
$619$	11.9446	−	23.4426i	0.480093	−	0.942236i	0.996314	−	0.0857804i	$-0.0273383\pi$
$620$	12.4941	−	10.4018i	0.501776	−	0.417748i
$621$	44.9046	+	14.5904i	1.80196	+	0.585492i
$622$	−19.6205	−	6.37509i	−0.786711	−	0.255618i
$623$	−0.884006	+	5.58139i	−0.0354169	+	0.223614i
$624$	−3.65423	−	0.938676i	−0.146286	−	0.0375771i
$625$	23.3574	+	8.91243i	0.934296	+	0.356497i
$626$	−20.5824	−	20.5824i	−0.822639	−	0.822639i
$627$	−0.0618595	+	0.390566i	−0.00247043	+	0.0155977i
$628$	7.74606	+	15.2025i	0.309101	+	0.606646i
$629$	0.918314	+	1.80229i	0.0366156	+	0.0718621i
$630$	−0.389140	+	4.25838i	−0.0155037	+	0.169658i
$631$	−27.4046	−	13.9633i	−1.09096	−	0.555872i	−0.186510	−	0.982453i	$-0.559718\pi$
$631$	−27.4046	−	13.9633i	−1.09096	−	0.555872i	−0.904449	+	0.426581i	$0.859718\pi$
$632$		−	8.99090i		−	0.357639i
$633$	1.79439	−	3.52169i	0.0713205	−	0.139974i
$634$	14.1423	+	10.2750i	0.561662	+	0.408071i
$635$	7.48063	−	29.5170i	0.296860	−	1.17135i
$636$	8.14816	+	11.2150i	0.323096	+	0.444703i
$637$	21.5095	+	2.03564i	0.852238	+	0.0806550i
$638$	0.208254	+	1.31487i	0.00824487	+	0.0520561i
$639$	−2.27571	+	14.3683i	−0.0900258	+	0.568400i
$640$	2.05492	+	0.881645i	0.0812279	+	0.0348501i
$641$	16.8785	−	23.2313i	0.666660	−	0.917579i	−0.333018	−	0.942920i	$-0.608067\pi$
$641$	16.8785	−	23.2313i	0.666660	−	0.917579i	0.999679	+	0.0253410i	$0.00806714\pi$
$642$	4.56921	+	14.0626i	0.180332	+	0.555005i
$643$		−	6.25746i		−	0.246770i	−0.992359	−	0.123385i	$-0.960625\pi$
$643$		−	6.25746i		−	0.246770i	0.992359	−	0.123385i	$-0.0393750\pi$
$644$	4.19228	−	8.22782i	0.165199	−	0.324222i
$645$	7.00923	+	3.00725i	0.275988	+	0.118410i
$646$	−0.0250964	+	0.0772388i	−0.000987405	+	0.00303892i
$647$	2.13953	−	1.09015i	0.0841137	−	0.0428581i	−0.411428	−	0.911442i	$-0.634970\pi$
$647$	2.13953	−	1.09015i	0.0841137	−	0.0428581i	0.495541	+	0.868584i	$0.334970\pi$
$648$	−0.278539	+	0.202370i	−0.0109420	+	0.00794985i
$649$	16.2876			0.639345
$650$	−16.9242	+	6.21050i	−0.663823	+	0.243596i
$651$	−7.63704			−0.299319
$652$	−15.6813	+	11.3931i	−0.614127	+	0.446189i
$653$	−28.4840	+	14.5133i	−1.11467	+	0.567951i	−0.911544	−	0.411203i	$-0.865109\pi$
$653$	−28.4840	+	14.5133i	−1.11467	+	0.567951i	−0.203122	+	0.979153i	$0.565109\pi$
$654$	−2.05522	+	6.32532i	−0.0803655	+	0.247340i
$655$	−8.29529	+	1.88140i	−0.324124	+	0.0735124i
$656$	1.67579	−	3.28892i	0.0654285	−	0.128411i
$657$			5.76026i			0.224729i
$658$	3.02551	+	9.31156i	0.117947	+	0.363003i
$659$	−7.33372	+	10.0940i	−0.285681	+	0.393207i	−0.927605	−	0.373562i	$-0.878136\pi$
$659$	−7.33372	+	10.0940i	−0.285681	+	0.393207i	0.641924	+	0.766768i	$0.278136\pi$
$660$	−0.902547	+	9.87662i	−0.0351316	+	0.384447i
$661$	−6.54930	+	41.3506i	−0.254738	+	1.60835i	0.446066	+	0.895000i	$0.352825\pi$
$661$	−6.54930	+	41.3506i	−0.254738	+	1.60835i	−0.700804	+	0.713353i	$0.747175\pi$
$662$	1.27038	+	8.02086i	0.0493747	+	0.311740i
$663$	0.323809	−	3.42152i	0.0125757	−	0.132881i
$664$	−6.53424	−	8.99360i	−0.253578	−	0.349019i
$665$	−0.169301	−	0.106702i	−0.00656520	−	0.00413774i
$666$	−3.42233	−	2.48647i	−0.132613	−	0.0963487i
$667$	−1.31166	+	2.57428i	−0.0507877	+	0.0996765i
$668$			16.3962i			0.634387i
$669$	−0.607717	−	0.309647i	−0.0234957	−	0.0119716i
$670$	13.0869	−	14.9379i	0.505592	−	0.577100i
$671$	−8.25089	−	16.1933i	−0.318522	−	0.625135i
$672$	−0.476878	−	0.935925i	−0.0183960	−	0.0361041i
$673$	−2.22505	+	14.0484i	−0.0857695	+	0.541527i	0.906965	+	0.421205i	$0.138393\pi$
$673$	−2.22505	+	14.0484i	−0.0857695	+	0.541527i	−0.992735	+	0.120322i	$0.961607\pi$
$674$	−22.6832	−	22.6832i	−0.873725	−	0.873725i
$675$	8.54234	−	24.1998i	0.328795	−	0.931451i
$676$	6.26531	−	11.3906i	0.240973	−	0.438100i
$677$	7.63640	−	48.2143i	0.293491	−	1.85303i	−0.195456	−	0.980713i	$-0.562619\pi$
$677$	7.63640	−	48.2143i	0.293491	−	1.85303i	0.488946	−	0.872314i	$-0.337381\pi$
$678$	−7.98952	−	2.59595i	−0.306836	−	0.0996969i
$679$	−6.58389	−	2.13924i	−0.252667	−	0.0820963i
$680$	−0.500400	+	1.97447i	−0.0191895	+	0.0757176i
$681$	−2.06377	+	4.05038i	−0.0790838	+	0.155211i
$682$	30.8173			1.18005
$683$	3.66717	+	11.2864i	0.140320	+	0.431862i	0.996380	−	0.0850161i	$-0.0270942\pi$
$683$	3.66717	+	11.2864i	0.140320	+	0.431862i	−0.856059	+	0.516878i	$0.827094\pi$
$684$	−0.0265694	−	0.167753i	−0.00101591	−	0.00641418i
$685$	14.8321	+	12.9942i	0.566704	+	0.496484i
$686$	7.66596	+	10.5513i	0.292688	+	0.402850i
$687$	−15.6169	+	21.4948i	−0.595820	+	0.820076i
$688$	3.21956	−	0.509927i	0.122744	−	0.0194408i
$689$	−44.4131	+	17.5787i	−1.69200	+	0.669696i
$690$	−14.1838	+	16.1899i	−0.539968	+	0.616337i
$691$	−1.78891	−	11.2948i	−0.0680535	−	0.429673i	−0.998067	−	0.0621474i	$-0.980205\pi$
$691$	−1.78891	−	11.2948i	−0.0680535	−	0.429673i	0.930013	−	0.367525i	$-0.119795\pi$
$692$	14.7605	+	7.52083i	0.561108	+	0.285899i
$693$	−5.73165	+	5.73165i	−0.217727	+	0.217727i
$694$	−29.5349	−	15.0488i	−1.12113	−	0.571243i
$695$	−22.8450	+	13.6069i	−0.866562	+	0.516138i
$696$	0.149203	+	0.292828i	0.00565553	+	0.0110996i
$697$	3.19788	+	1.03906i	0.121128	+	0.0393570i
$698$	−15.8654	−	2.51283i	−0.600514	−	0.0951121i
$699$	−29.7448			−1.12505
$700$	−4.41332	−	2.39052i	−0.166808	−	0.0903531i
$701$			27.4363i			1.03625i	0.855304	+	0.518127i	$0.173370\pi$
$701$			27.4363i			1.03625i	−0.855304	+	0.518127i	$0.826630\pi$
$702$	6.81063	+	17.2072i	0.257051	+	0.649445i
$703$	0.176395	−	0.0898778i	0.00665286	−	0.00338980i
$704$	1.92432	+	3.77668i	0.0725254	+	0.142339i
$705$	−1.50398	−	22.7716i	−0.0566433	−	0.857630i
$706$	−21.6128	+	7.02244i	−0.813410	+	0.264293i
$707$	7.43315			0.279552
$708$	3.82414	−	1.24254i	0.143720	−	0.0466974i
$709$	4.44716	+	28.0783i	0.167017	+	1.05450i	0.918694	+	0.394971i	$0.129245\pi$
$709$	4.44716	+	28.0783i	0.167017	+	1.05450i	−0.751677	+	0.659531i	$0.770755\pi$
$710$	−14.4455	−	9.10435i	−0.542131	−	0.341680i
$711$	−13.8569	+	10.0676i	−0.519673	+	0.377564i
$712$	−0.880631	−	5.56009i	−0.0330030	−	0.208373i
$713$	54.1085	+	39.3121i	2.02638	+	1.47225i
$714$	0.774109	−	0.562423i	0.0289703	−	0.0210482i
$715$	−32.1876	−	11.4790i	−1.20375	−	0.429290i
$716$	−19.9943	−	14.5267i	−0.747223	−	0.542889i
$717$	−1.12515	−	3.46285i	−0.0420194	−	0.129322i
$718$	15.4257	+	15.4257i	0.575683	+	0.575683i
$719$	−10.0741	−	31.0050i	−0.375702	−	1.15629i	−0.943004	−	0.332781i	$-0.892013\pi$
$719$	−10.0741	−	31.0050i	−0.375702	−	1.15629i	0.567302	−	0.823510i	$-0.307987\pi$
$720$	−0.942207	−	4.15429i	−0.0351140	−	0.154821i
$721$	−4.19957	+	2.13979i	−0.156400	+	0.0796898i
$722$	−18.0625	−	5.86887i	−0.672217	−	0.218417i
$723$	−17.2403	+	12.5258i	−0.641174	+	0.465840i
$724$		−	5.68456i		−	0.211265i
$725$	1.38082	+	0.747933i	0.0512823	+	0.0277775i
$726$	−5.15453	+	5.15453i	−0.191302	+	0.191302i
$727$	9.58403	+	1.51796i	0.355452	+	0.0562981i	0.331607	−	0.943418i	$-0.392409\pi$
$727$	9.58403	+	1.51796i	0.355452	+	0.0562981i	0.0238449	+	0.999716i	$0.492409\pi$
$728$	3.53229	−	0.789151i	0.130915	−	0.0292479i
$729$	−14.7001	−	4.77635i	−0.544448	−	0.176902i
$730$	−6.21346	−	2.66583i	−0.229970	−	0.0986667i
$731$	0.917577	+	2.82401i	0.0339378	+	0.104450i
$732$	−3.17255	−	3.17255i	−0.117261	−	0.117261i
$733$	47.0716	−	15.2945i	1.73863	−	0.564914i	0.743976	−	0.668206i	$-0.232937\pi$
$733$	47.0716	−	15.2945i	1.73863	−	0.564914i	0.994651	+	0.103291i	$0.0329374\pi$
$734$	−2.10931	+	0.334082i	−0.0778560	+	0.0123312i
$735$	−5.20211	−	13.0202i	−0.191883	−	0.480259i
$736$	−1.43905	+	9.08579i	−0.0530440	+	0.334907i
$737$	37.1824	−	5.88911i	1.36963	−	0.216928i
$738$	−6.94538	+	1.10004i	−0.255663	+	0.0404930i
$739$	35.3418	+	5.59759i	1.30007	+	0.205911i	0.767814	−	0.640673i	$-0.221344\pi$
$739$	35.3418	+	5.59759i	1.30007	+	0.205911i	0.532256	+	0.846584i	$0.321344\pi$
$740$	4.26594	−	2.54086i	0.156819	−	0.0934038i
$741$	−0.334873	−	0.0316921i	−0.0123019	−	0.00116424i
$742$	−11.8490	−	6.03739i	−0.434992	−	0.221640i
$743$			51.7685i			1.89920i	0.313461	+	0.949601i	$0.398511\pi$
$743$			51.7685i			1.89920i	−0.313461	+	0.949601i	$0.601489\pi$
$744$	7.23553	−	2.35097i	0.265267	−	0.0861906i
$745$	21.9567	+	26.3732i	0.804431	+	0.966239i
$746$	25.9634	−	13.2290i	0.950589	−	0.484349i
$747$	−6.54429	+	20.1412i	−0.239443	+	0.736930i
$748$	−3.12372	+	2.26951i	−0.114214	+	0.0829816i
$749$	−10.0301	−	10.0301i	−0.366492	−	0.366492i
$750$	8.60287	+	7.92848i	0.314132	+	0.289507i
$751$			17.2243i			0.628522i	0.949337	+	0.314261i	$0.101757\pi$
$751$			17.2243i			0.628522i	−0.949337	+	0.314261i	$0.898243\pi$
$752$	−5.73289	−	7.89065i	−0.209057	−	0.287742i
$753$	−2.29849	−	4.51105i	−0.0837617	−	0.164392i
$754$	−1.10517	+	0.246906i	−0.0402477	+	0.00899178i
$755$	−13.2211	−	15.8804i	−0.481164	−	0.577947i
$756$	−2.33910	+	4.59075i	−0.0850724	+	0.166964i
$757$	−12.5465	+	12.5465i	−0.456011	+	0.456011i	−0.897344	−	0.441333i	$-0.854506\pi$
$757$	−12.5465	+	12.5465i	−0.456011	+	0.456011i	0.441333	+	0.897344i	$0.354506\pi$
$758$	9.94788	+	5.06870i	0.361323	+	0.184103i
$759$	−40.2988	+	6.38270i	−1.46275	+	0.231677i
$760$	0.193247	+	0.0489755i	0.00700980	+	0.00177653i
$761$	−1.11561	+	7.04369i	−0.0404409	+	0.255334i	−0.999623	−	0.0274553i	$-0.991260\pi$
$761$	−1.11561	+	7.04369i	−0.0404409	+	0.255334i	0.959182	+	0.282789i	$0.0912596\pi$
$762$	8.37572	−	11.5282i	0.303420	−	0.417622i
$763$	−0.998092	−	6.30170i	−0.0361333	−	0.228137i
$764$	10.9674	−	7.96832i	0.396788	−	0.288284i
$765$	3.60340	−	1.43970i	0.130281	−	0.0520526i
$766$	8.45680	−	11.6398i	0.305556	−	0.420562i
$767$	0.868424	+	13.8275i	0.0313570	+	0.499283i
$768$	0.739919	+	0.739919i	0.0266995	+	0.0266995i
$769$	26.7859	+	13.6481i	0.965923	+	0.492162i	0.864473	−	0.502679i	$-0.167652\pi$
$769$	26.7859	+	13.6481i	0.965923	+	0.492162i	0.101449	+	0.994841i	$0.467652\pi$
$770$	−3.53001	−	8.83519i	−0.127213	−	0.318398i
$771$	−23.0412	−	7.48654i	−0.829809	−	0.269621i
$772$	−0.108956	+	0.335333i	−0.00392142	+	0.0120689i
$773$	−12.4816	−	17.1794i	−0.448931	−	0.617901i	0.523236	−	0.852188i	$-0.324725\pi$
$773$	−12.4816	−	17.1794i	−0.448931	−	0.617901i	−0.972168	+	0.234287i	$0.924725\pi$
$774$	−4.39102	−	4.39102i	−0.157832	−	0.157832i
$775$	22.1011	−	28.8626i	0.793896	−	1.03677i
$776$	6.89629			0.247562
$777$	−2.30378	−	0.364882i	−0.0826475	−	0.0130901i
$778$	−8.29084	+	25.5166i	−0.297241	+	0.914813i
$779$	0.101695	−	0.312985i	0.00364360	−	0.0112139i
$780$	−8.43297	−	0.239624i	−0.301949	−	0.00857991i
$781$	−10.0021	−	30.7834i	−0.357905	−	1.10152i
$782$	−8.37967			−0.299656
$783$	0.731847	−	1.43633i	0.0261541	−	0.0513303i
$784$	−4.84789	−	3.52220i	−0.173139	−	0.125793i
$785$	24.4107	+	29.3207i	0.871254	+	1.04650i
$786$	−3.93150	−	0.622688i	−0.140232	−	0.0222106i
$787$	−20.4215	+	28.1078i	−0.727948	+	1.00193i	0.271274	+	0.962502i	$0.412555\pi$
$787$	−20.4215	+	28.1078i	−0.727948	+	1.00193i	−0.999222	+	0.0394325i	$0.987445\pi$
$788$	9.38789	+	6.82070i	0.334430	+	0.242977i
$789$	6.43558	+	8.85782i	0.229113	+	0.315347i
$790$	−4.44678	−	19.6063i	−0.158209	−	0.697561i
$791$	7.95969	−	1.26069i	0.283014	−	0.0448250i
$792$	3.66590	−	7.19473i	0.130262	−	0.255654i
$793$	13.3075	−	7.86806i	0.472564	−	0.279403i
$794$	0.683206	−	0.221987i	0.0242461	−	0.00787803i
$795$	23.3153	+	20.4264i	0.826910	+	0.724448i
$796$	3.36515	−	10.3569i	0.119275	−	0.367090i
$797$	−1.64031	+	0.835778i	−0.0581026	+	0.0296048i	−0.482800	−	0.875730i	$-0.660380\pi$
$797$	−1.64031	+	0.835778i	−0.0581026	+	0.0296048i	0.424698	+	0.905335i	$0.360380\pi$
$798$	−0.0550458	−	0.0757641i	−0.00194860	−	0.00268202i
$799$	6.28238	−	6.28238i	0.222255	−	0.222255i
$800$	4.91718	+	0.906254i	0.173849	+	0.0320409i
$801$	−7.58317	+	7.58317i	−0.267938	+	0.267938i
$802$	1.97174	−	12.4491i	0.0696244	−	0.439591i
$803$	−5.81855	−	11.4196i	−0.205332	−	0.402987i
$804$	8.28071	−	4.21923i	0.292038	−	0.148801i
$805$	5.07268	−	20.0157i	0.178788	−	0.705462i
$806$	1.64312	+	26.1626i	0.0578764	+	0.921540i
$807$	14.1302	−	14.1302i	0.497407	−	0.497407i
$808$	−7.04235	+	2.28820i	−0.247749	+	0.0804986i
$809$	17.8522	−	24.5715i	0.627651	−	0.863887i	−0.370231	−	0.928940i	$-0.620722\pi$
$809$	17.8522	−	24.5715i	0.627651	−	0.863887i	0.997882	+	0.0650527i	$0.0207216\pi$
$810$	−0.507315	+	0.579067i	−0.0178252	+	0.0203463i
$811$	−38.9631	−	6.17115i	−1.36818	−	0.216698i	−0.571253	−	0.820774i	$-0.693542\pi$
$811$	−38.9631	−	6.17115i	−1.36818	−	0.216698i	−0.796927	+	0.604076i	$0.793542\pi$
$812$	−0.255065	−	0.185315i	−0.00895102	−	0.00650330i
$813$	−14.4137	−	10.4721i	−0.505509	−	0.367274i
$814$	9.29629	+	1.47239i	0.325835	+	0.0516072i
$815$	−28.5611	+	32.6006i	−1.00045	+	1.14195i
$816$	−0.560276	+	0.771154i	−0.0196136	+	0.0269958i
$817$	0.276393	−	0.0898056i	0.00966978	−	0.00314190i
$818$	−10.6970	+	10.6970i	−0.374013	+	0.374013i
$819$	−5.17154	−	4.56034i	−0.180708	−	0.159351i
$820$	2.02771	−	8.00091i	0.0708107	−	0.279404i
$821$	−37.5310	+	19.1230i	−1.30984	+	0.667397i	−0.962739	−	0.270431i	$-0.912834\pi$
$821$	−37.5310	+	19.1230i	−1.30984	+	0.667397i	−0.347101	+	0.937828i	$0.612834\pi$
$822$	4.18935	+	8.22206i	0.146120	+	0.286777i
$823$	2.59524	−	16.3857i	0.0904644	−	0.571170i	−0.900267	−	0.435337i	$-0.856629\pi$
$823$	2.59524	−	16.3857i	0.0904644	−	0.571170i	0.990732	−	0.135833i	$-0.0433709\pi$
$824$	3.32007	−	3.32007i	0.115660	−	0.115660i
$825$	2.91667	+	21.9842i	0.101545	+	0.765391i
$826$	−2.72756	+	2.72756i	−0.0949039	+	0.0949039i
$827$	−13.0845	−	18.0093i	−0.454993	−	0.626244i	0.518468	−	0.855097i	$-0.326503\pi$
$827$	−13.0845	−	18.0093i	−0.454993	−	0.626244i	−0.973461	+	0.228853i	$0.926503\pi$
$828$	15.6145	−	7.95598i	0.542641	−	0.276489i
$829$	−8.29063	+	25.5159i	−0.287945	+	0.886205i	0.697555	+	0.716531i	$0.254271\pi$
$829$	−8.29063	+	25.5159i	−0.287945	+	0.886205i	−0.985500	+	0.169673i	$0.945729\pi$
$830$	−18.6972	−	16.3805i	−0.648990	−	0.568574i
$831$	−24.3684	+	7.91776i	−0.845329	+	0.274664i
$832$	−3.10365	+	1.83503i	−0.107600	+	0.0636183i
$833$	2.47814	−	4.86363i	0.0858625	−	0.168515i
$834$	−12.2901	+	1.94657i	−0.425573	+	0.0674041i
$835$	8.10933	+	35.7549i	0.280635	+	1.23735i
$836$	0.222123	+	0.305726i	0.00768229	+	0.0105738i
$837$	−30.1901	−	21.9344i	−1.04352	−	0.758163i
$838$	22.5914	−	31.0944i	0.780407	−	1.07414i
$839$	28.6753	+	4.54173i	0.989982	+	0.156798i	0.630362	−	0.776301i	$-0.282906\pi$
$839$	28.6753	+	4.54173i	0.989982	+	0.156798i	0.359620	+	0.933099i	$0.382906\pi$
$840$	−1.50282	−	1.80510i	−0.0518521	−	0.0622819i
$841$	−23.3817	−	16.9878i	−0.806265	−	0.585786i
$842$	2.85104	−	5.59548i	0.0982533	−	0.192833i
$843$	32.1277			1.10654
$844$	−1.16722	−	3.59233i	−0.0401774	−	0.123653i
$845$	8.02902	−	27.9381i	0.276207	−	0.961098i
$846$	−5.74171	+	17.6712i	−0.197404	+	0.607548i
$847$	2.16097	−	6.65077i	0.0742517	−	0.228523i
$848$	13.0846	+	2.07240i	0.449328	+	0.0711666i
$849$	1.81081			0.0621469
$850$	−0.114667	+	4.55320i	−0.00393304	+	0.156173i
$851$	14.4440	+	14.4440i	0.495135	+	0.495135i
$852$	−4.69677	−	6.46454i	−0.160909	−	0.221472i
$853$	5.22280	−	16.0741i	0.178825	−	0.550367i	−0.820962	−	0.570982i	$-0.806562\pi$
$853$	5.22280	−	16.0741i	0.178825	−	0.550367i	0.999787	+	0.0206150i	$0.00656244\pi$
$854$	4.09347	+	1.33005i	0.140076	+	0.0455133i
$855$	−0.140908	−	0.352675i	−0.00481894	−	0.0120612i
$856$	12.5904	+	6.41514i	0.430331	+	0.219265i
$857$	−4.23773	−	4.23773i	−0.144758	−	0.144758i	0.631014	−	0.775772i	$-0.282639\pi$
$857$	−4.23773	−	4.23773i	−0.144758	−	0.144758i	−0.775772	+	0.631014i	$0.782639\pi$
$858$	−11.9946	−	10.5770i	−0.409487	−	0.361092i
$859$	20.4022	−	28.0812i	0.696113	−	0.958117i	−0.303873	−	0.952713i	$-0.598280\pi$
$859$	20.4022	−	28.0812i	0.696113	−	0.958117i	0.999985	−	0.00540436i	$-0.00172027\pi$
$860$	6.76863	−	2.70434i	0.230808	−	0.0922172i
$861$	−3.13682	+	2.27904i	−0.106903	+	0.0776693i
$862$	−5.33375	−	33.6760i	−0.181668	−	1.14701i
$863$	21.4819	−	29.5673i	0.731252	−	1.00648i	−0.267822	−	0.963468i	$-0.586304\pi$
$863$	21.4819	−	29.5673i	0.731252	−	1.00648i	0.999074	−	0.0430142i	$-0.0136961\pi$
$864$	0.802924	−	5.06946i	0.0273160	−	0.172467i
$865$	35.9076	+	9.10023i	1.22089	+	0.309417i
$866$	−5.45573	+	0.864103i	−0.185393	+	0.0293634i
$867$	15.0763	+	7.68178i	0.512019	+	0.260887i
$868$	−5.16073	+	5.16073i	−0.175166	+	0.175166i
$869$	17.3013	−	33.9558i	0.586908	−	1.15187i
$870$	0.470194	+	0.564771i	0.0159411	+	0.0191475i
$871$	6.98211	+	31.2524i	0.236580	+	1.05895i
$872$	2.88552	+	5.66315i	0.0977160	+	0.191778i
$873$	−7.72214	−	10.6286i	−0.261355	−	0.359724i
$874$			0.820140i			0.0277417i
$875$	−10.8064	−	3.03020i	−0.365322	−	0.102439i
$876$	−2.23729	−	2.23729i	−0.0755911	−	0.0755911i
$877$	−5.87006	+	4.26485i	−0.198218	+	0.144014i	−0.682467	−	0.730917i	$-0.739093\pi$
$877$	−5.87006	+	4.26485i	−0.198218	+	0.144014i	0.484249	+	0.874930i	$0.339093\pi$
$878$	−1.83928	+	5.66071i	−0.0620725	+	0.191040i
$879$	1.31331	−	0.669166i	0.0442969	−	0.0225704i
$880$	6.06422	+	7.28401i	0.204425	+	0.245544i
$881$	45.8353	−	14.8928i	1.54423	−	0.501751i	0.591691	−	0.806165i	$-0.298461\pi$
$881$	45.8353	−	14.8928i	1.54423	−	0.501751i	0.952540	+	0.304414i	$0.0984607\pi$
$882$			11.4156i			0.384383i
$883$	27.8383	+	14.1843i	0.936833	+	0.477340i	0.854608	−	0.519274i	$-0.173798\pi$
$883$	27.8383	+	14.1843i	0.936833	+	0.477340i	0.0822246	+	0.996614i	$0.473798\pi$
$884$	−2.09328	−	2.53090i	−0.0704045	−	0.0851235i
$885$	7.72469	−	4.60095i	0.259663	−	0.154659i
$886$	32.1424	+	5.09085i	1.07984	+	0.171030i
$887$	−37.1469	+	5.88348i	−1.24727	+	0.197548i	−0.744942	−	0.667129i	$-0.767523\pi$
$887$	−37.1469	+	5.88348i	−1.24727	+	0.197548i	−0.502328	+	0.864677i	$0.667523\pi$
$888$	2.29498	−	0.363490i	0.0770146	−	0.0121979i
$889$	−2.13844	+	13.5016i	−0.0717211	+	0.452829i
$890$	−4.67032	−	11.6892i	−0.156550	−	0.391824i
$891$	−1.44138	+	0.228292i	−0.0482879	+	0.00764806i
$892$	−0.619908	+	0.201420i	−0.0207561	+	0.00674405i
$893$	−0.614873	−	0.614873i	−0.0205759	−	0.0205759i
$894$	4.96253	+	15.2731i	0.165972	+	0.510809i
$895$	−50.7860	−	21.7893i	−1.69759	−	0.728335i
$896$	−0.954701	−	0.310201i	−0.0318943	−	0.0103631i
$897$	−7.56731	−	33.8717i	−0.252665	−	1.13094i
$898$	−13.7467	−	2.17726i	−0.458734	−	0.0726563i
$899$	1.61466	−	1.61466i	0.0538520	−	0.0538520i
$900$	−4.10931	−	8.59319i	−0.136977	−	0.286440i
$901$			12.0677i			0.402034i
$902$	12.6578	−	9.19646i	0.421460	−	0.306209i
$903$	−3.25644	−	1.05808i	−0.108367	−	0.0352107i
$904$	−7.15312	+	3.64470i	−0.237909	+	0.121221i
$905$	−2.81151	−	12.3962i	−0.0934577	−	0.412065i
$906$	−2.98815	−	9.19658i	−0.0992746	−	0.305536i
$907$	−16.0216	−	16.0216i	−0.531987	−	0.531987i	0.389176	−	0.921163i	$-0.372760\pi$
$907$	−16.0216	−	16.0216i	−0.531987	−	0.531987i	−0.921163	+	0.389176i	$0.872760\pi$
$908$	1.34245	+	4.13163i	0.0445507	+	0.137113i
$909$	11.4123	+	8.29152i	0.378522	+	0.275012i
$910$	7.31250	−	3.46791i	0.242407	−	0.114960i
$911$	−16.3475	+	11.8771i	−0.541616	+	0.393507i	−0.824685	−	0.565592i	$-0.808648\pi$
$911$	−16.3475	+	11.8771i	−0.541616	+	0.393507i	0.283069	+	0.959100i	$0.408648\pi$
$912$	0.0754748	+	0.0548357i	0.00249922	+	0.00181579i
$913$	−7.37120	−	46.5399i	−0.243951	−	1.54025i
$914$	−12.7481	+	9.26200i	−0.421668	+	0.306360i
$915$	−8.48743	−	5.34923i	−0.280586	−	0.176840i
$916$	3.97199	+	25.0781i	0.131238	+	0.828605i
$917$	3.63167	−	1.18000i	0.119928	−	0.0389671i
$918$	4.67548			0.154314
$919$	−31.5962	+	10.2662i	−1.04226	+	0.338652i	−0.779628	−	0.626243i	$-0.784592\pi$
$919$	−31.5962	+	10.2662i	−1.04226	+	0.338652i	−0.262636	+	0.964895i	$0.584592\pi$
$920$	1.35560	+	20.5250i	0.0446928	+	0.676688i
$921$	−4.62854	−	9.08403i	−0.152516	−	0.299329i
$922$	8.72431	−	4.44526i	0.287320	−	0.146397i
$923$	25.6006	−	10.1327i	0.842654	−	0.333523i
$924$		−	4.45236i		−	0.146472i
$925$	8.04599	−	7.65068i	0.264550	−	0.251553i
$926$	11.9409			0.392403
$927$	−8.83459	−	1.39926i	−0.290166	−	0.0459578i
$928$	0.298702	+	0.0970542i	0.00980538	+	0.00318596i
$929$	−18.0946	−	35.5127i	−0.593666	−	1.16513i	−0.971005	−	0.239060i	$-0.923161\pi$
$929$	−18.0946	−	35.5127i	−0.593666	−	1.16513i	0.377339	−	0.926075i	$-0.376839\pi$
$930$	14.6156	−	8.70531i	0.479266	−	0.285458i
$931$	−0.476016	−	0.242542i	−0.0156008	−	0.00794900i
$932$	−20.1000	+	20.1000i	−0.658399	+	0.658399i
$933$	−19.2347	−	9.80054i	−0.629714	−	0.320855i
$934$	1.82513	+	11.5234i	0.0597202	+	0.377058i
$935$	−5.68937	+	6.49404i	−0.186062	+	0.212378i
$936$	6.30350	+	2.72859i	0.206036	+	0.0891868i
$937$	53.9260	−	8.54103i	1.76168	−	0.279023i	0.810073	−	0.586329i	$-0.199427\pi$
$937$	53.9260	−	8.54103i	1.76168	−	0.279023i	0.951611	+	0.307305i	$0.0994273\pi$
$938$	−5.24043	+	7.21284i	−0.171106	+	0.235508i
$939$	−17.9031	−	24.6416i	−0.584247	−	0.804147i
$940$	−16.4042	−	14.3716i	−0.535047	−	0.468750i
$941$	3.08159	+	19.4564i	0.100457	+	0.634260i	0.985620	+	0.168979i	$0.0540469\pi$
$941$	3.08159	+	19.4564i	0.100457	+	0.634260i	−0.885163	+	0.465281i	$0.845953\pi$
$942$	5.51716	+	16.9801i	0.179759	+	0.553241i
$943$	33.9559			1.10576
$944$	1.74451	−	3.42380i	0.0567791	−	0.111435i
$945$	−2.83033	+	11.1679i	−0.0920705	+	0.363291i
$946$	13.1405	+	4.26961i	0.427235	+	0.138817i
$947$	−53.0272	−	17.2296i	−1.72315	−	0.559886i	−0.730720	−	0.682677i	$-0.760816\pi$
$947$	−53.0272	−	17.2296i	−1.72315	−	0.559886i	−0.992433	+	0.122791i	$0.960816\pi$
$948$	1.47175	−	9.29228i	0.0478003	−	0.301799i
$949$	9.38450	−	5.54858i	0.304634	−	0.180115i
$950$	0.445633	+	0.0112227i	0.0144583	+	0.000364114i
$951$	12.9344	+	12.9344i	0.419427	+	0.419427i
$952$	0.143047	−	0.903161i	0.00463617	−	0.0292716i
$953$	0.477583	+	0.937309i	0.0154704	+	0.0303624i	0.898612	−	0.438743i	$-0.144576\pi$
$953$	0.477583	+	0.937309i	0.0154704	+	0.0303624i	−0.883142	+	0.469106i	$0.844576\pi$
$954$	−11.4576	−	22.4867i	−0.370952	−	0.728035i
$955$	19.9755	−	22.8007i	0.646392	−	0.737814i
$956$	−3.10034	−	1.57970i	−0.100272	−	0.0510912i
$957$			1.39303i			0.0450303i
$958$	5.65744	−	11.1034i	0.182784	−	0.358733i
$959$	−7.16175	−	5.20331i	−0.231265	−	0.168024i
$960$	1.97948	+	1.24758i	0.0638876	+	0.0402653i
$961$	−12.8491	−	17.6853i	−0.414488	−	0.570494i
$962$	−0.754338	+	7.97068i	−0.0243208	+	0.256985i
$963$	−4.21110	−	26.5878i	−0.135701	−	0.856781i
$964$	−3.18581	+	20.1144i	−0.102608	+	0.647843i
$965$	−0.0717480	+	0.785143i	−0.00230965	+	0.0252746i
$966$	5.67965	−	7.81737i	0.182740	−	0.251520i
$967$	−10.8129	−	33.2786i	−0.347719	−	1.07017i	−0.960112	−	0.279615i	$-0.909793\pi$
$967$	−10.8129	−	33.2786i	−0.347719	−	1.07017i	0.612393	−	0.790553i	$-0.290207\pi$
$968$			6.96634i			0.223907i
$969$	−0.0385812	+	0.0757198i	−0.00123941	+	0.00243247i
$970$	15.0386	−	3.41081i	0.482861	−	0.109514i
$971$	−7.63154	+	23.4875i	−0.244908	+	0.753748i	0.750744	+	0.660593i	$0.229695\pi$
$971$	−7.63154	+	23.4875i	−0.244908	+	0.753748i	−0.995652	+	0.0931550i	$0.970305\pi$
$972$	−14.0407	+	7.15408i	−0.450355	+	0.229467i
$973$	9.65731	−	7.01645i	0.309599	−	0.224937i
$974$	19.7211			0.631904
$975$	−18.5082	+	3.64829i	−0.592736	+	0.116839i
$976$	−4.28770			−0.137246
$977$	−3.91111	+	2.84159i	−0.125127	+	0.0909104i	−0.648589	−	0.761139i	$-0.724640\pi$
$977$	−3.91111	+	2.84159i	−0.125127	+	0.0909104i	0.523461	+	0.852049i	$0.324640\pi$
$978$	−18.0719	+	9.20811i	−0.577877	+	0.294443i
$979$	7.37350	−	22.6933i	0.235658	−	0.725281i
$980$	−12.3137	−	5.28310i	−0.393348	−	0.168762i
$981$	5.49702	−	10.7885i	0.175506	−	0.344451i
$982$			5.68264i			0.181340i
$983$	2.47999	+	7.63261i	0.0790993	+	0.243443i	0.982785	−	0.184754i	$-0.0591490\pi$
$983$	2.47999	+	7.63261i	0.0790993	+	0.243443i	−0.903685	+	0.428197i	$0.859149\pi$
$984$	2.27034	−	3.12485i	0.0723757	−	0.0996165i
$985$	23.8454	+	10.2307i	0.759779	+	0.325976i
$986$	−0.0447557	+	0.282576i	−0.00142531	+	0.00899907i
$987$	1.60268	+	10.1189i	0.0510140	+	0.322090i
$988$	−0.247706	+	0.204874i	−0.00788058	+	0.00651792i
$989$	17.6253	+	24.2592i	0.560453	+	0.771398i
$990$	4.43575	−	17.5025i	0.140977	−	0.556267i
$991$	−27.0456	−	19.6498i	−0.859131	−	0.624195i	0.0685177	−	0.997650i	$-0.478173\pi$
$991$	−27.0456	−	19.6498i	−0.859131	−	0.624195i	−0.927648	+	0.373455i	$0.878173\pi$
$992$	3.30074	−	6.47807i	0.104799	−	0.205679i
$993$			8.49768i			0.269666i
$994$	6.83003	+	3.48008i	0.216636	+	0.110381i
$995$	2.21597	−	24.2494i	0.0702508	−	0.768759i
$996$	−5.28107	−	10.3647i	−0.167337	−	0.328418i
$997$	9.15058	+	17.9590i	0.289802	+	0.568768i	0.989305	−	0.145861i	$-0.0465953\pi$
$997$	9.15058	+	17.9590i	0.289802	+	0.568768i	−0.699503	+	0.714629i	$0.746595\pi$
$998$	2.33223	−	14.7251i	0.0738253	−	0.466115i
$999$	−8.05911	−	8.05911i	−0.254979	−	0.254979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.ba.b.73.13	✓	144
13.5	odd	4		650.2.bd.b.473.13	yes	144
25.12	odd	20		650.2.bd.b.437.13	yes	144
325.187	even	20	inner	650.2.ba.b.187.13	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.ba.b.73.13	✓	144	1.1	even	1	trivial
650.2.ba.b.187.13	yes	144	325.187	even	20	inner
650.2.bd.b.437.13	yes	144	25.12	odd	20
650.2.bd.b.473.13	yes	144	13.5	odd	4

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.ba (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.932353 - 0.475057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.203489 - 2.22679i) q^{5} +(0.475057 - 0.932353i) q^{6} +1.00383i q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.11975 + 1.54121i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.932353 - 0.475057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.203489 - 2.22679i) q^{5} +(0.475057 - 0.932353i) q^{6} +1.00383i q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.11975 + 1.54121i) q^{9} +(-1.14425 - 1.92112i) q^{10} +(0.663074 - 4.18649i) q^{11} +(-0.163694 - 1.03352i) q^{12} +(3.58951 + 0.339708i) q^{13} +(0.590038 + 0.812117i) q^{14} +(-0.868129 - 2.17282i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.413553 - 0.811643i) q^{17} +1.90504i q^{18} +(-0.0794376 - 0.0404755i) q^{19} +(-2.05492 - 0.881645i) q^{20} +(0.476878 + 0.935925i) q^{21} +(-1.92432 - 3.77668i) q^{22} +(1.43905 - 9.08579i) q^{23} +(-0.739919 - 0.739919i) q^{24} +(-4.91718 - 0.906254i) q^{25} +(3.10365 - 1.83503i) q^{26} +(-0.802924 + 5.06946i) q^{27} +(0.954701 + 0.310201i) q^{28} +(-0.298702 - 0.0970542i) q^{29} +(-1.97948 - 1.24758i) q^{30} +(-3.30074 + 6.47807i) q^{31} -1.00000 q^{32} +(-1.37060 - 4.21828i) q^{33} +(-0.142501 - 0.899713i) q^{34} +(2.23532 + 0.204269i) q^{35} +(1.11975 + 1.54121i) q^{36} +(-1.30521 + 1.79646i) q^{37} +(-0.0880573 + 0.0139469i) q^{38} +(3.50807 - 1.38850i) q^{39} +(-2.18068 + 0.494586i) q^{40} +(0.577437 + 3.64579i) q^{41} +(0.935925 + 0.476878i) q^{42} +(-2.30495 + 2.30495i) q^{43} +(-3.77668 - 1.92432i) q^{44} +(3.20409 + 2.80708i) q^{45} +(-4.17628 - 8.19641i) q^{46} +(9.27602 + 3.01396i) q^{47} +(-1.03352 - 0.163694i) q^{48} +5.99232 q^{49} +(-4.51077 + 2.15707i) q^{50} -0.953199i q^{51} +(1.43230 - 3.30885i) q^{52} +(-11.8038 + 6.01434i) q^{53} +(2.33017 + 4.57323i) q^{54} +(-9.18750 - 2.32843i) q^{55} +(0.954701 - 0.310201i) q^{56} -0.0932920 q^{57} +(-0.298702 + 0.0970542i) q^{58} +(0.601119 + 3.79531i) q^{59} +(-2.33474 + 0.154201i) q^{60} +(3.46882 - 2.52025i) q^{61} +(1.13736 + 7.18099i) q^{62} +(-1.54712 - 1.12405i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(1.48688 - 7.92396i) q^{65} +(-3.58828 - 2.60704i) q^{66} +(2.74454 + 8.44683i) q^{67} +(-0.644123 - 0.644123i) q^{68} +(-2.97457 - 9.15479i) q^{69} +(1.92848 - 1.14863i) q^{70} +(6.80396 - 3.46679i) q^{71} +(1.81180 + 0.588690i) q^{72} +(2.44622 - 1.77728i) q^{73} +2.22055i q^{74} +(-5.01507 + 1.49100i) q^{75} +(-0.0630420 + 0.0630420i) q^{76} +(4.20253 + 0.665615i) q^{77} +(2.02195 - 3.18531i) q^{78} +(8.55085 + 2.77834i) q^{79} +(-1.47350 + 1.68190i) q^{80} +(-0.106392 - 0.327442i) q^{81} +(2.61010 + 2.61010i) q^{82} +(10.5726 - 3.43525i) q^{83} +(1.03748 - 0.164321i) q^{84} +(-1.72320 - 1.08606i) q^{85} +(-0.509927 + 3.21956i) q^{86} +(-0.324602 + 0.0514119i) q^{87} +(-4.18649 + 0.663074i) q^{88} +(5.56009 + 0.880631i) q^{89} +(4.24212 + 0.387654i) q^{90} +(-0.341010 + 3.60327i) q^{91} +(-8.19641 - 4.17628i) q^{92} +7.60789i q^{93} +(9.27602 - 3.01396i) q^{94} +(-0.106295 + 0.168655i) q^{95} +(-0.932353 + 0.475057i) q^{96} +(-2.13107 + 6.55876i) q^{97} +(4.84789 - 3.52220i) q^{98} +(5.70977 + 5.70977i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9}+O(q^{10}) \) 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9	\( 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9} + 6 q^{13} + 8 q^{15} - 36 q^{16} - 6 q^{17} - 20 q^{19} - 6 q^{21} + 12 q^{23} + 2 q^{25} + 14 q^{26} - 24 q^{27} + 20 q^{29} + 12 q^{30} - 6 q^{31} - 144 q^{32} - 54 q^{33} + 6 q^{34} + 40 q^{35} + 20 q^{36} - 60 q^{37} + 20 q^{39} + 52 q^{41} + 6 q^{42} - 12 q^{43} - 6 q^{45} + 28 q^{46} + 50 q^{47} - 160 q^{49} - 22 q^{50} + 6 q^{52} + 20 q^{53} - 6 q^{54} - 32 q^{55} - 28 q^{57} + 20 q^{58} - 16 q^{59} - 12 q^{60} + 12 q^{61} + 6 q^{62} - 70 q^{63} - 36 q^{64} + 44 q^{65} - 16 q^{66} - 8 q^{67} - 6 q^{68} + 26 q^{69} + 10 q^{70} + 72 q^{71} - 52 q^{73} + 32 q^{75} - 56 q^{77} - 50 q^{78} - 20 q^{79} + 124 q^{81} - 22 q^{82} + 70 q^{83} - 6 q^{84} - 18 q^{85} - 8 q^{86} + 8 q^{87} + 28 q^{89} - 14 q^{90} - 26 q^{91} + 12 q^{92} + 50 q^{94} - 46 q^{95} + 28 q^{97} - 20 q^{98} + 40 q^{99}+O(q^{100}) \) 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9 + 6 * q^13 + 8 * q^15 - 36 * q^16 - 6 * q^17 - 20 * q^19 - 6 * q^21 + 12 * q^23 + 2 * q^25 + 14 * q^26 - 24 * q^27 + 20 * q^29 + 12 * q^30 - 6 * q^31 - 144 * q^32 - 54 * q^33 + 6 * q^34 + 40 * q^35 + 20 * q^36 - 60 * q^37 + 20 * q^39 + 52 * q^41 + 6 * q^42 - 12 * q^43 - 6 * q^45 + 28 * q^46 + 50 * q^47 - 160 * q^49 - 22 * q^50 + 6 * q^52 + 20 * q^53 - 6 * q^54 - 32 * q^55 - 28 * q^57 + 20 * q^58 - 16 * q^59 - 12 * q^60 + 12 * q^61 + 6 * q^62 - 70 * q^63 - 36 * q^64 + 44 * q^65 - 16 * q^66 - 8 * q^67 - 6 * q^68 + 26 * q^69 + 10 * q^70 + 72 * q^71 - 52 * q^73 + 32 * q^75 - 56 * q^77 - 50 * q^78 - 20 * q^79 + 124 * q^81 - 22 * q^82 + 70 * q^83 - 6 * q^84 - 18 * q^85 - 8 * q^86 + 8 * q^87 + 28 * q^89 - 14 * q^90 - 26 * q^91 + 12 * q^92 + 50 * q^94 - 46 * q^95 + 28 * q^97 - 20 * q^98 + 40 * q^99

Introduction

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