LMFDB - Embedded newform 980.2.x.m.67.13

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			67.13
Character	$\chi$	$=$	980.67
Dual form			980.2.x.m.863.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.952442 + 1.04540i) q^{2} +(-2.71477 + 0.727420i) q^{3} +(-0.185707 + 1.99136i) q^{4} +(2.01971 + 0.959579i) q^{5} +(-3.34610 - 2.14518i) q^{6} +(-2.25864 + 1.70252i) q^{8} +(4.24276 - 2.44956i) q^{9} +(0.920513 + 3.02534i) q^{10} +(-2.75736 - 1.59196i) q^{11} +(-0.944404 - 5.54117i) q^{12} +(-2.41925 + 2.41925i) q^{13} +(-6.18105 - 1.13586i) q^{15} +(-3.93103 - 0.739618i) q^{16} +(-2.24094 + 0.600458i) q^{17} +(6.60174 + 2.10230i) q^{18} +(-1.39787 - 2.42118i) q^{19} +(-2.28594 + 3.84376i) q^{20} +(-0.961994 - 4.39878i) q^{22} +(-1.39288 + 5.19830i) q^{23} +(4.89323 - 6.26492i) q^{24} +(3.15842 + 3.87613i) q^{25} +(-4.83327 - 0.224879i) q^{26} +(-3.77420 + 3.77420i) q^{27} -1.72334i q^{29} +(-4.69967 - 7.54349i) q^{30} +(-3.01685 - 1.74178i) q^{31} +(-2.97088 - 4.81392i) 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} +(1.19970 - 3.76736i) q^{38} +(4.80790 - 8.32752i) q^{39} +(-6.19548 + 1.27125i) q^{40} -2.72503 q^{41} +(-3.96477 - 3.96477i) q^{43} +(3.68223 - 5.19525i) q^{44} +(10.9197 - 0.876123i) q^{45} +(-6.76092 + 3.49497i) q^{46} +(6.10452 + 1.63570i) q^{47} +(11.2098 - 0.851615i) q^{48} +(-1.04388 + 6.99359i) q^{50} +(5.64685 - 3.26021i) q^{51} +(-4.36833 - 5.26687i) q^{52} +(-3.37866 - 12.6093i) q^{53} +(-7.54024 - 0.350826i) q^{54} +(-4.04144 - 5.86120i) q^{55} +(5.55610 + 5.55610i) q^{57} +(1.80158 - 1.64139i) q^{58} +(-0.951402 + 1.64788i) q^{59} +(3.40977 - 12.0978i) q^{60} +(-5.83980 - 10.1148i) q^{61} +(-1.05253 - 4.81275i) q^{62} +(2.20286 - 7.69073i) q^{64} +(-7.20764 + 2.56471i) q^{65} +(5.81136 + 11.2419i) q^{66} +(1.51938 + 5.67039i) q^{67} +(-0.779570 - 4.57403i) q^{68} -15.1254i q^{69} +0.562181i q^{71} +(-5.41242 + 12.7560i) q^{72} +(-0.866554 - 3.23402i) q^{73} +(-3.02695 + 1.56474i) q^{74} +(-11.3940 - 8.22531i) q^{75} +(5.08103 - 2.33403i) q^{76} +(13.2848 - 2.90533i) q^{78} +(4.13532 + 7.16259i) q^{79} +(-7.22979 - 5.26594i) q^{80} +(0.151981 - 0.263239i) q^{81} +(-2.59543 - 2.84874i) q^{82} +(4.38250 + 4.38250i) q^{83} +(-5.10222 - 0.937610i) q^{85} +(0.368541 - 7.92097i) q^{86} +(1.25360 + 4.67848i) q^{87} +(8.93821 - 1.09879i) q^{88} +(2.51180 - 1.45019i) q^{89} +(11.3162 + 10.5809i) q^{90} +(-10.0930 - 3.73908i) q^{92} +(9.45706 + 2.53401i) q^{93} +(4.10425 + 7.93955i) q^{94} +(-0.499970 - 6.23143i) q^{95} +(11.5670 + 10.9076i) 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 $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.952442	+	1.04540i	0.673478	+	0.739207i
$2$	0.952442	+	1.04540i	0.673478	+	0.739207i
$3$	−2.71477	+	0.727420i	−1.56737	+	0.419976i	−0.934988	−	0.354678i	$-0.884590\pi$
$3$	−2.71477	+	0.727420i	−1.56737	+	0.419976i	−0.632384	+	0.774655i	$0.717924\pi$
$4$	−0.185707	+	1.99136i	−0.0928534	+	0.995680i
$5$	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
$8$	−2.25864	+	1.70252i	−0.798548	+	0.601931i
$9$	4.24276	−	2.44956i	1.41425	−	0.816519i
$10$	0.920513	+	3.02534i	0.291092	+	0.956695i
$11$	−2.75736	−	1.59196i	−0.831375	−	0.479994i	0.0229484	−	0.999737i	$-0.492695\pi$
$11$	−2.75736	−	1.59196i	−0.831375	−	0.479994i	−0.854323	+	0.519742i	$0.826028\pi$
$12$	−0.944404	−	5.54117i	−0.272626	−	1.59960i
$13$	−2.41925	+	2.41925i	−0.670980	+	0.670980i	−0.957942	−	0.286962i	$-0.907355\pi$
$13$	−2.41925	+	2.41925i	−0.670980	+	0.670980i	0.286962	+	0.957942i	$0.407355\pi$
$14$		0			0
$15$	−6.18105	−	1.13586i	−1.59594	−	0.293278i
$16$	−3.93103	−	0.739618i	−0.982756	−	0.184905i
$17$	−2.24094	+	0.600458i	−0.543508	+	0.145632i	−0.520119	−	0.854094i	$-0.674112\pi$
$17$	−2.24094	+	0.600458i	−0.543508	+	0.145632i	−0.0233890	+	0.999726i	$0.507446\pi$
$18$	6.60174	+	2.10230i	1.55604	+	0.495517i
$19$	−1.39787	−	2.42118i	−0.320693	−	0.555456i	0.659938	−	0.751320i	$-0.270582\pi$
$19$	−1.39787	−	2.42118i	−0.320693	−	0.555456i	−0.980631	+	0.195863i	$0.937249\pi$
$20$	−2.28594	+	3.84376i	−0.511152	+	0.859491i
$21$		0			0
$22$	−0.961994	−	4.39878i	−0.205098	−	0.937824i
$23$	−1.39288	+	5.19830i	−0.290435	+	1.08392i	0.654340	+	0.756201i	$0.272947\pi$
$23$	−1.39288	+	5.19830i	−0.290435	+	1.08392i	−0.944775	+	0.327719i	$0.893720\pi$
$24$	4.89323	−	6.26492i	0.998826	−	1.27882i
$25$	3.15842	+	3.87613i	0.631683	+	0.775226i
$26$	−4.83327	−	0.224879i	−0.947883	−	0.0441024i
$27$	−3.77420	+	3.77420i	−0.726345	+	0.726345i
$28$		0			0
$29$		−	1.72334i		−	0.320017i	−0.987116	−	0.160009i	$-0.948848\pi$
$29$		−	1.72334i		−	0.320017i	0.987116	−	0.160009i	$-0.0511522\pi$
$30$	−4.69967	−	7.54349i	−0.858038	−	1.37725i
$31$	−3.01685	−	1.74178i	−0.541843	−	0.312833i	0.203983	−	0.978974i	$-0.434611\pi$
$31$	−3.01685	−	1.74178i	−0.541843	−	0.312833i	−0.745825	+	0.666141i	$0.767945\pi$
$32$	−2.97088	−	4.81392i	−0.525183	−	0.850990i
$33$	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	−0.998052	−	0.0623856i	$-0.980129\pi$
$37$	−0.623610	+	2.32734i	−0.102521	+	0.382613i	0.895531	+	0.444999i	$0.146796\pi$
$38$	1.19970	−	3.76736i	0.194617	−	0.611146i
$39$	4.80790	−	8.32752i	0.769880	−	1.33347i
$40$	−6.19548	+	1.27125i	−0.979591	+	0.201002i
$41$	−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	$-0.390617\pi$
$43$	−3.96477	−	3.96477i	−0.604622	−	0.604622i	−0.941536	+	0.336914i	$0.890617\pi$
$44$	3.68223	−	5.19525i	0.555117	−	0.783214i
$45$	10.9197	−	0.876123i	1.62781	−	0.130605i
$46$	−6.76092	+	3.49497i	−0.996843	+	0.515305i
$47$	6.10452	+	1.63570i	0.890435	+	0.238591i	0.674904	−	0.737905i	$-0.264185\pi$
$47$	6.10452	+	1.63570i	0.890435	+	0.238591i	0.215531	+	0.976497i	$0.430852\pi$
$48$	11.2098	−	0.851615i	1.61800	−	0.122920i
$49$		0			0
$50$	−1.04388	+	6.99359i	−0.147627	+	0.989043i
$51$	5.64685	−	3.26021i	0.790717	−	0.456521i
$52$	−4.36833	−	5.26687i	−0.605778	−	0.730384i
$53$	−3.37866	−	12.6093i	−0.464094	−	1.73202i	−0.659874	−	0.751376i	$-0.729390\pi$
$53$	−3.37866	−	12.6093i	−0.464094	−	1.73202i	0.195780	−	0.980648i	$-0.437276\pi$
$54$	−7.54024	−	0.350826i	−1.02610	−	0.0477414i
$55$	−4.04144	−	5.86120i	−0.544947	−	0.790323i
$56$		0			0
$57$	5.55610	+	5.55610i	0.735924	+	0.735924i
$58$	1.80158	−	1.64139i	0.236559	−	0.215525i
$59$	−0.951402	+	1.64788i	−0.123862	+	0.214535i	−0.921288	−	0.388882i	$-0.872861\pi$
$59$	−0.951402	+	1.64788i	−0.123862	+	0.214535i	0.797426	+	0.603417i	$0.206195\pi$
$60$	3.40977	−	12.0978i	0.440199	−	1.56181i
$61$	−5.83980	−	10.1148i	−0.747709	−	1.29507i	−0.948918	−	0.315522i	$-0.897820\pi$
$61$	−5.83980	−	10.1148i	−0.747709	−	1.29507i	0.201209	−	0.979548i	$-0.435513\pi$
$62$	−1.05253	−	4.81275i	−0.133671	−	0.611220i
$63$		0			0
$64$	2.20286	−	7.69073i	0.275358	−	0.961342i
$65$	−7.20764	+	2.56471i	−0.893997	+	0.318113i
$66$	5.81136	+	11.2419i	0.715329	+	1.38378i
$67$	1.51938	+	5.67039i	0.185621	+	0.692748i	0.994497	+	0.104768i	$0.0334100\pi$
$67$	1.51938	+	5.67039i	0.185621	+	0.692748i	−0.808875	+	0.587980i	$0.799923\pi$
$68$	−0.779570	−	4.57403i	−0.0945367	−	0.554682i
$69$		−	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	$0.989379\pi$
$72$	−5.41242	+	12.7560i	−0.637860	+	1.50331i
$73$	−0.866554	−	3.23402i	−0.101423	−	0.378514i	0.896492	−	0.443059i	$-0.146107\pi$
$73$	−0.866554	−	3.23402i	−0.101423	−	0.378514i	−0.997915	+	0.0645454i	$0.979440\pi$
$74$	−3.02695	+	1.56474i	−0.351876	+	0.181897i
$75$	−11.3940	−	8.22531i	−1.31566	−	0.949777i
$76$	5.08103	−	2.33403i	0.582834	−	0.267731i
$77$		0			0
$78$	13.2848	−	2.90533i	1.50421	−	0.328963i
$79$	4.13532	+	7.16259i	0.465260	+	0.805855i	0.999213	−	0.0396596i	$-0.0126274\pi$
$79$	4.13532	+	7.16259i	0.465260	+	0.805855i	−0.533953	+	0.845514i	$0.679294\pi$
$80$	−7.22979	−	5.26594i	−0.808315	−	0.588750i
$81$	0.151981	−	0.263239i	0.0168868	−	0.0292487i
$82$	−2.59543	−	2.84874i	−0.286618	−	0.314590i
$83$	4.38250	+	4.38250i	0.481042	+	0.481042i	0.905464	−	0.424423i	$-0.139523\pi$
$83$	4.38250	+	4.38250i	0.481042	+	0.481042i	−0.424423	+	0.905464i	$0.639523\pi$
$84$		0			0
$85$	−5.10222	−	0.937610i	−0.553414	−	0.101698i
$86$	0.368541	−	7.92097i	0.0397408	−	0.854141i
$87$	1.25360	+	4.67848i	0.134400	+	0.501586i
$88$	8.93821	−	1.09879i	0.952816	−	0.117132i
$89$	2.51180	−	1.45019i	0.266250	−	0.153720i	−0.360932	−	0.932592i	$-0.617541\pi$
$89$	2.51180	−	1.45019i	0.266250	−	0.153720i	0.627182	+	0.778872i	$0.284208\pi$
$90$	11.3162	+	10.5809i	1.19284	+	1.11533i
$91$		0			0
$92$	−10.0930	−	3.73908i	−1.05227	−	0.389826i
$93$	9.45706	+	2.53401i	0.980652	+	0.262765i
$94$	4.10425	+	7.93955i	0.423321	+	0.818902i
$95$	−0.499970	−	6.23143i	−0.0512958	−	0.639331i
$96$	11.5670	+	10.9076i	1.18055	+	1.11325i
$97$	10.9216	+	10.9216i	1.10892	+	1.10892i	0.993292	+	0.115629i	$0.0368885\pi$
$97$	10.9216	+	10.9216i	1.10892	+	1.10892i	0.115629	+	0.993292i	$0.463111\pi$
$98$		0			0
$99$	−15.5984			−1.56770
$100$	−8.30531	+	5.56972i	−0.830531	+	0.556972i
$101$	−5.73271	+	9.92934i	−0.570426	+	0.988007i	0.426096	+	0.904678i	$0.359889\pi$
$101$	−5.73271	+	9.92934i	−0.570426	+	0.988007i	−0.996522	+	0.0833288i	$0.973445\pi$
$102$	8.78651	+	2.79803i	0.869994	+	0.277047i
$103$	−3.39107	+	12.6556i	−0.334132	+	1.24700i	0.570676	+	0.821176i	$0.306681\pi$
$103$	−3.39107	+	12.6556i	−0.334132	+	1.24700i	−0.904807	+	0.425821i	$0.859985\pi$
$104$	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	$-0.410342\pi$
$107$	0.397018	+	0.106381i	0.0383812	+	0.0102842i	−0.239577	+	0.970877i	$0.577009\pi$
$108$	−6.81489	−	8.21668i	−0.655763	−	0.790650i
$109$	6.32499	+	3.65173i	0.605824	+	0.349773i	0.771329	−	0.636436i	$-0.219592\pi$
$109$	6.32499	+	3.65173i	0.605824	+	0.349773i	−0.165505	+	0.986209i	$0.552926\pi$
$110$	2.27803	−	9.80736i	0.217202	−	0.935095i
$111$		−	6.77183i		−	0.642753i
$112$		0			0
$113$	−11.6304	+	11.6304i	−1.09410	+	1.09410i	−0.0990127	+	0.995086i	$0.531568\pi$
$113$	−11.6304	+	11.6304i	−1.09410	+	1.09410i	−0.995086	+	0.0990127i	$0.968432\pi$
$114$	−0.516461	+	11.1002i	−0.0483710	+	1.03963i
$115$	−7.80138	+	9.16245i	−0.727482	+	0.854402i
$116$	3.43180	+	0.320037i	0.318635	+	0.0297147i
$117$	−4.33820	+	16.1904i	−0.401067	+	1.49680i
$118$	−2.62884	+	0.574915i	−0.242004	+	0.0529252i
$119$		0			0
$120$	15.8946	−	7.95785i	1.45097	−	0.726449i
$121$	−0.431317	−	0.747063i	−0.0392106	−	0.0679148i
$122$	5.01193	−	15.7387i	0.453759	−	1.42491i
$123$	7.39783	−	1.98224i	0.667040	−	0.178733i
$124$	4.02876	−	5.68418i	0.361793	−	0.510454i
$125$	2.65962	+	10.8594i	0.237883	+	0.971294i
$126$		0			0
$127$	−1.32146	+	1.32146i	−0.117261	+	0.117261i	−0.763302	−	0.646042i	$-0.776423\pi$
$127$	−1.32146	+	1.32146i	−0.117261	+	0.117261i	0.646042	+	0.763302i	$0.276423\pi$
$128$	10.1380	−	5.02211i	0.896078	−	0.443896i
$129$	13.6475	+	7.87939i	1.20159	+	0.693741i
$130$	−9.54600	−	5.09210i	−0.837239	−	0.446606i
$131$	−3.52422	+	2.03471i	−0.307912	+	0.177773i	−0.645992	−	0.763344i	$-0.723556\pi$
$131$	−3.52422	+	2.03471i	−0.307912	+	0.177773i	0.338080	+	0.941118i	$0.390223\pi$
$132$	−6.21727	+	16.7824i	−0.541144	+	1.46072i
$133$		0			0
$134$	−4.48068	+	6.98907i	−0.387072	+	0.603764i
$135$	−11.2444	+	4.00113i	−0.967765	+	0.344362i
$136$	4.03917	−	5.17146i	0.346356	−	0.443449i
$137$	−15.5676	+	4.17132i	−1.33003	+	0.356380i	−0.852726	−	0.522359i	$-0.825052\pi$
$137$	−15.5676	+	4.17132i	−1.33003	+	0.356380i	−0.477303	+	0.878739i	$0.658385\pi$
$138$	15.8120	−	14.4061i	1.34601	−	1.22632i
$139$	−17.0814			−1.44882			−0.724411	−	0.689369i	$-0.757888\pi$
$139$	−17.0814			−1.44882			−0.724411	+	0.689369i	$0.757888\pi$
$140$		0			0
$141$	−17.7622			−1.49585
$142$	−0.587702	+	0.535445i	−0.0493189	+	0.0449336i
$143$	10.5221	−	2.81939i	0.879902	−	0.235769i
$144$	−18.4901	+	6.49125i	−1.54084	+	0.540937i
$145$	1.65369	−	3.48065i	0.137331	−	0.289052i
$146$	2.55549	−	3.98611i	0.211494	−	0.329893i
$147$		0			0
$148$	−4.51877	−	1.67403i	−0.371441	−	0.137605i
$149$	7.75810	−	4.47914i	0.635569	−	0.366946i	−0.147337	−	0.989086i	$-0.547070\pi$
$149$	7.75810	−	4.47914i	0.635569	−	0.366946i	0.782905	+	0.622141i	$0.213737\pi$
$150$	−2.25338	−	19.7453i	−0.183987	−	1.61220i
$151$	−5.83274	−	3.36754i	−0.474662	−	0.274046i	0.243527	−	0.969894i	$-0.421695\pi$
$151$	−5.83274	−	3.36754i	−0.474662	−	0.274046i	−0.718189	+	0.695848i	$0.755029\pi$
$152$	7.27937	+	3.08866i	0.590435	+	0.250524i
$153$	−8.03690	+	8.03690i	−0.649745	+	0.649745i
$154$		0			0
$155$	−4.42178	−	6.41279i	−0.355166	−	0.515088i
$156$	15.6902	+	11.1207i	1.25622	+	0.890371i
$157$	−10.9964	+	2.94647i	−0.877606	+	0.235154i	−0.669374	−	0.742926i	$-0.733437\pi$
$157$	−10.9964	+	2.94647i	−0.877606	+	0.235154i	−0.208232	+	0.978080i	$0.566771\pi$
$158$	−3.54909	+	11.1450i	−0.282350	+	0.886649i
$159$	18.3446	+	31.7737i	1.45482	+	2.51982i
$160$	−1.38097	−	12.5735i	−0.109175	−	0.994023i
$161$		0			0
$162$	0.419942	−	0.0918394i	0.0329937	−	0.00721558i
$163$	0.000732309	−	0.00273302i	5.73589e−5	−	0.000214066i	−0.965897	−	0.258926i	$-0.916631\pi$
$163$	0.000732309	−	0.00273302i	5.73589e−5	−	0.000214066i	0.965954	+	0.258712i	$0.0832981\pi$
$164$	0.506057	−	5.42652i	0.0395164	−	0.423740i
$165$	15.2351	+	12.9720i	1.18605	+	1.00987i
$166$	−0.407370	+	8.75552i	−0.0316181	+	0.679560i
$167$	2.32482	−	2.32482i	0.179900	−	0.179900i	−0.611412	−	0.791312i	$-0.709398\pi$
$167$	2.32482	−	2.32482i	0.179900	−	0.179900i	0.791312	+	0.611412i	$0.209398\pi$
$168$		0			0
$169$			1.29445i			0.0995729i
$170$	−3.87940	−	6.22687i	−0.297536	−	0.477579i
$171$	−11.8616	−	6.84831i	−0.907081	−	0.523703i
$172$	8.63157	−	7.15900i	0.658151	−	0.545869i
$173$	−15.5233	−	4.15945i	−1.18021	−	0.316237i	−0.385201	−	0.922833i	$-0.625868\pi$
$173$	−15.5233	−	4.15945i	−1.18021	−	0.316237i	−0.795010	+	0.606596i	$0.792535\pi$
$174$	−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
$178$	3.90837	+	1.24461i	0.292945	+	0.0932871i
$179$	−9.08714	+	15.7394i	−0.679205	+	1.17642i	0.296016	+	0.955183i	$0.404342\pi$
$179$	−9.08714	+	15.7394i	−0.679205	+	1.17642i	−0.975221	+	0.221235i	$0.928991\pi$
$180$	−0.283180	+	21.9077i	−0.0211070	+	1.63290i
$181$	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
$184$	−5.70419	−	14.1125i	−0.420518	−	1.04038i
$185$	−3.49278	+	4.10214i	−0.256794	+	0.301596i
$186$	6.35826	+	12.2999i	0.466210	+	0.901871i
$187$	7.13498	+	1.91181i	0.521761	+	0.139806i
$188$	−4.39092	+	11.8525i	−0.320241	+	0.864434i
$189$		0			0
$190$	6.03812	−	6.45774i	0.438051	−	0.468494i
$191$	−10.0103	+	5.77946i	−0.724321	+	0.418187i	−0.816341	−	0.577570i	$-0.804001\pi$
$191$	−10.0103	+	5.77946i	−0.724321	+	0.418187i	0.0920200	+	0.995757i	$0.470668\pi$
$192$	−0.385874	+	22.4810i	−0.0278481	+	1.62242i
$193$	1.19666	+	4.46599i	0.0861374	+	0.321469i	0.995527	−	0.0944758i	$-0.0301175\pi$
$193$	1.19666	+	4.46599i	0.0861374	+	0.321469i	−0.909390	+	0.415945i	$0.863451\pi$
$194$	−1.01521	+	21.8196i	−0.0728876	+	1.56656i
$195$	17.7014	−	12.2056i	1.26763	−	0.874060i
$196$		0			0
$197$	6.77330	+	6.77330i	0.482578	+	0.482578i	0.905954	−	0.423376i	$-0.139155\pi$
$197$	6.77330	+	6.77330i	0.482578	+	0.482578i	−0.423376	+	0.905954i	$0.639155\pi$
$198$	−14.8566	−	16.3065i	−1.05581	−	1.15885i
$199$	0.869824	−	1.50658i	0.0616602	−	0.106799i	−0.833547	−	0.552448i	$-0.813694\pi$
$199$	0.869824	−	1.50658i	0.0616602	−	0.106799i	0.895208	+	0.445649i	$0.147027\pi$
$200$	−13.7329	−	3.37751i	−0.971062	−	0.238826i
$201$	−8.24951	−	14.2886i	−0.581876	−	1.00784i
$202$	−15.8402	+	3.46418i	−1.11451	+	0.243739i
$203$		0			0
$204$	5.44359	+	11.8504i	0.381128	+	0.829691i
$205$	−5.50376	−	2.61488i	−0.384399	−	0.182631i
$206$	−16.4599	+	8.50875i	−1.14682	+	0.592833i
$207$	6.82387	+	25.4670i	0.474292	+	1.77008i
$208$	11.2995	−	7.72082i	0.783477	−	0.535342i
$209$			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	$-0.304805\pi$
$212$	25.7371	−	4.38649i	1.76763	−	0.301265i
$213$	−0.408942	−	1.52619i	−0.0280202	−	0.104573i
$214$	0.266927	+	0.516363i	0.0182467	+	0.0352978i
$215$	−4.20316	−	11.8122i	−0.286653	−	0.805584i
$216$	2.09890	−	14.9502i	0.142812	−	1.01723i
$217$		0			0
$218$	2.20668	+	10.0902i	0.149455	+	0.683393i
$219$	4.70499	+	8.14928i	0.317934	+	0.550677i
$220$	12.4223	−	6.95949i	0.837509	−	0.469209i
$221$	3.96874	−	6.87406i	0.266966	−	0.462399i
$222$	7.07924	−	6.44977i	0.475128	−	0.432881i
$223$	13.2313	+	13.2313i	0.886031	+	0.886031i	0.994139	−	0.108108i	$-0.0344793\pi$
$223$	13.2313	+	13.2313i	0.886031	+	0.886031i	−0.108108	+	0.994139i	$0.534479\pi$
$224$		0			0
$225$	22.8952	+	8.70876i	1.52635	+	0.580584i
$226$	−23.2357	−	1.08109i	−1.54562	−	0.0719133i
$227$	5.38070	+	20.0810i	0.357130	+	1.33283i	0.877783	+	0.479058i	$0.159022\pi$
$227$	5.38070	+	20.0810i	0.357130	+	1.33283i	−0.520654	+	0.853768i	$0.674312\pi$
$228$	−12.0960	+	10.0324i	−0.801077	+	0.664411i
$229$	15.4800	−	8.93740i	1.02295	−	0.590600i	0.107992	−	0.994152i	$-0.465558\pi$
$229$	15.4800	−	8.93740i	1.02295	−	0.590600i	0.914957	+	0.403552i	$0.132224\pi$
$230$	−17.0088	+	0.571170i	−1.12152	+	0.0376618i
$231$		0			0
$232$	2.93403	+	3.89241i	0.192628	+	0.255549i
$233$	0.340822	+	0.0913229i	0.0223280	+	0.00598276i	0.269966	−	0.962870i	$-0.412988\pi$
$233$	0.340822	+	0.0913229i	0.0223280	+	0.00598276i	−0.247638	+	0.968853i	$0.579654\pi$
$234$	−21.0573	+	10.8853i	−1.37656	+	0.711592i
$235$	10.7597	+	9.16140i	0.701888	+	0.597624i
$236$	−3.10483	−	2.20061i	−0.202107	−	0.143247i
$237$	−16.4367	−	16.4367i	−1.06768	−	1.06768i
$238$		0			0
$239$	24.1080			1.55941			0.779707	−	0.626145i	$-0.215368\pi$
$239$	24.1080			1.55941			0.779707	+	0.626145i	$0.215368\pi$
$240$	23.4578	+	9.03672i	1.51419	+	0.583317i
$241$	2.17712	−	3.77087i	0.140240	−	0.242903i	−0.787347	−	0.616510i	$-0.788546\pi$
$241$	2.17712	−	3.77087i	0.140240	−	0.242903i	0.927587	+	0.373607i	$0.121879\pi$
$242$	0.370172	−	1.16243i	0.0237956	−	0.0747239i
$243$	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
$248$	9.77938	−	1.20220i	0.620991	−	0.0763397i
$249$	−15.0854	−	8.70955i	−0.955998	−	0.551945i
$250$	−8.81924	+	13.1233i	−0.557778	+	0.829990i
$251$			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
$254$	−2.64006	−	0.122835i	−0.165652	−	0.00770734i
$255$	14.5334	−	1.16607i	0.910117	−	0.0730219i
$256$	14.9059	+	5.81492i	0.931621	+	0.363432i
$257$	−2.60327	+	9.71554i	−0.162388	+	0.606039i	0.835971	+	0.548773i	$0.184905\pi$
$257$	−2.60327	+	9.71554i	−0.162388	+	0.606039i	−0.998359	+	0.0572656i	$0.981762\pi$
$258$	4.76137	+	21.7717i	0.296430	+	1.35545i
$259$		0			0
$260$	−3.76876	−	14.8293i	−0.233728	−	0.919673i
$261$	−4.22143	−	7.31173i	−0.261300	−	0.452585i
$262$	−5.48369	−	1.74626i	−0.338784	−	0.107884i
$263$	10.3861	−	2.78295i	0.640435	−	0.171604i	0.0760347	−	0.997105i	$-0.475774\pi$
$263$	10.3861	−	2.78295i	0.640435	−	0.171604i	0.564401	+	0.825501i	$0.309107\pi$
$264$	−23.4659	+	9.48480i	−1.44423	+	0.583749i
$265$	5.27575	−	28.7092i	0.324087	−	1.76359i
$266$		0			0
$267$	−5.76406	+	5.76406i	−0.352755	+	0.352755i
$268$	−11.5739	+	1.97259i	−0.706991	+	0.120495i
$269$	−8.18828	−	4.72750i	−0.499248	−	0.288241i	0.229155	−	0.973390i	$-0.426404\pi$
$269$	−8.18828	−	4.72750i	−0.499248	−	0.288241i	−0.728403	+	0.685149i	$0.759737\pi$
$270$	−14.8924	−	7.94402i	−0.906323	−	0.483458i
$271$	12.4949	−	7.21392i	0.759010	−	0.438214i	−0.0699304	−	0.997552i	$-0.522278\pi$
$271$	12.4949	−	7.21392i	0.759010	−	0.438214i	0.828940	+	0.559337i	$0.188944\pi$
$272$	9.25330	−	0.702976i	0.561064	−	0.0426242i
$273$		0			0
$274$	−19.1879	−	12.3013i	−1.15918	−	0.743152i
$275$	−2.53823	−	15.7160i	−0.153061	−	0.947708i
$276$	30.1201	+	2.80889i	1.81302	+	0.169075i
$277$	−31.9620	+	8.56419i	−1.92041	+	0.514572i	−0.932078	+	0.362259i	$0.882006\pi$
$277$	−31.9620	+	8.56419i	−1.92041	+	0.514572i	−0.988332	+	0.152314i	$0.951328\pi$
$278$	−16.2690	−	17.8568i	−0.975750	−	1.07098i
$279$	−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	$0.598074\pi$
$282$	−16.9175	−	18.5685i	−1.00742	−	1.10574i
$283$	−26.7548	+	7.16893i	−1.59041	+	0.426148i	−0.942128	−	0.335254i	$-0.891178\pi$
$283$	−26.7548	+	7.16893i	−1.59041	+	0.426148i	−0.648280	+	0.761402i	$0.724511\pi$
$284$	−1.11950	−	0.104401i	−0.0664304	−	0.00619505i
$285$	5.89017	+	16.5532i	0.348904	+	0.980527i
$286$	12.9691	+	8.31446i	0.766877	+	0.491644i
$287$		0			0
$288$	−24.3967	−	13.1470i	−1.43759	−	0.774692i
$289$	−10.0612	+	5.80882i	−0.591834	+	0.341695i
$290$	5.21370	−	1.58636i	0.306159	−	0.0931543i
$291$	−37.5943	−	21.7051i	−2.20381	−	1.27237i
$292$	6.60103	−	1.12504i	0.386296	−	0.0658380i
$293$	3.07964	−	3.07964i	0.179914	−	0.179914i	−0.611404	−	0.791318i	$-0.709395\pi$
$293$	3.07964	−	3.07964i	0.179914	−	0.179914i	0.791318	+	0.611404i	$0.209395\pi$
$294$		0			0
$295$	−3.50282	+	2.41528i	−0.203942	+	0.140623i
$296$	−2.55384	−	6.31833i	−0.148439	−	0.367245i
$297$	16.4152	−	4.39844i	0.952506	−	0.255223i
$298$	12.0716	+	3.84417i	0.699291	+	0.222687i
$299$	−9.20626	−	15.9457i	−0.532412	−	0.922164i
$300$	18.4955	−	21.1620i	1.06784	−	1.22179i
$301$		0			0
$302$	−2.03494	−	9.30491i	−0.117098	−	0.535437i
$303$	8.34018	−	31.1260i	0.479131	−	1.78814i
$304$	3.70431	+	10.5516i	0.212457	+	0.605176i
$305$	−2.08870	−	26.0327i	−0.119598	−	1.49063i
$306$	−16.0564	−	0.747062i	−0.917885	−	0.0427067i
$307$	13.3345	−	13.3345i	0.761042	−	0.761042i	−0.215469	−	0.976511i	$-0.569128\pi$
$307$	13.3345	−	13.3345i	0.761042	−	0.761042i	0.976511	+	0.215469i	$0.0691280\pi$
$308$		0			0
$309$		−	36.8239i		−	2.09484i
$310$	2.49242	−	10.7303i	0.141560	−	0.609441i
$311$	1.35454	+	0.782046i	0.0768091	+	0.0443457i	0.537913	−	0.843001i	$-0.319213\pi$
$311$	1.35454	+	0.782046i	0.0768091	+	0.0443457i	−0.461104	+	0.887346i	$0.652546\pi$
$312$	3.31847	+	26.9944i	0.187871	+	1.52825i
$313$	11.7632	+	3.15193i	0.664893	+	0.178157i	0.575453	−	0.817835i	$-0.304826\pi$
$313$	11.7632	+	3.15193i	0.664893	+	0.178157i	0.0894395	+	0.995992i	$0.471492\pi$
$314$	−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	0.418175	+	0.908366i	$0.362670\pi$
$317$	−7.08901	+	26.4565i	−0.398158	+	1.48595i	−0.816334	+	0.577581i	$0.803997\pi$
$318$	−15.7440	+	49.4400i	−0.882878	+	2.77245i
$319$	−2.74350	+	4.75188i	−0.153606	+	0.266054i
$320$	11.8290	−	13.4192i	0.661261	−	0.750156i
$321$	−1.15520			−0.0644768
$322$		0			0
$323$	4.58635	+	4.58635i	0.255191	+	0.255191i
$324$	0.495979	+	0.351534i	0.0275544	+	0.0195297i
$325$	−17.0183	−	1.73633i	−0.944008	−	0.0963144i
$326$	0.00355457	−	0.00183749i	0.000196869	−	0.000101769i
$327$	−19.8272	−	5.31269i	−1.09645	−	0.293792i
$328$	6.15485	−	4.63941i	0.339845	−	0.256169i
$329$		0			0
$330$	0.949729	+	28.2818i	0.0522809	+	1.55686i
$331$	3.38809	−	1.95612i	0.186226	−	0.107518i	−0.403988	−	0.914764i	$-0.632376\pi$
$331$	3.38809	−	1.95612i	0.186226	−	0.107518i	0.590215	+	0.807246i	$0.299043\pi$
$332$	−9.54099	+	7.91327i	−0.523630	+	0.434297i
$333$	3.05513	+	11.4019i	0.167420	+	0.624821i
$334$	4.64461	+	0.216101i	0.254142	+	0.0118245i
$335$	−2.37249	+	12.9105i	−0.129623	+	0.705374i
$336$		0			0
$337$	12.6447	+	12.6447i	0.688801	+	0.688801i	0.961967	−	0.273166i	$-0.0880709\pi$
$337$	12.6447	+	12.6447i	0.688801	+	0.688801i	−0.273166	+	0.961967i	$0.588071\pi$
$338$	−1.35321	+	1.23289i	−0.0736050	+	0.0670602i
$339$	23.1137	−	40.0341i	1.25537	−	2.17436i
$340$	2.81464	−	9.98624i	0.152645	−	0.541580i
$341$	5.54569	+	9.60542i	0.300316	+	0.520163i
$342$	−4.13831	−	18.9227i	−0.223774	−	1.02322i
$343$		0			0
$344$	15.7051	+	2.20488i	0.846761	+	0.118879i
$345$	14.5140	−	30.5488i	0.781407	−	1.64469i
$346$	−10.4367	−	20.1896i	−0.561083	−	1.08540i
$347$	1.55280	+	5.79511i	0.0833585	+	0.311098i	0.994998	−	0.0998921i	$-0.0318498\pi$
$347$	1.55280	+	5.79511i	0.0833585	+	0.311098i	−0.911640	+	0.410990i	$0.865183\pi$
$348$	−9.54934	+	1.62753i	−0.511899	+	0.0872450i
$349$			15.1860i			0.812888i	0.913676	+	0.406444i	$0.133231\pi$
$349$			15.1860i			0.812888i	−0.913676	+	0.406444i	$0.866769\pi$
$350$		0			0
$351$		−	18.2615i		−	0.974725i
$352$	0.528203	+	18.0032i	0.0281533	+	0.959576i
$353$	−8.90620	−	33.2384i	−0.474029	−	1.76910i	−0.625065	−	0.780573i	$-0.714927\pi$
$353$	−8.90620	−	33.2384i	−0.474029	−	1.76910i	0.151035	−	0.988528i	$-0.451739\pi$
$354$	6.71849	−	3.47303i	0.357084	−	0.184590i
$355$	−0.539457	+	1.13544i	−0.0286314	+	0.0602629i
$356$	2.42139	+	5.27121i	0.128333	+	0.279373i
$357$		0			0
$358$	−25.1089	+	5.49120i	−1.32705	+	0.290219i
$359$	−4.20241	−	7.27878i	−0.221795	−	0.384159i	0.733558	−	0.679626i	$-0.237858\pi$
$359$	−4.20241	−	7.27878i	−0.221795	−	0.384159i	−0.955353	+	0.295467i	$0.904525\pi$
$360$	−23.1719	+	20.5698i	−1.22127	+	1.08412i
$361$	5.59193	−	9.68551i	0.294312	−	0.509764i
$362$	4.08082	+	4.47909i	0.214483	+	0.235416i
$363$	1.71435	+	1.71435i	0.0899803	+	0.0899803i
$364$		0			0
$365$	1.35312	−	7.36330i	0.0708254	−	0.385413i
$366$	−2.15759	+	46.3727i	−0.112779	+	2.42394i
$367$	−7.95960	−	29.7056i	−0.415488	−	1.55062i	−0.783857	−	0.620941i	$-0.786751\pi$
$367$	−7.95960	−	29.7056i	−0.415488	−	1.55062i	0.368369	−	0.929679i	$-0.379916\pi$
$368$	9.32020	−	19.4044i	0.485849	−	1.01153i
$369$	−11.5616	+	6.67511i	−0.601875	+	0.347493i
$370$	−7.61504	+	0.255720i	−0.395887	+	0.0132943i
$371$		0			0
$372$	−6.80237	+	18.3618i	−0.352687	+	0.952017i
$373$	−14.5253	−	3.89204i	−0.752091	−	0.201522i	−0.137646	−	0.990482i	$-0.543954\pi$
$373$	−14.5253	−	3.89204i	−0.752091	−	0.201522i	−0.614446	+	0.788959i	$0.710620\pi$
$374$	4.79706	+	9.27977i	0.248050	+	0.479846i
$375$	−15.1196	−	27.5461i	−0.780772	−	1.42247i
$376$	−16.5727	+	6.69860i	−0.854671	+	0.345454i
$377$	4.16920	+	4.16920i	0.214725	+	0.214725i
$378$		0			0
$379$	1.92262			0.0987586			0.0493793	−	0.998780i	$-0.484276\pi$
$379$	1.92262			0.0987586			0.0493793	+	0.998780i	$0.484276\pi$
$380$	12.5019	+	0.161600i	0.641332	+	0.00828991i
$381$	2.62620	−	4.54871i	0.134544	−	0.233038i
$382$	−15.5761	−	4.96015i	−0.796941	−	0.253783i
$383$	−4.13733	+	15.4407i	−0.211408	+	0.788984i	0.775993	+	0.630742i	$0.217249\pi$
$383$	−4.13733	+	15.4407i	−0.211408	+	0.788984i	−0.987400	+	0.158242i	$0.949417\pi$
$384$	−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
$388$	−23.7771	+	19.7206i	−1.20710	+	1.00116i
$389$	9.81327	+	5.66569i	0.497552	+	0.287262i	0.727702	−	0.685893i	$-0.240588\pi$
$389$	9.81327	+	5.66569i	0.497552	+	0.287262i	−0.230150	+	0.973155i	$0.573922\pi$
$390$	29.6193	+	6.87991i	1.49983	+	0.348378i
$391$		−	12.4854i		−	0.631415i
$392$		0			0
$393$	8.08735	−	8.08735i	0.407953	−	0.407953i
$394$	−0.629605	+	13.5320i	−0.0317190	+	0.681730i
$395$	1.47906	+	18.4345i	0.0744198	+	0.927540i
$396$	2.89673	−	31.0620i	0.145566	−	1.56092i
$397$	−3.01844	+	11.2650i	−0.151491	+	0.565372i	0.847889	+	0.530173i	$0.177873\pi$
$397$	−3.01844	+	11.2650i	−0.151491	+	0.565372i	−0.999380	+	0.0351987i	$0.988794\pi$
$398$	2.40343	−	0.525620i	0.120473	−	0.0263469i
$399$		0			0
$400$	−9.54896	−	17.5732i	−0.477448	−	0.878660i
$401$	13.8361	+	23.9649i	0.690943	+	1.19675i	0.971529	+	0.236919i	$0.0761376\pi$
$401$	13.8361	+	23.9649i	0.690943	+	1.19675i	−0.280587	+	0.959829i	$0.590529\pi$
$402$	7.08004	−	22.2330i	0.353120	−	1.10888i
$403$	11.5123	−	3.08472i	0.573470	−	0.153661i
$404$	−18.7083	−	13.2598i	−0.930772	−	0.659701i
$405$	0.559555	−	0.385827i	0.0278045	−	0.0191719i
$406$		0			0
$407$	5.42456	−	5.42456i	0.268885	−	0.268885i
$408$	−7.20361	+	16.9775i	−0.356632	+	0.840511i
$409$	−11.9780	−	6.91550i	−0.592274	−	0.341950i	0.173722	−	0.984795i	$-0.444421\pi$
$409$	−11.9780	−	6.91550i	−0.592274	−	0.341950i	−0.765996	+	0.642845i	$0.777754\pi$
$410$	−2.50842	−	8.24413i	−0.123882	−	0.407149i
$411$	39.2281	−	22.6483i	1.93498	−	1.11716i
$412$	−24.5722	−	9.10307i	−1.21058	−	0.448476i
$413$		0			0
$414$	−20.1238	+	31.3895i	−0.989031	+	1.54271i
$415$	4.64600	+	13.0567i	0.228063	+	0.640928i
$416$	18.8334	+	4.45878i	0.923383	+	0.218610i
$417$	46.3719	−	12.4253i	2.27084	−	0.608471i
$418$	−9.30550	+	8.47808i	−0.455147	+	0.414676i
$419$	20.6976			1.01114			0.505572	−	0.862784i	$-0.331281\pi$
$419$	20.6976			1.01114			0.505572	+	0.862784i	$0.331281\pi$
$420$		0			0
$421$	26.7517			1.30380			0.651898	−	0.758306i	$-0.273973\pi$
$421$	26.7517			1.30380			0.651898	+	0.758306i	$0.273973\pi$
$422$	24.8369	−	22.6285i	1.20904	−	1.10154i
$423$	29.9067	−	8.01348i	1.45411	−	0.389629i
$424$	29.0988	+	22.7276i	1.41316	+	1.10375i
$425$	−9.40528	−	6.78968i	−0.456223	−	0.329348i
$426$	1.20598	−	1.88112i	0.0584300	−	0.0911404i
$427$		0			0
$428$	−0.285571	+	0.770850i	−0.0138036	+	0.0372605i
$429$	−26.5142	+	15.3080i	−1.28012	+	0.739076i
$430$	8.34514	−	15.6444i	0.402439	−	0.754439i
$431$	34.9346	+	20.1695i	1.68274	+	0.971531i	0.959827	+	0.280594i	$0.0905313\pi$
$431$	34.9346	+	20.1695i	1.68274	+	0.971531i	0.722914	+	0.690937i	$0.242802\pi$
$432$	17.6279	−	12.0450i	0.848125	−	0.579516i
$433$	−16.5835	+	16.5835i	−0.796954	+	0.796954i	−0.982614	−	0.185660i	$-0.940558\pi$
$433$	−16.5835	+	16.5835i	−0.796954	+	0.796954i	0.185660	+	0.982614i	$0.440558\pi$
$434$		0			0
$435$	−1.95748	+	10.6521i	−0.0938540	+	0.510728i
$436$	−8.44651	+	11.9172i	−0.404514	+	0.570729i
$437$	14.5331	−	3.89412i	0.695210	−	0.186281i
$438$	−4.03800	+	12.6803i	−0.192943	+	0.605888i
$439$	2.87067	+	4.97215i	0.137010	+	0.237308i	0.926363	−	0.376631i	$-0.122918\pi$
$439$	2.87067	+	4.97215i	0.137010	+	0.237308i	−0.789354	+	0.613939i	$0.789584\pi$
$440$	19.1069	+	6.35768i	0.910887	+	0.303091i
$441$		0			0
$442$	10.9661	−	2.39824i	0.521604	−	0.114073i
$443$	−0.221517	+	0.826713i	−0.0105246	+	0.0392783i	−0.970988	−	0.239126i	$-0.923139\pi$
$443$	−0.221517	+	0.826713i	−0.0105246	+	0.0392783i	0.960464	+	0.278405i	$0.0898056\pi$
$444$	13.4851	+	1.25757i	0.639976	+	0.0596819i
$445$	6.46467	−	0.518683i	0.306455	−	0.0245879i
$446$	−1.22990	+	26.4339i	−0.0582373	+	1.25168i
$447$	−17.8032	+	17.8032i	−0.842064	+	0.842064i
$448$		0			0
$449$			4.66158i			0.219993i	0.993932	+	0.109997i	$0.0350840\pi$
$449$			4.66158i			0.219993i	−0.993932	+	0.109997i	$0.964916\pi$
$450$	12.7022	+	32.2291i	0.598790	+	1.51930i
$451$	7.51388	+	4.33814i	0.353815	+	0.204275i
$452$	−21.0005	−	25.3202i	−0.987781	−	1.19096i
$453$	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	−0.452880	−	0.891572i	$-0.649603\pi$
$457$	8.23274	−	30.7250i	0.385111	−	1.43726i	0.837991	−	0.545684i	$-0.183730\pi$
$458$	24.0870	+	7.67041i	1.12551	+	0.358415i
$459$	6.19150	−	10.7240i	0.288995	−	0.500553i
$460$	−16.7970	−	17.2369i	−0.783162	−	0.803674i
$461$	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	$-0.269276\pi$
$463$	−1.84160	−	1.84160i	−0.0855866	−	0.0855866i	−0.748604	+	0.663017i	$0.769276\pi$
$464$	−1.27462	+	6.77451i	−0.0591726	+	0.314499i
$465$	16.6689	+	14.1928i	0.773001	+	0.658173i
$466$	0.229144	+	0.443274i	0.0106149	+	0.0205343i
$467$	−8.01462	−	2.14751i	−0.370872	−	0.0993749i	0.0685687	−	0.997646i	$-0.478157\pi$
$467$	−8.01462	−	2.14751i	−0.370872	−	0.0993749i	−0.439441	+	0.898271i	$0.644823\pi$
$468$	−31.4352	−	11.6456i	−1.45309	−	0.538317i
$469$		0			0
$470$	0.670742	+	19.9739i	0.0309390	+	0.921327i
$471$	27.7093	−	15.9980i	1.27678	−	0.737147i
$472$	−0.656670	−	5.34173i	−0.0302257	−	0.245873i
$473$	4.62053	+	17.2441i	0.212452	+	0.792883i
$474$	1.52785	−	32.8378i	0.0701766	−	1.50829i
$475$	4.96976	−	13.0654i	0.228028	−	0.599482i
$476$		0			0
$477$	−45.2221	−	45.2221i	−2.07058	−	2.07058i
$478$	22.9614	+	25.2024i	1.05023	+	1.15273i
$479$	−6.99926	+	12.1231i	−0.319805	+	0.553918i	−0.980447	−	0.196783i	$-0.936951\pi$
$479$	−6.99926	+	12.1231i	−0.319805	+	0.553918i	0.660643	+	0.750701i	$0.270284\pi$
$480$	12.8952	+	33.1296i	0.588584	+	1.51215i
$481$	−4.12176	−	7.13910i	−0.187936	−	0.325515i
$482$	6.01563	−	1.31559i	0.274005	−	0.0599236i
$483$		0			0
$484$	1.56777	−	0.720172i	0.0712622	−	0.0327351i
$485$	11.5783	+	32.5386i	0.525743	+	1.47750i
$486$	19.0431	−	9.84409i	0.863813	−	0.446537i
$487$	−6.87083	−	25.6423i	−0.311347	−	1.16196i	−0.927342	−	0.374214i	$-0.877913\pi$
$487$	−6.87083	−	25.6423i	−0.311347	−	1.16196i	0.615995	−	0.787750i	$-0.288754\pi$
$488$	30.4106	+	12.9033i	1.37662	+	0.584107i
$489$			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	$0.703234\pi$
$492$	2.57353	+	15.0999i	0.116024	+	0.680754i
$493$	1.03480	+	3.86191i	0.0466049	+	0.173932i
$494$	6.21181	+	12.0166i	0.279482	+	0.540651i
$495$	−31.5042	−	14.9679i	−1.41601	−	0.672757i
$496$	10.5711	+	9.07830i	0.474655	+	0.407628i
$497$		0			0
$498$	−5.26303	−	24.0656i	−0.235842	−	1.07840i
$499$	−4.94115	−	8.55833i	−0.221196	−	0.383123i	0.733975	−	0.679176i	$-0.237663\pi$
$499$	−4.94115	−	8.55833i	−0.221196	−	0.383123i	−0.955172	+	0.296053i	$0.904330\pi$
$500$	−22.1189	+	3.27959i	−0.989186	+	0.146668i
$501$	−4.62022	+	8.00245i	−0.206416	+	0.357523i
$502$	−13.9427	+	12.7030i	−0.622295	+	0.566962i
$503$	−16.5308	−	16.5308i	−0.737071	−	0.737071i	0.234939	−	0.972010i	$-0.424511\pi$
$503$	−16.5308	−	16.5308i	−0.737071	−	0.737071i	−0.972010	+	0.234939i	$0.924511\pi$
$504$		0			0
$505$	−21.1064	+	14.5534i	−0.939221	+	0.647616i
$506$	24.2061	+	1.12624i	1.07609	+	0.0500676i
$507$	−0.941607	−	3.51413i	−0.0418182	−	0.156068i
$508$	−2.38610	−	2.87690i	−0.105866	−	0.127642i
$509$	0.789343	−	0.455727i	0.0349870	−	0.0201998i	−0.482404	−	0.875949i	$-0.660236\pi$
$509$	0.789343	−	0.455727i	0.0349870	−	0.0201998i	0.517391	+	0.855749i	$0.326903\pi$
$510$	15.0612	+	14.0826i	0.666922	+	0.623586i
$511$		0			0
$512$	8.11815	+	21.1210i	0.358775	+	0.933424i
$513$	14.4138	+	3.86218i	0.636386	+	0.170519i
$514$	−12.6361	+	6.53204i	−0.557352	+	0.288116i
$515$	−18.9930	+	22.3067i	−0.836933	+	0.982949i
$516$	−18.2251	+	25.7138i	−0.802316	+	1.13199i
$517$	−14.2284	−	14.2284i	−0.625763	−	0.625763i
$518$		0			0
$519$	45.1677			1.98264
$520$	11.9130	−	18.0639i	0.522417	−	0.792153i
$521$	−3.24107	+	5.61370i	−0.141994	+	0.245941i	−0.928247	−	0.371963i	$-0.878685\pi$
$521$	−3.24107	+	5.61370i	−0.141994	+	0.245941i	0.786254	+	0.617904i	$0.212018\pi$
$522$	3.62299	−	11.3771i	0.158574	−	0.497961i
$523$	1.22075	−	4.55591i	0.0533798	−	0.199216i	−0.934086	−	0.357047i	$-0.883783\pi$
$523$	1.22075	−	4.55591i	0.0533798	−	0.199216i	0.987466	+	0.157831i	$0.0504502\pi$
$524$	−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
$528$	−32.2653	−	15.4974i	−1.40417	−	0.674439i
$529$	−5.16358	−	2.98119i	−0.224503	−	0.129617i
$530$	35.0373	−	21.8286i	1.52192	−	0.948175i
$531$			9.32205i			0.404542i
$532$		0			0
$533$	6.59253	−	6.59253i	0.285554	−	0.285554i
$534$	−11.5157	−	0.535792i	−0.498332	−	0.0231860i
$535$	0.699779	+	0.595828i	0.0302541	+	0.0257599i
$536$	−13.0857	−	10.2206i	−0.565214	−	0.441462i
$537$	13.2203	−	49.3390i	0.570500	−	2.12913i
$538$	−2.85675	−	13.0627i	−0.123163	−	0.563172i
$539$		0			0
$540$	−5.87952	−	23.1347i	−0.253014	−	0.995559i
$541$	−9.43554	−	16.3428i	−0.405666	−	0.702633i	0.588733	−	0.808328i	$-0.299627\pi$
$541$	−9.43554	−	16.3428i	−0.405666	−	0.702633i	−0.994399	+	0.105694i	$0.966294\pi$
$542$	19.4421	+	6.19125i	0.835108	+	0.265937i
$543$	−11.6317	+	3.11669i	−0.499162	+	0.133750i
$544$	9.54813	+	9.00382i	0.409373	+	0.386036i
$545$	9.27048	+	13.4447i	0.397104	+	0.575910i
$546$		0			0
$547$	−9.42028	+	9.42028i	−0.402782	+	0.402782i	−0.879212	−	0.476430i	$-0.841931\pi$
$547$	−9.42028	+	9.42028i	−0.402782	+	0.402782i	0.476430	+	0.879212i	$0.341931\pi$
$548$	−5.41559	−	31.7753i	−0.231343	−	1.35737i
$549$	−49.5537	−	28.6098i	−2.11490	−	1.22104i
$550$	14.0119	−	17.6220i	0.597469	−	0.751405i
$551$	−4.17252	+	2.40901i	−0.177756	+	0.102627i
$552$	25.7512	+	34.1627i	1.09605	+	1.45406i
$553$		0			0
$554$	−39.3949	−	25.2560i	−1.67373	−	1.07303i
$555$	6.49810	−	13.6771i	0.275829	−	0.580560i
$556$	3.17213	−	34.0151i	0.134528	−	1.44256i
$557$	36.6573	−	9.82230i	1.55322	−	0.416184i	0.622711	−	0.782452i	$-0.286031\pi$
$557$	36.6573	−	9.82230i	1.55322	−	0.416184i	0.930509	+	0.366268i	$0.119365\pi$
$558$	−16.2547	−	17.8411i	−0.688117	−	0.755274i
$559$	19.1836			0.811378
$560$		0			0
$561$	−20.7605			−0.876510
$562$	−9.68351	−	10.6286i	−0.408474	−	0.448339i
$563$	36.6293	−	9.81479i	1.54374	−	0.413644i	0.616269	−	0.787536i	$-0.288643\pi$
$563$	36.6293	−	9.81479i	1.54374	−	0.413644i	0.927472	+	0.373892i	$0.121977\pi$
$564$	3.29856	−	35.3709i	0.138895	−	1.48938i
$565$	−34.6504	+	12.3297i	−1.45775	+	0.518715i
$566$	−32.9768	−	21.1414i	−1.38612	−	0.888638i
$567$		0			0
$568$	−0.957124	−	1.26976i	−0.0401600	−	0.0532780i
$569$	−7.96777	+	4.60019i	−0.334026	+	0.192850i	−0.657627	−	0.753344i	$-0.728440\pi$
$569$	−7.96777	+	4.60019i	−0.334026	+	0.192850i	0.323601	+	0.946194i	$0.395106\pi$
$570$	−11.6946	+	21.9235i	−0.489833	+	0.918276i
$571$	−14.8692	−	8.58473i	−0.622256	−	0.359260i	0.155491	−	0.987837i	$-0.450304\pi$
$571$	−14.8692	−	8.58473i	−0.622256	−	0.359260i	−0.777747	+	0.628578i	$0.783637\pi$
$572$	3.66039	+	21.4769i	0.153049	+	0.897993i
$573$	22.9716	−	22.9716i	0.959652	−	0.959652i
$574$		0			0
$575$	−24.5486	+	11.0194i	−1.02375	+	0.459541i
$576$	−9.49267	−	38.0259i	−0.395528	−	1.58441i
$577$	29.5776	−	7.92529i	1.23133	−	0.329934i	0.416233	−	0.909258i	$-0.363350\pi$
$577$	29.5776	−	7.92529i	1.23133	−	0.329934i	0.815097	+	0.579324i	$0.196683\pi$
$578$	−15.6552	−	4.98534i	−0.651171	−	0.207363i
$579$	−6.49731	−	11.2537i	−0.270019	−	0.467687i
$580$	6.62412	+	3.93946i	0.275052	+	0.163577i
$581$		0			0
$582$	−13.1160	−	59.9737i	−0.543675	−	2.48599i
$583$	−10.7574	+	40.1471i	−0.445525	+	1.66272i
$584$	7.46322	+	5.82916i	0.308830	+	0.241212i
$585$	−24.2978	+	28.5370i	−1.00459	+	1.17986i
$586$	6.15262	+	0.286264i	0.254162	+	0.0118255i
$587$	−31.4917	+	31.4917i	−1.29980	+	1.29980i	−0.371283	+	0.928520i	$0.621082\pi$
$587$	−31.4917	+	31.4917i	−1.29980	+	1.29980i	−0.928520	+	0.371283i	$0.878918\pi$
$588$		0			0
$589$			9.73911i			0.401293i
$590$	−5.86116	−	1.36142i	−0.241300	−	0.0560487i
$591$	−23.3150	−	13.4609i	−0.959050	−	0.553708i
$592$	4.17277	−	8.68761i	0.171500	−	0.357059i
$593$	7.35708	+	1.97132i	0.302119	+	0.0809525i	0.406694	−	0.913564i	$-0.366682\pi$
$593$	7.35708	+	1.97132i	0.302119	+	0.0809525i	−0.104575	+	0.994517i	$0.533348\pi$
$594$	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
$598$	7.90115	−	24.8116i	0.323102	−	1.01462i
$599$	0.0710719	−	0.123100i	0.00290392	−	0.00502974i	−0.864570	−	0.502513i	$-0.832409\pi$
$599$	0.0710719	−	0.123100i	0.00290392	−	0.00502974i	0.867474	+	0.497483i	$0.165742\pi$
$600$	39.7385	−	0.820437i	1.62232	−	0.0334942i
$601$	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
$604$	7.78915	−	10.9897i	0.316936	−	0.447165i
$605$	−0.154267	−	1.92273i	−0.00627186	−	0.0781701i
$606$	40.4825	−	20.9269i	1.64449	−	0.850097i
$607$	−31.6805	−	8.48876i	−1.28587	−	0.344548i	−0.449781	−	0.893139i	$-0.648498\pi$
$607$	−31.6805	−	8.48876i	−1.28587	−	0.344548i	−0.836091	+	0.548591i	$0.815165\pi$
$608$	−7.50247	+	13.9223i	−0.304265	+	0.564622i
$609$		0			0
$610$	25.2251	−	26.9782i	1.02134	−	1.09231i
$611$	−18.7255	+	10.8112i	−0.757554	+	0.437374i
$612$	−14.5119	−	17.4969i	−0.586607	−	0.707269i
$613$	1.33983	+	5.00032i	0.0541153	+	0.201961i	0.987691	−	0.156420i	$-0.0499955\pi$
$613$	1.33983	+	5.00032i	0.0541153	+	0.201961i	−0.933575	+	0.358381i	$0.883329\pi$
$614$	26.6402	+	1.23950i	1.07511	+	0.0500220i
$615$	16.8435	+	3.09525i	0.679197	+	0.124813i
$616$		0			0
$617$	18.4714	+	18.4714i	0.743630	+	0.743630i	0.973275	−	0.229644i	$-0.0737563\pi$
$617$	18.4714	+	18.4714i	0.743630	+	0.743630i	−0.229644	+	0.973275i	$0.573756\pi$
$618$	38.4955	−	35.0726i	1.54852	−	1.41083i
$619$	4.38197	−	7.58980i	0.176126	−	0.305060i	−0.764424	−	0.644714i	$-0.776977\pi$
$619$	4.38197	−	7.58980i	0.176126	−	0.305060i	0.940551	+	0.339654i	$0.110310\pi$
$620$	13.5913	−	7.61445i	0.545841	−	0.305804i
$621$	−14.3624	−	24.8764i	−0.576343	−	0.998255i
$622$	0.472576	+	2.16089i	0.0189486	+	0.0866437i
$623$		0			0
$624$	−25.0592	+	29.1797i	−1.00317	+	1.16812i
$625$	−5.04880	+	24.4849i	−0.201952	+	0.979395i
$626$	7.90871	+	15.2992i	0.316096	+	0.611478i
$627$	−6.47506	−	24.1653i	−0.258589	−	0.965068i
$628$	−3.82538	−	22.4449i	−0.152649	−	0.895649i
$629$		−	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	$-0.213605\pi$
$632$	−21.5346	−	9.13722i	−0.856602	−	0.363459i
$633$	17.2823	+	64.4986i	0.686911	+	2.56359i
$634$	−34.4094	+	17.7875i	−1.36657	+	0.706432i
$635$	−3.93700	+	1.40091i	−0.156235	+	0.0555936i
$636$	−66.6796	+	30.6300i	−2.64402	+	1.21456i
$637$		0			0
$638$	−7.58062	+	1.65785i	−0.300120	+	0.0656348i
$639$	1.37709	+	2.38520i	0.0544770	+	0.0943569i
$640$	25.2948	−	0.415013i	0.999865	−	0.0164048i
$641$	−24.9696	+	43.2485i	−0.986238	+	1.70821i	−0.349939	+	0.936772i	$0.613798\pi$
$641$	−24.9696	+	43.2485i	−0.986238	+	1.70821i	−0.636299	+	0.771443i	$0.719535\pi$
$642$	−1.10026	−	1.20764i	−0.0434237	−	0.0476617i
$643$	−16.3136	−	16.3136i	−0.643345	−	0.643345i	0.308031	−	0.951376i	$-0.400330\pi$
$643$	−16.3136	−	16.3136i	−0.643345	−	0.643345i	−0.951376	+	0.308031i	$0.900330\pi$
$644$		0			0
$645$	20.0030	+	29.0099i	0.787618	+	1.14226i
$646$	−0.426319	+	9.16279i	−0.0167733	+	0.360505i
$647$	−4.17257	−	15.5722i	−0.164041	−	0.612208i	−0.998161	−	0.0606248i	$-0.980691\pi$
$647$	−4.17257	−	15.5722i	−0.164041	−	0.612208i	0.834120	−	0.551583i	$-0.185976\pi$
$648$	0.104899	+	0.853310i	0.00412083	+	0.0335212i
$649$	5.24671	−	3.02919i	0.205951	−	0.118906i
$650$	−14.3938	−	19.4447i	−0.564573	−	0.762683i
$651$		0			0
$652$	0.00530642	+	0.00196583i	0.000207816	+	7.69879e-5i
$653$	−21.8713	−	5.86041i	−0.855891	−	0.229335i	−0.195914	−	0.980621i	$-0.562767\pi$
$653$	−21.8713	−	5.86041i	−0.855891	−	0.229335i	−0.659977	+	0.751286i	$0.729434\pi$
$654$	−13.3304	−	25.7873i	−0.521261	−	1.00836i
$655$	−9.07034	+	0.727746i	−0.354408	+	0.0284354i
$656$	10.7122	+	2.01548i	0.418240	+	0.0786914i
$657$	−11.5985	−	11.5985i	−0.452501	−	0.452501i
$658$		0			0
$659$	0.119381			0.00465044			0.00232522	−	0.999997i	$-0.499260\pi$
$659$	0.119381			0.00465044			0.00232522	+	0.999997i	$0.499260\pi$
$660$	−28.6611	+	27.9296i	−1.11563	+	1.08716i
$661$	−10.3433	+	17.9151i	−0.402307	+	0.696816i	−0.994004	−	0.109344i	$-0.965125\pi$
$661$	−10.3433	+	17.9151i	−0.402307	+	0.696816i	0.591697	+	0.806161i	$0.298458\pi$
$662$	5.27188	+	1.67881i	0.204897	+	0.0652489i
$663$	−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
$668$	4.19781	+	5.06128i	0.162418	+	0.195827i
$669$	−45.5445	−	26.2951i	−1.76085	−	1.01663i
$670$	−15.7562	+	9.81629i	−0.608716	+	0.379236i
$671$			37.1869i			1.43559i
$672$		0			0
$673$	34.9098	−	34.9098i	1.34568	−	1.34568i	0.455376	−	0.890299i	$-0.349505\pi$
$673$	34.9098	−	34.9098i	1.34568	−	1.34568i	0.890299	−	0.455376i	$-0.150495\pi$
$674$	−1.17537	+	25.2621i	−0.0452737	+	0.973058i
$675$	−26.5498	−	2.70880i	−1.02190	−	0.104262i
$676$	−2.57771	−	0.240388i	−0.0991427	−	0.00924569i
$677$	1.32612	−	4.94915i	0.0509669	−	0.190211i	−0.935749	−	0.352667i	$-0.885275\pi$
$677$	1.32612	−	4.94915i	0.0509669	−	0.190211i	0.986716	+	0.162456i	$0.0519415\pi$
$678$	63.8660	−	13.9672i	2.45276	−	0.536408i
$679$		0			0
$680$	13.1204	−	6.56891i	0.503143	−	0.251906i
$681$	−29.2147	−	50.6014i	−1.11951	−	1.93905i
$682$	−4.75952	+	14.9461i	−0.182251	+	0.572314i
$683$	40.4498	−	10.8385i	1.54777	−	0.414724i	0.619003	−	0.785389i	$-0.287537\pi$
$683$	40.4498	−	10.8385i	1.54777	−	0.414724i	0.928767	+	0.370665i	$0.120870\pi$
$684$	15.8402	−	22.3490i	0.605666	−	0.854534i
$685$	−35.4446	−	6.51348i	−1.35427	−	0.248867i
$686$		0			0
$687$	−35.5235	+	35.5235i	−1.35530	+	1.35530i
$688$	12.6532	+	18.5180i	0.482399	+	0.705994i
$689$	38.6789	+	22.3313i	1.47355	+	0.850755i
$690$	45.7594	−	13.9231i	1.74203	−	0.530044i
$691$	−29.5825	+	17.0795i	−1.12537	+	0.649734i	−0.942767	−	0.333452i	$-0.891787\pi$
$691$	−29.5825	+	17.0795i	−1.12537	+	0.649734i	−0.182606	+	0.983186i	$0.558453\pi$
$692$	11.1657	−	30.1400i	0.424457	−	1.14575i
$693$		0			0
$694$	−4.57924	+	7.14280i	−0.173826	+	0.271137i
$695$	−34.4993	−	16.3909i	−1.30863	−	0.621742i
$696$	−10.7966	−	8.43272i	−0.409245	−	0.319641i
$697$	6.10663	−	1.63627i	0.231305	−	0.0619780i
$698$	−15.8754	+	14.4638i	−0.600892	+	0.547462i
$699$	−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	$0.678371\pi$
$702$	19.0905	−	17.3930i	0.720523	−	0.656456i
$703$	6.50664	−	1.74345i	0.245402	−	0.0657554i
$704$	−18.3174	+	17.6992i	−0.690364	+	0.667065i
$705$	−35.8744	−	17.0442i	−1.35111	−	0.641923i
$706$	26.2647	−	40.9682i	0.988483	−	1.54186i
$707$		0			0
$708$	10.0297	+	3.71562i	0.376938	+	0.139641i
$709$	3.23053	−	1.86515i	0.121325	−	0.0700471i	−0.438109	−	0.898922i	$-0.644352\pi$
$709$	3.23053	−	1.86515i	0.121325	−	0.0700471i	0.559434	+	0.828875i	$0.311018\pi$
$710$	−1.70079	+	0.517495i	−0.0638294	+	0.0194212i
$711$	35.0903	+	20.2594i	1.31599	+	0.759788i
$712$	−3.20427	+	7.55183i	−0.120085	+	0.283017i
$713$	13.2564	−	13.2564i	0.496456	−	0.496456i
$714$		0			0
$715$	23.9570	+	4.40245i	0.895939	+	0.164642i
$716$	−29.6553	−	21.0187i	−1.10827	−	0.785505i
$717$	−65.4475	+	17.5366i	−2.44418	+	0.654917i
$718$	3.60666	−	11.3258i	0.134599	−	0.422675i
$719$	14.3205	+	24.8039i	0.534066	+	0.925029i	0.999208	+	0.0397933i	$0.0126699\pi$
$719$	14.3205	+	24.8039i	0.534066	+	0.925029i	−0.465142	+	0.885236i	$0.653997\pi$
$720$	−43.5734	−	4.63232i	−1.62389	−	0.172636i
$721$		0			0
$722$	15.4512	−	3.37911i	0.575034	−	0.125757i
$723$	−3.16736	+	11.8207i	−0.117795	+	0.439618i
$724$	−0.795677	+	8.53215i	−0.0295711	+	0.317095i
$725$	6.67991	−	5.44304i	0.248086	−	0.202150i
$726$	−0.159356	+	3.42500i	−0.00591425	+	0.127114i
$727$	35.3576	−	35.3576i	1.31134	−	1.31134i	0.390911	−	0.920429i	$-0.372160\pi$
$727$	35.3576	−	35.3576i	1.31134	−	1.31134i	0.920429	−	0.390911i	$-0.127840\pi$
$728$		0			0
$729$			43.5147i			1.61166i
$730$	8.98634	−	5.59858i	0.332599	−	0.207213i
$731$	11.2655	+	6.50414i	0.416669	+	0.240564i
$732$	−50.5328	+	41.9118i	−1.86775	+	1.54910i
$733$	−19.8341	−	5.31453i	−0.732589	−	0.196297i	−0.126807	−	0.991927i	$-0.540473\pi$
$733$	−19.8341	−	5.31453i	−0.732589	−	0.196297i	−0.605782	+	0.795631i	$0.707140\pi$
$734$	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
$738$	−17.9899	−	5.72883i	−0.662219	−	0.210881i
$739$	24.2010	−	41.9174i	0.890249	−	1.54196i	0.0506730	−	0.998715i	$-0.483863\pi$
$739$	24.2010	−	41.9174i	0.890249	−	1.54196i	0.839576	−	0.543242i	$-0.182803\pi$
$740$	−7.52021	−	7.71717i	−0.276448	−	0.283689i
$741$	−26.8832			−0.987579
$742$		0			0
$743$	−3.78255	−	3.78255i	−0.138768	−	0.138768i	0.634310	−	0.773078i	$-0.281284\pi$
$743$	−3.78255	−	3.78255i	−0.138768	−	0.138768i	−0.773078	+	0.634310i	$0.781284\pi$
$744$	−25.6743	+	10.3774i	−0.941264	+	0.380454i
$745$	19.9672	−	1.60204i	0.731541	−	0.0586941i
$746$	−9.76578	−	18.8916i	−0.357551	−	0.691672i
$747$	29.3290	+	7.85869i	1.07309	+	0.287535i
$748$	−5.13212	+	13.8533i	−0.187649	+	0.506526i
$749$		0			0
$750$	14.3960	−	42.0420i	0.525669	−	1.53516i
$751$	15.5554	−	8.98090i	0.567623	−	0.327718i	−0.188576	−	0.982059i	$-0.560387\pi$
$751$	15.5554	−	8.98090i	0.567623	−	0.327718i	0.756200	+	0.654341i	$0.227054\pi$
$752$	−22.7872	−	10.9450i	−0.830964	−	0.399123i
$753$	−9.70180	−	36.2076i	−0.353553	−	1.31948i
$754$	−0.387544	+	8.32940i	−0.0141135	+	0.303339i
$755$	−8.54900	−	12.3984i	−0.311130	−	0.451224i
$756$		0			0
$757$	−35.0017	−	35.0017i	−1.27216	−	1.27216i	−0.944954	−	0.327204i	$-0.893894\pi$
$757$	−35.0017	−	35.0017i	−1.27216	−	1.27216i	−0.327204	−	0.944954i	$-0.606106\pi$
$758$	1.83119	+	2.00990i	0.0665118	+	0.0730030i
$759$	−24.0790	+	41.7061i	−0.874013	+	1.51384i
$760$	11.7384	+	13.2233i	0.425795	+	0.479660i
$761$	18.0493	+	31.2622i	0.654285	+	1.13325i	0.982073	+	0.188503i	$0.0603636\pi$
$761$	18.0493	+	31.2622i	0.654285	+	1.13325i	−0.327788	+	0.944751i	$0.606303\pi$
$762$	7.25651	−	1.58697i	0.262876	−	0.0574897i
$763$		0			0
$764$	−9.64999	−	21.0074i	−0.349125	−	0.760022i
$765$	−23.9442	+	8.52013i	−0.865705	+	0.308046i
$766$	−20.0822	+	10.3813i	−0.725601	+	0.375090i
$767$	−1.68495	−	6.28831i	−0.0608399	−	0.227058i
$768$	−44.6960	−	4.94329i	−1.61283	−	0.178375i
$769$		−	22.5137i		−	0.811865i	−0.913903	−	0.405933i	$-0.866947\pi$
$769$		−	22.5137i		−	0.811865i	0.913903	−	0.405933i	$-0.133053\pi$
$770$		0			0
$771$		−	28.2691i		−	1.01809i
$772$	−9.11563	+	1.55361i	−0.328079	+	0.0559158i
$773$	−5.98883	−	22.3506i	−0.215403	−	0.803896i	−0.986024	−	0.166602i	$-0.946720\pi$
$773$	−5.98883	−	22.3506i	−0.215403	−	0.803896i	0.770621	−	0.637294i	$-0.219946\pi$
$774$	−17.8392	−	34.5095i	−0.641218	−	1.24042i
$775$	−2.77711	−	17.1950i	−0.0997566	−	0.617662i
$776$	−43.2622	−	6.07370i	−1.55302	−	0.218033i
$777$		0			0
$778$	3.42368	+	15.6550i	0.122745	+	0.561259i
$779$	3.80923	+	6.59778i	0.136480	+	0.236390i
$780$	21.0184	+	37.5166i	0.752580	+	1.34331i
$781$	0.894971	−	1.55014i	0.0320246	−	0.0554682i
$782$	13.0522	−	11.8917i	0.466747	−	0.425245i
$783$	6.50425	+	6.50425i	0.232443	+	0.232443i
$784$		0			0
$785$	−25.0368	−	4.60088i	−0.893601	−	0.164213i
$786$	16.1572	+	0.751751i	0.576309	+	0.0268141i
$787$	9.53044	+	35.5681i	0.339724	+	1.26787i	0.898657	+	0.438653i	$0.144544\pi$
$787$	9.53044	+	35.5681i	0.339724	+	1.26787i	−0.558933	+	0.829213i	$0.688789\pi$
$788$	−14.7459	+	12.2302i	−0.525302	+	0.435684i
$789$	−26.1715	+	15.1101i	−0.931731	+	0.537935i
$790$	−17.8626	+	19.1040i	−0.635524	+	0.679690i
$791$		0			0
$792$	35.2311	−	26.5565i	1.25188	−	0.943646i
$793$	38.5982	+	10.3424i	1.37066	+	0.367268i
$794$	−14.6512	+	7.57376i	−0.519953	+	0.268783i
$795$	6.56122	+	81.7766i	0.232703	+	2.90032i
$796$	2.83861	+	2.01192i	0.100612	+	0.0713105i
$797$	8.30328	+	8.30328i	0.294117	+	0.294117i	0.838704	−	0.544587i	$-0.183314\pi$
$797$	8.30328	+	8.30328i	0.294117	+	0.294117i	−0.544587	+	0.838704i	$0.683314\pi$
$798$		0			0
$799$	−14.6620			−0.518705
$800$	9.27612	−	26.7199i	0.327960	−	0.944691i
$801$	7.10464	−	12.3056i	0.251030	−	0.434797i
$802$	−11.8747	+	37.2894i	−0.419309	+	1.31673i
$803$	−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
$808$	−3.95679	−	32.1868i	−0.139199	−	1.13233i
$809$	27.1489	+	15.6744i	0.954504	+	0.551083i	0.894477	−	0.447114i	$-0.147548\pi$
$809$	27.1489	+	15.6744i	0.954504	+	0.551083i	0.0600265	+	0.998197i	$0.480881\pi$
$810$	0.936286	+	0.217479i	0.0328977	+	0.00764142i
$811$		−	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
$814$	10.8374	+	0.504234i	0.379850	+	0.0176734i
$815$	0.00410159	−	0.00481718i	0.000143673	−	0.000168738i
$816$	−24.6092	+	8.63946i	−0.861495	+	0.302441i
$817$	−4.05719	+	15.1416i	−0.141943	+	0.529739i
$818$	−4.17892	−	19.1084i	−0.146112	−	0.668109i
$819$		0			0
$820$	6.22925	−	10.4744i	0.217535	−	0.365780i
$821$	3.83240	+	6.63791i	0.133752	+	0.231665i	0.925120	−	0.379675i	$-0.123964\pi$
$821$	3.83240	+	6.63791i	0.133752	+	0.231665i	−0.791368	+	0.611340i	$0.790631\pi$
$822$	61.0390	+	19.4377i	2.12898	+	0.677966i
$823$	−52.8907	+	14.1720i	−1.84365	+	0.494006i	−0.999138	−	0.0415239i	$-0.986779\pi$
$823$	−52.8907	+	14.1720i	−1.84365	+	0.494006i	−0.844517	+	0.535530i	$0.820112\pi$
$824$	−13.8873	−	34.3578i	−0.483786	−	1.19691i
$825$	18.3228	+	40.8189i	0.637919	+	1.42113i
$826$		0			0
$827$	35.5553	−	35.5553i	1.23638	−	1.23638i	0.274910	−	0.961470i	$-0.411352\pi$
$827$	35.5553	−	35.5553i	1.23638	−	1.23638i	0.961470	−	0.274910i	$-0.0886479\pi$
$828$	−51.9813	+	8.85938i	−1.80647	+	0.307885i
$829$	−23.4882	−	13.5609i	−0.815780	−	0.470991i	0.0331794	−	0.999449i	$-0.489437\pi$
$829$	−23.4882	−	13.5609i	−0.815780	−	0.470991i	−0.848959	+	0.528459i	$0.822770\pi$
$830$	−9.22438	+	17.2927i	−0.320183	+	0.600237i
$831$	80.5397	−	46.4996i	2.79389	−	1.61305i
$832$	13.2765	+	23.9351i	0.460281	+	0.829800i
$833$		0			0
$834$	57.1560	+	36.6426i	1.97915	+	1.26883i
$835$	6.92628	−	2.46460i	0.239694	−	0.0852909i
$836$	−17.7259	−	1.65305i	−0.613063	−	0.0571720i
$837$	17.9600	−	4.81237i	0.620789	−	0.166340i
$838$	19.7133	+	21.6372i	0.680984	+	0.747445i
$839$	−3.82948			−0.132208			−0.0661042	−	0.997813i	$-0.521057\pi$
$839$	−3.82948			−0.132208			−0.0661042	+	0.997813i	$0.521057\pi$
$840$		0			0
$841$	26.0301			0.897589
$842$	25.4794	+	27.9661i	0.878079	+	0.963775i
$843$	27.6011	−	7.39570i	0.950634	−	0.254722i
$844$	47.3115	+	4.41210i	1.62853	+	0.151871i
$845$	−1.24212	+	2.61440i	−0.0427304	+	0.0899382i
$846$	36.8617	+	23.6320i	1.26733	+	0.812485i
$847$		0			0
$848$	3.95551	+	52.0665i	0.135833	+	1.78797i
$849$	67.4183	−	38.9240i	2.31379	−	1.33587i
$850$	−1.86008	−	16.2990i	−0.0638001	−	0.559052i
$851$	−11.2296	−	6.48342i	−0.384946	−	0.222249i
$852$	3.11514	−	0.530926i	0.106723	−	0.0181892i
$853$	1.20013	−	1.20013i	0.0410916	−	0.0410916i	−0.686262	−	0.727354i	$-0.740750\pi$
$853$	1.20013	−	1.20013i	0.0410916	−	0.0410916i	0.727354	+	0.686262i	$0.240750\pi$
$854$		0			0
$855$	−17.3855	−	25.2137i	−0.594571	−	0.862291i
$856$	−1.07783	+	0.435655i	−0.0368396	+	0.0148904i
$857$	25.5819	−	6.85466i	0.873862	−	0.234151i	0.206105	−	0.978530i	$-0.433921\pi$
$857$	25.5819	−	6.85466i	0.873862	−	0.234151i	0.667757	+	0.744379i	$0.267254\pi$
$858$	−41.2561	−	13.1379i	−1.40846	−	0.448519i
$859$	19.8151	+	34.3208i	0.676083	+	1.17101i	0.976151	+	0.217093i	$0.0696574\pi$
$859$	19.8151	+	34.3208i	0.676083	+	1.17101i	−0.300068	+	0.953918i	$0.597009\pi$
$860$	24.3029	−	6.17640i	0.828720	−	0.210613i
$861$		0			0
$862$	12.1881	+	55.7308i	0.415128	+	1.89820i
$863$	−2.57861	+	9.62351i	−0.0877769	+	0.327588i	−0.995826	−	0.0912768i	$-0.970905\pi$
$863$	−2.57861	+	9.62351i	−0.0877769	+	0.327588i	0.908049	+	0.418865i	$0.137572\pi$
$864$	29.3814	+	6.95601i	0.999575	+	0.236648i
$865$	−27.3611	−	23.2966i	−0.930305	−	0.792110i
$866$	−33.1312	−	1.54150i	−1.12585	−	0.0523825i
$867$	23.0883	−	23.0883i	0.784120	−	0.784120i
$868$		0			0
$869$		−	26.3331i		−	0.893290i
$870$	−13.0000	+	8.09915i	−0.440742	+	0.274587i
$871$	−17.3938	−	10.0423i	−0.589368	−	0.340272i
$872$	−20.5030	+	2.52047i	−0.694318	+	0.0853540i
$873$	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	−0.953807	−	0.300420i	$-0.902873\pi$
$877$	0.664074	−	2.47836i	0.0224242	−	0.0836882i	0.976231	+	0.216732i	$0.0695398\pi$
$878$	−2.46372	+	7.73668i	−0.0831464	+	0.261100i
$879$	−6.12031	+	10.6007i	−0.206433	+	0.357553i
$880$	11.5519	+	26.0296i	0.389416	+	0.877459i
$881$	−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	$-0.468244\pi$
$883$	−26.6080	−	26.6080i	−0.895429	−	0.895429i	−0.995028	+	0.0995985i	$0.968244\pi$
$884$	12.9517	+	9.17974i	0.435613	+	0.308748i
$885$	7.75242	−	9.10495i	0.260595	−	0.306059i
$886$	−1.07522	+	0.555823i	−0.0361229	+	0.0186732i
$887$	−7.10873	−	1.90478i	−0.238688	−	0.0639562i	0.137492	−	0.990503i	$-0.456096\pi$
$887$	−7.10873	−	1.90478i	−0.238688	−	0.0639562i	−0.376180	+	0.926547i	$0.622762\pi$
$888$	11.5292	+	15.2951i	0.386893	+	0.513269i
$889$		0			0
$890$	6.69945	+	6.26412i	0.224566	+	0.209974i
$891$	−0.838132	+	0.483895i	−0.0280785	+	0.0162111i
$892$	−28.8053	+	23.8911i	−0.964474	+	0.799932i
$893$	−4.57299	−	17.0666i	−0.153029	−	0.571112i
$894$	−35.5680	−	1.65488i	−1.18957	−	0.0553475i
$895$	−33.4565	+	23.0691i	−1.11833	+	0.771115i
$896$		0			0
$897$	36.5921	+	36.5921i	1.22177	+	1.22177i
$898$	−4.87319	+	4.43988i	−0.162621	+	0.148161i
$899$	−3.00169	+	5.19908i	−0.100112	+	0.173399i
$900$	−21.5941	+	43.9753i	−0.719802	+	1.46584i
$901$	15.1427	+	26.2280i	0.504478	+	0.873781i
$902$	2.62146	+	11.9868i	0.0872852	+	0.399117i
$903$		0			0
$904$	6.46788	−	46.0699i	0.215119	−	1.53226i
$905$	8.65360	+	4.11140i	0.287655	+	0.136667i
$906$	12.2930	+	23.7804i	0.408407	+	0.790052i
$907$	3.60588	+	13.4573i	0.119731	+	0.446843i	0.999597	−	0.0283786i	$-0.00903439\pi$
$907$	3.60588	+	13.4573i	0.119731	+	0.446843i	−0.879866	+	0.475222i	$0.842368\pi$
$908$	−40.9878	+	6.98572i	−1.36023	+	0.231829i
$909$			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	$-0.0482031\pi$
$912$	−17.7318	−	25.9506i	−0.587158	−	0.859309i
$913$	−5.10735	−	19.0609i	−0.169029	−	0.630823i
$914$	39.9610	−	20.6573i	1.32179	−	0.683283i
$915$	24.6070	+	69.1534i	0.813484	+	2.28614i
$916$	14.9228	+	32.4860i	0.493064	+	1.07337i
$917$		0			0
$918$	17.1079	−	3.74142i	0.564644	−	0.123485i
$919$	−17.5872	−	30.4620i	−0.580149	−	1.00485i	−0.995461	−	0.0951683i	$-0.969661\pi$
$919$	−17.5872	−	30.4620i	−0.580149	−	1.00485i	0.415312	−	0.909679i	$-0.363672\pi$
$920$	2.02124	−	33.9766i	0.0666382	−	1.12018i
$921$	−26.5004	+	45.9000i	−0.873217	+	1.51246i
$922$	22.3295	+	24.5088i	0.735384	+	0.807154i
$923$	−1.36006	−	1.36006i	−0.0447668	−	0.0447668i
$924$		0			0
$925$	−10.9907	+	4.93353i	−0.361372	+	0.162213i
$926$	0.171184	−	3.67923i	0.00562546	−	0.120907i
$927$	16.6132	+	62.0014i	0.545650	+	2.03639i
$928$	−8.29605	+	5.11985i	−0.272331	+	0.168067i
$929$	32.5064	−	18.7676i	1.06650	−	0.615745i	0.139278	−	0.990253i	$-0.455522\pi$
$929$	32.5064	−	18.7676i	1.06650	−	0.615745i	0.927223	+	0.374509i	$0.122189\pi$
$930$	1.03911	+	30.9434i	0.0340737	+	1.01467i
$931$		0			0
$932$	−0.245150	+	0.661739i	−0.00803015	+	0.0216760i
$933$	−4.24615	−	1.13775i	−0.139013	−	0.0372483i
$934$	−5.38846	−	10.4238i	−0.176316	−	0.341078i
$935$	12.5760	+	10.7079i	0.411280	+	0.350185i
$936$	−17.7660	−	43.9540i	−0.580700	−	1.43668i
$937$	14.9371	+	14.9371i	0.487973	+	0.487973i	0.907666	−	0.419693i	$-0.137862\pi$
$937$	14.9371	+	14.9371i	0.487973	+	0.487973i	−0.419693	+	0.907666i	$0.637862\pi$
$938$		0			0
$939$	−34.2270			−1.11696
$940$	−20.2418	+	19.7252i	−0.660215	+	0.643364i
$941$	3.05589	−	5.29296i	0.0996192	−	0.172546i	−0.811908	−	0.583786i	$-0.801571\pi$
$941$	3.05589	−	5.29296i	0.0996192	−	0.172546i	0.911527	+	0.411240i	$0.134904\pi$
$942$	43.1157	+	13.7300i	1.40479	+	0.447349i
$943$	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	$-0.663753\pi$
$947$	−41.6507	−	11.1603i	−1.35347	−	0.362660i	−0.861413	+	0.507905i	$0.830420\pi$
$948$	35.7837	−	29.6789i	1.16220	−	0.963926i
$949$	9.92033	+	5.72751i	0.322028	+	0.185923i
$950$	18.3919	−	7.24868i	0.596713	−	0.235178i
$951$		−	76.9801i		−	2.49625i
$952$		0			0
$953$	26.8326	−	26.8326i	0.869193	−	0.869193i	−0.123190	−	0.992383i	$-0.539313\pi$
$953$	26.8326	−	26.8326i	0.869193	−	0.869193i	0.992383	+	0.123190i	$0.0393125\pi$
$954$	4.20357	−	90.3464i	0.136096	−	2.92507i
$955$	−25.7637	+	2.06711i	−0.833695	+	0.0668903i
$956$	−4.47701	+	48.0076i	−0.144797	+	1.55268i
$957$	3.99135	−	14.8959i	0.129022	−	0.481517i
$958$	−19.3398	+	4.22953i	−0.624841	+	0.136650i
$959$		0			0
$960$	−22.3516	+	45.0347i	−0.721395	+	1.45349i
$961$	−9.43240	−	16.3374i	−0.304271	−	0.527013i
$962$	3.53745	−	11.1085i	0.114052	−	0.358151i
$963$	1.94504	−	0.521171i	0.0626779	−	0.0167945i
$964$	7.10486	+	5.03570i	0.228832	+	0.162189i
$965$	−1.86857	+	10.1683i	−0.0601515	+	0.327329i
$966$		0			0
$967$	−9.65871	+	9.65871i	−0.310603	+	0.310603i	−0.845143	−	0.534540i	$-0.820485\pi$
$967$	−9.65871	+	9.65871i	−0.310603	+	0.310603i	0.534540	+	0.845143i	$0.320485\pi$
$968$	2.24608	+	0.953017i	0.0721916	+	0.0306311i
$969$	−15.7871	−	9.11468i	−0.507155	−	0.292806i
$970$	−22.9881	+	43.0950i	−0.738102	+	1.38370i
$971$	−18.9435	+	10.9371i	−0.607927	+	0.350987i	−0.772154	−	0.635436i	$-0.780821\pi$
$971$	−18.9435	+	10.9371i	−0.607927	+	0.350987i	0.164226	+	0.986423i	$0.447487\pi$
$972$	28.4284	+	10.5317i	0.911843	+	0.337804i
$973$		0			0
$974$	20.2623	−	31.6056i	0.649246	−	1.01271i
$975$	47.4639	−	7.66574i	1.52006	−	0.245500i
$976$	15.4753	+	44.0809i	0.495352	+	1.41099i
$977$	25.1707	−	6.74446i	0.805281	−	0.215774i	0.167380	−	0.985893i	$-0.446469\pi$
$977$	25.1707	−	6.74446i	0.805281	−	0.215774i	0.637901	+	0.770118i	$0.279803\pi$
$978$	−0.00831321	+	0.00757402i	−0.000265827	+	0.000242190i
$979$	−9.23458			−0.295138
$980$		0			0
$981$	35.7805			1.14238
$982$	−37.2023	+	33.8944i	−1.18717	+	1.08161i
$983$	−46.8710	+	12.5590i	−1.49495	+	0.400571i	−0.911406	−	0.411508i	$-0.865002\pi$
$983$	−46.8710	+	12.5590i	−1.49495	+	0.400571i	−0.583547	+	0.812080i	$0.698336\pi$
$984$	−13.3342	+	17.0721i	−0.425078	+	0.544239i
$985$	7.18055	+	20.1796i	0.228791	+	0.642975i
$986$	−3.05165	+	4.76002i	−0.0971842	+	0.151590i
$987$		0			0
$988$	−6.64569	+	17.9389i	−0.211427	+	0.570712i
$989$	26.1325	−	15.0876i	0.830965	−	0.479758i
$990$	−14.3585	−	47.1904i	−0.456344	−	1.49981i
$991$	3.40592	+	1.96641i	0.108193	+	0.0624650i	0.553120	−	0.833102i	$-0.313437\pi$
$991$	3.40592	+	1.96641i	0.108193	+	0.0624650i	−0.444927	+	0.895567i	$0.646770\pi$
$992$	0.577912	+	19.6975i	0.0183487	+	0.625397i
$993$	−7.77497	+	7.77497i	−0.246731	+	0.246731i
$994$		0			0
$995$	3.20247	−	2.20818i	0.101525	−	0.0700041i
$996$	20.1453	−	28.4230i	0.638329	−	0.900617i
$997$	49.5831	−	13.2857i	1.57031	−	0.420764i	0.634402	−	0.773004i	$-0.281247\pi$
$997$	49.5831	−	13.2857i	1.57031	−	0.420764i	0.935910	+	0.352240i	$0.114580\pi$
$998$	4.24068	−	13.3168i	0.134236	−	0.421535i
$999$	−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.67.13		72
4.3	odd	2	inner	980.2.x.m.67.3		72
5.3	odd	4	inner	980.2.x.m.263.15		72
7.2	even	3	inner	980.2.x.m.667.11		72
7.3	odd	6		980.2.k.k.687.2		36
7.4	even	3		980.2.k.j.687.2		36
7.5	odd	6		140.2.w.b.107.11	yes	72
7.6	odd	2		140.2.w.b.67.13	yes	72
20.3	even	4	inner	980.2.x.m.263.11		72
28.3	even	6		980.2.k.k.687.11		36
28.11	odd	6		980.2.k.j.687.11		36
28.19	even	6		140.2.w.b.107.15	yes	72
28.23	odd	6	inner	980.2.x.m.667.15		72
28.27	even	2		140.2.w.b.67.3	yes	72
35.3	even	12		980.2.k.k.883.11		36
35.12	even	12		700.2.be.e.443.16		72
35.13	even	4		140.2.w.b.123.15	yes	72
35.18	odd	12		980.2.k.j.883.11		36
35.19	odd	6		700.2.be.e.107.8		72
35.23	odd	12	inner	980.2.x.m.863.3		72
35.27	even	4		700.2.be.e.543.4		72
35.33	even	12		140.2.w.b.23.3	✓	72
35.34	odd	2		700.2.be.e.207.6		72
140.3	odd	12		980.2.k.k.883.2		36
140.19	even	6		700.2.be.e.107.4		72
140.23	even	12	inner	980.2.x.m.863.13		72
140.27	odd	4		700.2.be.e.543.8		72
140.47	odd	12		700.2.be.e.443.6		72
140.83	odd	4		140.2.w.b.123.11	yes	72
140.103	odd	12		140.2.w.b.23.13	yes	72
140.123	even	12		980.2.k.j.883.2		36
140.139	even	2		700.2.be.e.207.16		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.3	✓	72	35.33	even	12
140.2.w.b.23.13	yes	72	140.103	odd	12
140.2.w.b.67.3	yes	72	28.27	even	2
140.2.w.b.67.13	yes	72	7.6	odd	2
140.2.w.b.107.11	yes	72	7.5	odd	6
140.2.w.b.107.15	yes	72	28.19	even	6
140.2.w.b.123.11	yes	72	140.83	odd	4
140.2.w.b.123.15	yes	72	35.13	even	4
700.2.be.e.107.4		72	140.19	even	6
700.2.be.e.107.8		72	35.19	odd	6
700.2.be.e.207.6		72	35.34	odd	2
700.2.be.e.207.16		72	140.139	even	2
700.2.be.e.443.6		72	140.47	odd	12
700.2.be.e.443.16		72	35.12	even	12
700.2.be.e.543.4		72	35.27	even	4
700.2.be.e.543.8		72	140.27	odd	4
980.2.k.j.687.2		36	7.4	even	3
980.2.k.j.687.11		36	28.11	odd	6
980.2.k.j.883.2		36	140.123	even	12
980.2.k.j.883.11		36	35.18	odd	12
980.2.k.k.687.2		36	7.3	odd	6
980.2.k.k.687.11		36	28.3	even	6
980.2.k.k.883.2		36	140.3	odd	12
980.2.k.k.883.11		36	35.3	even	12
980.2.x.m.67.3		72	4.3	odd	2	inner
980.2.x.m.67.13		72	1.1	even	1	trivial
980.2.x.m.263.11		72	20.3	even	4	inner
980.2.x.m.263.15		72	5.3	odd	4	inner
980.2.x.m.667.11		72	7.2	even	3	inner
980.2.x.m.667.15		72	28.23	odd	6	inner
980.2.x.m.863.3		72	35.23	odd	12	inner
980.2.x.m.863.13		72	140.23	even	12	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+(0.952442 + 1.04540i) q^{2} +(-2.71477 + 0.727420i) q^{3} +(-0.185707 + 1.99136i) q^{4} +(2.01971 + 0.959579i) q^{5} +(-3.34610 - 2.14518i) q^{6} +(-2.25864 + 1.70252i) q^{8} +(4.24276 - 2.44956i) q^{9} +(0.920513 + 3.02534i) q^{10} +(-2.75736 - 1.59196i) q^{11} +(-0.944404 - 5.54117i) q^{12} +(-2.41925 + 2.41925i) q^{13} +(-6.18105 - 1.13586i) q^{15} +(-3.93103 - 0.739618i) q^{16} +(-2.24094 + 0.600458i) q^{17} +(6.60174 + 2.10230i) q^{18} +(-1.39787 - 2.42118i) q^{19} +(-2.28594 + 3.84376i) q^{20} +(-0.961994 - 4.39878i) q^{22} +(-1.39288 + 5.19830i) q^{23} +(4.89323 - 6.26492i) q^{24} +(3.15842 + 3.87613i) q^{25} +(-4.83327 - 0.224879i) q^{26} +(-3.77420 + 3.77420i) q^{27} -1.72334i q^{29} +(-4.69967 - 7.54349i) q^{30} +(-3.01685 - 1.74178i) q^{31} +(-2.97088 - 4.81392i) 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} +(1.19970 - 3.76736i) q^{38} +(4.80790 - 8.32752i) q^{39} +(-6.19548 + 1.27125i) q^{40} -2.72503 q^{41} +(-3.96477 - 3.96477i) q^{43} +(3.68223 - 5.19525i) q^{44} +(10.9197 - 0.876123i) q^{45} +(-6.76092 + 3.49497i) q^{46} +(6.10452 + 1.63570i) q^{47} +(11.2098 - 0.851615i) q^{48} +(-1.04388 + 6.99359i) q^{50} +(5.64685 - 3.26021i) q^{51} +(-4.36833 - 5.26687i) q^{52} +(-3.37866 - 12.6093i) q^{53} +(-7.54024 - 0.350826i) q^{54} +(-4.04144 - 5.86120i) q^{55} +(5.55610 + 5.55610i) q^{57} +(1.80158 - 1.64139i) q^{58} +(-0.951402 + 1.64788i) q^{59} +(3.40977 - 12.0978i) q^{60} +(-5.83980 - 10.1148i) q^{61} +(-1.05253 - 4.81275i) q^{62} +(2.20286 - 7.69073i) q^{64} +(-7.20764 + 2.56471i) q^{65} +(5.81136 + 11.2419i) q^{66} +(1.51938 + 5.67039i) q^{67} +(-0.779570 - 4.57403i) q^{68} -15.1254i q^{69} +0.562181i q^{71} +(-5.41242 + 12.7560i) q^{72} +(-0.866554 - 3.23402i) q^{73} +(-3.02695 + 1.56474i) q^{74} +(-11.3940 - 8.22531i) q^{75} +(5.08103 - 2.33403i) q^{76} +(13.2848 - 2.90533i) q^{78} +(4.13532 + 7.16259i) q^{79} +(-7.22979 - 5.26594i) q^{80} +(0.151981 - 0.263239i) q^{81} +(-2.59543 - 2.84874i) q^{82} +(4.38250 + 4.38250i) q^{83} +(-5.10222 - 0.937610i) q^{85} +(0.368541 - 7.92097i) q^{86} +(1.25360 + 4.67848i) q^{87} +(8.93821 - 1.09879i) q^{88} +(2.51180 - 1.45019i) q^{89} +(11.3162 + 10.5809i) q^{90} +(-10.0930 - 3.73908i) q^{92} +(9.45706 + 2.53401i) q^{93} +(4.10425 + 7.93955i) q^{94} +(-0.499970 - 6.23143i) q^{95} +(11.5670 + 10.9076i) 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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