LMFDB - Embedded newform 550.2.g.c.361.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(291,550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("550.291"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.g (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [60] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$15$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.4
Character	$\chi$	$=$	550.361
Dual form			550.2.g.c.291.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.391447 - 1.20475i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.60082 + 1.56121i) q^{5} +(1.02482 - 0.744577i) q^{6} +(-1.25694 - 0.913224i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.12886 - 0.820164i) q^{9} +(-1.97948 - 1.04003i) q^{10} +(2.51441 + 2.16281i) q^{11} +(1.02482 + 0.744577i) q^{12} +(-2.87302 + 2.08737i) q^{13} +(0.480110 - 1.47763i) q^{14} +(2.50751 + 1.31745i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-6.33003 + 4.59903i) q^{17} +(1.12886 + 0.820164i) q^{18} +(-6.06809 - 4.40873i) q^{19} +(0.377430 - 2.20398i) q^{20} +(-0.608179 + 1.87178i) q^{21} +(-1.27996 + 3.05969i) q^{22} +(-4.09001 + 2.97156i) q^{23} +(-0.391447 + 1.20475i) q^{24} +(0.125226 - 4.99843i) q^{25} +(-2.87302 - 2.08737i) q^{26} +(-4.50445 - 3.27267i) q^{27} +1.55367 q^{28} +(-2.29031 + 1.66401i) q^{29} +(-0.478109 + 2.79190i) q^{30} +0.336000 q^{31} +1.00000 q^{32} +(1.62139 - 3.87586i) q^{33} +(-6.33003 - 4.59903i) q^{34} +(3.43788 - 0.500455i) q^{35} +(-0.431186 + 1.32705i) q^{36} +(1.68155 + 5.17528i) q^{37} +(2.31780 - 7.13347i) q^{38} +(3.63939 + 2.64417i) q^{39} +(2.21275 - 0.322112i) q^{40} -6.25824 q^{41} -1.96811 q^{42} +5.91777 q^{43} +(-3.30547 - 0.271822i) q^{44} +(-0.526645 + 3.07532i) q^{45} +(-4.09001 - 2.97156i) q^{46} +(0.545087 + 1.67760i) q^{47} -1.26675 q^{48} +(-1.41719 - 4.36165i) q^{49} +(4.79249 - 1.42550i) q^{50} +(8.01856 + 5.82582i) q^{51} +(1.09739 - 3.37743i) q^{52} +(4.29125 + 3.11777i) q^{53} +(1.72055 - 5.29529i) q^{54} +(-7.40172 + 0.463256i) q^{55} +(0.480110 + 1.47763i) q^{56} +(-2.93608 + 9.03632i) q^{57} +(-2.29031 - 1.66401i) q^{58} +(0.0523156 + 0.161011i) q^{59} +(-2.80299 + 0.408035i) q^{60} +(4.17129 + 3.03062i) q^{61} +(0.103830 + 0.319555i) q^{62} -2.16791 q^{63} +(0.309017 + 0.951057i) q^{64} +(1.34034 - 7.82689i) q^{65} +(4.18720 + 0.344331i) q^{66} +(1.86161 + 5.72946i) q^{67} +(2.41786 - 7.44139i) q^{68} +(5.18101 + 3.76423i) q^{69} +(1.53832 + 3.11496i) q^{70} +10.3825 q^{71} -1.39535 q^{72} -12.2921 q^{73} +(-4.40236 + 3.19850i) q^{74} +(-6.07088 + 1.80575i) q^{75} +7.50057 q^{76} +(-1.18534 - 5.01475i) q^{77} +(-1.39012 + 4.27836i) q^{78} +(4.98259 + 3.62006i) q^{79} +(0.990123 + 2.00491i) q^{80} +(-0.885943 + 2.72665i) q^{81} +(-1.93390 - 5.95194i) q^{82} +(10.0939 - 7.33362i) q^{83} +(-0.608179 - 1.87178i) q^{84} +(2.95314 - 17.2447i) q^{85} +(1.82869 + 5.62813i) q^{86} +(2.90125 + 2.10788i) q^{87} +(-0.762927 - 3.22768i) q^{88} +(-2.72294 + 1.97833i) q^{89} +(-3.08755 + 0.449457i) q^{90} +5.51746 q^{91} +(1.56224 - 4.80809i) q^{92} +(-0.131526 - 0.404796i) q^{93} +(-1.42706 + 1.03682i) q^{94} +(16.5969 - 2.41602i) q^{95} +(-0.391447 - 1.20475i) q^{96} +(1.81374 + 1.31776i) q^{97} +(3.71024 - 2.69565i) q^{98} +(4.61227 + 0.379286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 15 q^{2} - 4 q^{3} - 15 q^{4} + q^{6} - 3 q^{7} - 15 q^{8} - 17 q^{9} - 5 q^{10} + 7 q^{11} + q^{12} + 12 q^{13} - 3 q^{14} + 12 q^{15} - 15 q^{16} + q^{17} - 17 q^{18} + 3 q^{19} - 5 q^{20} - 4 q^{21}+ \cdots + 21 q^{99}+O(q^{100}) $ 60 * q - 15 * q^2 - 4 * q^3 - 15 * q^4 + q^6 - 3 * q^7 - 15 * q^8 - 17 * q^9 - 5 * q^10 + 7 * q^11 + q^12 + 12 * q^13 - 3 * q^14 + 12 * q^15 - 15 * q^16 + q^17 - 17 * q^18 + 3 * q^19 - 5 * q^20 - 4 * q^21 - 3 * q^22 - 3 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 + 2 * q^27 + 12 * q^28 + 18 * q^29 + 2 * q^30 - 20 * q^31 + 60 * q^32 + 10 * q^33 + q^34 - 19 * q^35 - 12 * q^36 - 36 * q^37 - 22 * q^38 + 13 * q^39 + 64 * q^41 + 46 * q^42 + 40 * q^43 - 8 * q^44 - 20 * q^45 - 3 * q^46 - 9 * q^47 + 6 * q^48 - 30 * q^49 + 18 * q^50 - 48 * q^51 - 8 * q^52 + 31 * q^53 - 8 * q^54 - 42 * q^55 - 3 * q^56 + 30 * q^57 + 18 * q^58 + 23 * q^59 - 8 * q^60 - 41 * q^61 - 5 * q^62 + 6 * q^63 - 15 * q^64 - 7 * q^65 - 30 * q^66 - 40 * q^67 - 4 * q^68 - 22 * q^69 - 4 * q^70 + 4 * q^71 + 58 * q^72 + 74 * q^73 - 11 * q^74 + 35 * q^75 + 38 * q^76 + 22 * q^77 - 12 * q^78 - 45 * q^79 + 10 * q^80 + 24 * q^81 - 11 * q^82 + 16 * q^83 - 4 * q^84 + 9 * q^85 - 20 * q^86 + 68 * q^87 + 7 * q^88 + q^89 + 10 * q^90 + 10 * q^91 + 2 * q^92 - 40 * q^93 - 24 * q^94 + 24 * q^95 - 4 * q^96 + 6 * q^97 - 30 * q^98 + 21 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.391447	−	1.20475i	−0.226002	−	0.695563i	−0.998188	−	0.0601666i	$-0.980837\pi$
$3$	−0.391447	−	1.20475i	−0.226002	−	0.695563i	0.772186	−	0.635396i	$-0.219163\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−1.60082	+	1.56121i	−0.715907	+	0.698196i
$5$	−1.60082	+	1.56121i	−0.715907	+	0.698196i
$6$	1.02482	−	0.744577i	0.418382	−	0.303972i
$7$	−1.25694	−	0.913224i	−0.475081	−	0.345166i	0.324337	−	0.945941i	$-0.394859\pi$
$7$	−1.25694	−	0.913224i	−0.475081	−	0.345166i	−0.799418	+	0.600775i	$0.794859\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	1.12886	−	0.820164i	0.376286	−	0.273388i
$10$	−1.97948	−	1.04003i	−0.625967	−	0.328885i
$11$	2.51441	+	2.16281i	0.758122	+	0.652113i
$11$	2.51441	+	2.16281i	0.758122	+	0.652113i
$12$	1.02482	+	0.744577i	0.295841	+	0.214941i
$13$	−2.87302	+	2.08737i	−0.796832	+	0.578932i	−0.909983	−	0.414646i	$-0.863905\pi$
$13$	−2.87302	+	2.08737i	−0.796832	+	0.578932i	0.113151	+	0.993578i	$0.463905\pi$
$14$	0.480110	−	1.47763i	0.128315	−	0.394913i
$15$	2.50751	+	1.31745i	0.647436	+	0.340165i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−6.33003	+	4.59903i	−1.53526	+	1.11543i	−0.582033	+	0.813165i	$0.697742\pi$
$17$	−6.33003	+	4.59903i	−1.53526	+	1.11543i	−0.953224	+	0.302264i	$0.902258\pi$
$18$	1.12886	+	0.820164i	0.266075	+	0.193314i
$19$	−6.06809	−	4.40873i	−1.39212	−	1.01143i	−0.995630	−	0.0933906i	$-0.970229\pi$
$19$	−6.06809	−	4.40873i	−1.39212	−	1.01143i	−0.396486	−	0.918041i	$-0.629771\pi$
$20$	0.377430	−	2.20398i	0.0843958	−	0.492826i
$21$	−0.608179	+	1.87178i	−0.132716	+	0.408457i
$22$	−1.27996	+	3.05969i	−0.272889	+	0.652328i
$23$	−4.09001	+	2.97156i	−0.852825	+	0.619614i	−0.925924	−	0.377711i	$-0.876711\pi$
$23$	−4.09001	+	2.97156i	−0.852825	+	0.619614i	0.0730983	+	0.997325i	$0.476711\pi$
$24$	−0.391447	+	1.20475i	−0.0799038	+	0.245919i
$25$	0.125226	−	4.99843i	0.0250453	−	0.999686i
$26$	−2.87302	−	2.08737i	−0.563445	−	0.409367i
$27$	−4.50445	−	3.27267i	−0.866881	−	0.629826i
$28$	1.55367			0.293616
$29$	−2.29031	+	1.66401i	−0.425300	+	0.308998i	−0.779767	−	0.626070i	$-0.784662\pi$
$29$	−2.29031	+	1.66401i	−0.425300	+	0.308998i	0.354467	+	0.935069i	$0.384662\pi$
$30$	−0.478109	+	2.79190i	−0.0872903	+	0.509728i
$31$	0.336000			0.0603474			0.0301737	−	0.999545i	$-0.490394\pi$
$31$	0.336000			0.0603474			0.0301737	+	0.999545i	$0.490394\pi$
$32$	1.00000			0.176777
$33$	1.62139	−	3.87586i	0.282248	−	0.674700i
$34$	−6.33003	−	4.59903i	−1.08559	−	0.788728i
$35$	3.43788	−	0.500455i	0.581107	−	0.0845924i
$36$	−0.431186	+	1.32705i	−0.0718643	+	0.221175i
$37$	1.68155	+	5.17528i	0.276445	+	0.850812i	0.988833	+	0.149026i	$0.0476137\pi$
$37$	1.68155	+	5.17528i	0.276445	+	0.850812i	−0.712388	+	0.701786i	$0.752386\pi$
$38$	2.31780	−	7.13347i	0.375998	−	1.15720i
$39$	3.63939	+	2.64417i	0.582769	+	0.423407i
$40$	2.21275	−	0.322112i	0.349866	−	0.0509303i
$41$	−6.25824			−0.977373			−0.488687	−	0.872459i	$-0.662524\pi$
$41$	−6.25824			−0.977373			−0.488687	+	0.872459i	$0.662524\pi$
$42$	−1.96811			−0.303686
$43$	5.91777			0.902452			0.451226	−	0.892410i	$-0.350987\pi$
$43$	5.91777			0.902452			0.451226	+	0.892410i	$0.350987\pi$
$44$	−3.30547	−	0.271822i	−0.498318	−	0.0409788i
$45$	−0.526645	+	3.07532i	−0.0785076	+	0.458442i
$46$	−4.09001	−	2.97156i	−0.603039	−	0.438133i
$47$	0.545087	+	1.67760i	0.0795091	+	0.244704i	0.982908	−	0.184097i	$-0.0589361\pi$
$47$	0.545087	+	1.67760i	0.0795091	+	0.244704i	−0.903399	+	0.428801i	$0.858936\pi$
$48$	−1.26675			−0.182840
$49$	−1.41719	−	4.36165i	−0.202455	−	0.623093i
$50$	4.79249	−	1.42550i	0.677760	−	0.201597i
$51$	8.01856	+	5.82582i	1.12282	+	0.815778i
$52$	1.09739	−	3.37743i	0.152181	−	0.468366i
$53$	4.29125	+	3.11777i	0.589448	+	0.428259i	0.842118	−	0.539293i	$-0.181309\pi$
$53$	4.29125	+	3.11777i	0.589448	+	0.428259i	−0.252670	+	0.967553i	$0.581309\pi$
$54$	1.72055	−	5.29529i	0.234137	−	0.720598i
$55$	−7.40172	+	0.463256i	−0.998047	+	0.0624654i
$56$	0.480110	+	1.47763i	0.0641574	+	0.197456i
$57$	−2.93608	+	9.03632i	−0.388893	+	1.19689i
$58$	−2.29031	−	1.66401i	−0.300732	−	0.218495i
$59$	0.0523156	+	0.161011i	0.00681091	+	0.0209618i	0.954404	−	0.298517i	$-0.0964921\pi$
$59$	0.0523156	+	0.161011i	0.00681091	+	0.0209618i	−0.947593	+	0.319479i	$0.896492\pi$
$60$	−2.80299	+	0.408035i	−0.361865	+	0.0526771i
$61$	4.17129	+	3.03062i	0.534079	+	0.388031i	0.821881	−	0.569659i	$-0.192925\pi$
$61$	4.17129	+	3.03062i	0.534079	+	0.388031i	−0.287803	+	0.957690i	$0.592925\pi$
$62$	0.103830	+	0.319555i	0.0131864	+	0.0405835i
$63$	−2.16791			−0.273131
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	1.34034	−	7.82689i	0.166249	−	0.970806i
$66$	4.18720	+	0.344331i	0.515408	+	0.0423842i
$67$	1.86161	+	5.72946i	0.227432	+	0.699965i	0.998036	+	0.0626495i	$0.0199550\pi$
$67$	1.86161	+	5.72946i	0.227432	+	0.699965i	−0.770603	+	0.637315i	$0.780045\pi$
$68$	2.41786	−	7.44139i	0.293208	−	0.902401i
$69$	5.18101	+	3.76423i	0.623721	+	0.453160i
$70$	1.53832	+	3.11496i	0.183865	+	0.372309i
$71$	10.3825			1.23217			0.616087	−	0.787678i	$-0.288717\pi$
$71$	10.3825			1.23217			0.616087	+	0.787678i	$0.288717\pi$
$72$	−1.39535			−0.164443
$73$	−12.2921			−1.43868			−0.719340	−	0.694659i	$-0.755555\pi$
$73$	−12.2921			−1.43868			−0.719340	+	0.694659i	$0.755555\pi$
$74$	−4.40236	+	3.19850i	−0.511764	+	0.371818i
$75$	−6.07088	+	1.80575i	−0.701005	+	0.208511i
$76$	7.50057			0.860375
$77$	−1.18534	−	5.01475i	−0.135082	−	0.571484i
$78$	−1.39012	+	4.27836i	−0.157401	+	0.484429i
$79$	4.98259	+	3.62006i	0.560585	+	0.407289i	0.831673	−	0.555266i	$-0.187383\pi$
$79$	4.98259	+	3.62006i	0.560585	+	0.407289i	−0.271088	+	0.962555i	$0.587383\pi$
$80$	0.990123	+	2.00491i	0.110699	+	0.224156i
$81$	−0.885943	+	2.72665i	−0.0984381	+	0.302961i
$82$	−1.93390	−	5.95194i	−0.213564	−	0.657282i
$83$	10.0939	−	7.33362i	1.10794	−	0.804969i	0.125606	−	0.992080i	$-0.459912\pi$
$83$	10.0939	−	7.33362i	1.10794	−	0.804969i	0.982339	+	0.187111i	$0.0599124\pi$
$84$	−0.608179	−	1.87178i	−0.0663578	−	0.204228i
$85$	2.95314	−	17.2447i	0.320313	−	1.87045i
$86$	1.82869	+	5.62813i	0.197193	+	0.606897i
$87$	2.90125	+	2.10788i	0.311046	+	0.225988i
$88$	−0.762927	−	3.22768i	−0.0813283	−	0.344072i
$89$	−2.72294	+	1.97833i	−0.288631	+	0.209703i	−0.722673	−	0.691190i	$-0.757087\pi$
$89$	−2.72294	+	1.97833i	−0.288631	+	0.209703i	0.434042	+	0.900892i	$0.357087\pi$
$90$	−3.08755	+	0.449457i	−0.325456	+	0.0473770i
$91$	5.51746			0.578387
$92$	1.56224	−	4.80809i	0.162875	−	0.501278i
$93$	−0.131526	−	0.404796i	−0.0136386	−	0.0419754i
$94$	−1.42706	+	1.03682i	−0.147190	+	0.106939i
$95$	16.5969	−	2.41602i	1.70280	−	0.247879i
$96$	−0.391447	−	1.20475i	−0.0399519	−	0.122959i
$97$	1.81374	+	1.31776i	0.184157	+	0.133798i	0.676044	−	0.736861i	$-0.263693\pi$
$97$	1.81374	+	1.31776i	0.184157	+	0.133798i	−0.491887	+	0.870659i	$0.663693\pi$
$98$	3.71024	−	2.69565i	0.374791	−	0.272302i
$99$	4.61227	+	0.379286i	0.463551	+	0.0381197i
$100$	2.83669	+	4.11742i	0.283669	+	0.411742i
$101$	4.40772	−	13.5656i	0.438584	−	1.34982i	−0.450785	−	0.892633i	$-0.648856\pi$
$101$	4.40772	−	13.5656i	0.438584	−	1.34982i	0.889369	−	0.457190i	$-0.151144\pi$
$102$	−3.06282	+	9.42638i	−0.303264	+	0.933351i
$103$	−7.47500	+	5.43091i	−0.736534	+	0.535123i	−0.891624	−	0.452777i	$-0.850433\pi$
$103$	−7.47500	+	5.43091i	−0.736534	+	0.535123i	0.155090	+	0.987900i	$0.450433\pi$
$104$	3.55124			0.348228
$105$	−1.94867	−	3.94588i	−0.190171	−	0.385078i
$106$	−1.63911	+	5.04466i	−0.159205	+	0.489981i
$107$	2.02166	−	1.46882i	0.195441	−	0.141996i	−0.485761	−	0.874092i	$-0.661457\pi$
$107$	2.02166	−	1.46882i	0.195441	−	0.141996i	0.681202	+	0.732095i	$0.261457\pi$
$108$	5.56780			0.535762
$109$	−11.3204	−	8.22478i	−1.08430	−	0.787791i	−0.105873	−	0.994380i	$-0.533764\pi$
$109$	−11.3204	−	8.22478i	−1.08430	−	0.787791i	−0.978428	+	0.206589i	$0.933764\pi$
$110$	−2.72784	−	6.89630i	−0.260089	−	0.657536i
$111$	5.57669	−	4.05170i	0.529316	−	0.384570i
$112$	−1.25694	+	0.913224i	−0.118770	+	0.0862916i
$113$	−6.55605			−0.616742			−0.308371	−	0.951266i	$-0.599784\pi$
$113$	−6.55605			−0.616742			−0.308371	+	0.951266i	$0.599784\pi$
$114$	−9.50135			−0.889883
$115$	1.90810	−	11.1423i	0.177932	−	1.03902i
$116$	0.874820	−	2.69242i	0.0812250	−	0.249985i
$117$	−1.53125	+	4.71269i	−0.141564	+	0.435688i
$118$	−0.136964	+	0.0995102i	−0.0126086	+	0.00916066i
$119$	12.1564			1.11438
$120$	−1.25424	−	2.53972i	−0.114496	−	0.231843i
$121$	1.64447	+	10.8764i	0.149498	+	0.988762i
$122$	−1.59329	+	4.90364i	−0.144250	+	0.443955i
$123$	2.44977	+	7.53962i	0.220888	+	0.679824i
$124$	−0.271830	+	0.197496i	−0.0244110	+	0.0177357i
$125$	7.60315	+	8.19708i	0.680047	+	0.733169i
$126$	−0.669920	−	2.06180i	−0.0596812	−	0.183680i
$127$	−14.5804	−	10.5933i	−1.29380	−	0.940003i	−0.293929	−	0.955827i	$-0.594963\pi$
$127$	−14.5804	−	10.5933i	−1.29380	−	0.940003i	−0.999875	+	0.0158238i	$0.994963\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−2.31649	−	7.12944i	−0.203956	−	0.627712i
$130$	7.85800	−	1.14390i	0.689192	−	0.100326i
$131$	4.58161	+	14.1008i	0.400297	+	1.23199i	0.924759	+	0.380554i	$0.124267\pi$
$131$	4.58161	+	14.1008i	0.400297	+	1.23199i	−0.524461	+	0.851434i	$0.675733\pi$
$132$	0.966437	+	4.08867i	0.0841176	+	0.355873i
$133$	3.60110	+	11.0831i	0.312255	+	0.961023i
$134$	−4.87377	+	3.54100i	−0.421029	+	0.305896i
$135$	12.3201	−	1.79345i	1.06035	−	0.154356i
$136$	7.82434			0.670932
$137$	0.903732	−	2.78140i	0.0772110	−	0.237631i	−0.905000	−	0.425412i	$-0.860129\pi$
$137$	0.903732	−	2.78140i	0.0772110	−	0.237631i	0.982211	+	0.187780i	$0.0601293\pi$
$138$	−1.97897	+	6.09065i	−0.168461	+	0.518470i
$139$	1.66614			0.141320			0.0706602	−	0.997500i	$-0.477489\pi$
$139$	1.66614			0.141320			0.0706602	+	0.997500i	$0.477489\pi$
$140$	−2.48714	+	2.42561i	−0.210202	+	0.205001i
$141$	1.80772	−	1.31339i	0.152238	−	0.110607i
$142$	3.20837	+	9.87433i	0.269240	+	0.828636i
$143$	−11.7385	−	0.965308i	−0.981624	−	0.0807231i
$144$	−0.431186	−	1.32705i	−0.0359321	−	0.110588i
$145$	1.06849	−	6.23943i	0.0887337	−	0.518156i
$146$	−3.79846	−	11.6905i	−0.314363	−	0.967510i
$147$	−4.69995	+	3.41471i	−0.387645	+	0.281641i
$148$	−4.40236	−	3.19850i	−0.361872	−	0.262915i
$149$	1.92564	+	5.92652i	0.157755	+	0.485519i	0.998430	−	0.0560209i	$-0.0178414\pi$
$149$	1.92564	+	5.92652i	0.157755	+	0.485519i	−0.840675	+	0.541540i	$0.817841\pi$
$150$	−3.59338	−	5.21574i	−0.293398	−	0.425864i
$151$	−11.5000	+	8.35522i	−0.935854	+	0.679938i	−0.947419	−	0.319995i	$-0.896319\pi$
$151$	−11.5000	+	8.35522i	−0.935854	+	0.679938i	0.0115649	+	0.999933i	$0.496319\pi$
$152$	2.31780	+	7.13347i	0.187999	+	0.578601i
$153$	−3.37374	+	10.3833i	−0.272751	+	0.839441i
$154$	4.40302	−	2.67697i	0.354806	−	0.215716i
$155$	−0.537874	+	0.524568i	−0.0432031	+	0.0421343i
$156$	−4.49854			−0.360171
$157$	16.8290	−	12.2270i	1.34310	−	0.975822i	0.343780	−	0.939050i	$-0.388293\pi$
$157$	16.8290	−	12.2270i	1.34310	−	0.975822i	0.999324	−	0.0367718i	$-0.0117075\pi$
$158$	−1.90318	+	5.85739i	−0.151409	+	0.465989i
$159$	2.07634	−	6.39033i	0.164665	−	0.506786i
$160$	−1.60082	+	1.56121i	−0.126556	+	0.123425i
$161$	7.85462			0.619030
$162$	−2.86697			−0.225251
$163$	−12.6052	+	9.15818i	−0.987312	+	0.717324i	−0.959331	−	0.282284i	$-0.908908\pi$
$163$	−12.6052	+	9.15818i	−0.987312	+	0.717324i	−0.0279812	+	0.999608i	$0.508908\pi$
$164$	5.06302	−	3.67850i	0.395356	−	0.287243i
$165$	3.45549	+	8.73588i	0.269009	+	0.680087i
$166$	10.0939	+	7.33362i	0.783435	+	0.569199i
$167$	21.1947			1.64009			0.820047	−	0.572296i	$-0.193947\pi$
$167$	21.1947			1.64009			0.820047	+	0.572296i	$0.193947\pi$
$168$	1.59223	−	1.15683i	0.122844	−	0.0892511i
$169$	−0.120104	+	0.369641i	−0.00923875	+	0.0284340i
$170$	17.3133	−	2.52031i	1.32787	−	0.193299i
$171$	−10.4659			−0.800347
$172$	−4.78758	+	3.47838i	−0.365049	+	0.265224i
$173$	−6.36047	+	19.5755i	−0.483577	+	1.48830i	0.350453	+	0.936580i	$0.386028\pi$
$173$	−6.36047	+	19.5755i	−0.483577	+	1.48830i	−0.834031	+	0.551718i	$0.813972\pi$
$174$	−1.10818	+	3.41062i	−0.0840108	+	0.258559i
$175$	−4.72209	+	6.16839i	−0.356956	+	0.466287i
$176$	2.83395	−	1.72300i	0.213617	−	0.129876i
$177$	0.173499	−	0.126054i	0.0130410	−	0.00947484i
$178$	−2.72294	−	1.97833i	−0.204093	−	0.148282i
$179$	−1.82744	−	5.62428i	−0.136589	−	0.420379i	0.859245	−	0.511565i	$-0.170934\pi$
$179$	−1.82744	−	5.62428i	−0.136589	−	0.420379i	−0.995834	+	0.0911864i	$0.970934\pi$
$180$	−1.38156	−	2.79754i	−0.102976	−	0.208516i
$181$	−11.1611	+	8.10901i	−0.829598	+	0.602738i	−0.919445	−	0.393217i	$-0.871362\pi$
$181$	−11.1611	+	8.10901i	−0.829598	+	0.602738i	0.0898477	+	0.995956i	$0.471362\pi$
$182$	1.70499	+	5.24742i	0.126382	+	0.388964i
$183$	2.01830	−	6.21169i	0.149197	−	0.459181i
$184$	5.05553			0.372698
$185$	−10.7716	−	5.65942i	−0.791942	−	0.416089i
$186$	0.344340	−	0.250178i	0.0252482	−	0.0183439i
$187$	−25.8631	−	2.12683i	−1.89130	−	0.155529i
$188$	−1.42706	−	1.03682i	−0.104079	−	0.0756176i
$189$	2.67316	+	8.22714i	0.194444	+	0.598436i
$190$	7.42649	+	15.0380i	0.538774	+	1.09097i
$191$	−0.259848	−	0.799730i	−0.0188019	−	0.0578665i	0.941215	−	0.337807i	$-0.109685\pi$
$191$	−0.259848	−	0.799730i	−0.0188019	−	0.0578665i	−0.960017	+	0.279941i	$0.909685\pi$
$192$	1.02482	−	0.744577i	0.0739601	−	0.0537352i
$193$	−5.53337	−	17.0300i	−0.398301	−	1.22584i	−0.926361	−	0.376636i	$-0.877081\pi$
$193$	−5.53337	−	17.0300i	−0.398301	−	1.22584i	0.528061	−	0.849207i	$-0.322919\pi$
$194$	−0.692787	+	2.13218i	−0.0497392	+	0.153082i
$195$	−9.95412	+	1.44903i	−0.712829	+	0.103767i
$196$	3.71024	+	2.69565i	0.265017	+	0.192546i
$197$	−0.984307	+	3.02939i	−0.0701290	+	0.215835i	−0.979978	−	0.199104i	$-0.936197\pi$
$197$	−0.984307	+	3.02939i	−0.0701290	+	0.215835i	0.909849	+	0.414939i	$0.136197\pi$
$198$	1.06455	+	4.50374i	0.0756541	+	0.320067i
$199$	21.7336			1.54066			0.770328	−	0.637648i	$-0.220093\pi$
$199$	21.7336			1.54066			0.770328	+	0.637648i	$0.220093\pi$
$200$	−3.03931	+	3.97021i	−0.214912	+	0.280736i
$201$	6.17384	−	4.48556i	0.435469	−	0.316387i
$202$	14.2637			1.00359
$203$	4.39840			0.308707
$204$	−9.91148			−0.693943
$205$	10.0183	−	9.77045i	0.699708	−	0.682398i
$206$	−7.47500	−	5.43091i	−0.520808	−	0.378389i
$207$	−2.17987	+	6.70895i	−0.151511	+	0.466304i
$208$	1.09739	+	3.37743i	0.0760906	+	0.234183i
$209$	−5.72239	−	24.2095i	−0.395826	−	1.67460i
$210$	3.15058	−	3.07264i	0.217411	−	0.212032i
$211$	3.88619	+	11.9605i	0.267537	+	0.823393i	0.991098	+	0.133133i	$0.0425038\pi$
$211$	3.88619	+	11.9605i	0.267537	+	0.823393i	−0.723562	+	0.690260i	$0.757496\pi$
$212$	−5.30427			−0.364299
$213$	−4.06419	−	12.5083i	−0.278474	−	0.857055i
$214$	2.02166	+	1.46882i	0.138198	+	0.100406i
$215$	−9.47327	+	9.23890i	−0.646071	+	0.630088i
$216$	1.72055	+	5.29529i	0.117068	+	0.360299i
$217$	−0.422334	−	0.306843i	−0.0286699	−	0.0208299i
$218$	4.32402	−	13.3080i	0.292860	−	0.901329i
$219$	4.81170	+	14.8089i	0.325144	+	1.00069i
$220$	5.71582	−	4.72540i	0.385360	−	0.318586i
$221$	8.58639	−	26.4262i	0.577583	−	1.77762i
$222$	5.57669	+	4.05170i	0.374283	+	0.271932i
$223$	4.29881	−	13.2304i	0.287870	−	0.885972i	−0.697654	−	0.716435i	$-0.745773\pi$
$223$	4.29881	−	13.2304i	0.287870	−	0.885972i	0.985524	−	0.169537i	$-0.0542272\pi$
$224$	−1.25694	−	0.913224i	−0.0839832	−	0.0610173i
$225$	−3.95817	−	5.74523i	−0.263878	−	0.383015i
$226$	−2.02593	−	6.23518i	−0.134763	−	0.414758i
$227$	7.75142			0.514480			0.257240	−	0.966348i	$-0.417187\pi$
$227$	7.75142			0.514480			0.257240	+	0.966348i	$0.417187\pi$
$228$	−2.93608	−	9.03632i	−0.194447	−	0.598445i
$229$	−3.53716	−	2.56990i	−0.233742	−	0.169824i	0.464749	−	0.885443i	$-0.346145\pi$
$229$	−3.53716	−	2.56990i	−0.233742	−	0.169824i	−0.698491	+	0.715619i	$0.746145\pi$
$230$	11.1866	−	1.62844i	0.737622	−	0.107376i
$231$	−5.57753	+	3.39104i	−0.366974	+	0.223114i
$232$	2.83098			0.185863
$233$	−24.3461			−1.59497			−0.797483	−	0.603341i	$-0.793836\pi$
$233$	−24.3461			−1.59497			−0.797483	+	0.603341i	$0.793836\pi$
$234$	−4.95521			−0.323933
$235$	−3.49168	−	1.83454i	−0.227772	−	0.119672i
$236$	−0.136964	−	0.0995102i	−0.00891560	−	0.00647756i
$237$	2.41085	−	7.41984i	0.156602	−	0.481970i
$238$	3.75655	+	11.5615i	0.243501	+	0.749418i
$239$	−6.47926	+	19.9411i	−0.419109	+	1.28988i	0.489415	+	0.872051i	$0.337210\pi$
$239$	−6.47926	+	19.9411i	−0.419109	+	1.28988i	−0.908524	+	0.417833i	$0.862790\pi$
$240$	2.02783	−	1.97767i	0.130896	−	0.127658i
$241$	3.73477	+	2.71347i	0.240578	+	0.174790i	0.701541	−	0.712629i	$-0.252496\pi$
$241$	3.73477	+	2.71347i	0.240578	+	0.174790i	−0.460963	+	0.887419i	$0.652496\pi$
$242$	−9.83588	+	4.92497i	−0.632275	+	0.316589i
$243$	−13.0717			−0.838548
$244$	−5.15600			−0.330079
$245$	9.07812	+	4.76967i	0.579980	+	0.304723i
$246$	−6.41358	+	4.65974i	−0.408915	+	0.297094i
$247$	26.6364			1.69483
$248$	−0.271830	−	0.197496i	−0.0172612	−	0.0125410i
$249$	−12.7864	−	9.28986i	−0.810304	−	0.588721i
$250$	−5.44638	+	9.76406i	−0.344459	+	0.617534i
$251$	1.54790	−	4.76394i	0.0977025	−	0.300697i	−0.890246	−	0.455480i	$-0.849468\pi$
$251$	1.54790	−	4.76394i	0.0977025	−	0.300697i	0.987949	+	0.154783i	$0.0494677\pi$
$252$	1.75387	−	1.27426i	0.110484	−	0.0802710i
$253$	−16.7109	−	1.37421i	−1.05060	−	0.0863956i
$254$	5.56923	−	17.1403i	0.349444	−	1.07548i
$255$	−21.9316	+	3.19261i	−1.37341	+	0.199929i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−14.8465	−	10.7866i	−0.926098	−	0.672850i	0.0189362	−	0.999821i	$-0.493972\pi$
$257$	−14.8465	−	10.7866i	−0.926098	−	0.672850i	−0.945034	+	0.326971i	$0.893972\pi$
$258$	6.06466	−	4.40623i	0.377569	−	0.274320i
$259$	2.61258	−	8.04068i	0.162338	−	0.499624i
$260$	3.51617	+	7.11992i	0.218063	+	0.441559i
$261$	−1.22068	+	3.75686i	−0.0755580	+	0.232544i
$262$	−11.9948	+	8.71475i	−0.741042	+	0.538399i
$263$	−5.88804	−	4.27791i	−0.363072	−	0.263787i	0.391260	−	0.920280i	$-0.372039\pi$
$263$	−5.88804	−	4.27791i	−0.363072	−	0.263787i	−0.754332	+	0.656493i	$0.772039\pi$
$264$	−3.58991	+	2.18260i	−0.220944	+	0.134330i
$265$	−11.7370	+	1.70857i	−0.720999	+	0.104957i
$266$	−9.42781	+	6.84970i	−0.578056	+	0.419982i
$267$	3.44928	+	2.50605i	0.211093	+	0.153368i
$268$	−4.87377	−	3.54100i	−0.297713	−	0.216301i
$269$	16.0260	−	11.6435i	0.977120	−	0.709919i	0.0200568	−	0.999799i	$-0.493615\pi$
$269$	16.0260	−	11.6435i	0.977120	−	0.709919i	0.957063	+	0.289880i	$0.0936153\pi$
$270$	5.51281	+	11.1629i	0.335499	+	0.679354i
$271$	−6.05682	+	4.40054i	−0.367925	+	0.267313i	−0.756350	−	0.654167i	$-0.773019\pi$
$271$	−6.05682	+	4.40054i	−0.367925	+	0.267313i	0.388425	+	0.921480i	$0.373019\pi$
$272$	2.41786	+	7.44139i	0.146604	+	0.451201i
$273$	−2.15979	−	6.64716i	−0.130717	−	0.402304i
$274$	2.92454			0.176678
$275$	11.1255	−	12.2972i	0.670896	−	0.741552i
$276$	−6.40408			−0.385481
$277$	−7.46857	−	22.9859i	−0.448743	−	1.38109i	−0.878327	−	0.478061i	$-0.841340\pi$
$277$	−7.46857	−	22.9859i	−0.448743	−	1.38109i	0.429584	−	0.903027i	$-0.358660\pi$
$278$	0.514866	+	1.58460i	0.0308796	+	0.0950377i
$279$	0.379297	−	0.275575i	0.0227079	−	0.0164982i
$280$	−3.07546	−	1.61586i	−0.183794	−	0.0965658i
$281$	−2.25456	+	1.63803i	−0.134496	+	0.0977168i	−0.652999	−	0.757359i	$-0.726489\pi$
$281$	−2.25456	+	1.63803i	−0.134496	+	0.0977168i	0.518503	+	0.855076i	$0.326489\pi$
$282$	1.80772	+	1.31339i	0.107648	+	0.0782110i
$283$	−21.0372	−	15.2844i	−1.25053	−	0.908564i	−0.252278	−	0.967655i	$-0.581180\pi$
$283$	−21.0372	−	15.2844i	−1.25053	−	0.908564i	−0.998253	+	0.0590910i	$0.981180\pi$
$284$	−8.39961	+	6.10267i	−0.498425	+	0.362127i
$285$	−9.40750	−	19.0493i	−0.557252	−	1.12838i
$286$	−2.70934	−	11.4623i	−0.160207	−	0.677780i
$287$	7.86626	+	5.71518i	0.464331	+	0.337356i
$288$	1.12886	−	0.820164i	0.0665186	−	0.0483286i
$289$	13.6648	−	42.0561i	0.803814	−	2.47389i
$290$	6.26423	−	0.911891i	0.367848	−	0.0535481i
$291$	0.877588	−	2.70094i	0.0514451	−	0.158332i
$292$	9.94450	−	7.22510i	0.581958	−	0.422817i
$293$	18.5315	+	13.4639i	1.08262	+	0.786571i	0.978138	−	0.207956i	$-0.0666811\pi$
$293$	18.5315	+	13.4639i	1.08262	+	0.786571i	0.104483	+	0.994527i	$0.466681\pi$
$294$	−4.69995	−	3.41471i	−0.274106	−	0.199150i
$295$	−0.335120	−	0.176073i	−0.0195114	−	0.0102514i
$296$	1.68155	−	5.17528i	0.0977382	−	0.300807i
$297$	−4.24783	−	17.9711i	−0.246484	−	1.04279i
$298$	−5.04140	+	3.66279i	−0.292040	+	0.212180i
$299$	5.54791	−	17.0747i	0.320844	−	0.987456i
$300$	3.85005	−	5.02926i	0.222283	−	0.290365i
$301$	−7.43831	−	5.40425i	−0.428737	−	0.311496i
$302$	−11.5000	−	8.35522i	−0.661749	−	0.480789i
$303$	−18.0685			−1.03801
$304$	−6.06809	+	4.40873i	−0.348029	+	0.252858i
$305$	−11.4089	+	1.66081i	−0.653272	+	0.0950975i
$306$	−10.9177			−0.624121
$307$	12.2641			0.699947			0.349973	−	0.936760i	$-0.386191\pi$
$307$	12.2641			0.699947			0.349973	+	0.936760i	$0.386191\pi$
$308$	3.90656	+	3.36030i	0.222597	+	0.191471i
$309$	9.46896	+	6.87960i	0.538670	+	0.391367i
$310$	−0.665106	−	0.349449i	−0.0377755	−	0.0198473i
$311$	−8.54650	+	26.3034i	−0.484627	+	1.49153i	0.347892	+	0.937535i	$0.386897\pi$
$311$	−8.54650	+	26.3034i	−0.484627	+	1.49153i	−0.832520	+	0.553995i	$0.813103\pi$
$312$	−1.39012	−	4.27836i	−0.0787003	−	0.242215i
$313$	−7.03776	+	21.6600i	−0.397798	+	1.22430i	0.528963	+	0.848645i	$0.322581\pi$
$313$	−7.03776	+	21.6600i	−0.397798	+	1.22430i	−0.926761	+	0.375651i	$0.877419\pi$
$314$	16.8290	+	12.2270i	0.949718	+	0.690010i
$315$	3.47042	−	3.38456i	0.195536	−	0.190699i
$316$	−6.15882			−0.346461
$317$	−6.15260			−0.345564			−0.172782	−	0.984960i	$-0.555276\pi$
$317$	−6.15260			−0.345564			−0.172782	+	0.984960i	$0.555276\pi$
$318$	6.71919			0.376793
$319$	−9.35770	−	0.769523i	−0.523931	−	0.0430850i
$320$	−1.97948	−	1.04003i	−0.110656	−	0.0581392i
$321$	−2.56093	−	1.86063i	−0.142937	−	0.103850i
$322$	2.42721	+	7.47018i	0.135263	+	0.416297i
$323$	58.6871			3.26544
$324$	−0.885943	−	2.72665i	−0.0492190	−	0.151481i
$325$	10.0738	+	14.6220i	0.558794	+	0.811081i
$326$	−12.6052	−	9.15818i	−0.698135	−	0.507225i
$327$	−5.47745	+	16.8579i	−0.302904	+	0.932242i
$328$	5.06302	+	3.67850i	0.279559	+	0.203111i
$329$	0.846884	−	2.60644i	0.0466902	−	0.143698i
$330$	−7.24051	+	5.98590i	−0.398577	+	0.329513i
$331$	−0.818494	−	2.51906i	−0.0449885	−	0.138460i	0.926039	−	0.377427i	$-0.123191\pi$
$331$	−0.818494	−	2.51906i	−0.0449885	−	0.138460i	−0.971028	+	0.238967i	$0.923191\pi$
$332$	−3.85551	+	11.8660i	−0.211599	+	0.651234i
$333$	6.14282	+	4.46302i	0.336624	+	0.244572i
$334$	6.54952	+	20.1573i	0.358374	+	1.10296i
$335$	−11.9250	−	6.26543i	−0.651533	−	0.342317i
$336$	1.59223	+	1.15683i	0.0868635	+	0.0631100i
$337$	3.78516	+	11.6495i	0.206191	+	0.634590i	0.999662	+	0.0259829i	$0.00827155\pi$
$337$	3.78516	+	11.6495i	0.206191	+	0.634590i	−0.793471	+	0.608607i	$0.791728\pi$
$338$	−0.388664			−0.0211405
$339$	2.56635	+	7.89841i	0.139385	+	0.428983i
$340$	7.74706	+	15.6871i	0.420143	+	0.850752i
$341$	0.844840	+	0.726706i	0.0457507	+	0.0393533i
$342$	−3.23414	−	9.95366i	−0.174882	−	0.538232i
$343$	−5.56261	+	17.1200i	−0.300353	+	0.924391i
$344$	−4.78758	−	3.47838i	−0.258129	−	0.187542i
$345$	−14.1706	+	2.06283i	−0.762920	+	0.111059i
$346$	−20.5829			−1.10654
$347$	14.6953			0.788883			0.394441	−	0.918921i	$-0.370938\pi$
$347$	14.6953			0.788883			0.394441	+	0.918921i	$0.370938\pi$
$348$	−3.58614			−0.192237
$349$	−21.5887	+	15.6851i	−1.15562	+	0.839604i	−0.989217	−	0.146455i	$-0.953214\pi$
$349$	−21.5887	+	15.6851i	−1.15562	+	0.839604i	−0.166398	+	0.986059i	$0.553214\pi$
$350$	−7.32570	−	2.58484i	−0.391575	−	0.138165i
$351$	19.7726			1.05538
$352$	2.51441	+	2.16281i	0.134018	+	0.115278i
$353$	−7.10805	+	21.8763i	−0.378323	+	1.16436i	0.562886	+	0.826535i	$0.309691\pi$
$353$	−7.10805	+	21.8763i	−0.378323	+	1.16436i	−0.941209	+	0.337824i	$0.890309\pi$
$354$	0.173499	+	0.126054i	0.00922137	+	0.00669972i
$355$	−16.6205	+	16.2093i	−0.882122	+	0.860299i
$356$	1.04007	−	3.20101i	0.0551236	−	0.169653i
$357$	−4.75860	−	14.6455i	−0.251852	−	0.775121i
$358$	4.78430	−	3.47600i	0.252858	−	0.183712i
$359$	0.395995	+	1.21875i	0.0208998	+	0.0643230i	0.960962	−	0.276679i	$-0.0892338\pi$
$359$	0.395995	+	1.21875i	0.0208998	+	0.0643230i	−0.940063	+	0.341002i	$0.889234\pi$
$360$	2.23369	−	2.17843i	0.117726	−	0.114813i
$361$	11.5135	+	35.4350i	0.605976	+	1.86500i
$362$	−11.1611	−	8.10901i	−0.586614	−	0.426200i
$363$	12.4596	−	6.23871i	0.653959	−	0.327447i
$364$	−4.46372	+	3.24308i	−0.233962	+	0.169984i
$365$	19.6774	−	19.1906i	1.02996	−	1.00448i
$366$	6.53135			0.341399
$367$	1.01779	−	3.13242i	0.0531280	−	0.163511i	−0.920972	−	0.389629i	$-0.872603\pi$
$367$	1.01779	−	3.13242i	0.0531280	−	0.163511i	0.974100	+	0.226118i	$0.0726033\pi$
$368$	1.56224	+	4.80809i	0.0814376	+	0.250639i
$369$	−7.06467	+	5.13278i	−0.367772	+	0.267202i
$370$	2.05383	−	11.9932i	0.106773	−	0.623499i
$371$	−2.54664	−	7.83774i	−0.132215	−	0.406915i
$372$	0.344340	+	0.250178i	0.0178532	+	0.0129711i
$373$	−9.64327	+	7.00625i	−0.499310	+	0.362770i	−0.808753	−	0.588148i	$-0.799857\pi$
$373$	−9.64327	+	7.00625i	−0.499310	+	0.362770i	0.309444	+	0.950918i	$0.399857\pi$
$374$	−5.96940	−	25.2545i	−0.308670	−	1.30588i
$375$	6.89920	−	12.3686i	0.356273	−	0.638713i
$376$	0.545087	−	1.67760i	0.0281107	−	0.0865158i
$377$	3.10670	−	9.56144i	0.160003	−	0.492439i
$378$	−6.99842	+	5.08465i	−0.359960	+	0.261526i
$379$	−4.48407			−0.230331			−0.115166	−	0.993346i	$-0.536740\pi$
$379$	−4.48407			−0.230331			−0.115166	+	0.993346i	$0.536740\pi$
$380$	−12.0070	+	11.7100i	−0.615948	+	0.600710i
$381$	−7.05482	+	21.7125i	−0.361429	+	1.11236i
$382$	0.680291	−	0.494260i	0.0348067	−	0.0252886i
$383$	1.15620			0.0590793			0.0295396	−	0.999564i	$-0.490596\pi$
$383$	1.15620			0.0590793			0.0295396	+	0.999564i	$0.490596\pi$
$384$	1.02482	+	0.744577i	0.0522977	+	0.0379965i
$385$	9.72661	+	6.17714i	0.495714	+	0.314816i
$386$	14.4865	−	10.5251i	0.737346	−	0.535713i
$387$	6.68033	−	4.85354i	0.339580	−	0.246719i
$388$	−2.24191			−0.113816
$389$	−21.7354			−1.10203			−0.551014	−	0.834496i	$-0.685759\pi$
$389$	−21.7354			−1.10203			−0.551014	+	0.834496i	$0.685759\pi$
$390$	−4.45410	−	9.01915i	−0.225542	−	0.456703i
$391$	12.2235	−	37.6202i	0.618170	−	1.90253i
$392$	−1.41719	+	4.36165i	−0.0715787	+	0.220297i
$393$	15.1944	−	11.0394i	0.766458	−	0.556864i
$394$	−3.18528			−0.160472
$395$	−13.6279	+	1.98383i	−0.685694	+	0.0998172i
$396$	−3.95434	+	2.40418i	−0.198713	+	0.120814i
$397$	−0.764600	+	2.35320i	−0.0383742	+	0.118104i	−0.968409	−	0.249369i	$-0.919777\pi$
$397$	−0.764600	+	2.35320i	−0.0383742	+	0.118104i	0.930034	+	0.367473i	$0.119777\pi$
$398$	6.71606	+	20.6699i	0.336645	+	1.03609i
$399$	11.9427	−	8.67686i	0.597881	−	0.434386i
$400$	−4.71509	−	1.66370i	−0.235755	−	0.0831849i
$401$	−5.44575	−	16.7603i	−0.271948	−	0.836969i	−0.990011	−	0.140991i	$-0.954971\pi$
$401$	−5.44575	−	16.7603i	−0.271948	−	0.836969i	0.718063	−	0.695978i	$-0.245029\pi$
$402$	6.17384	+	4.48556i	0.307923	+	0.223719i
$403$	−0.965334	+	0.701356i	−0.0480867	+	0.0349370i
$404$	4.40772	+	13.5656i	0.219292	+	0.674912i
$405$	−2.83865	−	5.74801i	−0.141054	−	0.285621i
$406$	1.35918	+	4.18313i	0.0674550	+	0.207605i
$407$	−6.96507	+	16.6496i	−0.345246	+	0.825292i
$408$	−3.06282	−	9.42638i	−0.151632	−	0.466675i
$409$	−27.1875	+	19.7529i	−1.34434	+	0.976718i	−0.345064	+	0.938579i	$0.612143\pi$
$409$	−27.1875	+	19.7529i	−1.34434	+	0.976718i	−0.999272	+	0.0381383i	$0.987857\pi$
$410$	12.3881	+	6.50873i	0.611803	+	0.321443i
$411$	−3.70466			−0.182737
$412$	2.85520	−	8.78739i	0.140665	−	0.432924i
$413$	0.0812812	−	0.250158i	0.00399958	−	0.0123095i
$414$	−7.05421			−0.346695
$415$	−4.70907	+	27.4984i	−0.231159	+	1.34985i
$416$	−2.87302	+	2.08737i	−0.140861	+	0.102342i
$417$	−0.652206	−	2.00728i	−0.0319387	−	0.0982972i
$418$	21.2563	−	12.9235i	1.03968	−	0.632107i
$419$	−3.67671	−	11.3158i	−0.179619	−	0.552811i	0.820195	−	0.572084i	$-0.193865\pi$
$419$	−3.67671	−	11.3158i	−0.179619	−	0.552811i	−0.999814	+	0.0192731i	$0.993865\pi$
$420$	3.89584	+	2.04688i	0.190097	+	0.0998777i
$421$	11.5620	+	35.5843i	0.563499	+	1.73427i	0.672368	+	0.740217i	$0.265277\pi$
$421$	11.5620	+	35.5843i	0.563499	+	1.73427i	−0.108869	+	0.994056i	$0.534723\pi$
$422$	−10.1742	+	7.39198i	−0.495272	+	0.359836i
$423$	1.99124	+	1.44672i	0.0968172	+	0.0703418i
$424$	−1.63911	−	5.04466i	−0.0796023	−	0.244991i
$425$	22.1953	+	32.2161i	1.07663	+	1.56271i
$426$	10.6402	−	7.73056i	0.515519	−	0.374547i
$427$	−2.47545	−	7.61864i	−0.119795	−	0.368692i
$428$	−0.772205	+	2.37660i	−0.0373259	+	0.114877i
$429$	3.43205	+	14.5199i	0.165701	+	0.701025i
$430$	−11.7141	−	6.15463i	−0.564905	−	0.296803i
$431$	−4.93691			−0.237802			−0.118901	−	0.992906i	$-0.537937\pi$
$431$	−4.93691			−0.237802			−0.118901	+	0.992906i	$0.537937\pi$
$432$	−4.50445	+	3.27267i	−0.216720	+	0.157456i
$433$	9.68961	−	29.8216i	0.465653	−	1.43313i	−0.392507	−	0.919749i	$-0.628392\pi$
$433$	9.68961	−	29.8216i	0.465653	−	1.43313i	0.858159	−	0.513383i	$-0.171608\pi$
$434$	0.161317	−	0.496483i	0.00774347	−	0.0238319i
$435$	−7.93521	+	1.15514i	−0.380464	+	0.0553846i
$436$	13.9928			0.670135
$437$	37.9193			1.81393
$438$	−12.5972	+	9.15240i	−0.601917	+	0.437318i
$439$	−30.0613	+	21.8408i	−1.43475	+	1.04241i	−0.445642	+	0.895211i	$0.647024\pi$
$439$	−30.0613	+	21.8408i	−1.43475	+	1.04241i	−0.989108	+	0.147195i	$0.952976\pi$
$440$	6.26041	+	3.97584i	0.298453	+	0.189541i
$441$	−5.17707	−	3.76136i	−0.246527	−	0.179113i
$442$	27.7862			1.32165
$443$	26.7019	−	19.4000i	1.26864	−	0.921724i	0.269496	−	0.963001i	$-0.413143\pi$
$443$	26.7019	−	19.4000i	1.26864	−	0.921724i	0.999148	+	0.0412775i	$0.0131428\pi$
$444$	−2.13010	+	6.55579i	−0.101090	+	0.311124i
$445$	1.27033	−	7.41803i	0.0602193	−	0.351648i
$446$	13.9112			0.658717
$447$	6.38619	−	4.63984i	0.302056	−	0.219457i
$448$	0.480110	−	1.47763i	0.0226831	−	0.0698113i
$449$	0.0648666	−	0.199639i	0.00306124	−	0.00942153i	−0.949514	−	0.313724i	$-0.898423\pi$
$449$	0.0648666	−	0.199639i	0.00306124	−	0.00942153i	0.952575	+	0.304302i	$0.0984233\pi$
$450$	4.24090	−	5.53982i	0.199918	−	0.261149i
$451$	−15.7358	−	13.5354i	−0.740968	−	0.637358i
$452$	5.30396	−	3.85355i	0.249477	−	0.181256i
$453$	14.5676	+	10.5840i	0.684445	+	0.497278i
$454$	2.39532	+	7.37203i	0.112418	+	0.345987i
$455$	−8.83244	+	8.61393i	−0.414071	+	0.403827i
$456$	7.68675	−	5.58475i	0.359965	−	0.261530i
$457$	1.95366	+	6.01274i	0.0913883	+	0.281264i	0.986296	−	0.164988i	$-0.0527585\pi$
$457$	1.95366	+	6.01274i	0.0913883	+	0.281264i	−0.894907	+	0.446252i	$0.852758\pi$
$458$	1.35107	−	4.15818i	0.0631316	−	0.194299i
$459$	43.5644			2.03341
$460$	5.00559	+	10.1359i	0.233387	+	0.472587i
$461$	−23.7315	+	17.2419i	−1.10529	+	0.803037i	−0.981915	−	0.189323i	$-0.939371\pi$
$461$	−23.7315	+	17.2419i	−1.10529	+	0.803037i	−0.123371	+	0.992361i	$0.539371\pi$
$462$	−4.94863	−	4.25665i	−0.230231	−	0.198038i
$463$	−10.9360	−	7.94549i	−0.508241	−	0.369258i	0.303915	−	0.952699i	$-0.401706\pi$
$463$	−10.9360	−	7.94549i	−0.508241	−	0.369258i	−0.812156	+	0.583441i	$0.801706\pi$
$464$	0.874820	+	2.69242i	0.0406125	+	0.124992i
$465$	0.842522	+	0.442664i	0.0390710	+	0.0205280i
$466$	−7.52336	−	23.1545i	−0.348513	−	1.07261i
$467$	−14.9523	+	10.8635i	−0.691912	+	0.502703i	−0.877288	−	0.479964i	$-0.840650\pi$
$467$	−14.9523	+	10.8635i	−0.691912	+	0.502703i	0.185376	+	0.982668i	$0.440650\pi$
$468$	−1.53125	−	4.71269i	−0.0707818	−	0.217844i
$469$	2.89233	−	8.90168i	0.133555	−	0.411042i
$470$	0.665762	−	3.88769i	0.0307093	−	0.179326i
$471$	−21.3182	−	15.4886i	−0.982290	−	0.713675i
$472$	0.0523156	−	0.161011i	0.00240802	−	0.00741113i
$473$	14.8797	+	12.7990i	0.684168	+	0.588500i
$474$	7.80168			0.358343
$475$	−22.7966	+	29.7789i	−1.04598	+	1.36635i
$476$	−9.83477	+	7.14538i	−0.450776	+	0.327508i
$477$	7.40130			0.338882
$478$	−20.9673			−0.959024
$479$	−13.2613			−0.605925			−0.302962	−	0.953003i	$-0.597976\pi$
$479$	−13.2613			−0.605925			−0.302962	+	0.953003i	$0.597976\pi$
$480$	2.50751	+	1.31745i	0.114452	+	0.0601332i
$481$	−15.6339	−	11.3587i	−0.712842	−	0.517910i
$482$	−1.42656	+	4.39049i	−0.0649779	+	0.199981i
$483$	−3.07467	−	9.46285i	−0.139902	−	0.430575i
$484$	−7.72338	−	7.83258i	−0.351063	−	0.356026i
$485$	−4.96077	+	0.722144i	−0.225257	+	0.0327909i
$486$	−4.03937	−	12.4319i	−0.183229	−	0.563922i
$487$	−8.89210			−0.402940			−0.201470	−	0.979495i	$-0.564572\pi$
$487$	−8.89210			−0.402940			−0.201470	+	0.979495i	$0.564572\pi$
$488$	−1.59329	−	4.90364i	−0.0721249	−	0.221977i
$489$	15.9676	+	11.6011i	0.722079	+	0.524621i
$490$	−1.73093	+	10.1077i	−0.0781956	+	0.456620i
$491$	−8.48889	−	26.1261i	−0.383098	−	1.17905i	−0.937851	−	0.347039i	$-0.887187\pi$
$491$	−8.48889	−	26.1261i	−0.383098	−	1.17905i	0.554753	−	0.832015i	$-0.312813\pi$
$492$	−6.41358	−	4.65974i	−0.289147	−	0.210077i
$493$	6.84489	−	21.0664i	0.308279	−	0.948784i
$494$	8.23109	+	25.3327i	0.370334	+	1.13977i
$495$	−7.97555	+	6.59357i	−0.358474	+	0.296359i
$496$	0.103830	−	0.319555i	0.00466209	−	0.0143484i
$497$	−13.0502	−	9.48154i	−0.585382	−	0.425305i
$498$	4.88397	−	15.0313i	0.218856	−	0.673569i
$499$	28.8755	+	20.9793i	1.29265	+	0.939163i	0.999855	−	0.0170131i	$-0.00541571\pi$
$499$	28.8755	+	20.9793i	1.29265	+	0.939163i	0.292792	+	0.956176i	$0.405416\pi$
$500$	−10.9692	−	2.16255i	−0.490558	−	0.0967123i
$501$	−8.29660	−	25.5343i	−0.370665	−	1.14079i
$502$	5.00910			0.223567
$503$	−5.19118	−	15.9768i	−0.231463	−	0.712371i	−0.997571	−	0.0696587i	$-0.977809\pi$
$503$	−5.19118	−	15.9768i	−0.231463	−	0.712371i	0.766107	−	0.642713i	$-0.222191\pi$
$504$	1.75387	+	1.27426i	0.0781237	+	0.0567602i
$505$	14.1228	+	28.5973i	0.628455	+	1.27257i
$506$	−3.85700	−	16.3176i	−0.171464	−	0.725408i
$507$	0.492340			0.0218656
$508$	18.0224			0.799615
$509$	30.0719			1.33291			0.666456	−	0.745545i	$-0.267811\pi$
$509$	30.0719			1.33291			0.666456	+	0.745545i	$0.267811\pi$
$510$	−9.81358	−	19.8716i	−0.434553	−	0.879930i
$511$	15.4505	+	11.2254i	0.683488	+	0.496583i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	12.9051	+	39.7177i	0.569773	+	1.75358i
$514$	5.67085	−	17.4531i	0.250131	−	0.769823i
$515$	3.48730	−	20.3640i	0.153669	−	0.897343i
$516$	6.06466	+	4.40623i	0.266982	+	0.193974i
$517$	−2.25778	+	5.39710i	−0.0992969	+	0.237364i
$518$	8.45447			0.371468
$519$	26.0734			1.14449
$520$	−5.68489	+	5.54425i	−0.249299	+	0.243131i
$521$	−15.5915	+	11.3279i	−0.683075	+	0.496283i	−0.874376	−	0.485248i	$-0.838729\pi$
$521$	−15.5915	+	11.3279i	−0.683075	+	0.496283i	0.191302	+	0.981531i	$0.438729\pi$
$522$	−3.95019			−0.172895
$523$	9.00973	+	6.54595i	0.393968	+	0.286235i	0.767080	−	0.641552i	$-0.221709\pi$
$523$	9.00973	+	6.54595i	0.393968	+	0.286235i	−0.373112	+	0.927787i	$0.621709\pi$
$524$	−11.9948	−	8.71475i	−0.523996	−	0.380705i
$525$	9.27982	+	3.27434i	0.405005	+	0.142904i
$526$	2.24903	−	6.92181i	0.0980624	−	0.301805i
$527$	−2.12689	+	1.54528i	−0.0926488	+	0.0673133i
$528$	−3.18512	−	2.73974i	−0.138615	−	0.119232i
$529$	0.790571	−	2.43313i	0.0343727	−	0.105788i
$530$	−5.25188	−	10.6346i	−0.228127	−	0.461937i
$531$	0.191112	+	0.138851i	0.00829356	+	0.00602563i
$532$	−9.42781	−	6.84970i	−0.408747	−	0.296972i
$533$	17.9800	−	13.0633i	0.778802	−	0.565833i
$534$	−1.31751	+	4.05487i	−0.0570141	+	0.175471i
$535$	−0.943161	+	5.50755i	−0.0407764	+	0.238112i
$536$	1.86161	−	5.72946i	0.0804095	−	0.247475i
$537$	−6.06051	+	4.40322i	−0.261530	+	0.190013i
$538$	16.0260	+	11.6435i	0.690928	+	0.501989i
$539$	5.87006	−	14.0321i	0.252841	−	0.604404i
$540$	−8.91303	+	8.69253i	−0.383556	+	0.374067i
$541$	8.15618	−	5.92581i	0.350661	−	0.254770i	−0.398485	−	0.917175i	$-0.630464\pi$
$541$	8.15618	−	5.92581i	0.350661	−	0.254770i	0.749146	+	0.662404i	$0.230464\pi$
$542$	−6.05682	−	4.40054i	−0.260163	−	0.189019i
$543$	14.1383	+	10.2721i	0.606733	+	0.440817i
$544$	−6.33003	+	4.59903i	−0.271398	+	0.197182i
$545$	30.9626	−	4.50725i	1.32629	−	0.193070i
$546$	5.65441	−	4.10817i	0.241987	−	0.175813i
$547$	−4.83665	−	14.8857i	−0.206800	−	0.636466i	−0.999635	−	0.0270287i	$-0.991395\pi$
$547$	−4.83665	−	14.8857i	−0.206800	−	0.636466i	0.792834	−	0.609437i	$-0.208605\pi$
$548$	0.903732	+	2.78140i	0.0386055	+	0.118816i
$549$	7.19440			0.307049
$550$	15.1334	+	6.78097i	0.645289	+	0.289141i
$551$	21.2340			0.904597
$552$	−1.97897	−	6.09065i	−0.0842306	−	0.259235i
$553$	−2.95691	−	9.10044i	−0.125741	−	0.386990i
$554$	19.5530	−	14.2061i	0.830726	−	0.603558i
$555$	−2.60168	+	15.1924i	−0.110435	+	0.644883i
$556$	−1.34794	+	0.979334i	−0.0571653	+	0.0415330i
$557$	3.58167	+	2.60223i	0.151760	+	0.110260i	0.661074	−	0.750321i	$-0.270101\pi$
$557$	3.58167	+	2.60223i	0.151760	+	0.110260i	−0.509314	+	0.860581i	$0.670101\pi$
$558$	0.379297	+	0.275575i	0.0160569	+	0.0116660i
$559$	−17.0019	+	12.3526i	−0.719102	+	0.522458i
$560$	0.586401	−	3.42426i	0.0247800	−	0.144702i
$561$	7.56174	+	31.9911i	0.319257	+	1.35067i
$562$	−2.25456	−	1.63803i	−0.0951028	−	0.0690962i
$563$	−11.1242	+	8.08222i	−0.468830	+	0.340625i	−0.796985	−	0.603999i	$-0.793573\pi$
$563$	−11.1242	+	8.08222i	−0.468830	+	0.340625i	0.328155	+	0.944624i	$0.393573\pi$
$564$	−0.690488	+	2.12510i	−0.0290748	+	0.0894830i
$565$	10.4950	−	10.2354i	0.441530	−	0.430606i
$566$	8.03549	−	24.7307i	0.337757	−	1.03951i
$567$	3.60363	−	2.61819i	0.151338	−	0.109954i
$568$	−8.39961	−	6.10267i	−0.352440	−	0.256062i
$569$	6.99736	+	5.08388i	0.293345	+	0.213127i	0.724717	−	0.689047i	$-0.241970\pi$
$569$	6.99736	+	5.08388i	0.293345	+	0.213127i	−0.431372	+	0.902174i	$0.641970\pi$
$570$	15.2099	−	14.8336i	0.637073	−	0.621312i
$571$	13.5487	−	41.6987i	0.566996	−	1.74504i	−0.0949481	−	0.995482i	$-0.530269\pi$
$571$	13.5487	−	41.6987i	0.566996	−	1.74504i	0.661944	−	0.749553i	$-0.269731\pi$
$572$	10.0641	−	6.11878i	0.420799	−	0.255839i
$573$	−0.861758	+	0.626104i	−0.0360005	+	0.0261559i
$574$	−3.00465	+	9.24735i	−0.125411	+	0.385977i
$575$	14.3410	+	20.8157i	0.598060	+	0.868076i
$576$	1.12886	+	0.820164i	0.0470358	+	0.0341735i
$577$	15.1724	+	11.0234i	0.631635	+	0.458910i	0.856966	−	0.515372i	$-0.172346\pi$
$577$	15.1724	+	11.0234i	0.631635	+	0.458910i	−0.225331	+	0.974282i	$0.572346\pi$
$578$	44.2203			1.83932
$579$	−18.3508	+	13.3327i	−0.762634	+	0.554086i
$580$	2.80301	+	5.67585i	0.116389	+	0.235677i
$581$	−19.3847			−0.804211
$582$	2.83993			0.117719
$583$	4.04677	+	17.1205i	0.167600	+	0.709059i
$584$	9.94450	+	7.22510i	0.411506	+	0.298977i
$585$	−4.90627	−	9.93475i	−0.202849	−	0.410751i
$586$	−7.07840	+	21.7851i	−0.292406	+	0.899933i
$587$	−1.25004	−	3.84722i	−0.0515946	−	0.158792i	0.921939	−	0.387334i	$-0.126604\pi$
$587$	−1.25004	−	3.84722i	−0.0515946	−	0.158792i	−0.973534	+	0.228542i	$0.926604\pi$
$588$	1.79522	−	5.52512i	0.0740336	−	0.227852i
$589$	−2.03888	−	1.48133i	−0.0840105	−	0.0610372i
$590$	0.0638976	−	0.373128i	0.00263062	−	0.0153614i
$591$	4.03496			0.165976
$592$	5.44162			0.223649
$593$	9.35732			0.384259			0.192129	−	0.981370i	$-0.438461\pi$
$593$	9.35732			0.384259			0.192129	+	0.981370i	$0.438461\pi$
$594$	15.7789	−	9.59330i	0.647415	−	0.393618i
$595$	−19.4602	+	18.9788i	−0.797792	+	0.778055i
$596$	−5.04140	−	3.66279i	−0.206504	−	0.150034i
$597$	−8.50756	−	26.1836i	−0.348191	−	1.07162i
$598$	17.9534			0.734169
$599$	5.68647	+	17.5011i	0.232343	+	0.715078i	0.997463	+	0.0711898i	$0.0226796\pi$
$599$	5.68647	+	17.5011i	0.232343	+	0.715078i	−0.765120	+	0.643888i	$0.777320\pi$
$600$	5.97284	+	2.10749i	0.243840	+	0.0860378i
$601$	34.5582	+	25.1080i	1.40966	+	1.02418i	0.993372	+	0.114943i	$0.0366687\pi$
$601$	34.5582	+	25.1080i	1.40966	+	1.02418i	0.416287	+	0.909233i	$0.363331\pi$
$602$	2.84118	−	8.74426i	0.115798	−	0.356389i
$603$	6.80059	+	4.94092i	0.276942	+	0.201210i
$604$	4.39260	−	13.5190i	0.178732	−	0.550081i
$605$	−19.6129	−	14.8437i	−0.797376	−	0.603483i
$606$	−5.58347	−	17.1842i	−0.226813	−	0.698059i
$607$	12.2695	−	37.7616i	0.498003	−	1.53270i	−0.314221	−	0.949350i	$-0.601743\pi$
$607$	12.2695	−	37.7616i	0.498003	−	1.53270i	0.812224	−	0.583346i	$-0.198257\pi$
$608$	−6.06809	−	4.40873i	−0.246094	−	0.178797i
$609$	−1.72174	−	5.29898i	−0.0697685	−	0.214725i
$610$	−5.10507	−	10.3373i	−0.206698	−	0.418545i
$611$	−5.06782	−	3.68199i	−0.205022	−	0.148957i
$612$	−3.37374	−	10.3833i	−0.136376	−	0.419721i
$613$	−1.58462			−0.0640020			−0.0320010	−	0.999488i	$-0.510188\pi$
$613$	−1.58462			−0.0640020			−0.0320010	+	0.999488i	$0.510188\pi$
$614$	3.78980	+	11.6638i	0.152944	+	0.470713i
$615$	−15.6926	−	8.24493i	−0.632786	−	0.332468i
$616$	−1.98864	+	4.75374i	−0.0801246	+	0.191534i
$617$	−8.88849	−	27.3560i	−0.357837	−	1.10131i	−0.954346	−	0.298703i	$-0.903446\pi$
$617$	−8.88849	−	27.3560i	−0.357837	−	1.10131i	0.596509	−	0.802606i	$-0.296554\pi$
$618$	−3.61682	+	11.1314i	−0.145490	+	0.447772i
$619$	33.2988	+	24.1930i	1.33839	+	0.972399i	0.999501	+	0.0315738i	$0.0100519\pi$
$619$	33.2988	+	24.1930i	1.33839	+	0.972399i	0.338891	+	0.940825i	$0.389948\pi$
$620$	0.126816	−	0.740539i	0.00509307	−	0.0297408i
$621$	28.1482			1.12955
$622$	−27.6570			−1.10895
$623$	5.22924			0.209505
$624$	3.63939	−	2.64417i	0.145692	−	0.105852i
$625$	−24.9686	−	1.25187i	−0.998745	−	0.0500748i
$626$	−22.7747			−0.910259
$627$	−26.9264	+	16.3708i	−1.07534	+	0.653786i
$628$	−6.42812	+	19.7837i	−0.256510	+	0.789457i
$629$	−34.4456	−	25.0262i	−1.37344	−	0.997859i
$630$	4.29133	+	2.25468i	0.170971	+	0.0898285i
$631$	9.08399	−	27.9577i	0.361628	−	1.11298i	−0.590438	−	0.807083i	$-0.701045\pi$
$631$	9.08399	−	27.9577i	0.361628	−	1.11298i	0.952066	−	0.305893i	$-0.0989551\pi$
$632$	−1.90318	−	5.85739i	−0.0757044	−	0.232994i
$633$	12.8881	−	9.36379i	0.512258	−	0.372177i
$634$	−1.90126	−	5.85147i	−0.0755086	−	0.232392i
$635$	39.8790	−	5.80523i	1.58255	−	0.230373i
$636$	2.07634	+	6.39033i	0.0823323	+	0.253393i
$637$	13.1760	+	9.57291i	0.522051	+	0.379292i
$638$	−2.15983	−	9.13750i	−0.0855085	−	0.361757i
$639$	11.7204	−	8.51534i	0.463650	−	0.336862i
$640$	0.377430	−	2.20398i	0.0149192	−	0.0871201i
$641$	−44.0928			−1.74156			−0.870781	−	0.491671i	$-0.836386\pi$
$641$	−44.0928			−1.74156			−0.870781	+	0.491671i	$0.836386\pi$
$642$	0.978190	−	3.01056i	0.0386061	−	0.118817i
$643$	−11.2970	−	34.7686i	−0.445510	−	1.37114i	−0.881924	−	0.471392i	$-0.843752\pi$
$643$	−11.2970	−	34.7686i	−0.445510	−	1.37114i	0.436414	−	0.899746i	$-0.356248\pi$
$644$	−6.35452	+	4.61683i	−0.250403	+	0.181928i
$645$	14.8389	+	7.79638i	0.584279	+	0.306982i
$646$	18.1353	+	55.8147i	0.713524	+	2.19600i
$647$	−20.1250	−	14.6217i	−0.791196	−	0.574837i	0.117122	−	0.993118i	$-0.462633\pi$
$647$	−20.1250	−	14.6217i	−0.791196	−	0.574837i	−0.908318	+	0.418280i	$0.862633\pi$
$648$	2.31943	−	1.68516i	0.0911158	−	0.0661995i
$649$	−0.216694	+	0.517996i	−0.00850598	+	0.0203331i
$650$	−10.7933	+	14.0992i	−0.423350	+	0.553016i
$651$	−0.204348	+	0.628919i	−0.00800904	+	0.0246493i
$652$	4.81474	−	14.8183i	0.188560	−	0.580327i
$653$	14.6184	−	10.6209i	0.572063	−	0.415628i	−0.263791	−	0.964580i	$-0.584973\pi$
$653$	14.6184	−	10.6209i	0.572063	−	0.415628i	0.835854	+	0.548952i	$0.184973\pi$
$654$	−17.7254			−0.693118
$655$	−29.3486	−	15.4198i	−1.14674	−	0.602503i
$656$	−1.93390	+	5.95194i	−0.0755062	+	0.232384i
$657$	−13.8760	+	10.0815i	−0.541355	+	0.393318i
$658$	2.74058			0.106839
$659$	−13.1027	−	9.51968i	−0.510409	−	0.370834i	0.302570	−	0.953127i	$-0.402156\pi$
$659$	−13.1027	−	9.51968i	−0.510409	−	0.370834i	−0.812979	+	0.582293i	$0.802156\pi$
$660$	−7.93037	−	5.03639i	−0.308689	−	0.196041i
$661$	3.63128	−	2.63828i	0.141240	−	0.102617i	−0.514921	−	0.857237i	$-0.672179\pi$
$661$	3.63128	−	2.63828i	0.141240	−	0.102617i	0.656162	+	0.754620i	$0.272179\pi$
$662$	2.14284	−	1.55687i	0.0832840	−	0.0605094i
$663$	−35.1981			−1.36698
$664$	−12.4767			−0.484190
$665$	−23.0677	−	12.1198i	−0.894528	−	0.469987i
$666$	−2.34635	+	7.22131i	−0.0909191	+	0.279820i
$667$	4.42268	−	13.6116i	0.171247	−	0.527043i
$668$	−17.1469	+	12.4579i	−0.663432	+	0.482011i
$669$	−17.6221			−0.681308
$670$	2.27375	−	13.2775i	0.0878427	−	0.512954i
$671$	3.93365	+	16.6419i	0.151857	+	0.642454i
$672$	−0.608179	+	1.87178i	−0.0234610	+	0.0722056i
$673$	6.74999	+	20.7743i	0.260193	+	0.800791i	0.992762	+	0.120099i	$0.0383211\pi$
$673$	6.74999	+	20.7743i	0.260193	+	0.800791i	−0.732569	+	0.680693i	$0.761679\pi$
$674$	−9.90968	+	7.19981i	−0.381707	+	0.277326i
$675$	−16.9223	+	22.1053i	−0.651340	+	0.850835i
$676$	−0.120104	−	0.369641i	−0.00461938	−	0.0142170i
$677$	29.9443	+	21.7558i	1.15085	+	0.836145i	0.988594	−	0.150603i	$-0.0481216\pi$
$677$	29.9443	+	21.7558i	1.15085	+	0.836145i	0.162260	+	0.986748i	$0.448122\pi$
$678$	−6.71879	+	4.88148i	−0.258033	+	0.187472i
$679$	−1.07636	−	3.31270i	−0.0413070	−	0.127130i
$680$	−12.5253	+	12.2155i	−0.480325	+	0.468442i
$681$	−3.03427	−	9.33852i	−0.116273	−	0.357853i
$682$	−0.430068	+	1.02806i	−0.0164682	+	0.0393663i
$683$	11.5282	+	35.4801i	0.441113	+	1.35761i	0.886691	+	0.462363i	$0.152998\pi$
$683$	11.5282	+	35.4801i	0.441113	+	1.35761i	−0.445577	+	0.895243i	$0.647002\pi$
$684$	8.46709	−	6.15170i	0.323747	−	0.235216i
$685$	2.89565	+	5.86343i	0.110637	+	0.224030i
$686$	−18.0010			−0.687281
$687$	−1.71147	+	5.26737i	−0.0652967	+	0.200963i
$688$	1.82869	−	5.62813i	0.0697182	−	0.214571i
$689$	−18.8368			−0.717624
$690$	−6.34083	−	12.8396i	−0.241391	−	0.488795i
$691$	31.4510	−	22.8505i	1.19645	−	0.869275i	0.202523	−	0.979278i	$-0.435086\pi$
$691$	31.4510	−	22.8505i	1.19645	−	0.869275i	0.993931	+	0.110003i	$0.0350860\pi$
$692$	−6.36047	−	19.5755i	−0.241789	−	0.744149i
$693$	−5.45100	−	4.68878i	−0.207066	−	0.178112i
$694$	4.54109	+	13.9760i	0.172377	+	0.530523i
$695$	−2.66719	+	2.60120i	−0.101172	+	0.0986692i
$696$	−1.10818	−	3.41062i	−0.0420054	−	0.129279i
$697$	39.6148	−	28.7819i	1.50052	−	1.09019i
$698$	−21.5887	−	15.6851i	−0.817143	−	0.593689i
$699$	9.53021	+	29.3310i	0.360466	+	1.10940i
$700$	0.194560	−	7.76591i	0.00735369	−	0.293524i
$701$	−27.5908	+	20.0459i	−1.04209	+	0.757123i	−0.970693	−	0.240324i	$-0.922746\pi$
$701$	−27.5908	+	20.0459i	−1.04209	+	0.757123i	−0.0713984	+	0.997448i	$0.522746\pi$
$702$	6.11008	+	18.8049i	0.230610	+	0.709745i
$703$	12.6126	−	38.8176i	0.475693	−	1.46403i
$704$	−1.27996	+	3.05969i	−0.0482405	+	0.115316i
$705$	−0.843354	+	4.92473i	−0.0317625	+	0.185476i
$706$	−23.0021			−0.865696
$707$	−17.9286	+	13.0259i	−0.674276	+	0.489890i
$708$	−0.0662708	+	0.203960i	−0.00249061	+	0.00766530i
$709$	−12.5508	+	38.6274i	−0.471355	+	1.45068i	0.379455	+	0.925210i	$0.376111\pi$
$709$	−12.5508	+	38.6274i	−0.471355	+	1.45068i	−0.850811	+	0.525473i	$0.823889\pi$
$710$	−20.5519	−	10.7981i	−0.771301	−	0.405244i
$711$	8.59369			0.322288
$712$	3.36574			0.126136
$713$	−1.37424	+	0.998446i	−0.0514658	+	0.0373921i
$714$	12.4582	−	9.05140i	0.466236	−	0.338740i
$715$	20.2983	−	16.7811i	0.759112	−	0.627576i
$716$	4.78430	+	3.47600i	0.178798	+	0.129904i
$717$	26.5604			0.991915
$718$	−1.03673	+	0.753228i	−0.0386904	+	0.0281102i
$719$	−14.8243	+	45.6244i	−0.552851	+	1.70150i	0.148699	+	0.988882i	$0.452491\pi$
$719$	−14.8243	+	45.6244i	−0.552851	+	1.70150i	−0.701551	+	0.712619i	$0.747509\pi$
$720$	2.76206	+	1.45120i	0.102936	+	0.0540829i
$721$	14.3553			0.534619
$722$	−30.1428	+	21.9001i	−1.12180	+	0.815036i
$723$	1.80709	−	5.56165i	0.0672064	−	0.206840i
$724$	4.26316	−	13.1207i	0.158439	−	0.487625i
$725$	8.03062	+	11.6563i	0.298250	+	0.432905i
$726$	9.78359	+	9.92192i	0.363103	+	0.368237i
$727$	−26.0576	+	18.9319i	−0.966421	+	0.702146i	−0.954633	−	0.297784i	$-0.903752\pi$
$727$	−26.0576	+	18.9319i	−0.966421	+	0.702146i	−0.0117882	+	0.999931i	$0.503752\pi$
$728$	−4.46372	−	3.24308i	−0.165436	−	0.120197i
$729$	7.77470	+	23.9281i	0.287952	+	0.886224i
$730$	24.3319	+	12.7841i	0.900566	+	0.473160i
$731$	−37.4597	+	27.2160i	−1.38550	+	1.00662i
$732$	2.01830	+	6.21169i	0.0745985	+	0.229591i
$733$	−8.13868	+	25.0483i	−0.300609	+	0.925179i	0.680670	+	0.732590i	$0.261689\pi$
$733$	−8.13868	+	25.0483i	−0.300609	+	0.925179i	−0.981279	+	0.192590i	$0.938311\pi$
$734$	3.29363			0.121570
$735$	2.19266	−	12.8039i	0.0808775	−	0.472281i
$736$	−4.09001	+	2.97156i	−0.150760	+	0.109533i
$737$	−7.71090	+	18.4325i	−0.284035	+	0.678970i
$738$	−7.06467	−	5.13278i	−0.260054	−	0.188940i
$739$	−5.16534	−	15.8973i	−0.190010	−	0.584791i	0.809988	−	0.586446i	$-0.199473\pi$
$739$	−5.16534	−	15.8973i	−0.190010	−	0.584791i	−0.999999	+	0.00165467i	$0.999473\pi$
$740$	12.0409	−	1.75281i	0.442633	−	0.0644345i
$741$	−10.4267	−	32.0902i	−0.383035	−	1.17886i
$742$	6.66718	−	4.84399i	0.244760	−	0.177828i
$743$	−3.21071	−	9.88155i	−0.117790	−	0.362519i	0.874729	−	0.484612i	$-0.161039\pi$
$743$	−3.21071	−	9.88155i	−0.117790	−	0.362519i	−0.992519	+	0.122093i	$0.961039\pi$
$744$	−0.131526	+	0.404796i	−0.00482199	+	0.0148405i
$745$	−12.3352	−	6.48093i	−0.451925	−	0.237443i
$746$	−9.64327	−	7.00625i	−0.353065	−	0.256517i
$747$	5.37977	−	16.5572i	0.196836	−	0.605798i
$748$	22.1738	−	13.4813i	0.810755	−	0.492926i
$749$	−3.88247			−0.141863
$750$	13.8952	+	2.73941i	0.507382	+	0.100029i
$751$	23.6837	−	17.2073i	0.864232	−	0.627901i	−0.0648008	−	0.997898i	$-0.520641\pi$
$751$	23.6837	−	17.2073i	0.864232	−	0.627901i	0.929033	+	0.369997i	$0.120641\pi$
$752$	1.76394			0.0643242
$753$	−6.34528			−0.231235
$754$	10.0535			0.366127
$755$	5.36506	−	31.3291i	0.195255	−	1.14018i
$756$	−6.99842	−	5.08465i	−0.254530	−	0.184927i
$757$	−6.52331	+	20.0767i	−0.237094	+	0.729699i	0.759743	+	0.650223i	$0.225325\pi$
$757$	−6.52331	+	20.0767i	−0.237094	+	0.729699i	−0.996837	+	0.0794758i	$0.974675\pi$
$758$	−1.38565	−	4.26460i	−0.0503292	−	0.154897i
$759$	4.88585	+	20.6704i	0.177345	+	0.750286i
$760$	−14.8472	−	7.80079i	−0.538566	−	0.282964i
$761$	−5.89384	−	18.1394i	−0.213651	−	0.657552i	−0.999247	−	0.0388107i	$-0.987643\pi$
$761$	−5.89384	−	18.1394i	−0.213651	−	0.657552i	0.785595	−	0.618741i	$-0.212357\pi$
$762$	−22.8299			−0.827039
$763$	6.71810	+	20.6762i	0.243212	+	0.748528i
$764$	0.680291	+	0.494260i	0.0246121	+	0.0178817i
$765$	−10.8098	−	21.8889i	−0.390830	−	0.791396i
$766$	0.357287	+	1.09962i	0.0129093	+	0.0397307i
$767$	−0.486393	−	0.353385i	−0.0175626	−	0.0127600i
$768$	−0.391447	+	1.20475i	−0.0141251	+	0.0434727i
$769$	−12.7868	−	39.3538i	−0.461104	−	1.41913i	−0.863817	−	0.503806i	$-0.831933\pi$
$769$	−12.7868	−	39.3538i	−0.461104	−	1.41913i	0.402713	−	0.915327i	$-0.368067\pi$
$770$	−2.86912	+	11.1594i	−0.103396	+	0.402157i
$771$	−7.18355	+	22.1087i	−0.258709	+	0.796225i
$772$	14.4865	+	10.5251i	0.521382	+	0.378806i
$773$	−1.13154	+	3.48252i	−0.0406987	+	0.125258i	−0.969341	−	0.245717i	$-0.920976\pi$
$773$	−1.13154	+	3.48252i	−0.0406987	+	0.125258i	0.928643	+	0.370975i	$0.120976\pi$
$774$	6.68033	+	4.85354i	0.240119	+	0.174457i
$775$	0.0420761	−	1.67947i	0.00151142	−	0.0603285i
$776$	−0.692787	−	2.13218i	−0.0248696	−	0.0765408i
$777$	−10.7097			−0.384208
$778$	−6.71661	−	20.6716i	−0.240802	−	0.741112i
$779$	37.9756	+	27.5909i	1.36062	+	0.988546i
$780$	7.20133	−	7.02317i	0.257849	−	0.251470i
$781$	26.1058	+	22.4554i	0.934139	+	0.803517i
$782$	39.5562			1.41453
$783$	15.7623			0.563299
$784$	−4.58611			−0.163790
$785$	−7.85123	+	45.8469i	−0.280222	+	1.63635i
$786$	15.1944	+	11.0394i	0.541967	+	0.393762i
$787$	−2.11370	+	6.50531i	−0.0753453	+	0.231889i	−0.981635	−	0.190767i	$-0.938902\pi$
$787$	−2.11370	+	6.50531i	−0.0753453	+	0.231889i	0.906290	+	0.422657i	$0.138902\pi$
$788$	−0.984307	−	3.02939i	−0.0350645	−	0.107917i
$789$	−2.84896	+	8.76819i	−0.101426	+	0.312156i
$790$	−6.09799	−	12.3479i	−0.216957	−	0.439317i
$791$	8.24060	+	5.98715i	0.293002	+	0.212878i
$792$	−3.50847	−	3.01787i	−0.124668	−	0.107235i
$793$	−18.3102			−0.650214
$794$	−2.47430			−0.0878096
$795$	6.65282	+	13.4714i	0.235951	+	0.477780i
$796$	−17.5829	+	12.7747i	−0.623208	+	0.452787i
$797$	31.0141			1.09858			0.549289	−	0.835633i	$-0.314899\pi$
$797$	31.0141			1.09858			0.549289	+	0.835633i	$0.314899\pi$
$798$	11.9427	+	8.67686i	0.422766	+	0.307157i
$799$	−11.1658	−	8.11241i	−0.395017	−	0.286996i
$800$	0.125226	−	4.99843i	0.00442742	−	0.176721i
$801$	−1.45126	+	4.46651i	−0.0512777	+	0.157816i
$802$	14.2572	−	10.3584i	0.503437	−	0.365769i
$803$	−30.9073	−	26.5855i	−1.09069	−	0.938181i
$804$	−2.35820	+	7.25779i	−0.0831672	+	0.255962i
$805$	−12.5738	+	12.2627i	−0.443168	+	0.432204i
$806$	−0.965334	−	0.701356i	−0.0340024	−	0.0247042i
$807$	−20.3009	−	14.7494i	−0.714625	−	0.519205i
$808$	−11.5395	+	8.38397i	−0.405960	+	0.294947i
$809$	−12.2975	+	37.8477i	−0.432356	+	1.33066i	0.463416	+	0.886141i	$0.346624\pi$
$809$	−12.2975	+	37.8477i	−0.432356	+	1.33066i	−0.895772	+	0.444514i	$0.853376\pi$
$810$	4.58949	−	4.47595i	0.161258	−	0.157269i
$811$	0.654366	−	2.01393i	0.0229779	−	0.0707187i	−0.938910	−	0.344163i	$-0.888163\pi$
$811$	0.654366	−	2.01393i	0.0229779	−	0.0707187i	0.961888	+	0.273444i	$0.0881628\pi$
$812$	−3.55838	+	2.58532i	−0.124875	+	0.0907268i
$813$	7.67247	+	5.57438i	0.269085	+	0.195502i
$814$	−17.9871	−	1.47915i	−0.630447	−	0.0518443i
$815$	5.88067	−	34.3399i	0.205991	−	1.20287i
$816$	8.01856	−	5.82582i	0.280706	−	0.203945i
$817$	−35.9096	−	26.0898i	−1.25632	−	0.912768i
$818$	−27.1875	−	19.7529i	−0.950589	−	0.690644i
$819$	6.22843	−	4.52522i	0.217639	−	0.158124i
$820$	−2.36205	+	13.7931i	−0.0824862	+	0.481675i
$821$	0.445709	−	0.323827i	0.0155554	−	0.0113016i	−0.579980	−	0.814630i	$-0.696940\pi$
$821$	0.445709	−	0.323827i	0.0155554	−	0.0113016i	0.595536	+	0.803329i	$0.296940\pi$
$822$	−1.14480	−	3.52334i	−0.0399296	−	0.122891i
$823$	−4.10173	−	12.6238i	−0.142977	−	0.440039i	0.853768	−	0.520653i	$-0.174312\pi$
$823$	−4.10173	−	12.6238i	−0.142977	−	0.440039i	−0.996745	+	0.0806148i	$0.974312\pi$
$824$	9.23961			0.321877
$825$	−19.1702	−	8.58978i	−0.667420	−	0.299058i
$826$	0.263031			0.00915203
$827$	6.31684	+	19.4412i	0.219658	+	0.676037i	0.998790	+	0.0491778i	$0.0156601\pi$
$827$	6.31684	+	19.4412i	0.219658	+	0.676037i	−0.779132	+	0.626860i	$0.784340\pi$
$828$	−2.17987	−	6.70895i	−0.0757557	−	0.233152i
$829$	13.5841	−	9.86942i	0.471795	−	0.342779i	−0.326346	−	0.945251i	$-0.605817\pi$
$829$	13.5841	−	9.86942i	0.471795	−	0.342779i	0.798140	+	0.602472i	$0.205817\pi$
$830$	−27.6078	+	4.01889i	−0.958279	+	0.139498i
$831$	−24.7687	+	17.9955i	−0.859217	+	0.624257i
$832$	−2.87302	−	2.08737i	−0.0996039	−	0.0723665i
$833$	29.0302	+	21.0917i	1.00584	+	0.730783i
$834$	1.70750	−	1.24057i	0.0591258	−	0.0429574i
$835$	−33.9288	+	33.0894i	−1.17415	+	1.14511i
$836$	18.8595	+	16.2223i	0.652269	+	0.561062i
$837$	−1.51349	−	1.09962i	−0.0523140	−	0.0380084i
$838$	9.62575	−	6.99352i	0.332516	−	0.241587i
$839$	8.88416	−	27.3426i	0.306715	−	0.943973i	−0.672316	−	0.740264i	$-0.734700\pi$
$839$	8.88416	−	27.3426i	0.306715	−	0.943973i	0.979032	−	0.203709i	$-0.0652995\pi$
$840$	−0.742823	+	4.33768i	−0.0256298	+	0.149664i
$841$	−6.48490	+	19.9585i	−0.223617	+	0.688223i
$842$	−30.2698	+	21.9923i	−1.04317	+	0.757905i
$843$	2.85596	+	2.07498i	0.0983645	+	0.0714660i
$844$	−10.1742	−	7.39198i	−0.350210	−	0.254442i
$845$	−0.384825	−	0.779236i	−0.0132384	−	0.0268065i
$846$	−0.760584	+	2.34084i	−0.0261494	+	0.0804797i
$847$	7.86556	−	15.1728i	0.270264	−	0.521343i
$848$	4.29125	−	3.11777i	0.147362	−	0.107065i
$849$	−10.1790	+	31.3276i	−0.349341	+	1.07516i
$850$	−23.7806	+	31.0643i	−0.815669	+	1.06550i
$851$	−22.2562	−	16.1701i	−0.762934	−	0.554304i
$852$	10.6402	+	7.73056i	0.364527	+	0.264845i
$853$	24.6893			0.845347			0.422673	−	0.906282i	$-0.361092\pi$
$853$	24.6893			0.845347			0.422673	+	0.906282i	$0.361092\pi$
$854$	6.48080	−	4.70858i	0.221768	−	0.161124i
$855$	16.7540	−	16.3395i	0.572974	−	0.558799i
$856$	−2.49891			−0.0854109
$857$	−26.7150			−0.912567			−0.456283	−	0.889835i	$-0.650820\pi$
$857$	−26.7150			−0.912567			−0.456283	+	0.889835i	$0.650820\pi$
$858$	−12.7486	+	7.75096i	−0.435231	+	0.264613i
$859$	−18.0298	−	13.0994i	−0.615168	−	0.446946i	0.236062	−	0.971738i	$-0.424143\pi$
$859$	−18.0298	−	13.0994i	−0.615168	−	0.446946i	−0.851231	+	0.524792i	$0.824143\pi$
$860$	2.23354	−	13.0427i	0.0761631	−	0.444752i
$861$	3.80613	−	11.7141i	0.129713	−	0.399215i
$862$	−1.52559	−	4.69528i	−0.0519617	−	0.159922i
$863$	−2.16338	+	6.65821i	−0.0736425	+	0.226648i	−0.981102	−	0.193491i	$-0.938019\pi$
$863$	−2.16338	+	6.65821i	−0.0736425	+	0.226648i	0.907460	+	0.420140i	$0.138019\pi$
$864$	−4.50445	−	3.27267i	−0.153244	−	0.111339i
$865$	−20.3796	−	41.2668i	−0.692927	−	1.40311i
$866$	31.3562			1.06553
$867$	−56.0161			−1.90241
$868$	0.522033			0.0177190
$869$	4.69873	+	19.8787i	0.159393	+	0.674340i
$870$	−3.55072	−	7.18988i	−0.120381	−	0.243760i
$871$	−17.3079	−	12.5750i	−0.586457	−	0.426086i
$872$	4.32402	+	13.3080i	0.146430	+	0.450665i
$873$	3.12823			0.105875
$874$	11.7177	+	36.0634i	0.396358	+	1.21986i
$875$	−2.07098	−	17.2467i	−0.0700118	−	0.583043i
$876$	−12.5972	−	9.15240i	−0.425620	−	0.309231i
$877$	3.45437	−	10.6315i	0.116646	−	0.358999i	−0.875641	−	0.482963i	$-0.839561\pi$
$877$	3.45437	−	10.6315i	0.116646	−	0.358999i	0.992287	+	0.123964i	$0.0395607\pi$
$878$	−30.0613	−	21.8408i	−1.01452	−	0.737093i
$879$	8.96656	−	27.5962i	0.302435	−	0.930798i
$880$	−1.84667	+	7.18260i	−0.0622513	+	0.242126i
$881$	−10.7993	−	33.2369i	−0.363838	−	1.11978i	−0.950705	−	0.310096i	$-0.899639\pi$
$881$	−10.7993	−	33.2369i	−0.363838	−	1.11978i	0.586867	−	0.809683i	$-0.300361\pi$
$882$	1.97747	−	6.08601i	0.0665847	−	0.204927i
$883$	−23.1916	−	16.8497i	−0.780459	−	0.567037i	0.124657	−	0.992200i	$-0.460217\pi$
$883$	−23.1916	−	16.8497i	−0.780459	−	0.567037i	−0.905117	+	0.425163i	$0.860217\pi$
$884$	8.58639	+	26.4262i	0.288792	+	0.888809i
$885$	−0.0809423	+	0.472659i	−0.00272085	+	0.0158883i
$886$	26.7019	+	19.4000i	0.897067	+	0.651757i
$887$	6.00426	+	18.4792i	0.201603	+	0.620471i	0.999836	+	0.0181215i	$0.00576856\pi$
$887$	6.00426	+	18.4792i	0.201603	+	0.620471i	−0.798233	+	0.602349i	$0.794231\pi$
$888$	−6.89316			−0.231319
$889$	8.65274	+	26.6304i	0.290204	+	0.893155i
$890$	7.44752	−	1.08414i	0.249641	−	0.0363406i
$891$	−8.12486	+	4.93978i	−0.272193	+	0.165489i
$892$	4.29881	+	13.2304i	0.143935	+	0.442986i
$893$	4.08846	−	12.5830i	0.136815	−	0.421074i
$894$	6.38619	+	4.63984i	0.213586	+	0.155179i
$895$	11.7061	+	6.15042i	0.391292	+	0.205586i
$896$	1.55367			0.0519045
$897$	−22.7425			−0.759349
$898$	0.209913			0.00700487
$899$	−0.769544	+	0.559106i	−0.0256657	+	0.0186472i
$900$	6.57919	+	2.32143i	0.219306	+	0.0773811i
$901$	−41.5025			−1.38265
$902$	8.01032	−	19.1483i	0.266715	−	0.637568i
$903$	−3.59907	+	11.0768i	−0.119769	+	0.368612i
$904$	5.30396	+	3.85355i	0.176407	+	0.128167i
$905$	5.20697	−	30.4059i	0.173086	−	1.01073i
$906$	−5.56432	+	17.1252i	−0.184862	+	0.568947i
$907$	−4.77554	−	14.6976i	−0.158569	−	0.488025i	0.839936	−	0.542686i	$-0.182592\pi$
$907$	−4.77554	−	14.6976i	−0.158569	−	0.488025i	−0.998505	+	0.0546601i	$0.982592\pi$
$908$	−6.27103	+	4.55617i	−0.208111	+	0.151202i
$909$	−6.15029	−	18.9286i	−0.203992	−	0.627823i
$910$	−10.9217	−	5.73830i	−0.362051	−	0.190223i
$911$	1.46702	+	4.51502i	0.0486045	+	0.149589i	0.972413	−	0.233265i	$-0.0749410\pi$
$911$	1.46702	+	4.51502i	0.0486045	+	0.149589i	−0.923809	+	0.382855i	$0.874941\pi$
$912$	7.68675	+	5.58475i	0.254534	+	0.184930i
$913$	41.2413	+	3.39145i	1.36489	+	0.112240i
$914$	−5.11474	+	3.71608i	−0.169181	+	0.122917i
$915$	6.46684	+	13.0948i	0.213787	+	0.432900i
$916$	4.37217			0.144461
$917$	7.11831	−	21.9079i	0.235067	−	0.723463i
$918$	13.4621	+	41.4322i	0.444317	+	1.36747i
$919$	−31.8848	+	23.1657i	−1.05178	+	0.764165i	−0.972551	−	0.232691i	$-0.925247\pi$
$919$	−31.8848	+	23.1657i	−1.05178	+	0.764165i	−0.0792327	+	0.996856i	$0.525247\pi$
$920$	−8.09297	+	7.89275i	−0.266817	+	0.260216i
$921$	−4.80073	−	14.7751i	−0.158189	−	0.486857i
$922$	−23.7315	−	17.2419i	−0.781555	−	0.567833i
$923$	−29.8291	+	21.6721i	−0.981836	+	0.713345i
$924$	2.51911	−	6.02180i	0.0828726	−	0.198103i
$925$	26.0789	−	7.75704i	0.857468	−	0.255050i
$926$	4.17719	−	12.8561i	0.137271	−	0.422477i
$927$	−3.98399	+	12.2615i	−0.130851	+	0.402719i
$928$	−2.29031	+	1.66401i	−0.0751831	+	0.0546237i
$929$	15.5663			0.510714			0.255357	−	0.966847i	$-0.417807\pi$
$929$	15.5663			0.510714			0.255357	+	0.966847i	$0.417807\pi$
$930$	−0.160645	+	0.938077i	−0.00526774	+	0.0307608i
$931$	−10.6297	+	32.7149i	−0.348375	+	1.07219i
$932$	19.6964	−	14.3103i	0.645177	−	0.468749i
$933$	35.0345			1.14698
$934$	−14.9523	−	10.8635i	−0.489256	−	0.355465i
$935$	44.7225	−	36.9732i	1.46258	−	1.20915i
$936$	4.00885	−	2.91260i	0.131033	−	0.0952014i
$937$	43.7383	−	31.7778i	1.42887	−	1.03813i	0.438643	−	0.898661i	$-0.355459\pi$
$937$	43.7383	−	31.7778i	1.42887	−	1.03813i	0.990226	−	0.139473i	$-0.0445408\pi$
$938$	9.35978			0.305608
$939$	28.8498			0.941478
$940$	3.90315	−	0.568185i	0.127307	−	0.0185322i
$941$	0.994379	−	3.06039i	0.0324158	−	0.0997657i	−0.933540	−	0.358475i	$-0.883297\pi$
$941$	0.994379	−	3.06039i	0.0324158	−	0.0997657i	0.965955	+	0.258709i	$0.0832970\pi$
$942$	8.14282	−	25.0610i	0.265307	−	0.816532i
$943$	25.5962	−	18.5968i	0.833528	−	0.605594i
$944$	0.169297			0.00551014
$945$	−17.1236	−	8.99676i	−0.557029	−	0.292665i
$946$	−7.57453	+	18.1065i	−0.246269	+	0.588694i
$947$	−13.3796	+	41.1783i	−0.434779	+	1.33811i	0.458533	+	0.888677i	$0.348375\pi$
$947$	−13.3796	+	41.1783i	−0.434779	+	1.33811i	−0.893312	+	0.449436i	$0.851625\pi$
$948$	2.41085	+	7.41984i	0.0783008	+	0.240985i
$949$	35.3154	−	25.6581i	1.14638	−	0.832897i
$950$	−35.3659	−	12.4787i	−1.14742	−	0.404862i
$951$	2.40842	+	7.41235i	0.0780983	+	0.240362i
$952$	−9.83477	−	7.14538i	−0.318747	−	0.231583i
$953$	−32.3207	+	23.4823i	−1.04697	+	0.760668i	−0.971634	−	0.236490i	$-0.924003\pi$
$953$	−32.3207	+	23.4823i	−1.04697	+	0.760668i	−0.0753356	+	0.997158i	$0.524003\pi$
$954$	2.28713	+	7.03905i	0.0740485	+	0.227898i
$955$	1.66452	+	0.874543i	0.0538626	+	0.0282995i
$956$	−6.47926	−	19.9411i	−0.209554	−	0.644942i
$957$	2.73596	+	11.5749i	0.0884411	+	0.374164i
$958$	−4.09797	−	12.6123i	−0.132399	−	0.407484i
$959$	−3.67598	+	2.67076i	−0.118704	+	0.0862433i
$960$	−0.478109	+	2.79190i	−0.0154309	+	0.0901080i
$961$	−30.8871			−0.996358
$962$	5.97160	−	18.3787i	0.192532	−	0.592553i
$963$	1.07749	−	3.31618i	0.0347217	−	0.106862i
$964$	−4.61644			−0.148685
$965$	35.4453	+	18.6231i	1.14102	+	0.599498i
$966$	8.04958	−	5.84836i	0.258991	−	0.188168i
$967$	9.96047	+	30.6552i	0.320307	+	0.985804i	0.973515	+	0.228625i	$0.0734229\pi$
$967$	9.96047	+	30.6552i	0.320307	+	0.985804i	−0.653208	+	0.757179i	$0.726577\pi$
$968$	5.06257	−	9.76578i	0.162717	−	0.313884i
$969$	−22.9729	−	70.7033i	−0.737995	−	2.27132i
$970$	−2.21976	−	4.49482i	−0.0712722	−	0.144320i
$971$	−16.4415	−	50.6016i	−0.527631	−	1.62388i	−0.759053	−	0.651029i	$-0.774338\pi$
$971$	−16.4415	−	50.6016i	−0.527631	−	1.62388i	0.231422	−	0.972853i	$-0.425662\pi$
$972$	10.5752	−	7.68334i	0.339200	−	0.246443i
$973$	−2.09425	−	1.52156i	−0.0671385	−	0.0487790i
$974$	−2.74781	−	8.45689i	−0.0880455	−	0.270976i
$975$	13.6725	−	17.8601i	0.437869	−	0.571982i
$976$	4.17129	−	3.03062i	0.133520	−	0.0970077i
$977$	−3.22453	−	9.92409i	−0.103162	−	0.317500i	0.886133	−	0.463432i	$-0.153382\pi$
$977$	−3.22453	−	9.92409i	−0.103162	−	0.317500i	−0.989295	+	0.145932i	$0.953382\pi$
$978$	−6.09907	+	18.7710i	−0.195027	+	0.600231i
$979$	−11.1253	−	0.914883i	−0.355567	−	0.0292398i
$980$	−10.1479	+	1.47724i	−0.324163	+	0.0471887i
$981$	−19.5248			−0.623380
$982$	22.2242	−	16.1468i	0.709202	−	0.515266i
$983$	8.74790	−	26.9233i	0.279015	−	0.858719i	−0.709115	−	0.705093i	$-0.750905\pi$
$983$	8.74790	−	26.9233i	0.279015	−	0.858719i	0.988129	−	0.153625i	$-0.0490949\pi$
$984$	2.44977	−	7.53962i	0.0780958	−	0.240354i
$985$	−3.15382	−	6.38620i	−0.100489	−	0.203481i
$986$	22.1505			0.705417
$987$	−3.47162			−0.110503
$988$	−21.5493	+	15.6565i	−0.685574	+	0.498099i
$989$	−24.2037	+	17.5850i	−0.769634	+	0.559172i
$990$	−8.73544	−	5.54767i	−0.277630	−	0.176316i
$991$	20.5516	+	14.9316i	0.652843	+	0.474319i	0.864239	−	0.503082i	$-0.167801\pi$
$991$	20.5516	+	14.9316i	0.652843	+	0.474319i	−0.211395	+	0.977401i	$0.567801\pi$
$992$	0.336000			0.0106680
$993$	−2.71445	+	1.97216i	−0.0861404	+	0.0625846i
$994$	4.98474	−	15.3414i	0.158106	−	0.486601i
$995$	−34.7915	+	33.9308i	−1.10297	+	1.07568i
$996$	15.8048			0.500796
$997$	−1.25002	+	0.908194i	−0.0395886	+	0.0287628i	−0.607404	−	0.794393i	$-0.707789\pi$
$997$	−1.25002	+	0.908194i	−0.0395886	+	0.0287628i	0.567815	+	0.823156i	$0.307789\pi$
$998$	−11.0295	+	33.9452i	−0.349132	+	1.07452i
$999$	9.36255	−	28.8150i	0.296218	−	0.911665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.g.c.361.4	yes	60
11.5	even	5		550.2.j.c.511.12	yes	60
25.16	even	5		550.2.j.c.141.12	yes	60
275.16	even	5	inner	550.2.g.c.291.4	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.g.c.291.4	✓	60	275.16	even	5	inner
550.2.g.c.361.4	yes	60	1.1	even	1	trivial
550.2.j.c.141.12	yes	60	25.16	even	5
550.2.j.c.511.12	yes	60	11.5	even	5

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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.391447 - 1.20475i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.60082 + 1.56121i) q^{5} +(1.02482 - 0.744577i) q^{6} +(-1.25694 - 0.913224i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.12886 - 0.820164i) q^{9} +(-1.97948 - 1.04003i) q^{10} +(2.51441 + 2.16281i) q^{11} +(1.02482 + 0.744577i) q^{12} +(-2.87302 + 2.08737i) q^{13} +(0.480110 - 1.47763i) q^{14} +(2.50751 + 1.31745i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-6.33003 + 4.59903i) q^{17} +(1.12886 + 0.820164i) q^{18} +(-6.06809 - 4.40873i) q^{19} +(0.377430 - 2.20398i) q^{20} +(-0.608179 + 1.87178i) q^{21} +(-1.27996 + 3.05969i) q^{22} +(-4.09001 + 2.97156i) q^{23} +(-0.391447 + 1.20475i) q^{24} +(0.125226 - 4.99843i) q^{25} +(-2.87302 - 2.08737i) q^{26} +(-4.50445 - 3.27267i) q^{27} +1.55367 q^{28} +(-2.29031 + 1.66401i) q^{29} +(-0.478109 + 2.79190i) q^{30} +0.336000 q^{31} +1.00000 q^{32} +(1.62139 - 3.87586i) q^{33} +(-6.33003 - 4.59903i) q^{34} +(3.43788 - 0.500455i) q^{35} +(-0.431186 + 1.32705i) q^{36} +(1.68155 + 5.17528i) q^{37} +(2.31780 - 7.13347i) q^{38} +(3.63939 + 2.64417i) q^{39} +(2.21275 - 0.322112i) q^{40} -6.25824 q^{41} -1.96811 q^{42} +5.91777 q^{43} +(-3.30547 - 0.271822i) q^{44} +(-0.526645 + 3.07532i) q^{45} +(-4.09001 - 2.97156i) q^{46} +(0.545087 + 1.67760i) q^{47} -1.26675 q^{48} +(-1.41719 - 4.36165i) q^{49} +(4.79249 - 1.42550i) q^{50} +(8.01856 + 5.82582i) q^{51} +(1.09739 - 3.37743i) q^{52} +(4.29125 + 3.11777i) q^{53} +(1.72055 - 5.29529i) q^{54} +(-7.40172 + 0.463256i) q^{55} +(0.480110 + 1.47763i) q^{56} +(-2.93608 + 9.03632i) q^{57} +(-2.29031 - 1.66401i) q^{58} +(0.0523156 + 0.161011i) q^{59} +(-2.80299 + 0.408035i) q^{60} +(4.17129 + 3.03062i) q^{61} +(0.103830 + 0.319555i) q^{62} -2.16791 q^{63} +(0.309017 + 0.951057i) q^{64} +(1.34034 - 7.82689i) q^{65} +(4.18720 + 0.344331i) q^{66} +(1.86161 + 5.72946i) q^{67} +(2.41786 - 7.44139i) q^{68} +(5.18101 + 3.76423i) q^{69} +(1.53832 + 3.11496i) q^{70} +10.3825 q^{71} -1.39535 q^{72} -12.2921 q^{73} +(-4.40236 + 3.19850i) q^{74} +(-6.07088 + 1.80575i) q^{75} +7.50057 q^{76} +(-1.18534 - 5.01475i) q^{77} +(-1.39012 + 4.27836i) q^{78} +(4.98259 + 3.62006i) q^{79} +(0.990123 + 2.00491i) q^{80} +(-0.885943 + 2.72665i) q^{81} +(-1.93390 - 5.95194i) q^{82} +(10.0939 - 7.33362i) q^{83} +(-0.608179 - 1.87178i) q^{84} +(2.95314 - 17.2447i) q^{85} +(1.82869 + 5.62813i) q^{86} +(2.90125 + 2.10788i) q^{87} +(-0.762927 - 3.22768i) q^{88} +(-2.72294 + 1.97833i) q^{89} +(-3.08755 + 0.449457i) q^{90} +5.51746 q^{91} +(1.56224 - 4.80809i) q^{92} +(-0.131526 - 0.404796i) q^{93} +(-1.42706 + 1.03682i) q^{94} +(16.5969 - 2.41602i) q^{95} +(-0.391447 - 1.20475i) q^{96} +(1.81374 + 1.31776i) q^{97} +(3.71024 - 2.69565i) q^{98} +(4.61227 + 0.379286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 15 q^{2} - 4 q^{3} - 15 q^{4} + q^{6} - 3 q^{7} - 15 q^{8} - 17 q^{9} - 5 q^{10} + 7 q^{11} + q^{12} + 12 q^{13} - 3 q^{14} + 12 q^{15} - 15 q^{16} + q^{17} - 17 q^{18} + 3 q^{19} - 5 q^{20} - 4 q^{21}+ \cdots + 21 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 - 4 * q^3 - 15 * q^4 + q^6 - 3 * q^7 - 15 * q^8 - 17 * q^9 - 5 * q^10 + 7 * q^11 + q^12 + 12 * q^13 - 3 * q^14 + 12 * q^15 - 15 * q^16 + q^17 - 17 * q^18 + 3 * q^19 - 5 * q^20 - 4 * q^21 - 3 * q^22 - 3 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 + 2 * q^27 + 12 * q^28 + 18 * q^29 + 2 * q^30 - 20 * q^31 + 60 * q^32 + 10 * q^33 + q^34 - 19 * q^35 - 12 * q^36 - 36 * q^37 - 22 * q^38 + 13 * q^39 + 64 * q^41 + 46 * q^42 + 40 * q^43 - 8 * q^44 - 20 * q^45 - 3 * q^46 - 9 * q^47 + 6 * q^48 - 30 * q^49 + 18 * q^50 - 48 * q^51 - 8 * q^52 + 31 * q^53 - 8 * q^54 - 42 * q^55 - 3 * q^56 + 30 * q^57 + 18 * q^58 + 23 * q^59 - 8 * q^60 - 41 * q^61 - 5 * q^62 + 6 * q^63 - 15 * q^64 - 7 * q^65 - 30 * q^66 - 40 * q^67 - 4 * q^68 - 22 * q^69 - 4 * q^70 + 4 * q^71 + 58 * q^72 + 74 * q^73 - 11 * q^74 + 35 * q^75 + 38 * q^76 + 22 * q^77 - 12 * q^78 - 45 * q^79 + 10 * q^80 + 24 * q^81 - 11 * q^82 + 16 * q^83 - 4 * q^84 + 9 * q^85 - 20 * q^86 + 68 * q^87 + 7 * q^88 + q^89 + 10 * q^90 + 10 * q^91 + 2 * q^92 - 40 * q^93 - 24 * q^94 + 24 * q^95 - 4 * q^96 + 6 * q^97 - 30 * q^98 + 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more