LMFDB - Embedded newform 429.2.bj.a.424.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(73,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 14, 5]))

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

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

chi := DirichletCharacter("429.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bj (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			424.9
Character	$\chi$	$=$	429.424
Dual form			429.2.bj.a.343.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.396304 + 0.201927i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.05929 - 1.45799i) q^{4} +(-1.97703 + 1.00735i) q^{5} +(-0.201927 - 0.396304i) q^{6} +(0.380750 + 0.0603048i) q^{7} +(-0.264552 - 1.67032i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.396304 + 0.201927i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.05929 - 1.45799i) q^{4} +(-1.97703 + 1.00735i) q^{5} +(-0.201927 - 0.396304i) q^{6} +(0.380750 + 0.0603048i) q^{7} +(-0.264552 - 1.67032i) q^{8} +(0.309017 + 0.951057i) q^{9} -0.986916 q^{10} +(2.38874 + 2.30086i) q^{11} +1.80217i q^{12} +(-3.31298 + 1.42273i) q^{13} +(0.138715 + 0.100783i) q^{14} +(2.19156 + 0.347109i) q^{15} +(-0.881363 + 2.71256i) q^{16} +(-0.807047 + 2.48383i) q^{17} +(-0.0695793 + 0.439306i) q^{18} +(-6.72641 + 1.06536i) q^{19} +(3.56295 + 1.81541i) q^{20} +(-0.272587 - 0.272587i) q^{21} +(0.482060 + 1.39419i) q^{22} +3.32899i q^{23} +(-0.767760 + 1.50681i) q^{24} +(-0.0450191 + 0.0619635i) q^{25} +(-1.60023 - 0.105149i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.315400 - 0.619008i) q^{28} +(-0.151082 - 0.207946i) q^{29} +(0.798432 + 0.580095i) q^{30} +(-2.96320 + 5.81562i) q^{31} +(-3.28865 + 3.28865i) q^{32} +(-0.580118 - 3.26550i) q^{33} +(-0.821389 + 0.821389i) q^{34} +(-0.813503 + 0.264323i) q^{35} +(1.05929 - 1.45799i) q^{36} +(1.43319 - 9.04879i) q^{37} +(-2.88083 - 0.936037i) q^{38} +(3.51652 + 0.796314i) q^{39} +(2.20562 + 3.03577i) q^{40} +(9.16120 - 1.45099i) q^{41} +(-0.0529846 - 0.163070i) q^{42} +4.96533 q^{43} +(0.824256 - 5.92001i) q^{44} +(-1.56898 - 1.56898i) q^{45} +(-0.672213 + 1.31929i) q^{46} +(-6.66976 + 1.05639i) q^{47} +(2.30744 - 1.67645i) q^{48} +(-6.51606 - 2.11720i) q^{49} +(-0.0303534 + 0.0154658i) q^{50} +(2.11288 - 1.53509i) q^{51} +(5.58372 + 3.32320i) q^{52} +(0.308233 + 0.948645i) q^{53} +(0.314508 - 0.314508i) q^{54} +(-7.04037 - 2.14258i) q^{55} -0.651926i q^{56} +(6.06798 + 3.09179i) q^{57} +(-0.0178844 - 0.112917i) q^{58} +(1.40777 - 8.88833i) q^{59} +(-1.81541 - 3.56295i) q^{60} +(4.89107 + 1.58921i) q^{61} +(-2.34866 + 1.70640i) q^{62} +(0.0603048 + 0.380750i) q^{63} +(3.45774 - 1.12349i) q^{64} +(5.11669 - 6.15010i) q^{65} +(0.429489 - 1.41127i) q^{66} +(-4.47560 - 4.47560i) q^{67} +(4.47629 - 1.45443i) q^{68} +(1.95673 - 2.69321i) q^{69} +(-0.375768 - 0.0595158i) q^{70} +(-1.60883 + 0.819740i) q^{71} +(1.50681 - 0.767760i) q^{72} +(-14.8274 - 2.34843i) q^{73} +(2.39517 - 3.29667i) q^{74} +(0.0728425 - 0.0236680i) q^{75} +(8.67849 + 8.67849i) q^{76} +(0.770758 + 1.02010i) q^{77} +(1.23281 + 1.02566i) q^{78} +(-12.6789 + 4.11961i) q^{79} +(-0.990006 - 6.25065i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(3.92361 + 1.27486i) q^{82} +(-3.71205 - 7.28532i) q^{83} +(-0.108680 + 0.686175i) q^{84} +(-0.906529 - 5.72360i) q^{85} +(1.96778 + 1.00263i) q^{86} +0.257036i q^{87} +(3.21121 - 4.59864i) q^{88} +(-11.7782 + 11.7782i) q^{89} +(-0.304974 - 0.938613i) q^{90} +(-1.34721 + 0.341913i) q^{91} +(4.85362 - 3.52636i) q^{92} +(5.81562 - 2.96320i) q^{93} +(-2.85656 - 0.928154i) q^{94} +(12.2251 - 8.88209i) q^{95} +(4.59360 - 0.727555i) q^{96} +(-2.27838 + 4.47158i) q^{97} +(-2.15482 - 2.15482i) q^{98} +(-1.45009 + 2.98283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9	$ 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9} - 10 q^{11} + 10 q^{13} - 60 q^{14} + 4 q^{15} + 80 q^{16} - 74 q^{20} + 8 q^{22} + 30 q^{24} + 38 q^{26} - 28 q^{27} - 20 q^{29} - 8 q^{31} + 20 q^{33} - 48 q^{34} + 20 q^{35} + 12 q^{37} - 10 q^{39} + 40 q^{40} - 110 q^{41} + 20 q^{42} - 36 q^{44} + 4 q^{45} - 20 q^{46} - 30 q^{47} - 20 q^{48} + 90 q^{50} - 10 q^{52} + 52 q^{53} - 64 q^{55} + 30 q^{57} + 24 q^{58} - 36 q^{59} - 74 q^{60} - 60 q^{61} + 48 q^{66} + 60 q^{67} + 60 q^{68} + 116 q^{70} + 20 q^{71} - 30 q^{72} + 70 q^{73} + 120 q^{74} - 52 q^{78} - 120 q^{79} + 8 q^{80} - 28 q^{81} + 30 q^{83} + 30 q^{84} - 40 q^{85} + 62 q^{86} + 48 q^{89} - 4 q^{91} - 144 q^{92} - 8 q^{93} - 20 q^{94} + 82 q^{97} - 10 q^{99}+O(q^{100}) $ 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9 - 10 * q^11 + 10 * q^13 - 60 * q^14 + 4 * q^15 + 80 * q^16 - 74 * q^20 + 8 * q^22 + 30 * q^24 + 38 * q^26 - 28 * q^27 - 20 * q^29 - 8 * q^31 + 20 * q^33 - 48 * q^34 + 20 * q^35 + 12 * q^37 - 10 * q^39 + 40 * q^40 - 110 * q^41 + 20 * q^42 - 36 * q^44 + 4 * q^45 - 20 * q^46 - 30 * q^47 - 20 * q^48 + 90 * q^50 - 10 * q^52 + 52 * q^53 - 64 * q^55 + 30 * q^57 + 24 * q^58 - 36 * q^59 - 74 * q^60 - 60 * q^61 + 48 * q^66 + 60 * q^67 + 60 * q^68 + 116 * q^70 + 20 * q^71 - 30 * q^72 + 70 * q^73 + 120 * q^74 - 52 * q^78 - 120 * q^79 + 8 * q^80 - 28 * q^81 + 30 * q^83 + 30 * q^84 - 40 * q^85 + 62 * q^86 + 48 * q^89 - 4 * q^91 - 144 * q^92 - 8 * q^93 - 20 * q^94 + 82 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	0.396304	+	0.201927i	0.280229	+	0.142784i	0.588457	−	0.808529i	$-0.299736\pi$
$2$	0.396304	+	0.201927i	0.280229	+	0.142784i	−0.308227	+	0.951313i	$0.599736\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−1.05929	−	1.45799i	−0.529644	−	0.728993i
$5$	−1.97703	+	1.00735i	−0.884156	+	0.450500i	−0.836248	−	0.548352i	$-0.815255\pi$
$5$	−1.97703	+	1.00735i	−0.884156	+	0.450500i	−0.0479081	+	0.998852i	$0.515255\pi$
$6$	−0.201927	−	0.396304i	−0.0824363	−	0.161790i
$7$	0.380750	+	0.0603048i	0.143910	+	0.0227931i	0.227974	−	0.973667i	$-0.426790\pi$
$7$	0.380750	+	0.0603048i	0.143910	+	0.0227931i	−0.0840638	+	0.996460i	$0.526790\pi$
$8$	−0.264552	−	1.67032i	−0.0935333	−	0.590546i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−0.986916			−0.312090
$11$	2.38874	+	2.30086i	0.720231	+	0.693735i
$11$	2.38874	+	2.30086i	0.720231	+	0.693735i
$12$			1.80217i			0.520241i
$13$	−3.31298	+	1.42273i	−0.918856	+	0.394593i
$13$	−3.31298	+	1.42273i	−0.918856	+	0.394593i
$14$	0.138715	+	0.100783i	0.0370733	+	0.0269353i
$15$	2.19156	+	0.347109i	0.565858	+	0.0896231i
$16$	−0.881363	+	2.71256i	−0.220341	+	0.678139i
$17$	−0.807047	+	2.48383i	−0.195738	+	0.602418i	0.804230	+	0.594319i	$0.202578\pi$
$17$	−0.807047	+	2.48383i	−0.195738	+	0.602418i	−0.999967	+	0.00809960i	$0.997422\pi$
$18$	−0.0695793	+	0.439306i	−0.0164000	+	0.103545i
$19$	−6.72641	+	1.06536i	−1.54314	+	0.244410i	−0.869233	−	0.494402i	$-0.835387\pi$
$19$	−6.72641	+	1.06536i	−1.54314	+	0.244410i	−0.673911	+	0.738812i	$0.735387\pi$
$20$	3.56295	+	1.81541i	0.796699	+	0.405938i
$21$	−0.272587	−	0.272587i	−0.0594833	−	0.0594833i
$22$	0.482060	+	1.39419i	0.102776	+	0.297242i
$23$			3.32899i			0.694143i	0.937839	+	0.347072i	$0.112824\pi$
$23$			3.32899i			0.694143i	−0.937839	+	0.347072i	$0.887176\pi$
$24$	−0.767760	+	1.50681i	−0.156718	+	0.307577i
$25$	−0.0450191	+	0.0619635i	−0.00900383	+	0.0123927i
$26$	−1.60023	−	0.105149i	−0.313832	−	0.0206214i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−0.315400	−	0.619008i	−0.0596050	−	0.116981i
$29$	−0.151082	−	0.207946i	−0.0280552	−	0.0386147i	0.794759	−	0.606925i	$-0.207597\pi$
$29$	−0.151082	−	0.207946i	−0.0280552	−	0.0386147i	−0.822814	+	0.568311i	$0.807597\pi$
$30$	0.798432	+	0.580095i	0.145773	+	0.105910i
$31$	−2.96320	+	5.81562i	−0.532207	+	1.04452i	0.455796	+	0.890084i	$0.349355\pi$
$31$	−2.96320	+	5.81562i	−0.532207	+	1.04452i	−0.988004	+	0.154431i	$0.950645\pi$
$32$	−3.28865	+	3.28865i	−0.581357	+	0.581357i
$33$	−0.580118	−	3.26550i	−0.100986	−	0.568450i
$34$	−0.821389	+	0.821389i	−0.140867	+	0.140867i
$35$	−0.813503	+	0.264323i	−0.137507	+	0.0446788i
$36$	1.05929	−	1.45799i	0.176548	−	0.242998i
$37$	1.43319	−	9.04879i	0.235614	−	1.48761i	−0.532025	−	0.846729i	$-0.678569\pi$
$37$	1.43319	−	9.04879i	0.235614	−	1.48761i	0.767639	−	0.640882i	$-0.221431\pi$
$38$	−2.88083	−	0.936037i	−0.467332	−	0.151845i
$39$	3.51652	+	0.796314i	0.563093	+	0.127512i
$40$	2.20562	+	3.03577i	0.348739	+	0.479998i
$41$	9.16120	−	1.45099i	1.43074	−	0.226607i	0.607508	−	0.794313i	$-0.292169\pi$
$41$	9.16120	−	1.45099i	1.43074	−	0.226607i	0.823231	+	0.567706i	$0.192169\pi$
$42$	−0.0529846	−	0.163070i	−0.00817570	−	0.0251622i
$43$	4.96533			0.757206			0.378603	−	0.925559i	$-0.376405\pi$
$43$	4.96533			0.757206			0.378603	+	0.925559i	$0.376405\pi$
$44$	0.824256	−	5.92001i	0.124261	−	0.892475i
$45$	−1.56898	−	1.56898i	−0.233890	−	0.233890i
$46$	−0.672213	+	1.31929i	−0.0991125	+	0.194519i
$47$	−6.66976	+	1.05639i	−0.972885	+	0.154090i	−0.622589	−	0.782549i	$-0.713919\pi$
$47$	−6.66976	+	1.05639i	−0.972885	+	0.154090i	−0.350296	+	0.936639i	$0.613919\pi$
$48$	2.30744	−	1.67645i	0.333050	−	0.241975i
$49$	−6.51606	−	2.11720i	−0.930866	−	0.302457i
$50$	−0.0303534	+	0.0154658i	−0.00429261	+	0.00218720i
$51$	2.11288	−	1.53509i	0.295862	−	0.214956i
$52$	5.58372	+	3.32320i	0.774322	+	0.460845i
$53$	0.308233	+	0.948645i	0.0423391	+	0.130306i	0.969992	−	0.243138i	$-0.0781767\pi$
$53$	0.308233	+	0.948645i	0.0423391	+	0.130306i	−0.927653	+	0.373444i	$0.878177\pi$
$54$	0.314508	−	0.314508i	0.0427992	−	0.0427992i
$55$	−7.04037	−	2.14258i	−0.949324	−	0.288906i
$56$		−	0.651926i		−	0.0871173i
$57$	6.06798	+	3.09179i	0.803724	+	0.409518i
$58$	−0.0178844	−	0.112917i	−0.00234833	−	0.0148268i
$59$	1.40777	−	8.88833i	0.183276	−	1.15716i	−0.708845	−	0.705365i	$-0.750783\pi$
$59$	1.40777	−	8.88833i	0.183276	−	1.15716i	0.892121	−	0.451797i	$-0.149217\pi$
$60$	−1.81541	−	3.56295i	−0.234369	−	0.459974i
$61$	4.89107	+	1.58921i	0.626237	+	0.203477i	0.604908	−	0.796296i	$-0.293210\pi$
$61$	4.89107	+	1.58921i	0.626237	+	0.203477i	0.0213297	+	0.999772i	$0.493210\pi$
$62$	−2.34866	+	1.70640i	−0.298280	+	0.216713i
$63$	0.0603048	+	0.380750i	0.00759770	+	0.0479700i
$64$	3.45774	−	1.12349i	0.432217	−	0.140436i
$65$	5.11669	−	6.15010i	0.634648	−	0.762826i
$66$	0.429489	−	1.41127i	0.0528664	−	0.173715i
$67$	−4.47560	−	4.47560i	−0.546782	−	0.546782i	0.378727	−	0.925509i	$-0.376362\pi$
$67$	−4.47560	−	4.47560i	−0.546782	−	0.546782i	−0.925509	+	0.378727i	$0.876362\pi$
$68$	4.47629	−	1.45443i	0.542830	−	0.176376i
$69$	1.95673	−	2.69321i	0.235563	−	0.324225i
$70$	−0.375768	−	0.0595158i	−0.0449129	−	0.00711350i
$71$	−1.60883	+	0.819740i	−0.190933	+	0.0972852i	−0.546844	−	0.837235i	$-0.684171\pi$
$71$	−1.60883	+	0.819740i	−0.190933	+	0.0972852i	0.355911	+	0.934520i	$0.384171\pi$
$72$	1.50681	−	0.767760i	0.177580	−	0.0904814i
$73$	−14.8274	−	2.34843i	−1.73541	−	0.274863i	−0.792978	−	0.609250i	$-0.791471\pi$
$73$	−14.8274	−	2.34843i	−1.73541	−	0.274863i	−0.942436	+	0.334387i	$0.891471\pi$
$74$	2.39517	−	3.29667i	0.278433	−	0.383230i
$75$	0.0728425	−	0.0236680i	0.00841113	−	0.00273294i
$76$	8.67849	+	8.67849i	0.995491	+	0.995491i
$77$	0.770758	+	1.02010i	0.0878360	+	0.116252i
$78$	1.23281	+	1.02566i	0.139588	+	0.116133i
$79$	−12.6789	+	4.11961i	−1.42648	+	0.463492i	−0.917656	−	0.397377i	$-0.869921\pi$
$79$	−12.6789	+	4.11961i	−1.42648	+	0.463492i	−0.508827	+	0.860869i	$0.669921\pi$
$80$	−0.990006	−	6.25065i	−0.110686	−	0.698844i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	3.92361	+	1.27486i	0.433291	+	0.140785i
$83$	−3.71205	−	7.28532i	−0.407451	−	0.799667i	0.592532	−	0.805547i	$-0.298128\pi$
$83$	−3.71205	−	7.28532i	−0.407451	−	0.799667i	−0.999983	+	0.00587974i	$0.998128\pi$
$84$	−0.108680	+	0.686175i	−0.0118579	+	0.0748679i
$85$	−0.906529	−	5.72360i	−0.0983269	−	0.620811i
$86$	1.96778	+	1.00263i	0.212191	+	0.108117i
$87$			0.257036i			0.0275571i
$88$	3.21121	−	4.59864i	0.342317	−	0.490217i
$89$	−11.7782	+	11.7782i	−1.24849	+	1.24849i	−0.292097	+	0.956389i	$0.594353\pi$
$89$	−11.7782	+	11.7782i	−1.24849	+	1.24849i	−0.956389	+	0.292097i	$0.905647\pi$
$90$	−0.304974	−	0.938613i	−0.0321471	−	0.0989385i
$91$	−1.34721	+	0.341913i	−0.141226	+	0.0358423i
$92$	4.85362	−	3.52636i	0.506025	−	0.367649i
$93$	5.81562	−	2.96320i	0.603051	−	0.307270i
$94$	−2.85656	−	0.928154i	−0.294632	−	0.0957318i
$95$	12.2251	−	8.88209i	1.25427	−	0.911283i
$96$	4.59360	−	0.727555i	0.468832	−	0.0742557i
$97$	−2.27838	+	4.47158i	−0.231335	+	0.454020i	−0.977270	−	0.211999i	$-0.932003\pi$
$97$	−2.27838	+	4.47158i	−0.231335	+	0.454020i	0.745935	+	0.666018i	$0.232003\pi$
$98$	−2.15482	−	2.15482i	−0.217670	−	0.217670i
$99$	−1.45009	+	2.98283i	−0.145739	+	0.299785i
$100$	0.138030			0.0138030
$101$	2.67374	+	8.22892i	0.266047	+	0.818808i	0.991450	+	0.130484i	$0.0416531\pi$
$101$	2.67374	+	8.22892i	0.266047	+	0.818808i	−0.725404	+	0.688324i	$0.758347\pi$
$102$	1.14732	−	0.181717i	0.113601	−	0.0179927i
$103$	4.14904	+	5.71066i	0.408817	+	0.562688i	0.962929	−	0.269754i	$-0.0869423\pi$
$103$	4.14904	+	5.71066i	0.408817	+	0.562688i	−0.554113	+	0.832442i	$0.686942\pi$
$104$	3.25286	+	5.15734i	0.318969	+	0.505719i
$105$	0.813503	+	0.264323i	0.0793897	+	0.0257953i
$106$	−0.0694028	+	0.438192i	−0.00674100	+	0.0425610i
$107$	8.30131	−	11.4258i	0.802518	−	1.10457i	−0.189917	−	0.981800i	$-0.560822\pi$
$107$	8.30131	−	11.4258i	0.802518	−	1.10457i	0.992435	−	0.122771i	$-0.0391781\pi$
$108$	−1.71396	+	0.556901i	−0.164926	+	0.0535878i
$109$	−0.128910	+	0.128910i	−0.0123473	+	0.0123473i	−0.713254	−	0.700906i	$-0.752779\pi$
$109$	−0.128910	+	0.128910i	−0.0123473	+	0.0123473i	0.700906	+	0.713254i	$0.252779\pi$
$110$	−2.35748	−	2.27075i	−0.224777	−	0.216508i
$111$	−6.47822	+	6.47822i	−0.614885	+	0.614885i
$112$	−0.499159	+	0.979655i	−0.0471661	+	0.0925687i
$113$	13.3708	+	9.71443i	1.25782	+	0.913857i	0.998648	−	0.0519757i	$-0.0165518\pi$
$113$	13.3708	+	9.71443i	1.25782	+	0.913857i	0.259167	+	0.965832i	$0.416552\pi$
$114$	1.78045	+	2.45058i	0.166754	+	0.229518i
$115$	−3.35346	−	6.58153i	−0.312712	−	0.613731i
$116$	−0.143143	+	0.440550i	−0.0132905	+	0.0409041i
$117$	−2.37686	−	2.71119i	−0.219741	−	0.250649i
$118$	2.35270	−	3.23821i	0.216583	−	0.298101i
$119$	−0.457070	+	0.897051i	−0.0418996	+	0.0822325i
$120$		−	3.75242i		−	0.342548i
$121$	0.412114	+	10.9923i	0.0374649	+	0.999298i
$122$	1.61745	+	1.61745i	0.146437	+	0.146437i
$123$	−8.26444	−	4.21094i	−0.745179	−	0.379688i
$124$	11.6180	−	1.84011i	1.04332	−	0.165246i
$125$	1.76213	−	11.1256i	0.157610	−	0.995108i
$126$	−0.0529846	+	0.163070i	−0.00472024	+	0.0145274i
$127$	−0.318928	+	0.981558i	−0.0283002	+	0.0870992i	−0.964209	−	0.265143i	$-0.914581\pi$
$127$	−0.318928	+	0.981558i	−0.0283002	+	0.0870992i	0.935909	+	0.352242i	$0.114581\pi$
$128$	10.7844	+	1.70808i	0.953213	+	0.150974i
$129$	−4.01704	−	2.91855i	−0.353681	−	0.256964i
$130$	3.26964	−	1.40411i	0.286766	−	0.123149i
$131$		−	0.565920i		−	0.0494447i	−0.999694	−	0.0247223i	$-0.992130\pi$
$131$		−	0.565920i		−	0.0494447i	0.999694	−	0.0247223i	$-0.00787017\pi$
$132$	−4.14653	+	4.30490i	−0.360909	+	0.374694i
$133$	−2.62533			−0.227645
$134$	−0.869954	−	2.67744i	−0.0751526	−	0.231296i
$135$	0.347109	+	2.19156i	0.0298744	+	0.188619i
$136$	4.36229	+	0.690920i	0.374064	+	0.0592459i
$137$	3.49421	+	6.85778i	0.298531	+	0.585899i	0.990736	−	0.135801i	$-0.0433608\pi$
$137$	3.49421	+	6.85778i	0.298531	+	0.585899i	−0.692205	+	0.721700i	$0.743361\pi$
$138$	1.31929	−	0.672213i	0.112306	−	0.0572226i
$139$	0.607087	+	0.835584i	0.0514925	+	0.0708733i	0.833987	−	0.551784i	$-0.186053\pi$
$139$	0.607087	+	0.835584i	0.0514925	+	0.0708733i	−0.782494	+	0.622658i	$0.786053\pi$
$140$	1.24711	+	0.906081i	0.105400	+	0.0765778i
$141$	6.01688	+	3.06575i	0.506713	+	0.258183i
$142$	−0.803113			−0.0673957
$143$	−11.1873	−	4.22419i	−0.935531	−	0.353244i
$144$	−2.85215			−0.237679
$145$	0.508168	+	0.258925i	0.0422011	+	0.0215025i
$146$	−5.40194	−	3.92474i	−0.447068	−	0.324814i
$147$	4.02715	+	5.54289i	0.332154	+	0.457170i
$148$	−14.7112	+	7.49571i	−1.20925	+	0.616143i
$149$	9.09925	+	17.8583i	0.745440	+	1.46301i	0.881439	+	0.472299i	$0.156576\pi$
$149$	9.09925	+	17.8583i	0.745440	+	1.46301i	−0.135999	+	0.990709i	$0.543424\pi$
$150$	0.0336470	+	0.00532916i	0.00274726	+	0.000435124i
$151$	−2.45866	−	15.5234i	−0.200083	−	1.26328i	−0.859358	−	0.511374i	$-0.829137\pi$
$151$	−2.45866	−	15.5234i	−0.200083	−	1.26328i	0.659275	−	0.751902i	$-0.270863\pi$
$152$	3.55897	+	10.9534i	0.288671	+	0.888437i
$153$	−2.61166			−0.211140
$154$	0.0994680	+	0.559908i	0.00801536	+	0.0451186i
$155$		−	14.4826i		−	1.16327i
$156$	−2.56399	−	5.97055i	−0.205284	−	0.478027i
$157$	−6.00838	−	4.36535i	−0.479521	−	0.348393i	0.321619	−	0.946869i	$-0.395773\pi$
$157$	−6.00838	−	4.36535i	−0.479521	−	0.348393i	−0.801140	+	0.598477i	$0.795773\pi$
$158$	−5.85654	−	0.927584i	−0.465921	−	0.0737947i
$159$	0.308233	−	0.948645i	0.0244445	−	0.0752324i
$160$	3.18896	−	9.81460i	0.252109	−	0.775912i
$161$	−0.200755	+	1.26751i	−0.0158217	+	0.0998941i
$162$	−0.439306	+	0.0695793i	−0.0345152	+	0.00546666i
$163$	−3.82001	−	1.94639i	−0.299206	−	0.152453i	0.297942	−	0.954584i	$-0.403700\pi$
$163$	−3.82001	−	1.94639i	−0.299206	−	0.152453i	−0.597149	+	0.802131i	$0.703700\pi$
$164$	−11.8199	−	11.8199i	−0.922977	−	0.922977i
$165$	4.43640	+	5.87161i	0.345374	+	0.457104i
$166$		−	3.63676i		−	0.282267i
$167$	−2.24492	+	4.40591i	−0.173717	+	0.340939i	−0.961406	−	0.275134i	$-0.911278\pi$
$167$	−2.24492	+	4.40591i	−0.173717	+	0.340939i	0.787689	+	0.616074i	$0.211278\pi$
$168$	−0.383193	+	0.527420i	−0.0295640	+	0.0406913i
$169$	8.95171	−	9.42693i	0.688593	−	0.725148i
$170$	0.796487	−	2.45134i	0.0610878	−	0.188009i
$171$	−3.09179	−	6.06798i	−0.236435	−	0.464030i
$172$	−5.25972	−	7.23938i	−0.401050	−	0.551998i
$173$	−2.62900	−	1.91008i	−0.199879	−	0.145221i	0.483344	−	0.875431i	$-0.339422\pi$
$173$	−2.62900	−	1.91008i	−0.199879	−	0.145221i	−0.683223	+	0.730210i	$0.739422\pi$
$174$	−0.0519024	+	0.101864i	−0.00393471	+	0.00772231i
$175$	−0.0208777	+	0.0208777i	−0.00157821	+	0.00157821i
$176$	−8.34655	+	4.45169i	−0.629145	+	0.335559i
$177$	−6.36334	+	6.36334i	−0.478298	+	0.478298i
$178$	−7.04608	+	2.28941i	−0.528126	+	0.171598i
$179$	−5.67660	+	7.81316i	−0.424289	+	0.583983i	−0.966631	−	0.256175i	$-0.917538\pi$
$179$	−5.67660	+	7.81316i	−0.424289	+	0.583983i	0.542342	+	0.840158i	$0.317538\pi$
$180$	−0.625548	+	3.94956i	−0.0466256	+	0.294383i
$181$	21.2623	+	6.90853i	1.58041	+	0.513507i	0.962163	−	0.272475i	$-0.0878421\pi$
$181$	21.2623	+	6.90853i	1.58041	+	0.513507i	0.618250	+	0.785982i	$0.287842\pi$
$182$	−0.602948	−	0.136537i	−0.0446935	−	0.0101208i
$183$	−3.02285	−	4.16059i	−0.223455	−	0.307560i
$184$	5.56047	−	0.880692i	0.409924	−	0.0649255i
$185$	6.28182	+	19.3335i	0.461849	+	1.42142i
$186$	2.90310			0.212866
$187$	−7.64277	+	4.07632i	−0.558895	+	0.298090i
$188$	8.60539	+	8.60539i	0.627613	+	0.627613i
$189$	0.175011	−	0.343479i	0.0127302	−	0.0249844i
$190$	6.63841	−	1.05142i	0.481601	−	0.0762780i
$191$	−18.4652	+	13.4158i	−1.33609	+	0.970730i	−0.336517	+	0.941677i	$0.609249\pi$
$191$	−18.4652	+	13.4158i	−1.33609	+	0.970730i	−0.999578	+	0.0290525i	$0.990751\pi$
$192$	−3.45774	−	1.12349i	−0.249541	−	0.0810807i
$193$	16.9984	−	8.66112i	1.22357	−	0.623441i	0.281729	−	0.959494i	$-0.409092\pi$
$193$	16.9984	−	8.66112i	1.22357	−	0.623441i	0.941843	+	0.336053i	$0.109092\pi$
$194$	−1.80586	+	1.31204i	−0.129653	+	0.0941987i
$195$	−7.75443	+	1.96802i	−0.555306	+	0.140933i
$196$	3.81555	+	11.7430i	0.272539	+	0.838789i
$197$	−1.71679	+	1.71679i	−0.122316	+	0.122316i	−0.765615	−	0.643299i	$-0.777565\pi$
$197$	−1.71679	+	1.71679i	−0.122316	+	0.122316i	0.643299	+	0.765615i	$0.277565\pi$
$198$	−1.17699	+	0.889294i	−0.0836448	+	0.0631994i
$199$		−	12.2128i		−	0.865741i	−0.901456	−	0.432870i	$-0.857501\pi$
$199$		−	12.2128i		−	0.865741i	0.901456	−	0.432870i	$-0.142499\pi$
$200$	0.115409	+	0.0588036i	0.00816062	+	0.00415804i
$201$	0.990146	+	6.25153i	0.0698395	+	0.440949i
$202$	−0.602027	+	3.80105i	−0.0423585	+	0.267441i
$203$	−0.0449842	−	0.0882865i	−0.00315727	−	0.00619650i
$204$	−4.47629	−	1.45443i	−0.313403	−	0.101831i
$205$	−16.6503	+	12.0972i	−1.16291	+	0.844904i
$206$	0.491143	+	3.10096i	0.0342196	+	0.216054i
$207$	−3.16606	+	1.02872i	−0.220057	+	0.0715007i
$208$	−0.939281	−	10.2406i	−0.0651274	−	0.710057i
$209$	−18.5189	−	12.9317i	−1.28098	−	0.894501i
$210$	0.269020	+	0.269020i	0.0185642	+	0.0185642i
$211$	−5.63413	+	1.83064i	−0.387869	+	0.126026i	−0.496459	−	0.868060i	$-0.665367\pi$
$211$	−5.63413	+	1.83064i	−0.387869	+	0.126026i	0.108589	+	0.994087i	$0.465367\pi$
$212$	1.05660	−	1.45429i	0.0725677	−	0.0998809i
$213$	1.78340	+	0.282463i	0.122197	+	0.0193540i
$214$	5.59701	−	2.85182i	0.382604	−	0.194946i
$215$	−9.81663	+	5.00182i	−0.669489	+	0.341121i
$216$	−1.67032	−	0.264552i	−0.113651	−	0.0180005i
$217$	−1.47895	+	2.03560i	−0.100398	+	0.138185i
$218$	−0.0771180	+	0.0250571i	−0.00522309	+	0.00169708i
$219$	10.6152	+	10.6152i	0.717311	+	0.717311i
$220$	4.33393	+	12.5344i	0.292194	+	0.845067i
$221$	−0.860082	−	9.37711i	−0.0578553	−	0.630772i
$222$	−3.87547	+	1.25922i	−0.260104	+	0.0845130i
$223$	2.99250	+	18.8939i	0.200392	+	1.26523i	0.858700	+	0.512479i	$0.171273\pi$
$223$	2.99250	+	18.8939i	0.200392	+	1.26523i	−0.658308	+	0.752749i	$0.728727\pi$
$224$	−1.45048	+	1.05383i	−0.0969140	+	0.0704122i
$225$	−0.0728425	−	0.0236680i	−0.00485617	−	0.00157786i
$226$	3.33728	+	6.54978i	0.221993	+	0.435685i
$227$	1.62501	−	10.2599i	0.107856	−	0.680976i	−0.873216	−	0.487333i	$-0.837970\pi$
$227$	1.62501	−	10.2599i	0.107856	−	0.680976i	0.981072	−	0.193643i	$-0.0620303\pi$
$228$	−1.91996	−	12.1221i	−0.127152	−	0.802808i
$229$	−4.18528	−	2.13251i	−0.276571	−	0.140920i	0.310204	−	0.950670i	$-0.399603\pi$
$229$	−4.18528	−	2.13251i	−0.276571	−	0.140920i	−0.586775	+	0.809750i	$0.699603\pi$
$230$		−	3.28544i		−	0.216635i
$231$	−0.0239545	−	1.27832i	−0.00157609	−	0.0841073i
$232$	−0.307367	+	0.307367i	−0.0201796	+	0.0201796i
$233$	−5.34302	−	16.4441i	−0.350033	−	1.07729i	−0.958834	−	0.283968i	$-0.908349\pi$
$233$	−5.34302	−	16.4441i	−0.350033	−	1.07729i	0.608801	−	0.793323i	$-0.291651\pi$
$234$	−0.394497	−	1.55441i	−0.0257891	−	0.101615i
$235$	12.1222	−	8.80728i	0.790764	−	0.574524i
$236$	−14.4503	+	7.36279i	−0.940633	+	0.479277i
$237$	12.6789	+	4.11961i	0.823580	+	0.267597i
$238$	−0.362277	+	0.263210i	−0.0234829	+	0.0170614i
$239$	−8.64792	+	1.36970i	−0.559387	+	0.0885982i	−0.429725	−	0.902960i	$-0.641389\pi$
$239$	−8.64792	+	1.36970i	−0.559387	+	0.0885982i	−0.129663	+	0.991558i	$0.541389\pi$
$240$	−2.87311	+	5.63879i	−0.185458	+	0.363983i
$241$	10.7192	+	10.7192i	0.690487	+	0.690487i	0.962339	−	0.271852i	$-0.0876361\pi$
$241$	10.7192	+	10.7192i	0.690487	+	0.690487i	−0.271852	+	0.962339i	$0.587636\pi$
$242$	−2.05631	+	4.43950i	−0.132185	+	0.285382i
$243$	1.00000			0.0641500
$244$	−2.86402	−	8.81453i	−0.183350	−	0.564293i
$245$	15.0152	−	2.37818i	0.959287	−	0.151936i
$246$	−2.42493	−	3.33762i	−0.154608	−	0.212799i
$247$	20.7688	−	13.0993i	1.32149	−	0.833492i
$248$	10.4978	+	3.41096i	0.666614	+	0.216596i
$249$	−1.27909	+	8.07583i	−0.0810588	+	0.511785i
$250$	2.94490	−	4.05331i	0.186252	−	0.256354i
$251$	27.4820	−	8.92945i	1.73465	−	0.563622i	0.740541	−	0.672011i	$-0.234569\pi$
$251$	27.4820	−	8.92945i	1.73465	−	0.563622i	0.994109	+	0.108389i	$0.0345693\pi$
$252$	0.491247	−	0.491247i	0.0309457	−	0.0309457i
$253$	−7.65954	+	7.95209i	−0.481551	+	0.499943i
$254$	−0.324595	+	0.324595i	−0.0203669	+	0.0203669i
$255$	−2.63085	+	5.16333i	−0.164750	+	0.323340i
$256$	−1.95367	−	1.41943i	−0.122105	−	0.0887142i
$257$	1.72742	+	2.37759i	0.107754	+	0.148310i	0.859488	−	0.511156i	$-0.170782\pi$
$257$	1.72742	+	2.37759i	0.107754	+	0.148310i	−0.751734	+	0.659466i	$0.770782\pi$
$258$	−1.00263	−	1.96778i	−0.0624213	−	0.122509i
$259$	1.09137	−	3.35890i	0.0678145	−	0.208712i
$260$	−14.3868	−	0.945335i	−0.892232	−	0.0586272i
$261$	0.151082	−	0.207946i	0.00935173	−	0.0128716i
$262$	0.114274	−	0.224276i	0.00705990	−	0.0138558i
$263$			1.16190i			0.0716455i	0.999358	+	0.0358228i	$0.0114052\pi$
$263$			1.16190i			0.0716455i	−0.999358	+	0.0358228i	$0.988595\pi$
$264$	−5.30094	+	1.83287i	−0.326250	+	0.112806i
$265$	−1.56500	−	1.56500i	−0.0961374	−	0.0961374i
$266$	−1.04043	−	0.530124i	−0.0637927	−	0.0325040i
$267$	16.4518	−	2.60571i	1.00683	−	0.159467i
$268$	−1.78441	+	11.2663i	−0.109000	+	0.688200i
$269$	−8.03771	+	24.7375i	−0.490068	+	1.50827i	0.334437	+	0.942418i	$0.391454\pi$
$269$	−8.03771	+	24.7375i	−0.490068	+	1.50827i	−0.824505	+	0.565855i	$0.808546\pi$
$270$	−0.304974	+	0.938613i	−0.0185601	+	0.0571222i
$271$	−21.4411	−	3.39593i	−1.30245	−	0.206288i	−0.533612	−	0.845730i	$-0.679166\pi$
$271$	−21.4411	−	3.39593i	−1.30245	−	0.206288i	−0.768840	+	0.639442i	$0.779166\pi$
$272$	−6.02624	−	4.37832i	−0.365394	−	0.265475i
$273$	1.29089	+	0.515259i	0.0781283	+	0.0311849i
$274$			3.42334i			0.206811i
$275$	−0.250108	+	0.0444319i	−0.0150821	+	0.00267934i
$276$	−5.99941			−0.361122
$277$	4.82186	+	14.8402i	0.289718	+	0.891659i	0.984945	+	0.172869i	$0.0553038\pi$
$277$	4.82186	+	14.8402i	0.289718	+	0.891659i	−0.695227	+	0.718790i	$0.744696\pi$
$278$	0.0718641	+	0.453732i	0.00431013	+	0.0272131i
$279$	−6.44666	−	1.02105i	−0.385951	−	0.0611287i
$280$	0.656717	+	1.28888i	0.0392463	+	0.0770253i
$281$	−2.51416	+	1.28103i	−0.149982	+	0.0764196i	−0.527371	−	0.849635i	$-0.676822\pi$
$281$	−2.51416	+	1.28103i	−0.149982	+	0.0764196i	0.377389	+	0.926055i	$0.376822\pi$
$282$	1.76545	+	2.42994i	0.105131	+	0.144701i
$283$	−3.29625	−	2.39486i	−0.195942	−	0.142360i	0.485489	−	0.874243i	$-0.338642\pi$
$283$	−3.29625	−	2.39486i	−0.195942	−	0.142360i	−0.681430	+	0.731883i	$0.738642\pi$
$284$	2.89938	+	1.47731i	0.172047	+	0.0876622i
$285$	−15.1111			−0.895105
$286$	−3.58060	−	3.93308i	−0.211726	−	0.232568i
$287$	3.57563			0.211063
$288$	−4.14395	−	2.11145i	−0.244184	−	0.124418i
$289$	8.23518	+	5.98321i	0.484422	+	0.351953i
$290$	0.149105	+	0.205226i	0.00875576	+	0.0120513i
$291$	4.47158	−	2.27838i	0.262128	−	0.133561i
$292$	12.2825	+	24.1058i	0.718779	+	1.41068i
$293$	−1.76196	−	0.279067i	−0.102935	−	0.0163032i	0.104755	−	0.994498i	$-0.466594\pi$
$293$	−1.76196	−	0.279067i	−0.102935	−	0.0163032i	−0.207689	+	0.978195i	$0.566594\pi$
$294$	0.476715	+	3.00986i	0.0278026	+	0.175539i
$295$	6.17043	+	18.9906i	0.359256	+	1.10568i
$296$	−15.4935			−0.900541
$297$	2.92640	−	1.56082i	0.169807	−	0.0905679i
$298$			8.91469i			0.516414i
$299$	−4.73624	−	11.0289i	−0.273904	−	0.637818i
$300$	−0.111669	−	0.0811321i	−0.00644720	−	0.00468416i
$301$	1.89055	+	0.299434i	0.108970	+	0.0172591i
$302$	2.16021	−	6.64845i	0.124306	−	0.382575i
$303$	2.67374	−	8.22892i	0.153602	−	0.472739i
$304$	3.03856	−	19.1847i	0.174274	−	1.10032i
$305$	−11.2707	+	1.78510i	−0.645358	+	0.102215i
$306$	−1.03501	−	0.527364i	−0.0591676	−	0.0301474i
$307$	−3.67676	−	3.67676i	−0.209844	−	0.209844i	0.594357	−	0.804201i	$-0.297406\pi$
$307$	−3.67676	−	3.67676i	−0.209844	−	0.209844i	−0.804201	+	0.594357i	$0.797406\pi$
$308$	0.670841	−	2.20434i	0.0382247	−	0.125604i
$309$		−	7.05876i		−	0.401559i
$310$	2.92443	−	5.73953i	0.166097	−	0.325983i
$311$	−6.59864	+	9.08225i	−0.374174	+	0.515007i	−0.954029	−	0.299713i	$-0.903109\pi$
$311$	−6.59864	+	9.08225i	−0.374174	+	0.515007i	0.579855	+	0.814720i	$0.303109\pi$
$312$	0.399794	−	6.08436i	0.0226339	−	0.344459i
$313$	8.38630	−	25.8104i	0.474022	−	1.45889i	−0.373251	−	0.927730i	$-0.621757\pi$
$313$	8.38630	−	25.8104i	0.474022	−	1.45889i	0.847273	−	0.531158i	$-0.178243\pi$
$314$	−1.49966	−	2.94326i	−0.0846310	−	0.166098i
$315$	−0.502772	−	0.692007i	−0.0283280	−	0.0389902i
$316$	19.4369	+	14.1217i	1.09341	+	0.794409i
$317$	−12.0724	+	23.6934i	−0.678052	+	1.33075i	0.253568	+	0.967318i	$0.418396\pi$
$317$	−12.0724	+	23.6934i	−0.678052	+	1.33075i	−0.931620	+	0.363434i	$0.881604\pi$
$318$	0.313711	−	0.313711i	0.0175920	−	0.0175920i
$319$	0.117560	−	0.844347i	0.00658211	−	0.0472743i
$320$	−5.70432	+	5.70432i	−0.318881	+	0.318881i
$321$	−13.4318	+	4.36426i	−0.749690	+	0.243589i
$322$	−0.335505	+	0.461783i	−0.0186970	+	0.0257342i
$323$	2.78235	−	17.5671i	0.154814	−	0.977459i
$324$	1.71396	+	0.556901i	0.0952202	+	0.0309389i
$325$	0.0609906	−	0.269334i	0.00338315	−	0.0149400i
$326$	−1.12086	−	1.54273i	−0.0620785	−	0.0854437i
$327$	0.180062	−	0.0285190i	0.00995745	−	0.00157710i
$328$	−4.84723	−	14.9182i	−0.267644	−	0.823722i
$329$	−2.60322			−0.143520
$330$	0.572528	+	3.22277i	0.0315166	+	0.177408i
$331$	1.74600	+	1.74600i	0.0959687	+	0.0959687i	0.753461	−	0.657492i	$-0.228383\pi$
$331$	1.74600	+	1.74600i	0.0959687	+	0.0959687i	−0.657492	+	0.753461i	$0.728383\pi$
$332$	−6.68975	+	13.1294i	−0.367148	+	0.720568i
$333$	9.04879	−	1.43319i	0.495870	−	0.0785382i
$334$	−1.77934	+	1.29277i	−0.0973612	+	0.0707371i
$335$	13.3569	+	4.33992i	0.729766	+	0.237115i
$336$	0.979655	−	0.499159i	0.0534445	−	0.0272314i
$337$	25.6330	−	18.6235i	1.39632	−	1.01449i	0.401183	−	0.915998i	$-0.368599\pi$
$337$	25.6330	−	18.6235i	1.39632	−	1.01449i	0.995138	−	0.0984887i	$-0.0314008\pi$
$338$	5.45115	−	1.92834i	0.296503	−	0.104888i
$339$	−5.10718	−	15.7183i	−0.277384	−	0.853700i
$340$	−7.38465	+	7.38465i	−0.400489	+	0.400489i
$341$	−20.4592	+	7.07406i	−1.10793	+	0.383082i
$342$		−	3.02908i		−	0.163794i
$343$	−4.75767	−	2.42415i	−0.256890	−	0.130892i
$344$	−1.31359	−	8.29368i	−0.0708240	−	0.447165i
$345$	−1.15552	+	7.29568i	−0.0622112	+	0.392786i
$346$	−0.656186	−	1.28784i	−0.0352768	−	0.0692346i
$347$	−7.33825	−	2.38434i	−0.393938	−	0.127998i	0.105348	−	0.994435i	$-0.466404\pi$
$347$	−7.33825	−	2.38434i	−0.393938	−	0.127998i	−0.499286	+	0.866437i	$0.666404\pi$
$348$	0.374754	−	0.272275i	0.0200889	−	0.0145955i
$349$	−2.29985	−	14.5207i	−0.123108	−	0.777275i	−0.969568	−	0.244822i	$-0.921270\pi$
$349$	−2.29985	−	14.5207i	−0.123108	−	0.777275i	0.846460	−	0.532453i	$-0.178730\pi$
$350$	−0.0124897	+	0.00405815i	−0.000667603	+	0.000216917i
$351$	0.329324	+	3.59048i	0.0175780	+	0.191646i
$352$	−15.4224	+	0.289002i	−0.822019	+	0.0154038i
$353$	2.69782	+	2.69782i	0.143591	+	0.143591i	0.775248	−	0.631657i	$-0.217625\pi$
$353$	2.69782	+	2.69782i	0.143591	+	0.143591i	−0.631657	+	0.775248i	$0.717625\pi$
$354$	−3.80674	+	1.23689i	−0.202326	+	0.0657398i
$355$	2.35495	−	3.24130i	0.124988	−	0.172031i
$356$	29.6489	+	4.69593i	1.57139	+	0.248884i
$357$	0.897051	−	0.457070i	0.0474770	−	0.0241907i
$358$	−3.82734	+	1.95013i	−0.202281	+	0.103068i
$359$	15.2088	+	2.40883i	0.802687	+	0.127133i	0.544281	−	0.838903i	$-0.316803\pi$
$359$	15.2088	+	2.40883i	0.802687	+	0.127133i	0.258406	+	0.966036i	$0.416803\pi$
$360$	−2.20562	+	3.03577i	−0.116246	+	0.159999i
$361$	26.0395	−	8.46076i	1.37050	−	0.445303i
$362$	7.03130	+	7.03130i	0.369557	+	0.369557i
$363$	6.12769	−	9.13517i	0.321620	−	0.479472i
$364$	1.92559	+	1.60203i	0.100929	+	0.0839694i
$365$	31.6799	−	10.2934i	1.65820	−	0.538783i
$366$	−0.357831	−	2.25925i	−0.0187041	−	0.118093i
$367$	5.75639	−	4.18227i	0.300481	−	0.218312i	−0.427320	−	0.904100i	$-0.640542\pi$
$367$	5.75639	−	4.18227i	0.300481	−	0.218312i	0.727801	+	0.685788i	$0.240542\pi$
$368$	−9.03008	−	2.93405i	−0.470726	−	0.152948i
$369$	4.21094	+	8.26444i	0.219213	+	0.430230i
$370$	−1.41444	+	8.93039i	−0.0735330	+	0.464269i
$371$	0.0601519	+	0.379784i	0.00312293	+	0.0197174i
$372$	−10.4807	−	5.34019i	−0.543400	−	0.276876i
$373$		−	34.8639i		−	1.80518i	−0.430498	−	0.902591i	$-0.641662\pi$
$373$		−	34.8639i		−	1.80518i	0.430498	−	0.902591i	$-0.358338\pi$
$374$	−3.85198	+	0.0721823i	−0.199181	+	0.00373246i
$375$	−7.96508	+	7.96508i	−0.411315	+	0.411315i
$376$	3.52900	+	10.8611i	0.181994	+	0.560120i
$377$	0.796382	+	0.473975i	0.0410158	+	0.0244109i
$378$	0.138715	−	0.100783i	0.00713475	−	0.00518370i
$379$	−13.1848	+	6.71797i	−0.677255	+	0.345079i	−0.758553	−	0.651611i	$-0.774093\pi$
$379$	−13.1848	+	6.71797i	−0.677255	+	0.345079i	0.0812980	+	0.996690i	$0.474093\pi$
$380$	−25.8999	−	8.41539i	−1.32864	−	0.431700i
$381$	0.834963	−	0.606636i	0.0427765	−	0.0310789i
$382$	−10.0268	+	1.58809i	−0.513017	+	0.0812540i
$383$	−5.38640	+	10.5714i	−0.275232	+	0.540174i	−0.986701	−	0.162544i	$-0.948030\pi$
$383$	−5.38640	+	10.5714i	−0.275232	+	0.540174i	0.711469	+	0.702717i	$0.248030\pi$
$384$	−7.72076	−	7.72076i	−0.393998	−	0.393998i
$385$	−2.55141	−	1.24036i	−0.130032	−	0.0632144i
$386$	8.48544			0.431898
$387$	1.53437	+	4.72231i	0.0779966	+	0.240049i
$388$	8.93296	−	1.41484i	0.453502	−	0.0718277i
$389$	3.60828	+	4.96637i	0.182947	+	0.251805i	0.890634	−	0.454721i	$-0.150261\pi$
$389$	3.60828	+	4.96637i	0.182947	+	0.251805i	−0.707687	+	0.706526i	$0.750261\pi$
$390$	−3.47051	−	0.785895i	−0.175736	−	0.0397953i
$391$	−8.26867	−	2.68665i	−0.418165	−	0.135870i
$392$	−1.81255	+	11.4440i	−0.0915476	+	0.578009i
$393$	−0.332640	+	0.457839i	−0.0167794	+	0.0230949i
$394$	−1.02704	+	0.333705i	−0.0517414	+	0.0168118i
$395$	20.9166	−	20.9166i	1.05243	−	1.05243i
$396$	5.88497	−	1.04547i	0.295731	−	0.0525368i
$397$	−11.0966	+	11.0966i	−0.556920	+	0.556920i	−0.928429	−	0.371509i	$-0.878841\pi$
$397$	−11.0966	+	11.0966i	−0.556920	+	0.556920i	0.371509	+	0.928429i	$0.378841\pi$
$398$	2.46609	−	4.83997i	0.123614	−	0.242606i
$399$	2.12393	+	1.54313i	0.106330	+	0.0772530i
$400$	−0.128401	−	0.176729i	−0.00642007	−	0.00883647i
$401$	14.8832	+	29.2099i	0.743230	+	1.45867i	0.883437	+	0.468549i	$0.155223\pi$
$401$	14.8832	+	29.2099i	0.743230	+	1.45867i	−0.140207	+	0.990122i	$0.544777\pi$
$402$	−0.869954	+	2.67744i	−0.0433894	+	0.133539i
$403$	1.54302	−	23.4829i	0.0768634	−	1.16976i
$404$	9.16538	−	12.6151i	0.455995	−	0.627623i
$405$	1.00735	−	1.97703i	0.0500555	−	0.0982395i
$406$		−	0.0440718i		−	0.00218725i
$407$	24.2435	−	18.3176i	1.20170	−	0.907970i
$408$	−3.12306	−	3.12306i	−0.154614	−	0.154614i
$409$	6.44807	+	3.28546i	0.318837	+	0.162455i	0.606083	−	0.795401i	$-0.292740\pi$
$409$	6.44807	+	3.28546i	0.318837	+	0.162455i	−0.287246	+	0.957857i	$0.592740\pi$
$410$	−9.04134	+	1.43201i	−0.446520	+	0.0707218i
$411$	1.20402	−	7.60190i	0.0593901	−	0.374974i
$412$	3.93103	−	12.0985i	0.193668	−	0.596049i
$413$	1.07202	−	3.29933i	0.0527506	−	0.162350i
$414$	−1.46245	−	0.231629i	−0.0718754	−	0.0113839i
$415$	14.6777	+	10.6640i	0.720500	+	0.523474i
$416$	6.21640	−	15.5741i	0.304784	−	0.763583i
$417$		−	1.03284i		−	0.0505783i
$418$	−4.72785	−	8.86432i	−0.231246	−	0.433568i
$419$	18.0641			0.882487			0.441244	−	0.897387i	$-0.354537\pi$
$419$	18.0641			0.882487			0.441244	+	0.897387i	$0.354537\pi$
$420$	−0.476355	−	1.46607i	−0.0232437	−	0.0715369i
$421$	3.24407	+	20.4822i	0.158106	+	0.998243i	0.931348	+	0.364131i	$0.118634\pi$
$421$	3.24407	+	20.4822i	0.158106	+	0.998243i	−0.773241	+	0.634112i	$0.781366\pi$
$422$	−2.60248	−	0.412193i	−0.126687	−	0.0200652i
$423$	−3.06575	−	6.01688i	−0.149062	−	0.292551i
$424$	1.50299	−	0.765813i	0.0729918	−	0.0371912i
$425$	−0.117575	−	0.161828i	−0.00570321	−	0.00784979i
$426$	0.649732	+	0.472058i	0.0314796	+	0.0228713i
$427$	1.76644	+	0.900045i	0.0854839	+	0.0435562i
$428$	−25.4521			−1.23027
$429$	6.56782	+	9.99318i	0.317097	+	0.482475i
$430$	−4.90037			−0.236317
$431$	−1.18460	−	0.603585i	−0.0570603	−	0.0290737i	0.425228	−	0.905086i	$-0.360194\pi$
$431$	−1.18460	−	0.603585i	−0.0570603	−	0.0290737i	−0.482288	+	0.876013i	$0.660194\pi$
$432$	2.30744	+	1.67645i	0.111017	+	0.0806583i
$433$	−7.50809	−	10.3340i	−0.360816	−	0.496620i	0.589560	−	0.807725i	$-0.299301\pi$
$433$	−7.50809	−	10.3340i	−0.360816	−	0.496620i	−0.950376	+	0.311104i	$0.899301\pi$
$434$	−0.997156	+	0.508076i	−0.0478650	+	0.0243884i
$435$	−0.258925	−	0.508168i	−0.0124145	−	0.0243648i
$436$	0.324502	+	0.0513961i	0.0155408	+	0.00246142i
$437$	−3.54657	−	22.3922i	−0.169656	−	1.07116i
$438$	2.06336	+	6.35036i	0.0985910	+	0.303432i
$439$	12.2526			0.584785			0.292393	−	0.956298i	$-0.405549\pi$
$439$	12.2526			0.584785			0.292393	+	0.956298i	$0.405549\pi$
$440$	−1.71624	+	12.3265i	−0.0818186	+	0.587642i
$441$		−	6.85139i		−	0.326257i
$442$	1.55264	−	3.88986i	0.0738514	−	0.185022i
$443$	−28.9772	−	21.0532i	−1.37675	−	1.00027i	−0.997176	−	0.0751031i	$-0.976071\pi$
$443$	−28.9772	−	21.0532i	−1.37675	−	1.00027i	−0.379572	−	0.925162i	$-0.623929\pi$
$444$	16.3074	+	2.58284i	0.773917	+	0.122576i
$445$	11.4211	−	35.1506i	0.541413	−	1.66630i
$446$	−2.62924	+	8.09198i	−0.124498	+	0.383166i
$447$	3.13539	−	19.7961i	0.148299	−	0.936322i
$448$	1.38428	−	0.219249i	0.0654013	−	0.0103586i
$449$	20.5435	+	10.4674i	0.969507	+	0.493988i	0.865675	−	0.500606i	$-0.166890\pi$
$449$	20.5435	+	10.4674i	0.969507	+	0.493988i	0.103832	+	0.994595i	$0.466890\pi$
$450$	−0.0240886	−	0.0240886i	−0.00113555	−	0.00113555i
$451$	25.2222	+	17.6126i	1.18767	+	0.829344i
$452$		−	29.7848i		−	1.40096i
$453$	−7.13532	+	14.0039i	−0.335247	+	0.657959i
$454$	2.71576	−	3.73792i	0.127457	−	0.175429i
$455$	2.31906	−	2.03309i	0.108719	−	0.0953127i
$456$	3.55897	−	10.9534i	0.166664	−	0.512940i
$457$	−4.92163	−	9.65925i	−0.230224	−	0.451841i	0.746777	−	0.665075i	$-0.231600\pi$
$457$	−4.92163	−	9.65925i	−0.230224	−	0.451841i	−0.977001	+	0.213234i	$0.931600\pi$
$458$	−1.22803	−	1.69024i	−0.0573822	−	0.0789798i
$459$	2.11288	+	1.53509i	0.0986206	+	0.0716521i
$460$	−6.04350	+	11.8610i	−0.281779	+	0.553023i
$461$	19.8997	−	19.8997i	0.926821	−	0.926821i	−0.0706785	−	0.997499i	$-0.522516\pi$
$461$	19.8997	−	19.8997i	0.926821	−	0.926821i	0.997499	+	0.0706785i	$0.0225164\pi$
$462$	0.248634	−	0.511440i	0.0115675	−	0.0237944i
$463$	−0.807432	+	0.807432i	−0.0375245	+	0.0375245i	−0.725620	−	0.688096i	$-0.758447\pi$
$463$	−0.807432	+	0.807432i	−0.0375245	+	0.0375245i	0.688096	+	0.725620i	$0.258447\pi$
$464$	0.697224	−	0.226542i	0.0323678	−	0.0105169i
$465$	−8.51268	+	11.7167i	−0.394766	+	0.543349i
$466$	1.20305	−	7.59577i	0.0557303	−	0.351867i
$467$	13.8483	+	4.49958i	0.640821	+	0.208216i	0.611363	−	0.791350i	$-0.290622\pi$
$467$	13.8483	+	4.49958i	0.640821	+	0.208216i	0.0294587	+	0.999566i	$0.490622\pi$
$468$	−1.43509	+	6.33736i	−0.0663371	+	0.292944i
$469$	−1.43418	−	1.97399i	−0.0662245	−	0.0911502i
$470$	6.58250	−	1.04256i	0.303628	−	0.0480899i
$471$	2.29500	+	7.06328i	0.105748	+	0.325459i
$472$	−15.2187			−0.700499
$473$	11.8609	+	11.4245i	0.545363	+	0.525300i
$474$	4.19282	+	4.19282i	0.192583	+	0.192583i
$475$	0.236804	−	0.464754i	0.0108653	−	0.0213244i
$476$	1.79206	−	0.283834i	0.0821387	−	0.0130095i
$477$	−0.806965	+	0.586295i	−0.0369484	+	0.0268446i
$478$	−3.70378	−	1.20343i	−0.169407	−	0.0550437i
$479$	−24.4758	+	12.4711i	−1.11833	+	0.569817i	−0.912625	−	0.408797i	$-0.865948\pi$
$479$	−24.4758	+	12.4711i	−1.11833	+	0.569817i	−0.205704	+	0.978614i	$0.565948\pi$
$480$	−8.34879	+	6.06575i	−0.381069	+	0.276863i
$481$	8.12581	+	32.0175i	0.370505	+	1.45987i
$482$	2.08357	+	6.41258i	0.0949042	+	0.292085i
$483$	0.907440	−	0.907440i	0.0412899	−	0.0412899i
$484$	15.5900	−	12.2448i	0.708638	−	0.556584i
$485$		−	11.1356i		−	0.505641i
$486$	0.396304	+	0.201927i	0.0179767	+	0.00915959i
$487$	−3.57013	−	22.5409i	−0.161778	−	1.02143i	−0.926288	−	0.376815i	$-0.877019\pi$
$487$	−3.57013	−	22.5409i	−0.161778	−	1.02143i	0.764510	−	0.644611i	$-0.222981\pi$
$488$	1.36053	−	8.59006i	0.0615884	−	0.388854i
$489$	1.94639	+	3.82001i	0.0880189	+	0.172747i
$490$	6.43081	+	2.08950i	0.290514	+	0.0943938i
$491$	−9.75355	+	7.08637i	−0.440171	+	0.319803i	−0.785703	−	0.618604i	$-0.787699\pi$
$491$	−9.75355	+	7.08637i	−0.440171	+	0.319803i	0.345532	+	0.938407i	$0.387699\pi$
$492$	2.61493	+	16.5100i	0.117890	+	0.744330i
$493$	0.638434	−	0.207440i	0.0287536	−	0.00934262i
$494$	10.8759	−	0.997549i	0.489328	−	0.0448818i
$495$	−0.137880	−	7.35789i	−0.00619723	−	0.330712i
$496$	−13.1635	−	13.1635i	−0.591060	−	0.591060i
$497$	−0.661996	+	0.215095i	−0.0296946	+	0.00964835i
$498$	−2.13763	+	2.94220i	−0.0957897	+	0.131843i
$499$	−10.2391	−	1.62171i	−0.458364	−	0.0725977i	−0.0770170	−	0.997030i	$-0.524540\pi$
$499$	−10.2391	−	1.62171i	−0.458364	−	0.0725977i	−0.381347	+	0.924432i	$0.624540\pi$
$500$	−18.0876	+	9.21610i	−0.808903	+	0.412157i
$501$	4.40591	−	2.24492i	0.196841	−	0.100296i
$502$	12.6943	+	2.01058i	0.566575	+	0.0897367i
$503$	14.0248	−	19.3035i	0.625336	−	0.860702i	−0.372391	−	0.928076i	$-0.621462\pi$
$503$	14.0248	−	19.3035i	0.625336	−	0.860702i	0.997728	+	0.0673741i	$0.0214621\pi$
$504$	0.620019	−	0.201456i	0.0276178	−	0.00897358i
$505$	−13.5755	−	13.5755i	−0.604100	−	0.604100i
$506$	−4.64125	+	1.60478i	−0.206329	+	0.0713410i
$507$	−12.7831	+	2.36486i	−0.567717	+	0.105027i
$508$	1.76893	−	0.574761i	0.0784837	−	0.0255009i
$509$	5.77579	+	36.4669i	0.256008	+	1.61637i	0.695777	+	0.718258i	$0.255060\pi$
$509$	5.77579	+	36.4669i	0.256008	+	1.61637i	−0.439770	+	0.898111i	$0.644940\pi$
$510$	−2.08523	+	1.51501i	−0.0923356	+	0.0670857i
$511$	−5.50390	−	1.78833i	−0.243478	−	0.0791109i
$512$	−10.4017	−	20.4145i	−0.459694	−	0.902201i
$513$	−1.06536	+	6.72641i	−0.0470367	+	0.296978i
$514$	0.204484	+	1.29106i	0.00901941	+	0.0569463i
$515$	−13.9554	−	7.11063i	−0.614949	−	0.313332i
$516$			8.94837i			0.393930i
$517$	−18.3629	−	12.8227i	−0.807599	−	0.563943i
$518$	1.11077	−	1.11077i	0.0488043	−	0.0488043i
$519$	1.00419	+	3.09057i	0.0440790	+	0.135661i
$520$	−11.6262	−	6.91948i	−0.509845	−	0.303439i
$521$	−12.5729	+	9.13477i	−0.550830	+	0.400202i	−0.828092	−	0.560593i	$-0.810573\pi$
$521$	−12.5729	+	9.13477i	−0.550830	+	0.400202i	0.277261	+	0.960795i	$0.410573\pi$
$522$	0.101864	−	0.0519024i	0.00445848	−	0.00227171i
$523$	25.7427	+	8.36431i	1.12565	+	0.365746i	0.811921	−	0.583767i	$-0.198422\pi$
$523$	25.7427	+	8.36431i	1.12565	+	0.365746i	0.313729	+	0.949513i	$0.398422\pi$
$524$	−0.825103	+	0.599473i	−0.0360448	+	0.0261881i
$525$	0.0291621	−	0.00461882i	0.00127274	−	0.000201582i
$526$	−0.234618	+	0.460464i	−0.0102298	+	0.0200772i
$527$	−12.0536	−	12.0536i	−0.525062	−	0.525062i
$528$	9.36913	+	1.30449i	0.407739	+	0.0567704i
$529$	11.9178			0.518165
$530$	−0.304201	−	0.936233i	−0.0132136	−	0.0406674i
$531$	8.88833	−	1.40777i	0.385720	−	0.0610921i
$532$	2.78098	+	3.82769i	0.120571	+	0.165951i
$533$	−28.2865	+	17.8410i	−1.22523	+	0.772779i
$534$	7.04608	+	2.28941i	0.304914	+	0.0990724i
$535$	−4.90223	+	30.9514i	−0.211942	+	1.33815i
$536$	−6.29164	+	8.65971i	−0.271758	+	0.374042i
$537$	9.18492	−	2.98436i	0.396359	−	0.128785i
$538$	−8.18054	+	8.18054i	−0.352688	+	0.352688i
$539$	−10.6938	−	20.0499i	−0.460614	−	0.863612i
$540$	2.82757	−	2.82757i	0.121679	−	0.121679i
$541$	−11.3161	+	22.2090i	−0.486516	+	0.954841i	0.509047	+	0.860739i	$0.329998\pi$
$541$	−11.3161	+	22.2090i	−0.486516	+	0.954841i	−0.995563	+	0.0941022i	$0.970002\pi$
$542$	−7.81144	−	5.67535i	−0.335530	−	0.243777i
$543$	−13.1408	−	18.0868i	−0.563926	−	0.776178i
$544$	−5.51437	−	10.8226i	−0.236427	−	0.464014i
$545$	0.125002	−	0.384717i	0.00535450	−	0.0164795i
$546$	0.407540	+	0.464865i	0.0174411	+	0.0198944i
$547$	−24.3435	+	33.5060i	−1.04085	+	1.43261i	−0.144378	+	0.989523i	$0.546118\pi$
$547$	−24.3435	+	33.5060i	−1.04085	+	1.43261i	−0.896477	+	0.443091i	$0.853882\pi$
$548$	6.29716	−	12.3589i	0.269001	−	0.527945i
$549$			5.14278i			0.219488i
$550$	−0.108091	−	0.0328950i	−0.00460901	−	0.00140265i
$551$	1.23778	+	1.23778i	0.0527310	+	0.0527310i
$552$	−5.01618	−	2.55587i	−0.213503	−	0.108785i
$553$	−5.07590	+	0.803944i	−0.215849	+	0.0341872i
$554$	−1.08571	+	6.85488i	−0.0461272	+	0.291236i
$555$	6.28182	−	19.3335i	0.266649	−	0.820660i
$556$	0.575189	−	1.77025i	0.0243934	−	0.0750753i
$557$	13.4883	+	2.13634i	0.571518	+	0.0905195i	0.435503	−	0.900187i	$-0.356571\pi$
$557$	13.4883	+	2.13634i	0.571518	+	0.0905195i	0.136015	+	0.990707i	$0.456571\pi$
$558$	−2.34866	−	1.70640i	−0.0994266	−	0.0722377i
$559$	−16.4501	+	7.06431i	−0.695764	+	0.298788i
$560$		−	2.43964i		−	0.103093i
$561$	8.57913	+	1.19449i	0.362211	+	0.0504315i
$562$	−1.25504			−0.0529408
$563$	11.7761	+	36.2432i	0.496305	+	1.52747i	0.814913	+	0.579584i	$0.196785\pi$
$563$	11.7761	+	36.2432i	0.496305	+	1.52747i	−0.318608	+	0.947887i	$0.603215\pi$
$564$	−1.90379	−	12.0200i	−0.0801639	−	0.506135i
$565$	−36.2203	−	5.73672i	−1.52380	−	0.241346i
$566$	−0.822728	−	1.61470i	−0.0345819	−	0.0678707i
$567$	−0.343479	+	0.175011i	−0.0144248	+	0.00734979i
$568$	1.79484	+	2.47039i	0.0753100	+	0.103655i
$569$	15.3041	+	11.1191i	0.641581	+	0.466136i	0.860393	−	0.509631i	$-0.170218\pi$
$569$	15.3041	+	11.1191i	0.641581	+	0.466136i	−0.218812	+	0.975767i	$0.570218\pi$
$570$	−5.98859	−	3.05134i	−0.250835	−	0.127807i
$571$	0.477012			0.0199623			0.00998116	−	0.999950i	$-0.496823\pi$
$571$	0.477012			0.0199623			0.00998116	+	0.999950i	$0.496823\pi$
$572$	5.69180	+	20.7856i	0.237986	+	0.869089i
$573$	22.8242			0.953496
$574$	1.41703	+	0.722015i	0.0591459	+	0.0301363i
$575$	−0.206276	−	0.149868i	−0.00860232	−	0.00624995i
$576$	2.13700	+	2.94133i	0.0890417	+	0.122555i
$577$	−32.5584	+	16.5893i	−1.35542	+	0.690623i	−0.972445	−	0.233133i	$-0.925102\pi$
$577$	−32.5584	+	16.5893i	−1.35542	+	0.690623i	−0.382980	+	0.923757i	$0.625102\pi$
$578$	2.05546	+	4.03407i	0.0854960	+	0.167795i
$579$	−18.8429	−	2.98442i	−0.783083	−	0.124028i
$580$	−0.160788	−	1.01518i	−0.00667637	−	0.0421530i
$581$	−0.974024	−	2.99774i	−0.0404093	−	0.124367i
$582$	2.23217			0.0925264
$583$	−1.44641	+	2.97526i	−0.0599041	+	0.123223i
$584$			25.3877i			1.05055i
$585$	7.43024	+	2.96578i	0.307203	+	0.122620i
$586$	−0.641919	−	0.466382i	−0.0265174	−	0.0192661i
$587$	−3.70105	−	0.586189i	−0.152759	−	0.0241946i	0.0795866	−	0.996828i	$-0.474640\pi$
$587$	−3.70105	−	0.586189i	−0.152759	−	0.0241946i	−0.232345	+	0.972633i	$0.574640\pi$
$588$	3.81555	−	11.7430i	0.157350	−	0.484275i
$589$	13.7360	−	42.2751i	0.565983	−	1.74192i
$590$	−1.38935	+	8.77203i	−0.0571988	+	0.361139i
$591$	2.39802	−	0.379809i	0.0986414	−	0.0156233i
$592$	23.2822	+	11.8629i	0.956892	+	0.487561i
$593$	−14.1673	−	14.1673i	−0.581782	−	0.581782i	0.353611	−	0.935393i	$-0.384954\pi$
$593$	−14.1673	−	14.1673i	−0.581782	−	0.581782i	−0.935393	+	0.353611i	$0.884954\pi$
$594$	1.47492	−	0.0276385i	0.0605166	−	0.00113402i
$595$		−	2.23393i		−	0.0915821i
$596$	16.3984	−	32.1836i	0.671704	−	1.31829i
$597$	−7.17849	+	9.88034i	−0.293796	+	0.404375i
$598$	0.350040	−	5.32717i	0.0143142	−	0.217844i
$599$	−4.54074	+	13.9750i	−0.185530	+	0.571001i	−0.999957	−	0.00926397i	$-0.997051\pi$
$599$	−4.54074	+	13.9750i	−0.185530	+	0.571001i	0.814428	+	0.580265i	$0.197051\pi$
$600$	−0.0588036	−	0.115409i	−0.00240065	−	0.00471154i
$601$	9.87459	+	13.5912i	0.402793	+	0.554397i	0.961442	−	0.275007i	$-0.0886802\pi$
$601$	9.87459	+	13.5912i	0.402793	+	0.554397i	−0.558649	+	0.829404i	$0.688680\pi$
$602$	0.688769	+	0.500420i	0.0280721	+	0.0203956i
$603$	2.87351	−	5.63959i	0.117019	−	0.229662i
$604$	−20.0285	+	20.0285i	−0.814946	+	0.814946i
$605$	−11.8878	−	21.3169i	−0.483308	−	0.866657i
$606$	2.72125	−	2.72125i	0.110543	−	0.110543i
$607$	−10.7339	+	3.48766i	−0.435677	+	0.141560i	−0.518640	−	0.854993i	$-0.673562\pi$
$607$	−10.7339	+	3.48766i	−0.435677	+	0.141560i	0.0829634	+	0.996553i	$0.473562\pi$
$608$	18.6172	−	25.6244i	0.755029	−	1.03921i
$609$	−0.0155005	+	0.0978663i	−0.000628112	+	0.00396574i
$610$	−4.82708	−	1.56841i	−0.195443	−	0.0635032i
$611$	20.5939	−	12.9890i	0.833138	−	0.525480i
$612$	2.76650	+	3.80776i	0.111829	+	0.153920i
$613$	−2.60051	+	0.411881i	−0.105034	+	0.0166357i	−0.208730	−	0.977973i	$-0.566933\pi$
$613$	−2.60051	+	0.411881i	−0.105034	+	0.0166357i	0.103696	+	0.994609i	$0.466933\pi$
$614$	−0.714677	−	2.19955i	−0.0288420	−	0.0887666i
$615$	20.5810			0.829904
$616$	1.49999	−	1.55728i	0.0604363	−	0.0627446i
$617$	21.2916	+	21.2916i	0.857166	+	0.857166i	0.991003	−	0.133837i	$-0.0427300\pi$
$617$	21.2916	+	21.2916i	0.857166	+	0.857166i	−0.133837	+	0.991003i	$0.542730\pi$
$618$	1.42535	−	2.79741i	0.0573361	−	0.112529i
$619$	−5.69245	+	0.901596i	−0.228799	+	0.0362382i	−0.269781	−	0.962922i	$-0.586951\pi$
$619$	−5.69245	+	0.901596i	−0.228799	+	0.0362382i	0.0409821	+	0.999160i	$0.486951\pi$
$620$	−21.1155	+	15.3413i	−0.848018	+	0.616121i
$621$	3.16606	+	1.02872i	0.127050	+	0.0412809i
$622$	−4.44901	+	2.26689i	−0.178389	+	0.0908939i
$623$	−5.19483	+	3.77426i	−0.208126	+	0.151213i
$624$	−5.25937	+	8.83691i	−0.210543	+	0.353759i
$625$	7.60527	+	23.4066i	0.304211	+	0.936265i
$626$	8.53533	−	8.53533i	0.341140	−	0.341140i
$627$	7.38104	+	21.3470i	0.294770	+	0.852518i
$628$			13.3843i			0.534091i
$629$	21.3190	+	10.8626i	0.850046	+	0.433120i
$630$	−0.0595158	−	0.375768i	−0.00237117	−	0.0149710i
$631$	−1.32569	+	8.37006i	−0.0527748	+	0.333207i	0.947148	+	0.320796i	$0.103950\pi$
$631$	−1.32569	+	8.37006i	−0.0527748	+	0.333207i	−0.999923	+	0.0124105i	$0.996050\pi$
$632$	10.2353	+	20.0878i	0.407137	+	0.799051i
$633$	5.63413	+	1.83064i	0.223937	+	0.0727614i
$634$	−9.56865	+	6.95203i	−0.380020	+	0.276101i
$635$	−0.358241	−	2.26184i	−0.0142164	−	0.0897585i
$636$	−1.70962	+	0.555489i	−0.0677908	+	0.0220266i
$637$	24.5998	−	2.25633i	0.974679	−	0.0893990i
$638$	0.217086	−	0.310879i	0.00859451	−	0.0123078i
$639$	−1.27677	−	1.27677i	−0.0505084	−	0.0505084i
$640$	−23.0417	+	7.48670i	−0.910803	+	0.295938i
$641$	−10.3282	+	14.2156i	−0.407941	+	0.561482i	−0.962715	−	0.270519i	$-0.912805\pi$
$641$	−10.3282	+	14.2156i	−0.407941	+	0.561482i	0.554774	+	0.832001i	$0.312805\pi$
$642$	−6.20433	−	0.982670i	−0.244866	−	0.0387829i
$643$	−36.2748	+	18.4829i	−1.43054	+	0.728896i	−0.985982	−	0.166854i	$-0.946639\pi$
$643$	−36.2748	+	18.4829i	−1.43054	+	0.728896i	−0.444558	+	0.895750i	$0.646639\pi$
$644$	2.06067	−	1.04997i	0.0812019	−	0.0413744i
$645$	10.8818	+	1.72351i	0.428471	+	0.0678632i
$646$	4.64992	−	6.40007i	0.182949	−	0.251807i
$647$	−16.4672	+	5.35050i	−0.647391	+	0.210350i	−0.614263	−	0.789101i	$-0.710547\pi$
$647$	−16.4672	+	5.35050i	−0.647391	+	0.210350i	−0.0331275	+	0.999451i	$0.510547\pi$
$648$	1.19581	+	1.19581i	0.0469760	+	0.0469760i
$649$	23.8136	−	17.9928i	0.934764	−	0.706278i
$650$	0.0785566	−	0.0944225i	0.00308124	−	0.00370355i
$651$	2.39299	−	0.777530i	0.0937887	−	0.0304738i
$652$	1.20868	+	7.63131i	0.0473356	+	0.298865i
$653$	8.71482	−	6.33169i	0.341037	−	0.247778i	−0.404062	−	0.914732i	$-0.632402\pi$
$653$	8.71482	−	6.33169i	0.341037	−	0.247778i	0.745099	+	0.666953i	$0.232402\pi$
$654$	0.0771180	+	0.0250571i	0.00301555	+	0.000979812i
$655$	0.570079	+	1.11884i	0.0222748	+	0.0437168i
$656$	−4.13845	+	26.1291i	−0.161579	+	1.02017i
$657$	−2.34843	−	14.8274i	−0.0916209	−	0.578471i
$658$	−1.03166	−	0.525659i	−0.0402185	−	0.0204923i
$659$			24.8995i			0.969946i	0.874529	+	0.484973i	$0.161171\pi$
$659$			24.8995i			0.969946i	−0.874529	+	0.484973i	$0.838829\pi$
$660$	3.86129	−	12.6879i	0.150301	−	0.493877i
$661$	−33.5576	+	33.5576i	−1.30524	+	1.30524i	−0.380430	+	0.924810i	$0.624224\pi$
$661$	−33.5576	+	33.5576i	−1.30524	+	1.30524i	−0.924810	+	0.380430i	$0.875776\pi$
$662$	0.339382	+	1.04451i	0.0131904	+	0.0405960i
$663$	−4.81590	+	8.09178i	−0.187034	+	0.314259i
$664$	−11.1867	+	8.12765i	−0.434130	+	0.315414i
$665$	5.19036	−	2.64462i	0.201273	−	0.102554i
$666$	3.87547	+	1.25922i	0.150171	+	0.0487936i
$667$	0.692252	−	0.502951i	0.0268041	−	0.0194743i
$668$	8.80176	−	1.39406i	0.340550	−	0.0539379i
$669$	8.68456	−	17.0444i	0.335765	−	0.658975i
$670$	4.41705	+	4.41705i	0.170645	+	0.170645i
$671$	8.02694	+	15.0498i	0.309877	+	0.580993i
$672$	1.79289			0.0691621
$673$	0.819218	+	2.52130i	0.0315786	+	0.0971888i	0.965604	−	0.260019i	$-0.0837288\pi$
$673$	0.819218	+	2.52130i	0.0315786	+	0.0971888i	−0.934025	+	0.357208i	$0.883729\pi$
$674$	13.9191	−	2.20456i	0.536142	−	0.0849166i
$675$	0.0450191	+	0.0619635i	0.00173279	+	0.00238498i
$676$	−23.2268	−	3.06562i	−0.893337	−	0.117909i
$677$	−47.9537	−	15.5811i	−1.84301	−	0.598831i	−0.997938	−	0.0641811i	$-0.979556\pi$
$677$	−47.9537	−	15.5811i	−1.84301	−	0.598831i	−0.845074	−	0.534650i	$-0.820444\pi$
$678$	1.14995	−	7.26049i	0.0441635	−	0.278837i
$679$	−1.13715	+	1.56515i	−0.0436399	+	0.0600651i
$680$	−9.32040	+	3.02838i	−0.357421	+	0.116133i
$681$	−7.34530	+	7.34530i	−0.281473	+	0.281473i
$682$	−9.53651	−	1.32779i	−0.365172	−	0.0508437i
$683$	29.8197	−	29.8197i	1.14102	−	1.14102i	0.152755	−	0.988264i	$-0.451186\pi$
$683$	29.8197	−	29.8197i	1.14102	−	1.14102i	0.988264	−	0.152755i	$-0.0488144\pi$
$684$	−5.57193	+	10.9355i	−0.213048	+	0.418130i
$685$	−13.8163	−	10.0382i	−0.527895	−	0.383538i
$686$	−1.39598	−	1.92140i	−0.0532988	−	0.0733595i
$687$	2.13251	+	4.18528i	0.0813602	+	0.159678i
$688$	−4.37626	+	13.4687i	−0.166843	+	0.513491i
$689$	−2.37083	−	2.70431i	−0.0903215	−	0.103026i
$690$	−1.93113	+	2.65798i	−0.0735170	+	0.101187i
$691$	6.64247	−	13.0366i	0.252692	−	0.495935i	−0.729461	−	0.684023i	$-0.760229\pi$
$691$	6.64247	−	13.0366i	0.252692	−	0.495935i	0.982152	+	0.188088i	$0.0602289\pi$
$692$			5.85637i			0.222626i
$693$	−0.731999	+	1.04826i	−0.0278063	+	0.0398202i
$694$	−2.42671	−	2.42671i	−0.0921167	−	0.0921167i
$695$	−2.04196	−	1.04043i	−0.0774558	−	0.0394657i
$696$	0.429331	−	0.0679994i	0.0162738	−	0.00257751i
$697$	−3.78949	+	23.9259i	−0.143537	+	0.906259i
$698$	2.02068	−	6.21901i	0.0764838	−	0.235393i
$699$	−5.34302	+	16.4441i	−0.202092	+	0.621974i
$700$	0.0525550	+	0.00832389i	0.00198639	+	0.000314613i
$701$	−38.0939	−	27.6768i	−1.43879	−	1.04534i	−0.988295	−	0.152558i	$-0.951249\pi$
$701$	−38.0939	−	27.6768i	−1.43879	−	1.04534i	−0.450491	−	0.892781i	$-0.648751\pi$
$702$	−0.594502	+	1.48942i	−0.0224380	+	0.0562145i
$703$			62.3927i			2.35319i
$704$	10.8446	+	5.27205i	0.408721	+	0.198698i
$705$	−14.9838			−0.564324
$706$	0.524394	+	1.61392i	0.0197358	+	0.0607407i
$707$	0.521781	+	3.29440i	0.0196236	+	0.123899i
$708$	16.0183	+	2.53704i	0.602003	+	0.0953479i
$709$	3.26208	+	6.40219i	0.122510	+	0.240439i	0.944114	−	0.329619i	$-0.106920\pi$
$709$	3.26208	+	6.40219i	0.122510	+	0.240439i	−0.821604	+	0.570059i	$0.806920\pi$
$710$	1.58778	−	0.809014i	0.0595883	−	0.0303618i
$711$	−7.83596	−	10.7853i	−0.293872	−	0.404479i
$712$	22.7892	+	16.5574i	0.854063	+	0.620513i
$713$	−19.3602	−	9.86449i	−0.725043	−	0.369428i
$714$	0.447799			0.0167585
$715$	26.3729	−	2.91818i	0.986292	−	0.109134i
$716$	17.4046			0.650441
$717$	7.80140	+	3.97501i	0.291349	+	0.148450i
$718$	5.54088	+	4.02568i	0.206784	+	0.150237i
$719$	22.9815	+	31.6313i	0.857064	+	1.17965i	0.982262	+	0.187515i	$0.0600434\pi$
$719$	22.9815	+	31.6313i	0.857064	+	1.17965i	−0.125198	+	0.992132i	$0.539957\pi$
$720$	5.63879	−	2.87311i	0.210145	−	0.107074i
$721$	1.23536	+	2.42454i	0.0460074	+	0.0902946i
$722$	12.0280	+	1.90505i	0.447637	+	0.0708987i
$723$	−2.37144	−	14.9727i	−0.0881947	−	0.556839i
$724$	−12.4503	−	38.3182i	−0.462713	−	1.42409i
$725$	0.0196867			0.000731145
$726$	4.27306	−	2.38296i	0.158588	−	0.0884399i
$727$			20.3069i			0.753140i	0.926388	+	0.376570i	$0.122897\pi$
$727$			20.3069i			0.753140i	−0.926388	+	0.376570i	$0.877103\pi$
$728$	0.927512	+	2.15982i	0.0343759	+	0.0800483i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	14.6334	+	2.31770i	0.541606	+	0.0857820i
$731$	−4.00726	+	12.3331i	−0.148214	+	0.456155i
$732$	−2.86402	+	8.81453i	−0.105857	+	0.325795i
$733$	2.84575	−	17.9673i	0.105110	−	0.663639i	−0.877727	−	0.479162i	$-0.840941\pi$
$733$	2.84575	−	17.9673i	0.105110	−	0.663639i	0.982837	−	0.184477i	$-0.0590592\pi$
$734$	3.12579	−	0.495077i	0.115375	−	0.0182736i
$735$	−13.5454	−	6.90174i	−0.499631	−	0.254575i
$736$	−10.9479	−	10.9479i	−0.403545	−	0.403545i
$737$	−0.393309	−	20.9888i	−0.0144877	−	0.773131i
$738$			4.12553i			0.151863i
$739$	20.4893	−	40.2125i	0.753711	−	1.47924i	−0.119989	−	0.992775i	$-0.538286\pi$
$739$	20.4893	−	40.2125i	0.753711	−	1.47924i	0.873700	−	0.486466i	$-0.161714\pi$
$740$	21.5336	−	29.6385i	0.791592	−	1.08953i
$741$	−24.5019	−	1.60998i	−0.900100	−	0.0591441i
$742$	−0.0528502	+	0.162656i	−0.00194019	+	0.00597130i
$743$	−23.1725	−	45.4786i	−0.850117	−	1.66845i	−0.738049	−	0.674747i	$-0.764253\pi$
$743$	−23.1725	−	45.4786i	−0.850117	−	1.66845i	−0.112067	−	0.993701i	$-0.535747\pi$
$744$	−6.48802	−	8.93000i	−0.237862	−	0.327390i
$745$	−35.9790	−	26.1403i	−1.31817	−	0.957706i
$746$	7.03995	−	13.8167i	0.257751	−	0.505865i
$747$	5.78166	−	5.78166i	0.211540	−	0.211540i
$748$	14.0391	+	6.82504i	0.513321	+	0.249548i
$749$	3.84975	−	3.84975i	0.140667	−	0.140667i
$750$	−4.76496	+	1.54823i	−0.173992	+	0.0565333i
$751$	−24.9711	+	34.3698i	−0.911208	+	1.25417i	0.0555445	+	0.998456i	$0.482311\pi$
$751$	−24.9711	+	34.3698i	−0.911208	+	1.25417i	−0.966752	+	0.255714i	$0.917689\pi$
$752$	3.01297	−	19.0232i	0.109872	−	0.693703i
$753$	−27.4820	−	8.92945i	−1.00150	−	0.325407i
$754$	0.219901	+	0.348649i	0.00800832	+	0.0126970i
$755$	20.4983	+	28.2135i	0.746011	+	1.02680i
$756$	−0.686175	+	0.108680i	−0.0249560	+	0.00395264i
$757$	−12.8513	−	39.5523i	−0.467090	−	1.43755i	−0.856335	−	0.516420i	$-0.827264\pi$
$757$	−12.8513	−	39.5523i	−0.467090	−	1.43755i	0.389245	−	0.921134i	$-0.372736\pi$
$758$	−6.58171			−0.239058
$759$	10.8708	−	1.93121i	0.394586	−	0.0700984i
$760$	−18.0701	−	18.0701i	−0.655471	−	0.655471i
$761$	11.9838	−	23.5195i	0.434411	−	0.852579i	−0.565207	−	0.824949i	$-0.691204\pi$
$761$	11.9838	−	23.5195i	0.434411	−	0.852579i	0.999618	−	0.0276305i	$-0.00879619\pi$
$762$	0.453395	−	0.0718108i	0.0164248	−	0.00260143i
$763$	−0.0568564	+	0.0413086i	−0.00205834	+	0.00149547i
$764$	39.1199	+	12.7108i	1.41531	+	0.459862i
$765$	5.16333	−	2.63085i	0.186681	−	0.0951186i
$766$	−4.26930	+	3.10183i	−0.154256	+	0.112074i
$767$	7.98172	+	31.4497i	0.288203	+	1.13558i
$768$	0.746237	+	2.29668i	0.0269275	+	0.0828743i
$769$	−20.3148	+	20.3148i	−0.732570	+	0.732570i	−0.971128	−	0.238558i	$-0.923325\pi$
$769$	−20.3148	+	20.3148i	−0.732570	+	0.732570i	0.238558	+	0.971128i	$0.423325\pi$
$770$	−0.760673	−	1.00676i	−0.0274128	−	0.0362810i
$771$		−	2.93887i		−	0.105841i
$772$	−30.6340	−	15.6088i	−1.10254	−	0.561773i
$773$	−6.82575	−	43.0961i	−0.245505	−	1.55006i	−0.735009	−	0.678058i	$-0.762822\pi$
$773$	−6.82575	−	43.0961i	−0.245505	−	1.55006i	0.489504	−	0.872001i	$-0.337178\pi$
$774$	−0.345484	+	2.18130i	−0.0124182	+	0.0784053i
$775$	−0.226955	−	0.445425i	−0.00815247	−	0.0160001i
$776$	8.07170	+	2.62265i	0.289757	+	0.0941478i
$777$	−2.85725	+	2.07591i	−0.102503	+	0.0744729i
$778$	0.427131	+	2.69680i	0.0153134	+	0.0966849i
$779$	−60.0762	+	19.5199i	−2.15245	+	0.699374i
$780$	11.0835	+	9.22115i	0.396854	+	0.330170i
$781$	−5.72917	−	1.74355i	−0.205006	−	0.0623890i
$782$	−2.73440	−	2.73440i	−0.0977819	−	0.0977819i
$783$	−0.244456	+	0.0794284i	−0.00873613	+	0.00283854i
$784$	11.4860	−	15.8092i	0.410215	−	0.564613i
$785$	16.2762	+	2.57790i	0.580922	+	0.0920090i
$786$	−0.224276	+	0.114274i	−0.00799967	+	0.00407604i
$787$	−30.0559	+	15.3142i	−1.07138	+	0.545893i	−0.898465	−	0.439044i	$-0.855317\pi$
$787$	−30.0559	+	15.3142i	−1.07138	+	0.545893i	−0.172911	+	0.984938i	$0.555317\pi$
$788$	4.32164	+	0.684480i	0.153952	+	0.0243836i
$789$	0.682945	−	0.939993i	0.0243135	−	0.0334646i
$790$	12.5130	−	4.06571i	0.445191	−	0.144651i
$791$	4.50509	+	4.50509i	0.160183	+	0.160183i
$792$	5.36589	+	1.63299i	0.190668	+	0.0580257i
$793$	−18.4650	+	1.69364i	−0.655713	+	0.0601429i
$794$	−6.63830	+	2.15692i	−0.235585	+	0.0765461i
$795$	0.346228	+	2.18600i	0.0122795	+	0.0775294i
$796$	−17.8060	+	12.9368i	−0.631118	+	0.458534i
$797$	7.42963	+	2.41403i	0.263171	+	0.0855094i	0.437630	−	0.899155i	$-0.355818\pi$
$797$	7.42963	+	2.41403i	0.263171	+	0.0855094i	−0.174460	+	0.984664i	$0.555818\pi$
$798$	0.530124	+	1.04043i	0.0187662	+	0.0368307i
$799$	2.75892	−	17.4191i	0.0976036	−	0.616245i
$800$	−0.0557242	−	0.351829i	−0.00197015	−	0.0124390i
$801$	−14.8414	−	7.56206i	−0.524395	−	0.267192i
$802$			14.5813i			0.514884i
$803$	−30.0153	−	39.7255i	−1.05922	−	1.40188i
$804$	8.06579	−	8.06579i	0.284459	−	0.284459i
$805$	−0.879930	−	2.70815i	−0.0310135	−	0.0954496i
$806$	5.35333	−	8.99477i	0.188563	−	0.316827i
$807$	21.0430	−	15.2886i	0.740748	−	0.538185i
$808$	13.0375	−	6.64296i	0.458659	−	0.233699i
$809$	19.9073	+	6.46826i	0.699902	+	0.227412i	0.637288	−	0.770626i	$-0.280056\pi$
$809$	19.9073	+	6.46826i	0.699902	+	0.227412i	0.0626144	+	0.998038i	$0.480056\pi$
$810$	0.798432	−	0.580095i	0.0280540	−	0.0203825i
$811$	−27.5524	+	4.36387i	−0.967495	+	0.153236i	−0.620135	−	0.784495i	$-0.712922\pi$
$811$	−27.5524	+	4.36387i	−0.967495	+	0.153236i	−0.347361	+	0.937732i	$0.612922\pi$
$812$	−0.0810692	+	0.159107i	−0.00284497	+	0.00558357i
$813$	15.3501	+	15.3501i	0.538352	+	0.538352i
$814$	13.3066	−	2.36393i	0.466396	−	0.0828556i
$815$	9.51298			0.333225
$816$	2.30182	+	7.08427i	0.0805798	+	0.247999i
$817$	−33.3989	+	5.28986i	−1.16848	+	0.185069i
$818$	1.89197	+	2.60408i	0.0661513	+	0.0910495i
$819$	−0.741491	−	1.17562i	−0.0259098	−	0.0410795i
$820$	35.2750	+	11.4615i	1.23186	+	0.400255i
$821$	1.52253	−	9.61290i	0.0531368	−	0.335492i	−0.946771	−	0.321908i	$-0.895676\pi$
$821$	1.52253	−	9.61290i	0.0531368	−	0.335492i	0.999908	−	0.0135844i	$-0.00432417\pi$
$822$	2.01219	−	2.76954i	0.0701831	−	0.0965988i
$823$	−11.5040	+	3.73787i	−0.401004	+	0.130294i	−0.502574	−	0.864534i	$-0.667613\pi$
$823$	−11.5040	+	3.73787i	−0.401004	+	0.130294i	0.101570	+	0.994828i	$0.467613\pi$
$824$	8.44097	−	8.44097i	0.294055	−	0.294055i
$825$	0.228458	+	0.111064i	0.00795389	+	0.00386674i
$826$	1.09107	−	1.09107i	0.0379631	−	0.0379631i
$827$	4.55955	−	8.94862i	0.158551	−	0.311174i	−0.798042	−	0.602602i	$-0.794130\pi$
$827$	4.55955	−	8.94862i	0.158551	−	0.311174i	0.956593	+	0.291428i	$0.0941305\pi$
$828$	4.85362	+	3.52636i	0.168675	+	0.122550i
$829$	21.1123	+	29.0586i	0.733261	+	1.00925i	0.998978	+	0.0451963i	$0.0143913\pi$
$829$	21.1123	+	29.0586i	0.733261	+	1.00925i	−0.265717	+	0.964051i	$0.585609\pi$
$830$	3.66349	+	7.19000i	0.127161	+	0.249568i
$831$	4.82186	−	14.8402i	0.167269	−	0.514800i
$832$	−9.85701	+	8.64150i	−0.341730	+	0.299590i
$833$	10.5175	−	14.4761i	0.364411	−	0.501569i
$834$	0.208558	−	0.409318i	0.00722177	−	0.0141735i
$835$		−	10.9720i		−	0.379703i
$836$	0.762651	+	40.6986i	0.0263768	+	1.40759i
$837$	4.61530	+	4.61530i	0.159528	+	0.159528i
$838$	7.15886	+	3.64762i	0.247299	+	0.126005i
$839$	−18.3113	+	2.90022i	−0.632175	+	0.100127i	−0.464295	−	0.885681i	$-0.653692\pi$
$839$	−18.3113	+	2.90022i	−0.632175	+	0.100127i	−0.167880	+	0.985807i	$0.553692\pi$
$840$	0.226289	−	1.42873i	0.00780772	−	0.0492960i
$841$	8.94108	−	27.5178i	0.308313	−	0.948890i
$842$	−2.85028	+	8.77225i	−0.0982271	+	0.302312i
$843$	2.78696	+	0.441412i	0.0959881	+	0.0152030i
$844$	8.63721	+	6.27530i	0.297305	+	0.216005i
$845$	−8.20162	+	27.6548i	−0.282144	+	0.951355i
$846$		−	3.00357i		−	0.103265i
$847$	−0.505975	+	4.21016i	−0.0173855	+	0.144663i
$848$	−2.84492			−0.0976949
$849$	1.25906	+	3.87497i	0.0432107	+	0.132989i
$850$	−0.0139179	−	0.0878744i	−0.000477381	−	0.00301407i
$851$	30.1234	+	4.77107i	1.03262	+	0.163550i
$852$	−1.47731	−	2.89938i	−0.0506118	−	0.0993312i
$853$	22.1409	−	11.2814i	0.758091	−	0.386267i	−0.0318154	−	0.999494i	$-0.510129\pi$
$853$	22.1409	−	11.2814i	0.758091	−	0.386267i	0.789907	+	0.613227i	$0.210129\pi$
$854$	0.518303	+	0.713382i	0.0177360	+	0.0244114i
$855$	12.2251	+	8.88209i	0.418091	+	0.303761i
$856$	−21.2808	−	10.8431i	−0.727362	−	0.370609i
$857$	27.6610			0.944882			0.472441	−	0.881362i	$-0.343373\pi$
$857$	27.6610			0.944882			0.472441	+	0.881362i	$0.343373\pi$
$858$	0.584961	+	5.28656i	0.0199702	+	0.180480i
$859$	28.4817			0.971784			0.485892	−	0.874019i	$-0.338495\pi$
$859$	28.4817			0.971784			0.485892	+	0.874019i	$0.338495\pi$
$860$	17.6912	+	9.01413i	0.603266	+	0.307379i
$861$	−2.89274	−	2.10170i	−0.0985844	−	0.0716258i
$862$	−0.347582	−	0.478406i	−0.0118387	−	0.0162946i
$863$	−18.5627	+	9.45815i	−0.631881	+	0.321959i	−0.740432	−	0.672132i	$-0.765379\pi$
$863$	−18.5627	+	9.45815i	−0.631881	+	0.321959i	0.108551	+	0.994091i	$0.465379\pi$
$864$	2.11145	+	4.14395i	0.0718328	+	0.140980i
$865$	7.12173	+	1.12797i	0.242146	+	0.0383522i
$866$	−0.888773	−	5.61149i	−0.0302017	−	0.190686i
$867$	−3.14556	−	9.68104i	−0.106829	−	0.328785i
$868$	4.53451			0.153911
$869$	−39.7651	−	19.3316i	−1.34894	−	0.655779i
$870$		−	0.253673i		−	0.00860031i
$871$	21.1952	+	8.46005i	0.718170	+	0.286658i
$872$	0.249424	+	0.181217i	0.00844656	+	0.00613679i
$873$	−4.95678	−	0.785077i	−0.167762	−	0.0265708i
$874$	3.11606	−	9.59026i	0.105402	−	0.324395i
$875$	1.34186	−	4.12982i	0.0453632	−	0.139613i
$876$	4.23226	−	26.7215i	0.142995	−	0.902834i
$877$	1.27638	−	0.202159i	0.0431003	−	0.00682641i	−0.134847	−	0.990866i	$-0.543054\pi$
$877$	1.27638	−	0.202159i	0.0431003	−	0.00682641i	0.177947	+	0.984040i	$0.443054\pi$
$878$	4.85576	+	2.47413i	0.163874	+	0.0834979i
$879$	1.26142	+	1.26142i	0.0425467	+	0.0425467i
$880$	12.0170	−	17.2090i	0.405093	−	0.580116i
$881$		−	4.95329i		−	0.166881i	−0.996513	−	0.0834403i	$-0.973409\pi$
$881$		−	4.95329i		−	0.166881i	0.996513	−	0.0834403i	$-0.0265908\pi$
$882$	1.38348	−	2.71523i	0.0465842	−	0.0914267i
$883$	2.94534	−	4.05391i	0.0991186	−	0.136425i	−0.756577	−	0.653905i	$-0.773130\pi$
$883$	2.94534	−	4.05391i	0.0991186	−	0.136425i	0.855695	+	0.517480i	$0.173130\pi$
$884$	−12.7606	+	11.1870i	−0.429186	+	0.376261i
$885$	6.17043	−	18.9906i	0.207417	−	0.638363i
$886$	−7.23257	−	14.1947i	−0.242983	−	0.476881i
$887$	9.10439	+	12.5311i	0.305695	+	0.420754i	0.934033	−	0.357187i	$-0.116264\pi$
$887$	9.10439	+	12.5311i	0.305695	+	0.420754i	−0.628337	+	0.777941i	$0.716264\pi$
$888$	12.5345	+	9.10684i	0.420630	+	0.305606i
$889$	−0.180624	+	0.354495i	−0.00605795	+	0.0118894i
$890$	11.6241	−	11.6241i	0.389640	−	0.389640i
$891$	−3.28494	−	0.457369i	−0.110050	−	0.0153224i
$892$	24.3771	−	24.3771i	0.816205	−	0.816205i
$893$	43.7381	−	14.2114i	1.46364	−	0.475566i
$894$	5.23992	−	7.21214i	0.175249	−	0.241210i
$895$	3.35224	−	21.1652i	0.112053	−	0.707474i
$896$	4.00314	+	1.30070i	0.133736	+	0.0434533i
$897$	−2.65092	+	11.7065i	−0.0885118	+	0.390867i
$898$	6.02781	+	8.29656i	0.201150	+	0.276860i
$899$	1.65702	−	0.262447i	0.0552648	−	0.00875308i
$900$	0.0426537	+	0.131274i	0.00142179	+	0.00437582i
$901$	−2.60503			−0.0867863
$902$	6.43921	+	12.0730i	0.214402	+	0.401986i
$903$	−1.35348	−	1.35348i	−0.0450411	−	0.0450411i
$904$	12.6889	−	24.9034i	0.422027	−	0.828274i
$905$	−48.9955	+	7.76013i	−1.62867	+	0.257955i
$906$	−5.65551	+	4.10897i	−0.187892	+	0.136511i
$907$	30.7077	+	9.97754i	1.01963	+	0.331299i	0.770684	−	0.637218i	$-0.219915\pi$
$907$	30.7077	+	9.97754i	1.01963	+	0.331299i	0.248949	+	0.968517i	$0.419915\pi$
$908$	−16.6802	+	8.49898i	−0.553552	+	0.282049i
$909$	−6.99993	+	5.08575i	−0.232173	+	0.168684i
$910$	1.32959	−	0.337440i	0.0440754	−	0.0111860i
$911$	−11.9313	−	36.7208i	−0.395302	−	1.21661i	−0.928726	−	0.370766i	$-0.879095\pi$
$911$	−11.9313	−	36.7208i	−0.395302	−	1.21661i	0.533424	−	0.845848i	$-0.320905\pi$
$912$	−13.7348	+	13.7348i	−0.454803	+	0.454803i
$913$	7.89536	−	25.9436i	0.261298	−	0.858608i
$914$		−	4.82181i		−	0.159491i
$915$	10.1674	+	5.18057i	0.336125	+	0.171264i
$916$	1.32426	+	8.36102i	0.0437546	+	0.276256i
$917$	0.0341277	−	0.215474i	0.00112700	−	0.00711558i
$918$	0.527364	+	1.03501i	0.0174056	+	0.0341604i
$919$	−23.3217	−	7.57768i	−0.769312	−	0.249965i	−0.102042	−	0.994780i	$-0.532538\pi$
$919$	−23.3217	−	7.57768i	−0.769312	−	0.249965i	−0.667271	+	0.744815i	$0.732538\pi$
$920$	−10.1061	+	7.34249i	−0.333187	+	0.242075i
$921$	0.813416	+	5.13571i	0.0268030	+	0.169227i
$922$	11.9046	−	3.86804i	0.392057	−	0.127387i
$923$	4.16376	−	5.00470i	0.137052	−	0.164732i
$924$	−1.83840	+	1.38904i	−0.0604789	+	0.0456959i
$925$	0.496174	+	0.496174i	0.0163141	+	0.0163141i
$926$	−0.483031	+	0.156946i	−0.0158734	+	0.00515757i
$927$	−4.14904	+	5.71066i	−0.136272	+	0.187563i
$928$	1.18072	+	0.187008i	0.0387590	+	0.00613883i
$929$	19.3629	−	9.86589i	0.635276	−	0.323689i	−0.106524	−	0.994310i	$-0.533972\pi$
$929$	19.3629	−	9.86589i	0.635276	−	0.323689i	0.741800	+	0.670621i	$0.233972\pi$
$930$	−5.73953	+	2.92443i	−0.188206	+	0.0958960i
$931$	46.0853	+	7.29919i	1.51038	+	0.239221i
$932$	−18.3155	+	25.2091i	−0.599944	+	0.825752i
$933$	10.6768	−	3.46911i	0.349543	−	0.113574i
$934$	4.57954	+	4.57954i	0.149847	+	0.149847i
$935$	11.0037	−	15.7580i	0.359860	−	0.515340i
$936$	−3.89974	+	4.68736i	−0.127467	+	0.153211i
$937$	−25.7493	+	8.36645i	−0.841192	+	0.273320i	−0.697752	−	0.716339i	$-0.745816\pi$
$937$	−25.7493	+	8.36645i	−0.841192	+	0.273320i	−0.143440	+	0.989659i	$0.545816\pi$
$938$	−0.169772	−	1.07190i	−0.00554326	−	0.0349987i
$939$	−21.9556	+	15.9517i	−0.716494	+	0.520564i
$940$	−25.6818	−	8.34451i	−0.837647	−	0.272168i
$941$	−1.24907	−	2.45145i	−0.0407187	−	0.0799149i	0.869751	−	0.493491i	$-0.164279\pi$
$941$	−1.24907	−	2.45145i	−0.0407187	−	0.0799149i	−0.910469	+	0.413576i	$0.864279\pi$
$942$	−0.516749	+	3.26263i	−0.0168366	+	0.106302i
$943$	4.83034	+	30.4976i	0.157298	+	0.993138i
$944$	22.8693	+	11.6525i	0.744333	+	0.379257i
$945$			0.855367i			0.0278251i
$946$	2.39359	+	6.92261i	0.0778223	+	0.225074i
$947$	1.00243	−	1.00243i	0.0325747	−	0.0325747i	−0.690632	−	0.723207i	$-0.742667\pi$
$947$	1.00243	−	1.00243i	0.0325747	−	0.0325747i	0.723207	+	0.690632i	$0.242667\pi$
$948$	−7.42423	−	22.8494i	−0.241128	−	0.742115i
$949$	52.4640	−	13.3150i	1.70305	−	0.432223i
$950$	0.187693	−	0.136367i	0.00608955	−	0.00442432i
$951$	23.6934	−	12.0724i	0.768310	−	0.391474i
$952$	1.61928	+	0.526135i	0.0524811	+	0.0170521i
$953$	−21.6288	+	15.7142i	−0.700625	+	0.509034i	−0.880136	−	0.474722i	$-0.842549\pi$
$953$	−21.6288	+	15.7142i	−0.700625	+	0.509034i	0.179511	+	0.983756i	$0.442549\pi$
$954$	−0.438192	+	0.0694028i	−0.0141870	+	0.00224700i
$955$	22.9920	−	45.1243i	0.744003	−	1.46019i
$956$	11.1576	+	11.1576i	0.360864	+	0.360864i
$957$	−0.591403	+	0.613991i	−0.0191173	+	0.0198475i
$958$	−12.2181			−0.394749
$959$	0.916863	+	2.82182i	0.0296071	+	0.0911212i
$960$	7.96780	−	1.26198i	0.257160	−	0.0407301i
$961$	−6.81947	−	9.38620i	−0.219983	−	0.302781i
$962$	−3.24490	+	14.3295i	−0.104620	+	0.462001i
$963$	13.4318	+	4.36426i	0.432834	+	0.140636i
$964$	4.27373	−	26.9833i	0.137648	−	0.869072i
$965$	−24.8816	+	34.2466i	−0.800968	+	1.10244i
$966$	0.542858	−	0.176385i	0.0174662	−	0.00567511i
$967$	25.2913	−	25.2913i	0.813314	−	0.813314i	−0.171815	−	0.985129i	$-0.554963\pi$
$967$	25.2913	−	25.2913i	0.813314	−	0.813314i	0.985129	+	0.171815i	$0.0549631\pi$
$968$	18.2516	−	3.59639i	0.586627	−	0.115592i
$969$	−12.5766	+	12.5766i	−0.404020	+	0.404020i
$970$	2.24857	−	4.41307i	0.0721973	−	0.141695i
$971$	−38.8410	−	28.2196i	−1.24647	−	0.905611i	−0.248456	−	0.968643i	$-0.579923\pi$
$971$	−38.8410	−	28.2196i	−1.24647	−	0.905611i	−0.998012	+	0.0630318i	$0.979923\pi$
$972$	−1.05929	−	1.45799i	−0.0339767	−	0.0467649i
$973$	0.180759	+	0.354759i	0.00579486	+	0.0113730i
$974$	3.13676	−	9.65396i	0.100508	−	0.309333i
$975$	−0.207653	+	0.182046i	−0.00665022	+	0.00583015i
$976$	−8.62162	+	11.8666i	−0.275971	+	0.379842i
$977$	11.4121	−	22.3974i	0.365104	−	0.716557i	−0.633248	−	0.773949i	$-0.718279\pi$
$977$	11.4121	−	22.3974i	0.365104	−	0.716557i	0.998352	+	0.0573921i	$0.0182785\pi$
$978$			1.90691i			0.0609764i
$979$	−55.2349	+	1.03505i	−1.76532	+	0.0330803i
$980$	−19.3728	−	19.3728i	−0.618841	−	0.618841i
$981$	−0.162436	−	0.0827654i	−0.00518619	−	0.00264249i
$982$	−5.29630	+	0.838851i	−0.169012	+	0.0267688i
$983$	−9.56672	+	60.4019i	−0.305131	+	1.92652i	0.0657408	+	0.997837i	$0.479059\pi$
$983$	−9.56672	+	60.4019i	−0.305131	+	1.92652i	−0.370872	+	0.928684i	$0.620941\pi$
$984$	−4.84723	+	14.9182i	−0.154524	+	0.475576i
$985$	1.66475	−	5.12356i	0.0530432	−	0.163250i
$986$	0.294902	+	0.0467078i	0.00939158	+	0.00148748i
$987$	2.10605	+	1.53013i	0.0670362	+	0.0487046i
$988$	−41.0988	−	16.4046i	−1.30753	−	0.521899i
$989$			16.5296i			0.525610i
$990$	1.43111	−	2.94380i	0.0454837	−	0.0935601i
$991$	47.4094			1.50601			0.753004	−	0.658016i	$-0.228604\pi$
$991$	47.4094			1.50601			0.753004	+	0.658016i	$0.228604\pi$
$992$	−9.38060	−	28.8705i	−0.297834	−	0.916639i
$993$	−0.386270	−	2.43881i	−0.0122579	−	0.0773934i
$994$	−0.305785	−	0.0484316i	−0.00969891	−	0.00153616i
$995$	12.3025	+	24.1451i	0.390016	+	0.765450i
$996$	13.1294	−	6.68975i	0.416020	−	0.211973i
$997$	10.1882	+	14.0228i	0.322663	+	0.444108i	0.939278	−	0.343157i	$-0.111496\pi$
$997$	10.1882	+	14.0228i	0.322663	+	0.444108i	−0.616615	+	0.787265i	$0.711496\pi$
$998$	−3.73032	−	2.71023i	−0.118081	−	0.0857909i
$999$	−8.16303	−	4.15927i	−0.258267	−	0.131593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bj.a.424.9	yes	112
11.2	odd	10	inner	429.2.bj.a.112.9	✓	112
13.5	odd	4	inner	429.2.bj.a.226.9	yes	112
143.57	even	20	inner	429.2.bj.a.343.9	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bj.a.112.9	✓	112	11.2	odd	10	inner
429.2.bj.a.226.9	yes	112	13.5	odd	4	inner
429.2.bj.a.343.9	yes	112	143.57	even	20	inner
429.2.bj.a.424.9	yes	112	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.396304 + 0.201927i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.05929 - 1.45799i) q^{4} +(-1.97703 + 1.00735i) q^{5} +(-0.201927 - 0.396304i) q^{6} +(0.380750 + 0.0603048i) q^{7} +(-0.264552 - 1.67032i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.396304 + 0.201927i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.05929 - 1.45799i) q^{4} +(-1.97703 + 1.00735i) q^{5} +(-0.201927 - 0.396304i) q^{6} +(0.380750 + 0.0603048i) q^{7} +(-0.264552 - 1.67032i) q^{8} +(0.309017 + 0.951057i) q^{9} -0.986916 q^{10} +(2.38874 + 2.30086i) q^{11} +1.80217i q^{12} +(-3.31298 + 1.42273i) q^{13} +(0.138715 + 0.100783i) q^{14} +(2.19156 + 0.347109i) q^{15} +(-0.881363 + 2.71256i) q^{16} +(-0.807047 + 2.48383i) q^{17} +(-0.0695793 + 0.439306i) q^{18} +(-6.72641 + 1.06536i) q^{19} +(3.56295 + 1.81541i) q^{20} +(-0.272587 - 0.272587i) q^{21} +(0.482060 + 1.39419i) q^{22} +3.32899i q^{23} +(-0.767760 + 1.50681i) q^{24} +(-0.0450191 + 0.0619635i) q^{25} +(-1.60023 - 0.105149i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.315400 - 0.619008i) q^{28} +(-0.151082 - 0.207946i) q^{29} +(0.798432 + 0.580095i) q^{30} +(-2.96320 + 5.81562i) q^{31} +(-3.28865 + 3.28865i) q^{32} +(-0.580118 - 3.26550i) q^{33} +(-0.821389 + 0.821389i) q^{34} +(-0.813503 + 0.264323i) q^{35} +(1.05929 - 1.45799i) q^{36} +(1.43319 - 9.04879i) q^{37} +(-2.88083 - 0.936037i) q^{38} +(3.51652 + 0.796314i) q^{39} +(2.20562 + 3.03577i) q^{40} +(9.16120 - 1.45099i) q^{41} +(-0.0529846 - 0.163070i) q^{42} +4.96533 q^{43} +(0.824256 - 5.92001i) q^{44} +(-1.56898 - 1.56898i) q^{45} +(-0.672213 + 1.31929i) q^{46} +(-6.66976 + 1.05639i) q^{47} +(2.30744 - 1.67645i) q^{48} +(-6.51606 - 2.11720i) q^{49} +(-0.0303534 + 0.0154658i) q^{50} +(2.11288 - 1.53509i) q^{51} +(5.58372 + 3.32320i) q^{52} +(0.308233 + 0.948645i) q^{53} +(0.314508 - 0.314508i) q^{54} +(-7.04037 - 2.14258i) q^{55} -0.651926i q^{56} +(6.06798 + 3.09179i) q^{57} +(-0.0178844 - 0.112917i) q^{58} +(1.40777 - 8.88833i) q^{59} +(-1.81541 - 3.56295i) q^{60} +(4.89107 + 1.58921i) q^{61} +(-2.34866 + 1.70640i) q^{62} +(0.0603048 + 0.380750i) q^{63} +(3.45774 - 1.12349i) q^{64} +(5.11669 - 6.15010i) q^{65} +(0.429489 - 1.41127i) q^{66} +(-4.47560 - 4.47560i) q^{67} +(4.47629 - 1.45443i) q^{68} +(1.95673 - 2.69321i) q^{69} +(-0.375768 - 0.0595158i) q^{70} +(-1.60883 + 0.819740i) q^{71} +(1.50681 - 0.767760i) q^{72} +(-14.8274 - 2.34843i) q^{73} +(2.39517 - 3.29667i) q^{74} +(0.0728425 - 0.0236680i) q^{75} +(8.67849 + 8.67849i) q^{76} +(0.770758 + 1.02010i) q^{77} +(1.23281 + 1.02566i) q^{78} +(-12.6789 + 4.11961i) q^{79} +(-0.990006 - 6.25065i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(3.92361 + 1.27486i) q^{82} +(-3.71205 - 7.28532i) q^{83} +(-0.108680 + 0.686175i) q^{84} +(-0.906529 - 5.72360i) q^{85} +(1.96778 + 1.00263i) q^{86} +0.257036i q^{87} +(3.21121 - 4.59864i) q^{88} +(-11.7782 + 11.7782i) q^{89} +(-0.304974 - 0.938613i) q^{90} +(-1.34721 + 0.341913i) q^{91} +(4.85362 - 3.52636i) q^{92} +(5.81562 - 2.96320i) q^{93} +(-2.85656 - 0.928154i) q^{94} +(12.2251 - 8.88209i) q^{95} +(4.59360 - 0.727555i) q^{96} +(-2.27838 + 4.47158i) q^{97} +(-2.15482 - 2.15482i) q^{98} +(-1.45009 + 2.98283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9	\( 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9} - 10 q^{11} + 10 q^{13} - 60 q^{14} + 4 q^{15} + 80 q^{16} - 74 q^{20} + 8 q^{22} + 30 q^{24} + 38 q^{26} - 28 q^{27} - 20 q^{29} - 8 q^{31} + 20 q^{33} - 48 q^{34} + 20 q^{35} + 12 q^{37} - 10 q^{39} + 40 q^{40} - 110 q^{41} + 20 q^{42} - 36 q^{44} + 4 q^{45} - 20 q^{46} - 30 q^{47} - 20 q^{48} + 90 q^{50} - 10 q^{52} + 52 q^{53} - 64 q^{55} + 30 q^{57} + 24 q^{58} - 36 q^{59} - 74 q^{60} - 60 q^{61} + 48 q^{66} + 60 q^{67} + 60 q^{68} + 116 q^{70} + 20 q^{71} - 30 q^{72} + 70 q^{73} + 120 q^{74} - 52 q^{78} - 120 q^{79} + 8 q^{80} - 28 q^{81} + 30 q^{83} + 30 q^{84} - 40 q^{85} + 62 q^{86} + 48 q^{89} - 4 q^{91} - 144 q^{92} - 8 q^{93} - 20 q^{94} + 82 q^{97} - 10 q^{99}+O(q^{100}) \) 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9 - 10 * q^11 + 10 * q^13 - 60 * q^14 + 4 * q^15 + 80 * q^16 - 74 * q^20 + 8 * q^22 + 30 * q^24 + 38 * q^26 - 28 * q^27 - 20 * q^29 - 8 * q^31 + 20 * q^33 - 48 * q^34 + 20 * q^35 + 12 * q^37 - 10 * q^39 + 40 * q^40 - 110 * q^41 + 20 * q^42 - 36 * q^44 + 4 * q^45 - 20 * q^46 - 30 * q^47 - 20 * q^48 + 90 * q^50 - 10 * q^52 + 52 * q^53 - 64 * q^55 + 30 * q^57 + 24 * q^58 - 36 * q^59 - 74 * q^60 - 60 * q^61 + 48 * q^66 + 60 * q^67 + 60 * q^68 + 116 * q^70 + 20 * q^71 - 30 * q^72 + 70 * q^73 + 120 * q^74 - 52 * q^78 - 120 * q^79 + 8 * q^80 - 28 * q^81 + 30 * q^83 + 30 * q^84 - 40 * q^85 + 62 * q^86 + 48 * q^89 - 4 * q^91 - 144 * q^92 - 8 * q^93 - 20 * q^94 + 82 * q^97 - 10 * q^99

Introduction

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