LMFDB - Embedded newform 272.2.l.b.205.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,2,Mod(69,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			205.9
Character	$\chi$	$=$	272.205
Dual form			272.2.l.b.69.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.321310 - 1.37723i) q^{2} +(-2.20735 - 2.20735i) q^{3} +(-1.79352 - 0.885036i) q^{4} +(2.24231 - 2.24231i) q^{5} +(-3.74927 + 2.33078i) q^{6} -3.15246i q^{7} +(-1.79517 + 2.18572i) q^{8} +6.74479i q^{9} +(-2.36770 - 3.80866i) q^{10} +(2.18853 - 2.18853i) q^{11} +(2.00534 + 5.91251i) q^{12} +(1.93366 + 1.93366i) q^{13} +(-4.34166 - 1.01292i) q^{14} -9.89914 q^{15} +(2.43342 + 3.17466i) q^{16} -1.00000 q^{17} +(9.28912 + 2.16717i) q^{18} +(5.15715 + 5.15715i) q^{19} +(-6.00616 + 2.03710i) q^{20} +(-6.95858 + 6.95858i) q^{21} +(-2.31091 - 3.71730i) q^{22} +0.195308i q^{23} +(8.78721 - 0.862065i) q^{24} -5.05593i q^{25} +(3.28439 - 2.04178i) q^{26} +(8.26606 - 8.26606i) q^{27} +(-2.79004 + 5.65400i) q^{28} +(-0.528823 - 0.528823i) q^{29} +(-3.18069 + 13.6334i) q^{30} -6.11385 q^{31} +(5.15411 - 2.33133i) q^{32} -9.66169 q^{33} +(-0.321310 + 1.37723i) q^{34} +(-7.06880 - 7.06880i) q^{35} +(5.96938 - 12.0969i) q^{36} +(1.40762 - 1.40762i) q^{37} +(8.75961 - 5.44553i) q^{38} -8.53651i q^{39} +(0.875719 + 8.92640i) q^{40} -4.43656i q^{41} +(7.34770 + 11.8194i) q^{42} +(-0.190233 + 0.190233i) q^{43} +(-5.86209 + 1.98824i) q^{44} +(15.1239 + 15.1239i) q^{45} +(0.268984 + 0.0627545i) q^{46} +3.42093 q^{47} +(1.63616 - 12.3790i) q^{48} -2.93800 q^{49} +(-6.96317 - 1.62452i) q^{50} +(2.20735 + 2.20735i) q^{51} +(-1.75670 - 5.17941i) q^{52} +(8.10559 - 8.10559i) q^{53} +(-8.72828 - 14.0402i) q^{54} -9.81472i q^{55} +(6.89038 + 5.65921i) q^{56} -22.7673i q^{57} +(-0.898226 + 0.558394i) q^{58} +(-8.44870 + 8.44870i) q^{59} +(17.7543 + 8.76109i) q^{60} +(0.714780 + 0.714780i) q^{61} +(-1.96444 + 8.42018i) q^{62} +21.2627 q^{63} +(-1.55471 - 7.84748i) q^{64} +8.67172 q^{65} +(-3.10440 + 13.3064i) q^{66} +(-6.97933 - 6.97933i) q^{67} +(1.79352 + 0.885036i) q^{68} +(0.431113 - 0.431113i) q^{69} +(-12.0066 + 7.46408i) q^{70} +12.1516i q^{71} +(-14.7422 - 12.1081i) q^{72} +9.75624i q^{73} +(-1.48633 - 2.39089i) q^{74} +(-11.1602 + 11.1602i) q^{75} +(-4.68518 - 13.8137i) q^{76} +(-6.89924 - 6.89924i) q^{77} +(-11.7567 - 2.74287i) q^{78} -12.9230 q^{79} +(12.5751 + 1.66208i) q^{80} -16.2578 q^{81} +(-6.11016 - 1.42551i) q^{82} +(6.54131 + 6.54131i) q^{83} +(18.6389 - 6.32176i) q^{84} +(-2.24231 + 2.24231i) q^{85} +(0.200870 + 0.323118i) q^{86} +2.33459i q^{87} +(0.854714 + 8.71228i) q^{88} +5.65429i q^{89} +(25.6886 - 15.9696i) q^{90} +(6.09577 - 6.09577i) q^{91} +(0.172855 - 0.350289i) q^{92} +(13.4954 + 13.4954i) q^{93} +(1.09918 - 4.71141i) q^{94} +23.1279 q^{95} +(-16.5230 - 6.23087i) q^{96} -18.8256 q^{97} +(-0.944010 + 4.04630i) q^{98} +(14.7611 + 14.7611i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) $ 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	0.321310	−	1.37723i	0.227201	−	0.973848i
$2$	0.321310	−	1.37723i	0.227201	−	0.973848i
$3$	−2.20735	−	2.20735i	−1.27441	−	1.27441i	−0.943748	−	0.330666i	$-0.892727\pi$
$3$	−2.20735	−	2.20735i	−1.27441	−	1.27441i	−0.330666	−	0.943748i	$-0.607273\pi$
$4$	−1.79352	−	0.885036i	−0.896760	−	0.442518i
$5$	2.24231	−	2.24231i	1.00279	−	1.00279i	0.00279654	−	0.999996i	$-0.499110\pi$
$5$	2.24231	−	2.24231i	1.00279	−	1.00279i	0.999996	−	0.00279654i	$-0.000890169\pi$
$6$	−3.74927	+	2.33078i	−1.53063	+	0.951538i
$7$		−	3.15246i		−	1.19152i	−0.803163	−	0.595759i	$-0.796851\pi$
$7$		−	3.15246i		−	1.19152i	0.803163	−	0.595759i	$-0.203149\pi$
$8$	−1.79517	+	2.18572i	−0.634689	+	0.772767i
$9$			6.74479i			2.24826i
$10$	−2.36770	−	3.80866i	−0.748732	−	1.20440i
$11$	2.18853	−	2.18853i	0.659866	−	0.659866i	−0.295483	−	0.955348i	$-0.595480\pi$
$11$	2.18853	−	2.18853i	0.659866	−	0.659866i	0.955348	+	0.295483i	$0.0954804\pi$
$12$	2.00534	+	5.91251i	0.578892	+	1.70679i
$13$	1.93366	+	1.93366i	0.536300	+	0.536300i	0.922440	−	0.386140i	$-0.126192\pi$
$13$	1.93366	+	1.93366i	0.536300	+	0.536300i	−0.386140	+	0.922440i	$0.626192\pi$
$14$	−4.34166	−	1.01292i	−1.16036	−	0.270714i
$15$	−9.89914			−2.55595
$16$	2.43342	+	3.17466i	0.608356	+	0.793664i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$	9.28912	+	2.16717i	2.18947	+	0.510807i
$19$	5.15715	+	5.15715i	1.18313	+	1.18313i	0.978929	+	0.204202i	$0.0654598\pi$
$19$	5.15715	+	5.15715i	1.18313	+	1.18313i	0.204202	+	0.978929i	$0.434540\pi$
$20$	−6.00616	+	2.03710i	−1.34302	+	0.455510i
$21$	−6.95858	+	6.95858i	−1.51849	+	1.51849i
$22$	−2.31091	−	3.71730i	−0.492687	−	0.792531i
$23$			0.195308i			0.0407245i	0.999793	+	0.0203623i	$0.00648196\pi$
$23$			0.195308i			0.0407245i	−0.999793	+	0.0203623i	$0.993518\pi$
$24$	8.78721	−	0.862065i	1.79368	−	0.175968i
$25$		−	5.05593i		−	1.01119i
$26$	3.28439	−	2.04178i	0.644122	−	0.400427i
$27$	8.26606	−	8.26606i	1.59080	−	1.59080i
$28$	−2.79004	+	5.65400i	−0.527268	+	1.06851i
$29$	−0.528823	−	0.528823i	−0.0981999	−	0.0981999i	0.656300	−	0.754500i	$-0.272121\pi$
$29$	−0.528823	−	0.528823i	−0.0981999	−	0.0981999i	−0.754500	+	0.656300i	$0.772121\pi$
$30$	−3.18069	+	13.6334i	−0.580713	+	2.48910i
$31$	−6.11385			−1.09808			−0.549040	−	0.835796i	$-0.685007\pi$
$31$	−6.11385			−1.09808			−0.549040	+	0.835796i	$0.685007\pi$
$32$	5.15411	−	2.33133i	0.911127	−	0.412125i
$33$	−9.66169			−1.68188
$34$	−0.321310	+	1.37723i	−0.0551043	+	0.236193i
$35$	−7.06880	−	7.06880i	−1.19485	−	1.19485i
$36$	5.96938	−	12.0969i	0.994896	−	2.01615i
$37$	1.40762	−	1.40762i	0.231411	−	0.231411i	−0.581870	−	0.813281i	$-0.697679\pi$
$37$	1.40762	−	1.40762i	0.231411	−	0.231411i	0.813281	+	0.581870i	$0.197679\pi$
$38$	8.75961	−	5.44553i	1.42100	−	0.883381i
$39$		−	8.53651i		−	1.36694i
$40$	0.875719	+	8.92640i	0.138463	+	1.41139i
$41$		−	4.43656i		−	0.692874i	−0.938073	−	0.346437i	$-0.887391\pi$
$41$		−	4.43656i		−	0.692874i	0.938073	−	0.346437i	$-0.112609\pi$
$42$	7.34770	+	11.8194i	1.13377	+	1.82378i
$43$	−0.190233	+	0.190233i	−0.0290102	+	0.0290102i	−0.721463	−	0.692453i	$-0.756530\pi$
$43$	−0.190233	+	0.190233i	−0.0290102	+	0.0290102i	0.692453	+	0.721463i	$0.256530\pi$
$44$	−5.86209	+	1.98824i	−0.883743	+	0.299739i
$45$	15.1239	+	15.1239i	2.25454	+	2.25454i
$46$	0.268984	+	0.0627545i	0.0396595	+	0.00925264i
$47$	3.42093			0.498994			0.249497	−	0.968376i	$-0.419735\pi$
$47$	3.42093			0.498994			0.249497	+	0.968376i	$0.419735\pi$
$48$	1.63616	−	12.3790i	0.236160	−	1.78675i
$49$	−2.93800			−0.419715
$50$	−6.96317	−	1.62452i	−0.984742	−	0.229742i
$51$	2.20735	+	2.20735i	0.309091	+	0.309091i
$52$	−1.75670	−	5.17941i	−0.243610	−	0.718254i
$53$	8.10559	−	8.10559i	1.11339	−	1.11339i	0.120700	−	0.992689i	$-0.461486\pi$
$53$	8.10559	−	8.10559i	1.11339	−	1.11339i	0.992689	−	0.120700i	$-0.0385138\pi$
$54$	−8.72828	−	14.0402i	−1.18777	−	1.91063i
$55$		−	9.81472i		−	1.32342i
$56$	6.89038	+	5.65921i	0.920766	+	0.756244i
$57$		−	22.7673i		−	3.01560i
$58$	−0.898226	+	0.558394i	−0.117943	+	0.0733207i
$59$	−8.44870	+	8.44870i	−1.09993	+	1.09993i	−0.105509	+	0.994418i	$0.533647\pi$
$59$	−8.44870	+	8.44870i	−1.09993	+	1.09993i	−0.994418	+	0.105509i	$0.966353\pi$
$60$	17.7543	+	8.76109i	2.29207	+	1.13105i
$61$	0.714780	+	0.714780i	0.0915182	+	0.0915182i	0.751384	−	0.659866i	$-0.229387\pi$
$61$	0.714780	+	0.714780i	0.0915182	+	0.0915182i	−0.659866	+	0.751384i	$0.729387\pi$
$62$	−1.96444	+	8.42018i	−0.249485	+	1.06936i
$63$	21.2627			2.67884
$64$	−1.55471	−	7.84748i	−0.194339	−	0.980935i
$65$	8.67172			1.07560
$66$	−3.10440	+	13.3064i	−0.382125	+	1.63790i
$67$	−6.97933	−	6.97933i	−0.852661	−	0.852661i	0.137799	−	0.990460i	$-0.455997\pi$
$67$	−6.97933	−	6.97933i	−0.852661	−	0.852661i	−0.990460	+	0.137799i	$0.955997\pi$
$68$	1.79352	+	0.885036i	0.217496	+	0.107326i
$69$	0.431113	−	0.431113i	0.0518999	−	0.0518999i
$70$	−12.0066	+	7.46408i	−1.43507	+	0.892128i
$71$			12.1516i			1.44213i	0.692870	+	0.721063i	$0.256346\pi$
$71$			12.1516i			1.44213i	−0.692870	+	0.721063i	$0.743654\pi$
$72$	−14.7422	−	12.1081i	−1.73738	−	1.42695i
$73$			9.75624i			1.14188i	0.820991	+	0.570941i	$0.193421\pi$
$73$			9.75624i			1.14188i	−0.820991	+	0.570941i	$0.806579\pi$
$74$	−1.48633	−	2.39089i	−0.172782	−	0.277936i
$75$	−11.1602	+	11.1602i	−1.28867	+	1.28867i
$76$	−4.68518	−	13.8137i	−0.537427	−	1.58454i
$77$	−6.89924	−	6.89924i	−0.786242	−	0.786242i
$78$	−11.7567	−	2.74287i	−1.33119	−	0.310569i
$79$	−12.9230			−1.45396			−0.726978	−	0.686661i	$-0.759076\pi$
$79$	−12.9230			−1.45396			−0.726978	+	0.686661i	$0.759076\pi$
$80$	12.5751	+	1.66208i	1.40594	+	0.185826i
$81$	−16.2578			−1.80642
$82$	−6.11016	−	1.42551i	−0.674754	−	0.157422i
$83$	6.54131	+	6.54131i	0.718003	+	0.718003i	0.968196	−	0.250193i	$-0.0804942\pi$
$83$	6.54131	+	6.54131i	0.718003	+	0.718003i	−0.250193	+	0.968196i	$0.580494\pi$
$84$	18.6389	−	6.32176i	2.03368	−	0.689760i
$85$	−2.24231	+	2.24231i	−0.243213	+	0.243213i
$86$	0.200870	+	0.323118i	0.0216604	+	0.0348427i
$87$			2.33459i			0.250295i
$88$	0.854714	+	8.71228i	0.0911128	+	0.928732i
$89$			5.65429i			0.599353i	0.954041	+	0.299677i	$0.0968788\pi$
$89$			5.65429i			0.599353i	−0.954041	+	0.299677i	$0.903121\pi$
$90$	25.6886	−	15.9696i	2.70781	−	1.68335i
$91$	6.09577	−	6.09577i	0.639011	−	0.639011i
$92$	0.172855	−	0.350289i	0.0180213	−	0.0365201i
$93$	13.4954	+	13.4954i	1.39941	+	1.39941i
$94$	1.09918	−	4.71141i	0.113372	−	0.485944i
$95$	23.1279			2.37287
$96$	−16.5230	−	6.23087i	−1.68637	−	0.635935i
$97$	−18.8256			−1.91145			−0.955724	−	0.294264i	$-0.904926\pi$
$97$	−18.8256			−1.91145			−0.955724	+	0.294264i	$0.904926\pi$
$98$	−0.944010	+	4.04630i	−0.0953594	+	0.408738i
$99$	14.7611	+	14.7611i	1.48355	+	1.48355i
$100$	−4.47468	+	9.06791i	−0.447468	+	0.906791i
$101$	1.65020	−	1.65020i	0.164201	−	0.164201i	−0.620224	−	0.784425i	$-0.712958\pi$
$101$	1.65020	−	1.65020i	0.164201	−	0.164201i	0.784425	+	0.620224i	$0.212958\pi$
$102$	3.74927	−	2.33078i	0.371233	−	0.230782i
$103$		−	5.40899i		−	0.532963i	−0.963840	−	0.266482i	$-0.914139\pi$
$103$		−	5.40899i		−	0.532963i	0.963840	−	0.266482i	$-0.0858612\pi$
$104$	−7.69767	+	0.755176i	−0.754819	+	0.0740511i
$105$			31.2066i			3.04546i
$106$	−8.55885	−	13.7677i	−0.831309	−	1.33723i
$107$	7.65245	−	7.65245i	0.739790	−	0.739790i	−0.232747	−	0.972537i	$-0.574772\pi$
$107$	7.65245	−	7.65245i	0.739790	−	0.739790i	0.972537	+	0.232747i	$0.0747715\pi$
$108$	−22.1411	+	7.50958i	−2.13053	+	0.722609i
$109$	3.13945	+	3.13945i	0.300705	+	0.300705i	0.841290	−	0.540585i	$-0.181797\pi$
$109$	3.13945	+	3.13945i	0.300705	+	0.300705i	−0.540585	+	0.841290i	$0.681797\pi$
$110$	−13.5171	−	3.15357i	−1.28881	−	0.300681i
$111$	−6.21421			−0.589827
$112$	10.0080	−	7.67127i	0.945665	−	0.724867i
$113$	6.08014			0.571972			0.285986	−	0.958234i	$-0.407679\pi$
$113$	6.08014			0.571972			0.285986	+	0.958234i	$0.407679\pi$
$114$	−31.3557	−	7.31535i	−2.93673	−	0.685145i
$115$	0.437942	+	0.437942i	0.0408383	+	0.0408383i
$116$	0.480427	+	1.41648i	0.0446065	+	0.131517i
$117$	−13.0421	+	13.0421i	−1.20574	+	1.20574i
$118$	8.92114	+	14.3504i	0.821257	+	1.32107i
$119$			3.15246i			0.288986i
$120$	17.7707	−	21.6367i	1.62223	−	1.97515i
$121$			1.42070i			0.129155i
$122$	1.21408	−	0.754750i	0.109918	−	0.0683318i
$123$	−9.79304	+	9.79304i	−0.883009	+	0.883009i
$124$	10.9653	+	5.41098i	0.984714	+	0.485920i
$125$	−0.125414	−	0.125414i	−0.0112174	−	0.0112174i
$126$	6.83191	−	29.2836i	0.608635	−	2.60879i
$127$	18.1433			1.60995			0.804977	−	0.593306i	$-0.202178\pi$
$127$	18.1433			1.60995			0.804977	+	0.593306i	$0.202178\pi$
$128$	−11.3073	−	0.380286i	−0.999435	−	0.0336128i
$129$	0.839820			0.0739421
$130$	2.78631	−	11.9430i	0.244376	−	1.04747i
$131$	1.43989	+	1.43989i	0.125804	+	0.125804i	0.767205	−	0.641402i	$-0.221647\pi$
$131$	1.43989	+	1.43989i	0.125804	+	0.125804i	−0.641402	+	0.767205i	$0.721647\pi$
$132$	17.3284	+	8.55094i	1.50825	+	0.744264i
$133$	16.2577	−	16.2577i	1.40972	−	1.40972i
$134$	−11.8547	+	7.36961i	−1.02409	+	0.636637i
$135$		−	37.0702i		−	3.19049i
$136$	1.79517	−	2.18572i	0.153935	−	0.187424i
$137$		−	3.44420i		−	0.294258i	−0.989117	−	0.147129i	$-0.952997\pi$
$137$		−	3.44420i		−	0.294258i	0.989117	−	0.147129i	$-0.0470033\pi$
$138$	−0.455220	−	0.732263i	−0.0387509	−	0.0623343i
$139$	−3.26796	+	3.26796i	−0.277185	+	0.277185i	−0.831984	−	0.554799i	$-0.812795\pi$
$139$	−3.26796	+	3.26796i	−0.277185	+	0.277185i	0.554799	+	0.831984i	$0.312795\pi$
$140$	6.42189	+	18.9342i	0.542749	+	1.60023i
$141$	−7.55119	−	7.55119i	−0.635925	−	0.635925i
$142$	16.7355	+	3.90442i	1.40441	+	0.327652i
$143$	8.46372			0.707772
$144$	−21.4124	+	16.4129i	−1.78437	+	1.36774i
$145$	−2.37157			−0.196948
$146$	13.4366	+	3.13478i	1.11202	+	0.259436i
$147$	6.48520	+	6.48520i	0.534890	+	0.534890i
$148$	−3.77038	+	1.27880i	−0.309924	+	0.105117i
$149$	8.74820	−	8.74820i	0.716680	−	0.716680i	−0.251244	−	0.967924i	$-0.580840\pi$
$149$	8.74820	−	8.74820i	0.716680	−	0.716680i	0.967924	+	0.251244i	$0.0808395\pi$
$150$	11.7843	+	18.9561i	0.962182	+	1.54776i
$151$			6.28163i			0.511192i	0.966784	+	0.255596i	$0.0822717\pi$
$151$			6.28163i			0.511192i	−0.966784	+	0.255596i	$0.917728\pi$
$152$	−20.5300	+	2.01409i	−1.66520	+	0.163364i
$153$		−	6.74479i		−	0.545284i
$154$	−11.7186	+	7.28504i	−0.944314	+	0.587045i
$155$	−13.7092	+	13.7092i	−1.10115	+	1.10115i
$156$	−7.55512	+	15.3104i	−0.604894	+	1.22581i
$157$	−10.2980	−	10.2980i	−0.821870	−	0.821870i	0.164506	−	0.986376i	$-0.447397\pi$
$157$	−10.2980	−	10.2980i	−0.821870	−	0.821870i	−0.986376	+	0.164506i	$0.947397\pi$
$158$	−4.15231	+	17.7980i	−0.330340	+	1.41593i
$159$	−35.7838			−2.83784
$160$	6.32956	−	16.7847i	0.500396	−	1.32695i
$161$	0.615701			0.0485240
$162$	−5.22380	+	22.3907i	−0.410420	+	1.75918i
$163$	12.7512	+	12.7512i	0.998752	+	0.998752i	0.999999	−	0.00124705i	$-0.000396948\pi$
$163$	12.7512	+	12.7512i	0.998752	+	0.998752i	−0.00124705	+	0.999999i	$0.500397\pi$
$164$	−3.92651	+	7.95706i	−0.306609	+	0.621342i
$165$	−21.6645	+	21.6645i	−1.68658	+	1.68658i
$166$	11.1107	−	6.90710i	0.862356	−	0.536095i
$167$		−	8.20113i		−	0.634623i	−0.948321	−	0.317311i	$-0.897220\pi$
$167$		−	8.20113i		−	0.634623i	0.948321	−	0.317311i	$-0.102780\pi$
$168$	−2.71763	−	27.7013i	−0.209669	−	2.13720i
$169$		−	5.52194i		−	0.424765i
$170$	2.36770	+	3.80866i	0.181594	+	0.292111i
$171$	−34.7839	+	34.7839i	−2.65999	+	2.65999i
$172$	0.509549	−	0.172823i	0.0388527	−	0.0131777i
$173$	6.07174	+	6.07174i	0.461626	+	0.461626i	0.899188	−	0.437562i	$-0.144158\pi$
$173$	6.07174	+	6.07174i	0.461626	+	0.461626i	−0.437562	+	0.899188i	$0.644158\pi$
$174$	3.21527	+	0.750129i	0.243749	+	0.0568671i
$175$	−15.9386			−1.20485
$176$	12.2734	+	1.62221i	0.925145	+	0.122279i
$177$	37.2985			2.80352
$178$	7.78725	+	1.81678i	0.583679	+	0.136173i
$179$	−6.65485	−	6.65485i	−0.497407	−	0.497407i	0.413223	−	0.910630i	$-0.364403\pi$
$179$	−6.65485	−	6.65485i	−0.497407	−	0.497407i	−0.910630	+	0.413223i	$0.864403\pi$
$180$	−13.7398	−	40.5103i	−1.02411	−	3.01946i
$181$	5.84062	−	5.84062i	0.434130	−	0.434130i	−0.455901	−	0.890031i	$-0.650683\pi$
$181$	5.84062	−	5.84062i	0.434130	−	0.434130i	0.890031	+	0.455901i	$0.150683\pi$
$182$	−6.43664	−	10.3539i	−0.477116	−	0.767483i
$183$		−	3.15554i		−	0.233264i
$184$	−0.426888	−	0.350612i	−0.0314706	−	0.0258474i
$185$		−	6.31264i		−	0.464115i
$186$	22.9225	−	14.2501i	1.68076	−	1.04487i
$187$	−2.18853	+	2.18853i	−0.160041	+	0.160041i
$188$	−6.13551	−	3.02765i	−0.447478	−	0.220814i
$189$	−26.0584	−	26.0584i	−1.89547	−	1.89547i
$190$	7.43122	−	31.8524i	0.539117	−	2.31081i
$191$	7.20422			0.521279			0.260640	−	0.965436i	$-0.416067\pi$
$191$	7.20422			0.521279			0.260640	+	0.965436i	$0.416067\pi$
$192$	−13.8903	+	20.7539i	−1.00245	+	1.49778i
$193$	−22.5638			−1.62418			−0.812088	−	0.583535i	$-0.801669\pi$
$193$	−22.5638			−1.62418			−0.812088	+	0.583535i	$0.801669\pi$
$194$	−6.04885	+	25.9271i	−0.434282	+	1.86146i
$195$	−19.1415	−	19.1415i	−1.37075	−	1.37075i
$196$	5.26936	+	2.60024i	0.376383	+	0.185731i
$197$	−1.49672	+	1.49672i	−0.106637	+	0.106637i	−0.758412	−	0.651775i	$-0.774025\pi$
$197$	−1.49672	+	1.49672i	−0.106637	+	0.106637i	0.651775	+	0.758412i	$0.274025\pi$
$198$	25.0724	−	15.5866i	1.78182	−	1.10769i
$199$		−	4.78517i		−	0.339212i	−0.985512	−	0.169606i	$-0.945751\pi$
$199$		−	4.78517i		−	0.339212i	0.985512	−	0.169606i	$-0.0542495\pi$
$200$	11.0508	+	9.07627i	0.781412	+	0.641789i
$201$			30.8117i			2.17329i
$202$	−1.74248	−	2.80293i	−0.122600	−	0.197213i
$203$	−1.66709	+	1.66709i	−0.117007	+	0.117007i
$204$	−2.00534	−	5.91251i	−0.140402	−	0.413958i
$205$	−9.94816	−	9.94816i	−0.694809	−	0.694809i
$206$	−7.44941	−	1.73796i	−0.519025	−	0.121090i
$207$	−1.31731			−0.0915595
$208$	−1.43329	+	10.8441i	−0.0993808	+	0.751903i
$209$	22.5731			1.56141
$210$	42.9787	+	10.0270i	2.96581	+	0.691929i
$211$	−12.4302	−	12.4302i	−0.855729	−	0.855729i	0.135102	−	0.990832i	$-0.456864\pi$
$211$	−12.4302	−	12.4302i	−0.855729	−	0.855729i	−0.990832	+	0.135102i	$0.956864\pi$
$212$	−21.7113	+	7.36380i	−1.49114	+	0.505748i
$213$	26.8228	−	26.8228i	1.83787	−	1.83787i
$214$	−8.08036	−	12.9980i	−0.552362	−	0.888524i
$215$			0.853122i			0.0581825i
$216$	3.22825	+	32.9063i	0.219655	+	2.23899i
$217$			19.2737i			1.30838i
$218$	5.33249	−	3.31501i	0.361162	−	0.224521i
$219$	21.5354	−	21.5354i	1.45523	−	1.45523i
$220$	−8.68638	+	17.6029i	−0.585636	+	1.18679i
$221$	−1.93366	−	1.93366i	−0.130072	−	0.130072i
$222$	−1.99669	+	8.55839i	−0.134009	+	0.574402i
$223$	1.37935			0.0923681			0.0461840	−	0.998933i	$-0.485294\pi$
$223$	1.37935			0.0923681			0.0461840	+	0.998933i	$0.485294\pi$
$224$	−7.34943	−	16.2481i	−0.491054	−	1.08562i
$225$	34.1012			2.27341
$226$	1.95361	−	8.37375i	0.129952	−	0.557013i
$227$	−10.8928	−	10.8928i	−0.722981	−	0.722981i	0.246230	−	0.969211i	$-0.420808\pi$
$227$	−10.8928	−	10.8928i	−0.722981	−	0.722981i	−0.969211	+	0.246230i	$0.920808\pi$
$228$	−20.1498	+	40.8335i	−1.33445	+	2.70427i
$229$	6.47743	−	6.47743i	0.428040	−	0.428040i	−0.459920	−	0.887960i	$-0.652122\pi$
$229$	6.47743	−	6.47743i	0.428040	−	0.428040i	0.887960	+	0.459920i	$0.152122\pi$
$230$	0.743861	−	0.462431i	0.0490487	−	0.0304918i
$231$			30.4581i			2.00399i
$232$	2.10518	−	0.206528i	0.138212	−	0.0135592i
$233$		−	12.7932i		−	0.838110i	−0.907961	−	0.419055i	$-0.862361\pi$
$233$		−	12.7932i		−	0.838110i	0.907961	−	0.419055i	$-0.137639\pi$
$234$	13.7714	+	22.1525i	0.900265	+	1.44816i
$235$	7.67080	−	7.67080i	0.500388	−	0.500388i
$236$	22.6303	−	7.67551i	1.47311	−	0.499633i
$237$	28.5257	+	28.5257i	1.85294	+	1.85294i
$238$	4.34166	+	1.01292i	0.281428	+	0.0656577i
$239$	29.4415			1.90441			0.952205	−	0.305460i	$-0.0988101\pi$
$239$	29.4415			1.90441			0.952205	+	0.305460i	$0.0988101\pi$
$240$	−24.0888	−	31.4264i	−1.55493	−	2.02856i
$241$	2.50856			0.161590			0.0807952	−	0.996731i	$-0.474254\pi$
$241$	2.50856			0.161590			0.0807952	+	0.996731i	$0.474254\pi$
$242$	1.95663	+	0.456486i	0.125777	+	0.0293440i
$243$	11.0885	+	11.0885i	0.711326	+	0.711326i
$244$	−0.649366	−	1.91458i	−0.0415714	−	0.122568i
$245$	−6.58792	+	6.58792i	−0.420887	+	0.420887i
$246$	10.3407	+	16.6339i	0.659296	+	1.06054i
$247$			19.9443i			1.26903i
$248$	10.9754	−	13.3631i	0.696940	−	0.848561i
$249$		−	28.8779i		−	1.83007i
$250$	−0.213021	+	0.132427i	−0.0134726	+	0.00837542i
$251$	1.70198	−	1.70198i	0.107428	−	0.107428i	−0.651350	−	0.758778i	$-0.725797\pi$
$251$	1.70198	−	1.70198i	0.107428	−	0.107428i	0.758778	+	0.651350i	$0.225797\pi$
$252$	−38.1350	−	18.8182i	−2.40228	−	1.18544i
$253$	0.427437	+	0.427437i	0.0268727	+	0.0268727i
$254$	5.82962	−	24.9874i	0.365783	−	1.56785i
$255$	9.89914			0.619908
$256$	−4.15690	+	15.4506i	−0.259806	+	0.965661i
$257$	−18.3996			−1.14773			−0.573867	−	0.818949i	$-0.694557\pi$
$257$	−18.3996			−1.14773			−0.573867	+	0.818949i	$0.694557\pi$
$258$	0.269843	−	1.15662i	0.0167997	−	0.0720083i
$259$	−4.43746	−	4.43746i	−0.275730	−	0.275730i
$260$	−15.5529	−	7.67479i	−0.964550	−	0.475970i
$261$	3.56680	−	3.56680i	0.220779	−	0.220779i
$262$	2.44571	−	1.52041i	0.151096	−	0.0939310i
$263$			23.2237i			1.43203i	0.698083	+	0.716017i	$0.254037\pi$
$263$			23.2237i			1.43203i	−0.698083	+	0.716017i	$0.745963\pi$
$264$	17.3444	−	21.1177i	1.06747	−	1.29970i
$265$		−	36.3505i		−	2.23300i
$266$	−17.1668	−	27.6143i	−1.05256	−	1.69314i
$267$	12.4810	−	12.4810i	0.763824	−	0.763824i
$268$	6.34061	+	18.6945i	0.387314	+	1.14195i
$269$	15.2401	+	15.2401i	0.929208	+	0.929208i	0.997655	−	0.0684469i	$-0.0218044\pi$
$269$	15.2401	+	15.2401i	0.929208	+	0.929208i	−0.0684469	+	0.997655i	$0.521804\pi$
$270$	−51.0541	−	11.9110i	−3.10705	−	0.724882i
$271$	0.770720			0.0468179			0.0234089	−	0.999726i	$-0.492548\pi$
$271$	0.770720			0.0468179			0.0234089	+	0.999726i	$0.492548\pi$
$272$	−2.43342	−	3.17466i	−0.147548	−	0.192492i
$273$	−26.9110			−1.62873
$274$	−4.74346	−	1.10666i	−0.286563	−	0.0668557i
$275$	−11.0650	−	11.0650i	−0.667247	−	0.667247i
$276$	−1.15476	+	0.391659i	−0.0695084	+	0.0235751i
$277$	−9.64373	+	9.64373i	−0.579436	+	0.579436i	−0.934748	−	0.355312i	$-0.884375\pi$
$277$	−9.64373	+	9.64373i	−0.579436	+	0.579436i	0.355312	+	0.934748i	$0.384375\pi$
$278$	3.45071	+	5.55077i	0.206960	+	0.332913i
$279$		−	41.2366i		−	2.46877i
$280$	28.1401	−	2.76067i	1.68169	−	0.164982i
$281$		−	0.360033i		−	0.0214778i	−0.999942	−	0.0107389i	$-0.996582\pi$
$281$		−	0.360033i		−	0.0214778i	0.999942	−	0.0107389i	$-0.00341836\pi$
$282$	−12.8260	+	7.97345i	−0.763777	+	0.474812i
$283$	−11.5835	+	11.5835i	−0.688570	+	0.688570i	−0.961916	−	0.273346i	$-0.911870\pi$
$283$	−11.5835	+	11.5835i	−0.688570	+	0.688570i	0.273346	+	0.961916i	$0.411870\pi$
$284$	10.7546	−	21.7941i	0.638166	−	1.29324i
$285$	−51.0513	−	51.0513i	−3.02402	−	3.02402i
$286$	2.71948	−	11.6565i	0.160806	−	0.689262i
$287$	−13.9861			−0.825572
$288$	15.7243	+	34.7634i	0.926566	+	2.04845i
$289$	1.00000			0.0588235
$290$	−0.762010	+	3.26620i	−0.0447468	+	0.191798i
$291$	41.5547	+	41.5547i	2.43598	+	2.43598i
$292$	8.63462	−	17.4980i	0.505303	−	1.02399i
$293$	9.25792	−	9.25792i	0.540853	−	0.540853i	−0.382926	−	0.923779i	$-0.625084\pi$
$293$	9.25792	−	9.25792i	0.540853	−	0.540853i	0.923779	+	0.382926i	$0.125084\pi$
$294$	11.0154	−	6.84784i	0.642429	−	0.399374i
$295$			37.8892i			2.20600i
$296$	0.549735	+	5.60357i	0.0319527	+	0.325701i
$297$		−	36.1810i		−	2.09943i
$298$	−9.23739	−	14.8592i	−0.535107	−	0.860768i
$299$	−0.377659	+	0.377659i	−0.0218406	+	0.0218406i
$300$	29.8932	−	10.1389i	1.72589	−	0.585368i
$301$	0.599701	+	0.599701i	0.0345662	+	0.0345662i
$302$	8.65125	+	2.01835i	0.497823	+	0.116143i
$303$	−7.28514			−0.418520
$304$	−3.82265	+	28.9217i	−0.219244	+	1.65877i
$305$	3.20552			0.183548
$306$	−9.28912	−	2.16717i	−0.531023	−	0.123889i
$307$	13.8357	+	13.8357i	0.789643	+	0.789643i	0.981435	−	0.191793i	$-0.0614301\pi$
$307$	13.8357	+	13.8357i	0.789643	+	0.789643i	−0.191793	+	0.981435i	$0.561430\pi$
$308$	6.26785	+	18.4800i	0.357144	+	1.05300i
$309$	−11.9395	+	11.9395i	−0.679216	+	0.679216i
$310$	14.4758	+	23.2856i	0.822169	+	1.32253i
$311$			27.8292i			1.57805i	0.614362	+	0.789024i	$0.289413\pi$
$311$			27.8292i			1.57805i	−0.614362	+	0.789024i	$0.710587\pi$
$312$	18.6584	+	15.3245i	1.05632	+	0.867580i
$313$			16.0783i			0.908801i	0.890798	+	0.454400i	$0.150146\pi$
$313$			16.0783i			0.908801i	−0.890798	+	0.454400i	$0.849854\pi$
$314$	−17.4916	+	10.8739i	−0.987106	+	0.613647i
$315$	47.6776	−	47.6776i	2.68633	−	2.68633i
$316$	23.1777	+	11.4374i	1.30385	+	0.643401i
$317$	17.2656	+	17.2656i	0.969733	+	0.969733i	0.999555	−	0.0298218i	$-0.00949398\pi$
$317$	17.2656	+	17.2656i	0.969733	+	0.969733i	−0.0298218	+	0.999555i	$0.509494\pi$
$318$	−11.4977	+	49.2824i	−0.644758	+	2.76362i
$319$	−2.31468			−0.129597
$320$	−21.0826	−	14.1104i	−1.17856	−	0.788793i
$321$	−33.7833			−1.88560
$322$	0.197831	−	0.847961i	0.0110247	−	0.0472550i
$323$	−5.15715	−	5.15715i	−0.286951	−	0.286951i
$324$	29.1587	+	14.3887i	1.61993	+	0.799374i
$325$	9.77643	−	9.77643i	0.542299	−	0.542299i
$326$	21.6584	−	13.4642i	1.19955	−	0.745716i
$327$		−	13.8597i		−	0.766446i
$328$	9.69706	+	7.96439i	0.535431	+	0.439760i
$329$		−	10.7843i		−	0.594560i
$330$	22.8760	+	36.7980i	1.25928	+	2.02567i
$331$	9.14041	−	9.14041i	0.502403	−	0.502403i	−0.409781	−	0.912184i	$-0.634395\pi$
$331$	9.14041	−	9.14041i	0.502403	−	0.502403i	0.912184	+	0.409781i	$0.134395\pi$
$332$	−5.94268	−	17.5213i	−0.326147	−	0.961605i
$333$	9.49409	+	9.49409i	0.520273	+	0.520273i
$334$	−11.2948	−	2.63511i	−0.618026	−	0.144187i
$335$	−31.2997			−1.71008
$336$	−39.0243	−	5.15793i	−2.12895	−	0.281388i
$337$	−11.4915			−0.625980			−0.312990	−	0.949756i	$-0.601331\pi$
$337$	−11.4915			−0.625980			−0.312990	+	0.949756i	$0.601331\pi$
$338$	−7.60498	−	1.77426i	−0.413656	−	0.0965069i
$339$	−13.4210	−	13.4210i	−0.728929	−	0.728929i
$340$	6.00616	−	2.03710i	0.325730	−	0.110478i
$341$	−13.3803	+	13.3803i	−0.724586	+	0.724586i
$342$	36.7289	+	59.0817i	1.98607	+	3.19477i
$343$		−	12.8053i		−	0.691420i
$344$	−0.0742940	−	0.757295i	−0.00400567	−	0.0408306i
$345$		−	1.93338i		−	0.104090i
$346$	10.3131	−	6.41126i	0.554435	−	0.344672i
$347$	20.5442	−	20.5442i	1.10287	−	1.10287i	0.108807	−	0.994063i	$-0.465297\pi$
$347$	20.5442	−	20.5442i	1.10287	−	1.10287i	0.994063	−	0.108807i	$-0.0347031\pi$
$348$	2.06620	−	4.18714i	0.110760	−	0.224454i
$349$	−6.14836	−	6.14836i	−0.329114	−	0.329114i	0.523135	−	0.852250i	$-0.324762\pi$
$349$	−6.14836	−	6.14836i	−0.329114	−	0.329114i	−0.852250	+	0.523135i	$0.824762\pi$
$350$	−5.12124	+	21.9511i	−0.273742	+	1.17334i
$351$	31.9674			1.70630
$352$	6.17773	−	16.3821i	0.329274	−	0.873169i
$353$	2.95059			0.157044			0.0785220	−	0.996912i	$-0.474980\pi$
$353$	2.95059			0.157044			0.0785220	+	0.996912i	$0.474980\pi$
$354$	11.9844	−	51.3685i	0.636963	−	2.73021i
$355$	27.2476	+	27.2476i	1.44615	+	1.44615i
$356$	5.00425	−	10.1411i	0.265225	−	0.537476i
$357$	6.95858	−	6.95858i	0.368287	−	0.368287i
$358$	−11.3035	+	7.02698i	−0.597410	+	0.371387i
$359$			10.4590i			0.552004i	0.961157	+	0.276002i	$0.0890097\pi$
$359$			10.4590i			0.552004i	−0.961157	+	0.276002i	$0.910990\pi$
$360$	−60.2066	+	5.90654i	−3.17317	+	0.311302i
$361$			34.1923i			1.79960i
$362$	−6.16722	−	9.92052i	−0.324142	−	0.521411i
$363$	3.13599	−	3.13599i	0.164597	−	0.164597i
$364$	−16.3279	+	5.53791i	−0.855813	+	0.290265i
$365$	21.8765	+	21.8765i	1.14507	+	1.14507i
$366$	−4.34590	−	1.01391i	−0.227164	−	0.0529978i
$367$	−2.49608			−0.130294			−0.0651472	−	0.997876i	$-0.520752\pi$
$367$	−2.49608			−0.130294			−0.0651472	+	0.997876i	$0.520752\pi$
$368$	−0.620036	+	0.475267i	−0.0323216	+	0.0247750i
$369$	29.9237			1.55776
$370$	−8.69395	−	2.02832i	−0.451977	−	0.105447i
$371$	−25.5526	−	25.5526i	−1.32662	−	1.32662i
$372$	−12.2604	−	36.1482i	−0.635670	−	1.87420i
$373$	−6.88256	+	6.88256i	−0.356366	+	0.356366i	−0.862471	−	0.506106i	$-0.831085\pi$
$373$	−6.88256	+	6.88256i	−0.356366	+	0.356366i	0.506106	+	0.862471i	$0.331085\pi$
$374$	2.31091	+	3.71730i	0.119494	+	0.192217i
$375$			0.553665i			0.0285912i
$376$	−6.14116	+	7.47718i	−0.316706	+	0.385606i
$377$		−	2.04512i		−	0.105329i
$378$	−44.2612	+	27.5156i	−2.27655	+	1.41525i
$379$	−6.25007	+	6.25007i	−0.321045	+	0.321045i	−0.849168	−	0.528123i	$-0.822896\pi$
$379$	−6.25007	+	6.25007i	−0.321045	+	0.321045i	0.528123	+	0.849168i	$0.322896\pi$
$380$	−41.4803	−	20.4690i	−2.12789	−	1.05004i
$381$	−40.0485	−	40.0485i	−2.05175	−	2.05175i
$382$	2.31479	−	9.92187i	0.118435	−	0.507647i
$383$	−8.35445			−0.426892			−0.213446	−	0.976955i	$-0.568469\pi$
$383$	−8.35445			−0.426892			−0.213446	+	0.976955i	$0.568469\pi$
$384$	24.1198	+	25.7986i	1.23086	+	1.31653i
$385$	−30.9405			−1.57687
$386$	−7.24997	+	31.0755i	−0.369014	+	1.58170i
$387$	−1.28308	−	1.28308i	−0.0652226	−	0.0652226i
$388$	33.7641	+	16.6613i	1.71411	+	0.845850i
$389$	13.4682	−	13.4682i	0.682865	−	0.682865i	−0.277780	−	0.960645i	$-0.589598\pi$
$389$	13.4682	−	13.4682i	0.682865	−	0.682865i	0.960645	+	0.277780i	$0.0895985\pi$
$390$	−32.5126	+	20.2119i	−1.64634	+	1.02347i
$391$		−	0.195308i		−	0.00987715i
$392$	5.27422	−	6.42164i	0.266388	−	0.324342i
$393$		−	6.35668i		−	0.320652i
$394$	1.58042	+	2.54224i	0.0796204	+	0.128076i
$395$	−28.9775	+	28.9775i	−1.45802	+	1.45802i
$396$	−13.4103	−	39.5385i	−0.673891	−	1.98689i
$397$	−16.7653	−	16.7653i	−0.841427	−	0.841427i	0.147617	−	0.989045i	$-0.452840\pi$
$397$	−16.7653	−	16.7653i	−0.841427	−	0.841427i	−0.989045	+	0.147617i	$0.952840\pi$
$398$	−6.59028	−	1.53752i	−0.330341	−	0.0770691i
$399$	−71.7728			−3.59314
$400$	16.0508	−	12.3032i	0.802542	−	0.615161i
$401$	−4.92038			−0.245712			−0.122856	−	0.992424i	$-0.539205\pi$
$401$	−4.92038			−0.245712			−0.122856	+	0.992424i	$0.539205\pi$
$402$	42.4347	+	9.90010i	2.11645	+	0.493772i
$403$	−11.8221	−	11.8221i	−0.588900	−	0.588900i
$404$	−4.42015	+	1.49918i	−0.219911	+	0.0745870i
$405$	−36.4551	+	36.4551i	−1.81147	+	1.81147i
$406$	1.76031	+	2.83162i	0.0873629	+	0.140531i
$407$		−	6.16122i		−	0.305400i
$408$	−8.78721	+	0.862065i	−0.435032	+	0.0426786i
$409$		−	9.82430i		−	0.485780i	−0.970054	−	0.242890i	$-0.921905\pi$
$409$		−	9.82430i		−	0.485780i	0.970054	−	0.242890i	$-0.0780954\pi$
$410$	−16.8973	+	10.5044i	−0.834500	+	0.518778i
$411$	−7.60256	+	7.60256i	−0.375007	+	0.375007i
$412$	−4.78715	+	9.70112i	−0.235846	+	0.477940i
$413$	26.6342	+	26.6342i	1.31058	+	1.31058i
$414$	−0.423266	+	1.81424i	−0.0208024	+	0.0891650i
$415$	29.3353			1.44002
$416$	14.4743	+	5.45829i	0.709660	+	0.267615i
$417$	14.4271			0.706497
$418$	7.25297	−	31.0883i	0.354754	−	1.52058i
$419$	−7.47094	−	7.47094i	−0.364979	−	0.364979i	0.500663	−	0.865642i	$-0.333090\pi$
$419$	−7.47094	−	7.47094i	−0.364979	−	0.364979i	−0.865642	+	0.500663i	$0.833090\pi$
$420$	27.6190	−	55.9697i	1.34767	−	2.73104i
$421$	6.17663	−	6.17663i	0.301030	−	0.301030i	−0.540387	−	0.841417i	$-0.681722\pi$
$421$	6.17663	−	6.17663i	0.301030	−	0.301030i	0.841417	+	0.540387i	$0.181722\pi$
$422$	−21.1132	+	13.1253i	−1.02777	+	0.638928i
$423$			23.0735i			1.12187i
$424$	3.16558	+	32.2675i	0.153734	+	1.56705i
$425$			5.05593i			0.245249i
$426$	−28.3227	−	45.5595i	−1.37224	−	2.20737i
$427$	2.25332	−	2.25332i	0.109046	−	0.109046i
$428$	−20.4975	+	6.95212i	−0.990784	+	0.336044i
$429$	−18.6824	−	18.6824i	−0.901994	−	0.901994i
$430$	1.17494	+	0.274117i	0.0566609	+	0.0132191i
$431$	−1.57573			−0.0759005			−0.0379502	−	0.999280i	$-0.512083\pi$
$431$	−1.57573			−0.0759005			−0.0379502	+	0.999280i	$0.512083\pi$
$432$	46.3567	+	6.12708i	2.23034	+	0.294789i
$433$	−36.0809			−1.73394			−0.866968	−	0.498364i	$-0.833934\pi$
$433$	−36.0809			−1.73394			−0.866968	+	0.498364i	$0.833934\pi$
$434$	26.5443	+	6.19283i	1.27417	+	0.297265i
$435$	5.23489	+	5.23489i	0.250994	+	0.250994i
$436$	−2.85214	−	8.40920i	−0.136593	−	0.402728i
$437$	−1.00723	+	1.00723i	−0.0481824	+	0.0481824i
$438$	−22.7397	−	36.5788i	−1.08654	−	1.74780i
$439$			27.2574i			1.30092i	0.759539	+	0.650462i	$0.225425\pi$
$439$			27.2574i			1.30092i	−0.759539	+	0.650462i	$0.774575\pi$
$440$	21.4522	+	17.6191i	1.02269	+	0.839959i
$441$		−	19.8162i		−	0.943629i
$442$	−3.28439	+	2.04178i	−0.156223	+	0.0971178i
$443$	2.90063	−	2.90063i	0.137813	−	0.137813i	−0.634835	−	0.772648i	$-0.718932\pi$
$443$	2.90063	−	2.90063i	0.137813	−	0.137813i	0.772648	+	0.634835i	$0.218932\pi$
$444$	11.1453	+	5.49980i	0.528933	+	0.261009i
$445$	12.6787	+	12.6787i	0.601027	+	0.601027i
$446$	0.443199	−	1.89968i	0.0209861	−	0.0899524i
$447$	−38.6207			−1.82669
$448$	−24.7389	+	4.90115i	−1.16880	+	0.231558i
$449$	−23.3987			−1.10425			−0.552126	−	0.833761i	$-0.686183\pi$
$449$	−23.3987			−1.10425			−0.552126	+	0.833761i	$0.686183\pi$
$450$	10.9571	−	46.9651i	0.516521	−	2.21396i
$451$	−9.70953	−	9.70953i	−0.457204	−	0.457204i
$452$	−10.9049	−	5.38114i	−0.512921	−	0.253108i
$453$	13.8658	−	13.8658i	0.651471	−	0.651471i
$454$	−18.5019	+	11.5019i	−0.868336	+	0.539812i
$455$		−	27.3373i		−	1.28159i
$456$	49.7627	+	40.8712i	2.33035	+	1.91397i
$457$			35.4128i			1.65654i	0.560327	+	0.828271i	$0.310675\pi$
$457$			35.4128i			1.65654i	−0.560327	+	0.828271i	$0.689325\pi$
$458$	−6.83964	−	11.0022i	−0.319595	−	0.514097i
$459$	−8.26606	+	8.26606i	−0.385826	+	0.385826i
$460$	−0.397863	−	1.17305i	−0.0185505	−	0.0546938i
$461$	−23.7122	−	23.7122i	−1.10439	−	1.10439i	−0.993875	−	0.110512i	$-0.964751\pi$
$461$	−23.7122	−	23.7122i	−1.10439	−	1.10439i	−0.110512	−	0.993875i	$-0.535249\pi$
$462$	41.9478	+	9.78649i	1.95159	+	0.455309i
$463$	6.25453			0.290672			0.145336	−	0.989382i	$-0.453574\pi$
$463$	6.25453			0.290672			0.145336	+	0.989382i	$0.453574\pi$
$464$	0.391981	−	2.96568i	0.0181973	−	0.137678i
$465$	60.5219			2.80663
$466$	−17.6192	−	4.11059i	−0.816192	−	0.190419i
$467$	4.84326	+	4.84326i	0.224119	+	0.224119i	0.810231	−	0.586111i	$-0.199342\pi$
$467$	4.84326	+	4.84326i	0.224119	+	0.224119i	−0.586111	+	0.810231i	$0.699342\pi$
$468$	34.9340	−	11.8485i	1.61482	−	0.547699i
$469$	−22.0021	+	22.0021i	−1.01596	+	1.01596i
$470$	−8.09974	−	13.0292i	−0.373613	−	0.600990i
$471$			45.4626i			2.09481i
$472$	−3.29958	−	33.6333i	−0.151875	−	1.54810i
$473$			0.832659i			0.0382857i
$474$	48.4520	−	30.1208i	2.22547	−	1.38349i
$475$	26.0742	−	26.0742i	1.19637	−	1.19637i
$476$	2.79004	−	5.65400i	0.127881	−	0.259151i
$477$	54.6705	+	54.6705i	2.50319	+	2.50319i
$478$	9.45984	−	40.5476i	0.432683	−	1.85461i
$479$	0.158545			0.00724411			0.00362205	−	0.999993i	$-0.498847\pi$
$479$	0.158545			0.00724411			0.00362205	+	0.999993i	$0.498847\pi$
$480$	−51.0213	+	23.0782i	−2.32879	+	1.05337i
$481$	5.44370			0.248211
$482$	0.806025	−	3.45486i	0.0367134	−	0.157364i
$483$	−1.35907	−	1.35907i	−0.0618397	−	0.0618397i
$484$	1.25737	−	2.54806i	0.0571533	−	0.115821i
$485$	−42.2128	+	42.2128i	−1.91679	+	1.91679i
$486$	18.8342	−	11.7085i	0.854337	−	0.531110i
$487$		−	11.5290i		−	0.522428i	−0.965281	−	0.261214i	$-0.915877\pi$
$487$		−	11.5290i		−	0.522428i	0.965281	−	0.261214i	$-0.0841228\pi$
$488$	−2.84546	+	0.279152i	−0.128808	+	0.0126366i
$489$		−	56.2928i		−	2.54565i
$490$	6.95631	+	11.1898i	0.314254	+	0.505505i
$491$	−1.48385	+	1.48385i	−0.0669653	+	0.0669653i	−0.739796	−	0.672831i	$-0.765078\pi$
$491$	−1.48385	+	1.48385i	−0.0669653	+	0.0669653i	0.672831	+	0.739796i	$0.265078\pi$
$492$	26.2312	−	8.89682i	1.18259	−	0.401100i
$493$	0.528823	+	0.528823i	0.0238170	+	0.0238170i
$494$	27.4679	+	6.40831i	1.23584	+	0.288323i
$495$	66.1982			2.97539
$496$	−14.8776	−	19.4094i	−0.668024	−	0.871507i
$497$	38.3073			1.71832
$498$	−39.7715	−	9.27878i	−1.78221	−	0.415792i
$499$	15.9819	+	15.9819i	0.715448	+	0.715448i	0.967669	−	0.252222i	$-0.0811612\pi$
$499$	15.9819	+	15.9819i	0.715448	+	0.715448i	−0.252222	+	0.967669i	$0.581161\pi$
$500$	0.113937	+	0.335928i	0.00509540	+	0.0150232i
$501$	−18.1028	+	18.1028i	−0.808772	+	0.808772i
$502$	−1.79715	−	2.89087i	−0.0802107	−	0.129026i
$503$			4.42484i			0.197294i	0.995122	+	0.0986469i	$0.0314515\pi$
$503$			4.42484i			0.197294i	−0.995122	+	0.0986469i	$0.968549\pi$
$504$	−38.1702	+	46.4742i	−1.70023	+	2.07012i
$505$		−	7.40053i		−	0.329319i
$506$	0.726018	−	0.451339i	0.0322754	−	0.0200644i
$507$	−12.1889	+	12.1889i	−0.541326	+	0.541326i
$508$	−32.5403	−	16.0574i	−1.44374	−	0.712433i
$509$	12.6621	+	12.6621i	0.561238	+	0.561238i	0.929659	−	0.368421i	$-0.120102\pi$
$509$	12.6621	+	12.6621i	0.561238	+	0.561238i	−0.368421	+	0.929659i	$0.620102\pi$
$510$	3.18069	−	13.6334i	0.140844	−	0.603696i
$511$	30.7562			1.36057
$512$	19.9433	+	10.6894i	0.881379	+	0.472410i
$513$	85.2585			3.76426
$514$	−5.91197	+	25.3404i	−0.260766	+	1.11772i
$515$	−12.1286	−	12.1286i	−0.534452	−	0.534452i
$516$	−1.50623	−	0.743271i	−0.0663083	−	0.0327207i
$517$	7.48680	−	7.48680i	0.329269	−	0.329269i
$518$	−7.53720	+	4.68560i	−0.331166	+	0.205873i
$519$		−	26.8049i		−	1.17660i
$520$	−15.5672	+	18.9539i	−0.682669	+	0.831185i
$521$			26.6970i			1.16962i	0.811172	+	0.584808i	$0.198830\pi$
$521$			26.6970i			1.16962i	−0.811172	+	0.584808i	$0.801170\pi$
$522$	−3.76625	−	6.05834i	−0.164844	−	0.265166i
$523$	2.52409	−	2.52409i	0.110371	−	0.110371i	−0.649765	−	0.760135i	$-0.725133\pi$
$523$	2.52409	−	2.52409i	0.110371	−	0.110371i	0.760135	+	0.649765i	$0.225133\pi$
$524$	−1.30812	−	3.85682i	−0.0571453	−	0.168486i
$525$	35.1821	+	35.1821i	1.53547	+	1.53547i
$526$	31.9843	+	7.46201i	1.39458	+	0.325359i
$527$	6.11385			0.266324
$528$	−23.5110	−	30.6725i	−1.02318	−	1.33485i
$529$	22.9619			0.998342
$530$	−50.0630	−	11.6798i	−2.17460	−	0.507338i
$531$	−56.9847	−	56.9847i	−2.47292	−	2.47292i
$532$	−43.5471	+	14.7699i	−1.88801	+	0.640354i
$533$	8.57879	−	8.57879i	0.371588	−	0.371588i
$534$	−13.1789	−	21.1995i	−0.570307	−	0.917390i
$535$		−	34.3184i		−	1.48371i
$536$	27.7839	−	2.72573i	1.20008	−	0.117734i
$537$			29.3792i			1.26780i
$538$	25.8860	−	16.0924i	1.11602	−	0.693791i
$539$	−6.42990	+	6.42990i	−0.276955	+	0.276955i
$540$	−32.8084	+	66.4861i	−1.41185	+	2.86110i
$541$	7.52462	+	7.52462i	0.323509	+	0.323509i	0.850111	−	0.526603i	$-0.176534\pi$
$541$	7.52462	+	7.52462i	0.323509	+	0.323509i	−0.526603	+	0.850111i	$0.676534\pi$
$542$	0.247640	−	1.06146i	0.0106371	−	0.0455935i
$543$	−25.7846			−1.10652
$544$	−5.15411	+	2.33133i	−0.220981	+	0.0999550i
$545$	14.0793			0.603090
$546$	−8.64679	+	37.0626i	−0.370048	+	1.58613i
$547$	7.10779	+	7.10779i	0.303907	+	0.303907i	0.842540	−	0.538633i	$-0.181059\pi$
$547$	7.10779	+	7.10779i	0.303907	+	0.303907i	−0.538633	+	0.842540i	$0.681059\pi$
$548$	−3.04824	+	6.17725i	−0.130214	+	0.263879i
$549$	−4.82104	+	4.82104i	−0.205757	+	0.205757i
$550$	−18.7944	+	11.6838i	−0.801396	+	0.498198i
$551$		−	5.45443i		−	0.232367i
$552$	0.168368	+	1.71621i	0.00716623	+	0.0730469i
$553$			40.7394i			1.73241i
$554$	10.1830	+	16.3803i	0.432634	+	0.695930i
$555$	−13.9342	+	13.9342i	−0.591474	+	0.591474i
$556$	8.75342	−	2.96889i	0.371228	−	0.125909i
$557$	8.57204	+	8.57204i	0.363209	+	0.363209i	0.864993	−	0.501784i	$-0.167323\pi$
$557$	8.57204	+	8.57204i	0.363209	+	0.363209i	−0.501784	+	0.864993i	$0.667323\pi$
$558$	−56.7923	−	13.2498i	−2.40421	−	0.560907i
$559$	−0.735689			−0.0311163
$560$	5.23963	−	39.6424i	0.221415	−	1.67520i
$561$	9.66169			0.407917
$562$	−0.495848	−	0.115682i	−0.0209161	−	0.00487976i
$563$	−26.7190	−	26.7190i	−1.12607	−	1.12607i	−0.990810	−	0.135263i	$-0.956812\pi$
$563$	−26.7190	−	26.7190i	−1.12607	−	1.12607i	−0.135263	−	0.990810i	$-0.543188\pi$
$564$	6.86014	+	20.2263i	0.288864	+	0.851680i
$565$	13.6336	−	13.6336i	0.573569	−	0.573569i
$566$	12.2313	+	19.6751i	0.514119	+	0.827006i
$567$			51.2520i			2.15238i
$568$	−26.5599	−	21.8142i	−1.11443	−	0.915302i
$569$			0.399988i			0.0167684i	0.999965	+	0.00838419i	$0.00266880\pi$
$569$			0.399988i			0.0167684i	−0.999965	+	0.00838419i	$0.997331\pi$
$570$	−86.7126	+	53.9060i	−3.63199	+	2.25787i
$571$	14.3078	−	14.3078i	0.598764	−	0.598764i	−0.341219	−	0.939984i	$-0.610840\pi$
$571$	14.3078	−	14.3078i	0.598764	−	0.598764i	0.939984	+	0.341219i	$0.110840\pi$
$572$	−15.1798	−	7.49069i	−0.634701	−	0.313202i
$573$	−15.9022	−	15.9022i	−0.664326	−	0.664326i
$574$	−4.49387	+	19.2620i	−0.187571	+	0.803982i
$575$	0.987464			0.0411801
$576$	52.9296	−	10.4862i	2.20540	−	0.436924i
$577$	−22.4211			−0.933404			−0.466702	−	0.884415i	$-0.654558\pi$
$577$	−22.4211			−0.933404			−0.466702	+	0.884415i	$0.654558\pi$
$578$	0.321310	−	1.37723i	0.0133647	−	0.0572852i
$579$	49.8061	+	49.8061i	2.06987	+	2.06987i
$580$	4.25346	+	2.09892i	0.176615	+	0.0871531i
$581$	20.6212	−	20.6212i	0.855513	−	0.855513i
$582$	70.5822	−	43.8783i	2.92573	−	1.81882i
$583$		−	35.4786i		−	1.46937i
$584$	−21.3244	−	17.5141i	−0.882409	−	0.724740i
$585$			58.4889i			2.41822i
$586$	−9.77561	−	15.7249i	−0.403827	−	0.649591i
$587$	−3.09883	+	3.09883i	−0.127903	+	0.127903i	−0.768160	−	0.640258i	$-0.778828\pi$
$587$	−3.09883	+	3.09883i	−0.127903	+	0.127903i	0.640258	+	0.768160i	$0.278828\pi$
$588$	−5.89170	−	17.3710i	−0.242970	−	0.716366i
$589$	−31.5300	−	31.5300i	−1.29917	−	1.29917i
$590$	52.1822	+	12.1742i	2.14831	+	0.501204i
$591$	6.60759			0.271800
$592$	7.89404	+	1.04337i	0.324443	+	0.0428824i
$593$	−12.6744			−0.520477			−0.260238	−	0.965544i	$-0.583801\pi$
$593$	−12.6744			−0.520477			−0.260238	+	0.965544i	$0.583801\pi$
$594$	−49.8295	−	11.6253i	−2.04453	−	0.476993i
$595$	7.06880	+	7.06880i	0.289793	+	0.289793i
$596$	−23.4325	+	7.94760i	−0.959834	+	0.325546i
$597$	−10.5625	+	10.5625i	−0.432296	+	0.432296i
$598$	0.398777	+	0.641468i	0.0163072	+	0.0262316i
$599$		−	20.6642i		−	0.844317i	−0.906522	−	0.422158i	$-0.861273\pi$
$599$		−	20.6642i		−	0.844317i	0.906522	−	0.422158i	$-0.138727\pi$
$600$	−4.35854	−	44.4275i	−0.177937	−	1.81375i
$601$			18.5642i			0.757251i	0.925550	+	0.378625i	$0.123603\pi$
$601$			18.5642i			0.757251i	−0.925550	+	0.378625i	$0.876397\pi$
$602$	1.01862	−	0.633235i	0.0415157	−	0.0258087i
$603$	47.0741	−	47.0741i	1.91701	−	1.91701i
$604$	5.55947	−	11.2662i	0.226212	−	0.458417i
$605$	3.18566	+	3.18566i	0.129515	+	0.129515i
$606$	−2.34079	+	10.0333i	−0.0950881	+	0.407575i
$607$	22.7887			0.924965			0.462483	−	0.886628i	$-0.346959\pi$
$607$	22.7887			0.924965			0.462483	+	0.886628i	$0.346959\pi$
$608$	38.6035	+	14.5575i	1.56558	+	0.590385i
$609$	7.35971			0.298230
$610$	1.02997	−	4.41474i	0.0417021	−	0.178747i
$611$	6.61491	+	6.61491i	0.267610	+	0.267610i
$612$	−5.96938	+	12.0969i	−0.241298	+	0.488988i
$613$	−15.4128	+	15.4128i	−0.622519	+	0.622519i	−0.946175	−	0.323656i	$-0.895088\pi$
$613$	−15.4128	+	15.4128i	−0.622519	+	0.622519i	0.323656	+	0.946175i	$0.395088\pi$
$614$	23.5004	−	14.6093i	0.948399	−	0.589585i
$615$			43.9181i			1.77095i
$616$	27.4651	−	2.69445i	1.10660	−	0.108563i
$617$		−	15.5801i		−	0.627229i	−0.949550	−	0.313615i	$-0.898460\pi$
$617$		−	15.5801i		−	0.627229i	0.949550	−	0.313615i	$-0.101540\pi$
$618$	12.6072	+	20.2798i	0.507135	+	0.815771i
$619$	−22.7035	+	22.7035i	−0.912529	+	0.912529i	−0.996471	−	0.0839414i	$-0.973249\pi$
$619$	−22.7035	+	22.7035i	−0.912529	+	0.912529i	0.0839414	+	0.996471i	$0.473249\pi$
$620$	36.7208	−	12.4546i	1.47474	−	0.500187i
$621$	1.61443	+	1.61443i	0.0647847	+	0.0647847i
$622$	38.3272	+	8.94180i	1.53678	+	0.358534i
$623$	17.8249			0.714140
$624$	27.1005	−	20.7730i	1.08489	−	0.831584i
$625$	24.7172			0.988689
$626$	22.1435	+	5.16613i	0.885034	+	0.206480i
$627$	−49.8267	−	49.8267i	−1.98989	−	1.98989i
$628$	9.35557	+	27.5838i	0.373328	+	1.10071i
$629$	−1.40762	+	1.40762i	−0.0561254	+	0.0561254i
$630$	−50.3436	−	80.9822i	−2.00574	−	3.22641i
$631$			0.0996017i			0.00396508i	0.999998	+	0.00198254i	$0.000631063\pi$
$631$			0.0996017i			0.00396508i	−0.999998	+	0.00198254i	$0.999369\pi$
$632$	23.1991	−	28.2461i	0.922810	−	1.12357i
$633$			54.8756i			2.18111i
$634$	29.3263	−	18.2311i	1.16470	−	0.724049i
$635$	40.6829	−	40.6829i	1.61445	−	1.61445i
$636$	64.1789	+	31.6699i	2.54486	+	1.25579i
$637$	−5.68109	−	5.68109i	−0.225093	−	0.225093i
$638$	−0.743732	+	3.18785i	−0.0294446	+	0.126208i
$639$	−81.9597			−3.24228
$640$	−26.2073	+	24.5018i	−1.03593	+	0.968519i
$641$	−5.28531			−0.208757			−0.104379	−	0.994538i	$-0.533285\pi$
$641$	−5.28531			−0.208757			−0.104379	+	0.994538i	$0.533285\pi$
$642$	−10.8549	+	46.5273i	−0.428409	+	1.83629i
$643$	9.91275	+	9.91275i	0.390921	+	0.390921i	0.875016	−	0.484095i	$-0.160851\pi$
$643$	9.91275	+	9.91275i	0.390921	+	0.390921i	−0.484095	+	0.875016i	$0.660851\pi$
$644$	−1.10427	−	0.544917i	−0.0435144	−	0.0214727i
$645$	1.88314	−	1.88314i	0.0741485	−	0.0741485i
$646$	−8.75961	+	5.44553i	−0.344642	+	0.214251i
$647$		−	43.1203i		−	1.69523i	−0.530609	−	0.847617i	$-0.678037\pi$
$647$		−	43.1203i		−	1.69523i	0.530609	−	0.847617i	$-0.321963\pi$
$648$	29.1856	−	35.5349i	1.14652	−	1.39594i
$649$			36.9804i			1.45161i
$650$	−10.3231	−	16.6057i	−0.404906	−	0.651327i
$651$	42.5438	−	42.5438i	1.66742	−	1.66742i
$652$	−11.5843	−	34.1548i	−0.453675	−	1.33761i
$653$	−21.7617	−	21.7617i	−0.851603	−	0.851603i	0.138728	−	0.990331i	$-0.455699\pi$
$653$	−21.7617	−	21.7617i	−0.851603	−	0.851603i	−0.990331	+	0.138728i	$0.955699\pi$
$654$	−19.0880	−	4.45328i	−0.746402	−	0.174137i
$655$	6.45737			0.252310
$656$	14.0846	−	10.7960i	0.549910	−	0.421514i
$657$	−65.8038			−2.56725
$658$	−14.8525	−	3.46512i	−0.579011	−	0.135085i
$659$	15.3572	+	15.3572i	0.598231	+	0.598231i	0.939842	−	0.341610i	$-0.110972\pi$
$659$	15.3572	+	15.3572i	0.598231	+	0.598231i	−0.341610	+	0.939842i	$0.610972\pi$
$660$	58.0296	−	19.6819i	2.25880	−	0.766116i
$661$	−27.0072	+	27.0072i	−1.05046	+	1.05046i	−0.0517992	+	0.998658i	$0.516496\pi$
$661$	−27.0072	+	27.0072i	−1.05046	+	1.05046i	−0.998658	+	0.0517992i	$0.983504\pi$
$662$	−9.65153	−	15.5253i	−0.375117	−	0.603410i
$663$			8.53651i			0.331531i
$664$	−26.0402	+	2.55466i	−1.01056	+	0.0991402i
$665$		−	72.9097i		−	2.82732i
$666$	16.1261	−	10.0250i	0.624873	−	0.388460i
$667$	0.103283	−	0.103283i	0.00399915	−	0.00399915i
$668$	−7.25829	+	14.7089i	−0.280832	+	0.569104i
$669$	−3.04471	−	3.04471i	−0.117715	−	0.117715i
$670$	−10.0569	+	43.1068i	−0.388532	+	1.66536i
$671$	3.12863			0.120779
$672$	−19.6426	+	52.0881i	−0.757728	+	2.00934i
$673$	32.3134			1.24559			0.622796	−	0.782385i	$-0.285997\pi$
$673$	32.3134			1.24559			0.622796	+	0.782385i	$0.285997\pi$
$674$	−3.69232	+	15.8264i	−0.142223	+	0.609609i
$675$	−41.7926	−	41.7926i	−1.60860	−	1.60860i
$676$	−4.88712	+	9.90371i	−0.187966	+	0.380912i
$677$	1.35165	−	1.35165i	0.0519483	−	0.0519483i	−0.680655	−	0.732604i	$-0.738305\pi$
$677$	1.35165	−	1.35165i	0.0519483	−	0.0519483i	0.732604	+	0.680655i	$0.238305\pi$
$678$	−22.7961	+	14.1715i	−0.875479	+	0.544253i
$679$			59.3469i			2.27752i
$680$	−0.875719	−	8.92640i	−0.0335823	−	0.342312i
$681$			48.0885i			1.84276i
$682$	14.1285	+	22.7270i	0.541010	+	0.870263i
$683$	−22.3416	+	22.3416i	−0.854879	+	0.854879i	−0.990729	−	0.135850i	$-0.956623\pi$
$683$	−22.3416	+	22.3416i	−0.854879	+	0.854879i	0.135850	+	0.990729i	$0.456623\pi$
$684$	93.1705	−	31.6006i	3.56246	−	1.20828i
$685$	−7.72298	−	7.72298i	−0.295080	−	0.295080i
$686$	−17.6358	−	4.11447i	−0.673338	−	0.157091i
$687$	−28.5959			−1.09100
$688$	−1.06684	−	0.141007i	−0.0406729	−	0.00537583i
$689$	31.3469			1.19422
$690$	−2.66271	−	0.621215i	−0.101368	−	0.0236493i
$691$	−7.97997	−	7.97997i	−0.303572	−	0.303572i	0.538838	−	0.842410i	$-0.318864\pi$
$691$	−7.97997	−	7.97997i	−0.303572	−	0.303572i	−0.842410	+	0.538838i	$0.818864\pi$
$692$	−5.51608	−	16.2635i	−0.209690	−	0.618245i
$693$	46.5339	−	46.5339i	1.76768	−	1.76768i
$694$	−21.6930	−	34.8951i	−0.823455	−	1.32460i
$695$			14.6556i			0.555918i
$696$	−5.10276	−	4.19100i	−0.193419	−	0.158859i
$697$			4.43656i			0.168047i
$698$	−10.4432	+	6.49217i	−0.395282	+	0.245732i
$699$	−28.2391	+	28.2391i	−1.06810	+	1.06810i
$700$	28.5862	+	14.1062i	1.08046	+	0.533166i
$701$	−32.1528	−	32.1528i	−1.21439	−	1.21439i	−0.969567	−	0.244827i	$-0.921269\pi$
$701$	−32.1528	−	32.1528i	−1.21439	−	1.21439i	−0.244827	−	0.969567i	$-0.578731\pi$
$702$	10.2715	−	44.0265i	0.387671	−	1.66167i
$703$	14.5186			0.547579
$704$	−20.5769	−	13.7719i	−0.775522	−	0.519048i
$705$	−33.8643			−1.27540
$706$	0.948055	−	4.06364i	0.0356805	−	0.152937i
$707$	−5.20219	−	5.20219i	−0.195648	−	0.195648i
$708$	−66.8955	−	33.0105i	−2.51409	−	1.24061i
$709$	12.3116	−	12.3116i	0.462371	−	0.462371i	−0.437061	−	0.899432i	$-0.643981\pi$
$709$	12.3116	−	12.3116i	0.462371	−	0.462371i	0.899432	+	0.437061i	$0.143981\pi$
$710$	46.2811	−	28.7713i	1.73690	−	1.07977i
$711$		−	87.1632i		−	3.26887i
$712$	−12.3587	−	10.1504i	−0.463161	−	0.380403i
$713$		−	1.19408i		−	0.0447188i
$714$	−7.34770	−	11.8194i	−0.274981	−	0.442331i
$715$	18.9783	−	18.9783i	0.709748	−	0.709748i
$716$	6.04582	+	17.8254i	0.225943	+	0.666166i
$717$	−64.9876	−	64.9876i	−2.42701	−	2.42701i
$718$	14.4044	+	3.36058i	0.537568	+	0.125416i
$719$	20.4330			0.762023			0.381012	−	0.924570i	$-0.375576\pi$
$719$	20.4330			0.762023			0.381012	+	0.924570i	$0.375576\pi$
$720$	−11.2104	+	84.8162i	−0.417785	+	3.16091i
$721$	−17.0516			−0.635035
$722$	47.0906	+	10.9863i	1.75253	+	0.408869i
$723$	−5.53726	−	5.53726i	−0.205933	−	0.205933i
$724$	−15.6444	+	5.30611i	−0.581420	+	0.197200i
$725$	−2.67369	+	2.67369i	−0.0992984	+	0.0992984i
$726$	−3.31135	−	5.32660i	−0.122896	−	0.197688i
$727$			3.57951i			0.132757i	0.997795	+	0.0663783i	$0.0211444\pi$
$727$			3.57951i			0.132757i	−0.997795	+	0.0663783i	$0.978856\pi$
$728$	2.38066	+	24.2666i	0.0882332	+	0.899380i
$729$		−	0.178903i		−	0.00662603i
$730$	37.1582	−	23.0999i	1.37529	−	0.854964i
$731$	0.190233	−	0.190233i	0.00703601	−	0.00703601i
$732$	−2.79276	+	5.65952i	−0.103224	+	0.209182i
$733$	−13.5154	−	13.5154i	−0.499203	−	0.499203i	0.411987	−	0.911190i	$-0.364835\pi$
$733$	−13.5154	−	13.5154i	−0.499203	−	0.499203i	−0.911190	+	0.411987i	$0.864835\pi$
$734$	−0.802017	+	3.43768i	−0.0296030	+	0.126887i
$735$	29.0837			1.07277
$736$	0.455328	+	1.00664i	0.0167836	+	0.0371052i
$737$	−30.5489			−1.12528
$738$	9.61478	−	41.2117i	0.353925	−	1.51702i
$739$	14.7493	+	14.7493i	0.542563	+	0.542563i	0.924280	−	0.381716i	$-0.124667\pi$
$739$	14.7493	+	14.7493i	0.542563	+	0.542563i	−0.381716	+	0.924280i	$0.624667\pi$
$740$	−5.58691	+	11.3218i	−0.205379	+	0.416199i
$741$	44.0240	−	44.0240i	1.61726	−	1.61726i
$742$	−43.4020	+	26.9814i	−1.59334	+	0.990519i
$743$		−	32.8200i		−	1.20405i	−0.798478	−	0.602024i	$-0.794361\pi$
$743$		−	32.8200i		−	1.20405i	0.798478	−	0.602024i	$-0.205639\pi$
$744$	−53.7238	+	5.27054i	−1.96961	+	0.193227i
$745$		−	39.2324i		−	1.43736i
$746$	7.26743	+	11.6903i	0.266079	+	0.428013i
$747$	−44.1198	+	44.1198i	−1.61426	+	1.61426i
$748$	5.86209	−	1.98824i	0.214339	−	0.0726973i
$749$	−24.1240	−	24.1240i	−0.881473	−	0.881473i
$750$	0.762524	+	0.177898i	0.0278434	+	0.00649593i
$751$	−11.1026			−0.405140			−0.202570	−	0.979268i	$-0.564929\pi$
$751$	−11.1026			−0.405140			−0.202570	+	0.979268i	$0.564929\pi$
$752$	8.32458	+	10.8603i	0.303566	+	0.396034i
$753$	−7.51371			−0.273815
$754$	−2.81660	−	0.657119i	−0.102575	−	0.0239309i
$755$	14.0854	+	14.0854i	0.512620	+	0.512620i
$756$	23.6736	+	69.7989i	0.861002	+	2.53856i
$757$	−27.9594	+	27.9594i	−1.01620	+	1.01620i	−0.0163346	+	0.999867i	$0.505200\pi$
$757$	−27.9594	+	27.9594i	−1.01620	+	1.01620i	−0.999867	+	0.0163346i	$0.994800\pi$
$758$	6.59957	+	10.6160i	0.239707	+	0.385590i
$759$		−	1.88701i		−	0.0684940i
$760$	−41.5185	+	50.5509i	−1.50603	+	1.83368i
$761$			23.3144i			0.845145i	0.906329	+	0.422572i	$0.138873\pi$
$761$			23.3144i			0.845145i	−0.906329	+	0.422572i	$0.861127\pi$
$762$	−68.0240	+	42.2880i	−2.46425	+	1.53193i
$763$	9.89700	−	9.89700i	0.358296	−	0.358296i
$764$	−12.9209	−	6.37599i	−0.467462	−	0.230675i
$765$	−15.1239	−	15.1239i	−0.546807	−	0.546807i
$766$	−2.68437	+	11.5060i	−0.0969903	+	0.415728i
$767$	−32.6738			−1.17978
$768$	43.2805	−	24.9291i	1.56175	−	0.899551i
$769$	35.7148			1.28791			0.643955	−	0.765064i	$-0.277293\pi$
$769$	35.7148			1.28791			0.643955	+	0.765064i	$0.277293\pi$
$770$	−9.94150	+	42.6122i	−0.358267	+	1.53564i
$771$	40.6143	+	40.6143i	1.46269	+	1.46269i
$772$	40.4686	+	19.9697i	1.45650	+	0.718727i
$773$	−29.5816	+	29.5816i	−1.06398	+	1.06398i	−0.0661665	+	0.997809i	$0.521077\pi$
$773$	−29.5816	+	29.5816i	−1.06398	+	1.06398i	−0.997809	+	0.0661665i	$0.978923\pi$
$774$	−2.17936	+	1.35483i	−0.0783355	+	0.0486983i
$775$			30.9112i			1.11036i
$776$	33.7952	−	41.1474i	1.21318	−	1.47710i
$777$			19.5901i			0.702789i
$778$	−14.2213	−	22.8763i	−0.509859	−	0.820154i
$779$	22.8800	−	22.8800i	0.819761	−	0.819761i
$780$	17.3898	+	51.2716i	0.622654	+	1.83582i
$781$	26.5940	+	26.5940i	0.951609	+	0.951609i
$782$	−0.268984	−	0.0627545i	−0.00961884	−	0.00224410i
$783$	−8.74255			−0.312433
$784$	−7.14940	−	9.32715i	−0.255336	−	0.333112i
$785$	−46.1827			−1.64833
$786$	−8.75461	−	2.04247i	−0.312266	−	0.0728524i
$787$	−10.5768	−	10.5768i	−0.377023	−	0.377023i	0.493004	−	0.870027i	$-0.335899\pi$
$787$	−10.5768	−	10.5768i	−0.377023	−	0.377023i	−0.870027	+	0.493004i	$0.835899\pi$
$788$	4.00906	−	1.35975i	0.142817	−	0.0484391i
$789$	51.2628	−	51.2628i	1.82500	−	1.82500i
$790$	30.5979	+	49.2194i	1.08862	+	1.75115i
$791$		−	19.1674i		−	0.681514i
$792$	−58.7625	+	5.76486i	−2.08803	+	0.204845i
$793$			2.76428i			0.0981624i
$794$	−28.4766	+	17.7028i	−1.01060	+	0.628250i
$795$	−80.2384	+	80.2384i	−2.84576	+	2.84576i
$796$	−4.23505	+	8.58230i	−0.150107	+	0.304191i
$797$	20.4390	+	20.4390i	0.723987	+	0.723987i	0.969415	−	0.245428i	$-0.0789284\pi$
$797$	20.4390	+	20.4390i	0.723987	+	0.723987i	−0.245428	+	0.969415i	$0.578928\pi$
$798$	−23.0614	+	98.8476i	−0.816363	+	3.49917i
$799$	−3.42093			−0.121024
$800$	−11.7871	−	26.0588i	−0.416735	−	0.921319i
$801$	−38.1370			−1.34750
$802$	−1.58097	+	6.77650i	−0.0558260	+	0.239286i
$803$	21.3518	+	21.3518i	0.753489	+	0.753489i
$804$	27.2694	−	55.2613i	0.961718	−	1.94892i
$805$	1.38059	−	1.38059i	0.0486595	−	0.0486595i
$806$	−20.0803	+	12.4832i	−0.707298	+	0.439701i
$807$		−	67.2807i		−	2.36839i
$808$	0.644474	+	6.56926i	0.0226725	+	0.231106i
$809$		−	34.1334i		−	1.20007i	−0.799975	−	0.600033i	$-0.795154\pi$
$809$		−	34.1334i		−	1.20007i	0.799975	−	0.600033i	$-0.204846\pi$
$810$	38.4936	+	61.9203i	1.35253	+	2.17566i
$811$	36.4632	−	36.4632i	1.28040	−	1.28040i	0.339954	−	0.940442i	$-0.389589\pi$
$811$	36.4632	−	36.4632i	1.28040	−	1.28040i	0.940442	−	0.339954i	$-0.110411\pi$
$812$	4.46540	−	1.51453i	0.156705	−	0.0531494i
$813$	−1.70125	−	1.70125i	−0.0596654	−	0.0596654i
$814$	−8.48541	−	1.97966i	−0.297414	−	0.0693872i
$815$	57.1844			2.00308
$816$	−1.63616	+	12.3790i	−0.0572771	+	0.433352i
$817$	−1.96212			−0.0686457
$818$	−13.5303	−	3.15665i	−0.473076	−	0.110370i
$819$	41.1147	+	41.1147i	1.43666	+	1.43666i
$820$	9.03774	+	26.6467i	0.315612	+	0.930543i
$821$	−0.574860	+	0.574860i	−0.0200627	+	0.0200627i	−0.717067	−	0.697004i	$-0.754516\pi$
$821$	−0.574860	+	0.574860i	−0.0200627	+	0.0200627i	0.697004	+	0.717067i	$0.254516\pi$
$822$	8.02769	+	12.9133i	0.279998	+	0.450401i
$823$			5.47126i			0.190716i	0.995443	+	0.0953581i	$0.0303996\pi$
$823$			5.47126i			0.190716i	−0.995443	+	0.0953581i	$0.969600\pi$
$824$	11.8225	+	9.71007i	0.411857	+	0.338266i
$825$			48.8488i			1.70070i
$826$	45.2392	−	28.1235i	1.57407	−	0.978543i
$827$	−22.6045	+	22.6045i	−0.786036	+	0.786036i	−0.980842	−	0.194806i	$-0.937592\pi$
$827$	−22.6045	+	22.6045i	−0.786036	+	0.786036i	0.194806	+	0.980842i	$0.437592\pi$
$828$	2.36262	+	1.16587i	0.0821068	+	0.0405167i
$829$	33.2285	+	33.2285i	1.15407	+	1.15407i	0.985728	+	0.168345i	$0.0538423\pi$
$829$	33.2285	+	33.2285i	1.15407	+	1.15407i	0.168345	+	0.985728i	$0.446158\pi$
$830$	9.42575	−	40.4015i	0.327172	−	1.40236i
$831$	42.5742			1.47688
$832$	12.1681	−	18.1806i	0.421851	−	0.630299i
$833$	2.93800			0.101796
$834$	4.63557	−	19.8694i	0.160517	−	0.688021i
$835$	−18.3895	−	18.3895i	−0.636395	−	0.636395i
$836$	−40.4853	−	19.9780i	−1.40021	−	0.690954i
$837$	−50.5375	+	50.5375i	−1.74683	+	1.74683i
$838$	−12.6897	+	7.88871i	−0.438358	+	0.272511i
$839$		−	0.690285i		−	0.0238313i	−0.999929	−	0.0119156i	$-0.996207\pi$
$839$		−	0.690285i		−	0.0238313i	0.999929	−	0.0119156i	$-0.00379296\pi$
$840$	−68.2088	−	56.0213i	−2.35343	−	1.93292i
$841$		−	28.4407i		−	0.980714i
$842$	−6.52201	−	10.4912i	−0.224763	−	0.361552i
$843$	−0.794719	+	0.794719i	−0.0273716	+	0.0273716i
$844$	11.2926	+	33.2949i	0.388708	+	1.14606i
$845$	−12.3819	−	12.3819i	−0.425951	−	0.425951i
$846$	31.7774	+	7.41374i	1.09253	+	0.254890i
$847$	4.47871			0.153890
$848$	45.4568	+	6.00814i	1.56099	+	0.206320i
$849$	51.1379			1.75505
$850$	6.96317	+	1.62452i	0.238835	+	0.0557207i
$851$	0.274919	+	0.274919i	0.00942411	+	0.00942411i
$852$	−71.8462	+	24.3680i	−2.46141	+	0.834835i
$853$	−17.3394	+	17.3394i	−0.593690	+	0.593690i	−0.938626	−	0.344936i	$-0.887901\pi$
$853$	−17.3394	+	17.3394i	−0.593690	+	0.593690i	0.344936	+	0.938626i	$0.387901\pi$
$854$	−2.37932	−	3.82734i	−0.0814186	−	0.130969i
$855$			155.993i			5.33483i
$856$	2.98861	+	30.4635i	0.102149	+	1.04122i
$857$		−	19.7972i		−	0.676261i	−0.941099	−	0.338130i	$-0.890206\pi$
$857$		−	19.7972i		−	0.676261i	0.941099	−	0.338130i	$-0.109794\pi$
$858$	−31.7328	+	19.7271i	−1.08334	+	0.673472i
$859$	−32.1358	+	32.1358i	−1.09646	+	1.09646i	−0.101640	+	0.994821i	$0.532409\pi$
$859$	−32.1358	+	32.1358i	−1.09646	+	1.09646i	−0.994821	+	0.101640i	$0.967591\pi$
$860$	0.755044	−	1.53009i	0.0257468	−	0.0521757i
$861$	30.8722	+	30.8722i	1.05212	+	1.05212i
$862$	−0.506300	+	2.17015i	−0.0172446	+	0.0739155i
$863$	40.3820			1.37462			0.687309	−	0.726365i	$-0.258792\pi$
$863$	40.3820			1.37462			0.687309	+	0.726365i	$0.258792\pi$
$864$	23.3333	−	61.8751i	0.793814	−	2.10503i
$865$	27.2295			0.925830
$866$	−11.5931	+	49.6916i	−0.393951	+	1.68859i
$867$	−2.20735	−	2.20735i	−0.0749655	−	0.0749655i
$868$	17.0579	−	34.5677i	0.578983	−	1.17330i
$869$	−28.2824	+	28.2824i	−0.959416	+	0.959416i
$870$	8.89166	−	5.52761i	0.301456	−	0.187404i
$871$		−	26.9913i		−	0.914564i
$872$	−12.4978	+	1.22609i	−0.423230	+	0.0415207i
$873$		−	126.975i		−	4.29744i
$874$	1.06356	+	1.71082i	0.0359753	+	0.0578695i
$875$	−0.395363	+	0.395363i	−0.0133657	+	0.0133657i
$876$	−57.6839	+	19.5646i	−1.94896	+	0.661027i
$877$	−36.0783	−	36.0783i	−1.21828	−	1.21828i	−0.968235	−	0.250041i	$-0.919556\pi$
$877$	−36.0783	−	36.0783i	−1.21828	−	1.21828i	−0.250041	−	0.968235i	$-0.580444\pi$
$878$	37.5397	+	8.75808i	1.26690	+	0.295571i
$879$	−40.8709			−1.37854
$880$	31.1584	−	23.8834i	1.05035	−	0.805108i
$881$	2.81462			0.0948268			0.0474134	−	0.998875i	$-0.484902\pi$
$881$	2.81462			0.0948268			0.0474134	+	0.998875i	$0.484902\pi$
$882$	−27.2914	−	6.36715i	−0.918951	−	0.214393i
$883$	−33.5224	−	33.5224i	−1.12812	−	1.12812i	−0.990483	−	0.137634i	$-0.956050\pi$
$883$	−33.5224	−	33.5224i	−1.12812	−	1.12812i	−0.137634	−	0.990483i	$-0.543950\pi$
$884$	1.75670	+	5.17941i	0.0590841	+	0.174202i
$885$	83.6348	−	83.6348i	2.81135	−	2.81135i
$886$	−3.06283	−	4.92684i	−0.102898	−	0.165520i
$887$			39.8759i			1.33890i	0.742856	+	0.669452i	$0.233471\pi$
$887$			39.8759i			1.33890i	−0.742856	+	0.669452i	$0.766529\pi$
$888$	11.1556	−	13.5825i	0.374357	−	0.455799i
$889$		−	57.1959i		−	1.91829i
$890$	21.5352	−	13.3877i	0.721863	−	0.448755i
$891$	−35.5806	+	35.5806i	−1.19200	+	1.19200i
$892$	−2.47389	−	1.22077i	−0.0828320	−	0.0408745i
$893$	17.6422	+	17.6422i	0.590375	+	0.590375i
$894$	−12.4092	+	53.1895i	−0.415026	+	1.77892i
$895$	−29.8445			−0.997592
$896$	−1.19883	+	35.6459i	−0.0400503	+	1.19084i
$897$	1.66725			0.0556678
$898$	−7.51823	+	32.2253i	−0.250887	+	1.07537i
$899$	3.23314	+	3.23314i	0.107831	+	0.107831i
$900$	−61.1611	−	30.1808i	−2.03870	−	1.00603i
$901$	−8.10559	+	8.10559i	−0.270036	+	0.270036i
$902$	−16.4920	+	10.2525i	−0.549124	+	0.341370i
$903$		−	2.64750i		−	0.0881033i
$904$	−10.9149	+	13.2895i	−0.363024	+	0.442001i
$905$		−	26.1930i		−	0.870684i
$906$	−14.6411	−	23.5515i	−0.486419	−	0.782448i
$907$	15.3636	−	15.3636i	0.510141	−	0.510141i	−0.404428	−	0.914570i	$-0.632530\pi$
$907$	15.3636	−	15.3636i	0.510141	−	0.510141i	0.914570	+	0.404428i	$0.132530\pi$
$908$	9.89594	+	29.1770i	0.328408	+	0.968273i
$909$	11.1302	+	11.1302i	0.369167	+	0.369167i
$910$	−37.6497	−	8.78374i	−1.24807	−	0.291178i
$911$	−53.5523			−1.77427			−0.887134	−	0.461512i	$-0.847307\pi$
$911$	−53.5523			−1.77427			−0.887134	+	0.461512i	$0.847307\pi$
$912$	72.2782	−	55.4024i	2.39337	−	1.83456i
$913$	28.6317			0.947570
$914$	48.7716	+	11.3785i	1.61322	+	0.376368i
$915$	−7.07571	−	7.07571i	−0.233916	−	0.233916i
$916$	−17.3501	+	5.88464i	−0.573265	+	0.194434i
$917$	4.53919	−	4.53919i	0.149897	−	0.149897i
$918$	8.72828	+	14.0402i	0.288076	+	0.463396i
$919$		−	56.9562i		−	1.87881i	−0.342807	−	0.939406i	$-0.611378\pi$
$919$		−	56.9562i		−	1.87881i	0.342807	−	0.939406i	$-0.388622\pi$
$920$	−1.74340	+	0.171035i	−0.0574781	+	0.00563886i
$921$		−	61.0803i		−	2.01266i
$922$	−40.2761	+	25.0382i	−1.32642	+	0.824588i
$923$	−23.4970	+	23.4970i	−0.773412	+	0.773412i
$924$	26.9565	−	54.6272i	0.886803	−	1.79710i
$925$	−7.11682	−	7.11682i	−0.234000	−	0.234000i
$926$	2.00964	−	8.61391i	0.0660410	−	0.283071i
$927$	36.4825			1.19824
$928$	−3.95847	−	1.49275i	−0.129943	−	0.0490019i
$929$	42.6890			1.40058			0.700290	−	0.713858i	$-0.253054\pi$
$929$	42.6890			1.40058			0.700290	+	0.713858i	$0.253054\pi$
$930$	19.4463	−	83.3525i	0.637669	−	2.73324i
$931$	−15.1517	−	15.1517i	−0.496577	−	0.496577i
$932$	−11.3224	+	22.9448i	−0.370879	+	0.751584i
$933$	61.4288	−	61.4288i	2.01109	−	2.01109i
$934$	8.22647	−	5.11409i	0.269178	−	0.167338i
$935$			9.81472i			0.320976i
$936$	−5.09350	−	51.9192i	−0.166486	−	1.69703i
$937$			17.3653i			0.567299i	0.958928	+	0.283650i	$0.0915453\pi$
$937$			17.3653i			0.567299i	−0.958928	+	0.283650i	$0.908455\pi$
$938$	23.2324	+	37.3714i	0.758564	+	1.22022i
$939$	35.4905	−	35.4905i	1.15819	−	1.15819i
$940$	−20.5467	+	6.96880i	−0.670158	+	0.227297i
$941$	27.6766	+	27.6766i	0.902232	+	0.902232i	0.995629	−	0.0933974i	$-0.0297727\pi$
$941$	27.6766	+	27.6766i	0.902232	+	0.902232i	−0.0933974	+	0.995629i	$0.529773\pi$
$942$	62.6124	+	14.6076i	2.04002	+	0.475941i
$943$	0.866496			0.0282170
$944$	−47.3810	−	6.26246i	−1.54212	−	0.203826i
$945$	−116.862			−3.80153
$946$	1.14676	+	0.267542i	0.0372844	+	0.00869853i
$947$	27.5448	+	27.5448i	0.895084	+	0.895084i	0.994996	−	0.0999118i	$-0.0318561\pi$
$947$	27.5448	+	27.5448i	0.895084	+	0.895084i	−0.0999118	+	0.994996i	$0.531856\pi$
$948$	−25.9151	−	76.4076i	−0.841684	−	2.48160i
$949$	−18.8652	+	18.8652i	−0.612391	+	0.612391i
$950$	−27.5322	−	44.2880i	−0.893263	−	1.43689i
$951$		−	76.2225i		−	2.47168i
$952$	−6.89038	−	5.65921i	−0.223319	−	0.183416i
$953$			38.9899i			1.26301i	0.775374	+	0.631503i	$0.217562\pi$
$953$			38.9899i			1.26301i	−0.775374	+	0.631503i	$0.782438\pi$
$954$	92.8600	−	57.7276i	3.00645	−	1.86900i
$955$	16.1541	−	16.1541i	0.522735	−	0.522735i
$956$	−52.8038	−	26.0567i	−1.70780	−	0.842735i
$957$	5.10932	+	5.10932i	0.165161	+	0.165161i
$958$	0.0509422	−	0.218353i	0.00164587	−	0.00705466i
$959$	−10.8577			−0.350614
$960$	15.3903	+	77.6832i	0.496719	+	2.50722i
$961$	6.37921			0.205781
$962$	1.74912	−	7.49722i	0.0563938	−	0.241720i
$963$	51.6141	+	51.6141i	1.66324	+	1.66324i
$964$	−4.49915	−	2.22016i	−0.144908	−	0.0715066i
$965$	−50.5950	+	50.5950i	−1.62871	+	1.62871i
$966$	−2.30843	+	1.43506i	−0.0742725	+	0.0461724i
$967$		−	47.3576i		−	1.52292i	−0.648212	−	0.761460i	$-0.724483\pi$
$967$		−	47.3576i		−	1.52292i	0.648212	−	0.761460i	$-0.275517\pi$
$968$	−3.10525	−	2.55041i	−0.0998065	−	0.0819731i
$969$			22.7673i			0.731389i
$970$	44.5733	+	71.7002i	1.43116	+	2.30215i
$971$	−29.2058	+	29.2058i	−0.937258	+	0.937258i	−0.998145	−	0.0608866i	$-0.980607\pi$
$971$	−29.2058	+	29.2058i	−0.937258	+	0.937258i	0.0608866	+	0.998145i	$0.480607\pi$
$972$	−10.0737	−	29.7011i	−0.323114	−	0.952663i
$973$	10.3021	+	10.3021i	0.330271	+	0.330271i
$974$	−15.8780	−	3.70438i	−0.508765	−	0.118696i
$975$	−43.1600			−1.38223
$976$	−0.529819	+	4.00854i	−0.0169591	+	0.128310i
$977$	41.9415			1.34183			0.670914	−	0.741535i	$-0.265902\pi$
$977$	41.9415			1.34183			0.670914	+	0.741535i	$0.265902\pi$
$978$	−77.5281	−	18.0874i	−2.47907	−	0.578373i
$979$	12.3746	+	12.3746i	0.395493	+	0.395493i
$980$	17.6461	−	5.98502i	0.563684	−	0.191184i
$981$	−21.1750	+	21.1750i	−0.676064	+	0.676064i
$982$	1.56683	+	2.52038i	0.0499995	+	0.0804286i
$983$			38.0487i			1.21357i	0.794867	+	0.606783i	$0.207540\pi$
$983$			38.0487i			1.21357i	−0.794867	+	0.606783i	$0.792460\pi$
$984$	−3.82460	−	38.9850i	−0.121924	−	1.24280i
$985$			6.71225i			0.213870i
$986$	0.898226	−	0.558394i	0.0286053	−	0.0177829i
$987$	−23.8048	+	23.8048i	−0.757716	+	0.757716i
$988$	17.6514	−	35.7705i	0.561566	−	1.13801i
$989$	−0.0371540	−	0.0371540i	−0.00118143	−	0.00118143i
$990$	21.2702	−	91.1701i	0.676010	−	2.89758i
$991$	54.1271			1.71940			0.859702	−	0.510796i	$-0.170649\pi$
$991$	54.1271			1.71940			0.859702	+	0.510796i	$0.170649\pi$
$992$	−31.5115	+	14.2534i	−1.00049	+	0.452547i
$993$	−40.3522			−1.28054
$994$	12.3085	−	52.7580i	0.390403	−	1.67338i
$995$	−10.7298	−	10.7298i	−0.340159	−	0.340159i
$996$	−25.5580	+	51.7931i	−0.809836	+	1.64113i
$997$	−11.4688	+	11.4688i	−0.363221	+	0.363221i	−0.864998	−	0.501776i	$-0.832680\pi$
$997$	−11.4688	+	11.4688i	−0.363221	+	0.363221i	0.501776	+	0.864998i	$0.332680\pi$
$998$	27.1459	−	16.8756i	0.859288	−	0.534187i
$999$		−	23.2709i		−	0.736259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.b.205.9	yes	30
4.3	odd	2		1088.2.l.b.273.15		30
16.5	even	4	inner	272.2.l.b.69.9	✓	30
16.11	odd	4		1088.2.l.b.817.15		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.b.69.9	✓	30	16.5	even	4	inner
272.2.l.b.205.9	yes	30	1.1	even	1	trivial
1088.2.l.b.273.15		30	4.3	odd	2
1088.2.l.b.817.15		30	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.321310 - 1.37723i) q^{2} +(-2.20735 - 2.20735i) q^{3} +(-1.79352 - 0.885036i) q^{4} +(2.24231 - 2.24231i) q^{5} +(-3.74927 + 2.33078i) q^{6} -3.15246i q^{7} +(-1.79517 + 2.18572i) q^{8} +6.74479i q^{9} +(-2.36770 - 3.80866i) q^{10} +(2.18853 - 2.18853i) q^{11} +(2.00534 + 5.91251i) q^{12} +(1.93366 + 1.93366i) q^{13} +(-4.34166 - 1.01292i) q^{14} -9.89914 q^{15} +(2.43342 + 3.17466i) q^{16} -1.00000 q^{17} +(9.28912 + 2.16717i) q^{18} +(5.15715 + 5.15715i) q^{19} +(-6.00616 + 2.03710i) q^{20} +(-6.95858 + 6.95858i) q^{21} +(-2.31091 - 3.71730i) q^{22} +0.195308i q^{23} +(8.78721 - 0.862065i) q^{24} -5.05593i q^{25} +(3.28439 - 2.04178i) q^{26} +(8.26606 - 8.26606i) q^{27} +(-2.79004 + 5.65400i) q^{28} +(-0.528823 - 0.528823i) q^{29} +(-3.18069 + 13.6334i) q^{30} -6.11385 q^{31} +(5.15411 - 2.33133i) q^{32} -9.66169 q^{33} +(-0.321310 + 1.37723i) q^{34} +(-7.06880 - 7.06880i) q^{35} +(5.96938 - 12.0969i) q^{36} +(1.40762 - 1.40762i) q^{37} +(8.75961 - 5.44553i) q^{38} -8.53651i q^{39} +(0.875719 + 8.92640i) q^{40} -4.43656i q^{41} +(7.34770 + 11.8194i) q^{42} +(-0.190233 + 0.190233i) q^{43} +(-5.86209 + 1.98824i) q^{44} +(15.1239 + 15.1239i) q^{45} +(0.268984 + 0.0627545i) q^{46} +3.42093 q^{47} +(1.63616 - 12.3790i) q^{48} -2.93800 q^{49} +(-6.96317 - 1.62452i) q^{50} +(2.20735 + 2.20735i) q^{51} +(-1.75670 - 5.17941i) q^{52} +(8.10559 - 8.10559i) q^{53} +(-8.72828 - 14.0402i) q^{54} -9.81472i q^{55} +(6.89038 + 5.65921i) q^{56} -22.7673i q^{57} +(-0.898226 + 0.558394i) q^{58} +(-8.44870 + 8.44870i) q^{59} +(17.7543 + 8.76109i) q^{60} +(0.714780 + 0.714780i) q^{61} +(-1.96444 + 8.42018i) q^{62} +21.2627 q^{63} +(-1.55471 - 7.84748i) q^{64} +8.67172 q^{65} +(-3.10440 + 13.3064i) q^{66} +(-6.97933 - 6.97933i) q^{67} +(1.79352 + 0.885036i) q^{68} +(0.431113 - 0.431113i) q^{69} +(-12.0066 + 7.46408i) q^{70} +12.1516i q^{71} +(-14.7422 - 12.1081i) q^{72} +9.75624i q^{73} +(-1.48633 - 2.39089i) q^{74} +(-11.1602 + 11.1602i) q^{75} +(-4.68518 - 13.8137i) q^{76} +(-6.89924 - 6.89924i) q^{77} +(-11.7567 - 2.74287i) q^{78} -12.9230 q^{79} +(12.5751 + 1.66208i) q^{80} -16.2578 q^{81} +(-6.11016 - 1.42551i) q^{82} +(6.54131 + 6.54131i) q^{83} +(18.6389 - 6.32176i) q^{84} +(-2.24231 + 2.24231i) q^{85} +(0.200870 + 0.323118i) q^{86} +2.33459i q^{87} +(0.854714 + 8.71228i) q^{88} +5.65429i q^{89} +(25.6886 - 15.9696i) q^{90} +(6.09577 - 6.09577i) q^{91} +(0.172855 - 0.350289i) q^{92} +(13.4954 + 13.4954i) q^{93} +(1.09918 - 4.71141i) q^{94} +23.1279 q^{95} +(-16.5230 - 6.23087i) q^{96} -18.8256 q^{97} +(-0.944010 + 4.04630i) q^{98} +(14.7611 + 14.7611i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) \) 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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