LMFDB - Embedded newform 925.2.ba.b.99.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(99,925)] 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("925.99"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.ba (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72,0,0,6,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			99.3
Character	$\chi$	$=$	925.99
Dual form			925.2.ba.b.299.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.988334 + 0.829311i) q^{2} +(-1.05263 + 1.25448i) q^{3} +(-0.0582485 + 0.330344i) q^{4} -2.11280i q^{6} +(0.976055 + 2.68169i) q^{7} +(-1.50657 - 2.60945i) q^{8} +(0.0552654 + 0.313426i) q^{9} +(1.17577 + 2.03650i) q^{11} +(-0.353094 - 0.420801i) q^{12} +(-0.449906 + 2.55154i) q^{13} +(-3.18862 - 1.84095i) q^{14} +(3.02262 + 1.10014i) q^{16} +(1.16743 + 6.62084i) q^{17} +(-0.314548 - 0.263937i) q^{18} +(4.53076 - 5.39955i) q^{19} +(-4.39154 - 1.59839i) q^{21} +(-2.85095 - 1.03766i) q^{22} +(-4.47612 + 7.75287i) q^{23} +(4.85935 + 0.856835i) q^{24} +(-1.67136 - 2.89489i) q^{26} +(-4.70597 - 2.71699i) q^{27} +(-0.942733 + 0.166229i) q^{28} +(-0.496364 + 0.286576i) q^{29} +4.07319i q^{31} +(1.76313 - 0.641726i) q^{32} +(-3.79239 - 0.668701i) q^{33} +(-6.64455 - 5.57544i) q^{34} -0.106757 q^{36} +(2.46767 - 5.55973i) q^{37} +9.09397i q^{38} +(-2.72726 - 3.25023i) q^{39} +(-1.54272 + 8.74921i) q^{41} +(5.66587 - 2.06221i) q^{42} +1.85159 q^{43} +(-0.741232 + 0.269786i) q^{44} +(-2.00563 - 11.3745i) q^{46} +(4.32775 + 2.49863i) q^{47} +(-4.56180 + 2.63375i) q^{48} +(-0.876457 + 0.735435i) q^{49} +(-9.53456 - 5.50478i) q^{51} +(-0.816680 - 0.297247i) q^{52} +(4.67057 - 12.8323i) q^{53} +(6.90430 - 1.21742i) q^{54} +(5.52724 - 6.58711i) q^{56} +(2.00439 + 11.3675i) q^{57} +(0.252913 - 0.694873i) q^{58} +(0.214282 - 0.588735i) q^{59} +(-2.25236 - 0.397151i) q^{61} +(-3.37794 - 4.02567i) q^{62} +(-0.786568 + 0.454125i) q^{63} +(-4.42697 + 7.66773i) q^{64} +(4.30271 - 2.48417i) q^{66} +(-4.21171 - 11.5716i) q^{67} -2.25516 q^{68} +(-5.01409 - 13.7761i) q^{69} +(-2.29519 - 1.92589i) q^{71} +(0.734608 - 0.616409i) q^{72} -12.2346i q^{73} +(2.17186 + 7.54134i) q^{74} +(1.51980 + 1.81123i) q^{76} +(-4.31363 + 5.14079i) q^{77} +(5.39090 + 0.950560i) q^{78} +(-0.188725 - 0.518518i) q^{79} +(7.46485 - 2.71698i) q^{81} +(-5.73109 - 9.92654i) q^{82} +(-1.71921 + 0.303143i) q^{83} +(0.783819 - 1.35761i) q^{84} +(-1.82999 + 1.53554i) q^{86} +(0.162985 - 0.924336i) q^{87} +(3.54276 - 6.13624i) q^{88} +(2.18420 - 6.00103i) q^{89} +(-7.28157 + 1.28394i) q^{91} +(-2.30039 - 1.93025i) q^{92} +(-5.10971 - 4.28756i) q^{93} +(-6.34940 + 1.11957i) q^{94} +(-1.05089 + 2.88730i) q^{96} +(1.67596 - 2.90286i) q^{97} +(0.256328 - 1.45371i) q^{98} +(-0.573311 + 0.481065i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{4} - 6 q^{7} - 18 q^{8} - 42 q^{12} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 12 q^{17} + 24 q^{18} + 18 q^{19} + 24 q^{22} - 24 q^{23} + 30 q^{24} - 48 q^{28} - 18 q^{29} + 24 q^{33} - 66 q^{34}+ \cdots + 12 q^{99}+O(q^{100}) $ 72 * q + 6 * q^4 - 6 * q^7 - 18 * q^8 - 42 * q^12 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 12 * q^17 + 24 * q^18 + 18 * q^19 + 24 * q^22 - 24 * q^23 + 30 * q^24 - 48 * q^28 - 18 * q^29 + 24 * q^33 - 66 * q^34 - 12 * q^36 + 12 * q^37 - 24 * q^39 + 6 * q^41 + 12 * q^42 + 216 * q^43 - 24 * q^44 - 54 * q^46 - 252 * q^48 + 60 * q^49 - 180 * q^51 - 138 * q^52 + 66 * q^53 - 6 * q^54 - 156 * q^56 + 12 * q^57 + 60 * q^58 - 6 * q^59 - 36 * q^62 + 90 * q^63 + 126 * q^66 + 24 * q^67 - 72 * q^68 - 54 * q^69 - 60 * q^71 - 48 * q^72 - 6 * q^74 + 36 * q^76 + 174 * q^77 + 84 * q^78 + 72 * q^79 + 48 * q^81 + 96 * q^82 - 42 * q^83 - 12 * q^84 + 60 * q^86 + 42 * q^87 + 84 * q^88 - 12 * q^89 + 24 * q^91 + 42 * q^92 - 72 * q^93 + 66 * q^94 + 102 * q^96 - 24 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	−0.988334	+	0.829311i	−0.698858	+	0.586411i	−0.921448	−	0.388501i	$-0.872993\pi$
$2$	−0.988334	+	0.829311i	−0.698858	+	0.586411i	0.222591	+	0.974912i	$0.428549\pi$
$3$	−1.05263	+	1.25448i	−0.607736	+	0.724272i	−0.978910	−	0.204292i	$-0.934511\pi$
$3$	−1.05263	+	1.25448i	−0.607736	+	0.724272i	0.371174	+	0.928563i	$0.378955\pi$
$4$	−0.0582485	+	0.330344i	−0.0291243	+	0.165172i
$5$		0			0
$5$		0			0
$6$		−	2.11280i		−	0.862546i
$7$	0.976055	+	2.68169i	0.368914	+	1.01358i	0.975775	+	0.218775i	$0.0702061\pi$
$7$	0.976055	+	2.68169i	0.368914	+	1.01358i	−0.606861	+	0.794808i	$0.707572\pi$
$8$	−1.50657	−	2.60945i	−0.532652	−	0.922580i
$9$	0.0552654	+	0.313426i	0.0184218	+	0.104475i
$10$		0			0
$11$	1.17577	+	2.03650i	0.354509	+	0.614027i	0.987034	−	0.160513i	$-0.0513148\pi$
$11$	1.17577	+	2.03650i	0.354509	+	0.614027i	−0.632525	+	0.774540i	$0.717981\pi$
$12$	−0.353094	−	0.420801i	−0.101930	−	0.121475i
$13$	−0.449906	+	2.55154i	−0.124781	+	0.707671i	0.856656	+	0.515888i	$0.172538\pi$
$13$	−0.449906	+	2.55154i	−0.124781	+	0.707671i	−0.981437	+	0.191783i	$0.938573\pi$
$14$	−3.18862	−	1.84095i	−0.852195	−	0.492015i
$15$		0			0
$16$	3.02262	+	1.10014i	0.755654	+	0.275035i
$17$	1.16743	+	6.62084i	0.283144	+	1.60579i	0.711840	+	0.702342i	$0.247862\pi$
$17$	1.16743	+	6.62084i	0.283144	+	1.60579i	−0.428696	+	0.903449i	$0.641027\pi$
$18$	−0.314548	−	0.263937i	−0.0741396	−	0.0622105i
$19$	4.53076	−	5.39955i	1.03943	−	1.23874i	0.0689331	−	0.997621i	$-0.478040\pi$
$19$	4.53076	−	5.39955i	1.03943	−	1.23874i	0.970495	−	0.241121i	$-0.0775151\pi$
$20$		0			0
$21$	−4.39154	−	1.59839i	−0.958312	−	0.348797i
$22$	−2.85095	−	1.03766i	−0.607824	−	0.221230i
$23$	−4.47612	+	7.75287i	−0.933336	+	1.61659i	−0.155761	+	0.987795i	$0.549783\pi$
$23$	−4.47612	+	7.75287i	−0.933336	+	1.61659i	−0.777575	+	0.628790i	$0.783550\pi$
$24$	4.85935	+	0.856835i	0.991911	+	0.174901i
$25$		0			0
$26$	−1.67136	−	2.89489i	−0.327782	−	0.567734i
$27$	−4.70597	−	2.71699i	−0.905665	−	0.522886i
$28$	−0.942733	+	0.166229i	−0.178160	+	0.0314144i
$29$	−0.496364	+	0.286576i	−0.0921726	+	0.0532159i	−0.545378	−	0.838190i	$-0.683614\pi$
$29$	−0.496364	+	0.286576i	−0.0921726	+	0.0532159i	0.453205	+	0.891406i	$0.350280\pi$
$30$		0			0
$31$			4.07319i			0.731566i	0.930700	+	0.365783i	$0.119199\pi$
$31$			4.07319i			0.731566i	−0.930700	+	0.365783i	$0.880801\pi$
$32$	1.76313	−	0.641726i	0.311680	−	0.113442i
$33$	−3.79239	−	0.668701i	−0.660171	−	0.116406i
$34$	−6.64455	−	5.57544i	−1.13953	−	0.956180i
$35$		0			0
$36$	−0.106757			−0.0177929
$37$	2.46767	−	5.55973i	0.405683	−	0.914014i
$37$	2.46767	−	5.55973i	0.405683	−	0.914014i
$38$			9.09397i			1.47524i
$39$	−2.72726	−	3.25023i	−0.436712	−	0.520453i
$40$		0			0
$41$	−1.54272	+	8.74921i	−0.240933	+	1.36640i	0.588819	+	0.808265i	$0.299593\pi$
$41$	−1.54272	+	8.74921i	−0.240933	+	1.36640i	−0.829752	+	0.558133i	$0.811518\pi$
$42$	5.66587	−	2.06221i	0.874262	−	0.318205i
$43$	1.85159			0.282365			0.141182	−	0.989984i	$-0.454910\pi$
$43$	1.85159			0.282365			0.141182	+	0.989984i	$0.454910\pi$
$44$	−0.741232	+	0.269786i	−0.111745	+	0.0406718i
$45$		0			0
$46$	−2.00563	−	11.3745i	−0.295715	−	1.67708i
$47$	4.32775	+	2.49863i	0.631267	+	0.364462i	0.781243	−	0.624227i	$-0.214586\pi$
$47$	4.32775	+	2.49863i	0.631267	+	0.364462i	−0.149975	+	0.988690i	$0.547919\pi$
$48$	−4.56180	+	2.63375i	−0.658439	+	0.380150i
$49$	−0.876457	+	0.735435i	−0.125208	+	0.105062i
$50$		0			0
$51$	−9.53456	−	5.50478i	−1.33511	−	0.770824i
$52$	−0.816680	−	0.297247i	−0.113253	−	0.0412208i
$53$	4.67057	−	12.8323i	0.641552	−	1.76265i	−0.00524360	−	0.999986i	$-0.501669\pi$
$53$	4.67057	−	12.8323i	0.641552	−	1.76265i	0.646796	−	0.762663i	$-0.276109\pi$
$54$	6.90430	−	1.21742i	0.939557	−	0.165669i
$55$		0			0
$56$	5.52724	−	6.58711i	0.738609	−	0.880239i
$57$	2.00439	+	11.3675i	0.265488	+	1.50566i
$58$	0.252913	−	0.694873i	0.0332091	−	0.0912413i
$59$	0.214282	−	0.588735i	0.0278971	−	0.0766467i	−0.924962	−	0.380059i	$-0.875904\pi$
$59$	0.214282	−	0.588735i	0.0278971	−	0.0766467i	0.952859	+	0.303412i	$0.0981259\pi$
$60$		0			0
$61$	−2.25236	−	0.397151i	−0.288385	−	0.0508500i	0.0275844	−	0.999619i	$-0.491218\pi$
$61$	−2.25236	−	0.397151i	−0.288385	−	0.0508500i	−0.315969	+	0.948769i	$0.602330\pi$
$62$	−3.37794	−	4.02567i	−0.428998	−	0.511260i
$63$	−0.786568	+	0.454125i	−0.0990982	+	0.0572144i
$64$	−4.42697	+	7.66773i	−0.553371	+	0.958467i
$65$		0			0
$66$	4.30271	−	2.48417i	0.529627	−	0.305780i
$67$	−4.21171	−	11.5716i	−0.514542	−	1.41369i	−0.876456	−	0.481481i	$-0.840099\pi$
$67$	−4.21171	−	11.5716i	−0.514542	−	1.41369i	0.361914	−	0.932211i	$-0.382123\pi$
$68$	−2.25516			−0.273478
$69$	−5.01409	−	13.7761i	−0.603625	−	1.65845i
$70$		0			0
$71$	−2.29519	−	1.92589i	−0.272389	−	0.228562i	0.496353	−	0.868121i	$-0.334672\pi$
$71$	−2.29519	−	1.92589i	−0.272389	−	0.228562i	−0.768742	+	0.639559i	$0.779117\pi$
$72$	0.734608	−	0.616409i	0.0865743	−	0.0726445i
$73$		−	12.2346i		−	1.43196i	−0.698123	−	0.715978i	$-0.745981\pi$
$73$		−	12.2346i		−	1.43196i	0.698123	−	0.715978i	$-0.254019\pi$
$74$	2.17186	+	7.54134i	0.252474	+	0.876662i
$75$		0			0
$76$	1.51980	+	1.81123i	0.174333	+	0.207762i
$77$	−4.31363	+	5.14079i	−0.491584	+	0.585847i
$78$	5.39090	+	0.950560i	0.610399	+	0.107630i
$79$	−0.188725	−	0.518518i	−0.0212332	−	0.0583378i	0.928623	−	0.371024i	$-0.120993\pi$
$79$	−0.188725	−	0.518518i	−0.0212332	−	0.0583378i	−0.949856	+	0.312686i	$0.898771\pi$
$80$		0			0
$81$	7.46485	−	2.71698i	0.829428	−	0.301887i
$82$	−5.73109	−	9.92654i	−0.632893	−	1.09620i
$83$	−1.71921	+	0.303143i	−0.188708	+	0.0332743i	−0.267203	−	0.963640i	$-0.586100\pi$
$83$	−1.71921	+	0.303143i	−0.188708	+	0.0332743i	0.0784954	+	0.996914i	$0.474988\pi$
$84$	0.783819	−	1.35761i	0.0855216	−	0.148128i
$85$		0			0
$86$	−1.82999	+	1.53554i	−0.197333	+	0.165582i
$87$	0.162985	−	0.924336i	0.0174739	−	0.0990992i
$88$	3.54276	−	6.13624i	0.377660	−	0.654126i
$89$	2.18420	−	6.00103i	0.231524	−	0.636108i	−0.768469	−	0.639887i	$-0.778981\pi$
$89$	2.18420	−	6.00103i	0.231524	−	0.636108i	0.999993	+	0.00377986i	$0.00120317\pi$
$90$		0			0
$91$	−7.28157	+	1.28394i	−0.763316	+	0.134593i
$92$	−2.30039	−	1.93025i	−0.239832	−	0.201243i
$93$	−5.10971	−	4.28756i	−0.529852	−	0.444599i
$94$	−6.34940	+	1.11957i	−0.654891	+	0.115475i
$95$		0			0
$96$	−1.05089	+	2.88730i	−0.107256	+	0.294684i
$97$	1.67596	−	2.90286i	0.170168	−	0.294740i	−0.768310	−	0.640078i	$-0.778902\pi$
$97$	1.67596	−	2.90286i	0.170168	−	0.294740i	0.938479	+	0.345337i	$0.112235\pi$
$98$	0.256328	−	1.45371i	0.0258931	−	0.146847i
$99$	−0.573311	+	0.481065i	−0.0576199	+	0.0483489i
$100$		0			0
$101$	−0.441106	+	0.764018i	−0.0438917	+	0.0760226i	−0.887137	−	0.461507i	$-0.847309\pi$
$101$	−0.441106	+	0.764018i	−0.0438917	+	0.0760226i	0.843245	+	0.537529i	$0.180642\pi$
$102$	13.9885	−	2.46655i	1.38507	−	0.244225i
$103$	2.49722	+	4.32531i	0.246059	+	0.426186i	0.962429	−	0.271535i	$-0.0875311\pi$
$103$	2.49722	+	4.32531i	0.246059	+	0.426186i	−0.716370	+	0.697720i	$0.754198\pi$
$104$	7.33594	−	2.67006i	0.719348	−	0.261821i
$105$		0			0
$106$	6.02587	+	16.5559i	0.585284	+	1.60805i
$107$	7.46760	+	1.31674i	0.721920	+	0.127294i	0.522524	−	0.852625i	$-0.324991\pi$
$107$	7.46760	+	1.31674i	0.721920	+	0.127294i	0.199397	+	0.979919i	$0.436102\pi$
$108$	1.17166	−	1.39633i	0.112743	−	0.134362i
$109$	−2.70074	−	3.21862i	−0.258684	−	0.308288i	0.621034	−	0.783784i	$-0.286713\pi$
$109$	−2.70074	−	3.21862i	−0.258684	−	0.308288i	−0.879718	+	0.475496i	$0.842269\pi$
$110$		0			0
$111$	4.37700	+	8.94797i	0.415446	+	0.849304i
$112$			9.17951i			0.867382i
$113$	−10.5579	+	8.85914i	−0.993205	+	0.833398i	−0.986029	−	0.166576i	$-0.946729\pi$
$113$	−10.5579	+	8.85914i	−0.993205	+	0.833398i	−0.00717669	+	0.999974i	$0.502284\pi$
$114$	−11.4082	−	9.57259i	−1.06847	−	0.896555i
$115$		0			0
$116$	−0.0657562	−	0.180664i	−0.00610531	−	0.0167742i
$117$	−0.824583			−0.0762327
$118$	0.276462	+	0.759573i	0.0254504	+	0.0699243i
$119$	−16.6156	+	9.59300i	−1.52315	+	0.879389i
$120$		0			0
$121$	2.73512	−	4.73736i	0.248647	−	0.430669i
$122$	2.55544	−	1.47539i	0.231359	−	0.133575i
$123$	−9.35176	−	11.1450i	−0.843220	−	1.00491i
$124$	−1.34555	−	0.237257i	−0.120834	−	0.0213063i
$125$		0			0
$126$	0.400781	−	1.10114i	0.0357044	−	0.0980970i
$127$	−2.68696	+	7.38236i	−0.238429	+	0.655078i	0.761547	+	0.648110i	$0.224440\pi$
$127$	−2.68696	+	7.38236i	−0.238429	+	0.655078i	−0.999976	+	0.00696839i	$0.997782\pi$
$128$	−1.33198	−	7.55406i	−0.117732	−	0.667691i
$129$	−1.94904	+	2.32278i	−0.171603	+	0.204509i
$130$		0			0
$131$	0.191601	−	0.0337844i	0.0167402	−	0.00295175i	−0.165272	−	0.986248i	$-0.552850\pi$
$131$	0.191601	−	0.0337844i	0.0167402	−	0.00295175i	0.182012	+	0.983296i	$0.441739\pi$
$132$	0.441803	−	1.21384i	0.0384540	−	0.105651i
$133$	18.9022	+	6.87983i	1.63903	+	0.596557i
$134$	13.7590	+	7.94376i	1.18860	+	0.686237i
$135$		0			0
$136$	15.5180	−	13.0211i	1.33065	−	1.11655i
$137$	11.5272	−	6.65526i	0.984839	−	0.568597i	0.0811112	−	0.996705i	$-0.474153\pi$
$137$	11.5272	−	6.65526i	0.984839	−	0.568597i	0.903727	+	0.428108i	$0.140820\pi$
$138$	16.3802	+	9.45714i	1.39438	+	0.805045i
$139$	1.77564	+	10.0702i	0.150608	+	0.854140i	0.962692	+	0.270599i	$0.0872219\pi$
$139$	1.77564	+	10.0702i	0.150608	+	0.854140i	−0.812084	+	0.583540i	$0.801667\pi$
$140$		0			0
$141$	−7.68999	+	2.79893i	−0.647614	+	0.235712i
$142$	3.86558			0.324392
$143$	−5.72520	+	2.08380i	−0.478765	+	0.174256i
$144$	−0.177767	+	1.00816i	−0.0148139	+	0.0840137i
$145$		0			0
$146$	10.1463	+	12.0919i	0.839715	+	1.00073i
$147$		−	1.87364i		−	0.154535i
$148$	1.69288	+	1.13903i	0.139154	+	0.0936274i
$149$	−11.8503			−0.970814			−0.485407	−	0.874288i	$-0.661329\pi$
$149$	−11.8503			−0.970814			−0.485407	+	0.874288i	$0.661329\pi$
$150$		0			0
$151$	−10.0127	−	8.40164i	−0.814821	−	0.683716i	0.136932	−	0.990580i	$-0.456276\pi$
$151$	−10.0127	−	8.40164i	−0.814821	−	0.683716i	−0.951753	+	0.306864i	$0.900720\pi$
$152$	−20.9158	−	3.68801i	−1.69649	−	0.299137i
$153$	−2.01062	+	0.731807i	−0.162549	+	0.0591631i
$154$		−	8.65816i		−	0.697694i
$155$		0			0
$156$	1.23255	−	0.711614i	0.0986831	−	0.0569747i
$157$	−1.26517	+	0.223084i	−0.100972	+	0.0178040i	−0.223906	−	0.974611i	$-0.571881\pi$
$157$	−1.26517	+	0.223084i	−0.100972	+	0.0178040i	0.122934	+	0.992415i	$0.460770\pi$
$158$	0.616536	+	0.355957i	0.0490489	+	0.0283184i
$159$	11.1814	+	19.3668i	0.886743	+	1.53588i
$160$		0			0
$161$	−25.1597	−	4.43634i	−1.98286	−	0.349632i
$162$	−5.12454	+	8.87597i	−0.402622	+	0.697362i
$163$	12.3423	+	4.49222i	0.966720	+	0.351857i	0.776664	−	0.629916i	$-0.216911\pi$
$163$	12.3423	+	4.49222i	0.966720	+	0.351857i	0.190057	+	0.981773i	$0.439133\pi$
$164$	−2.80039	−	1.01926i	−0.218674	−	0.0795907i
$165$		0			0
$166$	1.44775	−	1.72537i	0.112368	−	0.133914i
$167$	−4.06035	−	3.40703i	−0.314199	−	0.263644i	0.472026	−	0.881585i	$-0.343523\pi$
$167$	−4.06035	−	3.40703i	−0.314199	−	0.263644i	−0.786225	+	0.617940i	$0.787967\pi$
$168$	2.44523	+	13.8676i	0.188653	+	1.06991i
$169$	5.90805	+	2.15035i	0.454465	+	0.165412i
$170$		0			0
$171$	1.94275	+	1.12165i	0.148566	+	0.0857746i
$172$	−0.107852	+	0.611662i	−0.00822368	+	0.0466388i
$173$	−7.06111	−	8.41510i	−0.536846	−	0.639788i	0.427631	−	0.903953i	$-0.359348\pi$
$173$	−7.06111	−	8.41510i	−0.536846	−	0.639788i	−0.964478	+	0.264165i	$0.914904\pi$
$174$	0.605478	+	1.04872i	0.0459011	+	0.0795031i
$175$		0			0
$176$	1.31347	+	7.44907i	0.0990066	+	0.561495i
$177$	0.512994	+	0.888531i	0.0385590	+	0.0667861i
$178$	2.81800	+	7.74240i	0.211218	+	0.580317i
$179$			23.6348i			1.76655i	0.468857	+	0.883274i	$0.344666\pi$
$179$			23.6348i			1.76655i	−0.468857	+	0.883274i	$0.655334\pi$
$180$		0			0
$181$	1.23808	−	7.02152i	0.0920260	−	0.521905i	−0.903592	−	0.428394i	$-0.859080\pi$
$181$	1.23808	−	7.02152i	0.0920260	−	0.521905i	0.995618	−	0.0935116i	$-0.0298092\pi$
$182$	6.13184	−	7.30765i	0.454522	−	0.541679i
$183$	2.86912	−	2.40747i	0.212091	−	0.177966i
$184$	26.9743			1.98857
$185$		0			0
$186$	8.60582			0.631009
$187$	−12.1107	+	10.1621i	−0.885622	+	0.743125i
$188$	−1.07749	+	1.28411i	−0.0785842	+	0.0936530i
$189$	2.69285	−	15.2719i	0.195876	−	1.11087i
$190$		0			0
$191$			22.0138i			1.59286i	0.604729	+	0.796431i	$0.293281\pi$
$191$			22.0138i			1.59286i	−0.604729	+	0.796431i	$0.706719\pi$
$192$	−4.95903	−	13.6248i	−0.357887	−	0.983286i
$193$	5.12800	+	8.88195i	0.369121	+	0.639337i	0.989428	−	0.145022i	$-0.0463253\pi$
$193$	5.12800	+	8.88195i	0.369121	+	0.639337i	−0.620307	+	0.784359i	$0.712992\pi$
$194$	0.750957	+	4.25889i	0.0539155	+	0.305770i
$195$		0			0
$196$	−0.191894	−	0.332370i	−0.0137067	−	0.0237407i
$197$	12.9244	+	15.4027i	0.920826	+	1.09740i	0.994972	+	0.100151i	$0.0319325\pi$
$197$	12.9244	+	15.4027i	0.920826	+	1.09740i	−0.0741458	+	0.997247i	$0.523623\pi$
$198$	0.167670	−	0.950906i	0.0119158	−	0.0675779i
$199$	10.1954	+	5.88631i	0.722732	+	0.417270i	0.815757	−	0.578394i	$-0.196320\pi$
$199$	10.1954	+	5.88631i	0.722732	+	0.417270i	−0.0930253	+	0.995664i	$0.529654\pi$
$200$		0			0
$201$	18.9496	+	6.89710i	1.33660	+	0.486484i
$202$	−0.197648	−	1.12092i	−0.0139065	−	0.0788676i
$203$	−1.25299	−	1.05138i	−0.0879424	−	0.0737925i
$204$	2.37385	−	2.82904i	0.166202	−	0.198072i
$205$		0			0
$206$	−6.05512	−	2.20388i	−0.421880	−	0.153552i
$207$	−2.67732	−	0.974466i	−0.186087	−	0.0677300i
$208$	−4.16695	+	7.21737i	−0.288926	+	0.500435i
$209$	16.3233	+	2.87824i	1.12911	+	0.199092i
$210$		0			0
$211$	7.26159	+	12.5774i	0.499909	+	0.865867i	1.00000		0.000105566i	$-3.36028e-5\pi$
$211$	7.26159	+	12.5774i	0.499909	+	0.865867i	−0.500091	+	0.865973i	$0.666700\pi$
$212$	3.96701	+	2.29036i	0.272456	+	0.157302i
$213$	4.83198	−	0.852008i	0.331081	−	0.0583786i
$214$	−8.47247	+	4.89158i	−0.579166	+	0.334382i
$215$		0			0
$216$			16.3733i			1.11406i
$217$	−10.9230	+	3.97565i	−0.741502	+	0.269885i
$218$	5.33847	+	0.941316i	0.361567	+	0.0637540i
$219$	15.3481	+	12.8785i	1.03713	+	0.870251i
$220$		0			0
$221$	−17.4186			−1.17170
$222$	−11.7466	−	5.21369i	−0.788379	−	0.349920i
$223$		−	8.41603i		−	0.563579i	−0.959476	−	0.281789i	$-0.909072\pi$
$223$		−	8.41603i		−	0.563579i	0.959476	−	0.281789i	$-0.0909280\pi$
$224$	3.44182	+	4.10180i	0.229966	+	0.274063i
$225$		0			0
$226$	3.08776	−	17.5116i	0.205395	−	1.16485i
$227$	−12.4512	+	4.53186i	−0.826413	+	0.300790i	−0.720386	−	0.693573i	$-0.756035\pi$
$227$	−12.4512	+	4.53186i	−0.826413	+	0.300790i	−0.106027	+	0.994363i	$0.533813\pi$
$228$	−3.87193			−0.256425
$229$	0.694444	−	0.252757i	0.0458902	−	0.0167026i	−0.318973	−	0.947764i	$-0.603338\pi$
$229$	0.694444	−	0.252757i	0.0458902	−	0.0167026i	0.364863	+	0.931061i	$0.381116\pi$
$230$		0			0
$231$	−1.90833	−	10.8227i	−0.125559	−	0.712081i
$232$	1.49561	+	0.863492i	0.0981918	+	0.0566911i
$233$	11.8437	−	6.83794i	0.775904	−	0.447968i	−0.0590727	−	0.998254i	$-0.518814\pi$
$233$	11.8437	−	6.83794i	0.775904	−	0.447968i	0.834977	+	0.550285i	$0.185481\pi$
$234$	0.814963	−	0.683835i	0.0532758	−	0.0447037i
$235$		0			0
$236$	0.182003	+	0.105080i	0.0118474	+	0.00684010i
$237$	0.849126	+	0.309056i	0.0551566	+	0.0200754i
$238$	8.46615	−	23.2605i	0.548779	−	1.50776i
$239$	−21.2667	+	3.74990i	−1.37563	+	0.242561i	−0.812092	−	0.583530i	$-0.801671\pi$
$239$	−21.2667	+	3.74990i	−1.37563	+	0.242561i	−0.563538	+	0.826090i	$0.690560\pi$
$240$		0			0
$241$	11.7564	−	14.0107i	0.757296	−	0.902510i	−0.240378	−	0.970679i	$-0.577271\pi$
$241$	11.7564	−	14.0107i	0.757296	−	0.902510i	0.997674	+	0.0681692i	$0.0217158\pi$
$242$	1.22554	+	6.95036i	0.0787804	+	0.446786i
$243$	1.12626	−	3.09439i	0.0722499	−	0.198505i
$244$	0.262393	−	0.720919i	0.0167980	−	0.0461521i
$245$		0			0
$246$	18.4853	+	3.25946i	1.17858	+	0.207816i
$247$	11.7388	+	13.9897i	0.746920	+	0.890145i
$248$	10.6288	−	6.13653i	0.674928	−	0.389670i
$249$	1.42941	−	2.47581i	0.0905850	−	0.156898i
$250$		0			0
$251$	−17.0537	+	9.84598i	−1.07642	+	0.621473i	−0.929929	−	0.367739i	$-0.880132\pi$
$251$	−17.0537	+	9.84598i	−1.07642	+	0.621473i	−0.146493	+	0.989212i	$0.546799\pi$
$252$	−0.104201	−	0.286290i	−0.00656405	−	0.0180346i
$253$	−21.0516			−1.32350
$254$	−3.46666	−	9.52456i	−0.217517	−	0.597624i
$255$		0			0
$256$	−5.98391	−	5.02110i	−0.373994	−	0.313818i
$257$	2.66645	−	2.23742i	0.166329	−	0.139566i	−0.555824	−	0.831300i	$-0.687597\pi$
$257$	2.66645	−	2.23742i	0.166329	−	0.139566i	0.722153	+	0.691734i	$0.243153\pi$
$258$		−	3.91204i		−	0.243553i
$259$	17.3180	+	1.19093i	1.07609	+	0.0740005i
$260$		0			0
$261$	−0.117252	−	0.139736i	−0.00725772	−	0.00864941i
$262$	−0.161348	+	0.192287i	−0.00996809	+	0.0118795i
$263$	−20.4036	−	3.59770i	−1.25814	−	0.221843i	−0.495464	−	0.868628i	$-0.665002\pi$
$263$	−20.4036	−	3.59770i	−1.25814	−	0.221843i	−0.762673	+	0.646785i	$0.776113\pi$
$264$	3.96855	+	10.9035i	0.244247	+	0.671064i
$265$		0			0
$266$	−24.3872	+	8.87621i	−1.49527	+	0.544235i
$267$	5.22899	+	9.05688i	0.320009	+	0.554272i
$268$	4.06793	−	0.717285i	0.248488	−	0.0438152i
$269$	3.40112	−	5.89091i	0.207370	−	0.359175i	−0.743515	−	0.668719i	$-0.766843\pi$
$269$	3.40112	−	5.89091i	0.207370	−	0.359175i	0.950885	+	0.309544i	$0.100176\pi$
$270$		0			0
$271$	15.4121	−	12.9323i	0.936219	−	0.785581i	−0.0407041	−	0.999171i	$-0.512960\pi$
$271$	15.4121	−	12.9323i	0.936219	−	0.785581i	0.976923	+	0.213590i	$0.0685156\pi$
$272$	−3.75517	+	21.2966i	−0.227690	+	1.29130i
$273$	6.05414	−	10.4861i	0.366413	−	0.634646i
$274$	−5.87349	+	16.1373i	−0.354830	+	0.974889i
$275$		0			0
$276$	4.84291	−	0.853936i	0.291509	−	0.0514009i
$277$	8.62832	+	7.24002i	0.518426	+	0.435011i	0.864082	−	0.503350i	$-0.167899\pi$
$277$	8.62832	+	7.24002i	0.518426	+	0.435011i	−0.345657	+	0.938361i	$0.612344\pi$
$278$	−10.1062	−	8.48012i	−0.606131	−	0.508604i
$279$	−1.27664	+	0.225106i	−0.0764305	+	0.0134768i
$280$		0			0
$281$	5.88669	−	16.1735i	0.351170	−	0.964833i	−0.630825	−	0.775925i	$-0.717283\pi$
$281$	5.88669	−	16.1735i	0.351170	−	0.964833i	0.981995	−	0.188907i	$-0.0604945\pi$
$282$	5.27910	−	9.14367i	0.314366	−	0.544497i
$283$	−3.80874	+	21.6004i	−0.226406	+	1.28401i	0.633573	+	0.773683i	$0.281588\pi$
$283$	−3.80874	+	21.6004i	−0.226406	+	1.28401i	−0.859979	+	0.510330i	$0.829523\pi$
$284$	0.769899	−	0.646022i	0.0456851	−	0.0383344i
$285$		0			0
$286$	3.93029	−	6.80746i	0.232403	−	0.402534i
$287$	−24.9684	+	4.40261i	−1.47384	+	0.259878i
$288$	0.298573	+	0.517144i	0.0175936	+	0.0304730i
$289$	−26.4979	+	9.64445i	−1.55870	+	0.567321i
$290$		0			0
$291$	1.87739	+	5.15809i	0.110055	+	0.302373i
$292$	4.04164	+	0.712650i	0.236519	+	0.0417047i
$293$	15.0632	−	17.9516i	0.880001	−	1.04874i	−0.118442	−	0.992961i	$-0.537790\pi$
$293$	15.0632	−	17.9516i	0.880001	−	1.04874i	0.998443	−	0.0557832i	$-0.0177656\pi$
$294$	1.55383	+	1.85178i	0.0906210	+	0.107998i
$295$		0			0
$296$	−18.2256	+	1.93684i	−1.05934	+	0.112576i
$297$		−	12.7783i		−	0.741471i
$298$	11.7120	−	9.82757i	0.678461	−	0.569296i
$299$	−17.7679	−	14.9091i	−1.02755	−	0.862214i
$300$		0			0
$301$	1.80725	+	4.96539i	0.104168	+	0.286200i
$302$	16.8635			0.970383
$303$	−0.494120	−	1.35758i	−0.0283865	−	0.0779912i
$304$	19.6350	−	11.3363i	1.12615	−	0.650181i
$305$		0			0
$306$	1.38027	−	2.39070i	0.0789049	−	0.136667i
$307$	10.1497	−	5.85992i	0.579273	−	0.334443i	−0.181571	−	0.983378i	$-0.558118\pi$
$307$	10.1497	−	5.85992i	0.579273	−	0.334443i	0.760844	+	0.648934i	$0.224785\pi$
$308$	−1.44697	−	1.72443i	−0.0824485	−	0.0982583i
$309$	−8.05465	−	1.42025i	−0.458213	−	0.0807953i
$310$		0			0
$311$	−4.31379	+	11.8520i	−0.244612	+	0.672067i	0.755249	+	0.655438i	$0.227516\pi$
$311$	−4.31379	+	11.8520i	−0.244612	+	0.672067i	−0.999862	+	0.0166295i	$0.994706\pi$
$312$	−4.37250	+	12.0133i	−0.247544	+	0.680122i
$313$	5.05637	+	28.6761i	0.285803	+	1.62087i	0.702404	+	0.711778i	$0.252110\pi$
$313$	5.05637	+	28.6761i	0.285803	+	1.62087i	−0.416602	+	0.909089i	$0.636779\pi$
$314$	1.06541	−	1.26970i	0.0601244	−	0.0716534i
$315$		0			0
$316$	0.182282	−	0.0321413i	0.0102542	−	0.00180809i
$317$	0.0415473	−	0.114150i	0.00233353	−	0.00641132i	−0.938520	−	0.345224i	$-0.887803\pi$
$317$	0.0415473	−	0.114150i	0.00233353	−	0.00641132i	0.940854	+	0.338812i	$0.110025\pi$
$318$	−27.1120	−	9.86797i	−1.52037	−	0.553368i
$319$	−1.16722	−	0.673897i	−0.0653520	−	0.0377310i
$320$		0			0
$321$	−9.51244	+	7.98189i	−0.530933	+	0.445505i
$322$	28.5453	−	16.4806i	1.59077	−	0.918430i
$323$	41.0390	+	23.6939i	2.28347	+	1.31836i
$324$	0.462722	+	2.62423i	0.0257068	+	0.145790i
$325$		0			0
$326$	−15.9237	+	5.79576i	−0.881933	+	0.320997i
$327$	6.88056			0.380496
$328$	25.1549	−	9.15562i	1.38894	−	0.505534i
$329$	−2.47642	+	14.0445i	−0.136529	+	0.774297i
$330$		0			0
$331$	16.9850	+	20.2419i	0.933579	+	1.11260i	0.993436	+	0.114389i	$0.0364909\pi$
$331$	16.9850	+	20.2419i	0.933579	+	1.11260i	−0.0598575	+	0.998207i	$0.519065\pi$
$332$		−	0.585589i		−	0.0321384i
$333$	1.87894	+	0.466171i	0.102965	+	0.0255460i
$334$	6.83847			0.374184
$335$		0			0
$336$	−11.5155	−	9.66263i	−0.628221	−	0.527140i
$337$	−30.7518	−	5.42237i	−1.67516	−	0.295375i	−0.746244	−	0.665673i	$-0.768145\pi$
$337$	−30.7518	−	5.42237i	−1.67516	−	0.295375i	−0.928913	+	0.370298i	$0.879256\pi$
$338$	−7.62244	+	2.77434i	−0.414606	+	0.150904i
$339$		−	22.5701i		−	1.22584i
$340$		0			0
$341$	−8.29504	+	4.78914i	−0.449201	+	0.259347i
$342$	−2.85028	+	0.502582i	−0.154126	+	0.0271765i
$343$	14.4725	+	8.35571i	0.781443	+	0.451166i
$344$	−2.78955	−	4.83164i	−0.150402	−	0.260504i
$345$		0			0
$346$	13.9575	+	2.46108i	0.750358	+	0.132308i
$347$	1.38753	−	2.40327i	0.0744863	−	0.129014i	−0.826376	−	0.563118i	$-0.809602\pi$
$347$	1.38753	−	2.40327i	0.0744863	−	0.129014i	0.900863	+	0.434104i	$0.142935\pi$
$348$	0.295855	+	0.107682i	0.0158595	+	0.00577238i
$349$	18.2247	+	6.63323i	0.975544	+	0.355069i	0.780106	−	0.625647i	$-0.215165\pi$
$349$	18.2247	+	6.63323i	0.975544	+	0.355069i	0.195438	+	0.980716i	$0.437387\pi$
$350$		0			0
$351$	9.04977	−	10.7851i	0.483041	−	0.575666i
$352$	3.37991	+	2.83608i	0.180150	+	0.151164i
$353$	−5.74182	−	32.5635i	−0.305606	−	1.73318i	−0.620637	−	0.784098i	$-0.713126\pi$
$353$	−5.74182	−	32.5635i	−0.305606	−	1.73318i	0.315030	−	0.949082i	$-0.397985\pi$
$354$	−1.24388	−	0.452734i	−0.0661113	−	0.0240626i
$355$		0			0
$356$	1.85518	+	1.07109i	0.0983242	+	0.0567675i
$357$	5.45586	−	30.9417i	0.288755	−	1.63761i
$358$	−19.6006	−	23.3591i	−1.03592	−	1.23457i
$359$	−2.73471	−	4.73666i	−0.144332	−	0.249991i	0.784791	−	0.619760i	$-0.212770\pi$
$359$	−2.73471	−	4.73666i	−0.144332	−	0.249991i	−0.929124	+	0.369769i	$0.879437\pi$
$360$		0			0
$361$	−5.32804	−	30.2168i	−0.280423	−	1.59036i
$362$	4.59938	+	7.96636i	0.241738	+	0.418703i
$363$	3.06384	+	8.41783i	0.160810	+	0.441821i
$364$		−	2.48021i		−	0.129998i
$365$		0			0
$366$	−0.839100	+	4.75878i	−0.0438605	+	0.248745i
$367$	−1.67622	+	1.99764i	−0.0874978	+	0.104276i	−0.808017	−	0.589159i	$-0.799459\pi$
$367$	−1.67622	+	1.99764i	−0.0874978	+	0.104276i	0.720519	+	0.693435i	$0.243904\pi$
$368$	−22.0588	+	18.5096i	−1.14990	+	0.964878i
$369$	−2.82749			−0.147193
$370$		0			0
$371$	38.9709			2.02327
$372$	1.71400	−	1.43822i	0.0888669	−	0.0745682i
$373$	−8.29681	+	9.88776i	−0.429593	+	0.511969i	−0.936805	−	0.349853i	$-0.886232\pi$
$373$	−8.29681	+	9.88776i	−0.429593	+	0.511969i	0.507212	+	0.861821i	$0.330676\pi$
$374$	3.54189	−	20.0871i	0.183147	−	1.03868i
$375$		0			0
$376$		−	15.0574i		−	0.776526i
$377$	−0.507894	−	1.39543i	−0.0261579	−	0.0718682i
$378$	10.0037	+	17.3269i	0.514535	+	0.891201i
$379$	−0.171916	−	0.974984i	−0.00883073	−	0.0500816i	0.980074	−	0.198633i	$-0.0636501\pi$
$379$	−0.171916	−	0.974984i	−0.00883073	−	0.0500816i	−0.988905	+	0.148551i	$0.952539\pi$
$380$		0			0
$381$	−6.43262	−	11.1416i	−0.329553	−	0.570802i
$382$	−18.2563	−	21.7570i	−0.934072	−	1.11318i
$383$	0.221686	−	1.25724i	0.0113276	−	0.0642422i	−0.978620	−	0.205677i	$-0.934060\pi$
$383$	0.221686	−	1.25724i	0.0113276	−	0.0642422i	0.989948	+	0.141435i	$0.0451715\pi$
$384$	10.8785	+	6.28069i	0.555140	+	0.320510i
$385$		0			0
$386$	−12.4341	−	4.52563i	−0.632878	−	0.230349i
$387$	0.102329	+	0.580336i	0.00520167	+	0.0295001i
$388$	0.861318	+	0.722732i	0.0437268	+	0.0366912i
$389$	−11.7099	+	13.9554i	−0.593718	+	0.707565i	−0.976316	−	0.216350i	$-0.930585\pi$
$389$	−11.7099	+	13.9554i	−0.593718	+	0.707565i	0.382598	+	0.923915i	$0.375029\pi$
$390$		0			0
$391$	−56.5561	−	20.5847i	−2.86017	−	1.04102i
$392$	3.23952	+	1.17909i	0.163621	+	0.0595530i
$393$	−0.159303	+	0.275921i	−0.00803577	+	0.0139184i
$394$	−25.5473	−	4.50467i	−1.28705	−	0.226942i
$395$		0			0
$396$	−0.125522	−	0.217411i	−0.00630774	−	0.0109253i
$397$	−5.42274	−	3.13082i	−0.272160	−	0.157131i	0.357709	−	0.933833i	$-0.383558\pi$
$397$	−5.42274	−	3.13082i	−0.272160	−	0.157131i	−0.629869	+	0.776702i	$0.716891\pi$
$398$	−14.9580	+	2.63750i	−0.749778	+	0.132206i
$399$	−28.5276	+	16.4704i	−1.42817	+	0.824552i
$400$		0			0
$401$			13.5132i			0.674817i	0.941358	+	0.337409i	$0.109550\pi$
$401$			13.5132i			0.674817i	−0.941358	+	0.337409i	$0.890450\pi$
$402$	−24.4484	+	8.89849i	−1.21938	+	0.443816i
$403$	−10.3929	−	1.83255i	−0.517708	−	0.0912858i
$404$	−0.226695	−	0.190220i	−0.0112785	−	0.00946378i
$405$		0			0
$406$	2.11029			0.104732
$407$	14.2238	−	1.51157i	0.705048	−	0.0749257i
$408$			33.1733i			1.64232i
$409$	−10.5817	−	12.6108i	−0.523234	−	0.623566i	0.438108	−	0.898922i	$-0.355649\pi$
$409$	−10.5817	−	12.6108i	−0.523234	−	0.623566i	−0.961342	+	0.275356i	$0.911204\pi$
$410$		0			0
$411$	−3.78506	+	21.4662i	−0.186703	+	1.05885i
$412$	−1.57430	+	0.572999i	−0.0775602	+	0.0282296i
$413$	1.78795			0.0879794
$414$	3.45422	−	1.25723i	0.169766	−	0.0617897i
$415$		0			0
$416$	0.844150	+	4.78741i	0.0413878	+	0.234722i
$417$	−14.5019	−	8.37265i	−0.710159	−	0.410011i
$418$	−18.5199	+	10.6924i	−0.905836	+	0.522984i
$419$	23.1506	−	19.4256i	1.13098	−	0.949005i	0.131874	−	0.991267i	$-0.457901\pi$
$419$	23.1506	−	19.4256i	1.13098	−	0.949005i	0.999107	+	0.0422615i	$0.0134563\pi$
$420$		0			0
$421$	0.289164	+	0.166949i	0.0140930	+	0.00813660i	0.507030	−	0.861928i	$-0.330743\pi$
$421$	0.289164	+	0.166949i	0.0140930	+	0.00813660i	−0.492937	+	0.870065i	$0.664077\pi$
$422$	−17.6075	−	6.40860i	−0.857119	−	0.311966i
$423$	−0.543959	+	1.49452i	−0.0264482	+	0.0726658i
$424$	−40.5217	+	7.14507i	−1.96791	+	0.346996i
$425$		0			0
$426$	−4.06903	+	4.84928i	−0.197145	+	0.234948i
$427$	−1.13339	−	6.42776i	−0.0548485	−	0.311061i
$428$	−0.869954	+	2.39018i	−0.0420508	+	0.115534i
$429$	3.41244	−	9.37560i	0.164754	−	0.452658i
$430$		0			0
$431$	36.9030	+	6.50699i	1.77755	+	0.313431i	0.963570	−	0.267456i	$-0.0861831\pi$
$431$	36.9030	+	6.50699i	1.77755	+	0.313431i	0.813984	+	0.580887i	$0.197294\pi$
$432$	−11.2353	−	13.3897i	−0.540557	−	0.644211i
$433$	−32.7443	+	18.9049i	−1.57359	+	0.908512i	−0.577866	+	0.816132i	$0.696114\pi$
$433$	−32.7443	+	18.9049i	−1.57359	+	0.908512i	−0.995724	+	0.0923806i	$0.970552\pi$
$434$	7.49853	−	12.9878i	0.359941	−	0.623436i
$435$		0			0
$436$	1.22057	−	0.704694i	0.0584545	−	0.0337487i
$437$	21.5818	+	59.2955i	1.03240	+	2.83649i
$438$	−25.8493			−1.23513
$439$	4.40358	+	12.0987i	0.210171	+	0.577441i	0.999324	−	0.0367557i	$-0.0117023\pi$
$439$	4.40358	+	12.0987i	0.210171	+	0.577441i	−0.789153	+	0.614197i	$0.789480\pi$
$440$		0			0
$441$	−0.278942	−	0.234060i	−0.0132829	−	0.0111457i
$442$	17.2154	−	14.4454i	0.818853	−	0.687099i
$443$		−	1.16412i		−	0.0553089i	−0.999618	−	0.0276545i	$-0.991196\pi$
$443$		−	1.16412i		−	0.0553089i	0.999618	−	0.0276545i	$-0.00880381\pi$
$444$	−3.21086	+	0.924709i	−0.152381	+	0.0438848i
$445$		0			0
$446$	6.97950	+	8.31784i	0.330489	+	0.393861i
$447$	12.4740	−	14.8659i	0.589999	−	0.703133i
$448$	−24.8834	−	4.38762i	−1.17563	−	0.207296i
$449$	−7.22003	−	19.8369i	−0.340734	−	0.936160i	−0.985182	−	0.171512i	$-0.945135\pi$
$449$	−7.22003	−	19.8369i	−0.340734	−	0.936160i	0.644448	−	0.764649i	$-0.277087\pi$
$450$		0			0
$451$	−19.6316	+	7.14534i	−0.924418	+	0.336461i
$452$	−2.31158	−	4.00378i	−0.108728	−	0.188322i
$453$	21.0793	−	3.71685i	0.990393	−	0.174633i
$454$	8.54760	−	14.8049i	0.401159	−	0.694827i
$455$		0			0
$456$	26.6431	−	22.3562i	1.24768	−	1.04693i
$457$	4.32794	−	24.5449i	0.202452	−	1.14816i	−0.698946	−	0.715174i	$-0.746347\pi$
$457$	4.32794	−	24.5449i	0.202452	−	1.14816i	0.901399	−	0.432990i	$-0.142541\pi$
$458$	−0.476729	+	0.825718i	−0.0222761	+	0.0385833i
$459$	12.4949	−	34.3294i	0.583211	−	1.60236i
$460$		0			0
$461$	−16.2811	+	2.87080i	−0.758288	+	0.133707i	−0.539407	−	0.842045i	$-0.681352\pi$
$461$	−16.2811	+	2.87080i	−0.758288	+	0.133707i	−0.218881	+	0.975752i	$0.570241\pi$
$462$	10.8615	+	9.11384i	0.505320	+	0.424014i
$463$	−26.2233	−	22.0040i	−1.21870	−	1.02261i	−0.998892	−	0.0470695i	$-0.985012\pi$
$463$	−26.2233	−	22.0040i	−1.21870	−	1.02261i	−0.219810	−	0.975543i	$-0.570544\pi$
$464$	−1.81559	+	0.320138i	−0.0842868	+	0.0148620i
$465$		0			0
$466$	−6.03471	+	16.5802i	−0.279553	+	0.768065i
$467$	13.5190	−	23.4156i	0.625586	−	1.08355i	−0.362842	−	0.931851i	$-0.618193\pi$
$467$	13.5190	−	23.4156i	0.625586	−	1.08355i	0.988427	−	0.151695i	$-0.0484733\pi$
$468$	0.0480308	−	0.272396i	0.00222022	−	0.0125915i
$469$	26.9205	−	22.5890i	1.24307	−	1.04306i
$470$		0			0
$471$	1.05190	−	1.82195i	0.0484692	−	0.0839511i
$472$	−1.85910	+	0.327810i	−0.0855722	+	0.0150887i
$473$	2.17705	+	3.77076i	0.100101	+	0.173380i
$474$	−1.09552	+	0.398738i	−0.0503191	+	0.0183146i
$475$		0			0
$476$	−2.20116	−	6.04763i	−0.100890	−	0.277193i
$477$	4.28009	+	0.754695i	0.195972	+	0.0345551i
$478$	17.9088	−	21.3429i	0.819129	−	0.976200i
$479$	0.187936	+	0.223973i	0.00858700	+	0.0102336i	0.770321	−	0.637656i	$-0.220096\pi$
$479$	0.187936	+	0.223973i	0.00858700	+	0.0102336i	−0.761734	+	0.647890i	$0.775652\pi$
$480$		0			0
$481$	13.0757	+	8.79773i	0.596199	+	0.401142i
$482$			23.5970i			1.07481i
$483$	32.0492	−	26.8924i	1.45829	−	1.22365i
$484$	1.40564	+	1.17947i	0.0638928	+	0.0536124i
$485$		0			0
$486$	1.45308	+	3.99231i	0.0659131	+	0.181095i
$487$	19.2312			0.871447			0.435723	−	0.900081i	$-0.356493\pi$
$487$	19.2312			0.871447			0.435723	+	0.900081i	$0.356493\pi$
$488$	2.35698	+	6.47575i	0.106695	+	0.293143i
$489$	−18.6272	+	10.7544i	−0.842352	+	0.486332i
$490$		0			0
$491$	14.6005	−	25.2888i	0.658912	−	1.14127i	−0.321986	−	0.946744i	$-0.604350\pi$
$491$	14.6005	−	25.2888i	0.658912	−	1.14127i	0.980898	−	0.194524i	$-0.0623162\pi$
$492$	4.22641	−	2.44012i	0.190541	−	0.110009i
$493$	−2.47685	−	2.95179i	−0.111552	−	0.132942i
$494$	−23.2037	−	4.09143i	−1.04398	−	0.184082i
$495$		0			0
$496$	−4.48108	+	12.3117i	−0.201207	+	0.552810i
$497$	2.92442	−	8.03477i	0.131178	−	0.360409i
$498$	0.640481	+	3.63235i	0.0287006	+	0.162769i
$499$	−9.17239	+	10.9312i	−0.410613	+	0.489349i	−0.931225	−	0.364444i	$-0.881259\pi$
$499$	−9.17239	+	10.9312i	−0.410613	+	0.489349i	0.520613	+	0.853793i	$0.325704\pi$
$500$		0			0
$501$	8.54809	−	1.50726i	0.381900	−	0.0673393i
$502$	8.68941	−	23.8740i	0.387827	−	1.06555i
$503$	20.9054	+	7.60895i	0.932127	+	0.339267i	0.763052	−	0.646337i	$-0.223700\pi$
$503$	20.9054	+	7.60895i	0.932127	+	0.339267i	0.169075	+	0.985603i	$0.445922\pi$
$504$	2.37003	+	1.36834i	0.105570	+	0.0609507i
$505$		0			0
$506$	20.8060	−	17.4583i	0.924940	−	0.776117i
$507$	−8.91656	+	5.14798i	−0.395998	+	0.228630i
$508$	−2.28221	−	1.31763i	−0.101257	−	0.0584605i
$509$	−1.69233	−	9.59770i	−0.0750114	−	0.425411i	−0.999068	−	0.0431559i	$-0.986259\pi$
$509$	−1.69233	−	9.59770i	−0.0750114	−	0.425411i	0.924057	−	0.382255i	$-0.124852\pi$
$510$		0			0
$511$	32.8095	−	11.9417i	1.45141	−	0.528269i
$512$	25.4193			1.12339
$513$	−35.9922	+	13.1001i	−1.58909	+	0.578383i
$514$	−0.779829	+	4.42263i	−0.0343968	+	0.195074i
$515$		0			0
$516$	−0.653786	−	0.779152i	−0.0287813	−	0.0343003i
$517$			11.7513i			0.516821i
$518$	−18.1037	+	13.1850i	−0.795429	+	0.579316i
$519$	17.9893			0.789642
$520$		0			0
$521$	−4.73873	−	3.97627i	−0.207608	−	0.174203i	0.533055	−	0.846081i	$-0.321044\pi$
$521$	−4.73873	−	3.97627i	−0.207608	−	0.174203i	−0.740663	+	0.671877i	$0.765488\pi$
$522$	0.231768	+	0.0408670i	0.0101442	+	0.00178870i
$523$	−4.42181	+	1.60941i	−0.193352	+	0.0703744i	−0.436881	−	0.899519i	$-0.643917\pi$
$523$	−4.42181	+	1.60941i	−0.193352	+	0.0703744i	0.243529	+	0.969894i	$0.421695\pi$
$524$			0.0652620i			0.00285098i
$525$		0			0
$526$	23.1491	−	13.3652i	1.00935	−	0.582748i
$527$	−26.9679	+	4.75517i	−1.17474	+	0.207139i
$528$	−10.7273	−	6.19339i	−0.466845	−	0.269533i
$529$	−28.5713	−	49.4870i	−1.24223	−	2.15161i
$530$		0			0
$531$	0.196367	+	0.0346248i	0.00852159	+	0.00150259i
$532$	−3.37374	+	5.84348i	−0.146270	+	0.253347i
$533$	−21.6299	−	7.87264i	−0.936895	−	0.341002i
$534$	−12.6790	−	4.61476i	−0.548672	−	0.199700i
$535$		0			0
$536$	−23.8502	+	28.4236i	−1.03017	+	1.22771i
$537$	−29.6493	−	24.8787i	−1.27946	−	1.07360i
$538$	1.52395	+	8.64276i	0.0657023	+	0.372616i
$539$	−2.52823	−	0.920199i	−0.108898	−	0.0396358i
$540$		0			0
$541$	−5.57730	−	3.22006i	−0.239787	−	0.138441i	0.375292	−	0.926907i	$-0.377542\pi$
$541$	−5.57730	−	3.22006i	−0.239787	−	0.138441i	−0.615079	+	0.788466i	$0.710876\pi$
$542$	−4.50742	+	25.5629i	−0.193610	+	1.09802i
$543$	7.50508	+	8.94421i	0.322074	+	0.383833i
$544$	6.30710	+	10.9242i	0.270415	+	0.468372i
$545$		0			0
$546$	2.71270	+	15.3845i	0.116093	+	0.658396i
$547$	−4.81629	−	8.34206i	−0.205930	−	0.356681i	0.744499	−	0.667624i	$-0.232688\pi$
$547$	−4.81629	−	8.34206i	−0.205930	−	0.356681i	−0.950429	+	0.310943i	$0.899355\pi$
$548$	1.52708	+	4.19561i	0.0652336	+	0.179228i
$549$		−	0.727895i		−	0.0310658i
$550$		0			0
$551$	−0.701526	+	3.97855i	−0.0298860	+	0.169492i
$552$	−28.3940	+	33.8386i	−1.20853	+	1.44027i
$553$	1.20630	−	1.01220i	0.0512970	−	0.0430433i
$554$	−14.5319			−0.617401
$555$		0			0
$556$	−3.43004			−0.145466
$557$	4.71112	−	3.95310i	0.199616	−	0.167498i	−0.537500	−	0.843264i	$-0.680631\pi$
$557$	4.71112	−	3.95310i	0.199616	−	0.167498i	0.737117	+	0.675766i	$0.236187\pi$
$558$	1.07506	−	1.28121i	0.0455111	−	0.0542380i
$559$	−0.833042	+	4.72441i	−0.0352339	+	0.199821i
$560$		0			0
$561$		−	25.8895i		−	1.09306i
$562$	7.59488	+	20.8668i	0.320371	+	0.880211i
$563$	12.1117	+	20.9781i	0.510448	+	0.884121i	0.999927	+	0.0121061i	$0.00385357\pi$
$563$	12.1117	+	20.9781i	0.510448	+	0.884121i	−0.489479	+	0.872015i	$0.662813\pi$
$564$	−0.476678	−	2.70338i	−0.0200718	−	0.113833i
$565$		0			0
$566$	−14.1492	−	24.5071i	−0.594734	−	1.03011i
$567$	14.5722	+	17.3665i	0.611975	+	0.729323i
$568$	−1.56767	+	8.89068i	−0.0657778	+	0.373045i
$569$	−8.71366	−	5.03083i	−0.365296	−	0.210904i	0.306106	−	0.951998i	$-0.400974\pi$
$569$	−8.71366	−	5.03083i	−0.365296	−	0.210904i	−0.671401	+	0.741094i	$0.734307\pi$
$570$		0			0
$571$	−12.1848	−	4.43491i	−0.509918	−	0.185595i	0.0742313	−	0.997241i	$-0.476350\pi$
$571$	−12.1848	−	4.43491i	−0.509918	−	0.185595i	−0.584150	+	0.811646i	$0.698572\pi$
$572$	−0.354887	−	2.01266i	−0.0148386	−	0.0841537i
$573$	−27.6158	−	23.1724i	−1.15367	−	0.968040i
$574$	21.0260	−	25.0578i	0.877609	−	1.04589i
$575$		0			0
$576$	−2.64792	−	0.963765i	−0.110330	−	0.0401569i
$577$	36.3948	+	13.2466i	1.51513	+	0.551464i	0.959927	−	0.280249i	$-0.0904169\pi$
$577$	36.3948	+	13.2466i	1.51513	+	0.551464i	0.555207	+	0.831712i	$0.312639\pi$
$578$	18.1905	−	31.5069i	0.756627	−	1.31052i
$579$	−16.5401	−	2.91646i	−0.687382	−	0.121204i
$580$		0			0
$581$	−2.49098	−	4.31450i	−0.103343	−	0.178996i
$582$	−6.13315	−	3.54098i	−0.254227	−	0.146778i
$583$	31.6244	−	5.57624i	1.30975	−	0.230944i
$584$	−31.9257	+	18.4323i	−1.32109	+	0.762734i
$585$		0			0
$586$			30.2342i			1.24897i
$587$	7.72288	−	2.81090i	0.318757	−	0.116018i	−0.177686	−	0.984087i	$-0.556861\pi$
$587$	7.72288	−	2.81090i	0.318757	−	0.116018i	0.496443	+	0.868069i	$0.334639\pi$
$588$	0.618944	+	0.109137i	0.0255248	+	0.00450072i
$589$	21.9934	+	18.4546i	0.906221	+	0.760410i
$590$		0			0
$591$	−32.9270			−1.35443
$592$	13.5753	−	14.0901i	0.557942	−	0.579101i
$593$			36.7123i			1.50759i	0.657107	+	0.753797i	$0.271780\pi$
$593$			36.7123i			1.50759i	−0.657107	+	0.753797i	$0.728220\pi$
$594$	10.5972	+	12.6292i	0.434807	+	0.518182i
$595$		0			0
$596$	0.690262	−	3.91467i	0.0282743	−	0.160351i
$597$	−18.1162	+	6.59376i	−0.741447	+	0.269865i
$598$	29.9249			1.22372
$599$	−2.30119	+	0.837565i	−0.0940241	+	0.0342220i	−0.388604	−	0.921405i	$-0.627043\pi$
$599$	−2.30119	+	0.837565i	−0.0940241	+	0.0342220i	0.294580	+	0.955627i	$0.404820\pi$
$600$		0			0
$601$	2.87747	+	16.3190i	0.117375	+	0.665664i	0.985547	+	0.169402i	$0.0541836\pi$
$601$	2.87747	+	16.3190i	0.117375	+	0.665664i	−0.868172	+	0.496263i	$0.834705\pi$
$602$	−5.90402	−	3.40869i	−0.240630	−	0.138928i
$603$	3.39407	−	1.95956i	0.138217	−	0.0797996i
$604$	3.35866	−	2.81825i	0.136662	−	0.114673i
$605$		0			0
$606$	1.61422	+	0.931968i	0.0655730	+	0.0378586i
$607$	10.0034	+	3.64095i	0.406026	+	0.147781i	0.536956	−	0.843610i	$-0.319574\pi$
$607$	10.0034	+	3.64095i	0.406026	+	0.147781i	−0.130930	+	0.991392i	$0.541796\pi$
$608$	4.52328	−	12.4276i	0.183443	−	0.504006i
$609$	2.63786	−	0.465126i	0.106892	−	0.0188479i
$610$		0			0
$611$	−8.32244	+	9.91830i	−0.336690	+	0.401251i
$612$	−0.124632	−	0.706824i	−0.00503796	−	0.0285717i
$613$	−12.6091	+	34.6433i	−0.509278	+	1.39923i	0.372705	+	0.927950i	$0.378430\pi$
$613$	−12.6091	+	34.6433i	−0.509278	+	1.39923i	−0.881983	+	0.471280i	$0.843792\pi$
$614$	−5.17158	+	14.2088i	−0.208708	+	0.573420i
$615$		0			0
$616$	19.9134	+	3.51127i	0.802334	+	0.141473i
$617$	−2.52478	−	3.00892i	−0.101644	−	0.121135i	0.712824	−	0.701343i	$-0.247416\pi$
$617$	−2.52478	−	3.00892i	−0.101644	−	0.121135i	−0.814468	+	0.580208i	$0.802971\pi$
$618$	9.13852	−	5.27612i	0.367605	−	0.212237i
$619$	−10.9070	+	18.8915i	−0.438390	+	0.759315i	−0.997566	−	0.0697351i	$-0.977785\pi$
$619$	−10.9070	+	18.8915i	−0.438390	+	0.759315i	0.559175	+	0.829050i	$0.311118\pi$
$620$		0			0
$621$	42.1290	−	24.3232i	1.69058	−	0.976056i
$622$	−5.56555	−	15.2912i	−0.223158	−	0.613123i
$623$	18.2248			0.730160
$624$	−4.66776	−	12.8246i	−0.186860	−	0.513393i
$625$		0			0
$626$	−28.7787	−	24.1482i	−1.15023	−	0.965158i
$627$	−20.7931	+	17.4475i	−0.830397	+	0.696786i
$628$		−	0.430936i		−	0.0171962i
$629$	39.6910	+	9.84746i	1.58258	+	0.392644i
$630$		0			0
$631$	−1.76384	−	2.10206i	−0.0702172	−	0.0836816i	0.729792	−	0.683669i	$-0.239617\pi$
$631$	−1.76384	−	2.10206i	−0.0702172	−	0.0836816i	−0.800010	+	0.599987i	$0.795172\pi$
$632$	−1.06872	+	1.27365i	−0.0425114	+	0.0506631i
$633$	−23.4219	−	4.12991i	−0.930936	−	0.164149i
$634$	0.0536034	+	0.147274i	0.00212886	+	0.00584901i
$635$		0			0
$636$	−7.04899	+	2.56562i	−0.279511	+	0.101734i
$637$	−1.48217	−	2.56719i	−0.0587257	−	0.101716i
$638$	1.71248	−	0.301956i	0.0677976	−	0.0119545i
$639$	0.476780	−	0.825807i	0.0188611	−	0.0326684i
$640$		0			0
$641$	1.69847	−	1.42518i	0.0670855	−	0.0562914i	−0.608628	−	0.793455i	$-0.708280\pi$
$641$	1.69847	−	1.42518i	0.0670855	−	0.0562914i	0.675714	+	0.737164i	$0.263836\pi$
$642$	2.78201	−	15.7775i	0.109797	−	0.622690i
$643$	8.79630	−	15.2356i	0.346892	−	0.600835i	−0.638804	−	0.769370i	$-0.720570\pi$
$643$	8.79630	−	15.2356i	0.346892	−	0.600835i	0.985696	+	0.168535i	$0.0539037\pi$
$644$	2.93103	−	8.05295i	0.115499	−	0.317331i
$645$		0			0
$646$	−60.2098	+	10.6166i	−2.36892	+	0.417705i
$647$	15.5558	+	13.0529i	0.611563	+	0.513162i	0.895139	−	0.445788i	$-0.147076\pi$
$647$	15.5558	+	13.0529i	0.611563	+	0.513162i	−0.283576	+	0.958950i	$0.591521\pi$
$648$	−18.3361	−	15.3858i	−0.720311	−	0.604413i
$649$	1.45090	−	0.255833i	0.0569529	−	0.0100423i
$650$		0			0
$651$	6.51053	−	17.8875i	0.255168	−	0.701068i
$652$	−2.20289	+	3.81553i	−0.0862720	+	0.149428i
$653$	−4.59929	+	26.0839i	−0.179984	+	1.02074i	0.752248	+	0.658880i	$0.228969\pi$
$653$	−4.59929	+	26.0839i	−0.179984	+	1.02074i	−0.932232	+	0.361860i	$0.882142\pi$
$654$	−6.80029	+	5.70612i	−0.265912	+	0.223127i
$655$		0			0
$656$	−14.2884	+	24.7483i	−0.557870	+	0.966258i
$657$	3.83465	−	0.676152i	0.149604	−	0.0263792i
$658$	−9.19970	−	15.9344i	−0.358642	−	0.621186i
$659$	−17.8919	+	6.51211i	−0.696969	+	0.253676i	−0.666116	−	0.745848i	$-0.732045\pi$
$659$	−17.8919	+	6.51211i	−0.696969	+	0.253676i	−0.0308527	+	0.999524i	$0.509822\pi$
$660$		0			0
$661$	−8.20350	−	22.5389i	−0.319079	−	0.876663i	−0.990736	−	0.135801i	$-0.956639\pi$
$661$	−8.20350	−	22.5389i	−0.319079	−	0.876663i	0.671657	−	0.740862i	$-0.265583\pi$
$662$	−33.5736	−	5.91994i	−1.30488	−	0.230085i
$663$	18.3353	−	21.8512i	0.712086	−	0.848631i
$664$	3.38114	+	4.02949i	0.131214	+	0.156375i
$665$		0			0
$666$	−2.24362	+	1.09749i	−0.0869385	+	0.0425269i
$667$		−	5.13100i		−	0.198673i
$668$	1.36200	−	1.14286i	0.0526975	−	0.0442184i
$669$	10.5577	+	8.85896i	0.408184	+	0.342507i
$670$		0			0
$671$	−1.83946	−	5.05388i	−0.0710116	−	0.195103i
$672$	−8.76857			−0.338255
$673$	4.77601	+	13.1220i	0.184102	+	0.505815i	0.997070	−	0.0764927i	$-0.0243722\pi$
$673$	4.77601	+	13.1220i	0.184102	+	0.505815i	−0.812969	+	0.582308i	$0.802150\pi$
$674$	34.8899	−	20.1437i	1.34391	−	0.775905i
$675$		0			0
$676$	−1.05449	+	1.82643i	−0.0405574	+	0.0702474i
$677$	22.8026	−	13.1651i	0.876375	−	0.505976i	0.00691375	−	0.999976i	$-0.497799\pi$
$677$	22.8026	−	13.1651i	0.876375	−	0.505976i	0.869462	+	0.494001i	$0.164466\pi$
$678$	18.7176	+	22.3067i	0.718844	+	0.856685i
$679$	9.42039	+	1.66107i	0.361521	+	0.0637460i
$680$		0			0
$681$	7.42138	−	20.3901i	0.284388	−	0.781349i
$682$	4.22658	−	11.6124i	0.161844	−	0.444663i
$683$	−4.35911	−	24.7217i	−0.166797	−	0.945951i	−0.947193	−	0.320665i	$-0.896094\pi$
$683$	−4.35911	−	24.7217i	−0.166797	−	0.945951i	0.780396	−	0.625286i	$-0.215018\pi$
$684$	−0.483692	+	0.576442i	−0.0184944	+	0.0220408i
$685$		0			0
$686$	−21.2332	+	3.74398i	−0.810686	+	0.142946i
$687$	−0.413915	+	1.13722i	−0.0157919	+	0.0433878i
$688$	5.59665	+	2.03701i	0.213370	+	0.0776604i
$689$	30.6408	+	17.6905i	1.16732	+	0.673953i
$690$		0			0
$691$	18.1417	−	15.2227i	0.690143	−	0.579099i	−0.228808	−	0.973472i	$-0.573483\pi$
$691$	18.1417	−	15.2227i	0.690143	−	0.579099i	0.918950	+	0.394373i	$0.129038\pi$
$692$	3.19118	−	1.84243i	0.121310	−	0.0700386i
$693$	−1.84965	−	1.06790i	−0.0702624	−	0.0405660i
$694$	0.621715	+	3.52592i	0.0236000	+	0.133842i
$695$		0			0
$696$	−2.65756	+	0.967272i	−0.100734	+	0.0366643i
$697$	−59.7282			−2.26237
$698$	−23.5131	+	8.55805i	−0.889982	+	0.323927i
$699$	−3.88896	+	22.0554i	−0.147094	+	0.834212i
$700$		0			0
$701$	20.2331	+	24.1129i	0.764194	+	0.910730i	0.998105	−	0.0615274i	$-0.0195972\pi$
$701$	20.2331	+	24.1129i	0.764194	+	0.910730i	−0.233912	+	0.972258i	$0.575153\pi$
$702$			18.1644i			0.685569i
$703$	−18.8396	−	38.5141i	−0.710550	−	1.45259i
$704$	−20.8204			−0.784700
$705$		0			0
$706$	32.6801	+	27.4218i	1.22993	+	1.03203i
$707$	−2.47940	−	0.437185i	−0.0932475	−	0.0164420i
$708$	−0.323402	+	0.117709i	−0.0121542	+	0.00442376i
$709$		−	28.7726i		−	1.08058i	−0.841480	−	0.540289i	$-0.818315\pi$
$709$		−	28.7726i		−	1.08058i	0.841480	−	0.540289i	$-0.181685\pi$
$710$		0			0
$711$	0.152087	−	0.0878073i	0.00570370	−	0.00329303i
$712$	−18.9500	+	3.34140i	−0.710182	+	0.125224i
$713$	−31.5789	−	18.2321i	−1.18264	−	0.682797i
$714$	20.2681	+	35.1053i	0.758513	+	1.31378i
$715$		0			0
$716$	−7.80761	−	1.37669i	−0.291784	−	0.0514494i
$717$	17.6818	−	30.6258i	0.660340	−	1.14374i
$718$	6.63096	+	2.41347i	0.247465	+	0.0900700i
$719$	15.1471	+	5.51309i	0.564891	+	0.205603i	0.608650	−	0.793439i	$-0.291711\pi$
$719$	15.1471	+	5.51309i	0.564891	+	0.205603i	−0.0437595	+	0.999042i	$0.513934\pi$
$720$		0			0
$721$	−9.16172	+	10.9185i	−0.341200	+	0.406627i
$722$	30.3250	+	25.4457i	1.12858	+	0.946991i
$723$	5.20098	+	29.4962i	0.193427	+	1.09698i
$724$	2.24740	+	0.817986i	0.0835239	+	0.0304002i
$725$		0			0
$726$	−10.0091	−	5.77875i	−0.371472	−	0.214470i
$727$	−5.49224	+	31.1480i	−0.203696	+	1.15522i	0.695783	+	0.718252i	$0.255058\pi$
$727$	−5.49224	+	31.1480i	−0.203696	+	1.15522i	−0.899479	+	0.436964i	$0.856054\pi$
$728$	14.3206	+	17.0666i	0.530755	+	0.632529i
$729$	14.6122	+	25.3090i	0.541192	+	0.937372i
$730$		0			0
$731$	2.16161	+	12.2591i	0.0799500	+	0.453419i
$732$	0.628172	+	1.08803i	0.0232179	+	0.0402146i
$733$	3.72052	+	10.2220i	0.137420	+	0.377560i	0.989245	−	0.146268i	$-0.0467260\pi$
$733$	3.72052	+	10.2220i	0.137420	+	0.377560i	−0.851825	+	0.523827i	$0.824504\pi$
$734$		−	3.36444i		−	0.124184i
$735$		0			0
$736$	−2.91675	+	16.5417i	−0.107513	+	0.609736i
$737$	18.6135	−	22.1827i	0.685636	−	0.817109i
$738$	2.79450	−	2.34486i	0.102867	−	0.0863156i
$739$	3.13742			0.115412			0.0577059	−	0.998334i	$-0.481621\pi$
$739$	3.13742			0.115412			0.0577059	+	0.998334i	$0.481621\pi$
$740$		0			0
$741$	−29.9064			−1.09864
$742$	−38.5163	+	32.3190i	−1.41398	+	1.18647i
$743$	−29.7002	+	35.3953i	−1.08959	+	1.29853i	−0.138250	+	0.990397i	$0.544148\pi$
$743$	−29.7002	+	35.3953i	−1.08959	+	1.29853i	−0.951344	+	0.308130i	$0.900297\pi$
$744$	−3.49005	+	19.7930i	−0.127951	+	0.725648i
$745$		0			0
$746$		−	16.6530i		−	0.609711i
$747$	−0.190026	−	0.522091i	−0.00695268	−	0.0191023i
$748$	−2.65155	−	4.59262i	−0.0969504	−	0.167923i
$749$	3.75770	+	21.3110i	0.137303	+	0.778687i
$750$		0			0
$751$	10.3282	+	17.8890i	0.376882	+	0.652779i	0.990607	−	0.136741i	$-0.0436628\pi$
$751$	10.3282	+	17.8890i	0.376882	+	0.652779i	−0.613724	+	0.789520i	$0.710329\pi$
$752$	10.3323	+	12.3135i	0.376780	+	0.449028i
$753$	5.59973	−	31.7577i	0.204066	−	1.15731i
$754$	1.65921	+	0.957946i	0.0604249	+	0.0348863i
$755$		0			0
$756$	4.88812	+	1.77913i	0.177779	+	0.0647064i
$757$	3.11344	+	17.6572i	0.113160	+	0.641761i	0.987645	+	0.156709i	$0.0500884\pi$
$757$	3.11344	+	17.6572i	0.113160	+	0.641761i	−0.874485	+	0.485053i	$0.838800\pi$
$758$	0.978475	+	0.821038i	0.0355398	+	0.0298215i
$759$	22.1596	−	26.4087i	0.804341	−	0.958576i
$760$		0			0
$761$	45.7740	+	16.6604i	1.65931	+	0.603938i	0.990254	−	0.139277i	$-0.0444777\pi$
$761$	45.7740	+	16.6604i	1.65931	+	0.603938i	0.669053	+	0.743215i	$0.266700\pi$
$762$	15.5974	+	5.67700i	0.565035	+	0.205656i
$763$	5.99526	−	10.3841i	0.217043	−	0.375929i
$764$	−7.27212	−	1.28227i	−0.263096	−	0.0463910i
$765$		0			0
$766$	0.823547	+	1.42642i	0.0297559	+	0.0515388i
$767$	1.40577	+	0.811624i	0.0507596	+	0.0293061i
$768$	12.5977	−	2.22131i	0.454580	−	0.0801547i
$769$	38.8454	−	22.4274i	1.40080	−	0.808754i	0.406327	−	0.913728i	$-0.366809\pi$
$769$	38.8454	−	22.4274i	1.40080	−	0.808754i	0.994475	+	0.104974i	$0.0334760\pi$
$770$		0			0
$771$			5.70017i			0.205287i
$772$	−3.23280	+	1.17664i	−0.116351	+	0.0423483i
$773$	17.1010	+	3.01536i	0.615079	+	0.108455i	0.472503	−	0.881329i	$-0.343350\pi$
$773$	17.1010	+	3.01536i	0.615079	+	0.108455i	0.142576	+	0.989784i	$0.454462\pi$
$774$	−0.582414	−	0.488703i	−0.0209344	−	0.0175661i
$775$		0			0
$776$	−10.0998			−0.362562
$777$	−19.7235	+	20.4715i	−0.707576	+	0.734410i
$778$		−	23.5037i		−	0.842650i
$779$	40.2521	+	47.9706i	1.44218	+	1.71873i
$780$		0			0
$781$	1.22346	−	6.93857i	0.0437787	−	0.248281i
$782$	72.9675	−	26.5580i	2.60931	−	0.949712i
$783$	3.11450			0.111303
$784$	−3.45828	+	1.25871i	−0.123510	+	0.0449539i
$785$		0			0
$786$	−0.0713795	−	0.404813i	−0.00254602	−	0.0144392i
$787$	−19.3240	−	11.1567i	−0.688826	−	0.397694i	0.114346	−	0.993441i	$-0.463523\pi$
$787$	−19.3240	−	11.1567i	−0.688826	−	0.397694i	−0.803172	+	0.595747i	$0.796856\pi$
$788$	−5.84102	+	3.37232i	−0.208078	+	0.120134i
$789$	25.9906	−	21.8087i	0.925290	−	0.776411i
$790$		0			0
$791$	−34.0626	−	19.6660i	−1.21113	−	0.699244i
$792$	2.11905	+	0.771270i	0.0752971	+	0.0274059i
$793$	2.02670	−	5.56830i	0.0719701	−	0.197736i
$794$	7.95590	−	1.40284i	0.282344	−	0.0497849i
$795$		0			0
$796$	−2.53837	+	3.02512i	−0.0899703	+	0.107222i
$797$	1.03433	+	5.86595i	0.0366377	+	0.207783i	0.997631	−	0.0687879i	$-0.0219132\pi$
$797$	1.03433	+	5.86595i	0.0366377	+	0.207783i	−0.960994	+	0.276571i	$0.910802\pi$
$798$	14.5357	−	39.9365i	0.514558	−	1.41374i
$799$	−11.4907	+	31.5704i	−0.406511	+	1.11688i
$800$		0			0
$801$	2.00159	+	0.352934i	0.0707226	+	0.0124703i
$802$	−11.2066	−	13.3556i	−0.395720	−	0.471601i
$803$	24.9158	−	14.3852i	0.879260	−	0.507641i
$804$	−3.38220	+	5.85815i	−0.119281	+	0.206601i
$805$		0			0
$806$	11.7914	−	6.80778i	0.415335	−	0.239794i
$807$	3.80988	+	10.4676i	0.134114	+	0.368476i
$808$	2.65822			0.0935159
$809$	−15.2385	−	41.8675i	−0.535758	−	1.47198i	−0.852121	−	0.523345i	$-0.824684\pi$
$809$	−15.2385	−	41.8675i	−0.535758	−	1.47198i	0.316363	−	0.948638i	$-0.397538\pi$
$810$		0			0
$811$	23.8129	+	19.9814i	0.836185	+	0.701643i	0.956702	−	0.291069i	$-0.0940108\pi$
$811$	23.8129	+	19.9814i	0.836185	+	0.701643i	−0.120517	+	0.992711i	$0.538455\pi$
$812$	0.420302	−	0.352675i	0.0147497	−	0.0123765i
$813$			32.9471i			1.15550i
$814$	−12.8043	+	13.2899i	−0.448791	+	0.465810i
$815$		0			0
$816$	−22.7633	−	27.1282i	−0.796874	−	0.949678i
$817$	8.38912	−	9.99776i	0.293498	−	0.349777i
$818$	20.9166	+	3.68816i	0.731332	+	0.128954i
$819$	−0.804838	−	2.21127i	−0.0281233	−	0.0772682i
$820$		0			0
$821$	−33.3141	+	12.1253i	−1.16267	+	0.423177i	−0.850050	−	0.526702i	$-0.823428\pi$
$821$	−33.3141	+	12.1253i	−1.16267	+	0.423177i	−0.312619	+	0.949879i	$0.601206\pi$
$822$	−14.0612	−	24.3547i	−0.490441	−	0.849469i
$823$	40.9950	−	7.22852i	1.42899	−	0.251970i	0.594992	−	0.803731i	$-0.297155\pi$
$823$	40.9950	−	7.22852i	1.42899	−	0.251970i	0.834002	+	0.551761i	$0.186044\pi$
$824$	7.52446	−	13.0328i	0.262127	−	0.454017i
$825$		0			0
$826$	−1.76709	+	1.48277i	−0.0614851	+	0.0515921i
$827$	−3.69582	+	20.9601i	−0.128516	+	0.728853i	0.850641	+	0.525748i	$0.176214\pi$
$827$	−3.69582	+	20.9601i	−0.128516	+	0.728853i	−0.979157	+	0.203105i	$0.934897\pi$
$828$	0.477859	−	0.827676i	0.0166067	−	0.0287637i
$829$	9.13523	−	25.0988i	0.317280	−	0.871719i	−0.673856	−	0.738863i	$-0.735363\pi$
$829$	9.13523	−	25.0988i	0.317280	−	0.871719i	0.991135	−	0.132856i	$-0.0424147\pi$
$830$		0			0
$831$	−18.1649	+	3.20296i	−0.630132	+	0.111109i
$832$	−17.5728	−	14.7454i	−0.609228	−	0.511203i
$833$	−5.89241	−	4.94432i	−0.204160	−	0.171310i
$834$	21.2762	−	3.75157i	0.736735	−	0.129906i
$835$		0			0
$836$	−1.90162	+	5.22466i	−0.0657689	+	0.180699i
$837$	11.0668	−	19.1683i	0.382525	−	0.662553i
$838$	−6.77061	+	38.3981i	−0.233887	+	1.32644i
$839$	−33.9082	+	28.4524i	−1.17064	+	0.982285i	−0.999995	−	0.00304679i	$-0.999030\pi$
$839$	−33.9082	+	28.4524i	−1.17064	+	0.982285i	−0.170647	+	0.985332i	$0.554586\pi$
$840$		0			0
$841$	−14.3357	+	24.8302i	−0.494336	+	0.856215i
$842$	−0.424243	+	0.0748055i	−0.0146204	+	0.00257797i
$843$	14.0928	+	24.4095i	0.485382	+	0.840707i
$844$	−4.57786	+	1.66620i	−0.157576	+	0.0573531i
$845$		0			0
$846$	−0.701804	−	1.92819i	−0.0241285	−	0.0662926i
$847$	15.3737	+	2.71081i	0.528248	+	0.0931444i
$848$	28.2347	−	33.6488i	0.969582	−	1.15550i
$849$	−23.0880	−	27.5152i	−0.792379	−	0.944321i
$850$		0			0
$851$	32.0583	+	44.0176i	1.09894	+	1.50890i
$852$			1.64584i			0.0563856i
$853$	6.00524	−	5.03899i	0.205615	−	0.172532i	−0.534165	−	0.845380i	$-0.679374\pi$
$853$	6.00524	−	5.03899i	0.205615	−	0.172532i	0.739780	+	0.672848i	$0.234929\pi$
$854$	6.45077	+	5.41284i	0.220741	+	0.185224i
$855$		0			0
$856$	−7.81448	−	21.4701i	−0.267093	−	0.733833i
$857$	1.42847			0.0487957			0.0243979	−	0.999702i	$-0.492233\pi$
$857$	1.42847			0.0487957			0.0243979	+	0.999702i	$0.492233\pi$
$858$	4.40265	+	12.0962i	0.150304	+	0.412957i
$859$	−21.2866	+	12.2898i	−0.726289	+	0.419323i	−0.817063	−	0.576548i	$-0.804399\pi$
$859$	−21.2866	+	12.2898i	−0.726289	+	0.419323i	0.0907740	+	0.995872i	$0.471066\pi$
$860$		0			0
$861$	20.7596	−	35.9566i	0.707484	−	1.22540i
$862$	−41.8688	+	24.1730i	−1.42606	+	0.823334i
$863$	26.1182	+	31.1265i	0.889074	+	1.05956i	0.997853	+	0.0654909i	$0.0208613\pi$
$863$	26.1182	+	31.1265i	0.889074	+	1.05956i	−0.108779	+	0.994066i	$0.534694\pi$
$864$	−10.0408	−	1.77046i	−0.341595	−	0.0602324i
$865$		0			0
$866$	16.6842	−	45.8395i	0.566953	−	1.55769i
$867$	15.7938	−	43.3930i	0.536384	−	1.47370i
$868$	−0.677083	−	3.83993i	−0.0229817	−	0.130336i
$869$	0.834063	−	0.993997i	0.0282936	−	0.0337190i
$870$		0			0
$871$	31.4202	−	5.54024i	1.06463	−	0.187724i
$872$	−4.32998	+	11.8965i	−0.146632	+	0.402867i
$873$	1.00245	+	0.364863i	0.0339279	+	0.0123487i
$874$	−70.5044	−	40.7057i	−2.38485	−	1.37689i
$875$		0			0
$876$	−5.14835	+	4.31998i	−0.173947	+	0.145959i
$877$	−17.3102	+	9.99404i	−0.584524	+	0.337475i	−0.762929	−	0.646482i	$-0.776239\pi$
$877$	−17.3102	+	9.99404i	−0.584524	+	0.337475i	0.178406	+	0.983957i	$0.442906\pi$
$878$	−14.3858	−	8.30565i	−0.485498	−	0.280302i
$879$	6.66389	+	37.7928i	0.224767	+	1.27472i
$880$		0			0
$881$	−1.61215	+	0.586774i	−0.0543146	+	0.0197689i	−0.369035	−	0.929416i	$-0.620312\pi$
$881$	−1.61215	+	0.586774i	−0.0543146	+	0.0197689i	0.314720	+	0.949185i	$0.398089\pi$
$882$	0.469796			0.0158189
$883$	−50.8554	+	18.5099i	−1.71142	+	0.622906i	−0.997042	−	0.0768530i	$-0.975513\pi$
$883$	−50.8554	+	18.5099i	−1.71142	+	0.622906i	−0.714379	+	0.699759i	$0.753291\pi$
$884$	1.01461	−	5.75413i	0.0341250	−	0.193532i
$885$		0			0
$886$	0.965415	+	1.15054i	0.0324338	+	0.0386530i
$887$			23.2394i			0.780304i	0.920750	+	0.390152i	$0.127578\pi$
$887$			23.2394i			0.780304i	−0.920750	+	0.390152i	$0.872422\pi$
$888$	16.7550	−	24.9023i	0.562263	−	0.835666i
$889$	−22.4198			−0.751936
$890$		0			0
$891$	14.3101	+	12.0076i	0.479406	+	0.402270i
$892$	2.78018	+	0.490221i	0.0930874	+	0.0164138i
$893$	33.0995	−	12.0472i	1.10763	−	0.403145i
$894$			25.0373i			0.837372i
$895$		0			0
$896$	18.9575	−	10.9451i	0.633327	−	0.365652i
$897$	37.4061	−	6.59571i	1.24895	−	0.220224i
$898$	23.5867	+	13.6178i	0.787100	+	0.454432i
$899$	−1.16728	−	2.02178i	−0.0389309	−	0.0674303i
$900$		0			0
$901$	90.4131	+	15.9423i	3.01210	+	0.531114i
$902$	13.4769	−	23.3427i	0.448732	−	0.777227i
$903$	−8.13133	−	2.95956i	−0.270594	−	0.0984881i
$904$	39.0237	+	14.2035i	1.29791	+	0.472400i
$905$		0			0
$906$	−17.7510	+	21.1548i	−0.589737	+	0.702821i
$907$	−25.8815	−	21.7171i	−0.859380	−	0.721105i	0.102455	−	0.994738i	$-0.467330\pi$
$907$	−25.8815	−	21.7171i	−0.859380	−	0.721105i	−0.961834	+	0.273633i	$0.911775\pi$
$908$	−0.771809	−	4.37714i	−0.0256134	−	0.145261i
$909$	−0.263841	−	0.0960301i	−0.00875104	−	0.00318512i
$910$		0			0
$911$	18.3374	+	10.5871i	0.607544	+	0.350766i	0.772004	−	0.635618i	$-0.219255\pi$
$911$	18.3374	+	10.5871i	0.607544	+	0.350766i	−0.164459	+	0.986384i	$0.552588\pi$
$912$	−6.44732	+	36.5646i	−0.213492	+	1.21077i
$913$	−2.63875	−	3.14474i	−0.0873300	−	0.104076i
$914$	16.0779	+	27.8478i	0.531811	+	0.921123i
$915$		0			0
$916$	0.0430464	+	0.244128i	0.00142229	+	0.00806622i
$917$	0.277612	+	0.480838i	0.00916755	+	0.0158787i
$918$	16.1206	+	44.2911i	0.532060	+	1.46182i
$919$		−	9.79121i		−	0.322982i	−0.986874	−	0.161491i	$-0.948370\pi$
$919$		−	9.79121i		−	0.322982i	0.986874	−	0.161491i	$-0.0516303\pi$
$920$		0			0
$921$	−3.33273	+	18.9009i	−0.109817	+	0.622805i
$922$	13.7104	−	16.3394i	0.451528	−	0.538111i
$923$	5.94662	−	4.98981i	0.195735	−	0.164242i
$924$	3.68637			0.121273
$925$		0			0
$926$	44.1656			1.45137
$927$	−1.21765	+	1.02173i	−0.0399930	+	0.0335581i
$928$	−0.691250	+	0.823800i	−0.0226914	+	0.0270426i
$929$	−6.20734	+	35.2036i	−0.203656	+	1.15499i	0.695884	+	0.718154i	$0.255013\pi$
$929$	−6.20734	+	35.2036i	−0.203656	+	1.15499i	−0.899540	+	0.436837i	$0.856099\pi$
$930$		0			0
$931$			8.06456i			0.264305i
$932$	1.56900	+	4.31078i	0.0513942	+	0.141204i
$933$	−10.3273	−	17.8873i	−0.338099	−	0.585605i
$934$	6.05752	+	34.3539i	0.198208	+	1.12409i
$935$		0			0
$936$	1.24229	+	2.15171i	0.0406055	+	0.0703308i
$937$	12.8049	+	15.2603i	0.418318	+	0.498532i	0.933514	−	0.358540i	$-0.116725\pi$
$937$	12.8049	+	15.2603i	0.418318	+	0.498532i	−0.515196	+	0.857072i	$0.672281\pi$
$938$	−7.87316	+	44.6509i	−0.257068	+	1.45790i
$939$	−41.2959	−	23.8422i	−1.34764	−	0.778061i
$940$		0			0
$941$	−25.6606	−	9.33970i	−0.836512	−	0.304465i	−0.111983	−	0.993710i	$-0.535720\pi$
$941$	−25.6606	−	9.33970i	−0.836512	−	0.304465i	−0.724529	+	0.689245i	$0.757943\pi$
$942$	0.471331	+	2.67305i	0.0153568	+	0.0870928i
$943$	−60.9261	−	51.1231i	−1.98403	−	1.66480i
$944$	1.29538	−	1.54378i	0.0421611	−	0.0502457i
$945$		0			0
$946$	−5.27879	−	1.92132i	−0.171628	−	0.0624675i
$947$	−51.8998	−	18.8900i	−1.68652	−	0.613843i	−0.692338	−	0.721573i	$-0.743419\pi$
$947$	−51.8998	−	18.8900i	−1.68652	−	0.613843i	−0.994180	+	0.107731i	$0.965642\pi$
$948$	−0.151555	+	0.262501i	−0.00492229	+	0.00852565i
$949$	31.2172	+	5.50443i	1.01335	+	0.178681i
$950$		0			0
$951$	0.0994648	+	0.172278i	0.00322537	+	0.00558650i
$952$	50.0649	+	28.9050i	1.62261	+	0.936816i
$953$	22.3301	−	3.93740i	0.723343	−	0.127545i	0.200158	−	0.979764i	$-0.435855\pi$
$953$	22.3301	−	3.93740i	0.723343	−	0.127545i	0.523186	+	0.852219i	$0.324743\pi$
$954$	−4.85603	+	2.80363i	−0.157220	+	0.0907709i
$955$		0			0
$956$		−	7.24376i		−	0.234280i
$957$	2.07404	−	0.754890i	0.0670443	−	0.0244021i
$958$	−0.371486	−	0.0655030i	−0.0120022	−	0.00211631i
$959$	29.0985	+	24.4166i	0.939641	+	0.788452i
$960$		0			0
$961$	14.4092			0.464812
$962$	−20.2192	+	2.14870i	−0.651892	+	0.0692769i
$963$			2.41331i			0.0777678i
$964$	3.94357	+	4.69976i	0.127014	+	0.151369i
$965$		0			0
$966$	−9.37308	+	53.1574i	−0.301574	+	1.71031i
$967$	29.7211	−	10.8176i	0.955766	−	0.347870i	0.183393	−	0.983040i	$-0.441292\pi$
$967$	29.7211	−	10.8176i	0.955766	−	0.347870i	0.772373	+	0.635169i	$0.219070\pi$
$968$	−16.4825			−0.529769
$969$	−72.9222	+	26.5415i	−2.34260	+	0.852636i
$970$		0			0
$971$	1.30092	+	7.37787i	0.0417484	+	0.236767i	0.998541	−	0.0540055i	$-0.0171988\pi$
$971$	1.30092	+	7.37787i	0.0417484	+	0.236767i	−0.956792	+	0.290772i	$0.906088\pi$
$972$	0.956609	+	0.552298i	0.0306832	+	0.0177150i
$973$	−25.2719	+	14.5907i	−0.810180	+	0.467758i
$974$	−19.0068	+	15.9486i	−0.609017	+	0.511026i
$975$		0			0
$976$	−6.37108	−	3.67835i	−0.203933	−	0.117741i
$977$	−2.87410	−	1.04609i	−0.0919505	−	0.0334672i	0.295635	−	0.955301i	$-0.404469\pi$
$977$	−2.87410	−	1.04609i	−0.0919505	−	0.0334672i	−0.387586	+	0.921834i	$0.626691\pi$
$978$	9.49114	−	26.0767i	0.303493	−	0.833841i
$979$	14.7892	−	2.60773i	0.472665	−	0.0833436i
$980$		0			0
$981$	0.859540	−	1.02436i	0.0274430	−	0.0327053i
$982$	6.54211	+	37.1021i	0.208767	+	1.18398i
$983$	16.2487	−	44.6429i	0.518252	−	1.42389i	−0.354192	−	0.935173i	$-0.615244\pi$
$983$	16.2487	−	44.6429i	0.518252	−	1.42389i	0.872444	−	0.488713i	$-0.162534\pi$
$984$	−14.9933	+	41.1936i	−0.477968	+	1.31320i
$985$		0			0
$986$	4.89591	+	0.863281i	0.155917	+	0.0274925i
$987$	−15.0117	−	17.8903i	−0.477828	−	0.569453i
$988$	−5.30519	+	3.06295i	−0.168780	+	0.0974455i
$989$	−8.28795	+	14.3551i	−0.263541	+	0.456467i
$990$		0			0
$991$	−39.9180	+	23.0467i	−1.26804	+	0.732102i	−0.974616	−	0.223882i	$-0.928127\pi$
$991$	−39.9180	+	23.0467i	−1.26804	+	0.732102i	−0.293421	+	0.955983i	$0.594794\pi$
$992$	2.61387	+	7.18154i	0.0829904	+	0.228014i
$993$	−43.2719			−1.37319
$994$	3.77302	+	10.3663i	0.119673	+	0.328798i
$995$		0			0
$996$	0.734607	+	0.616408i	0.0232769	+	0.0195316i
$997$	−14.0343	+	11.7761i	−0.444469	+	0.372954i	−0.837379	−	0.546623i	$-0.815913\pi$
$997$	−14.0343	+	11.7761i	−0.444469	+	0.372954i	0.392909	+	0.919577i	$0.371469\pi$
$998$		−	18.4105i		−	0.582773i
$999$	−26.7186	+	19.4593i	−0.845338	+	0.615665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.ba.b.99.3		72
5.2	odd	4		925.2.bb.b.876.3		72
5.3	odd	4		185.2.w.a.136.10	✓	72
5.4	even	2		925.2.ba.c.99.10		72
37.3	even	18		925.2.ba.c.299.10		72
185.3	odd	36		185.2.w.a.151.10	yes	72
185.77	odd	36		925.2.bb.b.151.3		72
185.114	even	18	inner	925.2.ba.b.299.3		72
185.133	even	36		6845.2.a.t.1.27		36
185.163	even	36		6845.2.a.u.1.10		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.w.a.136.10	✓	72	5.3	odd	4
185.2.w.a.151.10	yes	72	185.3	odd	36
925.2.ba.b.99.3		72	1.1	even	1	trivial
925.2.ba.b.299.3		72	185.114	even	18	inner
925.2.ba.c.99.10		72	5.4	even	2
925.2.ba.c.299.10		72	37.3	even	18
925.2.bb.b.151.3		72	185.77	odd	36
925.2.bb.b.876.3		72	5.2	odd	4
6845.2.a.t.1.27		36	185.133	even	36
6845.2.a.u.1.10		36	185.163	even	36

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.988334 + 0.829311i) q^{2} +(-1.05263 + 1.25448i) q^{3} +(-0.0582485 + 0.330344i) q^{4} -2.11280i q^{6} +(0.976055 + 2.68169i) q^{7} +(-1.50657 - 2.60945i) q^{8} +(0.0552654 + 0.313426i) q^{9} +(1.17577 + 2.03650i) q^{11} +(-0.353094 - 0.420801i) q^{12} +(-0.449906 + 2.55154i) q^{13} +(-3.18862 - 1.84095i) q^{14} +(3.02262 + 1.10014i) q^{16} +(1.16743 + 6.62084i) q^{17} +(-0.314548 - 0.263937i) q^{18} +(4.53076 - 5.39955i) q^{19} +(-4.39154 - 1.59839i) q^{21} +(-2.85095 - 1.03766i) q^{22} +(-4.47612 + 7.75287i) q^{23} +(4.85935 + 0.856835i) q^{24} +(-1.67136 - 2.89489i) q^{26} +(-4.70597 - 2.71699i) q^{27} +(-0.942733 + 0.166229i) q^{28} +(-0.496364 + 0.286576i) q^{29} +4.07319i q^{31} +(1.76313 - 0.641726i) q^{32} +(-3.79239 - 0.668701i) q^{33} +(-6.64455 - 5.57544i) q^{34} -0.106757 q^{36} +(2.46767 - 5.55973i) q^{37} +9.09397i q^{38} +(-2.72726 - 3.25023i) q^{39} +(-1.54272 + 8.74921i) q^{41} +(5.66587 - 2.06221i) q^{42} +1.85159 q^{43} +(-0.741232 + 0.269786i) q^{44} +(-2.00563 - 11.3745i) q^{46} +(4.32775 + 2.49863i) q^{47} +(-4.56180 + 2.63375i) q^{48} +(-0.876457 + 0.735435i) q^{49} +(-9.53456 - 5.50478i) q^{51} +(-0.816680 - 0.297247i) q^{52} +(4.67057 - 12.8323i) q^{53} +(6.90430 - 1.21742i) q^{54} +(5.52724 - 6.58711i) q^{56} +(2.00439 + 11.3675i) q^{57} +(0.252913 - 0.694873i) q^{58} +(0.214282 - 0.588735i) q^{59} +(-2.25236 - 0.397151i) q^{61} +(-3.37794 - 4.02567i) q^{62} +(-0.786568 + 0.454125i) q^{63} +(-4.42697 + 7.66773i) q^{64} +(4.30271 - 2.48417i) q^{66} +(-4.21171 - 11.5716i) q^{67} -2.25516 q^{68} +(-5.01409 - 13.7761i) q^{69} +(-2.29519 - 1.92589i) q^{71} +(0.734608 - 0.616409i) q^{72} -12.2346i q^{73} +(2.17186 + 7.54134i) q^{74} +(1.51980 + 1.81123i) q^{76} +(-4.31363 + 5.14079i) q^{77} +(5.39090 + 0.950560i) q^{78} +(-0.188725 - 0.518518i) q^{79} +(7.46485 - 2.71698i) q^{81} +(-5.73109 - 9.92654i) q^{82} +(-1.71921 + 0.303143i) q^{83} +(0.783819 - 1.35761i) q^{84} +(-1.82999 + 1.53554i) q^{86} +(0.162985 - 0.924336i) q^{87} +(3.54276 - 6.13624i) q^{88} +(2.18420 - 6.00103i) q^{89} +(-7.28157 + 1.28394i) q^{91} +(-2.30039 - 1.93025i) q^{92} +(-5.10971 - 4.28756i) q^{93} +(-6.34940 + 1.11957i) q^{94} +(-1.05089 + 2.88730i) q^{96} +(1.67596 - 2.90286i) q^{97} +(0.256328 - 1.45371i) q^{98} +(-0.573311 + 0.481065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{4} - 6 q^{7} - 18 q^{8} - 42 q^{12} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 12 q^{17} + 24 q^{18} + 18 q^{19} + 24 q^{22} - 24 q^{23} + 30 q^{24} - 48 q^{28} - 18 q^{29} + 24 q^{33} - 66 q^{34}+ \cdots + 12 q^{99}+O(q^{100}) \) 72 * q + 6 * q^4 - 6 * q^7 - 18 * q^8 - 42 * q^12 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 12 * q^17 + 24 * q^18 + 18 * q^19 + 24 * q^22 - 24 * q^23 + 30 * q^24 - 48 * q^28 - 18 * q^29 + 24 * q^33 - 66 * q^34 - 12 * q^36 + 12 * q^37 - 24 * q^39 + 6 * q^41 + 12 * q^42 + 216 * q^43 - 24 * q^44 - 54 * q^46 - 252 * q^48 + 60 * q^49 - 180 * q^51 - 138 * q^52 + 66 * q^53 - 6 * q^54 - 156 * q^56 + 12 * q^57 + 60 * q^58 - 6 * q^59 - 36 * q^62 + 90 * q^63 + 126 * q^66 + 24 * q^67 - 72 * q^68 - 54 * q^69 - 60 * q^71 - 48 * q^72 - 6 * q^74 + 36 * q^76 + 174 * q^77 + 84 * q^78 + 72 * q^79 + 48 * q^81 + 96 * q^82 - 42 * q^83 - 12 * q^84 + 60 * q^86 + 42 * q^87 + 84 * q^88 - 12 * q^89 + 24 * q^91 + 42 * q^92 - 72 * q^93 + 66 * q^94 + 102 * q^96 - 24 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more