LMFDB - Embedded newform 216.2.t.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34345 + 0.441744i) q^{2} +(1.73179 + 0.0302651i) q^{3} +(1.60972 - 1.18692i) q^{4} +(-0.721676 + 0.860059i) q^{5} +(-2.33994 + 0.724346i) q^{6} +(1.31793 + 0.479686i) q^{7} +(-1.63827 + 2.30566i) q^{8} +(2.99817 + 0.104825i) q^{9} +O(q^{10})$	\(q+(-1.34345 + 0.441744i) q^{2} +(1.73179 + 0.0302651i) q^{3} +(1.60972 - 1.18692i) q^{4} +(-0.721676 + 0.860059i) q^{5} +(-2.33994 + 0.724346i) q^{6} +(1.31793 + 0.479686i) q^{7} +(-1.63827 + 2.30566i) q^{8} +(2.99817 + 0.104825i) q^{9} +(0.589610 - 1.47424i) q^{10} +(1.05816 + 1.26106i) q^{11} +(2.82362 - 2.00678i) q^{12} +(-0.671077 - 0.118329i) q^{13} +(-1.98247 - 0.0622489i) q^{14} +(-1.27582 + 1.46760i) q^{15} +(1.18243 - 3.82124i) q^{16} +(0.907443 - 1.57174i) q^{17} +(-4.07420 + 1.18359i) q^{18} +(2.96777 - 1.71344i) q^{19} +(-0.140874 + 2.24103i) q^{20} +(2.26785 + 0.870601i) q^{21} +(-1.97865 - 1.22674i) q^{22} +(-3.62278 + 1.31858i) q^{23} +(-2.90692 + 3.94333i) q^{24} +(0.649354 + 3.68267i) q^{25} +(0.953831 - 0.137475i) q^{26} +(5.18901 + 0.272275i) q^{27} +(2.69085 - 0.792115i) q^{28} +(3.92395 - 0.691898i) q^{29} +(1.06570 - 2.53523i) q^{30} +(-6.21468 + 2.26196i) q^{31} +(0.0994769 + 5.65598i) q^{32} +(1.79434 + 2.21592i) q^{33} +(-0.524800 + 2.51241i) q^{34} +(-1.36367 + 0.787317i) q^{35} +(4.95064 - 3.38986i) q^{36} +(3.83532 + 2.21432i) q^{37} +(-3.23015 + 3.61292i) q^{38} +(-1.15858 - 0.225231i) q^{39} +(-0.800705 - 3.07295i) q^{40} +(0.952217 - 5.40029i) q^{41} +(-3.43133 - 0.167801i) q^{42} +(-7.26017 - 8.65234i) q^{43} +(3.20013 + 0.774013i) q^{44} +(-2.25386 + 2.50295i) q^{45} +(4.28455 - 3.37179i) q^{46} +(-11.5469 - 4.20273i) q^{47} +(2.16336 - 6.58178i) q^{48} +(-3.85548 - 3.23513i) q^{49} +(-2.49917 - 4.66064i) q^{50} +(1.61907 - 2.69445i) q^{51} +(-1.22070 + 0.606040i) q^{52} -6.89741i q^{53} +(-7.09147 + 1.92643i) q^{54} -1.84824 q^{55} +(-3.26511 + 2.25283i) q^{56} +(5.19140 - 2.87750i) q^{57} +(-4.96599 + 2.66291i) q^{58} +(-6.78921 + 8.09106i) q^{59} +(-0.311789 + 3.87673i) q^{60} +(1.24084 - 3.40917i) q^{61} +(7.34992 - 5.78413i) q^{62} +(3.90108 + 1.57633i) q^{63} +(-2.63214 - 7.55459i) q^{64} +(0.586070 - 0.491771i) q^{65} +(-3.38948 - 2.18434i) q^{66} +(-11.9425 - 2.10578i) q^{67} +(-0.404798 - 3.60713i) q^{68} +(-6.31378 + 2.17386i) q^{69} +(1.48424 - 1.66012i) q^{70} +(6.80355 - 11.7841i) q^{71} +(-5.15350 + 6.74102i) q^{72} +(4.73823 + 8.20685i) q^{73} +(-6.13073 - 1.28061i) q^{74} +(1.01309 + 6.39725i) q^{75} +(2.74357 - 6.28068i) q^{76} +(0.789660 + 2.16957i) q^{77} +(1.65599 - 0.209209i) q^{78} +(1.59290 + 9.03380i) q^{79} +(2.43316 + 3.77465i) q^{80} +(8.97802 + 0.628568i) q^{81} +(1.10629 + 7.67567i) q^{82} +(1.29853 - 0.228966i) q^{83} +(4.68395 - 1.29034i) q^{84} +(0.696908 + 1.91474i) q^{85} +(13.5758 + 8.41686i) q^{86} +(6.81638 - 1.07946i) q^{87} +(-4.64114 + 0.373789i) q^{88} +(-3.52339 - 6.10270i) q^{89} +(1.92229 - 4.35823i) q^{90} +(-0.827669 - 0.477855i) q^{91} +(-4.26662 + 6.42251i) q^{92} +(-10.8310 + 3.72914i) q^{93} +(17.3692 + 0.545389i) q^{94} +(-0.668104 + 3.78901i) q^{95} +(0.00109395 + 9.79796i) q^{96} +(-6.33275 + 5.31381i) q^{97} +(6.60875 + 2.64311i) q^{98} +(3.04035 + 3.89180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−1.34345	+	0.441744i	−0.949964	+	0.312360i
$2$	−1.34345	+	0.441744i	−0.949964	+	0.312360i
$3$	1.73179	+	0.0302651i	0.999847	+	0.0174736i
$3$	1.73179	+	0.0302651i	0.999847	+	0.0174736i
$4$	1.60972	−	1.18692i	0.804862	−	0.593462i
$5$	−0.721676	+	0.860059i	−0.322743	+	0.384630i	−0.902883	−	0.429887i	$-0.858553\pi$
$5$	−0.721676	+	0.860059i	−0.322743	+	0.384630i	0.580140	+	0.814517i	$0.302998\pi$
$6$	−2.33994	+	0.724346i	−0.955277	+	0.295713i
$7$	1.31793	+	0.479686i	0.498129	+	0.181304i	0.578852	−	0.815432i	$-0.303501\pi$
$7$	1.31793	+	0.479686i	0.498129	+	0.181304i	−0.0807232	+	0.996737i	$0.525723\pi$
$8$	−1.63827	+	2.30566i	−0.579216	+	0.815174i
$9$	2.99817	+	0.104825i	0.999389	+	0.0349418i
$10$	0.589610	−	1.47424i	0.186451	−	0.466197i
$11$	1.05816	+	1.26106i	0.319047	+	0.380225i	0.901602	−	0.432566i	$-0.142392\pi$
$11$	1.05816	+	1.26106i	0.319047	+	0.380225i	−0.582556	+	0.812791i	$0.697947\pi$
$12$	2.82362	−	2.00678i	0.815109	−	0.579307i
$13$	−0.671077	−	0.118329i	−0.186123	−	0.0328186i	0.0798095	−	0.996810i	$-0.474569\pi$
$13$	−0.671077	−	0.118329i	−0.186123	−	0.0328186i	−0.265933	+	0.963992i	$0.585680\pi$
$14$	−1.98247	−	0.0622489i	−0.529837	−	0.0166367i
$15$	−1.27582	+	1.46760i	−0.329415	+	0.378932i
$16$	1.18243	−	3.82124i	0.295607	−	0.955310i
$17$	0.907443	−	1.57174i	0.220087	−	0.381202i	−0.734747	−	0.678341i	$-0.762699\pi$
$17$	0.907443	−	1.57174i	0.220087	−	0.381202i	0.954834	+	0.297139i	$0.0960324\pi$
$18$	−4.07420	+	1.18359i	−0.960298	+	0.278976i
$19$	2.96777	−	1.71344i	0.680853	−	0.393091i	−0.119323	−	0.992855i	$-0.538073\pi$
$19$	2.96777	−	1.71344i	0.680853	−	0.393091i	0.800176	+	0.599765i	$0.204739\pi$
$20$	−0.140874	+	2.24103i	−0.0315004	+	0.501110i
$21$	2.26785	+	0.870601i	0.494885	+	0.189981i
$22$	−1.97865	−	1.22674i	−0.421850	−	0.261543i
$23$	−3.62278	+	1.31858i	−0.755401	+	0.274944i	−0.690877	−	0.722973i	$-0.742775\pi$
$23$	−3.62278	+	1.31858i	−0.755401	+	0.274944i	−0.0645244	+	0.997916i	$0.520553\pi$
$24$	−2.90692	+	3.94333i	−0.593372	+	0.804929i
$25$	0.649354	+	3.68267i	0.129871	+	0.736534i
$26$	0.953831	−	0.137475i	0.187062	−	0.0269611i
$27$	5.18901	+	0.272275i	0.998626	+	0.0523993i
$28$	2.69085	−	0.792115i	0.508522	−	0.149696i
$29$	3.92395	−	0.691898i	0.728659	−	0.128482i	0.203001	−	0.979179i	$-0.434930\pi$
$29$	3.92395	−	0.691898i	0.728659	−	0.128482i	0.525657	+	0.850696i	$0.323819\pi$
$30$	1.06570	−	2.53523i	0.194569	−	0.462868i
$31$	−6.21468	+	2.26196i	−1.11619	+	0.406260i	−0.833260	−	0.552881i	$-0.813529\pi$
$31$	−6.21468	+	2.26196i	−1.11619	+	0.406260i	−0.282930	+	0.959141i	$0.591306\pi$
$32$	0.0994769	+	5.65598i	0.0175852	+	0.999845i
$33$	1.79434	+	2.21592i	0.312354	+	0.385742i
$34$	−0.524800	+	2.51241i	−0.0900025	+	0.430875i
$35$	−1.36367	+	0.787317i	−0.230503	+	0.133081i
$36$	4.95064	−	3.38986i	0.825107	−	0.564976i
$37$	3.83532	+	2.21432i	0.630522	+	0.364032i	0.780954	−	0.624588i	$-0.214733\pi$
$37$	3.83532	+	2.21432i	0.630522	+	0.364032i	−0.150432	+	0.988620i	$0.548066\pi$
$38$	−3.23015	+	3.61292i	−0.524000	+	0.586093i
$39$	−1.15858	−	0.225231i	−0.185521	−	0.0360658i
$40$	−0.800705	−	3.07295i	−0.126603	−	0.485876i
$41$	0.952217	−	5.40029i	0.148711	−	0.843384i	−0.815601	−	0.578615i	$-0.803593\pi$
$41$	0.952217	−	5.40029i	0.148711	−	0.843384i	0.964312	−	0.264769i	$-0.0852956\pi$
$42$	−3.43133	−	0.167801i	−0.529465	−	0.0258923i
$43$	−7.26017	−	8.65234i	−1.10717	−	1.31947i	−0.942909	−	0.333051i	$-0.891922\pi$
$43$	−7.26017	−	8.65234i	−1.10717	−	1.31947i	−0.164257	−	0.986418i	$-0.552523\pi$
$44$	3.20013	+	0.774013i	0.482438	+	0.116687i
$45$	−2.25386	+	2.50295i	−0.335986	+	0.373118i
$46$	4.28455	−	3.37179i	0.631722	−	0.497144i
$47$	−11.5469	−	4.20273i	−1.68429	−	0.613031i	−0.690402	−	0.723426i	$-0.742566\pi$
$47$	−11.5469	−	4.20273i	−1.68429	−	0.613031i	−0.993888	+	0.110395i	$0.964788\pi$
$48$	2.16336	−	6.58178i	0.312254	−	0.949999i
$49$	−3.85548	−	3.23513i	−0.550783	−	0.462162i
$50$	−2.49917	−	4.66064i	−0.353437	−	0.659114i
$51$	1.61907	−	2.69445i	0.226715	−	0.377298i
$52$	−1.22070	+	0.606040i	−0.169280	+	0.0840426i
$53$		−	6.89741i		−	0.947432i	−0.880678	−	0.473716i	$-0.842912\pi$
$53$		−	6.89741i		−	0.947432i	0.880678	−	0.473716i	$-0.157088\pi$
$54$	−7.09147	+	1.92643i	−0.965026	+	0.262154i
$55$	−1.84824			−0.249216
$56$	−3.26511	+	2.25283i	−0.436319	+	0.301048i
$57$	5.19140	−	2.87750i	0.687618	−	0.381134i
$58$	−4.96599	+	2.66291i	−0.652067	+	0.349657i
$59$	−6.78921	+	8.09106i	−0.883880	+	1.05337i	0.114323	+	0.993444i	$0.463530\pi$
$59$	−6.78921	+	8.09106i	−0.883880	+	1.05337i	−0.998203	+	0.0599230i	$0.980914\pi$
$60$	−0.311789	+	3.87673i	−0.0402518	+	0.500483i
$61$	1.24084	−	3.40917i	0.158873	−	0.436499i	−0.834560	−	0.550917i	$-0.814278\pi$
$61$	1.24084	−	3.40917i	0.158873	−	0.436499i	0.993433	+	0.114418i	$0.0365003\pi$
$62$	7.34992	−	5.78413i	0.933441	−	0.734586i
$63$	3.90108	+	1.57633i	0.491490	+	0.198599i
$64$	−2.63214	−	7.55459i	−0.329017	−	0.944324i
$65$	0.586070	−	0.491771i	0.0726930	−	0.0609967i
$66$	−3.38948	−	2.18434i	−0.417216	−	0.268874i
$67$	−11.9425	−	2.10578i	−1.45901	−	0.257263i	−0.612852	−	0.790198i	$-0.709978\pi$
$67$	−11.9425	−	2.10578i	−1.45901	−	0.257263i	−0.846156	+	0.532935i	$0.821089\pi$
$68$	−0.404798	−	3.60713i	−0.0490890	−	0.437429i
$69$	−6.31378	+	2.17386i	−0.760090	+	0.261702i
$70$	1.48424	−	1.66012i	0.177400	−	0.198422i
$71$	6.80355	−	11.7841i	0.807432	−	1.39851i	−0.107204	−	0.994237i	$-0.534190\pi$
$71$	6.80355	−	11.7841i	0.807432	−	1.39851i	0.914637	−	0.404277i	$-0.132477\pi$
$72$	−5.15350	+	6.74102i	−0.607346	+	0.794437i
$73$	4.73823	+	8.20685i	0.554567	+	0.960539i	0.997937	+	0.0642000i	$0.0204496\pi$
$73$	4.73823	+	8.20685i	0.554567	+	0.960539i	−0.443370	+	0.896339i	$0.646217\pi$
$74$	−6.13073	−	1.28061i	−0.712682	−	0.148867i
$75$	1.01309	+	6.39725i	0.116981	+	0.738691i
$76$	2.74357	−	6.28068i	0.314709	−	0.720444i
$77$	0.789660	+	2.16957i	0.0899901	+	0.247246i
$78$	1.65599	−	0.209209i	0.187504	−	0.0236883i
$79$	1.59290	+	9.03380i	0.179215	+	1.01638i	0.933165	+	0.359449i	$0.117035\pi$
$79$	1.59290	+	9.03380i	0.179215	+	1.01638i	−0.753949	+	0.656933i	$0.771854\pi$
$80$	2.43316	+	3.77465i	0.272036	+	0.422019i
$81$	8.97802	+	0.628568i	0.997558	+	0.0698409i
$82$	1.10629	+	7.67567i	0.122169	+	0.847635i
$83$	1.29853	−	0.228966i	0.142532	−	0.0251322i	−0.101927	−	0.994792i	$-0.532501\pi$
$83$	1.29853	−	0.228966i	0.142532	−	0.0251322i	0.244459	+	0.969660i	$0.421390\pi$
$84$	4.68395	−	1.29034i	0.511061	−	0.140787i
$85$	0.696908	+	1.91474i	0.0755903	+	0.207683i
$86$	13.5758	+	8.41686i	1.46392	+	0.907613i
$87$	6.81638	−	1.07946i	0.730792	−	0.115730i
$88$	−4.64114	+	0.373789i	−0.494747	+	0.0398461i
$89$	−3.52339	−	6.10270i	−0.373479	−	0.646884i	0.616619	−	0.787262i	$-0.288502\pi$
$89$	−3.52339	−	6.10270i	−0.373479	−	0.646884i	−0.990098	+	0.140377i	$0.955168\pi$
$90$	1.92229	−	4.35823i	0.202627	−	0.459397i
$91$	−0.827669	−	0.477855i	−0.0867633	−	0.0500928i
$92$	−4.26662	+	6.42251i	−0.444825	+	0.669593i
$93$	−10.8310	+	3.72914i	−1.12312	+	0.386694i
$94$	17.3692	+	0.545389i	1.79150	+	0.0562525i
$95$	−0.668104	+	3.78901i	−0.0685460	+	0.388744i
$96$	0.00109395	+	9.79796i	0.000111651	+	1.00000i
$97$	−6.33275	+	5.31381i	−0.642993	+	0.539535i	−0.904936	−	0.425548i	$-0.860081\pi$
$97$	−6.33275	+	5.31381i	−0.642993	+	0.539535i	0.261943	+	0.965083i	$0.415637\pi$
$98$	6.60875	+	2.64311i	0.667585	+	0.266994i
$99$	3.04035	+	3.89180i	0.305566	+	0.391141i
$100$	5.41633	+	5.15735i	0.541633	+	0.515735i
$101$	6.04137	−	16.5985i	0.601139	−	1.65162i	−0.147832	−	0.989012i	$-0.547230\pi$
$101$	6.04137	−	16.5985i	0.601139	−	1.65162i	0.748971	−	0.662603i	$-0.230548\pi$
$102$	−0.984880	+	4.33508i	−0.0975177	+	0.429236i
$103$	−2.98038	−	2.50084i	−0.293666	−	0.246415i	0.484036	−	0.875048i	$-0.339170\pi$
$103$	−2.98038	−	2.50084i	−0.293666	−	0.246415i	−0.777702	+	0.628633i	$0.783615\pi$
$104$	1.37223	−	1.35342i	0.134558	−	0.132714i
$105$	−2.38542	+	1.32219i	−0.232793	+	0.129033i
$106$	3.04689	+	9.26634i	0.295940	+	0.900026i
$107$			4.16409i			0.402558i	0.979534	+	0.201279i	$0.0645098\pi$
$107$			4.16409i			0.402558i	−0.979534	+	0.201279i	$0.935490\pi$
$108$	8.67605	−	5.72067i	0.834854	−	0.550472i
$109$			20.6082i			1.97391i	0.161002	+	0.986954i	$0.448527\pi$
$109$			20.6082i			1.97391i	−0.161002	+	0.986954i	$0.551473\pi$
$110$	2.48302	−	0.816448i	0.236746	−	0.0778452i
$111$	6.57493	+	3.95081i	0.624065	+	0.374994i
$112$	3.39134	−	4.46892i	0.320452	−	0.422273i
$113$	2.03205	+	1.70510i	0.191160	+	0.160402i	0.733344	−	0.679857i	$-0.237958\pi$
$113$	2.03205	+	1.70510i	0.191160	+	0.160402i	−0.542185	+	0.840259i	$0.682403\pi$
$114$	−5.70328	+	6.15905i	−0.534161	+	0.576847i
$115$	1.48041	−	4.06739i	0.138049	−	0.379286i
$116$	5.49524	−	5.77119i	0.510221	−	0.535841i
$117$	−1.99960	−	0.425116i	−0.184863	−	0.0393020i
$118$	5.54679	−	13.8690i	0.510624	−	1.27675i
$119$	1.94988	−	1.63615i	0.178745	−	0.149985i
$120$	−1.29365	−	5.34592i	−0.118093	−	0.488014i
$121$	1.43955	−	8.16407i	0.130868	−	0.742188i
$122$	−0.161023	+	5.12818i	−0.0145784	+	0.464284i
$123$	1.81248	−	9.32333i	0.163426	−	0.840656i
$124$	−7.31916	+	11.0175i	−0.657280	+	0.989399i
$125$	−8.49749	−	4.90603i	−0.760039	−	0.438809i
$126$	−5.93725	−	0.394445i	−0.528932	−	0.0351400i
$127$	−2.14785	−	3.72019i	−0.190591	−	0.330113i	0.754855	−	0.655891i	$-0.227707\pi$
$127$	−2.14785	−	3.72019i	−0.190591	−	0.330113i	−0.945446	+	0.325778i	$0.894374\pi$
$128$	6.87334	+	8.98650i	0.607524	+	0.794302i
$129$	−12.3112	−	15.2037i	−1.08394	−	1.33861i
$130$	−0.570120	+	0.919563i	−0.0500028	+	0.0806510i
$131$	2.70846	+	7.44142i	0.236639	+	0.650160i	0.999991	+	0.00417788i	$0.00132986\pi$
$131$	2.70846	+	7.44142i	0.236639	+	0.650160i	−0.763352	+	0.645982i	$0.776448\pi$
$132$	5.51852	+	1.43728i	0.480325	+	0.125099i
$133$	4.73321	−	0.834593i	0.410422	−	0.0723684i
$134$	16.9744	−	2.44651i	1.46636	−	0.211346i
$135$	−3.97896	+	4.26637i	−0.342454	+	0.367190i
$136$	2.13726	+	4.66719i	0.183268	+	0.400208i
$137$	2.73472	+	15.5094i	0.233643	+	1.32506i	0.845452	+	0.534051i	$0.179331\pi$
$137$	2.73472	+	15.5094i	0.233643	+	1.32506i	−0.611809	+	0.791006i	$0.709558\pi$
$138$	7.52197	−	5.70955i	0.640313	−	0.486029i
$139$	0.133147	+	0.365819i	0.0112934	+	0.0310283i	0.945211	−	0.326459i	$-0.105856\pi$
$139$	0.133147	+	0.365819i	0.0112934	+	0.0310283i	−0.933918	+	0.357488i	$0.883633\pi$
$140$	−1.26065	+	2.88594i	−0.106545	+	0.243906i
$141$	−19.8696	−	7.62770i	−1.67332	−	0.642368i
$142$	−3.93469	+	18.8368i	−0.330191	+	1.58075i
$143$	−0.560885	−	0.971482i	−0.0469036	−	0.0812394i
$144$	3.94568	−	11.3328i	0.328806	−	0.944397i
$145$	−2.23674	+	3.87415i	−0.185751	+	0.321731i
$146$	−9.99090	−	8.93242i	−0.826853	−	0.739252i
$147$	−6.57896	−	5.71924i	−0.542623	−	0.471715i
$148$	8.80203	−	0.987780i	0.723523	−	0.0811950i
$149$	11.6562	+	2.05530i	0.954913	+	0.168377i	0.629331	−	0.777137i	$-0.283329\pi$
$149$	11.6562	+	2.05530i	0.954913	+	0.168377i	0.325581	+	0.945514i	$0.394440\pi$
$150$	−4.18698	−	8.14687i	−0.341866	−	0.665190i
$151$	7.05111	−	5.91658i	0.573811	−	0.481485i	−0.309097	−	0.951031i	$-0.600027\pi$
$151$	7.05111	−	5.91658i	0.573811	−	0.481485i	0.882908	+	0.469546i	$0.155582\pi$
$152$	−0.911394	+	9.64975i	−0.0739238	+	0.782698i
$153$	2.88542	−	4.61721i	0.233273	−	0.373279i
$154$	−2.01927	−	2.56589i	−0.162717	−	0.206765i
$155$	2.53957	−	6.97740i	0.203983	−	0.560438i
$156$	−2.13233	+	1.01259i	−0.170723	+	0.0810718i
$157$	−8.84016	+	10.5353i	−0.705521	+	0.840807i	−0.993139	−	0.116938i	$-0.962692\pi$
$157$	−8.84016	+	10.5353i	−0.705521	+	0.840807i	0.287618	+	0.957745i	$0.407137\pi$
$158$	−6.13061	−	11.4328i	−0.487725	−	0.909546i
$159$	0.208751	−	11.9448i	0.0165550	−	0.947288i
$160$	−4.93627	−	3.99623i	−0.390246	−	0.315929i
$161$	−5.40706			−0.426136
$162$	−12.3392	+	3.12154i	−0.969460	+	0.245251i
$163$			12.7196i			0.996272i	0.867099	+	0.498136i	$0.165982\pi$
$163$			12.7196i			0.996272i	−0.867099	+	0.498136i	$0.834018\pi$
$164$	−4.87692	−	9.82319i	−0.380824	−	0.767062i
$165$	−3.20075	−	0.0559371i	−0.249178	−	0.00435470i
$166$	−1.64337	+	0.881221i	−0.127550	+	0.0683960i
$167$	15.1696	+	12.7288i	1.17386	+	0.984986i	1.00000		0.000215714i	$6.86640e-5\pi$
$167$	15.1696	+	12.7288i	1.17386	+	0.984986i	0.173861	+	0.984770i	$0.444376\pi$
$168$	−5.72266	+	3.80261i	−0.441513	+	0.293378i
$169$	−11.7797	−	4.28745i	−0.906128	−	0.329804i
$170$	−1.78209	−	2.26450i	−0.136680	−	0.173680i
$171$	9.07748	−	4.82609i	0.694172	−	0.369060i
$172$	−21.9565	−	5.31061i	−1.67417	−	0.404930i
$173$	−3.14984	−	3.75384i	−0.239478	−	0.285399i	0.632897	−	0.774236i	$-0.281866\pi$
$173$	−3.14984	−	3.75384i	−0.239478	−	0.285399i	−0.872375	+	0.488837i	$0.837421\pi$
$174$	−8.68063	+	4.46130i	−0.658077	+	0.338210i
$175$	−0.910724	+	5.16497i	−0.0688443	+	0.390435i
$176$	6.07002	−	2.55236i	0.457545	−	0.192392i
$177$	−12.0023	+	13.8065i	−0.902151	+	1.03776i
$178$	7.42934	+	6.64224i	0.556852	+	0.497857i
$179$	−3.21176	−	1.85431i	−0.240058	−	0.138598i	0.375145	−	0.926966i	$-0.377593\pi$
$179$	−3.21176	−	1.85431i	−0.240058	−	0.138598i	−0.615204	+	0.788368i	$0.710926\pi$
$180$	−0.657282	+	6.70422i	−0.0489909	+	0.499703i
$181$	14.1322	−	8.15921i	1.05044	−	0.606470i	0.127665	−	0.991817i	$-0.459252\pi$
$181$	14.1322	−	8.15921i	1.05044	−	0.606470i	0.922771	+	0.385348i	$0.125919\pi$
$182$	1.32302	+	0.276357i	0.0980690	+	0.0204850i
$183$	2.25204	−	5.86640i	0.166476	−	0.433657i
$184$	2.89489	−	10.5131i	0.213414	−	0.775035i
$185$	−4.67230	+	1.70058i	−0.343515	+	0.125029i
$186$	12.9035	−	9.79444i	0.946134	−	0.718163i
$187$	2.94228	−	0.518804i	0.215161	−	0.0379387i
$188$	−23.5757	+	6.94005i	−1.71943	+	0.506155i
$189$	6.70813	+	2.84793i	0.487945	+	0.207157i
$190$	−0.776205	−	5.38548i	−0.0563118	−	0.390704i
$191$	1.19811	+	6.79482i	0.0866922	+	0.491656i	0.996979	+	0.0776767i	$0.0247502\pi$
$191$	1.19811	+	6.79482i	0.0866922	+	0.491656i	−0.910286	+	0.413979i	$0.864139\pi$
$192$	−4.32966	−	13.1626i	−0.312466	−	0.949929i
$193$	8.95564	−	3.25959i	0.644641	−	0.234630i	0.00104978	−	0.999999i	$-0.499666\pi$
$193$	8.95564	−	3.25959i	0.644641	−	0.234630i	0.643591	+	0.765369i	$0.277444\pi$
$194$	6.16040	−	9.93630i	0.442291	−	0.713385i
$195$	1.02983	−	0.833905i	0.0737477	−	0.0597172i
$196$	−10.0461	−	0.631512i	−0.717580	−	0.0451080i
$197$	1.74001	−	1.00460i	0.123971	−	0.0715746i	−0.436732	−	0.899592i	$-0.643864\pi$
$197$	1.74001	−	1.00460i	0.123971	−	0.0715746i	0.560703	+	0.828017i	$0.310531\pi$
$198$	−5.80374	−	3.88540i	−0.412454	−	0.276123i
$199$	10.6564	−	18.4573i	0.755409	−	1.30841i	−0.189762	−	0.981830i	$-0.560772\pi$
$199$	10.6564	−	18.4573i	0.755409	−	1.30841i	0.945171	−	0.326576i	$-0.105895\pi$
$200$	−9.55481	−	4.53602i	−0.675627	−	0.320745i
$201$	−20.6181	−	4.00821i	−1.45429	−	0.282717i
$202$	−0.783989	+	24.9681i	−0.0551613	+	1.75675i
$203$	5.50336	+	0.970392i	0.386260	+	0.0681081i
$204$	−0.591854	−	6.25903i	−0.0414381	−	0.438220i
$205$	3.95738	+	4.71622i	0.276395	+	0.329395i
$206$	5.10873	+	2.04319i	0.355942	+	0.142356i
$207$	−10.9999	+	3.57357i	−0.764547	+	0.248381i
$208$	−1.24566	+	2.42443i	−0.0863711	+	0.168104i
$209$	5.30113	+	1.92945i	0.366687	+	0.133463i
$210$	2.62062	−	2.83005i	0.180840	−	0.195292i
$211$	5.98817	−	7.13642i	0.412242	−	0.491291i	−0.519470	−	0.854489i	$-0.673870\pi$
$211$	5.98817	−	7.13642i	0.412242	−	0.491291i	0.931712	+	0.363197i	$0.118315\pi$
$212$	−8.18670	−	11.1029i	−0.562265	−	0.762552i
$213$	12.1389	−	20.2016i	0.831746	−	1.38419i
$214$	−1.83946	−	5.59426i	−0.125743	−	0.382416i
$215$	12.6810			0.864838
$216$	−9.12878	+	11.5180i	−0.621135	+	0.783704i
$217$	−9.27552			−0.629664
$218$	−9.10355	−	27.6861i	−0.616570	−	1.87514i
$219$	7.95721	+	14.3559i	0.537699	+	0.970083i
$220$	−2.97515	+	2.19372i	−0.200585	+	0.147900i
$221$	−0.794946	+	0.947380i	−0.0534739	+	0.0637277i
$222$	−10.5784	−	2.40328i	−0.709972	−	0.161298i
$223$	23.1313	+	8.41909i	1.54898	+	0.563784i	0.968179	−	0.250259i	$-0.0805157\pi$
$223$	23.1313	+	8.41909i	1.54898	+	0.563784i	0.580805	+	0.814043i	$0.302738\pi$
$224$	−2.58199	+	7.50188i	−0.172516	+	0.501240i
$225$	1.56084	+	11.1093i	0.104056	+	0.740622i
$226$	−3.48318	−	1.39307i	−0.231698	−	0.0926654i
$227$	2.62591	+	3.12944i	0.174288	+	0.207708i	0.846116	−	0.532999i	$-0.178935\pi$
$227$	2.62591	+	3.12944i	0.174288	+	0.207708i	−0.671828	+	0.740707i	$0.734491\pi$
$228$	4.94136	−	10.7938i	0.327249	−	0.714835i
$229$	12.4279	+	2.19138i	0.821261	+	0.144810i	0.568463	−	0.822709i	$-0.307538\pi$
$229$	12.4279	+	2.19138i	0.821261	+	0.144810i	0.252798	+	0.967519i	$0.418649\pi$
$230$	−0.192113	+	6.11831i	−0.0126675	+	0.403429i
$231$	1.30186	+	3.78114i	0.0856561	+	0.248781i
$232$	−4.83321	+	10.1808i	−0.317316	+	0.668402i
$233$	−12.2882	+	21.2839i	−0.805030	+	1.39435i	0.111241	+	0.993793i	$0.464517\pi$
$233$	−12.2882	+	21.2839i	−0.805030	+	1.39435i	−0.916271	+	0.400559i	$0.868816\pi$
$234$	2.87416	−	0.312187i	0.187889	−	0.0204083i
$235$	11.9477	−	6.89802i	0.779383	−	0.449977i
$236$	−1.32528	+	21.0827i	−0.0862686	+	1.37236i
$237$	2.48516	+	15.6928i	0.161428	+	1.01936i
$238$	−1.89682	+	3.05943i	−0.122952	+	0.198314i
$239$	−10.1778	+	3.70441i	−0.658346	+	0.239618i	−0.649522	−	0.760343i	$-0.725031\pi$
$239$	−10.1778	+	3.70441i	−0.658346	+	0.239618i	−0.00882395	+	0.999961i	$0.502809\pi$
$240$	4.09948	+	6.61053i	0.264620	+	0.426708i
$241$	−2.29103	−	12.9931i	−0.147579	−	0.836959i	−0.965261	−	0.261289i	$-0.915852\pi$
$241$	−2.29103	−	12.9931i	−0.147579	−	0.836959i	0.817682	−	0.575670i	$-0.195259\pi$
$242$	1.67247	+	11.6039i	0.107510	+	0.745930i
$243$	15.5290	+	1.36027i	0.996185	+	0.0872611i
$244$	−2.04902	−	6.96060i	−0.131175	−	0.445607i
$245$	5.56481	−	0.981227i	0.355523	−	0.0626883i
$246$	1.68355	+	13.3261i	0.107339	+	0.849641i
$247$	−2.19435	+	0.798678i	−0.139623	+	0.0508187i
$248$	4.96602	−	18.0347i	0.315343	−	1.14520i
$249$	2.25570	−	0.357219i	0.142949	−	0.0226379i
$250$	13.5832	+	2.83730i	0.859076	+	0.179446i
$251$	−17.6367	+	10.1826i	−1.11322	+	0.642717i	−0.939661	−	0.342106i	$-0.888860\pi$
$251$	−17.6367	+	10.1826i	−1.11322	+	0.642717i	−0.173558	+	0.984824i	$0.555526\pi$
$252$	8.15065	−	2.09282i	0.513443	−	0.131836i
$253$	−5.49629	−	3.17328i	−0.345549	−	0.199503i
$254$	4.52890	+	4.04909i	0.284169	+	0.254063i
$255$	1.14895	+	3.33701i	0.0719498	+	0.208972i
$256$	−13.2037	−	9.03667i	−0.825234	−	0.564792i
$257$	2.07937	−	11.7927i	0.129707	−	0.735606i	−0.848693	−	0.528886i	$-0.822610\pi$
$257$	2.07937	−	11.7927i	0.129707	−	0.735606i	0.978400	−	0.206720i	$-0.0662790\pi$
$258$	23.2557	+	14.9871i	1.44783	+	0.933054i
$259$	3.99249	+	4.75806i	0.248081	+	0.295651i
$260$	0.359717	−	1.48724i	0.0223087	−	0.0922344i
$261$	11.8372	−	1.66310i	0.732703	−	0.102943i
$262$	−6.92589	−	8.80075i	−0.427883	−	0.543712i
$263$	−9.28725	−	3.38028i	−0.572677	−	0.208437i	0.0394166	−	0.999223i	$-0.487450\pi$
$263$	−9.28725	−	3.38028i	−0.572677	−	0.208437i	−0.612093	+	0.790786i	$0.709672\pi$
$264$	−8.04877	+	0.506859i	−0.495368	+	0.0311950i
$265$	5.93218	+	4.97769i	0.364411	+	0.305777i
$266$	−5.99017	+	3.21210i	−0.367281	+	0.196947i
$267$	−5.91706	−	10.6752i	−0.362118	−	0.653312i
$268$	−21.7235	+	10.7851i	−1.32698	+	0.658805i
$269$			5.38944i			0.328600i	0.986410	+	0.164300i	$0.0525365\pi$
$269$			5.38944i			0.328600i	−0.986410	+	0.164300i	$0.947463\pi$
$270$	3.46089	−	7.48934i	0.210623	−	0.455787i
$271$	−6.24978			−0.379647			−0.189823	−	0.981818i	$-0.560792\pi$
$271$	−6.24978			−0.379647			−0.189823	+	0.981818i	$0.560792\pi$
$272$	−4.93300	−	5.32602i	−0.299107	−	0.322937i
$273$	−1.41888	−	0.852592i	−0.0858747	−	0.0516012i
$274$	−10.5252	−	19.6281i	−0.635848	−	1.18578i
$275$	−3.95697	+	4.71573i	−0.238614	+	0.284369i
$276$	−7.58324	+	10.9933i	−0.456458	+	0.661718i
$277$	4.85450	−	13.3376i	0.291679	−	0.801381i	−0.704143	−	0.710059i	$-0.748668\pi$
$277$	4.85450	−	13.3376i	0.291679	−	0.801381i	0.995821	−	0.0913223i	$-0.0291093\pi$
$278$	−0.340475	−	0.432643i	−0.0204203	−	0.0259482i
$279$	−18.8698	+	6.13028i	−1.12970	+	0.367010i
$280$	0.418780	−	4.43401i	0.0250269	−	0.264983i
$281$	21.3543	−	17.9184i	1.27389	−	1.06892i	0.279837	−	0.960047i	$-0.409720\pi$
$281$	21.3543	−	17.9184i	1.27389	−	1.06892i	0.994055	−	0.108875i	$-0.0347249\pi$
$282$	30.0633	+	1.47018i	1.79024	+	0.0875478i
$283$	−22.0316	−	3.88476i	−1.30964	−	0.230925i	−0.525121	−	0.851027i	$-0.675980\pi$
$283$	−22.0316	−	3.88476i	−1.30964	−	0.230925i	−0.784521	+	0.620102i	$0.787091\pi$
$284$	−3.03497	−	27.0444i	−0.180093	−	1.60479i
$285$	−1.27169	+	6.54153i	−0.0753283	+	0.387487i
$286$	1.18267	+	1.05737i	0.0699327	+	0.0625237i
$287$	3.84539	−	6.66042i	0.226986	−	0.393152i
$288$	−0.294642	+	16.9680i	−0.0173619	+	0.999849i
$289$	6.85309	+	11.8699i	0.403123	+	0.698230i
$290$	1.29357	−	6.19280i	0.0759612	−	0.363654i
$291$	−11.1278	+	9.01072i	−0.652323	+	0.528218i
$292$	17.3681	+	7.58685i	1.01639	+	0.443987i
$293$	−0.130208	−	0.357742i	−0.00760680	−	0.0208995i	0.935831	−	0.352449i	$-0.114651\pi$
$293$	−0.130208	−	0.357742i	−0.00760680	−	0.0208995i	−0.943438	+	0.331549i	$0.892429\pi$
$294$	11.3650	+	4.77731i	0.662817	+	0.278619i
$295$	−2.05919	−	11.6782i	−0.119891	−	0.679934i
$296$	−11.3888	+	5.21528i	−0.661958	+	0.303132i
$297$	5.14744	+	6.83179i	0.298685	+	0.396421i
$298$	−16.5675	+	2.38786i	−0.959727	+	0.138325i
$299$	2.58719	−	0.456191i	0.149621	−	0.0263822i
$300$	9.22384	+	9.09536i	0.532539	+	0.525121i
$301$	−5.41797	−	14.8857i	−0.312286	−	0.858000i
$302$	−6.85921	+	11.0634i	−0.394703	+	0.636629i
$303$	10.9647	−	28.5623i	0.629907	−	1.64086i
$304$	−3.03830	−	13.3666i	−0.174259	−	0.766626i
$305$	2.03661	+	3.52751i	0.116616	+	0.201984i
$306$	−1.83680	+	7.47762i	−0.105003	+	0.427467i
$307$	−9.47107	−	5.46813i	−0.540543	−	0.312083i	0.204756	−	0.978813i	$-0.434360\pi$
$307$	−9.47107	−	5.46813i	−0.540543	−	0.312083i	−0.745299	+	0.666731i	$0.767693\pi$
$308$	3.84625	+	2.55515i	0.219161	+	0.145593i
$309$	−5.08570	−	4.42112i	−0.289315	−	0.251509i
$310$	−0.329560	+	10.4956i	−0.0187177	+	0.596112i
$311$	−3.17033	+	17.9798i	−0.179773	+	1.01954i	0.752717	+	0.658344i	$0.228743\pi$
$311$	−3.17033	+	17.9798i	−0.179773	+	1.01954i	−0.932490	+	0.361197i	$0.882368\pi$
$312$	2.41737	−	2.30230i	0.136857	−	0.130342i
$313$	2.49125	−	2.09041i	0.140814	−	0.118157i	−0.569660	−	0.821880i	$-0.692925\pi$
$313$	2.49125	−	2.09041i	0.140814	−	0.118157i	0.710474	+	0.703724i	$0.248481\pi$
$314$	7.22242	−	18.0587i	0.407585	−	1.01911i
$315$	−4.17105	+	2.21756i	−0.235012	+	0.124945i
$316$	13.2866	+	12.6513i	0.747427	+	0.711690i
$317$	−5.82505	+	16.0042i	−0.327167	+	0.898885i	0.661658	+	0.749806i	$0.269853\pi$
$317$	−5.82505	+	16.0042i	−0.327167	+	0.898885i	−0.988825	+	0.149079i	$0.952369\pi$
$318$	4.99612	+	16.1395i	0.280168	+	0.905060i
$319$	5.02469	+	4.21621i	0.281328	+	0.236063i
$320$	8.39695	+	3.18817i	0.469404	+	0.178224i
$321$	−0.126027	+	7.21132i	−0.00703412	+	0.402497i
$322$	7.26412	−	2.38853i	0.404814	−	0.133108i
$323$		−	6.21940i		−	0.346057i
$324$	15.1982	−	9.64440i	0.844345	−	0.535800i
$325$		−	2.54819i		−	0.141348i
$326$	−5.61879	−	17.0881i	−0.311196	−	0.946423i
$327$	−0.623709	+	35.6890i	−0.0344912	+	1.97361i
$328$	10.8912	+	11.0426i	0.601368	+	0.609727i
$329$	−13.2020	−	11.0778i	−0.727849	−	0.610737i
$330$	4.32477	−	1.33876i	0.238071	−	0.0736966i
$331$	1.92215	−	5.28106i	0.105651	−	0.290273i	−0.875591	−	0.483053i	$-0.839528\pi$
$331$	1.92215	−	5.28106i	0.105651	−	0.290273i	0.981242	+	0.192780i	$0.0617502\pi$
$332$	1.81851	−	1.90983i	0.0998036	−	0.104815i
$333$	11.2668	+	7.04095i	0.617417	+	0.385841i
$334$	−26.0025	−	10.3995i	−1.42280	−	0.569034i
$335$	10.4297	−	8.75156i	0.569836	−	0.478149i
$336$	6.00834	−	7.63657i	0.327782	−	0.416609i
$337$	3.30062	−	18.7188i	0.179796	−	1.01968i	−0.752665	−	0.658404i	$-0.771232\pi$
$337$	3.30062	−	18.7188i	0.179796	−	1.01968i	0.932461	−	0.361271i	$-0.117657\pi$
$338$	17.7194	+	0.556382i	0.963806	+	0.0302632i
$339$	3.46748	+	3.01436i	0.188328	+	0.163718i
$340$	3.39448	+	2.25503i	0.184091	+	0.122296i
$341$	−9.42860	−	5.44360i	−0.510587	−	0.294788i
$342$	−10.0633	+	10.4935i	−0.544159	+	0.567426i
$343$	−8.43817	−	14.6153i	−0.455618	−	0.789154i
$344$	31.8435	−	2.56462i	1.71689	−	0.138275i
$345$	2.68685	−	6.99905i	0.144655	−	0.376816i
$346$	5.88990	+	3.65167i	0.316643	+	0.196315i
$347$	3.17358	+	8.71933i	0.170366	+	0.468078i	0.995265	−	0.0972035i	$-0.0309898\pi$
$347$	3.17358	+	8.71933i	0.170366	+	0.468078i	−0.824898	+	0.565282i	$0.808768\pi$
$348$	9.69125	−	9.82815i	0.519506	−	0.526844i
$349$	−7.31028	+	1.28900i	−0.391310	+	0.0689985i	−0.365842	−	0.930677i	$-0.619219\pi$
$349$	−7.31028	+	1.28900i	−0.391310	+	0.0689985i	−0.0254684	+	0.999676i	$0.508108\pi$
$350$	−1.05808	−	7.34120i	−0.0565569	−	0.392404i
$351$	−3.45001	−	0.796728i	−0.184148	−	0.0425262i
$352$	−7.02729	+	6.11037i	−0.374556	+	0.325684i
$353$	4.91102	+	27.8518i	0.261387	+	1.48240i	0.779129	+	0.626864i	$0.215662\pi$
$353$	4.91102	+	27.8518i	0.261387	+	1.48240i	−0.517742	+	0.855537i	$0.673227\pi$
$354$	10.0256	−	23.8503i	0.532855	−	1.26763i
$355$	5.22506	+	14.3557i	0.277318	+	0.761924i
$356$	−12.9151	−	5.64166i	−0.684500	−	0.299007i
$357$	3.42630	−	2.77444i	0.181339	−	0.146839i
$358$	5.13398	+	1.07240i	0.271339	+	0.0566782i
$359$	8.47821	+	14.6847i	0.447463	+	0.775029i	0.998220	−	0.0596369i	$-0.0189943\pi$
$359$	8.47821	+	14.6847i	0.447463	+	0.775029i	−0.550757	+	0.834666i	$0.685661\pi$
$360$	−2.07852	−	9.29715i	−0.109548	−	0.490003i
$361$	−3.62823	+	6.28428i	−0.190960	+	0.330752i
$362$	−15.3816	+	17.2043i	−0.808439	+	0.904239i
$363$	2.74007	−	14.0949i	0.143817	−	0.739788i
$364$	−1.89950	+	0.213165i	−0.0995607	+	0.0111729i
$365$	−10.4778	−	1.84753i	−0.548435	−	0.0967039i
$366$	−0.434063	+	8.87605i	−0.0226888	+	0.463958i
$367$	6.19539	−	5.19855i	0.323397	−	0.271362i	−0.466606	−	0.884465i	$-0.654523\pi$
$367$	6.19539	−	5.19855i	0.323397	−	0.271362i	0.790003	+	0.613103i	$0.210079\pi$
$368$	0.754954	+	15.4026i	0.0393547	+	0.802917i
$369$	3.42099	−	16.0912i	0.178090	−	0.837673i
$370$	5.52579	−	4.34861i	0.287272	−	0.226073i
$371$	3.30859	−	9.09028i	0.171773	−	0.471944i
$372$	−13.0087	+	18.8584i	−0.674468	+	0.977763i
$373$	−14.1644	+	16.8805i	−0.733405	+	0.874038i	−0.995859	−	0.0909062i	$-0.971024\pi$
$373$	−14.1644	+	16.8805i	−0.733405	+	0.874038i	0.262454	+	0.964944i	$0.415468\pi$
$374$	−3.72363	+	1.99672i	−0.192545	+	0.103248i
$375$	−14.5674	−	8.75337i	−0.752255	−	0.452022i
$376$	28.6070	−	19.7380i	1.47529	−	1.01791i
$377$	−2.71514			−0.139837
$378$	−10.2701	−	0.862787i	−0.528237	−	0.0443770i
$379$			9.42240i			0.483996i	0.970277	+	0.241998i	$0.0778027\pi$
$379$			9.42240i			0.483996i	−0.970277	+	0.241998i	$0.922197\pi$
$380$	3.42180	+	6.89225i	0.175534	+	0.353565i
$381$	−3.60703	−	6.50757i	−0.184794	−	0.333393i
$382$	−4.61117	−	8.59925i	−0.235928	−	0.439976i
$383$	−13.2473	−	11.1158i	−0.676904	−	0.567989i	0.238196	−	0.971217i	$-0.423444\pi$
$383$	−13.2473	−	11.1158i	−0.676904	−	0.567989i	−0.915100	+	0.403228i	$0.867888\pi$
$384$	11.6312	+	15.7707i	0.593552	+	0.804796i
$385$	−2.43584	−	0.886573i	−0.124142	−	0.0451840i
$386$	−10.5916	+	8.33520i	−0.539097	+	0.424250i
$387$	−20.8602	−	26.7022i	−1.06039	−	1.35735i
$388$	−3.88690	+	16.0703i	−0.197327	+	0.815844i
$389$	15.9667	+	19.0284i	0.809546	+	0.964780i	0.999856	−	0.0169443i	$-0.00539380\pi$
$389$	15.9667	+	19.0284i	0.809546	+	0.964780i	−0.190310	+	0.981724i	$0.560949\pi$
$390$	−1.01516	+	1.57523i	−0.0514044	+	0.0797650i
$391$	−1.21500	+	6.89059i	−0.0614451	+	0.348472i
$392$	13.7754	−	3.58940i	0.695765	−	0.181292i
$393$	4.46525	+	12.9689i	0.225242	+	0.654196i
$394$	−1.89385	+	2.11827i	−0.0954108	+	0.106717i
$395$	−8.91916	−	5.14948i	−0.448772	−	0.259098i
$396$	9.51339	+	2.65608i	0.478066	+	0.133473i
$397$	−5.94466	+	3.43215i	−0.298354	+	0.172255i	−0.641703	−	0.766953i	$-0.721772\pi$
$397$	−5.94466	+	3.43215i	−0.298354	+	0.172255i	0.343349	+	0.939208i	$0.388439\pi$
$398$	−6.16287	+	29.5039i	−0.308917	+	1.47890i
$399$	8.22217	−	1.30209i	0.411624	−	0.0651858i
$400$	14.8402	+	1.87315i	0.742009	+	0.0936574i
$401$	11.8463	−	4.31169i	0.591574	−	0.215315i	−0.0288475	−	0.999584i	$-0.509184\pi$
$401$	11.8463	−	4.31169i	0.591574	−	0.215315i	0.620422	+	0.784268i	$0.286961\pi$
$402$	29.4701	−	3.72310i	1.46983	−	0.185691i
$403$	4.43819	−	0.782572i	0.221082	−	0.0389827i
$404$	−9.97624	−	33.8897i	−0.496336	−	1.68608i
$405$	−7.01983	+	7.26801i	−0.348818	+	0.361150i
$406$	−7.82217	+	1.12740i	−0.388208	+	0.0559521i
$407$	1.26597	+	7.17969i	0.0627519	+	0.355884i
$408$	3.56002	+	8.14726i	0.176247	+	0.403349i
$409$	32.0334	−	11.6592i	1.58395	−	0.576510i	0.607891	−	0.794020i	$-0.292016\pi$
$409$	32.0334	−	11.6592i	1.58395	−	0.576510i	0.976058	+	0.217510i	$0.0697935\pi$
$410$	−7.39991	−	4.58787i	−0.365455	−	0.226579i
$411$	4.26657	+	26.9417i	0.210454	+	1.32894i
$412$	−7.76590	−	0.488175i	−0.382598	−	0.0240506i
$413$	−12.8288	+	7.40673i	−0.631266	+	0.364462i
$414$	13.1992	−	9.66007i	0.648708	−	0.474767i
$415$	−0.740192	+	1.28205i	−0.0363346	+	0.0629334i
$416$	0.602510	−	3.80737i	0.0295405	−	0.186672i
$417$	0.219511	+	0.637549i	0.0107495	+	0.0312209i
$418$	−7.97414	−	0.250385i	−0.390028	−	0.0122467i
$419$	−10.9419	−	1.92935i	−0.534545	−	0.0942547i	−0.100142	−	0.994973i	$-0.531930\pi$
$419$	−10.9419	−	1.92935i	−0.534545	−	0.0942547i	−0.434403	+	0.900718i	$0.643041\pi$
$420$	−2.27053	+	4.95968i	−0.110790	+	0.242007i
$421$	−12.6851	−	15.1175i	−0.618232	−	0.736780i	0.362533	−	0.931971i	$-0.381912\pi$
$421$	−12.6851	−	15.1175i	−0.618232	−	0.736780i	−0.980765	+	0.195190i	$0.937468\pi$
$422$	−4.89234	+	12.2327i	−0.238156	+	0.595477i
$423$	−34.1790	−	13.8109i	−1.66184	−	0.671509i
$424$	15.9031	+	11.2998i	0.772322	+	0.548768i
$425$	6.37744	+	2.32120i	0.309352	+	0.112595i
$426$	−7.38413	+	32.5022i	−0.357762	+	1.57474i
$427$	3.27066	−	3.89782i	0.158278	−	0.188629i
$428$	4.94246	+	6.70304i	0.238903	+	0.324004i
$429$	−0.941932	−	1.69937i	−0.0454769	−	0.0820466i
$430$	−17.0363	+	5.60176i	−0.821565	+	0.270141i
$431$	−0.293057			−0.0141161			−0.00705803	−	0.999975i	$-0.502247\pi$
$431$	−0.293057			−0.0141161			−0.00705803	+	0.999975i	$0.502247\pi$
$432$	7.17605	−	19.5065i	0.345258	−	0.938508i
$433$	18.2482			0.876954			0.438477	−	0.898742i	$-0.355518\pi$
$433$	18.2482			0.876954			0.438477	+	0.898742i	$0.355518\pi$
$434$	12.4612	−	4.09741i	0.598158	−	0.196682i
$435$	−3.99081	+	6.64151i	−0.191345	+	0.318436i
$436$	24.4604	+	33.1735i	1.17144	+	1.58872i
$437$	−8.49225	+	10.1207i	−0.406239	+	0.484137i
$438$	−17.0318	−	15.7714i	−0.813809	−	0.753588i
$439$	0.920498	+	0.335034i	0.0439330	+	0.0159903i	0.363893	−	0.931441i	$-0.381447\pi$
$439$	0.920498	+	0.335034i	0.0439330	+	0.0159903i	−0.319960	+	0.947431i	$0.603670\pi$
$440$	3.02791	−	4.26141i	0.144350	−	0.203155i
$441$	−11.2203	−	10.1036i	−0.534298	−	0.481125i
$442$	0.649472	−	1.62392i	0.0308923	−	0.0772421i
$443$	−3.31318	−	3.94849i	−0.157414	−	0.187599i	0.681573	−	0.731750i	$-0.261296\pi$
$443$	−3.31318	−	3.94849i	−0.157414	−	0.187599i	−0.838987	+	0.544151i	$0.816852\pi$
$444$	15.2731	−	1.44423i	0.724831	−	0.0685401i
$445$	7.79143	+	1.37384i	0.369349	+	0.0651262i
$446$	−34.7948	−	1.09255i	−1.64758	−	0.0517336i
$447$	20.1238	+	3.91212i	0.951825	+	0.185037i
$448$	0.154869	−	11.2190i	0.00731685	−	0.530048i
$449$	−6.21921	+	10.7720i	−0.293503	+	0.508362i	−0.974635	−	0.223798i	$-0.928154\pi$
$449$	−6.21921	+	10.7720i	−0.293503	+	0.508362i	0.681133	+	0.732160i	$0.261488\pi$
$450$	−7.00439	−	14.2354i	−0.330190	−	0.671062i
$451$	7.81771	−	4.51356i	0.368122	−	0.212535i
$452$	5.29486	+	0.332842i	0.249049	+	0.0156556i
$453$	12.3901	−	10.0329i	0.582137	−	0.471385i
$454$	−4.91019	−	3.04427i	−0.230447	−	0.142875i
$455$	1.00829	−	0.366988i	0.0472695	−	0.0172047i
$456$	−1.87039	+	16.6837i	−0.0875890	+	0.781287i
$457$	−4.18789	−	23.7507i	−0.195901	−	1.11101i	−0.911129	−	0.412121i	$-0.864788\pi$
$457$	−4.18789	−	23.7507i	−0.195901	−	1.11101i	0.715228	−	0.698891i	$-0.246323\pi$
$458$	−17.6644	+	2.54595i	−0.825401	+	0.118964i
$459$	5.13668	−	7.90869i	0.239760	−	0.369146i
$460$	−2.44463	−	8.30451i	−0.113981	−	0.387200i
$461$	−36.0117	+	6.34983i	−1.67723	+	0.295741i	−0.929654	−	0.368434i	$-0.879894\pi$
$461$	−36.0117	+	6.34983i	−1.67723	+	0.295741i	−0.747577	+	0.664175i	$0.768783\pi$
$462$	−3.41928	−	4.50469i	−0.159079	−	0.209577i
$463$	−21.2745	+	7.74329i	−0.988711	+	0.359861i	−0.785221	−	0.619216i	$-0.787451\pi$
$463$	−21.2745	+	7.74329i	−0.988711	+	0.359861i	−0.203490	+	0.979077i	$0.565228\pi$
$464$	1.99587	−	15.8125i	0.0926560	−	0.734075i
$465$	4.60916	−	12.0065i	0.213744	−	0.556788i
$466$	7.10665	−	34.0221i	0.329209	−	1.57604i
$467$	20.1982	−	11.6614i	0.934662	−	0.539628i	0.0463792	−	0.998924i	$-0.485232\pi$
$467$	20.1982	−	11.6614i	0.934662	−	0.539628i	0.888283	+	0.459296i	$0.151898\pi$
$468$	−3.72338	+	1.68905i	−0.172113	+	0.0780763i
$469$	−14.7292	−	8.50392i	−0.680132	−	0.392674i
$470$	−13.0040	+	14.5450i	−0.599831	+	0.670910i
$471$	−15.6281	+	17.9773i	−0.720105	+	0.828351i
$472$	−7.53268	−	28.9090i	−0.346720	−	1.33064i
$473$	3.22874	−	18.3111i	0.148458	−	0.841945i
$474$	−10.2709	−	19.9847i	−0.471758	−	0.917929i
$475$	8.23718	+	9.81669i	0.377948	+	0.450420i
$476$	1.19679	−	4.94811i	0.0548550	−	0.226796i
$477$	0.723024	−	20.6796i	0.0331050	−	0.946854i
$478$	12.0370	−	9.47267i	0.550558	−	0.433270i
$479$	−37.4812	−	13.6420i	−1.71256	−	0.623320i	−0.715405	−	0.698710i	$-0.753758\pi$
$479$	−37.4812	−	13.6420i	−1.71256	−	0.623320i	−0.997154	+	0.0753898i	$0.975980\pi$
$480$	−8.42762	−	7.07001i	−0.384666	−	0.322700i
$481$	−2.31177	−	1.93981i	−0.105408	−	0.0884477i
$482$	8.81752	+	16.4436i	0.401627	+	0.748983i
$483$	−9.36387	−	0.163645i	−0.426071	−	0.00744611i
$484$	−7.37286	−	14.8505i	−0.335130	−	0.675025i
$485$		−	9.28139i		−	0.421446i
$486$	−21.4633	+	5.03239i	−0.973597	+	0.228274i
$487$	−32.0323			−1.45152			−0.725762	−	0.687946i	$-0.758512\pi$
$487$	−32.0323			−1.45152			−0.725762	+	0.687946i	$0.758512\pi$
$488$	5.82756	+	8.44609i	0.263801	+	0.382336i
$489$	−0.384959	+	22.0276i	−0.0174084	+	0.996120i
$490$	−7.04260	+	3.77645i	−0.318152	+	0.170603i
$491$	16.9415	−	20.1901i	0.764559	−	0.911166i	−0.233568	−	0.972341i	$-0.575040\pi$
$491$	16.9415	−	20.1901i	0.764559	−	0.911166i	0.998127	+	0.0611743i	$0.0194845\pi$
$492$	−8.14849	−	17.1593i	−0.367362	−	0.773599i
$493$	2.47328	−	6.79527i	0.111391	−	0.306044i
$494$	2.59519	−	2.04233i	0.116763	−	0.0918886i
$495$	−5.54133	−	0.193742i	−0.249064	−	0.00870806i
$496$	1.29508	+	26.4224i	0.0581510	+	1.18640i
$497$	14.6192	−	12.2670i	0.655762	−	0.550250i
$498$	−2.87263	+	1.47635i	−0.128726	+	0.0661569i
$499$	0.796549	+	0.140453i	0.0356584	+	0.00628755i	0.191449	−	0.981503i	$-0.438681\pi$
$499$	0.796549	+	0.140453i	0.0356584	+	0.00628755i	−0.155790	+	0.987790i	$0.549792\pi$
$500$	−19.5017	+	2.18852i	−0.872143	+	0.0978734i
$501$	25.8853	+	22.5027i	1.15647	+	1.00535i
$502$	19.1960	−	21.4707i	0.856759	−	0.958284i
$503$	−0.838775	+	1.45280i	−0.0373991	+	0.0647772i	−0.884119	−	0.467262i	$-0.845241\pi$
$503$	−0.838775	+	1.45280i	−0.0373991	+	0.0647772i	0.846720	+	0.532039i	$0.178574\pi$
$504$	−10.0255	+	6.41211i	−0.446572	+	0.285618i
$505$	9.91581	+	17.1747i	0.441248	+	0.764264i
$506$	8.78578	+	1.83520i	0.390576	+	0.0815847i
$507$	−20.2701	−	7.78145i	−0.900227	−	0.345586i
$508$	−7.87302	−	3.43914i	−0.349309	−	0.152587i
$509$	2.89525	+	7.95462i	0.128330	+	0.352583i	0.987173	−	0.159656i	$-0.0510385\pi$
$509$	2.89525	+	7.95462i	0.128330	+	0.352583i	−0.858843	+	0.512239i	$0.828816\pi$
$510$	−3.01766	−	3.97557i	−0.133624	−	0.176041i
$511$	2.30792	+	13.0889i	0.102096	+	0.579018i
$512$	21.7305	+	6.30765i	0.960360	+	0.278762i
$513$	15.8663	−	8.08303i	0.700515	−	0.356874i
$514$	2.41581	+	16.7614i	0.106557	+	0.739315i
$515$	4.30174	−	0.758513i	0.189557	−	0.0334241i
$516$	−37.8633	−	9.86136i	−1.66684	−	0.434122i
$517$	−6.91855	−	19.0085i	−0.304277	−	0.835995i
$518$	−7.46555	−	4.62857i	−0.328018	−	0.203367i
$519$	−5.34124	−	6.59617i	−0.234455	−	0.289540i
$520$	0.173716	+	2.15693i	0.00761793	+	0.0945877i
$521$	1.96303	+	3.40007i	0.0860020	+	0.148960i	0.905818	−	0.423668i	$-0.139258\pi$
$521$	1.96303	+	3.40007i	0.0860020	+	0.148960i	−0.819816	+	0.572627i	$0.805924\pi$
$522$	−15.1680	+	7.46329i	−0.663886	+	0.326659i
$523$	14.9783	+	8.64774i	0.654956	+	0.378139i	0.790353	−	0.612652i	$-0.209897\pi$
$523$	14.9783	+	8.64774i	0.654956	+	0.378139i	−0.135396	+	0.990792i	$0.543231\pi$
$524$	13.1923	+	8.76391i	0.576307	+	0.382853i
$525$	−1.73350	+	8.91707i	−0.0756561	+	0.389173i
$526$	13.9702	+	0.438660i	0.609129	+	0.0191265i
$527$	−2.08426	+	11.8205i	−0.0907920	+	0.514907i
$528$	10.5892	−	4.23644i	0.460837	−	0.184367i
$529$	−6.23317	+	5.23025i	−0.271008	+	0.227402i
$530$	−10.1685	−	4.06678i	−0.441690	−	0.176650i
$531$	−21.2033	+	23.5467i	−0.920146	+	1.02184i
$532$	6.62857	−	6.96143i	0.287385	−	0.301816i
$533$	−1.27802	+	3.51134i	−0.0553573	+	0.152093i
$534$	12.6650	+	11.7278i	0.548068	+	0.507511i
$535$	−3.58137	−	3.00512i	−0.154836	−	0.129923i
$536$	24.4203	−	24.0855i	1.05480	−	1.04033i
$537$	−5.50597	−	3.30848i	−0.237600	−	0.142771i
$538$	−2.38075	−	7.24046i	−0.102642	−	0.312158i
$539$		−	8.28529i		−	0.356873i
$540$	−1.34118	+	11.5904i	−0.0577150	+	0.498771i
$541$		−	11.4118i		−	0.490630i	−0.969443	−	0.245315i	$-0.921109\pi$
$541$		−	11.4118i		−	0.490630i	0.969443	−	0.245315i	$-0.0788914\pi$
$542$	8.39627	−	2.76080i	0.360651	−	0.118587i
$543$	24.7208	−	13.7023i	1.06087	−	0.588022i
$544$	8.97999	+	4.97613i	0.385014	+	0.213350i
$545$	−17.7243	−	14.8724i	−0.759225	−	0.637065i
$546$	2.28283	+	0.518633i	0.0976961	+	0.0221954i
$547$	−4.84214	+	13.3037i	−0.207035	+	0.568824i	−0.999136	−	0.0415665i	$-0.986765\pi$
$547$	−4.84214	+	13.3037i	−0.207035	+	0.568824i	0.792101	+	0.610390i	$0.208987\pi$
$548$	22.8106	+	21.7199i	0.974421	+	0.927830i
$549$	4.07760	−	10.0912i	0.174028	−	0.430681i
$550$	3.23285	−	8.08332i	0.137849	−	0.344674i
$551$	10.4598	−	8.77685i	0.445604	−	0.373906i
$552$	5.33150	−	18.1188i	0.226924	−	0.771188i
$553$	−2.23406	+	12.6700i	−0.0950018	+	0.538782i
$554$	−0.629969	+	20.0629i	−0.0267648	+	0.852392i
$555$	−8.14290	+	2.80363i	−0.345647	+	0.119008i
$556$	0.648529	+	0.430832i	0.0275037	+	0.0182713i
$557$	29.6837	+	17.1379i	1.25774	+	0.726155i	0.972634	−	0.232342i	$-0.0746388\pi$
$557$	29.6837	+	17.1379i	1.25774	+	0.726155i	0.285103	+	0.958497i	$0.407972\pi$
$558$	22.6426	−	16.5713i	0.958538	−	0.701521i
$559$	3.84831	+	6.66547i	0.162766	+	0.281919i
$560$	1.39608	+	6.14187i	0.0589953	+	0.259541i
$561$	5.11110	−	0.809409i	0.215791	−	0.0341733i
$562$	−20.7732	+	33.5057i	−0.876263	+	1.41335i
$563$	−11.1729	−	30.6973i	−0.470882	−	1.29374i	−0.917044	−	0.398786i	$-0.869432\pi$
$563$	−11.1729	−	30.6973i	−0.470882	−	1.29374i	0.446162	−	0.894952i	$-0.352790\pi$
$564$	−41.0380	+	11.3052i	−1.72801	+	0.476034i
$565$	−2.93297	+	0.517161i	−0.123391	+	0.0217571i
$566$	31.3144	−	4.51333i	1.31624	−	0.189709i
$567$	11.5309	+	5.13504i	0.484250	+	0.215651i
$568$	16.0240	+	34.9922i	0.672354	+	1.46824i
$569$	4.57663	+	25.9553i	0.191862	+	1.08810i	0.916817	+	0.399308i	$0.130750\pi$
$569$	4.57663	+	25.9553i	0.191862	+	1.08810i	−0.724955	+	0.688797i	$0.758139\pi$
$570$	−1.18123	−	9.34999i	−0.0494763	−	0.391628i
$571$	14.3103	+	39.3171i	0.598865	+	1.64537i	0.753539	+	0.657404i	$0.228345\pi$
$571$	14.3103	+	39.3171i	0.598865	+	1.64537i	−0.154673	+	0.987966i	$0.549432\pi$
$572$	−2.05595	−	0.898091i	−0.0859634	−	0.0375511i
$573$	1.86922	+	11.8034i	0.0780880	+	0.493095i
$574$	−2.22390	+	10.6466i	−0.0928239	+	0.444382i
$575$	−7.20837	−	12.4853i	−0.300610	−	0.520672i
$576$	−7.09968	−	22.9258i	−0.295820	−	0.955244i
$577$	−6.39933	+	11.0840i	−0.266408	+	0.461431i	−0.967931	−	0.251215i	$-0.919170\pi$
$577$	−6.39933	+	11.0840i	−0.266408	+	0.461431i	0.701524	+	0.712646i	$0.252503\pi$
$578$	−14.4503	−	12.9193i	−0.601052	−	0.537373i
$579$	15.6079	−	5.37387i	0.648643	−	0.223330i
$580$	0.997782	+	8.89116i	0.0414306	+	0.369185i
$581$	1.82120	+	0.321126i	0.0755560	+	0.0133226i
$582$	10.9692	−	17.0211i	0.454689	−	0.705547i
$583$	8.69808	−	7.29856i	0.360238	−	0.302275i
$584$	−26.6847	−	2.52030i	−1.10422	−	0.104291i
$585$	1.80869	−	1.41298i	0.0747800	−	0.0584194i
$586$	0.332958	+	0.423091i	0.0137544	+	0.0174777i
$587$	4.86117	−	13.3560i	0.200642	−	0.551260i	−0.798039	−	0.602606i	$-0.794129\pi$
$587$	4.86117	−	13.3560i	0.200642	−	0.551260i	0.998681	+	0.0513464i	$0.0163513\pi$
$588$	−17.3786	−	1.39769i	−0.716682	−	0.0576398i
$589$	−14.5680	+	17.3615i	−0.600264	+	0.715367i
$590$	7.92522	+	14.7795i	0.326276	+	0.608463i
$591$	3.04374	−	1.68709i	0.125203	−	0.0693975i
$592$	12.9964	−	12.0374i	0.534150	−	0.494734i
$593$	−22.4225			−0.920782			−0.460391	−	0.887716i	$-0.652291\pi$
$593$	−22.4225			−0.920782			−0.460391	+	0.887716i	$0.652291\pi$
$594$	−9.93324	−	6.90433i	−0.407566	−	0.283288i
$595$			2.85778i			0.117158i
$596$	21.2027	−	10.5265i	0.868498	−	0.431184i
$597$	19.0131	−	31.6417i	0.778156	−	1.29501i
$598$	−3.27424	+	1.75575i	−0.133894	+	0.0717978i
$599$	3.21966	+	2.70162i	0.131552	+	0.110385i	0.706190	−	0.708023i	$-0.250413\pi$
$599$	3.21966	+	2.70162i	0.131552	+	0.110385i	−0.574638	+	0.818408i	$0.694857\pi$
$600$	−16.4096	−	8.14460i	−0.669919	−	0.332502i
$601$	−12.5218	−	4.55756i	−0.510775	−	0.185907i	0.0737590	−	0.997276i	$-0.476500\pi$
$601$	−12.5218	−	4.55756i	−0.510775	−	0.185907i	−0.584534	+	0.811369i	$0.698723\pi$
$602$	13.8545	+	17.6049i	0.564666	+	0.717523i
$603$	−35.5849	−	7.56537i	−1.44913	−	0.308086i
$604$	4.32781	−	17.8932i	0.176096	−	0.728064i
$605$	5.98270	+	7.12991i	0.243231	+	0.289872i
$606$	−2.11336	+	43.2156i	−0.0858495	+	1.75551i
$607$	−5.79180	+	32.8469i	−0.235082	+	1.33322i	0.607359	+	0.794428i	$0.292229\pi$
$607$	−5.79180	+	32.8469i	−0.235082	+	1.33322i	−0.842441	+	0.538789i	$0.818882\pi$
$608$	9.98642	+	16.6152i	0.405003	+	0.673835i
$609$	9.50128	+	1.84707i	0.385011	+	0.0748471i
$610$	−4.29434	−	3.83938i	−0.173873	−	0.155452i
$611$	7.25156	+	4.18669i	0.293367	+	0.169375i
$612$	−0.835535	−	10.8572i	−0.0337745	−	0.438877i
$613$	11.1640	−	6.44552i	0.450908	−	0.260332i	−0.257305	−	0.966330i	$-0.582835\pi$
$613$	11.1640	−	6.44552i	0.450908	−	0.260332i	0.708214	+	0.705998i	$0.249501\pi$
$614$	15.1394	+	3.16237i	0.610978	+	0.127623i
$615$	6.71060	+	8.28726i	0.270597	+	0.334174i
$616$	−6.29598	−	1.73366i	−0.253672	−	0.0698512i
$617$	20.7471	−	7.55132i	0.835246	−	0.304005i	0.111236	−	0.993794i	$-0.464519\pi$
$617$	20.7471	−	7.55132i	0.835246	−	0.304005i	0.724010	+	0.689789i	$0.242297\pi$
$618$	8.78539	+	3.69298i	0.353400	+	0.148554i
$619$	0.110454	−	0.0194760i	0.00443952	−	0.000782807i	−0.171428	−	0.985197i	$-0.554838\pi$
$619$	0.110454	−	0.0194760i	0.00443952	−	0.000782807i	0.175867	+	0.984414i	$0.443727\pi$
$620$	−4.19364	−	14.2460i	−0.168420	−	0.572131i
$621$	−19.1577	+	5.85575i	−0.768770	+	0.234983i
$622$	−3.68329	−	25.5555i	−0.147687	−	1.02468i
$623$	−1.71619	−	9.73302i	−0.0687579	−	0.389945i
$624$	−2.23060	+	4.16090i	−0.0892953	+	0.166569i
$625$	−7.21791	+	2.62710i	−0.288716	+	0.105084i
$626$	−2.42345	+	3.90885i	−0.0968604	+	0.156229i
$627$	9.12203	+	3.50184i	0.364299	+	0.139850i
$628$	−1.72564	+	27.4515i	−0.0688604	+	1.09543i
$629$	6.96066	−	4.01874i	0.277540	−	0.160238i
$630$	4.62401	−	4.82172i	0.184225	−	0.192102i
$631$	−7.25883	+	12.5727i	−0.288970	+	0.500510i	−0.973564	−	0.228414i	$-0.926646\pi$
$631$	−7.25883	+	12.5727i	−0.288970	+	0.500510i	0.684595	+	0.728924i	$0.259979\pi$
$632$	−23.4385	−	11.1271i	−0.932332	−	0.442613i
$633$	10.5862	−	12.1775i	0.420764	−	0.484013i
$634$	0.755917	−	24.0740i	0.0300213	−	0.956102i
$635$	4.74963	+	0.837488i	0.188483	+	0.0332347i
$636$	−13.8416	−	19.4757i	−0.548854	−	0.772261i
$637$	2.20451	+	2.62724i	0.0873460	+	0.104095i
$638$	−8.61291	−	3.44465i	−0.340988	−	0.136375i
$639$	21.6334	−	34.6175i	0.855806	−	1.36945i
$640$	−12.6892	−	0.573851i	−0.501586	−	0.0226835i
$641$	−26.9693	−	9.81603i	−1.06522	−	0.387710i	−0.250835	−	0.968030i	$-0.580705\pi$
$641$	−26.9693	−	9.81603i	−1.06522	−	0.387710i	−0.814389	+	0.580320i	$0.802928\pi$
$642$	−3.01625	−	9.74373i	−0.119042	−	0.384554i
$643$	16.9076	−	20.1497i	0.666772	−	0.794628i	−0.321569	−	0.946886i	$-0.604210\pi$
$643$	16.9076	−	20.1497i	0.666772	−	0.794628i	0.988341	+	0.152258i	$0.0486546\pi$
$644$	−8.70387	+	6.41776i	−0.342981	+	0.252895i
$645$	21.9608	+	0.383792i	0.864706	+	0.0151118i
$646$	2.74738	+	8.35547i	0.108094	+	0.328742i
$647$	31.9679			1.25679			0.628394	−	0.777895i	$-0.283713\pi$
$647$	31.9679			1.25679			0.628394	+	0.777895i	$0.283713\pi$
$648$	−16.1577	+	19.6705i	−0.634734	+	0.772730i
$649$	−17.3874			−0.682516
$650$	1.12565	+	3.42337i	0.0441516	+	0.134276i
$651$	−16.0632	−	0.280725i	−0.629567	−	0.0110025i
$652$	15.0971	+	20.4750i	0.591249	+	0.801862i
$653$	24.4383	−	29.1244i	0.956344	−	1.13973i	−0.0337653	−	0.999430i	$-0.510750\pi$
$653$	24.4383	−	29.1244i	0.956344	−	1.13973i	0.990109	−	0.140297i	$-0.0448057\pi$
$654$	−14.9275	−	48.2220i	−0.583711	−	1.88563i
$655$	−8.35469	−	3.04086i	−0.326445	−	0.118816i
$656$	−19.5099	−	10.0241i	−0.761733	−	0.391375i
$657$	13.3457	+	25.1022i	0.520666	+	0.979330i
$658$	22.6298	+	9.05056i	0.882200	+	0.352828i
$659$	13.8230	+	16.4736i	0.538469	+	0.641722i	0.964844	−	0.262825i	$-0.0846540\pi$
$659$	13.8230	+	16.4736i	0.538469	+	0.641722i	−0.426375	+	0.904546i	$0.640210\pi$
$660$	−5.21872	+	3.70900i	−0.203139	+	0.144373i
$661$	40.0325	+	7.05881i	1.55708	+	0.274556i	0.884883	−	0.465813i	$-0.154238\pi$
$661$	40.0325	+	7.05881i	1.55708	+	0.274556i	0.672201	+	0.740369i	$0.265349\pi$
$662$	−0.249437	+	7.94394i	−0.00969465	+	0.308750i
$663$	−1.40535	+	1.61660i	−0.0545793	+	0.0627836i
$664$	−1.59942	+	3.36907i	−0.0620697	+	0.130745i
$665$	−2.69804	+	4.67315i	−0.104626	+	0.181217i
$666$	−18.2467	−	4.48213i	−0.707046	−	0.173679i
$667$	−13.3033	+	7.68064i	−0.515104	+	0.297396i
$668$	39.5271	+	2.48472i	1.52935	+	0.0961368i
$669$	39.8036	+	15.2801i	1.53890	+	0.590764i
$670$	−10.1459	+	16.3646i	−0.391969	+	0.632218i
$671$	5.61218	−	2.04267i	0.216656	−	0.0788563i
$672$	−4.69850	+	12.9135i	−0.181249	+	0.498149i
$673$	7.13129	+	40.4435i	0.274891	+	1.55898i	0.739308	+	0.673367i	$0.235153\pi$
$673$	7.13129	+	40.4435i	0.274891	+	1.55898i	−0.464417	+	0.885616i	$0.653736\pi$
$674$	3.83467	+	26.6058i	0.147706	+	1.02482i
$675$	2.36681	+	19.2862i	0.0910985	+	0.742328i
$676$	−24.0509	+	7.07995i	−0.925034	+	0.272306i
$677$	17.2637	−	3.04406i	0.663499	−	0.116993i	0.168251	−	0.985744i	$-0.446188\pi$
$677$	17.2637	−	3.04406i	0.663499	−	0.116993i	0.495248	+	0.868752i	$0.335077\pi$
$678$	−5.98997	−	2.51791i	−0.230043	−	0.0966998i
$679$	−10.8951	+	3.96547i	−0.418114	+	0.152181i
$680$	−5.55646	−	1.53003i	−0.213081	−	0.0586739i
$681$	4.45280	+	5.49899i	0.170632	+	0.210722i
$682$	15.0715	+	3.14819i	0.577119	+	0.120551i
$683$	34.2463	−	19.7721i	1.31040	−	0.756558i	0.328235	−	0.944596i	$-0.393546\pi$
$683$	34.2463	−	19.7721i	1.31040	−	0.756558i	0.982162	+	0.188038i	$0.0602127\pi$
$684$	8.88405	−	18.5429i	0.339690	−	0.709007i
$685$	−15.3126	−	8.84073i	−0.585064	−	0.337787i
$686$	17.7925	+	15.9075i	0.679321	+	0.607351i
$687$	21.4562	+	4.17113i	0.818605	+	0.159139i
$688$	−41.6473	+	17.5121i	−1.58779	+	0.667643i
$689$	−0.816164	+	4.62869i	−0.0310934	+	0.176339i
$690$	−0.517870	+	10.5898i	−0.0197150	+	0.403146i
$691$	13.9569	+	16.6332i	0.530946	+	0.632757i	0.963133	−	0.269027i	$-0.0867022\pi$
$691$	13.9569	+	16.6332i	0.530946	+	0.632757i	−0.432186	+	0.901784i	$0.642258\pi$
$692$	−9.52589	−	2.30402i	−0.362120	−	0.0875857i
$693$	2.14011	+	6.58752i	0.0812960	+	0.250239i
$694$	−8.11526	−	10.3121i	−0.308051	−	0.391441i
$695$	−0.410715	−	0.149488i	−0.0155793	−	0.00567040i
$696$	−8.67820	+	17.4847i	−0.328946	+	0.662756i
$697$	−7.62376	−	6.39709i	−0.288770	−	0.242307i
$698$	9.25159	−	4.96098i	0.350178	−	0.187776i
$699$	−21.9248	+	36.4872i	−0.829271	+	1.38007i
$700$	4.66441	+	9.39515i	0.176298	+	0.355103i
$701$			24.5820i			0.928448i	0.885718	+	0.464224i	$0.153667\pi$
$701$			24.5820i			0.928448i	−0.885718	+	0.464224i	$0.846333\pi$
$702$	4.98687	−	0.453655i	0.188217	−	0.0171221i
$703$	15.1764			0.572390
$704$	6.74161	−	11.3133i	0.254084	−	0.426384i
$705$	20.8997	−	11.5843i	0.787127	−	0.436290i
$706$	−18.9011	−	35.2481i	−0.711351	−	1.32658i
$707$	15.9242	−	18.9777i	0.598889	−	0.713729i
$708$	−2.93318	+	36.4705i	−0.110236	+	1.37065i
$709$	−14.8834	+	40.8919i	−0.558959	+	1.53573i	0.262193	+	0.965016i	$0.415554\pi$
$709$	−14.8834	+	40.8919i	−0.558959	+	1.53573i	−0.821151	+	0.570711i	$0.806668\pi$
$710$	−13.3612	−	16.9781i	−0.501436	−	0.637177i
$711$	3.82882	+	27.2518i	0.143592	+	1.02202i
$712$	19.8430	+	1.87412i	0.743648	+	0.0702357i
$713$	19.5318	−	16.3891i	0.731473	−	0.613778i
$714$	−3.37747	+	5.24088i	−0.126399	+	0.196135i
$715$	1.24031	+	0.218700i	0.0463850	+	0.00817892i
$716$	−7.37098	+	0.827184i	−0.275466	+	0.0309133i
$717$	−17.7379	+	6.10722i	−0.662433	+	0.228078i
$718$	−17.8769	−	15.9830i	−0.667162	−	0.596480i
$719$	2.30085	−	3.98520i	0.0858074	−	0.148623i	−0.819928	−	0.572467i	$-0.805986\pi$
$719$	2.30085	−	3.98520i	0.0858074	−	0.148623i	0.905735	+	0.423844i	$0.139320\pi$
$720$	6.89936	+	11.5721i	0.257124	+	0.431267i
$721$	−2.72831	−	4.72557i	−0.101607	−	0.175989i
$722$	2.09831	−	10.0454i	0.0780910	−	0.373850i
$723$	−3.57434	−	22.5706i	−0.132931	−	0.839410i
$724$	13.0645	−	29.9079i	0.485540	−	1.11152i
$725$	5.09606	+	14.0013i	0.189263	+	0.519996i
$726$	2.54516	+	20.1462i	0.0944599	+	0.747695i
$727$	−0.922052	−	5.22921i	−0.0341970	−	0.193941i	0.962923	−	0.269775i	$-0.0869492\pi$
$727$	−0.922052	−	5.22921i	−0.0341970	−	0.193941i	−0.997120	+	0.0758339i	$0.975838\pi$
$728$	2.45772	−	1.12547i	0.0910891	−	0.0417126i
$729$	26.8517	+	2.82568i	0.994509	+	0.104655i
$730$	14.8926	−	2.14646i	0.551200	−	0.0794441i
$731$	−20.1874	+	3.55958i	−0.746658	+	0.131656i
$732$	−3.33780	−	12.1163i	−0.123369	−	0.447831i
$733$	−17.7690	−	48.8201i	−0.656315	−	1.80321i	−0.592980	−	0.805217i	$-0.702049\pi$
$733$	−17.7690	−	48.8201i	−0.656315	−	1.80321i	−0.0633350	−	0.997992i	$-0.520174\pi$
$734$	−6.02677	+	9.72077i	−0.222452	+	0.358800i
$735$	9.66676	−	1.53086i	0.356564	−	0.0564664i
$736$	−7.81826	−	20.3592i	−0.288185	−	0.750449i
$737$	−9.98153	−	17.2885i	−0.367674	−	0.636831i
$738$	2.51223	+	23.1289i	0.0924766	+	0.851387i
$739$	−8.21344	−	4.74203i	−0.302136	−	0.174439i	0.341266	−	0.939967i	$-0.389144\pi$
$739$	−8.21344	−	4.74203i	−0.302136	−	0.174439i	−0.643402	+	0.765528i	$0.722478\pi$
$740$	−5.50266	+	8.28313i	−0.202282	+	0.304494i
$741$	−3.82432	+	1.31673i	−0.140490	+	0.0483712i
$742$	−0.429356	+	13.6739i	−0.0157622	+	0.501985i
$743$	1.45201	−	8.23477i	0.0532691	−	0.302104i	−0.946520	−	0.322646i	$-0.895428\pi$
$743$	1.45201	−	8.23477i	0.0532691	−	0.302104i	0.999789	+	0.0205412i	$0.00653893\pi$
$744$	9.14591	−	31.0819i	0.335305	−	1.13952i
$745$	−10.1797	+	8.54176i	−0.372954	+	0.312946i
$746$	11.5723	−	28.9352i	0.423694	−	1.05939i
$747$	3.91721	−	0.550359i	0.143323	−	0.0201366i
$748$	4.12048	−	4.32739i	0.150660	−	0.158225i
$749$	−1.99746	+	5.48797i	−0.0729855	+	0.200526i
$750$	23.4373	+	5.32469i	0.855809	+	0.194430i
$751$	36.5089	+	30.6346i	1.33223	+	1.11787i	0.983551	+	0.180632i	$0.0578143\pi$
$751$	36.5089	+	30.6346i	1.33223	+	1.11787i	0.348680	+	0.937242i	$0.386630\pi$
$752$	−29.7130	+	39.1541i	−1.08352	+	1.42780i
$753$	−30.8512	+	17.1002i	−1.12428	+	0.623167i
$754$	3.64766	−	1.19940i	0.132840	−	0.0436795i
$755$			10.3342i			0.376101i
$756$	14.1785	−	3.37765i	0.515668	−	0.122844i
$757$		−	22.8271i		−	0.829666i	−0.909898	−	0.414833i	$-0.863840\pi$
$757$		−	22.8271i		−	0.829666i	0.909898	−	0.414833i	$-0.136160\pi$
$758$	−4.16229	−	12.6585i	−0.151181	−	0.459779i
$759$	−9.42236	−	5.66180i	−0.342010	−	0.205510i
$760$	−7.64163	−	7.74784i	−0.277191	−	0.281044i
$761$	−9.00453	−	7.55570i	−0.326414	−	0.273894i	0.464823	−	0.885404i	$-0.346118\pi$
$761$	−9.00453	−	7.55570i	−0.326414	−	0.273894i	−0.791237	+	0.611510i	$0.790562\pi$
$762$	7.72055	+	7.14923i	0.279686	+	0.258989i
$763$	−9.88546	+	27.1601i	−0.357878	+	0.983261i
$764$	9.99355	+	9.51572i	0.361554	+	0.344267i
$765$	1.88873	+	5.81376i	0.0682873	+	0.210197i
$766$	22.7074	+	9.08161i	0.820451	+	0.328132i
$767$	5.51349	−	4.62637i	0.199081	−	0.167048i
$768$	−22.5926	−	16.0492i	−0.815239	−	0.579125i
$769$	−3.03895	+	17.2347i	−0.109587	+	0.621501i	0.879701	+	0.475527i	$0.157743\pi$
$769$	−3.03895	+	17.2347i	−0.109587	+	0.621501i	−0.989288	+	0.145974i	$0.953369\pi$
$770$	3.66407	+	0.115051i	0.132044	+	0.00414614i
$771$	3.95792	−	20.3594i	0.142541	−	0.733228i
$772$	10.5472	−	15.8767i	0.379603	−	0.571415i
$773$	−20.9933	−	12.1205i	−0.755076	−	0.435943i	0.0724491	−	0.997372i	$-0.476919\pi$
$773$	−20.9933	−	12.1205i	−0.755076	−	0.435943i	−0.827525	+	0.561429i	$0.810252\pi$
$774$	39.8203	+	26.6582i	1.43131	+	0.958211i
$775$	−12.3656	−	21.4178i	−0.444185	−	0.769351i
$776$	−1.87708	−	23.3066i	−0.0673831	−	0.836659i
$777$	6.77013	+	8.36077i	0.242877	+	0.299941i
$778$	−29.8562	−	18.5106i	−1.07040	−	0.663636i
$779$	−6.42713	−	17.6584i	−0.230276	−	0.632677i
$780$	0.667964	−	2.56469i	0.0239169	−	0.0918305i
$781$	22.0597	−	3.88972i	0.789359	−	0.139185i
$782$	−1.41159	−	9.79390i	−0.0504783	−	0.350229i
$783$	20.5498	−	2.52187i	0.734390	−	0.0901244i
$784$	−16.9210	+	10.9074i	−0.604323	+	0.389550i
$785$	−2.68125	−	15.2061i	−0.0956979	−	0.542730i
$786$	−11.7278	−	15.4506i	−0.418317	−	0.551106i
$787$	2.60184	+	7.14850i	0.0927457	+	0.254817i	0.977388	−	0.211454i	$-0.0678197\pi$
$787$	2.60184	+	7.14850i	0.0927457	+	0.254817i	−0.884642	+	0.466270i	$0.845597\pi$
$788$	1.60856	−	3.68239i	0.0573027	−	0.131180i
$789$	−15.9812	−	6.13501i	−0.568947	−	0.218412i
$790$	14.2572	+	2.97809i	0.507249	+	0.105956i
$791$	1.86019	+	3.22194i	0.0661406	+	0.114559i
$792$	−13.9541	+	0.634174i	−0.495837	+	0.0225344i
$793$	−1.23610	+	2.14099i	−0.0438952	+	0.0760287i
$794$	6.47023	−	7.23694i	0.229620	−	0.256830i
$795$	10.1226	+	8.79984i	0.359012	+	0.312098i
$796$	−4.75366	−	42.3595i	−0.168489	−	1.50139i
$797$	−13.7809	−	2.42995i	−0.488146	−	0.0860733i	−0.0758424	−	0.997120i	$-0.524165\pi$
$797$	−13.7809	−	2.42995i	−0.488146	−	0.0860733i	−0.412304	+	0.911047i	$0.635276\pi$
$798$	−10.4709	+	5.38139i	−0.370666	+	0.190499i
$799$	−17.0837	+	14.3350i	−0.604380	+	0.507135i
$800$	−20.7645	+	4.03908i	−0.734137	+	0.142803i
$801$	−9.92401	−	18.6662i	−0.350648	−	0.659539i
$802$	−14.0102	+	11.0256i	−0.494718	+	0.389326i
$803$	−5.33557	+	14.6594i	−0.188288	+	0.517317i
$804$	−37.9469	+	18.0200i	−1.33829	+	0.635517i
$805$	3.90214	−	4.65039i	0.137532	−	0.163905i
$806$	−5.61679	+	3.01189i	−0.197843	+	0.106089i
$807$	−0.163112	+	9.33336i	−0.00574181	+	0.328550i
$808$	28.3732	+	41.1222i	0.998164	+	1.44667i
$809$	−20.7183			−0.728415			−0.364208	−	0.931318i	$-0.618660\pi$
$809$	−20.7183			−0.728415			−0.364208	+	0.931318i	$0.618660\pi$
$810$	6.22020	−	12.8652i	0.218555	−	0.452037i
$811$		−	43.7615i		−	1.53668i	−0.640045	−	0.768338i	$-0.721084\pi$
$811$		−	43.7615i		−	1.53668i	0.640045	−	0.768338i	$-0.278916\pi$
$812$	10.0107	−	4.97001i	0.351306	−	0.174413i
$813$	−10.8233	−	0.189150i	−0.379589	−	0.00663378i
$814$	−4.87236	−	9.08632i	−0.170776	−	0.318476i
$815$	−10.9396	−	9.17939i	−0.383197	−	0.321540i
$816$	−8.38171	−	9.37283i	−0.293419	−	0.328115i
$817$	−36.3718	−	13.2382i	−1.27249	−	0.463148i
$818$	−37.8849	+	29.8141i	−1.32462	+	1.04243i
$819$	−2.43140	−	1.51945i	−0.0849600	−	0.0530939i
$820$	11.9681	+	2.89471i	0.417944	+	0.101088i
$821$	−12.4887	−	14.8834i	−0.435858	−	0.519435i	0.502745	−	0.864435i	$-0.332323\pi$
$821$	−12.4887	−	14.8834i	−0.435858	−	0.519435i	−0.938603	+	0.345000i	$0.887879\pi$
$822$	−17.6333	−	34.3102i	−0.615031	−	1.19670i
$823$	6.24682	−	35.4275i	0.217750	−	1.23492i	−0.658319	−	0.752739i	$-0.728732\pi$
$823$	6.24682	−	35.4275i	0.217750	−	1.23492i	0.876069	−	0.482185i	$-0.160157\pi$
$824$	10.6488	−	2.77470i	0.370967	−	0.0966613i
$825$	−6.99534	+	8.04688i	−0.243547	+	0.280156i
$826$	13.9630	−	15.6177i	0.485837	−	0.543408i
$827$	35.6157	+	20.5627i	1.23848	+	0.715037i	0.968783	−	0.247909i	$-0.0797433\pi$
$827$	35.6157	+	20.5627i	1.23848	+	0.715037i	0.269697	+	0.962945i	$0.413077\pi$
$828$	−13.4653	+	18.8085i	−0.467951	+	0.653641i
$829$	−43.3862	+	25.0490i	−1.50687	+	0.869989i	−0.506897	+	0.862006i	$0.669208\pi$
$829$	−43.3862	+	25.0490i	−1.50687	+	0.869989i	−0.999968	+	0.00798294i	$0.997459\pi$
$830$	0.428074	−	2.04935i	0.0148587	−	0.0711339i
$831$	8.81063	−	22.9510i	0.305637	−	0.796162i
$832$	0.872440	+	5.38117i	0.0302464	+	0.186559i
$833$	−8.58341	+	3.12411i	−0.297397	+	0.108244i
$834$	−0.576536	−	0.759549i	−0.0199638	−	0.0263010i
$835$	−21.8951	+	3.86070i	−0.757711	+	0.133605i
$836$	10.8235	−	3.18615i	0.374338	−	0.110195i
$837$	−32.8640	+	10.0452i	−1.13594	+	0.347214i
$838$	15.5521	−	2.24152i	0.537240	−	0.0774320i
$839$	2.93816	+	16.6631i	0.101436	+	0.575275i	0.992584	+	0.121561i	$0.0387900\pi$
$839$	2.93816	+	16.6631i	0.101436	+	0.575275i	−0.891148	+	0.453714i	$0.850099\pi$
$840$	0.859434	−	7.66608i	0.0296533	−	0.264505i
$841$	−12.3325	+	4.48865i	−0.425257	+	0.154781i
$842$	23.7198	+	14.7060i	0.817439	+	0.506804i
$843$	37.5234	−	30.3846i	1.29238	−	1.04650i
$844$	1.16892	−	18.5952i	0.0402358	−	0.640072i
$845$	12.1886	−	7.03706i	0.419299	−	0.242082i
$846$	52.0187	+	3.45590i	1.78844	+	0.118816i
$847$	5.81341	−	10.0691i	0.199751	−	0.345979i
$848$	−26.3567	−	8.15568i	−0.905091	−	0.280067i
$849$	−38.0364	−	7.39437i	−1.30541	−	0.253774i
$850$	−9.59316	−	0.301222i	−0.329043	−	0.0103318i
$851$	−16.8143	−	2.96481i	−0.576385	−	0.101632i
$852$	−4.43742	−	46.9270i	−0.152024	−	1.60769i
$853$	−16.8126	−	20.0365i	−0.575653	−	0.686037i	0.397128	−	0.917763i	$-0.370007\pi$
$853$	−16.8126	−	20.0365i	−0.575653	−	0.686037i	−0.972781	+	0.231726i	$0.925563\pi$
$854$	−2.67213	+	6.68133i	−0.0914386	+	0.228630i
$855$	−2.40027	+	11.2900i	−0.0820876	+	0.386111i
$856$	−9.60099	−	6.82191i	−0.328155	−	0.233168i
$857$	−39.5672	−	14.4013i	−1.35159	−	0.491938i	−0.438146	−	0.898904i	$-0.644365\pi$
$857$	−39.5672	−	14.4013i	−1.35159	−	0.491938i	−0.913444	+	0.406965i	$0.866587\pi$
$858$	2.01613	+	1.86694i	0.0688295	+	0.0637361i
$859$	27.7503	−	33.0715i	0.946827	−	1.12838i	−0.0447668	−	0.998997i	$-0.514254\pi$
$859$	27.7503	−	33.0715i	0.946827	−	1.12838i	0.991594	−	0.129387i	$-0.0413011\pi$
$860$	20.4129	−	15.0514i	0.696075	−	0.513248i
$861$	6.86098	−	11.4180i	0.233822	−	0.389126i
$862$	0.393708	−	0.129456i	0.0134097	−	0.00440929i
$863$	−31.5239			−1.07308			−0.536542	−	0.843873i	$-0.680270\pi$
$863$	−31.5239			−1.07308			−0.536542	+	0.843873i	$0.680270\pi$
$864$	−1.02379	+	29.3760i	−0.0348302	+	0.999393i
$865$	5.50169			0.187063
$866$	−24.5156	+	8.06105i	−0.833075	+	0.273926i
$867$	11.5089	+	20.7636i	0.390861	+	0.705167i
$868$	−14.9310	+	11.0093i	−0.506792	+	0.373681i
$869$	−9.70666	+	11.5679i	−0.329276	+	0.392416i
$870$	2.42762	−	10.6855i	0.0823039	−	0.362271i
$871$	7.76516	+	2.82629i	0.263112	+	0.0957651i
$872$	−47.5155	−	33.7618i	−1.60908	−	1.14332i
$873$	−19.5437	+	15.2679i	−0.661453	+	0.516739i
$874$	6.93818	−	17.3480i	0.234687	−	0.586806i
$875$	−8.84571	−	10.5419i	−0.299040	−	0.356382i
$876$	29.8483	+	13.6645i	1.00848	+	0.461679i
$877$	22.1917	+	3.91299i	0.749360	+	0.132132i	0.535269	−	0.844681i	$-0.320210\pi$
$877$	22.1917	+	3.91299i	0.749360	+	0.132132i	0.214091	+	0.976814i	$0.431321\pi$
$878$	−1.38464	−	0.0434774i	−0.0467295	−	0.00146729i
$879$	−0.214665	−	0.623474i	−0.00724045	−	0.0210293i
$880$	−2.18540	+	7.06256i	−0.0736700	+	0.238079i
$881$	15.0315	−	26.0353i	0.506424	−	0.877153i	−0.493548	−	0.869719i	$-0.664300\pi$
$881$	15.0315	−	26.0353i	0.506424	−	0.877153i	0.999972	−	0.00743425i	$-0.00236642\pi$
$882$	19.5371	+	8.61725i	0.657848	+	0.290158i
$883$	−11.7757	+	6.79869i	−0.396283	+	0.228794i	−0.684879	−	0.728657i	$-0.740145\pi$
$883$	−11.7757	+	6.79869i	−0.396283	+	0.228794i	0.288596	+	0.957451i	$0.406812\pi$
$884$	−0.155177	+	2.46856i	−0.00521917	+	0.0830267i
$885$	−3.21263	−	20.2865i	−0.107991	−	0.681925i
$886$	6.19532	+	3.84103i	0.208136	+	0.129042i
$887$	34.6577	−	12.6144i	1.16369	−	0.423549i	0.313277	−	0.949662i	$-0.398573\pi$
$887$	34.6577	−	12.6144i	1.16369	−	0.423549i	0.850415	+	0.526112i	$0.176351\pi$
$888$	−19.8807	+	8.68707i	−0.667154	+	0.291519i
$889$	−1.04619	−	5.93322i	−0.0350880	−	0.198994i
$890$	−11.0743	+	1.59613i	−0.371211	+	0.0535024i
$891$	8.70751	+	11.9870i	0.291713	+	0.401579i
$892$	47.2278	−	13.9026i	1.58130	−	0.465494i
$893$	−41.4697	+	7.31222i	−1.38773	+	0.244694i
$894$	−28.7636	+	3.63384i	−0.961997	+	0.121534i
$895$	3.91267	−	1.42409i	0.130786	−	0.0476022i
$896$	4.74786	+	15.1406i	0.158615	+	0.505811i
$897$	4.49426	−	0.711724i	0.150059	−	0.0237638i
$898$	3.59675	−	17.2189i	0.120025	−	0.574604i
$899$	−22.8210	+	13.1757i	−0.761124	+	0.439435i
$900$	15.6984	+	16.0304i	0.523282	+	0.534346i
$901$	−10.8409	−	6.25901i	−0.361163	−	0.208518i
$902$	−8.50888	+	9.51717i	−0.283315	+	0.316887i
$903$	−8.93224	−	25.9429i	−0.297246	−	0.863326i
$904$	−7.26043	+	1.89182i	−0.241478	+	0.0629209i
$905$	−3.18143	+	18.0428i	−0.105754	+	0.599763i
$906$	−12.2135	+	18.9519i	−0.405767	+	0.629635i
$907$	2.75537	+	3.28372i	0.0914905	+	0.109034i	0.809847	−	0.586641i	$-0.199550\pi$
$907$	2.75537	+	3.28372i	0.0914905	+	0.109034i	−0.718357	+	0.695675i	$0.755105\pi$
$908$	7.94140	+	1.92078i	0.263544	+	0.0637433i
$909$	19.8530	−	49.1319i	0.658482	−	1.62960i
$910$	−1.19248	+	0.938438i	−0.0395302	+	0.0311089i
$911$	−26.1940	−	9.53385i	−0.867847	−	0.315871i	−0.130552	−	0.991441i	$-0.541675\pi$
$911$	−26.1940	−	9.53385i	−0.867847	−	0.315871i	−0.737295	+	0.675571i	$0.763897\pi$
$912$	−4.85715	−	23.2400i	−0.160836	−	0.769553i
$913$	1.66279	+	1.39525i	0.0550303	+	0.0461759i
$914$	16.1180	+	30.0580i	0.533135	+	0.994229i
$915$	3.42021	+	6.17053i	0.113069	+	0.203991i
$916$	22.6065	−	11.2235i	0.746941	−	0.370834i
$917$			11.1065i			0.366767i
$918$	−3.40726	+	12.8940i	−0.112456	+	0.425567i
$919$	54.1746			1.78705			0.893527	−	0.449009i	$-0.148223\pi$
$919$	54.1746			1.78705			0.893527	+	0.449009i	$0.148223\pi$
$920$	6.95271	+	10.0768i	0.229224	+	0.332223i
$921$	−16.2364	−	9.75627i	−0.535007	−	0.321480i
$922$	45.5750	−	24.4386i	1.50093	−	0.804844i
$923$	−5.96010	+	7.10297i	−0.196179	+	0.233797i
$924$	6.58356	+	4.54138i	0.216583	+	0.149400i
$925$	−5.66414	+	15.5621i	−0.186236	+	0.511678i
$926$	25.1607	−	19.8006i	0.826833	−	0.650689i
$927$	−8.67354	−	7.81035i	−0.284876	−	0.256526i
$928$	4.30370	+	22.1249i	0.141276	+	0.726287i
$929$	−26.4712	+	22.2120i	−0.868491	+	0.728751i	−0.963780	−	0.266699i	$-0.914067\pi$
$929$	−26.4712	+	22.2120i	−0.868491	+	0.728751i	0.0952887	+	0.995450i	$0.469623\pi$
$930$	−0.888378	+	18.1662i	−0.0291311	+	0.595694i
$931$	−16.9854	−	2.99498i	−0.556674	−	0.0981566i
$932$	5.48163	+	48.8464i	0.179557	+	1.60002i
$933$	−6.03449	+	31.0412i	−0.197560	+	1.01624i
$934$	−21.9840	+	24.5890i	−0.719337	+	0.804578i
$935$	−1.67717	+	2.90494i	−0.0548493	+	0.0950018i
$936$	4.25606	−	3.91394i	0.139114	−	0.127931i
$937$	−13.1443	−	22.7665i	−0.429404	−	0.743750i	0.567416	−	0.823431i	$-0.307943\pi$
$937$	−13.1443	−	22.7665i	−0.429404	−	0.743750i	−0.996820	+	0.0796811i	$0.974610\pi$
$938$	23.5445	+	4.91806i	0.768756	+	0.160580i
$939$	4.37758	−	3.54474i	0.142857	−	0.115678i
$940$	11.0451	−	25.2849i	0.360252	−	0.824704i
$941$	−13.8588	−	38.0767i	−0.451784	−	1.24127i	−0.931467	−	0.363825i	$-0.881471\pi$
$941$	−13.8588	−	38.0767i	−0.451784	−	1.24127i	0.479683	−	0.877442i	$-0.340752\pi$
$942$	13.0542	−	31.0553i	0.425330	−	1.01184i
$943$	3.67106	+	20.8196i	0.119546	+	0.677980i
$944$	22.8901	+	35.5103i	0.745011	+	1.15576i
$945$	−7.29049	+	3.71411i	−0.237160	+	0.120820i
$946$	3.75116	+	26.0263i	0.121961	+	0.846189i
$947$	−38.4009	+	6.77112i	−1.24786	+	0.220032i	−0.758282	−	0.651926i	$-0.773961\pi$
$947$	−38.4009	+	6.77112i	−1.24786	+	0.220032i	−0.489580	+	0.871958i	$0.662850\pi$
$948$	22.6266	+	22.3114i	0.734877	+	0.724641i
$949$	−2.20861	−	6.06810i	−0.0716944	−	0.196979i
$950$	−15.4027	−	9.54952i	−0.499730	−	0.309827i
$951$	−10.5721	+	27.5395i	−0.342824	+	0.893031i
$952$	0.577960	+	7.17622i	0.0187318	+	0.232583i
$953$	12.7586	+	22.0985i	0.413291	+	0.715842i	0.995247	−	0.0973785i	$-0.0310458\pi$
$953$	12.7586	+	22.0985i	0.413291	+	0.715842i	−0.581956	+	0.813220i	$0.697712\pi$
$954$	8.16374	+	28.1014i	0.264311	+	0.909817i
$955$	−6.70859	−	3.87321i	−0.217085	−	0.125334i
$956$	−11.9866	+	18.0433i	−0.387674	+	0.583563i
$957$	8.57408	+	7.45365i	0.277161	+	0.240942i
$958$	56.3804	+	1.77033i	1.82157	+	0.0571967i
$959$	−3.83547	+	21.7520i	−0.123854	+	0.702410i
$960$	14.4452	+	5.77536i	0.466218	+	0.186399i
$961$	9.75845	−	8.18831i	0.314789	−	0.264139i
$962$	3.96266	+	1.58483i	0.127761	+	0.0510969i
$963$	−0.436503	+	12.4847i	−0.0140661	+	0.402312i
$964$	−19.1098	−	18.1960i	−0.615484	−	0.586055i
$965$	−3.65963	+	10.0547i	−0.117808	+	0.323674i
$966$	12.6522	−	3.91658i	0.407078	−	0.126014i
$967$	−35.3489	−	29.6612i	−1.13674	−	0.953841i	−0.137416	−	0.990513i	$-0.543880\pi$
$967$	−35.3489	−	29.6612i	−1.13674	−	0.953841i	−0.999327	+	0.0366729i	$0.988324\pi$
$968$	16.4652	+	16.6941i	0.529212	+	0.536568i
$969$	0.188231	−	10.7707i	0.00604685	−	0.346004i
$970$	4.10000	+	12.4691i	0.131643	+	0.400358i
$971$		−	1.40859i		−	0.0452039i	−0.999745	−	0.0226020i	$-0.992805\pi$
$971$		−	1.40859i		−	0.0452039i	0.999745	−	0.0226020i	$-0.00719504\pi$
$972$	26.6119	−	16.2421i	0.853578	−	0.520965i
$973$			0.545991i			0.0175037i
$974$	43.0339	−	14.1501i	1.37889	−	0.453398i
$975$	0.0771213	−	4.41293i	0.00246986	−	0.141327i
$976$	−11.5601	−	8.77262i	−0.370028	−	0.280805i
$977$	36.5361	+	30.6574i	1.16889	+	0.980817i	0.999988	−	0.00481536i	$-0.00153278\pi$
$977$	36.5361	+	30.6574i	1.16889	+	0.980817i	0.168904	+	0.985633i	$0.445977\pi$
$978$	−9.21336	−	29.7630i	−0.294611	−	0.951716i
$979$	3.96758	−	10.9008i	0.126805	−	0.348393i
$980$	7.79317	−	8.18451i	0.248944	−	0.261445i
$981$	−2.16026	+	61.7869i	−0.0689719	+	1.97270i
$982$	−13.8412	+	34.6082i	−0.441692	+	1.10439i
$983$	13.2755	−	11.1394i	0.423421	−	0.355293i	−0.406041	−	0.913855i	$-0.633091\pi$
$983$	13.2755	−	11.1394i	0.423421	−	0.355293i	0.829463	+	0.558562i	$0.188647\pi$
$984$	18.5271	+	19.4531i	0.590623	+	0.620142i
$985$	−0.391712	+	2.22151i	−0.0124810	+	0.0707832i
$986$	−0.320957	+	10.2217i	−0.0102214	+	0.325524i
$987$	−22.5277	−	19.5839i	−0.717066	−	0.623362i
$988$	−2.58433	+	3.89018i	−0.0822185	+	0.123763i
$989$	37.7108	+	21.7723i	1.19913	+	0.692320i
$990$	7.53009	−	2.18756i	0.239322	−	0.0695254i
$991$	16.1511	+	27.9745i	0.513056	+	0.888638i	0.999885	+	0.0151416i	$0.00481989\pi$
$991$	16.1511	+	27.9745i	0.513056	+	0.888638i	−0.486830	+	0.873497i	$0.661847\pi$
$992$	−13.4118	−	34.9251i	−0.425826	−	1.10887i
$993$	3.48858	−	9.08749i	0.110707	−	0.288383i
$994$	−14.2214	+	22.9381i	−0.451074	+	0.727551i
$995$	8.18398	+	22.4853i	0.259450	+	0.712832i
$996$	3.20707	−	3.25237i	0.101620	−	0.103055i
$997$	−24.1513	+	4.25852i	−0.764879	+	0.134869i	−0.542459	−	0.840082i	$-0.682507\pi$
$997$	−24.1513	+	4.25852i	−0.764879	+	0.134869i	−0.222420	+	0.974951i	$0.571396\pi$
$998$	−1.13217	+	0.163179i	−0.0358382	+	0.00516534i
$999$	19.2986	+	12.5344i	0.610581	+	0.396571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.13.4	✓	204
3.2	odd	2		648.2.t.a.253.31		204
4.3	odd	2		864.2.bf.a.337.1		204
8.3	odd	2		864.2.bf.a.337.34		204
8.5	even	2	inner	216.2.t.a.13.34	yes	204
24.5	odd	2		648.2.t.a.253.1		204
27.2	odd	18		648.2.t.a.397.1		204
27.25	even	9	inner	216.2.t.a.133.34	yes	204
108.79	odd	18		864.2.bf.a.241.34		204
216.29	odd	18		648.2.t.a.397.31		204
216.133	even	18	inner	216.2.t.a.133.4	yes	204
216.187	odd	18		864.2.bf.a.241.1		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.4	✓	204	1.1	even	1	trivial
216.2.t.a.13.34	yes	204	8.5	even	2	inner
216.2.t.a.133.4	yes	204	216.133	even	18	inner
216.2.t.a.133.34	yes	204	27.25	even	9	inner
648.2.t.a.253.1		204	24.5	odd	2
648.2.t.a.253.31		204	3.2	odd	2
648.2.t.a.397.1		204	27.2	odd	18
648.2.t.a.397.31		204	216.29	odd	18
864.2.bf.a.241.1		204	216.187	odd	18
864.2.bf.a.241.34		204	108.79	odd	18
864.2.bf.a.337.1		204	4.3	odd	2
864.2.bf.a.337.34		204	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34345 + 0.441744i) q^{2} +(1.73179 + 0.0302651i) q^{3} +(1.60972 - 1.18692i) q^{4} +(-0.721676 + 0.860059i) q^{5} +(-2.33994 + 0.724346i) q^{6} +(1.31793 + 0.479686i) q^{7} +(-1.63827 + 2.30566i) q^{8} +(2.99817 + 0.104825i) q^{9} +O(q^{10})\)	\(q+(-1.34345 + 0.441744i) q^{2} +(1.73179 + 0.0302651i) q^{3} +(1.60972 - 1.18692i) q^{4} +(-0.721676 + 0.860059i) q^{5} +(-2.33994 + 0.724346i) q^{6} +(1.31793 + 0.479686i) q^{7} +(-1.63827 + 2.30566i) q^{8} +(2.99817 + 0.104825i) q^{9} +(0.589610 - 1.47424i) q^{10} +(1.05816 + 1.26106i) q^{11} +(2.82362 - 2.00678i) q^{12} +(-0.671077 - 0.118329i) q^{13} +(-1.98247 - 0.0622489i) q^{14} +(-1.27582 + 1.46760i) q^{15} +(1.18243 - 3.82124i) q^{16} +(0.907443 - 1.57174i) q^{17} +(-4.07420 + 1.18359i) q^{18} +(2.96777 - 1.71344i) q^{19} +(-0.140874 + 2.24103i) q^{20} +(2.26785 + 0.870601i) q^{21} +(-1.97865 - 1.22674i) q^{22} +(-3.62278 + 1.31858i) q^{23} +(-2.90692 + 3.94333i) q^{24} +(0.649354 + 3.68267i) q^{25} +(0.953831 - 0.137475i) q^{26} +(5.18901 + 0.272275i) q^{27} +(2.69085 - 0.792115i) q^{28} +(3.92395 - 0.691898i) q^{29} +(1.06570 - 2.53523i) q^{30} +(-6.21468 + 2.26196i) q^{31} +(0.0994769 + 5.65598i) q^{32} +(1.79434 + 2.21592i) q^{33} +(-0.524800 + 2.51241i) q^{34} +(-1.36367 + 0.787317i) q^{35} +(4.95064 - 3.38986i) q^{36} +(3.83532 + 2.21432i) q^{37} +(-3.23015 + 3.61292i) q^{38} +(-1.15858 - 0.225231i) q^{39} +(-0.800705 - 3.07295i) q^{40} +(0.952217 - 5.40029i) q^{41} +(-3.43133 - 0.167801i) q^{42} +(-7.26017 - 8.65234i) q^{43} +(3.20013 + 0.774013i) q^{44} +(-2.25386 + 2.50295i) q^{45} +(4.28455 - 3.37179i) q^{46} +(-11.5469 - 4.20273i) q^{47} +(2.16336 - 6.58178i) q^{48} +(-3.85548 - 3.23513i) q^{49} +(-2.49917 - 4.66064i) q^{50} +(1.61907 - 2.69445i) q^{51} +(-1.22070 + 0.606040i) q^{52} -6.89741i q^{53} +(-7.09147 + 1.92643i) q^{54} -1.84824 q^{55} +(-3.26511 + 2.25283i) q^{56} +(5.19140 - 2.87750i) q^{57} +(-4.96599 + 2.66291i) q^{58} +(-6.78921 + 8.09106i) q^{59} +(-0.311789 + 3.87673i) q^{60} +(1.24084 - 3.40917i) q^{61} +(7.34992 - 5.78413i) q^{62} +(3.90108 + 1.57633i) q^{63} +(-2.63214 - 7.55459i) q^{64} +(0.586070 - 0.491771i) q^{65} +(-3.38948 - 2.18434i) q^{66} +(-11.9425 - 2.10578i) q^{67} +(-0.404798 - 3.60713i) q^{68} +(-6.31378 + 2.17386i) q^{69} +(1.48424 - 1.66012i) q^{70} +(6.80355 - 11.7841i) q^{71} +(-5.15350 + 6.74102i) q^{72} +(4.73823 + 8.20685i) q^{73} +(-6.13073 - 1.28061i) q^{74} +(1.01309 + 6.39725i) q^{75} +(2.74357 - 6.28068i) q^{76} +(0.789660 + 2.16957i) q^{77} +(1.65599 - 0.209209i) q^{78} +(1.59290 + 9.03380i) q^{79} +(2.43316 + 3.77465i) q^{80} +(8.97802 + 0.628568i) q^{81} +(1.10629 + 7.67567i) q^{82} +(1.29853 - 0.228966i) q^{83} +(4.68395 - 1.29034i) q^{84} +(0.696908 + 1.91474i) q^{85} +(13.5758 + 8.41686i) q^{86} +(6.81638 - 1.07946i) q^{87} +(-4.64114 + 0.373789i) q^{88} +(-3.52339 - 6.10270i) q^{89} +(1.92229 - 4.35823i) q^{90} +(-0.827669 - 0.477855i) q^{91} +(-4.26662 + 6.42251i) q^{92} +(-10.8310 + 3.72914i) q^{93} +(17.3692 + 0.545389i) q^{94} +(-0.668104 + 3.78901i) q^{95} +(0.00109395 + 9.79796i) q^{96} +(-6.33275 + 5.31381i) q^{97} +(6.60875 + 2.64311i) q^{98} +(3.04035 + 3.89180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

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