LMFDB - Embedded newform 980.2.x.m.863.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72,2,0,0,8,16,0,-4,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			863.3
Character	$\chi$	$=$	980.863
Dual form			980.2.x.m.67.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34754 - 0.429119i) q^{2} +(2.71477 + 0.727420i) q^{3} +(1.63171 + 1.15651i) q^{4} +(2.01971 - 0.959579i) q^{5} +(-3.34610 - 2.14518i) q^{6} +(-1.70252 - 2.25864i) q^{8} +(4.24276 + 2.44956i) q^{9} +(-3.13340 + 0.426375i) q^{10} +(2.75736 - 1.59196i) q^{11} +(3.58846 + 4.32659i) q^{12} +(-2.41925 - 2.41925i) q^{13} +(6.18105 - 1.13586i) q^{15} +(1.32498 + 3.77418i) q^{16} +(-2.24094 - 0.600458i) q^{17} +(-4.66612 - 5.12151i) q^{18} +(1.39787 - 2.42118i) q^{19} +(4.40534 + 0.770044i) q^{20} +(-4.39878 + 0.961994i) q^{22} +(1.39288 + 5.19830i) q^{23} +(-2.97897 - 7.37012i) q^{24} +(3.15842 - 3.87613i) q^{25} +(2.22189 + 4.29818i) q^{26} +(3.77420 + 3.77420i) q^{27} +1.72334i q^{29} +(-8.81662 - 1.12179i) q^{30} +(3.01685 - 1.74178i) q^{31} +(-0.165897 - 5.65442i) q^{32} +(8.64362 - 2.31605i) q^{33} +(2.76208 + 1.77077i) q^{34} +(4.09004 + 8.90375i) q^{36} +(-0.623610 - 2.32734i) q^{37} +(-2.92265 + 2.66278i) q^{38} +(-4.80790 - 8.32752i) q^{39} +(-5.60592 - 2.92808i) q^{40} -2.72503 q^{41} +(3.96477 - 3.96477i) q^{43} +(6.34034 + 0.591276i) q^{44} +(10.9197 + 0.876123i) q^{45} +(0.353728 - 7.60261i) q^{46} +(-6.10452 + 1.63570i) q^{47} +(0.851615 + 11.2098i) q^{48} +(-5.91941 + 3.86790i) q^{50} +(-5.64685 - 3.26021i) q^{51} +(-1.14965 - 6.74541i) q^{52} +(-3.37866 + 12.6093i) q^{53} +(-3.46629 - 6.70545i) q^{54} +(4.04144 - 5.86120i) q^{55} +(5.55610 - 5.55610i) q^{57} +(0.739519 - 2.32227i) q^{58} +(0.951402 + 1.64788i) q^{59} +(11.3993 + 5.29503i) q^{60} +(-5.83980 + 10.1148i) q^{61} +(-4.81275 + 1.05253i) q^{62} +(-2.20286 + 7.69073i) q^{64} +(-7.20764 - 2.56471i) q^{65} +(-12.6415 - 0.588172i) q^{66} +(-1.51938 + 5.67039i) q^{67} +(-2.96214 - 3.57144i) q^{68} +15.1254i q^{69} +0.562181i q^{71} +(-1.69071 - 13.7532i) q^{72} +(-0.866554 + 3.23402i) q^{73} +(-0.158369 + 3.40378i) q^{74} +(11.3940 - 8.22531i) q^{75} +(5.08103 - 2.33403i) q^{76} +(2.90533 + 13.2848i) q^{78} +(-4.13532 + 7.16259i) q^{79} +(6.29770 + 6.35130i) q^{80} +(0.151981 + 0.263239i) q^{81} +(3.67208 + 1.16936i) q^{82} +(-4.38250 + 4.38250i) q^{83} +(-5.10222 + 0.937610i) q^{85} +(-7.04404 + 3.64132i) q^{86} +(-1.25360 + 4.67848i) q^{87} +(-8.29011 - 3.51752i) q^{88} +(2.51180 + 1.45019i) q^{89} +(-14.3387 - 5.86644i) q^{90} +(-3.73908 + 10.0930i) q^{92} +(9.45706 - 2.53401i) q^{93} +(8.92798 + 0.415394i) q^{94} +(0.499970 - 6.23143i) q^{95} +(3.66277 - 15.4711i) q^{96} +(10.9216 - 10.9216i) q^{97} +15.5984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) $ 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.34754	−	0.429119i	−0.952853	−	0.303433i
$2$	−1.34754	−	0.429119i	−0.952853	−	0.303433i
$3$	2.71477	+	0.727420i	1.56737	+	0.419976i	0.934988	−	0.354678i	$-0.115410\pi$
$3$	2.71477	+	0.727420i	1.56737	+	0.419976i	0.632384	+	0.774655i	$0.282076\pi$
$4$	1.63171	+	1.15651i	0.815857	+	0.578253i
$5$	2.01971	−	0.959579i	0.903240	−	0.429137i
$5$	2.01971	−	0.959579i	0.903240	−	0.429137i
$6$	−3.34610	−	2.14518i	−1.36604	−	0.875768i
$7$		0			0
$7$		0			0
$8$	−1.70252	−	2.25864i	−0.601931	−	0.798548i
$9$	4.24276	+	2.44956i	1.41425	+	0.816519i
$10$	−3.13340	+	0.426375i	−0.990869	+	0.134832i
$11$	2.75736	−	1.59196i	0.831375	−	0.479994i	−0.0229484	−	0.999737i	$-0.507305\pi$
$11$	2.75736	−	1.59196i	0.831375	−	0.479994i	0.854323	+	0.519742i	$0.173972\pi$
$12$	3.58846	+	4.32659i	1.03590	+	1.24898i
$13$	−2.41925	−	2.41925i	−0.670980	−	0.670980i	0.286962	−	0.957942i	$-0.407355\pi$
$13$	−2.41925	−	2.41925i	−0.670980	−	0.670980i	−0.957942	+	0.286962i	$0.907355\pi$
$14$		0			0
$15$	6.18105	−	1.13586i	1.59594	−	0.293278i
$16$	1.32498	+	3.77418i	0.331246	+	0.943544i
$17$	−2.24094	−	0.600458i	−0.543508	−	0.145632i	−0.0233890	−	0.999726i	$-0.507446\pi$
$17$	−2.24094	−	0.600458i	−0.543508	−	0.145632i	−0.520119	+	0.854094i	$0.674112\pi$
$18$	−4.66612	−	5.12151i	−1.09982	−	1.20715i
$19$	1.39787	−	2.42118i	0.320693	−	0.555456i	−0.659938	−	0.751320i	$-0.729418\pi$
$19$	1.39787	−	2.42118i	0.320693	−	0.555456i	0.980631	+	0.195863i	$0.0627510\pi$
$20$	4.40534	+	0.770044i	0.985064	+	0.172187i
$21$		0			0
$22$	−4.39878	+	0.961994i	−0.937824	+	0.205098i
$23$	1.39288	+	5.19830i	0.290435	+	1.08392i	0.944775	+	0.327719i	$0.106280\pi$
$23$	1.39288	+	5.19830i	0.290435	+	1.08392i	−0.654340	+	0.756201i	$0.727053\pi$
$24$	−2.97897	−	7.37012i	−0.608079	−	1.50442i
$25$	3.15842	−	3.87613i	0.631683	−	0.775226i
$26$	2.22189	+	4.29818i	0.435748	+	0.842942i
$27$	3.77420	+	3.77420i	0.726345	+	0.726345i
$28$		0			0
$29$			1.72334i			0.320017i	0.987116	+	0.160009i	$0.0511522\pi$
$29$			1.72334i			0.320017i	−0.987116	+	0.160009i	$0.948848\pi$
$30$	−8.81662	−	1.12179i	−1.60969	−	0.204810i
$31$	3.01685	−	1.74178i	0.541843	−	0.312833i	−0.203983	−	0.978974i	$-0.565389\pi$
$31$	3.01685	−	1.74178i	0.541843	−	0.312833i	0.745825	+	0.666141i	$0.232055\pi$
$32$	−0.165897	−	5.65442i	−0.0293267	−	0.999570i
$33$	8.64362	−	2.31605i	1.50466	−	0.403173i
$34$	2.76208	+	1.77077i	0.473693	+	0.303684i
$35$		0			0
$36$	4.09004	+	8.90375i	0.681673	+	1.48396i
$37$	−0.623610	−	2.32734i	−0.102521	−	0.382613i	0.895531	−	0.444999i	$-0.146796\pi$
$37$	−0.623610	−	2.32734i	−0.102521	−	0.382613i	−0.998052	+	0.0623856i	$0.980129\pi$
$38$	−2.92265	+	2.66278i	−0.474117	+	0.431959i
$39$	−4.80790	−	8.32752i	−0.769880	−	1.33347i
$40$	−5.60592	−	2.92808i	−0.886374	−	0.462970i
$41$	−2.72503			−0.425578			−0.212789	−	0.977098i	$-0.568255\pi$
$41$	−2.72503			−0.425578			−0.212789	+	0.977098i	$0.568255\pi$
$42$		0			0
$43$	3.96477	−	3.96477i	0.604622	−	0.604622i	−0.336914	−	0.941536i	$-0.609383\pi$
$43$	3.96477	−	3.96477i	0.604622	−	0.604622i	0.941536	+	0.336914i	$0.109383\pi$
$44$	6.34034	+	0.591276i	0.955842	+	0.0891383i
$45$	10.9197	+	0.876123i	1.62781	+	0.130605i
$46$	0.353728	−	7.60261i	0.0521544	−	1.12094i
$47$	−6.10452	+	1.63570i	−0.890435	+	0.238591i	−0.674904	−	0.737905i	$-0.735815\pi$
$47$	−6.10452	+	1.63570i	−0.890435	+	0.238591i	−0.215531	+	0.976497i	$0.569148\pi$
$48$	0.851615	+	11.2098i	0.122920	+	1.61800i
$49$		0			0
$50$	−5.91941	+	3.86790i	−0.837130	+	0.547003i
$51$	−5.64685	−	3.26021i	−0.790717	−	0.456521i
$52$	−1.14965	−	6.74541i	−0.159427	−	0.935420i
$53$	−3.37866	+	12.6093i	−0.464094	+	1.73202i	0.195780	+	0.980648i	$0.437276\pi$
$53$	−3.37866	+	12.6093i	−0.464094	+	1.73202i	−0.659874	+	0.751376i	$0.729390\pi$
$54$	−3.46629	−	6.70545i	−0.471703	−	0.912496i
$55$	4.04144	−	5.86120i	0.544947	−	0.790323i
$56$		0			0
$57$	5.55610	−	5.55610i	0.735924	−	0.735924i
$58$	0.739519	−	2.32227i	0.0971036	−	0.304929i
$59$	0.951402	+	1.64788i	0.123862	+	0.214535i	0.921288	−	0.388882i	$-0.127139\pi$
$59$	0.951402	+	1.64788i	0.123862	+	0.214535i	−0.797426	+	0.603417i	$0.793805\pi$
$60$	11.3993	+	5.29503i	1.47165	+	0.683585i
$61$	−5.83980	+	10.1148i	−0.747709	+	1.29507i	0.201209	+	0.979548i	$0.435513\pi$
$61$	−5.83980	+	10.1148i	−0.747709	+	1.29507i	−0.948918	+	0.315522i	$0.897820\pi$
$62$	−4.81275	+	1.05253i	−0.611220	+	0.133671i
$63$		0			0
$64$	−2.20286	+	7.69073i	−0.275358	+	0.961342i
$65$	−7.20764	−	2.56471i	−0.893997	−	0.318113i
$66$	−12.6415	−	0.588172i	−1.55606	−	0.0723990i
$67$	−1.51938	+	5.67039i	−0.185621	+	0.692748i	0.808875	+	0.587980i	$0.200077\pi$
$67$	−1.51938	+	5.67039i	−0.185621	+	0.692748i	−0.994497	+	0.104768i	$0.966590\pi$
$68$	−2.96214	−	3.57144i	−0.359212	−	0.433100i
$69$			15.1254i			1.82088i
$70$		0			0
$71$			0.562181i			0.0667186i	0.999443	+	0.0333593i	$0.0106206\pi$
$71$			0.562181i			0.0667186i	−0.999443	+	0.0333593i	$0.989379\pi$
$72$	−1.69071	−	13.7532i	−0.199253	−	1.62084i
$73$	−0.866554	+	3.23402i	−0.101423	+	0.378514i	−0.997915	−	0.0645454i	$-0.979440\pi$
$73$	−0.866554	+	3.23402i	−0.101423	+	0.378514i	0.896492	+	0.443059i	$0.146107\pi$
$74$	−0.158369	+	3.40378i	−0.0184100	+	0.395682i
$75$	11.3940	−	8.22531i	1.31566	−	0.949777i
$76$	5.08103	−	2.33403i	0.582834	−	0.267731i
$77$		0			0
$78$	2.90533	+	13.2848i	0.328963	+	1.50421i
$79$	−4.13532	+	7.16259i	−0.465260	+	0.805855i	−0.999213	−	0.0396596i	$-0.987373\pi$
$79$	−4.13532	+	7.16259i	−0.465260	+	0.805855i	0.533953	+	0.845514i	$0.320706\pi$
$80$	6.29770	+	6.35130i	0.704104	+	0.710097i
$81$	0.151981	+	0.263239i	0.0168868	+	0.0292487i
$82$	3.67208	+	1.16936i	0.405513	+	0.129134i
$83$	−4.38250	+	4.38250i	−0.481042	+	0.481042i	−0.905464	−	0.424423i	$-0.860477\pi$
$83$	−4.38250	+	4.38250i	−0.481042	+	0.481042i	0.424423	+	0.905464i	$0.360477\pi$
$84$		0			0
$85$	−5.10222	+	0.937610i	−0.553414	+	0.101698i
$86$	−7.04404	+	3.64132i	−0.759578	+	0.392654i
$87$	−1.25360	+	4.67848i	−0.134400	+	0.501586i
$88$	−8.29011	−	3.51752i	−0.883729	−	0.374969i
$89$	2.51180	+	1.45019i	0.266250	+	0.153720i	0.627182	−	0.778872i	$-0.284208\pi$
$89$	2.51180	+	1.45019i	0.266250	+	0.153720i	−0.360932	+	0.932592i	$0.617541\pi$
$90$	−14.3387	−	5.86644i	−1.51143	−	0.618377i
$91$		0			0
$92$	−3.73908	+	10.0930i	−0.389826	+	1.05227i
$93$	9.45706	−	2.53401i	0.980652	−	0.262765i
$94$	8.92798	+	0.415394i	0.920850	+	0.0428446i
$95$	0.499970	−	6.23143i	0.0512958	−	0.639331i
$96$	3.66277	−	15.4711i	0.373830	−	1.57902i
$97$	10.9216	−	10.9216i	1.10892	−	1.10892i	0.115629	−	0.993292i	$-0.463111\pi$
$97$	10.9216	−	10.9216i	1.10892	−	1.10892i	0.993292	−	0.115629i	$-0.0368885\pi$
$98$		0			0
$99$	15.5984			1.56770
$100$	9.63641	−	2.67201i	0.963641	−	0.267201i
$101$	−5.73271	−	9.92934i	−0.570426	−	0.988007i	−0.996522	−	0.0833288i	$-0.973445\pi$
$101$	−5.73271	−	9.92934i	−0.570426	−	0.988007i	0.426096	−	0.904678i	$-0.359889\pi$
$102$	6.21032	+	6.81642i	0.614914	+	0.674926i
$103$	3.39107	+	12.6556i	0.334132	+	1.24700i	0.904807	+	0.425821i	$0.140015\pi$
$103$	3.39107	+	12.6556i	0.334132	+	1.24700i	−0.570676	+	0.821176i	$0.693319\pi$
$104$	−1.34539	+	9.58302i	−0.131926	+	0.939693i
$105$		0			0
$106$	9.96376	−	15.5417i	0.967766	−	1.50954i
$107$	−0.397018	+	0.106381i	−0.0383812	+	0.0102842i	−0.277959	−	0.960593i	$-0.589658\pi$
$107$	−0.397018	+	0.106381i	−0.0383812	+	0.0102842i	0.239577	+	0.970877i	$0.422991\pi$
$108$	1.79353	+	10.5233i	0.172582	+	1.01260i
$109$	6.32499	−	3.65173i	0.605824	−	0.349773i	−0.165505	−	0.986209i	$-0.552926\pi$
$109$	6.32499	−	3.65173i	0.605824	−	0.349773i	0.771329	+	0.636436i	$0.219592\pi$
$110$	−7.96114	+	6.16392i	−0.759065	+	0.587707i
$111$		−	6.77183i		−	0.642753i
$112$		0			0
$113$	−11.6304	−	11.6304i	−1.09410	−	1.09410i	−0.995086	−	0.0990127i	$-0.968432\pi$
$113$	−11.6304	−	11.6304i	−1.09410	−	1.09410i	−0.0990127	−	0.995086i	$-0.531568\pi$
$114$	−9.87128	+	5.10283i	−0.924530	+	0.477924i
$115$	7.80138	+	9.16245i	0.727482	+	0.854402i
$116$	−1.99306	+	2.81201i	−0.185051	+	0.261088i
$117$	−4.33820	−	16.1904i	−0.401067	−	1.49680i
$118$	−0.574915	−	2.62884i	−0.0529252	−	0.242004i
$119$		0			0
$120$	−13.0888	−	12.0269i	−1.19484	−	1.09790i
$121$	−0.431317	+	0.747063i	−0.0392106	+	0.0679148i
$122$	12.2098	−	11.1241i	1.10542	−	1.00713i
$123$	−7.39783	−	1.98224i	−0.667040	−	0.178733i
$124$	6.93702	+	0.646921i	0.622963	+	0.0580952i
$125$	2.65962	−	10.8594i	0.237883	−	0.971294i
$126$		0			0
$127$	1.32146	+	1.32146i	0.117261	+	0.117261i	0.763302	−	0.646042i	$-0.223577\pi$
$127$	1.32146	+	1.32146i	0.117261	+	0.117261i	−0.646042	+	0.763302i	$0.723577\pi$
$128$	6.26868	−	9.41826i	0.554078	−	0.832465i
$129$	13.6475	−	7.87939i	1.20159	−	0.693741i
$130$	8.61199	+	6.54898i	0.755322	+	0.574383i
$131$	3.52422	+	2.03471i	0.307912	+	0.177773i	0.645992	−	0.763344i	$-0.276444\pi$
$131$	3.52422	+	2.03471i	0.307912	+	0.177773i	−0.338080	+	0.941118i	$0.609777\pi$
$132$	16.7824	+	6.21727i	1.46072	+	0.541144i
$133$		0			0
$134$	4.48068	−	6.98907i	0.387072	−	0.603764i
$135$	11.2444	+	4.00113i	0.967765	+	0.344362i
$136$	2.45903	+	6.08376i	0.210860	+	0.521678i
$137$	−15.5676	−	4.17132i	−1.33003	−	0.356380i	−0.477303	−	0.878739i	$-0.658385\pi$
$137$	−15.5676	−	4.17132i	−1.33003	−	0.356380i	−0.852726	+	0.522359i	$0.825052\pi$
$138$	6.49058	−	20.3820i	0.552515	−	1.73503i
$139$	17.0814			1.44882			0.724411	−	0.689369i	$-0.242112\pi$
$139$	17.0814			1.44882			0.724411	+	0.689369i	$0.242112\pi$
$140$		0			0
$141$	−17.7622			−1.49585
$142$	0.241242	−	0.757560i	0.0202446	−	0.0635730i
$143$	−10.5221	−	2.81939i	−0.879902	−	0.235769i
$144$	−3.62347	+	19.2585i	−0.301956	+	1.60488i
$145$	1.65369	+	3.48065i	0.137331	+	0.289052i
$146$	2.55549	−	3.98611i	0.211494	−	0.329893i
$147$		0			0
$148$	1.67403	−	4.51877i	0.137605	−	0.371441i
$149$	7.75810	+	4.47914i	0.635569	+	0.366946i	0.782905	−	0.622141i	$-0.213737\pi$
$149$	7.75810	+	4.47914i	0.635569	+	0.366946i	−0.147337	+	0.989086i	$0.547070\pi$
$150$	−18.8834	+	6.19456i	−1.54182	+	0.505783i
$151$	5.83274	−	3.36754i	0.474662	−	0.274046i	−0.243527	−	0.969894i	$-0.578305\pi$
$151$	5.83274	−	3.36754i	0.474662	−	0.274046i	0.718189	+	0.695848i	$0.244971\pi$
$152$	−7.84845	+	0.964826i	−0.636593	+	0.0782577i
$153$	−8.03690	−	8.03690i	−0.649745	−	0.649745i
$154$		0			0
$155$	4.42178	−	6.41279i	0.355166	−	0.515088i
$156$	1.78572	−	19.1485i	0.142972	−	1.53311i
$157$	−10.9964	−	2.94647i	−0.877606	−	0.235154i	−0.208232	−	0.978080i	$-0.566771\pi$
$157$	−10.9964	−	2.94647i	−0.877606	−	0.235154i	−0.669374	+	0.742926i	$0.733437\pi$
$158$	8.64611	−	7.87732i	0.687847	−	0.626686i
$159$	−18.3446	+	31.7737i	−1.45482	+	2.51982i
$160$	−5.76093	−	11.2611i	−0.455441	−	0.890266i
$161$		0			0
$162$	−0.0918394	−	0.419942i	−0.00721558	−	0.0329937i
$163$	−0.000732309	−	0.00273302i	−5.73589e−5	−	0.000214066i	0.965897	−	0.258926i	$-0.0833686\pi$
$163$	−0.000732309	−	0.00273302i	−5.73589e−5	−	0.000214066i	−0.965954	+	0.258712i	$0.916702\pi$
$164$	−4.44647	−	3.15152i	−0.347211	−	0.246092i
$165$	15.2351	−	12.9720i	1.18605	−	1.00987i
$166$	7.78619	−	4.02497i	0.604326	−	0.312398i
$167$	−2.32482	−	2.32482i	−0.179900	−	0.179900i	0.611412	−	0.791312i	$-0.290602\pi$
$167$	−2.32482	−	2.32482i	−0.179900	−	0.179900i	−0.791312	+	0.611412i	$0.790602\pi$
$168$		0			0
$169$		−	1.29445i		−	0.0995729i
$170$	7.27778	+	0.925994i	0.558181	+	0.0710205i
$171$	11.8616	−	6.84831i	0.907081	−	0.523703i
$172$	11.0547	−	1.88409i	0.842910	−	0.143661i
$173$	−15.5233	+	4.15945i	−1.18021	+	0.316237i	−0.795010	−	0.606596i	$-0.792535\pi$
$173$	−15.5233	+	4.15945i	−1.18021	+	0.316237i	−0.385201	+	0.922833i	$0.625868\pi$
$174$	3.69689	−	5.76649i	0.280261	−	0.437157i
$175$		0			0
$176$	9.66180	+	8.29743i	0.728286	+	0.625443i
$177$	1.38414	+	5.16567i	0.104038	+	0.388276i
$178$	−2.76244	−	3.03204i	−0.207054	−	0.227261i
$179$	9.08714	+	15.7394i	0.679205	+	1.17642i	0.975221	+	0.221235i	$0.0710086\pi$
$179$	9.08714	+	15.7394i	0.679205	+	1.17642i	−0.296016	+	0.955183i	$0.595658\pi$
$180$	16.8045	+	14.0582i	1.25254	+	1.04784i
$181$	4.28458			0.318471			0.159235	−	0.987241i	$-0.449097\pi$
$181$	4.28458			0.318471			0.159235	+	0.987241i	$0.449097\pi$
$182$		0			0
$183$	−23.2114	+	23.2114i	−1.71584	+	1.71584i
$184$	9.36965	−	11.9962i	0.690740	−	0.884371i
$185$	−3.49278	−	4.10214i	−0.256794	−	0.301596i
$186$	−13.8311	−	0.643525i	−1.01415	−	0.0471855i
$187$	−7.13498	+	1.91181i	−0.521761	+	0.139806i
$188$	−11.8525	−	4.39092i	−0.864434	−	0.320241i
$189$		0			0
$190$	−3.34775	+	8.18254i	−0.242871	+	0.593624i
$191$	10.0103	+	5.77946i	0.724321	+	0.418187i	0.816341	−	0.577570i	$-0.195999\pi$
$191$	10.0103	+	5.77946i	0.724321	+	0.418187i	−0.0920200	+	0.995757i	$0.529332\pi$
$192$	−11.5747	+	19.2762i	−0.835329	+	1.39114i
$193$	1.19666	−	4.46599i	0.0861374	−	0.321469i	−0.909390	−	0.415945i	$-0.863451\pi$
$193$	1.19666	−	4.46599i	0.0861374	−	0.321469i	0.995527	+	0.0944758i	$0.0301175\pi$
$194$	−19.4040	+	10.0306i	−1.39312	+	0.720156i
$195$	−17.7014	−	12.2056i	−1.26763	−	0.874060i
$196$		0			0
$197$	6.77330	−	6.77330i	0.482578	−	0.482578i	−0.423376	−	0.905954i	$-0.639155\pi$
$197$	6.77330	−	6.77330i	0.482578	−	0.482578i	0.905954	+	0.423376i	$0.139155\pi$
$198$	−21.0194	−	6.69356i	−1.49379	−	0.475691i
$199$	−0.869824	−	1.50658i	−0.0616602	−	0.106799i	0.833547	−	0.552448i	$-0.186306\pi$
$199$	−0.869824	−	1.50658i	−0.0616602	−	0.106799i	−0.895208	+	0.445649i	$0.852973\pi$
$200$	−14.1320	−	0.534527i	−0.999285	−	0.0377967i
$201$	−8.24951	+	14.2886i	−0.581876	+	1.00784i
$202$	3.46418	+	15.8402i	0.243739	+	1.11451i
$203$		0			0
$204$	−5.44359	−	11.8504i	−0.381128	−	0.829691i
$205$	−5.50376	+	2.61488i	−0.384399	+	0.182631i
$206$	0.861178	−	18.5091i	0.0600011	−	1.28959i
$207$	−6.82387	+	25.4670i	−0.474292	+	1.77008i
$208$	5.92521	−	12.3362i	0.410840	−	0.855358i
$209$		−	8.90141i		−	0.615723i
$210$		0			0
$211$		−	23.7584i		−	1.63560i	−0.575506	−	0.817798i	$-0.695195\pi$
$211$		−	23.7584i		−	1.63560i	0.575506	−	0.817798i	$-0.304805\pi$
$212$	−20.0958	+	16.6674i	−1.38018	+	1.14472i
$213$	−0.408942	+	1.52619i	−0.0280202	+	0.104573i
$214$	0.580647	+	0.0270159i	0.0396922	+	0.00184677i
$215$	4.20316	−	11.8122i	0.286653	−	0.805584i
$216$	2.09890	−	14.9502i	0.142812	−	1.01723i
$217$		0			0
$218$	−10.0902	+	2.20668i	−0.683393	+	0.149455i
$219$	−4.70499	+	8.14928i	−0.317934	+	0.550677i
$220$	13.3730	−	4.88985i	0.901606	−	0.329673i
$221$	3.96874	+	6.87406i	0.266966	+	0.462399i
$222$	−2.90592	+	9.12529i	−0.195032	+	0.612449i
$223$	−13.2313	+	13.2313i	−0.886031	+	0.886031i	−0.994139	−	0.108108i	$-0.965521\pi$
$223$	−13.2313	+	13.2313i	−0.886031	+	0.886031i	0.108108	+	0.994139i	$0.465521\pi$
$224$		0			0
$225$	22.8952	−	8.70876i	1.52635	−	0.580584i
$226$	10.6816	+	20.6633i	0.710530	+	1.37450i
$227$	−5.38070	+	20.0810i	−0.357130	+	1.33283i	0.520654	+	0.853768i	$0.325688\pi$
$227$	−5.38070	+	20.0810i	−0.357130	+	1.33283i	−0.877783	+	0.479058i	$0.840978\pi$
$228$	15.4916	−	2.64030i	1.02596	−	0.174858i
$229$	15.4800	+	8.93740i	1.02295	+	0.590600i	0.914957	−	0.403552i	$-0.132224\pi$
$229$	15.4800	+	8.93740i	1.02295	+	0.590600i	0.107992	+	0.994152i	$0.465558\pi$
$230$	−6.58087	−	15.6945i	−0.433930	−	1.03486i
$231$		0			0
$232$	3.89241	−	2.93403i	0.255549	−	0.192628i
$233$	0.340822	−	0.0913229i	0.0223280	−	0.00598276i	−0.247638	−	0.968853i	$-0.579654\pi$
$233$	0.340822	−	0.0913229i	0.0223280	−	0.00598276i	0.269966	+	0.962870i	$0.412988\pi$
$234$	−1.10171	+	23.6787i	−0.0720208	+	1.54793i
$235$	−10.7597	+	9.16140i	−0.701888	+	0.597624i
$236$	−0.353364	+	3.78917i	−0.0230020	+	0.246654i
$237$	−16.4367	+	16.4367i	−1.06768	+	1.06768i
$238$		0			0
$239$	−24.1080			−1.55941			−0.779707	−	0.626145i	$-0.784632\pi$
$239$	−24.1080			−1.55941			−0.779707	+	0.626145i	$0.784632\pi$
$240$	12.4767	+	21.8234i	0.805370	+	1.40869i
$241$	2.17712	+	3.77087i	0.140240	+	0.242903i	0.927587	−	0.373607i	$-0.121879\pi$
$241$	2.17712	+	3.77087i	0.140240	+	0.242903i	−0.787347	+	0.616510i	$0.788546\pi$
$242$	0.901794	−	0.821609i	0.0579695	−	0.0528150i
$243$	−3.92325	−	14.6418i	−0.251677	−	0.939270i
$244$	−21.2267	+	9.75074i	−1.35890	+	0.624227i
$245$		0			0
$246$	9.11823	+	5.84569i	0.581357	+	0.372708i
$247$	−9.23923	+	2.47564i	−0.587878	+	0.157521i
$248$	−9.07029	−	3.84856i	−0.575964	−	0.244384i
$249$	−15.0854	+	8.70955i	−0.955998	+	0.551945i
$250$	−8.24390	+	13.4921i	−0.521390	+	0.853318i
$251$			13.3373i			0.841841i	0.907098	+	0.420920i	$0.138293\pi$
$251$			13.3373i			0.841841i	−0.907098	+	0.420920i	$0.861707\pi$
$252$		0			0
$253$	12.1162	+	12.1162i	0.761736	+	0.761736i
$254$	−1.21365	−	2.34778i	−0.0761514	−	0.147313i
$255$	−14.5334	−	1.16607i	−0.910117	−	0.0730219i
$256$	−12.4888	+	10.0015i	−0.780552	+	0.625091i
$257$	−2.60327	−	9.71554i	−0.162388	−	0.606039i	−0.998359	−	0.0572656i	$-0.981762\pi$
$257$	−2.60327	−	9.71554i	−0.162388	−	0.606039i	0.835971	−	0.548773i	$-0.184905\pi$
$258$	−21.7717	+	4.76137i	−1.35545	+	0.296430i
$259$		0			0
$260$	−8.79470	−	12.5206i	−0.545424	−	0.776492i
$261$	−4.22143	+	7.31173i	−0.261300	+	0.452585i
$262$	−3.87589	−	4.25415i	−0.239453	−	0.262822i
$263$	−10.3861	−	2.78295i	−0.640435	−	0.171604i	−0.0760347	−	0.997105i	$-0.524226\pi$
$263$	−10.3861	−	2.78295i	−0.640435	−	0.171604i	−0.564401	+	0.825501i	$0.690893\pi$
$264$	−19.9470	−	15.5797i	−1.22765	−	0.958862i
$265$	5.27575	+	28.7092i	0.324087	+	1.76359i
$266$		0			0
$267$	5.76406	+	5.76406i	0.352755	+	0.352755i
$268$	−9.03703	+	7.49529i	−0.552024	+	0.457848i
$269$	−8.18828	+	4.72750i	−0.499248	+	0.288241i	−0.728403	−	0.685149i	$-0.759737\pi$
$269$	−8.18828	+	4.72750i	−0.499248	+	0.288241i	0.229155	+	0.973390i	$0.426404\pi$
$270$	−13.4353	−	10.2169i	−0.817646	−	0.621778i
$271$	−12.4949	−	7.21392i	−0.759010	−	0.438214i	0.0699304	−	0.997552i	$-0.477722\pi$
$271$	−12.4949	−	7.21392i	−0.759010	−	0.438214i	−0.828940	+	0.559337i	$0.811056\pi$
$272$	−0.702976	−	9.25330i	−0.0426242	−	0.561064i
$273$		0			0
$274$	19.1879	+	12.3013i	1.15918	+	0.743152i
$275$	2.53823	−	15.7160i	0.153061	−	0.947708i
$276$	−17.4926	+	24.6803i	−1.05293	+	1.48558i
$277$	−31.9620	−	8.56419i	−1.92041	−	0.514572i	−0.988332	−	0.152314i	$-0.951328\pi$
$277$	−31.9620	−	8.56419i	−1.92041	−	0.514572i	−0.932078	−	0.362259i	$-0.882006\pi$
$278$	−23.0178	−	7.32993i	−1.38051	−	0.439620i
$279$	17.0664			1.02174
$280$		0			0
$281$	−10.1670			−0.606514			−0.303257	−	0.952909i	$-0.598074\pi$
$281$	−10.1670			−0.606514			−0.303257	+	0.952909i	$0.598074\pi$
$282$	23.9352	+	7.62209i	1.42532	+	0.453889i
$283$	26.7548	+	7.16893i	1.59041	+	0.426148i	0.942128	−	0.335254i	$-0.108822\pi$
$283$	26.7548	+	7.16893i	1.59041	+	0.426148i	0.648280	+	0.761402i	$0.275489\pi$
$284$	−0.650166	+	0.917319i	−0.0385803	+	0.0544329i
$285$	5.89017	−	16.5532i	0.348904	−	0.980527i
$286$	12.9691	+	8.31446i	0.766877	+	0.491644i
$287$		0			0
$288$	13.1470	−	24.3967i	0.774692	−	1.43759i
$289$	−10.0612	−	5.80882i	−0.591834	−	0.341695i
$290$	−0.734792	−	5.39993i	−0.0431485	−	0.317095i
$291$	37.5943	−	21.7051i	2.20381	−	1.27237i
$292$	−5.15414	+	4.27483i	−0.301623	+	0.250165i
$293$	3.07964	+	3.07964i	0.179914	+	0.179914i	0.791318	−	0.611404i	$-0.209395\pi$
$293$	3.07964	+	3.07964i	0.179914	+	0.179914i	−0.611404	+	0.791318i	$0.709395\pi$
$294$		0			0
$295$	3.50282	+	2.41528i	0.203942	+	0.140623i
$296$	−4.19491	+	5.37085i	−0.243824	+	0.312174i
$297$	16.4152	+	4.39844i	0.952506	+	0.255223i
$298$	−8.53225	−	9.36496i	−0.494260	−	0.542498i
$299$	9.20626	−	15.9457i	0.532412	−	0.922164i
$300$	28.1043	−	0.244175i	1.62260	−	0.0140974i
$301$		0			0
$302$	−9.30491	+	2.03494i	−0.535437	+	0.117098i
$303$	−8.34018	−	31.1260i	−0.479131	−	1.78814i
$304$	10.9901	+	2.06778i	0.630326	+	0.118595i
$305$	−2.08870	+	26.0327i	−0.119598	+	1.49063i
$306$	7.38124	+	14.2788i	0.421958	+	0.816265i
$307$	−13.3345	−	13.3345i	−0.761042	−	0.761042i	0.215469	−	0.976511i	$-0.430872\pi$
$307$	−13.3345	−	13.3345i	−0.761042	−	0.761042i	−0.976511	+	0.215469i	$0.930872\pi$
$308$		0			0
$309$			36.8239i			2.09484i
$310$	−8.71036	+	6.74401i	−0.494715	+	0.383034i
$311$	−1.35454	+	0.782046i	−0.0768091	+	0.0443457i	−0.537913	−	0.843001i	$-0.680787\pi$
$311$	−1.35454	+	0.782046i	−0.0768091	+	0.0443457i	0.461104	+	0.887346i	$0.347454\pi$
$312$	−10.6233	+	25.0370i	−0.601426	+	1.41744i
$313$	11.7632	−	3.15193i	0.664893	−	0.178157i	0.0894395	−	0.995992i	$-0.471492\pi$
$313$	11.7632	−	3.15193i	0.664893	−	0.178157i	0.575453	+	0.817835i	$0.304826\pi$
$314$	13.5536	+	8.68922i	0.764876	+	0.490361i
$315$		0			0
$316$	−15.0313	+	6.90478i	−0.845574	+	0.388424i
$317$	−7.08901	−	26.4565i	−0.398158	−	1.48595i	−0.816334	−	0.577581i	$-0.803997\pi$
$317$	−7.08901	−	26.4565i	−0.398158	−	1.48595i	0.418175	−	0.908366i	$-0.362670\pi$
$318$	38.3547	−	34.9443i	2.15082	−	1.95958i
$319$	2.74350	+	4.75188i	0.153606	+	0.266054i
$320$	2.93073	+	17.6468i	0.163833	+	0.986488i
$321$	−1.15520			−0.0644768
$322$		0			0
$323$	−4.58635	+	4.58635i	−0.255191	+	0.255191i
$324$	−0.0564478	+	0.605297i	−0.00313599	+	0.0336276i
$325$	−17.0183	+	1.73633i	−0.944008	+	0.0963144i
$326$	−0.000185973		0.00399709i	−1.03001e−5		0.000221378i
$327$	19.8272	−	5.31269i	1.09645	−	0.293792i
$328$	4.63941	+	6.15485i	0.256169	+	0.339845i
$329$		0			0
$330$	−26.0964	+	10.9425i	−1.43656	+	0.602367i
$331$	−3.38809	−	1.95612i	−0.186226	−	0.107518i	0.403988	−	0.914764i	$-0.367624\pi$
$331$	−3.38809	−	1.95612i	−0.186226	−	0.107518i	−0.590215	+	0.807246i	$0.700957\pi$
$332$	−12.2194	+	2.08260i	−0.670625	+	0.114297i
$333$	3.05513	−	11.4019i	0.167420	−	0.624821i
$334$	2.13515	+	4.13040i	0.116830	+	0.226005i
$335$	2.37249	+	12.9105i	0.129623	+	0.705374i
$336$		0			0
$337$	12.6447	−	12.6447i	0.688801	−	0.688801i	−0.273166	−	0.961967i	$-0.588071\pi$
$337$	12.6447	−	12.6447i	0.688801	−	0.688801i	0.961967	+	0.273166i	$0.0880709\pi$
$338$	−0.555471	+	1.74432i	−0.0302137	+	0.0948783i
$339$	−23.1137	−	40.0341i	−1.25537	−	2.17436i
$340$	−9.40973	−	4.37084i	−0.510314	−	0.237042i
$341$	5.54569	−	9.60542i	0.300316	−	0.520163i
$342$	−18.9227	+	4.13831i	−1.02322	+	0.223774i
$343$		0			0
$344$	−15.7051	−	2.20488i	−0.846761	−	0.118879i
$345$	14.5140	+	30.5488i	0.781407	+	1.64469i
$346$	22.7031	+	1.05631i	1.22052	+	0.0567876i
$347$	−1.55280	+	5.79511i	−0.0833585	+	0.311098i	−0.994998	−	0.0998921i	$-0.968150\pi$
$347$	−1.55280	+	5.79511i	−0.0833585	+	0.311098i	0.911640	+	0.410990i	$0.134817\pi$
$348$	−7.45621	+	6.18416i	−0.399695	+	0.331506i
$349$		−	15.1860i		−	0.812888i	−0.913676	−	0.406444i	$-0.866769\pi$
$349$		−	15.1860i		−	0.812888i	0.913676	−	0.406444i	$-0.133231\pi$
$350$		0			0
$351$		−	18.2615i		−	0.974725i
$352$	−9.45906	−	15.3272i	−0.504169	−	0.816941i
$353$	−8.90620	+	33.2384i	−0.474029	+	1.76910i	0.151035	+	0.988528i	$0.451739\pi$
$353$	−8.90620	+	33.2384i	−0.474029	+	1.76910i	−0.625065	+	0.780573i	$0.714927\pi$
$354$	0.351508	−	7.55490i	0.0186825	−	0.401538i
$355$	0.539457	+	1.13544i	0.0286314	+	0.0602629i
$356$	2.42139	+	5.27121i	0.128333	+	0.279373i
$357$		0			0
$358$	−5.49120	−	25.1089i	−0.290219	−	1.32705i
$359$	4.20241	−	7.27878i	0.221795	−	0.384159i	−0.733558	−	0.679626i	$-0.762142\pi$
$359$	4.20241	−	7.27878i	0.221795	−	0.384159i	0.955353	+	0.295467i	$0.0954752\pi$
$360$	−16.6121	−	26.1551i	−0.875533	−	1.37850i
$361$	5.59193	+	9.68551i	0.294312	+	0.509764i
$362$	−5.77364	−	1.83859i	−0.303456	−	0.0966344i
$363$	−1.71435	+	1.71435i	−0.0899803	+	0.0899803i
$364$		0			0
$365$	1.35312	+	7.36330i	0.0708254	+	0.385413i
$366$	41.2387	−	21.3178i	2.15558	−	1.11430i
$367$	7.95960	−	29.7056i	0.415488	−	1.55062i	−0.368369	−	0.929679i	$-0.620084\pi$
$367$	7.95960	−	29.7056i	0.415488	−	1.55062i	0.783857	−	0.620941i	$-0.213249\pi$
$368$	−17.7737	+	12.1446i	−0.926521	+	0.633083i
$369$	−11.5616	−	6.67511i	−0.601875	−	0.347493i
$370$	2.94634	+	7.02661i	0.153173	+	0.365296i
$371$		0			0
$372$	18.3618	+	6.80237i	0.952017	+	0.352687i
$373$	−14.5253	+	3.89204i	−0.752091	+	0.201522i	−0.614446	−	0.788959i	$-0.710620\pi$
$373$	−14.5253	+	3.89204i	−0.752091	+	0.201522i	−0.137646	+	0.990482i	$0.543954\pi$
$374$	10.4350	+	0.485514i	0.539583	+	0.0251053i
$375$	15.1196	−	27.5461i	0.780772	−	1.42247i
$376$	14.0875	+	11.0031i	0.726507	+	0.567440i
$377$	4.16920	−	4.16920i	0.214725	−	0.214725i
$378$		0			0
$379$	−1.92262			−0.0987586			−0.0493793	−	0.998780i	$-0.515724\pi$
$379$	−1.92262			−0.0987586			−0.0493793	+	0.998780i	$0.515724\pi$
$380$	8.02250	−	9.58970i	0.411545	−	0.491941i
$381$	2.62620	+	4.54871i	0.134544	+	0.233038i
$382$	−11.0092	−	12.0836i	−0.563280	−	0.618253i
$383$	4.13733	+	15.4407i	0.211408	+	0.788984i	0.987400	+	0.158242i	$0.0505827\pi$
$383$	4.13733	+	15.4407i	0.211408	+	0.788984i	−0.775993	+	0.630742i	$0.782751\pi$
$384$	23.8691	−	21.0084i	1.21806	−	1.07208i
$385$		0			0
$386$	−3.52898	+	5.50459i	−0.179621	+	0.280176i
$387$	26.5335	−	7.10963i	1.34877	−	0.361403i
$388$	30.4519	−	5.19004i	1.54596	−	0.263484i
$389$	9.81327	−	5.66569i	0.497552	−	0.287262i	−0.230150	−	0.973155i	$-0.573922\pi$
$389$	9.81327	−	5.66569i	0.497552	−	0.287262i	0.727702	+	0.685893i	$0.240588\pi$
$390$	18.6157	+	24.0435i	0.942644	+	1.21749i
$391$		−	12.4854i		−	0.631415i
$392$		0			0
$393$	8.08735	+	8.08735i	0.407953	+	0.407953i
$394$	−12.0338	+	6.22073i	−0.606255	+	0.313396i
$395$	−1.47906	+	18.4345i	−0.0744198	+	0.927540i
$396$	25.4521	+	18.0396i	1.27902	+	0.906526i
$397$	−3.01844	−	11.2650i	−0.151491	−	0.565372i	−0.999380	−	0.0351987i	$-0.988794\pi$
$397$	−3.01844	−	11.2650i	−0.151491	−	0.565372i	0.847889	−	0.530173i	$-0.177873\pi$
$398$	0.525620	+	2.40343i	0.0263469	+	0.120473i
$399$		0			0
$400$	18.8141	+	6.78461i	0.940703	+	0.339231i
$401$	13.8361	−	23.9649i	0.690943	−	1.19675i	−0.280587	−	0.959829i	$-0.590529\pi$
$401$	13.8361	−	23.9649i	0.690943	−	1.19675i	0.971529	−	0.236919i	$-0.0761376\pi$
$402$	17.2480	−	15.7144i	0.860253	−	0.783761i
$403$	−11.5123	−	3.08472i	−0.573470	−	0.153661i
$404$	2.12921	−	22.8318i	0.105932	−	1.13592i
$405$	0.559555	+	0.385827i	0.0278045	+	0.0191719i
$406$		0			0
$407$	−5.42456	−	5.42456i	−0.268885	−	0.268885i
$408$	2.25024	+	18.3047i	0.111403	+	0.906220i
$409$	−11.9780	+	6.91550i	−0.592274	+	0.341950i	−0.765996	−	0.642845i	$-0.777754\pi$
$409$	−11.9780	+	6.91550i	−0.592274	+	0.341950i	0.173722	+	0.984795i	$0.444421\pi$
$410$	8.53861	−	1.16189i	0.421692	−	0.0573815i
$411$	−39.2281	−	22.6483i	−1.93498	−	1.11716i
$412$	−9.10307	+	24.5722i	−0.448476	+	1.21058i
$413$		0			0
$414$	20.1238	−	31.3895i	0.989031	−	1.54271i
$415$	−4.64600	+	13.0567i	−0.228063	+	0.640928i
$416$	−13.2781	+	14.0808i	−0.651013	+	0.690369i
$417$	46.3719	+	12.4253i	2.27084	+	0.608471i
$418$	−3.81976	+	11.9950i	−0.186830	+	0.586694i
$419$	−20.6976			−1.01114			−0.505572	−	0.862784i	$-0.668719\pi$
$419$	−20.6976			−1.01114			−0.505572	+	0.862784i	$0.668719\pi$
$420$		0			0
$421$	26.7517			1.30380			0.651898	−	0.758306i	$-0.273973\pi$
$421$	26.7517			1.30380			0.651898	+	0.758306i	$0.273973\pi$
$422$	−10.1952	+	32.0153i	−0.496293	+	1.55848i
$423$	−29.9067	−	8.01348i	−1.45411	−	0.389629i
$424$	34.2321	−	13.8364i	1.66246	−	0.671957i
$425$	−9.40528	+	6.78968i	−0.456223	+	0.329348i
$426$	1.20598	−	1.88112i	0.0584300	−	0.0911404i
$427$		0			0
$428$	−0.770850	−	0.285571i	−0.0372605	−	0.0138036i
$429$	−26.5142	−	15.3080i	−1.28012	−	0.739076i
$430$	−10.7327	+	14.1137i	−0.517579	+	0.680623i
$431$	−34.9346	+	20.1695i	−1.68274	+	0.971531i	−0.722914	+	0.690937i	$0.757198\pi$
$431$	−34.9346	+	20.1695i	−1.68274	+	0.971531i	−0.959827	+	0.280594i	$0.909469\pi$
$432$	−9.24374	+	19.2452i	−0.444740	+	0.925937i
$433$	−16.5835	−	16.5835i	−0.796954	−	0.796954i	0.185660	−	0.982614i	$-0.440558\pi$
$433$	−16.5835	−	16.5835i	−0.796954	−	0.796954i	−0.982614	+	0.185660i	$0.940558\pi$
$434$		0			0
$435$	1.95748	+	10.6521i	0.0938540	+	0.510728i
$436$	14.5438	+	1.35630i	0.696523	+	0.0649552i
$437$	14.5331	+	3.89412i	0.695210	+	0.186281i
$438$	9.83716	−	8.96246i	0.470038	−	0.428243i
$439$	−2.87067	+	4.97215i	−0.137010	+	0.237308i	−0.926363	−	0.376631i	$-0.877082\pi$
$439$	−2.87067	+	4.97215i	−0.137010	+	0.237308i	0.789354	+	0.613939i	$0.210416\pi$
$440$	−20.1189	+	0.850657i	−0.959132	+	0.0405535i
$441$		0			0
$442$	−2.39824	−	10.9661i	−0.114073	−	0.521604i
$443$	0.221517	+	0.826713i	0.0105246	+	0.0392783i	0.970988	−	0.239126i	$-0.0768610\pi$
$443$	0.221517	+	0.826713i	0.0105246	+	0.0392783i	−0.960464	+	0.278405i	$0.910194\pi$
$444$	7.83166	−	11.0497i	0.371674	−	0.524395i
$445$	6.46467	+	0.518683i	0.306455	+	0.0245879i
$446$	23.5074	−	12.1518i	1.11311	−	0.575407i
$447$	17.8032	+	17.8032i	0.842064	+	0.842064i
$448$		0			0
$449$		−	4.66158i		−	0.219993i	−0.993932	−	0.109997i	$-0.964916\pi$
$449$		−	4.66158i		−	0.219993i	0.993932	−	0.109997i	$-0.0350840\pi$
$450$	−34.5892	+	1.91063i	−1.63055	+	0.0900680i
$451$	−7.51388	+	4.33814i	−0.353815	+	0.204275i
$452$	−5.52687	−	32.4282i	−0.259962	−	1.52529i
$453$	18.2842	−	4.89923i	0.859065	−	0.230186i
$454$	15.8678	−	24.7510i	0.744715	−	1.16162i
$455$		0			0
$456$	−22.0086	−	3.08984i	−1.03065	−	0.144695i
$457$	8.23274	+	30.7250i	0.385111	+	1.43726i	0.837991	+	0.545684i	$0.183730\pi$
$457$	8.23274	+	30.7250i	0.385111	+	1.43726i	−0.452880	+	0.891572i	$0.649603\pi$
$458$	−17.0247	−	18.6863i	−0.795513	−	0.873151i
$459$	−6.19150	−	10.7240i	−0.288995	−	0.500553i
$460$	2.13319	+	23.9728i	0.0994606	+	1.11774i
$461$	23.4445			1.09192			0.545959	−	0.837812i	$-0.316165\pi$
$461$	23.4445			1.09192			0.545959	+	0.837812i	$0.316165\pi$
$462$		0			0
$463$	1.84160	−	1.84160i	0.0855866	−	0.0855866i	−0.663017	−	0.748604i	$-0.730724\pi$
$463$	1.84160	−	1.84160i	0.0855866	−	0.0855866i	0.748604	+	0.663017i	$0.230724\pi$
$464$	−6.50421	+	2.28341i	−0.301950	+	0.106004i
$465$	16.6689	−	14.1928i	0.773001	−	0.658173i
$466$	−0.498458	−	0.0231919i	−0.0230906	−	0.00107434i
$467$	8.01462	−	2.14751i	0.370872	−	0.0993749i	−0.0685687	−	0.997646i	$-0.521843\pi$
$467$	8.01462	−	2.14751i	0.370872	−	0.0993749i	0.439441	+	0.898271i	$0.355177\pi$
$468$	11.6456	−	31.4352i	0.538317	−	1.45309i
$469$		0			0
$470$	18.4305	−	7.72812i	0.850135	−	0.356472i
$471$	−27.7093	−	15.9980i	−1.27678	−	0.737147i
$472$	2.10217	−	4.95441i	0.0967603	−	0.228045i
$473$	4.62053	−	17.2441i	0.212452	−	0.792883i
$474$	29.2023	−	15.0957i	1.34131	−	0.693371i
$475$	−4.96976	−	13.0654i	−0.228028	−	0.599482i
$476$		0			0
$477$	−45.2221	+	45.2221i	−2.07058	+	2.07058i
$478$	32.4864	+	10.3452i	1.48589	+	0.473177i
$479$	6.99926	+	12.1231i	0.319805	+	0.553918i	0.980447	−	0.196783i	$-0.0630494\pi$
$479$	6.99926	+	12.1231i	0.319805	+	0.553918i	−0.660643	+	0.750701i	$0.729716\pi$
$480$	−7.44805	−	34.7618i	−0.339955	−	1.58665i
$481$	−4.12176	+	7.13910i	−0.187936	+	0.325515i
$482$	−1.31559	−	6.01563i	−0.0599236	−	0.274005i
$483$		0			0
$484$	−1.56777	+	0.720172i	−0.0712622	+	0.0327351i
$485$	11.5783	−	32.5386i	0.525743	−	1.47750i
$486$	−0.996328	+	21.4139i	−0.0451943	+	0.971353i
$487$	6.87083	−	25.6423i	0.311347	−	1.16196i	−0.615995	−	0.787750i	$-0.711246\pi$
$487$	6.87083	−	25.6423i	0.311347	−	1.16196i	0.927342	−	0.374214i	$-0.122087\pi$
$488$	32.7881	−	4.03070i	1.48425	−	0.182461i
$489$		−	0.00795220i		−	0.000359611i
$490$		0			0
$491$			35.5868i			1.60601i	0.595973	+	0.803004i	$0.296766\pi$
$491$			35.5868i			1.60601i	−0.595973	+	0.803004i	$0.703234\pi$
$492$	−9.77867	−	11.7901i	−0.440856	−	0.531538i
$493$	1.03480	−	3.86191i	0.0466049	−	0.173932i
$494$	13.5126	+	0.628702i	0.607959	+	0.0282866i
$495$	31.5042	−	14.9679i	1.41601	−	0.672757i
$496$	10.5711	+	9.07830i	0.474655	+	0.407628i
$497$		0			0
$498$	24.0656	−	5.26303i	1.07840	−	0.235842i
$499$	4.94115	−	8.55833i	0.221196	−	0.383123i	−0.733975	−	0.679176i	$-0.762337\pi$
$499$	4.94115	−	8.55833i	0.221196	−	0.383123i	0.955172	+	0.296053i	$0.0956705\pi$
$500$	16.8987	−	14.6436i	0.755733	−	0.654880i
$501$	−4.62022	−	8.00245i	−0.206416	−	0.357523i
$502$	5.72327	−	17.9725i	0.255442	−	0.802151i
$503$	16.5308	−	16.5308i	0.737071	−	0.737071i	−0.234939	−	0.972010i	$-0.575489\pi$
$503$	16.5308	−	16.5308i	0.737071	−	0.737071i	0.972010	+	0.234939i	$0.0754890\pi$
$504$		0			0
$505$	−21.1064	−	14.5534i	−0.939221	−	0.647616i
$506$	−11.1277	−	21.5262i	−0.494687	−	0.956958i
$507$	0.941607	−	3.51413i	0.0418182	−	0.156068i
$508$	0.627968	+	3.68452i	0.0278616	+	0.163474i
$509$	0.789343	+	0.455727i	0.0349870	+	0.0201998i	0.517391	−	0.855749i	$-0.326903\pi$
$509$	0.789343	+	0.455727i	0.0349870	+	0.0201998i	−0.482404	+	0.875949i	$0.660236\pi$
$510$	19.0839	+	7.80787i	0.845050	+	0.345738i
$511$		0			0
$512$	21.1210	−	8.11815i	0.933424	−	0.358775i
$513$	14.4138	−	3.86218i	0.636386	−	0.170519i
$514$	−0.661113	+	14.2092i	−0.0291604	+	0.626739i
$515$	18.9930	+	22.3067i	0.836933	+	0.982949i
$516$	31.3814	+	2.92651i	1.38149	+	0.128833i
$517$	−14.2284	+	14.2284i	−0.625763	+	0.625763i
$518$		0			0
$519$	−45.1677			−1.98264
$520$	6.47838	+	20.6459i	0.284096	+	0.905382i
$521$	−3.24107	−	5.61370i	−0.141994	−	0.245941i	0.786254	−	0.617904i	$-0.212018\pi$
$521$	−3.24107	−	5.61370i	−0.141994	−	0.245941i	−0.928247	+	0.371963i	$0.878685\pi$
$522$	8.82613	−	8.04134i	0.386309	−	0.351960i
$523$	−1.22075	−	4.55591i	−0.0533798	−	0.199216i	0.934086	−	0.357047i	$-0.116217\pi$
$523$	−1.22075	−	4.55591i	−0.0533798	−	0.199216i	−0.987466	+	0.157831i	$0.949550\pi$
$524$	3.39736	+	7.39585i	0.148415	+	0.323089i
$525$		0			0
$526$	12.8015	+	8.20701i	0.558170	+	0.357842i
$527$	−7.80645	+	2.09173i	−0.340054	+	0.0911173i
$528$	20.1938	+	29.5538i	0.878824	+	1.28616i
$529$	−5.16358	+	2.98119i	−0.224503	+	0.129617i
$530$	5.21039	−	40.9507i	0.226325	−	1.77878i
$531$			9.32205i			0.404542i
$532$		0			0
$533$	6.59253	+	6.59253i	0.285554	+	0.285554i
$534$	−5.29382	−	10.2408i	−0.229086	−	0.443161i
$535$	−0.699779	+	0.595828i	−0.0302541	+	0.0257599i
$536$	15.3941	−	6.22222i	0.664924	−	0.268759i
$537$	13.2203	+	49.3390i	0.570500	+	2.12913i
$538$	13.0627	−	2.85675i	0.563172	−	0.123163i
$539$		0			0
$540$	13.7203	+	19.5329i	0.590429	+	0.840563i
$541$	−9.43554	+	16.3428i	−0.405666	+	0.702633i	−0.994399	−	0.105694i	$-0.966294\pi$
$541$	−9.43554	+	16.3428i	−0.405666	+	0.702633i	0.588733	+	0.808328i	$0.299627\pi$
$542$	13.7417	+	15.0828i	0.590256	+	0.647862i
$543$	11.6317	+	3.11669i	0.499162	+	0.133750i
$544$	−3.02348	+	12.7708i	−0.129631	+	0.547545i
$545$	9.27048	−	13.4447i	0.397104	−	0.575910i
$546$		0			0
$547$	9.42028	+	9.42028i	0.402782	+	0.402782i	0.879212	−	0.476430i	$-0.158069\pi$
$547$	9.42028	+	9.42028i	0.402782	+	0.402782i	−0.476430	+	0.879212i	$0.658069\pi$
$548$	−20.5777	−	24.8104i	−0.879035	−	1.05985i
$549$	−49.5537	+	28.6098i	−2.11490	+	1.22104i
$550$	−10.1644	+	20.0886i	−0.433411	+	0.856583i
$551$	4.17252	+	2.40901i	0.177756	+	0.102627i
$552$	34.1627	−	25.7512i	1.45406	−	1.09605i
$553$		0			0
$554$	39.3949	+	25.2560i	1.67373	+	1.07303i
$555$	−6.49810	−	13.6771i	−0.275829	−	0.580560i
$556$	27.8719	+	19.7547i	1.18203	+	0.837786i
$557$	36.6573	+	9.82230i	1.55322	+	0.416184i	0.930509	−	0.366268i	$-0.119365\pi$
$557$	36.6573	+	9.82230i	1.55322	+	0.416184i	0.622711	+	0.782452i	$0.286031\pi$
$558$	−22.9976	−	7.32349i	−0.973564	−	0.310028i
$559$	−19.1836			−0.811378
$560$		0			0
$561$	−20.7605			−0.876510
$562$	13.7005	+	4.36286i	0.577919	+	0.184036i
$563$	−36.6293	−	9.81479i	−1.54374	−	0.413644i	−0.616269	−	0.787536i	$-0.711357\pi$
$563$	−36.6293	−	9.81479i	−1.54374	−	0.413644i	−0.927472	+	0.373892i	$0.878023\pi$
$564$	−28.9828	−	20.5421i	−1.22040	−	0.864978i
$565$	−34.6504	−	12.3297i	−1.45775	−	0.518715i
$566$	−32.9768	−	21.1414i	−1.38612	−	0.888638i
$567$		0			0
$568$	1.26976	−	0.957124i	0.0532780	−	0.0401600i
$569$	−7.96777	−	4.60019i	−0.334026	−	0.192850i	0.323601	−	0.946194i	$-0.395106\pi$
$569$	−7.96777	−	4.60019i	−0.334026	−	0.192850i	−0.657627	+	0.753344i	$0.728440\pi$
$570$	−15.0405	+	19.7785i	−0.629978	+	0.828429i
$571$	14.8692	−	8.58473i	0.622256	−	0.359260i	−0.155491	−	0.987837i	$-0.549696\pi$
$571$	14.8692	−	8.58473i	0.622256	−	0.359260i	0.777747	+	0.628578i	$0.216363\pi$
$572$	−13.9084	−	16.7693i	−0.581540	−	0.701160i
$573$	22.9716	+	22.9716i	0.959652	+	0.959652i
$574$		0			0
$575$	24.5486	+	11.0194i	1.02375	+	0.459541i
$576$	−28.1851	+	27.2339i	−1.17438	+	1.13474i
$577$	29.5776	+	7.92529i	1.23133	+	0.329934i	0.815097	−	0.579324i	$-0.196683\pi$
$577$	29.5776	+	7.92529i	1.23133	+	0.329934i	0.416233	+	0.909258i	$0.363350\pi$
$578$	11.0651	+	12.1450i	0.460249	+	0.505167i
$579$	6.49731	−	11.2537i	0.270019	−	0.467687i
$580$	−1.32705	+	7.59192i	−0.0551028	+	0.315237i
$581$		0			0
$582$	−59.9737	+	13.1160i	−2.48599	+	0.543675i
$583$	10.7574	+	40.1471i	0.445525	+	1.66272i
$584$	8.77981	−	3.54876i	0.363311	−	0.146849i
$585$	−24.2978	−	28.5370i	−1.00459	−	1.17986i
$586$	−2.82840	−	5.47146i	−0.116840	−	0.226024i
$587$	31.4917	+	31.4917i	1.29980	+	1.29980i	0.928520	+	0.371283i	$0.121082\pi$
$587$	31.4917	+	31.4917i	1.29980	+	1.29980i	0.371283	+	0.928520i	$0.378918\pi$
$588$		0			0
$589$		−	9.73911i		−	0.401293i
$590$	−3.68374	−	4.75780i	−0.151657	−	0.195876i
$591$	23.3150	−	13.4609i	0.959050	−	0.553708i
$592$	7.95753	−	5.43731i	0.327053	−	0.223472i
$593$	7.35708	−	1.97132i	0.302119	−	0.0809525i	−0.104575	−	0.994517i	$-0.533348\pi$
$593$	7.35708	−	1.97132i	0.302119	−	0.0809525i	0.406694	+	0.913564i	$0.366682\pi$
$594$	−20.2326	−	12.9711i	−0.830155	−	0.532212i
$595$		0			0
$596$	7.47885	+	16.2810i	0.306346	+	0.666895i
$597$	−1.26546	−	4.72275i	−0.0517917	−	0.193289i
$598$	−19.2484	+	17.5369i	−0.787125	+	0.717136i
$599$	−0.0710719	−	0.123100i	−0.00290392	−	0.00502974i	0.864570	−	0.502513i	$-0.167591\pi$
$599$	−0.0710719	−	0.123100i	−0.00290392	−	0.00502974i	−0.867474	+	0.497483i	$0.834258\pi$
$600$	−37.9764	−	11.7310i	−1.55038	−	0.478918i
$601$	13.9872			0.570550			0.285275	−	0.958446i	$-0.407915\pi$
$601$	13.9872			0.570550			0.285275	+	0.958446i	$0.407915\pi$
$602$		0			0
$603$	−20.3363	+	20.3363i	−0.828157	+	0.828157i
$604$	13.4119	+	1.25075i	0.545724	+	0.0508923i
$605$	−0.154267	+	1.92273i	−0.00627186	+	0.0781701i
$606$	−2.11803	+	45.5223i	−0.0860390	+	1.84922i
$607$	31.6805	−	8.48876i	1.28587	−	0.344548i	0.449781	−	0.893139i	$-0.351502\pi$
$607$	31.6805	−	8.48876i	1.28587	−	0.344548i	0.836091	+	0.548591i	$0.184835\pi$
$608$	−13.9223	−	7.50247i	−0.564622	−	0.304265i
$609$		0			0
$610$	13.9857	−	34.1837i	0.566265	−	1.38406i
$611$	18.7255	+	10.8112i	0.757554	+	0.437374i
$612$	−3.81920	−	22.4087i	−0.154382	−	0.905817i
$613$	1.33983	−	5.00032i	0.0541153	−	0.201961i	−0.933575	−	0.358381i	$-0.883329\pi$
$613$	1.33983	−	5.00032i	0.0541153	−	0.201961i	0.987691	+	0.156420i	$0.0499955\pi$
$614$	12.2467	+	23.6909i	0.494236	+	0.956086i
$615$	−16.8435	+	3.09525i	−0.679197	+	0.124813i
$616$		0			0
$617$	18.4714	−	18.4714i	0.743630	−	0.743630i	−0.229644	−	0.973275i	$-0.573756\pi$
$617$	18.4714	−	18.4714i	0.743630	−	0.743630i	0.973275	+	0.229644i	$0.0737563\pi$
$618$	15.8018	−	49.6215i	0.635642	−	1.99607i
$619$	−4.38197	−	7.58980i	−0.176126	−	0.305060i	0.764424	−	0.644714i	$-0.223023\pi$
$619$	−4.38197	−	7.58980i	−0.176126	−	0.305060i	−0.940551	+	0.339654i	$0.889690\pi$
$620$	14.6315	−	5.35003i	0.587616	−	0.214862i
$621$	−14.3624	+	24.8764i	−0.576343	+	0.998255i
$622$	2.16089	−	0.472576i	0.0866437	−	0.0189486i
$623$		0			0
$624$	25.0592	−	29.1797i	1.00317	−	1.16812i
$625$	−5.04880	−	24.4849i	−0.201952	−	0.979395i
$626$	−17.2038	−	0.800447i	−0.687604	−	0.0319923i
$627$	6.47506	−	24.1653i	0.258589	−	0.965068i
$628$	−14.5353	−	17.5252i	−0.580022	−	0.699330i
$629$			5.58989i			0.222883i
$630$		0			0
$631$		−	31.2397i		−	1.24363i	−0.783164	−	0.621816i	$-0.786395\pi$
$631$		−	31.2397i		−	1.24363i	0.783164	−	0.621816i	$-0.213605\pi$
$632$	23.2181	−	2.85425i	0.923568	−	0.113536i
$633$	17.2823	−	64.4986i	0.686911	−	2.56359i
$634$	−1.80029	+	38.6932i	−0.0714985	+	1.53670i
$635$	3.93700	+	1.40091i	0.156235	+	0.0555936i
$636$	−66.6796	+	30.6300i	−2.64402	+	1.21456i
$637$		0			0
$638$	−1.65785	−	7.58062i	−0.0656348	−	0.300120i
$639$	−1.37709	+	2.38520i	−0.0544770	+	0.0943569i
$640$	3.62332	−	25.0374i	0.143224	−	0.989690i
$641$	−24.9696	−	43.2485i	−0.986238	−	1.70821i	−0.636299	−	0.771443i	$-0.719535\pi$
$641$	−24.9696	−	43.2485i	−0.986238	−	1.70821i	−0.349939	−	0.936772i	$-0.613798\pi$
$642$	1.55667	+	0.495716i	0.0614369	+	0.0195644i
$643$	16.3136	−	16.3136i	0.643345	−	0.643345i	−0.308031	−	0.951376i	$-0.599670\pi$
$643$	16.3136	−	16.3136i	0.643345	−	0.643345i	0.951376	+	0.308031i	$0.0996701\pi$
$644$		0			0
$645$	20.0030	−	29.0099i	0.787618	−	1.14226i
$646$	8.14837	−	4.21219i	0.320593	−	0.165727i
$647$	4.17257	−	15.5722i	0.164041	−	0.612208i	−0.834120	−	0.551583i	$-0.814024\pi$
$647$	4.17257	−	15.5722i	0.164041	−	0.612208i	0.998161	−	0.0606248i	$-0.0193093\pi$
$648$	0.335810	−	0.791438i	0.0131919	−	0.0310906i
$649$	5.24671	+	3.02919i	0.205951	+	0.118906i
$650$	23.6779	+	4.96311i	0.928725	+	0.194669i
$651$		0			0
$652$	0.00196583	−	0.00530642i	7.69879e−5	−	0.000207816i
$653$	−21.8713	+	5.86041i	−0.855891	+	0.229335i	−0.659977	−	0.751286i	$-0.729434\pi$
$653$	−21.8713	+	5.86041i	−0.855891	+	0.229335i	−0.195914	+	0.980621i	$0.562767\pi$
$654$	−28.9977	−	1.34918i	−1.13390	−	0.0527572i
$655$	9.07034	+	0.727746i	0.354408	+	0.0284354i
$656$	−3.61062	−	10.2847i	−0.140971	−	0.401552i
$657$	−11.5985	+	11.5985i	−0.452501	+	0.452501i
$658$		0			0
$659$	−0.119381			−0.00465044			−0.00232522	−	0.999997i	$-0.500740\pi$
$659$	−0.119381			−0.00465044			−0.00232522	+	0.999997i	$0.500740\pi$
$660$	39.8615	−	3.54703i	1.55161	−	0.138068i
$661$	−10.3433	−	17.9151i	−0.402307	−	0.696816i	0.591697	−	0.806161i	$-0.298458\pi$
$661$	−10.3433	−	17.9151i	−0.402307	−	0.696816i	−0.994004	+	0.109344i	$0.965125\pi$
$662$	3.72618	+	4.08983i	0.144822	+	0.158956i
$663$	5.77388	+	21.5484i	0.224239	+	0.836871i
$664$	17.3597	+	2.43718i	0.673689	+	0.0945810i
$665$		0			0
$666$	−9.00968	+	14.0535i	−0.349118	+	0.544562i
$667$	−8.95846	+	2.40041i	−0.346873	+	0.0929443i
$668$	−1.10477	−	6.48210i	−0.0427449	−	0.250800i
$669$	−45.5445	+	26.2951i	−1.76085	+	1.01663i
$670$	2.34310	−	18.4154i	0.0905219	−	0.711450i
$671$			37.1869i			1.43559i
$672$		0			0
$673$	34.9098	+	34.9098i	1.34568	+	1.34568i	0.890299	+	0.455376i	$0.150495\pi$
$673$	34.9098	+	34.9098i	1.34568	+	1.34568i	0.455376	+	0.890299i	$0.349505\pi$
$674$	−22.4653	+	11.6131i	−0.865330	+	0.447321i
$675$	26.5498	−	2.70880i	1.02190	−	0.104262i
$676$	1.49704	−	2.11217i	0.0575784	−	0.0812373i
$677$	1.32612	+	4.94915i	0.0509669	+	0.190211i	0.986716	−	0.162456i	$-0.0519415\pi$
$677$	1.32612	+	4.94915i	0.0509669	+	0.190211i	−0.935749	+	0.352667i	$0.885275\pi$
$678$	13.9672	+	63.8660i	0.536408	+	2.45276i
$679$		0			0
$680$	10.8043	+	9.92776i	0.414328	+	0.380712i
$681$	−29.2147	+	50.6014i	−1.11951	+	1.93905i
$682$	−11.5949	+	10.5639i	−0.443992	+	0.404513i
$683$	−40.4498	−	10.8385i	−1.54777	−	0.414724i	−0.619003	−	0.785389i	$-0.712463\pi$
$683$	−40.4498	−	10.8385i	−1.54777	−	0.414724i	−0.928767	+	0.370665i	$0.879130\pi$
$684$	27.2749	+	2.54356i	1.04288	+	0.0972553i
$685$	−35.4446	+	6.51348i	−1.35427	+	0.248867i
$686$		0			0
$687$	35.5235	+	35.5235i	1.35530	+	1.35530i
$688$	20.2170	+	9.71049i	0.770766	+	0.370209i
$689$	38.6789	−	22.3313i	1.47355	−	0.850755i
$690$	−6.44909	−	47.3939i	−0.245513	−	1.80425i
$691$	29.5825	+	17.0795i	1.12537	+	0.649734i	0.942767	−	0.333452i	$-0.108213\pi$
$691$	29.5825	+	17.0795i	1.12537	+	0.649734i	0.182606	+	0.983186i	$0.441547\pi$
$692$	−30.1400	−	11.1657i	−1.14575	−	0.424457i
$693$		0			0
$694$	4.57924	−	7.14280i	0.173826	−	0.271137i
$695$	34.4993	−	16.3909i	1.30863	−	0.621742i
$696$	12.7013	−	5.13379i	0.481440	−	0.194596i
$697$	6.10663	+	1.63627i	0.231305	+	0.0619780i
$698$	−6.51659	+	20.4637i	−0.246657	+	0.774562i
$699$	0.991682			0.0375089
$700$		0			0
$701$	−28.1444			−1.06300			−0.531499	−	0.847059i	$-0.678371\pi$
$701$	−28.1444			−1.06300			−0.531499	+	0.847059i	$0.678371\pi$
$702$	−7.83633	+	24.6080i	−0.295763	+	0.928770i
$703$	−6.50664	−	1.74345i	−0.245402	−	0.0657554i
$704$	6.16927	+	24.7130i	0.232513	+	0.931406i
$705$	−35.8744	+	17.0442i	−1.35111	+	0.641923i
$706$	26.2647	−	40.9682i	0.988483	−	1.54186i
$707$		0			0
$708$	−3.71562	+	10.0297i	−0.139641	+	0.376938i
$709$	3.23053	+	1.86515i	0.121325	+	0.0700471i	0.559434	−	0.828875i	$-0.311018\pi$
$709$	3.23053	+	1.86515i	0.121325	+	0.0700471i	−0.438109	+	0.898922i	$0.644352\pi$
$710$	−0.239700	−	1.76154i	−0.00899579	−	0.0661094i
$711$	−35.0903	+	20.2594i	−1.31599	+	0.759788i
$712$	−1.00094	−	8.14221i	−0.0375118	−	0.305142i
$713$	13.2564	+	13.2564i	0.496456	+	0.496456i
$714$		0			0
$715$	−23.9570	+	4.40245i	−0.895939	+	0.164642i
$716$	−3.37509	+	36.1915i	−0.126133	+	1.35254i
$717$	−65.4475	−	17.5366i	−2.44418	−	0.654917i
$718$	−8.78636	+	8.00510i	−0.327904	+	0.298748i
$719$	−14.3205	+	24.8039i	−0.534066	+	0.925029i	0.465142	+	0.885236i	$0.346003\pi$
$719$	−14.3205	+	24.8039i	−0.534066	+	0.925029i	−0.999208	+	0.0397933i	$0.987330\pi$
$720$	11.1617	+	42.3736i	0.415973	+	1.57917i
$721$		0			0
$722$	−3.37911	−	15.4512i	−0.125757	−	0.575034i
$723$	3.16736	+	11.8207i	0.117795	+	0.439618i
$724$	6.99122	+	4.95515i	0.259827	+	0.184157i
$725$	6.67991	+	5.44304i	0.248086	+	0.202150i
$726$	3.04582	−	1.57450i	0.113041	−	0.0584350i
$727$	−35.3576	−	35.3576i	−1.31134	−	1.31134i	−0.920429	−	0.390911i	$-0.872160\pi$
$727$	−35.3576	−	35.3576i	−1.31134	−	1.31134i	−0.390911	−	0.920429i	$-0.627840\pi$
$728$		0			0
$729$		−	43.5147i		−	1.61166i
$730$	1.33635	−	10.5030i	0.0494607	−	0.388733i
$731$	−11.2655	+	6.50414i	−0.416669	+	0.240564i
$732$	−64.7186	+	11.0303i	−2.39207	+	0.407690i
$733$	−19.8341	+	5.31453i	−0.732589	+	0.196297i	−0.605782	−	0.795631i	$-0.707140\pi$
$733$	−19.8341	+	5.31453i	−0.732589	+	0.196297i	−0.126807	+	0.991927i	$0.540473\pi$
$734$	−23.4731	+	36.6138i	−0.866407	+	1.35144i
$735$		0			0
$736$	29.1623	−	8.73831i	1.07494	−	0.322098i
$737$	4.83758	+	18.0541i	0.178194	+	0.665031i
$738$	12.7153	+	13.9563i	0.468058	+	0.513738i
$739$	−24.2010	−	41.9174i	−0.890249	−	1.54196i	−0.839576	−	0.543242i	$-0.817197\pi$
$739$	−24.2010	−	41.9174i	−0.890249	−	1.54196i	−0.0506730	−	0.998715i	$-0.516137\pi$
$740$	−0.955058	−	10.7329i	−0.0351086	−	0.394551i
$741$	−26.8832			−0.987579
$742$		0			0
$743$	3.78255	−	3.78255i	0.138768	−	0.138768i	−0.634310	−	0.773078i	$-0.718716\pi$
$743$	3.78255	−	3.78255i	0.138768	−	0.138768i	0.773078	+	0.634310i	$0.218716\pi$
$744$	−21.8242	−	17.0459i	−0.800115	−	0.624931i
$745$	19.9672	+	1.60204i	0.731541	+	0.0586941i
$746$	21.2435	+	0.988403i	0.777781	+	0.0361880i
$747$	−29.3290	+	7.85869i	−1.07309	+	0.287535i
$748$	−13.8533	−	5.13212i	−0.506526	−	0.187649i
$749$		0			0
$750$	−32.1948	+	30.6313i	−1.17559	+	1.11850i
$751$	−15.5554	−	8.98090i	−0.567623	−	0.327718i	0.188576	−	0.982059i	$-0.439613\pi$
$751$	−15.5554	−	8.98090i	−0.567623	−	0.327718i	−0.756200	+	0.654341i	$0.772946\pi$
$752$	−14.2618	−	20.8723i	−0.520075	−	0.761133i
$753$	−9.70180	+	36.2076i	−0.353553	+	1.31948i
$754$	−7.40724	+	3.82908i	−0.269756	+	0.139447i
$755$	8.54900	−	12.3984i	0.311130	−	0.451224i
$756$		0			0
$757$	−35.0017	+	35.0017i	−1.27216	+	1.27216i	−0.327204	+	0.944954i	$0.606106\pi$
$757$	−35.0017	+	35.0017i	−1.27216	+	1.27216i	−0.944954	+	0.327204i	$0.893894\pi$
$758$	2.59081	+	0.825034i	0.0941024	+	0.0299666i
$759$	24.0790	+	41.7061i	0.874013	+	1.51384i
$760$	−14.9257	+	9.47987i	−0.541413	+	0.343871i
$761$	18.0493	−	31.2622i	0.654285	−	1.13325i	−0.327788	−	0.944751i	$-0.606303\pi$
$761$	18.0493	−	31.2622i	0.654285	−	1.13325i	0.982073	−	0.188503i	$-0.0603636\pi$
$762$	−1.58697	−	7.25651i	−0.0574897	−	0.262876i
$763$		0			0
$764$	9.64999	+	21.0074i	0.349125	+	0.760022i
$765$	−23.9442	−	8.52013i	−0.865705	−	0.308046i
$766$	1.05069	−	22.5824i	0.0379631	−	0.815934i
$767$	1.68495	−	6.28831i	0.0608399	−	0.227058i
$768$	−41.1796	+	18.0670i	−1.48594	+	0.651937i
$769$			22.5137i			0.811865i	0.913903	+	0.405933i	$0.133053\pi$
$769$			22.5137i			0.811865i	−0.913903	+	0.405933i	$0.866947\pi$
$770$		0			0
$771$		−	28.2691i		−	1.01809i
$772$	7.11756	−	5.90328i	0.256167	−	0.212464i
$773$	−5.98883	+	22.3506i	−0.215403	+	0.803896i	0.770621	+	0.637294i	$0.219946\pi$
$773$	−5.98883	+	22.3506i	−0.215403	+	0.803896i	−0.986024	+	0.166602i	$0.946720\pi$
$774$	−38.8057	−	1.80552i	−1.39484	−	0.0648982i
$775$	2.77711	−	17.1950i	0.0997566	−	0.617662i
$776$	−43.2622	−	6.07370i	−1.55302	−	0.218033i
$777$		0			0
$778$	−15.6550	+	3.42368i	−0.561259	+	0.122745i
$779$	−3.80923	+	6.59778i	−0.136480	+	0.236390i
$780$	−14.7679	−	40.3879i	−0.528775	−	1.44612i
$781$	0.894971	+	1.55014i	0.0320246	+	0.0554682i
$782$	−5.35773	+	16.8246i	−0.191592	+	0.601646i
$783$	−6.50425	+	6.50425i	−0.232443	+	0.232443i
$784$		0			0
$785$	−25.0368	+	4.60088i	−0.893601	+	0.164213i
$786$	−7.42758	−	14.3684i	−0.264933	−	0.512505i
$787$	−9.53044	+	35.5681i	−0.339724	+	1.26787i	0.558933	+	0.829213i	$0.311211\pi$
$787$	−9.53044	+	35.5681i	−0.339724	+	1.26787i	−0.898657	+	0.438653i	$0.855456\pi$
$788$	18.8855	−	3.21873i	0.672767	−	0.114662i
$789$	−26.1715	−	15.1101i	−0.931731	−	0.537935i
$790$	9.90368	−	24.2065i	0.352357	−	0.861228i
$791$		0			0
$792$	−26.5565	−	35.2311i	−0.943646	−	1.25188i
$793$	38.5982	−	10.3424i	1.37066	−	0.367268i
$794$	−0.766546	+	16.4752i	−0.0272037	+	0.584684i
$795$	−6.56122	+	81.7766i	−0.232703	+	2.90032i
$796$	0.323065	−	3.46427i	0.0114507	−	0.122788i
$797$	8.30328	−	8.30328i	0.294117	−	0.294117i	−0.544587	−	0.838704i	$-0.683314\pi$
$797$	8.30328	−	8.30328i	0.294117	−	0.294117i	0.838704	+	0.544587i	$0.183314\pi$
$798$		0			0
$799$	14.6620			0.518705
$800$	−22.4413	−	17.2160i	−0.793418	−	0.608677i
$801$	7.10464	+	12.3056i	0.251030	+	0.434797i
$802$	−28.9284	+	26.3562i	−1.02150	+	0.930670i
$803$	2.75904	+	10.2969i	0.0973645	+	0.363369i
$804$	−29.9857	+	13.7743i	−1.05751	+	0.485781i
$805$		0			0
$806$	14.1896	+	9.09693i	0.499807	+	0.320426i
$807$	−25.6682	+	6.87776i	−0.903562	+	0.242109i
$808$	−12.6667	+	29.8530i	−0.445614	+	1.05022i
$809$	27.1489	−	15.6744i	0.954504	−	0.551083i	0.0600265	−	0.998197i	$-0.480881\pi$
$809$	27.1489	−	15.6744i	0.954504	−	0.551083i	0.894477	+	0.447114i	$0.147548\pi$
$810$	−0.588456	−	0.760031i	−0.0206762	−	0.0267048i
$811$		−	9.76550i		−	0.342913i	−0.985192	−	0.171456i	$-0.945153\pi$
$811$		−	9.76550i		−	0.342913i	0.985192	−	0.171456i	$-0.0548473\pi$
$812$		0			0
$813$	−28.6732	−	28.6732i	−1.00561	−	1.00561i
$814$	4.98202	+	9.63757i	0.174620	+	0.337797i
$815$	−0.00410159	−	0.00481718i	−0.000143673	−	0.000168738i
$816$	4.82262	−	25.6319i	0.168826	−	0.897297i
$817$	−4.05719	−	15.1416i	−0.141943	−	0.529739i
$818$	19.1084	−	4.17892i	0.668109	−	0.146112i
$819$		0			0
$820$	−12.0047	−	2.09839i	−0.419222	−	0.0732790i
$821$	3.83240	−	6.63791i	0.133752	−	0.231665i	−0.791368	−	0.611340i	$-0.790631\pi$
$821$	3.83240	−	6.63791i	0.133752	−	0.231665i	0.925120	+	0.379675i	$0.123964\pi$
$822$	43.1425	+	47.3530i	1.50477	+	1.65163i
$823$	52.8907	+	14.1720i	1.84365	+	0.494006i	0.999138	−	0.0415239i	$-0.0132213\pi$
$823$	52.8907	+	14.1720i	1.84365	+	0.494006i	0.844517	+	0.535530i	$0.179888\pi$
$824$	22.8111	−	29.2056i	0.794663	−	1.01743i
$825$	18.3228	−	40.8189i	0.637919	−	1.42113i
$826$		0			0
$827$	−35.5553	−	35.5553i	−1.23638	−	1.23638i	−0.961470	−	0.274910i	$-0.911352\pi$
$827$	−35.5553	−	35.5553i	−1.23638	−	1.23638i	−0.274910	−	0.961470i	$-0.588648\pi$
$828$	−40.5874	+	33.6631i	−1.41051	+	1.16987i
$829$	−23.4882	+	13.5609i	−0.815780	+	0.470991i	−0.848959	−	0.528459i	$-0.822770\pi$
$829$	−23.4882	+	13.5609i	−0.815780	+	0.470991i	0.0331794	+	0.999449i	$0.489437\pi$
$830$	11.8635	−	15.6007i	0.411789	−	0.541509i
$831$	−80.5397	−	46.4996i	−2.79389	−	1.61305i
$832$	23.9351	−	13.2765i	0.829800	−	0.460281i
$833$		0			0
$834$	−57.1560	−	36.6426i	−1.97915	−	1.26883i
$835$	−6.92628	−	2.46460i	−0.239694	−	0.0852909i
$836$	10.2945	−	14.5246i	0.356044	−	0.502342i
$837$	17.9600	+	4.81237i	0.620789	+	0.166340i
$838$	27.8908	+	8.88173i	0.963472	+	0.306814i
$839$	3.82948			0.132208			0.0661042	−	0.997813i	$-0.478943\pi$
$839$	3.82948			0.132208			0.0661042	+	0.997813i	$0.478943\pi$
$840$		0			0
$841$	26.0301			0.897589
$842$	−36.0489	−	11.4796i	−1.24233	−	0.395614i
$843$	−27.6011	−	7.39570i	−0.950634	−	0.254722i
$844$	27.4767	−	38.7669i	0.945788	−	1.33441i
$845$	−1.24212	−	2.61440i	−0.0427304	−	0.0899382i
$846$	36.8617	+	23.6320i	1.26733	+	0.812485i
$847$		0			0
$848$	−52.0665	+	3.95551i	−1.78797	+	0.135833i
$849$	67.4183	+	38.9240i	2.31379	+	1.33587i
$850$	15.5875	−	5.11337i	0.534648	−	0.175387i
$851$	11.2296	−	6.48342i	0.384946	−	0.222249i
$852$	−2.43233	+	2.01737i	−0.0833302	+	0.0691138i
$853$	1.20013	+	1.20013i	0.0410916	+	0.0410916i	0.727354	−	0.686262i	$-0.240750\pi$
$853$	1.20013	+	1.20013i	0.0410916	+	0.0410916i	−0.686262	+	0.727354i	$0.740750\pi$
$854$		0			0
$855$	17.3855	−	25.2137i	0.594571	−	0.862291i
$856$	0.916206	+	0.715604i	0.0313153	+	0.0244588i
$857$	25.5819	+	6.85466i	0.873862	+	0.234151i	0.667757	−	0.744379i	$-0.267254\pi$
$857$	25.5819	+	6.85466i	0.873862	+	0.234151i	0.206105	+	0.978530i	$0.433921\pi$
$858$	29.1599	+	32.0058i	0.995503	+	1.09266i
$859$	−19.8151	+	34.3208i	−0.676083	+	1.17101i	0.300068	+	0.953918i	$0.402991\pi$
$859$	−19.8151	+	34.3208i	−0.676083	+	1.17101i	−0.976151	+	0.217093i	$0.930343\pi$
$860$	20.5192	−	14.4131i	0.699700	−	0.491483i
$861$		0			0
$862$	55.7308	−	12.1881i	1.89820	−	0.415128i
$863$	2.57861	+	9.62351i	0.0877769	+	0.327588i	0.995826	−	0.0912768i	$-0.0290948\pi$
$863$	2.57861	+	9.62351i	0.0877769	+	0.327588i	−0.908049	+	0.418865i	$0.862428\pi$
$864$	20.7148	−	21.9670i	0.704731	−	0.747334i
$865$	−27.3611	+	23.2966i	−0.930305	+	0.792110i
$866$	15.2306	+	29.4632i	0.517558	+	1.00120i
$867$	−23.0883	−	23.0883i	−0.784120	−	0.784120i
$868$		0			0
$869$			26.3331i			0.893290i
$870$	1.93323	−	15.1941i	0.0655426	−	0.515127i
$871$	17.3938	−	10.0423i	0.589368	−	0.340272i
$872$	−19.0163	−	8.06870i	−0.643974	−	0.273241i
$873$	73.0908	−	19.5846i	2.47375	−	0.662839i
$874$	−17.9128	−	11.4839i	−0.605909	−	0.388448i
$875$		0			0
$876$	−17.1019	+	7.85595i	−0.577820	+	0.265428i
$877$	0.664074	+	2.47836i	0.0224242	+	0.0836882i	0.976231	−	0.216732i	$-0.0695398\pi$
$877$	0.664074	+	2.47836i	0.0224242	+	0.0836882i	−0.953807	+	0.300420i	$0.902873\pi$
$878$	6.00198	−	5.46830i	0.202557	−	0.184546i
$879$	6.12031	+	10.6007i	0.206433	+	0.357553i
$880$	27.4760	+	7.48711i	0.926217	+	0.252390i
$881$	−20.5639			−0.692816			−0.346408	−	0.938084i	$-0.612599\pi$
$881$	−20.5639			−0.692816			−0.346408	+	0.938084i	$0.612599\pi$
$882$		0			0
$883$	26.6080	−	26.6080i	0.895429	−	0.895429i	−0.0995985	−	0.995028i	$-0.531756\pi$
$883$	26.6080	−	26.6080i	0.895429	−	0.895429i	0.995028	+	0.0995985i	$0.0317558\pi$
$884$	−1.47404	+	15.8064i	−0.0495775	+	0.531626i
$885$	7.75242	+	9.10495i	0.260595	+	0.306059i
$886$	0.0562553	−	1.20908i	0.00188993	−	0.0406199i
$887$	7.10873	−	1.90478i	0.238688	−	0.0639562i	−0.137492	−	0.990503i	$-0.543904\pi$
$887$	7.10873	−	1.90478i	0.238688	−	0.0639562i	0.376180	+	0.926547i	$0.377238\pi$
$888$	−15.2951	+	11.5292i	−0.513269	+	0.386893i
$889$		0			0
$890$	−8.48880	−	3.47305i	−0.284545	−	0.116417i
$891$	0.838132	+	0.483895i	0.0280785	+	0.0162111i
$892$	−36.8917	+	6.28760i	−1.23523	+	0.210524i
$893$	−4.57299	+	17.0666i	−0.153029	+	0.571112i
$894$	−16.3508	−	31.6302i	−0.546854	−	1.05787i
$895$	33.4565	+	23.0691i	1.11833	+	0.771115i
$896$		0			0
$897$	36.5921	−	36.5921i	1.22177	−	1.22177i
$898$	−2.00037	+	6.28165i	−0.0667532	+	0.209621i
$899$	3.00169	+	5.19908i	0.100112	+	0.173399i
$900$	47.4302	+	12.2682i	1.58101	+	0.408941i
$901$	15.1427	−	26.2280i	0.504478	−	0.873781i
$902$	11.9868	−	2.62146i	0.399117	−	0.0872852i
$903$		0			0
$904$	−6.46788	+	46.0699i	−0.215119	+	1.53226i
$905$	8.65360	−	4.11140i	0.287655	−	0.136667i
$906$	−26.7409	−	1.24418i	−0.888408	−	0.0413352i
$907$	−3.60588	+	13.4573i	−0.119731	+	0.446843i	−0.999597	−	0.0283786i	$-0.990966\pi$
$907$	−3.60588	+	13.4573i	−0.119731	+	0.446843i	0.879866	+	0.475222i	$0.157632\pi$
$908$	−32.0036	+	26.5437i	−1.06208	+	0.880884i
$909$		−	56.1704i		−	1.86305i
$910$		0			0
$911$		−	9.10653i		−	0.301713i	−0.988556	−	0.150856i	$-0.951797\pi$
$911$		−	9.10653i		−	0.301713i	0.988556	−	0.150856i	$-0.0482031\pi$
$912$	28.3315	+	13.6080i	0.938148	+	0.450605i
$913$	−5.10735	+	19.0609i	−0.169029	+	0.630823i
$914$	2.09074	−	44.9359i	0.0691557	−	1.48635i
$915$	−24.6070	+	69.1534i	−0.813484	+	2.28614i
$916$	14.9228	+	32.4860i	0.493064	+	1.07337i
$917$		0			0
$918$	3.74142	+	17.1079i	0.123485	+	0.564644i
$919$	17.5872	−	30.4620i	0.580149	−	1.00485i	−0.415312	−	0.909679i	$-0.636328\pi$
$919$	17.5872	−	30.4620i	0.580149	−	1.00485i	0.995461	−	0.0951683i	$-0.0303389\pi$
$920$	7.41263	−	33.2197i	0.244387	−	1.09522i
$921$	−26.5004	−	45.9000i	−0.873217	−	1.51246i
$922$	−31.5923	−	10.0605i	−1.04044	−	0.331324i
$923$	1.36006	−	1.36006i	0.0447668	−	0.0447668i
$924$		0			0
$925$	−10.9907	−	4.93353i	−0.361372	−	0.162213i
$926$	−3.27190	+	1.69136i	−0.107521	+	0.0555817i
$927$	−16.6132	+	62.0014i	−0.545650	+	2.03639i
$928$	9.74452	−	0.285898i	0.319879	−	0.00938505i
$929$	32.5064	+	18.7676i	1.06650	+	0.615745i	0.927223	−	0.374509i	$-0.122189\pi$
$929$	32.5064	+	18.7676i	1.06650	+	0.615745i	0.139278	+	0.990253i	$0.455522\pi$
$930$	−28.5523	+	11.9723i	−0.936268	+	0.392588i
$931$		0			0
$932$	0.661739	+	0.245150i	0.0216760	+	0.00803015i
$933$	−4.24615	+	1.13775i	−0.139013	+	0.0372483i
$934$	−11.7215	−	0.545370i	−0.383540	−	0.0178451i
$935$	−12.5760	+	10.7079i	−0.411280	+	0.350185i
$936$	−29.1823	+	37.3628i	−0.953853	+	1.22124i
$937$	14.9371	−	14.9371i	0.487973	−	0.487973i	−0.419693	−	0.907666i	$-0.637862\pi$
$937$	14.9371	−	14.9371i	0.487973	−	0.487973i	0.907666	+	0.419693i	$0.137862\pi$
$938$		0			0
$939$	34.2270			1.11696
$940$	−28.1520	+	2.50507i	−0.918218	+	0.0817065i
$941$	3.05589	+	5.29296i	0.0996192	+	0.172546i	0.911527	−	0.411240i	$-0.134904\pi$
$941$	3.05589	+	5.29296i	0.0996192	+	0.172546i	−0.811908	+	0.583786i	$0.801571\pi$
$942$	30.4743	+	33.4484i	0.992905	+	1.08981i
$943$	−3.79564	−	14.1655i	−0.123603	−	0.461293i
$944$	−4.95878	+	5.77417i	−0.161395	+	0.187933i
$945$		0			0
$946$	−13.6261	+	21.2543i	−0.443022	+	0.691036i
$947$	41.6507	−	11.1603i	1.35347	−	0.362660i	0.492053	−	0.870565i	$-0.336247\pi$
$947$	41.6507	−	11.1603i	1.35347	−	0.362660i	0.861413	+	0.507905i	$0.169580\pi$
$948$	−45.8291	+	7.81083i	−1.48846	+	0.253684i
$949$	9.92033	−	5.72751i	0.322028	−	0.185923i
$950$	1.09032	+	19.7387i	0.0353748	+	0.640409i
$951$		−	76.9801i		−	2.49625i
$952$		0			0
$953$	26.8326	+	26.8326i	0.869193	+	0.869193i	0.992383	−	0.123190i	$-0.0393125\pi$
$953$	26.8326	+	26.8326i	0.869193	+	0.869193i	−0.123190	+	0.992383i	$0.539313\pi$
$954$	80.3441	−	41.5328i	2.60123	−	1.34467i
$955$	25.7637	+	2.06711i	0.833695	+	0.0668903i
$956$	−39.3373	−	27.8810i	−1.27226	−	0.901736i
$957$	3.99135	+	14.8959i	0.129022	+	0.481517i
$958$	−4.22953	−	19.3398i	−0.136650	−	0.624841i
$959$		0			0
$960$	−4.88042	+	50.0390i	−0.157515	+	1.61500i
$961$	−9.43240	+	16.3374i	−0.304271	+	0.527013i
$962$	8.61774	−	7.85148i	0.277847	−	0.253142i
$963$	−1.94504	−	0.521171i	−0.0626779	−	0.0167945i
$964$	−0.808611	+	8.67084i	−0.0260436	+	0.279269i
$965$	−1.86857	−	10.1683i	−0.0601515	−	0.327329i
$966$		0			0
$967$	9.65871	+	9.65871i	0.310603	+	0.310603i	0.845143	−	0.534540i	$-0.179515\pi$
$967$	9.65871	+	9.65871i	0.310603	+	0.310603i	−0.534540	+	0.845143i	$0.679515\pi$
$968$	2.42167	−	0.297700i	0.0778353	−	0.00956845i
$969$	−15.7871	+	9.11468i	−0.507155	+	0.292806i
$970$	−29.5651	+	38.8785i	−0.949278	+	1.24831i
$971$	18.9435	+	10.9371i	0.607927	+	0.350987i	0.772154	−	0.635436i	$-0.219179\pi$
$971$	18.9435	+	10.9371i	0.607927	+	0.350987i	−0.164226	+	0.986423i	$0.552513\pi$
$972$	10.5317	−	28.4284i	0.337804	−	0.911843i
$973$		0			0
$974$	−20.2623	+	31.6056i	−0.649246	+	1.01271i
$975$	−47.4639	−	7.66574i	−1.52006	−	0.245500i
$976$	−45.9128	−	8.63844i	−1.46963	−	0.276510i
$977$	25.1707	+	6.74446i	0.805281	+	0.215774i	0.637901	−	0.770118i	$-0.279803\pi$
$977$	25.1707	+	6.74446i	0.805281	+	0.215774i	0.167380	+	0.985893i	$0.446469\pi$
$978$	−0.00341244	+	0.0107159i	−0.000109118	+	0.000342657i
$979$	9.23458			0.295138
$980$		0			0
$981$	35.7805			1.14238
$982$	15.2709	−	47.9545i	0.487315	−	1.53029i
$983$	46.8710	+	12.5590i	1.49495	+	0.400571i	0.911406	−	0.411508i	$-0.134998\pi$
$983$	46.8710	+	12.5590i	1.49495	+	0.400571i	0.583547	+	0.812080i	$0.301664\pi$
$984$	8.11777	+	20.0838i	0.258785	+	0.640248i
$985$	7.18055	−	20.1796i	0.228791	−	0.642975i
$986$	−3.05165	+	4.76002i	−0.0971842	+	0.151590i
$987$		0			0
$988$	−17.9389	−	6.64569i	−0.570712	−	0.211427i
$989$	26.1325	+	15.0876i	0.830965	+	0.479758i
$990$	−48.8760	+	6.65077i	−1.55338	+	0.211375i
$991$	−3.40592	+	1.96641i	−0.108193	+	0.0624650i	−0.553120	−	0.833102i	$-0.686563\pi$
$991$	−3.40592	+	1.96641i	−0.108193	+	0.0624650i	0.444927	+	0.895567i	$0.353230\pi$
$992$	−10.3492	−	16.7696i	−0.328589	−	0.532435i
$993$	−7.77497	−	7.77497i	−0.246731	−	0.246731i
$994$		0			0
$995$	−3.20247	−	2.20818i	−0.101525	−	0.0700041i
$996$	−34.6877	−	3.23485i	−1.09912	−	0.102500i
$997$	49.5831	+	13.2857i	1.57031	+	0.420764i	0.935910	−	0.352240i	$-0.114580\pi$
$997$	49.5831	+	13.2857i	1.57031	+	0.420764i	0.634402	+	0.773004i	$0.281247\pi$
$998$	−10.3309	+	9.41233i	−0.327020	+	0.297942i
$999$	6.43023	−	11.1375i	0.203443	−	0.352374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.m.863.3		72
4.3	odd	2	inner	980.2.x.m.863.13		72
5.2	odd	4	inner	980.2.x.m.667.11		72
7.2	even	3		980.2.k.j.883.11		36
7.3	odd	6		140.2.w.b.123.15	yes	72
7.4	even	3	inner	980.2.x.m.263.15		72
7.5	odd	6		980.2.k.k.883.11		36
7.6	odd	2		140.2.w.b.23.3	✓	72
20.7	even	4	inner	980.2.x.m.667.15		72
28.3	even	6		140.2.w.b.123.11	yes	72
28.11	odd	6	inner	980.2.x.m.263.11		72
28.19	even	6		980.2.k.k.883.2		36
28.23	odd	6		980.2.k.j.883.2		36
28.27	even	2		140.2.w.b.23.13	yes	72
35.2	odd	12		980.2.k.j.687.2		36
35.3	even	12		700.2.be.e.207.6		72
35.12	even	12		980.2.k.k.687.2		36
35.13	even	4		700.2.be.e.107.8		72
35.17	even	12		140.2.w.b.67.13	yes	72
35.24	odd	6		700.2.be.e.543.4		72
35.27	even	4		140.2.w.b.107.11	yes	72
35.32	odd	12	inner	980.2.x.m.67.13		72
35.34	odd	2		700.2.be.e.443.16		72
140.3	odd	12		700.2.be.e.207.16		72
140.27	odd	4		140.2.w.b.107.15	yes	72
140.47	odd	12		980.2.k.k.687.11		36
140.59	even	6		700.2.be.e.543.8		72
140.67	even	12	inner	980.2.x.m.67.3		72
140.83	odd	4		700.2.be.e.107.4		72
140.87	odd	12		140.2.w.b.67.3	yes	72
140.107	even	12		980.2.k.j.687.11		36
140.139	even	2		700.2.be.e.443.6		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.3	✓	72	7.6	odd	2
140.2.w.b.23.13	yes	72	28.27	even	2
140.2.w.b.67.3	yes	72	140.87	odd	12
140.2.w.b.67.13	yes	72	35.17	even	12
140.2.w.b.107.11	yes	72	35.27	even	4
140.2.w.b.107.15	yes	72	140.27	odd	4
140.2.w.b.123.11	yes	72	28.3	even	6
140.2.w.b.123.15	yes	72	7.3	odd	6
700.2.be.e.107.4		72	140.83	odd	4
700.2.be.e.107.8		72	35.13	even	4
700.2.be.e.207.6		72	35.3	even	12
700.2.be.e.207.16		72	140.3	odd	12
700.2.be.e.443.6		72	140.139	even	2
700.2.be.e.443.16		72	35.34	odd	2
700.2.be.e.543.4		72	35.24	odd	6
700.2.be.e.543.8		72	140.59	even	6
980.2.k.j.687.2		36	35.2	odd	12
980.2.k.j.687.11		36	140.107	even	12
980.2.k.j.883.2		36	28.23	odd	6
980.2.k.j.883.11		36	7.2	even	3
980.2.k.k.687.2		36	35.12	even	12
980.2.k.k.687.11		36	140.47	odd	12
980.2.k.k.883.2		36	28.19	even	6
980.2.k.k.883.11		36	7.5	odd	6
980.2.x.m.67.3		72	140.67	even	12	inner
980.2.x.m.67.13		72	35.32	odd	12	inner
980.2.x.m.263.11		72	28.11	odd	6	inner
980.2.x.m.263.15		72	7.4	even	3	inner
980.2.x.m.667.11		72	5.2	odd	4	inner
980.2.x.m.667.15		72	20.7	even	4	inner
980.2.x.m.863.3		72	1.1	even	1	trivial
980.2.x.m.863.13		72	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.34754 - 0.429119i) q^{2} +(2.71477 + 0.727420i) q^{3} +(1.63171 + 1.15651i) q^{4} +(2.01971 - 0.959579i) q^{5} +(-3.34610 - 2.14518i) q^{6} +(-1.70252 - 2.25864i) q^{8} +(4.24276 + 2.44956i) q^{9} +(-3.13340 + 0.426375i) q^{10} +(2.75736 - 1.59196i) q^{11} +(3.58846 + 4.32659i) q^{12} +(-2.41925 - 2.41925i) q^{13} +(6.18105 - 1.13586i) q^{15} +(1.32498 + 3.77418i) q^{16} +(-2.24094 - 0.600458i) q^{17} +(-4.66612 - 5.12151i) q^{18} +(1.39787 - 2.42118i) q^{19} +(4.40534 + 0.770044i) q^{20} +(-4.39878 + 0.961994i) q^{22} +(1.39288 + 5.19830i) q^{23} +(-2.97897 - 7.37012i) q^{24} +(3.15842 - 3.87613i) q^{25} +(2.22189 + 4.29818i) q^{26} +(3.77420 + 3.77420i) q^{27} +1.72334i q^{29} +(-8.81662 - 1.12179i) q^{30} +(3.01685 - 1.74178i) q^{31} +(-0.165897 - 5.65442i) q^{32} +(8.64362 - 2.31605i) q^{33} +(2.76208 + 1.77077i) q^{34} +(4.09004 + 8.90375i) q^{36} +(-0.623610 - 2.32734i) q^{37} +(-2.92265 + 2.66278i) q^{38} +(-4.80790 - 8.32752i) q^{39} +(-5.60592 - 2.92808i) q^{40} -2.72503 q^{41} +(3.96477 - 3.96477i) q^{43} +(6.34034 + 0.591276i) q^{44} +(10.9197 + 0.876123i) q^{45} +(0.353728 - 7.60261i) q^{46} +(-6.10452 + 1.63570i) q^{47} +(0.851615 + 11.2098i) q^{48} +(-5.91941 + 3.86790i) q^{50} +(-5.64685 - 3.26021i) q^{51} +(-1.14965 - 6.74541i) q^{52} +(-3.37866 + 12.6093i) q^{53} +(-3.46629 - 6.70545i) q^{54} +(4.04144 - 5.86120i) q^{55} +(5.55610 - 5.55610i) q^{57} +(0.739519 - 2.32227i) q^{58} +(0.951402 + 1.64788i) q^{59} +(11.3993 + 5.29503i) q^{60} +(-5.83980 + 10.1148i) q^{61} +(-4.81275 + 1.05253i) q^{62} +(-2.20286 + 7.69073i) q^{64} +(-7.20764 - 2.56471i) q^{65} +(-12.6415 - 0.588172i) q^{66} +(-1.51938 + 5.67039i) q^{67} +(-2.96214 - 3.57144i) q^{68} +15.1254i q^{69} +0.562181i q^{71} +(-1.69071 - 13.7532i) q^{72} +(-0.866554 + 3.23402i) q^{73} +(-0.158369 + 3.40378i) q^{74} +(11.3940 - 8.22531i) q^{75} +(5.08103 - 2.33403i) q^{76} +(2.90533 + 13.2848i) q^{78} +(-4.13532 + 7.16259i) q^{79} +(6.29770 + 6.35130i) q^{80} +(0.151981 + 0.263239i) q^{81} +(3.67208 + 1.16936i) q^{82} +(-4.38250 + 4.38250i) q^{83} +(-5.10222 + 0.937610i) q^{85} +(-7.04404 + 3.64132i) q^{86} +(-1.25360 + 4.67848i) q^{87} +(-8.29011 - 3.51752i) q^{88} +(2.51180 + 1.45019i) q^{89} +(-14.3387 - 5.86644i) q^{90} +(-3.73908 + 10.0930i) q^{92} +(9.45706 - 2.53401i) q^{93} +(8.92798 + 0.415394i) q^{94} +(0.499970 - 6.23143i) q^{95} +(3.66277 - 15.4711i) q^{96} +(10.9216 - 10.9216i) q^{97} +15.5984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) \) 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

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