LMFDB - Embedded newform 352.2.bf.a.5.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [352,2,Mod(5,352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("352.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(352, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([0, 5, 16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.bf (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$736$
Relative dimension:	$46$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	352.5
Dual form			352.2.bf.a.141.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23195 - 0.694480i) q^{2} +(-0.575954 + 2.39902i) q^{3} +(1.03539 + 1.71113i) q^{4} +(2.29907 - 2.69186i) q^{5} +(2.37562 - 2.55548i) q^{6} +(-4.37967 - 0.693671i) q^{7} +(-0.0872092 - 2.82708i) q^{8} +(-2.75055 - 1.40148i) q^{9} +(-4.70178 + 1.71958i) q^{10} +(0.461964 - 3.28429i) q^{11} +(-4.70137 + 1.49840i) q^{12} +(-3.43622 - 4.02330i) q^{13} +(4.91379 + 3.89616i) q^{14} +(5.13367 + 7.06589i) q^{15} +(-1.85592 + 3.54339i) q^{16} +(-0.893597 - 0.290347i) q^{17} +(2.41524 + 3.63675i) q^{18} +(4.35723 + 1.04608i) q^{19} +(6.98656 + 1.14686i) q^{20} +(4.18662 - 10.1074i) q^{21} +(-2.84999 + 3.72526i) q^{22} +(0.932759 - 0.932759i) q^{23} +(6.83245 + 1.41905i) q^{24} +(-1.17824 - 7.43910i) q^{25} +(1.43915 + 7.34289i) q^{26} +(0.139430 - 0.163251i) q^{27} +(-3.34773 - 8.21240i) q^{28} +(-3.19965 - 1.96075i) q^{29} +(-1.41730 - 12.2701i) q^{30} +(-2.75481 - 8.47844i) q^{31} +(4.74720 - 3.07637i) q^{32} +(7.61302 + 2.99986i) q^{33} +(0.899225 + 0.978278i) q^{34} +(-11.9364 + 10.1947i) q^{35} +(-0.449803 - 6.15763i) q^{36} +(3.50789 - 0.842170i) q^{37} +(-4.64141 - 4.31473i) q^{38} +(11.6311 - 5.92633i) q^{39} +(-7.81061 - 6.26490i) q^{40} +(3.59171 - 0.568871i) q^{41} +(-12.1771 + 9.54426i) q^{42} +(-2.45704 + 5.93182i) q^{43} +(6.09816 - 2.61006i) q^{44} +(-10.0963 + 4.18202i) q^{45} +(-1.79689 + 0.501329i) q^{46} +(1.58527 - 2.18194i) q^{47} +(-7.43173 - 6.49320i) q^{48} +(12.0429 + 3.91298i) q^{49} +(-3.71478 + 9.98285i) q^{50} +(1.21122 - 1.97653i) q^{51} +(3.32653 - 10.0455i) q^{52} +(1.36923 + 0.107761i) q^{53} +(-0.285145 + 0.104286i) q^{54} +(-7.77878 - 8.79435i) q^{55} +(-1.57912 + 12.4422i) q^{56} +(-5.01913 + 9.85060i) q^{57} +(2.58010 + 4.63763i) q^{58} +(-1.22541 + 0.294195i) q^{59} +(-6.77527 + 16.1004i) q^{60} +(0.554299 - 0.0436243i) q^{61} +(-2.49432 + 12.3582i) q^{62} +(11.0743 + 8.04598i) q^{63} +(-7.98479 + 0.493095i) q^{64} -18.7303 q^{65} +(-7.29550 - 8.98276i) q^{66} +(-0.826516 - 1.99539i) q^{67} +(-0.428404 - 1.82968i) q^{68} +(1.70048 + 2.77493i) q^{69} +(21.7850 - 4.26970i) q^{70} +(-8.52660 + 4.34452i) q^{71} +(-3.72222 + 7.89826i) q^{72} +(0.801014 - 5.05740i) q^{73} +(-4.90641 - 1.39865i) q^{74} +(18.5251 + 1.45796i) q^{75} +(2.72148 + 8.53889i) q^{76} +(-4.30147 + 14.0637i) q^{77} +(-18.4446 - 0.776618i) q^{78} +(13.2314 - 4.29916i) q^{79} +(5.27143 + 13.1423i) q^{80} +(-5.13217 - 7.06383i) q^{81} +(-4.81987 - 1.79355i) q^{82} +(-0.121231 - 1.54038i) q^{83} +(21.6298 - 3.30130i) q^{84} +(-2.83601 + 1.73791i) q^{85} +(7.14647 - 5.60133i) q^{86} +(6.54671 - 6.54671i) q^{87} +(-9.32526 - 1.01959i) q^{88} +(8.00433 + 8.00433i) q^{89} +(15.3424 + 1.85964i) q^{90} +(12.2587 + 20.0043i) q^{91} +(2.56184 + 0.630296i) q^{92} +(21.9266 - 1.72566i) q^{93} +(-3.46829 + 1.58710i) q^{94} +(12.8335 - 9.32406i) q^{95} +(4.64611 + 13.1605i) q^{96} +(-1.19043 - 3.66378i) q^{97} +(-12.1188 - 13.1842i) q^{98} +(-5.87352 + 8.38620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 736 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 12 q^{8} - 12 q^{9} - 32 q^{10} - 16 q^{11} - 64 q^{12} - 12 q^{13} - 28 q^{14} - 52 q^{16} + 48 q^{18} - 12 q^{19} - 28 q^{20}+ \cdots - 68 q^{99}+O(q^{100}) $ 736 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 12 * q^7 - 12 * q^8 - 12 * q^9 - 32 * q^10 - 16 * q^11 - 64 * q^12 - 12 * q^13 - 28 * q^14 - 52 * q^16 + 48 * q^18 - 12 * q^19 - 28 * q^20 - 32 * q^21 - 28 * q^22 - 48 * q^23 - 12 * q^24 - 12 * q^25 - 72 * q^26 - 12 * q^27 - 12 * q^28 - 12 * q^29 - 28 * q^30 - 24 * q^31 + 8 * q^32 - 32 * q^33 - 8 * q^34 - 12 * q^35 - 12 * q^36 - 12 * q^37 - 12 * q^38 - 12 * q^39 + 28 * q^40 - 12 * q^41 - 52 * q^42 - 48 * q^43 - 56 * q^44 - 56 * q^45 - 76 * q^46 - 12 * q^48 - 12 * q^50 - 36 * q^51 - 28 * q^52 + 36 * q^53 - 120 * q^54 + 16 * q^55 + 184 * q^56 - 12 * q^57 - 12 * q^58 + 20 * q^59 + 4 * q^60 - 12 * q^61 + 4 * q^62 + 56 * q^63 - 156 * q^64 - 64 * q^65 + 8 * q^66 + 48 * q^67 - 100 * q^68 - 12 * q^69 + 36 * q^70 + 20 * q^71 + 168 * q^72 - 12 * q^73 - 44 * q^74 - 148 * q^75 - 32 * q^76 - 32 * q^77 + 16 * q^78 - 148 * q^80 - 52 * q^82 - 12 * q^83 + 100 * q^84 - 52 * q^85 + 92 * q^86 - 32 * q^87 - 20 * q^88 - 32 * q^89 - 180 * q^90 + 132 * q^91 + 132 * q^92 + 12 * q^93 + 8 * q^94 - 152 * q^95 - 76 * q^96 - 24 * q^97 - 48 * q^98 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−1.23195	−	0.694480i	−0.871119	−	0.491072i
$2$	−1.23195	−	0.694480i	−0.871119	−	0.491072i
$3$	−0.575954	+	2.39902i	−0.332527	+	1.38507i	0.516302	+	0.856407i	$0.327308\pi$
$3$	−0.575954	+	2.39902i	−0.332527	+	1.38507i	−0.848829	+	0.528668i	$0.822692\pi$
$4$	1.03539	+	1.71113i	0.517697	+	0.855564i
$5$	2.29907	−	2.69186i	1.02817	−	1.20384i	0.0494243	−	0.998778i	$-0.484261\pi$
$5$	2.29907	−	2.69186i	1.02817	−	1.20384i	0.978750	−	0.205059i	$-0.0657387\pi$
$6$	2.37562	−	2.55548i	0.969841	−	1.04327i
$7$	−4.37967	−	0.693671i	−1.65536	−	0.262183i	−0.742317	−	0.670049i	$-0.766273\pi$
$7$	−4.37967	−	0.693671i	−1.65536	−	0.262183i	−0.913042	+	0.407866i	$0.866273\pi$
$8$	−0.0872092	−	2.82708i	−0.0308331	−	0.999525i
$9$	−2.75055	−	1.40148i	−0.916851	−	0.467159i
$10$	−4.70178	+	1.71958i	−1.48683	+	0.543779i
$11$	0.461964	−	3.28429i	0.139287	−	0.990252i
$11$	0.461964	−	3.28429i	0.139287	−	0.990252i
$12$	−4.70137	+	1.49840i	−1.35717	+	0.432551i
$13$	−3.43622	−	4.02330i	−0.953037	−	1.11586i	−0.993171	−	0.116668i	$-0.962779\pi$
$13$	−3.43622	−	4.02330i	−0.953037	−	1.11586i	0.0401342	−	0.999194i	$-0.487221\pi$
$14$	4.91379	+	3.89616i	1.31326	+	1.04129i
$15$	5.13367	+	7.06589i	1.32551	+	1.82441i
$16$	−1.85592	+	3.54339i	−0.463979	+	0.885846i
$17$	−0.893597	−	0.290347i	−0.216729	−	0.0704195i	0.198640	−	0.980073i	$-0.436348\pi$
$17$	−0.893597	−	0.290347i	−0.216729	−	0.0704195i	−0.415369	+	0.909653i	$0.636348\pi$
$18$	2.41524	+	3.63675i	0.569278	+	0.857191i
$19$	4.35723	+	1.04608i	0.999618	+	0.239987i	0.700055	−	0.714089i	$-0.253159\pi$
$19$	4.35723	+	1.04608i	0.999618	+	0.239987i	0.299563	+	0.954076i	$0.403159\pi$
$20$	6.98656	+	1.14686i	1.56224	+	0.256445i
$21$	4.18662	−	10.1074i	0.913595	−	2.20561i
$22$	−2.84999	+	3.72526i	−0.607620	+	0.794228i
$23$	0.932759	−	0.932759i	0.194494	−	0.194494i	−0.603141	−	0.797635i	$-0.706084\pi$
$23$	0.932759	−	0.932759i	0.194494	−	0.194494i	0.797635	+	0.603141i	$0.206084\pi$
$24$	6.83245	+	1.41905i	1.39467	+	0.289663i
$25$	−1.17824	−	7.43910i	−0.235647	−	1.48782i
$26$	1.43915	+	7.34289i	0.282240	+	1.44006i
$27$	0.139430	−	0.163251i	0.0268333	−	0.0314178i
$28$	−3.34773	−	8.21240i	−0.632661	−	1.55200i
$29$	−3.19965	−	1.96075i	−0.594159	−	0.364101i	0.192678	−	0.981262i	$-0.438283\pi$
$29$	−3.19965	−	1.96075i	−0.594159	−	0.364101i	−0.786837	+	0.617161i	$0.788283\pi$
$30$	−1.41730	−	12.2701i	−0.258762	−	2.24019i
$31$	−2.75481	−	8.47844i	−0.494779	−	1.52277i	−0.817302	−	0.576210i	$-0.804531\pi$
$31$	−2.75481	−	8.47844i	−0.494779	−	1.52277i	0.322523	−	0.946562i	$-0.395469\pi$
$32$	4.74720	−	3.07637i	0.839195	−	0.543831i
$33$	7.61302	+	2.99986i	1.32526	+	0.522209i
$34$	0.899225	+	0.978278i	0.154216	+	0.167773i
$35$	−11.9364	+	10.1947i	−2.01762	+	1.72321i
$36$	−0.449803	−	6.15763i	−0.0749671	−	1.02627i
$37$	3.50789	−	0.842170i	0.576694	−	0.138452i	0.0654019	−	0.997859i	$-0.479167\pi$
$37$	3.50789	−	0.842170i	0.576694	−	0.138452i	0.511292	+	0.859407i	$0.329167\pi$
$38$	−4.64141	−	4.31473i	−0.752936	−	0.699941i
$39$	11.6311	−	5.92633i	1.86246	−	0.948973i
$40$	−7.81061	−	6.26490i	−1.23497	−	0.990567i
$41$	3.59171	−	0.568871i	0.560931	−	0.0888427i	0.130470	−	0.991452i	$-0.458351\pi$
$41$	3.59171	−	0.568871i	0.560931	−	0.0888427i	0.430460	+	0.902610i	$0.358351\pi$
$42$	−12.1771	+	9.54426i	−1.87896	+	1.47271i
$43$	−2.45704	+	5.93182i	−0.374695	+	0.904594i	0.618246	+	0.785985i	$0.287844\pi$
$43$	−2.45704	+	5.93182i	−0.374695	+	0.904594i	−0.992941	+	0.118609i	$0.962156\pi$
$44$	6.09816	−	2.61006i	0.919332	−	0.393482i
$45$	−10.0963	+	4.18202i	−1.50507	+	0.623419i
$46$	−1.79689	+	0.501329i	−0.264938	+	0.0739169i
$47$	1.58527	−	2.18194i	0.231236	−	0.318268i	−0.677594	−	0.735436i	$-0.736977\pi$
$47$	1.58527	−	2.18194i	0.231236	−	0.318268i	0.908829	+	0.417168i	$0.136977\pi$
$48$	−7.43173	−	6.49320i	−1.07268	−	0.937213i
$49$	12.0429	+	3.91298i	1.72042	+	0.558998i
$50$	−3.71478	+	9.98285i	−0.525349	+	1.41179i
$51$	1.21122	−	1.97653i	0.169605	−	0.276769i
$52$	3.32653	−	10.0455i	0.461307	−	1.39306i
$53$	1.36923	+	0.107761i	0.188078	+	0.0148021i	0.172148	−	0.985071i	$-0.444929\pi$
$53$	1.36923	+	0.107761i	0.188078	+	0.0148021i	0.0159297	+	0.999873i	$0.494929\pi$
$54$	−0.285145	+	0.104286i	−0.0388034	+	0.0141915i
$55$	−7.77878	−	8.79435i	−1.04889	−	1.18583i
$56$	−1.57912	+	12.4422i	−0.211019	+	1.66266i
$57$	−5.01913	+	9.85060i	−0.664800	+	1.30474i
$58$	2.58010	+	4.63763i	0.338784	+	0.608950i
$59$	−1.22541	+	0.294195i	−0.159535	+	0.0383009i	−0.312426	−	0.949942i	$-0.601142\pi$
$59$	−1.22541	+	0.294195i	−0.159535	+	0.0383009i	0.152891	+	0.988243i	$0.451142\pi$
$60$	−6.77527	+	16.1004i	−0.874683	+	2.07855i
$61$	0.554299	−	0.0436243i	0.0709707	−	0.00558552i	−0.0429240	−	0.999078i	$-0.513667\pi$
$61$	0.554299	−	0.0436243i	0.0709707	−	0.00558552i	0.113895	+	0.993493i	$0.463667\pi$
$62$	−2.49432	+	12.3582i	−0.316779	+	1.56949i
$63$	11.0743	+	8.04598i	1.39524	+	1.01370i
$64$	−7.98479	+	0.493095i	−0.998099	+	0.0616369i
$65$	−18.7303			−2.32320
$66$	−7.29550	−	8.98276i	−0.898014	−	1.10570i
$67$	−0.826516	−	1.99539i	−0.100975	−	0.243775i	0.865316	−	0.501226i	$-0.167117\pi$
$67$	−0.826516	−	1.99539i	−0.100975	−	0.243775i	−0.966291	+	0.257451i	$0.917117\pi$
$68$	−0.428404	−	1.82968i	−0.0519516	−	0.221881i
$69$	1.70048	+	2.77493i	0.204714	+	0.334063i
$70$	21.7850	−	4.26970i	2.60381	−	0.510326i
$71$	−8.52660	+	4.34452i	−1.01192	+	0.515599i	−0.879654	−	0.475615i	$-0.842226\pi$
$71$	−8.52660	+	4.34452i	−1.01192	+	0.515599i	−0.132267	+	0.991214i	$0.542226\pi$
$72$	−3.72222	+	7.89826i	−0.438667	+	0.930819i
$73$	0.801014	−	5.05740i	0.0937516	−	0.591924i	−0.895427	−	0.445208i	$-0.853130\pi$
$73$	0.801014	−	5.05740i	0.0937516	−	0.591924i	0.989179	−	0.146716i	$-0.0468703\pi$
$74$	−4.90641	−	1.39865i	−0.570359	−	0.162590i
$75$	18.5251	+	1.45796i	2.13910	+	0.168351i
$76$	2.72148	+	8.53889i	0.312175	+	0.979478i
$77$	−4.30147	+	14.0637i	−0.490198	+	1.60270i
$78$	−18.4446	−	0.776618i	−2.08844	−	0.0879347i
$79$	13.2314	−	4.29916i	1.48865	−	0.483693i	0.551968	−	0.833865i	$-0.313877\pi$
$79$	13.2314	−	4.29916i	1.48865	−	0.483693i	0.936685	+	0.350172i	$0.113877\pi$
$80$	5.27143	+	13.1423i	0.589364	+	1.46936i
$81$	−5.13217	−	7.06383i	−0.570241	−	0.784870i
$82$	−4.81987	−	1.79355i	−0.532265	−	0.198064i
$83$	−0.121231	−	1.54038i	−0.0133068	−	0.169079i	−0.999980	−	0.00636306i	$-0.997975\pi$
$83$	−0.121231	−	1.54038i	−0.0133068	−	0.169079i	0.986673	−	0.162716i	$-0.0520254\pi$
$84$	21.6298	−	3.30130i	2.36001	−	0.360201i
$85$	−2.83601	+	1.73791i	−0.307609	+	0.188503i
$86$	7.14647	−	5.60133i	0.770624	−	0.604007i
$87$	6.54671	−	6.54671i	0.701881	−	0.701881i
$88$	−9.32526	−	1.01959i	−0.994076	−	0.108688i
$89$	8.00433	+	8.00433i	0.848457	+	0.848457i	0.989941	−	0.141484i	$-0.0451873\pi$
$89$	8.00433	+	8.00433i	0.848457	+	0.848457i	−0.141484	+	0.989941i	$0.545187\pi$
$90$	15.3424	+	1.85964i	1.61723	+	0.196023i
$91$	12.2587	+	20.0043i	1.28506	+	2.09702i
$92$	2.56184	+	0.630296i	0.267091	+	0.0657129i
$93$	21.9266	−	1.72566i	2.27368	−	0.178942i
$94$	−3.46829	+	1.58710i	−0.357726	+	0.163697i
$95$	12.8335	−	9.32406i	1.31669	−	0.956629i
$96$	4.64611	+	13.1605i	0.474192	+	1.34319i
$97$	−1.19043	−	3.66378i	−0.120870	−	0.372000i	0.872256	−	0.489050i	$-0.162656\pi$
$97$	−1.19043	−	3.66378i	−0.120870	−	0.372000i	−0.993126	+	0.117050i	$0.962656\pi$
$98$	−12.1188	−	13.1842i	−1.22418	−	1.33180i
$99$	−5.87352	+	8.38620i	−0.590311	+	0.842844i
$100$	11.5093	−	9.71852i	1.15093	−	0.971852i
$101$	−0.997626	+	12.6760i	−0.0992674	+	1.26131i	0.722452	+	0.691421i	$0.243015\pi$
$101$	−0.997626	+	12.6760i	−0.0992674	+	1.26131i	−0.821720	+	0.569892i	$0.806985\pi$
$102$	−2.86482	+	1.59382i	−0.283659	+	0.157811i
$103$	−14.2377	−	2.25504i	−1.40289	−	0.222195i	−0.591311	−	0.806444i	$-0.701389\pi$
$103$	−14.2377	−	2.25504i	−1.40289	−	0.222195i	−0.811575	+	0.584248i	$0.801389\pi$
$104$	−11.0745	+	10.0654i	−1.08595	+	0.986989i
$105$	−17.5824	−	34.5074i	−1.71586	−	3.36757i
$106$	−1.61198	−	1.08366i	−0.156569	−	0.105254i
$107$	−6.82974	+	4.18527i	−0.660256	+	0.404606i	−0.811873	−	0.583834i	$-0.801552\pi$
$107$	−6.82974	+	4.18527i	−0.660256	+	0.404606i	0.151617	+	0.988439i	$0.451552\pi$
$108$	0.423709	+	0.0695527i	0.0407714	+	0.00669271i
$109$	−12.3107	+	5.09928i	−1.17916	+	0.488422i	−0.884209	−	0.467091i	$-0.845302\pi$
$109$	−12.3107	+	5.09928i	−1.17916	+	0.488422i	−0.294947	+	0.955514i	$0.595302\pi$
$110$	3.47555	+	16.2364i	0.331381	+	1.54808i
$111$			8.90055i			0.844803i
$112$	10.5862	−	14.2315i	1.00031	−	1.34475i
$113$	4.20364	−	5.78581i	0.395445	−	0.544283i	−0.564149	−	0.825673i	$-0.690796\pi$
$113$	4.20364	−	5.78581i	0.395445	−	0.544283i	0.959593	+	0.281390i	$0.0907955\pi$
$114$	13.0244	−	8.64974i	1.21984	−	0.810123i
$115$	−0.366383	−	4.65533i	−0.0341654	−	0.434112i
$116$	0.0421890	−	7.50515i	0.00391715	−	0.696835i
$117$	3.81295	+	15.8821i	0.352508	+	1.46830i
$118$	1.71395	+	0.488589i	0.157782	+	0.0449783i
$119$	3.71225	+	1.89149i	0.340302	+	0.173392i
$120$	19.5282	−	15.1295i	1.78267	−	1.38113i
$121$	−10.5732	−	3.03445i	−0.961198	−	0.275859i
$122$	−0.713164	−	0.331207i	−0.0645668	−	0.0299861i
$123$	−0.703925	+	8.94422i	−0.0634708	+	0.806473i
$124$	11.6554	−	13.4924i	1.04668	−	1.21165i
$125$	−7.64199	−	4.68302i	−0.683521	−	0.418862i
$126$	−8.05525	−	17.6032i	−0.717619	−	1.56821i
$127$	−2.01535	+	6.20262i	−0.178834	+	0.550393i	−0.999788	−	0.0206008i	$-0.993442\pi$
$127$	−2.01535	+	6.20262i	−0.178834	+	0.550393i	0.820954	+	0.570994i	$0.193442\pi$
$128$	10.1793	+	4.93781i	0.899731	+	0.436445i
$129$	−12.8154	−	9.31094i	−1.12833	−	0.819782i
$130$	23.0747	+	13.0078i	2.02379	+	1.14086i
$131$	−3.07544	−	7.42477i	−0.268702	−	0.648705i	0.730720	−	0.682677i	$-0.239184\pi$
$131$	−3.07544	−	7.42477i	−0.268702	−	0.648705i	−0.999423	+	0.0339719i	$0.989184\pi$
$132$	2.74933	+	16.1329i	0.239299	+	1.40419i
$133$	−18.3576	−	7.60397i	−1.59181	−	0.659348i
$134$	−0.367531	+	3.03221i	−0.0317498	+	0.261943i
$135$	−0.118892	−	0.750652i	−0.0102326	−	0.0646059i
$136$	−0.742905	+	2.55159i	−0.0637036	+	0.218797i
$137$	3.20854	+	6.29711i	0.274124	+	0.537998i	0.986492	−	0.163807i	$-0.0523775\pi$
$137$	3.20854	+	6.29711i	0.274124	+	0.537998i	−0.712368	+	0.701806i	$0.752377\pi$
$138$	−0.167770	−	4.59953i	−0.0142815	−	0.391538i
$139$	−2.32229	−	9.67302i	−0.196974	−	0.820454i	−0.980086	−	0.198574i	$-0.936369\pi$
$139$	−2.32229	−	9.67302i	−0.196974	−	0.820454i	0.783112	−	0.621880i	$-0.213631\pi$
$140$	−29.8033	−	9.86923i	−2.51884	−	0.834102i
$141$	4.32147	+	5.05979i	0.363934	+	0.426111i
$142$	13.5215	+	0.569329i	1.13470	+	0.0477770i
$143$	−14.8011	+	9.42695i	−1.23773	+	0.788321i
$144$	10.0708	−	7.14525i	0.839230	−	0.595437i
$145$	−12.6343	+	4.10512i	−1.04922	+	0.340911i
$146$	−4.49907	+	5.67417i	−0.372346	+	0.469598i
$147$	−16.3235	+	26.6375i	−1.34634	+	2.19702i
$148$	5.07311	+	5.13047i	0.417007	+	0.421722i
$149$	7.25990	+	6.20054i	0.594754	+	0.507968i	0.895102	−	0.445862i	$-0.147103\pi$
$149$	7.25990	+	6.20054i	0.594754	+	0.507968i	−0.300348	+	0.953830i	$0.597103\pi$
$150$	−21.8095	−	14.6615i	−1.78074	−	1.19710i
$151$	2.71986	−	0.430783i	0.221339	−	0.0350566i	−0.0447800	−	0.998997i	$-0.514259\pi$
$151$	2.71986	−	0.430783i	0.221339	−	0.0350566i	0.266119	+	0.963940i	$0.414259\pi$
$152$	2.57736	−	12.4095i	0.209052	−	1.00654i
$153$	2.05097	+	2.05097i	0.165811	+	0.165811i
$154$	15.0661	−	14.3384i	1.21406	−	1.15542i
$155$	−29.1563	−	12.0769i	−2.34189	−	0.970042i
$156$	22.1835	+	13.7662i	1.77610	+	1.10218i
$157$	−2.18793	+	9.11337i	−0.174616	+	0.727326i	0.814497	+	0.580167i	$0.197013\pi$
$157$	−2.18793	+	9.11337i	−0.174616	+	0.727326i	−0.989113	+	0.147159i	$0.952987\pi$
$158$	−19.2861	−	3.89263i	−1.53432	−	0.309681i
$159$	−1.04713	+	3.22274i	−0.0830429	+	0.255580i
$160$	2.63297	−	19.8516i	0.208154	−	1.56941i
$161$	−4.73220	+	3.43815i	−0.372950	+	0.270964i
$162$	1.41688	+	12.2665i	0.111321	+	0.963745i
$163$	9.49887	−	8.11280i	0.744009	−	0.635443i	−0.194419	−	0.980919i	$-0.562282\pi$
$163$	9.49887	−	8.11280i	0.744009	−	0.635443i	0.938428	+	0.345475i	$0.112282\pi$
$164$	4.69225	+	5.55686i	0.366403	+	0.433918i
$165$	25.5780	−	13.5963i	1.99125	−	1.05847i
$166$	−0.920416	+	1.98187i	−0.0714381	+	0.153823i
$167$	8.42974	−	16.5443i	0.652313	−	1.28024i	−0.293635	−	0.955918i	$-0.594865\pi$
$167$	8.42974	−	16.5443i	0.652313	−	1.28024i	0.945948	−	0.324318i	$-0.105135\pi$
$168$	−28.9395	−	10.9545i	−2.23273	−	0.845155i
$169$	−2.34567	+	14.8100i	−0.180436	+	1.13923i
$170$	4.70077	−	0.171462i	0.360532	−	0.0131506i
$171$	−10.5187	−	8.98386i	−0.804389	−	0.687013i
$172$	−12.6941	+	1.93747i	−0.967916	+	0.147730i
$173$	16.1729	+	3.88278i	1.22961	+	0.295202i	0.795663	−	0.605739i	$-0.207122\pi$
$173$	16.1729	+	3.88278i	1.22961	+	0.295202i	0.433942	+	0.900941i	$0.357122\pi$
$174$	−12.6118	+	3.51865i	−0.956096	+	0.266748i
$175$			33.3981i			2.52466i
$176$	10.7802	+	7.73229i	0.812585	+	0.582843i
$177$		−	3.10922i		−	0.233703i
$178$	−4.30207	−	15.4198i	−0.322454	−	1.15576i
$179$	−15.6180	−	3.74955i	−1.16734	−	0.280254i	−0.396960	−	0.917836i	$-0.629935\pi$
$179$	−15.6180	−	3.74955i	−1.16734	−	0.280254i	−0.770383	+	0.637582i	$0.779935\pi$
$180$	−17.6096	−	12.9460i	−1.31254	−	0.964937i
$181$	0.248452	+	0.212198i	0.0184673	+	0.0157725i	0.658634	−	0.752464i	$-0.271135\pi$
$181$	0.248452	+	0.212198i	0.0184673	+	0.0157725i	−0.640167	+	0.768236i	$0.721135\pi$
$182$	−1.20944	−	33.1577i	−0.0896498	−	2.45781i
$183$	−0.214595	+	1.35490i	−0.0158633	+	0.100157i
$184$	−2.71833	−	2.55564i	−0.200398	−	0.188404i
$185$	5.79787	−	11.3790i	0.426268	−	0.836598i
$186$	−28.2109	−	13.1016i	−2.06852	−	0.960659i
$187$	−1.36639	+	2.80070i	−0.0999207	+	0.204808i
$188$	5.37496	+	0.453433i	0.392009	+	0.0330700i
$189$	−0.723900	+	0.618269i	−0.0526560	+	0.0449724i
$190$	−22.2856	+	2.57418i	−1.61676	+	0.186750i
$191$	17.3797	−	12.6271i	1.25755	−	0.913662i	0.258913	−	0.965901i	$-0.416636\pi$
$191$	17.3797	−	12.6271i	1.25755	−	0.913662i	0.998635	+	0.0522390i	$0.0166358\pi$
$192$	3.41592	−	19.4397i	0.246523	−	1.40294i
$193$	4.56055	−	14.0359i	0.328275	−	1.01033i	−0.641665	−	0.766985i	$-0.721756\pi$
$193$	4.56055	−	14.0359i	0.328275	−	1.01033i	0.969940	−	0.243343i	$-0.0782440\pi$
$194$	−1.07787	+	5.34032i	−0.0773864	+	0.383412i
$195$	10.7878	−	44.9343i	0.772528	−	3.21781i
$196$	5.77357	+	24.6585i	0.412398	+	1.76132i
$197$	−2.65390	−	1.09928i	−0.189083	−	0.0783207i	0.286133	−	0.958190i	$-0.407630\pi$
$197$	−2.65390	−	1.09928i	−0.189083	−	0.0783207i	−0.475216	+	0.879869i	$0.657630\pi$
$198$	13.0599	−	6.25232i	0.928128	−	0.444333i
$199$	9.76661	+	9.76661i	0.692337	+	0.692337i	0.962746	−	0.270409i	$-0.0871589\pi$
$199$	9.76661	+	9.76661i	0.692337	+	0.692337i	−0.270409	+	0.962746i	$0.587159\pi$
$200$	−20.9282	+	3.97973i	−1.47985	+	0.281409i
$201$	5.26300	−	0.833578i	0.371224	−	0.0587960i
$202$	10.0323	−	14.9234i	0.705869	−	1.05001i
$203$	12.6533	+	10.8069i	0.888086	+	0.758497i
$204$	4.63618	+	0.0260616i	0.324598	+	0.00182468i
$205$	6.72626	−	10.9763i	0.469782	−	0.766615i
$206$	15.9741	+	12.6659i	1.11297	+	0.882476i
$207$	−3.87284	+	1.25836i	−0.269181	+	0.0874623i
$208$	20.6334	−	4.70896i	1.43067	−	0.326507i
$209$	5.44852	−	13.8272i	0.376882	−	0.956447i
$210$	−2.30409	+	54.7219i	−0.158997	+	3.77617i
$211$	2.88529	+	3.37823i	0.198631	+	0.232567i	0.850778	−	0.525526i	$-0.176131\pi$
$211$	2.88529	+	3.37823i	0.198631	+	0.232567i	−0.652147	+	0.758093i	$0.726131\pi$
$212$	1.23330	+	2.45450i	0.0847033	+	0.168576i
$213$	−5.51166	−	22.9577i	−0.377653	−	1.57304i
$214$	11.3205	−	0.412919i	0.773852	−	0.0282266i
$215$	10.3187	+	20.2517i	0.703732	+	1.38115i
$216$	−0.473685	−	0.379943i	−0.0322302	−	0.0258518i
$217$	6.18391	+	39.0437i	0.419791	+	2.65046i
$218$	18.7076	+	2.26752i	1.26704	+	0.153576i
$219$	11.6715	+	4.83448i	0.788684	+	0.326684i
$220$	6.99415	−	22.4161i	0.471546	−	1.51129i
$221$	1.90244	+	4.59290i	0.127972	+	0.308952i
$222$	6.18126	−	10.9650i	0.414859	−	0.735924i
$223$	−19.6059	−	14.2446i	−1.31291	−	0.953886i	−0.999992	−	0.00410646i	$-0.998693\pi$
$223$	−19.6059	−	14.2446i	−1.31291	−	0.953886i	−0.312920	−	0.949780i	$-0.601307\pi$
$224$	−22.9252	+	10.1805i	−1.53175	+	0.680213i
$225$	−7.18492	+	22.1129i	−0.478995	+	1.47419i
$226$	−9.19679	+	4.20848i	−0.611762	+	0.279944i
$227$	11.2908	+	6.91902i	0.749398	+	0.459232i	0.844040	−	0.536280i	$-0.180171\pi$
$227$	11.2908	+	6.91902i	0.749398	+	0.459232i	−0.0946425	+	0.995511i	$0.530171\pi$
$228$	−22.0524	+	1.61089i	−1.46046	+	0.106683i
$229$	0.751694	−	9.55118i	0.0496733	−	0.631160i	−0.920813	−	0.390004i	$-0.872474\pi$
$229$	0.751694	−	9.55118i	0.0496733	−	0.631160i	0.970486	−	0.241156i	$-0.0775264\pi$
$230$	−2.78167	+	5.98958i	−0.183418	+	0.394941i
$231$	−31.2616	−	18.4193i	−2.05686	−	1.21190i
$232$	−5.26415	+	9.21666i	−0.345608	+	0.605103i
$233$	15.3467	+	7.81953i	1.00540	+	0.512275i	0.877533	−	0.479517i	$-0.159188\pi$
$233$	15.3467	+	7.81953i	1.00540	+	0.512275i	0.127863	+	0.991792i	$0.459188\pi$
$234$	6.33243	−	22.2139i	0.413964	−	1.45217i
$235$	−2.22883	−	9.28375i	−0.145393	−	0.605605i
$236$	−1.77219	−	1.79222i	−0.115359	−	0.116664i
$237$	2.69306	+	34.2186i	0.174933	+	2.22274i
$238$	−3.25970	−	4.90830i	−0.211295	−	0.318158i
$239$	12.9984	−	17.8907i	0.840794	−	1.15725i	−0.145023	−	0.989428i	$-0.546325\pi$
$239$	12.9984	−	17.8907i	0.840794	−	1.15725i	0.985817	−	0.167826i	$-0.0536745\pi$
$240$	−34.5648	+	5.07688i	−2.23115	+	0.327711i
$241$			6.98101i			0.449686i	0.974395	+	0.224843i	$0.0721870\pi$
$241$			6.98101i			0.449686i	−0.974395	+	0.224843i	$0.927813\pi$
$242$	10.9182	+	11.0811i	0.701852	+	0.712323i
$243$	20.4972	−	8.49022i	1.31490	−	0.544648i
$244$	0.648565	+	0.903308i	0.0415201	+	0.0578284i
$245$	38.2207	−	23.4217i	2.44183	−	1.49636i
$246$	7.07878	−	10.5300i	0.451327	−	0.671366i
$247$	−10.7637	−	21.1250i	−0.684880	−	1.34415i
$248$	−23.7290	+	8.52747i	−1.50679	+	0.541495i
$249$	3.76523	+	0.596354i	0.238612	+	0.0377924i
$250$	6.16228	+	11.0765i	0.389737	+	0.700536i
$251$	0.774322	−	9.83869i	0.0488748	−	0.621013i	−0.922890	−	0.385063i	$-0.874180\pi$
$251$	0.774322	−	9.83869i	0.0488748	−	0.621013i	0.971765	−	0.235950i	$-0.0758202\pi$
$252$	−2.30138	+	27.2804i	−0.144974	+	1.71850i
$253$	−2.63255	−	3.49436i	−0.165507	−	0.219688i
$254$	6.79041	−	6.24168i	0.426068	−	0.391638i
$255$	−2.53587	−	7.80461i	−0.158802	−	0.488743i
$256$	−9.11116	−	13.1524i	−0.569447	−	0.822028i
$257$	8.31255	−	6.03942i	0.518523	−	0.376729i	−0.297524	−	0.954714i	$-0.596161\pi$
$257$	8.31255	−	6.03942i	0.518523	−	0.376729i	0.816047	+	0.577985i	$0.196161\pi$
$258$	9.32166	+	20.3706i	0.580341	+	1.26822i
$259$	−15.9476	+	1.25510i	−0.990935	+	0.0779883i
$260$	−19.3932	−	32.0499i	−1.20272	−	1.98765i
$261$	6.05286	+	9.87736i	0.374662	+	0.611393i
$262$	−1.36757	+	11.2828i	−0.0844887	+	0.697051i
$263$	12.6196	+	12.6196i	0.778159	+	0.778159i	0.979518	−	0.201359i	$-0.0645358\pi$
$263$	12.6196	+	12.6196i	0.778159	+	0.778159i	−0.201359	+	0.979518i	$0.564536\pi$
$264$	7.81693	−	21.7842i	0.481099	−	1.34073i
$265$	3.43802	−	3.43802i	0.211196	−	0.211196i
$266$	17.3348	+	22.1167i	1.06287	+	1.35606i
$267$	−23.8127	+	14.5924i	−1.45731	+	0.893041i
$268$	2.55859	−	3.48029i	0.156291	−	0.212592i
$269$	1.75310	+	22.2752i	0.106888	+	1.35814i	0.783311	+	0.621630i	$0.213529\pi$
$269$	1.75310	+	22.2752i	0.106888	+	1.35814i	−0.676423	+	0.736514i	$0.736471\pi$
$270$	−0.374845	+	1.00733i	−0.0228123	+	0.0613043i
$271$	13.1404	+	18.0862i	0.798222	+	1.09866i	0.993035	+	0.117818i	$0.0375900\pi$
$271$	13.1404	+	18.0862i	0.798222	+	1.09866i	−0.194813	+	0.980840i	$0.562410\pi$
$272$	2.68725	−	2.62750i	0.162939	−	0.159315i
$273$	−55.0512	+	17.8872i	−3.33185	+	1.08258i
$274$	0.420464	−	9.98598i	0.0254011	−	0.603275i
$275$	−24.9765	+	0.433086i	−1.50614	+	0.0261161i
$276$	−2.98760	+	5.78289i	−0.179832	+	0.348089i
$277$	−7.06582	−	0.556092i	−0.424544	−	0.0334123i	−0.135612	−	0.990762i	$-0.543300\pi$
$277$	−7.06582	−	0.556092i	−0.424544	−	0.0334123i	−0.288932	+	0.957350i	$0.593300\pi$
$278$	−3.85678	+	13.5294i	−0.231314	+	0.811442i
$279$	−4.30508	+	27.1812i	−0.257738	+	1.62730i
$280$	29.8621	+	32.8562i	1.78460	+	1.96353i
$281$	17.8427	−	9.09131i	1.06441	−	0.542342i	0.168096	−	0.985771i	$-0.446238\pi$
$281$	17.8427	−	9.09131i	1.06441	−	0.542342i	0.896310	+	0.443429i	$0.146238\pi$
$282$	−1.80991	−	9.23458i	−0.107778	−	0.549911i
$283$	12.9552	+	21.1410i	0.770108	+	1.25670i	0.961396	+	0.275168i	$0.0887333\pi$
$283$	12.9552	+	21.1410i	0.770108	+	1.25670i	−0.191289	+	0.981534i	$0.561267\pi$
$284$	−16.2624	−	10.0918i	−0.964997	−	0.598838i
$285$	14.9771	+	36.1580i	0.887168	+	2.14181i
$286$	24.7810	−	1.33444i	1.46533	−	0.0789071i
$287$	−16.1251			−0.951835
$288$	−17.3689	+	1.80863i	−1.02347	+	0.106575i
$289$	−13.0391	−	9.47344i	−0.767004	−	0.557261i
$290$	18.4157	+	3.71694i	1.08141	+	0.218266i
$291$	9.47511	−	0.745707i	0.555441	−	0.0437141i
$292$	9.48323	−	3.86577i	0.554964	−	0.226227i
$293$	11.3155	−	2.71662i	0.661060	−	0.158706i	0.110985	−	0.993822i	$-0.464599\pi$
$293$	11.3155	−	2.71662i	0.661060	−	0.158706i	0.550074	+	0.835116i	$0.314599\pi$
$294$	38.6089	−	21.4797i	2.25172	−	1.25272i
$295$	−2.02536	+	3.97500i	−0.117921	+	0.231434i
$296$	−2.68681	−	9.84365i	−0.156167	−	0.572151i
$297$	−0.471754	−	0.533345i	−0.0273740	−	0.0309478i
$298$	−4.63767	−	12.6806i	−0.268653	−	0.734567i
$299$	−6.95794	−	0.547602i	−0.402388	−	0.0316686i
$300$	16.6861	+	33.2085i	0.963372	+	1.91729i
$301$	14.8757	−	24.2750i	0.857424	−	1.39919i
$302$	−3.64989	−	1.35818i	−0.210028	−	0.0781547i
$303$	−29.8355	−	9.69413i	−1.71400	−	0.556913i
$304$	−11.7933	+	13.4979i	−0.676393	+	0.774159i
$305$	1.15694	−	1.59239i	0.0662462	−	0.0911801i
$306$	−1.10233	−	3.95105i	−0.0630161	−	0.225866i
$307$	−18.9974	+	7.86900i	−1.08424	+	0.449108i	−0.851995	−	0.523549i	$-0.824608\pi$
$307$	−18.9974	+	7.86900i	−1.08424	+	0.449108i	−0.232246	+	0.972657i	$0.574608\pi$
$308$	−28.5185	+	7.20109i	−1.62499	+	0.410320i
$309$	13.6102	−	32.8578i	0.774255	−	1.86922i
$310$	27.5318	+	35.1266i	1.56370	+	1.99506i
$311$	17.2954	−	2.73933i	0.980734	−	0.155333i	0.354574	−	0.935028i	$-0.384626\pi$
$311$	17.2954	−	2.73933i	0.980734	−	0.155333i	0.626160	+	0.779695i	$0.284626\pi$
$312$	−17.7686	−	32.3652i	−1.00595	−	1.83232i
$313$	23.3225	−	11.8834i	1.31827	−	0.671690i	0.353656	−	0.935375i	$-0.384938\pi$
$313$	23.3225	−	11.8834i	1.31827	−	0.671690i	0.964609	+	0.263686i	$0.0849382\pi$
$314$	9.02447	−	9.70774i	0.509280	−	0.547839i
$315$	47.1193	−	11.3124i	2.65487	−	0.637379i
$316$	21.0562	+	18.1894i	1.18450	+	1.02323i
$317$	−13.7178	+	11.7161i	−0.770466	+	0.658040i	−0.945169	−	0.326581i	$-0.894103\pi$
$317$	−13.7178	+	11.7161i	−0.770466	+	0.658040i	0.174704	+	0.984621i	$0.444103\pi$
$318$	3.52814	−	3.24304i	0.197848	−	0.181861i
$319$	−7.91778	+	9.60278i	−0.443311	+	0.537653i
$320$	−17.0302	+	22.6276i	−0.952018	+	1.26492i
$321$	−6.10693	−	18.7952i	−0.340856	−	1.04905i
$322$	8.21756	−	0.949199i	0.457947	−	0.0528968i
$323$	−3.58988	−	2.19988i	−0.199746	−	0.122405i
$324$	6.77329	−	16.0957i	0.376294	−	0.894203i
$325$	−25.8810	+	30.3028i	−1.43562	+	1.68090i
$326$	−17.3363	+	3.39778i	−0.960168	+	0.188185i
$327$	−5.14285	−	32.4707i	−0.284400	−	1.79563i
$328$	−1.92147	−	10.1044i	−0.106096	−	0.557925i
$329$	−8.45651	+	8.45651i	−0.466223	+	0.466223i
$330$	−40.9532	−	1.01349i	−2.25440	−	0.0557909i
$331$	6.04916	−	14.6040i	0.332492	−	0.802706i	−0.665901	−	0.746040i	$-0.731953\pi$
$331$	6.04916	−	14.6040i	0.332492	−	0.802706i	0.998393	−	0.0566664i	$-0.0180472\pi$
$332$	2.51027	−	1.80235i	0.137769	−	0.0989166i
$333$	−10.8289	−	2.59979i	−0.593421	−	0.142468i
$334$	−21.8747	+	14.5274i	−1.19693	+	0.794906i
$335$	−7.27152	−	2.36266i	−0.397285	−	0.129086i
$336$	28.0444	+	33.5933i	1.52995	+	1.83266i
$337$	−8.23675	−	11.3369i	−0.448684	−	0.617561i	0.523430	−	0.852069i	$-0.324652\pi$
$337$	−8.23675	−	11.3369i	−0.448684	−	0.617561i	−0.972114	+	0.234508i	$0.924652\pi$
$338$	13.1750	−	16.6161i	0.716624	−	0.903796i
$339$	11.4592	+	13.4170i	0.622377	+	0.728709i
$340$	−5.91018	−	3.05336i	−0.320524	−	0.165591i
$341$	−29.1183	+	5.13088i	−1.57684	+	0.277853i
$342$	6.71945	+	18.3727i	0.363346	+	0.993483i
$343$	−22.3730	−	11.3996i	−1.20803	−	0.615521i
$344$	16.9840	+	6.42894i	0.915717	+	0.346625i
$345$	11.3793	+	1.80230i	0.612639	+	0.0970324i
$346$	−17.2277	−	16.0152i	−0.926167	−	0.860980i
$347$	14.6242	−	17.1228i	0.785070	−	0.919199i	−0.213258	−	0.976996i	$-0.568408\pi$
$347$	14.6242	−	17.1228i	0.785070	−	0.919199i	0.998328	+	0.0577968i	$0.0184076\pi$
$348$	17.9807	+	4.42383i	0.963867	+	0.237142i
$349$	3.83710	−	15.9827i	0.205395	−	0.855532i	−0.770526	−	0.637408i	$-0.780006\pi$
$349$	3.83710	−	15.9827i	0.205395	−	0.855532i	0.975921	−	0.218123i	$-0.0699935\pi$
$350$	23.1943	−	41.1447i	1.23979	−	2.19928i
$351$	−1.13592			−0.0606310
$352$	−7.91068	−	17.0124i	−0.421641	−	0.906763i
$353$	−5.79796			−0.308594			−0.154297	−	0.988024i	$-0.549311\pi$
$353$	−5.79796			−0.308594			−0.154297	+	0.988024i	$0.549311\pi$
$354$	−2.15929	+	3.83040i	−0.114765	+	0.203583i
$355$	−7.90837	+	32.9407i	−0.419733	+	1.74831i
$356$	−5.40878	+	21.9841i	−0.286665	+	1.16515i
$357$	−6.67580	+	7.81636i	−0.353321	+	0.413685i
$358$	16.6366	+	15.4656i	0.879270	+	0.817384i
$359$	−19.7596	−	3.12961i	−1.04287	−	0.165174i	−0.388577	−	0.921416i	$-0.627033\pi$
$359$	−19.7596	−	3.12961i	−1.04287	−	0.165174i	−0.654292	+	0.756242i	$0.727033\pi$
$360$	12.7034	+	28.1783i	0.669528	+	1.48513i
$361$	0.962083	+	0.490206i	0.0506359	+	0.0258003i
$362$	−0.158713	−	0.433961i	−0.00834174	−	0.0228085i
$363$	13.3694	−	23.6176i	0.701710	−	1.23960i
$364$	−21.5374	+	41.6885i	−1.12887	+	2.18507i
$365$	−11.7722	−	13.7835i	−0.616187	−	0.721463i
$366$	1.20532	−	1.52014i	0.0630031	−	0.0794587i
$367$	−5.59721	−	7.70390i	−0.292172	−	0.402140i	0.637546	−	0.770412i	$-0.279950\pi$
$367$	−5.59721	−	7.70390i	−0.292172	−	0.402140i	−0.929718	+	0.368272i	$0.879950\pi$
$368$	1.57400	+	5.03625i	0.0820506	+	0.262532i
$369$	−10.6764	−	3.46899i	−0.555793	−	0.180588i
$370$	−15.0451	+	9.99179i	−0.782160	+	0.519449i
$371$	−5.92201	−	1.42175i	−0.307456	−	0.0738136i
$372$	25.6555	+	35.7324i	1.33017	+	1.85264i
$373$	−6.86609	+	16.5762i	−0.355513	+	0.858284i	0.640407	+	0.768036i	$0.278766\pi$
$373$	−6.86609	+	16.5762i	−0.355513	+	0.858284i	−0.995919	+	0.0902475i	$0.971234\pi$
$374$	3.62836	−	2.50139i	0.187618	−	0.129344i
$375$	15.6361	−	15.6361i	0.807444	−	0.807444i
$376$	−6.30677	−	4.29141i	−0.325247	−	0.221312i
$377$	3.10603	+	19.6107i	0.159969	+	1.01000i
$378$	1.32118	−	0.258941i	0.0679543	−	0.0133185i
$379$	−2.53413	+	2.96708i	−0.130169	+	0.152409i	−0.821663	−	0.569974i	$-0.806953\pi$
$379$	−2.53413	+	2.96708i	−0.130169	+	0.152409i	0.691493	+	0.722383i	$0.256953\pi$
$380$	29.2424	+	12.3056i	1.50010	+	0.631265i
$381$	−13.7195	−	8.40729i	−0.702869	−	0.430719i
$382$	−30.1801	+	3.48606i	−1.54415	+	0.178362i
$383$	9.21374	+	28.3570i	0.470800	+	1.44897i	0.851539	+	0.524291i	$0.175670\pi$
$383$	9.21374	+	28.3570i	0.470800	+	1.44897i	−0.380739	+	0.924682i	$0.624330\pi$
$384$	−17.7087	+	21.5764i	−0.903694	+	1.10106i
$385$	27.9681	+	43.9123i	1.42539	+	2.23798i
$386$	−15.3660	+	14.1243i	−0.782110	+	0.718909i
$387$	15.0715	−	12.8723i	0.766128	−	0.654336i
$388$	5.03662	−	5.83044i	0.255696	−	0.295996i
$389$	13.7581	−	3.30303i	0.697563	−	0.167470i	0.130870	−	0.991399i	$-0.458223\pi$
$389$	13.7581	−	3.30303i	0.697563	−	0.167470i	0.566692	+	0.823929i	$0.308223\pi$
$390$	−44.4959	+	47.8648i	−2.25314	+	2.42373i
$391$	−1.10433	+	0.562686i	−0.0558486	+	0.0284563i
$392$	10.0121	−	34.3876i	0.505686	−	1.73684i
$393$	19.5835	−	3.10172i	0.987856	−	0.156461i
$394$	2.50604	+	3.19734i	0.126253	+	0.161080i
$395$	18.8472	−	45.5013i	0.948308	−	2.28942i
$396$	−20.4313	−	1.36732i	−1.02671	−	0.0687102i
$397$	20.0607	−	8.30940i	1.00682	−	0.417037i	0.182524	−	0.983201i	$-0.441573\pi$
$397$	20.0607	−	8.30940i	1.00682	−	0.417037i	0.824292	+	0.566165i	$0.191573\pi$
$398$	−5.24925	−	18.8147i	−0.263121	−	0.943095i
$399$	28.8152	−	39.6607i	1.44256	−	1.98552i
$400$	28.5463	+	9.63138i	1.42731	+	0.481569i
$401$	−6.19222	−	2.01197i	−0.309225	−	0.100473i	0.150294	−	0.988641i	$-0.451978\pi$
$401$	−6.19222	−	2.01197i	−0.309225	−	0.100473i	−0.459518	+	0.888168i	$0.651978\pi$
$402$	−7.06265	−	2.62813i	−0.352253	−	0.131079i
$403$	−24.6451	+	40.2172i	−1.22766	+	2.00336i
$404$	−22.7232	+	11.4176i	−1.13052	+	0.568049i
$405$	−30.8141	−	2.42512i	−1.53116	−	0.120505i
$406$	−8.08299	−	22.1010i	−0.401152	−	1.09685i
$407$	−1.14542	−	11.9100i	−0.0567762	−	0.590357i
$408$	−5.69344	−	3.25184i	−0.281867	−	0.160990i
$409$	−4.63776	+	9.10212i	−0.229323	+	0.450071i	−0.976782	−	0.214237i	$-0.931274\pi$
$409$	−4.63776	+	9.10212i	−0.229323	+	0.450071i	0.747459	+	0.664308i	$0.231274\pi$
$410$	−15.9092	+	8.85093i	−0.785699	+	0.437116i
$411$	−16.9549	+	4.07050i	−0.836322	+	0.200783i
$412$	−10.8830	−	26.6974i	−0.536168	−	1.31529i
$413$	5.57096	−	0.438444i	0.274129	−	0.0215744i
$414$	5.64505	+	1.13937i	0.277439	+	0.0559972i
$415$	−4.42522	−	3.21511i	−0.217225	−	0.157823i
$416$	−28.6896	−	8.52832i	−1.40662	−	0.418135i
$417$	24.5433			1.20189
$418$	−16.3150	+	13.2505i	−0.797993	+	0.648103i
$419$	7.57985	+	18.2994i	0.370300	+	0.893983i	0.993699	+	0.112080i	$0.0357512\pi$
$419$	7.57985	+	18.2994i	0.370300	+	0.893983i	−0.623399	+	0.781904i	$0.714249\pi$
$420$	40.8418	−	65.8144i	1.99288	−	3.21142i
$421$	−9.27147	−	15.1297i	−0.451864	−	0.737375i	0.542875	−	0.839813i	$-0.317336\pi$
$421$	−9.27147	−	15.1297i	−0.451864	−	0.737375i	−0.994739	+	0.102438i	$0.967336\pi$
$422$	−1.20841	−	6.16558i	−0.0588243	−	0.300136i
$423$	−7.41831	+	3.77982i	−0.360691	+	0.183781i
$424$	0.185239	−	3.88032i	0.00899599	−	0.188445i
$425$	−1.10705	+	6.98965i	−0.0536999	+	0.339048i
$426$	−9.15359	+	32.1105i	−0.443493	+	1.55576i
$427$	−2.45791	−	0.193441i	−0.118946	−	0.00936129i
$428$	−14.2330	−	7.35315i	−0.687979	−	0.355428i
$429$	−14.0907	−	40.9376i	−0.680305	−	1.97649i
$430$	1.35222	−	32.1151i	0.0652099	−	1.54873i
$431$	−34.1953	+	11.1107i	−1.64713	+	0.535185i	−0.978115	−	0.208065i	$-0.933283\pi$
$431$	−34.1953	+	11.1107i	−1.64713	+	0.535185i	−0.669014	+	0.743250i	$0.733283\pi$
$432$	0.319693	+	0.797035i	0.0153812	+	0.0383474i
$433$	17.5319	+	24.1305i	0.842527	+	1.15964i	0.985460	+	0.169907i	$0.0543466\pi$
$433$	17.5319	+	24.1305i	0.842527	+	1.15964i	−0.142933	+	0.989732i	$0.545653\pi$
$434$	19.4968	−	52.3944i	0.935876	−	2.51501i
$435$	−2.57151	−	32.6742i	−0.123295	−	1.56661i
$436$	−21.4720	−	15.7855i	−1.02832	−	0.755988i
$437$	5.03999	−	3.08851i	0.241095	−	0.147743i
$438$	−11.0212	−	14.0614i	−0.526613	−	0.671881i
$439$	26.1713	−	26.1713i	1.24909	−	1.24909i	0.292962	−	0.956124i	$-0.405359\pi$
$439$	26.1713	−	26.1713i	1.24909	−	1.24909i	0.956124	−	0.292962i	$-0.0946408\pi$
$440$	−24.1840	+	22.7582i	−1.15293	+	1.08495i
$441$	−27.6407	−	27.6407i	−1.31623	−	1.31623i
$442$	0.845968	−	6.97943i	0.0402386	−	0.331978i
$443$	11.9799	+	19.5494i	0.569182	+	0.928820i	0.999656	+	0.0262173i	$0.00834618\pi$
$443$	11.9799	+	19.5494i	0.569182	+	0.928820i	−0.430475	+	0.902603i	$0.641654\pi$
$444$	−15.2300	+	9.21559i	−0.722783	+	0.437352i
$445$	39.9490	−	3.14406i	1.89376	−	0.149043i
$446$	14.2610	+	31.1645i	0.675276	+	1.47568i
$447$	−19.0566	+	13.8454i	−0.901345	+	0.654866i
$448$	35.3128	+	3.37923i	1.66837	+	0.159653i
$449$	5.78970	+	17.8188i	0.273233	+	0.840923i	0.989682	+	0.143284i	$0.0457662\pi$
$449$	5.78970	+	17.8188i	0.273233	+	0.840923i	−0.716449	+	0.697639i	$0.754234\pi$
$450$	24.2084	−	22.2522i	1.14120	−	1.04898i
$451$	−0.209100	−	12.0590i	−0.00984616	−	0.567837i
$452$	14.2527	+	1.20236i	0.670390	+	0.0565543i
$453$	−0.533054	+	6.77310i	−0.0250451	+	0.318228i
$454$	−9.10458	−	16.3651i	−0.427299	−	0.768053i
$455$	82.0324	+	12.9927i	3.84574	+	0.609105i
$456$	28.2862	+	13.3304i	1.32462	+	0.624255i
$457$	−0.733634	−	1.43984i	−0.0343179	−	0.0673527i	0.873211	−	0.487342i	$-0.162034\pi$
$457$	−0.733634	−	1.43984i	−0.0343179	−	0.0673527i	−0.907529	+	0.419990i	$0.862034\pi$
$458$	−7.55915	+	11.2445i	−0.353216	+	0.525422i
$459$	−0.171994	+	0.105398i	−0.00802798	+	0.00491955i
$460$	7.58652	−	5.44704i	0.353723	−	0.253969i
$461$	−22.3450	+	9.25558i	−1.04071	+	0.431076i	−0.836566	−	0.547866i	$-0.815440\pi$
$461$	−22.3450	+	9.25558i	−1.04071	+	0.431076i	−0.204142	+	0.978941i	$0.565440\pi$
$462$	25.7208	+	44.4022i	1.19664	+	2.06578i
$463$			2.36837i			0.110067i	0.998485	+	0.0550336i	$0.0175266\pi$
$463$			2.36837i			0.110067i	−0.998485	+	0.0550336i	$0.982473\pi$
$464$	12.8859	−	7.69860i	0.598215	−	0.357399i
$465$	45.7654	−	62.9907i	2.12232	−	2.92112i
$466$	−13.4758	−	20.2912i	−0.624256	−	0.939974i
$467$	−1.25813	−	15.9860i	−0.0582192	−	0.739745i	−0.954873	−	0.297013i	$-0.904009\pi$
$467$	−1.25813	−	15.9860i	−0.0582192	−	0.739745i	0.896654	−	0.442732i	$-0.145991\pi$
$468$	−23.2284	+	22.9687i	−1.07373	+	1.06173i
$469$	2.23572	+	9.31246i	0.103236	+	0.430009i
$470$	−3.70158	+	12.9850i	−0.170741	+	0.598953i
$471$	−20.6030	−	10.4978i	−0.949337	−	0.483711i
$472$	0.938579	+	3.43867i	0.0432016	+	0.158278i
$473$	18.3468	+	10.8099i	0.843585	+	0.497041i
$474$	20.4464	−	44.0258i	0.939136	−	2.02217i
$475$	2.64803	−	33.6464i	0.121500	−	1.54380i
$476$	0.607071	+	8.31057i	0.0278251	+	0.380914i
$477$	−3.61511	−	2.21534i	−0.165525	−	0.101434i
$478$	−28.4381	+	13.0133i	−1.30073	+	0.595216i
$479$	8.11317	−	24.9698i	0.370700	−	1.14090i	−0.575634	−	0.817708i	$-0.695245\pi$
$479$	8.11317	−	24.9698i	0.370700	−	1.14090i	0.946334	−	0.323191i	$-0.104755\pi$
$480$	46.1079	+	17.7501i	2.10453	+	0.810179i
$481$	−15.4422	−	11.2194i	−0.704104	−	0.511561i
$482$	4.84817	−	8.60025i	0.220828	−	0.391731i
$483$	−5.52265	−	13.3329i	−0.251289	−	0.606666i
$484$	−5.75509	−	21.2339i	−0.261595	−	0.965178i
$485$	−12.5993	−	5.21879i	−0.572103	−	0.236973i
$486$	−31.1478	−	3.77539i	−1.41289	−	0.171255i
$487$	−1.88428	−	11.8969i	−0.0853847	−	0.539098i	−0.992888	−	0.119053i	$-0.962014\pi$
$487$	−1.88428	−	11.8969i	−0.0853847	−	0.539098i	0.907503	−	0.420045i	$-0.137986\pi$
$488$	−0.171669	−	1.56324i	−0.00777111	−	0.0707648i
$489$	13.9919	+	27.4606i	0.632734	+	1.24181i
$490$	−63.3518	+	2.31078i	−2.86194	+	0.104391i
$491$	0.479312	+	1.99648i	0.0216310	+	0.0900997i	0.982141	−	0.188145i	$-0.0602474\pi$
$491$	0.479312	+	1.99648i	0.0216310	+	0.0900997i	−0.960510	+	0.278245i	$0.910247\pi$
$492$	−16.0335	+	8.05629i	−0.722848	+	0.363206i
$493$	2.28990	+	2.68112i	0.103132	+	0.120752i
$494$	−1.41054	+	33.5001i	−0.0634631	+	1.50724i
$495$	9.07086	+	35.0911i	0.407705	+	1.57723i
$496$	35.1551	+	5.97390i	1.57851	+	0.268236i
$497$	40.3573	−	13.1129i	1.81027	−	0.588194i
$498$	−4.22442	−	3.34956i	−0.189301	−	0.150097i
$499$	−6.97958	+	11.3896i	−0.312449	+	0.509870i	−0.969860	−	0.243662i	$-0.921651\pi$
$499$	−6.97958	+	11.3896i	−0.312449	+	0.509870i	0.657411	+	0.753532i	$0.271651\pi$
$500$	0.100764	−	17.9252i	0.00450629	−	0.801639i
$501$	34.8349	+	29.7519i	1.55631	+	1.32921i
$502$	−7.78670	+	11.5830i	−0.347537	+	0.516975i
$503$	24.5442	−	3.88741i	1.09437	−	0.173331i	0.416952	−	0.908929i	$-0.363098\pi$
$503$	24.5442	−	3.88741i	1.09437	−	0.173331i	0.677419	+	0.735597i	$0.263098\pi$
$504$	21.7809	−	32.0098i	0.970197	−	1.42583i
$505$	31.8285	+	31.8285i	1.41635	+	1.41635i
$506$	0.816411	+	6.13312i	0.0362939	+	0.272651i
$507$	−34.1784	−	14.1572i	−1.51792	−	0.628741i
$508$	−12.7002	+	2.97363i	−0.563478	+	0.131934i
$509$	−8.70313	+	36.2511i	−0.385759	+	1.60680i	0.354888	+	0.934909i	$0.384519\pi$
$509$	−8.70313	+	36.2511i	−0.385759	+	1.60680i	−0.740647	+	0.671894i	$0.765481\pi$
$510$	−2.29608	+	11.3760i	−0.101672	+	0.503737i
$511$	−7.01635	+	21.5941i	−0.310385	+	0.955267i
$512$	2.09037	+	22.5307i	0.0923820	+	0.995724i
$513$	0.778303	−	0.565470i	0.0343629	−	0.0249661i
$514$	−14.4349	+	1.66736i	−0.636696	+	0.0735439i
$515$	−38.8038	+	33.1415i	−1.70990	+	1.46039i
$516$	2.66320	−	31.5693i	0.117241	−	1.38976i
$517$	−6.43379	−	6.21447i	−0.282958	−	0.273312i
$518$	20.5183	+	9.52906i	0.901521	+	0.418683i
$519$	−18.6297	+	36.5629i	−0.817754	+	1.60493i
$520$	1.63345	+	52.9520i	0.0716316	+	2.32210i
$521$	2.00798	−	12.6779i	0.0879713	−	0.555429i	−0.903855	−	0.427838i	$-0.859275\pi$
$521$	2.00798	−	12.6779i	0.0879713	−	0.555429i	0.991827	−	0.127591i	$-0.0407246\pi$
$522$	−0.597175	−	16.3720i	−0.0261377	−	0.716583i
$523$	3.54810	+	3.03036i	0.155148	+	0.132509i	0.723634	−	0.690184i	$-0.242471\pi$
$523$	3.54810	+	3.03036i	0.155148	+	0.132509i	−0.568486	+	0.822693i	$0.692471\pi$
$524$	9.52043	−	12.9500i	0.415902	−	0.565725i
$525$	−80.1227	−	19.2358i	−3.49684	−	0.839517i
$526$	−6.78264	−	24.3108i	−0.295737	−	1.06000i
$527$			8.37615i			0.364871i
$528$	−24.7588	+	21.4084i	−1.07749	+	0.931680i
$529$			21.2599i			0.924344i
$530$	−6.62311	+	1.84783i	−0.287689	+	0.0802646i
$531$	3.78286	+	0.908184i	0.164162	+	0.0394118i
$532$	−5.99601	−	39.2853i	−0.259960	−	1.70323i
$533$	−14.6306	−	12.4958i	−0.633724	−	0.541251i
$534$	39.4701	−	1.43969i	1.70804	−	0.0623014i
$535$	−4.43586	+	28.0069i	−0.191779	+	1.21085i
$536$	−5.56904	+	2.51064i	−0.240546	+	0.108443i
$537$	17.9905	−	35.3083i	0.776346	−	1.52367i
$538$	13.3100	−	28.6594i	0.573833	−	1.23560i
$539$	18.4148	−	37.7448i	0.793181	−	1.62579i
$540$	1.16136	−	0.980660i	0.0499771	−	0.0422009i
$541$	−6.98903	+	5.96919i	−0.300482	+	0.256636i	−0.786886	−	0.617098i	$-0.788308\pi$
$541$	−6.98903	+	5.96919i	−0.300482	+	0.256636i	0.486404	+	0.873734i	$0.338308\pi$
$542$	−3.62778	−	31.4070i	−0.155827	−	1.34905i
$543$	−0.652163	+	0.473824i	−0.0279870	+	0.0203337i
$544$	−5.13530	+	1.37070i	−0.220174	+	0.0587682i
$545$	−14.5767	+	44.8624i	−0.624396	+	1.92169i
$546$	80.2426	+	16.1958i	3.43407	+	0.693118i
$547$	−5.20609	+	21.6849i	−0.222596	+	0.927181i	0.743446	+	0.668796i	$0.233190\pi$
$547$	−5.20609	+	21.6849i	−0.222596	+	0.927181i	−0.966042	+	0.258385i	$0.916810\pi$
$548$	−7.45306	+	12.0102i	−0.318379	+	0.513051i
$549$	−1.58577	−	0.656846i	−0.0676789	−	0.0280335i
$550$	31.0705	+	16.8121i	1.32485	+	0.716872i
$551$	−11.8905	−	11.8905i	−0.506553	−	0.506553i
$552$	7.69667	−	5.04940i	0.327592	−	0.214917i
$553$	−60.9315	+	9.65061i	−2.59107	+	0.410386i
$554$	8.31853	+	5.59215i	0.353421	+	0.237588i
$555$	23.9591	+	20.4630i	1.01701	+	0.868604i
$556$	14.1473	−	13.9891i	0.599978	−	0.593271i
$557$	5.68963	−	9.28463i	0.241077	−	0.393402i	−0.709102	−	0.705106i	$-0.750900\pi$
$557$	5.68963	−	9.28463i	0.241077	−	0.393402i	0.950179	+	0.311703i	$0.100900\pi$
$558$	24.1804	−	30.4960i	1.02364	−	1.29100i
$559$	32.3084	−	10.4976i	1.36650	−	0.444003i
$560$	−13.9706	−	61.2158i	−0.590367	−	2.58684i
$561$	−5.93196	−	4.89108i	−0.250448	−	0.206502i
$562$	−28.2950	−	1.19137i	−1.19355	−	0.0502550i
$563$	0.371684	+	0.435186i	0.0156646	+	0.0183409i	0.768183	−	0.640230i	$-0.221161\pi$
$563$	0.371684	+	0.435186i	0.0156646	+	0.0183409i	−0.752518	+	0.658571i	$0.771161\pi$
$564$	−4.18352	+	12.6335i	−0.176158	+	0.531965i
$565$	−5.91015	−	24.6176i	−0.248642	−	1.03567i
$566$	−1.27816	−	35.0418i	−0.0537252	−	1.47291i
$567$	17.5772	+	34.4973i	0.738175	+	1.44875i
$568$	13.0259	+	23.7265i	0.546555	+	0.995542i
$569$	−3.43681	−	21.6991i	−0.144078	−	0.909676i	−0.948767	−	0.315978i	$-0.897667\pi$
$569$	−3.43681	−	21.6991i	−0.144078	−	0.909676i	0.804688	−	0.593698i	$-0.202333\pi$
$570$	6.65995	−	54.9461i	0.278955	−	2.30144i
$571$	−15.1387	−	6.27065i	−0.633534	−	0.262418i	0.0427197	−	0.999087i	$-0.486398\pi$
$571$	−15.1387	−	6.27065i	−0.633534	−	0.262418i	−0.676254	+	0.736669i	$0.736398\pi$
$572$	−31.4557	−	15.5660i	−1.31523	−	0.650846i
$573$	20.2827	+	48.9667i	0.847321	+	2.04561i
$574$	19.8653	+	11.1986i	0.829161	+	0.467419i
$575$	−8.03790	−	5.83987i	−0.335203	−	0.243540i
$576$	22.6536	+	9.83421i	0.943902	+	0.409759i
$577$	12.0366	−	37.0447i	0.501088	−	1.54219i	−0.306161	−	0.951980i	$-0.599045\pi$
$577$	12.0366	−	37.0447i	0.501088	−	1.54219i	0.807249	−	0.590211i	$-0.200955\pi$
$578$	9.48435	+	20.7262i	0.394497	+	0.862095i
$579$	31.0458	+	19.0249i	1.29022	+	0.790647i
$580$	−20.1058	−	17.3684i	−0.834849	−	0.721184i
$581$	−0.537569	+	6.83046i	−0.0223021	+	0.283375i
$582$	−12.1907	−	5.66160i	−0.505322	−	0.234681i
$583$	0.986451	−	4.44717i	0.0408546	−	0.184183i
$584$	−14.3676	−	1.82348i	−0.594533	−	0.0754562i
$585$	51.5186	+	26.2500i	2.13003	+	1.08531i
$586$	−15.8268	−	4.51167i	−0.653798	−	0.186376i
$587$	0.464308	+	1.93398i	0.0191640	+	0.0798240i	0.981132	−	0.193337i	$-0.0619310\pi$
$587$	0.464308	+	1.93398i	0.0191640	+	0.0798240i	−0.961968	+	0.273161i	$0.911931\pi$
$588$	−62.4814	−	0.351230i	−2.57669	−	0.0144845i
$589$	−3.13424	−	39.8243i	−0.129144	−	1.64093i
$590$	5.25571	−	3.49042i	0.216374	−	0.143698i
$591$	4.16573	−	5.73363i	0.171355	−	0.235850i
$592$	−3.52622	+	13.9928i	−0.144927	+	0.575101i
$593$		−	33.9177i		−	1.39283i	−0.717637	−	0.696417i	$-0.754776\pi$
$593$		−	33.9177i		−	1.39283i	0.717637	−	0.696417i	$-0.245224\pi$
$594$	0.210780	+	0.984678i	0.00864839	+	0.0404018i
$595$	13.6263	−	5.64421i	0.558625	−	0.231390i
$596$	−3.09305	+	18.8426i	−0.126696	+	0.771824i
$597$	−29.0554	+	17.8052i	−1.18916	+	0.728717i
$598$	8.19152	+	5.50677i	0.334976	+	0.225188i
$599$	−6.59568	−	12.9447i	−0.269492	−	0.528908i	0.716110	−	0.697987i	$-0.245921\pi$
$599$	−6.59568	−	12.9447i	−0.269492	−	0.528908i	−0.985603	+	0.169079i	$0.945921\pi$
$600$	2.50621	−	52.4993i	0.102316	−	2.14327i
$601$	−39.2790	−	6.22118i	−1.60222	−	0.253767i	−0.709611	−	0.704593i	$-0.751129\pi$
$601$	−39.2790	−	6.22118i	−1.60222	−	0.253767i	−0.892612	+	0.450826i	$0.851129\pi$
$602$	−35.1847	+	19.5747i	−1.43402	+	0.797804i
$603$	−0.523111	+	6.64676i	−0.0213027	+	0.270677i
$604$	3.55325	+	4.20799i	0.144580	+	0.171221i
$605$	−32.4768	+	21.4851i	−1.32037	+	0.873495i
$606$	30.0234	+	32.6628i	1.21962	+	1.32684i
$607$	−1.36526	−	4.20183i	−0.0554141	−	0.170547i	0.919519	−	0.393046i	$-0.128579\pi$
$607$	−1.36526	−	4.20183i	−0.0554141	−	0.170547i	−0.974933	+	0.222499i	$0.928579\pi$
$608$	23.9028	−	8.43852i	0.969387	−	0.342227i
$609$	−33.2137	+	24.1312i	−1.34589	+	0.977844i
$610$	−2.53117	+	1.15827i	−0.102484	+	0.0468971i
$611$	−14.2259	+	1.11961i	−0.575520	+	0.0452944i
$612$	−1.38591	+	5.63304i	−0.0560220	+	0.227702i
$613$	12.4078	+	20.2476i	0.501145	+	0.817794i	0.998769	−	0.0495989i	$-0.0157943\pi$
$613$	12.4078	+	20.2476i	0.501145	+	0.817794i	−0.497625	+	0.867392i	$0.665794\pi$
$614$	28.8687	+	3.49915i	1.16505	+	0.141214i
$615$	22.4582	+	22.4582i	0.905603	+	0.905603i
$616$	40.1343	+	10.9341i	1.61706	+	0.440548i
$617$	−4.57766	+	4.57766i	−0.184290	+	0.184290i	−0.793222	−	0.608933i	$-0.791598\pi$
$617$	−4.57766	+	4.57766i	−0.184290	+	0.184290i	0.608933	+	0.793222i	$0.291598\pi$
$618$	−39.5861	+	31.0272i	−1.59239	+	1.24810i
$619$	23.3126	−	14.2860i	0.937013	−	0.574203i	0.0319547	−	0.999489i	$-0.489827\pi$
$619$	23.3126	−	14.2860i	0.937013	−	0.574203i	0.905059	+	0.425287i	$0.139827\pi$
$620$	−9.52309	−	62.3945i	−0.382457	−	2.50582i
$621$	−0.0222198	−	0.282329i	−0.000891648	−	0.0113295i
$622$	−23.2095	−	8.63663i	−0.930616	−	0.346297i
$623$	−29.5039	−	40.6087i	−1.18205	−	1.62695i
$624$	−0.587024	+	52.2122i	−0.0234997	+	2.09016i
$625$	5.64046	−	1.83270i	0.225618	−	0.0733079i
$626$	−36.9849	−	1.55726i	−1.47821	−	0.0622408i
$627$	30.0336	+	21.0349i	1.19943	+	0.840054i
$628$	−17.8595	+	5.69212i	−0.712672	+	0.227140i
$629$	−3.37916	−	0.265946i	−0.134736	−	0.0106040i
$630$	−65.9048	−	18.7872i	−2.62571	−	0.748500i
$631$	−4.62150	+	29.1790i	−0.183979	+	1.16160i	0.706885	+	0.707328i	$0.250100\pi$
$631$	−4.62150	+	29.1790i	−0.183979	+	1.16160i	−0.890864	+	0.454270i	$0.849900\pi$
$632$	−13.3080	−	37.0315i	−0.529363	−	1.47303i
$633$	−9.76624	+	4.97615i	−0.388173	+	0.197784i
$634$	25.0361	−	4.90689i	0.994312	−	0.194877i
$635$	12.0632	+	19.6853i	0.478712	+	0.781187i
$636$	−6.59871	+	1.54503i	−0.261656	+	0.0612645i
$637$	−25.6391	−	61.8982i	−1.01586	−	2.45249i
$638$	16.4232	−	6.33139i	0.650203	−	0.250662i
$639$	29.5416			1.16865
$640$	36.6948	−	16.0489i	1.45049	−	0.634388i
$641$	−28.1325	−	20.4395i	−1.11117	−	0.807311i	−0.128321	−	0.991733i	$-0.540959\pi$
$641$	−28.1325	−	20.4395i	−1.11117	−	0.807311i	−0.982847	+	0.184422i	$0.940959\pi$
$642$	−5.52947	+	27.3959i	−0.218231	+	1.08123i
$643$	34.6065	−	2.72359i	1.36475	−	0.107408i	0.625175	−	0.780484i	$-0.285027\pi$
$643$	34.6065	−	2.72359i	1.36475	−	0.107408i	0.739573	+	0.673076i	$0.235027\pi$
$644$	−10.7828	−	4.53756i	−0.424902	−	0.178805i
$645$	−54.5272	+	13.0908i	−2.14701	+	0.515451i
$646$	2.89478	+	5.20325i	0.113893	+	0.204719i
$647$	16.3142	−	32.0185i	0.641379	−	1.25878i	−0.309994	−	0.950738i	$-0.600327\pi$
$647$	16.3142	−	32.0185i	0.641379	−	1.25878i	0.951374	−	0.308039i	$-0.0996729\pi$
$648$	−19.5225	+	15.1251i	−0.766914	+	0.594170i
$649$	0.400127	+	4.16051i	0.0157064	+	0.163314i
$650$	52.9288	−	19.3576i	2.07604	−	0.759268i
$651$	−97.2282	−	7.65202i	−3.81067	−	0.299906i
$652$	23.7171	+	7.85382i	0.928834	+	0.307579i
$653$	15.8767	−	25.9084i	0.621302	−	1.01387i	−0.374923	−	0.927056i	$-0.622331\pi$
$653$	15.8767	−	25.9084i	0.621302	−	1.01387i	0.996224	−	0.0868163i	$-0.0276693\pi$
$654$	−16.2145	+	43.5738i	−0.634038	+	1.70387i
$655$	−27.0571	−	8.79138i	−1.05721	−	0.343508i
$656$	−4.65018	+	13.7826i	−0.181559	+	0.538119i
$657$	−9.29106	+	12.7881i	−0.362479	+	0.498909i
$658$	16.2909	−	4.54511i	0.635084	−	0.177187i
$659$	−2.10714	+	0.872807i	−0.0820826	+	0.0339997i	−0.423347	−	0.905968i	$-0.639145\pi$
$659$	−2.10714	+	0.872807i	−0.0820826	+	0.0339997i	0.341264	+	0.939967i	$0.389145\pi$
$660$	49.7484	+	29.6898i	1.93645	+	1.15567i
$661$	17.1653	−	41.4407i	0.667653	−	1.61186i	−0.117873	−	0.993029i	$-0.537608\pi$
$661$	17.1653	−	41.4407i	0.667653	−	1.61186i	0.785526	−	0.618828i	$-0.212392\pi$
$662$	−17.5944	+	13.7903i	−0.683826	+	0.535976i
$663$	−12.1142	+	1.91870i	−0.470476	+	0.0745161i
$664$	−4.34422	+	0.477065i	−0.168588	+	0.0185137i
$665$	−62.6742	+	31.9341i	−2.43040	+	1.23835i
$666$	11.5352	+	10.7233i	0.446979	+	0.415519i
$667$	−4.81340	+	1.15560i	−0.186376	+	0.0447448i
$668$	37.0375	−	2.70552i	1.43302	−	0.104680i
$669$	45.4651	−	38.8309i	1.75778	−	1.50129i
$670$	7.31731	+	7.96060i	0.282693	+	0.307545i
$671$	0.112791	−	1.84063i	0.00435425	−	0.0710569i
$672$	−11.2194	−	60.8614i	−0.432797	−	2.34778i
$673$	2.13955	+	6.58487i	0.0824738	+	0.253828i	0.983787	−	0.179339i	$-0.0573959\pi$
$673$	2.13955	+	6.58487i	0.0824738	+	0.253828i	−0.901314	+	0.433167i	$0.857396\pi$
$674$	2.27399	+	19.6868i	0.0875909	+	0.758305i
$675$	−1.37873	−	0.844884i	−0.0530672	−	0.0325196i
$676$	−27.7704	+	11.3204i	−1.06809	+	0.435401i
$677$	−4.18012	+	4.89429i	−0.160655	+	0.188103i	−0.834895	−	0.550410i	$-0.814471\pi$
$677$	−4.18012	+	4.89429i	−0.160655	+	0.188103i	0.674240	+	0.738513i	$0.264471\pi$
$678$	−4.79929	−	24.4872i	−0.184316	−	0.940424i
$679$	2.67225	+	16.8719i	0.102551	+	0.647484i
$680$	5.16054	+	7.86608i	0.197898	+	0.301650i
$681$	−23.1019	+	23.1019i	−0.885265	+	0.885265i
$682$	39.4355	+	13.9011i	1.51006	+	0.532301i
$683$	−2.18769	+	5.28154i	−0.0837095	+	0.202093i	−0.960192	−	0.279341i	$-0.909884\pi$
$683$	−2.18769	+	5.28154i	−0.0837095	+	0.202093i	0.876482	+	0.481434i	$0.159884\pi$
$684$	4.48147	−	27.3008i	0.171353	−	1.04387i
$685$	24.3276	+	5.84054i	0.929510	+	0.223155i
$686$	19.6456	+	29.5813i	0.750072	+	1.12942i
$687$	22.4805	+	7.30437i	0.857686	+	0.278679i
$688$	−16.4587	−	19.7152i	−0.627480	−	0.751634i
$689$	−4.27142	−	5.87910i	−0.162728	−	0.223976i
$690$	−12.7670	−	10.1230i	−0.486031	−	0.385376i
$691$	8.90034	+	10.4210i	0.338585	+	0.396432i	0.903409	−	0.428779i	$-0.141056\pi$
$691$	8.90034	+	10.4210i	0.338585	+	0.396432i	−0.564825	+	0.825211i	$0.691056\pi$
$692$	10.1014	+	31.6942i	0.383999	+	1.20483i
$693$	31.5413	−	32.6545i	1.19816	−	1.24044i
$694$	−29.9077	+	10.9381i	−1.13528	+	0.415206i
$695$	−31.3775	−	15.9876i	−1.19022	−	0.606446i
$696$	−19.0790	−	17.9372i	−0.723189	−	0.679907i
$697$	−3.37471	−	0.534501i	−0.127826	−	0.0202457i
$698$	−15.8267	+	17.0250i	−0.599051	+	0.644406i
$699$	−27.5982	+	32.3133i	−1.04386	+	1.22220i
$700$	−57.1484	+	34.5802i	−2.16001	+	1.30701i
$701$	7.55779	−	31.4805i	0.285454	−	1.18900i	−0.626735	−	0.779232i	$-0.715609\pi$
$701$	7.55779	−	31.4805i	0.285454	−	1.18900i	0.912189	−	0.409769i	$-0.134391\pi$
$702$	1.39940	+	0.788875i	0.0528169	+	0.0297742i
$703$	16.1657			0.609700
$704$	−2.06921	+	26.4522i	−0.0779864	+	0.996954i
$705$	23.5556			0.887156
$706$	7.14279	+	4.02657i	0.268822	+	0.151542i
$707$	13.1623	−	54.8248i	0.495018	−	2.06190i
$708$	5.32027	−	3.21927i	0.199948	−	0.120988i
$709$	23.3119	−	27.2947i	0.875497	−	1.02508i	−0.123965	−	0.992287i	$-0.539561\pi$
$709$	23.3119	−	27.2947i	0.875497	−	1.02508i	0.999462	−	0.0327892i	$-0.0104390\pi$
$710$	32.6194	−	35.0891i	1.22418	−	1.31687i
$711$	−42.4190	−	6.71850i	−1.59084	−	0.251964i
$712$	21.9308	−	23.3269i	0.821893	−	0.874214i
$713$	−10.4779	−	5.33876i	−0.392401	−	0.199938i
$714$	13.6525	−	4.99314i	0.510934	−	0.186864i
$715$	−8.65270	+	61.5157i	−0.323593	+	2.30056i
$716$	−9.75483	−	30.6066i	−0.364555	−	1.14382i
$717$	35.4337	+	41.4875i	1.32330	+	1.54938i
$718$	22.1693	+	17.5781i	0.827351	+	0.656010i
$719$	12.7565	+	17.5579i	0.475739	+	0.654798i	0.977679	−	0.210104i	$-0.0673803\pi$
$719$	12.7565	+	17.5579i	0.475739	+	0.654798i	−0.501940	+	0.864902i	$0.667380\pi$
$720$	3.91935	−	43.5365i	0.146065	−	1.62251i
$721$	60.7923	+	19.7526i	2.26402	+	0.735626i
$722$	−0.844799	−	1.27206i	−0.0314401	−	0.0473410i
$723$	−16.7476	−	4.02074i	−0.622849	−	0.149533i
$724$	−0.105852	+	0.644841i	−0.00393395	+	0.0239653i
$725$	−10.8162	+	26.1127i	−0.401705	+	0.969801i
$726$	−32.8723	+	19.8109i	−1.22001	+	0.735250i
$727$	−24.9585	+	24.9585i	−0.925658	+	0.925658i	−0.997422	−	0.0717634i	$-0.977137\pi$
$727$	−24.9585	+	24.9585i	−0.925658	+	0.925658i	0.0717634	+	0.997422i	$0.477137\pi$
$728$	55.4848	−	36.4008i	2.05640	−	1.34910i
$729$	4.46510	+	28.1915i	0.165374	+	1.04413i
$730$	4.93041	+	25.1562i	0.182483	+	0.931072i
$731$	3.91789	−	4.58726i	0.144908	−	0.169666i
$732$	−2.54060	+	1.03566i	−0.0939032	+	0.0382790i
$733$	−45.0346	−	27.5973i	−1.66339	−	1.01933i	−0.946793	−	0.321843i	$-0.895698\pi$
$733$	−45.0346	−	27.5973i	−1.66339	−	1.01933i	−0.716599	−	0.697485i	$-0.754302\pi$
$734$	1.54527	+	13.3780i	0.0570370	+	0.493790i
$735$	34.1757	+	105.182i	1.26059	+	3.87970i
$736$	1.55848	−	7.29751i	0.0574464	−	0.268990i
$737$	−6.93525	+	1.79273i	−0.255463	+	0.0660359i
$738$	10.7437	+	11.6882i	0.395481	+	0.430248i
$739$	−10.6378	+	9.08553i	−0.391317	+	0.334217i	−0.823239	−	0.567694i	$-0.807836\pi$
$739$	−10.6378	+	9.08553i	−0.391317	+	0.334217i	0.431922	+	0.901911i	$0.357836\pi$
$740$	25.4739	−	1.86082i	0.936441	−	0.0684052i
$741$	56.8788	−	13.6554i	2.08949	−	0.501643i
$742$	6.30824	+	5.86424i	0.231583	+	0.215283i
$743$	−16.8779	+	8.59973i	−0.619191	+	0.315494i	−0.735299	−	0.677743i	$-0.762958\pi$
$743$	−16.8779	+	8.59973i	−0.619191	+	0.315494i	0.116108	+	0.993237i	$0.462958\pi$
$744$	−6.79078	−	61.8377i	−0.248962	−	2.26708i
$745$	33.3820	−	5.28719i	1.22302	−	0.193707i
$746$	19.9705	−	15.6527i	0.731173	−	0.573085i
$747$	−1.82536	+	4.40681i	−0.0667864	+	0.161237i
$748$	−6.20712	+	0.561759i	−0.226955	+	0.0205400i
$749$	32.8152	−	13.5925i	1.19904	−	0.496659i
$750$	−30.1218	+	8.40391i	−1.09989	+	0.306867i
$751$	−26.8339	+	36.9337i	−0.979182	+	1.34773i	−0.0419137	+	0.999121i	$0.513345\pi$
$751$	−26.8339	+	36.9337i	−0.979182	+	1.34773i	−0.937269	+	0.348608i	$0.886655\pi$
$752$	4.78932	+	9.66672i	0.174649	+	0.352509i
$753$	23.1572	+	7.52424i	0.843897	+	0.274199i
$754$	9.79277	−	26.3164i	0.356632	−	0.958388i
$755$	5.09352	−	8.31187i	0.185372	−	0.302500i
$756$	−1.80746	−	0.598533i	−0.0657367	−	0.0217684i
$757$	−28.6817	−	2.25730i	−1.04245	−	0.0820429i	−0.454346	−	0.890825i	$-0.650127\pi$
$757$	−28.6817	−	2.25730i	−1.04245	−	0.0820429i	−0.588108	+	0.808783i	$0.700127\pi$
$758$	5.18249	−	1.89539i	0.188237	−	0.0688437i
$759$	9.89926	−	4.30296i	0.359320	−	0.156188i
$760$	−27.4791	−	35.4681i	−0.996771	−	1.28656i
$761$	1.44311	−	2.83226i	0.0523127	−	0.102670i	−0.863370	−	0.504571i	$-0.831651\pi$
$761$	1.44311	−	2.83226i	0.0523127	−	0.102670i	0.915683	+	0.401902i	$0.131651\pi$
$762$	11.0630	+	19.8852i	0.400769	+	0.720366i
$763$	57.4542	−	13.7935i	2.07998	−	0.499360i
$764$	39.6013	+	16.6648i	1.43272	+	0.602912i
$765$	10.2362	−	0.805610i	0.370092	−	0.0291269i
$766$	8.34250	−	41.3331i	0.301427	−	1.49342i
$767$	5.39441	+	3.91927i	0.194781	+	0.141517i
$768$	36.8006	−	14.2826i	1.32793	−	0.515381i
$769$	−1.70553			−0.0615030			−0.0307515	−	0.999527i	$-0.509790\pi$
$769$	−1.70553			−0.0615030			−0.0307515	+	0.999527i	$0.509790\pi$
$770$	−3.95905	−	73.5209i	−0.142674	−	2.64951i
$771$	9.70105	+	23.4204i	0.349375	+	0.843465i
$772$	28.7392	−	6.72904i	1.03435	−	0.242184i
$773$	2.07292	+	3.38270i	0.0745577	+	0.121667i	0.887746	−	0.460333i	$-0.152270\pi$
$773$	2.07292	+	3.38270i	0.0745577	+	0.121667i	−0.813188	+	0.582001i	$0.802270\pi$
$774$	−27.5069	+	5.39113i	−0.988715	+	0.193780i
$775$	−59.8261	+	30.4829i	−2.14902	+	1.09498i
$776$	−10.2540	+	3.68497i	−0.368096	+	0.132283i
$777$	6.17406	−	38.9815i	0.221493	−	1.39845i
$778$	−19.2431	−	5.48556i	−0.689900	−	0.196667i
$779$	16.2450	+	1.27851i	0.582037	+	0.0458073i
$780$	88.0579	−	28.0655i	3.15298	−	1.00491i
$781$	10.3297	+	30.0109i	0.369626	+	1.07387i
$782$	1.75126	+	0.0737374i	0.0626248	+	0.00263684i
$783$	−0.766221	+	0.248960i	−0.0273825	+	0.00889712i
$784$	−36.2158	+	35.4105i	−1.29342	+	1.26466i
$785$	19.5017	+	26.8419i	0.696047	+	0.958027i
$786$	−26.2799	−	9.77918i	−0.937373	−	0.348812i
$787$	−1.02164	−	12.9812i	−0.0364175	−	0.462728i	−0.987907	−	0.155047i	$-0.950447\pi$
$787$	−1.02164	−	12.9812i	−0.0364175	−	0.462728i	0.951490	−	0.307681i	$-0.0995530\pi$
$788$	−0.866825	−	5.67936i	−0.0308794	−	0.202319i
$789$	−37.5430	+	23.0064i	−1.33657	+	0.819049i
$790$	−54.8186	+	42.9662i	−1.95036	+	1.52867i
$791$	−22.4240	+	22.4240i	−0.797305	+	0.797305i
$792$	24.2207	+	15.8736i	0.860645	+	0.564043i
$793$	−2.08021	−	2.08021i	−0.0738704	−	0.0738704i
$794$	−30.4844	−	3.69498i	−1.08185	−	0.131130i
$795$	6.26774	+	10.2280i	0.222294	+	0.362751i
$796$	−6.59962	+	26.8242i	−0.233917	+	0.950759i
$797$	−53.6641	+	4.22346i	−1.90088	+	0.149603i	−0.974117	−	0.226044i	$-0.927421\pi$
$797$	−53.6641	+	4.22346i	−1.90088	+	0.149603i	−0.926763	+	0.375647i	$0.877421\pi$
$798$	−63.0424	+	28.8484i	−2.23168	+	1.02122i
$799$	−2.05011	+	1.48949i	−0.0725278	+	0.0526945i
$800$	−28.4788	−	31.6902i	−1.00688	−	1.12042i
$801$	−10.7984	−	33.2342i	−0.381544	−	1.17427i
$802$	6.23122	+	6.77902i	0.220032	+	0.239375i
$803$	−16.2400	−	4.96710i	−0.573096	−	0.175285i
$804$	6.87564	+	8.14259i	0.242485	+	0.287167i
$805$	−1.62464	+	20.6430i	−0.0572609	+	0.727569i
$806$	58.2916	−	32.4300i	2.05323	−	1.14230i
$807$	−54.4484	−	8.62378i	−1.91667	−	0.303571i
$808$	35.9232	+	1.71490i	1.26377	+	0.0603301i
$809$	−2.42047	−	4.75045i	−0.0850994	−	0.167017i	0.844535	−	0.535501i	$-0.179877\pi$
$809$	−2.42047	−	4.75045i	−0.0850994	−	0.167017i	−0.929634	+	0.368484i	$0.879877\pi$
$810$	36.2771	+	24.3874i	1.27465	+	0.856885i
$811$	21.7227	−	13.3117i	0.762788	−	0.467437i	−0.0859178	−	0.996302i	$-0.527382\pi$
$811$	21.7227	−	13.3117i	0.762788	−	0.467437i	0.848706	+	0.528865i	$0.177382\pi$
$812$	−5.39088	+	32.8408i	−0.189183	+	1.15249i
$813$	−50.9574	+	21.1073i	−1.78715	+	0.740264i
$814$	−6.86016	+	15.4680i	−0.240449	+	0.542152i
$815$		−	44.2215i		−	1.54901i
$816$	4.75569	+	7.96008i	0.166482	+	0.278659i
$817$	−16.9110	+	23.2761i	−0.591643	+	0.814326i
$818$	12.0347	−	7.99251i	0.420784	−	0.279452i
$819$	−5.68252	−	72.2032i	−0.198563	−	2.52298i
$820$	25.7461	+	0.144728i	0.899093	+	0.00505411i
$821$	10.9027	+	45.4131i	0.380507	+	1.58493i	0.753729	+	0.657185i	$0.228253\pi$
$821$	10.9027	+	45.4131i	0.380507	+	1.58493i	−0.373222	+	0.927742i	$0.621747\pi$
$822$	23.7144	+	6.76016i	0.827135	+	0.235788i
$823$	14.5622	+	7.41981i	0.507606	+	0.258638i	0.688986	−	0.724775i	$-0.258056\pi$
$823$	14.5622	+	7.41981i	0.507606	+	0.258638i	−0.181379	+	0.983413i	$0.558056\pi$
$824$	−5.13351	+	40.4479i	−0.178834	+	1.40907i
$825$	13.3463	−	60.1685i	0.464659	−	2.09480i
$826$	−7.16762	−	3.32878i	−0.249393	−	0.115823i
$827$	−0.843489	+	10.7175i	−0.0293310	+	0.372685i	0.964682	+	0.263419i	$0.0848502\pi$
$827$	−0.843489	+	10.7175i	−0.0293310	+	0.372685i	−0.994012	+	0.109266i	$0.965150\pi$
$828$	−6.16314	−	5.32403i	−0.214184	−	0.185023i
$829$	5.45187	+	3.34091i	0.189351	+	0.116035i	0.613943	−	0.789350i	$-0.289582\pi$
$829$	5.45187	+	3.34091i	0.189351	+	0.116035i	−0.424592	+	0.905385i	$0.639582\pi$
$830$	3.21881	+	7.03407i	0.111727	+	0.244156i
$831$	5.40366	−	16.6308i	0.187451	−	0.576915i
$832$	29.4214	+	30.4308i	1.02000	+	1.05500i
$833$	−9.62539	−	6.99326i	−0.333500	−	0.242302i
$834$	−30.2361	−	17.0448i	−1.04699	−	0.590214i
$835$	−25.1544	−	60.7281i	−0.870504	−	2.10158i
$836$	29.3014	−	4.99349i	1.01341	−	0.172704i
$837$	−1.76822	−	0.732421i	−0.0611186	−	0.0253162i
$838$	3.37057	−	27.8080i	0.116434	−	0.960610i
$839$	−0.0848031	−	0.535426i	−0.00292773	−	0.0184849i	0.986181	−	0.165670i	$-0.0529787\pi$
$839$	−0.0848031	−	0.535426i	−0.00292773	−	0.0184849i	−0.989109	+	0.147185i	$0.952979\pi$
$840$	−96.0218	+	52.7162i	−3.31307	+	1.81888i
$841$	−6.77252	−	13.2918i	−0.233535	−	0.458338i
$842$	0.914724	+	25.0778i	0.0315235	+	0.864239i
$843$	11.5337	+	48.0411i	0.397240	+	1.65463i
$844$	−2.79318	+	8.43490i	−0.0961453	+	0.290341i
$845$	34.4735	+	40.3633i	1.18592	+	1.38854i
$846$	11.7640	+	0.495327i	0.404454	+	0.0170297i
$847$	44.2021	+	20.6242i	1.51880	+	0.708656i
$848$	−2.92301	+	4.65171i	−0.100377	+	0.159740i
$849$	−58.1793	+	18.9036i	−1.99671	+	0.648769i
$850$	6.21800	−	7.84206i	0.213276	−	0.268981i
$851$	2.48648	−	4.05756i	0.0852353	−	0.139091i
$852$	33.5768	−	33.2014i	1.15032	−	1.13746i
$853$	2.60873	+	2.22806i	0.0893211	+	0.0762874i	0.692987	−	0.720950i	$-0.256294\pi$
$853$	2.60873	+	2.22806i	0.0893211	+	0.0762874i	−0.603666	+	0.797237i	$0.706294\pi$
$854$	2.89367	+	1.94528i	0.0990195	+	0.0665660i
$855$	−48.3666	+	7.66052i	−1.65410	+	0.261984i
$856$	12.4277	+	18.9433i	0.424771	+	0.647467i
$857$	33.7386	+	33.7386i	1.15249	+	1.15249i	0.986052	+	0.166438i	$0.0532265\pi$
$857$	33.7386	+	33.7386i	1.15249	+	1.15249i	0.166438	+	0.986052i	$0.446773\pi$
$858$	−11.0714	+	60.2188i	−0.377971	+	2.05583i
$859$	−0.739980	−	0.306510i	−0.0252478	−	0.0104580i	0.370024	−	0.929022i	$-0.379350\pi$
$859$	−0.739980	−	0.306510i	−0.0252478	−	0.0104580i	−0.395272	+	0.918564i	$0.629350\pi$
$860$	−23.9692	+	38.6251i	−0.817343	+	1.31711i
$861$	9.28731	−	38.6844i	0.316511	−	1.31836i
$862$	49.8430	+	10.0601i	1.69766	+	0.342649i
$863$	2.20580	−	6.78875i	0.0750862	−	0.231092i	−0.906468	−	0.422274i	$-0.861232\pi$
$863$	2.20580	−	6.78875i	0.0750862	−	0.231092i	0.981555	+	0.191182i	$0.0612321\pi$
$864$	0.159680	−	1.20393i	0.00543242	−	0.0409584i
$865$	47.6345	−	34.6085i	1.61962	−	1.17673i
$866$	−4.84017	−	41.9031i	−0.164476	−	1.42392i
$867$	30.2369	−	25.8247i	1.02690	−	0.877054i
$868$	−60.4059	+	51.0071i	−2.05031	+	1.73129i
$869$	−8.00725	−	45.4420i	−0.271627	−	1.54151i
$870$	−19.5236	+	42.0388i	−0.661912	+	1.42525i
$871$	−5.18794	+	10.1819i	−0.175787	+	0.345001i
$872$	15.4897	+	34.3588i	0.524547	+	1.16354i
$873$	−1.86035	+	11.7458i	−0.0629632	+	0.397534i
$874$	−8.35392	+	0.304713i	−0.282575	+	0.0103071i
$875$	30.2209	+	25.8111i	1.02165	+	0.872575i
$876$	3.81216	+	24.9770i	0.128801	+	0.843893i
$877$	−40.2694	−	9.66782i	−1.35980	−	0.326459i	−0.513008	−	0.858384i	$-0.671469\pi$
$877$	−40.2694	−	9.66782i	−1.35980	−	0.326459i	−0.846792	+	0.531924i	$0.821469\pi$
$878$	−50.4171	+	14.0662i	−1.70149	+	0.474712i
$879$			28.7108i			0.968392i
$880$	45.5985	−	11.2416i	1.53713	−	0.378956i
$881$			10.0192i			0.337555i	0.985654	+	0.168777i	$0.0539819\pi$
$881$			10.0192i			0.337555i	−0.985654	+	0.168777i	$0.946018\pi$
$882$	14.8560	+	53.2479i	0.500229	+	1.79295i
$883$	29.6412	+	7.11623i	0.997507	+	0.239480i	0.699151	−	0.714974i	$-0.253562\pi$
$883$	29.6412	+	7.11623i	0.997507	+	0.239480i	0.298356	+	0.954455i	$0.403562\pi$
$884$	−5.88927	+	8.01079i	−0.198077	+	0.269432i
$885$	−8.36959	−	7.14831i	−0.281341	−	0.240288i
$886$	−1.18194	−	32.4036i	−0.0397079	−	1.08862i
$887$	4.31167	−	27.2228i	0.144772	−	0.914052i	−0.803203	−	0.595706i	$-0.796873\pi$
$887$	4.31167	−	27.2228i	0.144772	−	0.914052i	0.947974	−	0.318346i	$-0.103127\pi$
$888$	25.1626	−	0.776210i	0.844401	−	0.0260479i
$889$	13.1292	−	25.7674i	0.440338	−	0.864212i
$890$	−51.3986	−	23.8705i	−1.72289	−	0.800140i
$891$	−25.5706	+	13.5923i	−0.856646	+	0.455360i
$892$	4.07435	−	48.2970i	0.136419	−	1.61710i
$893$	9.18988	−	7.84890i	0.307528	−	0.262653i
$894$	33.0921	−	3.82242i	1.10676	−	0.127841i
$895$	−46.0001	+	33.4210i	−1.53761	+	1.11714i
$896$	−41.1567	−	28.6871i	−1.37495	−	0.958367i
$897$	5.32116	−	16.3768i	0.177668	−	0.546807i
$898$	5.24223	−	25.9727i	0.174935	−	0.866721i
$899$	−7.80963	+	32.5295i	−0.260466	+	1.08492i
$900$	−45.2772	+	10.6013i	−1.50924	+	0.353376i
$901$	−1.19225	−	0.493846i	−0.0397196	−	0.0164524i
$902$	−8.11715	+	15.0013i	−0.270272	+	0.499489i
$903$	49.6685	+	49.6685i	1.65286	+	1.65286i
$904$	−16.7236	−	11.3794i	−0.556217	−	0.378475i
$905$	1.14241	−	0.180941i	0.0379751	−	0.00601467i
$906$	5.36048	−	7.97391i	0.178090	−	0.264915i
$907$	−30.8362	−	26.3366i	−1.02390	−	0.874493i	−0.0317434	−	0.999496i	$-0.510106\pi$
$907$	−30.8362	−	26.3366i	−1.02390	−	0.874493i	−0.992156	+	0.125003i	$0.960106\pi$
$908$	−0.148875	+	26.4839i	−0.00494060	+	0.878901i
$909$	20.5092	−	33.4680i	0.680247	−	1.11006i
$910$	−92.0365	−	72.9761i	−3.05098	−	2.41914i
$911$	−22.5987	+	7.34276i	−0.748728	+	0.243276i	−0.658434	−	0.752639i	$-0.728781\pi$
$911$	−22.5987	+	7.34276i	−0.748728	+	0.243276i	−0.0902940	+	0.995915i	$0.528781\pi$
$912$	−25.5894	−	36.0666i	−0.847349	−	1.19428i
$913$	−5.11508	−	0.313443i	−0.169284	−	0.0103735i
$914$	−0.0961392	+	2.28330i	−0.00318000	+	0.0755248i
$915$	3.15383	+	3.69267i	0.104263	+	0.122076i
$916$	17.1216	−	8.60300i	0.565713	−	0.284251i
$917$	8.31906	+	34.6514i	0.274719	+	1.14429i
$918$	0.285084	−	0.0103986i	0.00940918	−	0.000343204i
$919$	14.6431	+	28.7387i	0.483031	+	0.948002i	0.995979	+	0.0895828i	$0.0285534\pi$
$919$	14.6431	+	28.7387i	0.483031	+	0.948002i	−0.512948	+	0.858420i	$0.671447\pi$
$920$	−13.1291	+	1.44178i	−0.432852	+	0.0475341i
$921$	−7.93624	−	50.1074i	−0.261508	−	1.65110i
$922$	33.9557	+	4.11572i	1.11827	+	0.135544i
$923$	46.7786	+	19.3763i	1.53974	+	0.637779i
$924$	−0.850250	−	72.5638i	−0.0279712	−	2.38717i
$925$	−10.3981	−	25.1033i	−0.341888	−	0.825390i
$926$	1.64478	−	2.91770i	0.0540509	−	0.0958817i
$927$	36.0013	+	26.1565i	1.18244	+	0.859091i
$928$	−21.2213	+	0.535246i	−0.696625	+	0.0175703i
$929$	−2.25977	+	6.95487i	−0.0741408	+	0.228182i	−0.981259	−	0.192694i	$-0.938277\pi$
$929$	−2.25977	+	6.95487i	−0.0741408	+	0.228182i	0.907118	+	0.420876i	$0.138277\pi$
$930$	−100.126	+	45.8181i	−3.28328	+	1.50244i
$931$	48.3805	+	29.6476i	1.58561	+	0.971662i
$932$	2.50967	+	34.3565i	0.0822071	+	1.12538i
$933$	−3.38967	+	43.0698i	−0.110973	+	1.41004i
$934$	−9.55202	+	20.5677i	−0.312552	+	0.672996i
$935$	4.39768	+	10.1172i	0.143819	+	0.330866i
$936$	44.5674	−	12.1646i	1.45673	−	0.397612i
$937$	−43.8740	−	22.3549i	−1.43330	−	0.730304i	−0.446889	−	0.894589i	$-0.647468\pi$
$937$	−43.8740	−	22.3549i	−1.43330	−	0.730304i	−0.986413	+	0.164286i	$0.947468\pi$
$938$	3.71302	−	13.0251i	0.121234	−	0.425286i
$939$	15.0758	+	62.7954i	0.491982	+	2.04925i
$940$	13.5780	−	13.4262i	0.442864	−	0.437913i
$941$	0.508181	+	6.45705i	0.0165662	+	0.210494i	0.999629	+	0.0272263i	$0.00866746\pi$
$941$	0.508181	+	6.45705i	0.0165662	+	0.210494i	−0.983063	+	0.183268i	$0.941333\pi$
$942$	18.0914	+	27.2411i	0.589449	+	0.887563i
$943$	2.81958	−	3.88082i	0.0918181	−	0.126377i
$944$	1.23181	−	4.88809i	0.0400920	−	0.159094i
$945$			3.37008i			0.109629i
$946$	−15.0950	−	26.0587i	−0.490781	−	0.847243i
$947$	44.4596	−	18.4158i	1.44474	−	0.598432i	0.483800	−	0.875178i	$-0.339256\pi$
$947$	44.4596	−	18.4158i	1.44474	−	0.598432i	0.960943	+	0.276746i	$0.0892561\pi$
$948$	−55.7640	+	40.0379i	−1.81113	+	1.30037i
$949$	−23.0999	+	14.1556i	−0.749855	+	0.459512i
$950$	−26.6290	+	39.6116i	−0.863959	+	1.28517i
$951$	−20.2063	−	39.6571i	−0.655234	−	1.28597i
$952$	5.02365	−	10.6598i	0.162817	−	0.345486i
$953$	13.4923	+	2.13697i	0.437058	+	0.0692232i	0.371087	−	0.928598i	$-0.378985\pi$
$953$	13.4923	+	2.13697i	0.437058	+	0.0692232i	0.0659717	+	0.997821i	$0.478985\pi$
$954$	2.91512	+	5.23981i	0.0943805	+	0.169645i
$955$	5.96670	−	75.8141i	0.193078	−	2.45329i
$956$	44.0717	+	3.71791i	1.42538	+	0.120246i
$957$	−18.4770	−	24.5257i	−0.597276	−	0.792803i
$958$	−27.3360	+	25.1270i	−0.883187	+	0.811818i
$959$	−9.68421	−	29.8049i	−0.312719	−	0.962451i
$960$	−44.4754	−	53.8883i	−1.43544	−	1.73924i
$961$	−39.2154	+	28.4916i	−1.26501	+	0.919085i
$962$	11.2323	+	24.5460i	0.362145	+	0.791396i
$963$	24.6511	−	1.94009i	0.794372	−	0.0625184i
$964$	−11.9454	+	7.22810i	−0.384735	+	0.232802i
$965$	−27.2978	−	44.5459i	−0.878746	−	1.43398i
$966$	−2.45578	+	20.2608i	−0.0790135	+	0.651880i
$967$	9.99708	+	9.99708i	0.321485	+	0.321485i	0.849336	−	0.527852i	$-0.177002\pi$
$967$	9.99708	+	9.99708i	0.321485	+	0.321485i	−0.527852	+	0.849336i	$0.677002\pi$
$968$	−7.65656	+	30.1559i	−0.246091	+	0.969247i
$969$	7.34517	−	7.34517i	0.235961	−	0.235961i
$970$	11.8973	+	15.1792i	0.381999	+	0.487375i
$971$	46.3054	−	28.3760i	1.48601	−	0.910628i	0.486697	−	0.873571i	$-0.338202\pi$
$971$	46.3054	−	28.3760i	1.48601	−	0.910628i	0.999313	−	0.0370574i	$-0.0117984\pi$
$972$	35.7505	+	26.2826i	1.14670	+	0.843015i
$973$	3.46095	+	43.9755i	0.110953	+	1.40979i
$974$	−5.94080	+	15.9649i	−0.190355	+	0.511549i
$975$	−57.7907	−	79.5421i	−1.85078	−	2.54739i
$976$	−0.874154	+	2.04506i	−0.0279810	+	0.0654607i
$977$	−33.8569	+	11.0008i	−1.08318	+	0.351946i	−0.795607	−	0.605813i	$-0.792848\pi$
$977$	−33.8569	+	11.0008i	−1.08318	+	0.351946i	−0.287572	+	0.957759i	$0.592848\pi$
$978$	1.83357	−	43.5471i	0.0586310	−	1.39248i
$979$	29.9863	−	22.5909i	0.958365	−	0.722007i
$980$	79.6510	+	41.1498i	2.54436	+	1.31448i
$981$	41.0079	+	3.22739i	1.30928	+	0.103043i
$982$	0.796026	−	2.79243i	0.0254022	−	0.0891100i
$983$	8.09732	−	51.1245i	0.258264	−	1.63062i	−0.428362	−	0.903607i	$-0.640909\pi$
$983$	8.09732	−	51.1245i	0.258264	−	1.63062i	0.686626	−	0.727010i	$-0.259091\pi$
$984$	25.3474	+	1.21004i	0.808047	+	0.0385746i
$985$	−9.06062	+	4.61662i	−0.288695	+	0.147098i
$986$	−0.959047	−	4.89329i	−0.0305423	−	0.155834i
$987$	−15.4168	−	25.1579i	−0.490721	−	0.800785i
$988$	25.0029	−	40.2909i	0.795448	−	1.28182i
$989$	3.24113	+	7.82478i	0.103062	+	0.248814i
$990$	13.1952	−	49.5300i	0.419372	−	1.57417i
$991$	−17.9304			−0.569576			−0.284788	−	0.958590i	$-0.591923\pi$
$991$	−17.9304			−0.569576			−0.284788	+	0.958590i	$0.591923\pi$
$992$	−39.1605	−	31.7740i	−1.24335	−	1.00883i
$993$	31.5512	+	22.9233i	1.00125	+	0.727448i
$994$	−58.8248	−	11.8730i	−1.86581	−	0.376587i
$995$	48.7445	−	3.83627i	1.54530	−	0.121618i
$996$	2.87807	+	7.06026i	0.0911950	+	0.223713i
$997$	28.8846	−	6.93459i	0.914786	−	0.219621i	0.251387	−	0.967887i	$-0.419113\pi$
$997$	28.8846	−	6.93459i	0.914786	−	0.219621i	0.663399	+	0.748266i	$0.269113\pi$
$998$	16.5084	−	9.18427i	0.522563	−	0.290723i
$999$	0.351620	−	0.690092i	0.0111248	−	0.0218336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.bf.a.5.8	✓	736
11.9	even	5	inner	352.2.bf.a.229.29	yes	736
32.13	even	8	inner	352.2.bf.a.269.29	yes	736
352.141	even	40	inner	352.2.bf.a.141.8	yes	736

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.bf.a.5.8	✓	736	1.1	even	1	trivial
352.2.bf.a.141.8	yes	736	352.141	even	40	inner
352.2.bf.a.229.29	yes	736	11.9	even	5	inner
352.2.bf.a.269.29	yes	736	32.13	even	8	inner

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:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.bf (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23195 - 0.694480i) q^{2} +(-0.575954 + 2.39902i) q^{3} +(1.03539 + 1.71113i) q^{4} +(2.29907 - 2.69186i) q^{5} +(2.37562 - 2.55548i) q^{6} +(-4.37967 - 0.693671i) q^{7} +(-0.0872092 - 2.82708i) q^{8} +(-2.75055 - 1.40148i) q^{9} +(-4.70178 + 1.71958i) q^{10} +(0.461964 - 3.28429i) q^{11} +(-4.70137 + 1.49840i) q^{12} +(-3.43622 - 4.02330i) q^{13} +(4.91379 + 3.89616i) q^{14} +(5.13367 + 7.06589i) q^{15} +(-1.85592 + 3.54339i) q^{16} +(-0.893597 - 0.290347i) q^{17} +(2.41524 + 3.63675i) q^{18} +(4.35723 + 1.04608i) q^{19} +(6.98656 + 1.14686i) q^{20} +(4.18662 - 10.1074i) q^{21} +(-2.84999 + 3.72526i) q^{22} +(0.932759 - 0.932759i) q^{23} +(6.83245 + 1.41905i) q^{24} +(-1.17824 - 7.43910i) q^{25} +(1.43915 + 7.34289i) q^{26} +(0.139430 - 0.163251i) q^{27} +(-3.34773 - 8.21240i) q^{28} +(-3.19965 - 1.96075i) q^{29} +(-1.41730 - 12.2701i) q^{30} +(-2.75481 - 8.47844i) q^{31} +(4.74720 - 3.07637i) q^{32} +(7.61302 + 2.99986i) q^{33} +(0.899225 + 0.978278i) q^{34} +(-11.9364 + 10.1947i) q^{35} +(-0.449803 - 6.15763i) q^{36} +(3.50789 - 0.842170i) q^{37} +(-4.64141 - 4.31473i) q^{38} +(11.6311 - 5.92633i) q^{39} +(-7.81061 - 6.26490i) q^{40} +(3.59171 - 0.568871i) q^{41} +(-12.1771 + 9.54426i) q^{42} +(-2.45704 + 5.93182i) q^{43} +(6.09816 - 2.61006i) q^{44} +(-10.0963 + 4.18202i) q^{45} +(-1.79689 + 0.501329i) q^{46} +(1.58527 - 2.18194i) q^{47} +(-7.43173 - 6.49320i) q^{48} +(12.0429 + 3.91298i) q^{49} +(-3.71478 + 9.98285i) q^{50} +(1.21122 - 1.97653i) q^{51} +(3.32653 - 10.0455i) q^{52} +(1.36923 + 0.107761i) q^{53} +(-0.285145 + 0.104286i) q^{54} +(-7.77878 - 8.79435i) q^{55} +(-1.57912 + 12.4422i) q^{56} +(-5.01913 + 9.85060i) q^{57} +(2.58010 + 4.63763i) q^{58} +(-1.22541 + 0.294195i) q^{59} +(-6.77527 + 16.1004i) q^{60} +(0.554299 - 0.0436243i) q^{61} +(-2.49432 + 12.3582i) q^{62} +(11.0743 + 8.04598i) q^{63} +(-7.98479 + 0.493095i) q^{64} -18.7303 q^{65} +(-7.29550 - 8.98276i) q^{66} +(-0.826516 - 1.99539i) q^{67} +(-0.428404 - 1.82968i) q^{68} +(1.70048 + 2.77493i) q^{69} +(21.7850 - 4.26970i) q^{70} +(-8.52660 + 4.34452i) q^{71} +(-3.72222 + 7.89826i) q^{72} +(0.801014 - 5.05740i) q^{73} +(-4.90641 - 1.39865i) q^{74} +(18.5251 + 1.45796i) q^{75} +(2.72148 + 8.53889i) q^{76} +(-4.30147 + 14.0637i) q^{77} +(-18.4446 - 0.776618i) q^{78} +(13.2314 - 4.29916i) q^{79} +(5.27143 + 13.1423i) q^{80} +(-5.13217 - 7.06383i) q^{81} +(-4.81987 - 1.79355i) q^{82} +(-0.121231 - 1.54038i) q^{83} +(21.6298 - 3.30130i) q^{84} +(-2.83601 + 1.73791i) q^{85} +(7.14647 - 5.60133i) q^{86} +(6.54671 - 6.54671i) q^{87} +(-9.32526 - 1.01959i) q^{88} +(8.00433 + 8.00433i) q^{89} +(15.3424 + 1.85964i) q^{90} +(12.2587 + 20.0043i) q^{91} +(2.56184 + 0.630296i) q^{92} +(21.9266 - 1.72566i) q^{93} +(-3.46829 + 1.58710i) q^{94} +(12.8335 - 9.32406i) q^{95} +(4.64611 + 13.1605i) q^{96} +(-1.19043 - 3.66378i) q^{97} +(-12.1188 - 13.1842i) q^{98} +(-5.87352 + 8.38620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 736 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 12 q^{8} - 12 q^{9} - 32 q^{10} - 16 q^{11} - 64 q^{12} - 12 q^{13} - 28 q^{14} - 52 q^{16} + 48 q^{18} - 12 q^{19} - 28 q^{20}+ \cdots - 68 q^{99}+O(q^{100}) \) 736 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 12 * q^7 - 12 * q^8 - 12 * q^9 - 32 * q^10 - 16 * q^11 - 64 * q^12 - 12 * q^13 - 28 * q^14 - 52 * q^16 + 48 * q^18 - 12 * q^19 - 28 * q^20 - 32 * q^21 - 28 * q^22 - 48 * q^23 - 12 * q^24 - 12 * q^25 - 72 * q^26 - 12 * q^27 - 12 * q^28 - 12 * q^29 - 28 * q^30 - 24 * q^31 + 8 * q^32 - 32 * q^33 - 8 * q^34 - 12 * q^35 - 12 * q^36 - 12 * q^37 - 12 * q^38 - 12 * q^39 + 28 * q^40 - 12 * q^41 - 52 * q^42 - 48 * q^43 - 56 * q^44 - 56 * q^45 - 76 * q^46 - 12 * q^48 - 12 * q^50 - 36 * q^51 - 28 * q^52 + 36 * q^53 - 120 * q^54 + 16 * q^55 + 184 * q^56 - 12 * q^57 - 12 * q^58 + 20 * q^59 + 4 * q^60 - 12 * q^61 + 4 * q^62 + 56 * q^63 - 156 * q^64 - 64 * q^65 + 8 * q^66 + 48 * q^67 - 100 * q^68 - 12 * q^69 + 36 * q^70 + 20 * q^71 + 168 * q^72 - 12 * q^73 - 44 * q^74 - 148 * q^75 - 32 * q^76 - 32 * q^77 + 16 * q^78 - 148 * q^80 - 52 * q^82 - 12 * q^83 + 100 * q^84 - 52 * q^85 + 92 * q^86 - 32 * q^87 - 20 * q^88 - 32 * q^89 - 180 * q^90 + 132 * q^91 + 132 * q^92 + 12 * q^93 + 8 * q^94 - 152 * q^95 - 76 * q^96 - 24 * q^97 - 48 * q^98 - 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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