LMFDB - Embedded newform 185.2.w.a.151.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(21,185)] 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("185.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.w (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			151.10
Character	$\chi$	$=$	185.151
Dual form			185.2.w.a.136.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.829311 - 0.988334i) q^{2} +(-1.25448 + 1.05263i) q^{3} +(0.0582485 + 0.330344i) q^{4} +(0.342020 - 0.939693i) q^{5} +2.11280i q^{6} +(2.68169 + 0.976055i) q^{7} +(2.60945 + 1.50657i) q^{8} +(-0.0552654 + 0.313426i) q^{9} +(-0.645089 - 1.11733i) q^{10} +(1.17577 - 2.03650i) q^{11} +(-0.420801 - 0.353094i) q^{12} +(-2.55154 + 0.449906i) q^{13} +(3.18862 - 1.84095i) q^{14} +(0.560093 + 1.53884i) q^{15} +(3.02262 - 1.10014i) q^{16} +(6.62084 + 1.16743i) q^{17} +(0.263937 + 0.314548i) q^{18} +(-4.53076 - 5.39955i) q^{19} +(0.330344 + 0.0582485i) q^{20} +(-4.39154 + 1.59839i) q^{21} +(-1.03766 - 2.85095i) q^{22} +(-7.75287 + 4.47612i) q^{23} +(-4.85935 + 0.856835i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-1.67136 + 2.89489i) q^{26} +(-2.71699 - 4.70597i) q^{27} +(-0.166229 + 0.942733i) q^{28} +(0.496364 + 0.286576i) q^{29} +(1.98538 + 0.722620i) q^{30} -4.07319i q^{31} +(-0.641726 + 1.76313i) q^{32} +(0.668701 + 3.79239i) q^{33} +(6.64455 - 5.57544i) q^{34} +(1.83438 - 2.18613i) q^{35} -0.106757 q^{36} +(-5.55973 + 2.46767i) q^{37} -9.09397 q^{38} +(2.72726 - 3.25023i) q^{39} +(2.30819 - 1.93681i) q^{40} +(-1.54272 - 8.74921i) q^{41} +(-2.06221 + 5.66587i) q^{42} -1.85159i q^{43} +(0.741232 + 0.269786i) q^{44} +(0.275622 + 0.159130i) q^{45} +(-2.00563 + 11.3745i) q^{46} +(2.49863 + 4.32775i) q^{47} +(-2.63375 + 4.56180i) q^{48} +(0.876457 + 0.735435i) q^{49} +(-1.27058 + 0.224037i) q^{50} +(-9.53456 + 5.50478i) q^{51} +(-0.297247 - 0.816680i) q^{52} +(12.8323 - 4.67057i) q^{53} +(-6.90430 - 1.21742i) q^{54} +(-1.51154 - 1.80139i) q^{55} +(5.52724 + 6.58711i) q^{56} +(11.3675 + 2.00439i) q^{57} +(0.694873 - 0.252913i) q^{58} +(-0.214282 - 0.588735i) q^{59} +(-0.475723 + 0.274659i) q^{60} +(-2.25236 + 0.397151i) q^{61} +(-4.02567 - 3.37794i) q^{62} +(-0.454125 + 0.786568i) q^{63} +(4.42697 + 7.66773i) q^{64} +(-0.449906 + 2.55154i) q^{65} +(4.30271 + 2.48417i) q^{66} +(-11.5716 - 4.21171i) q^{67} +2.25516i q^{68} +(5.01409 - 13.7761i) q^{69} +(-0.639355 - 3.62597i) q^{70} +(-2.29519 + 1.92589i) q^{71} +(-0.616409 + 0.734608i) q^{72} +12.2346 q^{73} +(-2.17186 + 7.54134i) q^{74} +1.63760 q^{75} +(1.51980 - 1.81123i) q^{76} +(5.14079 - 4.31363i) q^{77} +(-0.950560 - 5.39090i) q^{78} +(0.188725 - 0.518518i) q^{79} -3.21660i q^{80} +(7.46485 + 2.71698i) q^{81} +(-9.92654 - 5.73109i) q^{82} +(-0.303143 + 1.71921i) q^{83} +(-0.783819 - 1.35761i) q^{84} +(3.36149 - 5.82227i) q^{85} +(-1.82999 - 1.53554i) q^{86} +(-0.924336 + 0.162985i) q^{87} +(6.13624 - 3.54276i) q^{88} +(-2.18420 - 6.00103i) q^{89} +(0.385850 - 0.140438i) q^{90} +(-7.28157 - 1.28394i) q^{91} +(-1.93025 - 2.30039i) q^{92} +(4.28756 + 5.10971i) q^{93} +(6.34940 + 1.11957i) q^{94} +(-6.62353 + 2.41077i) q^{95} +(-1.05089 - 2.88730i) q^{96} +(-2.90286 + 1.67596i) q^{97} +(1.45371 - 0.256328i) q^{98} +(0.573311 + 0.481065i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{2} - 6 q^{4} - 6 q^{7} - 18 q^{8} + 6 q^{10} + 30 q^{12} - 30 q^{13} - 18 q^{14} - 18 q^{16} - 30 q^{18} - 18 q^{19} + 30 q^{22} - 30 q^{24} - 24 q^{27} + 30 q^{28} + 18 q^{29} + 24 q^{30} - 36 q^{32}+ \cdots - 12 q^{99}+O(q^{100}) $ 72 * q + 6 * q^2 - 6 * q^4 - 6 * q^7 - 18 * q^8 + 6 * q^10 + 30 * q^12 - 30 * q^13 - 18 * q^14 - 18 * q^16 - 30 * q^18 - 18 * q^19 + 30 * q^22 - 30 * q^24 - 24 * q^27 + 30 * q^28 + 18 * q^29 + 24 * q^30 - 36 * q^32 - 12 * q^33 + 66 * q^34 - 6 * q^35 - 12 * q^36 - 48 * q^37 - 48 * q^38 + 24 * q^39 + 6 * q^41 + 84 * q^42 + 24 * q^44 - 36 * q^45 - 54 * q^46 + 66 * q^47 - 24 * q^48 - 60 * q^49 + 6 * q^50 - 180 * q^51 - 42 * q^52 + 24 * q^53 + 6 * q^54 + 12 * q^55 - 156 * q^56 - 18 * q^57 + 54 * q^58 + 6 * q^59 + 48 * q^63 - 18 * q^65 + 126 * q^66 + 30 * q^67 + 54 * q^69 - 60 * q^71 + 30 * q^72 + 24 * q^73 + 6 * q^74 - 12 * q^75 + 36 * q^76 + 42 * q^77 + 96 * q^78 - 72 * q^79 + 48 * q^81 - 72 * q^82 + 48 * q^83 + 12 * q^84 - 12 * q^85 + 60 * q^86 + 84 * q^87 + 90 * q^88 + 12 * q^89 + 24 * q^90 + 24 * q^91 - 102 * q^92 + 18 * q^93 - 66 * q^94 + 24 * q^95 + 102 * q^96 - 72 * q^97 - 54 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

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 $

$2$	0.829311	−	0.988334i	0.586411	−	0.698858i	−0.388501	−	0.921448i	$-0.627007\pi$
$2$	0.829311	−	0.988334i	0.586411	−	0.698858i	0.974912	+	0.222591i	$0.0714514\pi$
$3$	−1.25448	+	1.05263i	−0.724272	+	0.607736i	−0.928563	−	0.371174i	$-0.878955\pi$
$3$	−1.25448	+	1.05263i	−0.724272	+	0.607736i	0.204292	+	0.978910i	$0.434511\pi$
$4$	0.0582485	+	0.330344i	0.0291243	+	0.165172i
$5$	0.342020	−	0.939693i	0.152956	−	0.420243i
$5$	0.342020	−	0.939693i	0.152956	−	0.420243i
$6$			2.11280i			0.862546i
$7$	2.68169	+	0.976055i	1.01358	+	0.368914i	0.794808	−	0.606861i	$-0.207572\pi$
$7$	2.68169	+	0.976055i	1.01358	+	0.368914i	0.218775	+	0.975775i	$0.429794\pi$
$8$	2.60945	+	1.50657i	0.922580	+	0.532652i
$9$	−0.0552654	+	0.313426i	−0.0184218	+	0.104475i
$10$	−0.645089	−	1.11733i	−0.203995	−	0.353330i
$11$	1.17577	−	2.03650i	0.354509	−	0.614027i	−0.632525	−	0.774540i	$-0.717981\pi$
$11$	1.17577	−	2.03650i	0.354509	−	0.614027i	0.987034	+	0.160513i	$0.0513148\pi$
$12$	−0.420801	−	0.353094i	−0.121475	−	0.101930i
$13$	−2.55154	+	0.449906i	−0.707671	+	0.124781i	−0.515888	−	0.856656i	$-0.672538\pi$
$13$	−2.55154	+	0.449906i	−0.707671	+	0.124781i	−0.191783	+	0.981437i	$0.561427\pi$
$14$	3.18862	−	1.84095i	0.852195	−	0.492015i
$15$	0.560093	+	1.53884i	0.144615	+	0.397327i
$16$	3.02262	−	1.10014i	0.755654	−	0.275035i
$17$	6.62084	+	1.16743i	1.60579	+	0.283144i	0.903449	−	0.428696i	$-0.141027\pi$
$17$	6.62084	+	1.16743i	1.60579	+	0.283144i	0.702342	+	0.711840i	$0.252138\pi$
$18$	0.263937	+	0.314548i	0.0622105	+	0.0741396i
$19$	−4.53076	−	5.39955i	−1.03943	−	1.23874i	−0.970495	−	0.241121i	$-0.922485\pi$
$19$	−4.53076	−	5.39955i	−1.03943	−	1.23874i	−0.0689331	−	0.997621i	$-0.521960\pi$
$20$	0.330344	+	0.0582485i	0.0738672	+	0.0130248i
$21$	−4.39154	+	1.59839i	−0.958312	+	0.348797i
$22$	−1.03766	−	2.85095i	−0.221230	−	0.607824i
$23$	−7.75287	+	4.47612i	−1.61659	+	0.933336i	−0.628790	+	0.777575i	$0.716450\pi$
$23$	−7.75287	+	4.47612i	−1.61659	+	0.933336i	−0.987795	+	0.155761i	$0.950217\pi$
$24$	−4.85935	+	0.856835i	−0.991911	+	0.174901i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	−1.67136	+	2.89489i	−0.327782	+	0.567734i
$27$	−2.71699	−	4.70597i	−0.522886	−	0.905665i
$28$	−0.166229	+	0.942733i	−0.0314144	+	0.178160i
$29$	0.496364	+	0.286576i	0.0921726	+	0.0532159i	0.545378	−	0.838190i	$-0.316386\pi$
$29$	0.496364	+	0.286576i	0.0921726	+	0.0532159i	−0.453205	+	0.891406i	$0.649720\pi$
$30$	1.98538	+	0.722620i	0.362479	+	0.131932i
$31$		−	4.07319i		−	0.731566i	−0.930700	−	0.365783i	$-0.880801\pi$
$31$		−	4.07319i		−	0.731566i	0.930700	−	0.365783i	$-0.119199\pi$
$32$	−0.641726	+	1.76313i	−0.113442	+	0.311680i
$33$	0.668701	+	3.79239i	0.116406	+	0.660171i
$34$	6.64455	−	5.57544i	1.13953	−	0.956180i
$35$	1.83438	−	2.18613i	0.310067	−	0.369524i
$36$	−0.106757			−0.0177929
$37$	−5.55973	+	2.46767i	−0.914014	+	0.405683i
$37$	−5.55973	+	2.46767i	−0.914014	+	0.405683i
$38$	−9.09397			−1.47524
$39$	2.72726	−	3.25023i	0.436712	−	0.520453i
$40$	2.30819	−	1.93681i	0.364958	−	0.306236i
$41$	−1.54272	−	8.74921i	−0.240933	−	1.36640i	−0.829752	−	0.558133i	$-0.811518\pi$
$41$	−1.54272	−	8.74921i	−0.240933	−	1.36640i	0.588819	−	0.808265i	$-0.299593\pi$
$42$	−2.06221	+	5.66587i	−0.318205	+	0.874262i
$43$		−	1.85159i		−	0.282365i	−0.989984	−	0.141182i	$-0.954910\pi$
$43$		−	1.85159i		−	0.282365i	0.989984	−	0.141182i	$-0.0450904\pi$
$44$	0.741232	+	0.269786i	0.111745	+	0.0406718i
$45$	0.275622	+	0.159130i	0.0410873	+	0.0237217i
$46$	−2.00563	+	11.3745i	−0.295715	+	1.67708i
$47$	2.49863	+	4.32775i	0.364462	+	0.631267i	0.988690	−	0.149975i	$-0.0479194\pi$
$47$	2.49863	+	4.32775i	0.364462	+	0.631267i	−0.624227	+	0.781243i	$0.714586\pi$
$48$	−2.63375	+	4.56180i	−0.380150	+	0.658439i
$49$	0.876457	+	0.735435i	0.125208	+	0.105062i
$50$	−1.27058	+	0.224037i	−0.179687	+	0.0316836i
$51$	−9.53456	+	5.50478i	−1.33511	+	0.770824i
$52$	−0.297247	−	0.816680i	−0.0412208	−	0.113253i
$53$	12.8323	−	4.67057i	1.76265	−	0.641552i	0.762663	−	0.646796i	$-0.223891\pi$
$53$	12.8323	−	4.67057i	1.76265	−	0.641552i	0.999986	+	0.00524360i	$0.00166910\pi$
$54$	−6.90430	−	1.21742i	−0.939557	−	0.165669i
$55$	−1.51154	−	1.80139i	−0.203817	−	0.242899i
$56$	5.52724	+	6.58711i	0.738609	+	0.880239i
$57$	11.3675	+	2.00439i	1.50566	+	0.265488i
$58$	0.694873	−	0.252913i	0.0912413	−	0.0332091i
$59$	−0.214282	−	0.588735i	−0.0278971	−	0.0766467i	0.924962	−	0.380059i	$-0.124096\pi$
$59$	−0.214282	−	0.588735i	−0.0278971	−	0.0766467i	−0.952859	+	0.303412i	$0.901874\pi$
$60$	−0.475723	+	0.274659i	−0.0614155	+	0.0354583i
$61$	−2.25236	+	0.397151i	−0.288385	+	0.0508500i	−0.315969	−	0.948769i	$-0.602330\pi$
$61$	−2.25236	+	0.397151i	−0.288385	+	0.0508500i	0.0275844	+	0.999619i	$0.491218\pi$
$62$	−4.02567	−	3.37794i	−0.511260	−	0.428998i
$63$	−0.454125	+	0.786568i	−0.0572144	+	0.0990982i
$64$	4.42697	+	7.66773i	0.553371	+	0.958467i
$65$	−0.449906	+	2.55154i	−0.0558040	+	0.316480i
$66$	4.30271	+	2.48417i	0.529627	+	0.305780i
$67$	−11.5716	−	4.21171i	−1.41369	−	0.514542i	−0.481481	−	0.876456i	$-0.659901\pi$
$67$	−11.5716	−	4.21171i	−1.41369	−	0.514542i	−0.932211	+	0.361914i	$0.882123\pi$
$68$			2.25516i			0.273478i
$69$	5.01409	−	13.7761i	0.603625	−	1.65845i
$70$	−0.639355	−	3.62597i	−0.0764176	−	0.433386i
$71$	−2.29519	+	1.92589i	−0.272389	+	0.228562i	−0.768742	−	0.639559i	$-0.779117\pi$
$71$	−2.29519	+	1.92589i	−0.272389	+	0.228562i	0.496353	+	0.868121i	$0.334672\pi$
$72$	−0.616409	+	0.734608i	−0.0726445	+	0.0865743i
$73$	12.2346			1.43196			0.715978	−	0.698123i	$-0.245981\pi$
$73$	12.2346			1.43196			0.715978	+	0.698123i	$0.245981\pi$
$74$	−2.17186	+	7.54134i	−0.252474	+	0.876662i
$75$	1.63760			0.189094
$76$	1.51980	−	1.81123i	0.174333	−	0.207762i
$77$	5.14079	−	4.31363i	0.585847	−	0.491584i
$78$	−0.950560	−	5.39090i	−0.107630	−	0.610399i
$79$	0.188725	−	0.518518i	0.0212332	−	0.0583378i	−0.928623	−	0.371024i	$-0.879007\pi$
$79$	0.188725	−	0.518518i	0.0212332	−	0.0583378i	0.949856	+	0.312686i	$0.101229\pi$
$80$		−	3.21660i		−	0.359627i
$81$	7.46485	+	2.71698i	0.829428	+	0.301887i
$82$	−9.92654	−	5.73109i	−1.09620	−	0.632893i
$83$	−0.303143	+	1.71921i	−0.0332743	+	0.188708i	−0.996914	−	0.0784954i	$-0.974988\pi$
$83$	−0.303143	+	1.71921i	−0.0332743	+	0.188708i	0.963640	+	0.267203i	$0.0860995\pi$
$84$	−0.783819	−	1.35761i	−0.0855216	−	0.148128i
$85$	3.36149	−	5.82227i	0.364605	−	0.631514i
$86$	−1.82999	−	1.53554i	−0.197333	−	0.165582i
$87$	−0.924336	+	0.162985i	−0.0990992	+	0.0174739i
$88$	6.13624	−	3.54276i	0.654126	−	0.377660i
$89$	−2.18420	−	6.00103i	−0.231524	−	0.636108i	0.768469	−	0.639887i	$-0.221019\pi$
$89$	−2.18420	−	6.00103i	−0.231524	−	0.636108i	−0.999993	+	0.00377986i	$0.998797\pi$
$90$	0.385850	−	0.140438i	0.0406722	−	0.0148035i
$91$	−7.28157	−	1.28394i	−0.763316	−	0.134593i
$92$	−1.93025	−	2.30039i	−0.201243	−	0.239832i
$93$	4.28756	+	5.10971i	0.444599	+	0.529852i
$94$	6.34940	+	1.11957i	0.654891	+	0.115475i
$95$	−6.62353	+	2.41077i	−0.679560	+	0.247340i
$96$	−1.05089	−	2.88730i	−0.107256	−	0.294684i
$97$	−2.90286	+	1.67596i	−0.294740	+	0.170168i	−0.640078	−	0.768310i	$-0.721098\pi$
$97$	−2.90286	+	1.67596i	−0.294740	+	0.170168i	0.345337	+	0.938479i	$0.387765\pi$
$98$	1.45371	−	0.256328i	0.146847	−	0.0258931i
$99$	0.573311	+	0.481065i	0.0576199	+	0.0483489i
$100$	0.167720	−	0.290500i	0.0167720	−	0.0290500i
$101$	−0.441106	−	0.764018i	−0.0438917	−	0.0760226i	0.843245	−	0.537529i	$-0.180642\pi$
$101$	−0.441106	−	0.764018i	−0.0438917	−	0.0760226i	−0.887137	+	0.461507i	$0.847309\pi$
$102$	−2.46655	+	13.9885i	−0.244225	+	1.38507i
$103$	−4.32531	−	2.49722i	−0.426186	−	0.246059i	0.271535	−	0.962429i	$-0.412469\pi$
$103$	−4.32531	−	2.49722i	−0.426186	−	0.246059i	−0.697720	+	0.716370i	$0.745802\pi$
$104$	−7.33594	−	2.67006i	−0.719348	−	0.261821i
$105$			4.67338i			0.456075i
$106$	6.02587	−	16.5559i	0.585284	−	1.60805i
$107$	1.31674	+	7.46760i	0.127294	+	0.721920i	0.979919	+	0.199397i	$0.0638983\pi$
$107$	1.31674	+	7.46760i	0.127294	+	0.721920i	−0.852625	+	0.522524i	$0.824991\pi$
$108$	1.39633	−	1.17166i	0.134362	−	0.112743i
$109$	2.70074	−	3.21862i	0.258684	−	0.308288i	−0.621034	−	0.783784i	$-0.713287\pi$
$109$	2.70074	−	3.21862i	0.258684	−	0.308288i	0.879718	+	0.475496i	$0.157731\pi$
$110$	−3.03391			−0.289272
$111$	4.37700	−	8.94797i	0.415446	−	0.849304i
$112$	9.17951			0.867382
$113$	−8.85914	+	10.5579i	−0.833398	+	0.993205i	0.166576	+	0.986029i	$0.446729\pi$
$113$	−8.85914	+	10.5579i	−0.833398	+	0.993205i	−0.999974	+	0.00717669i	$0.997716\pi$
$114$	11.4082	−	9.57259i	1.06847	−	0.896555i
$115$	1.55454	+	8.81624i	0.144962	+	0.822118i
$116$	−0.0657562	+	0.180664i	−0.00610531	+	0.0167742i
$117$		−	0.824583i		−	0.0762327i
$118$	−0.759573	−	0.276462i	−0.0699243	−	0.0254504i
$119$	16.6156	+	9.59300i	1.52315	+	0.879389i
$120$	−0.856835	+	4.85935i	−0.0782179	+	0.443596i
$121$	2.73512	+	4.73736i	0.248647	+	0.430669i
$122$	−1.47539	+	2.55544i	−0.133575	+	0.231359i
$123$	11.1450	+	9.35176i	1.00491	+	0.843220i
$124$	1.34555	−	0.237257i	0.120834	−	0.0213063i
$125$	−0.866025	+	0.500000i	−0.0774597	+	0.0447214i
$126$	0.400781	+	1.10114i	0.0357044	+	0.0980970i
$127$	7.38236	−	2.68696i	0.655078	−	0.238429i	0.00696839	−	0.999976i	$-0.497782\pi$
$127$	7.38236	−	2.68696i	0.655078	−	0.238429i	0.648110	+	0.761547i	$0.275560\pi$
$128$	7.55406	+	1.33198i	0.667691	+	0.117732i
$129$	1.94904	+	2.32278i	0.171603	+	0.204509i
$130$	2.14866	+	2.56068i	0.188450	+	0.224586i
$131$	0.191601	+	0.0337844i	0.0167402	+	0.00295175i	0.182012	−	0.983296i	$-0.441739\pi$
$131$	0.191601	+	0.0337844i	0.0167402	+	0.00295175i	−0.165272	+	0.986248i	$0.552850\pi$
$132$	−1.21384	+	0.441803i	−0.105651	+	0.0384540i
$133$	−6.87983	−	18.9022i	−0.596557	−	1.63903i
$134$	−13.7590	+	7.94376i	−1.18860	+	0.686237i
$135$	−5.35143	+	0.943602i	−0.460578	+	0.0812124i
$136$	15.5180	+	13.0211i	1.33065	+	1.11655i
$137$	−6.65526	+	11.5272i	−0.568597	+	0.984839i	0.428108	+	0.903727i	$0.359180\pi$
$137$	−6.65526	+	11.5272i	−0.568597	+	0.984839i	−0.996705	+	0.0811112i	$0.974153\pi$
$138$	−9.45714	−	16.3802i	−0.805045	−	1.39438i
$139$	−1.77564	+	10.0702i	−0.150608	+	0.854140i	0.812084	+	0.583540i	$0.198333\pi$
$139$	−1.77564	+	10.0702i	−0.150608	+	0.854140i	−0.962692	+	0.270599i	$0.912778\pi$
$140$	0.829026	+	0.478638i	0.0700655	+	0.0404523i
$141$	−7.68999	−	2.79893i	−0.647614	−	0.235712i
$142$			3.86558i			0.324392i
$143$	−2.08380	+	5.72520i	−0.174256	+	0.478765i
$144$	0.177767	+	1.00816i	0.0148139	+	0.0840137i
$145$	0.439060	−	0.368415i	0.0364620	−	0.0305952i
$146$	10.1463	−	12.0919i	0.839715	−	1.00073i
$147$	−1.87364			−0.154535
$148$	−1.13903	−	1.69288i	−0.0936274	−	0.139154i
$149$	11.8503			0.970814			0.485407	−	0.874288i	$-0.338671\pi$
$149$	11.8503			0.970814			0.485407	+	0.874288i	$0.338671\pi$
$150$	1.35808	−	1.61850i	0.110887	−	0.132150i
$151$	−10.0127	+	8.40164i	−0.814821	+	0.683716i	−0.951753	−	0.306864i	$-0.900720\pi$
$151$	−10.0127	+	8.40164i	−0.814821	+	0.683716i	0.136932	+	0.990580i	$0.456276\pi$
$152$	−3.68801	−	20.9158i	−0.299137	−	1.69649i
$153$	−0.731807	+	2.01062i	−0.0591631	+	0.162549i
$154$		−	8.65816i		−	0.697694i
$155$	−3.82754	−	1.39311i	−0.307436	−	0.111897i
$156$	1.23255	+	0.711614i	0.0986831	+	0.0569747i
$157$	0.223084	−	1.26517i	0.0178040	−	0.100972i	−0.974611	−	0.223906i	$-0.928119\pi$
$157$	0.223084	−	1.26517i	0.0178040	−	0.100972i	0.992415	+	0.122934i	$0.0392303\pi$
$158$	−0.355957	−	0.616536i	−0.0283184	−	0.0490489i
$159$	−11.1814	+	19.3668i	−0.886743	+	1.53588i
$160$	1.43731	+	1.20605i	0.113630	+	0.0953466i
$161$	−25.1597	+	4.43634i	−1.98286	+	0.349632i
$162$	8.87597	−	5.12454i	0.697362	−	0.402622i
$163$	−4.49222	−	12.3423i	−0.351857	−	0.966720i	−0.981773	−	0.190057i	$-0.939133\pi$
$163$	−4.49222	−	12.3423i	−0.351857	−	0.966720i	0.629916	−	0.776664i	$-0.283089\pi$
$164$	2.80039	−	1.01926i	0.218674	−	0.0795907i
$165$	3.79239	+	0.668701i	0.295237	+	0.0520583i
$166$	1.44775	+	1.72537i	0.112368	+	0.133914i
$167$	−3.40703	−	4.06035i	−0.263644	−	0.314199i	0.617940	−	0.786225i	$-0.287967\pi$
$167$	−3.40703	−	4.06035i	−0.263644	−	0.314199i	−0.881585	+	0.472026i	$0.843523\pi$
$168$	−13.8676	−	2.44523i	−1.06991	−	0.188653i
$169$	−5.90805	+	2.15035i	−0.454465	+	0.165412i
$170$	−2.96663	−	8.15075i	−0.227530	−	0.625134i
$171$	1.94275	−	1.12165i	0.148566	−	0.0857746i
$172$	0.611662	−	0.107852i	0.0466388	−	0.00822368i
$173$	8.41510	+	7.06111i	0.639788	+	0.536846i	0.903953	−	0.427631i	$-0.140652\pi$
$173$	8.41510	+	7.06111i	0.639788	+	0.536846i	−0.264165	+	0.964478i	$0.585096\pi$
$174$	−0.605478	+	1.04872i	−0.0459011	+	0.0795031i
$175$	−1.42690	−	2.47146i	−0.107863	−	0.186825i
$176$	1.31347	−	7.44907i	0.0990066	−	0.561495i
$177$	0.888531	+	0.512994i	0.0667861	+	0.0385590i
$178$	−7.74240	−	2.81800i	−0.580317	−	0.211218i
$179$			23.6348i			1.76655i	0.468857	+	0.883274i	$0.344666\pi$
$179$			23.6348i			1.76655i	−0.468857	+	0.883274i	$0.655334\pi$
$180$	−0.0365132	+	0.100319i	−0.00272153	+	0.00747734i
$181$	1.23808	+	7.02152i	0.0920260	+	0.521905i	0.995618	+	0.0935116i	$0.0298092\pi$
$181$	1.23808	+	7.02152i	0.0920260	+	0.521905i	−0.903592	+	0.428394i	$0.859080\pi$
$182$	−7.30765	+	6.13184i	−0.541679	+	0.454522i
$183$	2.40747	−	2.86912i	0.177966	−	0.212091i
$184$	−26.9743			−1.98857
$185$	0.417313	+	6.06843i	0.0306815	+	0.446160i
$186$	8.60582			0.631009
$187$	10.1621	−	12.1107i	0.743125	−	0.885622i
$188$	−1.28411	+	1.07749i	−0.0936530	+	0.0785842i
$189$	−2.69285	−	15.2719i	−0.195876	−	1.11087i
$190$	−3.11032	+	8.54554i	−0.225646	+	0.619958i
$191$		−	22.0138i		−	1.59286i	−0.604729	−	0.796431i	$-0.706719\pi$
$191$		−	22.0138i		−	1.59286i	0.604729	−	0.796431i	$-0.293281\pi$
$192$	−13.6248	−	4.95903i	−0.983286	−	0.357887i
$193$	−8.88195	−	5.12800i	−0.639337	−	0.369121i	0.145022	−	0.989428i	$-0.453675\pi$
$193$	−8.88195	−	5.12800i	−0.639337	−	0.369121i	−0.784359	+	0.620307i	$0.787008\pi$
$194$	−0.750957	+	4.25889i	−0.0539155	+	0.305770i
$195$	−2.12143	−	3.67443i	−0.151919	−	0.263132i
$196$	−0.191894	+	0.332370i	−0.0137067	+	0.0237407i
$197$	15.4027	+	12.9244i	1.09740	+	0.920826i	0.997247	−	0.0741458i	$-0.0236230\pi$
$197$	15.4027	+	12.9244i	1.09740	+	0.920826i	0.100151	+	0.994972i	$0.468067\pi$
$198$	0.950906	−	0.167670i	0.0675779	−	0.0119158i
$199$	−10.1954	+	5.88631i	−0.722732	+	0.417270i	−0.815757	−	0.578394i	$-0.803680\pi$
$199$	−10.1954	+	5.88631i	−0.722732	+	0.417270i	0.0930253	+	0.995664i	$0.470346\pi$
$200$	−1.03055	−	2.83142i	−0.0728711	−	0.200212i
$201$	18.9496	−	6.89710i	1.33660	−	0.486484i
$202$	−1.12092	−	0.197648i	−0.0788676	−	0.0139065i
$203$	1.05138	+	1.25299i	0.0737925	+	0.0879424i
$204$	−2.37385	−	2.82904i	−0.166202	−	0.198072i
$205$	−8.74921	−	1.54272i	−0.611072	−	0.107748i
$206$	−6.05512	+	2.20388i	−0.421880	+	0.153552i
$207$	−0.974466	−	2.67732i	−0.0677300	−	0.186087i
$208$	−7.21737	+	4.16695i	−0.500435	+	0.288926i
$209$	−16.3233	+	2.87824i	−1.12911	+	0.199092i
$210$	4.61886	+	3.87568i	0.318731	+	0.267447i
$211$	7.26159	−	12.5774i	0.499909	−	0.865867i	−0.500091	−	0.865973i	$-0.666700\pi$
$211$	7.26159	−	12.5774i	0.499909	−	0.865867i	1.00000		0.000105566i	$3.36028e-5\pi$
$212$	2.29036	+	3.96701i	0.157302	+	0.272456i
$213$	0.852008	−	4.83198i	0.0583786	−	0.331081i
$214$	8.47247	+	4.89158i	0.579166	+	0.334382i
$215$	−1.73993	−	0.633281i	−0.118662	−	0.0431894i
$216$		−	16.3733i		−	1.11406i
$217$	3.97565	−	10.9230i	0.269885	−	0.741502i
$218$	−0.941316	−	5.33847i	−0.0637540	−	0.361567i
$219$	−15.3481	+	12.8785i	−1.03713	+	0.870251i
$220$	0.507032	−	0.604258i	0.0341841	−	0.0407391i
$221$	−17.4186			−1.17170
$222$	−5.21369	−	11.7466i	−0.349920	−	0.788379i
$223$	8.41603			0.563579			0.281789	−	0.959476i	$-0.409072\pi$
$223$	8.41603			0.563579			0.281789	+	0.959476i	$0.409072\pi$
$224$	−3.44182	+	4.10180i	−0.229966	+	0.274063i
$225$	0.243802	−	0.204574i	0.0162535	−	0.0136383i
$226$	3.08776	+	17.5116i	0.205395	+	1.16485i
$227$	4.53186	−	12.4512i	0.300790	−	0.826413i	−0.693573	−	0.720386i	$-0.743965\pi$
$227$	4.53186	−	12.4512i	0.300790	−	0.826413i	0.994363	−	0.106027i	$-0.0338131\pi$
$228$			3.87193i			0.256425i
$229$	−0.694444	−	0.252757i	−0.0458902	−	0.0167026i	0.318973	−	0.947764i	$-0.396662\pi$
$229$	−0.694444	−	0.252757i	−0.0458902	−	0.0167026i	−0.364863	+	0.931061i	$0.618884\pi$
$230$	10.0026	+	5.77499i	0.659551	+	0.380792i
$231$	−1.90833	+	10.8227i	−0.125559	+	0.712081i
$232$	0.863492	+	1.49561i	0.0566911	+	0.0981918i
$233$	6.83794	−	11.8437i	0.447968	−	0.775904i	−0.550285	−	0.834977i	$-0.685481\pi$
$233$	6.83794	−	11.8437i	0.447968	−	0.775904i	0.998254	+	0.0590727i	$0.0188144\pi$
$234$	−0.814963	−	0.683835i	−0.0532758	−	0.0447037i
$235$	4.92134	−	0.867765i	0.321033	−	0.0566067i
$236$	0.182003	−	0.105080i	0.0118474	−	0.00684010i
$237$	0.309056	+	0.849126i	0.0200754	+	0.0551566i
$238$	23.2605	−	8.46615i	1.50776	−	0.548779i
$239$	21.2667	+	3.74990i	1.37563	+	0.242561i	0.812092	−	0.583530i	$-0.198329\pi$
$239$	21.2667	+	3.74990i	1.37563	+	0.242561i	0.563538	+	0.826090i	$0.309440\pi$
$240$	3.38589	+	4.03515i	0.218558	+	0.260468i
$241$	11.7564	+	14.0107i	0.757296	+	0.902510i	0.997674	−	0.0681692i	$-0.0217158\pi$
$241$	11.7564	+	14.0107i	0.757296	+	0.902510i	−0.240378	+	0.970679i	$0.577271\pi$
$242$	6.95036	+	1.22554i	0.446786	+	0.0787804i
$243$	3.09439	−	1.12626i	0.198505	−	0.0722499i
$244$	−0.262393	−	0.720919i	−0.0167980	−	0.0461521i
$245$	0.990849	−	0.572067i	0.0633030	−	0.0365480i
$246$	18.4853	−	3.25946i	1.17858	−	0.207816i
$247$	13.9897	+	11.7388i	0.890145	+	0.746920i
$248$	6.13653	−	10.6288i	0.389670	−	0.674928i
$249$	−1.42941	−	2.47581i	−0.0905850	−	0.156898i
$250$	−0.224037	+	1.27058i	−0.0141694	+	0.0803584i
$251$	−17.0537	−	9.84598i	−1.07642	−	0.621473i	−0.146493	−	0.989212i	$-0.546799\pi$
$251$	−17.0537	−	9.84598i	−1.07642	−	0.621473i	−0.929929	+	0.367739i	$0.880132\pi$
$252$	−0.286290	−	0.104201i	−0.0180346	−	0.00656405i
$253$			21.0516i			1.32350i
$254$	3.46666	−	9.52456i	0.217517	−	0.597624i
$255$	1.91179	+	10.8423i	0.119721	+	0.678972i
$256$	−5.98391	+	5.02110i	−0.373994	+	0.313818i
$257$	−2.23742	+	2.66645i	−0.139566	+	0.166329i	−0.831300	−	0.555824i	$-0.812403\pi$
$257$	−2.23742	+	2.66645i	−0.139566	+	0.166329i	0.691734	+	0.722153i	$0.256847\pi$
$258$	3.91204			0.243553
$259$	−17.3180	+	1.19093i	−1.07609	+	0.0740005i
$260$	−0.869093			−0.0538989
$261$	−0.117252	+	0.139736i	−0.00725772	+	0.00864941i
$262$	0.192287	−	0.161348i	0.0118795	−	0.00996809i
$263$	3.59770	+	20.4036i	0.221843	+	1.25814i	0.868628	+	0.495464i	$0.165002\pi$
$263$	3.59770	+	20.4036i	0.221843	+	1.25814i	−0.646785	+	0.762673i	$0.723887\pi$
$264$	−3.96855	+	10.9035i	−0.244247	+	0.671064i
$265$		−	13.6558i		−	0.838871i
$266$	−24.3872	−	8.87621i	−1.49527	−	0.544235i
$267$	9.05688	+	5.22899i	0.554272	+	0.320009i
$268$	0.717285	−	4.06793i	0.0438152	−	0.248488i
$269$	−3.40112	−	5.89091i	−0.207370	−	0.359175i	0.743515	−	0.668719i	$-0.233157\pi$
$269$	−3.40112	−	5.89091i	−0.207370	−	0.359175i	−0.950885	+	0.309544i	$0.899824\pi$
$270$	−3.50541	+	6.07154i	−0.213332	+	0.369502i
$271$	15.4121	+	12.9323i	0.936219	+	0.785581i	0.976923	−	0.213590i	$-0.0685156\pi$
$271$	15.4121	+	12.9323i	0.936219	+	0.785581i	−0.0407041	+	0.999171i	$0.512960\pi$
$272$	21.2966	−	3.75517i	1.29130	−	0.227690i
$273$	10.4861	−	6.05414i	0.634646	−	0.366413i
$274$	5.87349	+	16.1373i	0.354830	+	0.974889i
$275$	−2.20973	+	0.804276i	−0.133252	+	0.0484997i
$276$	4.84291	+	0.853936i	0.291509	+	0.0514009i
$277$	7.24002	+	8.62832i	0.435011	+	0.518426i	0.938361	−	0.345657i	$-0.112344\pi$
$277$	7.24002	+	8.62832i	0.435011	+	0.518426i	−0.503350	+	0.864082i	$0.667899\pi$
$278$	8.48012	+	10.1062i	0.508604	+	0.606131i
$279$	1.27664	+	0.225106i	0.0764305	+	0.0134768i
$280$	8.08029	−	2.94098i	0.482889	−	0.175757i
$281$	5.88669	+	16.1735i	0.351170	+	0.964833i	0.981995	+	0.188907i	$0.0604945\pi$
$281$	5.88669	+	16.1735i	0.351170	+	0.964833i	−0.630825	+	0.775925i	$0.717283\pi$
$282$	−9.14367	+	5.27910i	−0.544497	+	0.314366i
$283$	−21.6004	+	3.80874i	−1.28401	+	0.226406i	−0.773683	−	0.633573i	$-0.781588\pi$
$283$	−21.6004	+	3.80874i	−1.28401	+	0.226406i	−0.510330	+	0.859979i	$0.670477\pi$
$284$	−0.769899	−	0.646022i	−0.0456851	−	0.0383344i
$285$	5.77141	−	9.99638i	0.341869	−	0.592134i
$286$	3.93029	+	6.80746i	0.232403	+	0.402534i
$287$	4.40261	−	24.9684i	0.259878	−	1.47384i
$288$	−0.517144	−	0.298573i	−0.0304730	−	0.0175936i
$289$	26.4979	+	9.64445i	1.55870	+	0.567321i
$290$		−	0.739469i		−	0.0434231i
$291$	1.87739	−	5.15809i	0.110055	−	0.302373i
$292$	0.712650	+	4.04164i	0.0417047	+	0.236519i
$293$	17.9516	−	15.0632i	1.04874	−	0.880001i	0.0557832	−	0.998443i	$-0.482234\pi$
$293$	17.9516	−	15.0632i	1.04874	−	0.880001i	0.992961	+	0.118442i	$0.0377900\pi$
$294$	−1.55383	+	1.85178i	−0.0906210	+	0.107998i
$295$	−0.626518			−0.0364773
$296$	−18.2256	−	1.93684i	−1.05934	−	0.112576i
$297$	−12.7783			−0.741471
$298$	9.82757	−	11.7120i	0.569296	−	0.678461i
$299$	17.7679	−	14.9091i	1.02755	−	0.862214i
$300$	0.0953879	+	0.540972i	0.00550722	+	0.0312330i
$301$	1.80725	−	4.96539i	0.104168	−	0.286200i
$302$			16.8635i			0.970383i
$303$	1.35758	+	0.494120i	0.0779912	+	0.0283865i
$304$	−19.6350	−	11.3363i	−1.12615	−	0.650181i
$305$	−0.397151	+	2.25236i	−0.0227408	+	0.128970i
$306$	1.38027	+	2.39070i	0.0789049	+	0.136667i
$307$	−5.85992	+	10.1497i	−0.334443	+	0.579273i	−0.983378	−	0.181571i	$-0.941882\pi$
$307$	−5.85992	+	10.1497i	−0.334443	+	0.579273i	0.648934	+	0.760844i	$0.275215\pi$
$308$	1.72443	+	1.44697i	0.0982583	+	0.0824485i
$309$	8.05465	−	1.42025i	0.458213	−	0.0807953i
$310$	−4.55108	+	2.62757i	−0.258484	+	0.149236i
$311$	−4.31379	−	11.8520i	−0.244612	−	0.672067i	−0.999862	−	0.0166295i	$-0.994706\pi$
$311$	−4.31379	−	11.8520i	−0.244612	−	0.672067i	0.755249	−	0.655438i	$-0.227516\pi$
$312$	12.0133	−	4.37250i	0.680122	−	0.247544i
$313$	−28.6761	−	5.05637i	−1.62087	−	0.285803i	−0.711778	−	0.702404i	$-0.752110\pi$
$313$	−28.6761	−	5.05637i	−1.62087	−	0.285803i	−0.909089	+	0.416602i	$0.863221\pi$
$314$	−1.06541	−	1.26970i	−0.0601244	−	0.0716534i
$315$	0.583812	+	0.695760i	0.0328941	+	0.0392016i
$316$	0.182282	+	0.0321413i	0.0102542	+	0.00180809i
$317$	−0.114150	+	0.0415473i	−0.00641132	+	0.00233353i	−0.345224	−	0.938520i	$-0.612197\pi$
$317$	−0.114150	+	0.0415473i	−0.00641132	+	0.00233353i	0.338812	+	0.940854i	$0.389975\pi$
$318$	9.86797	+	27.1120i	0.553368	+	1.52037i
$319$	1.16722	−	0.673897i	0.0653520	−	0.0377310i
$320$	8.71943	−	1.53747i	0.487431	−	0.0859472i
$321$	−9.51244	−	7.98189i	−0.530933	−	0.445505i
$322$	−16.4806	+	28.5453i	−0.918430	+	1.59077i
$323$	−23.6939	−	41.0390i	−1.31836	−	2.28347i
$324$	−0.462722	+	2.62423i	−0.0257068	+	0.145790i
$325$	2.24379	+	1.29545i	0.124463	+	0.0718588i
$326$	−15.9237	−	5.79576i	−0.881933	−	0.320997i
$327$			6.88056i			0.380496i
$328$	9.15562	−	25.1549i	0.505534	−	1.38894i
$329$	2.47642	+	14.0445i	0.136529	+	0.774297i
$330$	3.80597	−	3.19359i	0.209512	−	0.175801i
$331$	16.9850	−	20.2419i	0.933579	−	1.11260i	−0.0598575	−	0.998207i	$-0.519065\pi$
$331$	16.9850	−	20.2419i	0.933579	−	1.11260i	0.993436	−	0.114389i	$-0.0364909\pi$
$332$	−0.585589			−0.0321384
$333$	−0.466171	−	1.87894i	−0.0255460	−	0.102965i
$334$	−6.83847			−0.374184
$335$	−7.91542	+	9.43323i	−0.432466	+	0.515393i
$336$	−11.5155	+	9.66263i	−0.628221	+	0.527140i
$337$	−5.42237	−	30.7518i	−0.295375	−	1.67516i	−0.665673	−	0.746244i	$-0.731855\pi$
$337$	−5.42237	−	30.7518i	−0.295375	−	1.67516i	0.370298	−	0.928913i	$-0.379256\pi$
$338$	−2.77434	+	7.62244i	−0.150904	+	0.414606i
$339$		−	22.5701i		−	1.22584i
$340$	2.11915	+	0.771309i	0.114927	+	0.0418301i
$341$	−8.29504	−	4.78914i	−0.449201	−	0.259347i
$342$	0.502582	−	2.85028i	0.0271765	−	0.154126i
$343$	−8.35571	−	14.4725i	−0.451166	−	0.781443i
$344$	2.78955	−	4.83164i	0.150402	−	0.260504i
$345$	−11.2304	−	9.42340i	−0.604623	−	0.507339i
$346$	13.9575	−	2.46108i	0.750358	−	0.132308i
$347$	−2.40327	+	1.38753i	−0.129014	+	0.0744863i	−0.563118	−	0.826376i	$-0.690398\pi$
$347$	−2.40327	+	1.38753i	−0.129014	+	0.0744863i	0.434104	+	0.900863i	$0.357065\pi$
$348$	−0.107682	−	0.295855i	−0.00577238	−	0.0158595i
$349$	−18.2247	+	6.63323i	−0.975544	+	0.355069i	−0.780106	−	0.625647i	$-0.784835\pi$
$349$	−18.2247	+	6.63323i	−0.975544	+	0.355069i	−0.195438	+	0.980716i	$0.562613\pi$
$350$	−3.62597	−	0.639355i	−0.193816	−	0.0341750i
$351$	9.04977	+	10.7851i	0.483041	+	0.575666i
$352$	2.83608	+	3.37991i	0.151164	+	0.180150i
$353$	32.5635	+	5.74182i	1.73318	+	0.305606i	0.949082	−	0.315030i	$-0.102015\pi$
$353$	32.5635	+	5.74182i	1.73318	+	0.305606i	0.784098	+	0.620637i	$0.213126\pi$
$354$	1.24388	−	0.452734i	0.0661113	−	0.0240626i
$355$	1.02475	+	2.81547i	0.0543879	+	0.149430i
$356$	1.85518	−	1.07109i	0.0983242	−	0.0567675i
$357$	−30.9417	+	5.45586i	−1.63761	+	0.288755i
$358$	23.3591	+	19.6006i	1.23457	+	1.03592i
$359$	2.73471	−	4.73666i	0.144332	−	0.249991i	−0.784791	−	0.619760i	$-0.787230\pi$
$359$	2.73471	−	4.73666i	0.144332	−	0.249991i	0.929124	+	0.369769i	$0.120563\pi$
$360$	0.479481	+	0.830485i	0.0252709	+	0.0437704i
$361$	−5.32804	+	30.2168i	−0.280423	+	1.59036i
$362$	7.96636	+	4.59938i	0.418703	+	0.241738i
$363$	−8.41783	−	3.06384i	−0.441821	−	0.160810i
$364$		−	2.48021i		−	0.129998i
$365$	4.18449	−	11.4968i	0.219026	−	0.601770i
$366$	−0.839100	−	4.75878i	−0.0438605	−	0.248745i
$367$	1.99764	−	1.67622i	0.104276	−	0.0874978i	−0.589159	−	0.808017i	$-0.700541\pi$
$367$	1.99764	−	1.67622i	0.104276	−	0.0874978i	0.693435	+	0.720519i	$0.256096\pi$
$368$	−18.5096	+	22.0588i	−0.964878	+	1.14990i
$369$	2.82749			0.147193
$370$	6.34372	+	4.62017i	0.329794	+	0.240191i
$371$	38.9709			2.02327
$372$	−1.43822	+	1.71400i	−0.0745682	+	0.0888669i
$373$	−9.88776	+	8.29681i	−0.511969	+	0.429593i	−0.861821	−	0.507212i	$-0.830676\pi$
$373$	−9.88776	+	8.29681i	−0.511969	+	0.429593i	0.349853	+	0.936805i	$0.386232\pi$
$374$	−3.54189	−	20.0871i	−0.183147	−	1.03868i
$375$	0.560093	−	1.53884i	0.0289231	−	0.0794655i
$376$			15.0574i			0.776526i
$377$	−1.39543	−	0.507894i	−0.0718682	−	0.0261579i
$378$	−17.3269	−	10.0037i	−0.891201	−	0.514535i
$379$	0.171916	−	0.974984i	0.00883073	−	0.0500816i	−0.980074	−	0.198633i	$-0.936350\pi$
$379$	0.171916	−	0.974984i	0.00883073	−	0.0500816i	0.988905	+	0.148551i	$0.0474610\pi$
$380$	−1.18219	−	2.04762i	−0.0606453	−	0.105041i
$381$	−6.43262	+	11.1416i	−0.329553	+	0.570802i
$382$	−21.7570	−	18.2563i	−1.11318	−	0.934072i
$383$	1.25724	−	0.221686i	0.0642422	−	0.0113276i	−0.141435	−	0.989948i	$-0.545172\pi$
$383$	1.25724	−	0.221686i	0.0642422	−	0.0113276i	0.205677	+	0.978620i	$0.434060\pi$
$384$	−10.8785	+	6.28069i	−0.555140	+	0.320510i
$385$	−2.29524	−	6.30611i	−0.116976	−	0.321389i
$386$	−12.4341	+	4.52563i	−0.632878	+	0.230349i
$387$	0.580336	+	0.102329i	0.0295001	+	0.00520167i
$388$	−0.722732	−	0.861318i	−0.0366912	−	0.0437268i
$389$	11.7099	+	13.9554i	0.593718	+	0.707565i	0.976316	−	0.216350i	$-0.0694151\pi$
$389$	11.7099	+	13.9554i	0.593718	+	0.707565i	−0.382598	+	0.923915i	$0.624971\pi$
$390$	−5.39090	−	0.950560i	−0.272979	−	0.0481335i
$391$	−56.5561	+	20.5847i	−2.86017	+	1.04102i
$392$	1.17909	+	3.23952i	0.0595530	+	0.163621i
$393$	−0.275921	+	0.159303i	−0.0139184	+	0.00803577i
$394$	25.5473	−	4.50467i	1.28705	−	0.226942i
$395$	−0.422700	−	0.354687i	−0.0212683	−	0.0178462i
$396$	−0.125522	+	0.217411i	−0.00630774	+	0.0109253i
$397$	−3.13082	−	5.42274i	−0.157131	−	0.272160i	0.776702	−	0.629869i	$-0.216891\pi$
$397$	−3.13082	−	5.42274i	−0.157131	−	0.272160i	−0.933833	+	0.357709i	$0.883558\pi$
$398$	−2.63750	+	14.9580i	−0.132206	+	0.749778i
$399$	28.5276	+	16.4704i	1.42817	+	0.824552i
$400$	−3.02262	−	1.10014i	−0.151131	−	0.0550071i
$401$		−	13.5132i		−	0.674817i	−0.941358	−	0.337409i	$-0.890450\pi$
$401$		−	13.5132i		−	0.674817i	0.941358	−	0.337409i	$-0.109550\pi$
$402$	8.89849	−	24.4484i	0.443816	−	1.21938i
$403$	1.83255	+	10.3929i	0.0912858	+	0.517708i
$404$	0.226695	−	0.190220i	0.0112785	−	0.00946378i
$405$	5.10626	−	6.08540i	0.253732	−	0.302386i
$406$	2.11029			0.104732
$407$	−1.51157	+	14.2238i	−0.0749257	+	0.705048i
$408$	−33.1733			−1.64232
$409$	10.5817	−	12.6108i	0.523234	−	0.623566i	−0.438108	−	0.898922i	$-0.644351\pi$
$409$	10.5817	−	12.6108i	0.523234	−	0.623566i	0.961342	+	0.275356i	$0.0887958\pi$
$410$	−8.78054	+	7.36775i	−0.433640	+	0.363867i
$411$	−3.78506	−	21.4662i	−0.186703	−	1.05885i
$412$	0.572999	−	1.57430i	0.0282296	−	0.0775602i
$413$		−	1.78795i		−	0.0879794i
$414$	−3.45422	−	1.25723i	−0.169766	−	0.0617897i
$415$	1.51185	+	0.872867i	0.0742138	+	0.0428473i
$416$	0.844150	−	4.78741i	0.0413878	−	0.234722i
$417$	−8.37265	−	14.5019i	−0.410011	−	0.710159i
$418$	−10.6924	+	18.5199i	−0.522984	+	0.905836i
$419$	−23.1506	−	19.4256i	−1.13098	−	0.949005i	−0.131874	−	0.991267i	$-0.542099\pi$
$419$	−23.1506	−	19.4256i	−1.13098	−	0.949005i	−0.999107	+	0.0422615i	$0.986544\pi$
$420$	−1.54382	+	0.272217i	−0.0753308	+	0.0132828i
$421$	0.289164	−	0.166949i	0.0140930	−	0.00813660i	−0.492937	−	0.870065i	$-0.664077\pi$
$421$	0.289164	−	0.166949i	0.0140930	−	0.00813660i	0.507030	+	0.861928i	$0.330743\pi$
$422$	−6.40860	−	17.6075i	−0.311966	−	0.857119i
$423$	−1.49452	+	0.543959i	−0.0726658	+	0.0264482i
$424$	40.5217	+	7.14507i	1.96791	+	0.346996i
$425$	−4.32145	−	5.15010i	−0.209621	−	0.249817i
$426$	−4.06903	−	4.84928i	−0.197145	−	0.234948i
$427$	−6.42776	−	1.13339i	−0.311061	−	0.0548485i
$428$	−2.39018	+	0.869954i	−0.115534	+	0.0420508i
$429$	−3.41244	−	9.37560i	−0.164754	−	0.452658i
$430$	−2.06883	+	1.19444i	−0.0997680	+	0.0576011i
$431$	36.9030	−	6.50699i	1.77755	−	0.313431i	0.813984	−	0.580887i	$-0.197294\pi$
$431$	36.9030	−	6.50699i	1.77755	−	0.313431i	0.963570	+	0.267456i	$0.0861831\pi$
$432$	−13.3897	−	11.2353i	−0.644211	−	0.540557i
$433$	−18.9049	+	32.7443i	−0.908512	+	1.57359i	−0.0923806	+	0.995724i	$0.529448\pi$
$433$	−18.9049	+	32.7443i	−0.908512	+	1.57359i	−0.816132	+	0.577866i	$0.803886\pi$
$434$	−7.49853	−	12.9878i	−0.359941	−	0.623436i
$435$	−0.162985	+	0.924336i	−0.00781455	+	0.0443185i
$436$	1.22057	+	0.704694i	0.0584545	+	0.0337487i
$437$	59.2955	+	21.5818i	2.83649	+	1.03240i
$438$			25.8493i			1.23513i
$439$	−4.40358	+	12.0987i	−0.210171	+	0.577441i	−0.999324	−	0.0367557i	$-0.988298\pi$
$439$	−4.40358	+	12.0987i	−0.210171	+	0.577441i	0.789153	+	0.614197i	$0.210520\pi$
$440$	−1.23039	−	6.97788i	−0.0586564	−	0.332657i
$441$	−0.278942	+	0.234060i	−0.0132829	+	0.0111457i
$442$	−14.4454	+	17.2154i	−0.687099	+	0.818853i
$443$	1.16412			0.0553089			0.0276545	−	0.999618i	$-0.491196\pi$
$443$	1.16412			0.0553089			0.0276545	+	0.999618i	$0.491196\pi$
$444$	3.21086	+	0.924709i	0.152381	+	0.0438848i
$445$	−6.38616			−0.302733
$446$	6.97950	−	8.31784i	0.330489	−	0.393861i
$447$	−14.8659	+	12.4740i	−0.703133	+	0.589999i
$448$	4.38762	+	24.8834i	0.207296	+	1.17563i
$449$	7.22003	−	19.8369i	0.340734	−	0.936160i	−0.644448	−	0.764649i	$-0.722913\pi$
$449$	7.22003	−	19.8369i	0.340734	−	0.936160i	0.985182	−	0.171512i	$-0.0548652\pi$
$450$		−	0.410613i		−	0.0193565i
$451$	−19.6316	−	7.14534i	−0.924418	−	0.336461i
$452$	−4.00378	−	2.31158i	−0.188322	−	0.108728i
$453$	3.71685	−	21.0793i	0.174633	−	0.990393i
$454$	−8.54760	−	14.8049i	−0.401159	−	0.694827i
$455$	−3.69695	+	6.40331i	−0.173316	+	0.300192i
$456$	26.6431	+	22.3562i	1.24768	+	1.04693i
$457$	−24.5449	+	4.32794i	−1.14816	+	0.202452i	−0.715174	−	0.698946i	$-0.753653\pi$
$457$	−24.5449	+	4.32794i	−1.14816	+	0.202452i	−0.432990	+	0.901399i	$0.642541\pi$
$458$	−0.825718	+	0.476729i	−0.0385833	+	0.0222761i
$459$	−12.4949	−	34.3294i	−0.583211	−	1.60236i
$460$	−2.82184	+	1.02707i	−0.131569	+	0.0478872i
$461$	−16.2811	−	2.87080i	−0.758288	−	0.133707i	−0.218881	−	0.975752i	$-0.570241\pi$
$461$	−16.2811	−	2.87080i	−0.758288	−	0.133707i	−0.539407	+	0.842045i	$0.681352\pi$
$462$	9.11384	+	10.8615i	0.424014	+	0.505320i
$463$	22.0040	+	26.2233i	1.02261	+	1.21870i	0.975543	+	0.219810i	$0.0705438\pi$
$463$	22.0040	+	26.2233i	1.02261	+	1.21870i	0.0470695	+	0.998892i	$0.485012\pi$
$464$	1.81559	+	0.320138i	0.0842868	+	0.0148620i
$465$	6.26799	−	2.28136i	0.290671	−	0.105796i
$466$	−6.03471	−	16.5802i	−0.279553	−	0.768065i
$467$	−23.4156	+	13.5190i	−1.08355	+	0.625586i	−0.931851	−	0.362842i	$-0.881807\pi$
$467$	−23.4156	+	13.5190i	−1.08355	+	0.625586i	−0.151695	+	0.988427i	$0.548473\pi$
$468$	0.272396	−	0.0480308i	0.0125915	−	0.00222022i
$469$	−26.9205	−	22.5890i	−1.24307	−	1.04306i
$470$	3.22368	−	5.58357i	0.148697	−	0.257551i
$471$	1.05190	+	1.82195i	0.0484692	+	0.0839511i
$472$	0.327810	−	1.85910i	0.0150887	−	0.0855722i
$473$	−3.77076	−	2.17705i	−0.173380	−	0.100101i
$474$	1.09552	+	0.398738i	0.0503191	+	0.0183146i
$475$			7.04861i			0.323413i
$476$	−2.20116	+	6.04763i	−0.100890	+	0.277193i
$477$	0.754695	+	4.28009i	0.0345551	+	0.195972i
$478$	21.3429	−	17.9088i	0.976200	−	0.819129i
$479$	−0.187936	+	0.223973i	−0.00858700	+	0.0102336i	−0.770321	−	0.637656i	$-0.779904\pi$
$479$	−0.187936	+	0.223973i	−0.00858700	+	0.0102336i	0.761734	+	0.647890i	$0.224348\pi$
$480$	−3.07260			−0.140244
$481$	13.0757	−	8.79773i	0.596199	−	0.401142i
$482$	23.5970			1.07481
$483$	26.8924	−	32.0492i	1.22365	−	1.45829i
$484$	−1.40564	+	1.17947i	−0.0638928	+	0.0536124i
$485$	0.582056	+	3.30101i	0.0264298	+	0.149891i
$486$	1.45308	−	3.99231i	0.0659131	−	0.181095i
$487$			19.2312i			0.871447i	0.900081	+	0.435723i	$0.143507\pi$
$487$			19.2312i			0.871447i	−0.900081	+	0.435723i	$0.856493\pi$
$488$	−6.47575	−	2.35698i	−0.293143	−	0.106695i
$489$	18.6272	+	10.7544i	0.842352	+	0.486332i
$490$	0.256328	−	1.45371i	0.0115797	−	0.0656720i
$491$	14.6005	+	25.2888i	0.658912	+	1.14127i	0.980898	+	0.194524i	$0.0623162\pi$
$491$	14.6005	+	25.2888i	0.658912	+	1.14127i	−0.321986	+	0.946744i	$0.604350\pi$
$492$	−2.44012	+	4.22641i	−0.110009	+	0.190541i
$493$	2.95179	+	2.47685i	0.132942	+	0.111552i
$494$	23.2037	−	4.09143i	1.04398	−	0.184082i
$495$	0.648137	−	0.374202i	0.0291316	−	0.0168191i
$496$	−4.48108	−	12.3117i	−0.201207	−	0.552810i
$497$	−8.03477	+	2.92442i	−0.360409	+	0.131178i
$498$	−3.63235	−	0.640481i	−0.162769	−	0.0287006i
$499$	9.17239	+	10.9312i	0.410613	+	0.489349i	0.931225	−	0.364444i	$-0.118741\pi$
$499$	9.17239	+	10.9312i	0.410613	+	0.489349i	−0.520613	+	0.853793i	$0.674296\pi$
$500$	−0.215617	−	0.256962i	−0.00964267	−	0.0114917i
$501$	8.54809	+	1.50726i	0.381900	+	0.0673393i
$502$	−23.8740	+	8.68941i	−1.06555	+	0.387827i
$503$	−7.60895	−	20.9054i	−0.339267	−	0.932127i	−0.985603	−	0.169075i	$-0.945922\pi$
$503$	−7.60895	−	20.9054i	−0.339267	−	0.932127i	0.646337	−	0.763052i	$-0.276300\pi$
$504$	−2.37003	+	1.36834i	−0.105570	+	0.0609507i
$505$	−0.868809	+	0.153194i	−0.0386615	+	0.00681706i
$506$	20.8060	+	17.4583i	0.924940	+	0.776117i
$507$	5.14798	−	8.91656i	0.228630	−	0.395998i
$508$	1.31763	+	2.28221i	0.0584605	+	0.101257i
$509$	1.69233	−	9.59770i	0.0750114	−	0.425411i	−0.924057	−	0.382255i	$-0.875148\pi$
$509$	1.69233	−	9.59770i	0.0750114	−	0.425411i	0.999068	−	0.0431559i	$-0.0137412\pi$
$510$	12.3013	+	7.10215i	0.544710	+	0.314489i
$511$	32.8095	+	11.9417i	1.45141	+	0.528269i
$512$			25.4193i			1.12339i
$513$	−13.1001	+	35.9922i	−0.578383	+	1.58909i
$514$	0.779829	+	4.42263i	0.0343968	+	0.195074i
$515$	−3.82596	+	3.21037i	−0.168592	+	0.141466i
$516$	−0.653786	+	0.779152i	−0.0287813	+	0.0343003i
$517$	11.7513			0.516821
$518$	−13.1850	+	18.1037i	−0.579316	+	0.795429i
$519$	−17.9893			−0.789642
$520$	−5.01808	+	5.98031i	−0.220057	+	0.262254i
$521$	−4.73873	+	3.97627i	−0.207608	+	0.174203i	−0.740663	−	0.671877i	$-0.765488\pi$
$521$	−4.73873	+	3.97627i	−0.207608	+	0.174203i	0.533055	+	0.846081i	$0.321044\pi$
$522$	0.0408670	+	0.231768i	0.00178870	+	0.0101442i
$523$	−1.60941	+	4.42181i	−0.0703744	+	0.193352i	−0.969894	−	0.243529i	$-0.921695\pi$
$523$	−1.60941	+	4.42181i	−0.0703744	+	0.193352i	0.899519	+	0.436881i	$0.143917\pi$
$524$			0.0652620i			0.00285098i
$525$	4.39154	+	1.59839i	0.191662	+	0.0697594i
$526$	23.1491	+	13.3652i	1.00935	+	0.582748i
$527$	4.75517	−	26.9679i	0.207139	−	1.17474i
$528$	6.19339	+	10.7273i	0.269533	+	0.466845i
$529$	28.5713	−	49.4870i	1.24223	−	2.15161i
$530$	−13.4965	−	11.3249i	−0.586251	−	0.491923i
$531$	0.196367	−	0.0346248i	0.00852159	−	0.00150259i
$532$	5.84348	−	3.37374i	0.253347	−	0.146270i
$533$	7.87264	+	21.6299i	0.341002	+	0.936895i
$534$	12.6790	−	4.61476i	0.548672	−	0.199700i
$535$	7.46760	+	1.31674i	0.322853	+	0.0569276i
$536$	−23.8502	−	28.4236i	−1.03017	−	1.22771i
$537$	−24.8787	−	29.6493i	−1.07360	−	1.27946i
$538$	−8.64276	−	1.52395i	−0.372616	−	0.0657023i
$539$	2.52823	−	0.920199i	0.108898	−	0.0396358i
$540$	−0.623427	−	1.71285i	−0.0268280	−	0.0737094i
$541$	−5.57730	+	3.22006i	−0.239787	+	0.138441i	−0.615079	−	0.788466i	$-0.710876\pi$
$541$	−5.57730	+	3.22006i	−0.239787	+	0.138441i	0.375292	+	0.926907i	$0.377542\pi$
$542$	25.5629	−	4.50742i	1.09802	−	0.193610i
$543$	−8.94421	−	7.50508i	−0.383833	−	0.322074i
$544$	−6.30710	+	10.9242i	−0.270415	+	0.468372i
$545$	−2.10080	−	3.63870i	−0.0899885	−	0.155865i
$546$	2.71270	−	15.3845i	0.116093	−	0.658396i
$547$	−8.34206	−	4.81629i	−0.356681	−	0.205930i	0.310943	−	0.950429i	$-0.399355\pi$
$547$	−8.34206	−	4.81629i	−0.356681	−	0.205930i	−0.667624	+	0.744499i	$0.732688\pi$
$548$	−4.19561	−	1.52708i	−0.179228	−	0.0652336i
$549$		−	0.727895i		−	0.0310658i
$550$	−1.03766	+	2.85095i	−0.0442459	+	0.121565i
$551$	−0.701526	−	3.97855i	−0.0298860	−	0.169492i
$552$	33.8386	−	28.3940i	1.44027	−	1.20853i
$553$	1.01220	−	1.20630i	0.0430433	−	0.0512970i
$554$	14.5319			0.617401
$555$	−6.91132	−	7.17342i	−0.293369	−	0.304495i
$556$	−3.43004			−0.145466
$557$	−3.95310	+	4.71112i	−0.167498	+	0.199616i	−0.843264	−	0.537500i	$-0.819369\pi$
$557$	−3.95310	+	4.71112i	−0.167498	+	0.199616i	0.675766	+	0.737117i	$0.263813\pi$
$558$	1.28121	−	1.07506i	0.0542380	−	0.0455111i
$559$	0.833042	+	4.72441i	0.0352339	+	0.199821i
$560$	3.13958	−	8.62592i	0.132671	−	0.364512i
$561$			25.8895i			1.09306i
$562$	20.8668	+	7.59488i	0.880211	+	0.320371i
$563$	−20.9781	−	12.1117i	−0.884121	−	0.510448i	−0.0121061	−	0.999927i	$-0.503854\pi$
$563$	−20.9781	−	12.1117i	−0.884121	−	0.510448i	−0.872015	+	0.489479i	$0.837187\pi$
$564$	0.476678	−	2.70338i	0.0200718	−	0.113833i
$565$	6.89119	+	11.9359i	0.289915	+	0.502147i
$566$	−14.1492	+	24.5071i	−0.594734	+	1.03011i
$567$	17.3665	+	14.5722i	0.729323	+	0.611975i
$568$	−8.89068	+	1.56767i	−0.373045	+	0.0657778i
$569$	8.71366	−	5.03083i	0.365296	−	0.210904i	−0.306106	−	0.951998i	$-0.599026\pi$
$569$	8.71366	−	5.03083i	0.365296	−	0.210904i	0.671401	+	0.741094i	$0.265693\pi$
$570$	−5.09347	−	13.9942i	−0.213342	−	0.586152i
$571$	−12.1848	+	4.43491i	−0.509918	+	0.185595i	−0.584150	−	0.811646i	$-0.698572\pi$
$571$	−12.1848	+	4.43491i	−0.509918	+	0.185595i	0.0742313	+	0.997241i	$0.476350\pi$
$572$	−2.01266	−	0.354887i	−0.0841537	−	0.0148386i
$573$	23.1724	+	27.6158i	0.968040	+	1.15367i
$574$	−21.0260	−	25.0578i	−0.877609	−	1.04589i
$575$	8.81624	+	1.55454i	0.367663	+	0.0648288i
$576$	−2.64792	+	0.963765i	−0.110330	+	0.0401569i
$577$	13.2466	+	36.3948i	0.551464	+	1.51513i	0.831712	+	0.555207i	$0.187361\pi$
$577$	13.2466	+	36.3948i	0.551464	+	1.51513i	−0.280249	+	0.959927i	$0.590417\pi$
$578$	31.5069	−	18.1905i	1.31052	−	0.756627i
$579$	16.5401	−	2.91646i	0.687382	−	0.121204i
$580$	0.147278	+	0.123581i	0.00611540	+	0.00513143i
$581$	−2.49098	+	4.31450i	−0.103343	+	0.178996i
$582$	−3.54098	−	6.13315i	−0.146778	−	0.254227i
$583$	5.57624	−	31.6244i	0.230944	−	1.30975i
$584$	31.9257	+	18.4323i	1.32109	+	0.762734i
$585$	−0.774855	−	0.282024i	−0.0320363	−	0.0116603i
$586$		−	30.2342i		−	1.24897i
$587$	−2.81090	+	7.72288i	−0.116018	+	0.318757i	−0.984087	−	0.177686i	$-0.943139\pi$
$587$	−2.81090	+	7.72288i	−0.116018	+	0.318757i	0.868069	+	0.496443i	$0.165361\pi$
$588$	−0.109137	−	0.618944i	−0.00450072	−	0.0255248i
$589$	−21.9934	+	18.4546i	−0.906221	+	0.760410i
$590$	−0.519578	+	0.619209i	−0.0213907	+	0.0254924i
$591$	−32.9270			−1.35443
$592$	−14.0901	+	13.5753i	−0.579101	+	0.557942i
$593$	−36.7123			−1.50759			−0.753797	−	0.657107i	$-0.771780\pi$
$593$	−36.7123			−1.50759			−0.753797	+	0.657107i	$0.771780\pi$
$594$	−10.5972	+	12.6292i	−0.434807	+	0.518182i
$595$	14.6973	−	12.3325i	0.602532	−	0.505584i
$596$	0.690262	+	3.91467i	0.0282743	+	0.160351i
$597$	6.59376	−	18.1162i	0.269865	−	0.741447i
$598$		−	29.9249i		−	1.22372i
$599$	2.30119	+	0.837565i	0.0940241	+	0.0342220i	0.388604	−	0.921405i	$-0.372957\pi$
$599$	2.30119	+	0.837565i	0.0940241	+	0.0342220i	−0.294580	+	0.955627i	$0.595180\pi$
$600$	4.27324	+	2.46716i	0.174454	+	0.100721i
$601$	2.87747	−	16.3190i	0.117375	−	0.665664i	−0.868172	−	0.496263i	$-0.834705\pi$
$601$	2.87747	−	16.3190i	0.117375	−	0.665664i	0.985547	−	0.169402i	$-0.0541836\pi$
$602$	−3.40869	−	5.90402i	−0.138928	−	0.240630i
$603$	1.95956	−	3.39407i	0.0797996	−	0.138217i
$604$	−3.35866	−	2.81825i	−0.136662	−	0.114673i
$605$	5.38713	−	0.949896i	0.219018	−	0.0386188i
$606$	1.61422	−	0.931968i	0.0655730	−	0.0378586i
$607$	3.64095	+	10.0034i	0.147781	+	0.406026i	0.991392	−	0.130930i	$-0.0417963\pi$
$607$	3.64095	+	10.0034i	0.147781	+	0.406026i	−0.843610	+	0.536956i	$0.819574\pi$
$608$	12.4276	−	4.52328i	0.504006	−	0.183443i
$609$	−2.63786	−	0.465126i	−0.106892	−	0.0188479i
$610$	1.89672	+	2.26042i	0.0767959	+	0.0915218i
$611$	−8.32244	−	9.91830i	−0.336690	−	0.401251i
$612$	−0.706824	−	0.124632i	−0.0285717	−	0.00503796i
$613$	−34.6433	+	12.6091i	−1.39923	+	0.509278i	−0.927950	−	0.372705i	$-0.878430\pi$
$613$	−34.6433	+	12.6091i	−1.39923	+	0.509278i	−0.471280	+	0.881983i	$0.656208\pi$
$614$	5.17158	+	14.2088i	0.208708	+	0.573420i
$615$	12.5996	−	7.27438i	0.508065	−	0.293331i
$616$	19.9134	−	3.51127i	0.802334	−	0.141473i
$617$	−3.00892	−	2.52478i	−0.121135	−	0.101644i	0.580208	−	0.814468i	$-0.302971\pi$
$617$	−3.00892	−	2.52478i	−0.121135	−	0.101644i	−0.701343	+	0.712824i	$0.747416\pi$
$618$	5.27612	−	9.13852i	0.212237	−	0.367605i
$619$	10.9070	+	18.8915i	0.438390	+	0.759315i	0.997566	−	0.0697351i	$-0.0222154\pi$
$619$	10.9070	+	18.8915i	0.438390	+	0.759315i	−0.559175	+	0.829050i	$0.688882\pi$
$620$	0.237257	−	1.34555i	0.00952848	−	0.0540387i
$621$	42.1290	+	24.3232i	1.69058	+	0.976056i
$622$	−15.2912	−	5.56555i	−0.613123	−	0.223158i
$623$		−	18.2248i		−	0.730160i
$624$	4.66776	−	12.8246i	0.186860	−	0.513393i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−28.7787	+	24.1482i	−1.15023	+	0.965158i
$627$	17.4475	−	20.7931i	0.696786	−	0.830397i
$628$	0.430936			0.0171962
$629$	−39.6910	+	9.84746i	−1.58258	+	0.392644i
$630$	1.17180			0.0466858
$631$	−1.76384	+	2.10206i	−0.0702172	+	0.0836816i	−0.800010	−	0.599987i	$-0.795172\pi$
$631$	−1.76384	+	2.10206i	−0.0702172	+	0.0836816i	0.729792	+	0.683669i	$0.239617\pi$
$632$	1.27365	−	1.06872i	0.0506631	−	0.0425114i
$633$	4.12991	+	23.4219i	0.164149	+	0.930936i
$634$	−0.0536034	+	0.147274i	−0.00212886	+	0.00584901i
$635$		−	7.85614i		−	0.311762i
$636$	−7.04899	−	2.56562i	−0.279511	−	0.101734i
$637$	−2.56719	−	1.48217i	−0.101716	−	0.0587257i
$638$	0.301956	−	1.71248i	0.0119545	−	0.0677976i
$639$	−0.476780	−	0.825807i	−0.0188611	−	0.0326684i
$640$	3.83530	−	6.64293i	0.151603	−	0.262585i
$641$	1.69847	+	1.42518i	0.0670855	+	0.0562914i	0.675714	−	0.737164i	$-0.263836\pi$
$641$	1.69847	+	1.42518i	0.0670855	+	0.0562914i	−0.608628	+	0.793455i	$0.708280\pi$
$642$	−15.7775	+	2.78201i	−0.622690	+	0.109797i
$643$	15.2356	−	8.79630i	0.600835	−	0.346892i	−0.168535	−	0.985696i	$-0.553904\pi$
$643$	15.2356	−	8.79630i	0.600835	−	0.346892i	0.769370	+	0.638804i	$0.220570\pi$
$644$	−2.93103	−	8.05295i	−0.115499	−	0.317331i
$645$	2.84931	−	1.03706i	0.112191	−	0.0408343i
$646$	−60.2098	−	10.6166i	−2.36892	−	0.417705i
$647$	13.0529	+	15.5558i	0.513162	+	0.611563i	0.958950	−	0.283576i	$-0.0915208\pi$
$647$	13.0529	+	15.5558i	0.513162	+	0.611563i	−0.445788	+	0.895139i	$0.647076\pi$
$648$	15.3858	+	18.3361i	0.604413	+	0.720311i
$649$	−1.45090	−	0.255833i	−0.0569529	−	0.0100423i
$650$	3.14114	−	1.14328i	0.123206	−	0.0448432i
$651$	6.51053	+	17.8875i	0.255168	+	0.701068i
$652$	3.81553	−	2.20289i	0.149428	−	0.0862720i
$653$	−26.0839	+	4.59929i	−1.02074	+	0.179984i	−0.658880	−	0.752248i	$-0.728969\pi$
$653$	−26.0839	+	4.59929i	−1.02074	+	0.179984i	−0.361860	+	0.932232i	$0.617858\pi$
$654$	6.80029	+	5.70612i	0.265912	+	0.223127i
$655$	0.0972782	−	0.168491i	0.00380097	−	0.00658348i
$656$	−14.2884	−	24.7483i	−0.557870	−	0.966258i
$657$	−0.676152	+	3.83465i	−0.0263792	+	0.149604i
$658$	15.9344	+	9.19970i	0.621186	+	0.358642i
$659$	17.8919	+	6.51211i	0.696969	+	0.253676i	0.666116	−	0.745848i	$-0.267955\pi$
$659$	17.8919	+	6.51211i	0.696969	+	0.253676i	0.0308527	+	0.999524i	$0.490178\pi$
$660$			1.29174i			0.0502811i
$661$	−8.20350	+	22.5389i	−0.319079	+	0.876663i	0.671657	+	0.740862i	$0.265583\pi$
$661$	−8.20350	+	22.5389i	−0.319079	+	0.876663i	−0.990736	+	0.135801i	$0.956639\pi$
$662$	−5.91994	−	33.5736i	−0.230085	−	1.30488i
$663$	21.8512	−	18.3353i	0.848631	−	0.712086i
$664$	−3.38114	+	4.02949i	−0.131214	+	0.156375i
$665$	−20.1153			−0.780037
$666$	−2.24362	−	1.09749i	−0.0869385	−	0.0425269i
$667$	−5.13100			−0.198673
$668$	1.14286	−	1.36200i	0.0442184	−	0.0526975i
$669$	−10.5577	+	8.85896i	−0.408184	+	0.342507i
$670$	2.75884	+	15.6462i	0.106583	+	0.604464i
$671$	−1.83946	+	5.05388i	−0.0710116	+	0.195103i
$672$		−	8.76857i		−	0.338255i
$673$	−13.1220	−	4.77601i	−0.505815	−	0.184102i	0.0764927	−	0.997070i	$-0.475628\pi$
$673$	−13.1220	−	4.77601i	−0.505815	−	0.184102i	−0.582308	+	0.812969i	$0.697850\pi$
$674$	−34.8899	−	20.1437i	−1.34391	−	0.775905i
$675$	−0.943602	+	5.35143i	−0.0363193	+	0.205977i
$676$	−1.05449	−	1.82643i	−0.0405574	−	0.0702474i
$677$	−13.1651	+	22.8026i	−0.505976	+	0.876375i	0.494001	+	0.869462i	$0.335534\pi$
$677$	−13.1651	+	22.8026i	−0.505976	+	0.876375i	−0.999976	+	0.00691375i	$0.997799\pi$
$678$	−22.3067	−	18.7176i	−0.856685	−	0.718844i
$679$	−9.42039	+	1.66107i	−0.361521	+	0.0637460i
$680$	17.5433	−	10.1286i	0.672754	−	0.388415i
$681$	7.42138	+	20.3901i	0.284388	+	0.781349i
$682$	−11.6124	+	4.22658i	−0.444663	+	0.161844i
$683$	24.7217	+	4.35911i	0.945951	+	0.166797i	0.625286	−	0.780396i	$-0.284982\pi$
$683$	24.7217	+	4.35911i	0.945951	+	0.166797i	0.320665	+	0.947193i	$0.396094\pi$
$684$	0.483692	+	0.576442i	0.0184944	+	0.0220408i
$685$	8.55583	+	10.1964i	0.326902	+	0.389586i
$686$	−21.2332	−	3.74398i	−0.810686	−	0.142946i
$687$	1.13722	−	0.413915i	0.0433878	−	0.0157919i
$688$	−2.03701	−	5.59665i	−0.0776604	−	0.213370i
$689$	−30.6408	+	17.6905i	−1.16732	+	0.673953i
$690$	−18.6269	+	3.28443i	−0.709115	+	0.125036i
$691$	18.1417	+	15.2227i	0.690143	+	0.579099i	0.918950	−	0.394373i	$-0.129038\pi$
$691$	18.1417	+	15.2227i	0.690143	+	0.579099i	−0.228808	+	0.973472i	$0.573483\pi$
$692$	−1.84243	+	3.19118i	−0.0700386	+	0.121310i
$693$	1.06790	+	1.84965i	0.0405660	+	0.0702624i
$694$	−0.621715	+	3.52592i	−0.0236000	+	0.133842i
$695$	8.85555	+	5.11275i	0.335910	+	0.193938i
$696$	−2.65756	−	0.967272i	−0.100734	−	0.0366643i
$697$		−	59.7282i		−	2.26237i
$698$	−8.55805	+	23.5131i	−0.323927	+	0.889982i
$699$	3.88896	+	22.0554i	0.147094	+	0.834212i
$700$	0.733316	−	0.615325i	0.0277167	−	0.0232571i
$701$	20.2331	−	24.1129i	0.764194	−	0.910730i	−0.233912	−	0.972258i	$-0.575153\pi$
$701$	20.2331	−	24.1129i	0.764194	−	0.910730i	0.998105	+	0.0615274i	$0.0195972\pi$
$702$	18.1644			0.685569
$703$	38.5141	+	18.8396i	1.45259	+	0.710550i
$704$	20.8204			0.784700
$705$	−5.26026	+	6.26894i	−0.198113	+	0.236102i
$706$	32.6801	−	27.4218i	1.22993	−	1.03203i
$707$	−0.437185	−	2.47940i	−0.0164420	−	0.0932475i
$708$	−0.117709	+	0.323402i	−0.00442376	+	0.0121542i
$709$		−	28.7726i		−	1.08058i	−0.841480	−	0.540289i	$-0.818315\pi$
$709$		−	28.7726i		−	1.08058i	0.841480	−	0.540289i	$-0.181685\pi$
$710$	3.63246	+	1.32211i	0.136324	+	0.0496178i
$711$	0.152087	+	0.0878073i	0.00570370	+	0.00329303i
$712$	3.34140	−	18.9500i	0.125224	−	0.710182i
$713$	18.2321	+	31.5789i	0.682797	+	1.18264i
$714$	−20.2681	+	35.1053i	−0.758513	+	1.31378i
$715$	4.66723	+	3.91627i	0.174544	+	0.146460i
$716$	−7.80761	+	1.37669i	−0.291784	+	0.0514494i
$717$	−30.6258	+	17.6818i	−1.14374	+	0.660340i
$718$	−2.41347	−	6.63096i	−0.0900700	−	0.247465i
$719$	−15.1471	+	5.51309i	−0.564891	+	0.205603i	−0.608650	−	0.793439i	$-0.708289\pi$
$719$	−15.1471	+	5.51309i	−0.564891	+	0.205603i	0.0437595	+	0.999042i	$0.486066\pi$
$720$	1.00816	+	0.177767i	0.0375721	+	0.00662497i
$721$	−9.16172	−	10.9185i	−0.341200	−	0.406627i
$722$	25.4457	+	30.3250i	0.946991	+	1.12858i
$723$	−29.4962	−	5.20098i	−1.09698	−	0.193427i
$724$	−2.24740	+	0.817986i	−0.0835239	+	0.0304002i
$725$	−0.196030	−	0.538587i	−0.00728036	−	0.0200026i
$726$	−10.0091	+	5.77875i	−0.371472	+	0.214470i
$727$	31.1480	−	5.49224i	1.15522	−	0.203696i	0.436964	−	0.899479i	$-0.356054\pi$
$727$	31.1480	−	5.49224i	1.15522	−	0.203696i	0.718252	+	0.695783i	$0.244942\pi$
$728$	−17.0666	−	14.3206i	−0.632529	−	0.530755i
$729$	−14.6122	+	25.3090i	−0.541192	+	0.937372i
$730$	−7.89243	−	13.6701i	−0.292112	−	0.505953i
$731$	2.16161	−	12.2591i	0.0799500	−	0.453419i
$732$	1.08803	+	0.628172i	0.0402146	+	0.0232179i
$733$	−10.2220	−	3.72052i	−0.377560	−	0.137420i	0.146268	−	0.989245i	$-0.453274\pi$
$733$	−10.2220	−	3.72052i	−0.377560	−	0.137420i	−0.523827	+	0.851825i	$0.675496\pi$
$734$		−	3.36444i		−	0.124184i
$735$	−0.640821	+	1.76064i	−0.0236370	+	0.0649422i
$736$	−2.91675	−	16.5417i	−0.107513	−	0.609736i
$737$	−22.1827	+	18.6135i	−0.817109	+	0.685636i
$738$	2.34486	−	2.79450i	0.0863156	−	0.102867i
$739$	−3.13742			−0.115412			−0.0577059	−	0.998334i	$-0.518379\pi$
$739$	−3.13742			−0.115412			−0.0577059	+	0.998334i	$0.518379\pi$
$740$	−1.98036	+	0.491334i	−0.0727995	+	0.0180618i
$741$	−29.9064			−1.09864
$742$	32.3190	−	38.5163i	1.18647	−	1.41398i
$743$	−35.3953	+	29.7002i	−1.29853	+	1.08959i	−0.308130	+	0.951344i	$0.599703\pi$
$743$	−35.3953	+	29.7002i	−1.29853	+	1.08959i	−0.990397	+	0.138250i	$0.955852\pi$
$744$	3.49005	+	19.7930i	0.127951	+	0.725648i
$745$	4.05304	−	11.1356i	0.148492	−	0.407978i
$746$			16.6530i			0.609711i
$747$	−0.522091	−	0.190026i	−0.0191023	−	0.00695268i
$748$	4.59262	+	2.65155i	0.167923	+	0.0969504i
$749$	−3.75770	+	21.3110i	−0.137303	+	0.778687i
$750$	−1.05640	−	1.82974i	−0.0385742	−	0.0668125i
$751$	10.3282	−	17.8890i	0.376882	−	0.652779i	−0.613724	−	0.789520i	$-0.710329\pi$
$751$	10.3282	−	17.8890i	0.376882	−	0.652779i	0.990607	+	0.136741i	$0.0436628\pi$
$752$	12.3135	+	10.3323i	0.449028	+	0.376780i
$753$	31.7577	−	5.59973i	1.15731	−	0.204066i
$754$	−1.65921	+	0.957946i	−0.0604249	+	0.0348863i
$755$	4.47042	+	12.2824i	0.162695	+	0.447002i
$756$	4.88812	−	1.77913i	0.177779	−	0.0647064i
$757$	17.6572	+	3.11344i	0.641761	+	0.113160i	0.485053	−	0.874485i	$-0.338800\pi$
$757$	17.6572	+	3.11344i	0.641761	+	0.113160i	0.156709	+	0.987645i	$0.449912\pi$
$758$	−0.821038	−	0.978475i	−0.0298215	−	0.0355398i
$759$	−22.1596	−	26.4087i	−0.804341	−	0.958576i
$760$	−20.9158	−	3.68801i	−0.758694	−	0.133778i
$761$	45.7740	−	16.6604i	1.65931	−	0.603938i	0.669053	−	0.743215i	$-0.266700\pi$
$761$	45.7740	−	16.6604i	1.65931	−	0.603938i	0.990254	+	0.139277i	$0.0444777\pi$
$762$	5.67700	+	15.5974i	0.205656	+	0.565035i
$763$	10.3841	−	5.99526i	0.375929	−	0.217043i
$764$	7.27212	−	1.28227i	0.263096	−	0.0463910i
$765$	1.63908	+	1.37535i	0.0592609	+	0.0497258i
$766$	0.823547	−	1.42642i	0.0297559	−	0.0515388i
$767$	0.811624	+	1.40577i	0.0293061	+	0.0507596i
$768$	2.22131	−	12.5977i	0.0801547	−	0.454580i
$769$	−38.8454	−	22.4274i	−1.40080	−	0.808754i	−0.406327	−	0.913728i	$-0.633191\pi$
$769$	−38.8454	−	22.4274i	−1.40080	−	0.808754i	−0.994475	+	0.104974i	$0.966524\pi$
$770$	−8.13601	−	2.96126i	−0.293201	−	0.106717i
$771$		−	5.70017i		−	0.205287i
$772$	1.17664	−	3.23280i	0.0423483	−	0.116351i
$773$	−3.01536	−	17.1010i	−0.108455	−	0.615079i	−0.989784	−	0.142576i	$-0.954462\pi$
$773$	−3.01536	−	17.1010i	−0.108455	−	0.615079i	0.881329	−	0.472503i	$-0.156650\pi$
$774$	0.582414	−	0.488703i	0.0209344	−	0.0175661i
$775$	−2.61819	+	3.12024i	−0.0940483	+	0.112082i
$776$	−10.0998			−0.362562
$777$	20.4715	−	19.7235i	0.734410	−	0.707576i
$778$	23.5037			0.842650
$779$	−40.2521	+	47.9706i	−1.44218	+	1.71873i
$780$	1.09026	−	0.914834i	0.0390374	−	0.0327563i
$781$	1.22346	+	6.93857i	0.0437787	+	0.248281i
$782$	−26.5580	+	72.9675i	−0.949712	+	2.60931i
$783$		−	3.11450i		−	0.111303i
$784$	3.45828	+	1.25871i	0.123510	+	0.0449539i
$785$	−1.11257	−	0.642345i	−0.0397095	−	0.0229263i
$786$	−0.0713795	+	0.404813i	−0.00254602	+	0.0144392i
$787$	−11.1567	−	19.3240i	−0.397694	−	0.688826i	0.595747	−	0.803172i	$-0.296856\pi$
$787$	−11.1567	−	19.3240i	−0.397694	−	0.688826i	−0.993441	+	0.114346i	$0.963523\pi$
$788$	−3.37232	+	5.84102i	−0.120134	+	0.208078i
$789$	−25.9906	−	21.8087i	−0.925290	−	0.776411i
$790$	−0.701098	+	0.123623i	−0.0249440	+	0.00439829i
$791$	−34.0626	+	19.6660i	−1.21113	+	0.699244i
$792$	0.771270	+	2.11905i	0.0274059	+	0.0752971i
$793$	5.56830	−	2.02670i	0.197736	−	0.0719701i
$794$	−7.95590	−	1.40284i	−0.282344	−	0.0497849i
$795$	14.3745	+	17.1309i	0.509812	+	0.607571i
$796$	−2.53837	−	3.02512i	−0.0899703	−	0.107222i
$797$	5.86595	+	1.03433i	0.207783	+	0.0366377i	0.276571	−	0.960994i	$-0.410802\pi$
$797$	5.86595	+	1.03433i	0.207783	+	0.0366377i	−0.0687879	+	0.997631i	$0.521913\pi$
$798$	39.9365	−	14.5357i	1.41374	−	0.514558i
$799$	11.4907	+	31.5704i	0.406511	+	1.11688i
$800$	1.62491	−	0.938140i	0.0574491	−	0.0331683i
$801$	2.00159	−	0.352934i	0.0707226	−	0.0124703i
$802$	−13.3556	−	11.2066i	−0.471601	−	0.395720i
$803$	14.3852	−	24.9158i	0.507641	−	0.879260i
$804$	3.38220	+	5.85815i	0.119281	+	0.206601i
$805$	−4.43634	+	25.1597i	−0.156360	+	0.886764i
$806$	11.7914	+	6.80778i	0.415335	+	0.239794i
$807$	10.4676	+	3.80988i	0.368476	+	0.134114i
$808$		−	2.65822i		−	0.0935159i
$809$	15.2385	−	41.8675i	0.535758	−	1.47198i	−0.316363	−	0.948638i	$-0.602462\pi$
$809$	15.2385	−	41.8675i	0.535758	−	1.47198i	0.852121	−	0.523345i	$-0.175316\pi$
$810$	−1.77973	−	10.0934i	−0.0625335	−	0.354645i
$811$	23.8129	−	19.9814i	0.836185	−	0.701643i	−0.120517	−	0.992711i	$-0.538455\pi$
$811$	23.8129	−	19.9814i	0.836185	−	0.701643i	0.956702	+	0.291069i	$0.0940108\pi$
$812$	−0.352675	+	0.420302i	−0.0123765	+	0.0147497i
$813$	−32.9471			−1.15550
$814$	12.8043	+	13.2899i	0.448791	+	0.465810i
$815$	−13.1344			−0.460077
$816$	−22.7633	+	27.1282i	−0.796874	+	0.949678i
$817$	−9.99776	+	8.38912i	−0.349777	+	0.293498i
$818$	−3.68816	−	20.9166i	−0.128954	−	0.731332i
$819$	0.804838	−	2.21127i	0.0281233	−	0.0772682i
$820$		−	2.98011i		−	0.104070i
$821$	−33.3141	−	12.1253i	−1.16267	−	0.423177i	−0.312619	−	0.949879i	$-0.601206\pi$
$821$	−33.3141	−	12.1253i	−1.16267	−	0.423177i	−0.850050	+	0.526702i	$0.823428\pi$
$822$	−24.3547	−	14.0612i	−0.849469	−	0.490441i
$823$	7.22852	−	40.9950i	0.251970	−	1.42899i	−0.551761	−	0.834002i	$-0.686044\pi$
$823$	7.22852	−	40.9950i	0.251970	−	1.42899i	0.803731	−	0.594992i	$-0.202845\pi$
$824$	−7.52446	−	13.0328i	−0.262127	−	0.454017i
$825$	1.92545	−	3.33497i	0.0670355	−	0.116109i
$826$	−1.76709	−	1.48277i	−0.0614851	−	0.0515921i
$827$	20.9601	−	3.69582i	0.728853	−	0.128516i	0.203105	−	0.979157i	$-0.434897\pi$
$827$	20.9601	−	3.69582i	0.728853	−	0.128516i	0.525748	+	0.850641i	$0.323786\pi$
$828$	0.827676	−	0.477859i	0.0287637	−	0.0166067i
$829$	−9.13523	−	25.0988i	−0.317280	−	0.871719i	−0.991135	−	0.132856i	$-0.957585\pi$
$829$	−9.13523	−	25.0988i	−0.317280	−	0.871719i	0.673856	−	0.738863i	$-0.264637\pi$
$830$	2.11648	−	0.770334i	0.0734640	−	0.0267387i
$831$	−18.1649	−	3.20296i	−0.630132	−	0.111109i
$832$	−14.7454	−	17.5728i	−0.511203	−	0.609228i
$833$	4.94432	+	5.89241i	0.171310	+	0.204160i
$834$	−21.2762	−	3.75157i	−0.736735	−	0.129906i
$835$	−4.98075	+	1.81285i	−0.172366	+	0.0627361i
$836$	−1.90162	−	5.22466i	−0.0657689	−	0.180699i
$837$	−19.1683	+	11.0668i	−0.662553	+	0.382525i
$838$	−38.3981	+	6.77061i	−1.32644	+	0.233887i
$839$	33.9082	+	28.4524i	1.17064	+	0.982285i	0.999995	−	0.00304679i	$-0.000969825\pi$
$839$	33.9082	+	28.4524i	1.17064	+	0.982285i	0.170647	+	0.985332i	$0.445414\pi$
$840$	−7.04075	+	12.1949i	−0.242929	+	0.420766i
$841$	−14.3357	−	24.8302i	−0.494336	−	0.856215i
$842$	0.0748055	−	0.424243i	0.00257797	−	0.0146204i
$843$	−24.4095	−	14.0928i	−0.840707	−	0.485382i
$844$	4.57786	+	1.66620i	0.157576	+	0.0573531i
$845$			6.28721i			0.216287i
$846$	−0.701804	+	1.92819i	−0.0241285	+	0.0662926i
$847$	2.71081	+	15.3737i	0.0931444	+	0.528248i
$848$	33.6488	−	28.2347i	1.15550	−	0.969582i
$849$	23.0880	−	27.5152i	0.792379	−	0.944321i
$850$	−8.67385			−0.297510
$851$	32.0583	−	44.0176i	1.09894	−	1.50890i
$852$	1.64584			0.0563856
$853$	5.03899	−	6.00524i	0.172532	−	0.205615i	−0.672848	−	0.739780i	$-0.734929\pi$
$853$	5.03899	−	6.00524i	0.172532	−	0.205615i	0.845380	+	0.534165i	$0.179374\pi$
$854$	−6.45077	+	5.41284i	−0.220741	+	0.185224i
$855$	−0.389544	−	2.20922i	−0.0133221	−	0.0755536i
$856$	−7.81448	+	21.4701i	−0.267093	+	0.733833i
$857$			1.42847i			0.0487957i	0.999702	+	0.0243979i	$0.00776685\pi$
$857$			1.42847i			0.0487957i	−0.999702	+	0.0243979i	$0.992233\pi$
$858$	−12.0962	−	4.40265i	−0.412957	−	0.150304i
$859$	21.2866	+	12.2898i	0.726289	+	0.419323i	0.817063	−	0.576548i	$-0.195601\pi$
$859$	21.2866	+	12.2898i	0.726289	+	0.419323i	−0.0907740	+	0.995872i	$0.528934\pi$
$860$	0.107852	−	0.611662i	0.00367774	−	0.0208575i
$861$	20.7596	+	35.9566i	0.707484	+	1.22540i
$862$	24.1730	−	41.8688i	0.823334	−	1.42606i
$863$	−31.1265	−	26.1182i	−1.05956	−	0.889074i	−0.0654909	−	0.997853i	$-0.520861\pi$
$863$	−31.1265	−	26.1182i	−1.05956	−	0.889074i	−0.994066	+	0.108779i	$0.965306\pi$
$864$	10.0408	−	1.77046i	0.341595	−	0.0602324i
$865$	9.51341	−	5.49257i	0.323466	−	0.186753i
$866$	16.6842	+	45.8395i	0.566953	+	1.55769i
$867$	−43.3930	+	15.7938i	−1.47370	+	0.536384i
$868$	3.83993	+	0.677083i	0.130336	+	0.0229817i
$869$	−0.834063	−	0.993997i	−0.0282936	−	0.0337190i
$870$	0.778387	+	0.927645i	0.0263898	+	0.0314501i
$871$	31.4202	+	5.54024i	1.06463	+	0.187724i
$872$	11.8965	−	4.32998i	0.402867	−	0.146632i
$873$	−0.364863	−	1.00245i	−0.0123487	−	0.0339279i
$874$	70.5044	−	40.7057i	2.38485	−	1.37689i
$875$	−2.81044	+	0.495556i	−0.0950101	+	0.0167528i
$876$	−5.14835	−	4.31998i	−0.173947	−	0.145959i
$877$	9.99404	−	17.3102i	0.337475	−	0.584524i	−0.646482	−	0.762929i	$-0.723761\pi$
$877$	9.99404	−	17.3102i	0.337475	−	0.584524i	0.983957	+	0.178406i	$0.0570939\pi$
$878$	8.30565	+	14.3858i	0.280302	+	0.485498i
$879$	−6.66389	+	37.7928i	−0.224767	+	1.27472i
$880$	−6.55060	−	3.78199i	−0.220821	−	0.127491i
$881$	−1.61215	−	0.586774i	−0.0543146	−	0.0197689i	0.314720	−	0.949185i	$-0.398089\pi$
$881$	−1.61215	−	0.586774i	−0.0543146	−	0.0197689i	−0.369035	+	0.929416i	$0.620312\pi$
$882$			0.469796i			0.0158189i
$883$	−18.5099	+	50.8554i	−0.622906	+	1.71142i	0.0768530	+	0.997042i	$0.475513\pi$
$883$	−18.5099	+	50.8554i	−0.622906	+	1.71142i	−0.699759	+	0.714379i	$0.746709\pi$
$884$	−1.01461	−	5.75413i	−0.0341250	−	0.193532i
$885$	0.785952	−	0.659492i	0.0264195	−	0.0221686i
$886$	0.965415	−	1.15054i	0.0324338	−	0.0386530i
$887$	23.2394			0.780304			0.390152	−	0.920750i	$-0.372422\pi$
$887$	23.2394			0.780304			0.390152	+	0.920750i	$0.372422\pi$
$888$	24.9023	−	16.7550i	0.835666	−	0.562263i
$889$	22.4198			0.751936
$890$	−5.29611	+	6.31166i	−0.177526	+	0.211567i
$891$	14.3101	−	12.0076i	0.479406	−	0.402270i
$892$	0.490221	+	2.78018i	0.0164138	+	0.0930874i
$893$	12.0472	−	33.0995i	0.403145	−	1.10763i
$894$			25.0373i			0.837372i
$895$	22.2095	+	8.08358i	0.742380	+	0.270204i
$896$	18.9575	+	10.9451i	0.633327	+	0.365652i
$897$	−6.59571	+	37.4061i	−0.220224	+	1.24895i
$898$	−13.6178	−	23.5867i	−0.454432	−	0.787100i
$899$	1.16728	−	2.02178i	0.0389309	−	0.0674303i
$900$	0.0817809	+	0.0686223i	0.00272603	+	0.00228741i
$901$	90.4131	−	15.9423i	3.01210	−	0.531114i
$902$	−23.3427	+	13.4769i	−0.777227	+	0.448732i
$903$	2.95956	+	8.13133i	0.0984881	+	0.270594i
$904$	−39.0237	+	14.2035i	−1.29791	+	0.472400i
$905$	7.02152	+	1.23808i	0.233403	+	0.0411553i
$906$	−17.7510	−	21.1548i	−0.589737	−	0.702821i
$907$	−21.7171	−	25.8815i	−0.721105	−	0.859380i	0.273633	−	0.961834i	$-0.411775\pi$
$907$	−21.7171	−	25.8815i	−0.721105	−	0.859380i	−0.994738	+	0.102455i	$0.967330\pi$
$908$	4.37714	+	0.771809i	0.145261	+	0.0256134i
$909$	0.263841	−	0.0960301i	0.00875104	−	0.00318512i
$910$	3.26269	+	8.96416i	0.108157	+	0.297159i
$911$	18.3374	−	10.5871i	0.607544	−	0.350766i	−0.164459	−	0.986384i	$-0.552588\pi$
$911$	18.3374	−	10.5871i	0.607544	−	0.350766i	0.772004	+	0.635618i	$0.219255\pi$
$912$	36.5646	−	6.44732i	1.21077	−	0.213492i
$913$	3.14474	+	2.63875i	0.104076	+	0.0873300i
$914$	−16.0779	+	27.8478i	−0.531811	+	0.921123i
$915$	−1.87268	−	3.24358i	−0.0619090	−	0.107229i
$916$	0.0430464	−	0.244128i	0.00142229	−	0.00806622i
$917$	0.480838	+	0.277612i	0.0158787	+	0.00916755i
$918$	−44.2911	−	16.1206i	−1.46182	−	0.532060i
$919$		−	9.79121i		−	0.322982i	−0.986874	−	0.161491i	$-0.948370\pi$
$919$		−	9.79121i		−	0.322982i	0.986874	−	0.161491i	$-0.0516303\pi$
$920$	−9.22576	+	25.3476i	−0.304164	+	0.835684i
$921$	−3.33273	−	18.9009i	−0.109817	−	0.622805i
$922$	−16.3394	+	13.7104i	−0.538111	+	0.451528i
$923$	4.98981	−	5.94662i	0.164242	−	0.195735i
$924$	−3.68637			−0.121273
$925$	5.84519	+	1.68338i	0.192189	+	0.0553492i
$926$	44.1656			1.45137
$927$	1.02173	−	1.21765i	0.0335581	−	0.0399930i
$928$	−0.823800	+	0.691250i	−0.0270426	+	0.0226914i
$929$	6.20734	+	35.2036i	0.203656	+	1.15499i	0.899540	+	0.436837i	$0.143901\pi$
$929$	6.20734	+	35.2036i	0.203656	+	1.15499i	−0.695884	+	0.718154i	$0.744987\pi$
$930$	2.94336	−	8.08682i	0.0965167	−	0.265177i
$931$		−	8.06456i		−	0.264305i
$932$	4.31078	+	1.56900i	0.141204	+	0.0513942i
$933$	17.8873	+	10.3273i	0.585605	+	0.338099i
$934$	−6.05752	+	34.3539i	−0.198208	+	1.12409i
$935$	−7.90470	−	13.6913i	−0.258511	−	0.447755i
$936$	1.24229	−	2.15171i	0.0406055	−	0.0703308i
$937$	15.2603	+	12.8049i	0.498532	+	0.418318i	0.857072	−	0.515196i	$-0.172281\pi$
$937$	15.2603	+	12.8049i	0.498532	+	0.418318i	−0.358540	+	0.933514i	$0.616725\pi$
$938$	−44.6509	+	7.87316i	−1.45790	+	0.257068i
$939$	41.2959	−	23.8422i	1.34764	−	0.778061i
$940$	0.573322	+	1.57519i	0.0186997	+	0.0513770i
$941$	−25.6606	+	9.33970i	−0.836512	+	0.304465i	−0.724529	−	0.689245i	$-0.757943\pi$
$941$	−25.6606	+	9.33970i	−0.836512	+	0.304465i	−0.111983	+	0.993710i	$0.535720\pi$
$942$	2.67305	+	0.471331i	0.0870928	+	0.0153568i
$943$	51.1231	+	60.9261i	1.66480	+	1.98403i
$944$	−1.29538	−	1.54378i	−0.0421611	−	0.0502457i
$945$	−15.2719	−	2.69285i	−0.496795	−	0.0875983i
$946$	−5.27879	+	1.92132i	−0.171628	+	0.0624675i
$947$	−18.8900	−	51.8998i	−0.613843	−	1.68652i	−0.721573	−	0.692338i	$-0.756581\pi$
$947$	−18.8900	−	51.8998i	−0.613843	−	1.68652i	0.107731	−	0.994180i	$-0.465642\pi$
$948$	−0.262501	+	0.151555i	−0.00852565	+	0.00492229i
$949$	−31.2172	+	5.50443i	−1.01335	+	0.178681i
$950$	6.96639	+	5.84549i	0.226019	+	0.189653i
$951$	0.0994648	−	0.172278i	0.00322537	−	0.00558650i
$952$	28.9050	+	50.0649i	0.936816	+	1.62261i
$953$	3.93740	−	22.3301i	0.127545	−	0.723343i	−0.852219	−	0.523186i	$-0.824743\pi$
$953$	3.93740	−	22.3301i	0.127545	−	0.723343i	0.979764	−	0.200158i	$-0.0641455\pi$
$954$	4.85603	+	2.80363i	0.157220	+	0.0907709i
$955$	−20.6862	−	7.52916i	−0.669390	−	0.243638i
$956$			7.24376i			0.234280i
$957$	−0.754890	+	2.07404i	−0.0244021	+	0.0670443i
$958$	0.0655030	+	0.371486i	0.00211631	+	0.0120022i
$959$	−29.0985	+	24.4166i	−0.939641	+	0.788452i
$960$	−9.31992	+	11.1070i	−0.300799	+	0.358478i
$961$	14.4092			0.464812
$962$	2.14870	−	20.2192i	0.0692769	−	0.651892i
$963$	−2.41331			−0.0777678
$964$	−3.94357	+	4.69976i	−0.127014	+	0.151369i
$965$	−7.85655	+	6.59243i	−0.252911	+	0.212218i
$966$	−9.37308	−	53.1574i	−0.301574	−	1.71031i
$967$	−10.8176	+	29.7211i	−0.347870	+	0.955766i	0.635169	+	0.772373i	$0.280930\pi$
$967$	−10.8176	+	29.7211i	−0.347870	+	0.955766i	−0.983040	+	0.183393i	$0.941292\pi$
$968$			16.4825i			0.529769i
$969$	72.9222	+	26.5415i	2.34260	+	0.852636i
$970$	3.74520	+	2.16229i	0.120251	+	0.0694271i
$971$	1.30092	−	7.37787i	0.0417484	−	0.236767i	−0.956792	−	0.290772i	$-0.906088\pi$
$971$	1.30092	−	7.37787i	0.0417484	−	0.236767i	0.998541	+	0.0540055i	$0.0171988\pi$
$972$	0.552298	+	0.956609i	0.0177150	+	0.0306832i
$973$	−14.5907	+	25.2719i	−0.467758	+	0.810180i
$974$	19.0068	+	15.9486i	0.609017	+	0.511026i
$975$	−4.17841	+	0.736767i	−0.133816	+	0.0235954i
$976$	−6.37108	+	3.67835i	−0.203933	+	0.117741i
$977$	−1.04609	−	2.87410i	−0.0334672	−	0.0919505i	0.921834	−	0.387586i	$-0.126691\pi$
$977$	−1.04609	−	2.87410i	−0.0334672	−	0.0919505i	−0.955301	+	0.295635i	$0.904469\pi$
$978$	26.0767	−	9.49114i	0.833841	−	0.303493i
$979$	−14.7892	−	2.60773i	−0.472665	−	0.0833436i
$980$	0.246694	+	0.293999i	0.00788036	+	0.00939145i
$981$	0.859540	+	1.02436i	0.0274430	+	0.0327053i
$982$	37.1021	+	6.54211i	1.18398	+	0.208767i
$983$	44.6429	−	16.2487i	1.42389	−	0.518252i	0.488713	−	0.872444i	$-0.337466\pi$
$983$	44.6429	−	16.2487i	1.42389	−	0.518252i	0.935173	+	0.354192i	$0.115244\pi$
$984$	14.9933	+	41.1936i	0.477968	+	1.31320i
$985$	17.4130	−	10.0534i	0.554825	−	0.320328i
$986$	4.89591	−	0.863281i	0.155917	−	0.0274925i
$987$	−17.8903	−	15.0117i	−0.569453	−	0.477828i
$988$	−3.06295	+	5.30519i	−0.0974455	+	0.168780i
$989$	8.28795	+	14.3551i	0.263541	+	0.456467i
$990$	0.167670	−	0.950906i	0.00532891	−	0.0302218i
$991$	−39.9180	−	23.0467i	−1.26804	−	0.732102i	−0.293421	−	0.955983i	$-0.594794\pi$
$991$	−39.9180	−	23.0467i	−1.26804	−	0.732102i	−0.974616	+	0.223882i	$0.928127\pi$
$992$	7.18154	+	2.61387i	0.228014	+	0.0829904i
$993$			43.2719i			1.37319i
$994$	−3.77302	+	10.3663i	−0.119673	+	0.328798i
$995$	2.04429	+	11.5938i	0.0648085	+	0.367547i
$996$	0.734607	−	0.616408i	0.0232769	−	0.0195316i
$997$	11.7761	−	14.0343i	0.372954	−	0.444469i	−0.546623	−	0.837379i	$-0.684087\pi$
$997$	11.7761	−	14.0343i	0.372954	−	0.444469i	0.919577	+	0.392909i	$0.128531\pi$
$998$	18.4105			0.582773
$999$	26.7186	+	19.4593i	0.845338	+	0.615665i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.w.a.136.10	✓	72	37.25	even	18	inner
185.2.w.a.151.10	yes	72	1.1	even	1	trivial
925.2.ba.b.99.3		72	185.62	odd	36
925.2.ba.b.299.3		72	5.3	odd	4
925.2.ba.c.99.10		72	185.173	odd	36
925.2.ba.c.299.10		72	5.2	odd	4
925.2.bb.b.151.3		72	5.4	even	2
925.2.bb.b.876.3		72	185.99	even	18
6845.2.a.t.1.27		36	37.32	odd	36
6845.2.a.u.1.10		36	37.5	odd	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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.w (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.829311 - 0.988334i) q^{2} +(-1.25448 + 1.05263i) q^{3} +(0.0582485 + 0.330344i) q^{4} +(0.342020 - 0.939693i) q^{5} +2.11280i q^{6} +(2.68169 + 0.976055i) q^{7} +(2.60945 + 1.50657i) q^{8} +(-0.0552654 + 0.313426i) q^{9} +(-0.645089 - 1.11733i) q^{10} +(1.17577 - 2.03650i) q^{11} +(-0.420801 - 0.353094i) q^{12} +(-2.55154 + 0.449906i) q^{13} +(3.18862 - 1.84095i) q^{14} +(0.560093 + 1.53884i) q^{15} +(3.02262 - 1.10014i) q^{16} +(6.62084 + 1.16743i) q^{17} +(0.263937 + 0.314548i) q^{18} +(-4.53076 - 5.39955i) q^{19} +(0.330344 + 0.0582485i) q^{20} +(-4.39154 + 1.59839i) q^{21} +(-1.03766 - 2.85095i) q^{22} +(-7.75287 + 4.47612i) q^{23} +(-4.85935 + 0.856835i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-1.67136 + 2.89489i) q^{26} +(-2.71699 - 4.70597i) q^{27} +(-0.166229 + 0.942733i) q^{28} +(0.496364 + 0.286576i) q^{29} +(1.98538 + 0.722620i) q^{30} -4.07319i q^{31} +(-0.641726 + 1.76313i) q^{32} +(0.668701 + 3.79239i) q^{33} +(6.64455 - 5.57544i) q^{34} +(1.83438 - 2.18613i) q^{35} -0.106757 q^{36} +(-5.55973 + 2.46767i) q^{37} -9.09397 q^{38} +(2.72726 - 3.25023i) q^{39} +(2.30819 - 1.93681i) q^{40} +(-1.54272 - 8.74921i) q^{41} +(-2.06221 + 5.66587i) q^{42} -1.85159i q^{43} +(0.741232 + 0.269786i) q^{44} +(0.275622 + 0.159130i) q^{45} +(-2.00563 + 11.3745i) q^{46} +(2.49863 + 4.32775i) q^{47} +(-2.63375 + 4.56180i) q^{48} +(0.876457 + 0.735435i) q^{49} +(-1.27058 + 0.224037i) q^{50} +(-9.53456 + 5.50478i) q^{51} +(-0.297247 - 0.816680i) q^{52} +(12.8323 - 4.67057i) q^{53} +(-6.90430 - 1.21742i) q^{54} +(-1.51154 - 1.80139i) q^{55} +(5.52724 + 6.58711i) q^{56} +(11.3675 + 2.00439i) q^{57} +(0.694873 - 0.252913i) q^{58} +(-0.214282 - 0.588735i) q^{59} +(-0.475723 + 0.274659i) q^{60} +(-2.25236 + 0.397151i) q^{61} +(-4.02567 - 3.37794i) q^{62} +(-0.454125 + 0.786568i) q^{63} +(4.42697 + 7.66773i) q^{64} +(-0.449906 + 2.55154i) q^{65} +(4.30271 + 2.48417i) q^{66} +(-11.5716 - 4.21171i) q^{67} +2.25516i q^{68} +(5.01409 - 13.7761i) q^{69} +(-0.639355 - 3.62597i) q^{70} +(-2.29519 + 1.92589i) q^{71} +(-0.616409 + 0.734608i) q^{72} +12.2346 q^{73} +(-2.17186 + 7.54134i) q^{74} +1.63760 q^{75} +(1.51980 - 1.81123i) q^{76} +(5.14079 - 4.31363i) q^{77} +(-0.950560 - 5.39090i) q^{78} +(0.188725 - 0.518518i) q^{79} -3.21660i q^{80} +(7.46485 + 2.71698i) q^{81} +(-9.92654 - 5.73109i) q^{82} +(-0.303143 + 1.71921i) q^{83} +(-0.783819 - 1.35761i) q^{84} +(3.36149 - 5.82227i) q^{85} +(-1.82999 - 1.53554i) q^{86} +(-0.924336 + 0.162985i) q^{87} +(6.13624 - 3.54276i) q^{88} +(-2.18420 - 6.00103i) q^{89} +(0.385850 - 0.140438i) q^{90} +(-7.28157 - 1.28394i) q^{91} +(-1.93025 - 2.30039i) q^{92} +(4.28756 + 5.10971i) q^{93} +(6.34940 + 1.11957i) q^{94} +(-6.62353 + 2.41077i) q^{95} +(-1.05089 - 2.88730i) q^{96} +(-2.90286 + 1.67596i) q^{97} +(1.45371 - 0.256328i) q^{98} +(0.573311 + 0.481065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{2} - 6 q^{4} - 6 q^{7} - 18 q^{8} + 6 q^{10} + 30 q^{12} - 30 q^{13} - 18 q^{14} - 18 q^{16} - 30 q^{18} - 18 q^{19} + 30 q^{22} - 30 q^{24} - 24 q^{27} + 30 q^{28} + 18 q^{29} + 24 q^{30} - 36 q^{32}+ \cdots - 12 q^{99}+O(q^{100}) \) 72 * q + 6 * q^2 - 6 * q^4 - 6 * q^7 - 18 * q^8 + 6 * q^10 + 30 * q^12 - 30 * q^13 - 18 * q^14 - 18 * q^16 - 30 * q^18 - 18 * q^19 + 30 * q^22 - 30 * q^24 - 24 * q^27 + 30 * q^28 + 18 * q^29 + 24 * q^30 - 36 * q^32 - 12 * q^33 + 66 * q^34 - 6 * q^35 - 12 * q^36 - 48 * q^37 - 48 * q^38 + 24 * q^39 + 6 * q^41 + 84 * q^42 + 24 * q^44 - 36 * q^45 - 54 * q^46 + 66 * q^47 - 24 * q^48 - 60 * q^49 + 6 * q^50 - 180 * q^51 - 42 * q^52 + 24 * q^53 + 6 * q^54 + 12 * q^55 - 156 * q^56 - 18 * q^57 + 54 * q^58 + 6 * q^59 + 48 * q^63 - 18 * q^65 + 126 * q^66 + 30 * q^67 + 54 * q^69 - 60 * q^71 + 30 * q^72 + 24 * q^73 + 6 * q^74 - 12 * q^75 + 36 * q^76 + 42 * q^77 + 96 * q^78 - 72 * q^79 + 48 * q^81 - 72 * q^82 + 48 * q^83 + 12 * q^84 - 12 * q^85 + 60 * q^86 + 84 * q^87 + 90 * q^88 + 12 * q^89 + 24 * q^90 + 24 * q^91 - 102 * q^92 + 18 * q^93 - 66 * q^94 + 24 * q^95 + 102 * q^96 - 72 * q^97 - 54 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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