LMFDB - Embedded newform 510.2.bd.a.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [510,2,Mod(7,510)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(510, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 4, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("510.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.bd (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	510.73
Dual form			510.2.bd.a.7.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.923880 + 0.382683i) q^{2} +(-0.195090 + 0.980785i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-2.08794 - 0.800320i) q^{5} +(-0.555570 + 0.831470i) q^{6} +(2.90113 + 1.93847i) q^{7} +(0.382683 + 0.923880i) q^{8} +(-0.923880 - 0.382683i) q^{9} +(-1.62273 - 1.53842i) q^{10} +(1.37169 + 0.916536i) q^{11} +(-0.831470 + 0.555570i) q^{12} +2.63079i q^{13} +(1.93847 + 2.90113i) q^{14} +(1.19228 - 1.89168i) q^{15} +1.00000i q^{16} +(-0.719107 + 4.05991i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(0.894550 - 0.370535i) q^{19} +(-0.910484 - 2.04231i) q^{20} +(-2.46721 + 2.46721i) q^{21} +(0.916536 + 1.37169i) q^{22} +(-7.17784 + 1.42776i) q^{23} +(-0.980785 + 0.195090i) q^{24} +(3.71898 + 3.34204i) q^{25} +(-1.00676 + 2.43054i) q^{26} +(0.555570 - 0.831470i) q^{27} +(0.680701 + 3.42212i) q^{28} +(-0.257536 + 1.29472i) q^{29} +(1.82544 - 1.29142i) q^{30} +(5.66944 - 3.78820i) q^{31} +(-0.382683 + 0.923880i) q^{32} +(-1.16653 + 1.16653i) q^{33} +(-2.21803 + 3.47568i) q^{34} +(-4.50598 - 6.36925i) q^{35} +(-0.382683 - 0.923880i) q^{36} +(-2.09782 - 0.417282i) q^{37} +0.968254 q^{38} +(-2.58024 - 0.513243i) q^{39} +(-0.0596204 - 2.23527i) q^{40} +(-0.591105 - 2.97169i) q^{41} +(-3.22356 + 1.33524i) q^{42} +(1.52446 - 0.631450i) q^{43} +(0.321845 + 1.61802i) q^{44} +(1.62273 + 1.53842i) q^{45} +(-7.17784 - 1.42776i) q^{46} +11.0116 q^{47} +(-0.980785 - 0.195090i) q^{48} +(1.98009 + 4.78037i) q^{49} +(2.15694 + 4.51083i) q^{50} +(-3.84161 - 1.49734i) q^{51} +(-1.86025 + 1.86025i) q^{52} +(2.23029 - 5.38439i) q^{53} +(0.831470 - 0.555570i) q^{54} +(-2.13049 - 3.01146i) q^{55} +(-0.680701 + 3.42212i) q^{56} +(0.188897 + 0.949649i) q^{57} +(-0.733401 + 1.09761i) q^{58} +(3.31805 - 8.01048i) q^{59} +(2.18069 - 0.494555i) q^{60} +(-0.308484 + 0.0613612i) q^{61} +(6.68755 - 1.33024i) q^{62} +(-1.93847 - 2.90113i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(2.10548 - 5.49294i) q^{65} +(-1.52414 + 0.631321i) q^{66} +(-2.83025 - 2.83025i) q^{67} +(-3.37928 + 2.36231i) q^{68} -7.31846i q^{69} +(-1.72558 - 7.60878i) q^{70} +(-7.65906 - 11.4626i) q^{71} -1.00000i q^{72} +(10.8701 - 7.26314i) q^{73} +(-1.77845 - 1.18832i) q^{74} +(-4.00336 + 2.99552i) q^{75} +(0.894550 + 0.370535i) q^{76} +(2.20278 + 5.31798i) q^{77} +(-2.18743 - 1.46159i) q^{78} +(-8.09620 + 12.1168i) q^{79} +(0.800320 - 2.08794i) q^{80} +(0.707107 + 0.707107i) q^{81} +(0.591105 - 2.97169i) q^{82} +(3.52958 + 1.46200i) q^{83} -3.48916 q^{84} +(4.75068 - 7.90133i) q^{85} +1.65006 q^{86} +(-1.21960 - 0.505176i) q^{87} +(-0.321845 + 1.61802i) q^{88} +(4.50143 + 4.50143i) q^{89} +(0.910484 + 2.04231i) q^{90} +(-5.09973 + 7.63228i) q^{91} +(-6.08507 - 4.06592i) q^{92} +(2.60935 + 6.29954i) q^{93} +(10.1734 + 4.21397i) q^{94} +(-2.16431 + 0.0577277i) q^{95} +(-0.831470 - 0.555570i) q^{96} +(11.5968 - 7.74876i) q^{97} +5.17424i q^{98} +(-0.916536 - 1.37169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 16 q^{15} + 16 q^{20} + 16 q^{25} - 16 q^{28} + 32 q^{29} + 16 q^{31} + 16 q^{33} + 32 q^{35} - 16 q^{37} - 16 q^{40} + 48 q^{41} + 16 q^{44} + 32 q^{47} - 64 q^{49} - 16 q^{50} + 32 q^{51} + 16 q^{52}+ \cdots - 80 q^{97}+O(q^{100}) $ 64 * q - 16 * q^15 + 16 * q^20 + 16 * q^25 - 16 * q^28 + 32 * q^29 + 16 * q^31 + 16 * q^33 + 32 * q^35 - 16 * q^37 - 16 * q^40 + 48 * q^41 + 16 * q^44 + 32 * q^47 - 64 * q^49 - 16 * q^50 + 32 * q^51 + 16 * q^52 + 80 * q^53 - 16 * q^55 + 16 * q^56 - 32 * q^57 + 64 * q^59 - 48 * q^61 + 32 * q^65 + 16 * q^67 - 48 * q^68 - 64 * q^71 + 16 * q^73 + 48 * q^74 - 32 * q^75 - 80 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 48 * q^82 - 32 * q^83 - 16 * q^85 - 64 * q^86 - 32 * q^87 - 16 * q^88 - 32 * q^89 - 16 * q^90 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 112 * q^95 - 80 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.923880	+	0.382683i	0.653281	+	0.270598i
$2$	0.923880	+	0.382683i	0.653281	+	0.270598i
$3$	−0.195090	+	0.980785i	−0.112635	+	0.566257i
$3$	−0.195090	+	0.980785i	−0.112635	+	0.566257i
$4$	0.707107	+	0.707107i	0.353553	+	0.353553i
$5$	−2.08794	−	0.800320i	−0.933755	−	0.357914i
$5$	−2.08794	−	0.800320i	−0.933755	−	0.357914i
$6$	−0.555570	+	0.831470i	−0.226811	+	0.339446i
$7$	2.90113	+	1.93847i	1.09652	+	0.732674i	0.965941	−	0.258763i	$-0.0833149\pi$
$7$	2.90113	+	1.93847i	1.09652	+	0.732674i	0.130583	+	0.991437i	$0.458315\pi$
$8$	0.382683	+	0.923880i	0.135299	+	0.326641i
$9$	−0.923880	−	0.382683i	−0.307960	−	0.127561i
$10$	−1.62273	−	1.53842i	−0.513154	−	0.486491i
$11$	1.37169	+	0.916536i	0.413581	+	0.276346i	0.744904	−	0.667171i	$-0.232495\pi$
$11$	1.37169	+	0.916536i	0.413581	+	0.276346i	−0.331323	+	0.943517i	$0.607495\pi$
$12$	−0.831470	+	0.555570i	−0.240025	+	0.160379i
$13$			2.63079i			0.729651i	0.931076	+	0.364826i	$0.118871\pi$
$13$			2.63079i			0.729651i	−0.931076	+	0.364826i	$0.881129\pi$
$14$	1.93847	+	2.90113i	0.518079	+	0.775360i
$15$	1.19228	−	1.89168i	0.307845	−	0.488431i
$16$			1.00000i			0.250000i
$17$	−0.719107	+	4.05991i	−0.174409	+	0.984673i
$17$	−0.719107	+	4.05991i	−0.174409	+	0.984673i
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	0.894550	−	0.370535i	0.205224	−	0.0850065i	−0.277704	−	0.960667i	$-0.589573\pi$
$19$	0.894550	−	0.370535i	0.205224	−	0.0850065i	0.482928	+	0.875660i	$0.339573\pi$
$20$	−0.910484	−	2.04231i	−0.203590	−	0.456674i
$21$	−2.46721	+	2.46721i	−0.538389	+	0.538389i
$22$	0.916536	+	1.37169i	0.195406	+	0.292446i
$23$	−7.17784	+	1.42776i	−1.49668	+	0.297709i	−0.874447	−	0.485122i	$-0.838775\pi$
$23$	−7.17784	+	1.42776i	−1.49668	+	0.297709i	−0.622235	+	0.782830i	$0.713775\pi$
$24$	−0.980785	+	0.195090i	−0.200202	+	0.0398226i
$25$	3.71898	+	3.34204i	0.743795	+	0.668408i
$26$	−1.00676	+	2.43054i	−0.197442	+	0.476668i
$27$	0.555570	−	0.831470i	0.106920	−	0.160016i
$28$	0.680701	+	3.42212i	0.128640	+	0.646719i
$29$	−0.257536	+	1.29472i	−0.0478233	+	0.240424i	−0.997302	−	0.0734074i	$-0.976613\pi$
$29$	−0.257536	+	1.29472i	−0.0478233	+	0.240424i	0.949479	+	0.313831i	$0.101613\pi$
$30$	1.82544	−	1.29142i	0.333278	−	0.235781i
$31$	5.66944	−	3.78820i	1.01826	−	0.680380i	0.0698934	−	0.997554i	$-0.477734\pi$
$31$	5.66944	−	3.78820i	1.01826	−	0.680380i	0.948367	+	0.317174i	$0.102734\pi$
$32$	−0.382683	+	0.923880i	−0.0676495	+	0.163320i
$33$	−1.16653	+	1.16653i	−0.203067	+	0.203067i
$34$	−2.21803	+	3.47568i	−0.380389	+	0.596074i
$35$	−4.50598	−	6.36925i	−0.761650	−	1.07660i
$36$	−0.382683	−	0.923880i	−0.0637806	−	0.153980i
$37$	−2.09782	−	0.417282i	−0.344880	−	0.0686008i	0.0196115	−	0.999808i	$-0.493757\pi$
$37$	−2.09782	−	0.417282i	−0.344880	−	0.0686008i	−0.364491	+	0.931207i	$0.618757\pi$
$38$	0.968254			0.157071
$39$	−2.58024	−	0.513243i	−0.413170	−	0.0821846i
$40$	−0.0596204	−	2.23527i	−0.00942681	−	0.353428i
$41$	−0.591105	−	2.97169i	−0.0923151	−	0.464099i	−0.999097	−	0.0424984i	$-0.986468\pi$
$41$	−0.591105	−	2.97169i	−0.0923151	−	0.464099i	0.906781	−	0.421601i	$-0.138532\pi$
$42$	−3.22356	+	1.33524i	−0.497407	+	0.206033i
$43$	1.52446	−	0.631450i	0.232477	−	0.0962952i	−0.263404	−	0.964686i	$-0.584845\pi$
$43$	1.52446	−	0.631450i	0.232477	−	0.0962952i	0.495881	+	0.868390i	$0.334845\pi$
$44$	0.321845	+	1.61802i	0.0485199	+	0.243926i
$45$	1.62273	+	1.53842i	0.241903	+	0.229334i
$46$	−7.17784	−	1.42776i	−1.05831	−	0.210512i
$47$	11.0116			1.60621			0.803107	−	0.595835i	$-0.203179\pi$
$47$	11.0116			1.60621			0.803107	+	0.595835i	$0.203179\pi$
$48$	−0.980785	−	0.195090i	−0.141564	−	0.0281589i
$49$	1.98009	+	4.78037i	0.282871	+	0.682910i
$50$	2.15694	+	4.51083i	0.305038	+	0.637928i
$51$	−3.84161	−	1.49734i	−0.537933	−	0.209669i
$52$	−1.86025	+	1.86025i	−0.257971	+	0.257971i
$53$	2.23029	−	5.38439i	0.306354	−	0.739603i	−0.693464	−	0.720491i	$-0.743916\pi$
$53$	2.23029	−	5.38439i	0.306354	−	0.739603i	0.999817	−	0.0191114i	$-0.00608371\pi$
$54$	0.831470	−	0.555570i	0.113149	−	0.0756035i
$55$	−2.13049	−	3.01146i	−0.287275	−	0.406066i
$56$	−0.680701	+	3.42212i	−0.0909625	+	0.457300i
$57$	0.188897	+	0.949649i	0.0250200	+	0.125784i
$58$	−0.733401	+	1.09761i	−0.0963003	+	0.144124i
$59$	3.31805	−	8.01048i	0.431973	−	1.04288i	−0.546677	−	0.837343i	$-0.684108\pi$
$59$	3.31805	−	8.01048i	0.431973	−	1.04288i	0.978650	−	0.205532i	$-0.0658924\pi$
$60$	2.18069	−	0.494555i	0.281526	−	0.0638468i
$61$	−0.308484	+	0.0613612i	−0.0394973	+	0.00785650i	−0.214799	−	0.976658i	$-0.568910\pi$
$61$	−0.308484	+	0.0613612i	−0.0394973	+	0.00785650i	0.175302	+	0.984515i	$0.443910\pi$
$62$	6.68755	−	1.33024i	0.849320	−	0.168940i
$63$	−1.93847	−	2.90113i	−0.244225	−	0.365508i
$64$	−0.707107	+	0.707107i	−0.0883883	+	0.0883883i
$65$	2.10548	−	5.49294i	0.261152	−	0.681315i
$66$	−1.52414	+	0.631321i	−0.187609	+	0.0777102i
$67$	−2.83025	−	2.83025i	−0.345771	−	0.345771i	0.512761	−	0.858531i	$-0.328623\pi$
$67$	−2.83025	−	2.83025i	−0.345771	−	0.345771i	−0.858531	+	0.512761i	$0.828623\pi$
$68$	−3.37928	+	2.36231i	−0.409797	+	0.286472i
$69$		−	7.31846i		−	0.881039i
$70$	−1.72558	−	7.60878i	−0.206246	−	0.909423i
$71$	−7.65906	−	11.4626i	−0.908963	−	1.36036i	−0.932705	−	0.360641i	$-0.882558\pi$
$71$	−7.65906	−	11.4626i	−0.908963	−	1.36036i	0.0237421	−	0.999718i	$-0.492442\pi$
$72$		−	1.00000i		−	0.117851i
$73$	10.8701	−	7.26314i	1.27224	−	0.850086i	0.278355	−	0.960478i	$-0.410211\pi$
$73$	10.8701	−	7.26314i	1.27224	−	0.850086i	0.993888	+	0.110392i	$0.0352107\pi$
$74$	−1.77845	−	1.18832i	−0.206740	−	0.138139i
$75$	−4.00336	+	2.99552i	−0.462268	+	0.345893i
$76$	0.894550	+	0.370535i	0.102612	+	0.0425032i
$77$	2.20278	+	5.31798i	0.251030	+	0.606040i
$78$	−2.18743	−	1.46159i	−0.247677	−	0.165493i
$79$	−8.09620	+	12.1168i	−0.910893	+	1.36325i	0.0207157	+	0.999785i	$0.493406\pi$
$79$	−8.09620	+	12.1168i	−0.910893	+	1.36325i	−0.931609	+	0.363462i	$0.881594\pi$
$80$	0.800320	−	2.08794i	0.0894785	−	0.233439i
$81$	0.707107	+	0.707107i	0.0785674	+	0.0785674i
$82$	0.591105	−	2.97169i	0.0652766	−	0.328168i
$83$	3.52958	+	1.46200i	0.387421	+	0.160475i	0.567888	−	0.823106i	$-0.307761\pi$
$83$	3.52958	+	1.46200i	0.387421	+	0.160475i	−0.180466	+	0.983581i	$0.557761\pi$
$84$	−3.48916			−0.380699
$85$	4.75068	−	7.90133i	0.515284	−	0.857020i
$86$	1.65006			0.177930
$87$	−1.21960	−	0.505176i	−0.130755	−	0.0541605i
$88$	−0.321845	+	1.61802i	−0.0343088	+	0.172482i
$89$	4.50143	+	4.50143i	0.477151	+	0.477151i	0.904219	−	0.427068i	$-0.140454\pi$
$89$	4.50143	+	4.50143i	0.477151	+	0.477151i	−0.427068	+	0.904219i	$0.640454\pi$
$90$	0.910484	+	2.04231i	0.0959734	+	0.215278i
$91$	−5.09973	+	7.63228i	−0.534597	+	0.800080i
$92$	−6.08507	−	4.06592i	−0.634413	−	0.423901i
$93$	2.60935	+	6.29954i	0.270577	+	0.653232i
$94$	10.1734	+	4.21397i	1.04931	+	0.434638i
$95$	−2.16431	+	0.0577277i	−0.222054	+	0.00592273i
$96$	−0.831470	−	0.555570i	−0.0848615	−	0.0567026i
$97$	11.5968	−	7.74876i	1.17748	−	0.786767i	0.196429	−	0.980518i	$-0.437065\pi$
$97$	11.5968	−	7.74876i	1.17748	−	0.786767i	0.981051	+	0.193751i	$0.0620654\pi$
$98$			5.17424i			0.522677i
$99$	−0.916536	−	1.37169i	−0.0921153	−	0.137860i
$100$	0.266536	+	4.99289i	0.0266536	+	0.499289i
$101$		−	13.5051i		−	1.34381i	−0.740636	−	0.671906i	$-0.765476\pi$
$101$		−	13.5051i		−	1.34381i	0.740636	−	0.671906i	$-0.234524\pi$
$102$	−2.97618	−	2.85348i	−0.294686	−	0.282537i
$103$	8.42263	+	8.42263i	0.829906	+	0.829906i	0.987503	−	0.157597i	$-0.0503748\pi$
$103$	8.42263	+	8.42263i	0.829906	+	0.829906i	−0.157597	+	0.987503i	$0.550375\pi$
$104$	−2.43054	+	1.00676i	−0.238334	+	0.0987211i
$105$	7.12594	−	3.17682i	0.695420	−	0.310026i
$106$	4.12103	−	4.12103i	0.400270	−	0.400270i
$107$	−1.65770	−	2.48092i	−0.160255	−	0.239839i	0.742649	−	0.669681i	$-0.233569\pi$
$107$	−1.65770	−	2.48092i	−0.160255	−	0.239839i	−0.902904	+	0.429842i	$0.858569\pi$
$108$	0.980785	−	0.195090i	0.0943761	−	0.0187726i
$109$	−2.72581	+	0.542197i	−0.261085	+	0.0519330i	−0.323897	−	0.946092i	$-0.604993\pi$
$109$	−2.72581	+	0.542197i	−0.261085	+	0.0519330i	0.0628120	+	0.998025i	$0.479993\pi$
$110$	−0.815878	−	3.59753i	−0.0777909	−	0.343011i
$111$	0.818529	−	1.97610i	0.0776913	−	0.187563i
$112$	−1.93847	+	2.90113i	−0.183169	+	0.274131i
$113$	3.46326	+	17.4110i	0.325796	+	1.63789i	0.702593	+	0.711592i	$0.252025\pi$
$113$	3.46326	+	17.4110i	0.325796	+	1.63789i	−0.376797	+	0.926296i	$0.622975\pi$
$114$	−0.188897	+	0.949649i	−0.0176918	+	0.0889428i
$115$	16.1295	+	2.76349i	1.50409	+	0.257697i
$116$	−1.09761	+	0.733401i	−0.101911	+	0.0680946i
$117$	1.00676	−	2.43054i	0.0930751	−	0.224703i
$118$	6.13095	−	6.13095i	0.564400	−	0.564400i
$119$	−9.95625	+	10.3844i	−0.912688	+	0.951933i
$120$	2.20395	+	0.377605i	0.201193	+	0.0344705i
$121$	−3.16801	−	7.64826i	−0.288001	−	0.695297i
$122$	−0.308484	−	0.0613612i	−0.0279288	−	0.00555538i
$123$	3.02990			0.273197
$124$	6.68755	+	1.33024i	0.600560	+	0.119459i
$125$	−5.09030	−	9.95434i	−0.455290	−	0.890343i
$126$	−0.680701	−	3.42212i	−0.0606417	−	0.304866i
$127$	−7.51461	+	3.11265i	−0.666814	+	0.276203i	−0.690303	−	0.723521i	$-0.742523\pi$
$127$	−7.51461	+	3.11265i	−0.666814	+	0.276203i	0.0234887	+	0.999724i	$0.492523\pi$
$128$	−0.923880	+	0.382683i	−0.0816602	+	0.0338248i
$129$	0.321910	+	1.61835i	0.0283426	+	0.142488i
$130$	4.04726	−	4.26908i	0.354969	−	0.374423i
$131$	−19.6918	−	3.91695i	−1.72048	−	0.342225i	−0.766536	−	0.642202i	$-0.778021\pi$
$131$	−19.6918	−	3.91695i	−1.72048	−	0.342225i	−0.953947	+	0.299977i	$0.903021\pi$
$132$	−1.64972			−0.143590
$133$	3.31348	+	0.659092i	0.287315	+	0.0571505i
$134$	−1.53172	−	3.69791i	−0.132321	−	0.319450i
$135$	−1.82544	+	1.29142i	−0.157109	+	0.111148i
$136$	−4.02606	+	0.889293i	−0.345232	+	0.0762562i
$137$	2.07939	−	2.07939i	0.177654	−	0.177654i	−0.612678	−	0.790332i	$-0.709908\pi$
$137$	2.07939	−	2.07939i	0.177654	−	0.177654i	0.790332	+	0.612678i	$0.209908\pi$
$138$	2.80065	−	6.76137i	0.238407	−	0.575566i
$139$	−6.06776	+	4.05435i	−0.514661	+	0.343885i	−0.785624	−	0.618704i	$-0.787658\pi$
$139$	−6.06776	+	4.05435i	−0.514661	+	0.343885i	0.270963	+	0.962590i	$0.412658\pi$
$140$	1.31753	−	7.68995i	0.111351	−	0.649919i
$141$	−2.14826	+	10.8001i	−0.180917	+	0.909529i
$142$	−2.68950	−	13.5210i	−0.225698	−	1.13466i
$143$	−2.41122	+	3.60864i	−0.201636	+	0.301770i
$144$	0.382683	−	0.923880i	0.0318903	−	0.0769900i
$145$	1.57391	−	2.49719i	0.130706	−	0.207380i
$146$	12.8221	−	2.55047i	1.06116	−	0.211079i
$147$	−5.07482	+	1.00944i	−0.418564	+	0.0832575i
$148$	−1.18832	−	1.77845i	−0.0976793	−	0.146187i
$149$	7.69536	−	7.69536i	0.630429	−	0.630429i	−0.317747	−	0.948176i	$-0.602926\pi$
$149$	7.69536	−	7.69536i	0.630429	−	0.630429i	0.948176	+	0.317747i	$0.102926\pi$
$150$	−4.84496	+	1.23548i	−0.395589	+	0.100876i
$151$	14.8602	−	6.15530i	1.20931	−	0.500911i	0.315311	−	0.948988i	$-0.397891\pi$
$151$	14.8602	−	6.15530i	1.20931	−	0.500911i	0.893995	+	0.448078i	$0.147891\pi$
$152$	0.684659	+	0.684659i	0.0555332	+	0.0555332i
$153$	2.21803	−	3.47568i	0.179317	−	0.280992i
$154$			5.75614i			0.463843i
$155$	−14.8692	+	3.37216i	−1.19432	+	0.270858i
$156$	−1.46159	−	2.18743i	−0.117021	−	0.175134i
$157$		−	6.97499i		−	0.556665i	−0.960485	−	0.278332i	$-0.910218\pi$
$157$		−	6.97499i		−	0.556665i	0.960485	−	0.278332i	$-0.0897817\pi$
$158$	−12.1168	+	8.09620i	−0.963962	+	0.644099i
$159$	4.84582	+	3.23788i	0.384299	+	0.256780i
$160$	1.53842	−	1.62273i	0.121623	−	0.128288i
$161$	−23.5915	−	9.77192i	−1.85927	−	0.770136i
$162$	0.382683	+	0.923880i	0.0300665	+	0.0725868i
$163$	−21.0143	−	14.0413i	−1.64596	−	1.09980i	−0.902162	−	0.431397i	$-0.858021\pi$
$163$	−21.0143	−	14.0413i	−1.64596	−	1.09980i	−0.743802	−	0.668400i	$-0.766979\pi$
$164$	1.68332	−	2.51927i	0.131446	−	0.196722i
$165$	3.36924	−	1.50204i	0.262295	−	0.116934i
$166$	2.70142	+	2.70142i	0.209671	+	0.209671i
$167$	0.906640	−	4.55798i	0.0701579	−	0.352707i	−0.929721	−	0.368264i	$-0.879952\pi$
$167$	0.906640	−	4.55798i	0.0701579	−	0.352707i	0.999879	+	0.0155569i	$0.00495213\pi$
$168$	−3.22356	−	1.33524i	−0.248703	−	0.103016i
$169$	6.07892			0.467609
$170$	7.41276	−	5.48187i	0.568533	−	0.420440i
$171$	−0.968254			−0.0740442
$172$	1.52446	+	0.631450i	0.116239	+	0.0481476i
$173$	−0.219886	+	1.10544i	−0.0167176	+	0.0840450i	−0.988243	−	0.152889i	$-0.951142\pi$
$173$	−0.219886	+	1.10544i	−0.0167176	+	0.0840450i	0.971526	+	0.236934i	$0.0761424\pi$
$174$	−0.933443	−	0.933443i	−0.0707641	−	0.0707641i
$175$	4.31078	+	16.9048i	0.325865	+	1.27788i
$176$	−0.916536	+	1.37169i	−0.0690865	+	0.103395i
$177$	7.20924	+	4.81706i	0.541879	+	0.362072i
$178$	2.43616	+	5.88140i	0.182598	+	0.440830i
$179$	5.76488	+	2.38789i	0.430888	+	0.178480i	0.587577	−	0.809168i	$-0.300082\pi$
$179$	5.76488	+	2.38789i	0.430888	+	0.178480i	−0.156689	+	0.987648i	$0.550082\pi$
$180$	0.0596204	+	2.23527i	0.00444384	+	0.166607i
$181$	−8.44320	−	5.64156i	−0.627578	−	0.419334i	0.200699	−	0.979653i	$-0.435679\pi$
$181$	−8.44320	−	5.64156i	−0.627578	−	0.419334i	−0.828277	+	0.560319i	$0.810679\pi$
$182$	−7.63228	+	5.09973i	−0.565742	+	0.378017i
$183$		−	0.314527i		−	0.0232505i
$184$	−4.06592	−	6.08507i	−0.299743	−	0.448598i
$185$	4.04616	+	2.55019i	0.297480	+	0.187494i
$186$			6.81857i			0.499962i
$187$	−4.70745	+	4.90987i	−0.344243	+	0.359045i
$188$	7.78641	+	7.78641i	0.567882	+	0.567882i
$189$	3.22356	−	1.33524i	0.234480	−	0.0971247i
$190$	−2.02165	−	0.774913i	−0.146666	−	0.0562181i
$191$	−6.25932	+	6.25932i	−0.452908	+	0.452908i	−0.896319	−	0.443410i	$-0.853768\pi$
$191$	−6.25932	+	6.25932i	−0.452908	+	0.452908i	0.443410	+	0.896319i	$0.353768\pi$
$192$	−0.555570	−	0.831470i	−0.0400948	−	0.0600062i
$193$	1.86148	−	0.370272i	0.133993	−	0.0266528i	−0.127638	−	0.991821i	$-0.540740\pi$
$193$	1.86148	−	0.370272i	0.133993	−	0.0266528i	0.261631	+	0.965168i	$0.415740\pi$
$194$	13.6794	−	2.72100i	0.982124	−	0.195357i
$195$	4.97663	+	3.13664i	0.356384	+	0.224619i
$196$	−1.98009	+	4.78037i	−0.141435	+	0.341455i
$197$	−12.1672	+	18.2096i	−0.866880	+	1.29738i	0.0866997	+	0.996234i	$0.472368\pi$
$197$	−12.1672	+	18.2096i	−0.866880	+	1.29738i	−0.953579	+	0.301142i	$0.902632\pi$
$198$	−0.321845	−	1.61802i	−0.0228725	−	0.114988i
$199$	−1.58342	+	7.96041i	−0.112246	+	0.564298i	0.883202	+	0.468992i	$0.155383\pi$
$199$	−1.58342	+	7.96041i	−0.112246	+	0.564298i	−0.995448	+	0.0953057i	$0.969617\pi$
$200$	−1.66445	+	4.71483i	−0.117694	+	0.333389i
$201$	3.32803	−	2.22372i	0.234741	−	0.156849i
$202$	5.16820	−	12.4771i	0.363633	−	0.877888i
$203$	−3.25693	+	3.25693i	−0.228592	+	0.228592i
$204$	−1.65765	−	3.77521i	−0.116059	−	0.264317i
$205$	−1.14411	+	6.67777i	−0.0799080	+	0.466396i
$206$	4.55829	+	11.0047i	0.317591	+	0.766733i
$207$	7.17784	+	1.42776i	0.498894	+	0.0992362i
$208$	−2.63079			−0.182413
$209$	1.56666	+	0.311627i	0.108368	+	0.0215557i
$210$	7.79923	−	0.208025i	0.538198	−	0.0143551i
$211$	0.593921	+	2.98584i	0.0408872	+	0.205554i	0.995829	−	0.0912393i	$-0.0290828\pi$
$211$	0.593921	+	2.98584i	0.0408872	+	0.205554i	−0.954942	+	0.296793i	$0.904083\pi$
$212$	5.38439	−	2.23029i	0.369801	−	0.153177i
$213$	12.7365	−	5.27565i	0.872694	−	0.361482i
$214$	−0.582105	−	2.92644i	−0.0397919	−	0.200047i
$215$	−3.68833	+	0.0983771i	−0.251542	+	0.00670927i
$216$	0.980785	+	0.195090i	0.0667340	+	0.0132742i
$217$	23.7911			1.61504
$218$	−2.72581	−	0.542197i	−0.184615	−	0.0367222i
$219$	5.00294	+	12.0782i	0.338067	+	0.816166i
$220$	0.622943	−	3.63591i	0.0419988	−	0.245133i
$221$	−10.6808	−	1.89182i	−0.718468	−	0.127258i
$222$	1.51244	−	1.51244i	0.101509	−	0.101509i
$223$	−3.27339	+	7.90267i	−0.219203	+	0.529202i	−0.994779	−	0.102052i	$-0.967459\pi$
$223$	−3.27339	+	7.90267i	−0.219203	+	0.529202i	0.775577	+	0.631253i	$0.217459\pi$
$224$	−2.90113	+	1.93847i	−0.193840	+	0.129520i
$225$	−2.15694	−	4.51083i	−0.143796	−	0.300722i
$226$	−3.46326	+	17.4110i	−0.230373	+	1.15816i
$227$	−0.544920	−	2.73950i	−0.0361676	−	0.181827i	0.958479	−	0.285164i	$-0.0920480\pi$
$227$	−0.544920	−	2.73950i	−0.0361676	−	0.181827i	−0.994646	+	0.103337i	$0.967048\pi$
$228$	−0.537933	+	0.805074i	−0.0356255	+	0.0533173i
$229$	−7.13304	+	17.2207i	−0.471364	+	1.13797i	0.492196	+	0.870484i	$0.336194\pi$
$229$	−7.13304	+	17.2207i	−0.471364	+	1.13797i	−0.963561	+	0.267490i	$0.913806\pi$
$230$	13.8442	+	8.72564i	0.912861	+	0.575352i
$231$	−5.64554	+	1.12297i	−0.371449	+	0.0738858i
$232$	−1.29472	+	0.257536i	−0.0850027	+	0.0169081i
$233$	15.6508	+	23.4232i	1.02532	+	1.53450i	0.833079	+	0.553154i	$0.186576\pi$
$233$	15.6508	+	23.4232i	1.02532	+	1.53450i	0.192242	+	0.981347i	$0.438424\pi$
$234$	1.86025	−	1.86025i	0.121609	−	0.121609i
$235$	−22.9916	−	8.81284i	−1.49981	−	0.574886i
$236$	8.01048	−	3.31805i	0.521438	−	0.215986i
$237$	−10.3045	−	10.3045i	−0.669349	−	0.669349i
$238$	−13.1723	+	5.78381i	−0.853834	+	0.374909i
$239$		−	15.5353i		−	1.00489i	−0.864608	−	0.502447i	$-0.832433\pi$
$239$		−	15.5353i		−	1.00489i	0.864608	−	0.502447i	$-0.167567\pi$
$240$	1.89168	+	1.19228i	0.122108	+	0.0769613i
$241$	−1.32613	−	1.98470i	−0.0854238	−	0.127846i	0.786297	−	0.617849i	$-0.211996\pi$
$241$	−1.32613	−	1.98470i	−0.0854238	−	0.127846i	−0.871721	+	0.490003i	$0.836996\pi$
$242$		−	8.27842i		−	0.532157i
$243$	−0.831470	+	0.555570i	−0.0533388	+	0.0356398i
$244$	−0.261520	−	0.174742i	−0.0167421	−	0.0111867i
$245$	−0.308490	−	11.5658i	−0.0197087	−	0.738914i
$246$	2.79927	+	1.15949i	0.178475	+	0.0739267i
$247$	0.974801	+	2.35338i	0.0620251	+	0.149742i
$248$	5.66944	+	3.78820i	0.360009	+	0.240551i
$249$	−2.12249	+	3.17653i	−0.134508	+	0.201305i
$250$	−0.893458	−	11.1446i	−0.0565073	−	0.704845i
$251$	9.56613	+	9.56613i	0.603809	+	0.603809i	0.941321	−	0.337512i	$-0.109585\pi$
$251$	9.56613	+	9.56613i	0.603809	+	0.603809i	−0.337512	+	0.941321i	$0.609585\pi$
$252$	0.680701	−	3.42212i	0.0428802	−	0.215573i
$253$	−11.1544	−	4.62030i	−0.701270	−	0.290476i
$254$	−8.13376			−0.510357
$255$	6.82270	+	6.20087i	0.427254	+	0.388314i
$256$	−1.00000			−0.0625000
$257$	28.4675	+	11.7916i	1.77575	+	0.735541i	0.993666	+	0.112372i	$0.0358449\pi$
$257$	28.4675	+	11.7916i	1.77575	+	0.735541i	0.782087	+	0.623169i	$0.214155\pi$
$258$	−0.321910	+	1.61835i	−0.0200413	+	0.100754i
$259$	−5.27716	−	5.27716i	−0.327907	−	0.327907i
$260$	5.37289	−	2.39530i	0.333213	−	0.148550i
$261$	0.733401	−	1.09761i	0.0453964	−	0.0679405i
$262$	−16.6939	−	11.1545i	−1.03135	−	0.689129i
$263$	−10.0539	−	24.2722i	−0.619948	−	1.49669i	−0.851763	−	0.523928i	$-0.824466\pi$
$263$	−10.0539	−	24.2722i	−0.619948	−	1.49669i	0.231814	−	0.972760i	$-0.425534\pi$
$264$	−1.52414	−	0.631321i	−0.0938046	−	0.0388551i
$265$	−8.96594	+	9.45733i	−0.550773	+	0.580959i
$266$	2.80903	+	1.87693i	0.172233	+	0.115082i
$267$	−5.29312	+	3.53675i	−0.323934	+	0.216446i
$268$		−	4.00258i		−	0.244497i
$269$	−7.07205	−	10.5841i	−0.431191	−	0.645322i	0.550715	−	0.834693i	$-0.314355\pi$
$269$	−7.07205	−	10.5841i	−0.431191	−	0.645322i	−0.981906	+	0.189371i	$0.939355\pi$
$270$	−2.18069	+	0.494555i	−0.132713	+	0.0300977i
$271$			9.65856i			0.586716i	0.956003	+	0.293358i	$0.0947727\pi$
$271$			9.65856i			0.586716i	−0.956003	+	0.293358i	$0.905227\pi$
$272$	−4.05991	−	0.719107i	−0.246168	−	0.0436023i
$273$	−6.49072	−	6.49072i	−0.392836	−	0.392836i
$274$	2.71685	−	1.12536i	0.164131	−	0.0679853i
$275$	2.03820	+	7.99283i	0.122908	+	0.481986i
$276$	5.17493	−	5.17493i	0.311494	−	0.311494i
$277$	13.2810	+	19.8764i	0.797977	+	1.19426i	0.977590	+	0.210520i	$0.0675157\pi$
$277$	13.2810	+	19.8764i	0.797977	+	1.19426i	−0.179612	+	0.983738i	$0.557484\pi$
$278$	−7.15741	+	1.42370i	−0.429273	+	0.0853877i
$279$	−6.68755	+	1.33024i	−0.400373	+	0.0796392i
$280$	4.16005	−	6.60039i	0.248611	−	0.394449i
$281$	−6.41043	+	15.4762i	−0.382414	+	0.923230i	0.609083	+	0.793106i	$0.291538\pi$
$281$	−6.41043	+	15.4762i	−0.382414	+	0.923230i	−0.991498	+	0.130124i	$0.958462\pi$
$282$	−6.11774	+	9.15585i	−0.364306	+	0.545223i
$283$	−4.47531	−	22.4989i	−0.266030	−	1.33742i	−0.850486	−	0.525997i	$-0.823692\pi$
$283$	−4.47531	−	22.4989i	−0.266030	−	1.33742i	0.584457	−	0.811425i	$-0.301308\pi$
$284$	2.68950	−	13.5210i	0.159593	−	0.802326i
$285$	0.365618	−	2.13399i	0.0216573	−	0.126406i
$286$	−3.60864	+	2.41122i	−0.213384	+	0.142578i
$287$	4.04566	−	9.76709i	0.238808	−	0.576533i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	−15.9658	−	5.83902i	−0.939163	−	0.343472i
$290$	2.40974	−	1.70479i	0.141505	−	0.100109i
$291$	5.33744	+	12.8857i	0.312886	+	0.755374i
$292$	12.8221	+	2.55047i	0.750357	+	0.149255i
$293$	15.4812			0.904420			0.452210	−	0.891912i	$-0.350636\pi$
$293$	15.4812			0.904420			0.452210	+	0.891912i	$0.350636\pi$
$294$	−5.07482	−	1.00944i	−0.295969	−	0.0588719i
$295$	−13.3388	+	14.0699i	−0.776616	+	0.819180i
$296$	−0.417282	−	2.09782i	−0.0242541	−	0.121933i
$297$	1.52414	−	0.631321i	0.0884398	−	0.0366330i
$298$	10.0545	−	4.16470i	0.582440	−	0.241255i
$299$	−3.75614	−	18.8834i	−0.217223	−	1.09206i
$300$	−4.94895	−	0.712650i	−0.285728	−	0.0411449i
$301$	5.64669	+	1.12320i	0.325470	+	0.0647400i
$302$	16.0846			0.925563
$303$	13.2456	+	2.63472i	0.760943	+	0.151361i
$304$	0.370535	+	0.894550i	0.0212516	+	0.0513059i
$305$	0.693204	+	0.118767i	0.0396927	+	0.00680059i
$306$	3.37928	−	2.36231i	0.193180	−	0.135044i
$307$	7.57075	−	7.57075i	0.432086	−	0.432086i	−0.457252	−	0.889337i	$-0.651166\pi$
$307$	7.57075	−	7.57075i	0.432086	−	0.432086i	0.889337	+	0.457252i	$0.151166\pi$
$308$	−2.20278	+	5.31798i	−0.125515	+	0.303020i
$309$	−9.90396	+	6.61762i	−0.563417	+	0.376463i
$310$	−15.0278	−	2.57473i	−0.853523	−	0.146235i
$311$	−4.29148	+	21.5747i	−0.243347	+	1.22339i	0.644988	+	0.764193i	$0.276863\pi$
$311$	−4.29148	+	21.5747i	−0.243347	+	1.22339i	−0.888335	+	0.459196i	$0.848137\pi$
$312$	−0.513243	−	2.58024i	−0.0290566	−	0.146078i
$313$	12.0901	−	18.0942i	0.683376	−	1.02274i	−0.313934	−	0.949445i	$-0.601647\pi$
$313$	12.0901	−	18.0942i	0.683376	−	1.02274i	0.997310	−	0.0732992i	$-0.0233528\pi$
$314$	2.66921	−	6.44405i	0.150632	−	0.363659i
$315$	1.72558	+	7.60878i	0.0972255	+	0.428706i
$316$	−14.2928	+	2.84301i	−0.804030	+	0.159932i
$317$	−18.7469	+	3.72899i	−1.05293	+	0.209441i	−0.691068	−	0.722790i	$-0.742859\pi$
$317$	−18.7469	+	3.72899i	−1.05293	+	0.209441i	−0.361863	+	0.932231i	$0.617859\pi$
$318$	3.23788	+	4.84582i	0.181571	+	0.271740i
$319$	−1.53992	+	1.53992i	−0.0862190	+	0.0862190i
$320$	2.04231	−	0.910484i	0.114168	−	0.0508976i
$321$	2.75665	−	1.14184i	0.153861	−	0.0637313i
$322$	−18.0562	−	18.0562i	−1.00623	−	1.00623i
$323$	0.861061	+	3.89825i	0.0479107	+	0.216904i
$324$			1.00000i			0.0555556i
$325$	−8.79222	+	9.78386i	−0.487704	+	0.542711i
$326$	−14.0413	−	21.0143i	−0.777674	−	1.16387i
$327$		−	2.77921i		−	0.153691i
$328$	2.51927	−	1.68332i	0.139104	−	0.0929461i
$329$	31.9462	+	21.3458i	1.76125	+	1.17683i
$330$	3.68758	−	0.0983570i	0.202994	−	0.00541438i
$331$	18.6582	+	7.72848i	1.02555	+	0.424796i	0.831103	−	0.556118i	$-0.187710\pi$
$331$	18.6582	+	7.72848i	1.02555	+	0.424796i	0.194444	+	0.980914i	$0.437710\pi$
$332$	1.46200	+	3.52958i	0.0802376	+	0.193711i
$333$	1.77845	+	1.18832i	0.0974583	+	0.0651195i
$334$	2.58189	−	3.86407i	0.141275	−	0.211433i
$335$	3.64429	+	8.17451i	0.199109	+	0.446621i
$336$	−2.46721	−	2.46721i	−0.134597	−	0.134597i
$337$	0.140908	−	0.708393i	0.00767575	−	0.0385886i	−0.976758	−	0.214347i	$-0.931238\pi$
$337$	0.140908	−	0.708393i	0.00767575	−	0.0385886i	0.984433	+	0.175758i	$0.0562377\pi$
$338$	5.61619	+	2.32630i	0.305480	+	0.126534i
$339$	−17.7521			−0.964161
$340$	8.94632	−	2.22785i	0.485182	−	0.120822i
$341$	11.2487			0.609154
$342$	−0.894550	−	0.370535i	−0.0483717	−	0.0200362i
$343$	1.24280	−	6.24797i	0.0671049	−	0.337359i
$344$	1.16677	+	1.16677i	0.0629079	+	0.0629079i
$345$	−5.85711	+	15.2805i	−0.315336	+	0.822674i
$346$	−0.626181	+	0.937147i	−0.0336637	+	0.0503813i
$347$	20.3060	+	13.5681i	1.09009	+	0.728372i	0.964598	−	0.263724i	$-0.0849507\pi$
$347$	20.3060	+	13.5681i	1.09009	+	0.728372i	0.125487	+	0.992095i	$0.459951\pi$
$348$	−0.505176	−	1.21960i	−0.0270803	−	0.0653775i
$349$	−30.0030	−	12.4277i	−1.60603	−	0.665238i	−0.613775	−	0.789481i	$-0.710350\pi$
$349$	−30.0030	−	12.4277i	−1.60603	−	0.665238i	−0.992252	+	0.124243i	$0.960350\pi$
$350$	−2.48655	+	17.2677i	−0.132912	+	0.922997i
$351$	2.18743	+	1.46159i	0.116756	+	0.0780140i
$352$	−1.37169	+	0.916536i	−0.0731115	+	0.0488515i
$353$			24.8745i			1.32393i	0.749533	+	0.661967i	$0.230278\pi$
$353$			24.8745i			1.32393i	−0.749533	+	0.661967i	$0.769722\pi$
$354$	4.81706	+	7.20924i	0.256024	+	0.383167i
$355$	6.81790	+	30.0629i	0.361857	+	1.59557i
$356$			6.36599i			0.337397i
$357$	−8.24246	−	11.7908i	−0.436237	−	0.624037i
$358$	4.41225	+	4.41225i	0.233195	+	0.233195i
$359$	−11.1261	+	4.60858i	−0.587213	+	0.243232i	−0.656451	−	0.754368i	$-0.727943\pi$
$359$	−11.1261	+	4.60858i	−0.587213	+	0.243232i	0.0692379	+	0.997600i	$0.477943\pi$
$360$	−0.800320	+	2.08794i	−0.0421806	+	0.110044i
$361$	−12.7721	+	12.7721i	−0.672216	+	0.672216i
$362$	−5.64156	−	8.44320i	−0.296514	−	0.443765i
$363$	8.11935	−	1.61504i	0.426155	−	0.0847676i
$364$	−9.00289	+	1.79079i	−0.471879	+	0.0938627i
$365$	−28.5088	+	6.46547i	−1.49222	+	0.338418i
$366$	0.120364	−	0.290585i	0.00629155	−	0.0151891i
$367$	−15.4629	+	23.1419i	−0.807158	+	1.20800i	0.167847	+	0.985813i	$0.446319\pi$
$367$	−15.4629	+	23.1419i	−0.807158	+	1.20800i	−0.975005	+	0.222184i	$0.928681\pi$
$368$	−1.42776	−	7.17784i	−0.0744271	−	0.374171i
$369$	−0.591105	+	2.97169i	−0.0307717	+	0.154700i
$370$	2.76225	+	3.90447i	0.143603	+	0.202983i
$371$	16.9079	−	11.2975i	0.877812	−	0.586535i
$372$	−2.60935	+	6.29954i	−0.135289	+	0.326616i
$373$	−3.95826	+	3.95826i	−0.204951	+	0.204951i	−0.802117	−	0.597166i	$-0.796293\pi$
$373$	−3.95826	+	3.95826i	−0.204951	+	0.204951i	0.597166	+	0.802117i	$0.296293\pi$
$374$	−6.22804	+	2.73466i	−0.322044	+	0.141406i
$375$	10.7561	−	3.05049i	0.555445	−	0.157527i
$376$	4.21397	+	10.1734i	0.217319	+	0.524655i
$377$	−3.40615	−	0.677525i	−0.175426	−	0.0348943i
$378$	3.48916			0.179463
$379$	17.4949	+	3.47996i	0.898654	+	0.178753i	0.622740	−	0.782429i	$-0.286019\pi$
$379$	17.4949	+	3.47996i	0.898654	+	0.178753i	0.275914	+	0.961182i	$0.411019\pi$
$380$	−1.57122	−	1.48958i	−0.0806018	−	0.0764138i
$381$	−1.58682	−	7.97747i	−0.0812951	−	0.408698i
$382$	−8.17820	+	3.38752i	−0.418433	+	0.173321i
$383$	−8.80128	+	3.64561i	−0.449724	+	0.186282i	−0.596038	−	0.802956i	$-0.703259\pi$
$383$	−8.80128	+	3.64561i	−0.449724	+	0.186282i	0.146313	+	0.989238i	$0.453259\pi$
$384$	−0.195090	−	0.980785i	−0.00995566	−	0.0500505i
$385$	−0.343183	−	12.8665i	−0.0174902	−	0.655740i
$386$	1.86148	+	0.370272i	0.0947471	+	0.0188464i
$387$	−1.65006			−0.0838772
$388$	13.6794	+	2.72100i	0.694466	+	0.138138i
$389$	6.99503	+	16.8875i	0.354662	+	0.856230i	0.996032	+	0.0889981i	$0.0283665\pi$
$389$	6.99503	+	16.8875i	0.354662	+	0.856230i	−0.641370	+	0.767232i	$0.721633\pi$
$390$	3.39747	+	4.80235i	0.172038	+	0.243177i
$391$	−0.634950	−	30.1681i	−0.0321108	−	1.52567i
$392$	−3.65874	+	3.65874i	−0.184794	+	0.184794i
$393$	7.68337	−	18.5493i	0.387575	−	0.935688i
$394$	−18.2096	+	12.1672i	−0.917384	+	0.612976i
$395$	26.6017	−	18.8196i	1.33848	−	0.946918i
$396$	0.321845	−	1.61802i	0.0161733	−	0.0813087i
$397$	−4.03879	−	20.3043i	−0.202701	−	1.01905i	−0.939399	−	0.342825i	$-0.888616\pi$
$397$	−4.03879	−	20.3043i	−0.202701	−	1.01905i	0.736699	−	0.676221i	$-0.236384\pi$
$398$	−4.50921	+	6.74851i	−0.226026	+	0.338272i
$399$	−1.29285	+	3.12123i	−0.0647237	+	0.156257i
$400$	−3.34204	+	3.71898i	−0.167102	+	0.185949i
$401$	25.8402	−	5.13993i	1.29040	−	0.256676i	0.498265	−	0.867025i	$-0.333971\pi$
$401$	25.8402	−	5.13993i	1.29040	−	0.256676i	0.792133	+	0.610349i	$0.208971\pi$
$402$	3.92568	−	0.780865i	0.195795	−	0.0389460i
$403$	9.96596	+	14.9151i	0.496440	+	0.742975i
$404$	9.54958	−	9.54958i	0.475109	−	0.475109i
$405$	−0.910484	−	2.04231i	−0.0452423	−	0.101483i
$406$	−4.25539	+	1.76264i	−0.211191	+	0.0874783i
$407$	−2.49511	−	2.49511i	−0.123678	−	0.123678i
$408$	−0.0867600	−	4.12219i	−0.00429526	−	0.204079i
$409$		−	20.5767i		−	1.01745i	−0.860928	−	0.508727i	$-0.830116\pi$
$409$		−	20.5767i		−	1.01745i	0.860928	−	0.508727i	$-0.169884\pi$
$410$	−3.61249	+	5.73163i	−0.178408	+	0.283065i
$411$	1.63377	+	2.44510i	0.0805877	+	0.120608i
$412$			11.9114i			0.586832i
$413$	25.1542	−	16.8075i	1.23776	−	0.827042i
$414$	6.08507	+	4.06592i	0.299065	+	0.199829i
$415$	−6.19947	−	5.87735i	−0.304320	−	0.288508i
$416$	−2.43054	−	1.00676i	−0.119167	−	0.0493605i
$417$	−2.79268	−	6.74213i	−0.136758	−	0.330164i
$418$	1.32815	+	0.887439i	0.0649618	+	0.0434061i
$419$	2.54927	−	3.81525i	0.124540	−	0.186387i	−0.763960	−	0.645263i	$-0.776748\pi$
$419$	2.54927	−	3.81525i	0.124540	−	0.186387i	0.888500	+	0.458876i	$0.151748\pi$
$420$	7.28515	+	2.79244i	0.355479	+	0.136257i
$421$	−4.73436	−	4.73436i	−0.230739	−	0.230739i	0.582262	−	0.813001i	$-0.302168\pi$
$421$	−4.73436	−	4.73436i	−0.230739	−	0.230739i	−0.813001	+	0.582262i	$0.802168\pi$
$422$	−0.593921	+	2.98584i	−0.0289116	+	0.145349i
$423$	−10.1734	−	4.21397i	−0.494649	−	0.204890i
$424$	5.82802			0.283034
$425$	−16.2427	+	12.6954i	−0.787888	+	0.615819i
$426$	13.7859			0.667931
$427$	−1.01390	−	0.419970i	−0.0490660	−	0.0203238i
$428$	0.582105	−	2.92644i	0.0281371	−	0.141455i
$429$	−3.06890	−	3.06890i	−0.148168	−	0.148168i
$430$	−3.44522	−	1.32057i	−0.166143	−	0.0636838i
$431$	19.3287	−	28.9275i	0.931032	−	1.39339i	0.0116880	−	0.999932i	$-0.496280\pi$
$431$	19.3287	−	28.9275i	0.931032	−	1.39339i	0.919344	−	0.393456i	$-0.128720\pi$
$432$	0.831470	+	0.555570i	0.0400041	+	0.0267299i
$433$	−1.79069	−	4.32312i	−0.0860552	−	0.207756i	0.874994	−	0.484135i	$-0.160866\pi$
$433$	−1.79069	−	4.32312i	−0.0860552	−	0.207756i	−0.961049	+	0.276379i	$0.910866\pi$
$434$	21.9801	+	9.10445i	1.05508	+	0.437028i
$435$	2.14215	+	2.03085i	0.102708	+	0.0973717i
$436$	−2.31083	−	1.54405i	−0.110669	−	0.0739464i
$437$	−5.89190	+	3.93684i	−0.281848	+	0.188325i
$438$			13.0733i			0.624667i
$439$	−17.1099	−	25.6067i	−0.816609	−	1.22214i	−0.972161	−	0.234314i	$-0.924715\pi$
$439$	−17.1099	−	25.6067i	−0.816609	−	1.22214i	0.155552	−	0.987828i	$-0.450285\pi$
$440$	1.96693	−	3.12075i	0.0937696	−	0.148776i
$441$		−	5.17424i		−	0.246392i
$442$	−9.14380	−	5.83518i	−0.434926	−	0.277551i
$443$	−22.1468	−	22.1468i	−1.05223	−	1.05223i	−0.998559	−	0.0536690i	$-0.982908\pi$
$443$	−22.1468	−	22.1468i	−1.05223	−	1.05223i	−0.0536690	−	0.998559i	$-0.517092\pi$
$444$	1.97610	−	0.818529i	0.0937817	−	0.0388457i
$445$	−5.79613	−	13.0013i	−0.274763	−	0.616321i
$446$	−6.04844	+	6.04844i	−0.286402	+	0.286402i
$447$	6.04621	+	9.04879i	0.285976	+	0.427993i
$448$	−3.42212	+	0.680701i	−0.161680	+	0.0321601i
$449$	21.7131	−	4.31901i	1.02471	−	0.203827i	0.345998	−	0.938235i	$-0.387540\pi$
$449$	21.7131	−	4.31901i	1.02471	−	0.203827i	0.678708	+	0.734409i	$0.262540\pi$
$450$	−0.266536	−	4.99289i	−0.0125646	−	0.235367i
$451$	1.91284	−	4.61801i	0.0900722	−	0.217454i
$452$	−9.86253	+	14.7603i	−0.463894	+	0.694267i
$453$	3.13794	+	15.7755i	0.147433	+	0.741198i
$454$	0.544920	−	2.73950i	0.0255744	−	0.128571i
$455$	16.7562	−	11.8543i	0.785542	−	0.555739i
$456$	−0.805074	+	0.537933i	−0.0377010	+	0.0251910i
$457$	2.27291	−	5.48728i	0.106322	−	0.256684i	−0.861761	−	0.507315i	$-0.830638\pi$
$457$	2.27291	−	5.48728i	0.106322	−	0.256684i	0.968083	+	0.250631i	$0.0806380\pi$
$458$	−13.1801	+	13.1801i	−0.615867	+	0.615867i
$459$	2.97618	+	2.85348i	0.138916	+	0.133189i
$460$	9.45123	+	13.3594i	0.440666	+	0.622885i
$461$	−7.89622	−	19.0632i	−0.367763	−	0.887860i	−0.994116	−	0.108320i	$-0.965453\pi$
$461$	−7.89622	−	19.0632i	−0.367763	−	0.887860i	0.626353	−	0.779540i	$-0.284547\pi$
$462$	−5.64554	−	1.12297i	−0.262654	−	0.0522452i
$463$	−30.3104			−1.40865			−0.704323	−	0.709880i	$-0.748749\pi$
$463$	−30.3104			−1.40865			−0.704323	+	0.709880i	$0.748749\pi$
$464$	−1.29472	−	0.257536i	−0.0601060	−	0.0119558i
$465$	−0.406526	−	15.2414i	−0.0188522	−	0.706802i
$466$	5.49585	+	27.6295i	0.254590	+	1.27991i
$467$	4.93732	−	2.04511i	0.228472	−	0.0946362i	−0.265511	−	0.964108i	$-0.585541\pi$
$467$	4.93732	−	2.04511i	0.228472	−	0.0946362i	0.493983	+	0.869472i	$0.335541\pi$
$468$	2.43054	−	1.00676i	0.112352	−	0.0465376i
$469$	−2.72456	−	13.6973i	−0.125809	−	0.632483i
$470$	−17.8690	−	16.9405i	−0.824234	−	0.781408i
$471$	6.84097	+	1.36075i	0.315215	+	0.0627002i
$472$	8.67048			0.399091
$473$	2.66983	+	0.531062i	0.122759	+	0.0244183i
$474$	−5.57676	−	13.4635i	−0.256149	−	0.618398i
$475$	4.56515	+	1.61161i	0.209463	+	0.0739457i
$476$	−14.3830	+	0.302720i	−0.659243	+	0.0138751i
$477$	−4.12103	+	4.12103i	−0.188689	+	0.188689i
$478$	5.94510	−	14.3527i	0.271922	−	0.656479i
$479$	3.28189	−	2.19289i	0.149953	−	0.100195i	−0.478330	−	0.878180i	$-0.658758\pi$
$479$	3.28189	−	2.19289i	0.149953	−	0.100195i	0.628283	+	0.777985i	$0.283758\pi$
$480$	1.29142	+	1.82544i	0.0589452	+	0.0833195i
$481$	1.09778	−	5.51894i	0.0500547	−	0.251642i
$482$	−0.465676	−	2.34111i	−0.0212110	−	0.106635i
$483$	14.1866	−	21.2318i	0.645514	−	0.966080i
$484$	3.16801	−	7.64826i	0.144001	−	0.347648i
$485$	−30.4150	+	6.89775i	−1.38107	+	0.313211i
$486$	−0.980785	+	0.195090i	−0.0444893	+	0.00884948i
$487$	−29.4659	+	5.86113i	−1.33523	+	0.265593i	−0.810531	−	0.585696i	$-0.800821\pi$
$487$	−29.4659	+	5.86113i	−1.33523	+	0.265593i	−0.524697	+	0.851289i	$0.675821\pi$
$488$	−0.174742	−	0.261520i	−0.00791020	−	0.0118384i
$489$	17.8712	−	17.8712i	0.808162	−	0.808162i
$490$	4.14104	−	10.8035i	0.187073	−	0.488052i
$491$	20.3436	−	8.42658i	0.918092	−	0.380286i	0.126943	−	0.991910i	$-0.459483\pi$
$491$	20.3436	−	8.42658i	0.918092	−	0.380286i	0.791149	+	0.611624i	$0.209483\pi$
$492$	2.14247	+	2.14247i	0.0965898	+	0.0965898i
$493$	−5.07126	−	1.97662i	−0.228398	−	0.0890224i
$494$			2.54728i			0.114607i
$495$	0.815878	+	3.59753i	0.0366710	+	0.161697i
$496$	3.78820	+	5.66944i	0.170095	+	0.254565i
$497$		−	48.1013i		−	2.15764i
$498$	−3.17653	+	2.12249i	−0.142344	+	0.0951112i
$499$	−29.8486	−	19.9442i	−1.33621	−	0.892825i	−0.337386	−	0.941366i	$-0.609543\pi$
$499$	−29.8486	−	19.9442i	−1.33621	−	0.892825i	−0.998821	+	0.0485410i	$0.984543\pi$
$500$	3.43940	−	10.6382i	0.153815	−	0.475753i
$501$	4.29353	+	1.77844i	0.191821	+	0.0794547i
$502$	5.17715	+	12.4988i	0.231068	+	0.557847i
$503$	−5.56741	−	3.72002i	−0.248238	−	0.165868i	0.425226	−	0.905087i	$-0.360195\pi$
$503$	−5.56741	−	3.72002i	−0.248238	−	0.165868i	−0.673465	+	0.739220i	$0.735195\pi$
$504$	1.93847	−	2.90113i	0.0863465	−	0.129227i
$505$	−10.8084	+	28.1979i	−0.480969	+	1.25479i
$506$	−8.53719	−	8.53719i	−0.379525	−	0.379525i
$507$	−1.18594	+	5.96211i	−0.0526694	+	0.264787i
$508$	−7.51461	−	3.11265i	−0.333407	−	0.138102i
$509$	13.1057			0.580901			0.290451	−	0.956890i	$-0.406195\pi$
$509$	13.1057			0.580901			0.290451	+	0.956890i	$0.406195\pi$
$510$	3.93038	+	8.33979i	0.174040	+	0.369292i
$511$	45.6148			2.01788
$512$	−0.923880	−	0.382683i	−0.0408301	−	0.0169124i
$513$	0.188897	−	0.949649i	0.00834000	−	0.0419280i
$514$	21.7881	+	21.7881i	0.961031	+	0.961031i
$515$	−10.8451	−	24.3267i	−0.477894	−	1.07196i
$516$	−0.916723	+	1.37197i	−0.0403565	+	0.0603978i
$517$	15.1046	+	10.0926i	0.664299	+	0.443871i
$518$	−2.85598	−	6.89494i	−0.125485	−	0.302946i
$519$	−1.04130	−	0.431321i	−0.0457081	−	0.0189329i
$520$	5.88054	−	0.156849i	0.257879	−	0.00687829i
$521$	20.6114	+	13.7721i	0.903003	+	0.603367i	0.918026	−	0.396520i	$-0.129782\pi$
$521$	20.6114	+	13.7721i	0.903003	+	0.603367i	−0.0150230	+	0.999887i	$0.504782\pi$
$522$	1.09761	−	0.733401i	0.0480412	−	0.0321001i
$523$		−	32.0074i		−	1.39959i	−0.714346	−	0.699793i	$-0.753276\pi$
$523$		−	32.0074i		−	1.39959i	0.714346	−	0.699793i	$-0.246724\pi$
$524$	−11.1545	−	16.6939i	−0.487287	−	0.729277i
$525$	−17.4210	+	0.929986i	−0.760315	+	0.0405879i
$526$		−	26.2720i		−	1.14552i
$527$	11.3028	+	25.7415i	0.492358	+	1.12132i
$528$	−1.16653	−	1.16653i	−0.0507667	−	0.0507667i
$529$	28.2336	−	11.6947i	1.22755	−	0.508467i
$530$	−11.9026	+	5.30632i	−0.517016	+	0.230492i
$531$	−6.13095	+	6.13095i	−0.266061	+	0.266061i
$532$	1.87693	+	2.80903i	0.0813754	+	0.121787i
$533$	7.81790	−	1.55508i	0.338631	−	0.0673578i
$534$	−6.24367	+	1.24194i	−0.270190	+	0.0537441i
$535$	1.47564	+	6.50669i	0.0637975	+	0.281309i
$536$	1.53172	−	3.69791i	0.0661603	−	0.159725i
$537$	−3.46668	+	5.18826i	−0.149598	+	0.223890i
$538$	−2.48337	−	12.4848i	−0.107066	−	0.538256i
$539$	−1.66530	+	8.37203i	−0.0717296	+	0.360609i
$540$	−2.20395	−	0.377605i	−0.0948431	−	0.0162495i
$541$	37.6410	−	25.1509i	1.61831	−	1.08132i	0.681315	−	0.731990i	$-0.261408\pi$
$541$	37.6410	−	25.1509i	1.61831	−	1.08132i	0.936999	−	0.349333i	$-0.113592\pi$
$542$	−3.69617	+	8.92334i	−0.158764	+	0.383290i
$543$	7.18035	−	7.18035i	0.308138	−	0.308138i
$544$	−3.47568	−	2.21803i	−0.149019	−	0.0950972i
$545$	6.12525	+	1.04944i	0.262377	+	0.0449532i
$546$	−3.51275	−	8.48053i	−0.150332	−	0.362933i
$547$	−25.4793	−	5.06815i	−1.08942	−	0.216698i	−0.382472	−	0.923967i	$-0.624927\pi$
$547$	−25.4793	−	5.06815i	−1.08942	−	0.216698i	−0.706945	+	0.707269i	$0.749927\pi$
$548$	2.94070			0.125620
$549$	0.308484	+	0.0613612i	0.0131658	+	0.00261883i
$550$	−1.17567	+	8.16439i	−0.0501309	+	0.348131i
$551$	0.249361	+	1.25362i	0.0106231	+	0.0534060i
$552$	6.76137	−	2.80065i	0.287783	−	0.119204i
$553$	−46.9762	+	19.4582i	−1.99763	+	0.827447i
$554$	4.66366	+	23.4458i	0.198140	+	0.996117i
$555$	−3.29055	+	3.47090i	−0.139676	+	0.147331i
$556$	−7.15741	−	1.42370i	−0.303542	−	0.0603782i
$557$	25.2990			1.07195			0.535976	−	0.844233i	$-0.319944\pi$
$557$	25.2990			1.07195			0.535976	+	0.844233i	$0.319944\pi$
$558$	−6.68755	−	1.33024i	−0.283107	−	0.0563134i
$559$	1.66122	+	4.01053i	0.0702619	+	0.169627i
$560$	6.36925	−	4.50598i	0.269150	−	0.190413i
$561$	−3.89715	−	5.57486i	−0.164538	−	0.235371i
$562$	−11.8449	+	11.8449i	−0.499649	+	0.499649i
$563$	−4.29740	+	10.3748i	−0.181114	+	0.437248i	−0.988197	−	0.153191i	$-0.951045\pi$
$563$	−4.29740	+	10.3748i	−0.181114	+	0.437248i	0.807083	+	0.590438i	$0.201045\pi$
$564$	−9.15585	+	6.11774i	−0.385531	+	0.257603i
$565$	6.70328	−	39.1248i	0.282009	−	1.64599i
$566$	4.47531	−	22.4989i	0.188111	−	0.945700i
$567$	0.680701	+	3.42212i	0.0285868	+	0.143715i
$568$	7.65906	−	11.4626i	0.321367	−	0.480959i
$569$	−7.25204	+	17.5080i	−0.304021	+	0.733973i	0.695854	+	0.718183i	$0.255026\pi$
$569$	−7.25204	+	17.5080i	−0.304021	+	0.733973i	−0.999875	+	0.0157892i	$0.994974\pi$
$570$	1.15443	−	1.83163i	0.0483537	−	0.0767186i
$571$	−0.250131	+	0.0497541i	−0.0104677	+	0.00208215i	−0.200321	−	0.979730i	$-0.564199\pi$
$571$	−0.250131	+	0.0497541i	−0.0104677	+	0.00208215i	0.189854	+	0.981812i	$0.439199\pi$
$572$	−4.25668	+	0.846707i	−0.177981	+	0.0354026i
$573$	−4.91792	−	7.36018i	−0.205449	−	0.307476i
$574$	7.47541	−	7.47541i	0.312017	−	0.312017i
$575$	−31.4658	−	18.6788i	−1.31222	−	0.778959i
$576$	0.923880	−	0.382683i	0.0384950	−	0.0159451i
$577$	13.8293	+	13.8293i	0.575723	+	0.575723i	0.933722	−	0.357999i	$-0.116541\pi$
$577$	13.8293	+	13.8293i	0.575723	+	0.575723i	−0.357999	+	0.933722i	$0.616541\pi$
$578$	−12.5160	−	11.5044i	−0.520595	−	0.478519i
$579$			1.89795i			0.0788762i
$580$	2.87870	−	0.652856i	0.119532	−	0.0271084i
$581$	7.40572	+	11.0834i	0.307241	+	0.459819i
$582$			13.9474i			0.578138i
$583$	7.99426	−	5.34159i	0.331088	−	0.221226i
$584$	10.8701	+	7.26314i	0.449806	+	0.300551i
$585$	−4.04726	+	4.26908i	−0.167334	+	0.176505i
$586$	14.3027	+	5.92439i	0.590841	+	0.244734i
$587$	−7.46527	−	18.0228i	−0.308125	−	0.743879i	−0.999766	−	0.0216374i	$-0.993112\pi$
$587$	−7.46527	−	18.0228i	−0.308125	−	0.743879i	0.691641	−	0.722241i	$-0.256888\pi$
$588$	−4.30222	−	2.87465i	−0.177421	−	0.118549i
$589$	3.66793	−	5.48945i	0.151135	−	0.226189i
$590$	−17.7078	+	7.89433i	−0.729018	+	0.325004i
$591$	−15.4860	−	15.4860i	−0.637007	−	0.637007i
$592$	0.417282	−	2.09782i	0.0171502	−	0.0862199i
$593$	−29.8738	−	12.3741i	−1.22677	−	0.508145i	−0.327215	−	0.944950i	$-0.606110\pi$
$593$	−29.8738	−	12.3741i	−1.22677	−	0.508145i	−0.899556	+	0.436805i	$0.856110\pi$
$594$	1.64972			0.0676889
$595$	29.0989	−	13.7137i	1.19294	−	0.562208i
$596$	10.8829			0.445780
$597$	−7.49854	−	3.10600i	−0.306895	−	0.127120i
$598$	3.75614	−	18.8834i	0.153600	−	0.772200i
$599$	−9.58466	−	9.58466i	−0.391619	−	0.391619i	0.483645	−	0.875264i	$-0.339312\pi$
$599$	−9.58466	−	9.58466i	−0.391619	−	0.391619i	−0.875264	+	0.483645i	$0.839312\pi$
$600$	−4.29952	−	2.55229i	−0.175527	−	0.104197i
$601$	−5.53485	+	8.28349i	−0.225771	+	0.337890i	−0.927010	−	0.375036i	$-0.877630\pi$
$601$	−5.53485	+	8.28349i	−0.225771	+	0.337890i	0.701239	+	0.712926i	$0.252630\pi$
$602$	4.78703	+	3.19859i	0.195105	+	0.130365i
$603$	1.53172	+	3.69791i	0.0623766	+	0.150590i
$604$	14.8602	+	6.15530i	0.604653	+	0.250455i
$605$	0.493563	+	18.5045i	0.0200662	+	0.752316i
$606$	11.2291	+	7.50306i	0.456152	+	0.304791i
$607$	−15.2038	+	10.1588i	−0.617103	+	0.412335i	−0.824452	−	0.565932i	$-0.808516\pi$
$607$	−15.2038	+	10.1588i	−0.617103	+	0.412335i	0.207349	+	0.978267i	$0.433516\pi$
$608$			0.968254i			0.0392679i
$609$	−2.55895	−	3.82975i	−0.103694	−	0.155189i
$610$	0.594986	+	0.375004i	0.0240903	+	0.0151835i
$611$			28.9694i			1.17198i
$612$	4.02606	−	0.889293i	0.162744	−	0.0359475i
$613$	−0.133400	−	0.133400i	−0.00538797	−	0.00538797i	0.704408	−	0.709796i	$-0.251213\pi$
$613$	−0.133400	−	0.133400i	−0.00538797	−	0.00538797i	−0.709796	+	0.704408i	$0.751213\pi$
$614$	9.89166	−	4.09726i	0.399195	−	0.165352i
$615$	−6.32626	−	2.42489i	−0.255099	−	0.0977811i
$616$	−4.07021	+	4.07021i	−0.163993	+	0.163993i
$617$	12.3721	+	18.5162i	0.498084	+	0.745435i	0.992294	−	0.123907i	$-0.0395426\pi$
$617$	12.3721	+	18.5162i	0.498084	+	0.745435i	−0.494210	+	0.869343i	$0.664543\pi$
$618$	−11.6825	+	2.32380i	−0.469940	+	0.0934769i
$619$	26.9188	−	5.35448i	1.08196	−	0.215215i	0.378249	−	0.925704i	$-0.376526\pi$
$619$	26.9188	−	5.35448i	1.08196	−	0.215215i	0.703708	+	0.710489i	$0.251526\pi$
$620$	−12.8986	−	8.12964i	−0.518020	−	0.326494i
$621$	−2.80065	+	6.76137i	−0.112386	+	0.271325i
$622$	−12.2211	+	18.2902i	−0.490021	+	0.733368i
$623$	4.33334	+	21.7851i	0.173611	+	0.872804i
$624$	0.513243	−	2.58024i	0.0205461	−	0.103292i
$625$	2.66157	+	24.8579i	0.106463	+	0.994317i
$626$	18.0942	−	12.0901i	0.723189	−	0.483220i
$627$	−0.611279	+	1.47576i	−0.0244121	+	0.0589361i
$628$	4.93206	−	4.93206i	0.196811	−	0.196811i
$629$	3.20269	−	8.21690i	0.127700	−	0.327629i
$630$	−1.31753	+	7.68995i	−0.0524915	+	0.306375i
$631$	−4.71842	−	11.3913i	−0.187837	−	0.453479i	0.801705	−	0.597719i	$-0.203926\pi$
$631$	−4.71842	−	11.3913i	−0.187837	−	0.453479i	−0.989543	+	0.144240i	$0.953926\pi$
$632$	−14.2928	−	2.84301i	−0.568535	−	0.113089i
$633$	−3.04434			−0.121002
$634$	−18.7469	−	3.72899i	−0.744535	−	0.148097i
$635$	18.1812	−	0.484938i	0.721498	−	0.0192442i
$636$	1.13699	+	5.71604i	0.0450846	+	0.226656i
$637$	−12.5762	+	5.20922i	−0.498286	+	0.206397i
$638$	−2.01200	+	0.833399i	−0.0796560	+	0.0329946i
$639$	2.68950	+	13.5210i	0.106395	+	0.534884i
$640$	2.23527	−	0.0596204i	0.0883569	−	0.00235670i
$641$	−35.0293	−	6.96776i	−1.38357	−	0.275210i	−0.553493	−	0.832854i	$-0.686706\pi$
$641$	−35.0293	−	6.96776i	−1.38357	−	0.275210i	−0.830081	+	0.557644i	$0.811706\pi$
$642$	2.98377			0.117760
$643$	39.0300	+	7.76354i	1.53919	+	0.306164i	0.890534	−	0.454917i	$-0.150331\pi$
$643$	39.0300	+	7.76354i	1.53919	+	0.306164i	0.648657	+	0.761081i	$0.275331\pi$
$644$	−9.77192	−	23.5915i	−0.385068	−	0.929636i
$645$	0.623071	−	3.63665i	0.0245334	−	0.143193i
$646$	−0.696278	+	3.93102i	−0.0273947	+	0.154664i
$647$	−17.4082	+	17.4082i	−0.684387	+	0.684387i	−0.960985	−	0.276599i	$-0.910793\pi$
$647$	−17.4082	+	17.4082i	−0.684387	+	0.684387i	0.276599	+	0.960985i	$0.410793\pi$
$648$	−0.382683	+	0.923880i	−0.0150332	+	0.0362934i
$649$	11.8932	−	7.94680i	0.466850	−	0.311939i
$650$	−11.8671	+	5.67448i	−0.465465	+	0.222571i
$651$	−4.64141	+	23.3339i	−0.181911	+	0.914530i
$652$	−4.93064	−	24.7880i	−0.193099	−	0.970773i
$653$	−27.5968	+	41.3016i	−1.07995	+	1.61625i	−0.344342	+	0.938844i	$0.611898\pi$
$653$	−27.5968	+	41.3016i	−1.07995	+	1.61625i	−0.735605	+	0.677411i	$0.763102\pi$
$654$	1.06356	−	2.56765i	0.0415884	−	0.100403i
$655$	37.9805	+	23.9381i	1.48402	+	0.935339i
$656$	2.97169	−	0.591105i	0.116025	−	0.0230788i
$657$	−12.8221	+	2.55047i	−0.500238	+	0.0995035i
$658$	21.3458	+	31.9462i	0.832145	+	1.24539i
$659$	−11.0000	+	11.0000i	−0.428498	+	0.428498i	−0.888116	−	0.459618i	$-0.847986\pi$
$659$	−11.0000	+	11.0000i	−0.428498	+	0.428498i	0.459618	+	0.888116i	$0.347986\pi$
$660$	3.44452	+	1.32030i	0.134078	+	0.0513928i
$661$	−22.2890	+	9.23242i	−0.866943	+	0.359100i	−0.771419	−	0.636327i	$-0.780453\pi$
$661$	−22.2890	+	9.23242i	−0.866943	+	0.359100i	−0.0955241	+	0.995427i	$0.530453\pi$
$662$	14.2804	+	14.2804i	0.555022	+	0.555022i
$663$	3.93919	−	10.1065i	0.152986	−	0.392504i
$664$			3.82039i			0.148260i
$665$	−6.39085	−	4.02798i	−0.247827	−	0.156199i
$666$	1.18832	+	1.77845i	0.0460465	+	0.0689134i
$667$		−	9.66101i		−	0.374076i
$668$	3.86407	−	2.58189i	0.149505	−	0.0998964i
$669$	−7.11221	−	4.75223i	−0.274974	−	0.183732i
$670$	0.238636	+	8.94687i	0.00921930	+	0.345648i
$671$	−0.479385	−	0.198568i	−0.0185064	−	0.00766562i
$672$	−1.33524	−	3.22356i	−0.0515081	−	0.124352i
$673$	11.4427	+	7.64578i	0.441084	+	0.294723i	0.756213	−	0.654326i	$-0.227048\pi$
$673$	11.4427	+	7.64578i	0.441084	+	0.294723i	−0.315128	+	0.949049i	$0.602048\pi$
$674$	0.401272	−	0.600546i	0.0154564	−	0.0231322i
$675$	4.84496	−	1.23548i	0.186482	−	0.0475536i
$676$	4.29844	+	4.29844i	0.165325	+	0.165325i
$677$	2.93813	−	14.7710i	0.112922	−	0.567695i	−0.882352	−	0.470589i	$-0.844041\pi$
$677$	2.93813	−	14.7710i	0.112922	−	0.567695i	0.995274	−	0.0971060i	$-0.0309586\pi$
$678$	−16.4008	−	6.79343i	−0.629868	−	0.260900i
$679$	48.6647			1.86758
$680$	9.11789	+	1.36535i	0.349655	+	0.0523587i
$681$	2.79317			0.107034
$682$	10.3925	+	4.30471i	0.397949	+	0.164836i
$683$	5.08150	−	25.5464i	0.194438	−	0.977508i	−0.753110	−	0.657895i	$-0.771447\pi$
$683$	5.08150	−	25.5464i	0.194438	−	0.977508i	0.947548	−	0.319613i	$-0.103553\pi$
$684$	−0.684659	−	0.684659i	−0.0261786	−	0.0261786i
$685$	−6.00581	+	2.67746i	−0.229470	+	0.102301i
$686$	3.53919	−	5.29678i	0.135127	−	0.202232i
$687$	−15.4982	−	10.3556i	−0.591293	−	0.395089i
$688$	0.631450	+	1.52446i	0.0240738	+	0.0581193i
$689$	14.1652	+	5.86743i	0.539652	+	0.223531i
$690$	−11.2589	+	11.8759i	−0.428617	+	0.452108i
$691$	13.6755	+	9.13769i	0.520241	+	0.347614i	0.787804	−	0.615926i	$-0.211218\pi$
$691$	13.6755	+	9.13769i	0.520241	+	0.347614i	−0.267562	+	0.963541i	$0.586218\pi$
$692$	−0.937147	+	0.626181i	−0.0356250	+	0.0238038i
$693$		−	5.75614i		−	0.218658i
$694$	13.5681	+	20.3060i	0.515037	+	0.770807i
$695$	15.9139	−	3.60908i	0.603648	−	0.136900i
$696$		−	1.32009i		−	0.0500378i
$697$	12.4899	−	0.262875i	0.473087	−	0.00995709i
$698$	−22.9633	−	22.9633i	−0.869175	−	0.869175i
$699$	−26.0264	+	10.7805i	−0.984409	+	0.407756i
$700$	−8.90533	+	15.0017i	−0.336590	+	0.567011i
$701$	−3.10963	+	3.10963i	−0.117449	+	0.117449i	−0.763389	−	0.645939i	$-0.776466\pi$
$701$	−3.10963	+	3.10963i	−0.117449	+	0.117449i	0.645939	+	0.763389i	$0.276466\pi$
$702$	1.46159	+	2.18743i	0.0551642	+	0.0825591i
$703$	−2.03122	+	0.404035i	−0.0766090	+	0.0152385i
$704$	−1.61802	+	0.321845i	−0.0609815	+	0.0121300i
$705$	13.1289	−	20.8306i	0.494465	−	0.784524i
$706$	−9.51905	+	22.9810i	−0.358254	+	0.864902i
$707$	26.1794	−	39.1802i	0.984576	−	1.47352i
$708$	1.69153	+	8.50388i	0.0635714	+	0.319595i
$709$	2.80441	−	14.0987i	0.105322	−	0.529488i	−0.891717	−	0.452593i	$-0.850499\pi$
$709$	2.80441	−	14.0987i	0.105322	−	0.529488i	0.997039	−	0.0768956i	$-0.0245008\pi$
$710$	−5.20564	+	30.3836i	−0.195364	+	1.14028i
$711$	12.1168	−	8.09620i	0.454416	−	0.303631i
$712$	−2.43616	+	5.88140i	−0.0912989	+	0.220415i
$713$	−35.2856	+	35.2856i	−1.32146	+	1.32146i
$714$	−3.10289	−	14.0476i	−0.116123	−	0.525717i
$715$	7.92254	−	5.60488i	0.296286	−	0.209611i
$716$	2.38789	+	5.76488i	0.0892398	+	0.215444i
$717$	15.2368	+	3.03078i	0.569028	+	0.113187i
$718$	−12.0428			−0.449434
$719$	14.6803	+	2.92009i	0.547483	+	0.108901i	0.461079	−	0.887359i	$-0.347462\pi$
$719$	14.6803	+	2.92009i	0.547483	+	0.108901i	0.0864039	+	0.996260i	$0.472462\pi$
$720$	−1.53842	+	1.62273i	−0.0573335	+	0.0604758i
$721$	8.10810	+	40.7622i	0.301962	+	1.51806i
$722$	−16.6876	+	6.91221i	−0.621047	+	0.257246i
$723$	2.20528	−	0.913457i	0.0820152	−	0.0339718i
$724$	−1.98105	−	9.95943i	−0.0736253	−	0.370139i
$725$	−5.28478	+	3.95435i	−0.196272	+	0.146861i
$726$	8.11935	+	1.61504i	0.301337	+	0.0599397i
$727$	−50.5177			−1.87360			−0.936799	−	0.349868i	$-0.886227\pi$
$727$	−50.5177			−1.87360			−0.936799	+	0.349868i	$0.886227\pi$
$728$	−9.00289	−	1.79079i	−0.333669	−	0.0663709i
$729$	−0.382683	−	0.923880i	−0.0141735	−	0.0342178i
$730$	−28.8130	−	4.93655i	−1.06642	−	0.182710i
$731$	1.46739	+	6.64323i	0.0542732	+	0.245709i
$732$	0.222404	−	0.222404i	0.00822030	−	0.00822030i
$733$	−2.01521	+	4.86514i	−0.0744333	+	0.179698i	−0.956717	−	0.291020i	$-0.906005\pi$
$733$	−2.01521	+	4.86514i	−0.0744333	+	0.179698i	0.882284	+	0.470718i	$0.156005\pi$
$734$	−23.1419	+	15.4629i	−0.854183	+	0.570747i
$735$	11.4038	+	1.95382i	0.420635	+	0.0720677i
$736$	1.42776	−	7.17784i	0.0526279	−	0.264579i
$737$	−1.28821	−	6.47627i	−0.0474518	−	0.238556i
$738$	−1.68332	+	2.51927i	−0.0619640	+	0.0927358i
$739$	−10.5105	+	25.3747i	−0.386637	+	0.933423i	0.604011	+	0.796976i	$0.293568\pi$
$739$	−10.5105	+	25.3747i	−0.386637	+	0.933423i	−0.990647	+	0.136447i	$0.956432\pi$
$740$	1.05781	+	4.66432i	0.0388860	+	0.171464i
$741$	−2.49833	+	0.496949i	−0.0917785	+	0.0182559i
$742$	19.9442	−	3.96714i	0.732174	−	0.145638i
$743$	−27.6002	−	41.3066i	−1.01255	−	1.51539i	−0.848677	−	0.528911i	$-0.822601\pi$
$743$	−27.6002	−	41.3066i	−1.01255	−	1.51539i	−0.163875	−	0.986481i	$-0.552399\pi$
$744$	−4.82146	+	4.82146i	−0.176763	+	0.176763i
$745$	−22.2262	+	9.90869i	−0.814305	+	0.363026i
$746$	−5.17171	+	2.14219i	−0.189350	+	0.0784313i
$747$	−2.70142	−	2.70142i	−0.0988398	−	0.0988398i
$748$	−6.80047	+	0.143130i	−0.248650	+	0.00523335i
$749$		−	10.4109i		−	0.380405i
$750$	11.1047	+	1.29791i	0.405488	+	0.0473930i
$751$	−12.5146	−	18.7294i	−0.456664	−	0.683446i	0.529670	−	0.848204i	$-0.322316\pi$
$751$	−12.5146	−	18.7294i	−0.456664	−	0.683446i	−0.986334	+	0.164758i	$0.947316\pi$
$752$			11.0116i			0.401553i
$753$	−11.2486	+	7.51606i	−0.409921	+	0.273901i
$754$	−2.88759	−	1.92943i	−0.105160	−	0.0702656i
$755$	−35.9534	+	0.958968i	−1.30848	+	0.0349004i
$756$	3.22356	+	1.33524i	0.117240	+	0.0485623i
$757$	−9.24350	−	22.3158i	−0.335961	−	0.811081i	−0.998095	−	0.0616955i	$-0.980349\pi$
$757$	−9.24350	−	22.3158i	−0.335961	−	0.811081i	0.662134	−	0.749385i	$-0.269651\pi$
$758$	14.8315	+	9.91008i	0.538704	+	0.359950i
$759$	6.70763	−	10.0387i	0.243472	−	0.364381i
$760$	−0.881580	−	1.97747i	−0.0319783	−	0.0717304i
$761$	25.7772	+	25.7772i	0.934421	+	0.934421i	0.997978	−	0.0635568i	$-0.0202444\pi$
$761$	25.7772	+	25.7772i	0.934421	+	0.934421i	−0.0635568	+	0.997978i	$0.520244\pi$
$762$	1.58682	−	7.97747i	0.0574843	−	0.288993i
$763$	−8.95896	−	3.71092i	−0.324336	−	0.134344i
$764$	−8.85201			−0.320255
$765$	−7.41276	+	5.48187i	−0.268009	+	0.198198i
$766$	−9.52644			−0.344204
$767$	21.0739	+	8.72910i	0.760935	+	0.315190i
$768$	0.195090	−	0.980785i	0.00703972	−	0.0353910i
$769$	−6.07250	−	6.07250i	−0.218980	−	0.218980i	0.589089	−	0.808068i	$-0.299487\pi$
$769$	−6.07250	−	6.07250i	−0.218980	−	0.218980i	−0.808068	+	0.589089i	$0.799487\pi$
$770$	4.60675	−	12.0185i	0.166016	−	0.433116i
$771$	−17.1188	+	25.6201i	−0.616518	+	0.922684i
$772$	1.57809	+	1.05445i	0.0567967	+	0.0379504i
$773$	18.8743	+	45.5667i	0.678863	+	1.63892i	0.766092	+	0.642731i	$0.222199\pi$
$773$	18.8743	+	45.5667i	0.678863	+	1.63892i	−0.0872288	+	0.996188i	$0.527801\pi$
$774$	−1.52446	−	0.631450i	−0.0547954	−	0.0226970i
$775$	33.7448	+	4.85926i	1.21215	+	0.174550i
$776$	11.5968	+	7.74876i	0.416302	+	0.278164i
$777$	6.20528	−	4.14624i	0.222613	−	0.148745i
$778$			18.2789i			0.655330i
$779$	−1.62989	−	2.43930i	−0.0583967	−	0.0873969i
$780$	1.30107	+	5.73695i	0.0465859	+	0.205416i
$781$		−	22.7430i		−	0.813807i
$782$	10.9582	−	28.1147i	0.391865	−	1.00538i
$783$	0.933443	+	0.933443i	0.0333585	+	0.0333585i
$784$	−4.78037	+	1.98009i	−0.170728	+	0.0707177i
$785$	−5.58222	+	14.5634i	−0.199238	+	0.519788i
$786$	14.1970	−	14.1970i	0.506391	−	0.506391i
$787$	22.6349	+	33.8755i	0.806846	+	1.20753i	0.975095	+	0.221786i	$0.0711885\pi$
$787$	22.6349	+	33.8755i	0.806846	+	1.20753i	−0.168250	+	0.985744i	$0.553811\pi$
$788$	−21.4796	+	4.27256i	−0.765180	+	0.152204i
$789$	25.7672	−	5.12542i	0.917338	−	0.182470i
$790$	31.7787	−	7.20703i	1.13064	−	0.256415i
$791$	−23.7034	+	57.2250i	−0.842794	+	2.03469i
$792$	0.916536	−	1.37169i	0.0325677	−	0.0487410i
$793$	−0.161429	−	0.811557i	−0.00573250	−	0.0288192i
$794$	4.03879	−	20.3043i	0.143331	−	0.720574i
$795$	−7.52645	−	10.6387i	−0.266936	−	0.377316i
$796$	−6.74851	+	4.50921i	−0.239194	+	0.159825i
$797$	−2.70436	+	6.52890i	−0.0957933	+	0.231265i	−0.964511	−	0.264041i	$-0.914944\pi$
$797$	−2.70436	+	6.52890i	−0.0957933	+	0.231265i	0.868718	+	0.495307i	$0.164944\pi$
$798$	−2.38888	+	2.38888i	−0.0845656	+	0.0845656i
$799$	−7.91855	+	44.7063i	−0.280138	+	1.58160i
$800$	−4.51083	+	2.15694i	−0.159482	+	0.0762595i
$801$	−2.43616	−	5.88140i	−0.0860774	−	0.207809i
$802$	25.8402	+	5.13993i	0.912449	+	0.181497i
$803$	21.5673			0.761094
$804$	3.92568	+	0.780865i	0.138448	+	0.0275390i
$805$	41.4370	+	39.2839i	1.46046	+	1.38458i
$806$	3.49958	+	17.5936i	0.123267	+	0.619708i
$807$	11.7604	−	4.87131i	0.413985	−	0.171478i
$808$	12.4771	−	5.16820i	0.438944	−	0.181816i
$809$	−5.10851	−	25.6822i	−0.179606	−	0.902939i	−0.960501	−	0.278277i	$-0.910237\pi$
$809$	−5.10851	−	25.6822i	−0.179606	−	0.902939i	0.780895	−	0.624662i	$-0.214763\pi$
$810$	−0.0596204	−	2.23527i	−0.00209485	−	0.0785395i
$811$	−39.8766	−	7.93196i	−1.40026	−	0.278529i	−0.563507	−	0.826112i	$-0.690548\pi$
$811$	−39.8766	−	7.93196i	−1.40026	−	0.278529i	−0.836751	+	0.547583i	$0.815548\pi$
$812$	−4.60600			−0.161639
$813$	−9.47297	−	1.88429i	−0.332232	−	0.0660850i
$814$	−1.35034	−	3.26002i	−0.0473296	−	0.114264i
$815$	32.6390	+	46.1355i	1.14329	+	1.61605i
$816$	1.49734	−	3.84161i	0.0524174	−	0.134483i
$817$	1.12973	−	1.12973i	0.0395241	−	0.0395241i
$818$	7.87437	−	19.0104i	0.275321	−	0.664684i
$819$	7.63228	−	5.09973i	0.266693	−	0.178199i
$820$	−5.53090	+	3.91289i	−0.193148	+	0.136644i
$821$	8.04829	−	40.4615i	0.280887	−	1.41212i	−0.540307	−	0.841468i	$-0.681692\pi$
$821$	8.04829	−	40.4615i	0.280887	−	1.41212i	0.821195	−	0.570648i	$-0.193308\pi$
$822$	0.573702	+	2.88420i	0.0200102	+	0.100598i
$823$	9.80162	−	14.6692i	0.341663	−	0.511335i	−0.620355	−	0.784321i	$-0.713011\pi$
$823$	9.80162	−	14.6692i	0.341663	−	0.511335i	0.962018	+	0.272986i	$0.0880114\pi$
$824$	−4.55829	+	11.0047i	−0.158796	+	0.383367i
$825$	−8.23688	+	0.439710i	−0.286771	+	0.0153087i
$826$	29.6714	−	5.90200i	1.03240	−	0.205357i
$827$	−29.0069	+	5.76983i	−1.00867	+	0.200637i	−0.671656	−	0.740864i	$-0.734416\pi$
$827$	−29.0069	+	5.76983i	−1.00867	+	0.200637i	−0.337013	+	0.941500i	$0.609416\pi$
$828$	4.06592	+	6.08507i	0.141300	+	0.211471i
$829$	−15.7047	+	15.7047i	−0.545446	+	0.545446i	−0.925120	−	0.379674i	$-0.876036\pi$
$829$	−15.7047	+	15.7047i	−0.545446	+	0.545446i	0.379674	+	0.925120i	$0.376036\pi$
$830$	−3.47840	−	7.80240i	−0.120737	−	0.270825i
$831$	−22.0855	+	9.14811i	−0.766137	+	0.317344i
$832$	−1.86025	−	1.86025i	−0.0644927	−	0.0644927i
$833$	−20.8318	+	4.60141i	−0.721779	+	0.159429i
$834$		−	7.29763i		−	0.252696i
$835$	−5.54085	+	8.79119i	−0.191749	+	0.304232i
$836$	0.887439	+	1.32815i	0.0306927	+	0.0459349i
$837$		−	6.81857i		−	0.235684i
$838$	3.81525	−	2.54927i	0.131796	−	0.0880630i
$839$	−9.37011	−	6.26091i	−0.323492	−	0.216151i	0.383211	−	0.923661i	$-0.374818\pi$
$839$	−9.37011	−	6.26091i	−0.323492	−	0.216151i	−0.706703	+	0.707510i	$0.749818\pi$
$840$	5.66198	+	5.36779i	0.195357	+	0.185206i
$841$	25.1825	+	10.4309i	0.868363	+	0.359688i
$842$	−2.56222	−	6.18574i	−0.0882998	−	0.213175i
$843$	−13.9282	−	9.30651i	−0.479712	−	0.320533i
$844$	−1.69134	+	2.53127i	−0.0582185	+	0.0871301i
$845$	−12.6924	−	4.86508i	−0.436632	−	0.167364i
$846$	−7.78641	−	7.78641i	−0.267702	−	0.267702i
$847$	5.63513	−	28.3297i	0.193625	−	0.973421i
$848$	5.38439	+	2.23029i	0.184901	+	0.0765884i
$849$	22.9397			0.787288
$850$	−19.8646	+	5.51323i	−0.681352	+	0.189102i
$851$	15.6536			0.536598
$852$	12.7365	+	5.27565i	0.436347	+	0.180741i
$853$	−2.17138	+	10.9163i	−0.0743467	+	0.373766i	−0.999989	−	0.00463286i	$-0.998525\pi$
$853$	−2.17138	+	10.9163i	−0.0743467	+	0.373766i	0.925643	+	0.378399i	$0.123525\pi$
$854$	−0.776004	−	0.776004i	−0.0265543	−	0.0265543i
$855$	2.02165	+	0.774913i	0.0691391	+	0.0265015i
$856$	1.65770	−	2.48092i	0.0566589	−	0.0847960i
$857$	27.9324	+	18.6639i	0.954154	+	0.637545i	0.932096	−	0.362212i	$-0.117978\pi$
$857$	27.9324	+	18.6639i	0.954154	+	0.637545i	0.0220578	+	0.999757i	$0.492978\pi$
$858$	−1.66088	−	4.00971i	−0.0567014	−	0.136889i
$859$	10.9930	+	4.55345i	0.375076	+	0.155362i	0.562254	−	0.826964i	$-0.309934\pi$
$859$	10.9930	+	4.55345i	0.375076	+	0.155362i	−0.187178	+	0.982326i	$0.559934\pi$
$860$	−2.67761	−	2.53848i	−0.0913056	−	0.0865615i
$861$	8.79015	+	5.87339i	0.299567	+	0.200165i
$862$	28.9275	−	19.3287i	0.985274	−	0.658339i
$863$			6.56672i			0.223534i	0.993734	+	0.111767i	$0.0356510\pi$
$863$			6.56672i			0.223534i	−0.993734	+	0.111767i	$0.964349\pi$
$864$	0.555570	+	0.831470i	0.0189009	+	0.0282872i
$865$	1.34381	−	2.13211i	0.0456910	−	0.0724940i
$866$		−	4.67931i		−	0.159009i
$867$	8.84159	−	14.5199i	0.300276	−	0.493120i
$868$	16.8228	+	16.8228i	0.571004	+	0.571004i
$869$	−22.2110	+	9.20009i	−0.753456	+	0.312092i
$870$	1.20192	+	2.69602i	0.0407489	+	0.0914038i
$871$	7.44582	−	7.44582i	0.252292	−	0.252292i
$872$	−1.54405	−	2.31083i	−0.0522880	−	0.0782545i
$873$	−13.6794	+	2.72100i	−0.462978	+	0.0920920i
$874$	−6.94997	+	1.38243i	−0.235086	+	0.0467615i
$875$	4.52861	−	38.7462i	0.153095	−	1.30986i
$876$	−5.00294	+	12.0782i	−0.169034	+	0.408083i
$877$	−22.6648	+	33.9203i	−0.765337	+	1.14541i	0.220118	+	0.975473i	$0.429356\pi$
$877$	−22.6648	+	33.9203i	−0.765337	+	1.14541i	−0.985455	+	0.169935i	$0.945644\pi$
$878$	−6.00819	−	30.2052i	−0.202766	−	1.01938i
$879$	−3.02023	+	15.1837i	−0.101870	+	0.512134i
$880$	3.01146	−	2.13049i	0.101516	−	0.0718188i
$881$	−29.1488	+	19.4766i	−0.982049	+	0.656184i	−0.939370	−	0.342905i	$-0.888589\pi$
$881$	−29.1488	+	19.4766i	−0.982049	+	0.656184i	−0.0426789	+	0.999089i	$0.513589\pi$
$882$	1.98009	−	4.78037i	0.0666733	−	0.160963i
$883$	−3.07055	+	3.07055i	−0.103332	+	0.103332i	−0.756883	−	0.653551i	$-0.773279\pi$
$883$	−3.07055	+	3.07055i	−0.103332	+	0.103332i	0.653551	+	0.756883i	$0.273279\pi$
$884$	−6.21474	−	8.89018i	−0.209024	−	0.299009i
$885$	−11.1973	−	15.8274i	−0.376392	−	0.532033i
$886$	−11.9858	−	28.9362i	−0.402670	−	0.972132i
$887$	10.0622	+	2.00149i	0.337854	+	0.0672034i	0.361102	−	0.932526i	$-0.382401\pi$
$887$	10.0622	+	2.00149i	0.337854	+	0.0672034i	−0.0232478	+	0.999730i	$0.507401\pi$
$888$	2.13892			0.0717774
$889$	−27.8347	−	5.53666i	−0.933545	−	0.185694i
$890$	−0.379543	−	14.2297i	−0.0127223	−	0.476981i
$891$	0.321845	+	1.61802i	0.0107822	+	0.0542058i
$892$	−7.90267	+	3.27339i	−0.264601	+	0.109601i
$893$	9.85046	−	4.08020i	0.329633	−	0.136539i
$894$	2.12315	+	10.6738i	0.0710086	+	0.356984i
$895$	−10.1256	−	9.59953i	−0.338463	−	0.320877i
$896$	−3.42212	−	0.680701i	−0.114325	−	0.0227406i
$897$	19.2534			0.642851
$898$	21.7131	+	4.31901i	0.724576	+	0.144127i
$899$	3.44458	+	8.31594i	0.114883	+	0.277352i
$900$	1.66445	−	4.71483i	0.0554817	−	0.157161i
$901$	20.2563	+	12.9267i	0.674836	+	0.430652i
$902$	3.53447	−	3.53447i	0.117685	−	0.117685i
$903$	−2.20323	+	5.31907i	−0.0733189	+	0.177007i
$904$	−14.7603	+	9.86253i	−0.490921	+	0.328023i
$905$	13.1138	+	18.5365i	0.435918	+	0.616174i
$906$	−3.13794	+	15.7755i	−0.104251	+	0.524106i
$907$	10.3361	+	51.9633i	0.343206	+	1.72541i	0.638161	+	0.769903i	$0.279695\pi$
$907$	10.3361	+	51.9633i	0.343206	+	1.72541i	−0.294955	+	0.955511i	$0.595305\pi$
$908$	1.55180	−	2.32243i	0.0514983	−	0.0770727i
$909$	−5.16820	+	12.4771i	−0.171418	+	0.413840i
$910$	20.0171	−	4.53965i	0.663562	−	0.150488i
$911$	24.6111	−	4.89545i	0.815401	−	0.162193i	0.230264	−	0.973128i	$-0.426041\pi$
$911$	24.6111	−	4.89545i	0.815401	−	0.162193i	0.585137	+	0.810935i	$0.301041\pi$
$912$	−0.949649	+	0.188897i	−0.0314460	+	0.00625500i
$913$	3.50152	+	5.24040i	0.115883	+	0.173432i
$914$	4.19978	−	4.19978i	0.138916	−	0.138916i
$915$	−0.251722	+	0.656714i	−0.00832168	+	0.0217103i
$916$	−17.2207	+	7.13304i	−0.568987	+	0.235682i
$917$	−49.5356	−	49.5356i	−1.63581	−	1.63581i
$918$	1.65765	+	3.77521i	0.0547106	+	0.124600i
$919$		−	45.6400i		−	1.50552i	−0.658293	−	0.752762i	$-0.728721\pi$
$919$		−	45.6400i		−	1.50552i	0.658293	−	0.752762i	$-0.271279\pi$
$920$	3.61938	+	15.9593i	0.119327	+	0.526162i
$921$	5.94830	+	8.90226i	0.196003	+	0.293339i
$922$		−	20.6338i		−	0.679538i
$923$	30.1557	−	20.1494i	0.992587	−	0.663226i
$924$	−4.78606	−	3.19794i	−0.157450	−	0.105205i
$925$	−6.40717	−	8.56286i	−0.210667	−	0.281545i
$926$	−28.0032	−	11.5993i	−0.920242	−	0.381177i
$927$	−4.55829	−	11.0047i	−0.149714	−	0.361442i
$928$	−1.09761	−	0.733401i	−0.0360309	−	0.0240751i
$929$	−7.70979	+	11.5385i	−0.252950	+	0.378566i	−0.936113	−	0.351700i	$-0.885604\pi$
$929$	−7.70979	+	11.5385i	−0.252950	+	0.378566i	0.683163	+	0.730266i	$0.260604\pi$
$930$	5.45704	−	14.2368i	0.178943	−	0.466842i
$931$	3.54259	+	3.54259i	0.116104	+	0.116104i
$932$	−5.49585	+	27.6295i	−0.180022	+	0.905034i
$933$	−20.3229	−	8.41803i	−0.665343	−	0.275594i
$934$	5.34412			0.174865
$935$	13.7583	−	6.48403i	0.449945	−	0.212051i
$936$	2.63079			0.0859902
$937$	24.7760	+	10.2625i	0.809396	+	0.335263i	0.748713	−	0.662894i	$-0.230672\pi$
$937$	24.7760	+	10.2625i	0.809396	+	0.335263i	0.0606829	+	0.998157i	$0.480672\pi$
$938$	2.72456	−	13.6973i	0.0889602	−	0.447233i
$939$	15.3878	+	15.3878i	0.502163	+	0.502163i
$940$	−10.0259	−	22.4892i	−0.327010	−	0.733515i
$941$	−0.812184	+	1.21552i	−0.0264764	+	0.0396248i	−0.844472	−	0.535600i	$-0.820085\pi$
$941$	−0.812184	+	1.21552i	−0.0264764	+	0.0396248i	0.817995	+	0.575225i	$0.195085\pi$
$942$	5.79949	+	3.87510i	0.188958	+	0.126258i
$943$	8.48571	+	20.4863i	0.276333	+	0.667126i
$944$	8.01048	+	3.31805i	0.260719	+	0.107993i
$945$	−7.79923	+	0.208025i	−0.253709	+	0.00676706i
$946$	2.26337	+	1.51234i	0.0735886	+	0.0491703i
$947$	−37.2429	+	24.8849i	−1.21023	+	0.808650i	−0.986139	−	0.165918i	$-0.946941\pi$
$947$	−37.2429	+	24.8849i	−1.21023	+	0.808650i	−0.224091	+	0.974568i	$0.571941\pi$
$948$		−	14.5728i		−	0.473301i
$949$	19.1078	+	28.5969i	0.620266	+	0.928294i
$950$	3.60091	+	3.23594i	0.116829	+	0.104988i
$951$		−	19.1142i		−	0.619820i
$952$	−13.4040	−	5.22446i	−0.434426	−	0.169326i
$953$	−25.2739	−	25.2739i	−0.818703	−	0.818703i	0.167217	−	0.985920i	$-0.446522\pi$
$953$	−25.2739	−	25.2739i	−0.818703	−	0.818703i	−0.985920	+	0.167217i	$0.946522\pi$
$954$	−5.38439	+	2.23029i	−0.174326	+	0.0722082i
$955$	18.0785	−	8.05962i	0.585008	−	0.260803i
$956$	10.9851	−	10.9851i	0.355284	−	0.355284i
$957$	−1.20991	−	1.81076i	−0.0391108	−	0.0585334i
$958$	3.87125	−	0.770039i	0.125074	−	0.0248788i
$959$	10.0634	−	2.00174i	0.324965	−	0.0646395i
$960$	0.494555	+	2.18069i	0.0159617	+	0.0703815i
$961$	5.92888	−	14.3136i	0.191254	−	0.461729i
$962$	3.12623	−	4.67873i	0.100794	−	0.150848i
$963$	0.582105	+	2.92644i	0.0187581	+	0.0943032i
$964$	0.465676	−	2.34111i	0.0149984	−	0.0754021i
$965$	−4.18300	−	0.716677i	−0.134656	−	0.0230707i
$966$	21.2318	−	14.1866i	0.683122	−	0.456448i
$967$	2.22653	−	5.37531i	0.0716002	−	0.172858i	−0.884028	−	0.467434i	$-0.845178\pi$
$967$	2.22653	−	5.37531i	0.0716002	−	0.172858i	0.955628	+	0.294576i	$0.0951784\pi$
$968$	5.85373	−	5.85373i	0.188146	−	0.188146i
$969$	−3.99133	+	0.0840057i	−0.128220	+	0.00269865i
$970$	−30.7394	−	5.26661i	−0.986983	−	0.169101i
$971$	5.30894	+	12.8169i	0.170372	+	0.411314i	0.985885	−	0.167425i	$-0.0535451\pi$
$971$	5.30894	+	12.8169i	0.170372	+	0.411314i	−0.815513	+	0.578739i	$0.803545\pi$
$972$	−0.980785	−	0.195090i	−0.0314587	−	0.00625752i
$973$	−25.4626			−0.816294
$974$	−29.4659	−	5.86113i	−0.944148	−	0.187803i
$975$	−7.88059	−	10.5320i	−0.252381	−	0.337294i
$976$	−0.0613612	−	0.308484i	−0.00196412	−	0.00987432i
$977$	−45.1718	+	18.7108i	−1.44517	+	0.598611i	−0.961047	−	0.276386i	$-0.910863\pi$
$977$	−45.1718	+	18.7108i	−1.44517	+	0.598611i	−0.484128	+	0.874997i	$0.660863\pi$
$978$	23.3498	−	9.67180i	0.746644	−	0.309270i
$979$	2.04886	+	10.3003i	0.0654818	+	0.329199i
$980$	7.96014	−	8.39641i	0.254277	−	0.268214i
$981$	2.72581	+	0.542197i	0.0870283	+	0.0173110i
$982$	22.0197			0.702677
$983$	3.36069	+	0.668484i	0.107189	+	0.0213213i	0.248394	−	0.968659i	$-0.420097\pi$
$983$	3.36069	+	0.668484i	0.107189	+	0.0213213i	−0.141204	+	0.989981i	$0.545097\pi$
$984$	1.15949	+	2.79927i	0.0369633	+	0.0892374i
$985$	39.9779	−	28.2827i	1.27380	−	0.901163i
$986$	−3.92882	−	3.76685i	−0.125119	−	0.119961i
$987$	−27.1680	+	27.1680i	−0.864768	+	0.864768i
$988$	−0.974801	+	2.35338i	−0.0310125	+	0.0748709i
$989$	−10.0407	+	6.70900i	−0.319277	+	0.213334i
$990$	−0.622943	+	3.63591i	−0.0197984	+	0.115557i
$991$	4.42734	−	22.2578i	0.140639	−	0.707041i	−0.844537	−	0.535497i	$-0.820124\pi$
$991$	4.42734	−	22.2578i	0.140639	−	0.707041i	0.985176	−	0.171544i	$-0.0548756\pi$
$992$	1.33024	+	6.68755i	0.0422351	+	0.212330i
$993$	−11.2200	+	16.7919i	−0.356056	+	0.532876i
$994$	18.4076	−	44.4398i	0.583853	−	1.40955i
$995$	9.67696	−	15.3536i	0.306780	−	0.486742i
$996$	−3.74698	+	0.745320i	−0.118728	+	0.0236164i
$997$	−46.5118	+	9.25177i	−1.47304	+	0.293007i	−0.865351	−	0.501166i	$-0.832905\pi$
$997$	−46.5118	+	9.25177i	−1.47304	+	0.293007i	−0.607692	+	0.794172i	$0.707905\pi$
$998$	−19.9442	−	29.8486i	−0.631323	−	0.944841i
$999$	−1.51244	+	1.51244i	−0.0478516	+	0.0478516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.bd.a.73.1	yes	64
5.2	odd	4		510.2.bi.a.277.8	yes	64
17.7	odd	16		510.2.bi.a.313.8	yes	64
85.7	even	16	inner	510.2.bd.a.7.1	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.bd.a.7.1	✓	64	85.7	even	16	inner
510.2.bd.a.73.1	yes	64	1.1	even	1	trivial
510.2.bi.a.277.8	yes	64	5.2	odd	4
510.2.bi.a.313.8	yes	64	17.7	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 + 0.382683i) q^{2} +(-0.195090 + 0.980785i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-2.08794 - 0.800320i) q^{5} +(-0.555570 + 0.831470i) q^{6} +(2.90113 + 1.93847i) q^{7} +(0.382683 + 0.923880i) q^{8} +(-0.923880 - 0.382683i) q^{9} +(-1.62273 - 1.53842i) q^{10} +(1.37169 + 0.916536i) q^{11} +(-0.831470 + 0.555570i) q^{12} +2.63079i q^{13} +(1.93847 + 2.90113i) q^{14} +(1.19228 - 1.89168i) q^{15} +1.00000i q^{16} +(-0.719107 + 4.05991i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(0.894550 - 0.370535i) q^{19} +(-0.910484 - 2.04231i) q^{20} +(-2.46721 + 2.46721i) q^{21} +(0.916536 + 1.37169i) q^{22} +(-7.17784 + 1.42776i) q^{23} +(-0.980785 + 0.195090i) q^{24} +(3.71898 + 3.34204i) q^{25} +(-1.00676 + 2.43054i) q^{26} +(0.555570 - 0.831470i) q^{27} +(0.680701 + 3.42212i) q^{28} +(-0.257536 + 1.29472i) q^{29} +(1.82544 - 1.29142i) q^{30} +(5.66944 - 3.78820i) q^{31} +(-0.382683 + 0.923880i) q^{32} +(-1.16653 + 1.16653i) q^{33} +(-2.21803 + 3.47568i) q^{34} +(-4.50598 - 6.36925i) q^{35} +(-0.382683 - 0.923880i) q^{36} +(-2.09782 - 0.417282i) q^{37} +0.968254 q^{38} +(-2.58024 - 0.513243i) q^{39} +(-0.0596204 - 2.23527i) q^{40} +(-0.591105 - 2.97169i) q^{41} +(-3.22356 + 1.33524i) q^{42} +(1.52446 - 0.631450i) q^{43} +(0.321845 + 1.61802i) q^{44} +(1.62273 + 1.53842i) q^{45} +(-7.17784 - 1.42776i) q^{46} +11.0116 q^{47} +(-0.980785 - 0.195090i) q^{48} +(1.98009 + 4.78037i) q^{49} +(2.15694 + 4.51083i) q^{50} +(-3.84161 - 1.49734i) q^{51} +(-1.86025 + 1.86025i) q^{52} +(2.23029 - 5.38439i) q^{53} +(0.831470 - 0.555570i) q^{54} +(-2.13049 - 3.01146i) q^{55} +(-0.680701 + 3.42212i) q^{56} +(0.188897 + 0.949649i) q^{57} +(-0.733401 + 1.09761i) q^{58} +(3.31805 - 8.01048i) q^{59} +(2.18069 - 0.494555i) q^{60} +(-0.308484 + 0.0613612i) q^{61} +(6.68755 - 1.33024i) q^{62} +(-1.93847 - 2.90113i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(2.10548 - 5.49294i) q^{65} +(-1.52414 + 0.631321i) q^{66} +(-2.83025 - 2.83025i) q^{67} +(-3.37928 + 2.36231i) q^{68} -7.31846i q^{69} +(-1.72558 - 7.60878i) q^{70} +(-7.65906 - 11.4626i) q^{71} -1.00000i q^{72} +(10.8701 - 7.26314i) q^{73} +(-1.77845 - 1.18832i) q^{74} +(-4.00336 + 2.99552i) q^{75} +(0.894550 + 0.370535i) q^{76} +(2.20278 + 5.31798i) q^{77} +(-2.18743 - 1.46159i) q^{78} +(-8.09620 + 12.1168i) q^{79} +(0.800320 - 2.08794i) q^{80} +(0.707107 + 0.707107i) q^{81} +(0.591105 - 2.97169i) q^{82} +(3.52958 + 1.46200i) q^{83} -3.48916 q^{84} +(4.75068 - 7.90133i) q^{85} +1.65006 q^{86} +(-1.21960 - 0.505176i) q^{87} +(-0.321845 + 1.61802i) q^{88} +(4.50143 + 4.50143i) q^{89} +(0.910484 + 2.04231i) q^{90} +(-5.09973 + 7.63228i) q^{91} +(-6.08507 - 4.06592i) q^{92} +(2.60935 + 6.29954i) q^{93} +(10.1734 + 4.21397i) q^{94} +(-2.16431 + 0.0577277i) q^{95} +(-0.831470 - 0.555570i) q^{96} +(11.5968 - 7.74876i) q^{97} +5.17424i q^{98} +(-0.916536 - 1.37169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 16 q^{15} + 16 q^{20} + 16 q^{25} - 16 q^{28} + 32 q^{29} + 16 q^{31} + 16 q^{33} + 32 q^{35} - 16 q^{37} - 16 q^{40} + 48 q^{41} + 16 q^{44} + 32 q^{47} - 64 q^{49} - 16 q^{50} + 32 q^{51} + 16 q^{52}+ \cdots - 80 q^{97}+O(q^{100}) \) 64 * q - 16 * q^15 + 16 * q^20 + 16 * q^25 - 16 * q^28 + 32 * q^29 + 16 * q^31 + 16 * q^33 + 32 * q^35 - 16 * q^37 - 16 * q^40 + 48 * q^41 + 16 * q^44 + 32 * q^47 - 64 * q^49 - 16 * q^50 + 32 * q^51 + 16 * q^52 + 80 * q^53 - 16 * q^55 + 16 * q^56 - 32 * q^57 + 64 * q^59 - 48 * q^61 + 32 * q^65 + 16 * q^67 - 48 * q^68 - 64 * q^71 + 16 * q^73 + 48 * q^74 - 32 * q^75 - 80 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 48 * q^82 - 32 * q^83 - 16 * q^85 - 64 * q^86 - 32 * q^87 - 16 * q^88 - 32 * q^89 - 16 * q^90 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 112 * q^95 - 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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