LMFDB - Embedded newform 216.2.t.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01573 - 0.984023i) q^{2} +(-1.62462 - 0.600509i) q^{3} +(0.0633965 + 1.99899i) q^{4} +(-0.765978 + 0.912857i) q^{5} +(1.05925 + 2.20862i) q^{6} +(0.820563 + 0.298660i) q^{7} +(1.90266 - 2.09281i) q^{8} +(2.27878 + 1.95120i) q^{9} +O(q^{10})$	\(q+(-1.01573 - 0.984023i) q^{2} +(-1.62462 - 0.600509i) q^{3} +(0.0633965 + 1.99899i) q^{4} +(-0.765978 + 0.912857i) q^{5} +(1.05925 + 2.20862i) q^{6} +(0.820563 + 0.298660i) q^{7} +(1.90266 - 2.09281i) q^{8} +(2.27878 + 1.95120i) q^{9} +(1.67630 - 0.173472i) q^{10} +(-0.659595 - 0.786075i) q^{11} +(1.09742 - 3.28568i) q^{12} +(5.47642 + 0.965640i) q^{13} +(-0.539578 - 1.11081i) q^{14} +(1.79260 - 1.02307i) q^{15} +(-3.99196 + 0.253458i) q^{16} +(1.12031 - 1.94043i) q^{17} +(-0.394587 - 4.22425i) q^{18} +(2.40409 - 1.38800i) q^{19} +(-1.87336 - 1.47331i) q^{20} +(-1.15375 - 0.977965i) q^{21} +(-0.103548 + 1.44749i) q^{22} +(3.96541 - 1.44329i) q^{23} +(-4.34786 + 2.25746i) q^{24} +(0.621655 + 3.52558i) q^{25} +(-4.61232 - 6.36975i) q^{26} +(-2.53043 - 4.53838i) q^{27} +(-0.545000 + 1.65923i) q^{28} +(1.65744 - 0.292252i) q^{29} +(-2.82751 - 0.724805i) q^{30} +(-1.20025 + 0.436854i) q^{31} +(4.30415 + 3.67074i) q^{32} +(0.599546 + 1.67317i) q^{33} +(-3.04735 + 0.868533i) q^{34} +(-0.901167 + 0.520289i) q^{35} +(-3.75597 + 4.67896i) q^{36} +(8.83390 + 5.10025i) q^{37} +(-3.80773 - 0.955852i) q^{38} +(-8.31722 - 4.85744i) q^{39} +(0.453041 + 3.33991i) q^{40} +(-1.93593 + 10.9792i) q^{41} +(0.209557 + 2.12866i) q^{42} +(-0.563024 - 0.670985i) q^{43} +(1.52954 - 1.36836i) q^{44} +(-3.52666 + 0.585623i) q^{45} +(-5.44800 - 2.43607i) q^{46} +(6.37901 + 2.32177i) q^{47} +(6.63762 + 1.98544i) q^{48} +(-4.77819 - 4.00937i) q^{49} +(2.83782 - 4.19275i) q^{50} +(-2.98531 + 2.47970i) q^{51} +(-1.58312 + 11.0085i) q^{52} -3.50342i q^{53} +(-1.89565 + 7.09975i) q^{54} +1.22281 q^{55} +(2.18630 - 1.14903i) q^{56} +(-4.73924 + 0.811297i) q^{57} +(-1.97109 - 1.33411i) q^{58} +(-7.30225 + 8.70248i) q^{59} +(2.15875 + 3.51854i) q^{60} +(1.86712 - 5.12986i) q^{61} +(1.64900 + 0.737347i) q^{62} +(1.28713 + 2.28166i) q^{63} +(-0.759738 - 7.96384i) q^{64} +(-5.07631 + 4.25953i) q^{65} +(1.03746 - 2.28944i) q^{66} +(-7.80090 - 1.37551i) q^{67} +(3.94992 + 2.11647i) q^{68} +(-7.30899 - 0.0364666i) q^{69} +(1.42732 + 0.358299i) q^{70} +(4.40148 - 7.62359i) q^{71} +(8.41924 - 1.05658i) q^{72} +(-5.37419 - 9.30837i) q^{73} +(-3.95405 - 13.8732i) q^{74} +(1.10719 - 6.10104i) q^{75} +(2.92702 + 4.71777i) q^{76} +(-0.306470 - 0.842019i) q^{77} +(3.66818 + 13.1182i) q^{78} +(1.26481 + 7.17310i) q^{79} +(2.82638 - 3.83823i) q^{80} +(1.38565 + 8.89269i) q^{81} +(12.7702 - 9.24687i) q^{82} +(6.42315 - 1.13258i) q^{83} +(1.88180 - 2.36835i) q^{84} +(0.913202 + 2.50900i) q^{85} +(-0.0883878 + 1.23557i) q^{86} +(-2.86821 - 0.520511i) q^{87} +(-2.90010 - 0.115227i) q^{88} +(-7.39005 - 12.7999i) q^{89} +(4.15838 + 2.87548i) q^{90} +(4.20535 + 2.42796i) q^{91} +(3.13653 + 7.83534i) q^{92} +(2.21228 + 0.0110377i) q^{93} +(-4.19465 - 8.63538i) q^{94} +(-0.574433 + 3.25777i) q^{95} +(-4.78829 - 8.54823i) q^{96} +(11.6240 - 9.75374i) q^{97} +(0.908008 + 8.77427i) q^{98} +(0.0307177 - 3.07829i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.01573	−	0.984023i	−0.718226	−	0.695810i
$2$	−1.01573	−	0.984023i	−0.718226	−	0.695810i
$3$	−1.62462	−	0.600509i	−0.937975	−	0.346704i
$3$	−1.62462	−	0.600509i	−0.937975	−	0.346704i
$4$	0.0633965	+	1.99899i	0.0316982	+	0.999497i
$5$	−0.765978	+	0.912857i	−0.342556	+	0.408242i	−0.909627	−	0.415427i	$-0.863632\pi$
$5$	−0.765978	+	0.912857i	−0.342556	+	0.408242i	0.567071	+	0.823669i	$0.308077\pi$
$6$	1.05925	+	2.20862i	0.432438	+	0.901664i
$7$	0.820563	+	0.298660i	0.310144	+	0.112883i	0.492403	−	0.870368i	$-0.336119\pi$
$7$	0.820563	+	0.298660i	0.310144	+	0.112883i	−0.182259	+	0.983251i	$0.558341\pi$
$8$	1.90266	−	2.09281i	0.672693	−	0.739921i
$9$	2.27878	+	1.95120i	0.759592	+	0.650399i
$10$	1.67630	−	0.173472i	0.530091	−	0.0548567i
$11$	−0.659595	−	0.786075i	−0.198875	−	0.237011i	0.657385	−	0.753555i	$-0.271663\pi$
$11$	−0.659595	−	0.786075i	−0.198875	−	0.237011i	−0.856260	+	0.516544i	$0.827218\pi$
$12$	1.09742	−	3.28568i	0.316798	−	0.948493i
$13$	5.47642	+	0.965640i	1.51888	+	0.267820i	0.869995	−	0.493061i	$-0.164122\pi$
$13$	5.47642	+	0.965640i	1.51888	+	0.267820i	0.648890	+	0.760882i	$0.275233\pi$
$14$	−0.539578	−	1.11081i	−0.144208	−	0.296876i
$15$	1.79260	−	1.02307i	0.462848	−	0.264155i
$16$	−3.99196	+	0.253458i	−0.997990	+	0.0633646i
$17$	1.12031	−	1.94043i	0.271714	−	0.470622i	−0.697587	−	0.716500i	$-0.745743\pi$
$17$	1.12031	−	1.94043i	0.271714	−	0.470622i	0.969301	+	0.245878i	$0.0790762\pi$
$18$	−0.394587	−	4.22425i	−0.0930052	−	0.995666i
$19$	2.40409	−	1.38800i	0.551537	−	0.318430i	−0.198205	−	0.980161i	$-0.563511\pi$
$19$	2.40409	−	1.38800i	0.551537	−	0.318430i	0.749742	+	0.661731i	$0.230178\pi$
$20$	−1.87336	−	1.47331i	−0.418895	−	0.329443i
$21$	−1.15375	−	0.977965i	−0.251770	−	0.213409i
$22$	−0.103548	+	1.44749i	−0.0220766	+	0.308607i
$23$	3.96541	−	1.44329i	0.826845	−	0.300947i	0.106282	−	0.994336i	$-0.466105\pi$
$23$	3.96541	−	1.44329i	0.826845	−	0.300947i	0.720563	+	0.693389i	$0.243883\pi$
$24$	−4.34786	+	2.25746i	−0.887503	+	0.460802i
$25$	0.621655	+	3.52558i	0.124331	+	0.705116i
$26$	−4.61232	−	6.36975i	−0.904551	−	1.24921i
$27$	−2.53043	−	4.53838i	−0.486982	−	0.873412i
$28$	−0.545000	+	1.65923i	−0.102995	+	0.313566i
$29$	1.65744	−	0.292252i	0.307779	−	0.0542698i	−0.0176254	−	0.999845i	$-0.505611\pi$
$29$	1.65744	−	0.292252i	0.307779	−	0.0542698i	0.325405	+	0.945575i	$0.394500\pi$
$30$	−2.82751	−	0.724805i	−0.516231	−	0.132331i
$31$	−1.20025	+	0.436854i	−0.215571	+	0.0784613i	−0.447548	−	0.894260i	$-0.647703\pi$
$31$	−1.20025	+	0.436854i	−0.215571	+	0.0784613i	0.231977	+	0.972721i	$0.425480\pi$
$32$	4.30415	+	3.67074i	0.760873	+	0.648901i
$33$	0.599546	+	1.67317i	0.104368	+	0.291261i
$34$	−3.04735	+	0.868533i	−0.522616	+	0.148952i
$35$	−0.901167	+	0.520289i	−0.152325	+	0.0879449i
$36$	−3.75597	+	4.67896i	−0.625995	+	0.779827i
$37$	8.83390	+	5.10025i	1.45228	+	0.838477i	0.998611	−	0.0526913i	$-0.0167799\pi$
$37$	8.83390	+	5.10025i	1.45228	+	0.838477i	0.453673	+	0.891168i	$0.350113\pi$
$38$	−3.80773	−	0.955852i	−0.617695	−	0.155060i
$39$	−8.31722	−	4.85744i	−1.33182	−	0.777813i
$40$	0.453041	+	3.33991i	0.0716321	+	0.528086i
$41$	−1.93593	+	10.9792i	−0.302342	+	1.71467i	0.333418	+	0.942779i	$0.391798\pi$
$41$	−1.93593	+	10.9792i	−0.302342	+	1.71467i	−0.635760	+	0.771887i	$0.719313\pi$
$42$	0.209557	+	2.12866i	0.0323353	+	0.328460i
$43$	−0.563024	−	0.670985i	−0.0858603	−	0.102324i	0.721404	−	0.692515i	$-0.243497\pi$
$43$	−0.563024	−	0.670985i	−0.0858603	−	0.102324i	−0.807264	+	0.590190i	$0.799053\pi$
$44$	1.52954	−	1.36836i	0.230587	−	0.206288i
$45$	−3.52666	+	0.585623i	−0.525723	+	0.0872995i
$46$	−5.44800	−	2.43607i	−0.803264	−	0.359179i
$47$	6.37901	+	2.32177i	0.930475	+	0.338665i	0.762398	−	0.647109i	$-0.224022\pi$
$47$	6.37901	+	2.32177i	0.930475	+	0.338665i	0.168077	+	0.985774i	$0.446244\pi$
$48$	6.63762	+	1.98544i	0.958058	+	0.286573i
$49$	−4.77819	−	4.00937i	−0.682598	−	0.572768i
$50$	2.83782	−	4.19275i	0.401329	−	0.592944i
$51$	−2.98531	+	2.47970i	−0.418027	+	0.347227i
$52$	−1.58312	+	11.0085i	−0.219540	+	1.52661i
$53$		−	3.50342i		−	0.481232i	−0.970620	−	0.240616i	$-0.922651\pi$
$53$		−	3.50342i		−	0.481232i	0.970620	−	0.240616i	$-0.0773494\pi$
$54$	−1.89565	+	7.09975i	−0.257965	+	0.966154i
$55$	1.22281			0.164884
$56$	2.18630	−	1.14903i	0.292156	−	0.153546i
$57$	−4.73924	+	0.811297i	−0.627728	+	0.107459i
$58$	−1.97109	−	1.33411i	−0.258816	−	0.175178i
$59$	−7.30225	+	8.70248i	−0.950672	+	1.13297i	0.0403389	+	0.999186i	$0.487156\pi$
$59$	−7.30225	+	8.70248i	−0.950672	+	1.13297i	−0.991011	+	0.133781i	$0.957288\pi$
$60$	2.15875	+	3.51854i	0.278694	+	0.454242i
$61$	1.86712	−	5.12986i	0.239060	−	0.656811i	−0.760909	−	0.648859i	$-0.775246\pi$
$61$	1.86712	−	5.12986i	0.239060	−	0.656811i	0.999968	−	0.00795221i	$-0.00253129\pi$
$62$	1.64900	+	0.737347i	0.209423	+	0.0936431i
$63$	1.28713	+	2.28166i	0.162164	+	0.287462i
$64$	−0.759738	−	7.96384i	−0.0949673	−	0.995480i
$65$	−5.07631	+	4.25953i	−0.629638	+	0.528329i
$66$	1.03746	−	2.28944i	0.127703	−	0.281811i
$67$	−7.80090	−	1.37551i	−0.953031	−	0.168045i	−0.324549	−	0.945869i	$-0.605213\pi$
$67$	−7.80090	−	1.37551i	−0.953031	−	0.168045i	−0.628482	+	0.777824i	$0.716324\pi$
$68$	3.94992	+	2.11647i	0.478999	+	0.256659i
$69$	−7.30899	−	0.0364666i	−0.879899	−	0.00439007i
$70$	1.42732	+	0.358299i	0.170597	+	0.0428249i
$71$	4.40148	−	7.62359i	0.522360	−	0.904754i	−0.477302	−	0.878740i	$-0.658385\pi$
$71$	4.40148	−	7.62359i	0.522360	−	0.904754i	0.999662	−	0.0260144i	$-0.00828159\pi$
$72$	8.41924	−	1.05658i	0.992217	−	0.124519i
$73$	−5.37419	−	9.30837i	−0.629001	−	1.08946i	−0.987752	−	0.156029i	$-0.950131\pi$
$73$	−5.37419	−	9.30837i	−0.629001	−	1.08946i	0.358751	−	0.933433i	$-0.383203\pi$
$74$	−3.95405	−	13.8732i	−0.459649	−	1.61273i
$75$	1.10719	−	6.10104i	0.127847	−	0.704487i
$76$	2.92702	+	4.71777i	0.335753	+	0.541166i
$77$	−0.306470	−	0.842019i	−0.0349255	−	0.0959570i
$78$	3.66818	+	13.1182i	0.415340	+	1.48534i
$79$	1.26481	+	7.17310i	0.142302	+	0.807037i	0.969494	+	0.245116i	$0.0788261\pi$
$79$	1.26481	+	7.17310i	0.142302	+	0.807037i	−0.827191	+	0.561920i	$0.810063\pi$
$80$	2.82638	−	3.83823i	0.315999	−	0.429128i
$81$	1.38565	+	8.89269i	0.153961	+	0.988077i
$82$	12.7702	−	9.24687i	1.41023	−	1.02115i
$83$	6.42315	−	1.13258i	0.705033	−	0.124316i	0.190374	−	0.981712i	$-0.439030\pi$
$83$	6.42315	−	1.13258i	0.705033	−	0.124316i	0.514659	+	0.857395i	$0.327919\pi$
$84$	1.88180	−	2.36835i	0.205322	−	0.258408i
$85$	0.913202	+	2.50900i	0.0990507	+	0.272139i
$86$	−0.0883878	+	1.23557i	−0.00953110	+	0.133234i
$87$	−2.86821	−	0.520511i	−0.307505	−	0.0558047i
$88$	−2.90010	−	0.115227i	−0.309151	−	0.0122832i
$89$	−7.39005	−	12.7999i	−0.783343	−	1.35679i	−0.929984	−	0.367600i	$-0.880179\pi$
$89$	−7.39005	−	12.7999i	−0.783343	−	1.35679i	0.146641	−	0.989190i	$-0.453154\pi$
$90$	4.15838	+	2.87548i	0.438332	+	0.303102i
$91$	4.20535	+	2.42796i	0.440840	+	0.254519i
$92$	3.13653	+	7.83534i	0.327005	+	0.816890i
$93$	2.21228	+	0.0110377i	0.229403	+	0.00114455i
$94$	−4.19465	−	8.63538i	−0.432645	−	0.890672i
$95$	−0.574433	+	3.25777i	−0.0589356	+	0.334240i
$96$	−4.78829	−	8.54823i	−0.488702	−	0.872450i
$97$	11.6240	−	9.75374i	1.18024	−	0.990342i	0.180266	−	0.983618i	$-0.442304\pi$
$97$	11.6240	−	9.75374i	1.18024	−	0.990342i	0.999977	−	0.00672396i	$-0.00214032\pi$
$98$	0.908008	+	8.77427i	0.0917226	+	0.886335i
$99$	0.0307177	−	3.07829i	0.00308724	−	0.309380i
$100$	−7.00821	+	1.46619i	−0.700821	+	0.146619i
$101$	−3.74650	+	10.2934i	−0.372791	+	1.02424i	0.601486	+	0.798883i	$0.294575\pi$
$101$	−3.74650	+	10.2934i	−0.372791	+	1.02424i	−0.974277	+	0.225352i	$0.927647\pi$
$102$	5.47234	+	0.418924i	0.541842	+	0.0414796i
$103$	−13.6774	−	11.4767i	−1.34767	−	1.13083i	−0.979583	−	0.201041i	$-0.935568\pi$
$103$	−13.6774	−	11.4767i	−1.34767	−	1.13083i	−0.368089	−	0.929790i	$-0.619988\pi$
$104$	12.4407	−	9.62383i	1.21991	−	0.943694i
$105$	1.77649	−	0.304113i	0.173368	−	0.0296784i
$106$	−3.44745	+	3.55851i	−0.334846	+	0.345633i
$107$			14.7884i			1.42965i	0.699306	+	0.714823i	$0.253493\pi$
$107$			14.7884i			1.42965i	−0.699306	+	0.714823i	$0.746507\pi$
$108$	8.91178	−	5.34604i	0.857537	−	0.514423i
$109$		−	7.25408i		−	0.694815i	−0.937714	−	0.347407i	$-0.887062\pi$
$109$		−	7.25408i		−	0.694815i	0.937714	−	0.347407i	$-0.112938\pi$
$110$	−1.24204	−	1.20327i	−0.118424	−	0.114728i
$111$	−11.2890	−	13.5908i	−1.07150	−	1.28998i
$112$	−3.35135	−	0.984262i	−0.316673	−	0.0930041i
$113$	−2.35446	−	1.97563i	−0.221489	−	0.185851i	0.525291	−	0.850923i	$-0.323957\pi$
$113$	−2.35446	−	1.97563i	−0.221489	−	0.185851i	−0.746780	+	0.665071i	$0.768401\pi$
$114$	5.61211	+	3.83947i	0.525622	+	0.359599i
$115$	−1.71990	+	4.72538i	−0.160381	+	0.440644i
$116$	0.689285	+	3.29469i	0.0639985	+	0.305904i
$117$	10.5954	+	12.8861i	0.979543	+	1.19132i
$118$	15.9805	−	1.65375i	1.47113	−	0.152240i
$119$	1.49881	−	1.25765i	0.137396	−	0.115289i
$120$	1.26963	−	5.69814i	0.115901	−	0.520166i
$121$	1.72728	−	9.79590i	0.157026	−	0.890537i
$122$	−6.94438	+	3.37324i	−0.628715	+	0.305399i
$123$	9.73828	−	16.6745i	0.878071	−	1.50349i
$124$	−0.949360	−	2.37159i	−0.0852551	−	0.212975i
$125$	−8.85452	−	5.11216i	−0.791973	−	0.457246i
$126$	0.937833	−	3.58411i	0.0835488	−	0.319298i
$127$	8.60715	+	14.9080i	0.763761	+	1.32287i	0.940899	+	0.338686i	$0.109983\pi$
$127$	8.60715	+	14.9080i	0.763761	+	1.32287i	−0.177139	+	0.984186i	$0.556684\pi$
$128$	−7.06492	+	8.83668i	−0.624457	+	0.781059i
$129$	0.511766	+	1.42820i	0.0450585	+	0.125746i
$130$	9.34761	+	0.668694i	0.819840	+	0.0586483i
$131$	2.26106	+	6.21220i	0.197549	+	0.542763i	0.998427	−	0.0560653i	$-0.0178555\pi$
$131$	2.26106	+	6.21220i	0.197549	+	0.542763i	−0.800878	+	0.598828i	$0.795633\pi$
$132$	−3.30664	+	1.30456i	−0.287806	+	0.113548i
$133$	2.38725	−	0.420937i	0.207001	−	0.0364998i
$134$	6.57004	+	9.07340i	0.567565	+	0.783823i
$135$	6.08115	+	1.16638i	0.523382	+	0.100386i
$136$	−1.92938	−	6.03657i	−0.165443	−	0.517631i
$137$	1.08490	+	6.15277i	0.0926892	+	0.525667i	0.995431	+	0.0954839i	$0.0304398\pi$
$137$	1.08490	+	6.15277i	0.0926892	+	0.525667i	−0.902742	+	0.430183i	$0.858449\pi$
$138$	7.38805	+	7.22926i	0.628912	+	0.615395i
$139$	−2.29890	−	6.31617i	−0.194990	−	0.535731i	0.803210	−	0.595695i	$-0.203123\pi$
$139$	−2.29890	−	6.31617i	−0.194990	−	0.535731i	−0.998201	+	0.0599646i	$0.980901\pi$
$140$	−1.09719	−	1.76844i	−0.0927292	−	0.149461i
$141$	−8.96923	−	7.60265i	−0.755345	−	0.640259i
$142$	−11.9725	+	3.41232i	−1.00471	+	0.286355i
$143$	−2.85315	−	4.94181i	−0.238593	−	0.413255i
$144$	−9.59134	−	7.21153i	−0.799278	−	0.600961i
$145$	−1.00278	+	1.73687i	−0.0832763	+	0.144239i
$146$	−3.70095	+	14.7431i	−0.306293	+	1.22015i
$147$	5.35507	+	9.38305i	0.441679	+	0.773901i
$148$	−9.63535	+	17.9823i	−0.792021	+	1.47813i
$149$	11.3946	+	2.00917i	0.933480	+	0.164598i	0.619647	−	0.784881i	$-0.287276\pi$
$149$	11.3946	+	2.00917i	0.933480	+	0.164598i	0.313833	+	0.949478i	$0.398387\pi$
$150$	−7.12817	+	5.10748i	−0.582012	+	0.417024i
$151$	−2.94313	+	2.46958i	−0.239509	+	0.200972i	−0.754639	−	0.656140i	$-0.772188\pi$
$151$	−2.94313	+	2.46958i	−0.239509	+	0.200972i	0.515130	+	0.857112i	$0.327744\pi$
$152$	1.66935	−	7.67222i	0.135402	−	0.622299i
$153$	6.33908	−	2.23586i	0.512484	−	0.180759i
$154$	−0.517277	+	1.15683i	−0.0416834	+	0.0932203i
$155$	0.520577	−	1.43027i	0.0418138	−	0.114882i
$156$	9.18271	−	16.9340i	0.735205	−	1.35581i
$157$	−1.15130	+	1.37207i	−0.0918840	+	0.109503i	−0.810027	−	0.586392i	$-0.800548\pi$
$157$	−1.15130	+	1.37207i	−0.0918840	+	0.109503i	0.718143	+	0.695895i	$0.244992\pi$
$158$	5.77379	−	8.53050i	0.459338	−	0.678650i
$159$	−2.10384	+	5.69172i	−0.166845	+	0.451383i
$160$	−6.64774	+	1.11737i	−0.525550	+	0.0883355i
$161$	3.68492			0.290413
$162$	7.34318	−	10.3960i	0.576934	−	0.816791i
$163$		−	9.49865i		−	0.743992i	−0.928234	−	0.371996i	$-0.878674\pi$
$163$		−	9.49865i		−	0.743992i	0.928234	−	0.371996i	$-0.121326\pi$
$164$	−22.0701	−	3.17388i	−1.72339	−	0.247838i
$165$	−1.98660	−	0.734309i	−0.154657	−	0.0571659i
$166$	−7.63864	−	5.17015i	−0.592874	−	0.401281i
$167$	−4.15650	−	3.48772i	−0.321640	−	0.269888i	0.467643	−	0.883917i	$-0.345103\pi$
$167$	−4.15650	−	3.48772i	−0.321640	−	0.269888i	−0.789283	+	0.614029i	$0.789548\pi$
$168$	−4.24190	+	0.553853i	−0.327270	+	0.0427307i
$169$	16.8427	+	6.13024i	1.29559	+	0.471557i
$170$	1.54135	−	3.44707i	0.118216	−	0.264378i
$171$	8.18666	+	1.52791i	0.626050	+	0.116842i
$172$	1.30560	−	1.16802i	0.0995513	−	0.0890607i
$173$	−9.81971	−	11.7027i	−0.746579	−	0.889738i	0.250341	−	0.968158i	$-0.419457\pi$
$173$	−9.81971	−	11.7027i	−0.746579	−	0.889738i	−0.996920	+	0.0784193i	$0.975013\pi$
$174$	2.40112	+	3.35108i	0.182028	+	0.254045i
$175$	−0.542845	+	3.07862i	−0.0410352	+	0.232722i
$176$	2.83232	+	2.97080i	0.213494	+	0.223933i
$177$	17.0893	−	9.75315i	1.28451	−	0.733092i
$178$	−5.08918	+	20.2732i	−0.381450	+	1.51954i
$179$	8.40518	+	4.85273i	0.628232	+	0.362710i	0.780067	−	0.625696i	$-0.215185\pi$
$179$	8.40518	+	4.85273i	0.628232	+	0.362710i	−0.151835	+	0.988406i	$0.548518\pi$
$180$	−1.39423	−	7.01265i	−0.103920	−	0.522692i
$181$	−21.1351	+	12.2024i	−1.57096	+	0.906995i	−0.574911	+	0.818216i	$0.694963\pi$
$181$	−21.1351	+	12.2024i	−1.57096	+	0.906995i	−0.996051	+	0.0887791i	$0.971703\pi$
$182$	−1.88231	−	6.60430i	−0.139526	−	0.489543i
$183$	−6.11388	+	7.21285i	−0.451951	+	0.533189i
$184$	4.52430	−	11.0450i	0.333536	−	0.814246i
$185$	−11.4224	+	4.15741i	−0.839790	+	0.305659i
$186$	−2.23621	−	2.18814i	−0.163967	−	0.160443i
$187$	−2.26427	+	0.399252i	−0.165580	+	0.0291962i
$188$	−4.23680	+	12.8988i	−0.309001	+	0.940742i
$189$	−0.720944	−	4.47977i	−0.0524410	−	0.325855i
$190$	3.78919	−	2.74375i	0.274897	−	0.199052i
$191$	1.75520	+	9.95423i	0.127002	+	0.720263i	0.980099	+	0.198510i	$0.0636104\pi$
$191$	1.75520	+	9.95423i	0.127002	+	0.720263i	−0.853097	+	0.521752i	$0.825279\pi$
$192$	−3.54808	+	13.3944i	−0.256060	+	0.966661i
$193$	−14.9119	+	5.42750i	−1.07338	+	0.390680i	−0.817441	−	0.576012i	$-0.804608\pi$
$193$	−14.9119	+	5.42750i	−1.07338	+	0.390680i	−0.255943	+	0.966692i	$0.582386\pi$
$194$	−21.4047	−	1.53122i	−1.53677	−	0.109935i
$195$	10.8050	−	3.87174i	0.773759	−	0.277261i
$196$	7.71180	−	9.80575i	0.550843	−	0.700411i
$197$	−9.56041	+	5.51970i	−0.681151	+	0.393263i	−0.800288	−	0.599615i	$-0.795320\pi$
$197$	−9.56041	+	5.51970i	−0.681151	+	0.393263i	0.119138	+	0.992878i	$0.461987\pi$
$198$	−3.06031	+	3.09647i	−0.217487	+	0.220057i
$199$	−11.9739	+	20.7394i	−0.848806	+	1.47018i	0.0334679	+	0.999440i	$0.489345\pi$
$199$	−11.9739	+	20.7394i	−0.848806	+	1.47018i	−0.882274	+	0.470736i	$0.843988\pi$
$200$	8.56119	+	5.40699i	0.605367	+	0.382332i
$201$	11.8475	+	6.91919i	0.835657	+	0.488042i
$202$	13.9344	−	6.76866i	0.980421	−	0.476241i
$203$	1.44732	+	0.255201i	0.101582	+	0.0179116i
$204$	−5.14616	−	5.81042i	−0.360304	−	0.406811i
$205$	−8.53958	−	10.1771i	−0.596430	−	0.710798i
$206$	2.59914	+	25.1160i	0.181091	+	1.74992i
$207$	11.8524	+	4.44836i	0.823801	+	0.309183i
$208$	−22.1064	−	2.46675i	−1.53280	−	0.171039i
$209$	−2.67680	−	0.974277i	−0.185158	−	0.0673921i
$210$	−2.10368	−	1.43922i	−0.145168	−	0.0993153i
$211$	−1.83510	+	2.18698i	−0.126333	+	0.150558i	−0.825503	−	0.564397i	$-0.809109\pi$
$211$	−1.83510	+	2.18698i	−0.126333	+	0.150558i	0.699170	+	0.714955i	$0.253553\pi$
$212$	7.00332	−	0.222104i	0.480990	−	0.0152542i
$213$	−11.7288	+	9.74231i	−0.803642	+	0.667532i
$214$	14.5521	−	15.0209i	0.994761	−	1.02681i
$215$	1.04378			0.0711850
$216$	−14.3126	−	3.33929i	−0.973846	−	0.227210i
$217$	−1.11535			−0.0757148
$218$	−7.13818	+	7.36815i	−0.483459	+	0.499034i
$219$	3.14125	+	18.3498i	0.212266	+	1.23997i
$220$	0.0775218	+	2.44439i	0.00522652	+	0.164801i
$221$	8.00901	−	9.54477i	0.538744	−	0.642051i
$222$	−1.90718	+	24.9132i	−0.128001	+	1.67206i
$223$	8.81118	+	3.20701i	0.590041	+	0.214757i	0.619747	−	0.784801i	$-0.287235\pi$
$223$	8.81118	+	3.20701i	0.590041	+	0.214757i	−0.0297067	+	0.999559i	$0.509457\pi$
$224$	2.43552	+	4.29755i	0.162730	+	0.287142i
$225$	−5.46250	+	9.24699i	−0.364166	+	0.616466i
$226$	0.447423	+	4.32354i	0.0297621	+	0.287598i
$227$	−14.0360	−	16.7275i	−0.931602	−	1.11024i	−0.993689	−	0.112169i	$-0.964220\pi$
$227$	−14.0360	−	16.7275i	−0.931602	−	1.11024i	0.0620871	−	0.998071i	$-0.480224\pi$
$228$	−1.92223	−	9.42229i	−0.127303	−	0.624006i
$229$	12.2439	+	2.15892i	0.809097	+	0.142666i	0.562869	−	0.826546i	$-0.309698\pi$
$229$	12.2439	+	2.15892i	0.809097	+	0.142666i	0.246228	+	0.969212i	$0.420809\pi$
$230$	6.39683	−	3.10727i	0.421795	−	0.204887i
$231$	−0.00774336	+	1.55200i	−0.000509475	+	0.102114i
$232$	2.54193	−	4.02477i	0.166886	−	0.264239i
$233$	9.39224	−	16.2678i	0.615306	−	1.06574i	−0.375025	−	0.927015i	$-0.622366\pi$
$233$	9.39224	−	16.2678i	0.615306	−	1.06574i	0.990331	−	0.138727i	$-0.0443009\pi$
$234$	1.91818	−	23.5148i	0.125395	−	1.53721i
$235$	−7.00563	+	4.04470i	−0.456997	+	0.263847i
$236$	−17.8592	−	14.0455i	−1.16253	−	0.914281i
$237$	2.25268	−	12.4131i	0.146327	−	0.806317i
$238$	−2.75994	−	0.197436i	−0.178900	−	0.0127979i
$239$	−10.0255	+	3.64897i	−0.648494	+	0.236033i	−0.645261	−	0.763962i	$-0.723251\pi$
$239$	−10.0255	+	3.64897i	−0.648494	+	0.236033i	−0.00323308	+	0.999995i	$0.501029\pi$
$240$	−6.89669	+	4.53840i	−0.445180	+	0.292953i
$241$	−1.87692	−	10.6445i	−0.120903	−	0.685674i	−0.983657	−	0.180051i	$-0.942374\pi$
$241$	−1.87692	−	10.6445i	−0.120903	−	0.685674i	0.862755	−	0.505623i	$-0.168737\pi$
$242$	−11.3938	+	8.25026i	−0.732424	+	0.530347i
$243$	3.08899	−	15.2793i	0.198159	−	0.980170i
$244$	10.3729	+	3.40714i	0.664059	+	0.218120i
$245$	7.31997	−	1.29071i	0.467656	−	0.0824603i
$246$	−26.2995	+	7.35403i	−1.67680	+	0.468876i
$247$	14.5061	−	5.27980i	0.923003	−	0.335945i
$248$	−1.36941	+	3.34308i	−0.0869577	+	0.212286i
$249$	−11.1153	−	2.01716i	−0.704404	−	0.127832i
$250$	3.96328	+	13.9056i	0.250660	+	0.879468i
$251$	16.5829	−	9.57417i	1.04671	−	0.604316i	0.124981	−	0.992159i	$-0.460113\pi$
$251$	16.5829	−	9.57417i	1.04671	−	0.604316i	0.921725	+	0.387843i	$0.126780\pi$
$252$	−4.47943	+	2.71762i	−0.282178	+	0.171194i
$253$	−3.75010	−	2.16512i	−0.235767	−	0.136120i
$254$	5.92734	−	23.6121i	0.371914	−	1.48155i
$255$	0.0230732	−	4.62456i	0.00144490	−	0.289601i
$256$	15.8715	−	2.02359i	0.991970	−	0.126475i
$257$	−0.770015	+	4.36697i	−0.0480322	+	0.272404i	−0.999360	−	0.0357772i	$-0.988609\pi$
$257$	−0.770015	+	4.36697i	−0.0480322	+	0.272404i	0.951328	+	0.308182i	$0.0997204\pi$
$258$	0.885565	−	1.95425i	0.0551329	−	0.121666i
$259$	5.72553	+	6.82342i	0.355767	+	0.423986i
$260$	−8.83659	−	9.87747i	−0.548022	−	0.612575i
$261$	4.34718	+	2.56802i	0.269084	+	0.158956i
$262$	3.81634	−	8.53483i	0.235774	−	0.527283i
$263$	28.6260	+	10.4190i	1.76516	+	0.642464i	0.999999	−	0.00138103i	$-0.000439595\pi$
$263$	28.6260	+	10.4190i	1.76516	+	0.642464i	0.765156	+	0.643845i	$0.222662\pi$
$264$	4.64236	+	1.92874i	0.285718	+	0.118705i
$265$	3.19812	+	2.68354i	0.196459	+	0.164849i
$266$	−2.83900	−	1.92155i	−0.174070	−	0.117818i
$267$	4.31953	+	25.2328i	0.264351	+	1.54422i
$268$	2.25509	−	15.6812i	0.137751	−	0.957879i
$269$		−	25.4966i		−	1.55455i	−0.629158	−	0.777277i	$-0.716600\pi$
$269$		−	25.4966i		−	1.55455i	0.629158	−	0.777277i	$-0.283400\pi$
$270$	−5.02904	−	7.16871i	−0.306057	−	0.436274i
$271$	3.87967			0.235673			0.117837	−	0.993033i	$-0.462404\pi$
$271$	3.87967			0.235673			0.117837	+	0.993033i	$0.462404\pi$
$272$	−3.98040	+	8.03005i	−0.241347	+	0.486894i
$273$	−5.37408	−	6.46986i	−0.325254	−	0.391574i
$274$	4.95251	−	7.31709i	0.299192	−	0.442042i
$275$	2.36133	−	2.81413i	0.142394	−	0.169698i
$276$	−0.390468	−	14.6130i	−0.0235034	−	0.879596i
$277$	4.85782	−	13.3467i	0.291878	−	0.801928i	−0.703914	−	0.710285i	$-0.748566\pi$
$277$	4.85782	−	13.3467i	0.291878	−	0.801928i	0.995792	−	0.0916426i	$-0.0292117\pi$
$278$	−3.88021	+	8.67767i	−0.232720	+	0.520452i
$279$	−3.58748	−	1.34643i	−0.214777	−	0.0806084i
$280$	−0.625750	+	2.87591i	−0.0373957	+	0.171869i
$281$	−4.95135	+	4.15467i	−0.295373	+	0.247847i	−0.778415	−	0.627750i	$-0.783976\pi$
$281$	−4.95135	+	4.15467i	−0.295373	+	0.247847i	0.483043	+	0.875597i	$0.339532\pi$
$282$	1.62908	+	16.5481i	0.0970106	+	0.985427i
$283$	−25.8655	−	4.56078i	−1.53754	−	0.271110i	−0.660242	−	0.751053i	$-0.729546\pi$
$283$	−25.8655	−	4.56078i	−1.53754	−	0.271110i	−0.877300	+	0.479943i	$0.840657\pi$
$284$	15.5186	+	8.31523i	0.920857	+	0.493418i
$285$	2.88956	−	4.94769i	0.171163	−	0.293076i
$286$	−1.96483	+	7.82709i	−0.116183	+	0.462826i
$287$	−4.86761	+	8.43095i	−0.287326	+	0.497663i
$288$	2.64585	+	16.7630i	0.155908	+	0.987772i
$289$	5.98983	+	10.3747i	0.352343	+	0.610276i
$290$	2.72766	−	0.777420i	0.160174	−	0.0456517i
$291$	−24.7419	+	8.86576i	−1.45039	+	0.519720i
$292$	18.2667	−	11.3331i	1.06898	−	0.663219i
$293$	−3.00287	−	8.25032i	−0.175430	−	0.481989i	0.820549	−	0.571576i	$-0.193668\pi$
$293$	−3.00287	−	8.25032i	−0.175430	−	0.481989i	−0.995979	+	0.0895867i	$0.971445\pi$
$294$	3.79386	−	14.8001i	0.221263	−	0.863160i
$295$	−2.35076	−	13.3318i	−0.136867	−	0.776209i
$296$	27.4818	−	8.78364i	1.59735	−	0.510538i
$297$	−1.89845	+	4.98261i	−0.110159	+	0.289120i
$298$	−9.59669	−	13.2533i	−0.555921	−	0.767743i
$299$	23.1099	−	4.07491i	1.33648	−	0.235658i
$300$	12.2661	+	1.82649i	0.708186	+	0.105452i
$301$	−0.261599	−	0.718739i	−0.0150783	−	0.0414274i
$302$	5.41954	+	0.387694i	0.311859	+	0.0223093i
$303$	12.2680	−	14.4731i	0.704775	−	0.831458i
$304$	−9.24524	+	6.15019i	−0.530251	+	0.352738i
$305$	3.25266	+	5.63377i	0.186247	+	0.322589i
$306$	−8.63890	−	3.96678i	−0.493853	−	0.226766i
$307$	18.3671	+	10.6042i	1.04826	+	0.605215i	0.922163	−	0.386802i	$-0.126420\pi$
$307$	18.3671	+	10.6042i	1.04826	+	0.605215i	0.126101	+	0.992017i	$0.459754\pi$
$308$	1.66376	−	0.666013i	0.0948017	−	0.0379496i
$309$	15.3287	+	26.8586i	0.872018	+	1.52793i
$310$	−1.93619	+	0.940506i	−0.109968	+	0.0534171i
$311$	1.64381	−	9.32250i	0.0932118	−	0.528630i	−0.902069	−	0.431592i	$-0.857952\pi$
$311$	1.64381	−	9.32250i	0.0932118	−	0.528630i	0.995281	−	0.0970383i	$-0.0309369\pi$
$312$	−25.9906	+	8.16432i	−1.47143	+	0.462213i
$313$	2.57412	−	2.15994i	0.145498	−	0.122087i	−0.567134	−	0.823626i	$-0.691948\pi$
$313$	2.57412	−	2.15994i	0.145498	−	0.122087i	0.712631	+	0.701539i	$0.247503\pi$
$314$	2.51956	−	0.260737i	0.142187	−	0.0147142i
$315$	−3.06875	−	0.572733i	−0.172904	−	0.0322699i
$316$	−14.2588	+	2.98310i	−0.802120	+	0.167812i
$317$	−2.51702	+	6.91547i	−0.141370	+	0.388411i	−0.990091	−	0.140431i	$-0.955151\pi$
$317$	−2.51702	+	6.91547i	−0.141370	+	0.388411i	0.848720	+	0.528842i	$0.177374\pi$
$318$	7.73771	−	3.71100i	0.433909	−	0.208103i
$319$	−1.32297	−	1.11011i	−0.0740722	−	0.0621540i
$320$	7.85179	+	5.40660i	0.438929	+	0.302238i
$321$	8.88055	−	24.0255i	0.495664	−	1.34097i
$322$	−3.74287	−	3.62605i	−0.208582	−	0.202072i
$323$		−	6.21995i		−	0.346087i
$324$	−17.6886	+	3.33367i	−0.982700	+	0.185204i
$325$			19.9079i			1.10429i
$326$	−9.34689	+	9.64802i	−0.517677	+	0.534355i
$327$	−4.35614	+	11.7851i	−0.240895	+	0.651719i
$328$	19.2940	+	24.9413i	1.06533	+	1.37715i
$329$	4.54096	+	3.81032i	0.250351	+	0.210070i
$330$	1.29526	+	2.70072i	0.0713019	+	0.148670i
$331$	−5.29806	+	14.5563i	−0.291208	+	0.800086i	0.704683	+	0.709522i	$0.251089\pi$
$331$	−5.29806	+	14.5563i	−0.291208	+	0.800086i	−0.995891	+	0.0905641i	$0.971133\pi$
$332$	2.67122	+	12.7681i	0.146602	+	0.700738i
$333$	10.1789	+	28.8590i	0.557799	+	1.58147i
$334$	0.789868	+	7.63266i	0.0432196	+	0.417640i
$335$	7.23096	−	6.06750i	0.395070	−	0.331503i
$336$	4.85361	+	3.61157i	0.264786	+	0.197027i
$337$	−0.204510	+	1.15983i	−0.0111404	+	0.0631802i	−0.989871	−	0.141969i	$-0.954657\pi$
$337$	−0.204510	+	1.15983i	−0.0111404	+	0.0631802i	0.978731	+	0.205149i	$0.0657679\pi$
$338$	−11.0753	−	22.8002i	−0.602414	−	1.24017i
$339$	2.63872	+	4.62352i	0.143316	+	0.251115i
$340$	−4.95759	+	1.98455i	−0.268863	+	0.107627i
$341$	1.13508	+	0.655337i	0.0614679	+	0.0354885i
$342$	−6.81190	−	9.60780i	−0.368345	−	0.519530i
$343$	−5.77965	−	10.0106i	−0.312072	−	0.540524i
$344$	−2.47549	−	0.0983563i	−0.133470	−	0.00530302i
$345$	5.63182	−	6.64413i	0.303207	−	0.357708i
$346$	−1.54158	+	21.5495i	−0.0828756	+	1.15851i
$347$	−5.38475	−	14.7945i	−0.289068	−	0.794209i	−0.996197	−	0.0871243i	$-0.972232\pi$
$347$	−5.38475	−	14.7945i	−0.289068	−	0.794209i	0.707129	−	0.707084i	$-0.249990\pi$
$348$	0.858665	−	5.76654i	0.0460293	−	0.309119i
$349$	−4.13570	+	0.729235i	−0.221379	+	0.0390351i	−0.283237	−	0.959050i	$-0.591408\pi$
$349$	−4.13570	+	0.729235i	−0.221379	+	0.0390351i	0.0618584	+	0.998085i	$0.480297\pi$
$350$	3.58082	−	2.59287i	0.191403	−	0.138595i
$351$	−9.47526	−	27.2976i	−0.505752	−	1.45704i
$352$	0.0464818	−	5.80459i	0.00247749	−	0.309385i
$353$	−3.37641	−	19.1485i	−0.179708	−	1.01917i	−0.932568	−	0.360994i	$-0.882438\pi$
$353$	−3.37641	−	19.1485i	−0.179708	−	1.01917i	0.752860	−	0.658180i	$-0.228674\pi$
$354$	−26.9554	−	6.90974i	−1.43266	−	0.367249i
$355$	3.58781	+	9.85743i	0.190421	+	0.523178i
$356$	25.1185	−	15.5841i	1.33128	−	0.825957i
$357$	−3.19022	+	1.14315i	−0.168845	+	0.0605021i
$358$	−3.76215	−	13.1999i	−0.198836	−	0.697638i
$359$	4.29826	+	7.44481i	0.226854	+	0.392922i	0.956874	−	0.290503i	$-0.0938227\pi$
$359$	4.29826	+	7.44481i	0.226854	+	0.392922i	−0.730020	+	0.683425i	$0.760489\pi$
$360$	−5.48445	+	8.49488i	−0.289056	+	0.447720i
$361$	−5.64689	+	9.78071i	−0.297205	+	0.514774i
$362$	33.4749	+	8.40320i	1.75940	+	0.441662i
$363$	−8.68871	+	14.8774i	−0.456039	+	0.780859i
$364$	−4.58687	+	8.56039i	−0.240417	+	0.448686i
$365$	12.6137	+	2.22414i	0.660232	+	0.116417i
$366$	13.3076	−	1.31007i	0.695601	−	0.0684786i
$367$	−3.84032	+	3.22241i	−0.200463	+	0.168208i	−0.737493	−	0.675355i	$-0.763991\pi$
$367$	−3.84032	+	3.22241i	−0.200463	+	0.168208i	0.537030	+	0.843563i	$0.319546\pi$
$368$	−15.4640	+	6.76663i	−0.806114	+	0.352735i
$369$	−25.8342	+	21.2418i	−1.34487	+	1.10580i
$370$	15.6930	+	7.01710i	0.815839	+	0.364802i
$371$	1.04633	−	2.87477i	0.0543229	−	0.149251i
$372$	0.118186	+	4.42303i	0.00612768	+	0.229324i
$373$	−9.63281	+	11.4799i	−0.498768	+	0.594409i	−0.955425	−	0.295234i	$-0.904602\pi$
$373$	−9.63281	+	11.4799i	−0.498768	+	0.594409i	0.456657	+	0.889643i	$0.349047\pi$
$374$	2.69275	+	1.82256i	0.139239	+	0.0942425i
$375$	11.3153	+	13.6225i	0.584321	+	0.703465i
$376$	16.9962	−	8.93254i	0.876510	−	0.460660i
$377$	9.35905			0.482016
$378$	−3.67591	+	5.25964i	−0.189069	+	0.270527i
$379$		−	34.5368i		−	1.77404i	−0.461733	−	0.887019i	$-0.652772\pi$
$379$		−	34.5368i		−	1.77404i	0.461733	−	0.887019i	$-0.347228\pi$
$380$	−6.54869	−	0.941758i	−0.335941	−	0.0483112i
$381$	−5.03094	−	29.3885i	−0.257743	−	1.50562i
$382$	8.01239	−	11.8379i	0.409950	−	0.605681i
$383$	−28.9473	−	24.2896i	−1.47914	−	1.24114i	−0.907100	−	0.420915i	$-0.861709\pi$
$383$	−28.9473	−	24.2896i	−1.47914	−	1.24114i	−0.572036	−	0.820228i	$-0.693846\pi$
$384$	16.7843	−	10.1137i	0.856521	−	0.516112i
$385$	1.00339	+	0.365205i	0.0511376	+	0.0186126i
$386$	20.4872	+	9.16084i	1.04277	+	0.466274i
$387$	0.0262203	−	2.62760i	0.00133285	−	0.133568i
$388$	20.2346	+	22.6181i	1.02726	+	1.14826i
$389$	5.52234	+	6.58127i	0.279994	+	0.333684i	0.887652	−	0.460515i	$-0.152335\pi$
$389$	5.52234	+	6.58127i	0.279994	+	0.333684i	−0.607658	+	0.794199i	$0.707891\pi$
$390$	−14.7848	−	6.69970i	−0.748655	−	0.339252i
$391$	1.64187	−	9.31151i	0.0830330	−	0.470903i
$392$	−17.4822	+	2.37136i	−0.882982	+	0.119772i
$393$	0.0571285	−	11.4503i	0.00288175	−	0.577589i
$394$	15.1423	+	3.80116i	0.762856	+	0.191500i
$395$	−7.51683	−	4.33984i	−0.378213	−	0.218361i
$396$	6.15544	−	0.133748i	0.309322	−	0.00672111i
$397$	−6.79437	+	3.92273i	−0.341000	+	0.196876i	−0.660714	−	0.750638i	$-0.729746\pi$
$397$	−6.79437	+	3.92273i	−0.341000	+	0.196876i	0.319714	+	0.947514i	$0.396413\pi$
$398$	32.5702	−	9.28293i	1.63260	−	0.465311i
$399$	−4.13115	−	0.749704i	−0.206816	−	0.0375322i
$400$	−3.37521	−	13.9164i	−0.168761	−	0.695821i
$401$	0.563801	−	0.205207i	0.0281549	−	0.0102475i	−0.327904	−	0.944711i	$-0.606342\pi$
$401$	0.563801	−	0.205207i	0.0281549	−	0.0102475i	0.356059	+	0.934463i	$0.384120\pi$
$402$	−5.22515	−	18.6862i	−0.260607	−	0.931983i
$403$	−6.99489	+	1.23339i	−0.348441	+	0.0614395i
$404$	−20.8140	−	6.83668i	−1.03554	−	0.340137i
$405$	−9.17914	−	5.54671i	−0.456115	−	0.275618i
$406$	−1.21895	−	1.68341i	−0.0604957	−	0.0835462i
$407$	−1.81762	−	10.3082i	−0.0900959	−	0.510959i
$408$	−0.490499	+	10.9657i	−0.0242833	+	0.542885i
$409$	−23.4551	+	8.53697i	−1.15978	+	0.422126i	−0.849019	−	0.528362i	$-0.822806\pi$
$409$	−23.4551	+	8.53697i	−1.15978	+	0.422126i	−0.310762	+	0.950488i	$0.600584\pi$
$410$	−1.34061	+	18.7403i	−0.0662080	+	0.925515i
$411$	1.93225	−	10.6474i	0.0953108	−	0.525198i
$412$	22.0747	−	28.0686i	1.08754	−	1.38284i
$413$	−8.59104	+	4.96004i	−0.422738	+	0.244068i
$414$	−7.66153	−	16.1814i	−0.376544	−	0.795272i
$415$	−3.88612	+	6.73095i	−0.190762	+	0.330409i
$416$	20.0267	+	24.2588i	0.981889	+	1.18938i
$417$	−0.0580846	+	11.6419i	−0.00284442	+	0.570106i
$418$	1.76019	+	3.62363i	0.0860935	+	0.177238i
$419$	−29.0531	−	5.12285i	−1.41934	−	0.250268i	−0.589273	−	0.807934i	$-0.700586\pi$
$419$	−29.0531	−	5.12285i	−1.41934	−	0.250268i	−0.830065	+	0.557666i	$0.811697\pi$
$420$	0.720543	+	3.53192i	0.0351589	+	0.172340i
$421$	1.77611	+	2.11669i	0.0865624	+	0.103161i	0.807587	−	0.589748i	$-0.200773\pi$
$421$	1.77611	+	2.11669i	0.0865624	+	0.103161i	−0.721025	+	0.692909i	$0.756329\pi$
$422$	4.01599	−	0.415596i	0.195495	−	0.0202309i
$423$	10.0061	+	17.7375i	0.486514	+	0.862428i
$424$	−7.33200	−	6.66583i	−0.356074	−	0.323721i
$425$	7.53757	+	2.74345i	0.365626	+	0.133077i
$426$	21.4999	+	1.64588i	1.04167	+	0.0797431i
$427$	3.06417	−	3.65174i	0.148286	−	0.176720i
$428$	−29.5619	+	0.937530i	−1.42893	+	0.0453172i
$429$	1.66769	+	9.74190i	0.0805167	+	0.470344i
$430$	−1.06019	−	1.02710i	−0.0511270	−	0.0495312i
$431$	−35.3625			−1.70335			−0.851675	−	0.524070i	$-0.824413\pi$
$431$	−35.3625			−1.70335			−0.851675	+	0.524070i	$0.824413\pi$
$432$	11.2517	+	17.4757i	0.541347	+	0.840799i
$433$	−25.3308			−1.21732			−0.608661	−	0.793430i	$-0.708293\pi$
$433$	−25.3308			−1.21732			−0.608661	+	0.793430i	$0.708293\pi$
$434$	1.13289	+	1.09753i	0.0543804	+	0.0526831i
$435$	2.67214	−	2.21957i	0.128119	−	0.106420i
$436$	14.5009	−	0.459883i	0.694466	−	0.0220244i
$437$	7.52992	−	8.97381i	0.360205	−	0.429275i
$438$	14.8660	−	21.7294i	0.710325	−	1.03827i
$439$	−24.5808	−	8.94668i	−1.17318	−	0.427002i	−0.319390	−	0.947623i	$-0.603478\pi$
$439$	−24.5808	−	8.94668i	−1.17318	−	0.427002i	−0.853787	+	0.520622i	$0.825700\pi$
$440$	2.32660	−	2.55911i	0.110916	−	0.122001i
$441$	−3.06534	−	18.4597i	−0.145968	−	0.879031i
$442$	−17.5272	+	1.81381i	−0.833685	+	0.0862742i
$443$	−15.4087	−	18.3634i	−0.732091	−	0.872472i	0.263655	−	0.964617i	$-0.415072\pi$
$443$	−15.4087	−	18.3634i	−0.732091	−	0.872472i	−0.995746	+	0.0921455i	$0.970628\pi$
$444$	26.4523	−	23.4282i	1.25537	−	1.11185i
$445$	17.3451	+	3.05841i	0.822238	+	0.144983i
$446$	−5.79397	−	11.9279i	−0.274353	−	0.564800i
$447$	−17.3053	−	10.1067i	−0.818514	−	0.478030i
$448$	1.75507	−	6.76174i	0.0829193	−	0.319462i
$449$	−8.35182	+	14.4658i	−0.394147	+	0.682682i	−0.992992	−	0.118183i	$-0.962293\pi$
$449$	−8.35182	+	14.4658i	−0.394147	+	0.682682i	0.598845	+	0.800865i	$0.295626\pi$
$450$	14.6476	−	4.01718i	0.690497	−	0.189372i
$451$	9.90743	−	5.72006i	0.466522	−	0.269347i
$452$	3.80000	−	4.83180i	0.178737	−	0.227269i
$453$	6.26447	−	2.24475i	0.294331	−	0.105468i
$454$	−2.20348	+	30.8022i	−0.103414	+	1.44562i
$455$	−5.43758	+	1.97912i	−0.254918	+	0.0927825i
$456$	−7.31930	+	11.4620i	−0.342757	+	0.536756i
$457$	1.32001	+	7.48613i	0.0617473	+	0.350186i	0.999991	+	0.00421154i	$0.00134058\pi$
$457$	1.32001	+	7.48613i	0.0617473	+	0.350186i	−0.938244	+	0.345975i	$0.887548\pi$
$458$	−10.3120	−	14.2411i	−0.481847	−	0.665444i
$459$	−11.6412	−	0.174256i	−0.543367	−	0.00813357i
$460$	−9.55505	−	3.13850i	−0.445507	−	0.146333i
$461$	29.9883	−	5.28774i	1.39669	−	0.246275i	0.575909	−	0.817513i	$-0.304648\pi$
$461$	29.9883	−	5.28774i	1.39669	−	0.246275i	0.820784	+	0.571239i	$0.193537\pi$
$462$	1.53507	−	1.56878i	0.0714178	−	0.0729865i
$463$	36.5232	−	13.2933i	1.69738	−	0.617794i	0.701854	−	0.712321i	$-0.252356\pi$
$463$	36.5232	−	13.2933i	1.69738	−	0.617794i	0.995522	+	0.0945267i	$0.0301338\pi$
$464$	−6.54237	+	1.58675i	−0.303722	+	0.0736630i
$465$	−1.70463	+	2.01104i	−0.0790505	+	0.0932597i
$466$	−25.5479	+	7.28147i	−1.18348	+	0.337308i
$467$	−22.9238	+	13.2351i	−1.06079	+	0.612445i	−0.925650	−	0.378382i	$-0.876481\pi$
$467$	−22.9238	+	13.2351i	−1.06079	+	0.612445i	−0.135136	+	0.990827i	$0.543147\pi$
$468$	−25.0875	+	21.9970i	−1.15967	+	1.01681i
$469$	−5.99032	−	3.45851i	−0.276607	−	0.159699i
$470$	11.0959	+	2.78540i	0.511815	+	0.128481i
$471$	2.69437	−	1.53772i	0.124150	−	0.0708546i
$472$	4.31895	+	31.8402i	0.198796	+	1.46556i
$473$	−0.156077	+	0.885158i	−0.00717644	+	0.0406996i
$474$	−14.5029	+	10.3916i	−0.666139	+	0.477302i
$475$	6.38804	+	7.61296i	0.293103	+	0.349307i
$476$	2.60906	+	2.91638i	0.119586	+	0.133672i
$477$	6.83586	−	7.98351i	0.312993	−	0.365540i
$478$	13.7738	+	6.15894i	0.629999	+	0.281704i
$479$	−14.1999	−	5.16834i	−0.648810	−	0.236148i	−0.00341243	−	0.999994i	$-0.501086\pi$
$479$	−14.1999	−	5.16834i	−0.648810	−	0.236148i	−0.645398	+	0.763847i	$0.723308\pi$
$480$	11.4710	+	2.17674i	0.523579	+	0.0993540i
$481$	43.4531	+	36.4615i	1.98129	+	1.66250i
$482$	−8.56802	+	12.6588i	−0.390263	+	0.576594i
$483$	−5.98660	−	2.21283i	−0.272400	−	0.100687i
$484$	19.6915	+	2.83180i	0.895066	+	0.128718i
$485$			18.0822i			0.821072i
$486$	−18.1728	+	12.4800i	−0.824334	+	0.566103i
$487$	7.24014			0.328082			0.164041	−	0.986454i	$-0.447547\pi$
$487$	7.24014			0.328082			0.164041	+	0.986454i	$0.447547\pi$
$488$	−7.18335	−	13.6679i	−0.325175	−	0.618718i
$489$	−5.70403	+	15.4317i	−0.257945	+	0.697845i
$490$	−8.70517	−	5.89202i	−0.393259	−	0.266174i
$491$	−7.12522	+	8.49150i	−0.321556	+	0.383216i	−0.902473	−	0.430747i	$-0.858250\pi$
$491$	−7.12522	+	8.49150i	−0.321556	+	0.383216i	0.580916	+	0.813963i	$0.302694\pi$
$492$	33.9496	+	18.4097i	1.53057	+	0.829972i
$493$	1.28975	−	3.54355i	0.0580873	−	0.159594i
$494$	−19.9297	−	8.91154i	−0.896679	−	0.400949i
$495$	2.78651	+	2.38594i	0.125244	+	0.107240i
$496$	4.68061	−	2.04812i	0.210166	−	0.0919632i
$497$	5.88856	−	4.94109i	0.264138	−	0.221638i
$498$	9.30517	+	12.9866i	0.416974	+	0.581943i
$499$	−10.5094	−	1.85310i	−0.470467	−	0.0829561i	−0.0666120	−	0.997779i	$-0.521219\pi$
$499$	−10.5094	−	1.85310i	−0.470467	−	0.0829561i	−0.403855	+	0.914823i	$0.632330\pi$
$500$	9.65784	−	18.0242i	0.431912	−	0.806069i
$501$	4.65832	+	8.16223i	0.208119	+	0.364662i
$502$	−26.2649	−	6.59328i	−1.17226	−	0.294272i
$503$	−5.44812	+	9.43641i	−0.242920	+	0.420749i	−0.961545	−	0.274649i	$-0.911438\pi$
$503$	−5.44812	+	9.43641i	−0.242920	+	0.420749i	0.718625	+	0.695398i	$0.244772\pi$
$504$	7.22408	+	1.64750i	0.321786	+	0.0733856i
$505$	−6.52670	−	11.3046i	−0.290434	−	0.503047i
$506$	1.67854	+	5.88936i	0.0746204	+	0.261814i
$507$	−23.6817	−	20.0735i	−1.05174	−	0.891495i
$508$	−29.2554	+	18.1508i	−1.29800	+	0.805310i
$509$	9.69169	+	26.6277i	0.429577	+	1.18025i	0.946070	+	0.323961i	$0.105015\pi$
$509$	9.69169	+	26.6277i	0.429577	+	1.18025i	−0.516493	+	0.856291i	$0.672763\pi$
$510$	−4.57411	+	4.67458i	−0.202545	+	0.206994i
$511$	−1.62982	−	9.24316i	−0.0720989	−	0.408893i
$512$	−18.1124	−	13.5625i	−0.800461	−	0.599385i
$513$	−12.3827	−	7.39844i	−0.546709	−	0.326649i
$514$	5.07933	−	3.67793i	0.224040	−	0.162227i
$515$	20.9531	−	3.69461i	0.923306	−	0.162804i
$516$	−2.82251	+	1.11356i	−0.124254	+	0.0490218i
$517$	−2.38248	−	6.54581i	−0.104781	−	0.287885i
$518$	0.898837	−	12.5648i	0.0394927	−	0.552064i
$519$	8.92573	+	24.9092i	0.391796	+	1.09339i
$520$	−0.744110	+	18.7282i	−0.0326314	+	0.821287i
$521$	3.13043	+	5.42206i	0.137147	+	0.237545i	0.926415	−	0.376503i	$-0.122874\pi$
$521$	3.13043	+	5.42206i	0.137147	+	0.237545i	−0.789269	+	0.614048i	$0.789540\pi$
$522$	−1.88855	−	6.88613i	−0.0826596	−	0.301398i
$523$	18.9647	+	10.9493i	0.829268	+	0.478778i	0.853602	−	0.520926i	$-0.174413\pi$
$523$	18.9647	+	10.9493i	0.829268	+	0.478778i	−0.0243339	+	0.999704i	$0.507746\pi$
$524$	−12.2748	+	4.91367i	−0.536228	+	0.214655i
$525$	2.73066	−	4.67561i	0.119176	−	0.204060i
$526$	−18.8236	−	38.7515i	−0.820748	−	1.68965i
$527$	−0.496960	+	2.81840i	−0.0216479	+	0.122771i
$528$	−2.81744	−	6.52726i	−0.122613	−	0.284062i
$529$	−3.97763	+	3.33763i	−0.172940	+	0.145114i
$530$	−0.607745	−	5.87277i	−0.0263988	−	0.255097i
$531$	−33.6205	+	5.58288i	−1.45900	+	0.242276i
$532$	0.992793	+	4.74541i	0.0430431	+	0.205740i
$533$	−21.2040	+	58.2574i	−0.918445	+	2.52341i
$534$	20.4422	−	29.8801i	0.884621	−	1.29304i
$535$	−13.4997	−	11.3276i	−0.583642	−	0.489733i
$536$	−17.7212	+	13.7087i	−0.765438	+	0.592125i
$537$	−10.7411	−	12.9312i	−0.463513	−	0.558024i
$538$	−25.0892	+	25.8975i	−1.08167	+	1.11652i
$539$			6.40058i			0.275692i
$540$	−1.94606	+	12.2301i	−0.0837450	+	0.526301i
$541$		−	20.0932i		−	0.863875i	−0.901903	−	0.431938i	$-0.857830\pi$
$541$		−	20.0932i		−	0.863875i	0.901903	−	0.431938i	$-0.142170\pi$
$542$	−3.94068	−	3.81769i	−0.169267	−	0.163984i
$543$	41.6642	−	7.13237i	1.78798	−	0.306079i
$544$	11.9448	−	4.23953i	0.512127	−	0.181768i
$545$	6.62194	+	5.55647i	0.283653	+	0.238013i
$546$	−0.907904	+	11.8598i	−0.0388547	+	0.507553i
$547$	1.25313	−	3.44296i	0.0535802	−	0.147210i	−0.910015	−	0.414574i	$-0.863930\pi$
$547$	1.25313	−	3.44296i	0.0535802	−	0.147210i	0.963596	+	0.267364i	$0.0861527\pi$
$548$	−12.2306	+	2.55877i	−0.522465	+	0.109305i
$549$	14.2641	−	8.04669i	0.608778	−	0.343424i
$550$	−5.16763	+	0.534774i	−0.220348	+	0.0228028i
$551$	3.57900	−	3.00313i	0.152470	−	0.127938i
$552$	−13.9829	+	15.2270i	−0.595151	+	0.648103i
$553$	−1.10446	+	6.26373i	−0.0469666	+	0.266361i
$554$	−18.0677	+	8.77642i	−0.767623	+	0.372874i
$555$	21.0536	+	0.105042i	0.893675	+	0.00445879i
$556$	12.4803	−	4.99591i	0.529281	−	0.211874i
$557$	−23.1155	−	13.3458i	−0.979437	−	0.565478i	−0.0773369	−	0.997005i	$-0.524642\pi$
$557$	−23.1155	−	13.3458i	−0.979437	−	0.565478i	−0.902100	+	0.431527i	$0.857975\pi$
$558$	2.31898	+	4.89777i	0.0981704	+	0.207339i
$559$	−2.43542	−	4.21827i	−0.103007	−	0.178414i
$560$	3.46555	−	2.30538i	0.146446	−	0.0974202i
$561$	3.91833	+	0.711082i	0.165432	+	0.0300219i
$562$	9.11750	+	0.652233i	0.384599	+	0.0275128i
$563$	−0.284822	−	0.782543i	−0.0120038	−	0.0329803i	0.933546	−	0.358458i	$-0.116697\pi$
$563$	−0.284822	−	0.782543i	−0.0120038	−	0.0329803i	−0.945550	+	0.325477i	$0.894475\pi$
$564$	14.6290	−	18.4114i	0.615994	−	0.775261i
$565$	3.60693	−	0.635999i	0.151745	−	0.0267567i
$566$	21.7843	+	30.0847i	0.915662	+	1.26455i
$567$	−1.51888	+	7.71085i	−0.0637871	+	0.323825i
$568$	−7.58021	−	23.7166i	−0.318059	−	0.995127i
$569$	−2.66725	−	15.1267i	−0.111817	−	0.634146i	−0.988277	−	0.152671i	$-0.951212\pi$
$569$	−2.66725	−	15.1267i	−0.111817	−	0.634146i	0.876460	−	0.481475i	$-0.159899\pi$
$570$	−7.80364	+	2.18210i	−0.326858	+	0.0913981i
$571$	5.21522	+	14.3287i	0.218250	+	0.599638i	0.999704	−	0.0243255i	$-0.00774380\pi$
$571$	5.21522	+	14.3287i	0.218250	+	0.599638i	−0.781454	+	0.623963i	$0.785522\pi$
$572$	9.69777	−	6.01673i	0.405484	−	0.251572i
$573$	3.12608	−	17.2258i	0.130594	−	0.719620i
$574$	13.2404	−	3.77369i	0.552644	−	0.157511i
$575$	7.55356	+	13.0831i	0.315005	+	0.545605i
$576$	13.8078	−	19.6302i	0.575323	−	0.817926i
$577$	0.429405	−	0.743751i	0.0178764	−	0.0309628i	−0.856949	−	0.515401i	$-0.827643\pi$
$577$	0.429405	−	0.743751i	0.0178764	−	0.0309628i	0.874825	+	0.484439i	$0.160976\pi$
$578$	4.12492	−	16.4320i	0.171574	−	0.683480i
$579$	27.4855	+	0.137133i	1.14226	+	0.00569904i
$580$	−3.53556	−	1.89444i	−0.146806	−	0.0786624i
$581$	5.60886	+	0.988993i	0.232695	+	0.0410303i
$582$	33.8551	+	15.3414i	1.40334	+	0.635921i
$583$	−2.75395	+	2.31084i	−0.114057	+	0.0957052i
$584$	−29.7060	−	6.46352i	−1.22924	−	0.267462i
$585$	−19.8790	−	0.198368i	−0.821894	−	0.00820152i
$586$	−5.06842	+	11.3350i	−0.209374	+	0.468243i
$587$	−8.47781	+	23.2926i	−0.349917	+	0.961388i	0.632479	+	0.774577i	$0.282037\pi$
$587$	−8.47781	+	23.2926i	−0.349917	+	0.961388i	−0.982396	+	0.186811i	$0.940185\pi$
$588$	−18.4172	+	11.2996i	−0.759512	+	0.465988i
$589$	−2.27915	+	2.71618i	−0.0939107	+	0.111918i
$590$	−10.7311	+	15.8547i	−0.441792	+	0.652727i
$591$	18.8467	−	3.22630i	0.775248	−	0.132712i
$592$	−36.5573	−	18.1210i	−1.50250	−	0.744768i
$593$	14.6588			0.601965			0.300983	−	0.953630i	$-0.402685\pi$
$593$	14.6588			0.601965			0.300983	+	0.953630i	$0.402685\pi$
$594$	6.83130	−	3.19284i	0.280292	−	0.131004i
$595$			2.33153i			0.0955834i
$596$	−3.29395	+	22.9051i	−0.134925	+	0.938228i
$597$	31.9072	−	26.5032i	1.30587	−	1.08470i
$598$	−27.4832	−	18.6017i	−1.12387	−	0.760682i
$599$	30.8377	+	25.8759i	1.26000	+	1.05726i	0.995682	+	0.0928254i	$0.0295898\pi$
$599$	30.8377	+	25.8759i	1.26000	+	1.05726i	0.264314	+	0.964437i	$0.414855\pi$
$600$	−10.6617	−	13.9254i	−0.435263	−	0.568501i
$601$	−10.8097	−	3.93440i	−0.440935	−	0.160487i	0.112006	−	0.993708i	$-0.464272\pi$
$601$	−10.8097	−	3.93440i	−0.440935	−	0.160487i	−0.552941	+	0.833220i	$0.686495\pi$
$602$	−0.441542	+	0.987461i	−0.0179959	+	0.0402459i
$603$	−15.0926	−	18.3556i	−0.614619	−	0.747497i
$604$	−5.12326	−	5.72674i	−0.208463	−	0.233018i
$605$	7.61920	+	9.08021i	0.309764	+	0.369163i
$606$	−26.7027	+	2.62876i	−1.08472	+	0.106786i
$607$	−0.434467	+	2.46399i	−0.0176345	+	0.100010i	−0.992355	−	0.123419i	$-0.960614\pi$
$607$	−0.434467	+	2.46399i	−0.0176345	+	0.100010i	0.974720	+	0.223429i	$0.0717252\pi$
$608$	15.4426	+	2.85063i	0.626279	+	0.115608i
$609$	−2.19809	−	1.28373i	−0.0890711	−	0.0520195i
$610$	2.23995	−	8.92306i	0.0906930	−	0.361284i
$611$	32.6922	+	18.8748i	1.32258	+	0.763594i
$612$	4.87135	+	12.5300i	0.196913	+	0.506497i
$613$	0.345283	−	0.199349i	0.0139458	−	0.00805163i	−0.493011	−	0.870023i	$-0.664104\pi$
$613$	0.345283	−	0.199349i	0.0139458	−	0.00805163i	0.506957	+	0.861972i	$0.330770\pi$
$614$	−8.22108	−	28.8446i	−0.331776	−	1.16407i
$615$	7.76214	+	21.6620i	0.313000	+	0.873495i
$616$	−2.34530	−	0.960695i	−0.0944948	−	0.0387075i
$617$	26.3403	−	9.58708i	1.06042	−	0.385961i	0.247834	−	0.968802i	$-0.420281\pi$
$617$	26.3403	−	9.58708i	1.06042	−	0.385961i	0.812586	+	0.582841i	$0.198059\pi$
$618$	10.8598	−	42.3648i	0.436845	−	1.70416i
$619$	26.4590	−	4.66543i	1.06348	−	0.187519i	0.385578	−	0.922675i	$-0.374002\pi$
$619$	26.4590	−	4.66543i	1.06348	−	0.187519i	0.677898	+	0.735156i	$0.262891\pi$
$620$	2.89211	+	0.949957i	0.116150	+	0.0381512i
$621$	−16.5844	−	14.3444i	−0.665510	−	0.575621i
$622$	−10.8432	+	7.85155i	−0.434773	+	0.314819i
$623$	−2.24116	−	12.7103i	−0.0897903	−	0.509226i
$624$	34.4332	+	17.2826i	1.37843	+	0.691859i
$625$	−5.37131	+	1.95500i	−0.214852	+	0.0781999i
$626$	−4.74003	−	0.339084i	−0.189450	−	0.0135525i
$627$	3.76372	+	3.19027i	0.150309	+	0.127407i
$628$	−2.81575	−	2.21447i	−0.112361	−	0.0883668i
$629$	19.7933	−	11.4277i	0.789212	−	0.455652i
$630$	2.55342	+	3.60146i	0.101731	+	0.143486i
$631$	19.9248	−	34.5108i	0.793194	−	1.37385i	−0.130785	−	0.991411i	$-0.541750\pi$
$631$	19.9248	−	34.5108i	0.793194	−	1.37385i	0.923980	−	0.382442i	$-0.124917\pi$
$632$	17.4185	+	11.0010i	0.692869	+	0.437596i
$633$	4.29463	−	2.45102i	0.170696	−	0.0974193i
$634$	9.36159	−	4.54741i	0.371796	−	0.180601i
$635$	−20.2018	−	3.56212i	−0.801683	−	0.141358i
$636$	−11.5111	−	3.84472i	−0.456445	−	0.152453i
$637$	−22.2957	−	26.5710i	−0.883389	−	1.05278i
$638$	0.251407	+	2.42940i	0.00995330	+	0.0961808i
$639$	24.9051	−	8.78430i	0.985232	−	0.347502i
$640$	−2.65505	−	13.2180i	−0.104950	−	0.522486i
$641$	15.7341	+	5.72673i	0.621458	+	0.226192i	0.633509	−	0.773735i	$-0.281614\pi$
$641$	15.7341	+	5.72673i	0.621458	+	0.226192i	−0.0120511	+	0.999927i	$0.503836\pi$
$642$	−32.6618	+	15.6646i	−1.28906	+	0.618233i
$643$	16.4380	−	19.5900i	0.648250	−	0.772555i	−0.337399	−	0.941362i	$-0.609547\pi$
$643$	16.4380	−	19.5900i	0.648250	−	0.772555i	0.985649	+	0.168807i	$0.0539915\pi$
$644$	0.233611	+	7.36614i	0.00920557	+	0.290267i
$645$	−1.69574	−	0.626798i	−0.0667698	−	0.0246802i
$646$	−6.12057	+	6.31776i	−0.240811	+	0.248569i
$647$	12.8399			0.504789			0.252394	−	0.967624i	$-0.418782\pi$
$647$	12.8399			0.504789			0.252394	+	0.967624i	$0.418782\pi$
$648$	21.2472	+	14.0199i	0.834668	+	0.550754i
$649$	11.6573			0.457591
$650$	19.5898	−	20.2209i	0.768375	−	0.793129i
$651$	1.81202	+	0.669777i	0.0710185	+	0.0262506i
$652$	18.9878	−	0.602181i	0.743618	−	0.0235832i
$653$	−4.75998	+	5.67272i	−0.186272	+	0.221991i	−0.851097	−	0.525009i	$-0.824062\pi$
$653$	−4.75998	+	5.67272i	−0.186272	+	0.221991i	0.664824	+	0.747000i	$0.268506\pi$
$654$	16.0215	−	7.68390i	0.626489	−	0.300464i
$655$	−7.40277	−	2.69439i	−0.289250	−	0.105278i
$656$	4.94539	−	44.3193i	0.193085	−	1.73038i
$657$	5.91589	−	31.6978i	0.230801	−	1.23665i
$658$	−0.862927	−	8.33865i	−0.0336404	−	0.325074i
$659$	−8.16716	−	9.73324i	−0.318147	−	0.379153i	0.583143	−	0.812370i	$-0.301823\pi$
$659$	−8.16716	−	9.73324i	−0.318147	−	0.379153i	−0.901290	+	0.433217i	$0.857378\pi$
$660$	1.34194	−	4.01776i	0.0522348	−	0.156391i
$661$	5.81255	+	1.02491i	0.226082	+	0.0398643i	0.285541	−	0.958366i	$-0.407827\pi$
$661$	5.81255	+	1.02491i	0.226082	+	0.0398643i	−0.0594595	+	0.998231i	$0.518938\pi$
$662$	19.7051	−	9.57179i	0.765861	−	0.372018i
$663$	−18.7433	+	10.6971i	−0.727930	+	0.415442i
$664$	9.85084	−	15.5974i	0.382287	−	0.605296i
$665$	−1.44433	+	2.50165i	−0.0560086	+	0.0970097i
$666$	18.0590	−	39.3291i	0.699773	−	1.52397i
$667$	6.15063	−	3.55107i	0.238153	−	0.137498i
$668$	6.70842	−	8.52993i	0.259557	−	0.330033i
$669$	−12.3890	−	10.5014i	−0.478986	−	0.406006i
$670$	−13.3152	−	0.952523i	−0.514412	−	0.0367992i
$671$	−5.26400	+	1.91594i	−0.203214	+	0.0739640i
$672$	−1.37607	−	8.44443i	−0.0530831	−	0.325751i
$673$	0.0417725	+	0.236903i	0.00161021	+	0.00913195i	0.985602	−	0.169080i	$-0.0540797\pi$
$673$	0.0417725	+	0.236903i	0.00161021	+	0.00913195i	−0.983992	+	0.178212i	$0.942969\pi$
$674$	1.34903	−	0.976830i	0.0519627	−	0.0376261i
$675$	14.4274	−	11.7426i	0.555310	−	0.451971i
$676$	−11.1865	+	34.0571i	−0.430252	+	1.30989i
$677$	−30.3395	+	5.34967i	−1.16604	+	0.205604i	−0.722968	−	0.690881i	$-0.757223\pi$
$677$	−30.3395	+	5.34967i	−1.16604	+	0.205604i	−0.443072	+	0.896486i	$0.646112\pi$
$678$	1.86943	−	7.29279i	0.0717952	−	0.280078i
$679$	12.4513	−	4.53191i	0.477838	−	0.173919i
$680$	6.98839	+	2.86263i	0.267993	+	0.109777i
$681$	12.7582	+	35.6045i	0.488894	+	1.36437i
$682$	−0.508060	−	1.78258i	−0.0194546	−	0.0682587i
$683$	20.4196	−	11.7893i	0.781336	−	0.451104i	−0.0555676	−	0.998455i	$-0.517697\pi$
$683$	20.4196	−	11.7893i	0.781336	−	0.451104i	0.836904	+	0.547350i	$0.184364\pi$
$684$	−2.53528	+	16.4620i	−0.0969389	+	0.629439i
$685$	−6.44761	−	3.72253i	−0.246351	−	0.142231i
$686$	−3.98017	+	15.8554i	−0.151964	+	0.605361i
$687$	−18.5952	−	10.8600i	−0.709449	−	0.414334i
$688$	2.41764	+	2.53585i	0.0921715	+	0.0966782i
$689$	3.38304	−	19.1862i	0.128884	−	0.730935i
$690$	−12.2584	+	1.20678i	−0.466668	+	0.0459412i
$691$	3.88838	+	4.63400i	0.147921	+	0.176286i	0.834917	−	0.550376i	$-0.185515\pi$
$691$	3.88838	+	4.63400i	0.147921	+	0.176286i	−0.686996	+	0.726661i	$0.741071\pi$
$692$	22.7711	−	20.3715i	0.865626	−	0.774407i
$693$	0.944570	−	2.51676i	0.0358812	−	0.0956037i
$694$	−9.08868	+	20.3258i	−0.345001	+	0.771558i
$695$	7.52667	+	2.73948i	0.285503	+	0.103915i
$696$	−6.54658	+	5.01227i	−0.248147	+	0.189990i
$697$	19.1355	+	16.0566i	0.724810	+	0.608187i
$698$	4.91832	+	3.32892i	0.186161	+	0.126002i
$699$	−25.0278	+	20.7889i	−0.946639	+	0.786309i
$700$	−6.18857	−	0.889970i	−0.233906	−	0.0336377i
$701$			6.37273i			0.240695i	0.992732	+	0.120347i	$0.0384008\pi$
$701$			6.37273i			0.240695i	−0.992732	+	0.120347i	$0.961599\pi$
$702$	−17.2372	+	37.0507i	−0.650575	+	1.39839i
$703$	28.3167			1.06798
$704$	−5.75906	+	5.85013i	−0.217053	+	0.220485i
$705$	13.8104	−	2.36416i	0.520128	−	0.0890393i
$706$	−15.4131	+	22.7721i	−0.580080	+	0.857040i
$707$	−6.14848	+	7.32748i	−0.231238	+	0.275578i
$708$	20.5799	+	33.5431i	0.773440	+	1.26063i
$709$	1.18619	−	3.25902i	0.0445482	−	0.122395i	−0.915424	−	0.402492i	$-0.868144\pi$
$709$	1.18619	−	3.25902i	0.0445482	−	0.122395i	0.959972	+	0.280096i	$0.0903665\pi$
$710$	6.05571	−	13.5429i	0.227267	−	0.508257i
$711$	−11.1139	+	18.8138i	−0.416804	+	0.705572i
$712$	−40.8486	−	8.88799i	−1.53087	−	0.333091i
$713$	−4.12896	+	3.46461i	−0.154631	+	0.129751i
$714$	4.36528	+	1.97812i	0.163367	+	0.0740294i
$715$	6.69662	+	1.18079i	0.250439	+	0.0441592i
$716$	−9.16773	+	17.1096i	−0.342614	+	0.639414i
$717$	18.4788	+	0.0921960i	0.690104	+	0.00344312i
$718$	2.96001	−	11.7915i	0.110467	−	0.440054i
$719$	−21.9558	+	38.0286i	−0.818814	+	1.41823i	0.0877429	+	0.996143i	$0.472035\pi$
$719$	−21.9558	+	38.0286i	−0.818814	+	1.41823i	−0.906557	+	0.422084i	$0.861299\pi$
$720$	13.9299	−	3.23165i	0.519135	−	0.120436i
$721$	−7.79552	−	13.5022i	−0.290320	−	0.502849i
$722$	15.3601	−	4.37784i	0.571645	−	0.162926i
$723$	−3.34286	+	18.4204i	−0.124322	+	0.685062i
$724$	−25.7324	−	41.4754i	−0.956336	−	1.54142i
$725$	2.06071	+	5.66176i	0.0765330	+	0.210273i
$726$	23.4650	−	6.56143i	0.870868	−	0.243517i
$727$	−0.602321	−	3.41593i	−0.0223389	−	0.126690i	0.971599	−	0.236634i	$-0.0760441\pi$
$727$	−0.602321	−	3.41593i	−0.0223389	−	0.126690i	−0.993938	+	0.109944i	$0.964933\pi$
$728$	13.0826	−	4.18142i	0.484874	−	0.154974i
$729$	−14.1938	+	22.9681i	−0.525697	+	0.850672i
$730$	−10.6235	−	14.6713i	−0.393192	−	0.543010i
$731$	−1.93276	+	0.340797i	−0.0714855	+	0.0126048i
$732$	−14.8060	−	11.7644i	−0.547247	−	0.434823i
$733$	−1.18277	−	3.24964i	−0.0436867	−	0.120028i	0.915931	−	0.401336i	$-0.131454\pi$
$733$	−1.18277	−	3.24964i	−0.0436867	−	0.120028i	−0.959618	+	0.281308i	$0.909232\pi$
$734$	7.07163	+	0.505879i	0.261019	+	0.0186723i
$735$	−12.6673	−	2.29880i	−0.467239	−	0.0847925i
$736$	22.3657	+	8.34385i	0.824409	+	0.307558i
$737$	4.06418	+	7.03937i	0.149706	+	0.259299i
$738$	47.1429	+	3.84560i	1.73535	+	0.141559i
$739$	−31.0668	−	17.9364i	−1.14281	−	0.659802i	−0.195685	−	0.980667i	$-0.562693\pi$
$739$	−31.0668	−	17.9364i	−1.14281	−	0.659802i	−0.947125	+	0.320865i	$0.896026\pi$
$740$	−9.03477	−	22.5697i	−0.332125	−	0.829679i
$741$	−26.7375	−	0.133401i	−0.982227	−	0.00490060i
$742$	−3.89163	+	1.89037i	−0.142866	+	0.0693975i
$743$	8.38647	−	47.5620i	0.307670	−	1.74488i	−0.302995	−	0.952992i	$-0.597987\pi$
$743$	8.38647	−	47.5620i	0.307670	−	1.74488i	0.610665	−	0.791889i	$-0.290902\pi$
$744$	4.23232	−	4.60889i	0.155164	−	0.168970i
$745$	−10.5621	+	8.86264i	−0.386965	+	0.324702i
$746$	21.0808	−	2.18155i	0.771824	−	0.0798724i
$747$	16.8468	+	9.95196i	0.616393	+	0.364123i
$748$	−0.941649	−	4.50095i	−0.0344301	−	0.164571i
$749$	−4.41670	+	12.1348i	−0.161383	+	0.443395i
$750$	1.91163	−	24.9713i	0.0698028	−	0.911823i
$751$	5.69735	+	4.78064i	0.207899	+	0.174448i	0.740792	−	0.671735i	$-0.234451\pi$
$751$	5.69735	+	4.78064i	0.207899	+	0.174448i	−0.532893	+	0.846183i	$0.678895\pi$
$752$	−26.0533	−	7.65161i	−0.950064	−	0.279025i
$753$	−32.6904	+	5.59617i	−1.19130	+	0.203936i
$754$	−9.50623	−	9.20952i	−0.346196	−	0.335391i
$755$		−	4.57830i		−	0.166621i
$756$	8.90933	−	1.72516i	0.324029	−	0.0627436i
$757$			11.0390i			0.401219i	0.979671	+	0.200610i	$0.0642923\pi$
$757$			11.0390i			0.401219i	−0.979671	+	0.200610i	$0.935708\pi$
$758$	−33.9850	+	35.0799i	−1.23439	+	1.27416i
$759$	4.79231	+	5.76947i	0.173950	+	0.209419i
$760$	5.72496	+	7.40063i	0.207666	+	0.268449i
$761$	27.5446	+	23.1126i	0.998490	+	0.837832i	0.986775	−	0.162099i	$-0.0518264\pi$
$761$	27.5446	+	23.1126i	0.998490	+	0.837832i	0.0117153	+	0.999931i	$0.496271\pi$
$762$	−23.8089	+	34.8012i	−0.862507	+	1.26072i
$763$	2.16651	−	5.95243i	0.0784328	−	0.215492i
$764$	−19.7872	+	4.13970i	−0.715875	+	0.149769i
$765$	−2.81458	+	7.49929i	−0.101761	+	0.271138i
$766$	5.50091	+	53.1564i	0.198756	+	1.92062i
$767$	−48.3936	+	40.6071i	−1.74739	+	1.46624i
$768$	−27.0004	−	6.24343i	−0.974292	−	0.225290i
$769$	4.52983	−	25.6899i	0.163350	−	0.926402i	−0.787400	−	0.616443i	$-0.788573\pi$
$769$	4.52983	−	25.6899i	0.163350	−	0.926402i	0.950750	−	0.309960i	$-0.100316\pi$
$770$	−0.659801	−	1.35831i	−0.0237776	−	0.0489501i
$771$	3.87339	−	6.63227i	0.139497	−	0.238855i
$772$	−11.7949	−	29.4648i	−0.424508	−	1.06046i
$773$	25.8130	+	14.9032i	0.928430	+	0.536029i	0.886315	−	0.463084i	$-0.153257\pi$
$773$	25.8130	+	14.9032i	0.928430	+	0.536029i	0.0421152	+	0.999113i	$0.486590\pi$
$774$	−2.61225	+	2.64312i	−0.0938954	+	0.0950048i
$775$	−2.28630	−	3.95999i	−0.0821265	−	0.142247i
$776$	1.70391	−	42.8851i	0.0611668	−	1.53948i
$777$	−5.20428	−	14.5237i	−0.186702	−	0.521034i
$778$	0.866940	−	12.1189i	0.0310813	−	0.434483i
$779$	10.5850	+	29.0821i	0.379248	+	1.04198i
$780$	8.42459	+	21.3536i	0.301649	+	0.764581i
$781$	−8.89591	+	1.56859i	−0.318321	+	0.0561286i
$782$	−10.8304	+	7.84230i	−0.387295	+	0.280440i
$783$	−5.52039	−	6.78258i	−0.197283	−	0.242390i
$784$	20.0905	+	14.7942i	0.717519	+	0.528364i
$785$	−0.370631	−	2.10195i	−0.0132284	−	0.0750219i
$786$	−11.3253	+	11.5741i	−0.403962	+	0.412834i
$787$	2.03191	+	5.58264i	0.0724299	+	0.198999i	0.970625	−	0.240598i	$-0.0773434\pi$
$787$	2.03191	+	5.58264i	0.0724299	+	0.198999i	−0.898195	+	0.439597i	$0.855121\pi$
$788$	−11.6400	−	18.7613i	−0.414656	−	0.668343i
$789$	−40.2497	−	34.1171i	−1.43293	−	1.21460i
$790$	3.36453	+	11.8048i	0.119705	+	0.419997i
$791$	−1.34194	−	2.32431i	−0.0477139	−	0.0826430i
$792$	−6.38385	−	5.92124i	−0.226840	−	0.210402i
$793$	15.1787	−	26.2903i	0.539012	−	0.933596i
$794$	10.7613	+	2.70140i	0.381903	+	0.0958691i
$795$	−3.58424	−	6.28024i	−0.127120	−	0.222737i
$796$	−42.2170	−	22.6209i	−1.49634	−	0.801778i
$797$	−29.5048	−	5.20250i	−1.04511	−	0.184282i	−0.375371	−	0.926875i	$-0.622485\pi$
$797$	−29.5048	−	5.20250i	−1.04511	−	0.184282i	−0.669743	+	0.742593i	$0.733596\pi$
$798$	3.45839	+	4.82664i	0.122426	+	0.170861i
$799$	11.6517	−	9.77691i	0.412206	−	0.345882i
$800$	−10.2658	+	17.4566i	−0.362951	+	0.617182i
$801$	8.13494	−	43.5876i	0.287434	−	1.54009i
$802$	−0.774595	−	0.346359i	−0.0273519	−	0.0122304i
$803$	−3.77229	+	10.3643i	−0.133121	+	0.365747i
$804$	−13.0803	+	24.1217i	−0.461308	+	0.850707i
$805$	−2.82257	+	3.36381i	−0.0994825	+	0.118559i
$806$	8.31858	+	5.63035i	0.293009	+	0.198321i
$807$	−15.3109	+	41.4222i	−0.538970	+	1.45813i
$808$	14.4139	+	27.4257i	0.507079	+	0.964832i
$809$	2.90808			0.102243			0.0511213	−	0.998692i	$-0.483720\pi$
$809$	2.90808			0.102243			0.0511213	+	0.998692i	$0.483720\pi$
$810$	3.86539	+	14.6664i	0.135816	+	0.515325i
$811$			34.5756i			1.21411i	0.794658	+	0.607057i	$0.207650\pi$
$811$			34.5756i			1.21411i	−0.794658	+	0.607057i	$0.792350\pi$
$812$	−0.418391	+	2.90936i	−0.0146827	+	0.102099i
$813$	−6.30299	−	2.32978i	−0.221055	−	0.0817089i
$814$	−8.29732	+	12.2589i	−0.290821	+	0.429674i
$815$	8.67091	+	7.27576i	0.303729	+	0.254859i
$816$	11.2888	−	10.6555i	0.395185	−	0.373018i
$817$	−2.28489	−	0.831632i	−0.0799382	−	0.0290951i
$818$	32.2245	+	14.4092i	1.12670	+	0.503805i
$819$	4.84562	+	13.7382i	0.169320	+	0.480053i
$820$	19.8025	−	17.7158i	0.691535	−	0.618661i
$821$	−29.4054	−	35.0440i	−1.02626	−	1.22304i	−0.974501	−	0.224385i	$-0.927963\pi$
$821$	−29.4054	−	35.0440i	−1.02626	−	1.22304i	−0.0517560	−	0.998660i	$-0.516482\pi$
$822$	−12.4399	+	8.91347i	−0.433892	+	0.310893i
$823$	−7.78187	+	44.1332i	−0.271259	+	1.53839i	0.479341	+	0.877629i	$0.340876\pi$
$823$	−7.78187	+	44.1332i	−0.271259	+	1.53839i	−0.750600	+	0.660757i	$0.770235\pi$
$824$	−50.0420	+	6.78793i	−1.74330	+	0.236469i
$825$	−5.52617	+	3.15388i	−0.192397	+	0.109804i
$826$	13.6069	+	3.41575i	0.473446	+	0.118849i
$827$	−26.1682	−	15.1082i	−0.909956	−	0.525364i	−0.0295392	−	0.999564i	$-0.509404\pi$
$827$	−26.1682	−	15.1082i	−0.909956	−	0.525364i	−0.880417	+	0.474200i	$0.842737\pi$
$828$	−8.14085	+	23.9750i	−0.282914	+	0.833188i
$829$	−7.34763	+	4.24216i	−0.255194	+	0.147336i	−0.622140	−	0.782906i	$-0.713737\pi$
$829$	−7.34763	+	4.24216i	−0.255194	+	0.147336i	0.366946	+	0.930242i	$0.380403\pi$
$830$	10.5706	−	3.01277i	0.366912	−	0.104575i
$831$	−15.9069	+	18.7662i	−0.551806	+	0.650992i
$832$	3.52956	−	44.3470i	0.122366	−	1.53745i
$833$	−13.1329	+	4.77999i	−0.455029	+	0.165617i
$834$	11.5149	−	11.7678i	0.398728	−	0.407486i
$835$	6.36758	−	1.12278i	0.220359	−	0.0388552i
$836$	1.77787	−	5.41268i	0.0614891	−	0.187202i
$837$	5.01975	+	4.34175i	0.173508	+	0.150073i
$838$	24.4690	+	33.7924i	0.845268	+	1.16734i
$839$	−0.547703	−	3.10618i	−0.0189088	−	0.107237i	0.973893	−	0.227009i	$-0.0728948\pi$
$839$	−0.547703	−	3.10618i	−0.0189088	−	0.107237i	−0.992801	+	0.119772i	$0.961784\pi$
$840$	2.74362	−	4.29649i	0.0946638	−	0.148243i
$841$	−24.5894	+	8.94980i	−0.847910	+	0.308614i
$842$	0.278828	−	3.89771i	0.00960904	−	0.134324i
$843$	10.5390	−	3.77643i	0.362982	−	0.130067i
$844$	−4.48810	−	3.52970i	−0.154487	−	0.121497i
$845$	−18.4972	+	10.6793i	−0.636322	+	0.367380i
$846$	7.29067	−	27.8627i	0.250658	−	0.957939i
$847$	4.34299	−	7.52228i	0.149227	−	0.258469i
$848$	0.887971	+	13.9855i	0.0304931	+	0.480265i
$849$	39.2827	+	22.9420i	1.34818	+	0.787366i
$850$	−4.95648	−	10.2037i	−0.170006	−	0.349985i
$851$	42.3912	+	7.47471i	1.45315	+	0.256230i
$852$	−20.2184	−	22.8281i	−0.692670	−	0.782079i
$853$	16.3176	+	19.4465i	0.558703	+	0.665836i	0.969272	−	0.245993i	$-0.0791141\pi$
$853$	16.3176	+	19.4465i	0.558703	+	0.665836i	−0.410568	+	0.911830i	$0.634670\pi$
$854$	−6.70575	+	0.693947i	−0.229466	+	0.0237464i
$855$	−7.66557	+	6.30290i	−0.262157	+	0.215555i
$856$	30.9493	+	28.1373i	1.05783	+	0.961713i
$857$	−49.7829	−	18.1195i	−1.70055	−	0.618950i	−0.704662	−	0.709543i	$-0.748901\pi$
$857$	−49.7829	−	18.1195i	−1.70055	−	0.618950i	−0.995888	+	0.0905935i	$0.971124\pi$
$858$	7.89235	−	11.5361i	0.269440	−	0.393837i
$859$	27.5561	−	32.8401i	0.940202	−	1.12049i	−0.0523449	−	0.998629i	$-0.516670\pi$
$859$	27.5561	−	32.8401i	0.940202	−	1.12049i	0.992547	−	0.121860i	$-0.0388860\pi$
$860$	0.0661718	+	2.08651i	0.00225644	+	0.0711493i
$861$	12.9709	−	10.7740i	0.442047	−	0.367178i
$862$	35.9186	+	34.7975i	1.22339	+	1.18521i
$863$	9.06092			0.308437			0.154219	−	0.988037i	$-0.450714\pi$
$863$	9.06092			0.308437			0.154219	+	0.988037i	$0.450714\pi$
$864$	5.76786	−	28.8224i	0.196227	−	0.980559i
$865$	18.2046			0.618974
$866$	25.7292	+	24.9261i	0.874313	+	0.847025i
$867$	−3.50110	−	20.4519i	−0.118904	−	0.694582i
$868$	−0.0707092	−	2.22958i	−0.00240003	−	0.0756767i
$869$	4.80433	−	5.72558i	0.162976	−	0.194227i
$870$	−4.89827	−	0.374977i	−0.166067	−	0.0127129i
$871$	−41.3927	−	15.0657i	−1.40254	−	0.510483i
$872$	−15.1814	−	13.8021i	−0.514108	−	0.467397i
$873$	45.5201	+	0.454236i	1.54062	+	0.0153736i
$874$	−16.4788	+	1.70531i	−0.557403	+	0.0576830i
$875$	−5.73889	−	6.83935i	−0.194010	−	0.231212i
$876$	−36.4820	+	7.44266i	−1.23261	+	0.251464i
$877$	56.5532	+	9.97185i	1.90966	+	0.336725i	0.997349	−	0.0727623i	$-0.0231814\pi$
$877$	56.5532	+	9.97185i	1.90966	+	0.336725i	0.912316	+	0.409488i	$0.134293\pi$
$878$	16.1636	+	33.2754i	0.545495	+	1.12299i
$879$	−0.0758714	+	15.2069i	−0.00255908	+	0.512916i
$880$	−4.88141	+	0.309932i	−0.164552	+	0.0104478i
$881$	21.5866	−	37.3891i	0.727271	−	1.25967i	−0.230761	−	0.973010i	$-0.574122\pi$
$881$	21.5866	−	37.3891i	0.727271	−	1.25967i	0.958032	−	0.286660i	$-0.0925451\pi$
$882$	−15.0512	+	21.7663i	−0.506800	+	0.732910i
$883$	23.2530	−	13.4252i	0.782527	−	0.451792i	−0.0547980	−	0.998497i	$-0.517451\pi$
$883$	23.2530	−	13.4252i	0.782527	−	0.451792i	0.837325	+	0.546705i	$0.184118\pi$
$884$	19.5877	+	15.4049i	0.658805	+	0.518122i
$885$	−4.18679	+	23.0708i	−0.140738	+	0.775516i
$886$	−2.41898	+	33.8147i	−0.0812673	+	1.13603i
$887$	11.5780	−	4.21405i	0.388751	−	0.141494i	−0.140247	−	0.990116i	$-0.544790\pi$
$887$	11.5780	−	4.21405i	0.388751	−	0.141494i	0.528999	+	0.848623i	$0.322568\pi$
$888$	−49.9222	−	2.23303i	−1.67528	−	0.0749355i
$889$	2.61027	+	14.8036i	0.0875456	+	0.496496i
$890$	−14.6083	−	20.1745i	−0.489672	−	0.676251i
$891$	6.07636	−	6.95480i	0.203566	−	0.232995i
$892$	−5.85220	+	17.8168i	−0.195946	+	0.596551i
$893$	18.5584	−	3.27234i	0.621032	−	0.109505i
$894$	7.63224	+	27.2945i	0.255260	+	0.912863i
$895$	−10.8680	+	3.95564i	−0.363278	+	0.132222i
$896$	−8.43638	+	5.14104i	−0.281840	+	0.171750i
$897$	−39.9919	−	7.25756i	−1.33529	−	0.242323i
$898$	22.7178	−	6.47487i	0.758103	−	0.216069i
$899$	−1.86167	+	1.07483i	−0.0620901	+	0.0358477i
$900$	−18.8310	−	10.3333i	−0.627699	−	0.344442i
$901$	−6.79812	−	3.92490i	−0.226478	−	0.130757i
$902$	−15.6919	−	3.93913i	−0.522483	−	0.131159i
$903$	−0.00660965	+	1.32477i	−0.000219955	+	0.0440856i
$904$	−8.61437	+	1.16849i	−0.286510	+	0.0388635i
$905$	5.05002	−	28.6401i	0.167868	−	0.952029i
$906$	−8.57187	−	3.88434i	−0.284781	−	0.129048i
$907$	29.6848	+	35.3769i	0.985666	+	1.17467i	0.984627	+	0.174672i	$0.0558865\pi$
$907$	29.6848	+	35.3769i	0.985666	+	1.17467i	0.00103965	+	0.999999i	$0.499669\pi$
$908$	32.5483	−	29.1184i	1.08015	−	0.966326i
$909$	−28.6220	+	16.1463i	−0.949331	+	0.535538i
$910$	7.47059	+	3.34047i	0.247648	+	0.110735i
$911$	−34.7008	−	12.6300i	−1.14969	−	0.418452i	−0.304285	−	0.952581i	$-0.598417\pi$
$911$	−34.7008	−	12.6300i	−1.14969	−	0.418452i	−0.845403	+	0.534129i	$0.820640\pi$
$912$	18.7133	−	4.43987i	0.619658	−	0.147019i
$913$	−5.12697	−	4.30204i	−0.169678	−	0.142377i
$914$	6.02576	−	8.90277i	0.199314	−	0.294477i
$915$	−1.90120	−	11.1060i	−0.0628518	−	0.367153i
$916$	−3.53946	+	24.6123i	−0.116947	+	0.813213i
$917$			5.77279i			0.190634i
$918$	11.6528	+	11.6323i	0.384601	+	0.383922i
$919$	−51.4933			−1.69861			−0.849303	−	0.527906i	$-0.822978\pi$
$919$	−51.4933			−1.69861			−0.849303	+	0.527906i	$0.822978\pi$
$920$	6.61696	+	12.5902i	0.218155	+	0.415088i
$921$	−23.4715	−	28.2574i	−0.773414	−	0.931114i
$922$	−35.6631	−	24.1383i	−1.17450	−	0.794952i
$923$	31.4660	−	37.4997i	1.03572	−	1.23432i
$924$	−3.10293	+	0.0829123i	−0.102079	+	0.00272761i
$925$	−12.4897	+	34.3152i	−0.410660	+	1.12828i
$926$	−50.1785	−	22.4373i	−1.64897	−	0.737334i
$927$	−8.77441	−	52.8401i	−0.288190	−	1.73550i
$928$	8.20665	+	4.82614i	0.269396	+	0.158426i
$929$	−17.6604	+	14.8188i	−0.579417	+	0.486189i	−0.884756	−	0.466055i	$-0.845675\pi$
$929$	−17.6604	+	14.8188i	−0.579417	+	0.486189i	0.305338	+	0.952244i	$0.401230\pi$
$930$	3.71035	−	0.365266i	0.121667	−	0.0119775i
$931$	−17.0522	−	3.00677i	−0.558864	−	0.0985428i
$932$	33.1148	+	17.7437i	1.08471	+	0.581215i
$933$	−8.26881	+	14.1584i	−0.270709	+	0.463525i
$934$	36.3079	+	9.11435i	1.18803	+	0.298231i
$935$	1.36992	−	2.37277i	0.0448012	−	0.0775979i
$936$	47.1276	+	2.34368i	1.54041	+	0.0766056i
$937$	−0.371339	−	0.643179i	−0.0121311	−	0.0210117i	0.859896	−	0.510469i	$-0.170528\pi$
$937$	−0.371339	−	0.643179i	−0.0121311	−	0.0210117i	−0.872027	+	0.489457i	$0.837195\pi$
$938$	2.68126	+	9.40751i	0.0875463	+	0.307166i
$939$	−5.47903	+	1.96330i	−0.178801	+	0.0640699i
$940$	−8.52947	−	13.7478i	−0.278201	−	0.448404i
$941$	−2.03139	−	5.58121i	−0.0662216	−	0.181942i	0.902168	−	0.431385i	$-0.141975\pi$
$941$	−2.03139	−	5.58121i	−0.0662216	−	0.181942i	−0.968390	+	0.249442i	$0.919753\pi$
$942$	−4.24990	−	1.08942i	−0.138469	−	0.0354952i
$943$	8.16945	+	46.3312i	0.266034	+	1.50875i
$944$	26.9446	−	36.5908i	0.876972	−	1.19093i
$945$	4.64161	+	2.77328i	0.150992	+	0.0902150i
$946$	1.02955	−	0.745494i	0.0334735	−	0.0242381i
$947$	−8.81540	+	1.55439i	−0.286462	+	0.0505110i	−0.315033	−	0.949081i	$-0.602016\pi$
$947$	−8.81540	+	1.55439i	−0.286462	+	0.0505110i	0.0285708	+	0.999592i	$0.490904\pi$
$948$	24.9565	+	3.71614i	0.810550	+	0.120695i
$949$	−20.4428	−	56.1661i	−0.663600	−	1.82323i
$950$	1.00284	−	14.0187i	0.0325365	−	0.454825i
$951$	8.24201	−	9.72351i	0.267265	−	0.315306i
$952$	0.219703	−	5.52961i	0.00712061	−	0.179216i
$953$	6.35244	+	11.0028i	0.205776	+	0.356414i	0.950380	−	0.311093i	$-0.100695\pi$
$953$	6.35244	+	11.0028i	0.205776	+	0.356414i	−0.744604	+	0.667507i	$0.767362\pi$
$954$	−14.7993	+	1.38241i	−0.479146	+	0.0447570i
$955$	−10.4312	−	6.02247i	−0.337547	−	0.194883i
$956$	−7.92986	−	19.8095i	−0.256470	−	0.640686i
$957$	1.48270	+	2.59796i	0.0479288	+	0.0839800i
$958$	9.33744	+	19.2227i	0.301679	+	0.621056i
$959$	−0.947361	+	5.37275i	−0.0305919	+	0.173495i
$960$	−9.50947	−	13.4987i	−0.306917	−	0.435670i
$961$	−22.4976	+	18.8778i	−0.725730	+	0.608960i
$962$	−8.25748	−	79.7937i	−0.266232	−	2.57265i
$963$	−28.8550	+	33.6994i	−0.929841	+	1.08595i
$964$	21.1593	−	4.42677i	0.681497	−	0.142577i
$965$	6.46768	−	17.7698i	0.208202	−	0.572030i
$966$	3.90326	+	8.13858i	0.125585	+	0.261854i
$967$	−35.5615	−	29.8396i	−1.14358	−	0.959578i	−0.144030	−	0.989573i	$-0.546006\pi$
$967$	−35.5615	−	29.8396i	−1.14358	−	0.959578i	−0.999550	+	0.0299954i	$0.990451\pi$
$968$	−17.2146	−	22.2532i	−0.553297	−	0.715245i
$969$	−3.73514	+	10.1050i	−0.119990	+	0.324621i
$970$	17.7933	−	18.3666i	0.571310	−	0.589716i
$971$			18.5720i			0.596004i	0.954565	+	0.298002i	$0.0963202\pi$
$971$			18.5720i			0.596004i	−0.954565	+	0.298002i	$0.903680\pi$
$972$	30.7391	+	5.20622i	0.985959	+	0.166990i
$973$		−	5.86941i		−	0.188165i
$974$	−7.35399	−	7.12446i	−0.235637	−	0.228283i
$975$	11.9549	−	32.3427i	0.382862	−	1.03579i
$976$	−6.15325	+	20.9514i	−0.196961	+	0.670639i
$977$	−1.57620	−	1.32259i	−0.0504270	−	0.0423133i	0.617226	−	0.786786i	$-0.288256\pi$
$977$	−1.57620	−	1.32259i	−0.0504270	−	0.0423133i	−0.667653	+	0.744473i	$0.732701\pi$
$978$	20.9789	−	10.0615i	0.670830	−	0.321730i
$979$	−5.18727	+	14.2519i	−0.165786	+	0.455493i
$980$	3.04418	+	14.5508i	0.0972428	+	0.464807i
$981$	14.1541	−	16.5304i	0.451907	−	0.527776i
$982$	15.5931	−	1.61366i	0.497596	−	0.0514938i
$983$	14.9247	−	12.5233i	0.476025	−	0.399433i	−0.372961	−	0.927847i	$-0.621658\pi$
$983$	14.9247	−	12.5233i	0.476025	−	0.399433i	0.848987	+	0.528414i	$0.177213\pi$
$984$	−16.3680	−	52.1064i	−0.521792	−	1.66109i
$985$	2.28436	−	12.9553i	0.0727858	−	0.412789i
$986$	−4.79697	+	2.33013i	−0.152767	+	0.0742066i
$987$	−5.08920	−	8.91721i	−0.161991	−	0.283838i
$988$	11.4739	+	28.6629i	0.365034	+	0.911890i
$989$	−3.20105	−	1.84813i	−0.101787	−	0.0587670i
$990$	−0.482505	−	5.16546i	−0.0153350	−	0.164169i
$991$	13.4703	+	23.3313i	0.427899	+	0.741142i	0.996686	−	0.0813423i	$-0.0259207\pi$
$991$	13.4703	+	23.3313i	0.427899	+	0.741142i	−0.568788	+	0.822484i	$0.692587\pi$
$992$	−6.76961	−	2.52551i	−0.214935	−	0.0801850i
$993$	17.3485	−	20.4669i	0.550539	−	0.649498i
$994$	−10.8433	−	0.775690i	−0.343929	−	0.0246034i
$995$	−9.76036	−	26.8164i	−0.309424	−	0.850136i
$996$	3.32762	−	22.3473i	0.105440	−	0.708102i
$997$	27.4422	−	4.83880i	0.869104	−	0.153246i	0.278723	−	0.960371i	$-0.410089\pi$
$997$	27.4422	−	4.83880i	0.869104	−	0.153246i	0.590381	+	0.807125i	$0.298978\pi$
$998$	8.85122	+	12.2238i	0.280180	+	0.386937i
$999$	0.793310	−	52.9975i	0.0250992	−	1.67677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.13.8	✓	204
3.2	odd	2		648.2.t.a.253.27		204
4.3	odd	2		864.2.bf.a.337.31		204
8.3	odd	2		864.2.bf.a.337.4		204
8.5	even	2	inner	216.2.t.a.13.23	yes	204
24.5	odd	2		648.2.t.a.253.12		204
27.2	odd	18		648.2.t.a.397.12		204
27.25	even	9	inner	216.2.t.a.133.23	yes	204
108.79	odd	18		864.2.bf.a.241.4		204
216.29	odd	18		648.2.t.a.397.27		204
216.133	even	18	inner	216.2.t.a.133.8	yes	204
216.187	odd	18		864.2.bf.a.241.31		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.8	✓	204	1.1	even	1	trivial
216.2.t.a.13.23	yes	204	8.5	even	2	inner
216.2.t.a.133.8	yes	204	216.133	even	18	inner
216.2.t.a.133.23	yes	204	27.25	even	9	inner
648.2.t.a.253.12		204	24.5	odd	2
648.2.t.a.253.27		204	3.2	odd	2
648.2.t.a.397.12		204	27.2	odd	18
648.2.t.a.397.27		204	216.29	odd	18
864.2.bf.a.241.4		204	108.79	odd	18
864.2.bf.a.241.31		204	216.187	odd	18
864.2.bf.a.337.4		204	8.3	odd	2
864.2.bf.a.337.31		204	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.01573 - 0.984023i) q^{2} +(-1.62462 - 0.600509i) q^{3} +(0.0633965 + 1.99899i) q^{4} +(-0.765978 + 0.912857i) q^{5} +(1.05925 + 2.20862i) q^{6} +(0.820563 + 0.298660i) q^{7} +(1.90266 - 2.09281i) q^{8} +(2.27878 + 1.95120i) q^{9} +O(q^{10})\)	\(q+(-1.01573 - 0.984023i) q^{2} +(-1.62462 - 0.600509i) q^{3} +(0.0633965 + 1.99899i) q^{4} +(-0.765978 + 0.912857i) q^{5} +(1.05925 + 2.20862i) q^{6} +(0.820563 + 0.298660i) q^{7} +(1.90266 - 2.09281i) q^{8} +(2.27878 + 1.95120i) q^{9} +(1.67630 - 0.173472i) q^{10} +(-0.659595 - 0.786075i) q^{11} +(1.09742 - 3.28568i) q^{12} +(5.47642 + 0.965640i) q^{13} +(-0.539578 - 1.11081i) q^{14} +(1.79260 - 1.02307i) q^{15} +(-3.99196 + 0.253458i) q^{16} +(1.12031 - 1.94043i) q^{17} +(-0.394587 - 4.22425i) q^{18} +(2.40409 - 1.38800i) q^{19} +(-1.87336 - 1.47331i) q^{20} +(-1.15375 - 0.977965i) q^{21} +(-0.103548 + 1.44749i) q^{22} +(3.96541 - 1.44329i) q^{23} +(-4.34786 + 2.25746i) q^{24} +(0.621655 + 3.52558i) q^{25} +(-4.61232 - 6.36975i) q^{26} +(-2.53043 - 4.53838i) q^{27} +(-0.545000 + 1.65923i) q^{28} +(1.65744 - 0.292252i) q^{29} +(-2.82751 - 0.724805i) q^{30} +(-1.20025 + 0.436854i) q^{31} +(4.30415 + 3.67074i) q^{32} +(0.599546 + 1.67317i) q^{33} +(-3.04735 + 0.868533i) q^{34} +(-0.901167 + 0.520289i) q^{35} +(-3.75597 + 4.67896i) q^{36} +(8.83390 + 5.10025i) q^{37} +(-3.80773 - 0.955852i) q^{38} +(-8.31722 - 4.85744i) q^{39} +(0.453041 + 3.33991i) q^{40} +(-1.93593 + 10.9792i) q^{41} +(0.209557 + 2.12866i) q^{42} +(-0.563024 - 0.670985i) q^{43} +(1.52954 - 1.36836i) q^{44} +(-3.52666 + 0.585623i) q^{45} +(-5.44800 - 2.43607i) q^{46} +(6.37901 + 2.32177i) q^{47} +(6.63762 + 1.98544i) q^{48} +(-4.77819 - 4.00937i) q^{49} +(2.83782 - 4.19275i) q^{50} +(-2.98531 + 2.47970i) q^{51} +(-1.58312 + 11.0085i) q^{52} -3.50342i q^{53} +(-1.89565 + 7.09975i) q^{54} +1.22281 q^{55} +(2.18630 - 1.14903i) q^{56} +(-4.73924 + 0.811297i) q^{57} +(-1.97109 - 1.33411i) q^{58} +(-7.30225 + 8.70248i) q^{59} +(2.15875 + 3.51854i) q^{60} +(1.86712 - 5.12986i) q^{61} +(1.64900 + 0.737347i) q^{62} +(1.28713 + 2.28166i) q^{63} +(-0.759738 - 7.96384i) q^{64} +(-5.07631 + 4.25953i) q^{65} +(1.03746 - 2.28944i) q^{66} +(-7.80090 - 1.37551i) q^{67} +(3.94992 + 2.11647i) q^{68} +(-7.30899 - 0.0364666i) q^{69} +(1.42732 + 0.358299i) q^{70} +(4.40148 - 7.62359i) q^{71} +(8.41924 - 1.05658i) q^{72} +(-5.37419 - 9.30837i) q^{73} +(-3.95405 - 13.8732i) q^{74} +(1.10719 - 6.10104i) q^{75} +(2.92702 + 4.71777i) q^{76} +(-0.306470 - 0.842019i) q^{77} +(3.66818 + 13.1182i) q^{78} +(1.26481 + 7.17310i) q^{79} +(2.82638 - 3.83823i) q^{80} +(1.38565 + 8.89269i) q^{81} +(12.7702 - 9.24687i) q^{82} +(6.42315 - 1.13258i) q^{83} +(1.88180 - 2.36835i) q^{84} +(0.913202 + 2.50900i) q^{85} +(-0.0883878 + 1.23557i) q^{86} +(-2.86821 - 0.520511i) q^{87} +(-2.90010 - 0.115227i) q^{88} +(-7.39005 - 12.7999i) q^{89} +(4.15838 + 2.87548i) q^{90} +(4.20535 + 2.42796i) q^{91} +(3.13653 + 7.83534i) q^{92} +(2.21228 + 0.0110377i) q^{93} +(-4.19465 - 8.63538i) q^{94} +(-0.574433 + 3.25777i) q^{95} +(-4.78829 - 8.54823i) q^{96} +(11.6240 - 9.75374i) q^{97} +(0.908008 + 8.77427i) q^{98} +(0.0307177 - 3.07829i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

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