LMFDB - Embedded newform 216.2.v.b.11.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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([9, 9, 13]))

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (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:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.30
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39125 + 0.253795i) q^{2} +(-1.72369 + 0.169964i) q^{3} +(1.87118 + 0.706186i) q^{4} +(-0.715441 - 0.260399i) q^{5} +(-2.44123 - 0.201001i) q^{6} +(3.32699 + 0.586638i) q^{7} +(2.42406 + 1.45738i) q^{8} +(2.94222 - 0.585931i) q^{9} +O(q^{10})$	\(q+(1.39125 + 0.253795i) q^{2} +(-1.72369 + 0.169964i) q^{3} +(1.87118 + 0.706186i) q^{4} +(-0.715441 - 0.260399i) q^{5} +(-2.44123 - 0.201001i) q^{6} +(3.32699 + 0.586638i) q^{7} +(2.42406 + 1.45738i) q^{8} +(2.94222 - 0.585931i) q^{9} +(-0.929272 - 0.543857i) q^{10} +(1.95175 + 5.36238i) q^{11} +(-3.34536 - 0.899214i) q^{12} +(-3.36983 - 4.01601i) q^{13} +(4.47981 + 1.66054i) q^{14} +(1.27746 + 0.327249i) q^{15} +(3.00260 + 2.64280i) q^{16} +(-2.95820 + 1.70792i) q^{17} +(4.24209 - 0.0684577i) q^{18} +(1.27164 - 2.20255i) q^{19} +(-1.15483 - 0.992487i) q^{20} +(-5.83441 - 0.445715i) q^{21} +(1.35443 + 7.95577i) q^{22} +(-0.947065 - 5.37107i) q^{23} +(-4.42603 - 2.10007i) q^{24} +(-3.38617 - 2.84134i) q^{25} +(-3.66905 - 6.44253i) q^{26} +(-4.97190 + 1.51004i) q^{27} +(5.81111 + 3.44718i) q^{28} +(-3.27434 - 2.74749i) q^{29} +(1.69421 + 0.779498i) q^{30} +(-2.33080 + 0.410982i) q^{31} +(3.50665 + 4.43885i) q^{32} +(-4.27562 - 8.91136i) q^{33} +(-4.54907 + 1.62537i) q^{34} +(-2.22751 - 1.28605i) q^{35} +(5.91920 + 0.981378i) q^{36} +(9.07767 - 5.24099i) q^{37} +(2.32817 - 2.74157i) q^{38} +(6.49112 + 6.34960i) q^{39} +(-1.35477 - 1.67389i) q^{40} +(1.88727 + 2.24916i) q^{41} +(-8.00403 - 2.10085i) q^{42} +(-5.95761 + 2.16839i) q^{43} +(-0.134776 + 11.4123i) q^{44} +(-2.25756 - 0.346954i) q^{45} +(0.0455422 - 7.71289i) q^{46} +(-0.625921 + 3.54977i) q^{47} +(-5.62474 - 4.04503i) q^{48} +(4.14688 + 1.50934i) q^{49} +(-3.98991 - 4.81242i) q^{50} +(4.80874 - 3.44671i) q^{51} +(-3.46950 - 9.89438i) q^{52} -8.06569 q^{53} +(-7.30042 + 0.839002i) q^{54} -4.34470i q^{55} +(7.20986 + 6.27073i) q^{56} +(-1.81756 + 4.01265i) q^{57} +(-3.85813 - 4.65347i) q^{58} +(-1.63379 + 4.48880i) q^{59} +(2.15925 + 1.51446i) q^{60} +(2.62747 + 0.463294i) q^{61} +(-3.34703 - 0.0197632i) q^{62} +(10.1325 - 0.223366i) q^{63} +(3.75209 + 7.06554i) q^{64} +(1.36515 + 3.75071i) q^{65} +(-3.68682 - 13.4831i) q^{66} +(2.16648 - 1.81790i) q^{67} +(-6.74143 + 1.10678i) q^{68} +(2.54534 + 9.09710i) q^{69} +(-2.77263 - 2.35455i) q^{70} +(-3.03884 - 5.26343i) q^{71} +(7.98604 + 2.86761i) q^{72} +(1.40736 - 2.43763i) q^{73} +(13.9595 - 4.98769i) q^{74} +(6.31965 + 4.32206i) q^{75} +(3.93488 - 3.22334i) q^{76} +(3.34767 + 18.9856i) q^{77} +(7.41930 + 10.4813i) q^{78} +(-7.42577 + 8.84969i) q^{79} +(-1.46000 - 2.67264i) q^{80} +(8.31337 - 3.44788i) q^{81} +(2.05484 + 3.60813i) q^{82} +(5.47239 - 6.52174i) q^{83} +(-10.6025 - 4.95419i) q^{84} +(2.56116 - 0.451602i) q^{85} +(-8.83888 + 1.50478i) q^{86} +(6.11092 + 4.17931i) q^{87} +(-3.08388 + 15.8431i) q^{88} +(-7.79000 - 4.49756i) q^{89} +(-3.05279 - 1.05566i) q^{90} +(-8.85545 - 15.3381i) q^{91} +(2.02085 - 10.7190i) q^{92} +(3.94772 - 1.10456i) q^{93} +(-1.77173 + 4.77978i) q^{94} +(-1.48333 + 1.24466i) q^{95} +(-6.79883 - 7.05520i) q^{96} +(13.6755 - 4.97747i) q^{97} +(5.38630 + 3.15233i) q^{98} +(8.88446 + 14.6337i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	1.39125	+	0.253795i	0.983765	+	0.179460i
$2$	1.39125	+	0.253795i	0.983765	+	0.179460i
$3$	−1.72369	+	0.169964i	−0.995174	+	0.0981288i
$3$	−1.72369	+	0.169964i	−0.995174	+	0.0981288i
$4$	1.87118	+	0.706186i	0.935588	+	0.353093i
$5$	−0.715441	−	0.260399i	−0.319955	−	0.116454i	0.177050	−	0.984202i	$-0.443345\pi$
$5$	−0.715441	−	0.260399i	−0.319955	−	0.116454i	−0.497005	+	0.867748i	$0.665567\pi$
$6$	−2.44123	−	0.201001i	−0.996628	−	0.0820582i
$7$	3.32699	+	0.586638i	1.25748	+	0.221728i	0.762394	−	0.647113i	$-0.224024\pi$
$7$	3.32699	+	0.586638i	1.25748	+	0.221728i	0.495091	+	0.868841i	$0.335135\pi$
$8$	2.42406	+	1.45738i	0.857033	+	0.515261i
$9$	2.94222	−	0.585931i	0.980741	−	0.195310i
$10$	−0.929272	−	0.543857i	−0.293862	−	0.171983i
$11$	1.95175	+	5.36238i	0.588474	+	1.61682i	0.773296	+	0.634046i	$0.218607\pi$
$11$	1.95175	+	5.36238i	0.588474	+	1.61682i	−0.184822	+	0.982772i	$0.559171\pi$
$12$	−3.34536	−	0.899214i	−0.965721	−	0.259581i
$13$	−3.36983	−	4.01601i	−0.934622	−	1.11384i	−0.993300	−	0.115563i	$-0.963133\pi$
$13$	−3.36983	−	4.01601i	−0.934622	−	1.11384i	0.0586778	−	0.998277i	$-0.481312\pi$
$14$	4.47981	+	1.66054i	1.19728	+	0.443797i
$15$	1.27746	+	0.327249i	0.329838	+	0.0844952i
$16$	3.00260	+	2.64280i	0.750651	+	0.660699i
$17$	−2.95820	+	1.70792i	−0.717470	+	0.414231i	−0.813821	−	0.581116i	$-0.802616\pi$
$17$	−2.95820	+	1.70792i	−0.717470	+	0.414231i	0.0963510	+	0.995347i	$0.469283\pi$
$18$	4.24209	−	0.0684577i	0.999870	−	0.0161356i
$19$	1.27164	−	2.20255i	0.291735	−	0.505299i	−0.682485	−	0.730899i	$-0.739101\pi$
$19$	1.27164	−	2.20255i	0.291735	−	0.505299i	0.974220	+	0.225600i	$0.0724342\pi$
$20$	−1.15483	−	0.992487i	−0.258227	−	0.221927i
$21$	−5.83441	−	0.445715i	−1.27317	−	0.0972629i
$22$	1.35443	+	7.95577i	0.288766	+	1.69618i
$23$	−0.947065	−	5.37107i	−0.197477	−	1.11995i	−0.908847	−	0.417129i	$-0.863036\pi$
$23$	−0.947065	−	5.37107i	−0.197477	−	1.11995i	0.711371	−	0.702817i	$-0.248075\pi$
$24$	−4.42603	−	2.10007i	−0.903459	−	0.428675i
$25$	−3.38617	−	2.84134i	−0.677235	−	0.568268i
$26$	−3.66905	−	6.44253i	−0.719559	−	1.26348i
$27$	−4.97190	+	1.51004i	−0.956843	+	0.290607i
$28$	5.81111	+	3.44718i	1.09820	+	0.651456i
$29$	−3.27434	−	2.74749i	−0.608029	−	0.510197i	0.285986	−	0.958234i	$-0.407679\pi$
$29$	−3.27434	−	2.74749i	−0.608029	−	0.510197i	−0.894015	+	0.448037i	$0.852123\pi$
$30$	1.69421	+	0.779498i	0.309320	+	0.142316i
$31$	−2.33080	+	0.410982i	−0.418623	+	0.0738146i	−0.378992	−	0.925400i	$-0.623729\pi$
$31$	−2.33080	+	0.410982i	−0.418623	+	0.0738146i	−0.0396309	+	0.999214i	$0.512618\pi$
$32$	3.50665	+	4.43885i	0.619895	+	0.784685i
$33$	−4.27562	−	8.91136i	−0.744290	−	1.55127i
$34$	−4.54907	+	1.62537i	−0.780160	+	0.278749i
$35$	−2.22751	−	1.28605i	−0.376517	−	0.217382i
$36$	5.91920	+	0.981378i	0.986533	+	0.163563i
$37$	9.07767	−	5.24099i	1.49236	−	0.861614i	0.492398	−	0.870370i	$-0.336121\pi$
$37$	9.07767	−	5.24099i	1.49236	−	0.861614i	0.999962	+	0.00875627i	$0.00278724\pi$
$38$	2.32817	−	2.74157i	0.377679	−	0.444741i
$39$	6.49112	+	6.34960i	1.03941	+	1.01675i
$40$	−1.35477	−	1.67389i	−0.214208	−	0.264665i
$41$	1.88727	+	2.24916i	0.294742	+	0.351259i	0.893010	−	0.450036i	$-0.148589\pi$
$41$	1.88727	+	2.24916i	0.294742	+	0.351259i	−0.598269	+	0.801296i	$0.704144\pi$
$42$	−8.00403	−	2.10085i	−1.23505	−	0.324168i
$43$	−5.95761	+	2.16839i	−0.908528	+	0.330677i	−0.753665	−	0.657259i	$-0.771716\pi$
$43$	−5.95761	+	2.16839i	−0.908528	+	0.330677i	−0.154863	+	0.987936i	$0.549494\pi$
$44$	−0.134776	+	11.4123i	−0.0203183	+	1.72046i
$45$	−2.25756	−	0.346954i	−0.336538	−	0.0517208i
$46$	0.0455422	−	7.71289i	0.00671483	−	1.13720i
$47$	−0.625921	+	3.54977i	−0.0913000	+	0.517788i	0.904519	+	0.426434i	$0.140230\pi$
$47$	−0.625921	+	3.54977i	−0.0913000	+	0.517788i	−0.995819	+	0.0913536i	$0.970881\pi$
$48$	−5.62474	−	4.04503i	−0.811861	−	0.583850i
$49$	4.14688	+	1.50934i	0.592412	+	0.215620i
$50$	−3.98991	−	4.81242i	−0.564259	−	0.680578i
$51$	4.80874	−	3.44671i	0.673359	−	0.482637i
$52$	−3.46950	−	9.89438i	−0.481133	−	1.37210i
$53$	−8.06569			−1.10791			−0.553954	−	0.832548i	$-0.686882\pi$
$53$	−8.06569			−1.10791			−0.553954	+	0.832548i	$0.686882\pi$
$54$	−7.30042	+	0.839002i	−0.993461	+	0.114174i
$55$		−	4.34470i		−	0.585839i
$56$	7.20986	+	6.27073i	0.963458	+	0.837962i
$57$	−1.81756	+	4.01265i	−0.240742	+	0.531488i
$58$	−3.85813	−	4.65347i	−0.506598	−	0.611031i
$59$	−1.63379	+	4.48880i	−0.212701	+	0.584392i	−0.999460	−	0.0328691i	$-0.989536\pi$
$59$	−1.63379	+	4.48880i	−0.212701	+	0.584392i	0.786758	+	0.617261i	$0.211758\pi$
$60$	2.15925	+	1.51446i	0.278758	+	0.195516i
$61$	2.62747	+	0.463294i	0.336413	+	0.0593187i	0.339303	−	0.940677i	$-0.389809\pi$
$61$	2.62747	+	0.463294i	0.336413	+	0.0593187i	−0.00289009	+	0.999996i	$0.500920\pi$
$62$	−3.34703	−	0.0197632i	−0.425074	−	0.00250993i
$63$	10.1325	−	0.223366i	1.27657	−	0.0281415i
$64$	3.75209	+	7.06554i	0.469011	+	0.883192i
$65$	1.36515	+	3.75071i	0.169326	+	0.465219i
$66$	−3.68682	−	13.4831i	−0.453816	−	1.65965i
$67$	2.16648	−	1.81790i	0.264678	−	0.222091i	−0.500784	−	0.865572i	$-0.666955\pi$
$67$	2.16648	−	1.81790i	0.264678	−	0.222091i	0.765462	+	0.643481i	$0.222510\pi$
$68$	−6.74143	+	1.10678i	−0.817518	+	0.134216i
$69$	2.54534	+	9.09710i	0.306422	+	1.09516i
$70$	−2.77263	−	2.35455i	−0.331393	−	0.281423i
$71$	−3.03884	−	5.26343i	−0.360644	−	0.624654i	0.627423	−	0.778679i	$-0.284110\pi$
$71$	−3.03884	−	5.26343i	−0.360644	−	0.624654i	−0.988067	+	0.154025i	$0.950776\pi$
$72$	7.98604	+	2.86761i	0.941164	+	0.337951i
$73$	1.40736	−	2.43763i	0.164720	−	0.285303i	−0.771836	−	0.635822i	$-0.780661\pi$
$73$	1.40736	−	2.43763i	0.164720	−	0.285303i	0.936556	+	0.350519i	$0.113995\pi$
$74$	13.9595	−	4.98769i	1.62276	−	0.579807i
$75$	6.31965	+	4.32206i	0.729730	+	0.499069i
$76$	3.93488	−	3.22334i	0.451361	−	0.369743i
$77$	3.34767	+	18.9856i	0.381502	+	2.16360i
$78$	7.41930	+	10.4813i	0.840071	+	1.18678i
$79$	−7.42577	+	8.84969i	−0.835464	+	0.995667i	0.164493	+	0.986378i	$0.447401\pi$
$79$	−7.42577	+	8.84969i	−0.835464	+	0.995667i	−0.999957	+	0.00928911i	$0.997043\pi$
$80$	−1.46000	−	2.67264i	−0.163233	−	0.298810i
$81$	8.31337	−	3.44788i	0.923708	−	0.383098i
$82$	2.05484	+	3.60813i	0.226919	+	0.398451i
$83$	5.47239	−	6.52174i	0.600673	−	0.715854i	−0.376947	−	0.926235i	$-0.623026\pi$
$83$	5.47239	−	6.52174i	0.600673	−	0.715854i	0.977620	+	0.210381i	$0.0674704\pi$
$84$	−10.6025	−	4.95419i	−1.15682	−	0.540547i
$85$	2.56116	−	0.451602i	0.277797	−	0.0489831i
$86$	−8.83888	+	1.50478i	−0.953121	+	0.162264i
$87$	6.11092	+	4.17931i	0.655159	+	0.448069i
$88$	−3.08388	+	15.8431i	−0.328743	+	1.68888i
$89$	−7.79000	−	4.49756i	−0.825739	−	0.476740i	0.0266528	−	0.999645i	$-0.491515\pi$
$89$	−7.79000	−	4.49756i	−0.825739	−	0.476740i	−0.852391	+	0.522904i	$0.824848\pi$
$90$	−3.05279	−	1.05566i	−0.321792	−	0.111276i
$91$	−8.85545	−	15.3381i	−0.928303	−	1.60787i
$92$	2.02085	−	10.7190i	0.210688	−	1.11754i
$93$	3.94772	−	1.10456i	0.409360	−	0.114537i
$94$	−1.77173	+	4.77978i	−0.182740	+	0.492997i
$95$	−1.48333	+	1.24466i	−0.152186	+	0.127699i
$96$	−6.79883	−	7.05520i	−0.693903	−	0.720068i
$97$	13.6755	−	4.97747i	1.38854	−	0.505386i	0.463781	−	0.885950i	$-0.346492\pi$
$97$	13.6755	−	4.97747i	1.38854	−	0.505386i	0.924755	+	0.380564i	$0.124270\pi$
$98$	5.38630	+	3.15233i	0.544099	+	0.318434i
$99$	8.88446	+	14.6337i	0.892922	+	1.47075i
$100$	−4.32962	−	7.70791i	−0.432962	−	0.770791i
$101$	−0.867234	+	4.91833i	−0.0862930	+	0.489392i	0.910777	+	0.412898i	$0.135484\pi$
$101$	−0.867234	+	4.91833i	−0.0862930	+	0.489392i	−0.997070	+	0.0764934i	$0.975628\pi$
$102$	7.56494	−	3.57482i	0.749041	−	0.353960i
$103$	1.64778	−	4.52724i	0.162360	−	0.446082i	−0.831659	−	0.555287i	$-0.812608\pi$
$103$	1.64778	−	4.52724i	0.162360	−	0.446082i	0.994019	+	0.109205i	$0.0348306\pi$
$104$	−2.31581	−	14.6461i	−0.227084	−	1.43617i
$105$	4.05811	+	1.83816i	0.396031	+	0.179386i
$106$	−11.2214	−	2.04703i	−1.08992	−	0.198825i
$107$		−	2.56818i		−	0.248275i	−0.992265	−	0.124138i	$-0.960384\pi$
$107$		−	2.56818i		−	0.248275i	0.992265	−	0.124138i	$-0.0396164\pi$
$108$	−10.3697	−	0.685542i	−0.997822	−	0.0659663i
$109$		−	7.69169i		−	0.736730i	−0.929681	−	0.368365i	$-0.879918\pi$
$109$		−	7.69169i		−	0.736730i	0.929681	−	0.368365i	$-0.120082\pi$
$110$	1.10266	−	6.04458i	0.105135	−	0.576328i
$111$	−14.7563	+	10.5767i	−1.40061	+	1.00390i
$112$	8.43927	+	10.5540i	0.797436	+	0.997260i
$113$	−2.07354	+	5.69700i	−0.195062	+	0.535928i	−0.998207	−	0.0598551i	$-0.980936\pi$
$113$	−2.07354	+	5.69700i	−0.195062	+	0.535928i	0.803145	+	0.595783i	$0.203158\pi$
$114$	−3.54708	+	5.12132i	−0.332215	+	0.479656i
$115$	−0.721054	+	4.08930i	−0.0672386	+	0.381329i
$116$	−4.18662	−	7.45334i	−0.388718	−	0.692025i
$117$	−12.2679	−	9.84150i	−1.13417	−	0.909847i
$118$	−3.41225	+	5.83042i	−0.314123	+	0.536733i
$119$	−10.8438	+	3.94684i	−0.994054	+	0.361806i
$120$	2.61970	+	2.65501i	0.239145	+	0.242368i
$121$	−16.5193	+	13.8613i	−1.50175	+	1.26012i
$122$	3.53789	+	1.31140i	0.320306	+	0.118728i
$123$	−3.63534	−	3.55609i	−0.327788	−	0.320641i
$124$	−4.65156	−	0.876956i	−0.417722	−	0.0787529i
$125$	3.58612	+	6.21133i	0.320752	+	0.555559i
$126$	14.1536	+	2.26081i	1.26090	+	0.201409i
$127$	2.68591	+	1.55071i	0.238336	+	0.137603i	0.614412	−	0.788986i	$-0.289393\pi$
$127$	2.68591	+	1.55071i	0.238336	+	0.137603i	−0.376076	+	0.926589i	$0.622727\pi$
$128$	3.42692	+	10.7822i	0.302899	+	0.953023i
$129$	9.90054	−	4.75022i	0.871694	−	0.418234i
$130$	0.947357	+	5.56466i	0.0830887	+	0.488053i
$131$	15.9872	−	2.81898i	1.39681	−	0.246295i	0.575978	−	0.817465i	$-0.304621\pi$
$131$	15.9872	−	2.81898i	1.39681	−	0.246295i	0.820832	+	0.571170i	$0.193510\pi$
$132$	−1.70736	−	19.6941i	−0.148607	−	1.71415i
$133$	5.52284	−	6.58187i	0.478891	−	0.570720i
$134$	3.47550	−	1.97931i	0.300238	−	0.170987i
$135$	3.95031	+	0.214337i	0.339989	+	0.0184472i
$136$	−9.65994	−	0.171133i	−0.828333	−	0.0146745i
$137$	0.0788460	−	0.0939650i	0.00673627	−	0.00802797i	−0.762666	−	0.646793i	$-0.776110\pi$
$137$	0.0788460	−	0.0939650i	0.00673627	−	0.00802797i	0.769402	+	0.638765i	$0.220554\pi$
$138$	1.23241	+	13.3024i	0.104910	+	1.13237i
$139$	2.78791	+	15.8110i	0.236467	+	1.34107i	0.839502	+	0.543357i	$0.182847\pi$
$139$	2.78791	+	15.8110i	0.236467	+	1.34107i	−0.603035	+	0.797715i	$0.706042\pi$
$140$	−3.25986	−	3.97946i	−0.275509	−	0.336326i
$141$	0.475561	−	6.22510i	0.0400494	−	0.524248i
$142$	−2.89197	−	8.09401i	−0.242689	−	0.679234i
$143$	14.9583	−	25.9085i	1.25088	−	2.16658i
$144$	10.3828	+	6.01639i	0.865236	+	0.501366i
$145$	1.62715	+	2.81830i	0.135127	+	0.234047i
$146$	2.57666	−	3.03418i	0.213246	−	0.251110i
$147$	−7.40448	−	1.89682i	−0.610711	−	0.156447i
$148$	20.6870	−	3.39630i	1.70046	−	0.279174i
$149$	14.4253	−	12.1043i	1.18177	−	0.991623i	0.181805	−	0.983335i	$-0.441806\pi$
$149$	14.4253	−	12.1043i	1.18177	−	0.991623i	0.999966	−	0.00828872i	$-0.00263841\pi$
$150$	7.69532	+	7.61698i	0.628320	+	0.621924i
$151$	5.65105	+	15.5261i	0.459876	+	1.26350i	0.925578	+	0.378557i	$0.123580\pi$
$151$	5.65105	+	15.5261i	0.459876	+	1.26350i	−0.465702	+	0.884942i	$0.654198\pi$
$152$	6.29248	−	3.48584i	0.510387	−	0.282739i
$153$	−7.70298	+	6.75839i	−0.622749	+	0.546383i
$154$	−0.160982	+	27.2634i	−0.0129723	+	2.19694i
$155$	1.77457	+	0.312904i	0.142537	+	0.0251330i
$156$	7.66203	+	16.4652i	0.613453	+	1.31827i
$157$	−3.99126	+	10.9659i	−0.318537	+	0.875174i	0.672320	+	0.740260i	$0.265298\pi$
$157$	−3.99126	+	10.9659i	−0.318537	+	0.875174i	−0.990857	+	0.134913i	$0.956924\pi$
$158$	−12.5771	+	10.4275i	−1.00058	+	0.829571i
$159$	13.9028	−	1.37088i	1.10256	−	0.108718i
$160$	−1.35293	−	4.08886i	−0.106959	−	0.323253i
$161$		−	18.4251i		−	1.45210i
$162$	12.4411	−	2.68699i	0.977462	−	0.211110i
$163$	2.29194			0.179518			0.0897591	−	0.995964i	$-0.471390\pi$
$163$	2.29194			0.179518			0.0897591	+	0.995964i	$0.471390\pi$
$164$	1.94309	+	5.54133i	0.151729	+	0.432705i
$165$	0.738442	+	7.48892i	0.0574876	+	0.583011i
$166$	9.26867	−	7.68454i	0.719388	−	0.596436i
$167$	−7.85034	−	2.85729i	−0.607478	−	0.221104i	0.0199215	−	0.999802i	$-0.493658\pi$
$167$	−7.85034	−	2.85729i	−0.607478	−	0.221104i	−0.627399	+	0.778698i	$0.715881\pi$
$168$	−13.4934	−	9.58339i	−1.04104	−	0.739375i
$169$	−2.51513	+	14.2640i	−0.193471	+	1.09723i
$170$	3.67784	+	0.0217165i	0.282077	+	0.00166558i
$171$	2.45091	−	7.22549i	0.187426	−	0.552547i
$172$	−12.6790	−	0.149737i	−0.966767	−	0.0114173i
$173$	−4.31220	+	1.56951i	−0.327850	+	0.119328i	−0.500701	−	0.865620i	$-0.666924\pi$
$173$	−4.31220	+	1.56951i	−0.327850	+	0.119328i	0.172851	+	0.984948i	$0.444702\pi$
$174$	7.44116	+	7.36541i	0.564113	+	0.558370i
$175$	−9.59894	−	11.4396i	−0.725611	−	0.864750i
$176$	−8.31136	+	21.2592i	−0.626493	+	1.60247i
$177$	2.05321	−	8.01499i	0.154329	−	0.602444i
$178$	−9.69641	−	8.23431i	−0.726777	−	0.617188i
$179$	−8.01534	+	4.62766i	−0.599094	+	0.345887i	−0.768685	−	0.639627i	$-0.779089\pi$
$179$	−8.01534	+	4.62766i	−0.599094	+	0.345887i	0.169591	+	0.985515i	$0.445755\pi$
$180$	−3.97928	−	2.24347i	−0.296598	−	0.167218i
$181$	10.1708	+	5.87212i	0.755990	+	0.436471i	0.827854	−	0.560943i	$-0.189561\pi$
$181$	10.1708	+	5.87212i	0.755990	+	0.436471i	−0.0718639	+	0.997414i	$0.522895\pi$
$182$	−8.42745	−	23.5866i	−0.624684	−	1.74836i
$183$	−4.60769	−	0.352000i	−0.340610	−	0.0260206i
$184$	5.53195	−	14.4000i	0.407821	−	1.06158i
$185$	−7.85928	+	1.38580i	−0.577826	+	0.101886i
$186$	5.77261	−	0.534810i	0.423269	−	0.0392142i
$187$	−14.9322	−	12.5296i	−1.09195	−	0.916254i
$188$	−3.67801	+	6.20024i	−0.268246	+	0.452199i
$189$	−17.4273	+	2.10717i	−1.26765	+	0.153274i
$190$	−2.37957	+	1.35518i	−0.172632	+	0.0983148i
$191$	−9.19786	−	7.71792i	−0.665534	−	0.558449i	0.246206	−	0.969218i	$-0.420816\pi$
$191$	−9.19786	−	7.71792i	−0.665534	−	0.558449i	−0.911740	+	0.410768i	$0.865260\pi$
$192$	−7.66833	−	11.5411i	−0.553414	−	0.832906i
$193$	0.0875504	+	0.496523i	0.00630202	+	0.0357405i	0.987797	−	0.155749i	$-0.0497792\pi$
$193$	0.0875504	+	0.496523i	0.00630202	+	0.0357405i	−0.981495	+	0.191490i	$0.938668\pi$
$194$	20.2893	−	3.45416i	1.45669	−	0.247994i
$195$	−2.99058	−	6.23305i	−0.214160	−	0.446358i
$196$	6.69367	+	5.75271i	0.478119	+	0.410908i
$197$	1.86464	−	3.22964i	0.132850	−	0.230103i	−0.791924	−	0.610619i	$-0.790921\pi$
$197$	1.86464	−	3.22964i	0.132850	−	0.230103i	0.924774	+	0.380517i	$0.124254\pi$
$198$	8.64657	+	22.6141i	0.614485	+	1.60711i
$199$	−22.4920	+	12.9857i	−1.59441	+	0.920534i	−0.601876	+	0.798590i	$0.705580\pi$
$199$	−22.4920	+	12.9857i	−1.59441	+	0.920534i	−0.992537	+	0.121945i	$0.961087\pi$
$200$	−4.06737	−	11.8225i	−0.287606	−	0.835977i
$201$	−3.42537	+	3.50171i	−0.241607	+	0.246992i
$202$	−2.45479	+	6.62254i	−0.172718	+	0.465960i
$203$	−9.28190	−	11.0617i	−0.651462	−	0.776382i
$204$	11.4320	−	3.05354i	0.800402	−	0.213791i
$205$	−0.764549	−	2.10058i	−0.0533984	−	0.146711i
$206$	3.44147	−	5.88034i	0.239778	−	0.409703i
$207$	−5.93355	−	15.2480i	−0.412411	−	1.05981i
$208$	0.495236	−	20.9642i	0.0343384	−	1.45361i
$209$	14.2928	+	2.52021i	0.988655	+	0.174327i
$210$	5.17935	+	3.58727i	0.357409	+	0.247545i
$211$	−5.28560	−	1.92380i	−0.363875	−	0.132440i	0.153611	−	0.988131i	$-0.450910\pi$
$211$	−5.28560	−	1.92380i	−0.363875	−	0.132440i	−0.517486	+	0.855692i	$0.673132\pi$
$212$	−15.0923	−	5.69588i	−1.03655	−	0.391194i
$213$	6.13262	+	8.55603i	0.420200	+	0.586250i
$214$	0.651790	−	3.57299i	0.0445555	−	0.244244i
$215$	4.82697			0.329196
$216$	−14.2529	−	3.58553i	−0.969784	−	0.243965i
$217$	−7.99564			−0.542779
$218$	1.95211	−	10.7011i	0.132214	−	0.724770i
$219$	−2.01155	+	4.44092i	−0.135928	+	0.300090i
$220$	3.06816	−	8.12969i	0.206856	−	0.548104i
$221$	16.8277	+	6.12476i	1.13195	+	0.411996i
$222$	−23.2141	+	10.9698i	−1.55803	+	0.736248i
$223$	−1.15220	−	0.203163i	−0.0771568	−	0.0136048i	0.134937	−	0.990854i	$-0.456917\pi$
$223$	−1.15220	−	0.203163i	−0.0771568	−	0.0136048i	−0.212093	+	0.977249i	$0.568028\pi$
$224$	9.06261	+	16.8252i	0.605521	+	1.12418i
$225$	−11.6277	−	6.37579i	−0.775181	−	0.425053i
$226$	−4.33069	+	7.39972i	−0.288073	+	0.492222i
$227$	−3.74301	−	10.2838i	−0.248432	−	0.682563i	−0.999744	−	0.0226152i	$-0.992801\pi$
$227$	−3.74301	−	10.2838i	−0.248432	−	0.682563i	0.751312	−	0.659947i	$-0.229421\pi$
$228$	−6.23466	+	6.22483i	−0.412900	+	0.412250i
$229$	3.60038	+	4.29076i	0.237920	+	0.283542i	0.871771	−	0.489913i	$-0.162971\pi$
$229$	3.60038	+	4.29076i	0.237920	+	0.283542i	−0.633852	+	0.773455i	$0.718527\pi$
$230$	−2.04101	+	5.50625i	−0.134580	+	0.363072i
$231$	−8.99720	−	32.1563i	−0.591973	−	2.11573i
$232$	−3.93303	−	11.4320i	−0.258216	−	0.750549i
$233$	−12.0089	+	6.93335i	−0.786730	+	0.454219i	−0.838810	−	0.544424i	$-0.816748\pi$
$233$	−12.0089	+	6.93335i	−0.786730	+	0.454219i	0.0520803	+	0.998643i	$0.483415\pi$
$234$	−14.5700	−	16.8056i	−0.952473	−	1.09861i
$235$	1.37217	−	2.37666i	0.0895103	−	0.155036i
$236$	−6.22704	+	7.24558i	−0.405346	+	0.471647i
$237$	11.2956	−	16.5162i	0.733728	−	1.07285i
$238$	−16.0882	+	2.73894i	−1.04285	+	0.177539i
$239$	3.00765	+	17.0573i	0.194549	+	1.10334i	0.913060	+	0.407826i	$0.133713\pi$
$239$	3.00765	+	17.0573i	0.194549	+	1.10334i	−0.718511	+	0.695516i	$0.755176\pi$
$240$	2.97084	+	4.35866i	0.191767	+	0.281350i
$241$	−1.47032	−	1.23374i	−0.0947115	−	0.0794724i	0.594202	−	0.804316i	$-0.297468\pi$
$241$	−1.47032	−	1.23374i	−0.0947115	−	0.0794724i	−0.688914	+	0.724843i	$0.741912\pi$
$242$	−26.5005	+	15.0921i	−1.70351	+	0.970159i
$243$	−13.7437	+	7.35606i	−0.881657	+	0.471891i
$244$	4.58929	+	2.72239i	0.293799	+	0.174283i
$245$	−2.57382	−	2.15969i	−0.164435	−	0.137977i
$246$	−4.15517	−	5.87005i	−0.264924	−	0.374261i
$247$	−13.1307	+	2.31529i	−0.835484	+	0.147318i
$248$	−6.24893	−	2.40061i	−0.396808	−	0.152439i
$249$	−8.32425	+	12.1716i	−0.527528	+	0.771343i
$250$	3.41279	+	9.55168i	0.215844	+	0.604101i
$251$	18.6528	+	10.7692i	1.17735	+	0.679746i	0.955401	−	0.295311i	$-0.0954234\pi$
$251$	18.6528	+	10.7692i	1.17735	+	0.679746i	0.221953	+	0.975057i	$0.428757\pi$
$252$	19.1174	+	6.73746i	1.20428	+	0.424420i
$253$	26.9533	−	15.5615i	1.69454	−	0.978342i
$254$	3.34322	+	2.83910i	0.209772	+	0.178141i
$255$	−4.33789	+	1.21373i	−0.271649	+	0.0760065i
$256$	2.03124	+	15.8705i	0.126952	+	0.991909i
$257$	−5.79174	−	6.90232i	−0.361279	−	0.430555i	0.554534	−	0.832161i	$-0.312897\pi$
$257$	−5.79174	−	6.90232i	−0.361279	−	0.430555i	−0.915813	+	0.401606i	$0.868452\pi$
$258$	14.9797	−	4.09606i	0.932598	−	0.255010i
$259$	33.2759	−	12.1114i	2.06766	−	0.752568i
$260$	−0.0942693	+	7.98230i	−0.00584634	+	0.495041i
$261$	−11.2437	−	6.16521i	−0.695966	−	0.381617i
$262$	22.9577	+	0.135558i	1.41833	+	0.00837482i
$263$	−1.07833	+	6.11552i	−0.0664927	+	0.377099i	0.933343	+	0.358985i	$0.116877\pi$
$263$	−1.07833	+	6.11552i	−0.0664927	+	0.377099i	−0.999836	+	0.0181137i	$0.994234\pi$
$264$	2.62289	−	27.8328i	0.161428	−	1.71299i
$265$	5.77052	+	2.10030i	0.354480	+	0.129020i
$266$	9.35412	−	7.75538i	0.573538	−	0.475513i
$267$	14.1920	+	6.42838i	0.868535	+	0.393411i
$268$	5.33764	−	1.87166i	0.326049	−	0.114330i
$269$	1.29437			0.0789188			0.0394594	−	0.999221i	$-0.487436\pi$
$269$	1.29437			0.0789188			0.0394594	+	0.999221i	$0.487436\pi$
$270$	5.44149	+	1.30077i	0.331159	+	0.0791621i
$271$		−	3.86099i		−	0.234539i	−0.993100	−	0.117269i	$-0.962586\pi$
$271$		−	3.86099i		−	0.234539i	0.993100	−	0.117269i	$-0.0374141\pi$
$272$	−13.3960	−	2.68973i	−0.812251	−	0.163089i
$273$	17.8710	+	24.9330i	1.08160	+	1.50902i
$274$	0.133543	−	0.110719i	0.00806761	−	0.00668875i
$275$	8.62737	−	23.7035i	0.520250	−	1.42938i
$276$	−1.66148	+	18.8198i	−0.100009	+	1.13282i
$277$	−24.2259	−	4.27169i	−1.45560	−	0.256661i	−0.610815	−	0.791774i	$-0.709158\pi$
$277$	−24.2259	−	4.27169i	−1.45560	−	0.256661i	−0.844780	+	0.535113i	$0.820269\pi$
$278$	−0.134064	+	22.7047i	−0.00804063	+	1.36174i
$279$	−6.61692	+	2.57489i	−0.396144	+	0.154154i
$280$	−3.52533	−	6.36378i	−0.210679	−	0.380309i
$281$	1.24545	+	3.42184i	0.0742972	+	0.204130i	0.971282	−	0.237932i	$-0.0764694\pi$
$281$	1.24545	+	3.42184i	0.0742972	+	0.204130i	−0.896985	+	0.442062i	$0.854247\pi$
$282$	2.24152	−	8.54000i	0.133481	−	0.508550i
$283$	2.81306	−	2.36044i	0.167219	−	0.140314i	−0.555338	−	0.831625i	$-0.687411\pi$
$283$	2.81306	−	2.36044i	0.167219	−	0.140314i	0.722557	+	0.691311i	$0.242967\pi$
$284$	−1.96925	−	11.9948i	−0.116853	−	0.711760i
$285$	2.34525	−	2.39752i	0.138921	−	0.142017i
$286$	27.3862	−	32.2490i	1.61938	−	1.90692i
$287$	4.95948	+	8.59007i	0.292749	+	0.507056i
$288$	12.9182	+	11.0054i	0.761214	+	0.648501i
$289$	−2.66602	+	4.61769i	−0.156825	+	0.271629i
$290$	1.54851	+	4.33394i	0.0909314	+	0.254498i
$291$	−22.7263	+	10.9040i	−1.33224	+	0.639202i
$292$	4.35485	−	3.56737i	0.254848	−	0.208765i
$293$	5.15756	+	29.2500i	0.301308	+	1.70880i	0.640394	+	0.768046i	$0.278771\pi$
$293$	5.15756	+	29.2500i	0.301308	+	1.70880i	−0.339086	+	0.940755i	$0.610118\pi$
$294$	−9.82011	−	4.51817i	−0.572720	−	0.263505i
$295$	2.33776	−	2.78603i	0.136110	−	0.162209i
$296$	29.6429	+	0.525145i	1.72296	+	0.0305235i
$297$	−17.8013	−	23.7140i	−1.03293	−	1.37603i
$298$	23.1413	−	13.1791i	1.34054	−	0.763444i
$299$	−18.3788	+	21.9030i	−1.06287	+	1.26668i
$300$	8.77299	+	12.5502i	0.506509	+	0.724585i
$301$	−21.0930	+	3.71926i	−1.21578	+	0.214375i
$302$	3.92160	+	23.0350i	0.225663	+	1.32552i
$303$	0.658905	−	8.62508i	0.0378531	−	0.495498i
$304$	9.63913	−	3.25268i	0.552842	−	0.186554i
$305$	−1.75916	−	1.01565i	−0.100729	−	0.0581559i
$306$	−12.4320	+	7.44766i	−0.710692	+	0.425754i
$307$	4.62536	+	8.01136i	0.263983	+	0.457232i	0.967297	−	0.253648i	$-0.0816303\pi$
$307$	4.62536	+	8.01136i	0.263983	+	0.457232i	−0.703314	+	0.710880i	$0.748297\pi$
$308$	−7.14326	+	37.8894i	−0.407025	+	2.15895i
$309$	−2.07080	+	8.08362i	−0.117803	+	0.459861i
$310$	2.38946	+	0.885704i	0.135712	+	0.0503046i
$311$	20.0930	−	16.8601i	1.13937	−	0.956046i	0.139953	−	0.990158i	$-0.455305\pi$
$311$	20.0930	−	16.8601i	1.13937	−	0.956046i	0.999418	+	0.0341122i	$0.0108604\pi$
$312$	6.48106	+	24.8518i	0.366918	+	1.40696i
$313$	18.7936	−	6.84033i	1.06228	−	0.386638i	0.248995	−	0.968505i	$-0.419900\pi$
$313$	18.7936	−	6.84033i	1.06228	−	0.386638i	0.813284	+	0.581866i	$0.197677\pi$
$314$	−8.33594	+	14.2434i	−0.470424	+	0.803801i
$315$	−7.30736	−	2.47869i	−0.411723	−	0.139658i
$316$	−20.1444	+	11.3153i	−1.13321	+	0.636538i
$317$	4.07115	−	23.0886i	0.228659	−	1.29679i	−0.626907	−	0.779094i	$-0.715680\pi$
$317$	4.07115	−	23.0886i	0.228659	−	1.29679i	0.855566	−	0.517694i	$-0.173209\pi$
$318$	19.6902	+	1.62121i	1.10417	+	0.0909129i
$319$	8.34243	−	22.9206i	0.467086	−	1.28331i
$320$	−0.844539	−	6.03201i	−0.0472112	−	0.337200i
$321$	0.436498	+	4.42675i	0.0243629	+	0.247077i
$322$	4.67619	−	25.6340i	0.260594	−	1.42853i
$323$			8.68745i			0.483383i
$324$	17.9906	−	0.580807i	0.999479	−	0.0322671i
$325$			23.1737i			1.28545i
$326$	3.18867	+	0.581681i	0.176604	+	0.0322164i
$327$	1.30731	+	13.2581i	0.0722945	+	0.733175i
$328$	1.29696	+	8.20254i	0.0716129	+	0.452910i
$329$	−4.16487	+	11.4429i	−0.229617	+	0.630866i
$330$	−0.873287	+	10.6064i	−0.0480729	+	0.583863i
$331$	−3.95158	+	22.4105i	−0.217198	+	1.23179i	0.659853	+	0.751395i	$0.270619\pi$
$331$	−3.95158	+	22.4105i	−0.217198	+	1.23179i	−0.877051	+	0.480397i	$0.840492\pi$
$332$	14.8454	−	8.33880i	0.814746	−	0.457651i
$333$	23.6377	−	20.7391i	1.29534	−	1.13649i
$334$	−10.1967	−	5.96759i	−0.557936	−	0.326532i
$335$	−2.02337	+	0.736446i	−0.110548	+	0.0402363i
$336$	−16.3405	−	16.7575i	−0.891447	−	0.914196i
$337$	24.5647	−	20.6122i	1.33812	−	1.12282i	0.356018	−	0.934479i	$-0.384134\pi$
$337$	24.5647	−	20.6122i	1.33812	−	1.12282i	0.982104	−	0.188338i	$-0.0603101\pi$
$338$	−7.11931	+	19.2065i	−0.387240	+	1.04470i
$339$	2.60585	−	10.1723i	0.141531	−	0.552483i
$340$	5.11130	+	0.963630i	0.277199	+	0.0522601i
$341$	−6.75296	−	11.6965i	−0.365693	−	0.633400i
$342$	5.24364	−	9.43046i	0.283543	−	0.509941i
$343$	−7.56875	−	4.36982i	−0.408674	−	0.235948i
$344$	−17.6018	−	3.42620i	−0.949023	−	0.184728i
$345$	0.547840	−	7.17124i	0.0294947	−	0.386087i
$346$	−6.39770	+	1.08918i	−0.343942	+	0.0585545i
$347$	14.5793	−	2.57072i	0.782658	−	0.138004i	0.231979	−	0.972721i	$-0.425480\pi$
$347$	14.5793	−	2.57072i	0.782658	−	0.138004i	0.550679	+	0.834717i	$0.314369\pi$
$348$	8.48324	+	12.1357i	0.454749	+	0.650541i
$349$	−16.2504	+	19.3665i	−0.869864	+	1.03666i	0.129121	+	0.991629i	$0.458784\pi$
$349$	−16.2504	+	19.3665i	−0.869864	+	1.03666i	−0.998985	+	0.0450350i	$0.985660\pi$
$350$	−10.4513	−	18.3515i	−0.558643	−	0.980929i
$351$	22.8188	+	14.8786i	1.21798	+	0.794162i
$352$	−16.9587	+	27.4675i	−0.903901	+	1.46402i
$353$	0.289344	−	0.344827i	0.0154002	−	0.0183533i	−0.758289	−	0.651918i	$-0.773965\pi$
$353$	0.289344	−	0.344827i	0.0154002	−	0.0183533i	0.773690	+	0.633565i	$0.218409\pi$
$354$	4.89071	−	10.6298i	0.259938	−	0.564967i
$355$	0.803519	+	4.55698i	0.0426464	+	0.241860i
$356$	−11.4004	−	13.9169i	−0.604217	−	0.737595i
$357$	18.0206	−	8.64620i	0.953753	−	0.457605i
$358$	−12.3258	+	4.40400i	−0.651441	+	0.232758i
$359$	−1.58856	+	2.75146i	−0.0838408	+	0.145216i	−0.904897	−	0.425631i	$-0.860052\pi$
$359$	−1.58856	+	2.75146i	−0.0838408	+	0.145216i	0.821056	+	0.570848i	$0.193385\pi$
$360$	−4.96682	−	4.13116i	−0.261774	−	0.217731i
$361$	6.26585	+	10.8528i	0.329782	+	0.571199i
$362$	12.6599	+	10.7509i	0.665388	+	0.565055i
$363$	26.1182	−	26.7003i	1.37085	−	1.40140i
$364$	−5.73856	−	34.9539i	−0.300782	−	1.83208i
$365$	−1.64164	+	1.37750i	−0.0859275	+	0.0721017i
$366$	−6.32113	−	1.65913i	−0.330411	−	0.0867241i
$367$	11.2504	+	30.9103i	0.587268	+	1.61351i	0.775476	+	0.631377i	$0.217510\pi$
$367$	11.2504	+	30.9103i	0.587268	+	1.61351i	−0.188208	+	0.982129i	$0.560268\pi$
$368$	11.3510	−	18.6301i	0.591712	−	0.971161i
$369$	6.87061	+	5.51172i	0.357670	+	0.286928i
$370$	−11.2860	−	0.0666402i	−0.586730	−	0.00346446i
$371$	−26.8345	−	4.73164i	−1.39318	−	0.245655i
$372$	8.16690	+	0.721003i	0.423434	+	0.0373823i
$373$	−4.07881	+	11.2064i	−0.211193	+	0.580247i	−0.999381	−	0.0351875i	$-0.988797\pi$
$373$	−4.07881	+	11.2064i	−0.211193	+	0.580247i	0.788188	+	0.615434i	$0.211019\pi$
$374$	−17.5945	−	21.2215i	−0.909790	−	1.09734i
$375$	−7.23706	−	10.0969i	−0.373720	−	0.521402i
$376$	−6.69064	+	7.69265i	−0.345043	+	0.396718i
$377$			22.4083i			1.15409i
$378$	−24.7806	−	1.49135i	−1.27458	−	0.0767068i
$379$	1.35817			0.0697646			0.0348823	−	0.999391i	$-0.488894\pi$
$379$	1.35817			0.0697646			0.0348823	+	0.999391i	$0.488894\pi$
$380$	−3.65453	+	1.28147i	−0.187473	+	0.0657381i
$381$	−4.89324	−	2.21644i	−0.250688	−	0.113551i
$382$	−10.8378	−	13.0720i	−0.554510	−	0.668819i
$383$	−27.9805	−	10.1841i	−1.42973	−	0.520381i	−0.492879	−	0.870098i	$-0.664056\pi$
$383$	−27.9805	−	10.1841i	−1.42973	−	0.520381i	−0.936855	+	0.349717i	$0.886278\pi$
$384$	−7.73953	−	18.0028i	−0.394956	−	0.918700i
$385$	2.54877	−	14.4548i	0.129897	−	0.736683i
$386$	−0.00421010	+	0.713010i	−0.000214289	+	0.0362912i
$387$	−16.2581	+	9.87065i	−0.826446	+	0.501753i
$388$	29.1043	+	0.343716i	1.47755	+	0.0174495i
$389$	5.43932	−	1.97975i	0.275784	−	0.100377i	−0.200426	−	0.979709i	$-0.564232\pi$
$389$	5.43932	−	1.97975i	0.275784	−	0.100377i	0.476210	+	0.879332i	$0.342010\pi$
$390$	−2.57874	−	9.43075i	−0.130580	−	0.477545i
$391$	11.9750	+	14.2712i	0.605600	+	0.721726i
$392$	7.85259	+	9.70231i	0.396616	+	0.490041i
$393$	−27.0779	+	7.57630i	−1.36590	+	0.382174i
$394$	3.41385	−	4.02002i	0.171987	−	0.202526i
$395$	7.61715	−	4.39776i	0.383260	−	0.221275i
$396$	6.29025	+	33.6564i	0.316097	+	1.69130i
$397$	−13.5494	−	7.82276i	−0.680026	−	0.392613i	0.119839	−	0.992793i	$-0.461762\pi$
$397$	−13.5494	−	7.82276i	−0.680026	−	0.392613i	−0.799865	+	0.600180i	$0.795096\pi$
$398$	−34.5877	+	12.3581i	−1.73373	+	0.619456i
$399$	−8.40099	+	12.2838i	−0.420576	+	0.614959i
$400$	−2.65825	−	17.4804i	−0.132913	−	0.874019i
$401$	32.9174	−	5.80423i	1.64382	−	0.289850i	0.726251	−	0.687429i	$-0.241261\pi$
$401$	32.9174	−	5.80423i	1.64382	−	0.289850i	0.917568	+	0.397580i	$0.130150\pi$
$402$	−5.65428	+	4.00243i	−0.282010	+	0.199623i
$403$	9.50489	+	7.97555i	0.473472	+	0.397290i
$404$	−5.09600	+	8.59063i	−0.253536	+	0.427400i
$405$	−6.84555	+	0.301961i	−0.340158	+	0.0150045i
$406$	−10.1061	−	17.7454i	−0.501556	−	0.880689i
$407$	45.8215	+	38.4488i	2.27129	+	1.90584i
$408$	16.6798	−	1.34686i	0.825775	−	0.0666796i
$409$	−4.03315	−	22.8731i	−0.199426	−	1.13100i	−0.905973	−	0.423336i	$-0.860859\pi$
$409$	−4.03315	−	22.8731i	−0.199426	−	1.13100i	0.706547	−	0.707666i	$-0.250252\pi$
$410$	−0.530565	−	3.11648i	−0.0262028	−	0.153912i
$411$	−0.119936	+	0.175368i	−0.00591598	+	0.00865025i
$412$	6.28036	−	7.30762i	0.309411	−	0.360020i
$413$	−8.06891	+	13.9758i	−0.397045	+	0.687702i
$414$	−4.38522	−	22.7197i	−0.215522	−	1.11661i
$415$	−5.61343	+	3.24091i	−0.275552	+	0.159090i
$416$	6.00962	−	29.0409i	0.294646	−	1.42385i
$417$	−7.49279	−	26.7794i	−0.366924	−	1.31139i
$418$	19.2453	+	7.13370i	0.941320	+	0.348920i
$419$	1.20391	+	1.43476i	0.0588147	+	0.0700926i	0.794650	−	0.607068i	$-0.207655\pi$
$419$	1.20391	+	1.43476i	0.0588147	+	0.0700926i	−0.735835	+	0.677161i	$0.763210\pi$
$420$	6.29536	+	6.30530i	0.307182	+	0.307667i
$421$	−6.15422	−	16.9086i	−0.299938	−	0.824073i	−0.994509	−	0.104649i	$-0.966628\pi$
$421$	−6.15422	−	16.9086i	−0.299938	−	0.824073i	0.694571	−	0.719424i	$-0.255594\pi$
$422$	−6.86536	−	4.01795i	−0.334200	−	0.195591i
$423$	0.238323	+	10.8110i	0.0115877	+	0.525648i
$424$	−19.5517	−	11.7548i	−0.949513	−	0.570862i
$425$	14.8698	+	2.62194i	0.721290	+	0.127183i
$426$	6.36056	+	13.4600i	0.308170	+	0.652141i
$427$	8.46978	+	3.08275i	0.409881	+	0.149185i
$428$	1.81361	−	4.80551i	0.0876642	−	0.232283i
$429$	−21.3800	+	47.2007i	−1.03223	+	2.27887i
$430$	6.71554	+	1.22506i	0.323852	+	0.0590776i
$431$	28.7176			1.38328			0.691640	−	0.722242i	$-0.256889\pi$
$431$	28.7176			1.38328			0.691640	+	0.722242i	$0.256889\pi$
$432$	−18.9194	−	8.60569i	−0.910258	−	0.414041i
$433$	−6.95359			−0.334168			−0.167084	−	0.985943i	$-0.553435\pi$
$433$	−6.95359			−0.334168			−0.167084	+	0.985943i	$0.553435\pi$
$434$	−11.1240	−	2.02925i	−0.533967	−	0.0974072i
$435$	−3.28371	−	4.58133i	−0.157442	−	0.219658i
$436$	5.43177	−	14.3925i	0.260134	−	0.689276i
$437$	−13.0344	−	4.74412i	−0.623519	−	0.226942i
$438$	−3.92567	+	5.66793i	−0.187576	+	0.270824i
$439$	32.5793	+	5.74462i	1.55493	+	0.274176i	0.884050	−	0.467393i	$-0.154807\pi$
$439$	32.5793	+	5.74462i	1.55493	+	0.274176i	0.670877	+	0.741568i	$0.265918\pi$
$440$	6.33187	−	10.5318i	0.301860	−	0.502083i
$441$	13.0854	+	2.01103i	0.623116	+	0.0957636i
$442$	21.8571	+	12.7919i	1.03964	+	0.608447i
$443$	6.00559	+	16.5002i	0.285334	+	0.783949i	0.996703	+	0.0811307i	$0.0258531\pi$
$443$	6.00559	+	16.5002i	0.285334	+	0.783949i	−0.711369	+	0.702818i	$0.751925\pi$
$444$	−35.0808	+	9.37023i	−1.66486	+	0.444691i
$445$	4.40212	+	5.24625i	0.208681	+	0.248696i
$446$	−1.55144	−	0.575073i	−0.0734626	−	0.0272305i
$447$	−22.8076	+	23.3159i	−1.07876	+	1.10280i
$448$	8.33826	+	25.7081i	0.393946	+	1.21459i
$449$	35.9869	−	20.7770i	1.69833	−	0.980529i	0.750974	−	0.660332i	$-0.229584\pi$
$449$	35.9869	−	20.7770i	1.69833	−	0.980529i	0.947351	−	0.320197i	$-0.103749\pi$
$450$	−14.5590	−	11.8214i	−0.686316	−	0.557266i
$451$	−8.37736	+	14.5100i	−0.394475	+	0.683250i
$452$	−7.90309	+	9.19578i	−0.371730	+	0.432533i
$453$	−12.3796	−	25.8018i	−0.581642	−	1.21227i
$454$	−2.59750	−	15.2574i	−0.121907	−	0.716065i
$455$	2.34152	+	13.2794i	0.109772	+	0.622550i
$456$	−10.2538	+	7.07800i	−0.480179	+	0.331458i
$457$	13.2175	+	11.0908i	0.618287	+	0.518804i	0.897265	−	0.441493i	$-0.145551\pi$
$457$	13.2175	+	11.0908i	0.618287	+	0.518804i	−0.278978	+	0.960298i	$0.589996\pi$
$458$	3.92007	+	6.88330i	0.183173	+	0.321635i
$459$	12.1289	−	12.9586i	0.566127	−	0.604856i
$460$	−4.23702	+	7.14260i	−0.197552	+	0.333025i
$461$	−12.7382	−	10.6886i	−0.593276	−	0.497817i	0.296001	−	0.955188i	$-0.404347\pi$
$461$	−12.7382	−	10.6886i	−0.593276	−	0.497817i	−0.889276	+	0.457370i	$0.848791\pi$
$462$	−4.35631	−	47.0210i	−0.202674	−	2.18761i
$463$	22.8699	−	4.03258i	1.06285	−	0.187410i	0.385232	−	0.922820i	$-0.374122\pi$
$463$	22.8699	−	4.03258i	1.06285	−	0.187410i	0.677622	+	0.735410i	$0.263010\pi$
$464$	−2.57046	−	16.9030i	−0.119330	−	0.784704i
$465$	−3.11199	−	0.237737i	−0.144315	−	0.0110248i
$466$	−18.4671	+	6.59825i	−0.855471	+	0.305658i
$467$	−19.4081	−	11.2053i	−0.898099	−	0.518518i	−0.0215159	−	0.999769i	$-0.506849\pi$
$467$	−19.4081	−	11.2053i	−0.898099	−	0.518518i	−0.876583	+	0.481251i	$0.840183\pi$
$468$	−16.0055	−	27.0786i	−0.739853	−	1.25171i
$469$	8.27432	−	4.77718i	0.382073	−	0.220590i
$470$	2.51222	−	2.95829i	0.115880	−	0.136456i
$471$	5.01589	−	19.5802i	0.231120	−	0.902207i
$472$	−10.5023	+	8.50005i	−0.483407	+	0.391247i
$473$	−23.2555	−	27.7148i	−1.06929	−	1.27433i
$474$	19.9068	−	20.1115i	0.914349	−	0.923753i
$475$	−10.5642	+	3.84505i	−0.484718	+	0.176423i
$476$	−23.0780	−	0.272546i	−1.05778	−	0.0124921i
$477$	−23.7311	+	4.72594i	−1.08657	+	0.216386i
$478$	−0.144631	+	24.4943i	−0.00661528	+	1.12034i
$479$	−5.11572	+	29.0127i	−0.233743	+	1.32562i	0.611502	+	0.791243i	$0.290566\pi$
$479$	−5.11572	+	29.0127i	−0.233743	+	1.32562i	−0.845245	+	0.534379i	$0.820545\pi$
$480$	3.02700	+	6.81799i	0.138163	+	0.311197i
$481$	−51.6380	−	18.7947i	−2.35449	−	0.856965i
$482$	−1.73247	−	2.08961i	−0.0789118	−	0.0951791i
$483$	3.13160	+	31.7592i	0.142493	+	1.44509i
$484$	−40.6992	+	14.2713i	−1.84996	+	0.648696i
$485$	−11.0801			−0.503123
$486$	−20.9879	+	6.74607i	−0.952029	+	0.306008i
$487$		−	27.2531i		−	1.23496i	−0.786587	−	0.617479i	$-0.788154\pi$
$487$		−	27.2531i		−	1.23496i	0.786587	−	0.617479i	$-0.211846\pi$
$488$	5.69393	+	4.95227i	0.257752	+	0.224179i
$489$	−3.95059	+	0.389547i	−0.178652	+	0.0176159i
$490$	−3.03272	−	3.65790i	−0.137004	−	0.165247i
$491$	−5.33019	+	14.6446i	−0.240548	+	0.660900i	0.759399	+	0.650625i	$0.225493\pi$
$491$	−5.33019	+	14.6446i	−0.240548	+	0.660900i	−0.999947	+	0.0102751i	$0.996729\pi$
$492$	−4.29111	−	9.22129i	−0.193458	−	0.415728i
$493$	14.3787	+	2.53534i	0.647582	+	0.114186i
$494$	−18.8557	−	0.111337i	−0.848358	−	0.00500929i
$495$	−2.54569	−	12.7831i	−0.114420	−	0.574556i
$496$	−8.08459	−	4.92581i	−0.363009	−	0.221175i
$497$	−7.02247	−	19.2941i	−0.315001	−	0.865458i
$498$	−14.6702	+	14.8211i	−0.657389	+	0.664150i
$499$	4.83664	−	4.05842i	0.216518	−	0.181680i	−0.528077	−	0.849196i	$-0.677087\pi$
$499$	4.83664	−	4.05842i	0.216518	−	0.181680i	0.744595	+	0.667516i	$0.232642\pi$
$500$	2.32390	+	14.1550i	0.103928	+	0.633029i
$501$	14.0172	+	3.59081i	0.626243	+	0.160426i
$502$	23.2176	+	19.7167i	1.03625	+	0.879998i
$503$	−3.45933	−	5.99174i	−0.154244	−	0.267159i	0.778539	−	0.627596i	$-0.215961\pi$
$503$	−3.45933	−	5.99174i	−0.154244	−	0.267159i	−0.932784	+	0.360437i	$0.882628\pi$
$504$	24.8872	+	14.2254i	1.10857	+	0.633651i
$505$	1.90118	−	3.29294i	0.0846015	−	0.146534i
$506$	41.4483	−	14.8094i	1.84260	−	0.658357i
$507$	1.91094	−	25.0142i	0.0848677	−	1.11092i
$508$	3.93072	+	4.79840i	0.174397	+	0.212895i
$509$	−6.85834	−	38.8956i	−0.303991	−	1.72402i	−0.628218	−	0.778037i	$-0.716215\pi$
$509$	−6.85834	−	38.8956i	−0.303991	−	1.72402i	0.324227	−	0.945979i	$-0.394896\pi$
$510$	−6.34315	+	0.587668i	−0.280879	+	0.0260224i
$511$	6.11230	−	7.28435i	0.270392	−	0.322241i
$512$	−1.20189	+	22.5955i	−0.0531166	+	0.998588i
$513$	−2.99655	+	12.8711i	−0.132301	+	0.568272i
$514$	−6.30600	−	11.0728i	−0.278146	−	0.488400i
$515$	−2.35778	+	2.80989i	−0.103896	+	0.123818i
$516$	21.8802	−	1.89688i	0.963222	−	0.0835055i
$517$	−20.2569	+	3.57183i	−0.890896	+	0.157089i
$518$	49.3690	−	8.40483i	2.16915	−	0.369287i
$519$	7.16614	−	3.43827i	0.314559	−	0.150923i
$520$	−2.15702	+	11.0815i	−0.0945915	+	0.485955i
$521$	0.808019	+	0.466510i	0.0353999	+	0.0204382i	0.517596	−	0.855625i	$-0.326827\pi$
$521$	0.808019	+	0.466510i	0.0353999	+	0.0204382i	−0.482196	+	0.876064i	$0.660161\pi$
$522$	−14.0781	−	11.4310i	−0.616182	−	0.500319i
$523$	−18.5482	−	32.1264i	−0.811057	−	1.40479i	−0.912125	−	0.409912i	$-0.865560\pi$
$523$	−18.5482	−	32.1264i	−0.811057	−	1.40479i	0.101069	−	0.994879i	$-0.467774\pi$
$524$	31.9056	+	6.01515i	1.39380	+	0.262773i
$525$	18.4899	+	18.0868i	0.806966	+	0.789373i
$526$	−3.05232	+	8.23457i	−0.133087	+	0.359044i
$527$	6.19304	−	5.19658i	0.269773	−	0.226367i
$528$	10.7129	−	38.0569i	0.466221	−	1.65621i
$529$	−6.33854	+	2.30704i	−0.275589	+	0.100306i
$530$	7.49522	+	4.38658i	0.325571	+	0.190541i
$531$	−2.17685	+	14.1643i	−0.0944672	+	0.614680i
$532$	14.9822	−	8.41568i	0.649562	−	0.364866i
$533$	2.67286	−	15.1585i	0.115774	−	0.656590i
$534$	18.1132	+	12.5454i	0.783833	+	0.542891i
$535$	−0.668751	+	1.83738i	−0.0289126	+	0.0794368i
$536$	7.90104	−	1.24929i	0.341273	−	0.0539612i
$537$	13.0294	−	9.33897i	0.562261	−	0.403006i
$538$	1.80079	+	0.328503i	0.0776376	+	0.0141628i
$539$			25.1830i			1.08471i
$540$	7.24037	+	3.19072i	0.311576	+	0.137307i
$541$			25.5189i			1.09714i	0.836104	+	0.548571i	$0.184828\pi$
$541$			25.5189i			1.09714i	−0.836104	+	0.548571i	$0.815172\pi$
$542$	0.979901	−	5.37163i	0.0420903	−	0.230731i
$543$	−18.5294	−	8.39305i	−0.795172	−	0.360180i
$544$	−17.9546	−	7.14193i	−0.769797	−	0.306208i
$545$	−2.00291	+	5.50295i	−0.0857952	+	0.235720i
$546$	18.5352	+	39.2237i	0.793234	+	1.67862i
$547$	−3.90042	+	22.1204i	−0.166770	+	0.945800i	0.780451	+	0.625218i	$0.214990\pi$
$547$	−3.90042	+	22.1204i	−0.166770	+	0.945800i	−0.947221	+	0.320582i	$0.896121\pi$
$548$	0.213892	−	0.120145i	0.00913700	−	0.00513235i
$549$	8.00206	−	0.176402i	0.341520	−	0.00752864i
$550$	18.0187	−	30.7880i	0.768320	−	1.31281i
$551$	−10.2153	+	3.71805i	−0.435185	+	0.158394i
$552$	−7.08789	+	25.7614i	−0.301681	+	1.09648i
$553$	−29.8970	+	25.0866i	−1.27135	+	1.06679i
$554$	−32.6203	−	12.0914i	−1.38590	−	0.513715i
$555$	13.3114	−	3.72449i	0.565039	−	0.158096i
$556$	−5.94885	+	31.5539i	−0.252287	+	1.33819i
$557$	−12.6918	−	21.9828i	−0.537768	−	0.931441i	−0.999024	−	0.0441741i	$-0.985934\pi$
$557$	−12.6918	−	21.9828i	−0.537768	−	0.931441i	0.461256	−	0.887267i	$-0.347399\pi$
$558$	−9.85931	+	1.90298i	−0.417378	+	0.0805597i
$559$	28.7844	+	16.6187i	1.21745	+	0.702896i
$560$	−3.28954	−	9.74835i	−0.139008	−	0.411943i
$561$	27.8680	+	19.0592i	1.17659	+	0.804680i
$562$	0.864290	+	5.07674i	0.0364579	+	0.214149i
$563$	−24.4865	+	4.31763i	−1.03198	+	0.181966i	−0.663896	−	0.747825i	$-0.731098\pi$
$563$	−24.4865	+	4.31763i	−1.03198	+	0.181966i	−0.368087	+	0.929791i	$0.619987\pi$
$564$	5.28594	−	11.3124i	0.222578	−	0.476339i
$565$	2.96699	−	3.53592i	0.124822	−	0.148757i
$566$	4.51275	−	2.57003i	0.189685	−	0.108026i
$567$	29.6812	−	6.59413i	1.24649	−	0.276927i
$568$	0.304491	−	17.1876i	0.0127761	−	0.721175i
$569$	−7.57957	+	9.03298i	−0.317752	+	0.378682i	−0.901152	−	0.433503i	$-0.857277\pi$
$569$	−7.57957	+	9.03298i	−0.317752	+	0.378682i	0.583400	+	0.812185i	$0.301722\pi$
$570$	3.87132	−	2.74035i	0.162152	−	0.114780i
$571$	−5.98228	−	33.9272i	−0.250351	−	1.41981i	−0.807731	−	0.589551i	$-0.799305\pi$
$571$	−5.98228	−	33.9272i	−0.250351	−	1.41981i	0.557380	−	0.830257i	$-0.311807\pi$
$572$	46.2858	−	37.9161i	1.93531	−	1.58535i
$573$	17.1660	+	11.7400i	0.717122	+	0.490446i
$574$	4.71978	+	13.2097i	0.197000	+	0.551361i
$575$	−12.0541	+	20.8783i	−0.502691	+	0.870686i
$576$	15.1794	+	18.5899i	0.632475	+	0.774580i
$577$	21.3516	+	36.9821i	0.888880	+	1.53958i	0.841201	+	0.540722i	$0.181849\pi$
$577$	21.3516	+	36.9821i	0.888880	+	1.53958i	0.0476781	+	0.998863i	$0.484818\pi$
$578$	−4.88106	+	5.74775i	−0.203025	+	0.239075i
$579$	−0.235301	−	0.840972i	−0.00977877	−	0.0349496i
$580$	1.05443	+	6.42261i	0.0437830	+	0.266684i
$581$	22.0325	−	18.4875i	0.914062	−	0.766989i
$582$	−34.3855	+	9.40236i	−1.42532	+	0.389741i
$583$	−15.7422	−	43.2513i	−0.651974	−	1.79128i
$584$	6.96408	−	3.85788i	0.288176	−	0.159640i
$585$	6.21423	+	10.2356i	0.256927	+	0.423188i
$586$	−0.248015	+	42.0031i	−0.0102454	+	1.73513i
$587$	−0.937739	−	0.165349i	−0.0387046	−	0.00682467i	0.154262	−	0.988030i	$-0.450700\pi$
$587$	−0.937739	−	0.165349i	−0.0387046	−	0.00682467i	−0.192967	+	0.981205i	$0.561811\pi$
$588$	−12.5156	−	8.77822i	−0.516134	−	0.362008i
$589$	−2.05873	+	5.65631i	−0.0848285	+	0.233064i
$590$	3.95950	−	3.28277i	0.163010	−	0.135149i
$591$	−2.66513	+	5.88383i	−0.109629	+	0.242028i
$592$	41.1075	+	8.25382i	1.68951	+	0.339230i
$593$		−	11.5209i		−	0.473108i	−0.971618	−	0.236554i	$-0.923982\pi$
$593$		−	11.5209i		−	0.473108i	0.971618	−	0.236554i	$-0.0760180\pi$
$594$	−18.7476	−	37.5101i	−0.769224	−	1.53906i
$595$	8.78588			0.360186
$596$	35.5403	−	12.4623i	1.45579	−	0.510476i
$597$	36.5621	−	26.2062i	1.49639	−	1.07255i
$598$	−31.1285	+	25.8082i	−1.27294	+	1.05538i
$599$	−45.3618	−	16.5103i	−1.85343	−	0.674594i	−0.983360	−	0.181668i	$-0.941851\pi$
$599$	−45.3618	−	16.5103i	−1.85343	−	0.674594i	−0.870071	−	0.492926i	$-0.835927\pi$
$600$	9.02029	+	19.6870i	0.368252	+	0.803720i
$601$	4.24537	−	24.0767i	0.173172	−	0.982109i	−0.767060	−	0.641575i	$-0.778281\pi$
$601$	4.24537	−	24.0767i	0.173172	−	0.982109i	0.940232	−	0.340534i	$-0.110608\pi$
$602$	−30.2896	−	0.178851i	−1.23451	−	0.00728943i
$603$	5.30912	−	6.61807i	0.216204	−	0.269508i
$604$	−0.390229	+	33.0428i	−0.0158782	+	1.34449i
$605$	15.4281	−	5.61535i	0.627240	−	0.228297i
$606$	3.10570	−	11.8324i	0.126161	−	0.480660i
$607$	−18.4241	−	21.9570i	−0.747812	−	0.891207i	0.249201	−	0.968452i	$-0.419832\pi$
$607$	−18.4241	−	21.9570i	−0.747812	−	0.891207i	−0.997012	+	0.0772447i	$0.975388\pi$
$608$	14.2360	−	2.07895i	0.577346	−	0.0843126i
$609$	17.8792	+	17.4894i	0.724503	+	0.708708i
$610$	−2.18967	−	1.85949i	−0.0886570	−	0.0752886i
$611$	16.3652	−	9.44843i	0.662064	−	0.382243i
$612$	−19.1863	+	7.20640i	−0.775560	+	0.291301i
$613$	−32.4005	−	18.7064i	−1.30864	−	0.755546i	−0.326774	−	0.945102i	$-0.605962\pi$
$613$	−32.4005	−	18.7064i	−1.30864	−	0.755546i	−0.981870	+	0.189556i	$0.939295\pi$
$614$	4.40181	+	12.3197i	0.177643	+	0.497184i
$615$	1.67487	+	3.49081i	0.0675373	+	0.140763i
$616$	−19.5542	+	50.9009i	−0.787862	+	2.05085i
$617$	6.61066	−	1.16564i	0.266135	−	0.0469268i	−0.0389880	−	0.999240i	$-0.512413\pi$
$617$	6.61066	−	1.16564i	0.266135	−	0.0469268i	0.305123	+	0.952313i	$0.401302\pi$
$618$	−4.93258	+	10.7208i	−0.198418	+	0.431254i
$619$	−5.88154	−	4.93520i	−0.236399	−	0.198362i	0.516890	−	0.856052i	$-0.327090\pi$
$619$	−5.88154	−	4.93520i	−0.236399	−	0.198362i	−0.753289	+	0.657689i	$0.771534\pi$
$620$	3.09956	+	1.83867i	0.124481	+	0.0738428i
$621$	12.8192	+	25.2743i	0.514418	+	1.01422i
$622$	32.2335	−	18.3571i	1.29245	−	0.736053i
$623$	−23.2788	−	19.5333i	−0.932647	−	0.782583i
$624$	2.70953	+	36.2201i	0.108468	+	1.44996i
$625$	2.88969	+	16.3882i	0.115588	+	0.655530i
$626$	27.8828	−	4.74691i	1.11442	−	0.189724i
$627$	−25.0648	−	1.91480i	−1.00099	−	0.0764697i
$628$	−15.2123	+	17.7005i	−0.607037	+	0.706329i
$629$	−17.9024	+	31.0079i	−0.713815	+	1.23636i
$630$	−9.53731	−	5.30305i	−0.379976	−	0.211279i
$631$	−2.13355	+	1.23181i	−0.0849353	+	0.0490374i	−0.541866	−	0.840465i	$-0.682282\pi$
$631$	−2.13355	+	1.23181i	−0.0849353	+	0.0490374i	0.456931	+	0.889502i	$0.348949\pi$
$632$	−30.8978	+	10.6300i	−1.22905	+	0.422837i
$633$	9.43771	+	2.41768i	0.375115	+	0.0960940i
$634$	11.5238	−	31.0889i	0.457668	−	1.23470i
$635$	−1.51780	−	1.80885i	−0.0602322	−	0.0717820i
$636$	26.9826	+	7.25278i	1.06993	+	0.287592i
$637$	−7.91276	−	21.7401i	−0.313515	−	0.861375i
$638$	17.4236	−	29.7712i	0.689806	−	1.17865i
$639$	−12.0250	−	13.7056i	−0.475700	−	0.542187i
$640$	0.355926	−	8.60640i	0.0140692	−	0.340198i
$641$	−34.3110	−	6.04995i	−1.35520	−	0.238959i	−0.551592	−	0.834114i	$-0.685979\pi$
$641$	−34.3110	−	6.04995i	−1.35520	−	0.238959i	−0.803610	+	0.595156i	$0.797090\pi$
$642$	−0.516206	+	6.26951i	−0.0203730	+	0.247438i
$643$	45.2740	+	16.4784i	1.78543	+	0.649844i	0.999503	+	0.0315285i	$0.0100375\pi$
$643$	45.2740	+	16.4784i	1.78543	+	0.649844i	0.785930	+	0.618316i	$0.212185\pi$
$644$	13.0115	−	34.4766i	0.512727	−	1.35857i
$645$	−8.32020	+	0.820411i	−0.327608	+	0.0323036i
$646$	−2.20483	+	12.0864i	−0.0867478	+	0.475535i
$647$	0.709735			0.0279025			0.0139513	−	0.999903i	$-0.495559\pi$
$647$	0.709735			0.0279025			0.0139513	+	0.999903i	$0.495559\pi$
$648$	25.1769	+	3.75788i	0.989044	+	0.147623i
$649$	−27.2594			−1.07002
$650$	−5.88137	+	32.2405i	−0.230686	+	1.26458i
$651$	13.7820	−	1.35897i	0.540160	−	0.0532623i
$652$	4.28862	+	1.61853i	0.167955	+	0.0633867i
$653$	−0.660215	−	0.240299i	−0.0258362	−	0.00940361i	0.329070	−	0.944306i	$-0.393265\pi$
$653$	−0.660215	−	0.240299i	−0.0258362	−	0.00940361i	−0.354906	+	0.934902i	$0.615487\pi$
$654$	−1.54604	+	18.7772i	−0.0604548	+	0.734246i
$655$	−12.1720	−	2.14625i	−0.475598	−	0.0838608i
$656$	−0.277356	+	11.7410i	−0.0108289	+	0.458409i
$657$	2.71250	−	7.99667i	0.105825	−	0.311980i
$658$	−8.69853	+	14.8629i	−0.339104	+	0.579418i
$659$	−12.8249	−	35.2362i	−0.499589	−	1.37261i	−0.891673	−	0.452680i	$-0.850468\pi$
$659$	−12.8249	−	35.2362i	−0.499589	−	1.37261i	0.392084	−	0.919929i	$-0.371754\pi$
$660$	−3.90681	+	14.5346i	−0.152073	+	0.565757i
$661$	−2.70452	−	3.22312i	−0.105194	−	0.125365i	0.710879	−	0.703314i	$-0.248297\pi$
$661$	−2.70452	−	3.22312i	−0.105194	−	0.125365i	−0.816072	+	0.577950i	$0.803853\pi$
$662$	−11.1853	+	30.1758i	−0.434730	+	1.17282i
$663$	−30.0467	−	7.69711i	−1.16692	−	0.298931i
$664$	22.7700	−	7.83371i	0.883649	−	0.304007i
$665$	−5.66518	+	3.27079i	−0.219686	+	0.126836i
$666$	38.1495	−	22.8542i	1.47826	−	0.885582i
$667$	−11.6560	+	20.1887i	−0.451321	+	0.781711i
$668$	−12.6716	−	10.8903i	−0.490279	−	0.421358i
$669$	2.02056	+	0.154359i	0.0781194	+	0.00596786i
$670$	−3.00193	+	0.511063i	−0.115975	+	0.0197441i
$671$	2.64380	+	14.9937i	0.102063	+	0.578826i
$672$	−18.4808	−	27.4611i	−0.712913	−	1.05933i
$673$	−30.4222	−	25.5272i	−1.17269	−	0.984002i	−0.172689	−	0.984976i	$-0.555245\pi$
$673$	−30.4222	−	25.5272i	−1.17269	−	0.984002i	−1.00000		0.000974390i	$0.999690\pi$
$674$	39.4069	−	22.4424i	1.51790	−	0.864449i
$675$	21.1262	+	9.01360i	0.813150	+	0.346934i
$676$	−14.7793	+	24.9143i	−0.568434	+	0.958243i
$677$	−2.47156	−	2.07389i	−0.0949899	−	0.0797060i	0.594056	−	0.804424i	$-0.297526\pi$
$677$	−2.47156	−	2.07389i	−0.0949899	−	0.0797060i	−0.689046	+	0.724718i	$0.741970\pi$
$678$	6.20708	−	13.4909i	0.238381	−	0.518115i
$679$	48.4182	−	8.53744i	1.85812	−	0.327637i
$680$	6.86655	+	2.63787i	0.263320	+	0.101158i
$681$	8.19968	+	17.0900i	0.314213	+	0.654890i
$682$	−6.42658	−	17.9866i	−0.246087	−	0.688744i
$683$	10.7853	+	6.22690i	0.412689	+	0.238266i	0.691944	−	0.721951i	$-0.256754\pi$
$683$	10.7853	+	6.22690i	0.412689	+	0.238266i	−0.279256	+	0.960217i	$0.590088\pi$
$684$	9.68863	−	11.7894i	0.370454	−	0.450777i
$685$	−0.0808781	+	0.0466950i	−0.00309019	+	0.00178412i
$686$	−9.42102	−	8.00044i	−0.359696	−	0.305458i
$687$	−6.93521	−	6.78402i	−0.264595	−	0.258826i
$688$	−23.6190	−	9.23394i	−0.900465	−	0.352041i
$689$	27.1800	+	32.3918i	1.03547	+	1.23403i
$690$	2.58221	−	9.83798i	0.0983030	−	0.374525i
$691$	−33.7240	+	12.2745i	−1.28292	+	0.466945i	−0.891397	−	0.453222i	$-0.850274\pi$
$691$	−33.7240	+	12.2745i	−1.28292	+	0.466945i	−0.391524	+	0.920168i	$0.628052\pi$
$692$	−9.17725	−	0.108382i	−0.348867	−	0.00412005i
$693$	20.9738	+	53.8983i	0.796729	+	2.04743i
$694$	20.9359	+	0.123620i	0.794718	+	0.00469256i
$695$	2.12259	−	12.0378i	0.0805144	−	0.456620i
$696$	8.72237	+	19.0368i	0.330620	+	0.721589i
$697$	−9.42430	−	3.43016i	−0.356971	−	0.129927i
$698$	−27.5236	+	22.8194i	−1.04178	+	0.863728i
$699$	19.5212	−	13.9920i	0.738361	−	0.529227i
$700$	−9.88284	−	28.1841i	−0.373536	−	1.06526i
$701$	−35.4138			−1.33756			−0.668781	−	0.743459i	$-0.733184\pi$
$701$	−35.4138			−1.33756			−0.668781	+	0.743459i	$0.733184\pi$
$702$	27.9706	+	26.4912i	1.05568	+	0.999847i
$703$		−	26.6587i		−	1.00545i
$704$	−30.5650	+	33.9103i	−1.15196	+	1.27804i
$705$	−1.96125	+	4.32985i	−0.0738648	+	0.163072i
$706$	0.490066	−	0.406308i	0.0184439	−	0.0152916i
$707$	−5.77056	+	15.8545i	−0.217024	+	0.596269i
$708$	9.50200	−	13.5475i	0.357107	−	0.509147i
$709$	2.07523	+	0.365919i	0.0779368	+	0.0137424i	0.212481	−	0.977165i	$-0.431846\pi$
$709$	2.07523	+	0.365919i	0.0779368	+	0.0137424i	−0.134544	+	0.990908i	$0.542957\pi$
$710$	−0.0386394	+	6.54385i	−0.00145011	+	0.245586i
$711$	−16.6630	+	30.3887i	−0.624910	+	1.13967i
$712$	−12.3287	−	22.2553i	−0.462039	−	0.834053i
$713$	4.41483	+	12.1296i	0.165337	+	0.454259i
$714$	27.2656	−	7.45551i	1.02039	−	0.279016i
$715$	−17.4483	+	14.6409i	−0.652530	+	0.547538i
$716$	−18.2661	+	2.99884i	−0.682636	+	0.112072i
$717$	−8.08339	−	28.8903i	−0.301880	−	1.07893i
$718$	−2.90839	+	3.42481i	−0.108540	+	0.127813i
$719$	2.79238	+	4.83654i	0.104138	+	0.180373i	0.913386	−	0.407095i	$-0.133458\pi$
$719$	2.79238	+	4.83654i	0.104138	+	0.180373i	−0.809248	+	0.587468i	$0.800125\pi$
$720$	−5.86164	−	7.00805i	−0.218450	−	0.261174i
$721$	8.13800	−	14.0954i	0.303075	−	0.524941i
$722$	5.96302	+	16.6892i	0.221920	+	0.621108i
$723$	2.74407	+	1.87669i	0.102053	+	0.0697949i
$724$	14.8846	+	18.1703i	0.553181	+	0.675292i
$725$	3.28091	+	18.6070i	0.121850	+	0.691046i
$726$	43.1135	−	30.5183i	1.60009	−	1.13264i
$727$	3.41147	−	4.06563i	0.126524	−	0.150786i	−0.699063	−	0.715060i	$-0.746399\pi$
$727$	3.41147	−	4.06563i	0.126524	−	0.150786i	0.825588	+	0.564274i	$0.190844\pi$
$728$	0.887312	−	50.0861i	0.0328860	−	1.85632i
$729$	22.4396	−	15.0155i	0.831095	−	0.556130i
$730$	−2.63354	+	1.49981i	−0.0974719	+	0.0555106i
$731$	13.9204	−	16.5897i	0.514864	−	0.613591i
$732$	−8.37322	−	3.91254i	−0.309483	−	0.144612i
$733$	44.4108	−	7.83081i	1.64035	−	0.289238i	0.724054	−	0.689743i	$-0.242277\pi$
$733$	44.4108	−	7.83081i	1.64035	−	0.289238i	0.916294	+	0.400505i	$0.131165\pi$
$734$	7.80734	+	45.8594i	0.288174	+	1.69270i
$735$	4.80354	+	3.28518i	0.177181	+	0.121176i
$736$	20.5203	−	23.0384i	0.756390	−	0.849205i
$737$	13.9767	+	8.06943i	0.514837	+	0.297241i
$738$	8.15992	+	9.41192i	0.300371	+	0.346458i
$739$	9.87524	+	17.1044i	0.363267	+	0.629196i	0.988496	−	0.151244i	$-0.0483280\pi$
$739$	9.87524	+	17.1044i	0.363267	+	0.629196i	−0.625230	+	0.780441i	$0.714995\pi$
$740$	−15.6847	−	2.95703i	−0.576583	−	0.108703i
$741$	22.2397	−	6.22259i	0.816996	−	0.228592i
$742$	−36.1327	−	13.3934i	−1.32647	−	0.491686i
$743$	−8.50460	+	7.13621i	−0.312004	+	0.261802i	−0.785320	−	0.619091i	$-0.787501\pi$
$743$	−8.50460	+	7.13621i	−0.312004	+	0.261802i	0.473316	+	0.880893i	$0.343057\pi$
$744$	11.1793	+	3.07582i	0.409851	+	0.112765i
$745$	−13.4724	+	4.90356i	−0.493592	+	0.179653i
$746$	−8.51879	+	14.5558i	−0.311895	+	0.532926i
$747$	12.2797	−	22.3949i	0.449291	−	0.819386i
$748$	−19.0925	−	33.9899i	−0.698091	−	1.24280i
$749$	1.50659	−	8.54431i	0.0550497	−	0.312202i
$750$	−7.50605	−	15.8841i	−0.274082	−	0.580005i
$751$	1.58243	−	4.34770i	0.0577439	−	0.158650i	−0.907467	−	0.420124i	$-0.861986\pi$
$751$	1.58243	−	4.34770i	0.0577439	−	0.158650i	0.965210	+	0.261474i	$0.0842087\pi$
$752$	−11.2607	+	9.00438i	−0.410637	+	0.328356i
$753$	−33.9821	−	15.3925i	−1.23837	−	0.560933i
$754$	−5.68712	+	31.1757i	−0.207113	+	1.13535i
$755$		−	12.5796i		−	0.457817i
$756$	−34.0976	−	8.36404i	−1.24012	−	0.304197i
$757$			11.0029i			0.399907i	0.979805	+	0.199954i	$0.0640792\pi$
$757$			11.0029i			0.399907i	−0.979805	+	0.199954i	$0.935921\pi$
$758$	1.88956	+	0.344697i	0.0686320	+	0.0125200i
$759$	−43.8142	+	31.4043i	−1.59036	+	1.13990i
$760$	−5.40960	+	0.855352i	−0.196227	+	0.0310269i
$761$	−3.02165	+	8.30192i	−0.109535	+	0.300944i	−0.982334	−	0.187135i	$-0.940080\pi$
$761$	−3.02165	+	8.30192i	−0.109535	+	0.300944i	0.872799	+	0.488079i	$0.162302\pi$
$762$	−6.24522	−	4.32551i	−0.226240	−	0.156697i
$763$	4.51224	−	25.5902i	0.163354	−	0.926427i
$764$	−11.7605	−	20.9370i	−0.425481	−	0.757474i
$765$	7.27090	−	2.82938i	0.262880	−	0.102296i
$766$	−36.3433	−	21.2699i	−1.31314	−	0.768513i
$767$	23.5326	−	8.56518i	0.849714	−	0.309271i
$768$	−6.19865	−	27.0107i	−0.223675	−	0.974664i
$769$	38.6343	−	32.4180i	1.39319	−	1.16902i	0.429158	−	0.903229i	$-0.358810\pi$
$769$	38.6343	−	32.4180i	1.39319	−	1.16902i	0.964030	−	0.265794i	$-0.0856342\pi$
$770$	7.21453	−	19.4634i	0.259993	−	0.701412i
$771$	11.1563	+	10.9131i	0.401785	+	0.393025i
$772$	−0.186815	+	0.990909i	−0.00672364	+	0.0356636i
$773$	10.6364	+	18.4228i	0.382565	+	0.662622i	0.991428	−	0.130653i	$-0.0417074\pi$
$773$	10.6364	+	18.4228i	0.382565	+	0.662622i	−0.608863	+	0.793275i	$0.708374\pi$
$774$	−25.1243	+	9.60636i	−0.903074	+	0.345294i
$775$	9.06022	+	5.23092i	0.325453	+	0.187900i
$776$	40.4042	+	7.86471i	1.45043	+	0.282327i
$777$	−55.2989	+	26.5321i	−1.98384	+	0.951833i
$778$	8.06992	−	1.37386i	0.289321	−	0.0492554i
$779$	7.35380	−	1.29667i	0.263477	−	0.0464582i
$780$	−1.19421	−	13.7750i	−0.0427597	−	0.493226i
$781$	22.2934	−	26.5683i	0.797722	−	0.950688i
$782$	13.0383	+	22.8941i	0.466247	+	0.818690i
$783$	20.4285	+	8.71590i	0.730055	+	0.311481i
$784$	8.46255	+	15.4913i	0.302234	+	0.553261i
$785$	5.71102	−	6.80613i	0.203835	−	0.242921i
$786$	−39.5951	+	3.66833i	−1.41231	+	0.130845i
$787$	−0.282984	−	1.60488i	−0.0100873	−	0.0572079i	0.979349	−	0.202179i	$-0.0648022\pi$
$787$	−0.282984	−	1.60488i	−0.0100873	−	0.0572079i	−0.989436	+	0.144971i	$0.953691\pi$
$788$	5.76979	−	4.72645i	0.205540	−	0.168373i
$789$	0.819292	−	10.7245i	0.0291676	−	0.381804i
$790$	11.7135	−	4.18521i	0.416748	−	0.148903i
$791$	−10.2407	+	17.7374i	−0.364118	+	0.630671i
$792$	0.209523	+	48.4210i	0.00744509	+	1.72057i
$793$	−6.99353	−	12.1131i	−0.248347	−	0.430150i
$794$	−16.8653	−	14.3222i	−0.598527	−	0.508277i
$795$	−10.3036	−	2.63948i	−0.365430	−	0.0936129i
$796$	−51.2568	+	8.41509i	−1.81675	+	0.298265i
$797$	−6.03133	+	5.06088i	−0.213641	+	0.179266i	−0.743328	−	0.668927i	$-0.766754\pi$
$797$	−6.03133	+	5.06088i	−0.213641	+	0.179266i	0.529687	+	0.848193i	$0.322309\pi$
$798$	−14.8055	+	14.9577i	−0.524108	+	0.529499i
$799$	−4.21113	−	11.5700i	−0.148979	−	0.409316i
$800$	0.738124	−	24.9943i	0.0260966	−	0.883682i
$801$	−25.5552	−	8.66843i	−0.902948	−	0.306284i
$802$	47.2696	+	0.279113i	1.66915	+	0.00985581i
$803$	15.8183	+	2.78919i	0.558216	+	0.0984285i
$804$	−8.88234	+	4.13338i	−0.313256	+	0.145773i
$805$	−4.79788	+	13.1821i	−0.169103	+	0.464607i
$806$	11.1996	+	13.5083i	0.394488	+	0.475810i
$807$	−2.23109	+	0.219995i	−0.0785379	+	0.00774421i
$808$	−9.27009	+	10.6584i	−0.326121	+	0.374961i
$809$			3.21158i			0.112913i	0.998405	+	0.0564566i	$0.0179802\pi$
$809$			3.21158i			0.112913i	−0.998405	+	0.0564566i	$0.982020\pi$
$810$	−9.60053	−	1.31726i	−0.337328	−	0.0462838i
$811$	20.5556			0.721806			0.360903	−	0.932603i	$-0.382469\pi$
$811$	20.5556			0.721806			0.360903	+	0.932603i	$0.382469\pi$
$812$	−9.55643	−	27.2532i	−0.335365	−	0.956401i
$813$	0.656230	+	6.65516i	0.0230150	+	0.233407i
$814$	53.9912	+	65.1213i	1.89239	+	2.28250i
$815$	−1.63974	−	0.596818i	−0.0574377	−	0.0209056i
$816$	23.5477	+	2.35943i	0.824335	+	0.0825965i
$817$	−2.79996	+	15.8794i	−0.0979581	+	0.555548i
$818$	0.193945	−	32.8459i	0.00678113	−	1.14843i
$819$	−35.0418	−	39.9394i	−1.22446	−	1.39560i
$820$	0.0527954	−	4.47047i	0.00184369	−	0.156116i
$821$	13.9182	−	5.06579i	0.485747	−	0.176797i	−0.0875255	−	0.996162i	$-0.527896\pi$
$821$	13.9182	−	5.06579i	0.485747	−	0.176797i	0.573272	+	0.819365i	$0.305674\pi$
$822$	−0.211368	+	0.213542i	−0.00737231	+	0.00744813i
$823$	−6.69751	−	7.98178i	−0.233460	−	0.278227i	0.636577	−	0.771213i	$-0.280350\pi$
$823$	−6.69751	−	7.98178i	−0.233460	−	0.278227i	−0.870037	+	0.492986i	$0.835905\pi$
$824$	10.5922	−	8.57283i	0.368997	−	0.298649i
$825$	−10.8422	+	42.3239i	−0.377476	+	1.47353i
$826$	−14.7729	+	17.3960i	−0.514014	+	0.605284i
$827$	−39.8873	+	23.0289i	−1.38702	+	0.800794i	−0.992978	−	0.118300i	$-0.962256\pi$
$827$	−39.8873	+	23.0289i	−1.38702	+	0.800794i	−0.394038	+	0.919094i	$0.628922\pi$
$828$	−0.334812	−	32.7219i	−0.0116355	−	1.13716i
$829$	−0.902728	−	0.521190i	−0.0313531	−	0.0181017i	0.484242	−	0.874934i	$-0.339096\pi$
$829$	−0.902728	−	0.521190i	−0.0313531	−	0.0181017i	−0.515595	+	0.856833i	$0.672429\pi$
$830$	−8.63223	+	3.08428i	−0.299629	+	0.107057i
$831$	42.4841	+	3.24553i	1.47376	+	0.112586i
$832$	15.7313	−	38.8781i	0.545386	−	1.34785i
$833$	−14.8452	+	2.61760i	−0.514354	+	0.0906945i
$834$	−3.62789	−	39.1586i	−0.125624	−	1.35595i
$835$	4.87242	+	4.08844i	0.168617	+	0.141486i
$836$	24.9646	+	14.8091i	0.863420	+	0.512185i
$837$	10.9679	−	5.56295i	0.379106	−	0.192284i
$838$	1.31081	+	2.30166i	0.0452810	+	0.0795095i
$839$	−8.47456	−	7.11100i	−0.292574	−	0.245499i	0.484671	−	0.874696i	$-0.338939\pi$
$839$	−8.47456	−	7.11100i	−0.292574	−	0.245499i	−0.777246	+	0.629197i	$0.783384\pi$
$840$	7.15820	+	10.3700i	0.246981	+	0.357799i
$841$	−1.86324	−	10.5670i	−0.0642498	−	0.364379i
$842$	−4.27077	−	25.0860i	−0.147180	−	0.864521i
$843$	−2.72836	−	5.68652i	−0.0939697	−	0.195854i
$844$	−8.53172	−	7.33238i	−0.293674	−	0.252391i
$845$	5.51376	−	9.55011i	0.189679	−	0.328534i
$846$	−2.41220	+	15.1013i	−0.0829332	+	0.519194i
$847$	−63.0911	+	36.4257i	−2.16784	+	1.25160i
$848$	−24.2180	−	21.3160i	−0.831651	−	0.731994i
$849$	−4.44766	+	4.54679i	−0.152643	+	0.156045i
$850$	20.0222	+	7.42166i	0.686756	+	0.254561i
$851$	−36.7469	−	43.7932i	−1.25967	−	1.50121i
$852$	5.43306	+	20.3406i	0.186134	+	0.696858i
$853$	6.84425	+	18.8044i	0.234343	+	0.643851i	1.00000		0.000602347i	$0.000191733\pi$
$853$	6.84425	+	18.8044i	0.234343	+	0.643851i	−0.765657	+	0.643249i	$0.777586\pi$
$854$	11.0012	+	6.43847i	0.376454	+	0.220320i
$855$	−3.63499	+	4.53119i	−0.124314	+	0.154963i
$856$	3.74281	−	6.22540i	0.127927	−	0.212780i
$857$	29.9891	+	5.28788i	1.02441	+	0.180631i	0.660517	−	0.750811i	$-0.270337\pi$
$857$	29.9891	+	5.28788i	1.02441	+	0.180631i	0.363890	+	0.931442i	$0.381448\pi$
$858$	−41.7242	+	60.2420i	−1.42444	+	2.05663i
$859$	−27.6630	−	10.0685i	−0.943851	−	0.343533i	−0.176165	−	0.984361i	$-0.556369\pi$
$859$	−27.6630	−	10.0685i	−0.943851	−	0.343533i	−0.767685	+	0.640827i	$0.778592\pi$
$860$	9.03211	+	3.40874i	0.307992	+	0.116237i
$861$	−10.0086	−	13.9637i	−0.341093	−	0.475882i
$862$	39.9535	+	7.28839i	1.36082	+	0.248243i
$863$	4.08631			0.139100			0.0695498	−	0.997578i	$-0.477844\pi$
$863$	4.08631			0.139100			0.0695498	+	0.997578i	$0.477844\pi$
$864$	−24.1376	−	16.7743i	−0.821176	−	0.570674i
$865$	3.49382			0.118794
$866$	−9.67421	−	1.76478i	−0.328743	−	0.0599698i
$867$	3.81056	−	8.41259i	0.129413	−	0.285707i
$868$	−14.9612	−	5.64641i	−0.507818	−	0.191652i
$869$	−61.9486	−	22.5474i	−2.10146	−	0.764869i
$870$	−3.40576	−	7.20718i	−0.115466	−	0.244346i
$871$	−14.6014	−	2.57461i	−0.494748	−	0.0872374i
$872$	11.2097	−	18.6451i	0.379609	−	0.631402i
$873$	37.3199	−	22.6577i	1.26309	−	0.766848i
$874$	−16.9301	−	9.90834i	−0.572669	−	0.335154i
$875$	8.28717	+	22.7688i	0.280157	+	0.769726i
$876$	−6.90009	+	6.88921i	−0.233132	+	0.232765i
$877$	34.0441	+	40.5721i	1.14959	+	1.37002i	0.917697	+	0.397282i	$0.130046\pi$
$877$	34.0441	+	40.5721i	1.14959	+	1.37002i	0.231890	+	0.972742i	$0.425509\pi$
$878$	43.8682	+	16.2607i	1.48048	+	0.548772i
$879$	−13.8615	−	49.5413i	−0.467536	−	1.67099i
$880$	11.4822	−	13.0454i	0.387063	−	0.439760i
$881$	−36.3618	+	20.9935i	−1.22506	+	0.707288i	−0.965992	−	0.258571i	$-0.916748\pi$
$881$	−36.3618	+	20.9935i	−1.22506	+	0.707288i	−0.259067	+	0.965859i	$0.583415\pi$
$882$	17.6948	+	6.11887i	0.595814	+	0.206033i
$883$	15.5284	−	26.8959i	0.522571	−	0.905120i	−0.477084	−	0.878858i	$-0.658306\pi$
$883$	15.5284	−	26.8959i	0.522571	−	0.905120i	0.999655	−	0.0262620i	$-0.00836041\pi$
$884$	27.1623	+	23.3440i	0.913566	+	0.785143i
$885$	−3.55605	+	5.19960i	−0.119535	+	0.174783i
$886$	4.16763	+	24.4802i	0.140014	+	0.822428i
$887$	−3.83931	−	21.7738i	−0.128911	−	0.731092i	−0.978908	−	0.204304i	$-0.934507\pi$
$887$	−3.83931	−	21.7738i	−0.128911	−	0.731092i	0.849996	−	0.526789i	$-0.176604\pi$
$888$	−51.1844	+	4.13304i	−1.71764	+	0.138696i
$889$	8.02628	+	6.73485i	0.269193	+	0.225880i
$890$	4.79300	+	8.41610i	0.160662	+	0.282108i
$891$	34.7144	+	37.8500i	1.16298	+	1.26802i
$892$	−2.01249	−	1.19382i	−0.0673832	−	0.0399720i
$893$	7.02260	+	5.89266i	0.235002	+	0.197190i
$894$	−37.6486	+	26.6499i	−1.25916	+	0.891305i
$895$	6.93953	−	1.22363i	0.231963	−	0.0409013i
$896$	5.07605	+	37.8827i	0.169579	+	1.26557i
$897$	27.9567	−	40.8778i	0.933446	−	1.36487i
$898$	55.3400	−	19.7728i	1.84672	−	0.659828i
$899$	8.76098	+	5.05815i	0.292195	+	0.168699i
$900$	−17.2550	−	20.1416i	−0.575167	−	0.671385i
$901$	23.8599	−	13.7755i	0.794890	−	0.458930i
$902$	−15.3376	+	18.0610i	−0.510687	+	0.601365i
$903$	35.7257	−	9.99591i	1.18888	−	0.332643i
$904$	−13.3291	+	10.7879i	−0.443318	+	0.358800i
$905$	−5.74752	−	6.84962i	−0.191054	−	0.227689i
$906$	−10.6747	−	39.0387i	−0.354645	−	1.29697i
$907$	−17.8490	+	6.49651i	−0.592666	+	0.215713i	−0.620902	−	0.783888i	$-0.713233\pi$
$907$	−17.8490	+	6.49651i	−0.592666	+	0.215713i	0.0282353	+	0.999601i	$0.491011\pi$
$908$	0.258471	−	21.8861i	0.00857766	−	0.726317i
$909$	0.330204	+	14.9790i	0.0109522	+	0.496821i
$910$	−0.112599	+	19.0694i	−0.00373261	+	0.632143i
$911$	−1.05476	+	5.98186i	−0.0349458	+	0.198188i	−0.997282	−	0.0736730i	$-0.976528\pi$
$911$	−1.05476	+	5.98186i	−0.0349458	+	0.198188i	0.962337	+	0.271861i	$0.0876390\pi$
$912$	−16.0620	+	7.24493i	−0.531867	+	0.239904i
$913$	45.6528	+	16.6162i	1.51089	+	0.549917i
$914$	15.5741	+	18.7846i	0.515145	+	0.621340i
$915$	3.20487	+	1.45167i	0.105950	+	0.0479908i
$916$	3.70686	+	10.5713i	0.122478	+	0.349286i
$917$	54.8431			1.81108
$918$	20.1632	−	14.9505i	0.665484	−	0.493439i
$919$		−	0.413428i		−	0.0136377i	−0.999977	−	0.00681886i	$-0.997829\pi$
$919$		−	0.413428i		−	0.0136377i	0.999977	−	0.00681886i	$-0.00217053\pi$
$920$	−7.70753	+	8.86184i	−0.254110	+	0.292166i
$921$	−9.33433	−	13.0230i	−0.307577	−	0.429121i
$922$	−15.0093	−	18.1034i	−0.494306	−	0.596205i
$923$	−10.8976	+	29.9409i	−0.358698	+	0.985515i
$924$	5.87295	−	66.5237i	0.193206	−	2.18847i
$925$	−45.6300	−	8.04580i	−1.50031	−	0.264544i
$926$	32.8413	+	0.193918i	1.07923	+	0.00637253i
$927$	2.19549	−	14.2856i	0.0721093	−	0.469202i
$928$	0.713746	−	24.1688i	0.0234299	−	0.793380i
$929$	9.19985	+	25.2764i	0.301837	+	0.829291i	0.994181	+	0.107723i	$0.0343561\pi$
$929$	9.19985	+	25.2764i	0.301837	+	0.829291i	−0.692344	+	0.721568i	$0.743422\pi$
$930$	−4.26923	−	1.12056i	−0.139993	−	0.0367446i
$931$	8.59775	−	7.21437i	0.281780	−	0.236441i
$932$	−27.3670	+	4.49299i	−0.896436	+	0.147173i
$933$	−31.7686	+	32.4766i	−1.04006	+	1.06324i
$934$	−24.1577	−	20.5150i	−0.790465	−	0.671272i
$935$	7.42039	+	12.8525i	0.242673	+	0.420322i
$936$	−15.3953	−	41.7353i	−0.503210	−	1.36416i
$937$	16.3866	−	28.3824i	0.535326	−	0.927211i	−0.463822	−	0.885928i	$-0.653522\pi$
$937$	16.3866	−	28.3824i	0.535326	−	0.927211i	0.999148	−	0.0412827i	$-0.0131444\pi$
$938$	12.7241	−	4.54629i	0.415457	−	0.148442i
$939$	−31.2318	+	14.9849i	−1.01921	+	0.489012i
$940$	4.24593	−	3.47815i	0.138487	−	0.113445i
$941$	2.14333	+	12.1554i	0.0698705	+	0.396255i	0.999607	+	0.0280300i	$0.00892339\pi$
$941$	2.14333	+	12.1554i	0.0698705	+	0.396255i	−0.929737	+	0.368225i	$0.879966\pi$
$942$	11.9477	−	25.9680i	0.389278	−	0.846083i
$943$	10.2930	−	12.2667i	0.335187	−	0.399460i
$944$	−16.7686	+	9.16031i	−0.545772	+	0.298143i
$945$	13.0169	+	3.03050i	0.423440	+	0.0985822i
$946$	−25.3204	−	44.4605i	−0.823238	−	1.44553i
$947$	6.78558	−	8.08674i	0.220502	−	0.262784i	−0.644441	−	0.764654i	$-0.722910\pi$
$947$	6.78558	−	8.08674i	0.220502	−	0.262784i	0.864943	+	0.501870i	$0.167354\pi$
$948$	32.7996	−	22.9280i	1.06528	−	0.744667i
$949$	−14.5321	+	2.56240i	−0.471732	+	0.0831791i
$950$	−15.6733	+	2.66831i	−0.508510	+	0.0865712i
$951$	−3.09317	+	40.4897i	−0.100303	+	1.31297i
$952$	−32.0381	−	6.23625i	−1.03836	−	0.202118i
$953$	−3.50537	−	2.02383i	−0.113550	−	0.0655581i	0.442149	−	0.896941i	$-0.354216\pi$
$953$	−3.50537	−	2.02383i	−0.113550	−	0.0655581i	−0.555699	+	0.831383i	$0.687549\pi$
$954$	−34.2154	+	0.552159i	−1.10776	+	0.0178768i
$955$	4.57078	+	7.91683i	0.147907	+	0.256183i
$956$	−6.41775	+	34.0411i	−0.207565	+	1.10097i
$957$	−10.4841	+	40.9260i	−0.338903	+	1.32295i
$958$	−14.4805	+	39.0656i	−0.467844	+	1.26215i
$959$	0.317444	−	0.266367i	0.0102508	−	0.00860143i
$960$	2.48095	+	10.2538i	0.0800723	+	0.330940i
$961$	−23.8668	+	8.68679i	−0.769896	+	0.280219i
$962$	−67.0716	−	39.2537i	−2.16248	−	1.26559i
$963$	−1.50477	−	7.55615i	−0.0484907	−	0.243494i
$964$	−1.87997	−	3.34687i	−0.0605498	−	0.107795i
$965$	0.0666570	−	0.378031i	0.00214577	−	0.0121692i
$966$	−3.70346	+	44.9799i	−0.119157	+	1.44720i
$967$	−5.69598	+	15.6496i	−0.183170	+	0.503256i	−0.996961	−	0.0779019i	$-0.975178\pi$
$967$	−5.69598	+	15.6496i	−0.183170	+	0.503256i	0.813791	+	0.581158i	$0.197400\pi$
$968$	−60.2449	+	9.52576i	−1.93634	+	0.306170i
$969$	−1.47655	−	14.9745i	−0.0474337	−	0.481050i
$970$	−15.4153	−	2.81208i	−0.494955	−	0.0902905i
$971$		−	0.618203i		−	0.0198391i	−0.999951	−	0.00991953i	$-0.996842\pi$
$971$		−	0.618203i		−	0.0198391i	0.999951	−	0.00991953i	$-0.00315754\pi$
$972$	−30.9116	+	4.05889i	−0.991489	+	0.130189i
$973$			54.2386i			1.73881i
$974$	6.91671	−	37.9160i	0.221626	−	1.21491i
$975$	−3.93870	−	39.9443i	−0.126139	−	1.27924i
$976$	6.66485	+	8.33495i	0.213337	+	0.266795i
$977$	−18.4051	+	50.5677i	−0.588833	+	1.61780i	0.183809	+	0.982962i	$0.441157\pi$
$977$	−18.4051	+	50.5677i	−0.588833	+	1.61780i	−0.772642	+	0.634842i	$0.781065\pi$
$978$	−5.59514	−	0.460681i	−0.178913	−	0.0147310i
$979$	8.91351	−	50.5510i	0.284877	−	1.61562i
$980$	−3.29092	−	5.85875i	−0.105125	−	0.187151i
$981$	−4.50680	−	22.6307i	−0.143891	−	0.722542i
$982$	−11.1324	+	19.0215i	−0.355248	+	0.607002i
$983$	14.7088	−	5.35358i	0.469139	−	0.170753i	−0.0966232	−	0.995321i	$-0.530804\pi$
$983$	14.7088	−	5.35358i	0.469139	−	0.170753i	0.565762	+	0.824568i	$0.308582\pi$
$984$	−3.62970	−	13.9182i	−0.115711	−	0.443697i
$985$	−2.17503	+	1.82507i	−0.0693023	+	0.0581515i
$986$	19.3609	+	7.17653i	0.616577	+	0.228547i
$987$	5.23407	−	20.4319i	0.166602	−	0.650354i
$988$	−26.2048	−	4.94038i	−0.833686	−	0.157174i
$989$	17.2888	+	29.9452i	0.549753	+	0.952201i
$990$	−0.297428	−	18.4306i	−0.00945288	−	0.585762i
$991$	13.5526	+	7.82457i	0.430511	+	0.248556i	0.699564	−	0.714570i	$-0.253377\pi$
$991$	13.5526	+	7.82457i	0.430511	+	0.248556i	−0.269053	+	0.963125i	$0.586711\pi$
$992$	−9.99758	−	8.90488i	−0.317424	−	0.282730i
$993$	3.00232	−	39.3004i	0.0952757	−	1.24716i
$994$	−4.87331	−	28.6252i	−0.154572	−	0.907938i
$995$	19.4731	−	3.43364i	0.617340	−	0.108854i
$996$	−24.1715	+	16.8967i	−0.765905	+	0.535392i
$997$	5.45472	−	6.50068i	0.172753	−	0.205879i	−0.672720	−	0.739897i	$-0.734874\pi$
$997$	5.45472	−	6.50068i	0.172753	−	0.205879i	0.845473	+	0.534018i	$0.179319\pi$
$998$	7.75901	−	4.41879i	0.245607	−	0.139874i
$999$	−37.2192	+	39.7653i	−1.17756	+	1.25812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.30	yes	192
3.2	odd	2		648.2.v.b.35.3		192
4.3	odd	2		864.2.bh.b.335.31		192
8.3	odd	2	inner	216.2.v.b.11.13	✓	192
8.5	even	2		864.2.bh.b.335.32		192
24.11	even	2		648.2.v.b.35.20		192
27.5	odd	18	inner	216.2.v.b.59.13	yes	192
27.22	even	9		648.2.v.b.611.20		192
108.59	even	18		864.2.bh.b.815.32		192
216.5	odd	18		864.2.bh.b.815.31		192
216.59	even	18	inner	216.2.v.b.59.30	yes	192
216.211	odd	18		648.2.v.b.611.3		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.13	✓	192	8.3	odd	2	inner
216.2.v.b.11.30	yes	192	1.1	even	1	trivial
216.2.v.b.59.13	yes	192	27.5	odd	18	inner
216.2.v.b.59.30	yes	192	216.59	even	18	inner
648.2.v.b.35.3		192	3.2	odd	2
648.2.v.b.35.20		192	24.11	even	2
648.2.v.b.611.3		192	216.211	odd	18
648.2.v.b.611.20		192	27.22	even	9
864.2.bh.b.335.31		192	4.3	odd	2
864.2.bh.b.335.32		192	8.5	even	2
864.2.bh.b.815.31		192	216.5	odd	18
864.2.bh.b.815.32		192	108.59	even	18

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.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39125 + 0.253795i) q^{2} +(-1.72369 + 0.169964i) q^{3} +(1.87118 + 0.706186i) q^{4} +(-0.715441 - 0.260399i) q^{5} +(-2.44123 - 0.201001i) q^{6} +(3.32699 + 0.586638i) q^{7} +(2.42406 + 1.45738i) q^{8} +(2.94222 - 0.585931i) q^{9} +O(q^{10})\)	\(q+(1.39125 + 0.253795i) q^{2} +(-1.72369 + 0.169964i) q^{3} +(1.87118 + 0.706186i) q^{4} +(-0.715441 - 0.260399i) q^{5} +(-2.44123 - 0.201001i) q^{6} +(3.32699 + 0.586638i) q^{7} +(2.42406 + 1.45738i) q^{8} +(2.94222 - 0.585931i) q^{9} +(-0.929272 - 0.543857i) q^{10} +(1.95175 + 5.36238i) q^{11} +(-3.34536 - 0.899214i) q^{12} +(-3.36983 - 4.01601i) q^{13} +(4.47981 + 1.66054i) q^{14} +(1.27746 + 0.327249i) q^{15} +(3.00260 + 2.64280i) q^{16} +(-2.95820 + 1.70792i) q^{17} +(4.24209 - 0.0684577i) q^{18} +(1.27164 - 2.20255i) q^{19} +(-1.15483 - 0.992487i) q^{20} +(-5.83441 - 0.445715i) q^{21} +(1.35443 + 7.95577i) q^{22} +(-0.947065 - 5.37107i) q^{23} +(-4.42603 - 2.10007i) q^{24} +(-3.38617 - 2.84134i) q^{25} +(-3.66905 - 6.44253i) q^{26} +(-4.97190 + 1.51004i) q^{27} +(5.81111 + 3.44718i) q^{28} +(-3.27434 - 2.74749i) q^{29} +(1.69421 + 0.779498i) q^{30} +(-2.33080 + 0.410982i) q^{31} +(3.50665 + 4.43885i) q^{32} +(-4.27562 - 8.91136i) q^{33} +(-4.54907 + 1.62537i) q^{34} +(-2.22751 - 1.28605i) q^{35} +(5.91920 + 0.981378i) q^{36} +(9.07767 - 5.24099i) q^{37} +(2.32817 - 2.74157i) q^{38} +(6.49112 + 6.34960i) q^{39} +(-1.35477 - 1.67389i) q^{40} +(1.88727 + 2.24916i) q^{41} +(-8.00403 - 2.10085i) q^{42} +(-5.95761 + 2.16839i) q^{43} +(-0.134776 + 11.4123i) q^{44} +(-2.25756 - 0.346954i) q^{45} +(0.0455422 - 7.71289i) q^{46} +(-0.625921 + 3.54977i) q^{47} +(-5.62474 - 4.04503i) q^{48} +(4.14688 + 1.50934i) q^{49} +(-3.98991 - 4.81242i) q^{50} +(4.80874 - 3.44671i) q^{51} +(-3.46950 - 9.89438i) q^{52} -8.06569 q^{53} +(-7.30042 + 0.839002i) q^{54} -4.34470i q^{55} +(7.20986 + 6.27073i) q^{56} +(-1.81756 + 4.01265i) q^{57} +(-3.85813 - 4.65347i) q^{58} +(-1.63379 + 4.48880i) q^{59} +(2.15925 + 1.51446i) q^{60} +(2.62747 + 0.463294i) q^{61} +(-3.34703 - 0.0197632i) q^{62} +(10.1325 - 0.223366i) q^{63} +(3.75209 + 7.06554i) q^{64} +(1.36515 + 3.75071i) q^{65} +(-3.68682 - 13.4831i) q^{66} +(2.16648 - 1.81790i) q^{67} +(-6.74143 + 1.10678i) q^{68} +(2.54534 + 9.09710i) q^{69} +(-2.77263 - 2.35455i) q^{70} +(-3.03884 - 5.26343i) q^{71} +(7.98604 + 2.86761i) q^{72} +(1.40736 - 2.43763i) q^{73} +(13.9595 - 4.98769i) q^{74} +(6.31965 + 4.32206i) q^{75} +(3.93488 - 3.22334i) q^{76} +(3.34767 + 18.9856i) q^{77} +(7.41930 + 10.4813i) q^{78} +(-7.42577 + 8.84969i) q^{79} +(-1.46000 - 2.67264i) q^{80} +(8.31337 - 3.44788i) q^{81} +(2.05484 + 3.60813i) q^{82} +(5.47239 - 6.52174i) q^{83} +(-10.6025 - 4.95419i) q^{84} +(2.56116 - 0.451602i) q^{85} +(-8.83888 + 1.50478i) q^{86} +(6.11092 + 4.17931i) q^{87} +(-3.08388 + 15.8431i) q^{88} +(-7.79000 - 4.49756i) q^{89} +(-3.05279 - 1.05566i) q^{90} +(-8.85545 - 15.3381i) q^{91} +(2.02085 - 10.7190i) q^{92} +(3.94772 - 1.10456i) q^{93} +(-1.77173 + 4.77978i) q^{94} +(-1.48333 + 1.24466i) q^{95} +(-6.79883 - 7.05520i) q^{96} +(13.6755 - 4.97747i) q^{97} +(5.38630 + 3.15233i) q^{98} +(8.88446 + 14.6337i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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