LMFDB - Embedded newform 603.2.e.b.202.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(202,603)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("603.202");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$33$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			202.15
Character	$\chi$	$=$	603.202
Dual form			603.2.e.b.403.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0950983 - 0.164715i) q^{2} +(-0.457819 - 1.67045i) q^{3} +(0.981913 - 1.70072i) q^{4} +(0.636538 - 1.10252i) q^{5} +(-0.231610 + 0.234267i) q^{6} +(-1.46668 - 2.54037i) q^{7} -0.753906 q^{8} +(-2.58080 + 1.52953i) q^{9} +O(q^{10})$	\(q+(-0.0950983 - 0.164715i) q^{2} +(-0.457819 - 1.67045i) q^{3} +(0.981913 - 1.70072i) q^{4} +(0.636538 - 1.10252i) q^{5} +(-0.231610 + 0.234267i) q^{6} +(-1.46668 - 2.54037i) q^{7} -0.753906 q^{8} +(-2.58080 + 1.52953i) q^{9} -0.242135 q^{10} +(0.448750 + 0.777258i) q^{11} +(-3.29051 - 0.861612i) q^{12} +(0.591437 - 1.02440i) q^{13} +(-0.278958 + 0.483169i) q^{14} +(-2.13312 - 0.558551i) q^{15} +(-1.89213 - 3.27727i) q^{16} +5.00024 q^{17} +(0.497366 + 0.279642i) q^{18} -4.48372 q^{19} +(-1.25005 - 2.16515i) q^{20} +(-3.57208 + 3.61305i) q^{21} +(0.0853508 - 0.147832i) q^{22} +(1.62896 - 2.82144i) q^{23} +(0.345153 + 1.25936i) q^{24} +(1.68964 + 2.92654i) q^{25} -0.224978 q^{26} +(3.73654 + 3.61085i) q^{27} -5.76061 q^{28} +(2.08779 + 3.61617i) q^{29} +(0.110854 + 0.404474i) q^{30} +(-3.76117 + 6.51453i) q^{31} +(-1.11378 + 1.92913i) q^{32} +(1.09292 - 1.10546i) q^{33} +(-0.475514 - 0.823614i) q^{34} -3.73439 q^{35} +(0.0671789 + 5.89109i) q^{36} +3.42365 q^{37} +(0.426394 + 0.738536i) q^{38} +(-1.98198 - 0.518976i) q^{39} +(-0.479890 + 0.831193i) q^{40} +(3.11885 - 5.40200i) q^{41} +(0.934822 + 0.244781i) q^{42} +(-0.847047 - 1.46713i) q^{43} +1.76253 q^{44} +(0.0435496 + 3.81898i) q^{45} -0.619646 q^{46} +(-2.79679 - 4.84417i) q^{47} +(-4.60825 + 4.66110i) q^{48} +(-0.802312 + 1.38965i) q^{49} +(0.321364 - 0.556618i) q^{50} +(-2.28920 - 8.35264i) q^{51} +(-1.16148 - 2.01174i) q^{52} -0.374255 q^{53} +(0.239424 - 0.958850i) q^{54} +1.14259 q^{55} +(1.10574 + 1.91520i) q^{56} +(2.05273 + 7.48983i) q^{57} +(0.397091 - 0.687782i) q^{58} +(1.27781 - 2.21323i) q^{59} +(-3.04447 + 3.07939i) q^{60} +(-6.23675 - 10.8024i) q^{61} +1.43072 q^{62} +(7.67078 + 4.31286i) q^{63} -7.14485 q^{64} +(-0.752943 - 1.30414i) q^{65} +(-0.286021 - 0.0748939i) q^{66} +(0.500000 - 0.866025i) q^{67} +(4.90979 - 8.50401i) q^{68} +(-5.45885 - 1.42939i) q^{69} +(0.355134 + 0.615111i) q^{70} -7.57087 q^{71} +(1.94568 - 1.15312i) q^{72} -6.20662 q^{73} +(-0.325583 - 0.563926i) q^{74} +(4.11509 - 4.16228i) q^{75} +(-4.40262 + 7.62556i) q^{76} +(1.31635 - 2.27998i) q^{77} +(0.102999 + 0.375815i) q^{78} +(0.114051 + 0.197543i) q^{79} -4.81765 q^{80} +(4.32109 - 7.89482i) q^{81} -1.18639 q^{82} +(5.63063 + 9.75254i) q^{83} +(2.63732 + 9.62282i) q^{84} +(3.18284 - 5.51284i) q^{85} +(-0.161105 + 0.279043i) q^{86} +(5.08479 - 5.14310i) q^{87} +(-0.338316 - 0.585980i) q^{88} +15.4222 q^{89} +(0.624902 - 0.370352i) q^{90} -3.46980 q^{91} +(-3.19900 - 5.54082i) q^{92} +(12.6041 + 3.30036i) q^{93} +(-0.531939 + 0.921345i) q^{94} +(-2.85406 + 4.94337i) q^{95} +(3.73242 + 0.977326i) q^{96} +(-2.53390 - 4.38884i) q^{97} +0.305194 q^{98} +(-2.34697 - 1.31958i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} - 33 q^{4} + 18 q^{5} - 3 q^{6} - 48 q^{8} + 4 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 - 33 * q^4 + 18 * q^5 - 3 * q^6 - 48 * q^8 + 4 * q^9	\( 66 q + 7 q^{2} - 33 q^{4} + 18 q^{5} - 3 q^{6} - 48 q^{8} + 4 q^{9} + 12 q^{11} + q^{12} + 9 q^{14} + 3 q^{15} - 33 q^{16} - 62 q^{17} + 7 q^{18} + 43 q^{20} + 17 q^{21} + 19 q^{23} - 17 q^{24} - 33 q^{25} - 28 q^{26} - 3 q^{27} + 54 q^{28} + 25 q^{29} + 24 q^{30} + 45 q^{32} - 32 q^{33} - 6 q^{34} - 50 q^{35} + 53 q^{36} - 24 q^{37} + 34 q^{38} + 19 q^{39} - 6 q^{40} + 34 q^{41} - 107 q^{42} - 98 q^{44} + 9 q^{45} + 12 q^{46} + 26 q^{47} + 49 q^{48} - 33 q^{49} + 39 q^{50} - 50 q^{51} + 9 q^{52} - 104 q^{53} + 70 q^{54} + 60 q^{55} + 16 q^{56} + 6 q^{57} + 3 q^{58} + 21 q^{59} - 161 q^{60} - 54 q^{62} + q^{63} - 12 q^{64} + 52 q^{65} + 52 q^{66} + 33 q^{67} + 98 q^{68} + 2 q^{69} - 6 q^{70} - 62 q^{71} + 66 q^{72} + 27 q^{74} + 21 q^{75} - 6 q^{76} + 85 q^{77} - 107 q^{78} - 172 q^{80} + 72 q^{81} + 102 q^{82} + 71 q^{83} - 54 q^{84} - 27 q^{85} + 9 q^{86} + 3 q^{87} - 12 q^{88} - 82 q^{89} + 153 q^{90} - 60 q^{91} + 67 q^{92} - 47 q^{93} + 15 q^{94} + 58 q^{95} - 136 q^{96} - 12 q^{97} - 172 q^{98} + 96 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 - 33 * q^4 + 18 * q^5 - 3 * q^6 - 48 * q^8 + 4 * q^9 + 12 * q^11 + q^12 + 9 * q^14 + 3 * q^15 - 33 * q^16 - 62 * q^17 + 7 * q^18 + 43 * q^20 + 17 * q^21 + 19 * q^23 - 17 * q^24 - 33 * q^25 - 28 * q^26 - 3 * q^27 + 54 * q^28 + 25 * q^29 + 24 * q^30 + 45 * q^32 - 32 * q^33 - 6 * q^34 - 50 * q^35 + 53 * q^36 - 24 * q^37 + 34 * q^38 + 19 * q^39 - 6 * q^40 + 34 * q^41 - 107 * q^42 - 98 * q^44 + 9 * q^45 + 12 * q^46 + 26 * q^47 + 49 * q^48 - 33 * q^49 + 39 * q^50 - 50 * q^51 + 9 * q^52 - 104 * q^53 + 70 * q^54 + 60 * q^55 + 16 * q^56 + 6 * q^57 + 3 * q^58 + 21 * q^59 - 161 * q^60 - 54 * q^62 + q^63 - 12 * q^64 + 52 * q^65 + 52 * q^66 + 33 * q^67 + 98 * q^68 + 2 * q^69 - 6 * q^70 - 62 * q^71 + 66 * q^72 + 27 * q^74 + 21 * q^75 - 6 * q^76 + 85 * q^77 - 107 * q^78 - 172 * q^80 + 72 * q^81 + 102 * q^82 + 71 * q^83 - 54 * q^84 - 27 * q^85 + 9 * q^86 + 3 * q^87 - 12 * q^88 - 82 * q^89 + 153 * q^90 - 60 * q^91 + 67 * q^92 - 47 * q^93 + 15 * q^94 + 58 * q^95 - 136 * q^96 - 12 * q^97 - 172 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.0950983	−	0.164715i	−0.0672446	−	0.116471i	0.830443	−	0.557104i	$-0.188087\pi$
$2$	−0.0950983	−	0.164715i	−0.0672446	−	0.116471i	−0.897687	+	0.440633i	$0.854754\pi$
$3$	−0.457819	−	1.67045i	−0.264322	−	0.964434i
$3$	−0.457819	−	1.67045i	−0.264322	−	0.964434i
$4$	0.981913	−	1.70072i	0.490956	−	0.850361i
$5$	0.636538	−	1.10252i	0.284668	−	0.493060i	−0.687860	−	0.725843i	$-0.741450\pi$
$5$	0.636538	−	1.10252i	0.284668	−	0.493060i	0.972529	+	0.232783i	$0.0747832\pi$
$6$	−0.231610	+	0.234267i	−0.0945545	+	0.0956389i
$7$	−1.46668	−	2.54037i	−0.554354	−	0.960169i	−0.997954	−	0.0639438i	$-0.979632\pi$
$7$	−1.46668	−	2.54037i	−0.554354	−	0.960169i	0.443600	−	0.896225i	$-0.353701\pi$
$8$	−0.753906			−0.266546
$9$	−2.58080	+	1.52953i	−0.860268	+	0.509843i
$10$	−0.242135			−0.0765697
$11$	0.448750	+	0.777258i	0.135303	+	0.234352i	0.925713	−	0.378226i	$-0.123466\pi$
$11$	0.448750	+	0.777258i	0.135303	+	0.234352i	−0.790410	+	0.612578i	$0.790132\pi$
$12$	−3.29051	−	0.861612i	−0.949888	−	0.248726i
$13$	0.591437	−	1.02440i	0.164035	−	0.284117i	−0.772277	−	0.635286i	$-0.780882\pi$
$13$	0.591437	−	1.02440i	0.164035	−	0.284117i	0.936312	+	0.351169i	$0.114216\pi$
$14$	−0.278958	+	0.483169i	−0.0745546	+	0.129132i
$15$	−2.13312	−	0.558551i	−0.550768	−	0.144217i
$16$	−1.89213	−	3.27727i	−0.473033	−	0.819316i
$17$	5.00024			1.21274			0.606368	−	0.795184i	$-0.292626\pi$
$17$	5.00024			1.21274			0.606368	+	0.795184i	$0.292626\pi$
$18$	0.497366	+	0.279642i	0.117230	+	0.0659122i
$19$	−4.48372			−1.02864			−0.514318	−	0.857600i	$-0.671955\pi$
$19$	−4.48372			−1.02864			−0.514318	+	0.857600i	$0.671955\pi$
$20$	−1.25005	−	2.16515i	−0.279519	−	0.484142i
$21$	−3.57208	+	3.61305i	−0.779492	+	0.788432i
$22$	0.0853508	−	0.147832i	0.0181968	−	0.0315179i
$23$	1.62896	−	2.82144i	0.339662	−	0.588312i	−0.644707	−	0.764430i	$-0.723021\pi$
$23$	1.62896	−	2.82144i	0.339662	−	0.588312i	0.984369	+	0.176118i	$0.0563540\pi$
$24$	0.345153	+	1.25936i	0.0704540	+	0.257066i
$25$	1.68964	+	2.92654i	0.337928	+	0.585308i
$26$	−0.224978			−0.0441219
$27$	3.73654	+	3.61085i	0.719097	+	0.694909i
$28$	−5.76061			−1.08865
$29$	2.08779	+	3.61617i	0.387694	+	0.671505i	0.992139	−	0.125142i	$-0.0399385\pi$
$29$	2.08779	+	3.61617i	0.387694	+	0.671505i	−0.604445	+	0.796647i	$0.706605\pi$
$30$	0.110854	+	0.404474i	0.0202391	+	0.0738464i
$31$	−3.76117	+	6.51453i	−0.675525	+	1.17004i	0.300790	+	0.953690i	$0.402750\pi$
$31$	−3.76117	+	6.51453i	−0.675525	+	1.17004i	−0.976315	+	0.216354i	$0.930584\pi$
$32$	−1.11378	+	1.92913i	−0.196891	+	0.341025i
$33$	1.09292	−	1.10546i	0.190254	−	0.192436i
$34$	−0.475514	−	0.823614i	−0.0815499	−	0.141249i
$35$	−3.73439			−0.631228
$36$	0.0671789	+	5.89109i	0.0111965	+	0.981849i
$37$	3.42365			0.562844			0.281422	−	0.959584i	$-0.409194\pi$
$37$	3.42365			0.562844			0.281422	+	0.959584i	$0.409194\pi$
$38$	0.426394	+	0.738536i	0.0691702	+	0.119806i
$39$	−1.98198	−	0.518976i	−0.317370	−	0.0831026i
$40$	−0.479890	+	0.831193i	−0.0758772	+	0.131423i
$41$	3.11885	−	5.40200i	0.487082	−	0.843651i	−0.512807	−	0.858504i	$-0.671394\pi$
$41$	3.11885	−	5.40200i	0.487082	−	0.843651i	0.999890	+	0.0148524i	$0.00472783\pi$
$42$	0.934822	+	0.244781i	0.144246	+	0.0377705i
$43$	−0.847047	−	1.46713i	−0.129173	−	0.223735i	0.794183	−	0.607678i	$-0.207899\pi$
$43$	−0.847047	−	1.46713i	−0.129173	−	0.223735i	−0.923357	+	0.383944i	$0.874566\pi$
$44$	1.76253			0.265712
$45$	0.0435496	+	3.81898i	0.00649199	+	0.569300i
$46$	−0.619646			−0.0913618
$47$	−2.79679	−	4.84417i	−0.407953	−	0.706595i	0.586707	−	0.809799i	$-0.300424\pi$
$47$	−2.79679	−	4.84417i	−0.407953	−	0.706595i	−0.994660	+	0.103204i	$0.967091\pi$
$48$	−4.60825	+	4.66110i	−0.665144	+	0.672772i
$49$	−0.802312	+	1.38965i	−0.114616	+	0.198521i
$50$	0.321364	−	0.556618i	0.0454477	−	0.0787177i
$51$	−2.28920	−	8.35264i	−0.320553	−	1.16960i
$52$	−1.16148	−	2.01174i	−0.161068	−	0.278978i
$53$	−0.374255			−0.0514079			−0.0257039	−	0.999670i	$-0.508183\pi$
$53$	−0.374255			−0.0514079			−0.0257039	+	0.999670i	$0.508183\pi$
$54$	0.239424	−	0.958850i	0.0325814	−	0.130483i
$55$	1.14259			0.154066
$56$	1.10574	+	1.91520i	0.147761	+	0.255929i
$57$	2.05273	+	7.48983i	0.271891	+	0.992052i
$58$	0.397091	−	0.687782i	0.0521406	−	0.0903102i
$59$	1.27781	−	2.21323i	0.166357	−	0.288139i	−0.770779	−	0.637102i	$-0.780133\pi$
$59$	1.27781	−	2.21323i	0.166357	−	0.288139i	0.937136	+	0.348964i	$0.113466\pi$
$60$	−3.04447	+	3.07939i	−0.393040	+	0.397548i
$61$	−6.23675	−	10.8024i	−0.798534	−	1.38310i	−0.920571	−	0.390576i	$-0.872276\pi$
$61$	−6.23675	−	10.8024i	−0.798534	−	1.38310i	0.122036	−	0.992526i	$-0.461058\pi$
$62$	1.43072			0.181702
$63$	7.67078	+	4.31286i	0.966427	+	0.543369i
$64$	−7.14485			−0.893106
$65$	−0.752943	−	1.30414i	−0.0933911	−	0.161758i
$66$	−0.286021	−	0.0748939i	−0.0352067	−	0.00921880i
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i
$68$	4.90979	−	8.50401i	0.595400	−	1.03126i
$69$	−5.45885	−	1.42939i	−0.657168	−	0.172078i
$70$	0.355134	+	0.615111i	0.0424467	+	0.0735198i
$71$	−7.57087			−0.898497			−0.449249	−	0.893407i	$-0.648308\pi$
$71$	−7.57087			−0.898497			−0.449249	+	0.893407i	$0.648308\pi$
$72$	1.94568	−	1.15312i	0.229301	−	0.135896i
$73$	−6.20662			−0.726430			−0.363215	−	0.931705i	$-0.618321\pi$
$73$	−6.20662			−0.726430			−0.363215	+	0.931705i	$0.618321\pi$
$74$	−0.325583	−	0.563926i	−0.0378482	−	0.0655551i
$75$	4.11509	−	4.16228i	0.475170	−	0.480619i
$76$	−4.40262	+	7.62556i	−0.505015	+	0.874712i
$77$	1.31635	−	2.27998i	0.150012	−	0.259828i
$78$	0.102999	+	0.375815i	0.0116624	+	0.0425527i
$79$	0.114051	+	0.197543i	0.0128318	+	0.0222253i	0.872370	−	0.488846i	$-0.162582\pi$
$79$	0.114051	+	0.197543i	0.0128318	+	0.0222253i	−0.859538	+	0.511071i	$0.829249\pi$
$80$	−4.81765			−0.538630
$81$	4.32109	−	7.89482i	0.480121	−	0.877202i
$82$	−1.18639			−0.131015
$83$	5.63063	+	9.75254i	0.618042	+	1.07048i	0.989843	+	0.142168i	$0.0454073\pi$
$83$	5.63063	+	9.75254i	0.618042	+	1.07048i	−0.371800	+	0.928313i	$0.621259\pi$
$84$	2.63732	+	9.62282i	0.287755	+	1.04994i
$85$	3.18284	−	5.51284i	0.345227	−	0.597951i
$86$	−0.161105	+	0.279043i	−0.0173724	+	0.0300900i
$87$	5.08479	−	5.14310i	0.545147	−	0.551399i
$88$	−0.338316	−	0.585980i	−0.0360646	−	0.0624656i
$89$	15.4222			1.63475			0.817373	−	0.576109i	$-0.195430\pi$
$89$	15.4222			1.63475			0.817373	+	0.576109i	$0.195430\pi$
$90$	0.624902	−	0.370352i	0.0658704	−	0.0390385i
$91$	−3.46980			−0.363734
$92$	−3.19900	−	5.54082i	−0.333518	−	0.577671i
$93$	12.6041	+	3.30036i	1.30699	+	0.342231i
$94$	−0.531939	+	0.921345i	−0.0548653	+	0.0950295i
$95$	−2.85406	+	4.94337i	−0.292820	+	0.507179i
$96$	3.73242	+	0.977326i	0.380939	+	0.0997479i
$97$	−2.53390	−	4.38884i	−0.257279	−	0.445620i	0.708233	−	0.705978i	$-0.249492\pi$
$97$	−2.53390	−	4.38884i	−0.257279	−	0.445620i	−0.965512	+	0.260359i	$0.916159\pi$
$98$	0.305194			0.0308293
$99$	−2.34697	−	1.31958i	−0.235880	−	0.132622i
$100$	6.63631			0.663631
$101$	−0.0293677	−	0.0508663i	−0.00292219	−	0.00506138i	0.864561	−	0.502529i	$-0.167597\pi$
$101$	−0.0293677	−	0.0508663i	−0.00292219	−	0.00506138i	−0.867483	+	0.497467i	$0.834263\pi$
$102$	−1.15811	+	1.17139i	−0.114670	+	0.115985i
$103$	−2.86696	+	4.96572i	−0.282490	+	0.489287i	−0.971997	−	0.234992i	$-0.924494\pi$
$103$	−2.86696	+	4.96572i	−0.282490	+	0.489287i	0.689508	+	0.724278i	$0.257827\pi$
$104$	−0.445887	+	0.772300i	−0.0437229	+	0.0757302i
$105$	1.70968	+	6.23812i	0.166847	+	0.608778i
$106$	0.0355910	+	0.0616454i	0.00345690	+	0.00598753i
$107$	1.64619			0.159143			0.0795714	−	0.996829i	$-0.474645\pi$
$107$	1.64619			0.159143			0.0795714	+	0.996829i	$0.474645\pi$
$108$	9.81002	−	2.80927i	0.943969	−	0.270323i
$109$	2.75469			0.263852			0.131926	−	0.991260i	$-0.457884\pi$
$109$	2.75469			0.263852			0.131926	+	0.991260i	$0.457884\pi$
$110$	−0.108658	−	0.188201i	−0.0103601	−	0.0179443i
$111$	−1.56741	−	5.71903i	−0.148772	−	0.542826i
$112$	−5.55031	+	9.61341i	−0.524455	+	0.908382i
$113$	5.69348	−	9.86140i	0.535598	−	0.927682i	−0.463537	−	0.886078i	$-0.653420\pi$
$113$	5.69348	−	9.86140i	0.535598	−	0.927682i	0.999134	−	0.0416044i	$-0.0132469\pi$
$114$	1.03848	−	1.05039i	0.0972622	−	0.0983776i
$115$	−2.07379	−	3.59191i	−0.193382	−	0.334948i
$116$	8.20013			0.761363
$117$	0.0404639	+	3.54839i	0.00374089	+	0.328049i
$118$	−0.486071			−0.0447464
$119$	−7.33376	−	12.7024i	−0.672284	−	1.16443i
$120$	1.60817	+	0.421095i	0.146805	+	0.0384406i
$121$	5.09725	−	8.82869i	0.463386	−	0.802608i
$122$	−1.18621	+	2.05457i	−0.107394	+	0.186012i
$123$	−10.4516	−	2.73674i	−0.942393	−	0.246763i
$124$	7.38627	+	12.7934i	0.663307	+	1.14888i
$125$	10.6675			0.954126
$126$	−0.0190853	−	1.67364i	−0.00170025	−	0.149100i
$127$	9.91351			0.879682			0.439841	−	0.898076i	$-0.355035\pi$
$127$	9.91351			0.879682			0.439841	+	0.898076i	$0.355035\pi$
$128$	2.90703	+	5.03512i	0.256947	+	0.445046i
$129$	−2.06297	+	2.08663i	−0.181634	+	0.183717i
$130$	−0.143207	+	0.248042i	−0.0125601	+	0.0217547i
$131$	6.97220	−	12.0762i	0.609164	−	1.05510i	−0.382215	−	0.924073i	$-0.624839\pi$
$131$	6.97220	−	12.0762i	0.609164	−	1.05510i	0.991379	−	0.131029i	$-0.0418281\pi$
$132$	−0.806922	−	2.94423i	−0.0702336	−	0.256262i
$133$	6.57619	+	11.3903i	0.570228	+	0.987664i
$134$	−0.190197			−0.0164305
$135$	6.35947	−	1.82115i	0.547336	−	0.156740i
$136$	−3.76971			−0.323250
$137$	7.60763	+	13.1768i	0.649964	+	1.12577i	0.983131	+	0.182903i	$0.0585494\pi$
$137$	7.60763	+	13.1768i	0.649964	+	1.12577i	−0.333167	+	0.942868i	$0.608117\pi$
$138$	0.283686	+	1.03509i	0.0241489	+	0.0881125i
$139$	9.36530	−	16.2212i	0.794354	−	1.37586i	−0.128894	−	0.991658i	$-0.541143\pi$
$139$	9.36530	−	16.2212i	0.794354	−	1.37586i	0.923248	−	0.384203i	$-0.125524\pi$
$140$	−3.66685	+	6.35117i	−0.309905	+	0.536772i
$141$	−6.81153	+	6.88965i	−0.573634	+	0.580213i
$142$	0.719977	+	1.24704i	0.0604191	+	0.104649i
$143$	1.06163			0.0887779
$144$	9.89588	+	5.56391i	0.824657	+	0.463659i
$145$	5.31584			0.441457
$146$	0.590239	+	1.02232i	0.0488485	+	0.0846081i
$147$	2.68865	+	0.704016i	0.221756	+	0.0580662i
$148$	3.36172	−	5.82267i	0.276332	−	0.478621i
$149$	0.315647	−	0.546717i	0.0258588	−	0.0447888i	−0.852806	−	0.522227i	$-0.825101\pi$
$149$	0.315647	−	0.546717i	0.0258588	−	0.0447888i	0.878665	+	0.477438i	$0.158435\pi$
$150$	−1.07693	−	0.281991i	−0.0879309	−	0.0230245i
$151$	−1.39591	−	2.41779i	−0.113598	−	0.196757i	0.803621	−	0.595142i	$-0.202904\pi$
$151$	−1.39591	−	2.41779i	−0.113598	−	0.196757i	−0.917218	+	0.398385i	$0.869571\pi$
$152$	3.38030			0.274179
$153$	−12.9046	+	7.64800i	−1.04328	+	0.618304i
$154$	−0.500730			−0.0403500
$155$	4.78825	+	8.29349i	0.384601	+	0.666149i
$156$	−2.82876	+	2.86120i	−0.226482	+	0.229080i
$157$	1.28427	−	2.22442i	0.102496	−	0.177528i	−0.810217	−	0.586131i	$-0.800651\pi$
$157$	1.28427	−	2.22442i	0.102496	−	0.177528i	0.912712	+	0.408603i	$0.133984\pi$
$158$	0.0216922	−	0.0375720i	0.00172574	−	0.00298907i
$159$	0.171341	+	0.625174i	0.0135882	+	0.0495795i
$160$	1.41793	+	2.45593i	0.112097	+	0.194158i
$161$	−9.55668			−0.753172
$162$	−1.71132	+	0.0390351i	−0.134454	+	0.00306689i
$163$	−2.93339			−0.229761			−0.114880	−	0.993379i	$-0.536648\pi$
$163$	−2.93339			−0.229761			−0.114880	+	0.993379i	$0.536648\pi$
$164$	−6.12487	−	10.6086i	−0.478272	−	0.828392i
$165$	−0.523098	−	1.90863i	−0.0407231	−	0.148587i
$166$	1.07093	−	1.85490i	0.0831200	−	0.143968i
$167$	−6.59632	+	11.4252i	−0.510438	+	0.884105i	0.489488	+	0.872010i	$0.337184\pi$
$167$	−6.59632	+	11.4252i	−0.510438	+	0.884105i	−0.999927	+	0.0120955i	$0.996150\pi$
$168$	2.69301	−	2.72390i	0.207770	−	0.210153i
$169$	5.80041	+	10.0466i	0.446185	+	0.772815i
$170$	−1.21073			−0.0928588
$171$	11.5716	−	6.85797i	0.884902	−	0.524442i
$172$	−3.32690			−0.253674
$173$	11.4521	+	19.8356i	0.870687	+	1.50807i	0.861287	+	0.508118i	$0.169659\pi$
$173$	11.4521	+	19.8356i	0.870687	+	1.50807i	0.00939958	+	0.999956i	$0.497008\pi$
$174$	−1.33070	−	0.348441i	−0.100880	−	0.0264152i
$175$	4.95633	−	8.58461i	0.374663	−	0.648935i
$176$	1.69819	−	2.94135i	0.128006	−	0.221712i
$177$	−4.28210	−	1.12126i	−0.321863	−	0.0842790i
$178$	−1.46662	−	2.54026i	−0.109928	−	0.190401i
$179$	−17.6006			−1.31553			−0.657767	−	0.753222i	$-0.728499\pi$
$179$	−17.6006			−1.31553			−0.657767	+	0.753222i	$0.728499\pi$
$180$	6.53779	+	3.67584i	0.487298	+	0.273981i
$181$	−24.8691			−1.84851			−0.924254	−	0.381777i	$-0.875312\pi$
$181$	−24.8691			−1.84851			−0.924254	+	0.381777i	$0.875312\pi$
$182$	0.329972	+	0.571528i	0.0244591	+	0.0423645i
$183$	−15.1895	+	15.3637i	−1.12284	+	1.13572i
$184$	−1.22808	+	2.12710i	−0.0905356	+	0.156812i
$185$	2.17928	−	3.77463i	0.160224	−	0.277516i
$186$	−0.655012	−	2.38995i	−0.0480278	−	0.175240i
$187$	2.24386	+	3.88648i	0.164087	+	0.284207i
$188$	−10.9848			−0.801149
$189$	3.69258	−	14.7882i	0.268596	−	1.07568i
$190$	1.08566			0.0787623
$191$	−1.82176	−	3.15539i	−0.131818	−	0.228316i	0.792559	−	0.609795i	$-0.208748\pi$
$191$	−1.82176	−	3.15539i	−0.131818	−	0.228316i	−0.924377	+	0.381479i	$0.875415\pi$
$192$	3.27105	+	11.9351i	0.236067	+	0.861342i
$193$	−1.66727	+	2.88780i	−0.120013	+	0.207868i	−0.919772	−	0.392452i	$-0.871627\pi$
$193$	−1.66727	+	2.88780i	−0.120013	+	0.207868i	0.799760	+	0.600320i	$0.204960\pi$
$194$	−0.481939	+	0.834743i	−0.0346012	+	0.0599311i
$195$	−1.83378	+	1.85481i	−0.131320	+	0.132826i
$196$	1.57560	+	2.72902i	0.112543	+	0.194930i
$197$	11.2300			0.800108			0.400054	−	0.916492i	$-0.368991\pi$
$197$	11.2300			0.800108			0.400054	+	0.916492i	$0.368991\pi$
$198$	0.00583939	+	0.512071i	0.000414987	+	0.0363913i
$199$	11.4048			0.808466			0.404233	−	0.914656i	$-0.367538\pi$
$199$	11.4048			0.808466			0.404233	+	0.914656i	$0.367538\pi$
$200$	−1.27383	−	2.20634i	−0.0900733	−	0.156012i
$201$	−1.67556	−	0.438742i	−0.118185	−	0.0309465i
$202$	−0.00558563	+	0.00967459i	−0.000393003	+	0.000680702i
$203$	6.12426	−	10.6075i	0.429839	−	0.744503i
$204$	−16.4533	−	4.30826i	−1.15196	−	0.301639i
$205$	−3.97053	−	6.87716i	−0.277314	−	0.480322i
$206$	1.09057			0.0759837
$207$	0.111448	+	9.77314i	0.00774614	+	0.679280i
$208$	−4.47630			−0.310376
$209$	−2.01207	−	3.48501i	−0.139178	−	0.241063i
$210$	0.864924	−	0.874844i	0.0596855	−	0.0603700i
$211$	3.18968	−	5.52469i	0.219587	−	0.380336i	−0.735095	−	0.677964i	$-0.762862\pi$
$211$	3.18968	−	5.52469i	0.219587	−	0.380336i	0.954682	+	0.297629i	$0.0961957\pi$
$212$	−0.367486	+	0.636504i	−0.0252390	+	0.0437153i
$213$	3.46609	+	12.6468i	0.237493	+	0.866542i
$214$	−0.156549	−	0.271152i	−0.0107015	−	0.0185355i
$215$	−2.15671			−0.147086
$216$	−2.81700	−	2.72224i	−0.191673	−	0.185225i
$217$	22.0657			1.49792
$218$	−0.261966	−	0.453739i	−0.0177426	−	0.0307311i
$219$	2.84151	+	10.3678i	0.192011	+	0.700594i
$220$	1.12192	−	1.94322i	0.0756398	−	0.131012i
$221$	2.95732	−	5.12223i	0.198931	−	0.344559i
$222$	−0.792952	+	0.802046i	−0.0532195	+	0.0538298i
$223$	−6.66976	−	11.5524i	−0.446640	−	0.773604i	0.551524	−	0.834159i	$-0.314046\pi$
$223$	−6.66976	−	11.5524i	−0.446640	−	0.773604i	−0.998165	+	0.0605548i	$0.980713\pi$
$224$	6.53426			0.436589
$225$	−8.83685	−	4.96848i	−0.589123	−	0.331232i
$226$	−2.16576			−0.144064
$227$	11.1168	+	19.2549i	0.737850	+	1.27799i	0.953461	+	0.301515i	$0.0974923\pi$
$227$	11.1168	+	19.2549i	0.737850	+	1.27799i	−0.215611	+	0.976479i	$0.569174\pi$
$228$	14.7537	+	3.86323i	0.977089	+	0.255848i
$229$	−3.82893	+	6.63190i	−0.253023	+	0.438248i	−0.964357	−	0.264606i	$-0.914758\pi$
$229$	−3.82893	+	6.63190i	−0.253023	+	0.438248i	0.711334	+	0.702854i	$0.248091\pi$
$230$	−0.394428	+	0.683169i	−0.0260078	+	0.0450469i
$231$	−4.41124	−	1.15507i	−0.290239	−	0.0759983i
$232$	−1.57400	−	2.72625i	−0.103338	−	0.178987i
$233$	−7.51027			−0.492014			−0.246007	−	0.969268i	$-0.579119\pi$
$233$	−7.51027			−0.492014			−0.246007	+	0.969268i	$0.579119\pi$
$234$	0.580625	−	0.344111i	0.0379566	−	0.0224952i
$235$	−7.12104			−0.464525
$236$	−2.50940	−	4.34641i	−0.163348	−	0.282927i
$237$	0.277771	−	0.280956i	0.0180431	−	0.0182501i
$238$	−1.39485	+	2.41596i	−0.0904150	+	0.156603i
$239$	10.9525	−	18.9704i	0.708461	−	1.22709i	−0.256967	−	0.966420i	$-0.582723\pi$
$239$	10.9525	−	18.9704i	0.708461	−	1.22709i	0.965428	−	0.260671i	$-0.0839437\pi$
$240$	2.20561	+	8.04764i	0.142372	+	0.519473i
$241$	−4.11959	−	7.13533i	−0.265366	−	0.459627i	0.702294	−	0.711887i	$-0.252159\pi$
$241$	−4.11959	−	7.13533i	−0.265366	−	0.459627i	−0.967659	+	0.252260i	$0.918826\pi$
$242$	−1.93896			−0.124641
$243$	−15.1662	−	3.60376i	−0.972911	−	0.231182i
$244$	−24.4958			−1.56818
$245$	1.02140	+	1.76912i	0.0652551	+	0.113025i
$246$	0.543151	+	1.98180i	0.0346301	+	0.126355i
$247$	−2.65183	+	4.59311i	−0.168732	+	0.292253i
$248$	2.83557	−	4.91134i	0.180059	−	0.311871i
$249$	13.7133	−	13.8706i	0.869046	−	0.879013i
$250$	−1.01446	−	1.75709i	−0.0641599	−	0.111128i
$251$	−23.0979			−1.45793			−0.728965	−	0.684551i	$-0.759998\pi$
$251$	−23.0979			−1.45793			−0.728965	+	0.684551i	$0.759998\pi$
$252$	14.8670	−	8.81102i	0.936534	−	0.555042i
$253$	2.92399			0.183830
$254$	−0.942758	−	1.63290i	−0.0591539	−	0.102458i
$255$	−10.6661	−	2.79289i	−0.667936	−	0.174897i
$256$	−6.59194	+	11.4176i	−0.411996	+	0.713598i
$257$	12.4199	−	21.5119i	0.774730	−	1.34187i	−0.160215	−	0.987082i	$-0.551219\pi$
$257$	12.4199	−	21.5119i	0.774730	−	1.34187i	0.934946	−	0.354790i	$-0.115448\pi$
$258$	0.539884	+	0.141367i	0.0336117	+	0.00880115i
$259$	−5.02140	−	8.69732i	−0.312015	−	0.540425i
$260$	−2.95730			−0.183404
$261$	−10.9192	−	6.13927i	−0.675882	−	0.380011i
$262$	−2.65218			−0.163852
$263$	7.02635	+	12.1700i	0.433263	+	0.750434i	0.997152	−	0.0754167i	$-0.0240287\pi$
$263$	7.02635	+	12.1700i	0.433263	+	0.750434i	−0.563889	+	0.825851i	$0.690695\pi$
$264$	−0.823962	+	0.833412i	−0.0507114	+	0.0512930i
$265$	−0.238228	+	0.412622i	−0.0146342	+	0.0253472i
$266$	1.25077	−	2.16639i	0.0766895	−	0.132830i
$267$	−7.06056	−	25.7619i	−0.432099	−	1.57661i
$268$	−0.981913	−	1.70072i	−0.0599799	−	0.103888i
$269$	−7.29295			−0.444659			−0.222329	−	0.974972i	$-0.571366\pi$
$269$	−7.29295			−0.444659			−0.222329	+	0.974972i	$0.571366\pi$
$270$	−0.904746	−	0.874313i	−0.0550611	−	0.0532090i
$271$	1.83918			0.111722			0.0558610	−	0.998439i	$-0.482210\pi$
$271$	1.83918			0.111722			0.0558610	+	0.998439i	$0.482210\pi$
$272$	−9.46110	−	16.3871i	−0.573663	−	0.993614i
$273$	1.58854	+	5.79612i	0.0961428	+	0.350797i
$274$	1.44695	−	2.50618i	0.0874132	−	0.151404i
$275$	−1.51645	+	2.62657i	−0.0914455	+	0.158388i
$276$	−7.79111	+	7.88046i	−0.468969	+	0.474348i
$277$	13.3021	+	23.0400i	0.799248	+	1.38434i	0.920107	+	0.391668i	$0.128102\pi$
$277$	13.3021	+	23.0400i	0.799248	+	1.38434i	−0.120859	+	0.992670i	$0.538565\pi$
$278$	−3.56249			−0.213664
$279$	−0.257325	−	22.5655i	−0.0154057	−	1.35096i
$280$	2.81538			0.168251
$281$	10.5125	+	18.2081i	0.627121	+	1.08620i	0.988127	+	0.153641i	$0.0491000\pi$
$281$	10.5125	+	18.2081i	0.627121	+	1.08620i	−0.361006	+	0.932563i	$0.617567\pi$
$282$	1.78259	+	0.466768i	0.106152	+	0.0277956i
$283$	12.4910	−	21.6350i	0.742512	−	1.28607i	−0.208836	−	0.977951i	$-0.566968\pi$
$283$	12.4910	−	21.6350i	0.742512	−	1.28607i	0.951348	−	0.308118i	$-0.0996990\pi$
$284$	−7.43394	+	12.8760i	−0.441123	+	0.764047i
$285$	9.56429	+	2.50439i	0.566540	+	0.148347i
$286$	−0.100959	−	0.174866i	−0.00596984	−	0.0103401i
$287$	−18.2974			−1.08006
$288$	−0.0762009	−	6.68226i	−0.00449018	−	0.393756i
$289$	8.00235			0.470727
$290$	−0.505527	−	0.875599i	−0.0296856	−	0.0514169i
$291$	−6.17127	+	6.24205i	−0.361767	+	0.365915i
$292$	−6.09436	+	10.5557i	−0.356645	+	0.617728i
$293$	−13.7583	+	23.8300i	−0.803766	+	1.39216i	0.113356	+	0.993554i	$0.463840\pi$
$293$	−13.7583	+	23.8300i	−0.803766	+	1.39216i	−0.917121	+	0.398608i	$0.869493\pi$
$294$	−0.139724	−	0.509811i	−0.00814885	−	0.0297328i
$295$	−1.62675	−	2.81762i	−0.0947131	−	0.164048i
$296$	−2.58111			−0.150024
$297$	−1.12979	+	4.52463i	−0.0655573	+	0.262546i
$298$	−0.120070			−0.00695546
$299$	−1.92686	−	3.33741i	−0.111433	−	0.193007i
$300$	−3.03823	−	11.0856i	−0.175412	−	0.640029i
$301$	−2.48470	+	4.30362i	−0.143216	+	0.248057i
$302$	−0.265498	+	0.459855i	−0.0152777	+	0.0264617i
$303$	−0.0715245	+	0.0723448i	−0.00410897	+	0.00415610i
$304$	8.48378	+	14.6943i	0.486578	+	0.842778i
$305$	−15.8797			−0.909270
$306$	2.48695	+	1.39827i	0.142169	+	0.0799340i
$307$	32.4477			1.85189			0.925944	−	0.377661i	$-0.123272\pi$
$307$	32.4477			1.85189			0.925944	+	0.377661i	$0.123272\pi$
$308$	−2.58508	−	4.47749i	−0.147298	−	0.255128i
$309$	9.60753	+	2.51571i	0.546553	+	0.143114i
$310$	0.910708	−	1.57739i	0.0517248	−	0.0895899i
$311$	−1.34357	+	2.32713i	−0.0761869	+	0.131960i	−0.901602	−	0.432567i	$-0.857608\pi$
$311$	−1.34357	+	2.32713i	−0.0761869	+	0.131960i	0.825415	+	0.564527i	$0.190941\pi$
$312$	1.49422	+	0.391259i	0.0845938	+	0.0221507i
$313$	−15.3596	−	26.6036i	−0.868176	−	1.50373i	−0.863858	−	0.503735i	$-0.831959\pi$
$313$	−15.3596	−	26.6036i	−0.868176	−	1.50373i	−0.00431789	−	0.999991i	$-0.501374\pi$
$314$	−0.488527			−0.0275692
$315$	9.63774	−	5.71186i	0.543025	−	0.321827i
$316$	0.447954			0.0251994
$317$	7.87046	+	13.6320i	0.442049	+	0.765652i	0.997841	−	0.0656695i	$-0.0209183\pi$
$317$	7.87046	+	13.6320i	0.442049	+	0.765652i	−0.555792	+	0.831321i	$0.687585\pi$
$318$	0.0866813	−	0.0876755i	0.00486085	−	0.00491660i
$319$	−1.87380	+	3.24551i	−0.104912	+	0.181714i
$320$	−4.54796	+	7.87731i	−0.254239	+	0.440355i
$321$	−0.753656	−	2.74987i	−0.0420650	−	0.153483i
$322$	0.908823	+	1.57413i	0.0506468	+	0.0877227i
$323$	−22.4196			−1.24746
$324$	−9.18396	−	15.1010i	−0.510220	−	0.838944i
$325$	3.99726			0.221728
$326$	0.278960	+	0.483173i	0.0154502	+	0.0267605i
$327$	−1.26115	−	4.60157i	−0.0697418	−	0.254468i
$328$	−2.35132	+	4.07260i	−0.129830	+	0.224872i
$329$	−8.20399	+	14.2097i	−0.452301	+	0.783408i
$330$	−0.264635	+	0.267670i	−0.0145677	+	0.0147347i
$331$	12.5804	+	21.7898i	0.691479	+	1.19768i	0.971353	+	0.237640i	$0.0763738\pi$
$331$	12.5804	+	21.7898i	0.691479	+	1.19768i	−0.279875	+	0.960037i	$0.590293\pi$
$332$	22.1152			1.21373
$333$	−8.83576	+	5.23656i	−0.484197	+	0.286962i
$334$	2.50919			0.137297
$335$	−0.636538	−	1.10252i	−0.0347778	−	0.0602369i
$336$	18.5998	+	4.87030i	1.01470	+	0.265697i
$337$	7.64242	−	13.2371i	0.416309	−	0.721068i	−0.579256	−	0.815146i	$-0.696657\pi$
$337$	7.64242	−	13.2371i	0.416309	−	0.721068i	0.995565	+	0.0940775i	$0.0299902\pi$
$338$	1.10322	−	1.91083i	0.0600071	−	0.103935i
$339$	−19.0796	−	4.99593i	−1.03626	−	0.271342i
$340$	−6.25054	−	10.8263i	−0.338983	−	0.587136i
$341$	−6.75130			−0.365603
$342$	−2.23005	−	1.25383i	−0.120587	−	0.0677996i
$343$	−15.8266			−0.854556
$344$	0.638594	+	1.10608i	0.0344307	+	0.0596357i
$345$	−5.05069	+	5.10861i	−0.271920	+	0.275038i
$346$	2.17815	−	3.77267i	0.117098	−	0.202820i
$347$	−12.5502	+	21.7375i	−0.673728	+	1.16693i	0.303111	+	0.952955i	$0.401975\pi$
$347$	−12.5502	+	21.7375i	−0.673728	+	1.16693i	−0.976839	+	0.213975i	$0.931359\pi$
$348$	−3.75418	−	13.6979i	−0.201245	−	0.734284i
$349$	7.20568	+	12.4806i	0.385711	+	0.668072i	0.991868	−	0.127274i	$-0.0406227\pi$
$349$	7.20568	+	12.4806i	0.385711	+	0.668072i	−0.606156	+	0.795346i	$0.707289\pi$
$350$	−1.88535			−0.100776
$351$	5.90888	−	1.69211i	0.315393	−	0.0903183i
$352$	−1.99924			−0.106560
$353$	2.93735	+	5.08764i	0.156340	+	0.270788i	0.933546	−	0.358458i	$-0.116697\pi$
$353$	2.93735	+	5.08764i	0.156340	+	0.270788i	−0.777206	+	0.629246i	$0.783364\pi$
$354$	0.222532	+	0.811957i	0.0118275	+	0.0431550i
$355$	−4.81915	+	8.34701i	−0.255774	+	0.443013i
$356$	15.1432	−	26.2288i	0.802589	−	1.39012i
$357$	−17.8612	+	18.0661i	−0.945317	+	0.956159i
$358$	1.67379	+	2.89909i	0.0884626	+	0.153222i
$359$	−23.5705			−1.24400			−0.622001	−	0.783016i	$-0.713680\pi$
$359$	−23.5705			−1.24400			−0.622001	+	0.783016i	$0.713680\pi$
$360$	−0.0328323	−	2.87915i	−0.00173041	−	0.151745i
$361$	1.10373			0.0580912
$362$	2.36501	+	4.09632i	0.124302	+	0.215298i
$363$	−17.0815	−	4.47275i	−0.896546	−	0.234758i
$364$	−3.40704	+	5.90116i	−0.178577	+	0.309305i
$365$	−3.95075	+	6.84290i	−0.206792	+	0.358174i
$366$	3.97513	+	1.04088i	0.207783	+	0.0544076i
$367$	−12.4350	−	21.5381i	−0.649103	−	1.12428i	−0.983337	−	0.181790i	$-0.941811\pi$
$367$	−12.4350	−	21.5381i	−0.649103	−	1.12428i	0.334234	−	0.942490i	$-0.391522\pi$
$368$	−12.3288			−0.642685
$369$	0.213380	+	18.7119i	0.0111081	+	0.974101i
$370$	−0.828983			−0.0430968
$371$	0.548913	+	0.950745i	0.0284982	+	0.0493602i
$372$	17.9892	−	18.1955i	0.932694	−	0.943391i
$373$	−11.0101	+	19.0700i	−0.570079	+	0.987406i	0.426478	+	0.904498i	$0.359754\pi$
$373$	−11.0101	+	19.0700i	−0.570079	+	0.987406i	−0.996557	+	0.0829084i	$0.973579\pi$
$374$	0.426774	−	0.739194i	0.0220680	−	0.0382228i
$375$	−4.88377	−	17.8194i	−0.252197	−	0.920192i
$376$	2.10851	+	3.65205i	0.108738	+	0.188340i
$377$	4.93919			0.254381
$378$	−2.78699	+	0.798105i	−0.143347	+	0.0410501i
$379$	14.9509			0.767976			0.383988	−	0.923338i	$-0.374550\pi$
$379$	14.9509			0.767976			0.383988	+	0.923338i	$0.374550\pi$
$380$	5.60487	+	9.70792i	0.287524	+	0.498006i
$381$	−4.53859	−	16.5600i	−0.232519	−	0.848395i
$382$	−0.346493	+	0.600143i	−0.0177281	+	0.0307060i
$383$	14.1029	−	24.4269i	0.720624	−	1.24816i	−0.240127	−	0.970742i	$-0.577189\pi$
$383$	14.1029	−	24.4269i	0.720624	−	1.24816i	0.960750	−	0.277415i	$-0.0894777\pi$
$384$	7.08002	−	7.16122i	0.361301	−	0.365444i
$385$	−1.67581	−	2.90259i	−0.0854072	−	0.147930i
$386$	0.634219			0.0322809
$387$	4.43007	+	2.49079i	0.225193	+	0.126614i
$388$	−9.95228			−0.505250
$389$	4.06406	+	7.03916i	0.206056	+	0.356899i	0.950469	−	0.310820i	$-0.100604\pi$
$389$	4.06406	+	7.03916i	0.206056	+	0.356899i	−0.744413	+	0.667720i	$0.767270\pi$
$390$	0.479905	+	0.125662i	0.0243009	+	0.00636314i
$391$	8.14519	−	14.1079i	0.411920	−	0.713467i
$392$	0.604868	−	1.04766i	0.0305504	−	0.0529149i
$393$	−23.3647	−	6.11799i	−1.17859	−	0.308612i
$394$	−1.06796	−	1.84976i	−0.0538030	−	0.0931894i
$395$	0.290392			0.0146112
$396$	−4.54876	+	2.69585i	−0.228584	+	0.135471i
$397$	3.74154			0.187782			0.0938912	−	0.995582i	$-0.470069\pi$
$397$	3.74154			0.187782			0.0938912	+	0.995582i	$0.470069\pi$
$398$	−1.08458	−	1.87855i	−0.0543650	−	0.0941630i
$399$	16.0162	−	16.1999i	0.801813	−	0.811009i
$400$	6.39403	−	11.0748i	0.319702	−	0.553740i
$401$	−3.61891	+	6.26813i	−0.180720	+	0.313016i	−0.942126	−	0.335259i	$-0.891176\pi$
$401$	−3.61891	+	6.26813i	−0.180720	+	0.313016i	0.761406	+	0.648275i	$0.224509\pi$
$402$	0.0870756	+	0.317714i	0.00434294	+	0.0158461i
$403$	4.44898	+	7.70586i	0.221620	+	0.383856i
$404$	−0.115346			−0.00573867
$405$	−5.95363	−	9.78942i	−0.295838	−	0.486440i
$406$	−2.32963			−0.115617
$407$	1.53636	+	2.66106i	0.0761547	+	0.131904i
$408$	1.72584	+	6.29710i	0.0854420	+	0.311753i
$409$	−7.90453	+	13.6910i	−0.390854	+	0.676978i	−0.992562	−	0.121737i	$-0.961153\pi$
$409$	−7.90453	+	13.6910i	−0.390854	+	0.676978i	0.601709	+	0.798716i	$0.294487\pi$
$410$	−0.755181	+	1.30801i	−0.0372957	+	0.0645981i
$411$	18.5283	−	18.7408i	0.913932	−	0.924414i
$412$	5.63020	+	9.75180i	0.277380	+	0.480437i
$413$	−7.49657			−0.368882
$414$	1.59918	−	0.947765i	0.0785956	−	0.0465801i
$415$	14.3364			0.703748
$416$	1.31746	+	2.28191i	0.0645940	+	0.111880i
$417$	−31.3843	−	8.21789i	−1.53689	−	0.402432i
$418$	−0.382689	+	0.662837i	−0.0187179	+	0.0324204i
$419$	−3.87280	+	6.70789i	−0.189199	+	0.327702i	−0.944983	−	0.327118i	$-0.893922\pi$
$419$	−3.87280	+	6.70789i	−0.189199	+	0.327702i	0.755784	+	0.654820i	$0.227256\pi$
$420$	12.2881	+	3.21760i	0.599596	+	0.157003i
$421$	−1.93242	−	3.34705i	−0.0941804	−	0.163125i	0.815086	−	0.579340i	$-0.196690\pi$
$421$	−1.93242	−	3.34705i	−0.0941804	−	0.163125i	−0.909266	+	0.416215i	$0.863356\pi$
$422$	−1.21333			−0.0590642
$423$	14.6273	+	8.22410i	0.711201	+	0.399869i
$424$	0.282153			0.0137026
$425$	8.44859	+	14.6334i	0.409817	+	0.709824i
$426$	1.75349	−	1.77360i	0.0849570	−	0.0859313i
$427$	−18.2947	+	31.6873i	−0.885341	+	1.53346i
$428$	1.61641	−	2.79971i	0.0781322	−	0.135329i
$429$	−0.486034	−	1.77340i	−0.0234660	−	0.0856205i
$430$	0.205099	+	0.355243i	0.00989077	+	0.0171313i
$431$	−7.97236			−0.384015			−0.192008	−	0.981393i	$-0.561500\pi$
$431$	−7.97236			−0.384015			−0.192008	+	0.981393i	$0.561500\pi$
$432$	4.76371	−	19.0778i	0.229194	−	0.917883i
$433$	12.4275			0.597225			0.298613	−	0.954374i	$-0.403476\pi$
$433$	12.4275			0.597225			0.298613	+	0.954374i	$0.403476\pi$
$434$	−2.09841	−	3.63456i	−0.100727	−	0.174464i
$435$	−2.43369	−	8.87984i	−0.116687	−	0.425756i
$436$	2.70487	−	4.68497i	0.129540	−	0.224369i
$437$	−7.30381	+	12.6506i	−0.349388	+	0.605159i
$438$	1.43752	−	1.45400i	0.0686872	−	0.0694750i
$439$	17.7188	+	30.6898i	0.845671	+	1.46475i	0.885037	+	0.465521i	$0.154133\pi$
$439$	17.7188	+	30.6898i	0.845671	+	1.46475i	−0.0393655	+	0.999225i	$0.512534\pi$
$440$	−0.861403			−0.0410658
$441$	−0.0548913	−	4.81356i	−0.00261387	−	0.229217i
$442$	−1.12494			−0.0535082
$443$	−3.34175	−	5.78809i	−0.158771	−	0.275000i	0.775654	−	0.631158i	$-0.217420\pi$
$443$	−3.34175	−	5.78809i	−0.158771	−	0.275000i	−0.934426	+	0.356158i	$0.884087\pi$
$444$	−11.2655	−	2.94986i	−0.534639	−	0.139994i
$445$	9.81679	−	17.0032i	0.465360	−	0.806028i
$446$	−1.26857	+	2.19722i	−0.0600683	+	0.104041i
$447$	−1.05777	−	0.276975i	−0.0500309	−	0.0131005i
$448$	10.4792	+	18.1505i	0.495096	+	0.857532i
$449$	−30.1437			−1.42257			−0.711285	−	0.702904i	$-0.751887\pi$
$449$	−30.1437			−1.42257			−0.711285	+	0.702904i	$0.751887\pi$
$450$	0.0219865	+	1.92806i	0.00103645	+	0.0908894i
$451$	5.59834			0.263615
$452$	−11.1810	−	19.3661i	−0.525910	−	0.910903i
$453$	−3.39972	+	3.43871i	−0.159733	+	0.161565i
$454$	2.11438	−	3.66222i	0.0992330	−	0.171877i
$455$	−2.20866	+	3.82551i	−0.103543	+	0.179343i
$456$	−1.54757	−	5.64662i	−0.0724715	−	0.264427i
$457$	12.3669	+	21.4201i	0.578499	+	1.00199i	0.995652	+	0.0931539i	$0.0296949\pi$
$457$	12.3669	+	21.4201i	0.578499	+	1.00199i	−0.417152	+	0.908837i	$0.636972\pi$
$458$	1.45650			0.0680577
$459$	18.6836	+	18.0551i	0.872075	+	0.842741i
$460$	−8.14513			−0.379769
$461$	−6.84093	−	11.8488i	−0.318614	−	0.551855i	0.661585	−	0.749870i	$-0.269884\pi$
$461$	−6.84093	−	11.8488i	−0.318614	−	0.551855i	−0.980199	+	0.198015i	$0.936551\pi$
$462$	0.229244	+	0.836444i	0.0106654	+	0.0389149i
$463$	10.3947	−	18.0041i	0.483083	−	0.836723i	−0.516729	−	0.856149i	$-0.672850\pi$
$463$	10.3947	−	18.0041i	0.483083	−	0.836723i	0.999811	+	0.0194257i	$0.00618378\pi$
$464$	7.90076	−	13.6845i	0.366783	−	0.635288i
$465$	11.6617	−	11.7954i	0.540799	−	0.547001i
$466$	0.714214	+	1.23705i	0.0330853	+	0.0573054i
$467$	−18.9536			−0.877067			−0.438533	−	0.898715i	$-0.644502\pi$
$467$	−18.9536			−0.877067			−0.438533	+	0.898715i	$0.644502\pi$
$468$	6.07456	+	3.41539i	0.280796	+	0.157876i
$469$	−2.93336			−0.135450
$470$	0.677199	+	1.17294i	0.0312368	+	0.0541038i
$471$	−4.30374	−	1.12692i	−0.198306	−	0.0519259i
$472$	−0.963350	+	1.66857i	−0.0443418	+	0.0768022i
$473$	0.760225	−	1.31675i	0.0349552	−	0.0605442i
$474$	−0.0726932	−	0.0190345i	−0.00333891	−	0.000874286i
$475$	−7.57587	−	13.1218i	−0.347605	−	0.602069i
$476$	−28.8044			−1.32025
$477$	0.965879	−	0.572433i	0.0442245	−	0.0262099i
$478$	−4.16627			−0.190561
$479$	13.2950	+	23.0277i	0.607466	+	1.05216i	0.991656	+	0.128909i	$0.0411474\pi$
$479$	13.2950	+	23.0277i	0.607466	+	1.05216i	−0.384190	+	0.923254i	$0.625519\pi$
$480$	3.45334	−	3.49295i	0.157623	−	0.159431i
$481$	2.02487	−	3.50718i	0.0923261	−	0.159914i
$482$	−0.783531	+	1.35712i	−0.0356889	+	0.0618149i
$483$	4.37523	+	15.9639i	0.199080	+	0.726385i
$484$	−10.0101	−	17.3380i	−0.455005	−	0.788091i
$485$	−6.45169			−0.292956
$486$	0.848683	+	2.84081i	0.0384970	+	0.128862i
$487$	−1.70719			−0.0773604			−0.0386802	−	0.999252i	$-0.512315\pi$
$487$	−1.70719			−0.0773604			−0.0386802	+	0.999252i	$0.512315\pi$
$488$	4.70192	+	8.14397i	0.212846	+	0.368660i
$489$	1.34296	+	4.90007i	0.0607308	+	0.221589i
$490$	0.194268	−	0.336481i	0.00877611	−	0.0152007i
$491$	2.30318	−	3.98922i	0.103941	−	0.180031i	−0.809364	−	0.587307i	$-0.800188\pi$
$491$	2.30318	−	3.98922i	0.103941	−	0.180031i	0.913305	+	0.407276i	$0.133521\pi$
$492$	−14.9170	+	15.0881i	−0.672512	+	0.680225i
$493$	10.4395	+	18.0817i	0.470170	+	0.814358i
$494$	1.00874			0.0453853
$495$	−2.94879	+	1.74762i	−0.132538	+	0.0785496i
$496$	28.4665			1.27818
$497$	11.1041	+	19.2328i	0.498085	+	0.862709i
$498$	−3.58881	−	0.939721i	−0.160818	−	0.0421099i
$499$	−18.8681	+	32.6805i	−0.844651	+	1.46298i	0.0412729	+	0.999148i	$0.486859\pi$
$499$	−18.8681	+	32.6805i	−0.844651	+	1.46298i	−0.885924	+	0.463831i	$0.846475\pi$
$500$	10.4745	−	18.1424i	0.468434	−	0.811352i
$501$	22.1051	+	5.78816i	0.987582	+	0.258596i
$502$	2.19657	+	3.80458i	0.0980379	+	0.169807i
$503$	−1.93700			−0.0863666			−0.0431833	−	0.999067i	$-0.513750\pi$
$503$	−1.93700			−0.0863666			−0.0431833	+	0.999067i	$0.513750\pi$
$504$	−5.78305	−	3.25149i	−0.257597	−	0.144833i
$505$	−0.0747745			−0.00332742
$506$	−0.278066	−	0.481625i	−0.0123616	−	0.0214108i
$507$	14.1268	−	14.2888i	0.627393	−	0.634588i
$508$	9.73420	−	16.8601i	0.431885	−	0.748047i
$509$	5.16345	−	8.94336i	0.228866	−	0.396407i	−0.728606	−	0.684933i	$-0.759832\pi$
$509$	5.16345	−	8.94336i	0.228866	−	0.396407i	0.957472	+	0.288525i	$0.0931650\pi$
$510$	0.554295	+	2.02246i	0.0245446	+	0.0895562i
$511$	9.10314	+	15.7671i	0.402699	+	0.697495i
$512$	14.1356			0.624713
$513$	−16.7536	−	16.1901i	−0.739689	−	0.714808i
$514$	−4.72443			−0.208386
$515$	3.64985	+	6.32173i	0.160832	+	0.278569i
$516$	1.52312	+	5.55743i	0.0670516	+	0.244652i
$517$	2.51012	−	4.34765i	0.110395	−	0.191209i
$518$	−0.955053	+	1.65420i	−0.0419626	+	0.0726814i
$519$	27.8914	−	28.2113i	1.22430	−	1.23834i
$520$	0.567649	+	0.983196i	0.0248930	+	0.0431160i
$521$	11.0587			0.484488			0.242244	−	0.970215i	$-0.422116\pi$
$521$	11.0587			0.484488			0.242244	+	0.970215i	$0.422116\pi$
$522$	0.0271675	+	2.38239i	0.00118909	+	0.104274i
$523$	28.6051			1.25082			0.625408	−	0.780298i	$-0.284933\pi$
$523$	28.6051			1.25082			0.625408	+	0.780298i	$0.284933\pi$
$524$	−13.6922	−	23.7155i	−0.598145	−	1.03602i
$525$	−16.6093	−	4.34909i	−0.724887	−	0.189810i
$526$	1.33639	−	2.31469i	0.0582693	−	0.100925i
$527$	−18.8067	+	32.5742i	−0.819233	+	1.41895i
$528$	−5.69084	−	1.49013i	−0.247662	−	0.0648497i
$529$	6.19297	+	10.7265i	0.269259	+	0.466371i
$530$	0.0906201			0.00393629
$531$	0.0874232	+	7.66637i	0.00379384	+	0.332692i
$532$	25.8290			1.11983
$533$	−3.68920	−	6.38989i	−0.159797	−	0.276777i
$534$	−3.57193	+	3.61290i	−0.154573	+	0.156345i
$535$	1.04786	−	1.81495i	0.0453029	−	0.0784670i
$536$	−0.376953	+	0.652902i	−0.0162819	+	0.0282011i
$537$	8.05791	+	29.4010i	0.347724	+	1.26875i
$538$	0.693547	+	1.20126i	0.0299009	+	0.0517899i
$539$	−1.44015			−0.0620317
$540$	3.14718	−	12.6039i	0.135433	−	0.542386i
$541$	−5.83972			−0.251069			−0.125534	−	0.992089i	$-0.540065\pi$
$541$	−5.83972			−0.251069			−0.125534	+	0.992089i	$0.540065\pi$
$542$	−0.174902	−	0.302940i	−0.00751270	−	0.0130124i
$543$	11.3856	+	41.5426i	0.488602	+	1.78277i
$544$	−5.56917	+	9.64609i	−0.238776	+	0.413573i
$545$	1.75347	−	3.03709i	0.0751102	−	0.130095i
$546$	0.803641	−	0.812857i	0.0343927	−	0.0347871i
$547$	10.8583	+	18.8071i	0.464267	+	0.804135i	0.999168	−	0.0407801i	$-0.0129843\pi$
$547$	10.8583	+	18.8071i	0.464267	+	0.804135i	−0.534901	+	0.844915i	$0.679651\pi$
$548$	29.8801			1.27642
$549$	32.6184	+	18.3395i	1.39212	+	0.782711i
$550$	0.576848			0.0245969
$551$	−9.36108	−	16.2139i	−0.398796	−	0.690734i
$552$	4.11546	+	1.07762i	0.175166	+	0.0458667i
$553$	0.334555	−	0.579466i	0.0142267	−	0.0246414i
$554$	2.53002	−	4.38212i	0.107490	−	0.186179i
$555$	−7.30304	−	1.91228i	−0.309997	−	0.0811719i
$556$	−18.3918	−	31.8555i	−0.779986	−	1.35098i
$557$	12.4068			0.525691			0.262846	−	0.964838i	$-0.415339\pi$
$557$	12.4068			0.525691			0.262846	+	0.964838i	$0.415339\pi$
$558$	−3.69241	+	2.18833i	−0.156312	+	0.0926393i
$559$	−2.00390			−0.0847559
$560$	7.06596	+	12.2386i	0.298591	+	0.517175i
$561$	5.46488	−	5.52755i	0.230727	−	0.233373i
$562$	1.99943	−	3.46312i	0.0843410	−	0.146083i
$563$	16.7745	−	29.0543i	0.706960	−	1.22449i	−0.259019	−	0.965872i	$-0.583399\pi$
$563$	16.7745	−	29.0543i	0.706960	−	1.22449i	0.965979	−	0.258619i	$-0.0832675\pi$
$564$	5.02905	+	18.3495i	0.211761	+	0.772655i
$565$	−7.24823	−	12.5543i	−0.304935	−	0.528164i
$566$	−4.75148			−0.199720
$567$	−26.3934	+	0.602031i	−1.10842	+	0.0252829i
$568$	5.70773			0.239491
$569$	7.93028	+	13.7356i	0.332455	+	0.575828i	0.982993	−	0.183646i	$-0.0587899\pi$
$569$	7.93028	+	13.7356i	0.332455	+	0.575828i	−0.650538	+	0.759474i	$0.725457\pi$
$570$	−0.497038	−	1.81355i	−0.0208186	−	0.0759611i
$571$	−18.2511	+	31.6118i	−0.763785	+	1.32291i	0.177102	+	0.984193i	$0.443328\pi$
$571$	−18.2511	+	31.6118i	−0.763785	+	1.32291i	−0.940887	+	0.338722i	$0.890005\pi$
$572$	1.04243	−	1.80554i	0.0435861	−	0.0754933i
$573$	−4.43687	+	4.48776i	−0.185353	+	0.187479i
$574$	1.74005	+	3.01386i	0.0726285	+	0.125796i
$575$	11.0094			0.459125
$576$	18.4394	−	10.9282i	0.768310	−	0.455343i
$577$	11.4794			0.477895			0.238948	−	0.971032i	$-0.423198\pi$
$577$	11.4794			0.477895			0.238948	+	0.971032i	$0.423198\pi$
$578$	−0.761010	−	1.31811i	−0.0316538	−	0.0548261i
$579$	5.58723	+	1.46300i	0.232197	+	0.0608003i
$580$	5.21969	−	9.04077i	0.216736	−	0.375398i
$581$	16.5167	−	28.6078i	0.685228	−	1.18685i
$582$	1.61504	+	0.422894i	0.0669454	+	0.0175295i
$583$	−0.167947	−	0.290893i	−0.00695566	−	0.0120476i
$584$	4.67921			0.193627
$585$	3.93791	+	2.21407i	0.162813	+	0.0915406i
$586$	5.23354			0.216196
$587$	−11.5816	−	20.0599i	−0.478022	−	0.827959i	0.521660	−	0.853153i	$-0.325313\pi$
$587$	−11.5816	−	20.0599i	−0.478022	−	0.827959i	−0.999683	+	0.0251943i	$0.991980\pi$
$588$	3.83735	−	3.88136i	0.158250	−	0.160065i
$589$	16.8640	−	29.2093i	0.694869	−	1.20355i
$590$	−0.309402	+	0.535901i	−0.0127379	+	0.0220627i
$591$	−5.14133	−	18.7592i	−0.211486	−	0.771651i
$592$	−6.47799	−	11.2202i	−0.266244	−	0.461147i
$593$	34.0685			1.39902			0.699512	−	0.714621i	$-0.253401\pi$
$593$	34.0685			1.39902			0.699512	+	0.714621i	$0.253401\pi$
$594$	0.852716	−	0.244190i	0.0349874	−	0.0100193i
$595$	−18.6729			−0.765512
$596$	−0.619875	−	1.07366i	−0.0253911	−	0.0439787i
$597$	−5.22135	−	19.0512i	−0.213695	−	0.779713i
$598$	−0.366481	+	0.634764i	−0.0149865	+	0.0259574i
$599$	−20.5911	+	35.6648i	−0.841330	+	1.45723i	0.0474408	+	0.998874i	$0.484893\pi$
$599$	−20.5911	+	35.6648i	−0.841330	+	1.45723i	−0.888771	+	0.458352i	$0.848440\pi$
$600$	−3.10239	+	3.13797i	−0.126655	+	0.128107i
$601$	−1.57086	−	2.72081i	−0.0640768	−	0.110984i	0.832207	−	0.554465i	$-0.187077\pi$
$601$	−1.57086	−	2.72081i	−0.0640768	−	0.110984i	−0.896284	+	0.443480i	$0.853744\pi$
$602$	0.945162			0.0385219
$603$	0.0342082	+	2.99980i	0.00139306	+	0.122162i
$604$	−5.48265			−0.223086
$605$	−6.48918	−	11.2396i	−0.263823	−	0.456954i
$606$	0.0187181	+	0.00490130i	0.000760372	+	0.000199102i
$607$	11.2311	−	19.4529i	0.455858	−	0.789569i	−0.542879	−	0.839811i	$-0.682666\pi$
$607$	11.2311	−	19.4529i	0.455858	−	0.789569i	0.998737	+	0.0502418i	$0.0159992\pi$
$608$	4.99389	−	8.64967i	0.202529	−	0.350790i
$609$	−20.5231	−	5.37394i	−0.831640	−	0.217763i
$610$	1.51013	+	2.61563i	0.0611435	+	0.105904i
$611$	−6.61648			−0.267674
$612$	0.335910	+	29.4568i	0.0135784	+	1.19072i
$613$	−22.9396			−0.926523			−0.463262	−	0.886222i	$-0.653321\pi$
$613$	−22.9396			−0.926523			−0.463262	+	0.886222i	$0.653321\pi$
$614$	−3.08572	−	5.34462i	−0.124530	−	0.215691i
$615$	−9.67016	+	9.78107i	−0.389939	+	0.394411i
$616$	−0.992403	+	1.71889i	−0.0399850	+	0.0692561i
$617$	−18.9951	+	32.9005i	−0.764715	+	1.32453i	0.175682	+	0.984447i	$0.443787\pi$
$617$	−18.9951	+	32.9005i	−0.764715	+	1.32453i	−0.940397	+	0.340079i	$0.889546\pi$
$618$	−0.499284	−	1.82174i	−0.0200842	−	0.0732813i
$619$	11.6056	+	20.1016i	0.466470	+	0.807950i	0.999267	−	0.0382933i	$-0.0121921\pi$
$619$	11.6056	+	20.1016i	0.466470	+	0.807950i	−0.532796	+	0.846244i	$0.678859\pi$
$620$	18.8066			0.755290
$621$	16.2745	−	4.66050i	0.653073	−	0.187019i
$622$	0.511085			0.0204926
$623$	−22.6194	−	39.1780i	−0.906227	−	1.56963i
$624$	2.04934	+	7.47743i	0.0820391	+	0.299337i
$625$	−1.65796	+	2.87166i	−0.0663183	+	0.114867i
$626$	−2.92134	+	5.05992i	−0.116760	+	0.202235i
$627$	−4.90037	+	4.95657i	−0.195702	+	0.197946i
$628$	−2.52208	−	4.36837i	−0.100642	−	0.174317i
$629$	17.1190			0.682581
$630$	−1.85736	−	1.04429i	−0.0739990	−	0.0416056i
$631$	−5.33193			−0.212261			−0.106130	−	0.994352i	$-0.533846\pi$
$631$	−5.33193			−0.212261			−0.106130	+	0.994352i	$0.533846\pi$
$632$	−0.0859841	−	0.148929i	−0.00342026	−	0.00592407i
$633$	−10.6890	−	2.79889i	−0.424850	−	0.111246i
$634$	1.49694	−	2.59277i	0.0594509	−	0.102972i
$635$	6.31032	−	10.9298i	0.250418	−	0.433736i
$636$	1.23149	+	0.322463i	0.0488318	+	0.0127865i
$637$	0.949034	+	1.64377i	0.0376021	+	0.0651287i
$638$	0.712779			0.0282192
$639$	19.5389	−	11.5799i	0.772948	−	0.458092i
$640$	7.40173			0.292579
$641$	−7.34447	−	12.7210i	−0.290089	−	0.502449i	0.683741	−	0.729724i	$-0.260352\pi$
$641$	−7.34447	−	12.7210i	−0.290089	−	0.502449i	−0.973831	+	0.227275i	$0.927018\pi$
$642$	−0.381274	+	0.385646i	−0.0150477	+	0.0152203i
$643$	−13.8607	+	24.0074i	−0.546613	+	0.946761i	0.451891	+	0.892073i	$0.350750\pi$
$643$	−13.8607	+	24.0074i	−0.546613	+	0.946761i	−0.998504	+	0.0546878i	$0.982584\pi$
$644$	−9.38382	+	16.2533i	−0.369774	+	0.640468i
$645$	0.987383	+	3.60267i	0.0388782	+	0.141855i
$646$	2.13207	+	3.69285i	0.0838852	+	0.145293i
$647$	39.7029			1.56088			0.780441	−	0.625229i	$-0.214995\pi$
$647$	39.7029			1.56088			0.780441	+	0.625229i	$0.214995\pi$
$648$	−3.25770	+	5.95195i	−0.127974	+	0.233815i
$649$	2.29367			0.0900346
$650$	−0.380132	−	0.658408i	−0.0149100	−	0.0258249i
$651$	−10.1021	−	36.8597i	−0.395933	−	1.44465i
$652$	−2.88033	+	4.98888i	−0.112802	+	0.195380i
$653$	−0.145885	+	0.252681i	−0.00570894	+	0.00988817i	−0.868866	−	0.495048i	$-0.835151\pi$
$653$	−0.145885	+	0.252681i	−0.00570894	+	0.00988817i	0.863157	+	0.504936i	$0.168484\pi$
$654$	−0.638015	+	0.645332i	−0.0249484	+	0.0252345i
$655$	−8.87613	−	15.3739i	−0.346819	−	0.600709i
$656$	−23.6051			−0.921623
$657$	16.0181	−	9.49320i	0.624924	−	0.370365i
$658$	3.12074			0.121659
$659$	19.2332	+	33.3128i	0.749217	+	1.29768i	0.948198	+	0.317679i	$0.102904\pi$
$659$	19.2332	+	33.3128i	0.749217	+	1.29768i	−0.198981	+	0.980003i	$0.563763\pi$
$660$	−3.75969	−	0.984466i	−0.146346	−	0.0383203i
$661$	4.13634	−	7.16435i	0.160885	−	0.278661i	−0.774301	−	0.632817i	$-0.781898\pi$
$661$	4.13634	−	7.16435i	0.160885	−	0.278661i	0.935186	+	0.354156i	$0.115232\pi$
$662$	2.39274	−	4.14435i	0.0929965	−	0.161075i
$663$	−9.91035	−	2.59500i	−0.384886	−	0.100781i
$664$	−4.24497	−	7.35250i	−0.164737	−	0.285332i
$665$	16.7440			0.649303
$666$	1.70281	+	0.957394i	0.0659824	+	0.0370983i
$667$	13.6037			0.526739
$668$	12.9540	+	22.4370i	0.501206	+	0.868114i
$669$	−16.2441	+	16.4304i	−0.628033	+	0.635236i
$670$	−0.121067	+	0.209695i	−0.00467724	+	0.00810121i
$671$	5.59749	−	9.69514i	0.216089	−	0.374277i
$672$	−2.99151	−	10.9152i	−0.115400	−	0.421061i
$673$	−19.2600	−	33.3593i	−0.742418	−	1.28591i	−0.951391	−	0.307985i	$-0.900345\pi$
$673$	−19.2600	−	33.3593i	−0.742418	−	1.28591i	0.208973	−	0.977921i	$-0.432988\pi$
$674$	−2.90712			−0.111978
$675$	−4.25391	+	17.0362i	−0.163733	+	0.655723i
$676$	22.7820			0.876229
$677$	5.17047	+	8.95551i	0.198717	+	0.344188i	0.948113	−	0.317934i	$-0.102989\pi$
$677$	5.17047	+	8.95551i	0.198717	+	0.344188i	−0.749396	+	0.662123i	$0.769656\pi$
$678$	0.991527	+	3.61779i	0.0380794	+	0.138941i
$679$	−7.43285	+	12.8741i	−0.285247	+	0.494062i
$680$	−2.39956	+	4.15616i	−0.0920190	+	0.159382i
$681$	27.0749	−	27.3854i	1.03751	−	1.04941i
$682$	0.642037	+	1.11204i	0.0245849	+	0.0425822i
$683$	52.2469			1.99917			0.999585	−	0.0288030i	$-0.00916955\pi$
$683$	52.2469			1.99917			0.999585	+	0.0288030i	$0.00916955\pi$
$684$	−0.301211	−	26.4140i	−0.0115171	−	1.00996i
$685$	19.3702			0.740097
$686$	1.50508	+	2.60688i	0.0574643	+	0.0995311i
$687$	12.8312	+	3.35982i	0.489541	+	0.128185i
$688$	−3.20545	+	5.55200i	−0.122206	+	0.211668i
$689$	−0.221348	+	0.383386i	−0.00843269	+	0.0146058i
$690$	1.32178	+	0.346104i	0.0503192	+	0.0131760i
$691$	−10.2020	−	17.6704i	−0.388103	−	0.672214i	0.604091	−	0.796915i	$-0.293536\pi$
$691$	−10.2020	−	17.6704i	−0.388103	−	0.672214i	−0.992194	+	0.124701i	$0.960203\pi$
$692$	44.9798			1.70988
$693$	0.0900597	+	7.89758i	0.00342109	+	0.300004i
$694$	4.77399			0.181218
$695$	−11.9227	−	20.6508i	−0.452255	−	0.783329i
$696$	−3.83345	+	3.87742i	−0.145307	+	0.146973i
$697$	15.5950	−	27.0113i	0.590702	−	1.02313i
$698$	1.37050	−	2.37377i	0.0518740	−	0.0898485i
$699$	3.43834	+	12.5455i	0.130050	+	0.474515i
$700$	−9.73336	−	16.8587i	−0.367886	−	0.637198i
$701$	−20.5437			−0.775923			−0.387961	−	0.921676i	$-0.626821\pi$
$701$	−20.5437			−0.775923			−0.387961	+	0.921676i	$0.626821\pi$
$702$	−0.840641	−	0.812364i	−0.0317279	−	0.0306607i
$703$	−15.3507			−0.578962
$704$	−3.20625	−	5.55339i	−0.120840	−	0.209301i
$705$	3.26015	+	11.8953i	0.122784	+	0.448004i
$706$	0.558674	−	0.967652i	0.0210260	−	0.0364181i
$707$	−0.0861460	+	0.149209i	−0.00323986	+	0.00561159i
$708$	−6.11160	+	6.18169i	−0.229688	+	0.232322i
$709$	−10.6049	−	18.3681i	−0.398274	−	0.689830i	0.595239	−	0.803548i	$-0.297057\pi$
$709$	−10.6049	−	18.3681i	−0.398274	−	0.689830i	−0.993513	+	0.113718i	$0.963724\pi$
$710$	1.83317			0.0687977
$711$	−0.596492	−	0.335375i	−0.0223702	−	0.0125775i
$712$	−11.6269			−0.435735
$713$	12.2536	+	21.2238i	0.458901	+	0.794839i
$714$	4.67433	+	1.22396i	0.174932	+	0.0458056i
$715$	0.675767	−	1.17046i	0.0252723	−	0.0437728i
$716$	−17.2823	+	29.9338i	−0.645869	+	1.11868i
$717$	−36.7033	−	9.61068i	−1.37071	−	0.358917i
$718$	2.24151	+	3.88241i	0.0836525	+	0.144890i
$719$	41.5523			1.54964			0.774821	−	0.632181i	$-0.217840\pi$
$719$	41.5523			1.54964			0.774821	+	0.632181i	$0.217840\pi$
$720$	12.4334	−	7.36873i	0.463366	−	0.274616i
$721$	16.8197			0.626397
$722$	−0.104963	−	0.181802i	−0.00390632	−	0.00676595i
$723$	−10.0332	+	10.1483i	−0.373138	+	0.377418i
$724$	−24.4193	+	42.2955i	−0.907537	+	1.57190i
$725$	−7.05524	+	12.2200i	−0.262025	+	0.453841i
$726$	0.887692	+	3.23893i	0.0329453	+	0.120208i
$727$	−5.29297	−	9.16769i	−0.196305	−	0.340011i	0.751022	−	0.660277i	$-0.229561\pi$
$727$	−5.29297	−	9.16769i	−0.196305	−	0.340011i	−0.947328	+	0.320266i	$0.896228\pi$
$728$	2.61590			0.0969517
$729$	0.923460	+	26.9842i	0.0342022	+	0.999415i
$730$	1.50284			0.0556225
$731$	−4.23543	−	7.33599i	−0.156653	−	0.271331i
$732$	11.2146	+	40.9190i	0.414505	+	1.51241i
$733$	−2.58780	+	4.48220i	−0.0955825	+	0.165554i	−0.909852	−	0.414934i	$-0.863805\pi$
$733$	−2.58780	+	4.48220i	−0.0955825	+	0.165554i	0.814269	+	0.580488i	$0.197138\pi$
$734$	−2.36510	+	4.09647i	−0.0872974	+	0.151204i
$735$	2.48761	−	2.51614i	0.0917570	−	0.0928093i
$736$	3.62862	+	6.28495i	0.133753	+	0.231666i
$737$	0.897501			0.0330599
$738$	3.06184	−	1.81461i	0.112708	−	0.0667969i
$739$	−45.5195			−1.67446			−0.837231	−	0.546849i	$-0.815827\pi$
$739$	−45.5195			−1.67446			−0.837231	+	0.546849i	$0.815827\pi$
$740$	−4.27973	−	7.41271i	−0.157326	−	0.272496i
$741$	8.88662	+	2.32694i	0.326458	+	0.0854823i
$742$	0.104401	−	0.180829i	0.00383270	−	0.00663842i
$743$	−0.195566	+	0.338730i	−0.00717461	+	0.0124268i	−0.869590	−	0.493774i	$-0.835617\pi$
$743$	−0.195566	+	0.338730i	−0.00717461	+	0.0124268i	0.862416	+	0.506201i	$0.168950\pi$
$744$	−9.50233	−	2.48816i	−0.348372	−	0.0912204i
$745$	−0.401842	−	0.696012i	−0.0147224	−	0.0254999i
$746$	4.18815			0.153339
$747$	−29.4483	−	16.5572i	−1.07746	−	0.605796i
$748$	8.81309			0.322238
$749$	−2.41443	−	4.18192i	−0.0882214	−	0.152804i
$750$	−2.47069	+	2.49903i	−0.0902170	+	0.0912516i
$751$	−2.06807	+	3.58200i	−0.0754648	+	0.130709i	−0.901288	−	0.433220i	$-0.857377\pi$
$751$	−2.06807	+	3.58200i	−0.0754648	+	0.130709i	0.825823	+	0.563929i	$0.190711\pi$
$752$	−10.5838	+	18.3316i	−0.385950	+	0.668485i
$753$	10.5747	+	38.5840i	0.385363	+	1.40608i
$754$	−0.469709	−	0.813559i	−0.0171058	−	0.0296281i
$755$	−3.55420			−0.129351
$756$	−21.5248	−	20.8007i	−0.782848	−	0.756516i
$757$	−9.46347			−0.343956			−0.171978	−	0.985101i	$-0.555016\pi$
$757$	−9.46347			−0.343956			−0.171978	+	0.985101i	$0.555016\pi$
$758$	−1.42181	−	2.46264i	−0.0516423	−	0.0894471i
$759$	−1.33866	−	4.88438i	−0.0485902	−	0.177292i
$760$	2.15169	−	3.72684i	0.0780500	−	0.135187i
$761$	0.191907	−	0.332393i	0.00695663	−	0.0120492i	−0.862526	−	0.506013i	$-0.831119\pi$
$761$	0.191907	−	0.332393i	0.00695663	−	0.0120492i	0.869483	+	0.493963i	$0.164452\pi$
$762$	−2.29607	+	2.32240i	−0.0831779	+	0.0841318i
$763$	−4.04026	−	6.99793i	−0.146267	−	0.253342i
$764$	−7.15525			−0.258868
$765$	0.217758	+	19.0958i	0.00787306	+	0.690410i
$766$	−5.36464			−0.193832
$767$	−1.51149	−	2.61798i	−0.0545767	−	0.0945296i
$768$	22.0904	+	5.78432i	0.797118	+	0.208724i
$769$	−11.5022	+	19.9225i	−0.414782	+	0.718423i	−0.995406	−	0.0957491i	$-0.969475\pi$
$769$	−11.5022	+	19.9225i	−0.414782	+	0.718423i	0.580624	+	0.814172i	$0.302809\pi$
$770$	−0.318733	+	0.552063i	−0.0114864	+	0.0198950i
$771$	−41.6205	−	10.8982i	−1.49893	−	0.392490i
$772$	3.27423	+	5.67113i	0.117842	+	0.204109i
$773$	−43.6554			−1.57018			−0.785088	−	0.619384i	$-0.787382\pi$
$773$	−43.6554			−1.57018			−0.785088	+	0.619384i	$0.787382\pi$
$774$	−0.0110222	−	0.966570i	−0.000396186	−	0.0347426i
$775$	−25.4201			−0.913115
$776$	1.91032	+	3.30878i	0.0685766	+	0.118778i
$777$	−12.2295	+	12.3698i	−0.438732	+	0.443764i
$778$	0.772970	−	1.33882i	0.0277123	−	0.0479991i
$779$	−13.9840	+	24.2211i	−0.501030	+	0.867810i
$780$	1.35391	+	4.94002i	0.0484777	+	0.176881i
$781$	−3.39743	−	5.88453i	−0.121570	−	0.210565i
$782$	−3.09838			−0.110798
$783$	−5.25632	+	21.0507i	−0.187846	+	0.752290i
$784$	6.07232			0.216868
$785$	−1.63497	−	2.83185i	−0.0583546	−	0.101073i
$786$	1.21422	+	4.43033i	0.0433097	+	0.158024i
$787$	24.9968	−	43.2958i	0.891041	−	1.54333i	0.0524123	−	0.998626i	$-0.483309\pi$
$787$	24.9968	−	43.2958i	0.891041	−	1.54333i	0.838629	−	0.544703i	$-0.183358\pi$
$788$	11.0269	−	19.0992i	0.392818	−	0.680381i
$789$	17.1126	−	17.3088i	0.609223	−	0.616210i
$790$	−0.0276158	−	0.0478320i	−0.000982527	−	0.00170179i
$791$	−33.4021			−1.18764
$792$	1.76940	+	0.994835i	0.0628728	+	0.0353499i
$793$	−14.7546			−0.523950
$794$	−0.355814	−	0.616287i	−0.0126274	−	0.0218712i
$795$	0.798330	+	0.209041i	0.0283138	+	0.00741391i
$796$	11.1985	−	19.3964i	0.396922	−	0.687488i
$797$	−24.0503	+	41.6563i	−0.851905	+	1.47554i	0.0275816	+	0.999620i	$0.491219\pi$
$797$	−24.0503	+	41.6563i	−0.851905	+	1.47554i	−0.879487	+	0.475923i	$0.842114\pi$
$798$	−4.19148	−	1.09753i	−0.148377	−	0.0388521i
$799$	−13.9846	−	24.2220i	−0.494739	−	0.856913i
$800$	−7.52756			−0.266140
$801$	−39.8016	+	23.5886i	−1.40632	+	0.833463i
$802$	1.37661			0.0486097
$803$	−2.78522	−	4.82415i	−0.0982884	−	0.170241i
$804$	−2.39143	+	2.41886i	−0.0843393	+	0.0853066i
$805$	−6.08319	+	10.5364i	−0.214404	+	0.371359i
$806$	0.846181	−	1.46563i	0.0298055	−	0.0516246i
$807$	3.33885	+	12.1825i	0.117533	+	0.428844i
$808$	0.0221405	+	0.0383484i	0.000778898	+	0.00134909i
$809$	51.2801			1.80291			0.901457	−	0.432869i	$-0.142499\pi$
$809$	51.2801			1.80291			0.901457	+	0.432869i	$0.142499\pi$
$810$	−1.04629	+	1.91161i	−0.0367627	+	0.0671671i
$811$	4.30946			0.151326			0.0756628	−	0.997133i	$-0.475893\pi$
$811$	4.30946			0.151326			0.0756628	+	0.997133i	$0.475893\pi$
$812$	−12.0270	−	20.8313i	−0.422064	−	0.731037i
$813$	−0.842010	−	3.07225i	−0.0295306	−	0.107749i
$814$	0.292211	−	0.506124i	0.0102420	−	0.0177396i
$815$	−1.86721	+	3.23411i	−0.0654056	+	0.113286i
$816$	−23.0423	+	23.3066i	−0.806644	+	0.815895i
$817$	3.79792	+	6.57819i	0.132872	+	0.230142i
$818$	3.00683			0.105131
$819$	8.95486	−	5.30715i	0.312908	−	0.185447i
$820$	−15.5949			−0.544596
$821$	−24.3713	−	42.2123i	−0.850564	−	1.47322i	−0.880700	−	0.473675i	$-0.842927\pi$
$821$	−24.3713	−	42.2123i	−0.850564	−	1.47322i	0.0301354	−	0.999546i	$-0.490406\pi$
$822$	−4.84889	−	1.26967i	−0.169125	−	0.0442849i
$823$	9.52386	−	16.4958i	0.331981	−	0.575008i	−0.650919	−	0.759147i	$-0.725616\pi$
$823$	9.52386	−	16.4958i	0.331981	−	0.575008i	0.982900	+	0.184139i	$0.0589497\pi$
$824$	2.16142	−	3.74368i	0.0752965	−	0.130417i
$825$	5.08182	+	1.33066i	0.176926	+	0.0463277i
$826$	0.712911	+	1.23480i	0.0248054	+	0.0429641i
$827$	−20.8177			−0.723901			−0.361951	−	0.932197i	$-0.617889\pi$
$827$	−20.8177			−0.723901			−0.361951	+	0.932197i	$0.617889\pi$
$828$	16.7308	+	9.40682i	0.581436	+	0.326910i
$829$	−41.0446			−1.42554			−0.712769	−	0.701399i	$-0.752559\pi$
$829$	−41.0446			−1.42554			−0.712769	+	0.701399i	$0.752559\pi$
$830$	−1.36337	−	2.36143i	−0.0473233	−	0.0819664i
$831$	32.3971	−	32.7687i	1.12384	−	1.13673i
$832$	−4.22572	+	7.31917i	−0.146501	+	0.253746i
$833$	−4.01175	+	6.94855i	−0.138999	+	0.240753i
$834$	1.63098	+	5.95097i	0.0564762	+	0.206065i
$835$	8.39761	+	14.5451i	0.290611	+	0.503354i
$836$	−7.90271			−0.273321
$837$	−37.5768	+	10.7608i	−1.29884	+	0.371947i
$838$	1.47319			0.0508904
$839$	−15.9911	−	27.6974i	−0.552074	−	0.956220i	−0.998125	−	0.0612126i	$-0.980503\pi$
$839$	−15.9911	−	27.6974i	−0.552074	−	0.956220i	0.446051	−	0.895008i	$-0.352830\pi$
$840$	−1.28894	−	4.70295i	−0.0444725	−	0.162267i
$841$	5.78223	−	10.0151i	0.199387	−	0.345349i
$842$	−0.367540	+	0.636597i	−0.0126663	+	0.0219386i
$843$	25.6029	−	25.8965i	0.881811	−	0.891924i
$844$	−6.26398	−	10.8495i	−0.215615	−	0.373456i
$845$	14.7687			0.508059
$846$	−0.0363933	−	3.19143i	−0.00125123	−	0.109723i
$847$	−29.9042			−1.02752
$848$	0.708139	+	1.22653i	0.0243176	+	0.0421193i
$849$	−41.8588	−	10.9606i	−1.43659	−	0.376168i
$850$	1.60689	−	2.78322i	0.0551160	−	0.0954637i
$851$	5.57699	−	9.65963i	0.191177	−	0.331128i
$852$	24.9120	+	6.52316i	0.853472	+	0.223480i
$853$	−10.3648	−	17.9523i	−0.354883	−	0.614676i	0.632215	−	0.774793i	$-0.282146\pi$
$853$	−10.3648	−	17.9523i	−0.354883	−	0.614676i	−0.987098	+	0.160117i	$0.948813\pi$
$854$	6.95916			0.238138
$855$	−0.195264	−	17.1232i	−0.00667789	−	0.585602i
$856$	−1.24107			−0.0424189
$857$	21.1224	+	36.5851i	0.721528	+	1.24972i	0.960387	+	0.278669i	$0.0898931\pi$
$857$	21.1224	+	36.5851i	0.721528	+	1.24972i	−0.238860	+	0.971054i	$0.576774\pi$
$858$	−0.245884	+	0.248704i	−0.00839435	+	0.00849062i
$859$	18.2776	−	31.6578i	0.623624	−	1.08015i	−0.365181	−	0.930936i	$-0.618993\pi$
$859$	18.2776	−	31.6578i	0.623624	−	1.08015i	0.988805	−	0.149212i	$-0.0476737\pi$
$860$	−2.11770	+	3.66796i	−0.0722130	+	0.125077i
$861$	8.37692	+	30.5649i	0.285485	+	1.04165i
$862$	0.758158	+	1.31317i	0.0258230	+	0.0447267i
$863$	47.9106			1.63090			0.815448	−	0.578830i	$-0.196490\pi$
$863$	47.9106			1.63090			0.815448	+	0.578830i	$0.196490\pi$
$864$	−11.1275	+	3.18656i	−0.378565	+	0.108409i
$865$	29.1588			0.991428
$866$	−1.18183	−	2.04699i	−0.0401602	−	0.0695595i
$867$	−3.66363	−	13.3675i	−0.124423	−	0.453985i
$868$	21.6666	−	37.5277i	0.735413	−	1.27377i
$869$	−0.102361	+	0.177295i	−0.00347237	+	0.00601432i
$870$	−1.23120	+	1.24532i	−0.0417417	+	0.0422204i
$871$	−0.591437	−	1.02440i	−0.0200401	−	0.0347104i
$872$	−2.07678			−0.0703286
$873$	13.2524	+	7.45107i	0.448524	+	0.252181i
$874$	2.77832			0.0939780
$875$	−15.6458	−	27.0993i	−0.528923	−	0.916122i
$876$	20.4229	+	5.34770i	0.690027	+	0.180682i
$877$	−18.9741	+	32.8642i	−0.640711	+	1.10974i	0.344563	+	0.938763i	$0.388027\pi$
$877$	−18.9741	+	32.8642i	−0.640711	+	1.10974i	−0.985274	+	0.170982i	$0.945306\pi$
$878$	3.37005	−	5.83710i	0.113734	−	0.196993i
$879$	46.1056	+	12.0726i	1.55510	+	0.407200i
$880$	−2.16192	−	3.74456i	−0.0728784	−	0.126229i
$881$	35.7432			1.20422			0.602110	−	0.798413i	$-0.294327\pi$
$881$	35.7432			1.20422			0.602110	+	0.798413i	$0.294327\pi$
$882$	−0.787646	+	0.466803i	−0.0265214	+	0.0157181i
$883$	−29.4351			−0.990570			−0.495285	−	0.868731i	$-0.664936\pi$
$883$	−29.4351			−0.990570			−0.495285	+	0.868731i	$0.664936\pi$
$884$	−5.80766	−	10.0592i	−0.195333	−	0.338326i
$885$	−3.96193	+	4.00736i	−0.133179	+	0.134706i
$886$	−0.635590	+	1.10087i	−0.0213531	+	0.0369846i
$887$	10.1192	−	17.5270i	0.339771	−	0.588500i	−0.644619	−	0.764504i	$-0.722984\pi$
$887$	10.1192	−	17.5270i	0.339771	−	0.588500i	0.984389	+	0.176004i	$0.0563172\pi$
$888$	1.18168	+	4.31161i	0.0396546	+	0.144688i
$889$	−14.5400	−	25.1840i	−0.487655	−	0.844643i
$890$	−3.73424			−0.125172
$891$	8.07541	−	0.184199i	0.270536	−	0.00617090i
$892$	−26.1965			−0.877124
$893$	12.5400	+	21.7199i	0.419635	+	0.726829i
$894$	0.0549703	+	0.200571i	0.00183848	+	0.00670809i
$895$	−11.2035	+	19.4050i	−0.374491	+	0.648637i
$896$	8.52737	−	14.7698i	0.284879	−	0.493426i
$897$	−4.69283	+	4.74664i	−0.156689	+	0.158486i
$898$	2.86662	+	4.96512i	0.0956602	+	0.165688i
$899$	−31.4102			−1.04759
$900$	−17.1270	+	10.1504i	−0.570901	+	0.338347i
$901$	−1.87136			−0.0623442
$902$	−0.532392	−	0.922130i	−0.0177267	−	0.0307036i
$903$	8.32652	+	2.18028i	0.277089	+	0.0725552i
$904$	−4.29235	+	7.43457i	−0.142761	+	0.247270i
$905$	−15.8301	+	27.4186i	−0.526212	+	0.911426i
$906$	0.889715	+	0.232970i	0.0295588	+	0.00773990i
$907$	16.7873	+	29.0765i	0.557414	+	0.965469i	0.997711	+	0.0676174i	$0.0215397\pi$
$907$	16.7873	+	29.0765i	0.557414	+	0.965469i	−0.440297	+	0.897852i	$0.645127\pi$
$908$	43.6631			1.44901
$909$	0.153594	+	0.0863572i	0.00509438	+	0.00286429i
$910$	0.840158			0.0278510
$911$	−15.6516	−	27.1093i	−0.518560	−	0.898172i	−0.999767	−	0.0215655i	$-0.993135\pi$
$911$	−15.6516	−	27.1093i	−0.518560	−	0.898172i	0.481207	−	0.876607i	$-0.340198\pi$
$912$	20.6621	−	20.8991i	0.684191	−	0.692037i
$913$	−5.05350	+	8.75291i	−0.167246	+	0.289679i
$914$	2.35214	−	4.07403i	0.0778020	−	0.134757i
$915$	7.27004	+	26.5263i	0.240340	+	0.876931i
$916$	7.51935	+	13.0239i	0.248446	+	0.430322i
$917$	−40.9040			−1.35077
$918$	1.19717	−	4.79448i	0.0395126	−	0.158241i
$919$	−5.64031			−0.186057			−0.0930284	−	0.995663i	$-0.529655\pi$
$919$	−5.64031			−0.186057			−0.0930284	+	0.995663i	$0.529655\pi$
$920$	1.56344	+	2.70796i	0.0515452	+	0.0892789i
$921$	−14.8552	−	54.2022i	−0.489495	−	1.78602i
$922$	−1.30112	+	2.25361i	−0.0428501	+	0.0742186i
$923$	−4.47769	+	7.75559i	−0.147385	+	0.255278i
$924$	−6.29592	+	6.36812i	−0.207120	+	0.209496i
$925$	5.78473	+	10.0194i	0.190201	+	0.329437i
$926$	−3.95407			−0.129939
$927$	−0.196147	−	17.2006i	−0.00644231	−	0.564943i
$928$	−9.30139			−0.305333
$929$	15.8317	+	27.4213i	0.519421	+	0.899663i	0.999745	+	0.0225721i	$0.00718552\pi$
$929$	15.8317	+	27.4213i	0.519421	+	0.899663i	−0.480325	+	0.877091i	$0.659481\pi$
$930$	−3.05190	−	0.799132i	−0.100076	−	0.0262046i
$931$	3.59734	−	6.23078i	0.117898	−	0.204206i
$932$	−7.37443	+	12.7729i	−0.241557	+	0.418390i
$933$	4.50247	+	1.17896i	0.147404	+	0.0385975i
$934$	1.80245	+	3.12194i	0.0589780	+	0.102153i
$935$	5.71320			0.186842
$936$	−0.0305060	−	2.67515i	−0.000997119	−	0.0874400i
$937$	35.6008			1.16303			0.581513	−	0.813537i	$-0.302461\pi$
$937$	35.6008			1.16303			0.581513	+	0.813537i	$0.302461\pi$
$938$	0.278958	+	0.483169i	0.00910830	+	0.0157760i
$939$	−37.4081	+	37.8371i	−1.22077	+	1.23477i
$940$	−6.99224	+	12.1109i	−0.228062	+	0.395014i
$941$	22.3555	−	38.7208i	0.728767	−	1.26226i	−0.228637	−	0.973512i	$-0.573427\pi$
$941$	22.3555	−	38.7208i	0.728767	−	1.26226i	0.957405	−	0.288750i	$-0.0932397\pi$
$942$	0.223657	+	0.816059i	0.00728713	+	0.0265886i
$943$	−10.1610	−	17.5993i	−0.330887	−	0.573113i
$944$	−9.67114			−0.314769
$945$	−13.9537	−	13.4844i	−0.453914	−	0.438646i
$946$	−0.289184			−0.00940220
$947$	−0.391990	−	0.678947i	−0.0127380	−	0.0220628i	0.859586	−	0.510991i	$-0.170721\pi$
$947$	−0.391990	−	0.678947i	−0.0127380	−	0.0220628i	−0.872324	+	0.488928i	$0.837388\pi$
$948$	−0.205082	−	0.748285i	−0.00666076	−	0.0243032i
$949$	−3.67082	+	6.35805i	−0.119160	+	0.206391i
$950$	−1.44090	+	2.49572i	−0.0467491	+	0.0809718i
$951$	19.1684	−	19.3882i	0.621578	−	0.628706i
$952$	5.52896	+	9.57644i	0.179195	+	0.310374i
$953$	21.4350			0.694347			0.347173	−	0.937801i	$-0.387142\pi$
$953$	21.4350			0.694347			0.347173	+	0.937801i	$0.387142\pi$
$954$	−0.186142	−	0.104657i	−0.00602656	−	0.00338841i
$955$	−4.63848			−0.150098
$956$	−21.5089	−	37.2545i	−0.695647	−	1.20490i
$957$	6.27932	+	1.64423i	0.202982	+	0.0531503i
$958$	2.52867	−	4.37979i	0.0816977	−	0.141505i
$959$	22.3160	−	38.6524i	0.720620	−	1.24815i
$960$	15.2408	+	3.99076i	0.491894	+	0.128801i
$961$	−12.7927	−	22.1577i	−0.412669	−	0.714764i
$962$	−0.770247			−0.0248337
$963$	−4.24848	+	2.51789i	−0.136905	+	0.0811378i
$964$	−16.1803			−0.521132
$965$	2.12256	+	3.67639i	0.0683277	+	0.118347i
$966$	2.21343	−	2.23881i	0.0712158	−	0.0720325i
$967$	−11.7946	+	20.4288i	−0.379289	+	0.656948i	−0.990959	−	0.134165i	$-0.957165\pi$
$967$	−11.7946	+	20.4288i	−0.379289	+	0.656948i	0.611670	+	0.791113i	$0.290498\pi$
$968$	−3.84284	+	6.65600i	−0.123514	+	0.213932i
$969$	10.2641	+	37.4509i	0.329732	+	1.20310i
$970$	0.613545	+	1.06269i	0.0196997	+	0.0341210i
$971$	−31.2839			−1.00395			−0.501973	−	0.864883i	$-0.667392\pi$
$971$	−31.2839			−1.00395			−0.501973	+	0.864883i	$0.667392\pi$
$972$	−21.0209	+	22.2549i	−0.674244	+	0.713825i
$973$	−54.9437			−1.76141
$974$	0.162351	+	0.281201i	0.00520207	+	0.00901025i
$975$	−1.83002	−	6.67722i	−0.0586076	−	0.213842i
$976$	−23.6015	+	40.8790i	−0.755465	+	1.30850i
$977$	−5.08226	+	8.80273i	−0.162596	+	0.281624i	−0.935799	−	0.352534i	$-0.885320\pi$
$977$	−5.08226	+	8.80273i	−0.162596	+	0.281624i	0.773203	+	0.634159i	$0.218653\pi$
$978$	0.679403	−	0.687195i	0.0217249	−	0.0219741i
$979$	6.92070	+	11.9870i	0.221187	+	0.383106i
$980$	4.01172			0.128150
$981$	−7.10932	+	4.21338i	−0.226983	+	0.134523i
$982$	−0.876113			−0.0279579
$983$	14.4091	+	24.9572i	0.459578	+	0.796012i	0.998939	−	0.0460628i	$-0.0146674\pi$
$983$	14.4091	+	24.9572i	0.459578	+	0.796012i	−0.539361	+	0.842075i	$0.681334\pi$
$984$	7.87956	+	2.06324i	0.251191	+	0.0657738i
$985$	7.14835	−	12.3813i	0.227765	−	0.394501i
$986$	1.98555	−	3.43907i	0.0632328	−	0.109522i
$987$	27.4926	+	7.19887i	0.875098	+	0.229142i
$988$	5.20774	+	9.02007i	0.165680	+	0.286967i
$989$	−5.51923			−0.175501
$990$	0.568284	+	0.319515i	0.0180612	+	0.0101548i
$991$	−40.2184			−1.27758			−0.638789	−	0.769382i	$-0.720564\pi$
$991$	−40.2184			−1.27758			−0.638789	+	0.769382i	$0.720564\pi$
$992$	−8.37824	−	14.5115i	−0.266009	−	0.460742i
$993$	30.6393	−	30.9906i	0.972307	−	0.983458i
$994$	2.11195	−	3.65801i	0.0669871	−	0.116025i
$995$	7.25960	−	12.5740i	0.230145	−	0.398622i
$996$	−10.1247	−	36.9423i	−0.320815	−	1.17056i
$997$	−15.8406	−	27.4367i	−0.501676	−	0.868928i	−0.999998	−	0.00193635i	$-0.999384\pi$
$997$	−15.8406	−	27.4367i	−0.501676	−	0.868928i	0.498322	−	0.866992i	$-0.333950\pi$
$998$	7.17729			0.227193
$999$	12.7926	+	12.3623i	0.404740	+	0.391126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.e.b.202.15	✓	66
9.4	even	3		5427.2.a.n.1.19		33
9.5	odd	6		5427.2.a.q.1.15		33
9.7	even	3	inner	603.2.e.b.403.15	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.e.b.202.15	✓	66	1.1	even	1	trivial
603.2.e.b.403.15	yes	66	9.7	even	3	inner
5427.2.a.n.1.19		33	9.4	even	3
5427.2.a.q.1.15		33	9.5	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0950983 - 0.164715i) q^{2} +(-0.457819 - 1.67045i) q^{3} +(0.981913 - 1.70072i) q^{4} +(0.636538 - 1.10252i) q^{5} +(-0.231610 + 0.234267i) q^{6} +(-1.46668 - 2.54037i) q^{7} -0.753906 q^{8} +(-2.58080 + 1.52953i) q^{9} +O(q^{10})\)	\(q+(-0.0950983 - 0.164715i) q^{2} +(-0.457819 - 1.67045i) q^{3} +(0.981913 - 1.70072i) q^{4} +(0.636538 - 1.10252i) q^{5} +(-0.231610 + 0.234267i) q^{6} +(-1.46668 - 2.54037i) q^{7} -0.753906 q^{8} +(-2.58080 + 1.52953i) q^{9} -0.242135 q^{10} +(0.448750 + 0.777258i) q^{11} +(-3.29051 - 0.861612i) q^{12} +(0.591437 - 1.02440i) q^{13} +(-0.278958 + 0.483169i) q^{14} +(-2.13312 - 0.558551i) q^{15} +(-1.89213 - 3.27727i) q^{16} +5.00024 q^{17} +(0.497366 + 0.279642i) q^{18} -4.48372 q^{19} +(-1.25005 - 2.16515i) q^{20} +(-3.57208 + 3.61305i) q^{21} +(0.0853508 - 0.147832i) q^{22} +(1.62896 - 2.82144i) q^{23} +(0.345153 + 1.25936i) q^{24} +(1.68964 + 2.92654i) q^{25} -0.224978 q^{26} +(3.73654 + 3.61085i) q^{27} -5.76061 q^{28} +(2.08779 + 3.61617i) q^{29} +(0.110854 + 0.404474i) q^{30} +(-3.76117 + 6.51453i) q^{31} +(-1.11378 + 1.92913i) q^{32} +(1.09292 - 1.10546i) q^{33} +(-0.475514 - 0.823614i) q^{34} -3.73439 q^{35} +(0.0671789 + 5.89109i) q^{36} +3.42365 q^{37} +(0.426394 + 0.738536i) q^{38} +(-1.98198 - 0.518976i) q^{39} +(-0.479890 + 0.831193i) q^{40} +(3.11885 - 5.40200i) q^{41} +(0.934822 + 0.244781i) q^{42} +(-0.847047 - 1.46713i) q^{43} +1.76253 q^{44} +(0.0435496 + 3.81898i) q^{45} -0.619646 q^{46} +(-2.79679 - 4.84417i) q^{47} +(-4.60825 + 4.66110i) q^{48} +(-0.802312 + 1.38965i) q^{49} +(0.321364 - 0.556618i) q^{50} +(-2.28920 - 8.35264i) q^{51} +(-1.16148 - 2.01174i) q^{52} -0.374255 q^{53} +(0.239424 - 0.958850i) q^{54} +1.14259 q^{55} +(1.10574 + 1.91520i) q^{56} +(2.05273 + 7.48983i) q^{57} +(0.397091 - 0.687782i) q^{58} +(1.27781 - 2.21323i) q^{59} +(-3.04447 + 3.07939i) q^{60} +(-6.23675 - 10.8024i) q^{61} +1.43072 q^{62} +(7.67078 + 4.31286i) q^{63} -7.14485 q^{64} +(-0.752943 - 1.30414i) q^{65} +(-0.286021 - 0.0748939i) q^{66} +(0.500000 - 0.866025i) q^{67} +(4.90979 - 8.50401i) q^{68} +(-5.45885 - 1.42939i) q^{69} +(0.355134 + 0.615111i) q^{70} -7.57087 q^{71} +(1.94568 - 1.15312i) q^{72} -6.20662 q^{73} +(-0.325583 - 0.563926i) q^{74} +(4.11509 - 4.16228i) q^{75} +(-4.40262 + 7.62556i) q^{76} +(1.31635 - 2.27998i) q^{77} +(0.102999 + 0.375815i) q^{78} +(0.114051 + 0.197543i) q^{79} -4.81765 q^{80} +(4.32109 - 7.89482i) q^{81} -1.18639 q^{82} +(5.63063 + 9.75254i) q^{83} +(2.63732 + 9.62282i) q^{84} +(3.18284 - 5.51284i) q^{85} +(-0.161105 + 0.279043i) q^{86} +(5.08479 - 5.14310i) q^{87} +(-0.338316 - 0.585980i) q^{88} +15.4222 q^{89} +(0.624902 - 0.370352i) q^{90} -3.46980 q^{91} +(-3.19900 - 5.54082i) q^{92} +(12.6041 + 3.30036i) q^{93} +(-0.531939 + 0.921345i) q^{94} +(-2.85406 + 4.94337i) q^{95} +(3.73242 + 0.977326i) q^{96} +(-2.53390 - 4.38884i) q^{97} +0.305194 q^{98} +(-2.34697 - 1.31958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} - 33 q^{4} + 18 q^{5} - 3 q^{6} - 48 q^{8} + 4 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 - 33 * q^4 + 18 * q^5 - 3 * q^6 - 48 * q^8 + 4 * q^9	\( 66 q + 7 q^{2} - 33 q^{4} + 18 q^{5} - 3 q^{6} - 48 q^{8} + 4 q^{9} + 12 q^{11} + q^{12} + 9 q^{14} + 3 q^{15} - 33 q^{16} - 62 q^{17} + 7 q^{18} + 43 q^{20} + 17 q^{21} + 19 q^{23} - 17 q^{24} - 33 q^{25} - 28 q^{26} - 3 q^{27} + 54 q^{28} + 25 q^{29} + 24 q^{30} + 45 q^{32} - 32 q^{33} - 6 q^{34} - 50 q^{35} + 53 q^{36} - 24 q^{37} + 34 q^{38} + 19 q^{39} - 6 q^{40} + 34 q^{41} - 107 q^{42} - 98 q^{44} + 9 q^{45} + 12 q^{46} + 26 q^{47} + 49 q^{48} - 33 q^{49} + 39 q^{50} - 50 q^{51} + 9 q^{52} - 104 q^{53} + 70 q^{54} + 60 q^{55} + 16 q^{56} + 6 q^{57} + 3 q^{58} + 21 q^{59} - 161 q^{60} - 54 q^{62} + q^{63} - 12 q^{64} + 52 q^{65} + 52 q^{66} + 33 q^{67} + 98 q^{68} + 2 q^{69} - 6 q^{70} - 62 q^{71} + 66 q^{72} + 27 q^{74} + 21 q^{75} - 6 q^{76} + 85 q^{77} - 107 q^{78} - 172 q^{80} + 72 q^{81} + 102 q^{82} + 71 q^{83} - 54 q^{84} - 27 q^{85} + 9 q^{86} + 3 q^{87} - 12 q^{88} - 82 q^{89} + 153 q^{90} - 60 q^{91} + 67 q^{92} - 47 q^{93} + 15 q^{94} + 58 q^{95} - 136 q^{96} - 12 q^{97} - 172 q^{98} + 96 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 - 33 * q^4 + 18 * q^5 - 3 * q^6 - 48 * q^8 + 4 * q^9 + 12 * q^11 + q^12 + 9 * q^14 + 3 * q^15 - 33 * q^16 - 62 * q^17 + 7 * q^18 + 43 * q^20 + 17 * q^21 + 19 * q^23 - 17 * q^24 - 33 * q^25 - 28 * q^26 - 3 * q^27 + 54 * q^28 + 25 * q^29 + 24 * q^30 + 45 * q^32 - 32 * q^33 - 6 * q^34 - 50 * q^35 + 53 * q^36 - 24 * q^37 + 34 * q^38 + 19 * q^39 - 6 * q^40 + 34 * q^41 - 107 * q^42 - 98 * q^44 + 9 * q^45 + 12 * q^46 + 26 * q^47 + 49 * q^48 - 33 * q^49 + 39 * q^50 - 50 * q^51 + 9 * q^52 - 104 * q^53 + 70 * q^54 + 60 * q^55 + 16 * q^56 + 6 * q^57 + 3 * q^58 + 21 * q^59 - 161 * q^60 - 54 * q^62 + q^63 - 12 * q^64 + 52 * q^65 + 52 * q^66 + 33 * q^67 + 98 * q^68 + 2 * q^69 - 6 * q^70 - 62 * q^71 + 66 * q^72 + 27 * q^74 + 21 * q^75 - 6 * q^76 + 85 * q^77 - 107 * q^78 - 172 * q^80 + 72 * q^81 + 102 * q^82 + 71 * q^83 - 54 * q^84 - 27 * q^85 + 9 * q^86 + 3 * q^87 - 12 * q^88 - 82 * q^89 + 153 * q^90 - 60 * q^91 + 67 * q^92 - 47 * q^93 + 15 * q^94 + 58 * q^95 - 136 * q^96 - 12 * q^97 - 172 * q^98 + 96 * q^99

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