LMFDB - Embedded newform 273.2.bt.a.136.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(136,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("273.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bt (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			136.6
Character	$\chi$	$=$	273.136
Dual form			273.2.bt.a.271.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.556084 - 0.556084i) q^{2} +(0.866025 - 0.500000i) q^{3} +1.38154i q^{4} +(0.542987 - 2.02645i) q^{5} +(0.203541 - 0.759625i) q^{6} +(-0.405927 - 2.61443i) q^{7} +(1.88042 + 1.88042i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.556084 - 0.556084i) q^{2} +(0.866025 - 0.500000i) q^{3} +1.38154i q^{4} +(0.542987 - 2.02645i) q^{5} +(0.203541 - 0.759625i) q^{6} +(-0.405927 - 2.61443i) q^{7} +(1.88042 + 1.88042i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.824932 - 1.42882i) q^{10} +(-0.632763 + 2.36150i) q^{11} +(0.690770 + 1.19645i) q^{12} +(1.96880 - 3.02057i) q^{13} +(-1.67957 - 1.22811i) q^{14} +(-0.542987 - 2.02645i) q^{15} -0.671737 q^{16} +6.55339 q^{17} +(-0.203541 - 0.759625i) q^{18} +(-7.74006 + 2.07394i) q^{19} +(2.79963 + 0.750158i) q^{20} +(-1.65876 - 2.06120i) q^{21} +(0.961326 + 1.66506i) q^{22} +3.84618i q^{23} +(2.56870 + 0.688282i) q^{24} +(0.518448 + 0.299326i) q^{25} +(-0.584868 - 2.77451i) q^{26} -1.00000i q^{27} +(3.61194 - 0.560804i) q^{28} +(-1.25425 + 2.17242i) q^{29} +(-1.42882 - 0.824932i) q^{30} +(-0.457027 + 0.122460i) q^{31} +(-4.13438 + 4.13438i) q^{32} +(0.632763 + 2.36150i) q^{33} +(3.64424 - 3.64424i) q^{34} +(-5.51843 - 0.597007i) q^{35} +(1.19645 + 0.690770i) q^{36} +(-5.00037 - 5.00037i) q^{37} +(-3.15084 + 5.45741i) q^{38} +(0.194751 - 3.60029i) q^{39} +(4.83163 - 2.78954i) q^{40} +(-11.0034 + 2.94834i) q^{41} +(-2.06861 - 0.223791i) q^{42} +(0.810492 - 0.467938i) q^{43} +(-3.26252 - 0.874188i) q^{44} +(-1.48347 - 1.48347i) q^{45} +(2.13880 + 2.13880i) q^{46} +(7.03848 + 1.88596i) q^{47} +(-0.581741 + 0.335869i) q^{48} +(-6.67045 + 2.12253i) q^{49} +(0.454751 - 0.121850i) q^{50} +(5.67540 - 3.27669i) q^{51} +(4.17303 + 2.71998i) q^{52} +(-1.08341 + 1.87652i) q^{53} +(-0.556084 - 0.556084i) q^{54} +(4.44190 + 2.56453i) q^{55} +(4.15291 - 5.67954i) q^{56} +(-5.66612 + 5.66612i) q^{57} +(0.510581 + 1.90552i) q^{58} +(-3.92820 + 3.92820i) q^{59} +(2.79963 - 0.750158i) q^{60} +(8.13407 + 4.69621i) q^{61} +(-0.186047 + 0.322243i) q^{62} +(-2.46712 - 0.955670i) q^{63} +3.25466i q^{64} +(-5.05200 - 5.62981i) q^{65} +(1.66506 + 0.961326i) q^{66} +(-11.1395 - 2.98482i) q^{67} +9.05378i q^{68} +(1.92309 + 3.33089i) q^{69} +(-3.40069 + 2.73672i) q^{70} +(9.44098 + 2.52970i) q^{71} +(2.56870 - 0.688282i) q^{72} +(2.62580 + 9.79963i) q^{73} -5.56125 q^{74} +0.598652 q^{75} +(-2.86524 - 10.6932i) q^{76} +(6.43083 + 0.695715i) q^{77} +(-1.89376 - 2.11036i) q^{78} +(1.07540 + 1.86264i) q^{79} +(-0.364744 + 1.36124i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.47927 + 7.75833i) q^{82} +(1.52436 + 1.52436i) q^{83} +(2.84763 - 2.29164i) q^{84} +(3.55840 - 13.2801i) q^{85} +(0.190489 - 0.710914i) q^{86} +2.50850i q^{87} +(-5.63048 + 3.25076i) q^{88} +(4.45304 - 4.45304i) q^{89} -1.64986 q^{90} +(-8.69623 - 3.92116i) q^{91} -5.31366 q^{92} +(-0.334567 + 0.334567i) q^{93} +(4.96274 - 2.86524i) q^{94} +16.8110i q^{95} +(-1.51329 + 5.64767i) q^{96} +(4.17950 - 15.5981i) q^{97} +(-2.52902 + 4.88964i) q^{98} +(1.72874 + 1.72874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7} + 18 q^{9}+O(q^{10}) $ 36 * q + 6 * q^7 + 18 * q^9	$ 36 q + 6 q^{7} + 18 q^{9} - 8 q^{11} - 16 q^{12} + 42 q^{14} - 24 q^{16} - 8 q^{17} - 18 q^{19} + 14 q^{20} - 4 q^{21} + 4 q^{22} + 18 q^{24} + 24 q^{25} - 50 q^{26} + 34 q^{28} + 8 q^{29} + 6 q^{31} - 50 q^{32} + 8 q^{33} - 24 q^{34} + 14 q^{35} - 14 q^{37} - 8 q^{38} - 2 q^{39} - 30 q^{40} + 34 q^{41} - 18 q^{42} + 30 q^{43} + 28 q^{44} - 32 q^{46} - 10 q^{47} + 24 q^{48} + 6 q^{49} - 20 q^{50} - 24 q^{51} + 4 q^{52} - 8 q^{53} - 30 q^{55} - 92 q^{56} - 24 q^{57} + 72 q^{58} - 70 q^{59} + 14 q^{60} - 60 q^{61} - 48 q^{62} + 6 q^{63} - 44 q^{65} + 18 q^{66} - 46 q^{67} + 4 q^{69} + 80 q^{70} + 42 q^{71} + 18 q^{72} - 56 q^{73} + 40 q^{74} - 20 q^{75} + 12 q^{76} + 24 q^{77} - 16 q^{78} + 170 q^{80} - 18 q^{81} + 24 q^{82} - 60 q^{83} + 2 q^{85} + 12 q^{86} + 84 q^{88} + 64 q^{89} - 86 q^{91} - 100 q^{92} + 12 q^{93} - 66 q^{94} + 46 q^{96} + 36 q^{97} - 22 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 6 * q^7 + 18 * q^9 - 8 * q^11 - 16 * q^12 + 42 * q^14 - 24 * q^16 - 8 * q^17 - 18 * q^19 + 14 * q^20 - 4 * q^21 + 4 * q^22 + 18 * q^24 + 24 * q^25 - 50 * q^26 + 34 * q^28 + 8 * q^29 + 6 * q^31 - 50 * q^32 + 8 * q^33 - 24 * q^34 + 14 * q^35 - 14 * q^37 - 8 * q^38 - 2 * q^39 - 30 * q^40 + 34 * q^41 - 18 * q^42 + 30 * q^43 + 28 * q^44 - 32 * q^46 - 10 * q^47 + 24 * q^48 + 6 * q^49 - 20 * q^50 - 24 * q^51 + 4 * q^52 - 8 * q^53 - 30 * q^55 - 92 * q^56 - 24 * q^57 + 72 * q^58 - 70 * q^59 + 14 * q^60 - 60 * q^61 - 48 * q^62 + 6 * q^63 - 44 * q^65 + 18 * q^66 - 46 * q^67 + 4 * q^69 + 80 * q^70 + 42 * q^71 + 18 * q^72 - 56 * q^73 + 40 * q^74 - 20 * q^75 + 12 * q^76 + 24 * q^77 - 16 * q^78 + 170 * q^80 - 18 * q^81 + 24 * q^82 - 60 * q^83 + 2 * q^85 + 12 * q^86 + 84 * q^88 + 64 * q^89 - 86 * q^91 - 100 * q^92 + 12 * q^93 - 66 * q^94 + 46 * q^96 + 36 * q^97 - 22 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.556084	−	0.556084i	0.393211	−	0.393211i	−0.482619	−	0.875830i	$-0.660315\pi$
$2$	0.556084	−	0.556084i	0.393211	−	0.393211i	0.875830	+	0.482619i	$0.160315\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$			1.38154i			0.690770i
$5$	0.542987	−	2.02645i	0.242831	−	0.906258i	−0.731630	−	0.681702i	$-0.761240\pi$
$5$	0.542987	−	2.02645i	0.242831	−	0.906258i	0.974461	−	0.224556i	$-0.0720931\pi$
$6$	0.203541	−	0.759625i	0.0830952	−	0.310116i
$7$	−0.405927	−	2.61443i	−0.153426	−	0.988160i
$7$	−0.405927	−	2.61443i	−0.153426	−	0.988160i
$8$	1.88042	+	1.88042i	0.664829	+	0.664829i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.824932	−	1.42882i	−0.260867	−	0.451834i
$11$	−0.632763	+	2.36150i	−0.190785	+	0.712020i	0.802532	+	0.596608i	$0.203485\pi$
$11$	−0.632763	+	2.36150i	−0.190785	+	0.712020i	−0.993318	+	0.115412i	$0.963181\pi$
$12$	0.690770	+	1.19645i	0.199408	+	0.345385i
$13$	1.96880	−	3.02057i	0.546048	−	0.837754i
$13$	1.96880	−	3.02057i	0.546048	−	0.837754i
$14$	−1.67957	−	1.22811i	−0.448884	−	0.328227i
$15$	−0.542987	−	2.02645i	−0.140199	−	0.523228i
$16$	−0.671737			−0.167934
$17$	6.55339			1.58943			0.794715	−	0.606983i	$-0.207620\pi$
$17$	6.55339			1.58943			0.794715	+	0.606983i	$0.207620\pi$
$18$	−0.203541	−	0.759625i	−0.0479751	−	0.179045i
$19$	−7.74006	+	2.07394i	−1.77569	+	0.475795i	−0.989787	−	0.142552i	$-0.954469\pi$
$19$	−7.74006	+	2.07394i	−1.77569	+	0.475795i	−0.785905	+	0.618347i	$0.787803\pi$
$20$	2.79963	+	0.750158i	0.626016	+	0.167740i
$21$	−1.65876	−	2.06120i	−0.361970	−	0.449790i
$22$	0.961326	+	1.66506i	0.204955	+	0.354993i
$23$			3.84618i			0.801984i	0.916082	+	0.400992i	$0.131335\pi$
$23$			3.84618i			0.801984i	−0.916082	+	0.400992i	$0.868665\pi$
$24$	2.56870	+	0.688282i	0.524334	+	0.140495i
$25$	0.518448	+	0.299326i	0.103690	+	0.0598652i
$26$	−0.584868	−	2.77451i	−0.114702	−	0.544126i
$27$		−	1.00000i		−	0.192450i
$28$	3.61194	−	0.560804i	0.682592	−	0.105982i
$29$	−1.25425	+	2.17242i	−0.232908	+	0.403408i	−0.958663	−	0.284545i	$-0.908157\pi$
$29$	−1.25425	+	2.17242i	−0.232908	+	0.403408i	0.725755	+	0.687954i	$0.241491\pi$
$30$	−1.42882	−	0.824932i	−0.260867	−	0.150611i
$31$	−0.457027	+	0.122460i	−0.0820844	+	0.0219945i	−0.299628	−	0.954056i	$-0.596862\pi$
$31$	−0.457027	+	0.122460i	−0.0820844	+	0.0219945i	0.217543	+	0.976051i	$0.430196\pi$
$32$	−4.13438	+	4.13438i	−0.730863	+	0.730863i
$33$	0.632763	+	2.36150i	0.110150	+	0.411085i
$34$	3.64424	−	3.64424i	0.624981	−	0.624981i
$35$	−5.51843	−	0.597007i	−0.932784	−	0.100913i
$36$	1.19645	+	0.690770i	0.199408	+	0.115128i
$37$	−5.00037	−	5.00037i	−0.822055	−	0.822055i	0.164347	−	0.986403i	$-0.447448\pi$
$37$	−5.00037	−	5.00037i	−0.822055	−	0.822055i	−0.986403	+	0.164347i	$0.947448\pi$
$38$	−3.15084	+	5.45741i	−0.511134	+	0.885309i
$39$	0.194751	−	3.60029i	0.0311851	−	0.576507i
$40$	4.83163	−	2.78954i	0.763948	−	0.441065i
$41$	−11.0034	+	2.94834i	−1.71844	+	0.460454i	−0.977468	−	0.211084i	$-0.932301\pi$
$41$	−11.0034	+	2.94834i	−1.71844	+	0.460454i	−0.740970	+	0.671538i	$0.765634\pi$
$42$	−2.06861	−	0.223791i	−0.319193	−	0.0345316i
$43$	0.810492	−	0.467938i	0.123599	−	0.0713598i	−0.436926	−	0.899497i	$-0.643933\pi$
$43$	0.810492	−	0.467938i	0.123599	−	0.0713598i	0.560525	+	0.828138i	$0.310599\pi$
$44$	−3.26252	−	0.874188i	−0.491843	−	0.131789i
$45$	−1.48347	−	1.48347i	−0.221142	−	0.221142i
$46$	2.13880	+	2.13880i	0.315349	+	0.315349i
$47$	7.03848	+	1.88596i	1.02667	+	0.275095i	0.732578	−	0.680683i	$-0.238317\pi$
$47$	7.03848	+	1.88596i	1.02667	+	0.275095i	0.294090	+	0.955778i	$0.404983\pi$
$48$	−0.581741	+	0.335869i	−0.0839672	+	0.0484785i
$49$	−6.67045	+	2.12253i	−0.952921	+	0.303219i
$50$	0.454751	−	0.121850i	0.0643115	−	0.0172322i
$51$	5.67540	−	3.27669i	0.794715	−	0.458829i
$52$	4.17303	+	2.71998i	0.578696	+	0.377194i
$53$	−1.08341	+	1.87652i	−0.148818	+	0.257760i	−0.930791	−	0.365552i	$-0.880880\pi$
$53$	−1.08341	+	1.87652i	−0.148818	+	0.257760i	0.781973	+	0.623312i	$0.214213\pi$
$54$	−0.556084	−	0.556084i	−0.0756735	−	0.0756735i
$55$	4.44190	+	2.56453i	0.598945	+	0.345801i
$56$	4.15291	−	5.67954i	0.554956	−	0.758960i
$57$	−5.66612	+	5.66612i	−0.750496	+	0.750496i
$58$	0.510581	+	1.90552i	0.0670426	+	0.250206i
$59$	−3.92820	+	3.92820i	−0.511408	+	0.511408i	−0.914958	−	0.403550i	$-0.867776\pi$
$59$	−3.92820	+	3.92820i	−0.511408	+	0.511408i	0.403550	+	0.914958i	$0.367776\pi$
$60$	2.79963	−	0.750158i	0.361430	−	0.0968450i
$61$	8.13407	+	4.69621i	1.04146	+	0.601288i	0.920247	−	0.391339i	$-0.127988\pi$
$61$	8.13407	+	4.69621i	1.04146	+	0.601288i	0.121214	+	0.992626i	$0.461321\pi$
$62$	−0.186047	+	0.322243i	−0.0236280	+	0.0409249i
$63$	−2.46712	−	0.955670i	−0.310828	−	0.120403i
$64$			3.25466i			0.406832i
$65$	−5.05200	−	5.62981i	−0.626624	−	0.698293i
$66$	1.66506	+	0.961326i	0.204955	+	0.118331i
$67$	−11.1395	−	2.98482i	−1.36091	−	0.364653i	−0.496756	−	0.867890i	$-0.665476\pi$
$67$	−11.1395	−	2.98482i	−1.36091	−	0.364653i	−0.864149	+	0.503237i	$0.832142\pi$
$68$			9.05378i			1.09793i
$69$	1.92309	+	3.33089i	0.231513	+	0.400992i
$70$	−3.40069	+	2.73672i	−0.406461	+	0.327101i
$71$	9.44098	+	2.52970i	1.12044	+	0.300221i	0.771061	−	0.636762i	$-0.219726\pi$
$71$	9.44098	+	2.52970i	1.12044	+	0.300221i	0.349377	+	0.936982i	$0.386393\pi$
$72$	2.56870	−	0.688282i	0.302725	−	0.0811148i
$73$	2.62580	+	9.79963i	0.307327	+	1.14696i	0.930924	+	0.365214i	$0.119004\pi$
$73$	2.62580	+	9.79963i	0.307327	+	1.14696i	−0.623597	+	0.781746i	$0.714329\pi$
$74$	−5.56125			−0.646482
$75$	0.598652			0.0691264
$76$	−2.86524	−	10.6932i	−0.328665	−	1.22660i
$77$	6.43083	+	0.695715i	0.732862	+	0.0792841i
$78$	−1.89376	−	2.11036i	−0.214427	−	0.238951i
$79$	1.07540	+	1.86264i	0.120992	+	0.209564i	0.920159	−	0.391545i	$-0.128059\pi$
$79$	1.07540	+	1.86264i	0.120992	+	0.209564i	−0.799167	+	0.601109i	$0.794726\pi$
$80$	−0.364744	+	1.36124i	−0.0407796	+	0.152192i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.47927	+	7.75833i	−0.494653	+	0.856764i
$83$	1.52436	+	1.52436i	0.167320	+	0.167320i	0.785801	−	0.618480i	$-0.212251\pi$
$83$	1.52436	+	1.52436i	0.167320	+	0.167320i	−0.618480	+	0.785801i	$0.712251\pi$
$84$	2.84763	−	2.29164i	0.310702	−	0.250038i
$85$	3.55840	−	13.2801i	0.385963	−	1.44043i
$86$	0.190489	−	0.710914i	0.0205409	−	0.0766598i
$87$			2.50850i			0.268939i
$88$	−5.63048	+	3.25076i	−0.600212	+	0.346532i
$89$	4.45304	−	4.45304i	0.472021	−	0.472021i	−0.430547	−	0.902568i	$-0.641679\pi$
$89$	4.45304	−	4.45304i	0.472021	−	0.472021i	0.902568	+	0.430547i	$0.141679\pi$
$90$	−1.64986			−0.173911
$91$	−8.69623	−	3.92116i	−0.911613	−	0.411050i
$92$	−5.31366			−0.553987
$93$	−0.334567	+	0.334567i	−0.0346930	+	0.0346930i
$94$	4.96274	−	2.86524i	0.511867	−	0.295527i
$95$			16.8110i			1.72477i
$96$	−1.51329	+	5.64767i	−0.154449	+	0.576413i
$97$	4.17950	−	15.5981i	0.424363	−	1.58375i	−0.340946	−	0.940083i	$-0.610747\pi$
$97$	4.17950	−	15.5981i	0.424363	−	1.58375i	0.765309	−	0.643663i	$-0.222586\pi$
$98$	−2.52902	+	4.88964i	−0.255470	+	0.493928i
$99$	1.72874	+	1.72874i	0.173745	+	0.173745i
$100$	−0.413531	+	0.716257i	−0.0413531	+	0.0716257i
$101$	−1.76991	−	3.06558i	−0.176113	−	0.305037i	0.764433	−	0.644703i	$-0.223019\pi$
$101$	−1.76991	−	3.06558i	−0.176113	−	0.305037i	−0.940546	+	0.339667i	$0.889686\pi$
$102$	1.33388	−	4.97812i	0.132074	−	0.492907i
$103$	−4.58234	−	7.93684i	−0.451511	−	0.782041i	0.546969	−	0.837153i	$-0.315782\pi$
$103$	−4.58234	−	7.93684i	−0.451511	−	0.782041i	−0.998480	+	0.0551124i	$0.982448\pi$
$104$	9.38211	−	1.97776i	0.919992	−	0.193935i
$105$	−5.07760	+	2.24219i	−0.495523	+	0.218815i
$106$	0.441036	+	1.64597i	0.0428372	+	0.159871i
$107$	−2.01759			−0.195048			−0.0975240	−	0.995233i	$-0.531092\pi$
$107$	−2.01759			−0.195048			−0.0975240	+	0.995233i	$0.531092\pi$
$108$	1.38154			0.132939
$109$	−1.45769	−	5.44016i	−0.139621	−	0.521073i	−0.999936	−	0.0113102i	$-0.996400\pi$
$109$	−1.45769	−	5.44016i	−0.139621	−	0.521073i	0.860315	−	0.509763i	$-0.170267\pi$
$110$	3.89616	−	1.04397i	0.371485	−	0.0995390i
$111$	−6.83063	−	1.83026i	−0.648335	−	0.173721i
$112$	0.272676	+	1.75621i	0.0257655	+	0.165946i
$113$	−6.20648	−	10.7499i	−0.583857	−	1.01127i	−0.995017	−	0.0997064i	$-0.968210\pi$
$113$	−6.20648	−	10.7499i	−0.583857	−	1.01127i	0.411160	−	0.911563i	$-0.365124\pi$
$114$			6.30168i			0.590206i
$115$	7.79411	+	2.08842i	0.726804	+	0.194747i
$116$	−3.00129	−	1.73279i	−0.278663	−	0.160886i
$117$	−1.63148	−	3.21532i	−0.150831	−	0.297256i
$118$			4.36881i			0.402182i
$119$	−2.66020	−	17.1334i	−0.243860	−	1.57061i
$120$	2.78954	−	4.83163i	0.254649	−	0.441065i
$121$	4.34997	+	2.51145i	0.395451	+	0.228314i
$122$	7.13471	−	1.91174i	0.645947	−	0.173081i
$123$	−8.05503	+	8.05503i	−0.726297	+	0.726297i
$124$	−0.169183	−	0.631401i	−0.0151931	−	0.0567015i
$125$	8.30541	−	8.30541i	0.742859	−	0.742859i
$126$	−1.90336	+	0.840495i	−0.169565	+	0.0748772i
$127$	−9.05461	−	5.22768i	−0.803467	−	0.463882i	0.0412153	−	0.999150i	$-0.486877\pi$
$127$	−9.05461	−	5.22768i	−0.803467	−	0.463882i	−0.844682	+	0.535269i	$0.820210\pi$
$128$	−6.45891	−	6.45891i	−0.570892	−	0.570892i
$129$	0.467938	−	0.810492i	0.0411996	−	0.0713598i
$130$	−5.93999	−	0.321313i	−0.520971	−	0.0281810i
$131$	18.0680	−	10.4315i	1.57860	−	0.911408i	0.583550	−	0.812077i	$-0.301663\pi$
$131$	18.0680	−	10.4315i	1.57860	−	0.911408i	0.995055	−	0.0993303i	$-0.0316700\pi$
$132$	−3.26252	+	0.874188i	−0.283965	+	0.0760883i
$133$	8.56407	+	19.3940i	0.742599	+	1.68167i
$134$	−7.85430	+	4.53468i	−0.678508	+	0.391737i
$135$	−2.02645	−	0.542987i	−0.174409	−	0.0467328i
$136$	12.3231	+	12.3231i	1.05670	+	1.05670i
$137$	7.97181	+	7.97181i	0.681078	+	0.681078i	0.960243	−	0.279165i	$-0.0900577\pi$
$137$	7.97181	+	7.97181i	0.681078	+	0.681078i	−0.279165	+	0.960243i	$0.590058\pi$
$138$	2.92166	+	0.782855i	0.248708	+	0.0666411i
$139$	−8.83314	+	5.09981i	−0.749217	+	0.432561i	−0.825411	−	0.564532i	$-0.809057\pi$
$139$	−8.83314	+	5.09981i	−0.749217	+	0.432561i	0.0761940	+	0.997093i	$0.475723\pi$
$140$	0.824789	−	7.62393i	0.0697074	−	0.644340i
$141$	7.03848	−	1.88596i	0.592747	−	0.158826i
$142$	6.65671	−	3.84325i	0.558618	−	0.322518i
$143$	5.88729	+	6.56064i	0.492320	+	0.548628i
$144$	−0.335869	+	0.581741i	−0.0279891	+	0.0484785i
$145$	3.72127	+	3.72127i	0.309035	+	0.309035i
$146$	6.90958	+	3.98925i	0.571841	+	0.330153i
$147$	−4.71551	+	5.17339i	−0.388929	+	0.426694i
$148$	6.90821	−	6.90821i	0.567852	−	0.567852i
$149$	−1.21789	−	4.54523i	−0.0997734	−	0.372359i	0.897926	−	0.440145i	$-0.145073\pi$
$149$	−1.21789	−	4.54523i	−0.0997734	−	0.372359i	−0.997700	+	0.0677861i	$0.978406\pi$
$150$	0.332901	−	0.332901i	0.0271813	−	0.0271813i
$151$	0.563961	−	0.151113i	0.0458945	−	0.0122974i	−0.235799	−	0.971802i	$-0.575771\pi$
$151$	0.563961	−	0.151113i	0.0458945	−	0.0122974i	0.281693	+	0.959505i	$0.409104\pi$
$152$	−18.4545	−	10.6547i	−1.49685	−	0.864210i
$153$	3.27669	−	5.67540i	0.264905	−	0.458829i
$154$	3.96296	−	3.18921i	0.319344	−	0.256994i
$155$			0.992638i			0.0797306i
$156$	4.97394	+	0.269057i	0.398234	+	0.0215418i
$157$	−9.61395	−	5.55061i	−0.767276	−	0.442987i	0.0646257	−	0.997910i	$-0.479415\pi$
$157$	−9.61395	−	5.55061i	−0.767276	−	0.442987i	−0.831902	+	0.554922i	$0.812748\pi$
$158$	1.63380	+	0.437774i	0.129978	+	0.0348275i
$159$			2.16682i			0.171840i
$160$	6.13322	+	10.6231i	0.484874	+	0.839826i
$161$	10.0556	−	1.56127i	0.792489	−	0.123045i
$162$	−0.759625	−	0.203541i	−0.0596818	−	0.0159917i
$163$	15.9158	−	4.26463i	1.24662	−	0.334031i	0.425592	−	0.904915i	$-0.360066\pi$
$163$	15.9158	−	4.26463i	1.24662	−	0.334031i	0.821031	+	0.570884i	$0.193399\pi$
$164$	−4.07326	−	15.2016i	−0.318068	−	1.18705i
$165$	5.12906			0.399297
$166$	1.69535			0.131584
$167$	0.00245012	+	0.00914399i	0.000189596	+	0.000707583i	0.966021	−	0.258465i	$-0.0832167\pi$
$167$	0.00245012	+	0.00914399i	0.000189596	+	0.000707583i	−0.965831	+	0.259173i	$0.916550\pi$
$168$	0.756757	−	6.99508i	0.0583851	−	0.539682i
$169$	−5.24763	−	11.8938i	−0.403664	−	0.914907i
$170$	−5.40610	−	9.36364i	−0.414629	−	0.718159i
$171$	−2.07394	+	7.74006i	−0.158598	+	0.591897i
$172$	0.646475	+	1.11973i	0.0492933	+	0.0853784i
$173$	10.4806	−	18.1529i	0.796823	−	1.38014i	−0.124852	−	0.992175i	$-0.539846\pi$
$173$	10.4806	−	18.1529i	0.796823	−	1.38014i	0.921675	−	0.387963i	$-0.126821\pi$
$174$	1.39493	+	1.39493i	0.105750	+	0.105750i
$175$	0.572114	−	1.47695i	0.0432478	−	0.111647i
$176$	0.425051	−	1.58631i	0.0320394	−	0.119573i
$177$	−1.43782	+	5.36602i	−0.108073	+	0.403334i
$178$		−	4.95253i		−	0.371208i
$179$	−8.35625	+	4.82448i	−0.624576	+	0.360599i	−0.778648	−	0.627461i	$-0.784094\pi$
$179$	−8.35625	+	4.82448i	−0.624576	+	0.360599i	0.154073	+	0.988060i	$0.450761\pi$
$180$	2.04947	−	2.04947i	0.152758	−	0.152758i
$181$	1.25766			0.0934813			0.0467407	−	0.998907i	$-0.485117\pi$
$181$	1.25766			0.0934813			0.0467407	+	0.998907i	$0.485117\pi$
$182$	−7.01633	+	2.65534i	−0.520085	+	0.196827i
$183$	9.39241			0.694307
$184$	−7.23244	+	7.23244i	−0.533183	+	0.533183i
$185$	−12.8481	+	7.41788i	−0.944614	+	0.545373i
$186$			0.372095i			0.0272833i
$187$	−4.14674	+	15.4759i	−0.303240	+	1.13171i
$188$	−2.60552	+	9.72395i	−0.190027	+	0.709192i
$189$	−2.61443	+	0.405927i	−0.190172	+	0.0295268i
$190$	9.34833	+	9.34833i	0.678199	+	0.678199i
$191$	−1.22251	+	2.11745i	−0.0884578	+	0.153213i	−0.906859	−	0.421433i	$-0.861527\pi$
$191$	−1.22251	+	2.11745i	−0.0884578	+	0.153213i	0.818402	+	0.574647i	$0.194861\pi$
$192$	1.62733	+	2.81862i	0.117442	+	0.203416i
$193$	4.45444	−	16.6242i	0.320638	−	1.19664i	−0.597987	−	0.801506i	$-0.704033\pi$
$193$	4.45444	−	16.6242i	0.320638	−	1.19664i	0.918625	−	0.395131i	$-0.129301\pi$
$194$	−6.34970	−	10.9980i	−0.455882	−	0.789610i
$195$	−7.19007	−	2.34956i	−0.514891	−	0.168256i
$196$	−2.93236	−	9.21550i	−0.209454	−	0.658250i
$197$	6.05858	+	22.6109i	0.431656	+	1.61096i	0.748944	+	0.662634i	$0.230561\pi$
$197$	6.05858	+	22.6109i	0.431656	+	1.61096i	−0.317287	+	0.948329i	$0.602772\pi$
$198$	1.92265			0.136637
$199$	−18.6415			−1.32146			−0.660732	−	0.750622i	$-0.729754\pi$
$199$	−18.6415			−1.32146			−0.660732	+	0.750622i	$0.729754\pi$
$200$	0.412042	+	1.53776i	0.0291357	+	0.108736i
$201$	−11.1395	+	2.98482i	−0.785719	+	0.210533i
$202$	−2.68894	−	0.720500i	−0.189193	−	0.0506942i
$203$	6.18877	+	2.39729i	0.434366	+	0.168257i
$204$	4.52689	+	7.84080i	0.316946	+	0.548966i
$205$			23.8987i			1.66916i
$206$	−6.96172	−	1.86539i	−0.485046	−	0.129968i
$207$	3.33089	+	1.92309i	0.231513	+	0.133664i
$208$	−1.32252	+	2.02903i	−0.0917002	+	0.140688i
$209$		−	19.5905i		−	1.35510i
$210$	−1.57673	+	4.07042i	−0.108804	+	0.280886i
$211$	−5.61294	+	9.72190i	−0.386411	+	0.669283i	−0.991964	−	0.126522i	$-0.959619\pi$
$211$	−5.61294	+	9.72190i	−0.386411	+	0.669283i	0.605553	+	0.795805i	$0.292952\pi$
$212$	−2.59249	−	1.49677i	−0.178053	−	0.102799i
$213$	9.44098	−	2.52970i	0.646885	−	0.173332i
$214$	−1.12195	+	1.12195i	−0.0766950	+	0.0766950i
$215$	−0.508168	−	1.89651i	−0.0346567	−	0.129341i
$216$	1.88042	−	1.88042i	0.127946	−	0.127946i
$217$	0.505682	+	1.14515i	0.0343279	+	0.0777381i
$218$	−3.83579	−	2.21459i	−0.259792	−	0.149991i
$219$	7.17382	+	7.17382i	0.484762	+	0.484762i
$220$	−3.54300	+	6.13666i	−0.238869	+	0.413734i
$221$	12.9023	−	19.7949i	0.867905	−	1.33155i
$222$	−4.81618	+	2.78062i	−0.323241	+	0.186623i
$223$	9.81982	−	2.63121i	0.657584	−	0.176199i	0.0854284	−	0.996344i	$-0.472774\pi$
$223$	9.81982	−	2.63121i	0.657584	−	0.176199i	0.572155	+	0.820145i	$0.306107\pi$
$224$	12.4873	+	9.13079i	0.834343	+	0.610076i
$225$	0.518448	−	0.299326i	0.0345632	−	0.0199551i
$226$	−9.42920	−	2.52655i	−0.627221	−	0.168063i
$227$	−4.65548	−	4.65548i	−0.308995	−	0.308995i	0.535524	−	0.844520i	$-0.320114\pi$
$227$	−4.65548	−	4.65548i	−0.308995	−	0.308995i	−0.844520	+	0.535524i	$0.820114\pi$
$228$	−7.82798	−	7.82798i	−0.518420	−	0.518420i
$229$	1.20056	+	0.321690i	0.0793354	+	0.0212578i	0.298268	−	0.954482i	$-0.403591\pi$
$229$	1.20056	+	0.321690i	0.0793354	+	0.0212578i	−0.218933	+	0.975740i	$0.570258\pi$
$230$	5.49552	−	3.17284i	0.362364	−	0.209211i
$231$	5.91712	−	2.61291i	0.389318	−	0.171917i
$232$	−6.44358	+	1.72655i	−0.423042	+	0.113354i
$233$	12.6928	−	7.32822i	0.831536	−	0.480088i	−0.0228423	−	0.999739i	$-0.507272\pi$
$233$	12.6928	−	7.32822i	0.831536	−	0.480088i	0.854378	+	0.519652i	$0.173938\pi$
$234$	−2.69523	−	0.880744i	−0.176193	−	0.0575760i
$235$	7.64360	−	13.2391i	0.498614	−	0.863624i
$236$	−5.42696	−	5.42696i	−0.353265	−	0.353265i
$237$	1.86264	+	1.07540i	0.120992	+	0.0698545i
$238$	−11.0069	−	8.04829i	−0.713470	−	0.521693i
$239$	−4.85743	+	4.85743i	−0.314201	+	0.314201i	−0.846535	−	0.532334i	$-0.821315\pi$
$239$	−4.85743	+	4.85743i	−0.314201	+	0.314201i	0.532334	+	0.846535i	$0.321315\pi$
$240$	0.364744	+	1.36124i	0.0235441	+	0.0878679i
$241$	−13.5158	+	13.5158i	−0.870627	+	0.870627i	−0.992541	−	0.121914i	$-0.961097\pi$
$241$	−13.5158	+	13.5158i	−0.870627	+	0.870627i	0.121914	+	0.992541i	$0.461097\pi$
$242$	3.81553	−	1.02237i	0.245271	−	0.0657202i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−6.48800	+	11.2375i	−0.415352	+	0.719410i
$245$	0.679246	+	14.6699i	0.0433955	+	0.937223i
$246$			8.95855i			0.571176i
$247$	−8.97418	+	27.4626i	−0.571013	+	1.74740i
$248$	−1.08968	−	0.629127i	−0.0691947	−	0.0399496i
$249$	2.08232	+	0.557955i	0.131961	+	0.0353590i
$250$		−	9.23702i		−	0.584200i
$251$	−1.37023	−	2.37330i	−0.0864880	−	0.149802i	0.819536	−	0.573027i	$-0.194231\pi$
$251$	−1.37023	−	2.37330i	−0.0864880	−	0.149802i	−0.906024	+	0.423226i	$0.860898\pi$
$252$	1.32030	−	3.40843i	0.0831709	−	0.214711i
$253$	−9.08277	−	2.43372i	−0.571029	−	0.153007i
$254$	−7.94215	+	2.12809i	−0.498335	+	0.133528i
$255$	−3.55840	−	13.2801i	−0.222836	−	0.831634i
$256$	−13.6927			−0.855794
$257$	−10.9615			−0.683758			−0.341879	−	0.939744i	$-0.611063\pi$
$257$	−10.9615			−0.683758			−0.341879	+	0.939744i	$0.611063\pi$
$258$	−0.190489	−	0.710914i	−0.0118593	−	0.0442596i
$259$	−11.0433	+	15.1029i	−0.686198	+	0.938447i
$260$	7.77782	−	6.97955i	0.482360	−	0.432853i
$261$	1.25425	+	2.17242i	0.0776360	+	0.134469i
$262$	4.24649	−	15.8481i	0.262349	−	0.979100i
$263$	11.0595	+	19.1556i	0.681958	+	1.18119i	0.974383	+	0.224897i	$0.0722046\pi$
$263$	11.0595	+	19.1556i	0.681958	+	1.18119i	−0.292425	+	0.956289i	$0.594462\pi$
$264$	−3.25076	+	5.63048i	−0.200071	+	0.346532i
$265$	3.21440	+	3.21440i	0.197459	+	0.197459i
$266$	15.5470	+	6.02233i	0.953249	+	0.369252i
$267$	1.62993	−	6.08297i	0.0997498	−	0.372271i
$268$	4.12365	−	15.3897i	0.251892	−	0.940073i
$269$			9.12867i			0.556585i	0.960496	+	0.278292i	$0.0897684\pi$
$269$			9.12867i			0.556585i	−0.960496	+	0.278292i	$0.910232\pi$
$270$	−1.42882	+	0.824932i	−0.0869555	+	0.0502038i
$271$	13.7284	−	13.7284i	0.833942	−	0.833942i	−0.154112	−	0.988053i	$-0.549252\pi$
$271$	13.7284	−	13.7284i	0.833942	−	0.833942i	0.988053	+	0.154112i	$0.0492516\pi$
$272$	−4.40216			−0.266920
$273$	−9.49174	+	0.952290i	−0.574466	+	0.0576352i
$274$	8.86600			0.535614
$275$	−1.03491	+	1.03491i	−0.0624077	+	0.0624077i
$276$	−4.60176	+	2.65683i	−0.276994	+	0.159922i
$277$			28.0822i			1.68730i	0.536896	+	0.843649i	$0.319597\pi$
$277$			28.0822i			1.68730i	−0.536896	+	0.843649i	$0.680403\pi$
$278$	−2.07604	+	7.74789i	−0.124513	+	0.464688i
$279$	−0.122460	+	0.457027i	−0.00733149	+	0.0273615i
$280$	−9.25434	−	11.4996i	−0.553053	−	0.687232i
$281$	3.79779	+	3.79779i	0.226557	+	0.226557i	0.811253	−	0.584695i	$-0.198786\pi$
$281$	3.79779	+	3.79779i	0.226557	+	0.226557i	−0.584695	+	0.811253i	$0.698786\pi$
$282$	2.86524	−	4.96274i	0.170622	−	0.295527i
$283$	0.692540	+	1.19951i	0.0411672	+	0.0713037i	0.885875	−	0.463924i	$-0.153559\pi$
$283$	0.692540	+	1.19951i	0.0411672	+	0.0713037i	−0.844708	+	0.535228i	$0.820226\pi$
$284$	−3.49489	+	13.0431i	−0.207383	+	0.773966i
$285$	8.40550	+	14.5588i	0.497899	+	0.862386i
$286$	6.92210	+	0.374439i	0.409312	+	0.0221410i
$287$	12.1748	+	27.5707i	0.718655	+	1.62745i
$288$	1.51329	+	5.64767i	0.0891715	+	0.332792i
$289$	25.9469			1.52629
$290$	4.13868			0.243032
$291$	−4.17950	−	15.5981i	−0.245006	−	0.914376i
$292$	−13.5386	+	3.62765i	−0.792286	+	0.212292i
$293$	−17.3288	−	4.64324i	−1.01236	−	0.271261i	−0.285745	−	0.958306i	$-0.592241\pi$
$293$	−17.3288	−	4.64324i	−1.01236	−	0.271261i	−0.726615	+	0.687045i	$0.758908\pi$
$294$	0.254618	+	5.49906i	0.0148497	+	0.320712i
$295$	5.82735	+	10.0933i	0.339281	+	0.587653i
$296$		−	18.8056i		−	1.09305i
$297$	2.36150	+	0.632763i	0.137028	+	0.0367166i
$298$	−3.20478	−	1.85028i	−0.185648	−	0.107184i
$299$	11.6176	+	7.57237i	0.671866	+	0.437922i
$300$			0.827063i			0.0477505i
$301$	−1.55239	−	1.92902i	−0.0894782	−	0.111187i
$302$	0.229578	−	0.397641i	0.0132107	−	0.0228817i
$303$	−3.06558	−	1.76991i	−0.176113	−	0.101679i
$304$	5.19929	−	1.39315i	0.298200	−	0.0799024i
$305$	13.9333	−	13.9333i	0.797820	−	0.797820i
$306$	−1.33388	−	4.97812i	−0.0762530	−	0.284580i
$307$	−5.47242	+	5.47242i	−0.312327	+	0.312327i	−0.845811	−	0.533483i	$-0.820883\pi$
$307$	−5.47242	+	5.47242i	−0.312327	+	0.312327i	0.533483	+	0.845811i	$0.320883\pi$
$308$	−0.961159	+	8.88446i	−0.0547671	+	0.506239i
$309$	−7.93684	−	4.58234i	−0.451511	−	0.260680i
$310$	0.551990	+	0.551990i	0.0313509	+	0.0313509i
$311$	3.27357	−	5.66998i	0.185627	−	0.321515i	−0.758161	−	0.652068i	$-0.773902\pi$
$311$	3.27357	−	5.66998i	0.185627	−	0.321515i	0.943788	+	0.330553i	$0.107235\pi$
$312$	7.13627	−	6.40384i	0.404012	−	0.362546i
$313$	−14.8538	+	8.57583i	−0.839585	+	0.484735i	−0.857123	−	0.515111i	$-0.827751\pi$
$313$	−14.8538	+	8.57583i	−0.839585	+	0.484735i	0.0175379	+	0.999846i	$0.494417\pi$
$314$	−8.43277	+	2.25955i	−0.475889	+	0.127514i
$315$	−3.27624	+	4.48059i	−0.184595	+	0.252453i
$316$	−2.57332	+	1.48570i	−0.144760	+	0.0835774i
$317$	−15.5081	−	4.15537i	−0.871019	−	0.233389i	−0.204491	−	0.978869i	$-0.565554\pi$
$317$	−15.5081	−	4.15537i	−0.871019	−	0.233389i	−0.666528	+	0.745480i	$0.732220\pi$
$318$	1.20493	+	1.20493i	0.0675693	+	0.0675693i
$319$	−4.33654	−	4.33654i	−0.242800	−	0.242800i
$320$	6.59541	+	1.76723i	0.368695	+	0.0987914i
$321$	−1.74729	+	1.00880i	−0.0975240	+	0.0563055i
$322$	4.72354	−	6.45993i	0.263233	−	0.359998i
$323$	−50.7236	+	13.5914i	−2.82234	+	0.756243i
$324$	1.19645	−	0.690770i	0.0664694	−	0.0383761i
$325$	1.92486	−	0.976692i	0.106772	−	0.0541771i
$326$	6.47904	−	11.2220i	0.358841	−	0.621530i
$327$	−3.98248	−	3.98248i	−0.220231	−	0.220231i
$328$	−26.2351	−	15.1468i	−1.44859	−	0.836345i
$329$	2.07358	−	19.1672i	0.114320	−	1.05672i
$330$	2.85219	−	2.85219i	0.157008	−	0.157008i
$331$	−1.47690	−	5.51186i	−0.0811776	−	0.302959i	0.913385	−	0.407096i	$-0.133459\pi$
$331$	−1.47690	−	5.51186i	−0.0811776	−	0.302959i	−0.994563	+	0.104137i	$0.966792\pi$
$332$	−2.10597	+	2.10597i	−0.115580	+	0.115580i
$333$	−6.83063	+	1.83026i	−0.374316	+	0.100298i
$334$	0.00644730	+	0.00372235i	0.000352781	+	0.000203678i
$335$	−12.0972	+	20.9529i	−0.660940	+	1.14478i
$336$	1.11425	+	1.38458i	0.0607872	+	0.0755351i
$337$		−	6.54996i		−	0.356799i	−0.983958	−	0.178399i	$-0.942908\pi$
$337$		−	6.54996i		−	0.356799i	0.983958	−	0.178399i	$-0.0570919\pi$
$338$	−9.53207	−	3.69583i	−0.518476	−	0.201027i
$339$	−10.7499	−	6.20648i	−0.583857	−	0.337090i
$340$	18.3471	+	4.91608i	0.995009	+	0.266612i
$341$		−	1.15676i		−	0.0626420i
$342$	3.15084	+	5.45741i	0.170378	+	0.295103i
$343$	8.25691	+	16.5778i	0.445831	+	0.895117i
$344$	2.40399	+	0.644146i	0.129614	+	0.0347300i
$345$	7.79411	−	2.08842i	0.419621	−	0.112437i
$346$	−4.26645	−	15.9226i	−0.229366	−	0.856005i
$347$	−22.8051			−1.22424			−0.612120	−	0.790765i	$-0.709683\pi$
$347$	−22.8051			−1.22424			−0.612120	+	0.790765i	$0.709683\pi$
$348$	−3.46559			−0.185775
$349$	−0.529316	−	1.97543i	−0.0283336	−	0.105743i	0.950311	−	0.311302i	$-0.100765\pi$
$349$	−0.529316	−	1.97543i	−0.0283336	−	0.105743i	−0.978645	+	0.205560i	$0.934099\pi$
$350$	−0.503164	−	1.13945i	−0.0268953	−	0.0609062i
$351$	−3.02057	−	1.96880i	−0.161226	−	0.105087i
$352$	−7.14728	−	12.3795i	−0.380951	−	0.659827i
$353$	6.69454	−	24.9843i	0.356314	−	1.32978i	−0.522508	−	0.852634i	$-0.675004\pi$
$353$	6.69454	−	24.9843i	0.356314	−	1.32978i	0.878823	−	0.477149i	$-0.158330\pi$
$354$	2.18441	+	3.78350i	0.116100	+	0.201091i
$355$	10.2527	−	17.7581i	0.544154	−	0.942503i
$356$	6.15206	+	6.15206i	0.326058	+	0.326058i
$357$	−10.8705	−	13.5078i	−0.575326	−	0.714910i
$358$	−1.96396	+	7.32960i	−0.103798	+	0.387381i
$359$	−3.89528	+	14.5374i	−0.205585	+	0.767255i	0.783685	+	0.621158i	$0.213338\pi$
$359$	−3.89528	+	14.5374i	−0.205585	+	0.767255i	−0.989270	+	0.146096i	$0.953329\pi$
$360$		−	5.57908i		−	0.294044i
$361$	39.1529	−	22.6049i	2.06068	−	1.18973i
$362$	0.699366	−	0.699366i	0.0367579	−	0.0367579i
$363$	5.02291			0.263634
$364$	5.41725	−	12.0142i	0.283941	−	0.629715i
$365$	21.2843			1.11407
$366$	5.22297	−	5.22297i	0.273009	−	0.273009i
$367$	13.2477	−	7.64858i	0.691526	−	0.399253i	−0.112657	−	0.993634i	$-0.535936\pi$
$367$	13.2477	−	7.64858i	0.691526	−	0.399253i	0.804184	+	0.594381i	$0.202603\pi$
$368$		−	2.58362i		−	0.134681i
$369$	−2.94834	+	11.0034i	−0.153485	+	0.572813i
$370$	−3.01968	+	11.2696i	−0.156986	+	0.585879i
$371$	5.34581	+	2.07076i	0.277540	+	0.107509i
$372$	−0.462218	−	0.462218i	−0.0239649	−	0.0239649i
$373$	10.2210	−	17.7032i	0.529221	−	0.916638i	−0.470198	−	0.882561i	$-0.655817\pi$
$373$	10.2210	−	17.7032i	0.529221	−	0.916638i	0.999419	−	0.0340771i	$-0.0108492\pi$
$374$	6.29994	+	10.9118i	0.325762	+	0.564237i
$375$	3.03999	−	11.3454i	0.156985	−	0.585874i
$376$	9.68892	+	16.7817i	0.499668	+	0.865450i
$377$	4.09257	+	8.06561i	0.210778	+	0.415400i
$378$	−1.22811	+	1.67957i	−0.0631672	+	0.0863878i
$379$	−1.64237	−	6.12940i	−0.0843628	−	0.314846i	0.910830	−	0.412782i	$-0.135443\pi$
$379$	−1.64237	−	6.12940i	−0.0843628	−	0.314846i	−0.995193	+	0.0979355i	$0.968776\pi$
$380$	−23.2251			−1.19142
$381$	−10.4554			−0.535644
$382$	0.497662	+	1.85730i	0.0254626	+	0.0950277i
$383$	−6.04679	+	1.62023i	−0.308976	+	0.0827899i	−0.409975	−	0.912097i	$-0.634463\pi$
$383$	−6.04679	+	1.62023i	−0.308976	+	0.0827899i	0.100999	+	0.994887i	$0.467796\pi$
$384$	−8.82303	−	2.36412i	−0.450248	−	0.120644i
$385$	4.90169	−	12.6540i	0.249813	−	0.644909i
$386$	−6.76741	−	11.7215i	−0.344452	−	0.596609i
$387$		−	0.935875i		−	0.0475732i
$388$	21.5494	+	5.77414i	1.09400	+	0.293138i
$389$	4.72095	+	2.72564i	0.239362	+	0.138196i	0.614883	−	0.788618i	$-0.289203\pi$
$389$	4.72095	+	2.72564i	0.239362	+	0.138196i	−0.375522	+	0.926814i	$0.622536\pi$
$390$	−5.30484	+	2.69173i	−0.268621	+	0.136301i
$391$			25.2055i			1.27470i
$392$	−16.5345	−	8.55200i	−0.835118	−	0.431941i
$393$	10.4315	−	18.0680i	0.526201	−	0.911408i
$394$	15.9427	+	9.20450i	0.803180	+	0.463716i
$395$	4.35848	−	1.16785i	0.219299	−	0.0587610i
$396$	−2.38833	+	2.38833i	−0.120018	+	0.120018i
$397$	2.48129	+	9.26032i	0.124533	+	0.464762i	0.999823	−	0.0188365i	$-0.00599620\pi$
$397$	2.48129	+	9.26032i	0.124533	+	0.464762i	−0.875290	+	0.483598i	$0.839330\pi$
$398$	−10.3663	+	10.3663i	−0.519614	+	0.519614i
$399$	17.1137	+	12.5136i	0.856756	+	0.626465i
$400$	−0.348261	−	0.201069i	−0.0174130	−	0.0100534i
$401$	26.5226	+	26.5226i	1.32447	+	1.32447i	0.910112	+	0.414362i	$0.135995\pi$
$401$	26.5226	+	26.5226i	1.32447	+	1.32447i	0.414362	+	0.910112i	$0.364005\pi$
$402$	−4.53468	+	7.85430i	−0.226169	+	0.391737i
$403$	−0.529898	+	1.62158i	−0.0263961	+	0.0807766i
$404$	4.23523	−	2.44521i	0.210710	−	0.121654i
$405$	−2.02645	+	0.542987i	−0.100695	+	0.0269812i
$406$	4.77457	−	2.10838i	0.236958	−	0.104637i
$407$	14.9724	−	8.64434i	0.742156	−	0.428484i
$408$	16.8337	+	4.51058i	0.833393	+	0.223307i
$409$	−21.7339	−	21.7339i	−1.07467	−	1.07467i	−0.996977	−	0.0776962i	$-0.975244\pi$
$409$	−21.7339	−	21.7339i	−1.07467	−	1.07467i	−0.0776962	−	0.996977i	$-0.524756\pi$
$410$	13.2897	+	13.2897i	0.656332	+	0.656332i
$411$	10.8897	+	2.91789i	0.537149	+	0.143929i
$412$	10.9651	−	6.33069i	0.540210	−	0.311891i
$413$	11.8645	+	8.67542i	0.583816	+	0.426889i
$414$	2.92166	−	0.782855i	0.143592	−	0.0384752i
$415$	3.91676	−	2.26134i	0.192266	−	0.111005i
$416$	4.34839	+	20.6280i	0.213197	+	1.01137i
$417$	−5.09981	+	8.83314i	−0.249739	+	0.432561i
$418$	−10.8940	−	10.8940i	−0.532842	−	0.532842i
$419$	20.2493	+	11.6909i	0.989241	+	0.571138i	0.905047	−	0.425311i	$-0.139835\pi$
$419$	20.2493	+	11.6909i	0.989241	+	0.571138i	0.0841936	+	0.996449i	$0.473169\pi$
$420$	−3.09768	−	7.01491i	−0.151151	−	0.342293i
$421$	14.1492	−	14.1492i	0.689589	−	0.689589i	−0.272552	−	0.962141i	$-0.587868\pi$
$421$	14.1492	−	14.1492i	0.689589	−	0.689589i	0.962141	+	0.272552i	$0.0878676\pi$
$422$	2.28493	+	8.52747i	0.111229	+	0.415111i
$423$	5.15253	−	5.15253i	0.250524	−	0.250524i
$424$	−5.56591	+	1.49138i	−0.270305	+	0.0724279i
$425$	3.39759	+	1.96160i	0.164807	+	0.0951516i
$426$	3.84325	−	6.65671i	0.186206	−	0.322518i
$427$	8.97605	−	23.1722i	0.434382	−	1.12138i
$428$		−	2.78739i		−	0.134733i
$429$	8.37886	+	2.73804i	0.404535	+	0.132194i
$430$	−1.33720	−	0.772034i	−0.0644856	−	0.0372308i
$431$	−12.7388	−	3.41335i	−0.613606	−	0.164415i	−0.0613869	−	0.998114i	$-0.519552\pi$
$431$	−12.7388	−	3.41335i	−0.613606	−	0.164415i	−0.552220	+	0.833699i	$0.686219\pi$
$432$			0.671737i			0.0323190i
$433$	−5.53868	−	9.59327i	−0.266172	−	0.461023i	0.701698	−	0.712474i	$-0.252426\pi$
$433$	−5.53868	−	9.59327i	−0.266172	−	0.461023i	−0.967870	+	0.251451i	$0.919092\pi$
$434$	0.918003	+	0.355600i	0.0440656	+	0.0170693i
$435$	5.08335	+	1.36208i	0.243728	+	0.0653067i
$436$	7.51581	−	2.01385i	0.359942	−	0.0964462i
$437$	−7.97676	−	29.7697i	−0.381580	−	1.42408i
$438$	7.97850			0.381227
$439$	13.2330			0.631578			0.315789	−	0.948829i	$-0.397731\pi$
$439$	13.2330			0.631578			0.315789	+	0.948829i	$0.397731\pi$
$440$	3.53024	+	13.1750i	0.168298	+	0.628095i
$441$	−1.49706	+	6.83804i	−0.0712885	+	0.325621i
$442$	−3.83287	−	18.1824i	−0.182311	−	0.864850i
$443$	2.45582	+	4.25360i	0.116679	+	0.202095i	0.918450	−	0.395537i	$-0.129442\pi$
$443$	2.45582	+	4.25360i	0.116679	+	0.202095i	−0.801770	+	0.597632i	$0.796108\pi$
$444$	2.52858	−	9.43679i	0.120001	−	0.447850i
$445$	−6.60594	−	11.4418i	−0.313151	−	0.542394i
$446$	3.99747	−	6.92382i	0.189286	−	0.327852i
$447$	−3.32734	−	3.32734i	−0.157378	−	0.157378i
$448$	8.50906	−	1.32115i	0.402015	−	0.0624186i
$449$	0.246197	−	0.918821i	0.0116188	−	0.0433618i	−0.959873	−	0.280435i	$-0.909521\pi$
$449$	0.246197	−	0.918821i	0.0116188	−	0.0433618i	0.971492	+	0.237073i	$0.0761880\pi$
$450$	0.121850	−	0.454751i	0.00574407	−	0.0214372i
$451$		−	27.8501i		−	1.31141i
$452$	14.8515	−	8.57451i	0.698555	−	0.403311i
$453$	0.412848	−	0.412848i	0.0193973	−	0.0193973i
$454$	−5.17768			−0.243001
$455$	−12.6680	+	15.4934i	−0.593885	+	0.726341i
$456$	−21.3094			−0.997903
$457$	−13.6046	+	13.6046i	−0.636394	+	0.636394i	−0.949664	−	0.313270i	$-0.898576\pi$
$457$	−13.6046	+	13.6046i	−0.636394	+	0.636394i	0.313270	+	0.949664i	$0.398576\pi$
$458$	0.846500	−	0.488727i	0.0395543	−	0.0228367i
$459$		−	6.55339i		−	0.305886i
$460$	−2.88524	+	10.7679i	−0.134525	+	0.502055i
$461$	1.66867	−	6.22758i	0.0777179	−	0.290047i	−0.916118	−	0.400909i	$-0.868694\pi$
$461$	1.66867	−	6.22758i	0.0777179	−	0.290047i	0.993836	+	0.110862i	$0.0353610\pi$
$462$	1.83742	−	4.74342i	0.0854845	−	0.220684i
$463$	7.67988	+	7.67988i	0.356914	+	0.356914i	0.862674	−	0.505760i	$-0.168788\pi$
$463$	7.67988	+	7.67988i	0.356914	+	0.356914i	−0.505760	+	0.862674i	$0.668788\pi$
$464$	0.842525	−	1.45930i	0.0391132	−	0.0677461i
$465$	0.496319	+	0.859649i	0.0230162	+	0.0398653i
$466$	2.98318	−	11.1334i	0.138193	−	0.515745i
$467$	−10.7238	−	18.5741i	−0.496236	−	0.859507i	0.503754	−	0.863847i	$-0.331952\pi$
$467$	−10.7238	−	18.5741i	−0.496236	−	0.859507i	−0.999991	+	0.00434034i	$0.998618\pi$
$468$	4.44209	−	2.25396i	0.205336	−	0.104189i
$469$	−3.28177	+	30.3350i	−0.151538	+	1.40074i
$470$	−3.11157	−	11.6125i	−0.143526	−	0.535647i
$471$	−11.1012			−0.511518
$472$	−14.7733			−0.679997
$473$	0.592187	+	2.21007i	0.0272288	+	0.101619i
$474$	1.63380	−	0.437774i	0.0750428	−	0.0201076i
$475$	−4.63361	−	1.24157i	−0.212604	−	0.0569672i
$476$	23.6704	−	3.67517i	1.08493	−	0.168451i
$477$	1.08341	+	1.87652i	0.0496059	+	0.0859199i
$478$			5.40228i			0.247095i
$479$	−17.4860	−	4.68536i	−0.798956	−	0.214080i	−0.163831	−	0.986489i	$-0.552385\pi$
$479$	−17.4860	−	4.68536i	−0.798956	−	0.214080i	−0.635126	+	0.772409i	$0.719052\pi$
$480$	10.6231	+	6.13322i	0.484874	+	0.279942i
$481$	−24.9487	+	5.25920i	−1.13756	+	0.239799i
$482$			15.0318i			0.684680i
$483$	7.92773	−	6.37988i	0.360724	−	0.290294i
$484$	−3.46968	+	6.00966i	−0.157713	+	0.273166i
$485$	−29.3394	−	16.9391i	−1.33223	−	0.769165i
$486$	−0.759625	+	0.203541i	−0.0344573	+	0.00923280i
$487$	5.09200	−	5.09200i	0.230740	−	0.230740i	−0.582261	−	0.813002i	$-0.697832\pi$
$487$	5.09200	−	5.09200i	0.230740	−	0.230740i	0.813002	+	0.582261i	$0.197832\pi$
$488$	6.46463	+	24.1263i	0.292640	+	1.09215i
$489$	11.6512	−	11.6512i	0.526885	−	0.526885i
$490$	8.53539	+	7.77996i	0.385590	+	0.351463i
$491$	−24.3966	−	14.0854i	−1.10101	−	0.635666i	−0.164520	−	0.986374i	$-0.552608\pi$
$491$	−24.3966	−	14.0854i	−1.10101	−	0.635666i	−0.936485	+	0.350708i	$0.885941\pi$
$492$	−11.1284	−	11.1284i	−0.501705	−	0.501705i
$493$	−8.21957	+	14.2367i	−0.370191	+	0.641190i
$494$	10.2811	+	20.2619i	0.462568	+	0.911625i
$495$	4.44190	−	2.56453i	0.199648	−	0.115267i
$496$	0.307002	−	0.0822609i	0.0137848	−	0.00369362i
$497$	2.78138	−	25.7096i	0.124762	−	1.15323i
$498$	1.46821	−	0.847673i	0.0657922	−	0.0379852i
$499$	−20.3207	−	5.44491i	−0.909678	−	0.243748i	−0.226510	−	0.974009i	$-0.572732\pi$
$499$	−20.3207	−	5.44491i	−0.909678	−	0.243748i	−0.683168	+	0.730261i	$0.739398\pi$
$500$	11.4743	+	11.4743i	0.513145	+	0.513145i
$501$	0.00669386	+	0.00669386i	0.000299060	+	0.000299060i
$502$	−2.08172	−	0.557794i	−0.0929116	−	0.0248956i
$503$	−18.9822	+	10.9594i	−0.846374	+	0.488655i	−0.859426	−	0.511260i	$-0.829179\pi$
$503$	−18.9822	+	10.9594i	−0.846374	+	0.488655i	0.0130514	+	0.999915i	$0.495845\pi$
$504$	−2.84217	−	6.43629i	−0.126600	−	0.286695i
$505$	−7.17330	+	1.92208i	−0.319208	+	0.0855314i
$506$	−6.40414	+	3.69743i	−0.284699	+	0.164371i
$507$	−10.4915	−	7.67652i	−0.465943	−	0.340926i
$508$	7.22226	−	12.5093i	0.320436	−	0.555011i
$509$	−2.12967	−	2.12967i	−0.0943961	−	0.0943961i	0.658332	−	0.752728i	$-0.271262\pi$
$509$	−2.12967	−	2.12967i	−0.0943961	−	0.0943961i	−0.752728	+	0.658332i	$0.771262\pi$
$510$	−9.36364	−	5.40610i	−0.414629	−	0.239386i
$511$	24.5545	−	10.8429i	1.08623	−	0.479661i
$512$	5.30352	−	5.30352i	0.234385	−	0.234385i
$513$	2.07394	+	7.74006i	0.0915668	+	0.341732i
$514$	−6.09550	+	6.09550i	−0.268861	+	0.268861i
$515$	−18.5718	+	4.97630i	−0.818371	+	0.219282i
$516$	1.11973	+	0.646475i	0.0492933	+	0.0284595i
$517$	−8.90738	+	15.4280i	−0.391746	+	0.678525i
$518$	2.25746	+	14.5395i	0.0991871	+	0.638828i
$519$		−	20.9611i		−	0.920092i
$520$	1.08653	−	20.0863i	0.0476476	−	0.880843i
$521$	20.7786	+	11.9965i	0.910328	+	0.525578i	0.880537	−	0.473978i	$-0.157182\pi$
$521$	20.7786	+	11.9965i	0.910328	+	0.525578i	0.0297912	+	0.999556i	$0.490516\pi$
$522$	1.90552	+	0.510581i	0.0834022	+	0.0223475i
$523$		−	9.58298i		−	0.419034i	−0.977805	−	0.209517i	$-0.932811\pi$
$523$		−	9.58298i		−	0.419034i	0.977805	−	0.209517i	$-0.0671892\pi$
$524$	14.4116	+	24.9616i	0.629573	+	1.09045i
$525$	−0.243009	−	1.56513i	−0.0106058	−	0.0683080i
$526$	16.8021	+	4.50212i	0.732608	+	0.196302i
$527$	−2.99507	+	0.802528i	−0.130467	+	0.0349587i
$528$	−0.425051	−	1.58631i	−0.0184980	−	0.0690353i
$529$	8.20689			0.356821
$530$	3.57496			0.155286
$531$	1.43782	+	5.36602i	0.0623961	+	0.232865i
$532$	−26.7935	+	11.8316i	−1.16165	+	0.512966i
$533$	−12.7578	+	39.0411i	−0.552602	+	1.69106i
$534$	−2.47626	−	4.28902i	−0.107158	−	0.185604i
$535$	−1.09553	+	4.08856i	−0.0473637	+	0.176764i
$536$	−15.3342	−	26.5596i	−0.662337	−	1.14720i
$537$	−4.82448	+	8.35625i	−0.208192	+	0.360599i
$538$	5.07631	+	5.07631i	0.218855	+	0.218855i
$539$	−0.791552	−	17.0953i	−0.0340946	−	0.736349i
$540$	0.750158	−	2.79963i	0.0322817	−	0.120477i
$541$	−5.61424	+	20.9526i	−0.241375	+	0.900823i	0.733796	+	0.679370i	$0.237747\pi$
$541$	−5.61424	+	20.9526i	−0.241375	+	0.900823i	−0.975171	+	0.221454i	$0.928920\pi$
$542$		−	15.2683i		−	0.655830i
$543$	1.08917	−	0.628831i	0.0467407	−	0.0269857i
$544$	−27.0942	+	27.0942i	−1.16166	+	1.16166i
$545$	−11.8157			−0.506131
$546$	−4.74865	+	5.80776i	−0.203224	+	0.248549i
$547$	−24.6132			−1.05238			−0.526191	−	0.850366i	$-0.676380\pi$
$547$	−24.6132			−1.05238			−0.526191	+	0.850366i	$0.676380\pi$
$548$	−11.0134	+	11.0134i	−0.470468	+	0.470468i
$549$	8.13407	−	4.69621i	0.347154	−	0.200429i
$550$			1.15100i			0.0490788i
$551$	5.20248	−	19.4159i	0.221633	−	0.827146i
$552$	−2.64726	+	9.87970i	−0.112675	+	0.420508i
$553$	4.43321	−	3.56764i	0.188519	−	0.151712i
$554$	15.6161	+	15.6161i	0.663464	+	0.663464i
$555$	−7.41788	+	12.8481i	−0.314871	+	0.545373i
$556$	−7.04560	−	12.2033i	−0.298800	−	0.517537i
$557$	0.132844	−	0.495782i	0.00562880	−	0.0210070i	−0.963054	−	0.269307i	$-0.913205\pi$
$557$	0.132844	−	0.495782i	0.00562880	−	0.0210070i	0.968683	+	0.248300i	$0.0798720\pi$
$558$	0.186047	+	0.322243i	0.00787601	+	0.0136416i
$559$	0.182263	−	3.36942i	0.00770889	−	0.142511i
$560$	3.70693	+	0.401032i	0.156646	+	0.0169467i
$561$	4.14674	+	15.4759i	0.175076	+	0.653391i
$562$	4.22379			0.178170
$563$	−43.2008			−1.82070			−0.910349	−	0.413842i	$-0.864187\pi$
$563$	−43.2008			−1.82070			−0.910349	+	0.413842i	$0.864187\pi$
$564$	2.60552	+	9.72395i	0.109712	+	0.409452i
$565$	−25.1543	+	6.74007i	−1.05825	+	0.283557i
$566$	1.05214	+	0.281920i	0.0442248	+	0.0118500i
$567$	−2.06120	+	1.65876i	−0.0865621	+	0.0696612i
$568$	12.9961	+	22.5099i	0.545305	+	0.944496i
$569$			30.7249i			1.28805i	0.765003	+	0.644027i	$0.222737\pi$
$569$			30.7249i			1.28805i	−0.765003	+	0.644027i	$0.777263\pi$
$570$	12.7701	+	3.42173i	0.534879	+	0.143320i
$571$	18.1885	+	10.5012i	0.761167	+	0.439460i	0.829715	−	0.558188i	$-0.188503\pi$
$571$	18.1885	+	10.5012i	0.761167	+	0.439460i	−0.0685475	+	0.997648i	$0.521836\pi$
$572$	−9.06379	+	8.13353i	−0.378976	+	0.340080i
$573$			2.44502i			0.102142i
$574$	22.1018	+	8.56142i	0.922513	+	0.357347i
$575$	−1.15126	+	1.99405i	−0.0480110	+	0.0831574i
$576$	2.81862	+	1.62733i	0.117442	+	0.0678054i
$577$	−8.56673	+	2.29545i	−0.356638	+	0.0955608i	−0.432689	−	0.901543i	$-0.642435\pi$
$577$	−8.56673	+	2.29545i	−0.356638	+	0.0955608i	0.0760516	+	0.997104i	$0.475769\pi$
$578$	14.4287	−	14.4287i	0.600153	−	0.600153i
$579$	−4.45444	−	16.6242i	−0.185120	−	0.690878i
$580$	−5.14109	+	5.14109i	−0.213472	+	0.213472i
$581$	3.36655	−	4.60411i	0.139668	−	0.191011i
$582$	−10.9980	−	6.34970i	−0.455882	−	0.263203i
$583$	−3.74587	−	3.74587i	−0.155138	−	0.155138i
$584$	−13.4898	+	23.3650i	−0.558212	+	0.966852i
$585$	−7.40156	+	1.56025i	−0.306017	+	0.0645086i
$586$	−12.2183	+	7.05424i	−0.504734	+	0.291408i
$587$	30.5954	−	8.19801i	1.26281	−	0.338368i	0.435536	−	0.900171i	$-0.356559\pi$
$587$	30.5954	−	8.19801i	1.26281	−	0.338368i	0.827271	+	0.561803i	$0.189892\pi$
$588$	−7.14725	−	6.51467i	−0.294748	−	0.268661i
$589$	3.28344	−	1.89570i	0.135292	−	0.0781108i
$590$	8.85320	+	2.37221i	0.364480	+	0.0976622i
$591$	16.5524	+	16.5524i	0.680873	+	0.680873i
$592$	3.35893	+	3.35893i	0.138051	+	0.138051i
$593$	−5.48978	−	1.47098i	−0.225438	−	0.0604060i	0.144332	−	0.989529i	$-0.453897\pi$
$593$	−5.48978	−	1.47098i	−0.225438	−	0.0604060i	−0.369770	+	0.929123i	$0.620563\pi$
$594$	1.66506	−	0.961326i	0.0683184	−	0.0394437i
$595$	−36.1644	−	3.91242i	−1.48260	−	0.160393i
$596$	6.27941	−	1.68256i	0.257215	−	0.0689205i
$597$	−16.1440	+	9.32077i	−0.660732	+	0.381474i
$598$	10.6713	−	2.24951i	0.436380	−	0.0919892i
$599$	5.44521	−	9.43138i	0.222485	−	0.385356i	−0.733077	−	0.680146i	$-0.761916\pi$
$599$	5.44521	−	9.43138i	0.222485	−	0.385356i	0.955562	+	0.294790i	$0.0952498\pi$
$600$	1.12572	+	1.12572i	0.0459573	+	0.0459573i
$601$	−1.42936	−	0.825243i	−0.0583049	−	0.0336624i	0.470564	−	0.882366i	$-0.344050\pi$
$601$	−1.42936	−	0.825243i	−0.0583049	−	0.0336624i	−0.528869	+	0.848703i	$0.677384\pi$
$602$	−1.93596	−	0.209440i	−0.0789037	−	0.00853614i
$603$	−8.15467	+	8.15467i	−0.332084	+	0.332084i
$604$	0.208769	+	0.779135i	0.00849468	+	0.0317026i
$605$	7.45132	−	7.45132i	0.302939	−	0.302939i
$606$	−2.68894	+	0.720500i	−0.109231	+	0.0292683i
$607$	22.6877	+	13.0987i	0.920865	+	0.531662i	0.883911	−	0.467655i	$-0.154901\pi$
$607$	22.6877	+	13.0987i	0.920865	+	0.531662i	0.0369540	+	0.999317i	$0.488234\pi$
$608$	23.4259	−	40.5749i	0.950046	−	1.64553i
$609$	6.55828	−	1.01827i	0.265755	−	0.0412622i
$610$		−	15.4962i		−	0.627423i
$611$	19.5540	−	17.5471i	0.791072	−	0.709880i
$612$	7.84080	+	4.52689i	0.316946	+	0.182989i
$613$	22.6882	+	6.07928i	0.916367	+	0.245540i	0.686032	−	0.727571i	$-0.259351\pi$
$613$	22.6882	+	6.07928i	0.916367	+	0.245540i	0.230335	+	0.973111i	$0.426018\pi$
$614$			6.08625i			0.245621i
$615$	11.9494	+	20.6969i	0.481845	+	0.834580i
$616$	10.7844	+	13.4009i	0.434517	+	0.539938i
$617$	−7.41451	−	1.98671i	−0.298497	−	0.0799820i	0.106462	−	0.994317i	$-0.466048\pi$
$617$	−7.41451	−	1.98671i	−0.298497	−	0.0799820i	−0.404959	+	0.914335i	$0.632714\pi$
$618$	−6.96172	+	1.86539i	−0.280041	+	0.0750369i
$619$	−7.36942	−	27.5031i	−0.296202	−	1.10544i	−0.940258	−	0.340463i	$-0.889416\pi$
$619$	−7.36942	−	27.5031i	−0.296202	−	1.10544i	0.644056	−	0.764978i	$-0.277250\pi$
$620$	−1.37137			−0.0550755
$621$	3.84618			0.154342
$622$	−1.33261	−	4.97337i	−0.0534328	−	0.199414i
$623$	−13.4498	−	9.83454i	−0.538853	−	0.394012i
$624$	−0.130822	+	2.41845i	−0.00523706	+	0.0968154i
$625$	−10.8242	−	18.7480i	−0.432967	−	0.749921i
$626$	−3.49107	+	13.0288i	−0.139531	+	0.520737i
$627$	−9.79525	−	16.9659i	−0.391185	−	0.677552i
$628$	7.66840	−	13.2821i	0.306003	−	0.530012i
$629$	−32.7694	−	32.7694i	−1.30660	−	1.30660i
$630$	0.669724	+	4.31345i	0.0266824	+	0.171852i
$631$	−2.62809	+	9.80818i	−0.104623	+	0.390458i	−0.998302	−	0.0582487i	$-0.981448\pi$
$631$	−2.62809	+	9.80818i	−0.104623	+	0.390458i	0.893679	+	0.448706i	$0.148115\pi$
$632$	−1.48035	+	5.52475i	−0.0588852	+	0.219763i
$633$			11.2259i			0.446189i
$634$	−10.9345	+	6.31305i	−0.434265	+	0.250723i
$635$	−15.5102	+	15.5102i	−0.615503	+	0.615503i
$636$	−2.99355			−0.118702
$637$	−6.72156	+	24.3274i	−0.266318	+	0.963885i
$638$	−4.82296			−0.190943
$639$	6.91128	−	6.91128i	0.273406	−	0.273406i
$640$	−16.5958	+	9.58157i	−0.656005	+	0.378745i
$641$			23.1705i			0.915180i	0.889163	+	0.457590i	$0.151287\pi$
$641$			23.1705i			0.915180i	−0.889163	+	0.457590i	$0.848713\pi$
$642$	−0.410663	+	1.53261i	−0.0162076	+	0.0604875i
$643$	6.46488	−	24.1273i	0.254950	−	0.951486i	−0.713168	−	0.700993i	$-0.752741\pi$
$643$	6.46488	−	24.1273i	0.254950	−	0.951486i	0.968118	−	0.250493i	$-0.0805928\pi$
$644$	2.15696	+	13.8922i	0.0849959	+	0.547428i
$645$	−1.38834	−	1.38834i	−0.0546658	−	0.0546658i
$646$	−20.6487	+	35.7646i	−0.812411	+	1.40714i
$647$	2.29221	+	3.97022i	0.0901160	+	0.156085i	0.907560	−	0.419923i	$-0.137943\pi$
$647$	2.29221	+	3.97022i	0.0901160	+	0.156085i	−0.817444	+	0.576008i	$0.804610\pi$
$648$	0.688282	−	2.56870i	0.0270383	−	0.100908i
$649$	−6.79083	−	11.7621i	−0.266564	−	0.461702i
$650$	0.527259	−	1.61350i	0.0206808	−	0.0632869i
$651$	1.01051	+	0.738891i	0.0396050	+	0.0289594i
$652$	5.89176	+	21.9883i	0.230739	+	0.861130i
$653$	−25.4566			−0.996192			−0.498096	−	0.867122i	$-0.665967\pi$
$653$	−25.4566			−0.996192			−0.498096	+	0.867122i	$0.665967\pi$
$654$	−4.42918			−0.173195
$655$	−11.3284	−	42.2780i	−0.442636	−	1.65194i
$656$	7.39138	−	1.98051i	0.288585	−	0.0773260i
$657$	9.79963	+	2.62580i	0.382320	+	0.102442i
$658$	−9.50546	−	11.8116i	−0.370561	−	0.460465i
$659$	−6.21741	−	10.7689i	−0.242196	−	0.419496i	0.719144	−	0.694861i	$-0.244534\pi$
$659$	−6.21741	−	10.7689i	−0.242196	−	0.419496i	−0.961339	+	0.275366i	$0.911201\pi$
$660$			7.08601i			0.275822i
$661$	36.4077	+	9.75540i	1.41609	+	0.379441i	0.884096	−	0.467305i	$-0.154775\pi$
$661$	36.4077	+	9.75540i	1.41609	+	0.379441i	0.531998	+	0.846746i	$0.321442\pi$
$662$	−3.88634	−	2.24378i	−0.151047	−	0.0872069i
$663$	1.27628	−	23.5941i	0.0495666	−	0.916318i
$664$			5.73288i			0.222479i
$665$	43.9511	−	6.82403i	1.70435	−	0.264625i
$666$	−2.78062	+	4.81618i	−0.107747	+	0.186623i
$667$	−8.35552	−	4.82406i	−0.323527	−	0.186788i
$668$	−0.0126328	+	0.00338495i	−0.000488778	+	0.000130968i
$669$	7.18861	−	7.18861i	0.277928	−	0.277928i
$670$	4.92454	+	18.3786i	0.190252	+	0.710029i
$671$	−16.2371	+	16.2371i	−0.626825	+	0.626825i
$672$	15.3797	+	1.66384i	0.593285	+	0.0641841i
$673$	21.1591	+	12.2162i	0.815624	+	0.470901i	0.848905	−	0.528545i	$-0.177262\pi$
$673$	21.1591	+	12.2162i	0.815624	+	0.470901i	−0.0332811	+	0.999446i	$0.510596\pi$
$674$	−3.64233	−	3.64233i	−0.140297	−	0.140297i
$675$	0.299326	−	0.518448i	0.0115211	−	0.0199551i
$676$	16.4318	−	7.24981i	0.631991	−	0.278839i
$677$	−3.00229	+	1.73338i	−0.115388	+	0.0666190i	−0.556583	−	0.830792i	$-0.687888\pi$
$677$	−3.00229	+	1.73338i	−0.115388	+	0.0666190i	0.441195	+	0.897411i	$0.354555\pi$
$678$	−9.42920	+	2.52655i	−0.362126	+	0.0970314i
$679$	−42.4766	−	4.59530i	−1.63010	−	0.176351i
$680$	31.6635	−	18.2810i	1.21424	−	0.701043i
$681$	−6.35951	−	1.70402i	−0.243697	−	0.0652984i
$682$	−0.643255	−	0.643255i	−0.0246315	−	0.0246315i
$683$	26.9394	+	26.9394i	1.03081	+	1.03081i	0.999510	+	0.0312978i	$0.00996401\pi$
$683$	26.9394	+	26.9394i	1.03081	+	1.03081i	0.0312978	+	0.999510i	$0.490036\pi$
$684$	−10.6932	−	2.86524i	−0.408865	−	0.109555i
$685$	20.4831	−	11.8259i	0.782619	−	0.451845i
$686$	13.8102	+	4.62711i	0.527275	+	0.176664i
$687$	1.20056	−	0.321690i	0.0458043	−	0.0122732i
$688$	−0.544437	+	0.314331i	−0.0207565	+	0.0119838i
$689$	3.53513	+	6.96700i	0.134678	+	0.265422i
$690$	3.17284	−	5.49552i	0.120788	−	0.209211i
$691$	15.8802	+	15.8802i	0.604110	+	0.604110i	0.941401	−	0.337290i	$-0.109510\pi$
$691$	15.8802	+	15.8802i	0.604110	+	0.604110i	−0.337290	+	0.941401i	$0.609510\pi$
$692$	25.0789	+	14.4793i	0.953359	+	0.550422i
$693$	3.81792	−	5.22141i	0.145031	−	0.198345i
$694$	−12.6815	+	12.6815i	−0.481384	+	0.481384i
$695$	5.53826	+	20.6691i	0.210078	+	0.784023i
$696$	−4.71703	+	4.71703i	−0.178798	+	0.178798i
$697$	−72.1094	+	19.3217i	−2.73134	+	0.731860i
$698$	−1.39285	−	0.804163i	−0.0527202	−	0.0304380i
$699$	7.32822	−	12.6928i	0.277179	−	0.480088i
$700$	2.04047	+	0.790399i	0.0771223	+	0.0298743i
$701$		−	43.0296i		−	1.62520i	−0.582819	−	0.812602i	$-0.698050\pi$
$701$		−	43.0296i		−	1.62520i	0.582819	−	0.812602i	$-0.301950\pi$
$702$	−2.77451	+	0.584868i	−0.104717	+	0.0220744i
$703$	49.0736	+	28.3327i	1.85085	+	1.06859i
$704$	−7.68589	−	2.05943i	−0.289673	−	0.0776176i
$705$		−	15.2872i		−	0.575749i
$706$	−10.1707	−	17.6161i	−0.382778	−	0.662992i
$707$	−7.29628	+	5.87171i	−0.274405	+	0.220829i
$708$	−7.41337	−	1.98641i	−0.278611	−	0.0746537i
$709$	19.1430	−	5.12936i	0.718932	−	0.192637i	0.119237	−	0.992866i	$-0.461955\pi$
$709$	19.1430	−	5.12936i	0.718932	−	0.192637i	0.599695	+	0.800228i	$0.295288\pi$
$710$	−4.17367	−	15.5763i	−0.156635	−	0.584570i
$711$	2.15079			0.0806610
$712$	16.7472			0.627627
$713$	−0.471003	−	1.75781i	−0.0176392	−	0.0658304i
$714$	−13.5564	−	1.46659i	−0.507335	−	0.0548856i
$715$	16.4916	−	8.36798i	0.616749	−	0.312945i
$716$	−6.66522	−	11.5445i	−0.249091	−	0.431438i
$717$	−1.77794	+	6.63538i	−0.0663985	+	0.247803i
$718$	5.91791	+	10.2501i	0.220854	+	0.382531i
$719$	23.2898	−	40.3391i	0.868563	−	1.50440i	0.00509796	−	0.999987i	$-0.498377\pi$
$719$	23.2898	−	40.3391i	0.868563	−	1.50440i	0.863465	−	0.504408i	$-0.168289\pi$
$720$	0.996500	+	0.996500i	0.0371374	+	0.0371374i
$721$	−18.8902	+	15.2020i	−0.703508	+	0.566151i
$722$	9.20205	−	34.3425i	0.342465	−	1.27810i
$723$	−4.94711	+	18.4629i	−0.183985	+	0.686641i
$724$			1.73751i			0.0645742i
$725$	−1.30052	+	0.750858i	−0.0483003	+	0.0278862i
$726$	2.79316	−	2.79316i	0.103664	−	0.103664i
$727$	38.0896			1.41266			0.706332	−	0.707880i	$-0.250348\pi$
$727$	38.0896			1.41266			0.706332	+	0.707880i	$0.250348\pi$
$728$	−8.97914	−	23.7260i	−0.332789	−	0.879345i
$729$	−1.00000			−0.0370370
$730$	11.8358	−	11.8358i	0.438064	−	0.438064i
$731$	5.31147	−	3.06658i	0.196452	−	0.113421i
$732$			12.9760i			0.479607i
$733$	8.16549	−	30.4740i	0.301599	−	1.12558i	−0.634234	−	0.773141i	$-0.718684\pi$
$733$	8.16549	−	30.4740i	0.301599	−	1.12558i	0.935833	−	0.352443i	$-0.114649\pi$
$734$	3.11360	−	11.6201i	0.114925	−	0.428906i
$735$	7.92317	+	12.3648i	0.292251	+	0.456084i
$736$	−15.9016	−	15.9016i	−0.586140	−	0.586140i
$737$	14.0973	−	24.4173i	0.519281	−	0.899422i
$738$	4.47927	+	7.75833i	0.164884	+	0.285588i
$739$	−7.67265	+	28.6347i	−0.282243	+	1.05335i	0.668587	+	0.743634i	$0.266899\pi$
$739$	−7.67265	+	28.6347i	−0.282243	+	1.05335i	−0.950830	+	0.309712i	$0.899767\pi$
$740$	−10.2481	−	17.7502i	−0.376728	−	0.652512i
$741$	5.95941	+	28.2704i	0.218924	+	1.03854i
$742$	4.12424	−	1.82120i	0.151405	−	0.0668583i
$743$	6.49849	+	24.2527i	0.238406	+	0.889745i	0.976584	+	0.215138i	$0.0690201\pi$
$743$	6.49849	+	24.2527i	0.238406	+	0.889745i	−0.738177	+	0.674607i	$0.764313\pi$
$744$	−1.25825			−0.0461298
$745$	−9.87198			−0.361682
$746$	−4.16077	−	15.5282i	−0.152337	−	0.568528i
$747$	2.08232	−	0.557955i	0.0761880	−	0.0204145i
$748$	−21.3805	−	5.72890i	−0.781750	−	0.209469i
$749$	0.818995	+	5.27485i	0.0299254	+	0.192739i
$750$	−4.61851	−	7.99949i	−0.168644	−	0.292100i
$751$		−	31.1328i		−	1.13605i	−0.823011	−	0.568025i	$-0.807707\pi$
$751$		−	31.1328i		−	1.13605i	0.823011	−	0.568025i	$-0.192293\pi$
$752$	−4.72801	−	1.26687i	−0.172413	−	0.0461979i
$753$	−2.37330	−	1.37023i	−0.0864880	−	0.0499338i
$754$	6.76097	+	2.20934i	0.246220	+	0.0804595i
$755$		−	1.22489i		−	0.0445784i
$756$	−0.560804	−	3.61194i	−0.0203963	−	0.131365i
$757$	1.51455	−	2.62328i	0.0550472	−	0.0953446i	−0.837189	−	0.546914i	$-0.815802\pi$
$757$	1.51455	−	2.62328i	0.0550472	−	0.0953446i	0.892236	+	0.451570i	$0.149136\pi$
$758$	−4.32176	−	2.49517i	−0.156973	−	0.0906286i
$759$	−9.08277	+	2.43372i	−0.329684	+	0.0883385i
$760$	−31.6118	+	31.6118i	−1.14668	+	1.14668i
$761$	7.59236	+	28.3351i	0.275223	+	1.02715i	0.955692	+	0.294369i	$0.0951095\pi$
$761$	7.59236	+	28.3351i	0.275223	+	1.02715i	−0.680469	+	0.732777i	$0.738224\pi$
$762$	−5.81406	+	5.81406i	−0.210621	+	0.210621i
$763$	−13.6312	+	6.01932i	−0.493482	+	0.217914i
$764$	−2.92535	−	1.68895i	−0.105835	−	0.0611040i
$765$	−9.72174	−	9.72174i	−0.351490	−	0.351490i
$766$	−2.46154	+	4.26351i	−0.0889389	+	0.154047i
$767$	4.13153	+	19.5992i	0.149181	+	0.707687i
$768$	−11.8582	+	6.84635i	−0.427897	+	0.247046i
$769$	−30.9694	+	8.29823i	−1.11679	+	0.299242i	−0.769582	−	0.638548i	$-0.779535\pi$
$769$	−30.9694	+	8.29823i	−1.11679	+	0.299242i	−0.347203	+	0.937790i	$0.612869\pi$
$770$	−4.31095	−	9.76245i	−0.155356	−	0.351814i
$771$	−9.49291	+	5.48074i	−0.341879	+	0.197384i
$772$	22.9670	+	6.15399i	0.826601	+	0.221487i
$773$	−31.5168	−	31.5168i	−1.13358	−	1.13358i	−0.989577	−	0.144005i	$-0.954002\pi$
$773$	−31.5168	−	31.5168i	−1.13358	−	1.13358i	−0.144005	−	0.989577i	$-0.545998\pi$
$774$	−0.520425	−	0.520425i	−0.0187063	−	0.0187063i
$775$	−0.273600	−	0.0733109i	−0.00982801	−	0.00263341i
$776$	37.1902	−	21.4718i	1.33505	−	0.770791i
$777$	−2.01235	+	18.6011i	−0.0721926	+	0.667312i
$778$	4.14094	−	1.10956i	0.148460	−	0.0397797i
$779$	79.0521	−	45.6408i	2.83234	−	1.63525i
$780$	3.24602	−	9.93337i	0.116226	−	0.355672i
$781$	−11.9478	+	20.6942i	−0.427526	+	0.740497i
$782$	14.0164	+	14.0164i	0.501225	+	0.501225i
$783$	2.17242	+	1.25425i	0.0776360	+	0.0448232i
$784$	4.48079	−	1.42578i	0.160028	−	0.0509208i
$785$	−16.4683	+	16.4683i	−0.587779	+	0.587779i
$786$	−4.24649	−	15.8481i	−0.151467	−	0.565283i
$787$	13.0345	−	13.0345i	0.464631	−	0.464631i	−0.435539	−	0.900170i	$-0.643442\pi$
$787$	13.0345	−	13.0345i	0.464631	−	0.464631i	0.900170	+	0.435539i	$0.143442\pi$
$788$	−31.2379	+	8.37018i	−1.11281	+	0.298175i
$789$	19.1556	+	11.0595i	0.681958	+	0.393729i
$790$	1.77426	−	3.07311i	0.0631253	−	0.109336i
$791$	−25.5856	+	20.5901i	−0.909718	+	0.732099i
$792$			6.50152i			0.231022i
$793$	30.1996	−	15.3236i	1.07242	−	0.544156i
$794$	6.52932	+	3.76971i	0.231717	+	0.133782i
$795$	4.39096	+	1.17655i	0.155731	+	0.0417280i
$796$		−	25.7540i		−	0.912828i
$797$	−6.45241	−	11.1759i	−0.228556	−	0.395871i	0.728824	−	0.684701i	$-0.240067\pi$
$797$	−6.45241	−	11.1759i	−0.228556	−	0.395871i	−0.957380	+	0.288830i	$0.906734\pi$
$798$	16.4753	−	2.55802i	0.583218	−	0.0905529i
$799$	46.1259	+	12.3594i	1.63182	+	0.437244i
$800$	−3.38099	+	0.905934i	−0.119536	+	0.0320296i
$801$	−1.62993	−	6.08297i	−0.0575906	−	0.214931i
$802$	29.4976			1.04160
$803$	−24.8034			−0.875292
$804$	−4.12365	−	15.3897i	−0.145430	−	0.542751i
$805$	2.29620	−	21.2249i	0.0809303	−	0.748078i
$806$	0.607067	+	1.19640i	0.0213830	+	0.0421415i
$807$	4.56433	+	7.90566i	0.160672	+	0.278292i
$808$	2.43640	−	9.09277i	0.0857123	−	0.319883i
$809$	−19.0726	−	33.0347i	−0.670558	−	1.16144i	−0.977746	−	0.209791i	$-0.932722\pi$
$809$	−19.0726	−	33.0347i	−0.670558	−	1.16144i	0.307189	−	0.951649i	$-0.400612\pi$
$810$	−0.824932	+	1.42882i	−0.0289852	+	0.0502038i
$811$	−10.6932	−	10.6932i	−0.375490	−	0.375490i	0.493982	−	0.869472i	$-0.335541\pi$
$811$	−10.6932	−	10.6932i	−0.375490	−	0.375490i	−0.869472	+	0.493982i	$0.835541\pi$
$812$	−3.31196	+	8.55003i	−0.116227	+	0.300047i
$813$	5.02495	−	18.7534i	0.176233	−	0.657709i
$814$	3.51895	−	13.1329i	0.123339	−	0.460308i
$815$		−	34.5683i		−	1.21087i
$816$	−3.81238	+	2.20108i	−0.133460	+	0.0770531i
$817$	−5.30278	+	5.30278i	−0.185521	+	0.185521i
$818$	−24.1718			−0.845146
$819$	−7.74394	+	5.57058i	−0.270595	+	0.194652i
$820$	−33.0171			−1.15301
$821$	−17.3195	+	17.3195i	−0.604455	+	0.604455i	−0.941492	−	0.337036i	$-0.890575\pi$
$821$	−17.3195	+	17.3195i	−0.604455	+	0.604455i	0.337036	+	0.941492i	$0.390575\pi$
$822$	7.67818	−	4.43300i	0.267807	−	0.154619i
$823$			13.5237i			0.471408i	0.971825	+	0.235704i	$0.0757396\pi$
$823$			13.5237i			0.471408i	−0.971825	+	0.235704i	$0.924260\pi$
$824$	6.30788	−	23.5413i	0.219746	−	0.820101i
$825$	−0.378805	+	1.41372i	−0.0131883	+	0.0492194i
$826$	11.4219	−	1.77342i	0.397420	−	0.0617051i
$827$	24.6131	+	24.6131i	0.855881	+	0.855881i	0.990850	−	0.134969i	$-0.0430935\pi$
$827$	24.6131	+	24.6131i	0.855881	+	0.855881i	−0.134969	+	0.990850i	$0.543094\pi$
$828$	−2.65683	+	4.60176i	−0.0923312	+	0.159922i
$829$	9.85463	+	17.0687i	0.342266	+	0.592821i	0.984853	−	0.173391i	$-0.0554724\pi$
$829$	9.85463	+	17.0687i	0.342266	+	0.592821i	−0.642588	+	0.766212i	$0.722139\pi$
$830$	0.920551	−	3.43554i	0.0319528	−	0.119249i
$831$	14.0411	+	24.3199i	0.487081	+	0.843649i
$832$	9.83090	+	6.40778i	0.340825	+	0.222150i
$833$	−43.7140	+	13.9098i	−1.51460	+	0.481945i
$834$	2.07604	+	7.74789i	0.0718874	+	0.268288i
$835$	0.0198603			0.000687292
$836$	27.0651			0.936066
$837$	0.122460	+	0.457027i	0.00423284	+	0.0157972i
$838$	17.7614	−	4.75916i	0.613558	−	0.164402i
$839$	22.4087	+	6.00440i	0.773635	+	0.207295i	0.623977	−	0.781443i	$-0.285516\pi$
$839$	22.4087	+	6.00440i	0.773635	+	0.207295i	0.149658	+	0.988738i	$0.452183\pi$
$840$	−13.7643	−	5.33177i	−0.474913	−	0.183963i
$841$	11.3537	+	19.6652i	0.391508	+	0.678111i
$842$		−	15.7363i		−	0.542308i
$843$	5.18788	+	1.39009i	0.178680	+	0.0478772i
$844$	−13.4312	−	7.75451i	−0.462321	−	0.266921i
$845$	−26.9516	+	4.17590i	−0.927164	+	0.143655i
$846$		−	5.73048i		−	0.197018i
$847$	4.80024	−	12.3921i	0.164938	−	0.425799i
$848$	0.727766	−	1.26053i	0.0249916	−	0.0432867i
$849$	1.19951	+	0.692540i	0.0411672	+	0.0237679i
$850$	2.98016	−	0.798532i	0.102219	−	0.0273894i
$851$	19.2323	−	19.2323i	0.659275	−	0.659275i
$852$	3.49489	+	13.0431i	0.119733	+	0.446849i
$853$	−25.2631	+	25.2631i	−0.864993	+	0.864993i	−0.991913	−	0.126920i	$-0.959491\pi$
$853$	−25.2631	+	25.2631i	−0.864993	+	0.864993i	0.126920	+	0.991913i	$0.459491\pi$
$854$	−7.89427	−	17.8772i	−0.270137	−	0.611744i
$855$	14.5588	+	8.40550i	0.497899	+	0.287462i
$856$	−3.79392	−	3.79392i	−0.129674	−	0.129674i
$857$	−3.17108	+	5.49248i	−0.108322	+	0.187619i	−0.915091	−	0.403248i	$-0.867881\pi$
$857$	−3.17108	+	5.49248i	−0.108322	+	0.187619i	0.806769	+	0.590868i	$0.201214\pi$
$858$	6.18193	−	3.13678i	0.211048	−	0.107088i
$859$	12.1601	−	7.02065i	0.414898	−	0.239541i	−0.277994	−	0.960583i	$-0.589670\pi$
$859$	12.1601	−	7.02065i	0.414898	−	0.239541i	0.692892	+	0.721041i	$0.256336\pi$
$860$	2.62010	−	0.702054i	0.0893448	−	0.0239399i
$861$	24.3290	+	17.7895i	0.829131	+	0.606265i
$862$	−8.98196	+	5.18573i	−0.305927	+	0.176627i
$863$	33.5781	+	8.99722i	1.14301	+	0.306269i	0.780161	−	0.625579i	$-0.215137\pi$
$863$	33.5781	+	8.99722i	1.14301	+	0.306269i	0.362850	+	0.931848i	$0.381804\pi$
$864$	4.13438	+	4.13438i	0.140655	+	0.140655i
$865$	−31.0952	−	31.0952i	−1.05727	−	1.05727i
$866$	−8.41464	−	2.25470i	−0.285941	−	0.0766177i
$867$	22.4707	−	12.9735i	0.763144	−	0.440602i
$868$	−1.58208	+	0.698620i	−0.0536991	+	0.0237127i
$869$	−5.07911	+	1.36094i	−0.172297	+	0.0461668i
$870$	3.58420	−	2.06934i	0.121516	−	0.0701572i
$871$	−30.9473	+	27.7710i	−1.04861	+	0.940986i
$872$	7.48873	−	12.9709i	0.253600	−	0.439249i
$873$	−11.4186	−	11.4186i	−0.386461	−	0.386461i
$874$	−20.9902	−	12.1187i	−0.710004	−	0.409921i
$875$	−25.0853	−	18.3425i	−0.848037	−	0.620090i
$876$	−9.91093	+	9.91093i	−0.334859	+	0.334859i
$877$	7.21350	+	26.9211i	0.243583	+	0.909062i	0.974091	+	0.226158i	$0.0726167\pi$
$877$	7.21350	+	26.9211i	0.243583	+	0.909062i	−0.730508	+	0.682904i	$0.760717\pi$
$878$	7.35868	−	7.35868i	0.248343	−	0.248343i
$879$	−17.3288	+	4.64324i	−0.584486	+	0.156613i
$880$	−2.98379	−	1.72269i	−0.100583	−	0.0580719i
$881$	4.46832	−	7.73936i	0.150542	−	0.260746i	−0.780885	−	0.624675i	$-0.785232\pi$
$881$	4.46832	−	7.73936i	0.150542	−	0.260746i	0.931427	+	0.363929i	$0.118565\pi$
$882$	2.97004	+	4.63502i	0.100006	+	0.156069i
$883$		−	17.8140i		−	0.599488i	−0.954020	−	0.299744i	$-0.903099\pi$
$883$		−	17.8140i		−	0.599488i	0.954020	−	0.299744i	$-0.0969012\pi$
$884$	27.3475	+	17.8251i	0.919797	+	0.599523i
$885$	10.0933	+	5.82735i	0.339281	+	0.195884i
$886$	3.73100	+	0.999719i	0.125345	+	0.0335862i
$887$			43.3313i			1.45492i	0.686149	+	0.727461i	$0.259300\pi$
$887$			43.3313i			1.45492i	−0.686149	+	0.727461i	$0.740700\pi$
$888$	−9.40280	−	16.2861i	−0.315537	−	0.546526i
$889$	−9.99188	+	25.7947i	−0.335117	+	0.865125i
$890$	−10.0361	−	2.68916i	−0.336410	−	0.0901407i
$891$	2.36150	−	0.632763i	0.0791134	−	0.0211984i
$892$	3.63513	+	13.5665i	0.121713	+	0.454239i
$893$	−58.3897			−1.95394
$894$	−3.70056			−0.123765
$895$	5.23926	+	19.5532i	0.175129	+	0.653591i
$896$	−14.2645	+	19.5082i	−0.476543	+	0.651722i
$897$	13.8474	+	0.749048i	0.462350	+	0.0250100i
$898$	−0.374035	−	0.647848i	−0.0124817	−	0.0216190i
$899$	0.307190	−	1.14645i	0.0102454	−	0.0382362i
$900$	0.413531	+	0.716257i	0.0137844	+	0.0238752i
$901$	−7.10000	+	12.2976i	−0.236535	+	0.409691i
$902$	−15.4870	−	15.4870i	−0.515661	−	0.515661i
$903$	−2.30892	−	0.894388i	−0.0768360	−	0.0297634i
$904$	8.54362	−	31.8852i	0.284157	−	1.06049i
$905$	0.682894	−	2.54860i	0.0227002	−	0.0847182i
$906$		−	0.459157i		−	0.0152545i
$907$	30.7649	−	17.7621i	1.02153	−	0.589781i	0.106984	−	0.994261i	$-0.465881\pi$
$907$	30.7649	−	17.7621i	1.02153	−	0.589781i	0.914547	+	0.404480i	$0.132547\pi$
$908$	6.43174	−	6.43174i	0.213445	−	0.213445i
$909$	−3.53983			−0.117409
$910$	1.57115	+	15.6601i	0.0520831	+	0.519127i
$911$	−56.1740			−1.86113			−0.930564	−	0.366130i	$-0.880682\pi$
$911$	−56.1740			−1.86113			−0.930564	+	0.366130i	$0.880682\pi$
$912$	3.80614	−	3.80614i	0.126034	−	0.126034i
$913$	−4.56435	+	2.63523i	−0.151058	+	0.0872133i
$914$			15.1306i			0.500474i
$915$	5.09995	−	19.0333i	0.168599	−	0.629221i
$916$	−0.444427	+	1.65863i	−0.0146843	+	0.0548025i
$917$	−34.6067	−	43.0029i	−1.14282	−	1.42008i
$918$	−3.64424	−	3.64424i	−0.120278	−	0.120278i
$919$	21.2328	−	36.7763i	0.700405	−	1.21314i	−0.267919	−	0.963441i	$-0.586336\pi$
$919$	21.2328	−	36.7763i	0.700405	−	1.21314i	0.968324	−	0.249696i	$-0.0803306\pi$
$920$	10.7291	+	18.5833i	0.353727	+	0.612674i
$921$	−2.00304	+	7.47546i	−0.0660025	+	0.246325i
$922$	−2.53513	−	4.39098i	−0.0834902	−	0.144609i
$923$	26.2286	−	23.5366i	0.863324	−	0.774717i
$924$	3.60984	+	8.17475i	0.118755	+	0.268929i
$925$	−1.09569	−	4.08917i	−0.0360261	−	0.134451i
$926$	8.54132			0.280685
$927$	−9.16468			−0.301008
$928$	−3.79608	−	14.1672i	−0.124612	−	0.465060i
$929$	27.8702	−	7.46779i	0.914391	−	0.245010i	0.229205	−	0.973378i	$-0.426388\pi$
$929$	27.8702	−	7.46779i	0.914391	−	0.245010i	0.685186	+	0.728368i	$0.259721\pi$
$930$	0.754032	+	0.202042i	0.0247257	+	0.00662523i
$931$	47.2277	−	30.2627i	1.54782	−	0.991818i
$932$	10.1242	+	17.5357i	0.331630	+	0.574400i
$933$		−	6.54713i		−	0.214344i
$934$	−16.2921	−	4.36545i	−0.533093	−	0.142842i
$935$	29.1095	+	16.8064i	0.951982	+	0.549627i
$936$	2.97827	−	9.11403i	0.0973478	−	0.297901i
$937$		−	15.4230i		−	0.503847i	−0.967747	−	0.251923i	$-0.918937\pi$
$937$		−	15.4230i		−	0.503847i	0.967747	−	0.251923i	$-0.0810631\pi$
$938$	15.0439	+	18.6937i	0.491200	+	0.610372i
$939$	−8.57583	+	14.8538i	−0.279862	+	0.484735i
$940$	18.2904	+	10.5599i	0.596566	+	0.344428i
$941$	31.8491	−	8.53393i	1.03825	−	0.278198i	0.300862	−	0.953668i	$-0.402726\pi$
$941$	31.8491	−	8.53393i	1.03825	−	0.278198i	0.737388	+	0.675470i	$0.236059\pi$
$942$	−6.17322	+	6.17322i	−0.201134	+	0.201134i
$943$	−11.3399	−	42.3210i	−0.369277	−	1.37816i
$944$	2.63872	−	2.63872i	0.0858829	−	0.0858829i
$945$	−0.597007	+	5.51843i	−0.0194206	+	0.179514i
$946$	1.55829	+	0.899681i	0.0506645	+	0.0292511i
$947$	−17.4962	−	17.4962i	−0.568550	−	0.568550i	0.363172	−	0.931722i	$-0.381694\pi$
$947$	−17.4962	−	17.4962i	−0.568550	−	0.568550i	−0.931722	+	0.363172i	$0.881694\pi$
$948$	−1.48570	+	2.57332i	−0.0482534	+	0.0835774i
$949$	34.7701	+	11.3621i	1.12869	+	0.368830i
$950$	−3.26709	+	1.88626i	−0.105998	+	0.0611983i
$951$	−15.5081	+	4.15537i	−0.502883	+	0.134747i
$952$	27.2156	−	37.2202i	0.882064	−	1.20631i
$953$	38.7397	−	22.3663i	1.25490	−	0.724517i	0.282822	−	0.959172i	$-0.408729\pi$
$953$	38.7397	−	22.3663i	1.25490	−	0.724517i	0.972079	+	0.234655i	$0.0753962\pi$
$954$	1.64597	+	0.441036i	0.0532902	+	0.0142791i
$955$	3.62711	+	3.62711i	0.117371	+	0.117371i
$956$	−6.71074	−	6.71074i	−0.217041	−	0.217041i
$957$	−5.92382	−	1.58728i	−0.191490	−	0.0513096i
$958$	−12.3291	+	7.11824i	−0.398337	+	0.229980i
$959$	17.6057	−	24.0777i	0.568519	−	0.777509i
$960$	6.59541	−	1.76723i	0.212866	−	0.0570373i
$961$	−26.6529	+	15.3881i	−0.859771	+	0.496389i
$962$	−10.9490	+	16.7981i	−0.353010	+	0.541593i
$963$	−1.00880	+	1.74729i	−0.0325080	+	0.0563055i
$964$	−18.6726	−	18.6726i	−0.601403	−	0.601403i
$965$	−31.2695	−	18.0534i	−1.00660	−	0.581161i
$966$	0.860739	−	7.95623i	0.0276938	−	0.255988i
$967$	−7.27104	+	7.27104i	−0.233821	+	0.233821i	−0.814285	−	0.580465i	$-0.802871\pi$
$967$	−7.27104	+	7.27104i	−0.233821	+	0.233821i	0.580465	+	0.814285i	$0.302871\pi$
$968$	3.45718	+	12.9024i	0.111118	+	0.414697i
$969$	−37.1323	+	37.1323i	−1.19286	+	1.19286i
$970$	−25.7347	+	6.89560i	−0.826293	+	0.221404i
$971$	18.9111	+	10.9184i	0.606887	+	0.350387i	0.771746	−	0.635931i	$-0.219384\pi$
$971$	18.9111	+	10.9184i	0.606887	+	0.350387i	−0.164859	+	0.986317i	$0.552717\pi$
$972$	0.690770	−	1.19645i	0.0221565	−	0.0383761i
$973$	16.9187	+	21.0234i	0.542388	+	0.673980i
$974$		−	5.66316i		−	0.181459i
$975$	1.17863	−	1.80827i	0.0377463	−	0.0579109i
$976$	−5.46396	−	3.15462i	−0.174897	−	0.100977i
$977$	−3.64839	−	0.977584i	−0.116722	−	0.0312757i	0.199985	−	0.979799i	$-0.435911\pi$
$977$	−3.64839	−	0.977584i	−0.116722	−	0.0312757i	−0.316707	+	0.948523i	$0.602577\pi$
$978$		−	12.9581i		−	0.414353i
$979$	7.69815	+	13.3336i	0.246034	+	0.426143i
$980$	−20.2670	+	0.938407i	−0.647406	+	0.0299763i
$981$	−5.44016	−	1.45769i	−0.173691	−	0.0465404i
$982$	−21.3993	+	5.73392i	−0.682878	+	0.182977i
$983$	12.2540	+	45.7327i	0.390843	+	1.45865i	0.828746	+	0.559625i	$0.189055\pi$
$983$	12.2540	+	45.7327i	0.390843	+	1.45865i	−0.437903	+	0.899022i	$0.644279\pi$
$984$	−30.2937			−0.965728
$985$	49.1098			1.56477
$986$	3.34604	+	12.4876i	0.106560	+	0.397686i
$987$	−7.78780	−	17.6360i	−0.247888	−	0.561361i
$988$	−37.9406	−	12.3982i	−1.20705	−	0.394439i
$989$	1.79977	+	3.11730i	0.0572294	+	0.0991243i
$990$	1.04397	−	3.89616i	0.0331797	−	0.123828i
$991$	5.24867	+	9.09095i	0.166729	+	0.288784i	0.937268	−	0.348610i	$-0.113346\pi$
$991$	5.24867	+	9.09095i	0.166729	+	0.288784i	−0.770539	+	0.637393i	$0.780013\pi$
$992$	1.38323	−	2.39582i	0.0439175	−	0.0760674i
$993$	−4.03496	−	4.03496i	−0.128046	−	0.128046i
$994$	−12.7500	−	15.8434i	−0.404406	−	0.502522i
$995$	−10.1221	+	37.7762i	−0.320892	+	1.19759i
$996$	−0.770838	+	2.87681i	−0.0244249	+	0.0911551i
$997$			37.0853i			1.17450i	0.809405	+	0.587251i	$0.199790\pi$
$997$			37.0853i			1.17450i	−0.809405	+	0.587251i	$0.800210\pi$
$998$	−14.3278	+	8.27218i	−0.453540	+	0.261851i
$999$	−5.00037	+	5.00037i	−0.158205	+	0.158205i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bt.a.136.6	✓	36
3.2	odd	2		819.2.et.c.136.4		36
7.5	odd	6		273.2.cg.a.19.4	yes	36
13.11	odd	12		273.2.cg.a.115.4	yes	36
21.5	even	6		819.2.gh.c.19.6		36
39.11	even	12		819.2.gh.c.388.6		36
91.89	even	12	inner	273.2.bt.a.271.6	yes	36
273.89	odd	12		819.2.et.c.271.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.6	✓	36	1.1	even	1	trivial
273.2.bt.a.271.6	yes	36	91.89	even	12	inner
273.2.cg.a.19.4	yes	36	7.5	odd	6
273.2.cg.a.115.4	yes	36	13.11	odd	12
819.2.et.c.136.4		36	3.2	odd	2
819.2.et.c.271.4		36	273.89	odd	12
819.2.gh.c.19.6		36	21.5	even	6
819.2.gh.c.388.6		36	39.11	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.556084 - 0.556084i) q^{2} +(0.866025 - 0.500000i) q^{3} +1.38154i q^{4} +(0.542987 - 2.02645i) q^{5} +(0.203541 - 0.759625i) q^{6} +(-0.405927 - 2.61443i) q^{7} +(1.88042 + 1.88042i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.556084 - 0.556084i) q^{2} +(0.866025 - 0.500000i) q^{3} +1.38154i q^{4} +(0.542987 - 2.02645i) q^{5} +(0.203541 - 0.759625i) q^{6} +(-0.405927 - 2.61443i) q^{7} +(1.88042 + 1.88042i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.824932 - 1.42882i) q^{10} +(-0.632763 + 2.36150i) q^{11} +(0.690770 + 1.19645i) q^{12} +(1.96880 - 3.02057i) q^{13} +(-1.67957 - 1.22811i) q^{14} +(-0.542987 - 2.02645i) q^{15} -0.671737 q^{16} +6.55339 q^{17} +(-0.203541 - 0.759625i) q^{18} +(-7.74006 + 2.07394i) q^{19} +(2.79963 + 0.750158i) q^{20} +(-1.65876 - 2.06120i) q^{21} +(0.961326 + 1.66506i) q^{22} +3.84618i q^{23} +(2.56870 + 0.688282i) q^{24} +(0.518448 + 0.299326i) q^{25} +(-0.584868 - 2.77451i) q^{26} -1.00000i q^{27} +(3.61194 - 0.560804i) q^{28} +(-1.25425 + 2.17242i) q^{29} +(-1.42882 - 0.824932i) q^{30} +(-0.457027 + 0.122460i) q^{31} +(-4.13438 + 4.13438i) q^{32} +(0.632763 + 2.36150i) q^{33} +(3.64424 - 3.64424i) q^{34} +(-5.51843 - 0.597007i) q^{35} +(1.19645 + 0.690770i) q^{36} +(-5.00037 - 5.00037i) q^{37} +(-3.15084 + 5.45741i) q^{38} +(0.194751 - 3.60029i) q^{39} +(4.83163 - 2.78954i) q^{40} +(-11.0034 + 2.94834i) q^{41} +(-2.06861 - 0.223791i) q^{42} +(0.810492 - 0.467938i) q^{43} +(-3.26252 - 0.874188i) q^{44} +(-1.48347 - 1.48347i) q^{45} +(2.13880 + 2.13880i) q^{46} +(7.03848 + 1.88596i) q^{47} +(-0.581741 + 0.335869i) q^{48} +(-6.67045 + 2.12253i) q^{49} +(0.454751 - 0.121850i) q^{50} +(5.67540 - 3.27669i) q^{51} +(4.17303 + 2.71998i) q^{52} +(-1.08341 + 1.87652i) q^{53} +(-0.556084 - 0.556084i) q^{54} +(4.44190 + 2.56453i) q^{55} +(4.15291 - 5.67954i) q^{56} +(-5.66612 + 5.66612i) q^{57} +(0.510581 + 1.90552i) q^{58} +(-3.92820 + 3.92820i) q^{59} +(2.79963 - 0.750158i) q^{60} +(8.13407 + 4.69621i) q^{61} +(-0.186047 + 0.322243i) q^{62} +(-2.46712 - 0.955670i) q^{63} +3.25466i q^{64} +(-5.05200 - 5.62981i) q^{65} +(1.66506 + 0.961326i) q^{66} +(-11.1395 - 2.98482i) q^{67} +9.05378i q^{68} +(1.92309 + 3.33089i) q^{69} +(-3.40069 + 2.73672i) q^{70} +(9.44098 + 2.52970i) q^{71} +(2.56870 - 0.688282i) q^{72} +(2.62580 + 9.79963i) q^{73} -5.56125 q^{74} +0.598652 q^{75} +(-2.86524 - 10.6932i) q^{76} +(6.43083 + 0.695715i) q^{77} +(-1.89376 - 2.11036i) q^{78} +(1.07540 + 1.86264i) q^{79} +(-0.364744 + 1.36124i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.47927 + 7.75833i) q^{82} +(1.52436 + 1.52436i) q^{83} +(2.84763 - 2.29164i) q^{84} +(3.55840 - 13.2801i) q^{85} +(0.190489 - 0.710914i) q^{86} +2.50850i q^{87} +(-5.63048 + 3.25076i) q^{88} +(4.45304 - 4.45304i) q^{89} -1.64986 q^{90} +(-8.69623 - 3.92116i) q^{91} -5.31366 q^{92} +(-0.334567 + 0.334567i) q^{93} +(4.96274 - 2.86524i) q^{94} +16.8110i q^{95} +(-1.51329 + 5.64767i) q^{96} +(4.17950 - 15.5981i) q^{97} +(-2.52902 + 4.88964i) q^{98} +(1.72874 + 1.72874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7} + 18 q^{9}+O(q^{10}) \) 36 * q + 6 * q^7 + 18 * q^9	\( 36 q + 6 q^{7} + 18 q^{9} - 8 q^{11} - 16 q^{12} + 42 q^{14} - 24 q^{16} - 8 q^{17} - 18 q^{19} + 14 q^{20} - 4 q^{21} + 4 q^{22} + 18 q^{24} + 24 q^{25} - 50 q^{26} + 34 q^{28} + 8 q^{29} + 6 q^{31} - 50 q^{32} + 8 q^{33} - 24 q^{34} + 14 q^{35} - 14 q^{37} - 8 q^{38} - 2 q^{39} - 30 q^{40} + 34 q^{41} - 18 q^{42} + 30 q^{43} + 28 q^{44} - 32 q^{46} - 10 q^{47} + 24 q^{48} + 6 q^{49} - 20 q^{50} - 24 q^{51} + 4 q^{52} - 8 q^{53} - 30 q^{55} - 92 q^{56} - 24 q^{57} + 72 q^{58} - 70 q^{59} + 14 q^{60} - 60 q^{61} - 48 q^{62} + 6 q^{63} - 44 q^{65} + 18 q^{66} - 46 q^{67} + 4 q^{69} + 80 q^{70} + 42 q^{71} + 18 q^{72} - 56 q^{73} + 40 q^{74} - 20 q^{75} + 12 q^{76} + 24 q^{77} - 16 q^{78} + 170 q^{80} - 18 q^{81} + 24 q^{82} - 60 q^{83} + 2 q^{85} + 12 q^{86} + 84 q^{88} + 64 q^{89} - 86 q^{91} - 100 q^{92} + 12 q^{93} - 66 q^{94} + 46 q^{96} + 36 q^{97} - 22 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 6 * q^7 + 18 * q^9 - 8 * q^11 - 16 * q^12 + 42 * q^14 - 24 * q^16 - 8 * q^17 - 18 * q^19 + 14 * q^20 - 4 * q^21 + 4 * q^22 + 18 * q^24 + 24 * q^25 - 50 * q^26 + 34 * q^28 + 8 * q^29 + 6 * q^31 - 50 * q^32 + 8 * q^33 - 24 * q^34 + 14 * q^35 - 14 * q^37 - 8 * q^38 - 2 * q^39 - 30 * q^40 + 34 * q^41 - 18 * q^42 + 30 * q^43 + 28 * q^44 - 32 * q^46 - 10 * q^47 + 24 * q^48 + 6 * q^49 - 20 * q^50 - 24 * q^51 + 4 * q^52 - 8 * q^53 - 30 * q^55 - 92 * q^56 - 24 * q^57 + 72 * q^58 - 70 * q^59 + 14 * q^60 - 60 * q^61 - 48 * q^62 + 6 * q^63 - 44 * q^65 + 18 * q^66 - 46 * q^67 + 4 * q^69 + 80 * q^70 + 42 * q^71 + 18 * q^72 - 56 * q^73 + 40 * q^74 - 20 * q^75 + 12 * q^76 + 24 * q^77 - 16 * q^78 + 170 * q^80 - 18 * q^81 + 24 * q^82 - 60 * q^83 + 2 * q^85 + 12 * q^86 + 84 * q^88 + 64 * q^89 - 86 * q^91 - 100 * q^92 + 12 * q^93 - 66 * q^94 + 46 * q^96 + 36 * q^97 - 22 * q^98 - 4 * q^99

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