LMFDB - Embedded newform 160.2.ba.a.107.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,2,Mod(3,160)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("160.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 3, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.ba (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.1
Character	$\chi$	$=$	160.107
Dual form			160.2.ba.a.3.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36334 + 0.375898i) q^{2} +(1.22690 + 0.508197i) q^{3} +(1.71740 - 1.02496i) q^{4} +(0.868914 + 2.06034i) q^{5} +(-1.86371 - 0.231658i) q^{6} +0.810621 q^{7} +(-1.95613 + 2.04293i) q^{8} +(-0.874309 - 0.874309i) q^{9} +(-1.95910 - 2.48232i) q^{10} +(0.353731 - 0.853982i) q^{11} +(2.62795 - 0.384736i) q^{12} +(3.86563 + 1.60120i) q^{13} +(-1.10515 + 0.304711i) q^{14} +(0.0190103 + 2.96940i) q^{15} +(1.89893 - 3.52052i) q^{16} +(-4.37679 + 4.37679i) q^{17} +(1.52063 + 0.863331i) q^{18} +(0.285895 + 0.690211i) q^{19} +(3.60403 + 2.64783i) q^{20} +(0.994548 + 0.411955i) q^{21} +(-0.161246 + 1.29724i) q^{22} +5.36098 q^{23} +(-3.43818 + 1.51237i) q^{24} +(-3.48998 + 3.58051i) q^{25} +(-5.87207 - 0.729895i) q^{26} +(-2.15296 - 5.19770i) q^{27} +(1.39216 - 0.830850i) q^{28} +(-1.48464 - 3.58424i) q^{29} +(-1.14211 - 4.04116i) q^{30} -9.06865i q^{31} +(-1.26554 + 5.51348i) q^{32} +(0.867982 - 0.867982i) q^{33} +(4.32183 - 7.61229i) q^{34} +(0.704360 + 1.67015i) q^{35} +(-2.39767 - 0.605412i) q^{36} +(-0.870467 + 0.360559i) q^{37} +(-0.649221 - 0.833526i) q^{38} +(3.92901 + 3.92901i) q^{39} +(-5.90883 - 2.25515i) q^{40} +(0.572180 - 0.572180i) q^{41} +(-1.51076 - 0.187787i) q^{42} +(-4.42382 - 10.6801i) q^{43} +(-0.267796 - 1.82919i) q^{44} +(1.04167 - 2.56107i) q^{45} +(-7.30885 + 2.01518i) q^{46} +(-1.59734 - 1.59734i) q^{47} +(4.11891 - 3.35428i) q^{48} -6.34289 q^{49} +(3.41212 - 6.19334i) q^{50} +(-7.59414 + 3.14560i) q^{51} +(8.28000 - 1.21220i) q^{52} +(-4.62712 + 1.91662i) q^{53} +(4.88902 + 6.27695i) q^{54} +(2.06685 - 0.0132321i) q^{55} +(-1.58568 + 1.65604i) q^{56} +0.992109i q^{57} +(3.37138 + 4.32846i) q^{58} +(0.996806 - 2.40650i) q^{59} +(3.07615 + 5.08017i) q^{60} +(5.76047 - 2.38607i) q^{61} +(3.40889 + 12.3637i) q^{62} +(-0.708734 - 0.708734i) q^{63} +(-0.347145 - 7.99246i) q^{64} +(0.0598966 + 9.35581i) q^{65} +(-0.857084 + 1.50963i) q^{66} +(2.34497 - 5.66126i) q^{67} +(-3.03069 + 12.0027i) q^{68} +(6.57737 + 2.72444i) q^{69} +(-1.58809 - 2.01222i) q^{70} +(-1.22326 + 1.22326i) q^{71} +(3.49641 - 0.0758959i) q^{72} +11.4586i q^{73} +(1.05121 - 0.818772i) q^{74} +(-6.10145 + 2.61932i) q^{75} +(1.19843 + 0.892340i) q^{76} +(0.286742 - 0.692256i) q^{77} +(-6.83349 - 3.87967i) q^{78} +17.0418i q^{79} +(8.90346 + 0.853413i) q^{80} -3.76178i q^{81} +(-0.564996 + 0.995159i) q^{82} +(3.28569 - 7.93236i) q^{83} +(2.13027 - 0.311875i) q^{84} +(-12.8207 - 5.21461i) q^{85} +(10.0458 + 12.8977i) q^{86} -5.15198i q^{87} +(1.05269 + 2.39314i) q^{88} +(7.65721 - 7.65721i) q^{89} +(-0.457453 + 3.88318i) q^{90} +(3.13356 + 1.29796i) q^{91} +(9.20696 - 5.49477i) q^{92} +(4.60866 - 11.1263i) q^{93} +(2.77815 + 1.57728i) q^{94} +(-1.17365 + 1.18877i) q^{95} +(-4.35462 + 6.12132i) q^{96} +(-2.02530 - 2.02530i) q^{97} +(8.64753 - 2.38428i) q^{98} +(-1.05591 + 0.437374i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 8 q^{7} + 8 q^{8} + 8 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} - 16 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 16 q^{19} - 32 q^{20} - 8 q^{21} - 20 q^{22}+ \cdots + 16 q^{98}+O(q^{100}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 8 * q^7 + 8 * q^8 + 8 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 - 16 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 16 * q^19 - 32 * q^20 - 8 * q^21 - 20 * q^22 - 8 * q^23 + 32 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 - 20 * q^28 + 64 * q^30 + 16 * q^32 - 8 * q^33 - 8 * q^34 - 48 * q^35 - 8 * q^36 - 4 * q^37 - 4 * q^38 + 16 * q^40 - 8 * q^41 - 68 * q^42 + 28 * q^43 - 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 88 * q^48 + 40 * q^49 + 4 * q^50 + 8 * q^51 + 48 * q^52 - 4 * q^53 + 56 * q^54 + 28 * q^55 + 40 * q^56 - 36 * q^58 + 12 * q^60 - 40 * q^61 - 32 * q^62 - 56 * q^63 - 48 * q^64 - 8 * q^65 + 72 * q^66 - 28 * q^67 + 8 * q^68 - 24 * q^69 + 4 * q^70 + 24 * q^71 + 88 * q^72 - 16 * q^75 + 56 * q^76 - 32 * q^77 + 112 * q^78 + 80 * q^80 + 68 * q^82 + 36 * q^83 - 56 * q^84 - 4 * q^85 + 24 * q^86 - 24 * q^88 - 84 * q^90 - 8 * q^91 + 92 * q^92 + 8 * q^93 + 32 * q^94 + 24 * q^96 - 8 * q^97 + 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$	−1.36334	+	0.375898i	−0.964028	+	0.265800i
$2$	−1.36334	+	0.375898i	−0.964028	+	0.265800i
$3$	1.22690	+	0.508197i	0.708349	+	0.293408i	0.707621	−	0.706592i	$-0.249768\pi$
$3$	1.22690	+	0.508197i	0.708349	+	0.293408i	0.000727832		1.00000i	$0.499768\pi$
$4$	1.71740	−	1.02496i	0.858701	−	0.512478i
$5$	0.868914	+	2.06034i	0.388590	+	0.921411i
$5$	0.868914	+	2.06034i	0.388590	+	0.921411i
$6$	−1.86371	−	0.231658i	−0.760856	−	0.0945741i
$7$	0.810621			0.306386			0.153193	−	0.988196i	$-0.451044\pi$
$7$	0.810621			0.306386			0.153193	+	0.988196i	$0.451044\pi$
$8$	−1.95613	+	2.04293i	−0.691595	+	0.722286i
$9$	−0.874309	−	0.874309i	−0.291436	−	0.291436i
$10$	−1.95910	−	2.48232i	−0.619523	−	0.784978i
$11$	0.353731	−	0.853982i	0.106654	−	0.257485i	−0.861538	−	0.507692i	$-0.830499\pi$
$11$	0.353731	−	0.853982i	0.106654	−	0.257485i	0.968192	+	0.250207i	$0.0804987\pi$
$12$	2.62795	−	0.384736i	0.758625	−	0.111064i
$13$	3.86563	+	1.60120i	1.07213	+	0.444092i	0.847743	−	0.530407i	$-0.177961\pi$
$13$	3.86563	+	1.60120i	1.07213	+	0.444092i	0.224391	+	0.974499i	$0.427961\pi$
$14$	−1.10515	+	0.304711i	−0.295365	+	0.0814374i
$15$	0.0190103	+	2.96940i	0.00490845	+	0.766696i
$16$	1.89893	−	3.52052i	0.474733	−	0.880130i
$17$	−4.37679	+	4.37679i	−1.06153	+	1.06153i	−0.0635485	+	0.997979i	$0.520242\pi$
$17$	−4.37679	+	4.37679i	−1.06153	+	1.06153i	−0.997979	+	0.0635485i	$0.979758\pi$
$18$	1.52063	+	0.863331i	0.358417	+	0.203489i
$19$	0.285895	+	0.690211i	0.0655888	+	0.158345i	0.953275	−	0.302103i	$-0.0976887\pi$
$19$	0.285895	+	0.690211i	0.0655888	+	0.158345i	−0.887687	+	0.460448i	$0.847689\pi$
$20$	3.60403	+	2.64783i	0.805885	+	0.592072i
$21$	0.994548	+	0.411955i	0.217028	+	0.0898960i
$22$	−0.161246	+	1.29724i	−0.0343777	+	0.276572i
$23$	5.36098			1.11784			0.558921	−	0.829221i	$-0.311215\pi$
$23$	5.36098			1.11784			0.558921	+	0.829221i	$0.311215\pi$
$24$	−3.43818	+	1.51237i	−0.701815	+	0.308711i
$25$	−3.48998	+	3.58051i	−0.697995	+	0.716102i
$26$	−5.87207	−	0.729895i	−1.15161	−	0.143144i
$27$	−2.15296	−	5.19770i	−0.414337	−	1.00030i
$28$	1.39216	−	0.830850i	0.263094	−	0.157016i
$29$	−1.48464	−	3.58424i	−0.275691	−	0.665576i	0.724016	−	0.689783i	$-0.242294\pi$
$29$	−1.48464	−	3.58424i	−0.275691	−	0.665576i	−0.999707	+	0.0242069i	$0.992294\pi$
$30$	−1.14211	−	4.04116i	−0.208520	−	0.737812i
$31$		−	9.06865i		−	1.62878i	−0.580319	−	0.814389i	$-0.697072\pi$
$31$		−	9.06865i		−	1.62878i	0.580319	−	0.814389i	$-0.302928\pi$
$32$	−1.26554	+	5.51348i	−0.223718	+	0.974654i
$33$	0.867982	−	0.867982i	0.151096	−	0.151096i
$34$	4.32183	−	7.61229i	0.741188	−	1.30550i
$35$	0.704360	+	1.67015i	0.119059	+	0.282307i
$36$	−2.39767	−	0.605412i	−0.399611	−	0.100902i
$37$	−0.870467	+	0.360559i	−0.143104	+	0.0592756i	−0.453086	−	0.891467i	$-0.649677\pi$
$37$	−0.870467	+	0.360559i	−0.143104	+	0.0592756i	0.309982	+	0.950742i	$0.399677\pi$
$38$	−0.649221	−	0.833526i	−0.105318	−	0.135216i
$39$	3.92901	+	3.92901i	0.629145	+	0.629145i
$40$	−5.90883	−	2.25515i	−0.934269	−	0.356570i
$41$	0.572180	−	0.572180i	0.0893596	−	0.0893596i	−0.661014	−	0.750374i	$-0.729874\pi$
$41$	0.572180	−	0.572180i	0.0893596	−	0.0893596i	0.750374	+	0.661014i	$0.229874\pi$
$42$	−1.51076	−	0.187787i	−0.233116	−	0.0289762i
$43$	−4.42382	−	10.6801i	−0.674627	−	1.62869i	−0.773654	−	0.633608i	$-0.781573\pi$
$43$	−4.42382	−	10.6801i	−0.674627	−	1.62869i	0.0990273	−	0.995085i	$-0.468427\pi$
$44$	−0.267796	−	1.82919i	−0.0403717	−	0.275760i
$45$	1.04167	−	2.56107i	0.155283	−	0.381782i
$46$	−7.30885	+	2.01518i	−1.07763	+	0.297123i
$47$	−1.59734	−	1.59734i	−0.232995	−	0.232995i	0.580946	−	0.813942i	$-0.302683\pi$
$47$	−1.59734	−	1.59734i	−0.232995	−	0.232995i	−0.813942	+	0.580946i	$0.802683\pi$
$48$	4.11891	−	3.35428i	0.594514	−	0.484149i
$49$	−6.34289			−0.906128
$50$	3.41212	−	6.19334i	0.482547	−	0.875870i
$51$	−7.59414	+	3.14560i	−1.06339	+	0.440471i
$52$	8.28000	−	1.21220i	1.14823	−	0.168102i
$53$	−4.62712	+	1.91662i	−0.635584	+	0.263268i	−0.677124	−	0.735869i	$-0.736774\pi$
$53$	−4.62712	+	1.91662i	−0.635584	+	0.263268i	0.0415393	+	0.999137i	$0.486774\pi$
$54$	4.88902	+	6.27695i	0.665312	+	0.854184i
$55$	2.06685	−	0.0132321i	0.278694	−	0.00178422i
$56$	−1.58568	+	1.65604i	−0.211895	+	0.221298i
$57$			0.992109i			0.131408i
$58$	3.37138	+	4.32846i	0.442684	+	0.568355i
$59$	0.996806	−	2.40650i	0.129773	−	0.313300i	−0.845616	−	0.533792i	$-0.820766\pi$
$59$	0.996806	−	2.40650i	0.129773	−	0.313300i	0.975389	+	0.220492i	$0.0707664\pi$
$60$	3.07615	+	5.08017i	0.397129	+	0.655847i
$61$	5.76047	−	2.38607i	0.737553	−	0.305504i	0.0179014	−	0.999840i	$-0.494301\pi$
$61$	5.76047	−	2.38607i	0.737553	−	0.305504i	0.719652	+	0.694335i	$0.244301\pi$
$62$	3.40889	+	12.3637i	0.432929	+	1.57019i
$63$	−0.708734	−	0.708734i	−0.0892920	−	0.0892920i
$64$	−0.347145	−	7.99246i	−0.0433931	−	0.999058i
$65$	0.0598966	+	9.35581i	0.00742926	+	1.16045i
$66$	−0.857084	+	1.50963i	−0.105500	+	0.185823i
$67$	2.34497	−	5.66126i	0.286484	−	0.691633i	−0.713475	−	0.700680i	$-0.752880\pi$
$67$	2.34497	−	5.66126i	0.286484	−	0.691633i	0.999959	+	0.00904731i	$0.00287989\pi$
$68$	−3.03069	+	12.0027i	−0.367525	+	1.45554i
$69$	6.57737	+	2.72444i	0.791822	+	0.327984i
$70$	−1.58809	−	2.01222i	−0.189813	−	0.240506i
$71$	−1.22326	+	1.22326i	−0.145174	+	0.145174i	−0.775958	−	0.630784i	$-0.782733\pi$
$71$	−1.22326	+	1.22326i	−0.145174	+	0.145174i	0.630784	+	0.775958i	$0.282733\pi$
$72$	3.49641	−	0.0758959i	0.412056	−	0.00894442i
$73$			11.4586i			1.34113i	0.741851	+	0.670565i	$0.233948\pi$
$73$			11.4586i			1.34113i	−0.741851	+	0.670565i	$0.766052\pi$
$74$	1.05121	−	0.818772i	0.122201	−	0.0951804i
$75$	−6.10145	+	2.61932i	−0.704534	+	0.302453i
$76$	1.19843	+	0.892340i	0.137470	+	0.102358i
$77$	0.286742	−	0.692256i	0.0326773	−	0.0788899i
$78$	−6.83349	−	3.87967i	−0.773740	−	0.439287i
$79$			17.0418i			1.91736i	0.284493	+	0.958678i	$0.408175\pi$
$79$			17.0418i			1.91736i	−0.284493	+	0.958678i	$0.591825\pi$
$80$	8.90346	+	0.853413i	0.995438	+	0.0954145i
$81$		−	3.76178i		−	0.417976i
$82$	−0.564996	+	0.995159i	−0.0623933	+	0.109897i
$83$	3.28569	−	7.93236i	0.360651	−	0.870689i	−0.634554	−	0.772879i	$-0.718816\pi$
$83$	3.28569	−	7.93236i	0.360651	−	0.870689i	0.995205	−	0.0978105i	$-0.0311839\pi$
$84$	2.13027	−	0.311875i	0.232432	−	0.0340283i
$85$	−12.8207	−	5.21461i	−1.39060	−	0.565603i
$86$	10.0458	+	12.8977i	1.08327	+	1.39079i
$87$		−	5.15198i		−	0.552350i
$88$	1.05269	+	2.39314i	0.112217	+	0.255110i
$89$	7.65721	−	7.65721i	0.811663	−	0.811663i	−0.173220	−	0.984883i	$-0.555417\pi$
$89$	7.65721	−	7.65721i	0.811663	−	0.811663i	0.984883	+	0.173220i	$0.0554172\pi$
$90$	−0.457453	+	3.88318i	−0.0482198	+	0.409323i
$91$	3.13356	+	1.29796i	0.328487	+	0.136064i
$92$	9.20696	−	5.49477i	0.959892	−	0.572869i
$93$	4.60866	−	11.1263i	0.477896	−	1.15374i
$94$	2.77815	+	1.57728i	0.286544	+	0.162684i
$95$	−1.17365	+	1.18877i	−0.120414	+	0.121966i
$96$	−4.35462	+	6.12132i	−0.444441	+	0.624755i
$97$	−2.02530	−	2.02530i	−0.205638	−	0.205638i	0.596772	−	0.802411i	$-0.296450\pi$
$97$	−2.02530	−	2.02530i	−0.205638	−	0.205638i	−0.802411	+	0.596772i	$0.796450\pi$
$98$	8.64753	−	2.38428i	0.873533	−	0.240849i
$99$	−1.05591	+	0.437374i	−0.106123	+	0.0439578i
$100$	−2.32382	+	9.72624i	−0.232382	+	0.972624i
$101$	0.295173	−	0.712610i	0.0293708	−	0.0709073i	−0.908514	−	0.417855i	$-0.862782\pi$
$101$	0.295173	−	0.712610i	0.0293708	−	0.0709073i	0.937884	+	0.346948i	$0.112782\pi$
$102$	9.17098	−	7.14314i	0.908063	−	0.707277i
$103$			9.73185i			0.958908i	0.877567	+	0.479454i	$0.159165\pi$
$103$			9.73185i			0.958908i	−0.877567	+	0.479454i	$0.840835\pi$
$104$	−10.8328	+	4.76508i	−1.06224	+	0.467255i
$105$	0.0154102	+	2.40706i	0.00150388	+	0.234905i
$106$	5.58790	−	4.35233i	0.542745	−	0.422736i
$107$	−6.55453	+	2.71497i	−0.633650	+	0.262466i	−0.676303	−	0.736624i	$-0.736419\pi$
$107$	−6.55453	+	2.71497i	−0.633650	+	0.262466i	0.0426531	+	0.999090i	$0.486419\pi$
$108$	−9.02490	−	6.71985i	−0.868421	−	0.646618i
$109$	10.2140	−	4.23080i	0.978328	−	0.405237i	0.164522	−	0.986373i	$-0.447392\pi$
$109$	10.2140	−	4.23080i	0.978328	−	0.405237i	0.813806	+	0.581137i	$0.197392\pi$
$110$	−2.81285	+	0.794966i	−0.268195	+	0.0757970i
$111$	−1.25121			−0.118759
$112$	1.53932	−	2.85381i	0.145452	−	0.269659i
$113$	−14.5463	−	14.5463i	−1.36841	−	1.36841i	−0.862715	−	0.505690i	$-0.831238\pi$
$113$	−14.5463	−	14.5463i	−1.36841	−	1.36841i	−0.505690	−	0.862715i	$-0.668762\pi$
$114$	−0.372932	−	1.35258i	−0.0349283	−	0.126681i
$115$	4.65823	+	11.0454i	0.434383	+	1.02999i
$116$	−6.22340	−	4.63388i	−0.577828	−	0.430245i
$117$	−1.97982	−	4.77970i	−0.183034	−	0.441884i
$118$	−0.454387	+	3.65558i	−0.0418297	+	0.336524i
$119$	−3.54792	+	3.54792i	−0.325237	+	0.325237i
$120$	−6.10347	−	5.76968i	−0.557168	−	0.526698i
$121$	7.17401	+	7.17401i	0.652183	+	0.652183i
$122$	−6.95658	+	5.41838i	−0.629819	+	0.490557i
$123$	0.992787	−	0.411226i	0.0895166	−	0.0370790i
$124$	−9.29496	−	15.5745i	−0.834712	−	1.39863i
$125$	−10.4096	−	4.07937i	−0.931058	−	0.364870i
$126$	1.23266	+	0.699834i	0.109814	+	0.0623462i
$127$	−12.0188	+	12.0188i	−1.06649	+	1.06649i	−0.0688681	+	0.997626i	$0.521939\pi$
$127$	−12.0188	+	12.0188i	−1.06649	+	1.06649i	−0.997626	+	0.0688681i	$0.978061\pi$
$128$	3.47763	+	10.7660i	0.307382	+	0.951586i
$129$		−	15.3515i		−	1.35162i
$130$	−3.59849	−	12.7327i	−0.315609	−	1.11673i
$131$	4.28707	+	10.3499i	0.374563	+	0.904274i	0.992965	+	0.118412i	$0.0377805\pi$
$131$	4.28707	+	10.3499i	0.374563	+	0.904274i	−0.618402	+	0.785862i	$0.712220\pi$
$132$	0.601031	−	2.38032i	0.0523130	−	0.207180i
$133$	0.231752	+	0.559500i	0.0200955	+	0.0485148i
$134$	−1.06894	+	8.59970i	−0.0923423	+	0.742901i
$135$	8.83828	−	8.95217i	0.760678	−	0.770480i
$136$	−0.379935	−	17.5030i	−0.0325791	−	1.50087i
$137$	1.71157			0.146229			0.0731145	−	0.997324i	$-0.476706\pi$
$137$	1.71157			0.146229			0.0731145	+	0.997324i	$0.476706\pi$
$138$	−9.99132	−	1.24192i	−0.850517	−	0.105719i
$139$	−1.54808	−	0.641236i	−0.131306	−	0.0543889i	0.316063	−	0.948738i	$-0.397639\pi$
$139$	−1.54808	−	0.641236i	−0.131306	−	0.0543889i	−0.447369	+	0.894349i	$0.647639\pi$
$140$	2.92150	+	2.14638i	0.246912	+	0.181403i
$141$	−1.14800	−	2.77153i	−0.0966794	−	0.233405i
$142$	1.20790	−	2.12754i	0.101365	−	0.178539i
$143$	2.73479	−	2.73479i	0.228694	−	0.228694i
$144$	−4.73828	+	1.41777i	−0.394857	+	0.118147i
$145$	6.09471	−	6.17325i	0.506138	−	0.512660i
$146$	−4.30727	−	15.6220i	−0.356473	−	1.29289i
$147$	−7.78207	−	3.22344i	−0.641855	−	0.265865i
$148$	−1.12538	+	1.51141i	−0.0925060	+	0.124238i
$149$	−7.10915	+	17.1630i	−0.582404	+	1.40605i	0.308223	+	0.951314i	$0.400266\pi$
$149$	−7.10915	+	17.1630i	−0.582404	+	1.40605i	−0.890627	+	0.454734i	$0.849734\pi$
$150$	7.33376	−	5.86455i	0.598799	−	0.478839i
$151$	7.59514	+	7.59514i	0.618083	+	0.618083i	0.945040	−	0.326956i	$-0.106023\pi$
$151$	7.59514	+	7.59514i	0.618083	+	0.618083i	−0.326956	+	0.945040i	$0.606023\pi$
$152$	−1.96930	−	0.766076i	−0.159731	−	0.0621370i
$153$	7.65334			0.618736
$154$	−0.130709	+	1.05157i	−0.0105329	+	0.0847377i
$155$	18.6845	−	7.87988i	1.50077	−	0.632927i
$156$	10.7747	+	2.72062i	0.862670	+	0.217824i
$157$	13.5947	+	5.63110i	1.08497	+	0.449411i	0.852251	−	0.523133i	$-0.175237\pi$
$157$	13.5947	+	5.63110i	1.08497	+	0.449411i	0.232722	+	0.972543i	$0.425237\pi$
$158$	−6.40600	−	23.2338i	−0.509634	−	1.84839i
$159$	−6.65102			−0.527460
$160$	−12.4593	+	2.18330i	−0.984991	+	0.172605i
$161$	4.34573			0.342491
$162$	1.41405	+	5.12860i	0.111098	+	0.402941i
$163$	−4.78964	−	1.98393i	−0.375154	−	0.155394i	0.187136	−	0.982334i	$-0.440079\pi$
$163$	−4.78964	−	1.98393i	−0.375154	−	0.155394i	−0.562290	+	0.826940i	$0.690079\pi$
$164$	0.396204	−	1.56912i	0.0309383	−	0.122528i
$165$	2.54254	+	1.03413i	0.197936	+	0.0805072i
$166$	−1.49776	+	12.0496i	−0.116249	+	0.935230i
$167$	−7.59626			−0.587817			−0.293908	−	0.955834i	$-0.594956\pi$
$167$	−7.59626			−0.587817			−0.293908	+	0.955834i	$0.594956\pi$
$168$	−2.78706	+	1.22596i	−0.215026	+	0.0945847i
$169$	3.18690	+	3.18690i	0.245146	+	0.245146i
$170$	19.4392	+	2.29001i	1.49092	+	0.175635i
$171$	0.353498	−	0.853419i	0.0270326	−	0.0652626i
$172$	−18.5441	−	13.8077i	−1.41397	−	1.05283i
$173$	0.0431970	+	0.0178928i	0.00328421	+	0.00136036i	0.384325	−	0.923198i	$-0.374434\pi$
$173$	0.0431970	+	0.0178928i	0.00328421	+	0.00136036i	−0.381041	+	0.924558i	$0.624434\pi$
$174$	1.93662	+	7.02390i	0.146815	+	0.532481i
$175$	−2.82905	+	2.90244i	−0.213856	+	0.219404i
$176$	−2.33475	−	2.86697i	−0.175988	−	0.216106i
$177$	2.44595	−	2.44595i	0.183849	−	0.183849i
$178$	−7.56106	+	13.3177i	−0.566726	+	0.998206i
$179$	7.55581	+	18.2413i	0.564748	+	1.36342i	0.905931	+	0.423425i	$0.139172\pi$
$179$	7.55581	+	18.2413i	0.564748	+	1.36342i	−0.341183	+	0.939997i	$0.610828\pi$
$180$	−0.836015	−	5.46606i	−0.0623129	−	0.407416i
$181$	22.1793	+	9.18697i	1.64858	+	0.682862i	0.997121	−	0.0758260i	$-0.0241593\pi$
$181$	22.1793	+	9.18697i	1.64858	+	0.682862i	0.651454	+	0.758688i	$0.274159\pi$
$182$	−4.76002	−	0.591668i	−0.352836	−	0.0438574i
$183$	8.28010			0.612082
$184$	−10.4868	+	10.9521i	−0.773094	+	0.807401i
$185$	−1.49923	−	1.48016i	−0.110226	−	0.108824i
$186$	−2.10083	+	16.9013i	−0.154040	+	1.23927i
$187$	2.18949	+	5.28590i	0.160112	+	0.386544i
$188$	−4.38046	−	1.10607i	−0.319478	−	0.0806683i
$189$	−1.74523	−	4.21336i	−0.126947	−	0.306477i
$190$	1.15323	−	2.06188i	0.0836639	−	0.149584i
$191$		−	10.7326i		−	0.776586i	−0.921536	−	0.388293i	$-0.873065\pi$
$191$		−	10.7326i		−	0.776586i	0.921536	−	0.388293i	$-0.126935\pi$
$192$	3.63584	−	9.98235i	0.262394	−	0.720414i
$193$	−13.3767	+	13.3767i	−0.962880	+	0.962880i	−0.999335	−	0.0364558i	$-0.988393\pi$
$193$	−13.3767	+	13.3767i	−0.962880	+	0.962880i	0.0364558	+	0.999335i	$0.488393\pi$
$194$	3.52249	+	1.99987i	0.252900	+	0.143582i
$195$	−4.68111	+	11.5091i	−0.335221	+	0.824180i
$196$	−10.8933	+	6.50118i	−0.778092	+	0.464370i
$197$	7.08755	−	2.93576i	0.504967	−	0.209164i	−0.115632	−	0.993292i	$-0.536889\pi$
$197$	7.08755	−	2.93576i	0.504967	−	0.209164i	0.620599	+	0.784128i	$0.286889\pi$
$198$	1.27516	−	0.993207i	0.0906220	−	0.0705841i
$199$	−15.2564	−	15.2564i	−1.08149	−	1.08149i	−0.996370	−	0.0851236i	$-0.972871\pi$
$199$	−15.2564	−	15.2564i	−1.08149	−	1.08149i	−0.0851236	−	0.996370i	$-0.527129\pi$
$200$	−0.487911	−	14.1337i	−0.0345005	−	0.999405i
$201$	5.75407	−	5.75407i	0.405861	−	0.405861i
$202$	−0.134552	+	1.08249i	−0.00946708	+	0.0761634i
$203$	−1.20348	−	2.90546i	−0.0844677	−	0.203923i
$204$	−9.81809	+	13.1859i	−0.687404	+	0.923198i
$205$	1.67606	+	0.681709i	0.117061	+	0.0476126i
$206$	−3.65818	−	13.2678i	−0.254878	−	0.924414i
$207$	−4.68716	−	4.68716i	−0.325780	−	0.325780i
$208$	12.9776	−	10.5685i	0.899836	−	0.732791i
$209$	0.690558			0.0477669
$210$	−0.925818	−	3.27585i	−0.0638875	−	0.226055i
$211$	−12.4406	+	5.15308i	−0.856449	+	0.354753i	−0.767318	−	0.641267i	$-0.778409\pi$
$211$	−12.4406	+	5.15308i	−0.856449	+	0.354753i	−0.0891311	+	0.996020i	$0.528409\pi$
$212$	−5.98218	+	8.03420i	−0.410858	+	0.551791i
$213$	−2.12247	+	0.879155i	−0.145429	+	0.0602387i
$214$	7.91550	−	6.16527i	0.541093	−	0.421449i
$215$	18.1606	−	18.3946i	1.23854	−	1.25450i
$216$	14.8300	+	5.76901i	1.00905	+	0.392531i
$217$		−	7.35124i		−	0.499035i
$218$	−12.3349	+	9.60746i	−0.835424	+	0.650699i
$219$	−5.82324	+	14.0585i	−0.393498	+	0.949988i
$220$	3.53605	−	2.14116i	0.238401	−	0.144357i
$221$	−23.9272	+	9.91096i	−1.60952	+	0.666683i
$222$	1.70582	−	0.470327i	0.114487	−	0.0315663i
$223$	18.6893	+	18.6893i	1.25153	+	1.25153i	0.955035	+	0.296495i	$0.0958177\pi$
$223$	18.6893	+	18.6893i	1.25153	+	1.25153i	0.296495	+	0.955035i	$0.404182\pi$
$224$	−1.02587	+	4.46934i	−0.0685439	+	0.298620i
$225$	6.18179	−	0.0791559i	0.412120	−	0.00527706i
$226$	25.2996	+	14.3637i	1.68290	+	0.955459i
$227$	8.91547	−	21.5239i	0.591741	−	1.42859i	−0.290080	−	0.957003i	$-0.593682\pi$
$227$	8.91547	−	21.5239i	0.591741	−	1.42859i	0.881820	−	0.471586i	$-0.156318\pi$
$228$	1.01687	+	1.70385i	0.0673437	+	0.112840i
$229$	−9.93553	−	4.11543i	−0.656558	−	0.271955i	0.0294313	−	0.999567i	$-0.490630\pi$
$229$	−9.93553	−	4.11543i	−0.656558	−	0.271955i	−0.685989	+	0.727612i	$0.740630\pi$
$230$	−10.5027	−	13.3077i	−0.692529	−	0.877482i
$231$	0.703605	−	0.703605i	0.0462938	−	0.0462938i
$232$	10.2265	+	3.97820i	0.671402	+	0.261181i
$233$			16.9133i			1.10803i	0.832507	+	0.554014i	$0.186905\pi$
$233$			16.9133i			1.10803i	−0.832507	+	0.554014i	$0.813095\pi$
$234$	4.49585	+	5.77216i	0.293903	+	0.377338i
$235$	1.90310	−	4.67900i	0.124145	−	0.305224i
$236$	−0.754642	−	5.15461i	−0.0491230	−	0.335536i
$237$	−8.66061	+	20.9086i	−0.562567	+	1.35816i
$238$	3.50337	−	6.17068i	0.227090	−	0.399986i
$239$		−	16.3930i		−	1.06038i	−0.847880	−	0.530189i	$-0.822121\pi$
$239$		−	16.3930i		−	1.06038i	0.847880	−	0.530189i	$-0.177879\pi$
$240$	10.4899	+	5.57177i	0.677122	+	0.359656i
$241$			2.00046i			0.128861i	0.997922	+	0.0644306i	$0.0205231\pi$
$241$			2.00046i			0.128861i	−0.997922	+	0.0644306i	$0.979477\pi$
$242$	−12.4773	−	7.08393i	−0.802073	−	0.455373i
$243$	−4.54714	+	10.9778i	−0.291699	+	0.704225i
$244$	7.44743	−	10.0021i	0.476773	−	0.640316i
$245$	−5.51143	−	13.0685i	−0.352112	−	0.834916i
$246$	−1.19893	+	0.933828i	−0.0764409	+	0.0595387i
$247$			3.12588i			0.198895i
$248$	18.5266	+	17.7394i	1.17644	+	1.12645i
$249$	8.06240	−	8.06240i	0.510934	−	0.510934i
$250$	15.7252	+	1.64864i	0.994549	+	0.104269i
$251$	2.14679	+	0.889229i	0.135504	+	0.0561277i	0.449405	−	0.893328i	$-0.351636\pi$
$251$	2.14679	+	0.889229i	0.135504	+	0.0561277i	−0.313901	+	0.949456i	$0.601636\pi$
$252$	−1.94360	−	0.490760i	−0.122435	−	0.0309149i
$253$	1.89635	−	4.57818i	0.119222	−	0.287828i
$254$	11.8679	−	20.9035i	0.744656	−	1.31160i
$255$	−13.0796	−	12.9132i	−0.819079	−	0.808658i
$256$	−8.78811	−	13.3705i	−0.549257	−	0.835654i
$257$	5.89815	+	5.89815i	0.367916	+	0.367916i	0.866717	−	0.498800i	$-0.166226\pi$
$257$	5.89815	+	5.89815i	0.367916	+	0.367916i	−0.498800	+	0.866717i	$0.666226\pi$
$258$	5.77060	+	20.9293i	0.359262	+	1.30300i
$259$	−0.705619	+	0.292277i	−0.0438450	+	0.0181612i
$260$	9.69215	+	16.0063i	0.601082	+	0.992668i
$261$	−1.83570	+	4.43176i	−0.113627	+	0.274319i
$262$	−9.73524	−	12.4989i	−0.601445	−	0.772187i
$263$		−	6.25098i		−	0.385452i	−0.981253	−	0.192726i	$-0.938267\pi$
$263$		−	6.25098i		−	0.385452i	0.981253	−	0.192726i	$-0.0617328\pi$
$264$	0.0753467	+	3.47111i	0.00463727	+	0.213632i
$265$	−7.96945	−	7.86806i	−0.489560	−	0.483331i
$266$	−0.526273	−	0.675674i	−0.0322678	−	0.0414282i
$267$	13.2860	−	5.50323i	0.813089	−	0.336792i
$268$	−1.77528	−	12.1261i	−0.108443	−	0.740722i
$269$	−5.81666	+	2.40934i	−0.354648	+	0.146900i	−0.552893	−	0.833252i	$-0.686476\pi$
$269$	−5.81666	+	2.40934i	−0.354648	+	0.146900i	0.198244	+	0.980153i	$0.436476\pi$
$270$	−8.68448	+	15.5272i	−0.528521	+	0.944953i
$271$	−15.8408			−0.962258			−0.481129	−	0.876650i	$-0.659773\pi$
$271$	−15.8408			−0.962258			−0.481129	+	0.876650i	$0.659773\pi$
$272$	7.09734	+	23.7198i	0.430339	+	1.43822i
$273$	3.18494	+	3.18494i	0.192761	+	0.192761i
$274$	−2.33345	+	0.643375i	−0.140969	+	0.0388677i
$275$	1.82318	+	4.24691i	0.109942	+	0.256099i
$276$	14.0884	−	2.06256i	0.848023	−	0.124152i
$277$	4.18090	+	10.0936i	0.251206	+	0.606465i	0.998302	−	0.0582513i	$-0.0185525\pi$
$277$	4.18090	+	10.0936i	0.251206	+	0.606465i	−0.747096	+	0.664716i	$0.768552\pi$
$278$	2.35160	+	0.292303i	0.141040	+	0.0175312i
$279$	−7.92881	+	7.92881i	−0.474685	+	0.474685i
$280$	−4.78983	−	1.82807i	−0.286247	−	0.109248i
$281$	−4.80986	−	4.80986i	−0.286932	−	0.286932i	0.548934	−	0.835866i	$-0.315034\pi$
$281$	−4.80986	−	4.80986i	−0.286932	−	0.286932i	−0.835866	+	0.548934i	$0.815034\pi$
$282$	2.60693	+	3.34700i	0.155241	+	0.199311i
$283$	−24.3013	+	10.0659i	−1.44456	+	0.598358i	−0.960900	−	0.276897i	$-0.910694\pi$
$283$	−24.3013	+	10.0659i	−1.44456	+	0.598358i	−0.483663	+	0.875254i	$0.660694\pi$
$284$	−0.847040	+	3.35461i	−0.0502626	+	0.199060i
$285$	−2.04408	+	0.862057i	−0.121081	+	0.0510639i
$286$	−2.70045	+	4.75645i	−0.159681	+	0.281255i
$287$	0.463821	−	0.463821i	0.0273785	−	0.0273785i
$288$	5.92696	−	3.71401i	0.349249	−	0.218850i
$289$		−	21.3126i		−	1.25368i
$290$	−5.98866	+	10.7072i	−0.351666	+	0.628751i
$291$	−1.45558	−	3.51409i	−0.0853278	−	0.206000i
$292$	11.7446	+	19.6790i	0.687299	+	1.15163i
$293$	−7.47876	−	18.0553i	−0.436914	−	1.05480i	−0.977009	−	0.213199i	$-0.931612\pi$
$293$	−7.47876	−	18.0553i	−0.436914	−	1.05480i	0.540095	−	0.841604i	$-0.318388\pi$
$294$	11.8213	+	1.46938i	0.689433	+	0.0856962i
$295$	5.82434	−	0.0372879i	0.339106	−	0.00217098i
$296$	0.966145	−	2.48360i	0.0561560	−	0.144357i
$297$	−5.20031			−0.301753
$298$	3.24066	−	26.0713i	0.187726	−	1.51027i
$299$	20.7236	+	8.58399i	1.19848	+	0.496425i
$300$	−7.79394	+	10.7521i	−0.449984	+	0.620775i
$301$	−3.58604	−	8.65748i	−0.206696	−	0.499009i
$302$	−13.2098	−	7.49977i	−0.760136	−	0.431563i
$303$	0.724293	−	0.724293i	0.0416095	−	0.0416095i
$304$	2.97280	+	0.304167i	0.170502	+	0.0174452i
$305$	9.92146	+	9.79523i	0.568101	+	0.560873i
$306$	−10.4341	+	2.87688i	−0.596479	+	0.164460i
$307$	30.3123	+	12.5558i	1.73001	+	0.716595i	0.999430	+	0.0337730i	$0.0107523\pi$
$307$	30.3123	+	12.5558i	1.73001	+	0.716595i	0.730585	+	0.682822i	$0.239248\pi$
$308$	−0.217081	−	1.48278i	−0.0123693	−	0.0844891i
$309$	−4.94570	+	11.9400i	−0.281351	+	0.679241i
$310$	−22.5113	+	17.7664i	−1.27856	+	1.00907i
$311$	−9.72842	−	9.72842i	−0.551648	−	0.551648i	0.375268	−	0.926916i	$-0.377551\pi$
$311$	−9.72842	−	9.72842i	−0.551648	−	0.551648i	−0.926916	+	0.375268i	$0.877551\pi$
$312$	−15.7123	+	0.341064i	−0.889536	+	0.0193090i
$313$	−12.4426			−0.703299			−0.351649	−	0.936132i	$-0.614379\pi$
$313$	−12.4426			−0.703299			−0.351649	+	0.936132i	$0.614379\pi$
$314$	−20.6509	−	2.56690i	−1.16540	−	0.144858i
$315$	0.844401	−	2.07606i	0.0475766	−	0.116973i
$316$	17.4671	+	29.2677i	0.982602	+	1.64644i
$317$	19.8193	+	8.20943i	1.11316	+	0.461087i	0.862026	−	0.506864i	$-0.169195\pi$
$317$	19.8193	+	8.20943i	1.11316	+	0.461087i	0.251138	+	0.967951i	$0.419195\pi$
$318$	9.06762	−	2.50011i	0.508487	−	0.140199i
$319$	−3.58604			−0.200779
$320$	16.1655	−	7.66000i	0.903681	−	0.428207i
$321$	−9.42147			−0.525855
$322$	−5.92471	+	1.63355i	−0.330171	+	0.0910342i
$323$	−4.27221	−	1.76961i	−0.237712	−	0.0984636i
$324$	−3.85566	−	6.46049i	−0.214203	−	0.358916i
$325$	−19.2241	+	8.25280i	−1.06636	+	0.457783i
$326$	7.27567	+	0.904363i	0.402962	+	0.0500880i
$327$	14.6817			0.811897
$328$	0.0496691	+	2.28818i	0.00274252	+	0.126344i
$329$	−1.29483	−	1.29483i	−0.0713865	−	0.0713865i
$330$	−3.85508	−	0.454142i	−0.212215	−	0.0249997i
$331$	8.99571	−	21.7176i	0.494449	−	1.19371i	−0.457985	−	0.888960i	$-0.651429\pi$
$331$	8.99571	−	21.7176i	0.494449	−	1.19371i	0.952434	−	0.304746i	$-0.0985714\pi$
$332$	−2.48746	−	16.9907i	−0.136517	−	0.932487i
$333$	1.07630	+	0.445817i	0.0589808	+	0.0244306i
$334$	10.3563	−	2.85542i	0.566672	−	0.156242i
$335$	13.7017	−	0.0877192i	0.748603	−	0.00479261i
$336$	3.33888	−	2.71905i	0.182151	−	0.148336i
$337$	6.90744	−	6.90744i	0.376272	−	0.376272i	−0.493483	−	0.869755i	$-0.664277\pi$
$337$	6.90744	−	6.90744i	0.376272	−	0.376272i	0.869755	+	0.493483i	$0.164277\pi$
$338$	−5.54278	−	3.14688i	−0.301488	−	0.171168i
$339$	−10.4545	−	25.2393i	−0.567808	−	1.37081i
$340$	−27.3630	+	4.18509i	−1.48397	+	0.226968i
$341$	−7.74446	−	3.20786i	−0.419386	−	0.173715i
$342$	−0.161139	+	1.29638i	−0.00871342	+	0.0701002i
$343$	−10.8160			−0.584011
$344$	30.4722	+	11.8540i	1.64295	+	0.639123i
$345$	0.101914	+	15.9189i	0.00548687	+	0.857045i
$346$	−0.0656181	−	0.00815630i	−0.00352765	−	0.000438486i
$347$	−2.89398	−	6.98669i	−0.155357	−	0.375065i	0.826968	−	0.562249i	$-0.190064\pi$
$347$	−2.89398	−	6.98669i	−0.155357	−	0.375065i	−0.982325	+	0.187184i	$0.940064\pi$
$348$	−5.28055	−	8.84801i	−0.283067	−	0.474303i
$349$	−1.31230	−	3.16817i	−0.0702457	−	0.169588i	0.884857	−	0.465862i	$-0.154256\pi$
$349$	−1.31230	−	3.16817i	−0.0702457	−	0.169588i	−0.955103	+	0.296274i	$0.904256\pi$
$350$	2.76594	−	5.02045i	0.147846	−	0.268354i
$351$		−	23.5397i		−	1.25646i
$352$	4.26075	+	3.03103i	0.227099	+	0.161555i
$353$	7.05995	−	7.05995i	0.375763	−	0.375763i	−0.493808	−	0.869571i	$-0.664395\pi$
$353$	7.05995	−	7.05995i	0.375763	−	0.375763i	0.869571	+	0.493808i	$0.164395\pi$
$354$	−2.41524	+	4.25410i	−0.128369	+	0.226103i
$355$	−3.58323	−	1.45742i	−0.190178	−	0.0773517i
$356$	5.30220	−	20.9988i	0.281016	−	1.11293i
$357$	−6.15597	+	2.54989i	−0.325808	+	0.134954i
$358$	−17.1580	−	22.0290i	−0.906830	−	1.16427i
$359$	−6.96604	−	6.96604i	−0.367654	−	0.367654i	0.498967	−	0.866621i	$-0.333713\pi$
$359$	−6.96604	−	6.96604i	−0.367654	−	0.367654i	−0.866621	+	0.498967i	$0.833713\pi$
$360$	3.19445	+	7.13784i	0.168363	+	0.376197i
$361$	13.0404	−	13.0404i	0.686335	−	0.686335i
$362$	−33.6913	−	4.18782i	−1.77078	−	0.220107i
$363$	5.15596	+	12.4476i	0.270618	+	0.653329i
$364$	6.71194	−	0.982637i	0.351801	−	0.0515042i
$365$	−23.6086	+	9.95656i	−1.23573	+	0.521150i
$366$	−11.2886	+	3.11247i	−0.590065	+	0.162692i
$367$	−10.5140	−	10.5140i	−0.548826	−	0.548826i	0.377275	−	0.926101i	$-0.376861\pi$
$367$	−10.5140	−	10.5140i	−0.548826	−	0.548826i	−0.926101	+	0.377275i	$0.876861\pi$
$368$	10.1801	−	18.8734i	0.530677	−	0.983846i
$369$	−1.00053			−0.0520853
$370$	2.60036	+	1.45440i	0.135186	+	0.0756109i
$371$	−3.75084	+	1.55365i	−0.194734	+	0.0806615i
$372$	−3.48903	−	23.8320i	−0.180898	−	1.23563i
$373$	14.8828	−	6.16467i	0.770604	−	0.319195i	0.0374868	−	0.999297i	$-0.488065\pi$
$373$	14.8828	−	6.16467i	0.770604	−	0.319195i	0.733117	+	0.680103i	$0.238065\pi$
$374$	−4.97199	−	6.38347i	−0.257095	−	0.330081i
$375$	−10.6983	−	10.2951i	−0.552459	−	0.531635i
$376$	6.38784	−	0.138659i	0.329427	−	0.00715081i
$377$		−	16.2325i		−	0.836018i
$378$	3.96314	+	5.08822i	0.203842	+	0.261710i
$379$	4.07716	−	9.84314i	0.209430	−	0.505608i	−0.783904	−	0.620882i	$-0.786775\pi$
$379$	4.07716	−	9.84314i	0.209430	−	0.505608i	0.993334	+	0.115274i	$0.0367746\pi$
$380$	−0.797187	+	3.24454i	−0.0408948	+	0.166441i
$381$	−20.8537	+	8.63789i	−1.06837	+	0.442532i
$382$	4.03438	+	14.6322i	0.206417	+	0.748651i
$383$	−0.245014	−	0.245014i	−0.0125196	−	0.0125196i	0.700819	−	0.713339i	$-0.252818\pi$
$383$	−0.245014	−	0.245014i	−0.0125196	−	0.0125196i	−0.713339	+	0.700819i	$0.752818\pi$
$384$	−1.20454	+	14.9761i	−0.0614691	+	0.764243i
$385$	1.67543	−	0.0107263i	0.0853880	−	0.000546661i
$386$	13.2088	−	23.2654i	0.672309	−	1.18418i
$387$	−5.46988	+	13.2055i	−0.278050	+	0.671271i
$388$	−5.55410	−	1.40241i	−0.281967	−	0.0711967i
$389$	9.70866	+	4.02146i	0.492248	+	0.203896i	0.614978	−	0.788544i	$-0.289165\pi$
$389$	9.70866	+	4.02146i	0.492248	+	0.203896i	−0.122730	+	0.992440i	$0.539165\pi$
$390$	2.05572	−	17.4504i	0.104095	−	0.883635i
$391$	−23.4639	+	23.4639i	−1.18662	+	1.18662i
$392$	12.4075	−	12.9581i	0.626673	−	0.654483i
$393$			14.8769i			0.750442i
$394$	−8.55921	+	6.66664i	−0.431207	+	0.335860i
$395$	−35.1119	+	14.8079i	−1.76667	+	0.745066i
$396$	−1.36514	+	1.83341i	−0.0686009	+	0.0921324i
$397$	−5.50244	+	13.2841i	−0.276159	+	0.666708i	−0.999723	−	0.0235503i	$-0.992503\pi$
$397$	−5.50244	+	13.2841i	−0.276159	+	0.666708i	0.723563	+	0.690258i	$0.242503\pi$
$398$	26.5345	+	15.0648i	1.33005	+	0.755129i
$399$			0.804224i			0.0402616i
$400$	5.97803	+	19.0857i	0.298901	+	0.954284i
$401$			36.3553i			1.81550i	0.419515	+	0.907748i	$0.362200\pi$
$401$			36.3553i			1.81550i	−0.419515	+	0.907748i	$0.637800\pi$
$402$	−5.68182	+	10.0077i	−0.283384	+	0.499139i
$403$	14.5207	−	35.0561i	0.723328	−	1.74627i
$404$	−0.223463	−	1.52638i	−0.0111177	−	0.0759400i
$405$	7.75054	−	3.26867i	0.385128	−	0.162421i
$406$	2.73291	+	3.50874i	0.135632	+	0.174136i
$407$			0.870904i			0.0431691i
$408$	8.42885	−	21.6675i	0.417290	−	1.07270i
$409$	−1.73940	+	1.73940i	−0.0860076	+	0.0860076i	−0.748802	−	0.662794i	$-0.769370\pi$
$409$	−1.73940	+	1.73940i	−0.0860076	+	0.0860076i	0.662794	+	0.748802i	$0.269370\pi$
$410$	−2.54130	−	0.299374i	−0.125506	−	0.0147850i
$411$	2.09991	+	0.869813i	0.103581	+	0.0429047i
$412$	9.97471	+	16.7135i	0.491419	+	0.823415i
$413$	0.808032	−	1.95076i	0.0397606	−	0.0959907i
$414$	8.15209	+	4.62830i	0.400653	+	0.227469i
$415$	19.1983	−	0.122909i	0.942408	−	0.00603337i
$416$	−13.7203	+	19.2867i	−0.672692	+	0.945608i
$417$	−1.57346	−	1.57346i	−0.0770527	−	0.0770527i
$418$	−0.941466	+	0.259579i	−0.0460486	+	0.0126964i
$419$	30.4757	−	12.6234i	1.48883	−	0.616695i	0.517771	−	0.855519i	$-0.326762\pi$
$419$	30.4757	−	12.6234i	1.48883	−	0.616695i	0.971063	+	0.238824i	$0.0767620\pi$
$420$	2.49359	+	4.11809i	0.121675	+	0.200942i
$421$	−2.20626	+	5.32637i	−0.107526	+	0.259591i	−0.968480	−	0.249092i	$-0.919868\pi$
$421$	−2.20626	+	5.32637i	−0.107526	+	0.259591i	0.860953	+	0.508684i	$0.169868\pi$
$422$	15.0238	−	11.7018i	0.731347	−	0.569636i
$423$			2.79313i			0.135807i
$424$	5.13572	−	13.2020i	0.249412	−	0.641148i
$425$	−0.396254	−	30.9460i	−0.0192211	−	1.50110i
$426$	2.56318	−	1.99642i	0.124186	−	0.0967269i
$427$	4.66956	−	1.93420i	0.225976	−	0.0936023i
$428$	−8.47402	+	11.3808i	−0.409607	+	0.550111i
$429$	4.74511	−	1.96549i	0.229096	−	0.0948948i
$430$	−17.8446	+	31.9047i	−0.860542	+	1.53858i
$431$	11.5520			0.556441			0.278220	−	0.960517i	$-0.410255\pi$
$431$	11.5520			0.556441			0.278220	+	0.960517i	$0.410255\pi$
$432$	−22.3869	−	2.29056i	−1.07709	−	0.110204i
$433$	4.86860	+	4.86860i	0.233970	+	0.233970i	0.814348	−	0.580378i	$-0.197095\pi$
$433$	4.86860	+	4.86860i	0.233970	+	0.233970i	−0.580378	+	0.814348i	$0.697095\pi$
$434$	2.76332	+	10.0223i	0.132643	+	0.481083i
$435$	10.6148	−	4.47662i	0.508941	−	0.214638i
$436$	13.2052	−	17.7349i	0.632416	−	0.849348i
$437$	1.53268	+	3.70021i	0.0733179	+	0.177005i
$438$	2.65448	−	21.3555i	0.126836	−	1.02041i
$439$	−12.4739	+	12.4739i	−0.595347	+	0.595347i	−0.939071	−	0.343724i	$-0.888312\pi$
$439$	−12.4739	+	12.4739i	−0.595347	+	0.595347i	0.343724	+	0.939071i	$0.388312\pi$
$440$	−4.01599	+	4.24832i	−0.191455	+	0.202531i
$441$	5.54565	+	5.54565i	0.264079	+	0.264079i
$442$	28.8954	−	22.5062i	1.37441	−	1.07051i
$443$	−10.2113	+	4.22965i	−0.485152	+	0.200957i	−0.611833	−	0.790987i	$-0.709568\pi$
$443$	−10.2113	+	4.22965i	−0.485152	+	0.200957i	0.126681	+	0.991944i	$0.459568\pi$
$444$	−2.14883	+	1.28243i	−0.101979	+	0.0608616i
$445$	22.4299	+	9.12298i	1.06328	+	0.432471i
$446$	−32.5052	−	18.4546i	−1.53917	−	0.873853i
$447$	−17.4444	+	17.4444i	−0.825091	+	0.825091i
$448$	−0.281403	−	6.47886i	−0.0132950	−	0.306097i
$449$			23.5370i			1.11078i	0.831589	+	0.555391i	$0.187431\pi$
$449$			23.5370i			1.11078i	−0.831589	+	0.555391i	$0.812569\pi$
$450$	−8.39814	+	2.43164i	−0.395892	+	0.114629i
$451$	−0.286234	−	0.691030i	−0.0134782	−	0.0325393i
$452$	−39.8913	−	10.0726i	−1.87633	−	0.473773i
$453$	5.45862	+	13.1783i	0.256468	+	0.619169i
$454$	−4.06406	+	32.6957i	−0.190736	+	1.53448i
$455$	0.0485535	+	7.58402i	0.00227622	+	0.355544i
$456$	−2.02681	−	1.94069i	−0.0949141	−	0.0908811i
$457$	−9.83092			−0.459871			−0.229936	−	0.973206i	$-0.573852\pi$
$457$	−9.83092			−0.459871			−0.229936	+	0.973206i	$0.573852\pi$
$458$	15.0925	+	1.87599i	0.705226	+	0.0876593i
$459$	32.1723	+	13.3262i	1.50167	+	0.622013i
$460$	19.3211	+	14.1950i	0.900852	+	0.661843i
$461$	−8.56757	−	20.6839i	−0.399031	−	0.963347i	−0.987896	−	0.155116i	$-0.950425\pi$
$461$	−8.56757	−	20.6839i	−0.399031	−	0.963347i	0.588865	−	0.808231i	$-0.299575\pi$
$462$	−0.694770	+	1.22374i	−0.0323236	+	0.0569334i
$463$	10.2145	−	10.2145i	0.474707	−	0.474707i	−0.428727	−	0.903434i	$-0.641038\pi$
$463$	10.2145	−	10.2145i	0.474707	−	0.474707i	0.903434	+	0.428727i	$0.141038\pi$
$464$	−15.4376	−	1.57952i	−0.716673	−	0.0733276i
$465$	26.9285	−	0.172398i	1.24878	−	0.00799477i
$466$	−6.35769	−	23.0586i	−0.294514	−	1.06817i
$467$	1.32214	+	0.547649i	0.0611814	+	0.0253422i	0.413064	−	0.910702i	$-0.364458\pi$
$467$	1.32214	+	0.547649i	0.0611814	+	0.0253422i	−0.351883	+	0.936044i	$0.614458\pi$
$468$	−8.29912	−	6.17944i	−0.383627	−	0.285645i
$469$	1.90088	−	4.58914i	0.0877746	−	0.211907i
$470$	−0.835752	+	7.09444i	−0.0385503	+	0.327242i
$471$	13.8176	+	13.8176i	0.636679	+	0.636679i
$472$	2.96644	+	6.74383i	0.136542	+	0.310410i
$473$	−10.6854			−0.491316
$474$	3.94788	−	31.7610i	0.181332	−	1.45883i
$475$	−3.46908	−	1.38517i	−0.159172	−	0.0635560i
$476$	−2.45674	+	9.72965i	−0.112605	+	0.445958i
$477$	5.72126	+	2.36982i	0.261958	+	0.108507i
$478$	6.16211	+	22.3493i	0.281848	+	1.02223i
$479$	31.8238			1.45407			0.727033	−	0.686602i	$-0.240899\pi$
$479$	31.8238			1.45407			0.727033	+	0.686602i	$0.240899\pi$
$480$	−16.3958	−	3.65308i	−0.748361	−	0.166739i
$481$	−3.94223			−0.179750
$482$	−0.751971	−	2.72732i	−0.0342513	−	0.124226i
$483$	5.33176	+	2.20849i	0.242603	+	0.100490i
$484$	19.6737	+	4.96762i	0.894259	+	0.225801i
$485$	2.41299	−	5.93262i	0.109568	−	0.269386i
$486$	2.07278	−	16.6757i	0.0940234	−	0.756426i
$487$	9.67742			0.438526			0.219263	−	0.975666i	$-0.429635\pi$
$487$	9.67742			0.438526			0.219263	+	0.975666i	$0.429635\pi$
$488$	−6.39364	+	16.4357i	−0.289426	+	0.744009i
$489$	−4.86816	−	4.86816i	−0.220146	−	0.220146i
$490$	12.4264	+	15.7451i	0.561367	+	0.711291i
$491$	−9.42241	+	22.7477i	−0.425227	+	1.02659i	0.555554	+	0.831480i	$0.312506\pi$
$491$	−9.42241	+	22.7477i	−0.425227	+	1.02659i	−0.980781	+	0.195109i	$0.937494\pi$
$492$	1.28352	−	1.72380i	0.0578658	−	0.0777150i
$493$	22.1854	+	9.18949i	0.999180	+	0.413874i
$494$	−1.17501	−	4.26164i	−0.0528663	−	0.191740i
$495$	−1.81864	−	1.79550i	−0.0817417	−	0.0807017i
$496$	−31.9264	−	17.2208i	−1.43354	−	0.773235i
$497$	−0.991599	+	0.991599i	−0.0444793	+	0.0444793i
$498$	−7.96117	+	14.0225i	−0.356748	+	0.628361i
$499$	−7.85461	−	18.9627i	−0.351621	−	0.848887i	−0.996420	−	0.0845356i	$-0.973059\pi$
$499$	−7.85461	−	18.9627i	−0.351621	−	0.848887i	0.644800	−	0.764351i	$-0.276941\pi$
$500$	−22.0585	+	3.66341i	−0.986488	+	0.163833i
$501$	−9.31983	−	3.86040i	−0.416379	−	0.172470i
$502$	−3.26107	−	0.405349i	−0.145549	−	0.0180916i
$503$	−20.3583			−0.907731			−0.453865	−	0.891070i	$-0.649955\pi$
$503$	−20.3583			−0.907731			−0.453865	+	0.891070i	$0.649955\pi$
$504$	2.83427	−	0.0615228i	0.126248	−	0.00274044i
$505$	1.72470	−	0.0110416i	0.0767480	−	0.000491346i
$506$	−0.864436	+	6.95446i	−0.0384289	+	0.309163i
$507$	2.29042	+	5.52957i	0.101721	+	0.245577i
$508$	−8.32235	+	32.9598i	−0.369245	+	1.46235i
$509$	1.82470	+	4.40522i	0.0808785	+	0.195258i	0.959146	−	0.282912i	$-0.0913004\pi$
$509$	1.82470	+	4.40522i	0.0808785	+	0.195258i	−0.878267	+	0.478170i	$0.841300\pi$
$510$	22.6861	+	12.6885i	1.00456	+	0.561858i
$511$			9.28860i			0.410903i
$512$	17.0071	+	14.9251i	0.751616	+	0.659601i
$513$	2.97199	−	2.97199i	0.131217	−	0.131217i
$514$	−10.2583	−	5.82409i	−0.452474	−	0.256890i
$515$	−20.0509	+	8.45614i	−0.883548	+	0.372622i
$516$	−15.7346	−	26.3647i	−0.692677	−	1.16064i
$517$	−1.92912	+	0.799069i	−0.0848427	+	0.0351430i
$518$	0.852133	−	0.663714i	0.0374406	−	0.0291619i
$519$	0.0439052	+	0.0439052i	0.00192722	+	0.00192722i
$520$	−19.2305	−	18.1788i	−0.843311	−	0.797192i
$521$	7.13106	−	7.13106i	0.312417	−	0.312417i	−0.533428	−	0.845845i	$-0.679097\pi$
$521$	7.13106	−	7.13106i	0.312417	−	0.312417i	0.845845	+	0.533428i	$0.179097\pi$
$522$	0.836790	−	6.73205i	0.0366253	−	0.294654i
$523$	5.75338	+	13.8899i	0.251578	+	0.607363i	0.998332	−	0.0577377i	$-0.0183887\pi$
$523$	5.75338	+	13.8899i	0.251578	+	0.607363i	−0.746754	+	0.665100i	$0.768389\pi$
$524$	17.9708	+	13.3809i	0.785058	+	0.584546i
$525$	−4.94596	+	2.12328i	−0.215859	+	0.0926674i
$526$	2.34973	+	8.52222i	0.102453	+	0.371586i
$527$	39.6916	+	39.6916i	1.72899	+	1.72899i
$528$	−1.40751	−	4.70399i	−0.0612539	−	0.204715i
$529$	5.74014			0.249571
$530$	13.8227	+	7.73115i	0.600419	+	0.335820i
$531$	−2.97554	+	1.23251i	−0.129128	+	0.0534864i
$532$	0.971474	+	0.723349i	0.0421187	+	0.0313612i
$533$	3.12801	−	1.29567i	0.135489	−	0.0561215i
$534$	−16.0447	+	12.4970i	−0.694321	+	0.540797i
$535$	−11.2891	−	11.1455i	−0.488070	−	0.481860i
$536$	6.97852	+	15.8648i	0.301426	+	0.685253i
$537$			26.2201i			1.13148i
$538$	7.02443	−	5.47123i	0.302845	−	0.235881i
$539$	−2.24368	+	5.41672i	−0.0966420	+	0.233315i
$540$	6.00329	−	24.4333i	0.258340	−	1.05144i
$541$	16.0301	−	6.63988i	0.689187	−	0.285471i	−0.0104742	−	0.999945i	$-0.503334\pi$
$541$	16.0301	−	6.63988i	0.689187	−	0.285471i	0.699662	+	0.714474i	$0.253334\pi$
$542$	21.5964	−	5.95451i	0.927644	−	0.255768i
$543$	22.5429	+	22.5429i	0.967410	+	0.967410i
$544$	−18.5923	−	29.6703i	−0.797139	−	1.27210i
$545$	17.5920	+	17.3682i	0.753558	+	0.743971i
$546$	−5.53937	−	3.14494i	−0.237063	−	0.134591i
$547$	−7.54852	+	18.2237i	−0.322751	+	0.779191i	0.676341	+	0.736589i	$0.263565\pi$
$547$	−7.54852	+	18.2237i	−0.322751	+	0.779191i	−0.999092	+	0.0426017i	$0.986435\pi$
$548$	2.93945	−	1.75428i	0.125567	−	0.0749391i
$549$	−7.12260	−	2.95028i	−0.303985	−	0.125915i
$550$	−4.08202	−	5.10467i	−0.174058	−	0.217664i
$551$	2.04943	−	2.04943i	0.0873086	−	0.0873086i
$552$	−18.4320	+	8.10778i	−0.784518	+	0.345090i
$553$			13.8145i			0.587451i
$554$	−9.49416	−	12.1894i	−0.403368	−	0.517879i
$555$	−1.08719	−	2.57791i	−0.0461488	−	0.109426i
$556$	−3.31591	+	0.485454i	−0.140626	+	0.0205878i
$557$	9.98481	−	24.1055i	0.423070	−	1.02138i	−0.558367	−	0.829594i	$-0.688572\pi$
$557$	9.98481	−	24.1055i	0.423070	−	1.02138i	0.981437	−	0.191787i	$-0.0614282\pi$
$558$	7.82925	−	13.7901i	0.331439	−	0.583781i
$559$		−	48.3686i		−	2.04577i
$560$	7.21734	+	0.691795i	0.304988	+	0.0292337i
$561$			7.59795i			0.320786i
$562$	8.36550	+	4.74946i	0.352877	+	0.200344i
$563$	8.21473	−	19.8321i	0.346210	−	0.835824i	−0.650851	−	0.759206i	$-0.725588\pi$
$563$	8.21473	−	19.8321i	0.346210	−	0.835824i	0.997060	−	0.0766186i	$-0.0244124\pi$
$564$	−4.81227	−	3.58317i	−0.202633	−	0.150879i
$565$	17.3309	−	42.6099i	0.729114	−	1.79261i
$566$	29.3472	−	22.8581i	1.23356	−	0.960799i
$567$		−	3.04938i		−	0.128062i
$568$	−0.106187	−	4.89188i	−0.00445551	−	0.205259i
$569$	−14.8979	+	14.8979i	−0.624551	+	0.624551i	−0.946692	−	0.322141i	$-0.895597\pi$
$569$	−14.8979	+	14.8979i	−0.624551	+	0.624551i	0.322141	+	0.946692i	$0.395597\pi$
$570$	2.46273	−	1.94364i	0.103152	−	0.0814103i
$571$	6.23047	+	2.58075i	0.260737	+	0.108001i	0.509223	−	0.860635i	$-0.329933\pi$
$571$	6.23047	+	2.58075i	0.260737	+	0.108001i	−0.248486	+	0.968636i	$0.579933\pi$
$572$	1.89369	−	7.49976i	0.0791793	−	0.313581i
$573$	5.45429	−	13.1678i	0.227856	−	0.550094i
$574$	−0.457997	+	0.806697i	−0.0191164	+	0.0336709i
$575$	−18.7097	+	19.1951i	−0.780249	+	0.800489i
$576$	−6.68438	+	7.29140i	−0.278516	+	0.303808i
$577$	−18.1617	−	18.1617i	−0.756080	−	0.756080i	0.219526	−	0.975607i	$-0.429549\pi$
$577$	−18.1617	−	18.1617i	−0.756080	−	0.756080i	−0.975607	+	0.219526i	$0.929549\pi$
$578$	8.01135	+	29.0563i	0.333228	+	1.20858i
$579$	−23.2099	+	9.61386i	−0.964571	+	0.399538i
$580$	4.13975	−	16.8487i	0.171894	−	0.699606i
$581$	2.66345	−	6.43014i	0.110498	−	0.266767i
$582$	3.30540	+	4.24375i	0.137013	+	0.175909i
$583$			4.62945i			0.191732i
$584$	−23.4092	−	22.4145i	−0.968679	−	0.927519i
$585$	8.12751	−	8.23224i	0.336031	−	0.340361i
$586$	16.9831	+	21.8043i	0.701564	+	0.900728i
$587$	−22.7897	+	9.43980i	−0.940631	+	0.389622i	−0.799702	−	0.600398i	$-0.795009\pi$
$587$	−22.7897	+	9.43980i	−0.940631	+	0.389622i	−0.140929	+	0.990020i	$0.545009\pi$
$588$	−16.6688	+	2.44034i	−0.687411	+	0.100638i
$589$	6.25928	−	2.59268i	0.257909	−	0.106830i
$590$	−7.92655	+	2.24020i	−0.326331	+	0.0922274i
$591$	10.1876			0.419063
$592$	−0.383603	+	3.74917i	−0.0157660	+	0.154090i
$593$	−6.73738	−	6.73738i	−0.276671	−	0.276671i	0.555107	−	0.831779i	$-0.312677\pi$
$593$	−6.73738	−	6.73738i	−0.276671	−	0.276671i	−0.831779	+	0.555107i	$0.812677\pi$
$594$	7.08980	−	1.95479i	0.290898	−	0.0802059i
$595$	−10.3927	−	4.22707i	−0.426061	−	0.173293i
$596$	5.38205	+	36.7623i	0.220457	+	1.50584i
$597$	−10.9647	−	26.4712i	−0.448757	−	1.08339i
$598$	−31.4800	−	3.91295i	−1.28731	−	0.160013i
$599$	−17.9363	+	17.9363i	−0.732856	+	0.732856i	−0.971185	−	0.238328i	$-0.923401\pi$
$599$	−17.9363	+	17.9363i	−0.732856	+	0.732856i	0.238328	+	0.971185i	$0.423401\pi$
$600$	6.58410	−	17.5886i	0.268795	−	0.718050i
$601$	−29.0033	−	29.0033i	−1.18307	−	1.18307i	−0.978945	−	0.204126i	$-0.934565\pi$
$601$	−29.0033	−	29.0033i	−1.18307	−	1.18307i	−0.204126	−	0.978945i	$-0.565435\pi$
$602$	8.14333	+	10.4551i	0.331897	+	0.426119i
$603$	−6.99992	+	2.89946i	−0.285059	+	0.118075i
$604$	20.8286	+	5.25922i	0.847502	+	0.213995i
$605$	−8.54728	+	21.0145i	−0.347497	+	0.854361i
$606$	−0.715198	+	1.25972i	−0.0290529	+	0.0511726i
$607$	9.76508	−	9.76508i	0.396352	−	0.396352i	−0.480592	−	0.876944i	$-0.659578\pi$
$607$	9.76508	−	9.76508i	0.396352	−	0.396352i	0.876944	+	0.480592i	$0.159578\pi$
$608$	−4.16727	+	0.702786i	−0.169005	+	0.0285017i
$609$		−	4.17630i		−	0.169232i
$610$	−17.2083	−	9.62479i	−0.696746	−	0.389696i
$611$	−3.61706	−	8.73236i	−0.146331	−	0.353274i
$612$	13.1438	−	7.84433i	0.531309	−	0.317088i
$613$	−2.09885	−	5.06707i	−0.0847717	−	0.204657i	0.875809	−	0.482657i	$-0.160328\pi$
$613$	−2.09885	−	5.06707i	−0.0847717	−	0.204657i	−0.960581	+	0.278000i	$0.910328\pi$
$614$	−46.0457	−	5.72346i	−1.85825	−	0.230980i
$615$	1.70991	+	1.68816i	0.0689502	+	0.0680730i
$616$	0.853329	+	1.93993i	0.0343816	+	0.0781621i
$617$	−27.5407			−1.10875			−0.554374	−	0.832268i	$-0.687042\pi$
$617$	−27.5407			−1.10875			−0.554374	+	0.832268i	$0.687042\pi$
$618$	2.25446	−	18.1373i	0.0906878	−	0.729591i
$619$	−18.0221	−	7.46500i	−0.724370	−	0.300044i	−0.0101336	−	0.999949i	$-0.503226\pi$
$619$	−18.0221	−	7.46500i	−0.724370	−	0.300044i	−0.714236	+	0.699905i	$0.753226\pi$
$620$	24.0122	−	32.6837i	0.964354	−	1.31261i
$621$	−11.5420	−	27.8648i	−0.463163	−	1.11817i
$622$	16.9201	+	9.60627i	0.678433	+	0.385176i
$623$	6.20710	−	6.20710i	0.248682	−	0.248682i
$624$	21.2931	−	6.37122i	0.852405	−	0.255053i
$625$	−0.640129	−	24.9918i	−0.0256052	−	0.999672i
$626$	16.9636	−	4.67716i	0.678000	−	0.186937i
$627$	0.847243	+	0.350939i	0.0338356	+	0.0140152i
$628$	29.1191	−	4.26308i	1.16198	−	0.170115i
$629$	2.23176	−	5.38794i	0.0889861	−	0.214831i
$630$	−0.370821	+	3.14779i	−0.0147739	+	0.125411i
$631$	25.8413	+	25.8413i	1.02873	+	1.02873i	0.999575	+	0.0291526i	$0.00928088\pi$
$631$	25.8413	+	25.8413i	1.02873	+	1.02873i	0.0291526	+	0.999575i	$0.490719\pi$
$632$	−34.8153	−	33.3360i	−1.38488	−	1.32603i
$633$	−17.8822			−0.710752
$634$	−30.1064	−	3.74221i	−1.19568	−	0.148622i
$635$	−35.2060	−	14.3194i	−1.39711	−	0.568250i
$636$	−11.4225	+	6.81700i	−0.452931	+	0.270312i
$637$	−24.5193	−	10.1562i	−0.971490	−	0.402404i
$638$	4.88899	−	1.34798i	0.193557	−	0.0533672i
$639$	2.13901			0.0846180
$640$	−19.1598	+	16.5198i	−0.757356	+	0.653002i
$641$	10.5781			0.417809			0.208904	−	0.977936i	$-0.433010\pi$
$641$	10.5781			0.417809			0.208904	+	0.977936i	$0.433010\pi$
$642$	12.8447	−	3.54151i	0.506939	−	0.139772i
$643$	−37.7706	−	15.6451i	−1.48953	−	0.616982i	−0.518312	−	0.855192i	$-0.673439\pi$
$643$	−37.7706	−	15.6451i	−1.48953	−	0.616982i	−0.971214	+	0.238210i	$0.923439\pi$
$644$	7.46335	−	4.45417i	0.294097	−	0.175519i
$645$	31.6293	−	13.3391i	1.24540	−	0.525228i
$646$	6.48967	+	0.806663i	0.255333	+	0.0317377i
$647$	−2.74049			−0.107740			−0.0538699	−	0.998548i	$-0.517156\pi$
$647$	−2.74049			−0.107740			−0.0538699	+	0.998548i	$0.517156\pi$
$648$	7.68507	+	7.35852i	0.301898	+	0.289070i
$649$	−1.70251	−	1.70251i	−0.0668293	−	0.0668293i
$650$	23.1068	−	18.4777i	0.906322	−	0.724754i
$651$	3.73588	−	9.01921i	0.146421	−	0.353491i
$652$	−10.2592	+	1.50196i	−0.401780	+	0.0588212i
$653$	18.0867	+	7.49175i	0.707787	+	0.293175i	0.707388	−	0.706825i	$-0.249873\pi$
$653$	18.0867	+	7.49175i	0.707787	+	0.293175i	0.000398301		1.00000i	$0.499873\pi$
$654$	−20.0161	+	5.51881i	−0.782692	+	0.215802i
$655$	−17.5992	+	17.8260i	−0.687657	+	0.696518i
$656$	−0.927840	−	3.10090i	−0.0362261	−	0.121070i
$657$	10.0184	−	10.0184i	0.390854	−	0.390854i
$658$	2.25203	+	1.27857i	0.0877931	+	0.0498440i
$659$	−12.5791	−	30.3686i	−0.490012	−	1.18299i	−0.954714	−	0.297526i	$-0.903839\pi$
$659$	−12.5791	−	30.3686i	−0.490012	−	1.18299i	0.464702	−	0.885467i	$-0.346161\pi$
$660$	5.42650	−	0.829966i	0.211226	−	0.0323064i
$661$	23.3971	+	9.69138i	0.910041	+	0.376951i	0.788072	−	0.615583i	$-0.211079\pi$
$661$	23.3971	+	9.69138i	0.910041	+	0.376951i	0.121968	+	0.992534i	$0.461079\pi$
$662$	−4.10063	+	32.9899i	−0.159376	+	1.28219i
$663$	−34.3929			−1.33571
$664$	9.77805	+	22.2291i	0.379462	+	0.862657i
$665$	−0.951385	+	0.963645i	−0.0368931	+	0.0373686i
$666$	−1.63494	−	0.203223i	−0.0633528	−	0.00787472i
$667$	−7.95912	−	19.2150i	−0.308179	−	0.744009i
$668$	−13.0458	+	7.78583i	−0.504758	+	0.301243i
$669$	13.4320	+	32.4277i	0.519311	+	1.25373i
$670$	−18.6471	+	5.27003i	−0.720400	+	0.203599i
$671$		−	5.76337i		−	0.222492i
$672$	−3.52994	+	4.96207i	−0.136171	+	0.191416i
$673$	−20.6746	+	20.6746i	−0.796946	+	0.796946i	−0.982613	−	0.185667i	$-0.940555\pi$
$673$	−20.6746	+	20.6746i	−0.796946	+	0.796946i	0.185667	+	0.982613i	$0.440555\pi$
$674$	−6.82070	+	12.0137i	−0.262724	+	0.462750i
$675$	26.1242	+	10.4312i	1.00552	+	0.401495i
$676$	8.73961	+	2.20675i	0.336139	+	0.0848752i
$677$	34.6696	−	14.3606i	1.33246	−	0.551924i	0.401106	−	0.916032i	$-0.368626\pi$
$677$	34.6696	−	14.3606i	1.33246	−	0.551924i	0.931357	+	0.364107i	$0.118626\pi$
$678$	23.7404	+	30.4800i	0.911744	+	1.17058i
$679$	−1.64175	−	1.64175i	−0.0630047	−	0.0630047i
$680$	35.7320	−	15.9914i	1.37026	−	0.613243i
$681$	21.8767	−	21.8767i	0.838318	−	0.838318i
$682$	11.7642	+	1.46228i	0.450474	+	0.0559937i
$683$	7.42928	+	17.9359i	0.284274	+	0.686297i	0.999926	−	0.0121593i	$-0.00387051\pi$
$683$	7.42928	+	17.9359i	0.284274	+	0.686297i	−0.715652	+	0.698457i	$0.753871\pi$
$684$	−0.267619	−	1.82798i	−0.0102327	−	0.0698946i
$685$	1.48720	+	3.52640i	0.0568231	+	0.134737i
$686$	14.7459	−	4.06573i	0.563003	−	0.155230i
$687$	−10.0984	−	10.0984i	−0.385279	−	0.385279i
$688$	−45.9999	−	4.70655i	−1.75373	−	0.179436i
$689$	−20.9557			−0.798347
$690$	−6.12283	−	21.6646i	−0.233092	−	0.824757i
$691$	−10.7885	+	4.46873i	−0.410413	+	0.169999i	−0.578331	−	0.815802i	$-0.696296\pi$
$691$	−10.7885	+	4.46873i	−0.410413	+	0.169999i	0.167918	+	0.985801i	$0.446296\pi$
$692$	0.0925259	−	0.0135459i	0.00351731	−	0.000514938i
$693$	−0.855947	+	0.354545i	−0.0325147	+	0.0134680i
$694$	6.57177	+	8.43740i	0.249461	+	0.320279i
$695$	−0.0239870	−	3.74675i	−0.000909877	−	0.142122i
$696$	10.5251	+	10.0779i	0.398954	+	0.382002i
$697$			5.00863i			0.189715i
$698$	2.98002	+	3.82601i	0.112795	+	0.144816i
$699$	−8.59530	+	20.7509i	−0.325104	+	0.784871i
$700$	−1.88374	+	7.88430i	−0.0711987	+	0.297998i
$701$	−47.2867	+	19.5868i	−1.78599	+	0.739782i	−0.794879	+	0.606769i	$0.792465\pi$
$701$	−47.2867	+	19.5868i	−1.78599	+	0.739782i	−0.991114	+	0.133014i	$0.957535\pi$
$702$	8.84853	+	32.0927i	0.333966	+	1.21126i
$703$	−0.497724	−	0.497724i	−0.0187720	−	0.0187720i
$704$	−6.94822	−	2.53073i	−0.261871	−	0.0953803i
$705$	4.71276	−	4.77349i	0.177493	−	0.179780i
$706$	−6.97130	+	12.2790i	−0.262369	+	0.462124i
$707$	0.239273	−	0.577657i	0.00899879	−	0.0217250i
$708$	1.69369	−	6.70768i	0.0636528	−	0.252090i
$709$	−0.906566	−	0.375512i	−0.0340468	−	0.0141027i	0.365595	−	0.930774i	$-0.380866\pi$
$709$	−0.906566	−	0.375512i	−0.0340468	−	0.0141027i	−0.399642	+	0.916671i	$0.630866\pi$
$710$	5.43301	+	0.640029i	0.203897	+	0.0240198i
$711$	14.8998	−	14.8998i	0.558788	−	0.558788i
$712$	0.664697	+	30.6216i	0.0249106	+	1.14759i
$713$		−	48.6169i		−	1.82072i
$714$	7.43419	−	5.79038i	0.278218	−	0.216700i
$715$	8.01088	+	3.25829i	0.299590	+	0.121853i
$716$	31.6729	+	23.5833i	1.18367	+	0.881350i
$717$	8.33090	−	20.1126i	0.311123	−	0.751117i
$718$	12.1156	+	6.87857i	0.452151	+	0.256706i
$719$			42.1446i			1.57173i	0.618399	+	0.785864i	$0.287782\pi$
$719$			42.1446i			1.57173i	−0.618399	+	0.785864i	$0.712218\pi$
$720$	−7.03824	−	8.53053i	−0.262300	−	0.317914i
$721$			7.88884i			0.293796i
$722$	−12.8766	+	22.6803i	−0.479219	+	0.844075i
$723$	−1.01663	+	2.45436i	−0.0378089	+	0.0912787i
$724$	47.5070	−	6.95509i	1.76558	−	0.258484i
$725$	18.0148	+	7.19313i	0.669051	+	0.267146i
$726$	−11.7084	−	15.0322i	−0.434538	−	0.557897i
$727$			17.3527i			0.643576i	0.946812	+	0.321788i	$0.104284\pi$
$727$			17.3527i			0.643576i	−0.946812	+	0.321788i	$0.895716\pi$
$728$	−8.78130	+	3.86268i	−0.325457	+	0.143160i
$729$	−19.1377	+	19.1377i	−0.708804	+	0.708804i
$730$	28.4440	−	22.4486i	1.05276	−	0.830861i
$731$	66.1065	+	27.3822i	2.44504	+	1.01277i
$732$	14.2202	−	8.48673i	0.525596	−	0.313679i
$733$	−1.67662	+	4.04772i	−0.0619273	+	0.149506i	−0.951814	−	0.306676i	$-0.900783\pi$
$733$	−1.67662	+	4.04772i	−0.0619273	+	0.149506i	0.889887	+	0.456182i	$0.150783\pi$
$734$	18.2864	+	10.3820i	0.674962	+	0.383206i
$735$	−0.120580	−	18.8346i	−0.00444768	−	0.694724i
$736$	−6.78453	+	29.5576i	−0.250081	+	1.08951i
$737$	−4.00513	−	4.00513i	−0.147531	−	0.147531i
$738$	1.36406	−	0.376096i	0.0502117	−	0.0138443i
$739$	27.4135	−	11.3551i	1.00842	−	0.417703i	0.183544	−	0.983011i	$-0.441243\pi$
$739$	27.4135	−	11.3551i	1.00842	−	0.417703i	0.824879	+	0.565309i	$0.191243\pi$
$740$	−4.09189	−	1.00538i	−0.150421	−	0.0369585i
$741$	−1.58856	+	3.83513i	−0.0583573	+	0.140887i
$742$	4.52967	−	3.52809i	0.166289	−	0.129520i
$743$		−	23.9173i		−	0.877440i	−0.898624	−	0.438720i	$-0.855432\pi$
$743$		−	23.9173i		−	0.877440i	0.898624	−	0.438720i	$-0.144568\pi$
$744$	13.7151	+	31.1796i	0.502822	+	1.14310i
$745$	−41.5388	+	0.265935i	−1.52186	+	0.00974309i
$746$	−17.9731	+	13.9990i	−0.658042	+	0.512539i
$747$	−9.80804	+	4.06262i	−0.358858	+	0.148644i
$748$	9.17805	+	6.83389i	0.335583	+	0.249872i
$749$	−5.31324	+	2.20081i	−0.194141	+	0.0804160i
$750$	18.4554	+	10.0142i	0.673894	+	0.365668i
$751$	−22.5603			−0.823236			−0.411618	−	0.911357i	$-0.635036\pi$
$751$	−22.5603			−0.823236			−0.411618	+	0.911357i	$0.635036\pi$
$752$	−8.65668	+	2.59022i	−0.315677	+	0.0944555i
$753$	2.18198	+	2.18198i	0.0795159	+	0.0795159i
$754$	6.10178	+	22.1305i	0.222214	+	0.805945i
$755$	−9.04902	+	22.2481i	−0.329327	+	0.809690i
$756$	−7.31577	−	5.44725i	−0.266072	−	0.198115i
$757$	−9.21573	−	22.2487i	−0.334951	−	0.808644i	−0.998184	−	0.0602313i	$-0.980816\pi$
$757$	−9.21573	−	22.2487i	−0.334951	−	0.808644i	0.663233	−	0.748413i	$-0.269184\pi$
$758$	−1.85855	+	14.9522i	−0.0675054	+	0.543087i
$759$	4.65324	−	4.65324i	0.168902	−	0.168902i
$760$	−0.132779	−	4.72308i	−0.00481639	−	0.171324i
$761$	−8.29763	−	8.29763i	−0.300789	−	0.300789i	0.540534	−	0.841322i	$-0.318222\pi$
$761$	−8.29763	−	8.29763i	−0.300789	−	0.300789i	−0.841322	+	0.540534i	$0.818222\pi$
$762$	25.1838	−	19.6153i	0.912311	−	0.710586i
$763$	8.27972	−	3.42957i	0.299746	−	0.124159i
$764$	−11.0005	−	18.4322i	−0.397983	−	0.666855i
$765$	6.65009	+	15.7685i	0.240435	+	0.570110i
$766$	0.426137	+	0.241937i	0.0153970	+	0.00874154i
$767$	7.70657	−	7.70657i	0.278268	−	0.278268i
$768$	−3.98727	−	20.8703i	−0.143878	−	0.753091i
$769$			22.7180i			0.819233i	0.912258	+	0.409616i	$0.134337\pi$
$769$			22.7180i			0.819233i	−0.912258	+	0.409616i	$0.865663\pi$
$770$	−2.28016	+	0.644416i	−0.0821712	+	0.0232231i
$771$	4.23900	+	10.2338i	0.152664	+	0.368563i
$772$	−9.26267	+	36.6838i	−0.333371	+	1.32028i
$773$	−1.94650	−	4.69925i	−0.0700106	−	0.169020i	0.885001	−	0.465589i	$-0.154158\pi$
$773$	−1.94650	−	4.69925i	−0.0700106	−	0.169020i	−0.955011	+	0.296569i	$0.904158\pi$
$774$	2.49341	−	20.0597i	0.0896237	−	0.721030i
$775$	32.4704	+	31.6494i	1.16637	+	1.13688i
$776$	8.09930	−	0.175810i	0.290748	−	0.00631120i
$777$	−1.01426			−0.0363862
$778$	−14.7479	−	1.83315i	−0.528737	−	0.0657217i
$779$	0.558509	+	0.231342i	0.0200106	+	0.00828868i
$780$	3.75692	+	24.5636i	0.134519	+	0.879517i
$781$	0.611936	+	1.47735i	0.0218968	+	0.0528636i
$782$	23.1693	−	40.8093i	0.828531	−	1.45934i
$783$	−15.4334	+	15.4334i	−0.551545	+	0.551545i
$784$	−12.0447	+	22.3303i	−0.430169	+	0.797510i
$785$	0.210645	+	32.9025i	0.00751823	+	1.17434i
$786$	−5.59221	−	20.2823i	−0.199468	−	0.723447i
$787$	−29.8282	−	12.3552i	−1.06326	−	0.440417i	−0.218653	−	0.975803i	$-0.570166\pi$
$787$	−29.8282	−	12.3552i	−1.06326	−	0.440417i	−0.844608	+	0.535386i	$0.820166\pi$
$788$	9.16314	−	12.3063i	0.326423	−	0.438394i
$789$	3.17673	−	7.66930i	0.113095	−	0.273034i
$790$	42.3033	−	33.3867i	1.50508	−	1.18785i
$791$	−11.7916	−	11.7916i	−0.419260	−	0.419260i
$792$	1.17198	−	3.01272i	0.0416444	−	0.107052i
$793$	26.0884			0.926428
$794$	2.50825	−	20.1791i	0.0890144	−	0.716128i
$795$	−5.77917	−	13.7033i	−0.204966	−	0.486008i
$796$	−41.8384	−	10.5642i	−1.48292	−	0.374438i
$797$	−14.4591	−	5.98915i	−0.512167	−	0.212147i	0.111605	−	0.993753i	$-0.464401\pi$
$797$	−14.4591	−	5.98915i	−0.512167	−	0.212147i	−0.623772	+	0.781606i	$0.714401\pi$
$798$	−0.302306	−	1.09643i	−0.0107015	−	0.0388133i
$799$	13.9824			0.494662
$800$	−15.3244	−	23.7732i	−0.541798	−	0.840509i
$801$	−13.3895			−0.473096
$802$	−13.6659	−	49.5647i	−0.482559	−	1.75019i
$803$	9.78546	+	4.05327i	0.345321	+	0.143037i
$804$	3.98438	−	15.7797i	0.140518	−	0.556508i
$805$	3.77606	+	8.95366i	0.133089	+	0.315575i
$806$	−6.61916	+	53.2517i	−0.233150	+	1.87571i
$807$	−8.36087			−0.294316
$808$	0.878419	+	1.99697i	0.0309027	+	0.0702532i
$809$	36.9823	+	36.9823i	1.30023	+	1.30023i	0.928236	+	0.371991i	$0.121325\pi$
$809$	36.9823	+	36.9823i	1.30023	+	1.30023i	0.371991	+	0.928236i	$0.378675\pi$
$810$	−9.33795	+	7.36973i	−0.328102	+	0.258946i
$811$	16.7840	−	40.5201i	0.589365	−	1.42285i	−0.294745	−	0.955576i	$-0.595235\pi$
$811$	16.7840	−	40.5201i	0.589365	−	1.42285i	0.884111	−	0.467278i	$-0.154765\pi$
$812$	−5.04482	−	3.75632i	−0.177038	−	0.131821i
$813$	−19.4350	−	8.05023i	−0.681614	−	0.282334i
$814$	−0.327371	−	1.18734i	−0.0114744	−	0.0416162i
$815$	−0.0742138	−	11.5921i	−0.00259960	−	0.406055i
$816$	−3.34663	+	32.7086i	−0.117156	+	1.14503i
$817$	6.10674	−	6.10674i	0.213648	−	0.213648i
$818$	1.71756	−	3.02523i	0.0600529	−	0.105775i
$819$	−1.60488	−	3.87453i	−0.0560791	−	0.135387i
$820$	3.57719	−	0.547119i	0.124921	−	0.0191062i
$821$	41.4829	+	17.1828i	1.44776	+	0.599682i	0.961666	−	0.274223i	$-0.0884207\pi$
$821$	41.4829	+	17.1828i	1.44776	+	0.599682i	0.486095	+	0.873906i	$0.338421\pi$
$822$	−3.18986	−	0.396498i	−0.111259	−	0.0138295i
$823$	5.15995			0.179865			0.0899323	−	0.995948i	$-0.471335\pi$
$823$	5.15995			0.179865			0.0899323	+	0.995948i	$0.471335\pi$
$824$	−19.8815	−	19.0367i	−0.692605	−	0.663176i
$825$	0.0785831	+	6.13706i	0.00273591	+	0.213665i
$826$	−0.368336	+	2.96329i	−0.0128160	+	0.103106i
$827$	−1.85424	−	4.47653i	−0.0644782	−	0.155664i	0.888356	−	0.459155i	$-0.151848\pi$
$827$	−1.85424	−	4.47653i	−0.0644782	−	0.155664i	−0.952834	+	0.303491i	$0.901848\pi$
$828$	−12.8539	−	3.24560i	−0.446702	−	0.112792i
$829$	7.40324	+	17.8730i	0.257125	+	0.620755i	0.998746	−	0.0500640i	$-0.0159425\pi$
$829$	7.40324	+	17.8730i	0.257125	+	0.620755i	−0.741621	+	0.670819i	$0.765943\pi$
$830$	−26.1277	+	7.38418i	−0.906904	+	0.256309i
$831$			14.5085i			0.503295i
$832$	11.4556	−	31.4518i	0.397151	−	1.09039i
$833$	27.7615	−	27.7615i	0.961879	−	0.961879i
$834$	2.73662	+	1.55370i	0.0947616	+	0.0538003i
$835$	−6.60050	−	15.6509i	−0.228420	−	0.541621i
$836$	1.18596	−	0.707791i	0.0410174	−	0.0244795i
$837$	−47.1361	+	19.5244i	−1.62926	+	0.674863i
$838$	−36.8036	+	28.6658i	−1.27136	+	0.990244i
$839$	11.2001	+	11.2001i	0.386669	+	0.386669i	0.873498	−	0.486828i	$-0.161846\pi$
$839$	11.2001	+	11.2001i	0.386669	+	0.386669i	−0.486828	+	0.873498i	$0.661846\pi$
$840$	−4.94760	−	4.67703i	−0.170708	−	0.161373i
$841$	9.86351	−	9.86351i	0.340121	−	0.340121i
$842$	1.00571	−	8.09099i	0.0346589	−	0.278834i
$843$	−3.45684	−	8.34556i	−0.119060	−	0.287436i
$844$	−16.0839	+	21.6010i	−0.553630	+	0.743537i
$845$	−3.79694	+	9.33523i	−0.130619	+	0.321142i
$846$	−1.04993	−	3.80799i	−0.0360974	−	0.130921i
$847$	5.81541	+	5.81541i	0.199820	+	0.199820i
$848$	−2.03911	+	19.9294i	−0.0700234	+	0.684379i
$849$	−34.9307			−1.19882
$850$	12.1728	+	42.0411i	0.417523	+	1.44200i
$851$	−4.66656	+	1.93295i	−0.159968	+	0.0662607i
$852$	−2.74403	+	3.68530i	−0.0940091	+	0.126256i
$853$	−1.97932	+	0.819862i	−0.0677707	+	0.0280715i	−0.416311	−	0.909222i	$-0.636677\pi$
$853$	−1.97932	+	0.819862i	−0.0677707	+	0.0280715i	0.348541	+	0.937294i	$0.386677\pi$
$854$	−5.63915	+	4.39225i	−0.192968	+	0.150300i
$855$	2.06549	−	0.0132234i	0.0706382	−	0.000452231i
$856$	7.27497	−	18.7013i	0.248653	−	0.639197i
$857$		−	15.5286i		−	0.530448i	−0.964187	−	0.265224i	$-0.914554\pi$
$857$		−	15.5286i		−	0.530448i	0.964187	−	0.265224i	$-0.0854460\pi$
$858$	−5.73039	+	4.46331i	−0.195632	+	0.152375i
$859$	14.0088	−	33.8203i	0.477974	−	1.15393i	−0.482583	−	0.875850i	$-0.660301\pi$
$859$	14.0088	−	33.8203i	0.477974	−	1.15393i	0.960557	−	0.278082i	$-0.0896987\pi$
$860$	12.3354	−	50.2047i	0.420632	−	1.71197i
$861$	0.804774	−	0.333348i	0.0274266	−	0.0113605i
$862$	−15.7493	+	4.34238i	−0.536425	+	0.147902i
$863$	13.2837	+	13.2837i	0.452182	+	0.452182i	0.896078	−	0.443896i	$-0.146404\pi$
$863$	13.2837	+	13.2837i	0.452182	+	0.452182i	−0.443896	+	0.896078i	$0.646404\pi$
$864$	31.3820	−	5.29239i	1.06764	−	0.180051i
$865$	0.000669322		0.104548i	2.27576e−5		0.00355473i
$866$	−8.46766	−	4.80747i	−0.287743	−	0.163364i
$867$	10.8310	−	26.1483i	0.367840	−	0.888043i
$868$	−7.53469	−	12.6250i	−0.255744	−	0.428521i
$869$	14.5534	+	6.02822i	0.493691	+	0.204494i
$870$	−12.7889	+	10.0933i	−0.433583	+	0.342193i
$871$	18.1296	−	18.1296i	0.614298	−	0.614298i
$872$	−11.3367	+	29.1426i	−0.383910	+	0.986892i
$873$			3.54148i			0.119861i
$874$	−3.48046	−	4.46852i	−0.117728	−	0.151150i
$875$	−8.43820	−	3.30682i	−0.285263	−	0.111791i
$876$	4.40854	+	30.1127i	0.148951	+	1.01741i
$877$	−1.17244	+	2.83052i	−0.0395905	+	0.0955799i	−0.942438	−	0.334381i	$-0.891473\pi$
$877$	−1.17244	+	2.83052i	−0.0395905	+	0.0955799i	0.902847	+	0.429961i	$0.141473\pi$
$878$	12.3173	−	21.6951i	0.415688	−	0.732175i
$879$		−	25.9527i		−	0.875362i
$880$	3.87823	−	7.30152i	0.130735	−	0.246134i
$881$			32.6206i			1.09902i	0.835488	+	0.549508i	$0.185185\pi$
$881$			32.6206i			1.09902i	−0.835488	+	0.549508i	$0.814815\pi$
$882$	−9.64522	−	5.47602i	−0.324771	−	0.184387i
$883$	5.81184	−	14.0310i	0.195584	−	0.472181i	−0.795413	−	0.606068i	$-0.792746\pi$
$883$	5.81184	−	14.0310i	0.195584	−	0.472181i	0.990997	+	0.133887i	$0.0427459\pi$
$884$	−30.9343	+	41.5454i	−1.04043	+	1.39732i
$885$	7.16482	+	2.91417i	0.240843	+	0.0979586i
$886$	12.3315	−	9.60485i	0.414286	−	0.322681i
$887$		−	26.0808i		−	0.875708i	−0.899046	−	0.437854i	$-0.855739\pi$
$887$		−	26.0808i		−	0.875708i	0.899046	−	0.437854i	$-0.144261\pi$
$888$	2.44752	−	2.55613i	0.0821334	−	0.0857782i
$889$	−9.74267	+	9.74267i	−0.326759	+	0.326759i
$890$	−34.0089	−	4.00638i	−1.13998	−	0.134294i
$891$	−3.21250	−	1.33066i	−0.107623	−	0.0445788i
$892$	51.2528	+	12.9413i	1.71607	+	0.433308i
$893$	0.645829	−	1.55917i	0.0216118	−	0.0521756i
$894$	17.2253	−	30.3400i	0.576101	−	1.01472i
$895$	−31.0180	+	31.4177i	−1.03682	+	1.05018i
$896$	2.81904	+	8.72712i	0.0941775	+	0.291553i
$897$	21.0633	+	21.0633i	0.703285	+	0.703285i
$898$	−8.84753	−	32.0890i	−0.295246	−	1.07082i
$899$	−32.5042	+	13.4637i	−1.08408	+	0.449039i
$900$	10.5355	−	6.47201i	0.351183	−	0.215734i
$901$	11.8633	−	28.6406i	0.395224	−	0.954156i
$902$	0.649991	+	0.834515i	0.0216423	+	0.0277863i
$903$		−	12.4442i		−	0.414119i
$904$	58.1717	−	1.26272i	1.93476	−	0.0419974i
$905$	0.343661	+	53.6795i	0.0114237	+	1.78437i
$906$	−12.3957	−	15.9146i	−0.411818	−	0.528727i
$907$	22.6408	−	9.37811i	0.751774	−	0.311395i	0.0263091	−	0.999654i	$-0.491625\pi$
$907$	22.6408	−	9.37811i	0.751774	−	0.311395i	0.725465	+	0.688259i	$0.241625\pi$
$908$	−6.74955	−	46.1031i	−0.223992	−	1.52998i
$909$	−0.881114	+	0.364969i	−0.0292247	+	0.0121053i
$910$	−2.91701	−	10.3214i	−0.0966980	−	0.342150i
$911$	19.6911			0.652395			0.326198	−	0.945302i	$-0.394233\pi$
$911$	19.6911			0.652395			0.326198	+	0.945302i	$0.394233\pi$
$912$	3.49274	+	1.88395i	0.115656	+	0.0623837i
$913$	−5.61184	−	5.61184i	−0.185725	−	0.185725i
$914$	13.4029	−	3.69542i	0.443329	−	0.122234i
$915$	7.19469	+	17.0598i	0.237849	+	0.563979i
$916$	−21.2814	+	3.11563i	−0.703158	+	0.102943i
$917$	3.47519	+	8.38984i	0.114761	+	0.277057i
$918$	−48.8711	−	6.07465i	−1.61299	−	0.200493i
$919$	14.8097	−	14.8097i	0.488526	−	0.488526i	−0.419315	−	0.907841i	$-0.637730\pi$
$919$	14.8097	−	14.8097i	0.488526	−	0.488526i	0.907841	+	0.419315i	$0.137730\pi$
$920$	−31.6772	−	12.0898i	−1.04436	−	0.398589i
$921$	30.8092	+	30.8092i	1.01520	+	1.01520i
$922$	19.4556	+	24.9787i	0.640735	+	0.822631i
$923$	−6.68735	+	2.76999i	−0.220117	+	0.0911753i
$924$	0.487208	−	1.92954i	0.0160280	−	0.0634771i
$925$	1.74692	−	4.37506i	0.0574385	−	0.143851i
$926$	−10.0862	+	17.7654i	−0.331454	+	0.583808i
$927$	8.50865	−	8.50865i	0.279461	−	0.279461i
$928$	21.6405	−	3.64953i	0.710383	−	0.119802i
$929$			2.48749i			0.0816119i	0.999167	+	0.0408059i	$0.0129925\pi$
$929$			2.48749i			0.0816119i	−0.999167	+	0.0408059i	$0.987007\pi$
$930$	−36.6479	+	10.3574i	−1.20173	+	0.339632i
$931$	−1.81340	−	4.37794i	−0.0594318	−	0.143481i
$932$	17.3354	+	29.0469i	0.567840	+	0.951464i
$933$	−6.99181	−	16.8797i	−0.228902	−	0.552618i
$934$	−2.00839	−	0.249642i	−0.0657166	−	0.00816854i
$935$	−8.98826	+	9.10409i	−0.293948	+	0.297736i
$936$	13.6374	+	5.30506i	0.445752	+	0.173401i
$937$	−29.6925			−0.970013			−0.485006	−	0.874511i	$-0.661183\pi$
$937$	−29.6925			−0.970013			−0.485006	+	0.874511i	$0.661183\pi$
$938$	−0.866504	+	6.97110i	−0.0282924	+	0.227614i
$939$	−15.2658	−	6.32331i	−0.498181	−	0.206353i
$940$	−1.52737	−	9.98631i	−0.0498174	−	0.325717i
$941$	15.1479	+	36.5702i	0.493807	+	1.19215i	0.952768	+	0.303698i	$0.0982215\pi$
$941$	15.1479	+	36.5702i	0.493807	+	1.19215i	−0.458962	+	0.888456i	$0.651778\pi$
$942$	−24.0320	−	13.6440i	−0.783006	−	0.444547i
$943$	3.06745	−	3.06745i	0.0998899	−	0.0998899i
$944$	−6.57927	−	8.07906i	−0.214137	−	0.262951i
$945$	7.16449	−	7.25682i	0.233061	−	0.236064i
$946$	14.5679	−	4.01663i	0.473642	−	0.130592i
$947$	35.1138	+	14.5446i	1.14104	+	0.472636i	0.871521	−	0.490358i	$-0.163134\pi$
$947$	35.1138	+	14.5446i	1.14104	+	0.472636i	0.269523	+	0.962994i	$0.413134\pi$
$948$	6.55660	+	44.7851i	0.212949	+	1.45455i
$949$	−18.3475	+	44.2948i	−0.595586	+	1.43787i
$950$	5.25022	+	0.584442i	0.170340	+	0.0189618i
$951$	20.1442	+	20.1442i	0.653222	+	0.653222i
$952$	−0.307983	−	14.1883i	−0.00998178	−	0.459846i
$953$	34.9734			1.13290			0.566450	−	0.824096i	$-0.308316\pi$
$953$	34.9734			1.13290			0.566450	+	0.824096i	$0.308316\pi$
$954$	−8.69084	−	1.08027i	−0.281376	−	0.0349749i
$955$	22.1128	−	9.32573i	0.715554	−	0.301774i
$956$	−16.8021	−	28.1534i	−0.543420	−	0.910547i
$957$	−4.39969	−	1.82241i	−0.142222	−	0.0589102i
$958$	−43.3867	+	11.9625i	−1.40176	+	0.386491i
$959$	1.38743			0.0448025
$960$	23.7262	−	1.18275i	0.765761	−	0.0381731i
$961$	−51.2404			−1.65292
$962$	5.37461	−	1.48188i	0.173284	−	0.0477777i
$963$	8.10441	+	3.35696i	0.261161	+	0.108176i
$964$	2.05039	+	3.43560i	0.0660385	+	0.110653i
$965$	−39.1839	−	15.9374i	−1.26137	−	0.513042i
$966$	−8.09917	−	1.00672i	−0.260587	−	0.0323908i
$967$	−11.5019			−0.369876			−0.184938	−	0.982750i	$-0.559208\pi$
$967$	−11.5019			−0.369876			−0.184938	+	0.982750i	$0.559208\pi$
$968$	−28.6893	+	0.622752i	−0.922109	+	0.0200160i
$969$	−4.34225	−	4.34225i	−0.139493	−	0.139493i
$970$	−1.05967	+	8.99523i	−0.0340240	+	0.288819i
$971$	−12.3780	+	29.8832i	−0.397230	+	0.958998i	0.591090	+	0.806606i	$0.298698\pi$
$971$	−12.3780	+	29.8832i	−0.397230	+	0.958998i	−0.988320	+	0.152393i	$0.951302\pi$
$972$	3.44246	+	23.5139i	0.110417	+	0.754207i
$973$	−1.25491	−	0.519799i	−0.0402305	−	0.0166640i
$974$	−13.1936	+	3.63772i	−0.422751	+	0.116560i
$975$	−27.7800	+	0.355714i	−0.889672	+	0.0113920i
$976$	2.53856	−	24.8108i	0.0812574	−	0.794176i
$977$	13.9126	−	13.9126i	0.445104	−	0.445104i	−0.448619	−	0.893723i	$-0.648084\pi$
$977$	13.9126	−	13.9126i	0.445104	−	0.445104i	0.893723	+	0.448619i	$0.148084\pi$
$978$	8.46690	+	4.80704i	0.270742	+	0.153712i
$979$	−3.83053	−	9.24771i	−0.122424	−	0.295558i
$980$	−22.8600	−	16.7949i	−0.730235	−	0.536493i
$981$	−12.6293	−	5.23121i	−0.403221	−	0.167020i
$982$	4.29514	−	34.5548i	0.137063	−	1.10269i
$983$	−29.1931			−0.931115			−0.465557	−	0.885018i	$-0.654146\pi$
$983$	−29.1931			−0.931115			−0.465557	+	0.885018i	$0.654146\pi$
$984$	−1.10191	+	2.83261i	−0.0351276	+	0.0903002i
$985$	12.2071	+	12.0518i	0.388951	+	0.384003i
$986$	−33.7006	−	4.18897i	−1.07325	−	0.133404i
$987$	−0.930596	−	2.24666i	−0.0296212	−	0.0715119i
$988$	3.20388	+	5.36838i	0.101929	+	0.170791i
$989$	−23.7160	−	57.2556i	−0.754126	−	1.82062i
$990$	3.15435	+	1.76426i	0.100252	+	0.0560718i
$991$		−	16.1180i		−	0.512006i	−0.966676	−	0.256003i	$-0.917594\pi$
$991$		−	16.1180i		−	0.512006i	0.966676	−	0.256003i	$-0.0824057\pi$
$992$	49.9998	+	11.4767i	1.58749	+	0.364386i
$993$	22.0736	−	22.0736i	0.700485	−	0.700485i
$994$	0.979148	−	1.72463i	0.0310567	−	0.0547019i
$995$	18.1768	−	44.6897i	0.576242	−	1.41676i
$996$	5.58278	−	22.1100i	0.176897	−	0.700582i
$997$	−4.69692	+	1.94553i	−0.148753	+	0.0616154i	−0.455818	−	0.890073i	$-0.650653\pi$
$997$	−4.69692	+	1.94553i	−0.148753	+	0.0616154i	0.307065	+	0.951689i	$0.400653\pi$
$998$	17.8366	+	22.9001i	0.564606	+	0.724890i
$999$	3.74816	+	3.74816i	0.118586	+	0.118586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.ba.a.107.1	yes	88
4.3	odd	2		640.2.ba.a.207.7		88
5.2	odd	4		800.2.v.b.43.10		88
5.3	odd	4		160.2.u.a.43.13	✓	88
5.4	even	2		800.2.bb.b.107.22		88
20.3	even	4		640.2.u.a.463.16		88
32.3	odd	8		160.2.u.a.67.13	yes	88
32.29	even	8		640.2.u.a.47.16		88
160.3	even	8	inner	160.2.ba.a.3.1	yes	88
160.67	even	8		800.2.bb.b.643.22		88
160.93	odd	8		640.2.ba.a.303.7		88
160.99	odd	8		800.2.v.b.707.10		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.13	✓	88	5.3	odd	4
160.2.u.a.67.13	yes	88	32.3	odd	8
160.2.ba.a.3.1	yes	88	160.3	even	8	inner
160.2.ba.a.107.1	yes	88	1.1	even	1	trivial
640.2.u.a.47.16		88	32.29	even	8
640.2.u.a.463.16		88	20.3	even	4
640.2.ba.a.207.7		88	4.3	odd	2
640.2.ba.a.303.7		88	160.93	odd	8
800.2.v.b.43.10		88	5.2	odd	4
800.2.v.b.707.10		88	160.99	odd	8
800.2.bb.b.107.22		88	5.4	even	2
800.2.bb.b.643.22		88	160.67	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.ba (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36334 + 0.375898i) q^{2} +(1.22690 + 0.508197i) q^{3} +(1.71740 - 1.02496i) q^{4} +(0.868914 + 2.06034i) q^{5} +(-1.86371 - 0.231658i) q^{6} +0.810621 q^{7} +(-1.95613 + 2.04293i) q^{8} +(-0.874309 - 0.874309i) q^{9} +(-1.95910 - 2.48232i) q^{10} +(0.353731 - 0.853982i) q^{11} +(2.62795 - 0.384736i) q^{12} +(3.86563 + 1.60120i) q^{13} +(-1.10515 + 0.304711i) q^{14} +(0.0190103 + 2.96940i) q^{15} +(1.89893 - 3.52052i) q^{16} +(-4.37679 + 4.37679i) q^{17} +(1.52063 + 0.863331i) q^{18} +(0.285895 + 0.690211i) q^{19} +(3.60403 + 2.64783i) q^{20} +(0.994548 + 0.411955i) q^{21} +(-0.161246 + 1.29724i) q^{22} +5.36098 q^{23} +(-3.43818 + 1.51237i) q^{24} +(-3.48998 + 3.58051i) q^{25} +(-5.87207 - 0.729895i) q^{26} +(-2.15296 - 5.19770i) q^{27} +(1.39216 - 0.830850i) q^{28} +(-1.48464 - 3.58424i) q^{29} +(-1.14211 - 4.04116i) q^{30} -9.06865i q^{31} +(-1.26554 + 5.51348i) q^{32} +(0.867982 - 0.867982i) q^{33} +(4.32183 - 7.61229i) q^{34} +(0.704360 + 1.67015i) q^{35} +(-2.39767 - 0.605412i) q^{36} +(-0.870467 + 0.360559i) q^{37} +(-0.649221 - 0.833526i) q^{38} +(3.92901 + 3.92901i) q^{39} +(-5.90883 - 2.25515i) q^{40} +(0.572180 - 0.572180i) q^{41} +(-1.51076 - 0.187787i) q^{42} +(-4.42382 - 10.6801i) q^{43} +(-0.267796 - 1.82919i) q^{44} +(1.04167 - 2.56107i) q^{45} +(-7.30885 + 2.01518i) q^{46} +(-1.59734 - 1.59734i) q^{47} +(4.11891 - 3.35428i) q^{48} -6.34289 q^{49} +(3.41212 - 6.19334i) q^{50} +(-7.59414 + 3.14560i) q^{51} +(8.28000 - 1.21220i) q^{52} +(-4.62712 + 1.91662i) q^{53} +(4.88902 + 6.27695i) q^{54} +(2.06685 - 0.0132321i) q^{55} +(-1.58568 + 1.65604i) q^{56} +0.992109i q^{57} +(3.37138 + 4.32846i) q^{58} +(0.996806 - 2.40650i) q^{59} +(3.07615 + 5.08017i) q^{60} +(5.76047 - 2.38607i) q^{61} +(3.40889 + 12.3637i) q^{62} +(-0.708734 - 0.708734i) q^{63} +(-0.347145 - 7.99246i) q^{64} +(0.0598966 + 9.35581i) q^{65} +(-0.857084 + 1.50963i) q^{66} +(2.34497 - 5.66126i) q^{67} +(-3.03069 + 12.0027i) q^{68} +(6.57737 + 2.72444i) q^{69} +(-1.58809 - 2.01222i) q^{70} +(-1.22326 + 1.22326i) q^{71} +(3.49641 - 0.0758959i) q^{72} +11.4586i q^{73} +(1.05121 - 0.818772i) q^{74} +(-6.10145 + 2.61932i) q^{75} +(1.19843 + 0.892340i) q^{76} +(0.286742 - 0.692256i) q^{77} +(-6.83349 - 3.87967i) q^{78} +17.0418i q^{79} +(8.90346 + 0.853413i) q^{80} -3.76178i q^{81} +(-0.564996 + 0.995159i) q^{82} +(3.28569 - 7.93236i) q^{83} +(2.13027 - 0.311875i) q^{84} +(-12.8207 - 5.21461i) q^{85} +(10.0458 + 12.8977i) q^{86} -5.15198i q^{87} +(1.05269 + 2.39314i) q^{88} +(7.65721 - 7.65721i) q^{89} +(-0.457453 + 3.88318i) q^{90} +(3.13356 + 1.29796i) q^{91} +(9.20696 - 5.49477i) q^{92} +(4.60866 - 11.1263i) q^{93} +(2.77815 + 1.57728i) q^{94} +(-1.17365 + 1.18877i) q^{95} +(-4.35462 + 6.12132i) q^{96} +(-2.02530 - 2.02530i) q^{97} +(8.64753 - 2.38428i) q^{98} +(-1.05591 + 0.437374i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 8 q^{7} + 8 q^{8} + 8 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} - 16 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 16 q^{19} - 32 q^{20} - 8 q^{21} - 20 q^{22}+ \cdots + 16 q^{98}+O(q^{100}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 8 * q^7 + 8 * q^8 + 8 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 - 16 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 16 * q^19 - 32 * q^20 - 8 * q^21 - 20 * q^22 - 8 * q^23 + 32 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 - 20 * q^28 + 64 * q^30 + 16 * q^32 - 8 * q^33 - 8 * q^34 - 48 * q^35 - 8 * q^36 - 4 * q^37 - 4 * q^38 + 16 * q^40 - 8 * q^41 - 68 * q^42 + 28 * q^43 - 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 88 * q^48 + 40 * q^49 + 4 * q^50 + 8 * q^51 + 48 * q^52 - 4 * q^53 + 56 * q^54 + 28 * q^55 + 40 * q^56 - 36 * q^58 + 12 * q^60 - 40 * q^61 - 32 * q^62 - 56 * q^63 - 48 * q^64 - 8 * q^65 + 72 * q^66 - 28 * q^67 + 8 * q^68 - 24 * q^69 + 4 * q^70 + 24 * q^71 + 88 * q^72 - 16 * q^75 + 56 * q^76 - 32 * q^77 + 112 * q^78 + 80 * q^80 + 68 * q^82 + 36 * q^83 - 56 * q^84 - 4 * q^85 + 24 * q^86 - 24 * q^88 - 84 * q^90 - 8 * q^91 + 92 * q^92 + 8 * q^93 + 32 * q^94 + 24 * q^96 - 8 * q^97 + 16 * q^98

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