LMFDB - Embedded newform 980.2.x.k.67.11

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)

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);

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")

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 = [72,0,0,0,0,-16,0,0,0,16,0] 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			67.11
Character	$\chi$	$=$	980.67
Dual form			980.2.x.k.863.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.370738 + 1.36475i) q^{2} +(1.72922 - 0.463343i) q^{3} +(-1.72511 + 1.01193i) q^{4} +(-0.0513098 - 2.23548i) q^{5} +(1.27344 + 2.18818i) q^{6} +(-2.02060 - 1.97918i) q^{8} +(0.177443 - 0.102447i) q^{9} +(3.03186 - 0.898803i) q^{10} +(1.83014 + 1.05663i) q^{11} +(-2.51422 + 2.54917i) q^{12} +(2.86476 - 2.86476i) q^{13} +(-1.12452 - 3.84186i) q^{15} +(1.95198 - 3.49138i) q^{16} +(6.10660 - 1.63626i) q^{17} +(0.205599 + 0.204185i) q^{18} +(-1.47623 - 2.55691i) q^{19} +(2.35067 + 3.80452i) q^{20} +(-0.763541 + 2.88943i) q^{22} +(1.44328 - 5.38640i) q^{23} +(-4.41111 - 2.48621i) q^{24} +(-4.99473 + 0.229404i) q^{25} +(4.97177 + 2.84762i) q^{26} +(-3.53826 + 3.53826i) q^{27} +2.86818i q^{29} +(4.82630 - 2.95902i) q^{30} +(5.20796 + 3.00682i) q^{31} +(5.48855 + 1.36959i) q^{32} +(3.65431 + 0.979169i) q^{33} +(4.49704 + 7.72739i) q^{34} +(-0.202439 + 0.356292i) q^{36} +(1.43278 - 5.34722i) q^{37} +(2.94225 - 2.96264i) q^{38} +(3.62644 - 6.28117i) q^{39} +(-4.32075 + 4.61857i) q^{40} -7.98984 q^{41} +(5.64967 + 5.64967i) q^{43} +(-4.22644 + 0.0291770i) q^{44} +(-0.238122 - 0.391413i) q^{45} +(7.88619 - 0.0272206i) q^{46} +(5.87853 + 1.57515i) q^{47} +(1.75770 - 6.94181i) q^{48} +(-2.16482 - 6.73153i) q^{50} +(9.80152 - 5.65891i) q^{51} +(-2.04307 + 7.84096i) q^{52} +(-0.205406 - 0.766587i) q^{53} +(-6.14063 - 3.51709i) q^{54} +(2.26818 - 4.14546i) q^{55} +(-3.73746 - 3.73746i) q^{57} +(-3.91435 + 1.06334i) q^{58} +(-2.48910 + 4.31124i) q^{59} +(5.82763 + 5.48968i) q^{60} +(-0.843662 - 1.46127i) q^{61} +(-2.17278 + 8.22233i) q^{62} +(0.165668 + 7.99828i) q^{64} +(-6.55110 - 6.25712i) q^{65} +(0.0184674 + 5.35025i) q^{66} +(-2.95071 - 11.0122i) q^{67} +(-8.87876 + 9.00220i) q^{68} -9.98301i q^{69} +0.610925i q^{71} +(-0.561302 - 0.144188i) q^{72} +(-1.18312 - 4.41548i) q^{73} +(7.82883 - 0.0270227i) q^{74} +(-8.53071 + 2.71097i) q^{75} +(5.13407 + 2.91709i) q^{76} +(9.91671 + 2.62052i) q^{78} +(7.12694 + 12.3442i) q^{79} +(-7.90507 - 4.18448i) q^{80} +(-4.78635 + 8.29020i) q^{81} +(-2.96214 - 10.9042i) q^{82} +(5.51624 + 5.51624i) q^{83} +(-3.97115 - 13.5672i) q^{85} +(-5.61586 + 9.80496i) q^{86} +(1.32895 + 4.95971i) q^{87} +(-1.60672 - 5.75723i) q^{88} +(1.80030 - 1.03940i) q^{89} +(0.445902 - 0.470090i) q^{90} +(2.96086 + 10.7526i) q^{92} +(10.3989 + 2.78638i) q^{93} +(0.0297077 + 8.60672i) q^{94} +(-5.64017 + 3.43128i) q^{95} +(10.1255 - 0.174767i) q^{96} +(-1.95542 - 1.95542i) q^{97} +0.432994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 16 q^{6} + 16 q^{10} + 16 q^{12} - 8 q^{13} + 8 q^{16} + 20 q^{17} - 28 q^{18} + 40 q^{20} + 8 q^{22} + 20 q^{25} + 32 q^{26} + 4 q^{30} - 20 q^{37} + 36 q^{40} - 20 q^{45} - 16 q^{46} - 48 q^{48}+ \cdots + 40 q^{97}+O(q^{100}) $ 72 * q - 16 * q^6 + 16 * q^10 + 16 * q^12 - 8 * q^13 + 8 * q^16 + 20 * q^17 - 28 * q^18 + 40 * q^20 + 8 * q^22 + 20 * q^25 + 32 * q^26 + 4 * q^30 - 20 * q^37 + 36 * q^40 - 20 * q^45 - 16 * q^46 - 48 * q^48 + 80 * q^50 - 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 + 64 * q^61 + 80 * q^62 - 4 * q^65 - 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 16 * q^76 - 152 * q^78 + 20 * q^80 + 36 * q^81 - 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 - 32 * q^90 - 112 * q^92 - 32 * q^93 - 120 * q^96 + 40 * 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 $

$2$	0.370738	+	1.36475i	0.262152	+	0.965027i
$2$	0.370738	+	1.36475i	0.262152	+	0.965027i
$3$	1.72922	−	0.463343i	0.998366	−	0.267511i	0.277605	−	0.960695i	$-0.410459\pi$
$3$	1.72922	−	0.463343i	0.998366	−	0.267511i	0.720761	+	0.693184i	$0.243793\pi$
$4$	−1.72511	+	1.01193i	−0.862553	+	0.505967i
$5$	−0.0513098	−	2.23548i	−0.0229464	−	0.999737i
$5$	−0.0513098	−	2.23548i	−0.0229464	−	0.999737i
$6$	1.27344	+	2.18818i	0.519879	+	0.893322i
$7$		0			0
$7$		0			0
$8$	−2.02060	−	1.97918i	−0.714391	−	0.699747i
$9$	0.177443	−	0.102447i	0.0591476	−	0.0341489i
$10$	3.03186	−	0.898803i	0.958757	−	0.284226i
$11$	1.83014	+	1.05663i	0.551809	+	0.318587i	0.749851	−	0.661606i	$-0.230125\pi$
$11$	1.83014	+	1.05663i	0.551809	+	0.318587i	−0.198042	+	0.980193i	$0.563458\pi$
$12$	−2.51422	+	2.54917i	−0.725792	+	0.735883i
$13$	2.86476	−	2.86476i	0.794542	−	0.794542i	−0.187687	−	0.982229i	$-0.560099\pi$
$13$	2.86476	−	2.86476i	0.794542	−	0.794542i	0.982229	+	0.187687i	$0.0600992\pi$
$14$		0			0
$15$	−1.12452	−	3.84186i	−0.290350	−	0.991965i
$16$	1.95198	−	3.49138i	0.487996	−	0.872846i
$17$	6.10660	−	1.63626i	1.48107	−	0.396851i	0.574358	−	0.818604i	$-0.305252\pi$
$17$	6.10660	−	1.63626i	1.48107	−	0.396851i	0.906711	+	0.421753i	$0.138585\pi$
$18$	0.205599	+	0.204185i	0.0484602	+	0.0481268i
$19$	−1.47623	−	2.55691i	−0.338671	−	0.586595i	0.645512	−	0.763750i	$-0.276644\pi$
$19$	−1.47623	−	2.55691i	−0.338671	−	0.586595i	−0.984183	+	0.177155i	$0.943311\pi$
$20$	2.35067	+	3.80452i	0.525626	+	0.850716i
$21$		0			0
$22$	−0.763541	+	2.88943i	−0.162788	+	0.616029i
$23$	1.44328	−	5.38640i	0.300945	−	1.12314i	−0.635435	−	0.772154i	$-0.719179\pi$
$23$	1.44328	−	5.38640i	0.300945	−	1.12314i	0.936380	−	0.350988i	$-0.114154\pi$
$24$	−4.41111	−	2.48621i	−0.900414	−	0.507496i
$25$	−4.99473	+	0.229404i	−0.998947	+	0.0458808i
$26$	4.97177	+	2.84762i	0.975044	+	0.558464i
$27$	−3.53826	+	3.53826i	−0.680939	+	0.680939i
$28$		0			0
$29$			2.86818i			0.532607i	0.963889	+	0.266303i	$0.0858023\pi$
$29$			2.86818i			0.532607i	−0.963889	+	0.266303i	$0.914198\pi$
$30$	4.82630	−	2.95902i	0.881157	−	0.540241i
$31$	5.20796	+	3.00682i	0.935378	+	0.540041i	0.888508	−	0.458860i	$-0.151742\pi$
$31$	5.20796	+	3.00682i	0.935378	+	0.540041i	0.0468695	+	0.998901i	$0.485076\pi$
$32$	5.48855	+	1.36959i	0.970249	+	0.242111i
$33$	3.65431	+	0.979169i	0.636133	+	0.170451i
$34$	4.49704	+	7.72739i	0.771237	+	1.32524i
$35$		0			0
$36$	−0.202439	+	0.356292i	−0.0337398	+	0.0593819i
$37$	1.43278	−	5.34722i	0.235548	−	0.879078i	−0.742353	−	0.670009i	$-0.766290\pi$
$37$	1.43278	−	5.34722i	0.235548	−	0.879078i	0.977901	−	0.209069i	$-0.0670432\pi$
$38$	2.94225	−	2.96264i	0.477297	−	0.480603i
$39$	3.62644	−	6.28117i	0.580695	−	1.00579i
$40$	−4.32075	+	4.61857i	−0.683170	+	0.730259i
$41$	−7.98984			−1.24780			−0.623902	−	0.781503i	$-0.714453\pi$
$41$	−7.98984			−1.24780			−0.623902	+	0.781503i	$0.714453\pi$
$42$		0			0
$43$	5.64967	+	5.64967i	0.861567	+	0.861567i	0.991520	−	0.129954i	$-0.0414828\pi$
$43$	5.64967	+	5.64967i	0.861567	+	0.861567i	−0.129954	+	0.991520i	$0.541483\pi$
$44$	−4.22644	+	0.0291770i	−0.637159	+	0.00439860i
$45$	−0.238122	−	0.391413i	−0.0354971	−	0.0583484i
$46$	7.88619	−	0.0272206i	1.16275	−	0.00401346i
$47$	5.87853	+	1.57515i	0.857472	+	0.229759i	0.660663	−	0.750683i	$-0.270275\pi$
$47$	5.87853	+	1.57515i	0.857472	+	0.229759i	0.196810	+	0.980442i	$0.436942\pi$
$48$	1.75770	−	6.94181i	0.253702	−	1.00196i
$49$		0			0
$50$	−2.16482	−	6.73153i	−0.306152	−	0.951983i
$51$	9.80152	−	5.65891i	1.37249	−	0.792406i
$52$	−2.04307	+	7.84096i	−0.283323	+	1.08735i
$53$	−0.205406	−	0.766587i	−0.0282147	−	0.105299i	0.950383	−	0.311084i	$-0.100692\pi$
$53$	−0.205406	−	0.766587i	−0.0282147	−	0.105299i	−0.978597	+	0.205785i	$0.934025\pi$
$54$	−6.14063	−	3.51709i	−0.835634	−	0.478615i
$55$	2.26818	−	4.14546i	0.305841	−	0.558974i
$56$		0			0
$57$	−3.73746	−	3.73746i	−0.495038	−	0.495038i
$58$	−3.91435	+	1.06334i	−0.513980	+	0.139624i
$59$	−2.48910	+	4.31124i	−0.324053	+	0.561276i	−0.981320	−	0.192382i	$-0.938379\pi$
$59$	−2.48910	+	4.31124i	−0.324053	+	0.561276i	0.657268	+	0.753657i	$0.271712\pi$
$60$	5.82763	+	5.48968i	0.752343	+	0.708715i
$61$	−0.843662	−	1.46127i	−0.108020	−	0.187096i	0.806948	−	0.590622i	$-0.201118\pi$
$61$	−0.843662	−	1.46127i	−0.108020	−	0.187096i	−0.914968	+	0.403526i	$0.867784\pi$
$62$	−2.17278	+	8.22233i	−0.275943	+	1.04424i
$63$		0			0
$64$	0.165668	+	7.99828i	0.0207085	+	0.999786i
$65$	−6.55110	−	6.25712i	−0.812564	−	0.776100i
$66$	0.0184674	+	5.35025i	0.00227318	+	0.658570i
$67$	−2.95071	−	11.0122i	−0.360486	−	1.34535i	−0.873438	−	0.486935i	$-0.838115\pi$
$67$	−2.95071	−	11.0122i	−0.360486	−	1.34535i	0.512952	−	0.858417i	$-0.328552\pi$
$68$	−8.87876	+	9.00220i	−1.07671	+	1.09168i
$69$		−	9.98301i		−	1.20181i
$70$		0			0
$71$			0.610925i			0.0725035i	0.999343	+	0.0362518i	$0.0115418\pi$
$71$			0.610925i			0.0725035i	−0.999343	+	0.0362518i	$0.988458\pi$
$72$	−0.561302	−	0.144188i	−0.0661501	−	0.0169927i
$73$	−1.18312	−	4.41548i	−0.138474	−	0.516793i	−0.999959	−	0.00901016i	$-0.997132\pi$
$73$	−1.18312	−	4.41548i	−0.138474	−	0.516793i	0.861485	−	0.507783i	$-0.169535\pi$
$74$	7.82883	−	0.0270227i	0.910083	−	0.00314132i
$75$	−8.53071	+	2.71097i	−0.985041	+	0.313036i
$76$	5.13407	+	2.91709i	0.588919	+	0.334613i
$77$		0			0
$78$	9.91671	+	2.62052i	1.12285	+	0.296716i
$79$	7.12694	+	12.3442i	0.801843	+	1.38883i	0.918401	+	0.395650i	$0.129481\pi$
$79$	7.12694	+	12.3442i	0.801843	+	1.38883i	−0.116558	+	0.993184i	$0.537186\pi$
$80$	−7.90507	−	4.18448i	−0.883814	−	0.467839i
$81$	−4.78635	+	8.29020i	−0.531817	+	0.921133i
$82$	−2.96214	−	10.9042i	−0.327114	−	1.20416i
$83$	5.51624	+	5.51624i	0.605486	+	0.605486i	0.941763	−	0.336277i	$-0.109168\pi$
$83$	5.51624	+	5.51624i	0.605486	+	0.605486i	−0.336277	+	0.941763i	$0.609168\pi$
$84$		0			0
$85$	−3.97115	−	13.5672i	−0.430732	−	1.47157i
$86$	−5.61586	+	9.80496i	−0.605574	+	1.05730i
$87$	1.32895	+	4.95971i	0.142478	+	0.531737i
$88$	−1.60672	−	5.75723i	−0.171277	−	0.613723i
$89$	1.80030	−	1.03940i	0.190831	−	0.110176i	−0.401540	−	0.915841i	$-0.631525\pi$
$89$	1.80030	−	1.03940i	0.190831	−	0.110176i	0.592372	+	0.805665i	$0.298192\pi$
$90$	0.445902	−	0.470090i	0.0470022	−	0.0495518i
$91$		0			0
$92$	2.96086	+	10.7526i	0.308691	+	1.12104i
$93$	10.3989	+	2.78638i	1.07832	+	0.288934i
$94$	0.0297077	+	8.60672i	0.00306411	+	0.887715i
$95$	−5.64017	+	3.43128i	−0.578669	+	0.352042i
$96$	10.1255	−	0.174767i	1.03343	−	0.0178371i
$97$	−1.95542	−	1.95542i	−0.198543	−	0.198543i	0.600832	−	0.799375i	$-0.294836\pi$
$97$	−1.95542	−	1.95542i	−0.198543	−	0.198543i	−0.799375	+	0.600832i	$0.794836\pi$
$98$		0			0
$99$	0.432994			0.0435176
$100$	8.38431	−	5.45008i	0.838431	−	0.545008i
$101$	−0.631568	+	1.09391i	−0.0628434	+	0.108848i	−0.895735	−	0.444588i	$-0.853350\pi$
$101$	−0.631568	+	1.09391i	−0.0628434	+	0.108848i	0.832892	+	0.553436i	$0.186684\pi$
$102$	11.3568	+	11.2787i	1.12449	+	1.11676i
$103$	−3.36344	+	12.5525i	−0.331409	+	1.23684i	0.576300	+	0.817238i	$0.304496\pi$
$103$	−3.36344	+	12.5525i	−0.331409	+	1.23684i	−0.907710	+	0.419599i	$0.862171\pi$
$104$	−11.4584	+	0.118656i	−1.12359	+	0.0116352i
$105$		0			0
$106$	0.970051	−	0.564533i	0.0942197	−	0.0548322i
$107$	−18.6606	−	5.00010i	−1.80399	−	0.483378i	−0.809402	−	0.587255i	$-0.800209\pi$
$107$	−18.6606	−	5.00010i	−1.80399	−	0.483378i	−0.994590	+	0.103877i	$0.966875\pi$
$108$	2.52339	−	9.68437i	0.242814	−	0.931879i
$109$	−11.7830	−	6.80291i	−1.12860	−	0.651600i	−0.185021	−	0.982735i	$-0.559235\pi$
$109$	−11.7830	−	6.80291i	−1.12860	−	0.651600i	−0.943584	+	0.331134i	$0.892569\pi$
$110$	6.49844	+	1.55862i	0.619602	+	0.148609i
$111$		−	9.91040i		−	0.940654i
$112$		0			0
$113$	−7.72607	+	7.72607i	−0.726807	+	0.726807i	−0.969982	−	0.243175i	$-0.921811\pi$
$113$	−7.72607	+	7.72607i	−0.726807	+	0.726807i	0.243175	+	0.969982i	$0.421811\pi$
$114$	3.71509	−	6.48633i	0.347950	−	0.607500i
$115$	−12.1152	−	2.95005i	−1.12975	−	0.275094i
$116$	−2.90240	−	4.94791i	−0.269481	−	0.459402i
$117$	0.214846	−	0.801816i	0.0198625	−	0.0741279i
$118$	−6.80658	−	1.79866i	−0.626597	−	0.165580i
$119$		0			0
$120$	−5.33154	+	9.98851i	−0.486701	+	0.911822i
$121$	−3.26705	−	5.65869i	−0.297004	−	0.514427i
$122$	1.68149	−	1.69314i	0.152235	−	0.153290i
$123$	−13.8162	+	3.70204i	−1.24576	+	0.333802i
$124$	−12.0270	+	0.0830278i	−1.08006	+	0.00745611i
$125$	0.769107	+	11.1539i	0.0687910	+	0.997631i
$126$		0			0
$127$	−3.84193	+	3.84193i	−0.340917	+	0.340917i	−0.856712	−	0.515795i	$-0.827496\pi$
$127$	−3.84193	+	3.84193i	−0.340917	+	0.340917i	0.515795	+	0.856712i	$0.327496\pi$
$128$	−10.8543	+	3.19137i	−0.959391	+	0.282080i
$129$	12.3873	+	7.15179i	1.09064	+	0.629680i
$130$	6.11069	−	11.2604i	0.535943	−	0.987602i
$131$	10.0683	−	5.81295i	0.879674	−	0.507880i	0.00912320	−	0.999958i	$-0.497096\pi$
$131$	10.0683	−	5.81295i	0.879674	−	0.507880i	0.870551	+	0.492078i	$0.163763\pi$
$132$	−7.29492	+	2.00874i	−0.634942	+	0.174839i
$133$		0			0
$134$	13.9350	−	8.10963i	1.20380	−	0.700565i
$135$	8.09126	+	7.72817i	0.696385	+	0.665135i
$136$	−15.5775	−	8.77986i	−1.33576	−	0.752867i
$137$	−20.6120	+	5.52298i	−1.76101	+	0.471860i	−0.986919	−	0.161219i	$-0.948457\pi$
$137$	−20.6120	+	5.52298i	−1.76101	+	0.471860i	−0.774087	+	0.633079i	$0.781791\pi$
$138$	13.6244	−	3.70108i	1.15978	−	0.315057i
$139$	5.05787			0.429003			0.214501	−	0.976724i	$-0.431187\pi$
$139$	5.05787			0.429003			0.214501	+	0.976724i	$0.431187\pi$
$140$		0			0
$141$	10.8951			0.917535
$142$	−0.833763	+	0.226493i	−0.0699678	+	0.0190069i
$143$	8.26993	−	2.21592i	0.691566	−	0.185305i
$144$	−0.0113152	−	0.819495i	−0.000942936	−	0.0682912i
$145$	6.41175	−	0.147165i	0.532466	−	0.0122214i
$146$	5.58741	−	3.25166i	0.462418	−	0.269109i
$147$		0			0
$148$	2.93933	+	10.6744i	0.241611	+	0.877431i
$149$	−6.53199	+	3.77124i	−0.535121	+	0.308952i	−0.743099	−	0.669181i	$-0.766645\pi$
$149$	−6.53199	+	3.77124i	−0.535121	+	0.308952i	0.207978	+	0.978133i	$0.433312\pi$
$150$	−6.86246	−	10.6373i	−0.560318	−	0.868528i
$151$	12.0674	+	6.96711i	0.982030	+	0.566975i	0.902883	−	0.429887i	$-0.141447\pi$
$151$	12.0674	+	6.96711i	0.982030	+	0.566975i	0.0791478	+	0.996863i	$0.474780\pi$
$152$	−2.07771	+	8.08822i	−0.168525	+	0.656042i
$153$	0.915944	−	0.915944i	0.0740496	−	0.0740496i
$154$		0			0
$155$	6.45446	−	11.7966i	0.518435	−	0.947524i
$156$	0.100137	+	14.5054i	0.00801740	+	1.16136i
$157$	7.70790	−	2.06532i	0.615157	−	0.164831i	0.0622318	−	0.998062i	$-0.480178\pi$
$157$	7.70790	−	2.06532i	0.615157	−	0.164831i	0.552925	+	0.833231i	$0.313512\pi$
$158$	−14.2046	+	14.3030i	−1.13006	+	1.13789i
$159$	−0.710386	−	1.23043i	−0.0563373	−	0.0975791i
$160$	2.78007	−	12.3398i	0.219784	−	0.975549i
$161$		0			0
$162$	−13.0886	−	3.45869i	−1.02833	−	0.271741i
$163$	−3.60545	+	13.4557i	−0.282400	+	1.05393i	0.668318	+	0.743876i	$0.267015\pi$
$163$	−3.60545	+	13.4557i	−0.282400	+	1.05393i	−0.950718	+	0.310057i	$0.899652\pi$
$164$	13.7833	−	8.08518i	1.07630	−	0.631347i
$165$	2.00141	−	8.21937i	0.155810	−	0.639877i
$166$	−5.48323	+	9.57339i	−0.425581	+	0.743039i
$167$	14.0288	−	14.0288i	1.08558	−	1.08558i	0.0896054	−	0.995977i	$-0.471439\pi$
$167$	14.0288	−	14.0288i	1.08558	−	1.08558i	0.995977	−	0.0896054i	$-0.0285606\pi$
$168$		0			0
$169$		−	3.41370i		−	0.262592i
$170$	17.0437	−	10.4495i	1.30719	−	0.801443i
$171$	−0.523893	−	0.302470i	−0.0400631	−	0.0231304i
$172$	−15.4634	−	4.02919i	−1.17907	−	0.307223i
$173$	−12.1268	−	3.24936i	−0.921982	−	0.247044i	−0.233550	−	0.972345i	$-0.575034\pi$
$173$	−12.1268	−	3.24936i	−0.921982	−	0.247044i	−0.688432	+	0.725300i	$0.741701\pi$
$174$	−6.27609	+	3.65244i	−0.475789	+	0.276891i
$175$		0			0
$176$	7.26153	−	4.32720i	0.547358	−	0.326175i
$177$	−2.30661	+	8.60839i	−0.173376	+	0.647046i
$178$	2.08597	+	2.07162i	0.156350	+	0.155274i
$179$	1.72867	−	2.99414i	0.129207	−	0.223792i	−0.794163	−	0.607705i	$-0.792090\pi$
$179$	1.72867	−	2.99414i	0.129207	−	0.223792i	0.923369	+	0.383913i	$0.125424\pi$
$180$	0.806869	+	0.434266i	0.0601405	+	0.0323683i
$181$	−16.0960			−1.19640			−0.598202	−	0.801345i	$-0.704118\pi$
$181$	−16.0960			−1.19640			−0.598202	+	0.801345i	$0.704118\pi$
$182$		0			0
$183$	−2.13595	−	2.13595i	−0.157894	−	0.157894i
$184$	−13.5770	+	8.02725i	−1.00091	+	0.591777i
$185$	−12.0271	−	2.92859i	−0.884251	−	0.215314i
$186$	0.0525518	+	15.2250i	0.00385329	+	1.11635i
$187$	12.9049	+	3.45786i	0.943699	+	0.252863i
$188$	−11.7350	+	3.23138i	−0.855866	+	0.235673i
$189$		0			0
$190$	−6.77388	−	6.42533i	−0.491429	−	0.466143i
$191$	−4.59262	+	2.65155i	−0.332310	+	0.191860i	−0.656866	−	0.754007i	$-0.728118\pi$
$191$	−4.59262	+	2.65155i	−0.332310	+	0.191860i	0.324556	+	0.945866i	$0.394785\pi$
$192$	3.99243	+	13.7540i	0.288129	+	0.992612i
$193$	5.79200	+	21.6160i	0.416917	+	1.55596i	0.780964	+	0.624576i	$0.214728\pi$
$193$	5.79200	+	21.6160i	0.416917	+	1.55596i	−0.364047	+	0.931381i	$0.618605\pi$
$194$	1.94372	−	3.39361i	0.139551	−	0.243647i
$195$	−14.2275	−	7.78454i	−1.01885	−	0.557462i
$196$		0			0
$197$	5.33556	+	5.33556i	0.380143	+	0.380143i	0.871154	−	0.491011i	$-0.163372\pi$
$197$	5.33556	+	5.33556i	0.380143	+	0.380143i	−0.491011	+	0.871154i	$0.663372\pi$
$198$	0.160528	+	0.590931i	0.0114082	+	0.0419956i
$199$	−5.94289	+	10.2934i	−0.421280	+	0.729679i	−0.996065	−	0.0886258i	$-0.971752\pi$
$199$	−5.94289	+	10.2934i	−0.421280	+	0.729679i	0.574785	+	0.818305i	$0.305086\pi$
$200$	10.5464	+	9.42196i	0.745743	+	0.666233i
$201$	−10.2048	−	17.6753i	−0.719795	−	1.24672i
$202$	−1.72706	−	0.456381i	−0.121516	−	0.0321109i
$203$		0			0
$204$	−11.1822	+	19.6807i	−0.782912	+	1.37792i
$205$	0.409957	+	17.8611i	0.0286326	+	1.24747i
$206$	−18.3781	+	0.0634353i	−1.28046	+	0.00441974i
$207$	−0.295719	−	1.10364i	−0.0205539	−	0.0767081i
$208$	−4.41001	−	15.5939i	−0.305779	−	1.08125i
$209$		−	6.23934i		−	0.431584i
$210$		0			0
$211$		−	2.04430i		−	0.140735i	−0.997521	−	0.0703677i	$-0.977583\pi$
$211$		−	2.04430i		−	0.140735i	0.997521	−	0.0703677i	$-0.0224173\pi$
$212$	1.13008	+	1.11459i	0.0776144	+	0.0765502i
$213$	0.283068	+	1.05643i	0.0193955	+	0.0723851i
$214$	−0.0943032	−	27.3209i	−0.00644643	−	1.86762i
$215$	12.3398	−	12.9196i	0.841570	−	0.881110i
$216$	14.1523	−	0.146552i	0.962942	−	0.00997163i
$217$		0			0
$218$	4.91589	−	18.6030i	0.332946	−	1.25995i
$219$	−4.09177	−	7.08715i	−0.276496	−	0.478905i
$220$	0.282082	+	9.44661i	0.0190180	+	0.636890i
$221$	12.8065	−	22.1815i	0.861456	−	1.49209i
$222$	13.5253	−	3.67416i	0.907756	−	0.246594i
$223$	13.1600	+	13.1600i	0.881261	+	0.881261i	0.993663	−	0.112402i	$-0.0358544\pi$
$223$	13.1600	+	13.1600i	0.881261	+	0.881261i	−0.112402	+	0.993663i	$0.535854\pi$
$224$		0			0
$225$	−0.862778	+	0.552400i	−0.0575185	+	0.0368267i
$226$	−13.4085	−	7.67983i	−0.891922	−	0.510855i
$227$	−1.44049	−	5.37597i	−0.0956085	−	0.356816i	0.901502	−	0.432774i	$-0.142465\pi$
$227$	−1.44049	−	5.37597i	−0.0956085	−	0.356816i	−0.997111	+	0.0759580i	$0.975798\pi$
$228$	10.2296	+	2.66545i	0.677469	+	0.176524i
$229$	7.11068	−	4.10535i	0.469887	−	0.271289i	−0.246305	−	0.969192i	$-0.579217\pi$
$229$	7.11068	−	4.10535i	0.469887	−	0.271289i	0.716192	+	0.697903i	$0.245883\pi$
$230$	−0.465490	−	17.6280i	−0.0306935	−	1.16236i
$231$		0			0
$232$	5.67664	−	5.79544i	0.372690	−	0.380489i
$233$	11.5815	+	3.10326i	0.758732	+	0.203302i	0.617388	−	0.786659i	$-0.288191\pi$
$233$	11.5815	+	3.10326i	0.758732	+	0.203302i	0.141344	+	0.989961i	$0.454858\pi$
$234$	1.17393	−	0.00405205i	0.0767424	−	0.000264891i
$235$	3.21959	−	13.2222i	0.210023	−	0.862519i
$236$	−0.0687318	−	9.95614i	−0.00447406	−	0.648090i
$237$	18.0437	+	18.0437i	1.17206	+	1.17206i
$238$		0			0
$239$	−18.5038			−1.19691			−0.598456	−	0.801155i	$-0.704219\pi$
$239$	−18.5038			−1.19691			−0.598456	+	0.801155i	$0.704219\pi$
$240$	−15.6085	−	3.57312i	−1.00752	−	0.230644i
$241$	−0.0411841	+	0.0713330i	−0.00265290	+	0.00459496i	−0.867349	−	0.497701i	$-0.834178\pi$
$241$	−0.0411841	+	0.0713330i	−0.00265290	+	0.00459496i	0.864696	+	0.502296i	$0.167511\pi$
$242$	6.51150	−	6.55661i	0.418575	−	0.421475i
$243$	−0.550164	+	2.05324i	−0.0352930	+	0.131715i
$244$	2.93411	+	1.66711i	0.187837	+	0.106726i
$245$		0			0
$246$	−10.1746	−	17.4832i	−0.648707	−	1.11469i
$247$	−11.5540	−	3.09588i	−0.735162	−	0.196986i
$248$	−4.57218	−	16.3831i	−0.290334	−	1.04033i
$249$	12.0947	+	6.98289i	0.766471	+	0.442522i
$250$	−14.9371	+	5.18480i	−0.944707	+	0.327916i
$251$			9.07743i			0.572963i	0.958086	+	0.286481i	$0.0924856\pi$
$251$			9.07743i			0.572963i	−0.958086	+	0.286481i	$0.907514\pi$
$252$		0			0
$253$	8.33287	−	8.33287i	0.523883	−	0.523883i
$254$	−6.66765	−	3.81894i	−0.418365	−	0.239622i
$255$	−13.1533	−	21.6207i	−0.823691	−	1.35394i
$256$	−8.37952	−	13.6302i	−0.523720	−	0.851890i
$257$	−1.88616	+	7.03925i	−0.117656	+	0.439097i	−0.999472	−	0.0324965i	$-0.989654\pi$
$257$	−1.88616	+	7.03925i	−0.117656	+	0.439097i	0.881816	+	0.471593i	$0.156321\pi$
$258$	−5.16800	+	19.5570i	−0.321746	+	1.21757i
$259$		0			0
$260$	17.6331	+	4.16492i	1.09356	+	0.258298i
$261$	0.293835	+	0.508937i	0.0181879	+	0.0315024i
$262$	11.6660	+	11.5857i	0.720726	+	0.715768i
$263$	−5.18349	+	1.38891i	−0.319628	+	0.0856441i	−0.415066	−	0.909791i	$-0.636241\pi$
$263$	−5.18349	+	1.38891i	−0.319628	+	0.0856441i	0.0954380	+	0.995435i	$0.469575\pi$
$264$	−5.44595	−	9.21106i	−0.335175	−	0.566901i
$265$	−1.70315	+	0.498515i	−0.104624	+	0.0306236i
$266$		0			0
$267$	2.63151	−	2.63151i	0.161046	−	0.161046i
$268$	16.2339	+	16.0113i	0.991642	+	0.978044i
$269$	−4.69186	−	2.70885i	−0.286068	−	0.165161i	0.350099	−	0.936713i	$-0.386148\pi$
$269$	−4.69186	−	2.70885i	−0.286068	−	0.165161i	−0.636167	+	0.771551i	$0.719481\pi$
$270$	−7.54731	+	13.9077i	−0.459314	+	0.846396i
$271$	7.10365	−	4.10129i	0.431516	−	0.249136i	−0.268476	−	0.963286i	$-0.586520\pi$
$271$	7.10365	−	4.10129i	0.431516	−	0.249136i	0.699992	+	0.714151i	$0.253187\pi$
$272$	6.20718	−	24.5145i	0.376365	−	1.48641i
$273$		0			0
$274$	−15.1792	−	26.0828i	−0.917008	−	1.57572i
$275$	−9.38348	−	4.85776i	−0.565845	−	0.292934i
$276$	10.1021	+	17.2218i	0.608077	+	1.03663i
$277$	14.6458	−	3.92432i	0.879979	−	0.235790i	0.209581	−	0.977791i	$-0.432790\pi$
$277$	14.6458	−	3.92432i	0.879979	−	0.235790i	0.670398	+	0.742002i	$0.266123\pi$
$278$	1.87515	+	6.90275i	0.112464	+	0.413999i
$279$	1.23215			0.0737671
$280$		0			0
$281$	−23.7586			−1.41732			−0.708659	−	0.705551i	$-0.750700\pi$
$281$	−23.7586			−1.41732			−0.708659	+	0.705551i	$0.750700\pi$
$282$	4.03924	+	14.8692i	0.240533	+	0.885446i
$283$	22.8818	−	6.13117i	1.36018	−	0.364460i	0.496300	−	0.868151i	$-0.334692\pi$
$283$	22.8818	−	6.13117i	1.36018	−	0.364460i	0.863884	+	0.503691i	$0.168025\pi$
$284$	−0.618216	−	1.05391i	−0.0366843	−	0.0625381i
$285$	−8.16324	+	8.54677i	−0.483548	+	0.506267i
$286$	6.09016	+	10.4649i	0.360119	+	0.618802i
$287$		0			0
$288$	1.11421	−	0.319261i	0.0656557	−	0.0188126i
$289$	19.8908	−	11.4840i	1.17005	−	0.675528i
$290$	2.57792	+	8.69589i	0.151381	+	0.510641i
$291$	−4.28738	−	2.47532i	−0.251331	−	0.145106i
$292$	6.50919	+	6.41993i	0.380921	+	0.375698i
$293$	18.6078	−	18.6078i	1.08708	−	1.08708i	0.0912527	−	0.995828i	$-0.470913\pi$
$293$	18.6078	−	18.6078i	1.08708	−	1.08708i	0.995828	−	0.0912527i	$-0.0290871\pi$
$294$		0			0
$295$	9.76540	+	5.34311i	0.568564	+	0.311088i
$296$	−13.4782	+	7.96887i	−0.783405	+	0.463181i
$297$	−10.2142	+	2.73688i	−0.592687	+	0.158810i
$298$	−7.56848	−	7.51641i	−0.438430	−	0.435414i
$299$	−11.2961	−	19.5654i	−0.653270	−	1.13150i
$300$	11.9731	−	13.3092i	0.691265	−	0.768408i
$301$		0			0
$302$	−5.03455	+	19.0520i	−0.289706	+	1.09632i
$303$	−0.585266	+	2.18424i	−0.0336226	+	0.125481i
$304$	−11.8087	+	0.163050i	−0.677277	+	0.00935154i
$305$	−3.22334	+	1.96097i	−0.184568	+	0.112285i
$306$	1.58961	+	0.910462i	0.0908721	+	0.0520477i
$307$	−19.1930	+	19.1930i	−1.09540	+	1.09540i	−0.100459	+	0.994941i	$0.532031\pi$
$307$	−19.1930	+	19.1930i	−1.09540	+	1.09540i	−0.994941	+	0.100459i	$0.967969\pi$
$308$		0			0
$309$			23.2645i			1.32347i
$310$	18.4923	+	4.43531i	1.05029	+	0.251909i
$311$	−11.9923	−	6.92373i	−0.680018	−	0.392609i	0.119844	−	0.992793i	$-0.461761\pi$
$311$	−11.9923	−	6.92373i	−0.680018	−	0.392609i	−0.799862	+	0.600184i	$0.795094\pi$
$312$	−19.7592	+	5.51437i	−1.11864	+	0.312190i
$313$	22.7192	+	6.08759i	1.28417	+	0.344091i	0.835441	−	0.549579i	$-0.185212\pi$
$313$	22.7192	+	6.08759i	1.28417	+	0.344091i	0.448724	+	0.893670i	$0.351879\pi$
$314$	5.67627	+	9.75368i	0.320331	+	0.550432i
$315$		0			0
$316$	−24.7863	−	14.0831i	−1.39434	−	0.792237i
$317$	−0.213444	+	0.796585i	−0.0119882	+	0.0447407i	−0.971661	−	0.236379i	$-0.924039\pi$
$317$	−0.213444	+	0.796585i	−0.0119882	+	0.0447407i	0.959673	+	0.281120i	$0.0907059\pi$
$318$	1.41586	−	1.42567i	0.0793975	−	0.0799475i
$319$	−3.03061	+	5.24917i	−0.169682	+	0.293897i
$320$	17.8715	−	0.780739i	0.999047	−	0.0436446i
$321$	−34.5851			−1.93035
$322$		0			0
$323$	−13.1985	−	13.1985i	−0.734386	−	0.734386i
$324$	−0.132166	−	19.1449i	−0.00734257	−	1.06361i
$325$	−13.6515	+	14.9659i	−0.757251	+	0.830159i
$326$	−19.7004	+	0.0679996i	−1.09110	+	0.00376615i
$327$	−23.5275	−	6.30416i	−1.30107	−	0.348621i
$328$	16.1443	+	15.8134i	0.891419	+	0.873146i
$329$		0			0
$330$	11.9594	−	0.315804i	0.658344	−	0.0173844i
$331$	12.4271	−	7.17480i	0.683056	−	0.394363i	−0.117949	−	0.993020i	$-0.537632\pi$
$331$	12.4271	−	7.17480i	0.683056	−	0.394363i	0.801006	+	0.598657i	$0.204299\pi$
$332$	−15.0982	−	3.93404i	−0.828620	−	0.215908i
$333$	−0.293568	−	1.09561i	−0.0160874	−	0.0600390i
$334$	24.3469	+	13.9449i	1.33220	+	0.763029i
$335$	−24.4661	+	7.16128i	−1.33673	+	0.391262i
$336$		0			0
$337$	0.0624771	+	0.0624771i	0.00340335	+	0.00340335i	0.708806	−	0.705403i	$-0.249234\pi$
$337$	0.0624771	+	0.0624771i	0.00340335	+	0.00340335i	−0.705403	+	0.708806i	$0.749234\pi$
$338$	4.65886	−	1.26559i	0.253409	−	0.0688390i
$339$	−9.78026	+	16.9399i	−0.531191	+	0.920049i
$340$	20.5798	+	19.3864i	1.11610	+	1.05137i
$341$	6.35422	+	11.0058i	0.344100	+	0.595999i
$342$	0.218570	−	0.827122i	0.0118189	−	0.0447256i
$343$		0			0
$344$	−0.234005	−	22.5975i	−0.0126167	−	1.21837i
$345$	−22.3168	+	0.512226i	−1.20150	+	0.0275773i
$346$	−0.0612838	−	17.7547i	−0.00329464	−	0.954501i
$347$	2.28336	+	8.52161i	0.122577	+	0.457464i	0.999742	−	0.0227259i	$-0.00723449\pi$
$347$	2.28336	+	8.52161i	0.122577	+	0.457464i	−0.877165	+	0.480190i	$0.840568\pi$
$348$	−7.31147	−	7.21122i	−0.391936	−	0.386562i
$349$		−	3.77799i		−	0.202231i	−0.994875	−	0.101116i	$-0.967759\pi$
$349$		−	3.77799i		−	0.202231i	0.994875	−	0.101116i	$-0.0322412\pi$
$350$		0			0
$351$			20.2726i			1.08207i
$352$	8.59769	+	8.30594i	0.458259	+	0.442708i
$353$	−0.321686	−	1.20055i	−0.0171216	−	0.0638987i	0.956836	−	0.290627i	$-0.0938638\pi$
$353$	−0.321686	−	1.20055i	−0.0171216	−	0.0638987i	−0.973958	+	0.226728i	$0.927197\pi$
$354$	−12.6035	+	0.0435033i	−0.669868	+	0.00231217i
$355$	1.36571	−	0.0313465i	0.0724844	−	0.00166370i
$356$	−2.05390	+	3.61486i	−0.108856	+	0.191587i
$357$		0			0
$358$	4.72714	+	1.24916i	0.249837	+	0.0660203i
$359$	−8.75216	−	15.1592i	−0.461922	−	0.800072i	0.537135	−	0.843496i	$-0.319507\pi$
$359$	−8.75216	−	15.1592i	−0.461922	−	0.800072i	−0.999057	+	0.0434246i	$0.986173\pi$
$360$	−0.293529	+	1.26218i	−0.0154703	+	0.0665226i
$361$	5.14148	−	8.90531i	0.270604	−	0.468701i
$362$	−5.96740	−	21.9671i	−0.313639	−	1.15456i
$363$	−8.27137	−	8.27137i	−0.434134	−	0.434134i
$364$		0			0
$365$	−9.81001	+	2.87141i	−0.513479	+	0.150296i
$366$	2.12316	−	3.70692i	0.110980	−	0.193764i
$367$	4.02948	+	15.0382i	0.210337	+	0.784988i	0.987756	+	0.156006i	$0.0498618\pi$
$367$	4.02948	+	15.0382i	0.210337	+	0.784988i	−0.777419	+	0.628983i	$0.783472\pi$
$368$	−15.9887	−	15.5532i	−0.833470	−	0.810767i
$369$	−1.41774	+	0.818532i	−0.0738046	+	0.0426111i
$370$	−0.462104	−	17.4998i	−0.0240237	−	0.909771i
$371$		0			0
$372$	−20.7589	+	5.71620i	−1.07630	+	0.296371i
$373$	−0.759994	−	0.203640i	−0.0393510	−	0.0105441i	0.239090	−	0.970997i	$-0.423151\pi$
$373$	−0.759994	−	0.203640i	−0.0393510	−	0.0105441i	−0.278441	+	0.960453i	$0.589818\pi$
$374$	0.0652160	+	18.8940i	0.00337224	+	0.976984i
$375$	6.49802	+	18.9311i	0.335556	+	0.977599i
$376$	−8.76067	−	14.8174i	−0.451797	−	0.764151i
$377$	8.21663	+	8.21663i	0.423178	+	0.423178i
$378$		0			0
$379$	9.14995			0.470001			0.235001	−	0.971995i	$-0.424491\pi$
$379$	9.14995			0.470001			0.235001	+	0.971995i	$0.424491\pi$
$380$	6.25766	−	11.6268i	0.321011	−	0.596442i
$381$	−4.86342	+	8.42369i	−0.249161	+	0.431559i
$382$	−5.32138	−	5.28477i	−0.272265	−	0.270392i
$383$	−2.18517	+	8.15515i	−0.111657	+	0.416709i	−0.999015	−	0.0443718i	$-0.985871\pi$
$383$	−2.18517	+	8.15515i	−0.111657	+	0.416709i	0.887358	+	0.461080i	$0.152538\pi$
$384$	−17.2907	+	10.5478i	−0.882364	+	0.538267i
$385$		0			0
$386$	−27.3533	+	15.9185i	−1.39224	+	0.810233i
$387$	1.58128	+	0.423703i	0.0803811	+	0.0215381i
$388$	5.35206	+	1.39455i	0.271709	+	0.0707976i
$389$	24.8832	+	14.3663i	1.26163	+	0.728400i	0.973389	−	0.229159i	$-0.0735976\pi$
$389$	24.8832	+	14.3663i	1.26163	+	0.728400i	0.288237	+	0.957559i	$0.406931\pi$
$390$	5.34930	−	22.3031i	0.270872	−	1.12936i
$391$		−	35.2542i		−	1.78288i
$392$		0			0
$393$	14.7170	−	14.7170i	0.742373	−	0.742373i
$394$	−5.30363	+	9.25983i	−0.267193	+	0.466503i
$395$	27.2296	−	16.5655i	1.37007	−	0.833501i
$396$	−0.746961	+	0.438161i	−0.0375362	+	0.0220184i
$397$	−6.60652	+	24.6559i	−0.331572	+	1.23744i	0.575967	+	0.817473i	$0.304626\pi$
$397$	−6.60652	+	24.6559i	−0.331572	+	1.23744i	−0.907538	+	0.419969i	$0.862041\pi$
$398$	−16.2512	−	4.29443i	−0.814599	−	0.215260i
$399$		0			0
$400$	−8.94870	+	17.8863i	−0.447435	+	0.894316i
$401$	−13.0839	−	22.6620i	−0.653380	−	1.13169i	−0.982297	−	0.187329i	$-0.940017\pi$
$401$	−13.0839	−	22.6620i	−0.653380	−	1.13169i	0.328917	−	0.944359i	$-0.393316\pi$
$402$	20.3391	−	20.4800i	1.01442	−	1.02145i
$403$	23.5334	−	6.30575i	1.17228	−	0.314112i
$404$	−0.0174396	−	2.52621i	−0.000867652	−	0.125684i
$405$	18.7782	+	10.2744i	0.933094	+	0.510540i
$406$		0			0
$407$	8.27226	−	8.27226i	0.410041	−	0.410041i
$408$	−31.0050	−	7.96460i	−1.53498	−	0.394306i
$409$	−0.853122	−	0.492550i	−0.0421842	−	0.0243550i	0.478760	−	0.877946i	$-0.341087\pi$
$409$	−0.853122	−	0.492550i	−0.0421842	−	0.0243550i	−0.520944	+	0.853591i	$0.674420\pi$
$410$	−24.2240	+	7.18129i	−1.19634	+	0.354659i
$411$	−33.0837	+	19.1009i	−1.63190	+	0.942178i
$412$	−6.90002	−	25.0580i	−0.339940	−	1.23452i
$413$		0			0
$414$	1.39656	−	0.812743i	0.0686371	−	0.0399442i
$415$	12.0484	−	12.6145i	0.591433	−	0.619220i
$416$	19.6469	−	11.7999i	0.963270	−	0.578535i
$417$	8.74617	−	2.34353i	0.428302	−	0.114763i
$418$	8.51517	−	2.31316i	0.416491	−	0.113141i
$419$	−16.7317			−0.817399			−0.408699	−	0.912669i	$-0.634018\pi$
$419$	−16.7317			−0.817399			−0.408699	+	0.912669i	$0.634018\pi$
$420$		0			0
$421$	35.5024			1.73028			0.865140	−	0.501530i	$-0.167229\pi$
$421$	35.5024			1.73028			0.865140	+	0.501530i	$0.167229\pi$
$422$	2.78996	−	0.757900i	0.135813	−	0.0368940i
$423$	1.20447	−	0.322737i	0.0585634	−	0.0156920i
$424$	−1.10217	+	1.95551i	−0.0535262	+	0.0949677i
$425$	−30.1255	+	9.57356i	−1.46130	+	0.464386i
$426$	−1.33682	+	0.777976i	−0.0647689	+	0.0376930i
$427$		0			0
$428$	37.2514	−	10.2576i	1.80061	−	0.495820i
$429$	13.2738	−	7.66363i	0.640865	−	0.370004i
$430$	22.2069	+	12.0510i	1.07091	+	0.581153i
$431$	0.906153	+	0.523167i	0.0436478	+	0.0252001i	0.521665	−	0.853150i	$-0.325311\pi$
$431$	0.906153	+	0.523167i	0.0436478	+	0.0252001i	−0.478017	+	0.878350i	$0.658644\pi$
$432$	5.44681	+	19.2601i	0.262060	+	0.926650i
$433$	9.24591	−	9.24591i	0.444330	−	0.444330i	−0.449134	−	0.893464i	$-0.648267\pi$
$433$	9.24591	−	9.24591i	0.444330	−	0.444330i	0.893464	+	0.449134i	$0.148267\pi$
$434$		0			0
$435$	11.0191	−	3.22532i	0.528327	−	0.154642i
$436$	27.2110	−	0.187850i	1.30317	−	0.00899637i
$437$	−15.9031	+	4.26123i	−0.760750	+	0.203842i
$438$	8.15524	−	8.21173i	0.389672	−	0.392372i
$439$	11.3657	+	19.6860i	0.542455	+	0.939559i	0.998762	+	0.0497373i	$0.0158384\pi$
$439$	11.3657	+	19.6860i	0.542455	+	0.939559i	−0.456307	+	0.889822i	$0.650828\pi$
$440$	−12.7877	+	3.88719i	−0.609631	+	0.185315i
$441$		0			0
$442$	35.0201	+	9.25416i	1.66573	+	0.440176i
$443$	−6.04148	+	22.5471i	−0.287040	+	1.07125i	0.660296	+	0.751005i	$0.270431\pi$
$443$	−6.04148	+	22.5471i	−0.287040	+	1.07125i	−0.947336	+	0.320241i	$0.896236\pi$
$444$	10.0287	+	17.0965i	0.475939	+	0.811364i
$445$	−2.41594	−	3.97120i	−0.114526	−	0.188253i
$446$	−13.0813	+	22.8391i	−0.619416	+	1.08146i
$447$	−9.54787	+	9.54787i	−0.451599	+	0.451599i
$448$		0			0
$449$			18.0937i			0.853895i	0.904276	+	0.426947i	$0.140411\pi$
$449$			18.0937i			0.853895i	−0.904276	+	0.426947i	$0.859589\pi$
$450$	−1.07375	−	0.972684i	−0.0506173	−	0.0458527i
$451$	−14.6226	−	8.44234i	−0.688549	−	0.397534i
$452$	5.51003	−	21.1466i	0.259170	−	0.994650i
$453$	24.0954	+	6.45633i	1.13210	+	0.303345i
$454$	6.80284	−	3.95899i	0.319273	−	0.185805i
$455$		0			0
$456$	0.154803	+	14.9490i	0.00724931	+	0.700052i
$457$	−4.70586	+	17.5625i	−0.220131	+	0.821540i	0.764166	+	0.645020i	$0.223151\pi$
$457$	−4.70586	+	17.5625i	−0.220131	+	0.821540i	−0.984297	+	0.176520i	$0.943516\pi$
$458$	8.23900	+	8.18232i	0.384983	+	0.382334i
$459$	−15.8173	+	27.3963i	−0.738286	+	1.27875i
$460$	23.8853	−	7.17066i	1.11366	−	0.334334i
$461$	30.3805			1.41496			0.707481	−	0.706733i	$-0.249832\pi$
$461$	30.3805			1.41496			0.707481	+	0.706733i	$0.249832\pi$
$462$		0			0
$463$	20.1652	+	20.1652i	0.937156	+	0.937156i	0.998139	−	0.0609833i	$-0.0194236\pi$
$463$	20.1652	+	20.1652i	0.937156	+	0.937156i	−0.0609833	+	0.998139i	$0.519424\pi$
$464$	10.0139	+	5.59863i	0.464884	+	0.259910i
$465$	5.69533	−	23.3895i	0.264115	−	1.08466i
$466$	0.0585283	+	16.9564i	0.00271127	+	0.785492i
$467$	−20.2575	−	5.42798i	−0.937405	−	0.251177i	−0.242396	−	0.970177i	$-0.577933\pi$
$467$	−20.2575	−	5.42798i	−0.937405	−	0.251177i	−0.695009	+	0.719001i	$0.744600\pi$
$468$	0.440752	+	1.60063i	0.0203738	+	0.0739890i
$469$		0			0
$470$	19.2386	−	0.508020i	0.887411	−	0.0234332i
$471$	12.3717	−	7.14281i	0.570058	−	0.329123i
$472$	13.5622	−	3.78493i	0.624251	−	0.174215i
$473$	4.37008	+	16.3093i	0.200936	+	0.749904i
$474$	−17.9357	+	31.3147i	−0.823814	+	1.43833i
$475$	7.95995	+	12.4324i	0.365227	+	0.570439i
$476$		0			0
$477$	−0.114982	−	0.114982i	−0.00526467	−	0.00526467i
$478$	−6.86007	−	25.2532i	−0.313773	−	1.15505i
$479$	13.9452	−	24.1538i	0.637172	−	1.10361i	−0.348879	−	0.937168i	$-0.613438\pi$
$479$	13.9452	−	24.1538i	0.637172	−	1.10361i	0.986051	−	0.166446i	$-0.0532292\pi$
$480$	−0.910226	−	22.6264i	−0.0415460	−	1.03275i
$481$	−11.2139	−	19.4231i	−0.511311	−	0.885617i
$482$	−0.112621	−	0.0297603i	−0.00512972	−	0.00135555i
$483$		0			0
$484$	11.3622	+	6.45581i	0.516465	+	0.293446i
$485$	−4.27096	+	4.47163i	−0.193934	+	0.203046i
$486$	−3.00613	+	0.0103762i	−0.136361	+	0.000470675i
$487$	1.00721	+	3.75898i	0.0456412	+	0.170335i	0.984984	−	0.172643i	$-0.0552308\pi$
$487$	1.00721	+	3.75898i	0.0456412	+	0.170335i	−0.939343	+	0.342979i	$0.888564\pi$
$488$	−1.18741	+	4.62240i	−0.0537514	+	0.209246i
$489$			24.9385i			1.12776i
$490$		0			0
$491$			14.4151i			0.650544i	0.945620	+	0.325272i	$0.105456\pi$
$491$			14.4151i			0.650544i	−0.945620	+	0.325272i	$0.894544\pi$
$492$	20.0882	−	20.3675i	0.905646	−	0.918237i
$493$	4.69308	+	17.5148i	0.211366	+	0.788827i
$494$	−0.0583890	−	16.9161i	−0.00262705	−	0.761091i
$495$	−0.0222169	−	0.967950i	−0.000998573	−	0.0435061i
$496$	20.6638	−	12.3137i	0.927833	−	0.552903i
$497$		0			0
$498$	−5.04595	+	19.0951i	−0.226114	+	0.855673i
$499$	1.47517	+	2.55507i	0.0660377	+	0.114381i	0.897154	−	0.441718i	$-0.145631\pi$
$499$	1.47517	+	2.55507i	0.0660377	+	0.114381i	−0.831116	+	0.556099i	$0.812298\pi$
$500$	−12.6137	−	18.4633i	−0.564104	−	0.825704i
$501$	17.7588	−	30.7591i	0.793403	−	1.37422i
$502$	−12.3885	+	3.36535i	−0.552924	+	0.150203i
$503$	17.2036	+	17.2036i	0.767071	+	0.767071i	0.977590	−	0.210518i	$-0.0675152\pi$
$503$	17.2036	+	17.2036i	0.767071	+	0.767071i	−0.210518	+	0.977590i	$0.567515\pi$
$504$		0			0
$505$	2.47781	+	1.35573i	0.110261	+	0.0603291i
$506$	14.4616	+	8.28300i	0.642898	+	0.368224i
$507$	−1.58172	−	5.90305i	−0.0702465	−	0.262163i
$508$	2.73996	−	10.5155i	0.121566	−	0.466551i
$509$	2.32094	−	1.34000i	0.102874	−	0.0593944i	−0.447680	−	0.894194i	$-0.647750\pi$
$509$	2.32094	−	1.34000i	0.102874	−	0.0593944i	0.550554	+	0.834799i	$0.314416\pi$
$510$	24.6306	−	25.9666i	1.09066	−	1.14982i
$511$		0			0
$512$	15.4953	−	16.4892i	0.684803	−	0.728728i
$513$	14.2703	+	3.82372i	0.630049	+	0.168821i
$514$	−10.3061	+	0.0355735i	−0.454584	+	0.00156908i
$515$	28.2335	+	6.87483i	1.24412	+	0.302941i
$516$	−28.6065	+	0.197484i	−1.25933	+	0.00869373i
$517$	9.09421	+	9.09421i	0.399963	+	0.399963i
$518$		0			0
$519$	−22.4755			−0.986563
$520$	0.853183	+	25.6090i	0.0374146	+	1.12303i
$521$	22.5104	−	38.9891i	0.986196	−	1.70814i	0.349702	−	0.936861i	$-0.386283\pi$
$521$	22.5104	−	38.9891i	0.986196	−	1.70814i	0.636495	−	0.771281i	$-0.280384\pi$
$522$	−0.585638	+	0.589695i	−0.0256327	+	0.0258102i
$523$	1.63883	−	6.11620i	0.0716610	−	0.267443i	−0.920794	−	0.390048i	$-0.872458\pi$
$523$	1.63883	−	6.11620i	0.0716610	−	0.267443i	0.992455	+	0.122606i	$0.0391250\pi$
$524$	−11.4866	+	20.2164i	−0.501795	+	0.883159i
$525$		0			0
$526$	−3.81724	−	6.55927i	−0.166440	−	0.285998i
$527$	36.7229	+	9.83987i	1.59968	+	0.428632i
$528$	10.5518	−	10.8473i	0.459208	−	0.472067i
$529$	−7.01165	−	4.04818i	−0.304854	−	0.176008i
$530$	−1.31177	−	2.13956i	−0.0569798	−	0.0929367i
$531$			1.02000i			0.0442641i
$532$		0			0
$533$	−22.8890	+	22.8890i	−0.991432	+	0.991432i
$534$	4.56697	+	2.61577i	0.197632	+	0.113195i
$535$	−10.2202	+	41.9720i	−0.441856	+	1.81461i
$536$	−15.8329	+	28.0912i	−0.683878	+	1.21336i
$537$	1.60193	−	5.97849i	0.0691285	−	0.257991i
$538$	1.95746	−	7.40751i	0.0843919	−	0.319360i
$539$		0			0
$540$	−21.7787	−	5.14409i	−0.937205	−	0.221367i
$541$	−8.37685	−	14.5091i	−0.360149	−	0.623796i	0.627836	−	0.778345i	$-0.283941\pi$
$541$	−8.37685	−	14.5091i	−0.360149	−	0.623796i	−0.987985	+	0.154549i	$0.950607\pi$
$542$	8.23085	+	8.17422i	0.353545	+	0.351113i
$543$	−27.8335	+	7.45797i	−1.19445	+	0.320052i
$544$	35.7574	−	0.617176i	1.53309	−	0.0264612i
$545$	−14.6032	+	26.6897i	−0.625531	+	1.14326i
$546$		0			0
$547$	−12.5910	+	12.5910i	−0.538352	+	0.538352i	−0.923045	−	0.384693i	$-0.874307\pi$
$547$	−12.5910	+	12.5910i	−0.538352	+	0.538352i	0.384693	+	0.923045i	$0.374307\pi$
$548$	29.9691	−	30.3857i	1.28022	−	1.29801i
$549$	−0.299404	−	0.172861i	−0.0127782	−	0.00737752i
$550$	3.15084	−	14.6071i	0.134352	−	0.622849i
$551$	7.33366	−	4.23409i	0.312424	−	0.180378i
$552$	−19.7582	+	20.1717i	−0.840965	+	0.858564i
$553$		0			0
$554$	10.7855	+	18.5330i	0.458231	+	0.787391i
$555$	−22.1545	+	0.508501i	−0.940406	+	0.0215847i
$556$	−8.72536	+	5.11822i	−0.370038	+	0.217061i
$557$	31.9653	−	8.56509i	1.35441	−	0.362914i	0.492652	−	0.870226i	$-0.336027\pi$
$557$	31.9653	−	8.56509i	1.35441	−	0.362914i	0.861763	+	0.507312i	$0.169361\pi$
$558$	0.456807	+	1.68159i	0.0193382	+	0.0711872i
$559$	32.3699			1.36910
$560$		0			0
$561$	23.9176			1.00980
$562$	−8.80822	−	32.4246i	−0.371552	−	1.36775i
$563$	−18.8737	+	5.05720i	−0.795433	+	0.213136i	−0.633578	−	0.773679i	$-0.718414\pi$
$563$	−18.8737	+	5.05720i	−0.795433	+	0.213136i	−0.161855	+	0.986815i	$0.551748\pi$
$564$	−18.7952	+	11.0251i	−0.791422	+	0.464242i
$565$	17.6679	+	16.8750i	0.743294	+	0.709938i
$566$	16.8507	+	28.9550i	0.708288	+	1.21707i
$567$		0			0
$568$	1.20913	−	1.23444i	0.0507341	−	0.0517958i
$569$	−33.7127	+	19.4640i	−1.41331	+	0.815974i	−0.995699	−	0.0926518i	$-0.970466\pi$
$569$	−33.7127	+	19.4640i	−1.41331	+	0.815974i	−0.417610	+	0.908626i	$0.637132\pi$
$570$	−14.6907	−	7.97219i	−0.615324	−	0.333918i
$571$	17.7481	+	10.2468i	0.742733	+	0.428817i	0.823062	−	0.567951i	$-0.192264\pi$
$571$	17.7481	+	10.2468i	0.742733	+	0.428817i	−0.0803293	+	0.996768i	$0.525597\pi$
$572$	−12.0241	+	12.1913i	−0.502755	+	0.509744i
$573$	−6.71308	+	6.71308i	−0.280443	+	0.280443i
$574$		0			0
$575$	−5.97315	+	27.2347i	−0.249097	+	1.13577i
$576$	0.848794	+	1.40227i	0.0353664	+	0.0584277i
$577$	6.79196	−	1.81990i	0.282753	−	0.0757634i	−0.114655	−	0.993405i	$-0.536576\pi$
$577$	6.79196	−	1.81990i	0.282753	−	0.0757634i	0.397408	+	0.917642i	$0.369910\pi$
$578$	23.0471	+	22.8886i	0.958633	+	0.952038i
$579$	20.0313	+	34.6952i	0.832472	+	1.44188i
$580$	−10.9120	+	6.74213i	−0.453097	+	0.279952i
$581$		0			0
$582$	1.78871	−	6.76892i	0.0741443	−	0.280581i
$583$	0.434079	−	1.62000i	0.0179777	−	0.0670937i
$584$	−6.34842	+	11.2636i	−0.262699	+	0.466089i
$585$	−1.80347	−	0.439143i	−0.0745642	−	0.0181563i
$586$	32.2937	+	18.4965i	1.33404	+	0.764082i
$587$	−4.00401	+	4.00401i	−0.165263	+	0.165263i	−0.784894	−	0.619631i	$-0.787282\pi$
$587$	−4.00401	+	4.00401i	−0.165263	+	0.165263i	0.619631	+	0.784894i	$0.287282\pi$
$588$		0			0
$589$		−	17.7550i		−	0.731584i
$590$	−3.67162	+	15.3083i	−0.151158	+	0.630231i
$591$	11.6986	+	6.75417i	0.481215	+	0.277829i
$592$	−15.8724	−	15.4401i	−0.652353	−	0.634584i
$593$	−33.9171	−	9.08806i	−1.39281	−	0.373202i	−0.517051	−	0.855954i	$-0.672970\pi$
$593$	−33.9171	−	9.08806i	−1.39281	−	0.373202i	−0.875757	+	0.482753i	$0.839637\pi$
$594$	−7.52196	−	12.9252i	−0.308630	−	0.530326i
$595$		0			0
$596$	7.45212	−	13.1157i	0.305251	−	0.537241i
$597$	−5.50720	+	20.5531i	−0.225395	+	0.841184i
$598$	22.5141	−	22.6700i	0.920668	−	0.927046i
$599$	−0.687491	+	1.19077i	−0.0280901	+	0.0486535i	−0.879729	−	0.475476i	$-0.842276\pi$
$599$	−0.687491	+	1.19077i	−0.0280901	+	0.0486535i	0.851639	+	0.524129i	$0.175609\pi$
$600$	22.6027	+	11.4060i	0.922750	+	0.465650i
$601$	−8.86739			−0.361708			−0.180854	−	0.983510i	$-0.557886\pi$
$601$	−8.86739			−0.361708			−0.180854	+	0.983510i	$0.557886\pi$
$602$		0			0
$603$	−1.65174	−	1.65174i	−0.0672642	−	0.0672642i
$604$	−27.8678	+	0.192384i	−1.13392	+	0.00782799i
$605$	−12.4823	+	7.59377i	−0.507476	+	0.308730i
$606$	−3.19793	+	0.0110383i	−0.129907	+	0.000448398i
$607$	−16.4539	−	4.40882i	−0.667845	−	0.178948i	−0.0910609	−	0.995845i	$-0.529026\pi$
$607$	−16.4539	−	4.40882i	−0.667845	−	0.178948i	−0.576784	+	0.816897i	$0.695692\pi$
$608$	−4.60047	−	16.0556i	−0.186574	−	0.651139i
$609$		0			0
$610$	−3.87125	−	3.67206i	−0.156742	−	0.148677i
$611$	21.3530	−	12.3282i	0.863851	−	0.498744i
$612$	−0.653226	+	2.50697i	−0.0264051	+	0.101338i
$613$	−7.36973	−	27.5042i	−0.297661	−	1.11088i	−0.939081	−	0.343695i	$-0.888321\pi$
$613$	−7.36973	−	27.5042i	−0.297661	−	1.11088i	0.641421	−	0.767189i	$-0.278345\pi$
$614$	−33.3092	−	19.0781i	−1.34425	−	0.769930i
$615$	8.98474	+	30.6959i	0.362300	+	1.23778i
$616$		0			0
$617$	0.247352	+	0.247352i	0.00995801	+	0.00995801i	0.712068	−	0.702110i	$-0.247759\pi$
$617$	0.247352	+	0.247352i	0.00995801	+	0.00995801i	−0.702110	+	0.712068i	$0.747759\pi$
$618$	−31.7503	+	8.62504i	−1.27719	+	0.346950i
$619$	−4.44950	+	7.70677i	−0.178841	+	0.309761i	−0.941484	−	0.337059i	$-0.890568\pi$
$619$	−4.44950	+	7.70677i	−0.178841	+	0.309761i	0.762643	+	0.646820i	$0.223901\pi$
$620$	0.802709	+	26.8818i	0.0322376	+	1.07960i
$621$	13.9518	+	24.1652i	0.559866	+	0.969716i
$622$	5.00320	−	18.9334i	0.200610	−	0.759159i
$623$		0			0
$624$	−14.8512	−	24.9220i	−0.594525	−	0.997679i
$625$	24.8947	−	2.29162i	0.995790	−	0.0916650i
$626$	0.114813	+	33.2630i	0.00458887	+	1.32946i
$627$	−2.89096	−	10.7892i	−0.115454	−	0.430879i
$628$	−11.2070	+	11.3628i	−0.447207	+	0.453424i
$629$		−	34.9978i		−	1.39545i
$630$		0			0
$631$		−	30.9594i		−	1.23248i	−0.787560	−	0.616238i	$-0.788656\pi$
$631$		−	30.9594i		−	1.23248i	0.787560	−	0.616238i	$-0.211344\pi$
$632$	10.0308	−	39.0483i	0.399002	−	1.55326i
$633$	−0.947212	−	3.53505i	−0.0376483	−	0.140505i
$634$	−1.16628	+	0.00402561i	−0.0463187	+	0.000159878i
$635$	8.78569	+	8.39143i	0.348650	+	0.333004i
$636$	2.47060	+	1.40375i	0.0979657	+	0.0556624i
$637$		0			0
$638$	−8.28739	−	2.18997i	−0.328101	−	0.0867017i
$639$	0.0625872	+	0.108404i	0.00247591	+	0.00428841i
$640$	7.69116	+	24.1007i	0.304020	+	0.952666i
$641$	−6.18079	+	10.7055i	−0.244127	+	0.422840i	−0.961886	−	0.273452i	$-0.911835\pi$
$641$	−6.18079	+	10.7055i	−0.244127	+	0.422840i	0.717759	+	0.696292i	$0.245168\pi$
$642$	−12.8220	−	47.2002i	−0.506045	−	1.86284i
$643$	2.95024	+	2.95024i	0.116346	+	0.116346i	0.762883	−	0.646537i	$-0.223783\pi$
$643$	2.95024	+	2.95024i	0.116346	+	0.116346i	−0.646537	+	0.762883i	$0.723783\pi$
$644$		0			0
$645$	15.3521	−	28.0584i	0.604488	−	1.10480i
$646$	13.1195	−	22.9059i	0.516181	−	0.901222i
$647$	−1.23483	−	4.60847i	−0.0485464	−	0.181178i	0.937395	−	0.348267i	$-0.113230\pi$
$647$	−1.23483	−	4.60847i	−0.0485464	−	0.181178i	−0.985942	+	0.167090i	$0.946563\pi$
$648$	26.0791	−	7.27814i	1.02449	−	0.285912i
$649$	−9.11081	+	5.26013i	−0.357630	+	0.206478i
$650$	−25.4859	−	13.0825i	−0.999640	−	0.513140i
$651$		0			0
$652$	−7.39650	−	26.8610i	−0.289669	−	1.05196i
$653$	−8.09326	−	2.16858i	−0.316714	−	0.0848632i	0.0969603	−	0.995288i	$-0.469088\pi$
$653$	−8.09326	−	2.16858i	−0.316714	−	0.0848632i	−0.413674	+	0.910425i	$0.635755\pi$
$654$	−0.118898	−	34.4464i	−0.00464928	−	1.34696i
$655$	−13.5113	−	22.2093i	−0.527932	−	0.867788i
$656$	−15.5960	+	27.8956i	−0.608923	+	1.08914i
$657$	−0.662288	−	0.662288i	−0.0258383	−	0.0258383i
$658$		0			0
$659$	−35.0426			−1.36507			−0.682534	−	0.730854i	$-0.739122\pi$
$659$	−35.0426			−1.36507			−0.682534	+	0.730854i	$0.739122\pi$
$660$	4.86481	+	16.2046i	0.189362	+	0.630762i
$661$	−9.52109	+	16.4910i	−0.370328	+	0.641426i	−0.989616	−	0.143737i	$-0.954088\pi$
$661$	−9.52109	+	16.4910i	−0.370328	+	0.641426i	0.619288	+	0.785164i	$0.287421\pi$
$662$	14.3990	+	14.3000i	0.559635	+	0.555785i
$663$	11.8676	−	44.2904i	0.460899	−	1.72010i
$664$	−0.228479	−	22.0638i	−0.00886670	−	0.856241i
$665$		0			0
$666$	1.38640	−	0.806832i	0.0537219	−	0.0312641i
$667$	15.4491	+	4.13958i	0.598193	+	0.160285i
$668$	−10.0050	+	38.3974i	−0.387104	+	1.48564i
$669$	28.8542	+	16.6590i	1.11557	+	0.644074i
$670$	−18.8439	−	30.7353i	−0.728004	−	1.18741i
$671$		−	3.56577i		−	0.137655i
$672$		0			0
$673$	−25.9196	+	25.9196i	−0.999127	+	0.999127i	−1.00000		0.000872915i	$-0.999722\pi$
$673$	−25.9196	+	25.9196i	−0.999127	+	0.999127i	0.000872915		1.00000i	$0.499722\pi$
$674$	−0.0621032	+	0.108429i	−0.00239213	+	0.00417651i
$675$	16.8610	−	18.4844i	0.648980	−	0.711464i
$676$	3.45444	+	5.88900i	0.132863	+	0.226500i
$677$	3.56148	−	13.2916i	0.136879	−	0.510838i	−0.863104	−	0.505026i	$-0.831483\pi$
$677$	3.56148	−	13.2916i	0.136879	−	0.510838i	0.999983	−	0.00581271i	$-0.00185025\pi$
$678$	−26.7447	−	7.06737i	−1.02712	−	0.271421i
$679$		0			0
$680$	−18.8279	+	35.2736i	−0.722018	+	1.35268i
$681$	−4.98184	−	8.62881i	−0.190905	−	0.330657i
$682$	−12.6645	+	12.7522i	−0.484948	+	0.488308i
$683$	−8.02293	+	2.14974i	−0.306989	+	0.0822574i	−0.409025	−	0.912523i	$-0.634131\pi$
$683$	−8.02293	+	2.14974i	−0.306989	+	0.0822574i	0.102036	+	0.994781i	$0.467464\pi$
$684$	1.20985	−	0.00835214i	0.0462598	−	0.000319352i
$685$	13.4041	+	45.7944i	0.512145	+	1.74971i
$686$		0			0
$687$	10.3937	−	10.3937i	0.396546	−	0.396546i
$688$	30.7532	−	8.69711i	1.17246	−	0.331574i
$689$	−2.78453	−	1.60765i	−0.106082	−	0.0612465i
$690$	−8.97276	−	30.2671i	−0.341587	−	1.15225i
$691$	7.15943	−	4.13350i	0.272357	−	0.157246i	−0.357601	−	0.933874i	$-0.616405\pi$
$691$	7.15943	−	4.13350i	0.272357	−	0.157246i	0.629958	+	0.776629i	$0.283072\pi$
$692$	24.2081	−	6.66600i	0.920255	−	0.253403i
$693$		0			0
$694$	−10.7834	+	6.27551i	−0.409331	+	0.238215i
$695$	−0.259518	−	11.3068i	−0.00984409	−	0.428890i
$696$	7.13089	−	12.6518i	0.270296	−	0.479567i
$697$	−48.7908	+	13.0735i	−1.84808	+	0.495192i
$698$	5.15603	−	1.40065i	0.195159	−	0.0530153i
$699$	21.4649			0.811878
$700$		0			0
$701$	−14.1462			−0.534296			−0.267148	−	0.963656i	$-0.586081\pi$
$701$	−14.1462			−0.534296			−0.267148	+	0.963656i	$0.586081\pi$
$702$	−27.6670	+	7.51581i	−1.04423	+	0.283666i
$703$	−15.7875	+	4.23024i	−0.595436	+	0.159547i
$704$	−8.14806	+	14.8131i	−0.307092	+	0.558288i
$705$	−0.559026	−	24.3558i	−0.0210542	−	0.917293i
$706$	1.51919	−	0.884111i	0.0571755	−	0.0332740i
$707$		0			0
$708$	−4.73197	−	17.1845i	−0.177838	−	0.645834i
$709$	10.2057	−	5.89228i	0.383284	−	0.221289i	−0.295962	−	0.955200i	$-0.595640\pi$
$709$	10.2057	−	5.89228i	0.383284	−	0.221289i	0.679246	+	0.733910i	$0.262307\pi$
$710$	0.549102	+	1.85224i	0.0206074	+	0.0695133i
$711$	2.52925	+	1.46026i	0.0948542	+	0.0547641i
$712$	−5.69486	−	1.46290i	−0.213424	−	0.0548245i
$713$	23.7125	−	23.7125i	0.888039	−	0.888039i
$714$		0			0
$715$	−5.37797	−	18.3736i	−0.201125	−	0.687132i
$716$	0.0477339	+	6.91450i	0.00178390	+	0.258407i
$717$	−31.9972	+	8.57362i	−1.19496	+	0.320188i
$718$	17.4438	−	17.5646i	0.650997	−	0.655507i
$719$	9.74435	+	16.8777i	0.363403	+	0.629433i	0.988519	−	0.151100i	$-0.0482815\pi$
$719$	9.74435	+	16.8777i	0.363403	+	0.629433i	−0.625115	+	0.780532i	$0.714948\pi$
$720$	−1.83138	+	0.0673431i	−0.0682516	+	0.00250973i
$721$		0			0
$722$	14.0597	+	3.71532i	0.523248	+	0.138270i
$723$	−0.0381648	+	0.142433i	−0.00141936	+	0.00529714i
$724$	27.7673	−	16.2881i	1.03196	−	0.605341i
$725$	−0.657971	−	14.3258i	−0.0244364	−	0.532046i
$726$	8.22187	−	14.3549i	0.305142	−	0.532760i
$727$	−21.7062	+	21.7062i	−0.805039	+	0.805039i	−0.983878	−	0.178839i	$-0.942766\pi$
$727$	−21.7062	+	21.7062i	−0.805039	+	0.805039i	0.178839	+	0.983878i	$0.442766\pi$
$728$		0			0
$729$		−	24.9127i		−	0.922692i
$730$	−7.55571	−	12.3237i	−0.279649	−	0.456121i
$731$	43.7446	+	25.2560i	1.61795	+	0.934126i
$732$	5.84617	+	1.52330i	0.216081	+	0.0563028i
$733$	22.5783	+	6.04984i	0.833949	+	0.223456i	0.650436	−	0.759561i	$-0.274586\pi$
$733$	22.5783	+	6.04984i	0.833949	+	0.223456i	0.183513	+	0.983017i	$0.441253\pi$
$734$	−19.0296	+	11.0745i	−0.702395	+	0.408767i
$735$		0			0
$736$	15.2987	−	27.5868i	0.563916	−	1.01686i
$737$	6.23563	−	23.2717i	0.229693	−	0.857224i
$738$	−1.64271	−	1.63140i	−0.0604688	−	0.0600528i
$739$	−4.82260	+	8.35299i	−0.177402	+	0.307270i	−0.940990	−	0.338434i	$-0.890103\pi$
$739$	−4.82260	+	8.35299i	−0.177402	+	0.307270i	0.763588	+	0.645704i	$0.223436\pi$
$740$	23.7116	−	7.11850i	0.871656	−	0.261681i
$741$	−21.4138			−0.786657
$742$		0			0
$743$	−24.5711	−	24.5711i	−0.901426	−	0.901426i	0.0941337	−	0.995560i	$-0.469992\pi$
$743$	−24.5711	−	24.5711i	−0.901426	−	0.901426i	−0.995560	+	0.0941337i	$0.969992\pi$
$744$	−15.4973	−	26.2115i	−0.568159	−	0.960961i
$745$	8.76569	+	14.4086i	0.321150	+	0.527891i
$746$	−0.00384070	−	1.11270i	−0.000140618	−	0.0407389i
$747$	1.54394	+	0.413697i	0.0564897	+	0.0151364i
$748$	−25.7614	+	7.09372i	−0.941931	+	0.259372i
$749$		0			0
$750$	−23.4273	+	15.8867i	−0.855442	+	0.580100i
$751$	−45.6939	+	26.3814i	−1.66739	+	0.962671i	−0.698359	+	0.715747i	$0.746086\pi$
$751$	−45.6939	+	26.3814i	−1.66739	+	0.962671i	−0.969035	+	0.246923i	$0.920581\pi$
$752$	16.9742	−	17.4496i	0.618987	−	0.636320i
$753$	4.20597	+	15.6969i	0.153274	+	0.572027i
$754$	−8.16746	+	14.2599i	−0.297441	+	0.519315i
$755$	14.9557	−	27.3339i	0.544292	−	0.994782i
$756$		0			0
$757$	−4.54052	−	4.54052i	−0.165028	−	0.165028i	0.619762	−	0.784790i	$-0.287229\pi$
$757$	−4.54052	−	4.54052i	−0.165028	−	0.165028i	−0.784790	+	0.619762i	$0.787229\pi$
$758$	3.39224	+	12.4874i	0.123212	+	0.453564i
$759$	10.5484	−	18.2703i	0.382882	−	0.663172i
$760$	18.1877	+	4.22968i	0.659736	+	0.153426i
$761$	−5.96614	−	10.3337i	−0.216272	−	0.374595i	0.737393	−	0.675464i	$-0.236057\pi$
$761$	−5.96614	−	10.3337i	−0.216272	−	0.374595i	−0.953665	+	0.300869i	$0.902723\pi$
$762$	−13.2993	−	3.51439i	−0.481783	−	0.127313i
$763$		0			0
$764$	5.23957	−	9.22163i	0.189561	−	0.333627i
$765$	−2.09457	−	2.00058i	−0.0757293	−	0.0723310i
$766$	−11.9399	+	0.0412128i	−0.431406	+	0.00148908i
$767$	5.22001	+	19.4813i	0.188484	+	0.703430i
$768$	−20.8055	−	19.6871i	−0.750755	−	0.710397i
$769$		−	29.2063i		−	1.05321i	−0.850111	−	0.526603i	$-0.823465\pi$
$769$		−	29.2063i		−	1.05321i	0.850111	−	0.526603i	$-0.176535\pi$
$770$		0			0
$771$			13.0464i			0.469854i
$772$	−31.8658	−	31.4288i	−1.14688	−	1.13115i
$773$	−9.31348	−	34.7584i	−0.334982	−	1.25017i	−0.903888	−	0.427769i	$-0.859300\pi$
$773$	−9.31348	−	34.7584i	−0.334982	−	1.25017i	0.568906	−	0.822403i	$-0.307367\pi$
$774$	0.00799115	+	2.31514i	0.000287236	+	0.0832162i
$775$	−26.7022	−	13.8235i	−0.959170	−	0.496556i
$776$	0.0809921	+	7.82125i	0.00290745	+	0.280767i
$777$		0			0
$778$	−10.3813	+	39.2855i	−0.372188	+	1.40845i
$779$	11.7948	+	20.4293i	0.422594	+	0.731955i
$780$	32.4214	−	0.968124i	1.16087	−	0.0346644i
$781$	−0.645525	+	1.11808i	−0.0230987	+	0.0400081i
$782$	48.1133	−	13.0701i	1.72053	−	0.467385i
$783$	−10.1484	−	10.1484i	−0.362673	−	0.362673i
$784$		0			0
$785$	−5.01248	−	17.1249i	−0.178903	−	0.611213i
$786$	25.5412	+	14.6289i	0.911024	+	0.521796i
$787$	−4.65805	−	17.3841i	−0.166042	−	0.619675i	−0.997905	−	0.0646952i	$-0.979392\pi$
$787$	−4.65805	−	17.3841i	−0.166042	−	0.619675i	0.831864	−	0.554980i	$-0.187274\pi$
$788$	−14.6036	−	3.80518i	−0.520233	−	0.135554i
$789$	−8.31986	+	4.80348i	−0.296195	+	0.171008i
$790$	32.7029	+	31.0202i	1.16352	+	1.10365i
$791$		0			0
$792$	−0.874910	−	0.856975i	−0.0310886	−	0.0304513i
$793$	−6.60307	−	1.76929i	−0.234482	−	0.0628292i
$794$	−36.0985	+	0.124601i	−1.28109	+	0.00442191i
$795$	−2.71414	+	1.65119i	−0.0962607	+	0.0585616i
$796$	−0.164102	−	23.7710i	−0.00581644	−	0.842541i
$797$	−26.2293	−	26.2293i	−0.929091	−	0.929091i	0.0685567	−	0.997647i	$-0.478161\pi$
$797$	−26.2293	−	26.2293i	−0.929091	−	0.929091i	−0.997647	+	0.0685567i	$0.978161\pi$
$798$		0			0
$799$	38.4752			1.36116
$800$	−27.7281	−	5.58163i	−0.980335	−	0.197340i
$801$	0.212967	−	0.368869i	0.00752481	−	0.0130333i
$802$	26.0774	−	26.2580i	0.920824	−	0.927203i
$803$	2.50026	−	9.33109i	0.0882322	−	0.329287i
$804$	35.4907	+	20.1652i	1.25166	+	0.711171i
$805$		0			0
$806$	17.3305	+	29.7795i	0.610442	+	1.04894i
$807$	−9.36839	−	2.51025i	−0.329783	−	0.0883651i
$808$	3.44119	−	0.960364i	0.121061	−	0.0337855i
$809$	−28.7418	−	16.5941i	−1.01051	−	0.583418i	−0.0991688	−	0.995071i	$-0.531618\pi$
$809$	−28.7418	−	16.5941i	−1.01051	−	0.583418i	−0.911341	+	0.411653i	$0.864952\pi$
$810$	−7.06027	+	29.4367i	−0.248073	+	1.03430i
$811$		−	44.6901i		−	1.56928i	−0.619950	−	0.784641i	$-0.712847\pi$
$811$		−	44.6901i		−	1.56928i	0.619950	−	0.784641i	$-0.287153\pi$
$812$		0			0
$813$	10.3835	−	10.3835i	0.364164	−	0.364164i
$814$	14.3564	+	8.22275i	0.503193	+	0.288207i
$815$	30.2650	+	7.36949i	1.06014	+	0.258142i
$816$	−0.625027	−	45.2670i	−0.0218803	−	1.58466i
$817$	6.10546	−	22.7859i	0.213603	−	0.797178i
$818$	0.355925	−	1.34691i	0.0124446	−	0.0470936i
$819$		0			0
$820$	−18.7815	−	30.3975i	−0.655878	−	1.06153i
$821$	3.13055	+	5.42227i	0.109257	+	0.189238i	0.915469	−	0.402388i	$-0.131820\pi$
$821$	3.13055	+	5.42227i	0.109257	+	0.189238i	−0.806213	+	0.591626i	$0.798486\pi$
$822$	−38.3334	−	38.0697i	−1.33703	−	1.32783i
$823$	20.8940	−	5.59854i	0.728320	−	0.195153i	0.124439	−	0.992227i	$-0.460287\pi$
$823$	20.8940	−	5.59854i	0.728320	−	0.195153i	0.603881	+	0.797074i	$0.293620\pi$
$824$	31.6399	−	18.7068i	1.10223	−	0.651682i
$825$	−18.4769	−	4.05238i	−0.643284	−	0.141086i
$826$		0			0
$827$	−2.73070	+	2.73070i	−0.0949558	+	0.0949558i	−0.752989	−	0.658033i	$-0.771389\pi$
$827$	−2.73070	+	2.73070i	−0.0949558	+	0.0949558i	0.658033	+	0.752989i	$0.271389\pi$
$828$	1.62695	+	1.60464i	0.0565405	+	0.0557652i
$829$	36.5986	+	21.1302i	1.27112	+	0.733883i	0.975199	−	0.221328i	$-0.0710392\pi$
$829$	36.5986	+	21.1302i	1.27112	+	0.733883i	0.295924	+	0.955212i	$0.404373\pi$
$830$	21.6825	+	11.7664i	0.752609	+	0.408419i
$831$	23.5075	−	13.5720i	0.815465	−	0.470809i
$832$	23.3878	+	22.4386i	0.810825	+	0.777917i
$833$		0			0
$834$	6.44088	+	11.0675i	0.223030	+	0.383238i
$835$	−32.0810	−	30.6413i	−1.11021	−	1.06039i
$836$	6.31380	+	10.7635i	0.218367	+	0.372265i
$837$	−29.0661	+	7.78823i	−1.00467	+	0.269201i
$838$	−6.20310	−	22.8347i	−0.214282	−	0.788812i
$839$	−27.3666			−0.944801			−0.472400	−	0.881384i	$-0.656612\pi$
$839$	−27.3666			−0.944801			−0.472400	+	0.881384i	$0.656612\pi$
$840$		0			0
$841$	20.7736			0.716330
$842$	13.1621	+	48.4520i	0.453596	+	1.66977i
$843$	−41.0838	+	11.0084i	−1.41500	+	0.379149i
$844$	2.06869	+	3.52663i	0.0712074	+	0.121392i
$845$	−7.63126	+	0.175156i	−0.262523	+	0.00602556i
$846$	0.887001	+	1.52416i	0.0304957	+	0.0524016i
$847$		0			0
$848$	−3.07740	−	0.779213i	−0.105678	−	0.0267583i
$849$	36.7269	−	21.2043i	1.26046	−	0.727729i
$850$	−24.2342	−	37.5646i	−0.831227	−	1.28846i
$851$	−26.7344	−	15.4351i	−0.916442	−	0.529108i
$852$	−1.55735	−	1.53600i	−0.0533541	−	0.0526225i
$853$	−15.4514	+	15.4514i	−0.529044	+	0.529044i	−0.920287	−	0.391243i	$-0.872045\pi$
$853$	−15.4514	+	15.4514i	−0.529044	+	0.529044i	0.391243	+	0.920287i	$0.372045\pi$
$854$		0			0
$855$	−0.649284	+	1.18667i	−0.0222050	+	0.0405833i
$856$	27.8096	+	47.0360i	0.950513	+	1.60766i
$857$	17.1024	−	4.58257i	0.584206	−	0.156537i	0.0454021	−	0.998969i	$-0.485543\pi$
$857$	17.1024	−	4.58257i	0.584206	−	0.156537i	0.538804	+	0.842431i	$0.318876\pi$
$858$	15.3801	+	15.2743i	0.525067	+	0.521455i
$859$	−4.41256	−	7.64278i	−0.150555	−	0.260768i	0.780877	−	0.624685i	$-0.214773\pi$
$859$	−4.41256	−	7.64278i	−0.150555	−	0.260768i	−0.931432	+	0.363917i	$0.881439\pi$
$860$	−8.21376	+	34.7748i	−0.280087	+	1.18581i
$861$		0			0
$862$	−0.378049	+	1.43063i	−0.0128764	+	0.0487276i
$863$	8.17206	−	30.4985i	0.278180	−	1.03818i	−0.675500	−	0.737360i	$-0.736072\pi$
$863$	8.17206	−	30.4985i	0.278180	−	1.03818i	0.953680	−	0.300822i	$-0.0972611\pi$
$864$	−24.2659	+	14.5740i	−0.825543	+	0.495817i
$865$	−6.64166	+	27.2759i	−0.225823	+	0.927408i
$866$	16.0462	+	9.19058i	0.545272	+	0.312309i
$867$	29.0746	−	29.0746i	0.987427	−	0.987427i
$868$		0			0
$869$			30.1223i			1.02183i
$870$	8.48699	+	13.8427i	0.287736	+	0.469310i
$871$	−40.0003	−	23.0942i	−1.35536	−	0.782517i
$872$	10.3445	+	37.0666i	0.350310	+	1.25523i
$873$	−0.547301	−	0.146649i	−0.0185233	−	0.00496331i
$874$	−11.7114	−	20.1241i	−0.396145	−	0.680707i
$875$		0			0
$876$	14.2305	+	8.08549i	0.480803	+	0.273183i
$877$	−4.12581	+	15.3977i	−0.139319	+	0.519945i	0.860624	+	0.509241i	$0.170074\pi$
$877$	−4.12581	+	15.3977i	−0.139319	+	0.519945i	−0.999943	+	0.0107038i	$0.996593\pi$
$878$	−22.6528	+	22.8097i	−0.764495	+	0.769790i
$879$	23.5552	−	40.7988i	0.794498	−	1.37611i
$880$	−10.0460	−	16.0110i	−0.338649	−	0.539729i
$881$	−33.9704			−1.14449			−0.572245	−	0.820082i	$-0.693927\pi$
$881$	−33.9704			−1.14449			−0.572245	+	0.820082i	$0.693927\pi$
$882$		0			0
$883$	−5.75604	−	5.75604i	−0.193706	−	0.193706i	0.603589	−	0.797295i	$-0.293737\pi$
$883$	−5.75604	−	5.75604i	−0.193706	−	0.193706i	−0.797295	+	0.603589i	$0.793737\pi$
$884$	0.353627	+	51.2246i	0.0118938	+	1.72287i
$885$	19.3622	+	4.71469i	0.650854	+	0.158483i
$886$	−33.0111	+	0.113944i	−1.10903	+	0.00382802i
$887$	−17.5583	−	4.70474i	−0.589551	−	0.157970i	−0.0483029	−	0.998833i	$-0.515381\pi$
$887$	−17.5583	−	4.70474i	−0.589551	−	0.157970i	−0.541248	+	0.840863i	$0.682048\pi$
$888$	−19.6145	+	20.0250i	−0.658219	+	0.671994i
$889$		0			0
$890$	4.52403	−	4.76943i	0.151646	−	0.159872i
$891$	−17.5194	+	10.1148i	−0.586923	+	0.338860i
$892$	−36.0195	−	9.38538i	−1.20602	−	0.314246i
$893$	−4.65057	−	17.3562i	−0.155625	−	0.580801i
$894$	−16.5703	−	9.49073i	−0.554192	−	0.317418i
$895$	−6.78203	−	3.71077i	−0.226698	−	0.124037i
$896$		0			0
$897$	−28.5989	−	28.5989i	−0.954890	−	0.954890i
$898$	−24.6935	+	6.70803i	−0.824031	+	0.223850i
$899$	−8.62408	+	14.9374i	−0.287629	+	0.498189i
$900$	0.929392	−	1.82602i	0.0309797	−	0.0608674i
$901$	−2.50867	−	4.34515i	−0.0835760	−	0.144758i
$902$	6.10057	−	23.0861i	0.203127	−	0.768683i
$903$		0			0
$904$	30.9026	−	0.320008i	1.02781	−	0.0106433i
$905$	0.825881	+	35.9822i	0.0274532	+	1.19609i
$906$	0.121768	+	35.2778i	0.00404547	+	1.17203i
$907$	−11.7282	−	43.7702i	−0.389428	−	1.45337i	−0.831067	−	0.556172i	$-0.812269\pi$
$907$	−11.7282	−	43.7702i	−0.389428	−	1.45337i	0.441639	−	0.897193i	$-0.354397\pi$
$908$	7.92512	+	7.81645i	0.263004	+	0.259398i
$909$			0.258808i			0.00858412i
$910$		0			0
$911$		−	55.7310i		−	1.84645i	−0.384261	−	0.923225i	$-0.625544\pi$
$911$		−	55.7310i		−	1.84645i	0.384261	−	0.923225i	$-0.374456\pi$
$912$	−20.3443	+	5.75344i	−0.673669	+	0.190516i
$913$	4.26687	+	15.9242i	0.141213	+	0.527013i
$914$	−25.7132	+	0.0887537i	−0.850516	+	0.00293571i
$915$	−4.66527	+	4.88446i	−0.154229	+	0.161475i
$916$	−8.11234	+	14.2777i	−0.268039	+	0.471748i
$917$		0			0
$918$	−43.2533	−	11.4298i	−1.42757	−	0.377240i
$919$	1.00568	+	1.74189i	0.0331743	+	0.0574596i	0.882136	−	0.470995i	$-0.156105\pi$
$919$	1.00568	+	1.74189i	0.0331743	+	0.0574596i	−0.848962	+	0.528455i	$0.822772\pi$
$920$	18.6414	+	29.9392i	0.614588	+	0.987065i
$921$	−24.2959	+	42.0818i	−0.800579	+	1.38664i
$922$	11.2632	+	41.4619i	0.370934	+	1.36548i
$923$	1.75015	+	1.75015i	0.0576070	+	0.0576070i
$924$		0			0
$925$	−5.92970	+	27.0366i	−0.194967	+	0.888959i
$926$	−20.0445	+	34.9965i	−0.658703	+	1.15006i
$927$	0.689146	+	2.57193i	0.0226345	+	0.0844731i
$928$	−3.92821	+	15.7421i	−0.128950	+	0.516761i
$929$	12.0757	−	6.97192i	0.396192	−	0.228741i	−0.288648	−	0.957435i	$-0.593206\pi$
$929$	12.0757	−	6.97192i	0.396192	−	0.228741i	0.684839	+	0.728694i	$0.259872\pi$
$930$	34.0324	−	0.898669i	1.11597	−	0.0294685i
$931$		0			0
$932$	−23.1197	+	6.36628i	−0.757310	+	0.208534i
$933$	−23.9453	−	6.41613i	−0.783935	−	0.210055i
$934$	−0.102373	−	29.6589i	−0.00334975	−	0.970467i
$935$	7.06782	−	29.0260i	0.231142	−	0.949253i
$936$	−2.02106	+	1.19493i	−0.0660604	+	0.0390576i
$937$	−10.0820	−	10.0820i	−0.329363	−	0.329363i	0.522981	−	0.852344i	$-0.324820\pi$
$937$	−10.0820	−	10.0820i	−0.329363	−	0.329363i	−0.852344	+	0.522981i	$0.824820\pi$
$938$		0			0
$939$	42.1072			1.37412
$940$	7.82582	+	26.0676i	0.255250	+	0.850233i
$941$	−8.57804	+	14.8576i	−0.279636	+	0.484344i	−0.971294	−	0.237881i	$-0.923547\pi$
$941$	−8.57804	+	14.8576i	−0.279636	+	0.484344i	0.691658	+	0.722225i	$0.256881\pi$
$942$	14.3348	+	14.2362i	0.467054	+	0.463841i
$943$	−11.5316	+	43.0365i	−0.375520	+	1.40146i
$944$	10.1935	+	17.1059i	0.331771	+	0.556748i
$945$		0			0
$946$	−20.6381	+	12.0106i	−0.671002	+	0.390497i
$947$	29.3795	+	7.87222i	0.954707	+	0.255813i	0.702358	−	0.711824i	$-0.252130\pi$
$947$	29.3795	+	7.87222i	0.954707	+	0.255813i	0.252348	+	0.967636i	$0.418797\pi$
$948$	−49.3862	−	12.8683i	−1.60399	−	0.417942i
$949$	−16.0387	−	9.25992i	−0.520637	−	0.300590i
$950$	−14.0161	+	15.4725i	−0.454743	+	0.501996i
$951$			1.47637i			0.0478746i
$952$		0			0
$953$	−36.7987	+	36.7987i	−1.19203	+	1.19203i	−0.215529	+	0.976497i	$0.569148\pi$
$953$	−36.7987	+	36.7987i	−1.19203	+	1.19203i	−0.976497	+	0.215529i	$0.930852\pi$
$954$	0.114294	−	0.199551i	0.00370041	−	0.00646069i
$955$	6.16314	+	10.1307i	0.199434	+	0.327820i
$956$	31.9211	−	18.7246i	1.03240	−	0.605598i
$957$	−2.80843	+	10.4812i	−0.0907836	+	0.338809i
$958$	38.1340	+	10.0770i	1.23205	+	0.325574i
$959$		0			0
$960$	30.5420	−	9.63071i	0.985740	−	0.310830i
$961$	2.58192	+	4.47202i	0.0832878	+	0.144259i
$962$	22.3503	−	22.5051i	0.720603	−	0.725595i
$963$	−3.82344	+	1.02449i	−0.123209	+	0.0330137i
$964$	−0.00113722	−	0.164733i	−3.66275e−5	−	0.00530568i
$965$	48.0250	−	14.0570i	1.54598	−	0.452511i
$966$		0			0
$967$	2.22247	−	2.22247i	0.0714698	−	0.0714698i	−0.670468	−	0.741938i	$-0.733907\pi$
$967$	2.22247	−	2.22247i	0.0714698	−	0.0714698i	0.741938	+	0.670468i	$0.233907\pi$
$968$	−4.59819	+	17.9001i	−0.147791	+	0.575330i
$969$	−28.9386	−	16.7077i	−0.929642	−	0.536729i
$970$	−7.68608	−	4.17101i	−0.246785	−	0.133923i
$971$	28.5473	−	16.4818i	0.916127	−	0.528926i	0.0337295	−	0.999431i	$-0.489262\pi$
$971$	28.5473	−	16.4818i	0.916127	−	0.528926i	0.882397	+	0.470505i	$0.155928\pi$
$972$	−1.12865	−	4.09879i	−0.0362015	−	0.131469i
$973$		0			0
$974$	−4.75666	+	2.76820i	−0.152413	+	0.0886987i
$975$	−16.6722	+	32.2047i	−0.533936	+	1.03138i
$976$	−6.74865	+	0.0931825i	−0.216019	+	0.00298270i
$977$	−6.89664	+	1.84795i	−0.220643	+	0.0591211i	−0.367447	−	0.930044i	$-0.619768\pi$
$977$	−6.89664	+	1.84795i	−0.220643	+	0.0591211i	0.146804	+	0.989166i	$0.453101\pi$
$978$	−34.0349	+	9.24564i	−1.08831	+	0.295643i
$979$	4.39307			0.140403
$980$		0			0
$981$	−2.78774			−0.0890057
$982$	−19.6731	+	5.34423i	−0.627793	+	0.170541i
$983$	−33.0575	+	8.85773i	−1.05437	+	0.282518i	−0.744057	−	0.668116i	$-0.767101\pi$
$983$	−33.0575	+	8.85773i	−1.05437	+	0.282518i	−0.310314	+	0.950634i	$0.600434\pi$
$984$	35.2441	+	19.8644i	1.12354	+	0.633255i
$985$	11.6538	−	12.2013i	0.371320	−	0.388766i
$986$	−22.1635	+	12.8983i	−0.705830	+	0.410766i
$987$		0			0
$988$	23.0647	−	6.35113i	0.733784	−	0.202056i
$989$	38.5854	−	22.2773i	1.22695	−	0.708377i
$990$	1.31278	−	0.389177i	0.0417228	−	0.0123688i
$991$	−27.9661	−	16.1462i	−0.888373	−	0.512902i	−0.0149631	−	0.999888i	$-0.504763\pi$
$991$	−27.9661	−	16.1462i	−0.888373	−	0.512902i	−0.873410	+	0.486986i	$0.838096\pi$
$992$	24.4661	+	23.6358i	0.776799	+	0.750439i
$993$	18.1648	−	18.1648i	0.576444	−	0.576444i
$994$		0			0
$995$	23.3156	+	12.7571i	0.739154	+	0.404426i
$996$	−27.9309	+	0.192820i	−0.885024	+	0.00610972i
$997$	25.5236	−	6.83904i	0.808342	−	0.216594i	0.169098	−	0.985599i	$-0.445914\pi$
$997$	25.5236	−	6.83904i	0.808342	−	0.216594i	0.639243	+	0.769005i	$0.279248\pi$
$998$	−2.94014	+	2.96051i	−0.0930685	+	0.0937132i
$999$	13.8503	+	23.9894i	0.438205	+	0.758993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.k.67.11		72
4.3	odd	2	inner	980.2.x.k.67.6		72
5.3	odd	4	inner	980.2.x.k.263.17		72
7.2	even	3	inner	980.2.x.k.667.14		72
7.3	odd	6		980.2.k.l.687.2		36
7.4	even	3		140.2.k.a.127.2	yes	36
7.5	odd	6		980.2.x.l.667.14		72
7.6	odd	2		980.2.x.l.67.11		72
20.3	even	4	inner	980.2.x.k.263.14		72
28.3	even	6		980.2.k.l.687.9		36
28.11	odd	6		140.2.k.a.127.9	yes	36
28.19	even	6		980.2.x.l.667.17		72
28.23	odd	6	inner	980.2.x.k.667.17		72
28.27	even	2		980.2.x.l.67.6		72
35.3	even	12		980.2.k.l.883.9		36
35.4	even	6		700.2.k.b.407.17		36
35.13	even	4		980.2.x.l.263.17		72
35.18	odd	12		140.2.k.a.43.9	yes	36
35.23	odd	12	inner	980.2.x.k.863.6		72
35.32	odd	12		700.2.k.b.43.10		36
35.33	even	12		980.2.x.l.863.6		72
140.3	odd	12		980.2.k.l.883.2		36
140.23	even	12	inner	980.2.x.k.863.11		72
140.39	odd	6		700.2.k.b.407.10		36
140.67	even	12		700.2.k.b.43.17		36
140.83	odd	4		980.2.x.l.263.14		72
140.103	odd	12		980.2.x.l.863.11		72
140.123	even	12		140.2.k.a.43.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.2	✓	36	140.123	even	12
140.2.k.a.43.9	yes	36	35.18	odd	12
140.2.k.a.127.2	yes	36	7.4	even	3
140.2.k.a.127.9	yes	36	28.11	odd	6
700.2.k.b.43.10		36	35.32	odd	12
700.2.k.b.43.17		36	140.67	even	12
700.2.k.b.407.10		36	140.39	odd	6
700.2.k.b.407.17		36	35.4	even	6
980.2.k.l.687.2		36	7.3	odd	6
980.2.k.l.687.9		36	28.3	even	6
980.2.k.l.883.2		36	140.3	odd	12
980.2.k.l.883.9		36	35.3	even	12
980.2.x.k.67.6		72	4.3	odd	2	inner
980.2.x.k.67.11		72	1.1	even	1	trivial
980.2.x.k.263.14		72	20.3	even	4	inner
980.2.x.k.263.17		72	5.3	odd	4	inner
980.2.x.k.667.14		72	7.2	even	3	inner
980.2.x.k.667.17		72	28.23	odd	6	inner
980.2.x.k.863.6		72	35.23	odd	12	inner
980.2.x.k.863.11		72	140.23	even	12	inner
980.2.x.l.67.6		72	28.27	even	2
980.2.x.l.67.11		72	7.6	odd	2
980.2.x.l.263.14		72	140.83	odd	4
980.2.x.l.263.17		72	35.13	even	4
980.2.x.l.667.14		72	7.5	odd	6
980.2.x.l.667.17		72	28.19	even	6
980.2.x.l.863.6		72	35.33	even	12
980.2.x.l.863.11		72	140.103	odd	12

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+(0.370738 + 1.36475i) q^{2} +(1.72922 - 0.463343i) q^{3} +(-1.72511 + 1.01193i) q^{4} +(-0.0513098 - 2.23548i) q^{5} +(1.27344 + 2.18818i) q^{6} +(-2.02060 - 1.97918i) q^{8} +(0.177443 - 0.102447i) q^{9} +(3.03186 - 0.898803i) q^{10} +(1.83014 + 1.05663i) q^{11} +(-2.51422 + 2.54917i) q^{12} +(2.86476 - 2.86476i) q^{13} +(-1.12452 - 3.84186i) q^{15} +(1.95198 - 3.49138i) q^{16} +(6.10660 - 1.63626i) q^{17} +(0.205599 + 0.204185i) q^{18} +(-1.47623 - 2.55691i) q^{19} +(2.35067 + 3.80452i) q^{20} +(-0.763541 + 2.88943i) q^{22} +(1.44328 - 5.38640i) q^{23} +(-4.41111 - 2.48621i) q^{24} +(-4.99473 + 0.229404i) q^{25} +(4.97177 + 2.84762i) q^{26} +(-3.53826 + 3.53826i) q^{27} +2.86818i q^{29} +(4.82630 - 2.95902i) q^{30} +(5.20796 + 3.00682i) q^{31} +(5.48855 + 1.36959i) q^{32} +(3.65431 + 0.979169i) q^{33} +(4.49704 + 7.72739i) q^{34} +(-0.202439 + 0.356292i) q^{36} +(1.43278 - 5.34722i) q^{37} +(2.94225 - 2.96264i) q^{38} +(3.62644 - 6.28117i) q^{39} +(-4.32075 + 4.61857i) q^{40} -7.98984 q^{41} +(5.64967 + 5.64967i) q^{43} +(-4.22644 + 0.0291770i) q^{44} +(-0.238122 - 0.391413i) q^{45} +(7.88619 - 0.0272206i) q^{46} +(5.87853 + 1.57515i) q^{47} +(1.75770 - 6.94181i) q^{48} +(-2.16482 - 6.73153i) q^{50} +(9.80152 - 5.65891i) q^{51} +(-2.04307 + 7.84096i) q^{52} +(-0.205406 - 0.766587i) q^{53} +(-6.14063 - 3.51709i) q^{54} +(2.26818 - 4.14546i) q^{55} +(-3.73746 - 3.73746i) q^{57} +(-3.91435 + 1.06334i) q^{58} +(-2.48910 + 4.31124i) q^{59} +(5.82763 + 5.48968i) q^{60} +(-0.843662 - 1.46127i) q^{61} +(-2.17278 + 8.22233i) q^{62} +(0.165668 + 7.99828i) q^{64} +(-6.55110 - 6.25712i) q^{65} +(0.0184674 + 5.35025i) q^{66} +(-2.95071 - 11.0122i) q^{67} +(-8.87876 + 9.00220i) q^{68} -9.98301i q^{69} +0.610925i q^{71} +(-0.561302 - 0.144188i) q^{72} +(-1.18312 - 4.41548i) q^{73} +(7.82883 - 0.0270227i) q^{74} +(-8.53071 + 2.71097i) q^{75} +(5.13407 + 2.91709i) q^{76} +(9.91671 + 2.62052i) q^{78} +(7.12694 + 12.3442i) q^{79} +(-7.90507 - 4.18448i) q^{80} +(-4.78635 + 8.29020i) q^{81} +(-2.96214 - 10.9042i) q^{82} +(5.51624 + 5.51624i) q^{83} +(-3.97115 - 13.5672i) q^{85} +(-5.61586 + 9.80496i) q^{86} +(1.32895 + 4.95971i) q^{87} +(-1.60672 - 5.75723i) q^{88} +(1.80030 - 1.03940i) q^{89} +(0.445902 - 0.470090i) q^{90} +(2.96086 + 10.7526i) q^{92} +(10.3989 + 2.78638i) q^{93} +(0.0297077 + 8.60672i) q^{94} +(-5.64017 + 3.43128i) q^{95} +(10.1255 - 0.174767i) q^{96} +(-1.95542 - 1.95542i) q^{97} +0.432994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 16 q^{6} + 16 q^{10} + 16 q^{12} - 8 q^{13} + 8 q^{16} + 20 q^{17} - 28 q^{18} + 40 q^{20} + 8 q^{22} + 20 q^{25} + 32 q^{26} + 4 q^{30} - 20 q^{37} + 36 q^{40} - 20 q^{45} - 16 q^{46} - 48 q^{48}+ \cdots + 40 q^{97}+O(q^{100}) \) 72 * q - 16 * q^6 + 16 * q^10 + 16 * q^12 - 8 * q^13 + 8 * q^16 + 20 * q^17 - 28 * q^18 + 40 * q^20 + 8 * q^22 + 20 * q^25 + 32 * q^26 + 4 * q^30 - 20 * q^37 + 36 * q^40 - 20 * q^45 - 16 * q^46 - 48 * q^48 + 80 * q^50 - 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 + 64 * q^61 + 80 * q^62 - 4 * q^65 - 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 16 * q^76 - 152 * q^78 + 20 * q^80 + 36 * q^81 - 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 - 32 * q^90 - 112 * q^92 - 32 * q^93 - 120 * q^96 + 40 * q^97

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