LMFDB - Embedded newform 216.2.t.a.205.20

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			205.20
Character	$\chi$	$=$	216.205
Dual form			216.2.t.a.157.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.139081 - 1.40736i) q^{2} +(1.67311 - 0.447985i) q^{3} +(-1.96131 - 0.391473i) q^{4} +(0.141945 - 0.389992i) q^{5} +(-0.397778 - 2.41698i) q^{6} +(0.275847 - 1.56441i) q^{7} +(-0.823724 + 2.70582i) q^{8} +(2.59862 - 1.49906i) q^{9} +O(q^{10})$	\(q+(0.139081 - 1.40736i) q^{2} +(1.67311 - 0.447985i) q^{3} +(-1.96131 - 0.391473i) q^{4} +(0.141945 - 0.389992i) q^{5} +(-0.397778 - 2.41698i) q^{6} +(0.275847 - 1.56441i) q^{7} +(-0.823724 + 2.70582i) q^{8} +(2.59862 - 1.49906i) q^{9} +(-0.529116 - 0.254008i) q^{10} +(-0.0599272 - 0.164649i) q^{11} +(-3.45687 + 0.223660i) q^{12} +(-2.46059 - 2.93241i) q^{13} +(-2.16332 - 0.605795i) q^{14} +(0.0627802 - 0.716090i) q^{15} +(3.69350 + 1.53560i) q^{16} +(2.86613 + 4.96428i) q^{17} +(-1.74830 - 3.86568i) q^{18} +(-1.93026 - 1.11443i) q^{19} +(-0.431071 + 0.709328i) q^{20} +(-0.239308 - 2.74101i) q^{21} +(-0.240054 + 0.0614396i) q^{22} +(0.766596 + 4.34758i) q^{23} +(-0.166015 + 4.89617i) q^{24} +(3.69828 + 3.10322i) q^{25} +(-4.46917 + 3.05508i) q^{26} +(3.67623 - 3.67224i) q^{27} +(-1.15345 + 2.96031i) q^{28} +(-4.91044 + 5.85204i) q^{29} +(-0.999064 - 0.187949i) q^{30} +(-0.320688 - 1.81871i) q^{31} +(2.67484 - 4.98450i) q^{32} +(-0.174025 - 0.248629i) q^{33} +(7.38514 - 3.34323i) q^{34} +(-0.570951 - 0.329639i) q^{35} +(-5.68355 + 1.92284i) q^{36} +(1.08361 - 0.625621i) q^{37} +(-1.83687 + 2.56157i) q^{38} +(-5.43052 - 3.80395i) q^{39} +(0.938325 + 0.705325i) q^{40} +(-3.02029 + 2.53433i) q^{41} +(-3.89086 - 0.0444299i) q^{42} +(0.731061 + 2.00857i) q^{43} +(0.0530805 + 0.346388i) q^{44} +(-0.215760 - 1.22622i) q^{45} +(6.22522 - 0.474209i) q^{46} +(1.57990 - 8.96007i) q^{47} +(6.86757 + 0.914606i) q^{48} +(4.20657 + 1.53107i) q^{49} +(4.88171 - 4.77320i) q^{50} +(7.01928 + 7.02182i) q^{51} +(3.67802 + 6.71463i) q^{52} +13.3090i q^{53} +(-4.65687 - 5.68451i) q^{54} -0.0727180 q^{55} +(4.00579 + 2.03504i) q^{56} +(-3.72879 - 0.999849i) q^{57} +(7.55296 + 7.72466i) q^{58} +(1.89616 - 5.20965i) q^{59} +(-0.403462 + 1.37990i) q^{60} +(5.96533 + 1.05185i) q^{61} +(-2.60418 + 0.198374i) q^{62} +(-1.62832 - 4.47881i) q^{63} +(-6.64296 - 4.45770i) q^{64} +(-1.49289 + 0.543366i) q^{65} +(-0.374114 + 0.210336i) q^{66} +(-9.26414 - 11.0406i) q^{67} +(-3.67799 - 10.8585i) q^{68} +(3.23026 + 6.93058i) q^{69} +(-0.543328 + 0.757686i) q^{70} +(3.41074 + 5.90757i) q^{71} +(1.91565 + 8.26621i) q^{72} +(-4.55745 + 7.89374i) q^{73} +(-0.729764 - 1.61204i) q^{74} +(7.57784 + 3.53527i) q^{75} +(3.34957 + 2.94140i) q^{76} +(-0.274109 + 0.0483327i) q^{77} +(-6.10880 + 7.11362i) q^{78} +(-6.16792 - 5.17550i) q^{79} +(1.12315 - 1.22246i) q^{80} +(4.50563 - 7.79097i) q^{81} +(3.14664 + 4.60311i) q^{82} +(-2.20213 + 2.62440i) q^{83} +(-0.603674 + 5.46966i) q^{84} +(2.34286 - 0.413110i) q^{85} +(2.92846 - 0.749510i) q^{86} +(-5.59410 + 11.9909i) q^{87} +(0.494874 - 0.0265273i) q^{88} +(4.28674 - 7.42485i) q^{89} +(-1.75575 + 0.133106i) q^{90} +(-5.26623 + 3.04046i) q^{91} +(0.198428 - 8.82707i) q^{92} +(-1.35130 - 2.89925i) q^{93} +(-12.3903 - 3.46966i) q^{94} +(-0.708612 + 0.594596i) q^{95} +(2.24233 - 9.53792i) q^{96} +(-15.8647 + 5.77429i) q^{97} +(2.73981 - 5.70720i) q^{98} +(-0.402546 - 0.338025i) 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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.139081	−	1.40736i	0.0983451	−	0.995152i
$2$	0.139081	−	1.40736i	0.0983451	−	0.995152i
$3$	1.67311	−	0.447985i	0.965973	−	0.258644i
$3$	1.67311	−	0.447985i	0.965973	−	0.258644i
$4$	−1.96131	−	0.391473i	−0.980656	−	0.195737i
$5$	0.141945	−	0.389992i	0.0634799	−	0.174410i	−0.903898	−	0.427749i	$-0.859307\pi$
$5$	0.141945	−	0.389992i	0.0634799	−	0.174410i	0.967377	+	0.253339i	$0.0815289\pi$
$6$	−0.397778	−	2.41698i	−0.162392	−	0.986726i
$7$	0.275847	−	1.56441i	0.104261	−	0.591291i	−0.887253	−	0.461284i	$-0.847389\pi$
$7$	0.275847	−	1.56441i	0.104261	−	0.591291i	0.991513	−	0.130007i	$-0.0414999\pi$
$8$	−0.823724	+	2.70582i	−0.291231	+	0.956653i
$9$	2.59862	−	1.49906i	0.866206	−	0.499687i
$10$	−0.529116	−	0.254008i	−0.167321	−	0.0803245i
$11$	−0.0599272	−	0.164649i	−0.0180687	−	0.0496434i	0.930330	−	0.366723i	$-0.119520\pi$
$11$	−0.0599272	−	0.164649i	−0.0180687	−	0.0496434i	−0.948399	+	0.317079i	$0.897298\pi$
$12$	−3.45687	+	0.223660i	−0.997913	+	0.0645652i
$13$	−2.46059	−	2.93241i	−0.682444	−	0.813305i	0.307976	−	0.951394i	$-0.400348\pi$
$13$	−2.46059	−	2.93241i	−0.682444	−	0.813305i	−0.990420	+	0.138089i	$0.955904\pi$
$14$	−2.16332	−	0.605795i	−0.578171	−	0.161906i
$15$	0.0627802	−	0.716090i	0.0162098	−	0.184894i
$16$	3.69350	+	1.53560i	0.923374	+	0.383901i
$17$	2.86613	+	4.96428i	0.695138	+	1.20401i	0.970134	+	0.242569i	$0.0779902\pi$
$17$	2.86613	+	4.96428i	0.695138	+	1.20401i	−0.274996	+	0.961445i	$0.588676\pi$
$18$	−1.74830	−	3.86568i	−0.412078	−	0.911149i
$19$	−1.93026	−	1.11443i	−0.442831	−	0.255669i	0.261966	−	0.965077i	$-0.415629\pi$
$19$	−1.93026	−	1.11443i	−0.442831	−	0.255669i	−0.704798	+	0.709408i	$0.748962\pi$
$20$	−0.431071	+	0.709328i	−0.0963904	+	0.158611i
$21$	−0.239308	−	2.74101i	−0.0522213	−	0.598137i
$22$	−0.240054	+	0.0614396i	−0.0511798	+	0.0130990i
$23$	0.766596	+	4.34758i	0.159846	+	0.906534i	0.954220	+	0.299105i	$0.0966880\pi$
$23$	0.766596	+	4.34758i	0.159846	+	0.906534i	−0.794374	+	0.607429i	$0.792201\pi$
$24$	−0.166015	+	4.89617i	−0.0338877	+	0.999426i
$25$	3.69828	+	3.10322i	0.739655	+	0.620645i
$26$	−4.46917	+	3.05508i	−0.876477	+	0.599151i
$27$	3.67623	−	3.67224i	0.707490	−	0.706723i
$28$	−1.15345	+	2.96031i	−0.217981	+	0.559445i
$29$	−4.91044	+	5.85204i	−0.911846	+	1.08670i	0.0840741	+	0.996460i	$0.473207\pi$
$29$	−4.91044	+	5.85204i	−0.911846	+	1.08670i	−0.995920	+	0.0902366i	$0.971238\pi$
$30$	−0.999064	−	0.187949i	−0.182403	−	0.0343146i
$31$	−0.320688	−	1.81871i	−0.0575972	−	0.326650i	0.942371	−	0.334568i	$-0.108591\pi$
$31$	−0.320688	−	1.81871i	−0.0575972	−	0.326650i	−0.999969	+	0.00791850i	$0.997479\pi$
$32$	2.67484	−	4.98450i	0.472849	−	0.881143i
$33$	−0.174025	−	0.248629i	−0.0302939	−	0.0432808i
$34$	7.38514	−	3.34323i	1.26654	−	0.573360i
$35$	−0.570951	−	0.329639i	−0.0965084	−	0.0557191i
$36$	−5.68355	+	1.92284i	−0.947258	+	0.320473i
$37$	1.08361	−	0.625621i	0.178144	−	0.102851i	−0.408276	−	0.912858i	$-0.633870\pi$
$37$	1.08361	−	0.625621i	0.178144	−	0.102851i	0.586420	+	0.810007i	$0.300537\pi$
$38$	−1.83687	+	2.56157i	−0.297980	+	0.415541i
$39$	−5.43052	−	3.80395i	−0.869579	−	0.609120i
$40$	0.938325	+	0.705325i	0.148362	+	0.111522i
$41$	−3.02029	+	2.53433i	−0.471691	+	0.395795i	−0.847411	−	0.530938i	$-0.821840\pi$
$41$	−3.02029	+	2.53433i	−0.471691	+	0.395795i	0.375720	+	0.926733i	$0.377395\pi$
$42$	−3.89086	−	0.0444299i	−0.600373	−	0.00685569i
$43$	0.731061	+	2.00857i	0.111486	+	0.306305i	0.982871	−	0.184295i	$-0.0590001\pi$
$43$	0.731061	+	2.00857i	0.111486	+	0.306305i	−0.871385	+	0.490599i	$0.836778\pi$
$44$	0.0530805	+	0.346388i	0.00800218	+	0.0522199i
$45$	−0.215760	−	1.22622i	−0.0321635	−	0.182795i
$46$	6.22522	−	0.474209i	0.917859	−	0.0699184i
$47$	1.57990	−	8.96007i	0.230452	−	1.30696i	−0.621530	−	0.783390i	$-0.713489\pi$
$47$	1.57990	−	8.96007i	0.230452	−	1.30696i	0.851983	−	0.523570i	$-0.175400\pi$
$48$	6.86757	+	0.914606i	0.991248	+	0.132012i
$49$	4.20657	+	1.53107i	0.600938	+	0.218724i
$50$	4.88171	−	4.77320i	0.690377	−	0.675033i
$51$	7.01928	+	7.02182i	0.982896	+	0.983252i
$52$	3.67802	+	6.71463i	0.510049	+	0.931152i
$53$			13.3090i			1.82813i	0.405567	+	0.914065i	$0.367074\pi$
$53$			13.3090i			1.82813i	−0.405567	+	0.914065i	$0.632926\pi$
$54$	−4.65687	−	5.68451i	−0.633719	−	0.773563i
$55$	−0.0727180			−0.00980530
$56$	4.00579	+	2.03504i	0.535296	+	0.271943i
$57$	−3.72879	−	0.999849i	−0.493890	−	0.132433i
$58$	7.55296	+	7.72466i	0.991753	+	1.01430i
$59$	1.89616	−	5.20965i	0.246859	−	0.678239i	−0.752938	−	0.658091i	$-0.771364\pi$
$59$	1.89616	−	5.20965i	0.246859	−	0.678239i	0.999797	−	0.0201475i	$-0.00641359\pi$
$60$	−0.403462	+	1.37990i	−0.0520867	+	0.178144i
$61$	5.96533	+	1.05185i	0.763782	+	0.134675i	0.541951	−	0.840410i	$-0.317686\pi$
$61$	5.96533	+	1.05185i	0.763782	+	0.134675i	0.221831	+	0.975085i	$0.428797\pi$
$62$	−2.60418	+	0.198374i	−0.330731	+	0.0251936i
$63$	−1.62832	−	4.47881i	−0.205149	−	0.564277i
$64$	−6.64296	−	4.45770i	−0.830370	−	0.557213i
$65$	−1.49289	+	0.543366i	−0.185170	+	0.0673962i
$66$	−0.374114	+	0.210336i	−0.0460503	+	0.0258906i
$67$	−9.26414	−	11.0406i	−1.13180	−	1.34882i	−0.929208	−	0.369557i	$-0.879509\pi$
$67$	−9.26414	−	11.0406i	−1.13180	−	1.34882i	−0.202587	−	0.979264i	$-0.564935\pi$
$68$	−3.67799	−	10.8585i	−0.446022	−	1.31679i
$69$	3.23026	+	6.93058i	0.388877	+	0.834343i
$70$	−0.543328	+	0.757686i	−0.0649401	+	0.0905608i
$71$	3.41074	+	5.90757i	0.404780	+	0.701100i	0.994296	−	0.106657i	$-0.0340147\pi$
$71$	3.41074	+	5.90757i	0.404780	+	0.701100i	−0.589516	+	0.807757i	$0.700681\pi$
$72$	1.91565	+	8.26621i	0.225761	+	0.974183i
$73$	−4.55745	+	7.89374i	−0.533409	+	0.923892i	0.465829	+	0.884875i	$0.345756\pi$
$73$	−4.55745	+	7.89374i	−0.533409	+	0.923892i	−0.999239	+	0.0390176i	$0.987577\pi$
$74$	−0.729764	−	1.61204i	−0.0848333	−	0.187395i
$75$	7.57784	+	3.53527i	0.875013	+	0.408218i
$76$	3.34957	+	2.94140i	0.384222	+	0.337402i
$77$	−0.274109	+	0.0483327i	−0.0312376	+	0.00550803i
$78$	−6.10880	+	7.11362i	−0.691686	+	0.805459i
$79$	−6.16792	−	5.17550i	−0.693945	−	0.582289i	0.226099	−	0.974104i	$-0.427403\pi$
$79$	−6.16792	−	5.17550i	−0.693945	−	0.582289i	−0.920044	+	0.391815i	$0.871847\pi$
$80$	1.12315	−	1.22246i	0.125572	−	0.136675i
$81$	4.50563	−	7.79097i	0.500626	−	0.865664i
$82$	3.14664	+	4.60311i	0.347488	+	0.508329i
$83$	−2.20213	+	2.62440i	−0.241716	+	0.288065i	−0.873240	−	0.487291i	$-0.837985\pi$
$83$	−2.20213	+	2.62440i	−0.241716	+	0.288065i	0.631524	+	0.775356i	$0.282430\pi$
$84$	−0.603674	+	5.46966i	−0.0658662	+	0.596789i
$85$	2.34286	−	0.413110i	0.254119	−	0.0448081i
$86$	2.92846	−	0.749510i	0.315784	−	0.0808218i
$87$	−5.59410	+	11.9909i	−0.599751	+	1.28556i
$88$	0.494874	−	0.0265273i	0.0527537	−	0.00282782i
$89$	4.28674	−	7.42485i	0.454393	−	0.787032i	−0.544260	−	0.838917i	$-0.683189\pi$
$89$	4.28674	−	7.42485i	0.454393	−	0.787032i	0.998653	+	0.0518843i	$0.0165227\pi$
$90$	−1.75575	+	0.133106i	−0.185072	+	0.0140307i
$91$	−5.26623	+	3.04046i	−0.552051	+	0.318727i
$92$	0.198428	−	8.82707i	0.0206875	−	0.920286i
$93$	−1.35130	−	2.89925i	−0.140124	−	0.300638i
$94$	−12.3903	−	3.46966i	−1.27796	−	0.357868i
$95$	−0.708612	+	0.594596i	−0.0727020	+	0.0610042i
$96$	2.24233	−	9.53792i	0.228856	−	0.973460i
$97$	−15.8647	+	5.77429i	−1.61082	+	0.586291i	−0.981602	−	0.190938i	$-0.938847\pi$
$97$	−15.8647	+	5.77429i	−1.61082	+	0.586291i	−0.629219	+	0.777228i	$0.716625\pi$
$98$	2.73981	−	5.70720i	0.276763	−	0.576515i
$99$	−0.402546	−	0.338025i	−0.0404574	−	0.0339727i
$100$	−6.03865	−	7.53417i	−0.603865	−	0.753417i
$101$	−9.80937	−	1.72966i	−0.976069	−	0.172107i	−0.337208	−	0.941430i	$-0.609483\pi$
$101$	−9.80937	−	1.72966i	−0.976069	−	0.172107i	−0.638860	+	0.769323i	$0.720594\pi$
$102$	10.8585	−	8.90204i	1.07515	−	0.881434i
$103$	−3.75903	−	1.36817i	−0.370388	−	0.134810i	0.150118	−	0.988668i	$-0.452035\pi$
$103$	−3.75903	−	1.36817i	−0.370388	−	0.134810i	−0.520506	+	0.853858i	$0.674257\pi$
$104$	9.96143	−	4.24241i	0.976799	−	0.416003i
$105$	−1.10294	−	0.295745i	−0.107636	−	0.0288618i
$106$	18.7305	+	1.85103i	1.81927	+	0.179788i
$107$		−	5.21018i		−	0.503688i	−0.967768	−	0.251844i	$-0.918963\pi$
$107$		−	5.21018i		−	0.503688i	0.967768	−	0.251844i	$-0.0810369\pi$
$108$	−8.64781	+	5.76327i	−0.832136	+	0.554571i
$109$		−	10.9921i		−	1.05285i	−0.850221	−	0.526426i	$-0.823532\pi$
$109$		−	10.9921i		−	1.05285i	0.850221	−	0.526426i	$-0.176468\pi$
$110$	−0.0101137	+	0.102340i	−0.000964303	+	0.00975777i
$111$	1.53273	−	1.53218i	0.145480	−	0.145428i
$112$	3.42115	−	5.35455i	0.323268	−	0.505957i
$113$	−15.5673	−	5.66605i	−1.46445	−	0.533017i	−0.517864	−	0.855463i	$-0.673273\pi$
$113$	−15.5673	−	5.66605i	−1.46445	−	0.533017i	−0.946588	+	0.322446i	$0.895495\pi$
$114$	−1.92575	+	5.10868i	−0.180363	+	0.478472i
$115$	1.80434	+	0.318153i	0.168255	+	0.0296679i
$116$	11.9218	−	9.55537i	1.10691	−	0.887194i
$117$	−10.7900	−	3.93165i	−0.997534	−	0.363481i
$118$	−7.06812	−	3.39313i	−0.650673	−	0.312363i
$119$	8.55677	−	3.11441i	0.784398	−	0.285498i
$120$	1.88590	+	0.759733i	0.172158	+	0.0693538i
$121$	8.40297	−	7.05093i	0.763906	−	0.640994i
$122$	2.30999	−	8.24906i	0.209137	−	0.746835i
$123$	−3.91795	+	5.59327i	−0.353270	+	0.504328i
$124$	−0.0830075	+	3.69260i	−0.00745430	+	0.331605i
$125$	3.53228	−	2.03936i	0.315937	−	0.182406i
$126$	−6.52976	+	1.66871i	−0.581717	+	0.148661i
$127$	1.71084	−	2.96325i	0.151812	−	0.262946i	−0.780082	−	0.625678i	$-0.784822\pi$
$127$	1.71084	−	2.96325i	0.151812	−	0.262946i	0.931894	+	0.362732i	$0.118156\pi$
$128$	−7.19749	+	8.72904i	−0.636175	+	0.771545i
$129$	2.12296	+	3.03307i	0.186916	+	0.267047i
$130$	0.557078	+	2.17660i	0.0488590	+	0.190900i
$131$	−6.19124	+	1.09168i	−0.540931	+	0.0953807i	−0.437436	−	0.899249i	$-0.644113\pi$
$131$	−6.19124	+	1.09168i	−0.540931	+	0.0953807i	−0.103494	+	0.994630i	$0.533002\pi$
$132$	0.243986	+	0.555766i	0.0212363	+	0.0483733i
$133$	−2.27589	+	2.71230i	−0.197344	+	0.235186i
$134$	−16.8265	+	11.5024i	−1.45359	+	0.993659i
$135$	−0.910321	−	1.95496i	−0.0783480	−	0.168256i
$136$	−15.7934	+	3.66604i	−1.35427	+	0.314360i
$137$	−6.32766	−	5.30954i	−0.540608	−	0.453624i	0.331138	−	0.943583i	$-0.392568\pi$
$137$	−6.32766	−	5.30954i	−0.540608	−	0.453624i	−0.871746	+	0.489958i	$0.837012\pi$
$138$	10.2031	−	3.58222i	0.868543	−	0.304938i
$139$	−9.54087	+	1.68231i	−0.809246	+	0.142692i	−0.562937	−	0.826500i	$-0.690329\pi$
$139$	−9.54087	+	1.68231i	−0.809246	+	0.142692i	−0.246309	+	0.969191i	$0.579218\pi$
$140$	0.990769	+	0.870037i	0.0837353	+	0.0735316i
$141$	−1.37062	−	15.6990i	−0.115427	−	1.32209i
$142$	8.78844	−	3.97850i	0.737509	−	0.333868i
$143$	−0.335362	+	0.580863i	−0.0280444	+	0.0485742i
$144$	11.9000	−	1.54633i	0.991663	−	0.128861i
$145$	1.58523	+	2.74570i	0.131646	+	0.228018i
$146$	10.4755	+	7.51184i	0.866955	+	0.621684i
$147$	7.72396	+	0.677166i	0.637061	+	0.0558517i
$148$	−2.37021	+	0.802835i	−0.194830	+	0.0659927i
$149$	10.8188	+	12.8933i	0.886308	+	1.05626i	0.998044	+	0.0625230i	$0.0199147\pi$
$149$	10.8188	+	12.8933i	0.886308	+	1.05626i	−0.111735	+	0.993738i	$0.535641\pi$
$150$	6.02932	−	10.1730i	0.492292	−	0.830625i
$151$	−19.2524	+	7.00729i	−1.56674	+	0.570245i	−0.972267	−	0.233873i	$-0.924860\pi$
$151$	−19.2524	+	7.00729i	−1.56674	+	0.570245i	−0.594469	+	0.804118i	$0.702638\pi$
$152$	4.60546	−	4.30495i	0.373552	−	0.349177i
$153$	14.8897	+	8.60377i	1.20376	+	0.695573i
$154$	0.0298982	+	0.392491i	0.00240926	+	0.0316278i
$155$	−0.754802	−	0.133092i	−0.0606272	−	0.0106902i
$156$	9.16180	+	9.58664i	0.733531	+	0.767546i
$157$	5.19403	−	14.2705i	0.414529	−	1.13891i	−0.540228	−	0.841519i	$-0.681662\pi$
$157$	5.19403	−	14.2705i	0.414529	−	1.13891i	0.954756	−	0.297389i	$-0.0961159\pi$
$158$	−8.14162	+	7.96066i	−0.647713	+	0.633316i
$159$	5.96223	+	22.2675i	0.472836	+	1.76592i
$160$	−1.56423	−	1.75069i	−0.123664	−	0.138404i
$161$	7.01286			0.552691
$162$	−10.3380	−	7.42461i	−0.812233	−	0.583333i
$163$			20.1038i			1.57465i	0.616540	+	0.787324i	$0.288534\pi$
$163$			20.1038i			1.57465i	−0.616540	+	0.787324i	$0.711466\pi$
$164$	6.91586	−	3.78824i	0.540038	−	0.295812i
$165$	−0.121666	+	0.0325766i	−0.00947165	+	0.00253609i
$166$	3.38720	+	3.46420i	0.262897	+	0.268874i
$167$	11.4766	+	4.17713i	0.888084	+	0.323236i	0.745468	−	0.666542i	$-0.232226\pi$
$167$	11.4766	+	4.17713i	0.888084	+	0.323236i	0.142617	+	0.989778i	$0.454448\pi$
$168$	7.61381	+	1.61031i	0.587418	+	0.124238i
$169$	−0.287130	+	1.62840i	−0.0220869	+	0.125261i
$170$	−0.255546	−	3.35470i	−0.0195995	−	0.257294i
$171$	−6.68661	−	0.00241689i	−0.511338	−	0.000184824i
$172$	−0.647537	−	4.22563i	−0.0493742	−	0.322201i
$173$	0.129408	+	0.355545i	0.00983868	+	0.0270316i	0.944515	−	0.328469i	$-0.106533\pi$
$173$	0.129408	+	0.355545i	0.00983868	+	0.0270316i	−0.934676	+	0.355501i	$0.884310\pi$
$174$	16.0975	+	9.54061i	1.22035	+	0.723272i
$175$	5.87487	−	4.92960i	0.444098	−	0.372643i
$176$	0.0314940	−	0.700154i	0.00237395	−	0.0527761i
$177$	0.838640	−	9.56579i	0.0630360	−	0.719008i
$178$	−9.85322	−	7.06563i	−0.738530	−	0.529591i
$179$	13.7833	−	7.95779i	1.03021	−	0.594793i	0.113167	−	0.993576i	$-0.463901\pi$
$179$	13.7833	−	7.95779i	1.03021	−	0.594793i	0.917045	+	0.398783i	$0.130567\pi$
$180$	−0.0568622	+	2.48947i	−0.00423826	+	0.185554i
$181$	8.74868	+	5.05105i	0.650284	+	0.375442i	0.788565	−	0.614951i	$-0.210824\pi$
$181$	8.74868	+	5.05105i	0.650284	+	0.375442i	−0.138281	+	0.990393i	$0.544158\pi$
$182$	3.54659	+	7.83435i	0.262890	+	0.580720i
$183$	10.4519	−	0.912518i	0.772626	−	0.0674553i
$184$	−12.3953	−	1.50694i	−0.913790	−	0.111093i
$185$	−0.0901740	−	0.511402i	−0.00662972	−	0.0375990i
$186$	−4.26822	+	1.49854i	−0.312961	+	0.109878i
$187$	0.645603	−	0.769400i	0.0472112	−	0.0562641i
$188$	−6.60631	+	16.9550i	−0.481815	+	1.23657i
$189$	−4.73081	−	6.76410i	−0.344116	−	0.492016i
$190$	0.738255	+	1.07997i	0.0535586	+	0.0783491i
$191$	−8.91900	−	7.48393i	−0.645356	−	0.541518i	0.260302	−	0.965527i	$-0.416178\pi$
$191$	−8.91900	−	7.48393i	−0.645356	−	0.541518i	−0.905658	+	0.424009i	$0.860622\pi$
$192$	−13.1114	−	4.48230i	−0.946234	−	0.323482i
$193$	−4.01975	−	22.7971i	−0.289348	−	1.64097i	−0.689329	−	0.724449i	$-0.742094\pi$
$193$	−4.01975	−	22.7971i	−0.289348	−	1.64097i	0.399981	−	0.916523i	$-0.369017\pi$
$194$	5.92002	+	23.1305i	0.425032	+	1.66067i
$195$	−2.25435	+	1.57790i	−0.161437	+	0.112996i
$196$	−7.65102	−	4.64966i	−0.546502	−	0.332118i
$197$	8.46293	+	4.88607i	0.602959	+	0.348118i	0.770205	−	0.637797i	$-0.220154\pi$
$197$	8.46293	+	4.88607i	0.602959	+	0.348118i	−0.167246	+	0.985915i	$0.553487\pi$
$198$	−0.531708	+	0.519514i	−0.0377868	+	0.0369203i
$199$	12.5020	+	21.6540i	0.886240	+	1.53501i	0.844286	+	0.535893i	$0.180025\pi$
$199$	12.5020	+	21.6540i	0.886240	+	1.53501i	0.0419537	+	0.999120i	$0.486642\pi$
$200$	−11.4431	+	7.45068i	−0.809152	+	0.526843i
$201$	−20.4460	−	14.3219i	−1.44215	−	1.01019i
$202$	−3.79854	+	13.5647i	−0.267264	+	0.954411i
$203$	7.80044	+	9.29621i	0.547484	+	0.652466i
$204$	−11.0182	−	16.5199i	−0.771425	−	1.15662i
$205$	0.559650	+	1.53763i	0.0390877	+	0.107392i
$206$	−2.44832	+	5.10001i	−0.170583	+	0.355335i
$207$	8.50938	+	10.1485i	0.591443	+	0.705372i
$208$	−4.58514	−	14.6093i	−0.317923	−	1.01298i
$209$	−0.0678152	+	0.384599i	−0.00469088	+	0.0266033i
$210$	−0.569618	+	1.51110i	−0.0393073	+	0.104276i
$211$	−2.42068	+	6.65077i	−0.166647	+	0.457858i	−0.994703	−	0.102786i	$-0.967224\pi$
$211$	−2.42068	+	6.65077i	−0.166647	+	0.457858i	0.828057	+	0.560644i	$0.189446\pi$
$212$	5.21011	−	26.1031i	0.357832	−	1.79277i
$213$	8.35306	+	8.35608i	0.572342	+	0.572549i
$214$	−7.33260	−	0.724637i	−0.501246	−	0.0495352i
$215$	0.887098			0.0604996
$216$	6.90824	+	12.9721i	0.470046	+	0.882642i
$217$	−2.93367			−0.199150
$218$	−15.4698	−	1.52879i	−1.04775	−	0.103543i
$219$	−4.08886	+	15.2488i	−0.276299	+	1.03042i
$220$	0.142623	+	0.0284672i	0.00961563	+	0.00191926i
$221$	7.50496	−	20.6197i	0.504838	−	1.38703i
$222$	−1.94315	−	2.37020i	−0.130415	−	0.159077i
$223$	4.40167	−	24.9631i	0.294757	−	1.67165i	−0.373429	−	0.927659i	$-0.621818\pi$
$223$	4.40167	−	24.9631i	0.294757	−	1.67165i	0.668187	−	0.743994i	$-0.267071\pi$
$224$	−7.05995	−	5.55950i	−0.471712	−	0.371460i
$225$	14.2623	+	2.52015i	0.950822	+	0.168010i
$226$	−10.1393	+	21.1208i	−0.674455	+	1.40493i
$227$	−4.11151	−	11.2963i	−0.272891	−	0.749761i	−0.998122	−	0.0612559i	$-0.980489\pi$
$227$	−4.11151	−	11.2963i	−0.272891	−	0.749761i	0.725231	−	0.688505i	$-0.241733\pi$
$228$	6.92191	+	3.42074i	0.458415	+	0.226544i
$229$	16.6781	+	19.8762i	1.10212	+	1.31346i	0.945435	+	0.325810i	$0.105637\pi$
$229$	16.6781	+	19.8762i	1.10212	+	1.31346i	0.156687	+	0.987648i	$0.449919\pi$
$230$	0.698704	−	2.49510i	0.0460712	−	0.164522i
$231$	−0.436962	+	0.203663i	−0.0287500	+	0.0134000i
$232$	−11.7897	−	18.1073i	−0.774034	−	1.18880i
$233$	0.498504	+	0.863434i	0.0326581	+	0.0565655i	0.881892	−	0.471451i	$-0.156269\pi$
$233$	0.498504	+	0.863434i	0.0326581	+	0.0565655i	−0.849234	+	0.528016i	$0.822936\pi$
$234$	−7.03392	+	14.6386i	−0.459822	+	0.956952i
$235$	−3.27009	−	1.88799i	−0.213317	−	0.123159i
$236$	−5.75840	+	9.47546i	−0.374840	+	0.616800i
$237$	−12.6382	−	5.89606i	−0.820938	−	0.382990i
$238$	−3.19301	−	12.4756i	−0.206972	−	0.808673i
$239$	3.64160	+	20.6525i	0.235555	+	1.33590i	0.841441	+	0.540349i	$0.181708\pi$
$239$	3.64160	+	20.6525i	0.235555	+	1.33590i	−0.605886	+	0.795552i	$0.707181\pi$
$240$	1.33151	−	2.54847i	0.0859485	−	0.164503i
$241$	15.3537	+	12.8833i	0.989018	+	0.829884i	0.985425	−	0.170109i	$-0.0544120\pi$
$241$	15.3537	+	12.8833i	0.989018	+	0.829884i	0.00359245	+	0.999994i	$0.498856\pi$
$242$	−8.75449	−	12.8066i	−0.562760	−	0.823242i
$243$	4.04819	−	15.0536i	0.259692	−	0.965692i
$244$	−11.2881	−	4.39827i	−0.722647	−	0.281570i
$245$	1.19421	−	1.42320i	0.0762950	−	0.0909249i
$246$	7.32681	+	6.29188i	0.467141	+	0.401156i
$247$	1.48158	+	8.40247i	0.0942708	+	0.534636i
$248$	5.18527	+	0.630392i	0.329265	+	0.0400299i
$249$	−2.50873	+	5.37745i	−0.158984	+	0.340782i
$250$	−2.37884	−	5.25482i	−0.150451	−	0.332344i
$251$	−15.4089	−	8.89636i	−0.972604	−	0.561533i	−0.0725750	−	0.997363i	$-0.523122\pi$
$251$	−15.4089	−	8.89636i	−0.972604	−	0.561533i	−0.900029	+	0.435830i	$0.856455\pi$
$252$	1.44031	+	9.42180i	0.0907311	+	0.593517i
$253$	0.669884	−	0.386758i	0.0421152	−	0.0243152i
$254$	−3.93241	−	2.81989i	−0.246742	−	0.176936i
$255$	3.73481	−	1.74075i	0.233883	−	0.109010i
$256$	11.2838	+	11.3435i	0.705240	+	0.708968i
$257$	−2.62380	+	2.20163i	−0.163668	+	0.137334i	−0.720943	−	0.692994i	$-0.756291\pi$
$257$	−2.62380	+	2.20163i	−0.163668	+	0.137334i	0.557275	+	0.830328i	$0.311847\pi$
$258$	4.56387	−	2.56592i	0.284134	−	0.159747i
$259$	−0.679816	−	1.86778i	−0.0422417	−	0.116058i
$260$	3.14073	−	0.481286i	0.194780	−	0.0298481i
$261$	−3.98781	+	22.5683i	−0.246839	+	1.39694i
$262$	0.675305	+	8.86512i	0.0417205	+	0.547689i
$263$	2.78285	−	15.7823i	0.171598	−	0.973179i	−0.770400	−	0.637560i	$-0.779944\pi$
$263$	2.78285	−	15.7823i	0.171598	−	0.973179i	0.941998	−	0.335618i	$-0.108945\pi$
$264$	0.816096	−	0.266079i	0.0502272	−	0.0163761i
$265$	5.19040	+	1.88915i	0.318844	+	0.116050i
$266$	3.50064	+	3.58022i	0.214638	+	0.219517i
$267$	3.84598	−	14.3430i	0.235370	−	0.877778i
$268$	13.8478	+	25.2807i	0.845889	+	1.54426i
$269$		−	16.0010i		−	0.975599i	−0.872956	−	0.487800i	$-0.837800\pi$
$269$		−	16.0010i		−	0.975599i	0.872956	−	0.487800i	$-0.162200\pi$
$270$	−2.87793	+	1.00925i	−0.175145	+	0.0614210i
$271$	27.8409			1.69122			0.845608	−	0.533804i	$-0.179238\pi$
$271$	27.8409			1.69122			0.845608	+	0.533804i	$0.179238\pi$
$272$	2.96287	+	22.7368i	0.179651	+	1.37862i
$273$	−7.44893	+	7.44623i	−0.450830	+	0.450667i
$274$	−8.35248	+	8.16683i	−0.504591	+	0.493376i
$275$	0.289314	−	0.794884i	0.0174463	−	0.0479333i
$276$	−3.62241	−	14.8576i	−0.218043	−	0.894322i
$277$	−5.82356	−	1.02685i	−0.349904	−	0.0616975i	−0.00406597	−	0.999992i	$-0.501294\pi$
$277$	−5.82356	−	1.02685i	−0.349904	−	0.0616975i	−0.345838	+	0.938294i	$0.612405\pi$
$278$	1.04066	+	13.6614i	0.0624148	+	0.819356i
$279$	−3.55970	−	4.24540i	−0.213114	−	0.254166i
$280$	1.36225	−	1.27336i	0.0814101	−	0.0760979i
$281$	−9.94539	+	3.61983i	−0.593292	+	0.215941i	−0.621177	−	0.783670i	$-0.713345\pi$
$281$	−9.94539	+	3.61983i	−0.593292	+	0.215941i	0.0278845	+	0.999611i	$0.491123\pi$
$282$	−22.2847	−	0.254470i	−1.32704	−	0.0151535i
$283$	3.90228	+	4.65056i	0.231967	+	0.276447i	0.869454	−	0.494014i	$-0.164471\pi$
$283$	3.90228	+	4.65056i	0.231967	+	0.276447i	−0.637488	+	0.770461i	$0.720026\pi$
$284$	−4.37687	−	12.9218i	−0.259719	−	0.766768i
$285$	−0.919218	+	1.31227i	−0.0544498	+	0.0777324i
$286$	0.770840	+	0.552761i	0.0455807	+	0.0326854i
$287$	3.13158	+	5.42406i	0.184851	+	0.320172i
$288$	−0.521184	−	16.9626i	−0.0307111	−	0.999528i
$289$	−7.92938	+	13.7341i	−0.466434	+	0.807888i
$290$	4.08466	−	1.84911i	0.239860	−	0.108584i
$291$	−23.9567	+	16.7682i	−1.40437	+	0.982971i
$292$	12.0288	−	13.6980i	0.703931	−	0.801613i
$293$	−9.84448	+	1.73585i	−0.575120	+	0.101409i	−0.453641	−	0.891185i	$-0.649875\pi$
$293$	−9.84448	+	1.73585i	−0.575120	+	0.101409i	−0.121480	+	0.992594i	$0.538764\pi$
$294$	2.02727	−	10.7762i	0.118233	−	0.628480i
$295$	−1.76257	−	1.47897i	−0.102621	−	0.0861091i
$296$	0.800226	+	3.44739i	0.0465122	+	0.200375i
$297$	−0.824936	−	0.385219i	−0.0478676	−	0.0223526i
$298$	19.6502	−	13.4327i	1.13830	−	0.778134i
$299$	10.8626	−	12.9456i	0.628202	−	0.748662i
$300$	−13.4785	−	9.90029i	−0.778184	−	0.571594i
$301$	3.34389	−	0.589618i	0.192739	−	0.0339850i
$302$	7.18413	+	28.0696i	0.413400	+	1.61522i
$303$	−17.1871	+	1.50054i	−0.987370	+	0.0862039i
$304$	−5.41807	−	7.08027i	−0.310748	−	0.406081i
$305$	1.25696	−	2.17712i	0.0719735	−	0.124662i
$306$	14.1795	−	19.7586i	0.810586	−	1.12952i
$307$	19.1701	−	11.0679i	1.09410	−	0.631677i	0.159432	−	0.987209i	$-0.449034\pi$
$307$	19.1701	−	11.0679i	1.09410	−	0.631677i	0.934664	+	0.355532i	$0.115700\pi$
$308$	0.556534	+	0.0125106i	0.0317114	+	0.000712855i
$309$	−6.90220	−	0.605122i	−0.392653	−	0.0344242i
$310$	−0.292287	+	1.04377i	−0.0166008	+	0.0592820i
$311$	−0.101641	+	0.0852868i	−0.00576352	+	0.00483617i	−0.645665	−	0.763621i	$-0.723420\pi$
$311$	−0.101641	+	0.0852868i	−0.00576352	+	0.00483617i	0.639901	+	0.768457i	$0.278975\pi$
$312$	14.7661	−	11.5606i	0.835964	−	0.654491i
$313$	3.80750	−	1.38582i	0.215212	−	0.0783309i	−0.232164	−	0.972677i	$-0.574581\pi$
$313$	3.80750	−	1.38582i	0.215212	−	0.0783309i	0.447377	+	0.894346i	$0.352358\pi$
$314$	−19.3613	−	9.29461i	−1.09262	−	0.524525i
$315$	−1.97783		0.000714891i	−0.111438		4.02796e-5i
$316$	10.0712	+	12.5654i	0.566547	+	0.706856i
$317$	−9.00181	−	1.58726i	−0.505592	−	0.0891495i	−0.0849663	−	0.996384i	$-0.527078\pi$
$317$	−9.00181	−	1.58726i	−0.505592	−	0.0891495i	−0.420626	+	0.907234i	$0.638189\pi$
$318$	32.1675	−	5.29402i	1.80386	−	0.296874i
$319$	1.25780	+	0.457802i	0.0704233	+	0.0256320i
$320$	−2.68141	+	1.95795i	−0.149895	+	0.109453i
$321$	−2.33409	−	8.71723i	−0.130276	−	0.486548i
$322$	0.975355	−	9.86960i	0.0543544	−	0.550011i
$323$		−	12.7765i		−	0.710901i
$324$	−11.8869	+	13.5167i	−0.660384	+	0.750928i
$325$		−	18.4806i		−	1.02512i
$326$	28.2932	+	2.79605i	1.56701	+	0.154859i
$327$	−4.92430	−	18.3910i	−0.272314	−	1.01703i
$328$	−4.36955	−	10.2600i	−0.241268	−	0.566512i
$329$	−13.5814	−	4.94322i	−0.748766	−	0.272529i
$330$	0.0289256	+	0.175758i	0.00159230	+	0.00967515i
$331$	16.6781	+	2.94080i	0.916710	+	0.161641i	0.612049	−	0.790820i	$-0.290346\pi$
$331$	16.6781	+	2.94080i	0.916710	+	0.161641i	0.304661	+	0.952461i	$0.401457\pi$
$332$	5.34646	−	4.28520i	0.293425	−	0.235181i
$333$	1.87804	−	3.25014i	0.102916	−	0.178107i
$334$	7.47490	−	15.5707i	0.409008	−	0.851991i
$335$	−5.62074	+	2.04578i	−0.307094	+	0.111773i
$336$	3.32522	−	10.4914i	0.181406	−	0.572352i
$337$	17.0213	−	14.2826i	0.927209	−	0.778021i	−0.0481053	−	0.998842i	$-0.515318\pi$
$337$	17.0213	−	14.2826i	0.927209	−	0.778021i	0.975314	+	0.220822i	$0.0708739\pi$
$338$	2.25180	+	0.630574i	0.122482	+	0.0342987i
$339$	−28.5842	−	2.50600i	−1.55248	−	0.136107i
$340$	−4.75681	−	0.106930i	−0.257974	−	0.00579911i
$341$	−0.280230	+	0.161791i	−0.0151753	+	0.00876148i
$342$	−0.933381	+	9.41012i	−0.0504715	+	0.508841i
$343$	9.11548	−	15.7885i	0.492190	−	0.852497i
$344$	−6.03704	+	0.323611i	−0.325495	+	0.0174479i
$345$	3.16139	−	0.276010i	0.170203	−	0.0148599i
$346$	0.518377	−	0.132673i	0.0278681	−	0.00713257i
$347$	−24.5082	+	4.32146i	−1.31567	+	0.231988i	−0.787060	−	0.616877i	$-0.788398\pi$
$347$	−24.5082	+	4.32146i	−1.31567	+	0.231988i	−0.528610	+	0.848865i	$0.677287\pi$
$348$	15.6659	−	21.3280i	0.839781	−	1.14330i
$349$	−12.8010	+	15.2557i	−0.685223	+	0.816617i	−0.990769	−	0.135560i	$-0.956717\pi$
$349$	−12.8010	+	15.2557i	−0.685223	+	0.816617i	0.305546	+	0.952177i	$0.401161\pi$
$350$	−6.12063	−	8.95365i	−0.327161	−	0.478593i
$351$	−19.8142	−	1.74434i	−1.05760	−	0.0931061i
$352$	−0.980987	−	0.141701i	−0.0522868	−	0.00755271i
$353$	5.58988	+	4.69047i	0.297519	+	0.249648i	0.779311	−	0.626637i	$-0.215569\pi$
$353$	5.58988	+	4.69047i	0.297519	+	0.249648i	−0.481792	+	0.876286i	$0.660014\pi$
$354$	−13.3458	−	2.51068i	−0.709324	−	0.133441i
$355$	2.78804	−	0.491607i	0.147974	−	0.0260918i
$356$	−11.3143	+	12.8843i	−0.599655	+	0.682867i
$357$	12.9212	−	9.04407i	0.683865	−	0.478663i
$358$	−9.28246	−	20.5048i	−0.490594	−	1.08371i
$359$	−3.04491	+	5.27394i	−0.160704	+	0.278348i	−0.935121	−	0.354327i	$-0.884710\pi$
$359$	−3.04491	+	5.27394i	−0.160704	+	0.278348i	0.774417	+	0.632675i	$0.218043\pi$
$360$	3.49567	+	0.426264i	0.184238	+	0.0224661i
$361$	−7.01607	−	12.1522i	−0.369267	−	0.639589i
$362$	8.32541	−	11.6100i	0.437574	−	0.610209i
$363$	10.9004	−	15.5614i	0.572123	−	0.816762i
$364$	11.5190	−	3.90171i	0.603759	−	0.204505i
$365$	2.43158	+	2.89785i	0.127275	+	0.151680i
$366$	0.169418	−	14.8365i	0.00885563	−	0.775514i
$367$	−8.97268	+	3.26579i	−0.468370	+	0.170473i	−0.565414	−	0.824807i	$-0.691284\pi$
$367$	−8.97268	+	3.26579i	−0.468370	+	0.170473i	0.0970437	+	0.995280i	$0.469061\pi$
$368$	−3.84474	+	17.2350i	−0.200421	+	0.898435i
$369$	−4.04948	+	11.1134i	−0.210807	+	0.578538i
$370$	−0.732267	+	0.0557808i	−0.0380688	+	0.00289991i
$371$	20.8207	+	3.67125i	1.08096	+	0.190602i
$372$	1.51535	+	6.21533i	0.0785672	+	0.322250i
$373$	−10.1367	+	27.8503i	−0.524857	+	1.44203i	0.340197	+	0.940354i	$0.389506\pi$
$373$	−10.1367	+	27.8503i	−0.524857	+	1.44203i	−0.865054	+	0.501679i	$0.832716\pi$
$374$	−0.993030	−	1.01560i	−0.0513484	−	0.0525156i
$375$	4.99630	−	4.99449i	0.258008	−	0.257914i
$376$	22.9430	+	11.6556i	1.18319	+	0.601090i
$377$	29.2431			1.50610
$378$	−10.1775	+	5.71718i	−0.523473	+	0.294060i
$379$			11.8593i			0.609171i	0.952485	+	0.304585i	$0.0985179\pi$
$379$			11.8593i			0.609171i	−0.952485	+	0.304585i	$0.901482\pi$
$380$	1.62258	−	0.888786i	0.0832365	−	0.0455938i
$381$	1.53493	−	5.72429i	0.0786367	−	0.293264i
$382$	−11.7730	+	11.5114i	−0.602361	+	0.588972i
$383$	−26.9019	−	9.79149i	−1.37462	−	0.500322i	−0.454079	−	0.890961i	$-0.650032\pi$
$383$	−26.9019	−	9.79149i	−1.37462	−	0.500322i	−0.920544	+	0.390640i	$0.872254\pi$
$384$	−8.13174	+	17.8290i	−0.414971	+	0.909834i
$385$	−0.0200591	+	0.113761i	−0.00102231	+	0.00579778i
$386$	−32.6428	+	2.48658i	−1.66147	+	0.126563i
$387$	4.91072	+	4.12361i	0.249626	+	0.209615i
$388$	33.3762	−	5.11458i	1.69442	−	0.259653i
$389$	−2.40763	−	6.61492i	−0.122072	−	0.335390i	0.863572	−	0.504225i	$-0.168222\pi$
$389$	−2.40763	−	6.61492i	−0.122072	−	0.335390i	−0.985644	+	0.168835i	$0.945999\pi$
$390$	1.90714	+	3.39213i	0.0965717	+	0.171767i
$391$	−19.3855	+	16.2663i	−0.980365	+	0.822624i
$392$	−7.60784	+	10.1211i	−0.384254	+	0.511190i
$393$	−9.86958	+	4.60009i	−0.497855	+	0.232044i
$394$	8.05349	−	11.2308i	0.405729	−	0.565800i
$395$	−2.89391	+	1.67080i	−0.145608	+	0.0840671i
$396$	0.657192	+	0.820558i	0.0330251	+	0.0412346i
$397$	12.2406	+	7.06713i	0.614339	+	0.354689i	0.774662	−	0.632376i	$-0.217920\pi$
$397$	12.2406	+	7.06713i	0.614339	+	0.354689i	−0.160322	+	0.987065i	$0.551253\pi$
$398$	32.2137	−	14.5831i	1.61473	−	0.730983i
$399$	−2.59275	+	5.55755i	−0.129800	+	0.278225i
$400$	8.89426	+	17.1408i	0.444713	+	0.857042i
$401$	0.0872296	+	0.494703i	0.00435604	+	0.0247043i	0.986908	−	0.161282i	$-0.0515630\pi$
$401$	0.0872296	+	0.494703i	0.00435604	+	0.0247043i	−0.982552	+	0.185987i	$0.940452\pi$
$402$	−22.9997	+	26.7829i	−1.14712	+	1.33581i
$403$	−4.54413	+	5.41548i	−0.226359	+	0.269764i
$404$	18.5621	+	7.23250i	0.923500	+	0.359831i
$405$	−2.39886	−	2.86305i	−0.119200	−	0.142266i
$406$	14.1680	−	9.68509i	0.703145	−	0.480663i
$407$	−0.167945	−	0.140923i	−0.00832474	−	0.00698529i
$408$	−24.7818	+	13.2089i	−1.22688	+	0.653938i
$409$	0.176738	+	1.00233i	0.00873915	+	0.0495622i	0.988865	−	0.148812i	$-0.0475450\pi$
$409$	0.176738	+	1.00233i	0.00873915	+	0.0495622i	−0.980126	+	0.198374i	$0.936434\pi$
$410$	2.24183	−	0.573774i	0.110716	−	0.0283367i
$411$	−12.9655	−	6.04876i	−0.639540	−	0.298363i
$412$	6.83703	+	4.15498i	0.336836	+	0.204701i
$413$	−7.62697	−	4.40343i	−0.375299	−	0.216679i
$414$	15.4661	−	10.5643i	0.760118	−	0.519206i
$415$	0.710912	+	1.23134i	0.0348973	+	0.0604439i
$416$	−21.1983	+	4.42106i	−1.03933	+	0.216760i
$417$	−15.2093	+	7.08887i	−0.744803	+	0.347143i
$418$	0.531837	+	0.148931i	0.0260130	+	0.00728444i
$419$	20.7981	+	24.7862i	1.01605	+	1.21089i	0.977349	+	0.211636i	$0.0678790\pi$
$419$	20.7981	+	24.7862i	1.01605	+	1.21089i	0.0387057	+	0.999251i	$0.487677\pi$
$420$	2.04743	+	1.01182i	0.0999045	+	0.0493718i
$421$	2.72967	+	7.49969i	0.133036	+	0.365513i	0.988267	−	0.152733i	$-0.0488075\pi$
$421$	2.72967	+	7.49969i	0.133036	+	0.365513i	−0.855232	+	0.518246i	$0.826585\pi$
$422$	9.02334	+	4.33176i	0.439249	+	0.210867i
$423$	−9.32613	−	25.6522i	−0.453452	−	1.24725i
$424$	−36.0118	−	10.9629i	−1.74889	−	0.532407i
$425$	−4.80553	+	27.2535i	−0.233102	+	1.32199i
$426$	12.9217	−	10.5936i	0.626060	−	0.513260i
$427$	3.29104	−	9.04206i	0.159265	−	0.437576i
$428$	−2.03965	+	10.2188i	−0.0985901	+	0.493944i
$429$	−0.300880	+	1.12209i	−0.0145266	+	0.0541749i
$430$	0.123378	−	1.24846i	0.00594984	−	0.0602063i
$431$	−40.3264			−1.94246			−0.971228	−	0.238151i	$-0.923459\pi$
$431$	−40.3264			−1.94246			−0.971228	+	0.238151i	$0.923459\pi$
$432$	19.2172	−	7.91819i	0.924590	−	0.380964i
$433$	−0.347828			−0.0167155			−0.00835777	−	0.999965i	$-0.502660\pi$
$433$	−0.347828			−0.0167155			−0.00835777	+	0.999965i	$0.502660\pi$
$434$	−0.408017	+	4.12872i	−0.0195854	+	0.198185i
$435$	3.88231	+	3.88371i	0.186142	+	0.186210i
$436$	−4.30311	+	21.5589i	−0.206082	+	1.03249i
$437$	3.36537	−	9.24628i	0.160987	−	0.442309i
$438$	20.8918	+	7.87530i	0.998250	+	0.376296i
$439$	2.54785	−	14.4496i	0.121602	−	0.689640i	−0.861666	−	0.507476i	$-0.830579\pi$
$439$	2.54785	−	14.4496i	0.121602	−	0.689640i	0.983268	−	0.182164i	$-0.0583102\pi$
$440$	0.0598996	−	0.196762i	0.00285560	−	0.00938027i
$441$	13.2264	−	2.32725i	0.629830	−	0.110821i
$442$	−27.9755	−	13.4300i	−1.33066	−	0.638798i
$443$	13.7397	+	37.7495i	0.652792	+	1.79353i	0.607169	+	0.794573i	$0.292305\pi$
$443$	13.7397	+	37.7495i	0.652792	+	1.79353i	0.0456232	+	0.998959i	$0.485473\pi$
$444$	−3.60597	+	2.40505i	−0.171132	+	0.114139i
$445$	−2.28715	−	2.72572i	−0.108421	−	0.129211i
$446$	−34.5198	−	9.66661i	−1.63456	−	0.457727i
$447$	23.8770	+	16.7253i	1.12935	+	0.791080i
$448$	−8.80611	+	9.16265i	−0.416050	+	0.432895i
$449$	2.52521	+	4.37380i	0.119172	+	0.206412i	0.919440	−	0.393231i	$-0.128643\pi$
$449$	2.52521	+	4.37380i	0.119172	+	0.206412i	−0.800268	+	0.599643i	$0.795309\pi$
$450$	5.53037	−	19.7217i	0.260704	−	0.929690i
$451$	0.598272	+	0.345412i	0.0281715	+	0.0162648i
$452$	28.3143	+	17.2071i	1.33179	+	0.809354i
$453$	−29.0722	+	20.3488i	−1.36593	+	0.956069i
$454$	−16.4698	+	4.21527i	−0.772964	+	0.197833i
$455$	0.438237	+	2.48537i	0.0205449	+	0.116516i
$456$	5.77691	−	9.26585i	0.270529	−	0.433913i
$457$	−1.57729	−	1.32350i	−0.0737824	−	0.0619108i	0.605151	−	0.796111i	$-0.293113\pi$
$457$	−1.57729	−	1.32350i	−0.0737824	−	0.0619108i	−0.678933	+	0.734200i	$0.737557\pi$
$458$	30.2926	−	20.7077i	1.41548	−	0.967607i
$459$	28.7666	+	7.72470i	1.34271	+	0.360558i
$460$	−3.41432	−	1.33035i	−0.159194	−	0.0620278i
$461$	9.53518	−	11.3636i	0.444098	−	0.529255i	−0.496837	−	0.867844i	$-0.665505\pi$
$461$	9.53518	−	11.3636i	0.444098	−	0.529255i	0.940934	+	0.338589i	$0.109950\pi$
$462$	0.225853	+	0.643288i	0.0105076	+	0.0299285i
$463$	0.666314	+	3.77886i	0.0309662	+	0.175618i	0.996368	−	0.0851474i	$-0.0271361\pi$
$463$	0.666314	+	3.77886i	0.0309662	+	0.175618i	−0.965402	+	0.260766i	$0.916025\pi$
$464$	−27.1231	+	14.0740i	−1.25916	+	0.653369i
$465$	−1.32249	+	0.115462i	−0.0613292	+	0.00535444i
$466$	1.28449	−	0.581486i	0.0595030	−	0.0269368i
$467$	−2.93590	−	1.69504i	−0.135857	−	0.0784371i	0.430531	−	0.902576i	$-0.358326\pi$
$467$	−2.93590	−	1.69504i	−0.135857	−	0.0784371i	−0.566388	+	0.824139i	$0.691660\pi$
$468$	19.6234	+	11.9352i	0.907092	+	0.551704i
$469$	−19.8275	+	11.4474i	−0.915547	+	0.528591i
$470$	−3.11189	+	4.33961i	−0.143541	+	0.200171i
$471$	2.29724	−	26.2030i	0.105851	−	1.20737i
$472$	12.5345	+	9.42198i	0.576946	+	0.433682i
$473$	0.286899	−	0.240736i	0.0131916	−	0.0110691i
$474$	−10.0556	+	16.9664i	−0.461869	+	0.779293i
$475$	−3.68029	−	10.1115i	−0.168863	−	0.463948i
$476$	−18.0017	+	2.75859i	−0.825108	+	0.126440i
$477$	19.9510	+	34.5850i	0.913493	+	1.58354i
$478$	29.5720	−	2.25266i	1.35259	−	0.103034i
$479$	1.35147	−	7.66457i	0.0617503	−	0.350203i	−0.938241	−	0.345983i	$-0.887546\pi$
$479$	1.35147	−	7.66457i	0.0617503	−	0.350203i	0.999991	−	0.00422030i	$-0.00134337\pi$
$480$	−3.40142	−	2.22835i	−0.155253	−	0.101710i
$481$	−4.50089	−	1.63819i	−0.205223	−	0.0746950i
$482$	20.2668	−	19.8163i	0.923126	−	0.902608i
$483$	11.7333	−	3.14166i	0.533884	−	0.142950i
$484$	−19.2411	+	10.5395i	−0.874596	+	0.479070i
$485$			7.00676i			0.318160i
$486$	−20.6228	−	7.79093i	−0.935471	−	0.353404i
$487$	−35.0900			−1.59008			−0.795041	−	0.606556i	$-0.792550\pi$
$487$	−35.0900			−1.59008			−0.795041	+	0.606556i	$0.792550\pi$
$488$	−7.75990	+	15.2747i	−0.351274	+	0.691453i
$489$	9.00619	+	33.6359i	0.407274	+	1.52107i
$490$	−1.83686	−	1.87862i	−0.0829809	−	0.0848672i
$491$	0.860058	−	2.36299i	0.0388139	−	0.106640i	−0.918772	−	0.394789i	$-0.870818\pi$
$491$	0.860058	−	2.36299i	0.0388139	−	0.106640i	0.957586	+	0.288149i	$0.0930398\pi$
$492$	9.87395	−	9.43637i	0.445152	−	0.425424i
$493$	−43.1251	−	7.60412i	−1.94226	−	0.342472i
$494$	12.0313	−	0.916493i	0.541316	−	0.0412350i
$495$	−0.188966	+	0.109009i	−0.00849341	+	0.00489958i
$496$	1.60836	−	7.20985i	0.0722174	−	0.323732i
$497$	10.1827	−	3.70620i	0.456756	−	0.166246i
$498$	7.21907	+	4.27858i	0.323494	+	0.191728i
$499$	1.81333	+	2.16105i	0.0811760	+	0.0967418i	0.805104	−	0.593134i	$-0.202110\pi$
$499$	1.81333	+	2.16105i	0.0811760	+	0.0967418i	−0.723928	+	0.689876i	$0.757665\pi$
$500$	−7.72626	+	2.61703i	−0.345529	+	0.117037i
$501$	21.0729	+	1.84748i	0.941468	+	0.0825393i
$502$	−14.6635	+	20.4486i	−0.654462	+	0.912665i
$503$	−10.1002	−	17.4940i	−0.450344	−	0.780018i	0.548064	−	0.836437i	$-0.315365\pi$
$503$	−10.1002	−	17.4940i	−0.450344	−	0.780018i	−0.998407	+	0.0564186i	$0.982032\pi$
$504$	13.4602	−	0.716643i	0.599563	−	0.0319218i
$505$	−2.06695	+	3.58006i	−0.0919779	+	0.159310i
$506$	−0.451138	−	0.996557i	−0.0200555	−	0.0443024i
$507$	0.249096	+	2.85312i	0.0110628	+	0.126712i
$508$	−4.51552	+	5.14212i	−0.200344	+	0.228145i
$509$	0.00532574		0.000939071i	0.000236059		4.16236e-5i	−0.173530	−	0.984829i	$-0.555517\pi$
$509$	0.00532574		0.000939071i	0.000236059		4.16236e-5i	0.173766	+	0.984787i	$0.444406\pi$
$510$	−1.93042	−	5.49832i	−0.0854802	−	0.243470i
$511$	11.0919	+	9.30718i	0.490675	+	0.411726i
$512$	17.5337	−	14.3027i	0.774888	−	0.632098i
$513$	−11.1885	+	2.99146i	−0.493986	+	0.132076i
$514$	2.73356	+	3.99883i	0.120572	+	0.176381i
$515$	−1.06715	+	1.27178i	−0.0470244	+	0.0560415i
$516$	−2.97642	−	6.77988i	−0.131030	−	0.298467i
$517$	−1.56994	+	0.276823i	−0.0690460	+	0.0121747i
$518$	−2.72319	+	0.696973i	−0.119650	+	0.0306232i
$519$	0.375793	+	0.536894i	0.0164955	+	0.0235670i
$520$	−0.240526	−	4.48707i	−0.0105478	−	0.196771i
$521$	7.16840	−	12.4160i	0.314053	−	0.543956i	−0.665183	−	0.746681i	$-0.731646\pi$
$521$	7.16840	−	12.4160i	0.314053	−	0.543956i	0.979236	+	0.202725i	$0.0649796\pi$
$522$	31.2070	+	8.75108i	1.36589	+	0.383025i
$523$	31.9572	−	18.4505i	1.39739	−	0.806784i	0.403271	−	0.915080i	$-0.367873\pi$
$523$	31.9572	−	18.4505i	1.39739	−	0.806784i	0.994119	+	0.108297i	$0.0345397\pi$
$524$	12.5703	+	0.282573i	0.549137	+	0.0123443i
$525$	7.62093	−	10.8796i	0.332605	−	0.474826i
$526$	−21.8243	−	6.11148i	−0.951585	−	0.266473i
$527$	8.10945	−	6.80464i	0.353253	−	0.296415i
$528$	−0.260966	−	1.18555i	−0.0113571	−	0.0515943i
$529$	3.29912	−	1.20078i	0.143440	−	0.0522079i
$530$	3.38060	−	7.04200i	0.146844	−	0.305885i
$531$	−2.88219	−	16.3803i	−0.125076	−	0.710846i
$532$	5.52552	−	4.42871i	0.239562	−	0.192009i
$533$	14.8634	+	2.62082i	0.643804	+	0.113520i
$534$	−19.6509	−	7.40751i	−0.850376	−	0.320554i
$535$	−2.03193	−	0.739562i	−0.0878480	−	0.0319741i
$536$	37.5050	−	15.9727i	1.61997	−	0.689918i
$537$	19.4960	−	19.4890i	0.841316	−	0.841012i
$538$	−22.5192	−	2.22544i	−0.970870	−	0.0959454i
$539$		−	0.784358i		−	0.0337847i
$540$	1.02011	+	4.19065i	0.0438986	+	0.180337i
$541$		−	30.3968i		−	1.30686i	−0.756987	−	0.653430i	$-0.773329\pi$
$541$		−	30.3968i		−	1.30686i	0.756987	−	0.653430i	$-0.226671\pi$
$542$	3.87214	−	39.1822i	0.166323	−	1.68302i
$543$	16.9003	+	4.53170i	0.725263	+	0.194474i
$544$	32.4109	−	1.00757i	1.38961	−	0.0431992i
$545$	−4.28683	−	1.56028i	−0.183628	−	0.0668350i
$546$	9.44351	+	11.5189i	0.404145	+	0.492965i
$547$	5.50047	+	0.969880i	0.235183	+	0.0414691i	0.289997	−	0.957027i	$-0.406346\pi$
$547$	5.50047	+	0.969880i	0.235183	+	0.0414691i	−0.0548144	+	0.998497i	$0.517457\pi$
$548$	10.3320	+	12.8908i	0.441360	+	0.550667i
$549$	17.0784	−	6.20904i	0.728888	−	0.264995i
$550$	−1.07845	−	0.517722i	−0.0459852	−	0.0220757i
$551$	16.0001	−	5.82357i	0.681629	−	0.248093i
$552$	−21.4138	+	3.03162i	−0.911430	+	0.129034i
$553$	−9.79800	+	8.22150i	−0.416653	+	0.349614i
$554$	−2.25509	+	8.05302i	−0.0958098	+	0.342140i
$555$	−0.379972	−	0.815237i	−0.0161289	−	0.0346049i
$556$	19.3712	+	0.435454i	0.821522	+	0.0184673i
$557$	−23.1205	+	13.3486i	−0.979647	+	0.565599i	−0.902164	−	0.431394i	$-0.858022\pi$
$557$	−23.1205	+	13.3486i	−0.979647	+	0.565599i	−0.0774834	+	0.996994i	$0.524688\pi$
$558$	−6.46989	+	4.41932i	−0.273892	+	0.187085i
$559$	4.09113	−	7.08604i	0.173036	−	0.299707i
$560$	−1.60261	−	2.09427i	−0.0677227	−	0.0884993i
$561$	0.735487	−	1.57651i	0.0310523	−	0.0665605i
$562$	3.71118	+	14.5002i	0.156547	+	0.611653i
$563$	−37.1869	+	6.55705i	−1.56724	+	0.276347i	−0.888796	−	0.458304i	$-0.848457\pi$
$563$	−37.1869	+	6.55705i	−1.56724	+	0.276347i	−0.678445	+	0.734651i	$0.737346\pi$
$564$	−3.45751	+	31.3272i	−0.145587	+	1.31911i
$565$	−4.41943	+	5.26687i	−0.185927	+	0.221579i
$566$	7.08773	−	4.84510i	0.297920	−	0.203655i
$567$	−10.9454	−	9.19777i	−0.459663	−	0.386270i
$568$	−18.7943	+	4.36264i	−0.788593	+	0.183052i
$569$	22.9957	+	19.2957i	0.964029	+	0.808917i	0.981604	−	0.190929i	$-0.0611500\pi$
$569$	22.9957	+	19.2957i	0.964029	+	0.808917i	−0.0175746	+	0.999846i	$0.505594\pi$
$570$	1.71899	+	1.47618i	0.0720007	+	0.0618304i
$571$	−12.6544	+	2.23132i	−0.529572	+	0.0933779i	−0.432040	−	0.901854i	$-0.642206\pi$
$571$	−12.6544	+	2.23132i	−0.529572	+	0.0933779i	−0.0975323	+	0.995232i	$0.531095\pi$
$572$	0.885142	−	1.00797i	0.0370096	−	0.0421453i
$573$	−18.2752	−	8.52588i	−0.763457	−	0.356174i
$574$	8.06914	−	3.65287i	0.336799	−	0.152468i
$575$	−10.6564	+	18.4575i	−0.444404	+	0.769730i
$576$	−23.9449	−	1.62568i	−0.997703	−	0.0677365i
$577$	−20.5100	−	35.5243i	−0.853841	−	1.47890i	−0.877716	−	0.479180i	$-0.840934\pi$
$577$	−20.5100	−	35.5243i	−0.853841	−	1.47890i	0.0238757	−	0.999715i	$-0.492399\pi$
$578$	18.2260	+	13.0696i	0.758100	+	0.543625i
$579$	−16.9383	−	36.3414i	−0.703930	−	1.51030i
$580$	−2.03427	−	6.00576i	−0.0844684	−	0.249376i
$581$	3.49818	+	4.16897i	0.145129	+	0.172958i
$582$	20.2670	+	36.0478i	0.840093	+	1.49423i
$583$	2.19131	−	0.797571i	0.0907547	−	0.0330320i
$584$	−17.6050	−	18.8339i	−0.728499	−	0.779353i
$585$	−3.06490	+	3.64993i	−0.126718	+	0.150906i
$586$	1.07378	+	14.0961i	0.0443574	+	0.582306i
$587$	5.11310	+	0.901578i	0.211040	+	0.0372121i	0.278169	−	0.960532i	$-0.410273\pi$
$587$	5.11310	+	0.901578i	0.211040	+	0.0372121i	−0.0671284	+	0.997744i	$0.521384\pi$
$588$	−14.8840	−	4.35186i	−0.613806	−	0.179468i
$589$	−1.40782	+	3.86796i	−0.0580084	+	0.159377i
$590$	−2.32658	+	2.27487i	−0.0957839	+	0.0936549i
$591$	16.3483	+	4.38369i	0.672480	+	0.180321i
$592$	4.96301	−	0.646739i	0.203978	−	0.0265808i
$593$	5.36613			0.220360			0.110180	−	0.993912i	$-0.464857\pi$
$593$	5.36613			0.220360			0.110180	+	0.993912i	$0.464857\pi$
$594$	−0.656873	+	1.10740i	−0.0269518	+	0.0454373i
$595$		−	3.77915i		−	0.154930i
$596$	−16.1716	−	29.5231i	−0.662415	−	1.20931i
$597$	30.6179	+	30.6289i	1.25311	+	1.25356i
$598$	−16.7083	−	17.0881i	−0.683252	−	0.698784i
$599$	28.3431	+	10.3160i	1.15807	+	0.421502i	0.848406	−	0.529346i	$-0.177563\pi$
$599$	28.3431	+	10.3160i	1.15807	+	0.421502i	0.309660	+	0.950847i	$0.399785\pi$
$600$	−15.8079	+	17.5922i	−0.645353	+	0.718198i
$601$	−0.320606	+	1.81824i	−0.0130778	+	0.0741677i	−0.990648	−	0.136441i	$-0.956434\pi$
$601$	−0.320606	+	1.81824i	−0.0130778	+	0.0741677i	0.977570	+	0.210609i	$0.0675446\pi$
$602$	−0.364732	−	4.78806i	−0.0148654	−	0.195147i
$603$	−40.6245	−	14.8027i	−1.65436	−	0.602814i
$604$	40.5031	−	6.20670i	1.64805	−	0.252547i
$605$	−1.55704	−	4.27794i	−0.0633028	−	0.173923i
$606$	−0.278591	+	24.3970i	−0.0113170	+	0.991062i
$607$	−13.5490	+	11.3689i	−0.549936	+	0.461451i	−0.874919	−	0.484269i	$-0.839086\pi$
$607$	−13.5490	+	11.3689i	−0.549936	+	0.461451i	0.324983	+	0.945720i	$0.394641\pi$
$608$	−10.7180	+	6.64044i	−0.434673	+	0.269305i
$609$	17.2156	+	12.0591i	0.697611	+	0.488660i
$610$	−2.88917	−	2.07179i	−0.116979	−	0.0838845i
$611$	−30.1621	+	17.4141i	−1.22023	+	0.704499i
$612$	−25.8353	−	22.7036i	−1.04433	−	0.917739i
$613$	−16.1809	−	9.34204i	−0.653540	−	0.377321i	0.136271	−	0.990672i	$-0.456488\pi$
$613$	−16.1809	−	9.34204i	−0.653540	−	0.377321i	−0.789811	+	0.613350i	$0.789821\pi$
$614$	−12.9103	−	28.5185i	−0.521016	−	1.15091i
$615$	1.62519	+	2.32191i	0.0655341	+	0.0936284i
$616$	0.0950100	−	0.781502i	0.00382806	−	0.0314876i
$617$	−3.69099	−	20.9327i	−0.148594	−	0.842718i	−0.964411	−	0.264408i	$-0.914824\pi$
$617$	−3.69099	−	20.9327i	−0.148594	−	0.842718i	0.815817	−	0.578310i	$-0.196288\pi$
$618$	−1.81159	+	9.62971i	−0.0728727	+	0.387364i
$619$	23.6791	−	28.2197i	0.951744	−	1.13424i	−0.0391005	−	0.999235i	$-0.512449\pi$
$619$	23.6791	−	28.2197i	0.951744	−	1.13424i	0.990844	−	0.135009i	$-0.0431063\pi$
$620$	1.42830	+	0.556520i	0.0573620	+	0.0223504i
$621$	18.7836	+	13.1676i	0.753758	+	0.528396i
$622$	0.105893	+	0.154907i	0.00424591	+	0.00621119i
$623$	−10.4330	−	8.75433i	−0.417990	−	0.350735i
$624$	−14.2162	−	22.3890i	−0.569105	−	0.896277i
$625$	3.89771	+	22.1050i	0.155909	+	0.884201i
$626$	−1.42079	−	5.55125i	−0.0567861	−	0.221873i
$627$	0.0588323	+	0.673859i	0.00234953	+	0.0269113i
$628$	−15.7736	+	25.9555i	−0.629436	+	1.03574i
$629$	6.21152	+	3.58622i	0.247669	+	0.142992i
$630$	−0.276085	+	2.78342i	−0.0109995	+	0.110894i
$631$	17.3832	+	30.1086i	0.692014	+	1.19860i	0.971177	+	0.238359i	$0.0766095\pi$
$631$	17.3832	+	30.1086i	0.692014	+	1.19860i	−0.279164	+	0.960244i	$0.590057\pi$
$632$	19.0847	−	12.4261i	0.759147	−	0.494284i
$633$	−1.07063	+	12.2119i	−0.0425537	+	0.485380i
$634$	−3.48582	+	12.4480i	−0.138440	+	0.494374i
$635$	−0.912800	−	1.08783i	−0.0362233	−	0.0431693i
$636$	−2.97669	−	46.0075i	−0.118034	−	1.82432i
$637$	−5.86090	−	16.1027i	−0.232217	−	0.638012i
$638$	0.819227	−	1.70650i	0.0324335	−	0.0675611i
$639$	17.7190	+	10.2386i	0.700953	+	0.405033i
$640$	2.38260	+	4.04601i	0.0941806	+	0.159933i
$641$	−1.09984	+	6.23751i	−0.0434411	+	0.246367i	−0.998794	−	0.0491010i	$-0.984364\pi$
$641$	−1.09984	+	6.23751i	−0.0434411	+	0.246367i	0.955353	+	0.295468i	$0.0954755\pi$
$642$	−12.5929	+	2.07249i	−0.497002	+	0.0817948i
$643$	8.02118	−	22.0380i	0.316324	−	0.869094i	−0.675019	−	0.737800i	$-0.735865\pi$
$643$	8.02118	−	22.0380i	0.316324	−	0.869094i	0.991344	−	0.131294i	$-0.0419131\pi$
$644$	−13.7544	−	2.74535i	−0.542000	−	0.108182i
$645$	1.48422	−	0.397407i	0.0584409	−	0.0156479i
$646$	−17.9810	−	1.77696i	−0.707455	−	0.0699136i
$647$	36.2379			1.42466			0.712329	−	0.701846i	$-0.247640\pi$
$647$	36.2379			1.42466			0.712329	+	0.701846i	$0.247640\pi$
$648$	17.3696	+	18.6091i	0.682342	+	0.731033i
$649$	−0.971393			−0.0381305
$650$	−26.0088	−	2.57030i	−1.02015	−	0.100815i
$651$	−4.90836	+	1.31424i	−0.192374	+	0.0515091i
$652$	7.87008	−	39.4298i	0.308216	−	1.54419i
$653$	13.3926	−	36.7959i	0.524093	−	1.43993i	−0.341832	−	0.939761i	$-0.611047\pi$
$653$	13.3926	−	36.7959i	0.524093	−	1.43993i	0.865925	−	0.500173i	$-0.166730\pi$
$654$	−26.5676	+	4.37241i	−1.03888	+	0.170975i
$655$	−0.453071	+	2.56949i	−0.0177029	+	0.100398i
$656$	−15.0472	+	4.72256i	−0.587493	+	0.184385i
$657$	−0.00988380	+	27.3447i	−0.000385604	+	1.06682i
$658$	−8.84580	+	18.4264i	−0.344845	+	0.718335i
$659$	−0.151479	−	0.416185i	−0.00590079	−	0.0162123i	0.936707	−	0.350114i	$-0.113857\pi$
$659$	−0.151479	−	0.416185i	−0.00590079	−	0.0162123i	−0.942608	+	0.333901i	$0.891635\pi$
$660$	0.251377	−	0.0162641i	0.00978484	−	0.000633081i
$661$	−6.98818	−	8.32819i	−0.271809	−	0.323929i	0.612822	−	0.790221i	$-0.290034\pi$
$661$	−6.98818	−	8.32819i	−0.271809	−	0.323929i	−0.884631	+	0.466292i	$0.845590\pi$
$662$	6.45836	−	23.0630i	0.251011	−	0.896370i
$663$	3.31932	−	37.8612i	0.128912	−	1.47041i
$664$	−5.28721	−	8.12037i	−0.205184	−	0.315131i
$665$	0.734722	+	1.27258i	0.0284913	+	0.0493484i
$666$	−4.31292	−	3.09510i	−0.167122	−	0.119933i
$667$	−29.2065	−	16.8624i	−1.13088	−	0.652915i
$668$	−20.8739	−	12.6854i	−0.807637	−	0.490814i
$669$	−3.81861	−	43.7380i	−0.147636	−	1.69101i
$670$	2.09741	+	8.19492i	0.0810300	+	0.316597i
$671$	−0.184300	−	1.04522i	−0.00711483	−	0.0403502i
$672$	−14.3027	−	6.13892i	−0.551737	−	0.236814i
$673$	8.86370	+	7.43753i	0.341670	+	0.286696i	0.797435	−	0.603405i	$-0.206190\pi$
$673$	8.86370	+	7.43753i	0.341670	+	0.286696i	−0.455765	+	0.890100i	$0.650634\pi$
$674$	−17.7333	−	25.9415i	−0.683063	−	0.999229i
$675$	24.9915	−	2.17282i	0.961923	−	0.0836318i
$676$	1.20063	−	3.08139i	0.0461779	−	0.118515i
$677$	−5.48261	+	6.53392i	−0.210714	+	0.251119i	−0.861041	−	0.508535i	$-0.830187\pi$
$677$	−5.48261	+	6.53392i	−0.210714	+	0.251119i	0.650327	+	0.759654i	$0.274632\pi$
$678$	−7.50237	+	39.8797i	−0.288127	+	1.53157i
$679$	4.65711	+	26.4118i	0.178723	+	1.01359i
$680$	−0.812071	+	6.67966i	−0.0311415	+	0.256153i
$681$	−11.9396	−	17.0581i	−0.457527	−	0.653667i
$682$	0.188723	+	0.416886i	0.00722659	+	0.0159634i
$683$	25.2170	+	14.5590i	0.964900	+	0.557085i	0.897678	−	0.440653i	$-0.145253\pi$
$683$	25.2170	+	14.5590i	0.964900	+	0.557085i	0.0672223	+	0.997738i	$0.478586\pi$
$684$	13.1136	+	2.62237i	0.501410	+	0.100269i
$685$	−2.96886	+	1.71407i	−0.113434	+	0.0654913i
$686$	−20.9522	−	15.0246i	−0.799960	−	0.573642i
$687$	36.8087	+	25.7836i	1.40434	+	0.983707i
$688$	−0.384200	+	8.54128i	−0.0146475	+	0.325633i
$689$	39.0274	−	32.7479i	1.48683	−	1.24760i
$690$	0.0512440	−	4.48759i	0.00195083	−	0.170840i
$691$	−3.45954	−	9.50501i	−0.131607	−	0.361588i	0.856333	−	0.516424i	$-0.172737\pi$
$691$	−3.45954	−	9.50501i	−0.131607	−	0.361588i	−0.987940	+	0.154836i	$0.950515\pi$
$692$	−0.114623	−	0.747994i	−0.00435730	−	0.0284345i
$693$	−0.639850	+	0.536504i	−0.0243059	+	0.0203801i
$694$	2.67322	+	35.0929i	0.101474	+	1.33211i
$695$	−0.698194	+	3.95966i	−0.0264840	+	0.150198i
$696$	−27.8373	−	25.0139i	−1.05517	−	0.948148i
$697$	−21.2377	−	7.72988i	−0.804434	−	0.292790i
$698$	19.6898	+	20.1374i	0.745270	+	0.762212i
$699$	1.22086	+	1.22130i	0.0461772	+	0.0461938i
$700$	−13.4523	+	7.36863i	−0.508448	+	0.278508i
$701$			2.89056i			0.109175i	0.998509	+	0.0545874i	$0.0173844\pi$
$701$			2.89056i			0.109175i	−0.998509	+	0.0545874i	$0.982616\pi$
$702$	−5.21069	+	27.6431i	−0.196665	+	1.04332i
$703$	−2.78886			−0.105184
$704$	−0.335861	+	1.36089i	−0.0126582	+	0.0512905i
$705$	−6.31703	−	1.69387i	−0.237913	−	0.0637947i
$706$	7.37861	−	7.21461i	0.277698	−	0.271525i
$707$	−5.41178	+	14.8687i	−0.203531	+	0.559196i
$708$	−5.38958	+	18.4332i	−0.202553	+	0.692762i
$709$	26.6028	+	4.69079i	0.999090	+	0.176166i	0.649195	−	0.760622i	$-0.275106\pi$
$709$	26.6028	+	4.69079i	0.999090	+	0.176166i	0.349895	+	0.936789i	$0.386217\pi$
$710$	−0.304104	−	3.99215i	−0.0114128	−	0.149823i
$711$	−23.7865	−	4.20306i	−0.892062	−	0.157627i
$712$	16.5592	+	17.7152i	0.620584	+	0.663905i
$713$	7.66115	−	2.78843i	0.286913	−	0.104428i
$714$	−10.9312	−	19.4427i	−0.409088	−	0.727624i
$715$	0.178929	+	0.213239i	0.00669156	+	0.00797469i
$716$	−30.1486	+	10.2119i	−1.12671	+	0.381638i
$717$	15.3448	+	32.9226i	0.573063	+	1.22952i
$718$	6.99883	+	5.01878i	0.261194	+	0.187299i
$719$	−17.0798	−	29.5830i	−0.636968	−	1.10326i	−0.986095	−	0.166185i	$-0.946855\pi$
$719$	−17.0798	−	29.5830i	−0.636968	−	1.10326i	0.349126	−	0.937076i	$-0.386478\pi$
$720$	1.08609	−	4.86038i	0.0404761	−	0.181136i
$721$	−3.17730	+	5.50325i	−0.118329	+	0.204952i
$722$	−18.0783	+	8.18398i	−0.672804	+	0.304576i
$723$	31.4600	+	14.6769i	1.17001	+	0.545842i
$724$	−15.1815	−	13.3316i	−0.564218	−	0.495464i
$725$	−36.3204	+	6.40426i	−1.34890	+	0.237848i
$726$	−20.3844	−	17.5051i	−0.756538	−	0.649674i
$727$	2.59111	+	2.17420i	0.0960990	+	0.0806366i	0.689571	−	0.724218i	$-0.257799\pi$
$727$	2.59111	+	2.17420i	0.0960990	+	0.0806366i	−0.593472	+	0.804854i	$0.702243\pi$
$728$	−3.88903	−	16.7540i	−0.144137	−	0.620945i
$729$	0.0292776	−	27.0000i	0.00108436	−	0.999999i
$730$	4.41650	−	3.01907i	0.163462	−	0.111741i
$731$	−7.87581	+	9.38602i	−0.291297	+	0.347155i
$732$	−20.8566	−	2.30190i	−0.770884	−	0.0850807i
$733$	−2.03469	+	0.358771i	−0.0751530	+	0.0132515i	−0.211098	−	0.977465i	$-0.567704\pi$
$733$	−2.03469	+	0.358771i	−0.0751530	+	0.0132515i	0.135945	+	0.990716i	$0.456593\pi$
$734$	3.34821	+	13.0820i	0.123585	+	0.482865i
$735$	1.36047	−	2.91616i	0.0501817	−	0.107564i
$736$	23.7210	+	7.80798i	0.874369	+	0.287806i
$737$	−1.26264	+	2.18696i	−0.0465100	+	0.0805577i
$738$	15.0773	+	7.24472i	0.555002	+	0.266682i
$739$	−10.6217	+	6.13246i	−0.390727	+	0.225586i	−0.682475	−	0.730909i	$-0.739096\pi$
$739$	−10.6217	+	6.13246i	−0.390727	+	0.225586i	0.291748	+	0.956495i	$0.405763\pi$
$740$	−0.0233408	+	1.03832i	−0.000858027	+	0.0381694i
$741$	6.24304	+	13.3946i	0.229344	+	0.492062i
$742$	8.06252	−	28.7916i	0.295985	−	1.05697i
$743$	20.9883	−	17.6113i	0.769987	−	0.646096i	−0.170718	−	0.985320i	$-0.554609\pi$
$743$	20.9883	−	17.6113i	0.769987	−	0.646096i	0.940706	+	0.339224i	$0.110164\pi$
$744$	8.95794	−	1.26821i	0.328414	−	0.0464947i
$745$	6.56396	−	2.38909i	0.240485	−	0.0875294i
$746$	37.7855	+	18.1394i	1.38343	+	0.664130i
$747$	−1.78837	+	10.1209i	−0.0654330	+	0.370306i
$748$	−1.56743	+	1.25630i	−0.0573109	+	0.0459348i
$749$	−8.15086	−	1.43722i	−0.297826	−	0.0525147i
$750$	−6.33415	−	7.72622i	−0.231290	−	0.282122i
$751$	5.65802	+	2.05935i	0.206464	+	0.0751468i	0.443182	−	0.896432i	$-0.353850\pi$
$751$	5.65802	+	2.05935i	0.206464	+	0.0751468i	−0.236718	+	0.971578i	$0.576072\pi$
$752$	19.5945	−	30.6679i	0.714537	−	1.11834i
$753$	−29.7664	−	7.98164i	−1.08475	−	0.290867i
$754$	4.06716	−	41.1556i	0.148117	−	1.49880i
$755$			8.50292i			0.309453i
$756$	6.63063	+	15.1185i	0.241154	+	0.549854i
$757$		−	8.96216i		−	0.325735i	−0.986648	−	0.162868i	$-0.947926\pi$
$757$		−	8.96216i		−	0.325735i	0.986648	−	0.162868i	$-0.0520743\pi$
$758$	16.6903	+	1.64940i	0.606217	+	0.0599089i
$759$	0.947530	−	0.947188i	0.0343932	−	0.0343807i
$760$	−1.02517	−	2.40716i	−0.0371868	−	0.0873169i
$761$	10.8588	+	3.95227i	0.393630	+	0.143270i	0.531249	−	0.847215i	$-0.321723\pi$
$761$	10.8588	+	3.95227i	0.393630	+	0.143270i	−0.137619	+	0.990485i	$0.543945\pi$
$762$	−7.84264	−	2.95633i	−0.284109	−	0.107097i
$763$	−17.1961	−	3.03214i	−0.622542	−	0.109771i
$764$	14.5632	+	18.1699i	0.526878	+	0.657363i
$765$	5.46893	−	4.58561i	0.197730	−	0.165793i
$766$	−17.5217	+	36.4988i	−0.633084	+	1.31875i
$767$	−19.9425	+	7.25847i	−0.720082	+	0.262088i
$768$	23.9609	+	13.9240i	0.864614	+	0.502437i
$769$	−11.3522	+	9.52567i	−0.409373	+	0.343504i	−0.824103	−	0.566440i	$-0.808320\pi$
$769$	−11.3522	+	9.52567i	−0.409373	+	0.343504i	0.414730	+	0.909944i	$0.363876\pi$
$770$	0.157312	+	0.0440523i	0.00566914	+	0.00158753i
$771$	−3.40362	+	4.85900i	−0.122578	+	0.174993i
$772$	−1.04048	+	46.2859i	−0.0374477	+	1.66587i
$773$	23.5727	−	13.6097i	0.847850	−	0.489506i	−0.0120749	−	0.999927i	$-0.503844\pi$
$773$	23.5727	−	13.6097i	0.847850	−	0.489506i	0.859925	+	0.510421i	$0.170510\pi$
$774$	6.48638	−	6.33763i	0.233148	−	0.227801i
$775$	4.45787	−	7.72126i	0.160131	−	0.277356i
$776$	−2.55604	−	47.6836i	−0.0917567	−	1.71174i
$777$	−1.97415	−	2.82046i	−0.0708222	−	0.101183i
$778$	−9.64442	+	2.46839i	−0.345769	+	0.0884962i
$779$	8.65429	−	1.52598i	0.310072	−	0.0546741i
$780$	5.03919	−	2.21225i	0.180432	−	0.0792111i
$781$	0.768278	−	0.915598i	0.0274911	−	0.0327627i
$782$	20.1964	+	29.5446i	0.722222	+	1.05651i
$783$	3.43820	+	39.5457i	0.122871	+	1.41325i
$784$	13.1858	+	12.1146i	0.470923	+	0.432664i
$785$	−4.82810	−	4.05126i	−0.172322	−	0.144596i
$786$	5.10130	+	14.5298i	0.181957	+	0.518262i
$787$	20.6527	−	3.64163i	0.736191	−	0.129810i	0.207033	−	0.978334i	$-0.433619\pi$
$787$	20.6527	−	3.64163i	0.736191	−	0.129810i	0.529157	+	0.848524i	$0.322508\pi$
$788$	−14.6857	−	12.8961i	−0.523156	−	0.459406i
$789$	−2.41422	−	27.6523i	−0.0859487	−	0.984447i
$790$	1.94893	+	4.30515i	0.0693397	+	0.153170i
$791$	−13.1582	+	22.7907i	−0.467853	+	0.810345i
$792$	1.24622	−	0.810780i	0.0442826	−	0.0288098i
$793$	−11.5937	−	20.0810i	−0.411706	−	0.713096i
$794$	11.6484	−	16.2440i	0.413387	−	0.576479i
$795$	9.53044	+	0.835541i	0.338010	+	0.0296336i
$796$	−16.0433	−	47.3645i	−0.568639	−	1.67879i
$797$	15.9123	+	18.9635i	0.563642	+	0.671722i	0.970313	−	0.241852i	$-0.0777550\pi$
$797$	15.9123	+	18.9635i	0.563642	+	0.671722i	−0.406671	+	0.913575i	$0.633311\pi$
$798$	7.46085	+	4.42187i	0.264111	+	0.156533i
$799$	49.0085	−	17.8376i	1.73380	−	0.631050i
$800$	25.3603	−	10.1334i	0.896622	−	0.358271i
$801$	0.00929670	−	25.7204i	0.000328483	−	0.908787i
$802$	0.708357	−	0.0539594i	0.0250129	−	0.00190537i
$803$	1.57281	+	0.277329i	0.0555032	+	0.00978672i
$804$	34.4943	+	36.0939i	1.21652	+	1.27293i
$805$	0.995443	−	2.73496i	0.0350848	−	0.0963946i
$806$	6.98952	+	7.14840i	0.246195	+	0.251792i
$807$	−7.16822	−	26.7715i	−0.252333	−	0.942402i
$808$	12.7604	−	25.1177i	0.448908	−	0.883636i
$809$	−22.8474			−0.803271			−0.401635	−	0.915800i	$-0.631558\pi$
$809$	−22.8474			−0.803271			−0.401635	+	0.915800i	$0.631558\pi$
$810$	−4.36298	+	2.97786i	−0.153299	+	0.104631i
$811$			49.0261i			1.72154i	0.508995	+	0.860769i	$0.330017\pi$
$811$			49.0261i			1.72154i	−0.508995	+	0.860769i	$0.669983\pi$
$812$	−11.6599	−	21.2864i	−0.409182	−	0.747007i
$813$	46.5810	−	12.4723i	1.63367	−	0.437424i
$814$	−0.221687	+	0.216759i	−0.00777012	+	0.00759742i
$815$	7.84030	+	2.85364i	0.274634	+	0.0999585i
$816$	15.1430	+	36.7139i	0.530110	+	1.28524i
$817$	0.827288	−	4.69178i	0.0289431	−	0.164145i
$818$	1.43522	−	0.109329i	0.0501814	−	0.00382259i
$819$	−9.12710	+	15.7954i	−0.318927	+	0.551936i
$820$	−0.495710	−	3.23485i	−0.0173109	−	0.112966i
$821$	−6.95176	−	19.0998i	−0.242618	−	0.666587i	−0.999909	−	0.0135096i	$-0.995700\pi$
$821$	−6.95176	−	19.0998i	−0.242618	−	0.666587i	0.757291	−	0.653078i	$-0.226523\pi$
$822$	−10.3160	+	17.4058i	−0.359813	+	0.607098i
$823$	−18.9998	+	15.9427i	−0.662291	+	0.555728i	−0.910772	−	0.412909i	$-0.864513\pi$
$823$	−18.9998	+	15.9427i	−0.662291	+	0.555728i	0.248482	+	0.968637i	$0.420068\pi$
$824$	6.79844	−	9.04427i	0.236835	−	0.315072i
$825$	0.127959	−	1.45954i	0.00445496	−	0.0508147i
$826$	−7.25797	+	10.1214i	−0.252537	+	0.352170i
$827$	−19.3353	+	11.1632i	−0.672354	+	0.388184i	−0.796968	−	0.604021i	$-0.793564\pi$
$827$	−19.3353	+	11.1632i	−0.672354	+	0.388184i	0.124614	+	0.992205i	$0.460231\pi$
$828$	−12.7167	−	23.2356i	−0.441935	−	0.807495i
$829$	37.4638	+	21.6297i	1.30117	+	0.751232i	0.980605	−	0.195994i	$-0.0627934\pi$
$829$	37.4638	+	21.6297i	1.30117	+	0.751232i	0.320566	+	0.947226i	$0.396127\pi$
$830$	1.83181	−	0.829253i	0.0635829	−	0.0287838i
$831$	−10.2035	+	0.890832i	−0.353955	+	0.0309026i
$832$	3.27374	+	30.4484i	0.113496	+	1.05561i
$833$	4.45592	+	25.2708i	0.154389	+	0.875582i
$834$	7.86125	+	22.3909i	0.272213	+	0.775332i
$835$	3.25810	−	3.88285i	0.112751	−	0.134371i
$836$	0.283567	−	0.727772i	0.00980738	−	0.0251705i
$837$	−7.85766	−	5.50835i	−0.271601	−	0.190396i
$838$	37.7757	−	25.8231i	1.30494	−	0.892044i
$839$	27.4815	+	23.0597i	0.948765	+	0.796109i	0.979089	−	0.203431i	$-0.0652094\pi$
$839$	27.4815	+	23.0597i	0.948765	+	0.796109i	−0.0303238	+	0.999540i	$0.509654\pi$
$840$	1.70875	−	2.74075i	0.0589576	−	0.0945647i
$841$	−5.09810	−	28.9128i	−0.175797	−	0.996992i
$842$	10.9344	−	2.79855i	0.376824	−	0.0964445i
$843$	−15.0181	+	10.5118i	−0.517252	+	0.362045i
$844$	7.35131	−	12.0966i	0.253043	−	0.416382i
$845$	0.594304	+	0.343122i	0.0204447	+	0.0118037i
$846$	−37.3989	+	9.55747i	−1.28580	+	0.328593i
$847$	−8.71260	−	15.0907i	−0.299368	−	0.518521i
$848$	−20.4373	+	49.1567i	−0.701821	+	1.68805i
$849$	8.61234	+	6.03275i	0.295575	+	0.207043i
$850$	37.6871	+	10.5535i	1.29266	+	0.361984i
$851$	3.55063	+	4.23147i	0.121714	+	0.145053i
$852$	−13.1118	−	19.6589i	−0.449202	−	0.673502i
$853$	−9.03106	−	24.8126i	−0.309217	−	0.849568i	−0.992810	−	0.119704i	$-0.961806\pi$
$853$	−9.03106	−	24.8126i	−0.309217	−	0.849568i	0.683592	−	0.729864i	$-0.260417\pi$
$854$	−12.2677	−	5.88925i	−0.419792	−	0.201526i
$855$	−0.950076	+	2.60738i	−0.0324919	+	0.0891705i
$856$	14.0978	+	4.29176i	0.481854	+	0.146689i
$857$	0.634748	−	3.59984i	0.0216826	−	0.122968i	−0.972045	−	0.234793i	$-0.924559\pi$
$857$	0.634748	−	3.59984i	0.0216826	−	0.122968i	0.993728	+	0.111825i	$0.0356697\pi$
$858$	1.53733	+	0.579507i	0.0524837	+	0.0197840i
$859$	−7.11419	+	19.5461i	−0.242733	+	0.666903i	0.757173	+	0.653214i	$0.226580\pi$
$859$	−7.11419	+	19.5461i	−0.242733	+	0.666903i	−0.999906	+	0.0136894i	$0.995642\pi$
$860$	−1.73988	−	0.347275i	−0.0593293	−	0.0118420i
$861$	7.66939	+	7.67217i	0.261372	+	0.261467i
$862$	−5.60864	+	56.7537i	−0.191031	+	1.93304i
$863$	−33.2434			−1.13162			−0.565809	−	0.824536i	$-0.691436\pi$
$863$	−33.2434			−1.13162			−0.565809	+	0.824536i	$0.691436\pi$
$864$	−8.47098	−	28.1468i	−0.288189	−	0.957574i
$865$	0.157028			0.00533912
$866$	−0.0483762	+	0.489518i	−0.00164389	+	0.0166345i
$867$	−7.11409	+	26.5310i	−0.241607	+	0.901038i
$868$	5.75384	+	1.14845i	0.195298	+	0.0389810i
$869$	−0.482513	+	1.32569i	−0.0163681	+	0.0449711i
$870$	6.00573	−	4.92365i	0.203613	−	0.166927i
$871$	−9.58030	+	54.3326i	−0.324616	+	1.84099i
$872$	29.7427	+	9.05446i	1.00721	+	0.306623i
$873$	−32.5704	+	38.7874i	−1.10234	+	1.31275i
$874$	−12.5448	−	6.02226i	−0.424333	−	0.203706i
$875$	−2.21602	−	6.08848i	−0.0749153	−	0.205828i
$876$	13.9890	−	28.3070i	0.472645	−	0.956404i
$877$	−14.1420	−	16.8538i	−0.477543	−	0.569114i	0.472461	−	0.881352i	$-0.343366\pi$
$877$	−14.1420	−	16.8538i	−0.477543	−	0.569114i	−0.950004	+	0.312238i	$0.898921\pi$
$878$	−19.9813	−	5.59539i	−0.674338	−	0.188835i
$879$	−15.6933	+	7.31445i	−0.529322	+	0.246710i
$880$	−0.268584	−	0.111666i	−0.00905396	−	0.00376426i
$881$	−23.4256	−	40.5742i	−0.789227	−	1.36698i	−0.926441	−	0.376440i	$-0.877148\pi$
$881$	−23.4256	−	40.5742i	−0.789227	−	1.36698i	0.137214	−	0.990541i	$-0.456185\pi$
$882$	−1.43573	−	18.9380i	−0.0483434	−	0.637675i
$883$	−19.8318	−	11.4499i	−0.667394	−	0.385320i	0.127695	−	0.991814i	$-0.459242\pi$
$883$	−19.8318	−	11.4499i	−0.667394	−	0.385320i	−0.795088	+	0.606494i	$0.792576\pi$
$884$	−22.7916	+	37.5037i	−0.766566	+	1.26139i
$885$	−3.61154	−	1.68488i	−0.121401	−	0.0566367i
$886$	55.0379	−	14.0864i	1.84904	−	0.473243i
$887$	3.23660	+	18.3557i	0.108674	+	0.616323i	0.989689	+	0.143234i	$0.0457501\pi$
$887$	3.23660	+	18.3557i	0.108674	+	0.616323i	−0.881014	+	0.473089i	$0.843139\pi$
$888$	2.88325	+	5.40938i	0.0967555	+	0.181527i
$889$	−4.16381	−	3.49385i	−0.139650	−	0.117180i
$890$	−4.15416	+	2.83974i	−0.139248	+	0.0951883i
$891$	−1.55278	−	0.274955i	−0.0520202	−	0.00921135i
$892$	−18.4054	+	47.2373i	−0.616259	+	1.58162i
$893$	−13.0350	+	15.5345i	−0.436201	+	0.519844i
$894$	26.8594	−	31.2774i	0.898311	−	1.04607i
$895$	−1.14700	−	6.50494i	−0.0383399	−	0.217436i
$896$	11.6704	+	13.6677i	0.389880	+	0.456606i
$897$	12.3750	−	26.5257i	0.413189	−	0.885668i
$898$	6.50671	−	2.94557i	0.217132	−	0.0982949i
$899$	12.2179	+	7.05399i	0.407489	+	0.235264i
$900$	−26.9863	−	10.5261i	−0.899544	−	0.350871i
$901$	−66.0696	+	38.1453i	−2.20110	+	1.27080i
$902$	0.569327	−	0.793942i	0.0189565	−	0.0264354i
$903$	5.33057	−	2.48451i	0.177390	−	0.0826794i
$904$	28.1545	−	37.4552i	0.936406	−	1.24574i
$905$	3.21170	−	2.69494i	0.106761	−	0.0895828i
$906$	24.5946	+	43.7452i	0.817102	+	1.45334i
$907$	4.56947	+	12.5545i	0.151727	+	0.416866i	0.992148	−	0.125068i	$-0.0399147\pi$
$907$	4.56947	+	12.5545i	0.151727	+	0.416866i	−0.840421	+	0.541933i	$0.817693\pi$
$908$	3.64177	+	23.7651i	0.120856	+	0.788673i
$909$	−28.0837	+	10.2101i	−0.931476	+	0.338648i
$910$	3.55875	−	0.271090i	0.117972	−	0.00898654i
$911$	−9.26802	+	52.5616i	−0.307063	+	1.74144i	0.306568	+	0.951849i	$0.400819\pi$
$911$	−9.26802	+	52.5616i	−0.307063	+	1.74144i	−0.613631	+	0.789593i	$0.710292\pi$
$912$	−12.2369	−	9.41888i	−0.405204	−	0.311890i
$913$	0.564072	+	0.205305i	0.0186681	+	0.00679462i
$914$	−2.08201	+	2.03573i	−0.0688668	+	0.0673361i
$915$	1.12772	−	4.20568i	0.0372814	−	0.139035i
$916$	−24.9300	−	45.5125i	−0.823711	−	1.50378i
$917$			9.98676i			0.329792i
$918$	14.8723	−	39.4105i	0.490859	−	1.30074i
$919$	−29.3286			−0.967460			−0.483730	−	0.875217i	$-0.660718\pi$
$919$	−29.3286			−0.967460			−0.483730	+	0.875217i	$0.660718\pi$
$920$	−2.34714	+	4.62015i	−0.0773830	+	0.152322i
$921$	27.1155	−	27.1057i	0.893487	−	0.893164i
$922$	−14.6665	−	14.9999i	−0.483015	−	0.493994i
$923$	8.93102	−	24.5378i	0.293968	−	0.807670i
$924$	0.936748	−	0.228387i	0.0308168	−	0.00751339i
$925$	5.94892	+	1.04896i	0.195599	+	0.0344894i
$926$	5.41087	−	0.412176i	0.177812	−	0.0135449i
$927$	−11.8193	+	2.07965i	−0.388195	+	0.0683046i
$928$	16.0348	+	40.1294i	0.526369	+	1.31731i
$929$	−41.2440	+	15.0116i	−1.35317	+	0.492514i	−0.913936	−	0.405859i	$-0.866972\pi$
$929$	−41.2440	+	15.0116i	−1.35317	+	0.492514i	−0.439234	+	0.898373i	$0.644750\pi$
$930$	−0.0214367	+	1.87728i	−0.000702938	+	0.0615584i
$931$	−6.41349	−	7.64329i	−0.210194	−	0.250499i
$932$	−0.639711	−	1.88862i	−0.0209544	−	0.0618637i
$933$	−0.131849	+	0.188228i	−0.00431655	+	0.00616231i
$934$	−2.79386	+	3.89611i	−0.0914177	+	0.127485i
$935$	−0.208419	−	0.360993i	−0.00681604	−	0.0118057i
$936$	19.5263	−	25.9572i	0.638238	−	0.848437i
$937$	−2.28782	+	3.96262i	−0.0747397	+	0.129453i	−0.900973	−	0.433875i	$-0.857146\pi$
$937$	−2.28782	+	3.96262i	−0.0747397	+	0.129453i	0.826233	+	0.563328i	$0.190479\pi$
$938$	13.3530	+	29.4964i	0.435989	+	0.963093i
$939$	5.74955	−	4.02433i	0.187629	−	0.131329i
$940$	5.67458	+	4.98309i	0.185084	+	0.162531i
$941$	20.4961	−	3.61402i	0.668155	−	0.117814i	0.170726	−	0.985319i	$-0.445389\pi$
$941$	20.4961	−	3.61402i	0.668155	−	0.117814i	0.497429	+	0.867505i	$0.334278\pi$
$942$	−36.5575	−	6.87737i	−1.19111	−	0.224077i
$943$	−13.3335	−	11.1882i	−0.434200	−	0.364337i
$944$	15.0034	−	16.3301i	0.488319	−	0.531499i
$945$	−3.30946	+	0.884844i	−0.107657	+	0.0287840i
$946$	−0.298900	−	0.437251i	−0.00971809	−	0.0142163i
$947$	−19.2312	+	22.9188i	−0.624929	+	0.744762i	−0.981910	−	0.189350i	$-0.939362\pi$
$947$	−19.2312	+	22.9188i	−0.624929	+	0.744762i	0.356980	+	0.934112i	$0.383806\pi$
$948$	22.4793	+	16.5115i	0.730093	+	0.536270i
$949$	34.3617	−	6.05889i	1.11543	−	0.196680i
$950$	−14.7424	+	3.77316i	−0.478306	+	0.122418i
$951$	−15.7721	+	1.37701i	−0.511446	+	0.0446526i
$952$	1.37862	+	25.7185i	0.0446814	+	0.833542i
$953$	−22.8497	+	39.5768i	−0.740174	+	1.28202i	0.212242	+	0.977217i	$0.431924\pi$
$953$	−22.8497	+	39.5768i	−0.740174	+	1.28202i	−0.952416	+	0.304802i	$0.901410\pi$
$954$	51.4483	−	23.2681i	1.66570	−	0.753332i
$955$	−4.18468	+	2.41603i	−0.135413	+	0.0781808i
$956$	0.942599	−	41.9316i	0.0304858	−	1.35617i
$957$	2.30953	+	0.202478i	0.0746565	+	0.00654519i
$958$	−10.5988	−	2.96800i	−0.342433	−	0.0958917i
$959$	−10.0518	+	8.43442i	−0.324588	+	0.272362i
$960$	−3.60916	+	4.47710i	−0.116485	+	0.144498i
$961$	25.9256	−	9.43615i	0.836310	−	0.304392i
$962$	−2.93151	+	6.10652i	−0.0945155	+	0.196882i
$963$	−7.81038	−	13.5393i	−0.251686	−	0.436297i
$964$	−25.0699	−	31.2787i	−0.807448	−	1.00742i
$965$	−9.46127	−	1.66828i	−0.304569	−	0.0537038i
$966$	−2.78956	−	16.9499i	−0.0897526	−	0.545354i
$967$	5.78938	+	2.10716i	0.186174	+	0.0677617i	0.433425	−	0.901190i	$-0.357305\pi$
$967$	5.78938	+	2.10716i	0.186174	+	0.0677617i	−0.247251	+	0.968951i	$0.579527\pi$
$968$	12.1568	+	28.5450i	0.390736	+	0.917470i
$969$	−5.72366	−	21.3765i	−0.183871	−	0.686711i
$970$	9.86101	+	0.974506i	0.316618	+	0.0312895i
$971$			0.579394i			0.0185936i	0.999957	+	0.00929682i	$0.00295931\pi$
$971$			0.579394i			0.0185936i	−0.999957	+	0.00929682i	$0.997041\pi$
$972$	−13.8329	+	27.9401i	−0.443690	+	0.896181i
$973$			15.3899i			0.493377i
$974$	−4.88035	+	49.3842i	−0.156377	+	1.58237i
$975$	−8.27904	−	30.9202i	−0.265142	−	0.990238i
$976$	20.4177	+	13.0454i	0.653555	+	0.417572i
$977$	1.17972	+	0.429383i	0.0377426	+	0.0137372i	0.360822	−	0.932635i	$-0.382496\pi$
$977$	1.17972	+	0.429383i	0.0377426	+	0.0137372i	−0.323080	+	0.946372i	$0.604718\pi$
$978$	48.5903	−	7.99682i	1.55375	−	0.255710i
$979$	−1.47938	−	0.260855i	−0.0472813	−	0.00833697i
$980$	−2.89936	+	2.32384i	−0.0926165	+	0.0742323i
$981$	−16.4778	−	28.5643i	−0.526096	−	0.911987i
$982$	−3.20596	−	1.53906i	−0.102306	−	0.0491133i
$983$	−0.302913	+	0.110251i	−0.00966143	+	0.00351647i	−0.346846	−	0.937922i	$-0.612747\pi$
$983$	−0.302913	+	0.110251i	−0.00966143	+	0.00351647i	0.337185	+	0.941438i	$0.390525\pi$
$984$	−11.9071	−	15.2086i	−0.379584	−	0.484832i
$985$	3.10680	−	2.60692i	0.0989910	−	0.0830633i
$986$	−16.6996	+	59.6349i	−0.531824	+	1.89916i
$987$	−24.9377	−	2.18631i	−0.793776	−	0.0695910i
$988$	0.383496	−	17.0599i	0.0122006	−	0.542747i
$989$	−8.17201	+	4.71811i	−0.259855	+	0.150027i
$990$	0.127133	+	0.281104i	0.00404054	+	0.00893409i
$991$	30.3683	−	52.5994i	0.964681	−	1.67088i	0.254210	−	0.967149i	$-0.418185\pi$
$991$	30.3683	−	52.5994i	0.964681	−	1.67088i	0.710471	−	0.703727i	$-0.248482\pi$
$992$	−9.92315	−	3.26629i	−0.315060	−	0.103705i
$993$	29.2218	−	2.55125i	0.927324	−	0.0809615i
$994$	−3.79973	−	14.8462i	−0.120520	−	0.470892i
$995$	10.2195	−	1.80197i	0.323979	−	0.0571263i
$996$	7.02553	−	9.56475i	0.222612	−	0.303071i
$997$	36.6115	−	43.6319i	1.15950	−	1.38184i	0.248906	−	0.968528i	$-0.419929\pi$
$997$	36.6115	−	43.6319i	1.15950	−	1.38184i	0.910592	−	0.413307i	$-0.135626\pi$
$998$	3.29357	−	2.25145i	0.104256	−	0.0712684i
$999$	1.68615	−	6.27919i	0.0533476	−	0.198665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.205.20	yes	204
3.2	odd	2		648.2.t.a.613.15		204
4.3	odd	2		864.2.bf.a.529.3		204
8.3	odd	2		864.2.bf.a.529.32		204
8.5	even	2	inner	216.2.t.a.205.3	yes	204
24.5	odd	2		648.2.t.a.613.32		204
27.5	odd	18		648.2.t.a.37.32		204
27.22	even	9	inner	216.2.t.a.157.3	✓	204
108.103	odd	18		864.2.bf.a.49.32		204
216.5	odd	18		648.2.t.a.37.15		204
216.157	even	18	inner	216.2.t.a.157.20	yes	204
216.211	odd	18		864.2.bf.a.49.3		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.3	✓	204	27.22	even	9	inner
216.2.t.a.157.20	yes	204	216.157	even	18	inner
216.2.t.a.205.3	yes	204	8.5	even	2	inner
216.2.t.a.205.20	yes	204	1.1	even	1	trivial
648.2.t.a.37.15		204	216.5	odd	18
648.2.t.a.37.32		204	27.5	odd	18
648.2.t.a.613.15		204	3.2	odd	2
648.2.t.a.613.32		204	24.5	odd	2
864.2.bf.a.49.3		204	216.211	odd	18
864.2.bf.a.49.32		204	108.103	odd	18
864.2.bf.a.529.3		204	4.3	odd	2
864.2.bf.a.529.32		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)

\(f(q)\)	\(=\)	\(q+(0.139081 - 1.40736i) q^{2} +(1.67311 - 0.447985i) q^{3} +(-1.96131 - 0.391473i) q^{4} +(0.141945 - 0.389992i) q^{5} +(-0.397778 - 2.41698i) q^{6} +(0.275847 - 1.56441i) q^{7} +(-0.823724 + 2.70582i) q^{8} +(2.59862 - 1.49906i) q^{9} +O(q^{10})\)	\(q+(0.139081 - 1.40736i) q^{2} +(1.67311 - 0.447985i) q^{3} +(-1.96131 - 0.391473i) q^{4} +(0.141945 - 0.389992i) q^{5} +(-0.397778 - 2.41698i) q^{6} +(0.275847 - 1.56441i) q^{7} +(-0.823724 + 2.70582i) q^{8} +(2.59862 - 1.49906i) q^{9} +(-0.529116 - 0.254008i) q^{10} +(-0.0599272 - 0.164649i) q^{11} +(-3.45687 + 0.223660i) q^{12} +(-2.46059 - 2.93241i) q^{13} +(-2.16332 - 0.605795i) q^{14} +(0.0627802 - 0.716090i) q^{15} +(3.69350 + 1.53560i) q^{16} +(2.86613 + 4.96428i) q^{17} +(-1.74830 - 3.86568i) q^{18} +(-1.93026 - 1.11443i) q^{19} +(-0.431071 + 0.709328i) q^{20} +(-0.239308 - 2.74101i) q^{21} +(-0.240054 + 0.0614396i) q^{22} +(0.766596 + 4.34758i) q^{23} +(-0.166015 + 4.89617i) q^{24} +(3.69828 + 3.10322i) q^{25} +(-4.46917 + 3.05508i) q^{26} +(3.67623 - 3.67224i) q^{27} +(-1.15345 + 2.96031i) q^{28} +(-4.91044 + 5.85204i) q^{29} +(-0.999064 - 0.187949i) q^{30} +(-0.320688 - 1.81871i) q^{31} +(2.67484 - 4.98450i) q^{32} +(-0.174025 - 0.248629i) q^{33} +(7.38514 - 3.34323i) q^{34} +(-0.570951 - 0.329639i) q^{35} +(-5.68355 + 1.92284i) q^{36} +(1.08361 - 0.625621i) q^{37} +(-1.83687 + 2.56157i) q^{38} +(-5.43052 - 3.80395i) q^{39} +(0.938325 + 0.705325i) q^{40} +(-3.02029 + 2.53433i) q^{41} +(-3.89086 - 0.0444299i) q^{42} +(0.731061 + 2.00857i) q^{43} +(0.0530805 + 0.346388i) q^{44} +(-0.215760 - 1.22622i) q^{45} +(6.22522 - 0.474209i) q^{46} +(1.57990 - 8.96007i) q^{47} +(6.86757 + 0.914606i) q^{48} +(4.20657 + 1.53107i) q^{49} +(4.88171 - 4.77320i) q^{50} +(7.01928 + 7.02182i) q^{51} +(3.67802 + 6.71463i) q^{52} +13.3090i q^{53} +(-4.65687 - 5.68451i) q^{54} -0.0727180 q^{55} +(4.00579 + 2.03504i) q^{56} +(-3.72879 - 0.999849i) q^{57} +(7.55296 + 7.72466i) q^{58} +(1.89616 - 5.20965i) q^{59} +(-0.403462 + 1.37990i) q^{60} +(5.96533 + 1.05185i) q^{61} +(-2.60418 + 0.198374i) q^{62} +(-1.62832 - 4.47881i) q^{63} +(-6.64296 - 4.45770i) q^{64} +(-1.49289 + 0.543366i) q^{65} +(-0.374114 + 0.210336i) q^{66} +(-9.26414 - 11.0406i) q^{67} +(-3.67799 - 10.8585i) q^{68} +(3.23026 + 6.93058i) q^{69} +(-0.543328 + 0.757686i) q^{70} +(3.41074 + 5.90757i) q^{71} +(1.91565 + 8.26621i) q^{72} +(-4.55745 + 7.89374i) q^{73} +(-0.729764 - 1.61204i) q^{74} +(7.57784 + 3.53527i) q^{75} +(3.34957 + 2.94140i) q^{76} +(-0.274109 + 0.0483327i) q^{77} +(-6.10880 + 7.11362i) q^{78} +(-6.16792 - 5.17550i) q^{79} +(1.12315 - 1.22246i) q^{80} +(4.50563 - 7.79097i) q^{81} +(3.14664 + 4.60311i) q^{82} +(-2.20213 + 2.62440i) q^{83} +(-0.603674 + 5.46966i) q^{84} +(2.34286 - 0.413110i) q^{85} +(2.92846 - 0.749510i) q^{86} +(-5.59410 + 11.9909i) q^{87} +(0.494874 - 0.0265273i) q^{88} +(4.28674 - 7.42485i) q^{89} +(-1.75575 + 0.133106i) q^{90} +(-5.26623 + 3.04046i) q^{91} +(0.198428 - 8.82707i) q^{92} +(-1.35130 - 2.89925i) q^{93} +(-12.3903 - 3.46966i) q^{94} +(-0.708612 + 0.594596i) q^{95} +(2.24233 - 9.53792i) q^{96} +(-15.8647 + 5.77429i) q^{97} +(2.73981 - 5.70720i) q^{98} +(-0.402546 - 0.338025i) 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

Fields

Representations

Groups

Database

Properties

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