LMFDB - Embedded newform 81.2.g.a.22.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(4,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("81.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			22.8
Character	$\chi$	$=$	81.22
Dual form			81.2.g.a.70.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71221 + 1.81484i) q^{2} +(-1.10419 - 1.33445i) q^{3} +(-0.245679 + 4.21814i) q^{4} +(1.39804 - 0.163408i) q^{5} +(0.531205 - 4.28879i) q^{6} +(-2.85083 - 1.43174i) q^{7} +(-4.25325 + 3.56890i) q^{8} +(-0.561524 + 2.94698i) q^{9} +(2.69030 + 2.25743i) q^{10} +(-1.87624 - 4.34961i) q^{11} +(5.90018 - 4.32979i) q^{12} +(2.07522 + 0.491837i) q^{13} +(-2.28284 - 7.62523i) q^{14} +(-1.76177 - 1.68519i) q^{15} +(-5.36597 - 0.627192i) q^{16} +(0.520249 - 2.95048i) q^{17} +(-6.30973 + 4.02677i) q^{18} +(1.23380 + 6.99724i) q^{19} +(0.345808 + 5.93730i) q^{20} +(1.23727 + 5.38521i) q^{21} +(4.68131 - 10.8525i) q^{22} +(-2.70239 + 1.35719i) q^{23} +(9.45892 + 1.73501i) q^{24} +(-2.93740 + 0.696176i) q^{25} +(2.66061 + 4.60832i) q^{26} +(4.55263 - 2.50470i) q^{27} +(6.73968 - 11.6735i) q^{28} +(-0.631591 + 2.10966i) q^{29} +(0.0418260 - 6.08272i) q^{30} +(3.14652 + 2.06950i) q^{31} +(-1.41830 - 1.90511i) q^{32} +(-3.73262 + 7.30654i) q^{33} +(6.24541 - 4.10767i) q^{34} +(-4.21955 - 1.53579i) q^{35} +(-12.2928 - 3.09260i) q^{36} +(-6.31317 + 2.29781i) q^{37} +(-10.5863 + 14.2199i) q^{38} +(-1.63511 - 3.31237i) q^{39} +(-5.36304 + 5.68449i) q^{40} +(2.90628 - 3.08048i) q^{41} +(-7.65481 + 11.4661i) q^{42} +(0.474097 - 0.636822i) q^{43} +(18.8082 - 6.84563i) q^{44} +(-0.303475 + 4.21177i) q^{45} +(-7.09015 - 2.58060i) q^{46} +(4.83370 - 3.17917i) q^{47} +(5.08810 + 7.85317i) q^{48} +(1.89725 + 2.54844i) q^{49} +(-6.29289 - 4.13890i) q^{50} +(-4.51172 + 2.56364i) q^{51} +(-2.58448 + 8.63275i) q^{52} +(4.83254 - 8.37020i) q^{53} +(12.3407 + 3.97371i) q^{54} +(-3.33382 - 5.77435i) q^{55} +(17.2350 - 4.08478i) q^{56} +(7.97512 - 9.37273i) q^{57} +(-4.91010 + 2.46595i) q^{58} +(-0.636054 + 1.47454i) q^{59} +(7.54120 - 7.01737i) q^{60} +(0.0674875 + 1.15872i) q^{61} +(1.63170 + 9.25383i) q^{62} +(5.82012 - 7.59739i) q^{63} +(-0.847235 + 4.80491i) q^{64} +(2.98162 + 0.348502i) q^{65} +(-19.6512 + 5.73625i) q^{66} +(1.71558 + 5.73045i) q^{67} +(12.3177 + 2.91935i) q^{68} +(4.79507 + 2.10761i) q^{69} +(-4.43754 - 10.2874i) q^{70} +(2.74773 + 2.30562i) q^{71} +(-8.12917 - 14.5383i) q^{72} +(8.55952 - 7.18229i) q^{73} +(-14.9796 - 7.52304i) q^{74} +(4.17246 + 3.15111i) q^{75} +(-29.8185 + 3.48528i) q^{76} +(-0.878675 + 15.0863i) q^{77} +(3.21175 - 8.63892i) q^{78} +(-3.21730 - 3.41014i) q^{79} -7.60435 q^{80} +(-8.36938 - 3.30960i) q^{81} +10.5667 q^{82} +(-10.2659 - 10.8812i) q^{83} +(-23.0196 + 3.89596i) q^{84} +(0.245199 - 4.20991i) q^{85} +(1.96748 - 0.229966i) q^{86} +(3.51264 - 1.48664i) q^{87} +(23.5034 + 11.8038i) q^{88} +(3.17449 - 2.66371i) q^{89} +(-8.16328 + 6.66067i) q^{90} +(-5.21193 - 4.37333i) q^{91} +(-5.06091 - 11.7325i) q^{92} +(-0.712713 - 6.48400i) q^{93} +(14.0460 + 3.32896i) q^{94} +(2.86831 + 9.58083i) q^{95} +(-0.976202 + 3.99627i) q^{96} +(-12.5027 - 1.46135i) q^{97} +(-1.37652 + 7.80666i) q^{98} +(13.8718 - 3.08682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	1.71221	+	1.81484i	1.21071	+	1.28328i	0.947949	+	0.318423i	$0.103153\pi$
$2$	1.71221	+	1.81484i	1.21071	+	1.28328i	0.262766	+	0.964860i	$0.415365\pi$
$3$	−1.10419	−	1.33445i	−0.637505	−	0.770446i
$3$	−1.10419	−	1.33445i	−0.637505	−	0.770446i
$4$	−0.245679	+	4.21814i	−0.122839	+	2.10907i
$5$	1.39804	−	0.163408i	0.625224	−	0.0730783i	0.202419	−	0.979299i	$-0.435120\pi$
$5$	1.39804	−	0.163408i	0.625224	−	0.0730783i	0.422805	+	0.906221i	$0.361046\pi$
$6$	0.531205	−	4.28879i	0.216863	−	1.75089i
$7$	−2.85083	−	1.43174i	−1.07751	−	0.541147i	−0.180691	−	0.983540i	$-0.557834\pi$
$7$	−2.85083	−	1.43174i	−1.07751	−	0.541147i	−0.896822	+	0.442393i	$0.854130\pi$
$8$	−4.25325	+	3.56890i	−1.50375	+	1.26180i
$9$	−0.561524	+	2.94698i	−0.187175	+	0.982327i
$10$	2.69030	+	2.25743i	0.850749	+	0.713863i
$11$	−1.87624	−	4.34961i	−0.565707	−	1.31146i	−0.925615	−	0.378468i	$-0.876451\pi$
$11$	−1.87624	−	4.34961i	−0.565707	−	1.31146i	0.359908	−	0.932988i	$-0.382808\pi$
$12$	5.90018	−	4.32979i	1.70324	−	1.24990i
$13$	2.07522	+	0.491837i	0.575563	+	0.136411i	0.508081	−	0.861309i	$-0.330355\pi$
$13$	2.07522	+	0.491837i	0.575563	+	0.136411i	0.0674826	+	0.997720i	$0.478503\pi$
$14$	−2.28284	−	7.62523i	−0.610116	−	2.03793i
$15$	−1.76177	−	1.68519i	−0.454887	−	0.435114i
$16$	−5.36597	−	0.627192i	−1.34149	−	0.156798i
$17$	0.520249	−	2.95048i	0.126179	−	0.715596i	−0.854422	−	0.519580i	$-0.826088\pi$
$17$	0.520249	−	2.95048i	0.126179	−	0.715596i	0.980601	−	0.196016i	$-0.0628004\pi$
$18$	−6.30973	+	4.02677i	−1.48722	+	0.949120i
$19$	1.23380	+	6.99724i	0.283053	+	1.60528i	0.712157	+	0.702020i	$0.247718\pi$
$19$	1.23380	+	6.99724i	0.283053	+	1.60528i	−0.429103	+	0.903255i	$0.641170\pi$
$20$	0.345808	+	5.93730i	0.0773250	+	1.32762i
$21$	1.23727	+	5.38521i	0.269995	+	1.17515i
$22$	4.68131	−	10.8525i	0.998059	−	2.31376i
$23$	−2.70239	+	1.35719i	−0.563488	+	0.282994i	−0.707654	−	0.706559i	$-0.750246\pi$
$23$	−2.70239	+	1.35719i	−0.563488	+	0.282994i	0.144166	+	0.989554i	$0.453950\pi$
$24$	9.45892	+	1.73501i	1.93079	+	0.354157i
$25$	−2.93740	+	0.696176i	−0.587480	+	0.139235i
$26$	2.66061	+	4.60832i	0.521789	+	0.903765i
$27$	4.55263	−	2.50470i	0.876155	−	0.482030i
$28$	6.73968	−	11.6735i	1.27368	−	2.20608i
$29$	−0.631591	+	2.10966i	−0.117284	+	0.391754i	−0.996392	−	0.0848670i	$-0.972953\pi$
$29$	−0.631591	+	2.10966i	−0.117284	+	0.391754i	0.879109	+	0.476621i	$0.158139\pi$
$30$	0.0418260	−	6.08272i	0.00763634	−	1.11055i
$31$	3.14652	+	2.06950i	0.565132	+	0.371693i	0.799694	−	0.600408i	$-0.204995\pi$
$31$	3.14652	+	2.06950i	0.565132	+	0.371693i	−0.234562	+	0.972101i	$0.575366\pi$
$32$	−1.41830	−	1.90511i	−0.250723	−	0.336779i
$33$	−3.73262	+	7.30654i	−0.649765	+	1.27191i
$34$	6.24541	−	4.10767i	1.07108	−	0.704459i
$35$	−4.21955	−	1.53579i	−0.713233	−	0.259596i
$36$	−12.2928	−	3.09260i	−2.04880	−	0.515433i
$37$	−6.31317	+	2.29781i	−1.03788	+	0.377757i	−0.804076	−	0.594527i	$-0.797339\pi$
$37$	−6.31317	+	2.29781i	−1.03788	+	0.377757i	−0.233803	+	0.972284i	$0.575117\pi$
$38$	−10.5863	+	14.2199i	−1.71733	+	2.30677i
$39$	−1.63511	−	3.31237i	−0.261827	−	0.530403i
$40$	−5.36304	+	5.68449i	−0.847971	+	0.898797i
$41$	2.90628	−	3.08048i	0.453884	−	0.481089i	−0.459506	−	0.888175i	$-0.651973\pi$
$41$	2.90628	−	3.08048i	0.453884	−	0.481089i	0.913390	+	0.407085i	$0.133455\pi$
$42$	−7.65481	+	11.4661i	−1.18116	+	1.76925i
$43$	0.474097	−	0.636822i	0.0722991	−	0.0971145i	−0.764503	−	0.644621i	$-0.777015\pi$
$43$	0.474097	−	0.636822i	0.0722991	−	0.0971145i	0.836802	+	0.547506i	$0.184423\pi$
$44$	18.8082	−	6.84563i	2.83544	−	1.03202i
$45$	−0.303475	+	4.21177i	−0.0452394	+	0.627853i
$46$	−7.09015	−	2.58060i	−1.04538	−	0.380489i
$47$	4.83370	−	3.17917i	0.705067	−	0.463730i	−0.145662	−	0.989334i	$-0.546531\pi$
$47$	4.83370	−	3.17917i	0.705067	−	0.463730i	0.850729	+	0.525605i	$0.176161\pi$
$48$	5.08810	+	7.85317i	0.734404	+	1.13351i
$49$	1.89725	+	2.54844i	0.271035	+	0.364063i
$50$	−6.29289	−	4.13890i	−0.889949	−	0.585328i
$51$	−4.51172	+	2.56364i	−0.631768	+	0.358982i
$52$	−2.58448	+	8.63275i	−0.358402	+	1.19715i
$53$	4.83254	−	8.37020i	0.663800	−	1.14973i	−0.315809	−	0.948823i	$-0.602276\pi$
$53$	4.83254	−	8.37020i	0.663800	−	1.14973i	0.979609	−	0.200912i	$-0.0643906\pi$
$54$	12.3407	+	3.97371i	1.67935	+	0.540753i
$55$	−3.33382	−	5.77435i	−0.449532	−	0.778613i
$56$	17.2350	−	4.08478i	2.30313	−	0.545851i
$57$	7.97512	−	9.37273i	1.05633	−	1.24145i
$58$	−4.91010	+	2.46595i	−0.644728	+	0.323795i
$59$	−0.636054	+	1.47454i	−0.0828072	+	0.191969i	−0.954589	−	0.297926i	$-0.903705\pi$
$59$	−0.636054	+	1.47454i	−0.0828072	+	0.191969i	0.871782	+	0.489894i	$0.162965\pi$
$60$	7.54120	−	7.01737i	0.973564	−	0.905939i
$61$	0.0674875	+	1.15872i	0.00864089	+	0.148358i	0.999869	+	0.0161951i	$0.00515528\pi$
$61$	0.0674875	+	1.15872i	0.00864089	+	0.148358i	−0.991228	+	0.132163i	$0.957808\pi$
$62$	1.63170	+	9.25383i	0.207226	+	1.17524i
$63$	5.82012	−	7.59739i	0.733266	−	0.957181i
$64$	−0.847235	+	4.80491i	−0.105904	+	0.600613i
$65$	2.98162	+	0.348502i	0.369825	+	0.0432263i
$66$	−19.6512	+	5.73625i	−2.41890	+	0.706083i
$67$	1.71558	+	5.73045i	0.209592	+	0.700085i	0.996544	+	0.0830710i	$0.0264728\pi$
$67$	1.71558	+	5.73045i	0.209592	+	0.700085i	−0.786952	+	0.617014i	$0.788342\pi$
$68$	12.3177	+	2.91935i	1.49374	+	0.354024i
$69$	4.79507	+	2.10761i	0.577258	+	0.253727i
$70$	−4.43754	−	10.2874i	−0.530388	−	1.22958i
$71$	2.74773	+	2.30562i	0.326095	+	0.273626i	0.791107	−	0.611678i	$-0.209505\pi$
$71$	2.74773	+	2.30562i	0.326095	+	0.273626i	−0.465011	+	0.885305i	$0.653950\pi$
$72$	−8.12917	−	14.5383i	−0.958032	−	1.71335i
$73$	8.55952	−	7.18229i	1.00182	−	0.840623i	0.0145810	−	0.999894i	$-0.495359\pi$
$73$	8.55952	−	7.18229i	1.00182	−	0.840623i	0.987235	+	0.159270i	$0.0509141\pi$
$74$	−14.9796	−	7.52304i	−1.74134	−	0.874536i
$75$	4.17246	+	3.15111i	0.481795	+	0.363858i
$76$	−29.8185	+	3.48528i	−3.42041	+	0.399789i
$77$	−0.878675	+	15.0863i	−0.100134	+	1.71924i
$78$	3.21175	−	8.63892i	0.363659	−	0.978165i
$79$	−3.21730	−	3.41014i	−0.361975	−	0.383671i	0.520633	−	0.853780i	$-0.325696\pi$
$79$	−3.21730	−	3.41014i	−0.361975	−	0.383671i	−0.882608	+	0.470110i	$0.844214\pi$
$80$	−7.60435			−0.850192
$81$	−8.36938	−	3.30960i	−0.929931	−	0.367733i
$82$	10.5667			1.16690
$83$	−10.2659	−	10.8812i	−1.12683	−	1.19437i	−0.978677	−	0.205406i	$-0.934148\pi$
$83$	−10.2659	−	10.8812i	−1.12683	−	1.19437i	−0.148154	−	0.988964i	$-0.547333\pi$
$84$	−23.0196	+	3.89596i	−2.51164	+	0.425084i
$85$	0.245199	−	4.20991i	0.0265956	−	0.456629i
$86$	1.96748	−	0.229966i	0.212159	−	0.0247978i
$87$	3.51264	−	1.48664i	0.376594	−	0.159385i
$88$	23.5034	+	11.8038i	2.50547	+	1.25829i
$89$	3.17449	−	2.66371i	0.336495	−	0.282353i	−0.458845	−	0.888516i	$-0.651737\pi$
$89$	3.17449	−	2.66371i	0.336495	−	0.282353i	0.795340	+	0.606164i	$0.207292\pi$
$90$	−8.16328	+	6.66067i	−0.860485	+	0.702096i
$91$	−5.21193	−	4.37333i	−0.546358	−	0.458449i
$92$	−5.06091	−	11.7325i	−0.527637	−	1.22320i
$93$	−0.712713	−	6.48400i	−0.0739049	−	0.672360i
$94$	14.0460	+	3.32896i	1.44873	+	0.343356i
$95$	2.86831	+	9.58083i	0.294283	+	0.982973i
$96$	−0.976202	+	3.99627i	−0.0996332	+	0.407867i
$97$	−12.5027	−	1.46135i	−1.26946	−	0.148378i	−0.545433	−	0.838154i	$-0.683635\pi$
$97$	−12.5027	−	1.46135i	−1.26946	−	0.148378i	−0.724023	+	0.689776i	$0.757709\pi$
$98$	−1.37652	+	7.80666i	−0.139050	+	0.788591i
$99$	13.8718	−	3.08682i	1.39416	−	0.310238i
$100$	−2.21491	−	12.5614i	−0.221491	−	1.25614i
$101$	0.261942	+	4.49737i	0.0260642	+	0.447505i	0.985942	+	0.167087i	$0.0534361\pi$
$101$	0.261942	+	4.49737i	0.0260642	+	0.447505i	−0.959878	+	0.280418i	$0.909527\pi$
$102$	−12.3776	−	3.79854i	−1.22557	−	0.376112i
$103$	5.52933	−	12.8184i	0.544821	−	1.26304i	−0.394152	−	0.919045i	$-0.628962\pi$
$103$	5.52933	−	12.8184i	0.544821	−	1.26304i	0.938973	−	0.343992i	$-0.111779\pi$
$104$	−10.5817	+	5.31435i	−1.03763	+	0.521115i
$105$	2.60975	+	7.32659i	0.254685	+	0.715002i
$106$	23.4648	−	5.56127i	2.27911	−	0.540158i
$107$	−2.27719	−	3.94420i	−0.220144	−	0.381301i	0.734708	−	0.678384i	$-0.237319\pi$
$107$	−2.27719	−	3.94420i	−0.220144	−	0.381301i	−0.954852	+	0.297083i	$0.903986\pi$
$108$	9.44671	+	19.8190i	0.909010	+	1.90708i
$109$	−3.56879	+	6.18132i	−0.341828	+	0.592063i	−0.984772	−	0.173850i	$-0.944379\pi$
$109$	−3.56879	+	6.18132i	−0.341828	+	0.592063i	0.642944	+	0.765913i	$0.277713\pi$
$110$	4.77129	−	15.9372i	0.454925	−	1.51956i
$111$	10.0373	+	5.88741i	0.952695	+	0.558808i
$112$	14.3995	+	9.47070i	1.36062	+	0.894897i
$113$	4.67557	+	6.28038i	0.439840	+	0.590808i	0.965667	−	0.259784i	$-0.0836513\pi$
$113$	4.67557	+	6.28038i	0.439840	+	0.590808i	−0.525826	+	0.850592i	$0.676244\pi$
$114$	30.6651	−	1.57455i	2.87205	−	0.147470i
$115$	−3.55629	+	2.33901i	−0.331626	+	0.218114i
$116$	−8.74368	−	3.18244i	−0.811830	−	0.295482i
$117$	−2.61472	+	5.83946i	−0.241731	+	0.539859i
$118$	−3.76510	+	1.37039i	−0.346606	+	0.126154i
$119$	−5.70746	+	7.66645i	−0.523202	+	0.702782i
$120$	13.5075	+	0.879955i	1.23306	+	0.0803285i
$121$	−7.85014	+	8.32067i	−0.713649	+	0.756424i
$122$	−1.98733	+	2.10644i	−0.179924	+	0.190708i
$123$	−7.31983	−	0.476855i	−0.660007	−	0.0429966i
$124$	−9.50247	+	12.7640i	−0.853347	+	1.14624i
$125$	−10.6062	+	3.86035i	−0.948650	+	0.345280i
$126$	23.7533	−	2.44575i	2.11611	−	0.217885i
$127$	9.61531	+	3.49969i	0.853220	+	0.310547i	0.731353	−	0.681999i	$-0.238889\pi$
$127$	9.61531	+	3.49969i	0.853220	+	0.310547i	0.121868	+	0.992546i	$0.461112\pi$
$128$	−14.1395	+	9.29968i	−1.24976	+	0.821983i
$129$	−1.37330	+	0.0705144i	−0.120913	+	0.00620845i
$130$	4.47269	+	6.00787i	0.392281	+	0.526925i
$131$	−7.19028	−	4.72912i	−0.628218	−	0.413185i	0.195086	−	0.980786i	$-0.437501\pi$
$131$	−7.19028	−	4.72912i	−0.628218	−	0.413185i	−0.823304	+	0.567601i	$0.807872\pi$
$132$	−29.9030	−	17.5398i	−2.60272	−	1.52664i
$133$	6.50087	−	21.7144i	0.563697	−	1.88288i
$134$	−7.46238	+	12.9252i	−0.644652	+	1.11657i
$135$	5.95549	−	4.24562i	0.512567	−	0.365405i
$136$	8.31720	+	14.4058i	0.713194	+	1.23529i
$137$	1.03986	−	0.246452i	0.0888413	−	0.0210558i	−0.185955	−	0.982558i	$-0.559538\pi$
$137$	1.03986	−	0.246452i	0.0888413	−	0.0210558i	0.274796	+	0.961503i	$0.411390\pi$
$138$	4.38519	+	12.3109i	0.373292	+	1.04798i
$139$	−6.65577	+	3.34265i	−0.564535	+	0.283520i	−0.708090	−	0.706122i	$-0.750443\pi$
$139$	−6.65577	+	3.34265i	−0.564535	+	0.283520i	0.143555	+	0.989642i	$0.454147\pi$
$140$	7.51483	−	17.4213i	0.635119	−	1.47237i
$141$	−9.57978	−	2.93992i	−0.806763	−	0.247586i
$142$	0.520368	+	8.93437i	0.0436683	+	0.749756i
$143$	−1.75431	−	9.94920i	−0.146703	−	0.831994i
$144$	4.86144	−	15.4612i	0.405120	−	1.28844i
$145$	−0.538257	+	3.05261i	−0.0446998	+	0.253505i
$146$	27.6904	+	3.23654i	2.29167	+	0.267858i
$147$	1.30585	−	5.34575i	0.107705	−	0.440910i
$148$	−8.14146	−	27.1944i	−0.669224	−	2.23536i
$149$	−2.37562	−	0.563032i	−0.194618	−	0.0461254i	0.132151	−	0.991230i	$-0.457812\pi$
$149$	−2.37562	−	0.563032i	−0.194618	−	0.0461254i	−0.326769	+	0.945104i	$0.605960\pi$
$150$	1.42539	+	12.9677i	0.116383	+	1.05881i
$151$	8.46731	+	19.6294i	0.689060	+	1.59742i	0.797501	+	0.603318i	$0.206155\pi$
$151$	8.46731	+	19.6294i	0.689060	+	1.59742i	−0.108440	+	0.994103i	$0.534586\pi$
$152$	−30.2201	−	25.3577i	−2.45117	−	2.05678i
$153$	8.40287	+	3.18993i	0.679331	+	0.257890i
$154$	−28.8836	+	24.2362i	−2.32751	+	1.95301i
$155$	4.73715	+	2.37908i	0.380497	+	0.191093i
$156$	14.3737	−	6.08335i	1.15082	−	0.487058i
$157$	6.41788	−	0.750143i	0.512203	−	0.0598679i	0.143934	−	0.989587i	$-0.454025\pi$
$157$	6.41788	−	0.750143i	0.512203	−	0.0598679i	0.368269	+	0.929719i	$0.379951\pi$
$158$	0.680151	−	11.6777i	0.0541099	−	0.929031i
$159$	−16.5057	+	2.79351i	−1.30898	+	0.221540i
$160$	−2.29416	−	2.43167i	−0.181369	−	0.192240i
$161$	9.64722			0.760307
$162$	−8.32376	−	20.8558i	−0.653976	−	1.63858i
$163$	−6.49040			−0.508367			−0.254184	−	0.967156i	$-0.581807\pi$
$163$	−6.49040			−0.508367			−0.254184	+	0.967156i	$0.581807\pi$
$164$	12.2799	+	13.0159i	0.958897	+	1.01637i
$165$	−4.02441	+	10.8248i	−0.313300	+	0.842710i
$166$	2.17026	−	37.2619i	0.168445	−	2.89208i
$167$	3.87721	−	0.453181i	0.300028	−	0.0350682i	0.0352527	−	0.999378i	$-0.488776\pi$
$167$	3.87721	−	0.453181i	0.300028	−	0.0350682i	0.264775	+	0.964310i	$0.414702\pi$
$168$	−24.4817	−	18.4889i	−1.88880	−	1.42645i
$169$	−7.55258	−	3.79305i	−0.580967	−	0.291773i
$170$	8.06013	−	6.76325i	0.618184	−	0.518718i
$171$	−21.3135	−	0.293126i	−1.62989	−	0.0224159i
$172$	2.56973	+	2.15626i	0.195940	+	0.164413i
$173$	6.46827	+	14.9951i	0.491774	+	1.14006i	0.965739	+	0.259516i	$0.0835630\pi$
$173$	6.46827	+	14.9951i	0.491774	+	1.14006i	−0.473965	+	0.880544i	$0.657178\pi$
$174$	8.71238	+	3.82942i	0.660484	+	0.290308i
$175$	9.37077	+	2.22091i	0.708364	+	0.167885i
$176$	7.33979	+	24.5166i	0.553258	+	1.84801i
$177$	2.67003	−	0.779389i	0.200691	−	0.0585825i
$178$	10.2696	+	1.20034i	0.769737	+	0.0899694i
$179$	−3.76729	+	21.3654i	−0.281581	+	1.59692i	0.435670	+	0.900107i	$0.356512\pi$
$179$	−3.76729	+	21.3654i	−0.281581	+	1.59692i	−0.717250	+	0.696816i	$0.754599\pi$
$180$	−17.6913	−	2.31484i	−1.31863	−	0.172538i
$181$	−1.10326	−	6.25687i	−0.0820043	−	0.465070i	−0.997963	−	0.0637968i	$-0.979679\pi$
$181$	−1.10326	−	6.25687i	−0.0820043	−	0.465070i	0.915959	−	0.401273i	$-0.131432\pi$
$182$	−0.987041	−	16.9468i	−0.0731644	−	1.25618i
$183$	1.47173	−	1.36950i	0.108794	−	0.101237i
$184$	6.65026	−	15.4170i	0.490264	−	1.13656i
$185$	−8.45061	+	4.24406i	−0.621301	+	0.312029i
$186$	10.5471	−	12.3954i	0.773350	−	0.908877i
$187$	−13.8095	+	3.27292i	−1.00985	+	0.239339i
$188$	12.2227	+	21.1703i	0.891429	+	1.54400i
$189$	−16.5649	+	0.622293i	−1.20492	+	0.0452652i
$190$	−12.4765	+	21.6099i	−0.905139	+	1.56775i
$191$	−3.95814	+	13.2211i	−0.286401	+	0.956646i	0.686830	+	0.726818i	$0.259002\pi$
$191$	−3.95814	+	13.2211i	−0.286401	+	0.956646i	−0.973231	+	0.229828i	$0.926184\pi$
$192$	7.34743	−	4.17494i	0.530255	−	0.301301i
$193$	−3.15541	−	2.07534i	−0.227131	−	0.149387i	0.430843	−	0.902427i	$-0.358216\pi$
$193$	−3.15541	−	2.07534i	−0.227131	−	0.149387i	−0.657974	+	0.753040i	$0.728587\pi$
$194$	−18.7551	−	25.1925i	−1.34654	−	1.80871i
$195$	−2.82722	−	4.36365i	−0.202462	−	0.312487i
$196$	−11.2158	+	7.37675i	−0.801129	+	0.526911i
$197$	−5.18414	−	1.88687i	−0.369355	−	0.134434i	0.150673	−	0.988584i	$-0.451856\pi$
$197$	−5.18414	−	1.88687i	−0.369355	−	0.134434i	−0.520027	+	0.854150i	$0.674078\pi$
$198$	29.3534	+	19.8897i	2.08606	+	1.41350i
$199$	15.9504	−	5.80546i	1.13069	−	0.411538i	0.292148	−	0.956373i	$-0.405630\pi$
$199$	15.9504	−	5.80546i	1.13069	−	0.411538i	0.838543	+	0.544835i	$0.183408\pi$
$200$	10.0089	−	13.4443i	0.707736	−	0.950654i
$201$	5.75267	−	8.61687i	0.405762	−	0.607787i
$202$	−7.71350	+	8.17583i	−0.542720	+	0.575249i
$203$	4.82105	−	5.11001i	0.338371	−	0.358653i
$204$	−9.70538	−	19.6609i	−0.679513	−	1.37654i
$205$	3.55973	−	4.78155i	0.248622	−	0.333958i
$206$	32.7307	−	11.9130i	2.28046	−	0.830018i
$207$	−2.48216	−	8.72599i	−0.172522	−	0.606499i
$208$	−10.8271	−	3.94075i	−0.750725	−	0.273242i
$209$	28.1203	−	18.4950i	1.94512	−	1.27933i
$210$	−8.82812	+	17.2809i	−0.609198	+	1.19250i
$211$	11.5293	+	15.4866i	0.793712	+	1.06614i	0.996221	+	0.0868601i	$0.0276833\pi$
$211$	11.5293	+	15.4866i	0.793712	+	1.06614i	−0.202508	+	0.979281i	$0.564909\pi$
$212$	34.1194	+	22.4407i	2.34333	+	1.54123i
$213$	0.0427187	−	6.21255i	0.00292704	−	0.425677i
$214$	3.25906	−	10.8860i	0.222785	−	0.744153i
$215$	0.558746	−	0.967777i	0.0381062	−	0.0660018i
$216$	−10.4244	+	26.9010i	−0.709293	+	1.83038i
$217$	−6.00721	−	10.4048i	−0.407796	−	0.706323i
$218$	−17.3286	+	4.10695i	−1.17364	+	0.278158i
$219$	−19.0358	−	3.49165i	−1.28632	−	0.235944i
$220$	25.1761	−	12.6439i	1.69737	−	0.852452i
$221$	2.53079	−	5.86702i	0.170239	−	0.394659i
$222$	6.50122	+	28.2965i	0.436333	+	1.89913i
$223$	0.880079	+	15.1104i	0.0589345	+	1.01187i	0.890078	+	0.455808i	$0.150650\pi$
$223$	0.880079	+	15.1104i	0.0589345	+	1.01187i	−0.831144	+	0.556058i	$0.812313\pi$
$224$	1.31572	+	7.46180i	0.0879100	+	0.498562i
$225$	−0.402198	−	9.04737i	−0.0268132	−	0.603158i
$226$	−3.39230	+	19.2387i	−0.225653	+	1.27974i
$227$	−6.25901	−	0.731573i	−0.415425	−	0.0485562i	−0.0941866	−	0.995555i	$-0.530025\pi$
$227$	−6.25901	−	0.731573i	−0.415425	−	0.0485562i	−0.321238	+	0.946998i	$0.604099\pi$
$228$	37.5762	+	35.9429i	2.48854	+	2.38038i
$229$	−2.67203	−	8.92519i	−0.176572	−	0.589793i	−0.999758	−	0.0220199i	$-0.992990\pi$
$229$	−2.67203	−	8.92519i	−0.176572	−	0.589793i	0.823185	−	0.567773i	$-0.192195\pi$
$230$	−10.3340	−	2.44921i	−0.681406	−	0.161496i
$231$	21.1021	−	15.4856i	1.38842	−	1.01888i
$232$	−4.84285	−	11.2270i	−0.317949	−	0.737088i
$233$	−16.1221	−	13.5280i	−1.05619	−	0.886251i	−0.0624612	−	0.998047i	$-0.519895\pi$
$233$	−16.1221	−	13.5280i	−1.05619	−	0.886251i	−0.993731	+	0.111797i	$0.964339\pi$
$234$	−15.0746	+	5.25309i	−0.985458	+	0.343406i
$235$	6.23822	−	5.23449i	0.406937	−	0.341460i
$236$	−6.06355	−	3.04523i	−0.394703	−	0.198227i
$237$	−0.998152	+	8.05878i	−0.0648369	+	0.523474i
$238$	−23.6857	+	2.76846i	−1.53532	+	0.179453i
$239$	0.953580	−	16.3723i	0.0616819	−	1.05904i	−0.815462	−	0.578811i	$-0.803517\pi$
$239$	0.953580	−	16.3723i	0.0616819	−	1.05904i	0.877144	−	0.480227i	$-0.159446\pi$
$240$	8.39666	+	10.1476i	0.542002	+	0.655027i
$241$	−1.13385	−	1.20181i	−0.0730377	−	0.0774155i	0.689824	−	0.723977i	$-0.257688\pi$
$241$	−1.13385	−	1.20181i	−0.0730377	−	0.0774155i	−0.762862	+	0.646562i	$0.776206\pi$
$242$	−28.5417			−1.83473
$243$	4.82490	+	14.8230i	0.309517	+	0.950894i
$244$	−4.90421			−0.313960
$245$	3.06887	+	3.25281i	0.196063	+	0.207814i
$246$	−11.6677	−	14.1008i	−0.743904	−	0.899032i
$247$	−0.881085	+	15.1277i	−0.0560621	+	0.962549i
$248$	−20.7688	+	2.42752i	−1.31882	+	0.154148i
$249$	−3.18495	+	25.7143i	−0.201838	+	1.62958i
$250$	−25.1660	−	12.6388i	−1.59164	−	0.799350i
$251$	−16.6349	+	13.9583i	−1.04998	+	0.881040i	−0.993092	−	0.117340i	$-0.962563\pi$
$251$	−16.6349	+	13.9583i	−1.04998	+	0.881040i	−0.0568910	+	0.998380i	$0.518119\pi$
$252$	30.6170	+	26.4166i	1.92869	+	1.66409i
$253$	10.9736	+	9.20793i	0.689903	+	0.578898i
$254$	10.1121	+	23.4424i	0.634487	+	1.47091i
$255$	−5.88867	+	4.32134i	−0.368763	+	0.270613i
$256$	−31.5921	−	7.48747i	−1.97451	−	0.467967i
$257$	−1.76523	−	5.89628i	−0.110112	−	0.367800i	0.885117	−	0.465369i	$-0.154078\pi$
$257$	−1.76523	−	5.89628i	−0.110112	−	0.367800i	−0.995229	+	0.0975692i	$0.968893\pi$
$258$	−2.47935	−	2.37158i	−0.154358	−	0.147648i
$259$	21.2876	+	2.48817i	1.32275	+	0.154607i
$260$	−2.20255	+	12.4913i	−0.136596	+	0.774677i
$261$	−5.86248	−	3.04591i	−0.362878	−	0.188537i
$262$	−3.72869	−	21.1464i	−0.230359	−	1.30643i
$263$	−1.48444	−	25.4869i	−0.0915345	−	1.57159i	−0.661517	−	0.749930i	$-0.730087\pi$
$263$	−1.48444	−	25.4869i	−0.0915345	−	1.57159i	0.569983	−	0.821657i	$-0.306950\pi$
$264$	−10.2006	−	44.3978i	−0.627802	−	2.73250i
$265$	5.38834	−	12.4916i	0.331003	−	0.767352i
$266$	50.5390	−	25.3816i	3.09874	−	1.55625i
$267$	−7.05983	−	1.29495i	−0.432055	−	0.0792499i
$268$	−24.5933	+	5.82872i	−1.50228	+	0.356046i
$269$	8.19176	+	14.1885i	0.499460	+	0.865091i	1.00000		0.000622889i	$-0.000198272\pi$
$269$	8.19176	+	14.1885i	0.499460	+	0.865091i	−0.500539	+	0.865714i	$0.666865\pi$
$270$	17.9022	+	3.53885i	1.08949	+	0.215368i
$271$	13.6365	−	23.6192i	0.828361	−	1.43476i	−0.0709627	−	0.997479i	$-0.522607\pi$
$271$	13.6365	−	23.6192i	0.828361	−	1.43476i	0.899323	−	0.437284i	$-0.144060\pi$
$272$	−4.64215	+	15.5059i	−0.281472	+	0.940182i
$273$	−0.0810295	+	11.7841i	−0.00490413	+	0.713203i
$274$	2.22773	+	1.46520i	0.134582	+	0.0885160i
$275$	8.53935	+	11.4703i	0.514942	+	0.691687i
$276$	−10.0683	+	19.7085i	−0.606038	+	1.18631i
$277$	19.1354	−	12.5855i	1.14973	−	0.756192i	0.176115	−	0.984370i	$-0.443647\pi$
$277$	19.1354	−	12.5855i	1.14973	−	0.756192i	0.973620	+	0.228177i	$0.0732766\pi$
$278$	−17.4624	−	6.35580i	−1.04733	−	0.381196i
$279$	−7.86562	+	8.11066i	−0.470902	+	0.485572i
$280$	23.4278	−	8.52704i	1.40008	−	0.509588i
$281$	17.9072	−	24.0535i	1.06825	−	1.43491i	0.175439	−	0.984490i	$-0.443866\pi$
$281$	17.9072	−	24.0535i	1.06825	−	1.43491i	0.892815	−	0.450424i	$-0.148727\pi$
$282$	−11.0671	−	22.4195i	−0.659037	−	1.33506i
$283$	−10.6483	+	11.2865i	−0.632975	+	0.670914i	−0.961887	−	0.273446i	$-0.911836\pi$
$283$	−10.6483	+	11.2865i	−0.632975	+	0.670914i	0.328912	+	0.944360i	$0.393318\pi$
$284$	−10.4005	+	11.0239i	−0.617155	+	0.654146i
$285$	9.61799	−	14.4067i	0.569721	−	0.853379i
$286$	15.0524	−	20.2189i	0.890068	−	1.19557i
$287$	−12.6958	+	4.62088i	−0.749407	+	0.272762i
$288$	6.41074	−	3.10995i	0.377756	−	0.183255i
$289$	7.54012	+	2.74438i	0.443536	+	0.161434i
$290$	−6.46159	+	4.24985i	−0.379438	+	0.249560i
$291$	11.8553	+	18.2979i	0.694967	+	1.07264i
$292$	28.1930	+	37.8698i	1.64987	+	2.21616i
$293$	6.43251	+	4.23073i	0.375791	+	0.247162i	0.723328	−	0.690505i	$-0.242612\pi$
$293$	6.43251	+	4.23073i	0.375791	+	0.247162i	−0.347537	+	0.937666i	$0.612982\pi$
$294$	11.9376	−	6.78313i	0.696212	−	0.395600i
$295$	−0.648280	+	2.16541i	−0.0377443	+	0.126075i
$296$	18.6508	−	32.3042i	1.08406	−	1.87764i
$297$	−19.4363	−	15.1027i	−1.12781	−	0.876350i
$298$	−3.04574	−	5.27538i	−0.176435	−	0.305595i
$299$	−6.27559	+	1.48734i	−0.362927	+	0.0860152i
$300$	−14.3169	+	16.8259i	−0.826586	+	0.971443i
$301$	−2.26333	+	1.13669i	−0.130456	+	0.0655177i
$302$	−21.1264	+	48.9765i	−1.21569	+	2.81828i
$303$	5.71230	−	5.31551i	0.328163	−	0.305368i
$304$	−2.23193	−	38.3208i	−0.128010	−	2.19785i
$305$	0.283694	+	1.60891i	0.0162443	+	0.0921258i
$306$	8.59827	+	20.7116i	0.491531	+	1.18401i
$307$	2.28454	−	12.9563i	0.130386	−	0.739454i	−0.847577	−	0.530673i	$-0.821939\pi$
$307$	2.28454	−	12.9563i	0.130386	−	0.739454i	0.977962	−	0.208781i	$-0.0669496\pi$
$308$	−63.4202	−	7.41276i	−3.61370	−	0.422381i
$309$	−23.2110	+	6.77537i	−1.32043	+	0.385437i
$310$	3.79334	+	12.6706i	0.215447	+	0.719644i
$311$	−5.33273	−	1.26388i	−0.302391	−	0.0716681i	0.0766191	−	0.997060i	$-0.475587\pi$
$311$	−5.33273	−	1.26388i	−0.302391	−	0.0716681i	−0.379011	+	0.925392i	$0.623736\pi$
$312$	18.7760	+	8.25277i	1.06298	+	0.467221i
$313$	9.57732	+	22.2027i	0.541342	+	1.25497i	0.941031	+	0.338321i	$0.109859\pi$
$313$	9.57732	+	22.2027i	0.541342	+	1.25497i	−0.399688	+	0.916651i	$0.630882\pi$
$314$	12.3501	+	10.3630i	0.696959	+	0.584818i
$315$	6.89532	−	11.5725i	0.388507	−	0.652039i
$316$	15.1749	−	12.7332i	0.853653	−	0.716300i
$317$	9.24502	+	4.64302i	0.519252	+	0.260778i	0.689067	−	0.724698i	$-0.258021\pi$
$317$	9.24502	+	4.64302i	0.519252	+	0.260778i	−0.169815	+	0.985476i	$0.554317\pi$
$318$	−33.3309	−	25.1720i	−1.86911	−	1.41158i
$319$	10.3612	−	1.21105i	0.580116	−	0.0678059i
$320$	−0.399312	+	6.85592i	−0.0223222	+	0.383258i
$321$	−2.74890	+	7.39395i	−0.153429	+	0.412690i
$322$	16.5181	+	17.5081i	0.920515	+	0.975689i
$323$	21.2871			1.18444
$324$	16.0165	−	34.4901i	0.889808	−	1.91612i
$325$	−6.43816			−0.357125
$326$	−11.1129	−	11.7790i	−0.615488	−	0.652379i
$327$	12.1893	−	2.06298i	0.674070	−	0.114083i
$328$	−1.36722	+	23.4742i	−0.0754920	+	1.29615i
$329$	−18.3318	+	2.14268i	−1.01066	+	0.118130i
$330$	−26.5359	+	11.2307i	−1.46075	+	0.618229i
$331$	−27.4917	−	13.8069i	−1.51108	−	0.758894i	−0.515873	−	0.856665i	$-0.672532\pi$
$331$	−27.4917	−	13.8069i	−1.51108	−	0.758894i	−0.995209	+	0.0977711i	$0.968829\pi$
$332$	48.4207	−	40.6298i	2.65743	−	2.22985i
$333$	−3.22659	−	19.8951i	−0.176816	−	1.09024i
$334$	7.46105	+	6.26056i	0.408250	+	0.342563i
$335$	3.33486	+	7.73108i	0.182203	+	0.422394i
$336$	−3.26161	−	29.6729i	−0.177935	−	1.61879i
$337$	−32.0522	−	7.59650i	−1.74599	−	0.413808i	−0.771141	−	0.636664i	$-0.780314\pi$
$337$	−32.0522	−	7.59650i	−1.74599	−	0.413808i	−0.974851	+	0.222856i	$0.928462\pi$
$338$	−6.04784	−	20.2012i	−0.328959	−	1.09880i
$339$	3.21814	−	13.1741i	0.174785	−	0.715517i
$340$	17.6978	+	2.06857i	0.959796	+	0.112184i
$341$	3.09789	−	17.5690i	0.167760	−	0.951414i
$342$	−35.9612	−	39.1824i	−1.94456	−	2.11874i
$343$	2.11774	+	12.0103i	0.114347	+	0.648496i
$344$	0.256304	+	4.40056i	0.0138190	+	0.237263i
$345$	7.04812	+	2.16298i	0.379458	+	0.116451i
$346$	−16.1387	+	37.4137i	−0.867621	+	2.01137i
$347$	−23.1751	+	11.6390i	−1.24410	+	0.624812i	−0.944268	−	0.329178i	$-0.893228\pi$
$347$	−23.1751	+	11.6390i	−1.24410	+	0.624812i	−0.299836	+	0.953991i	$0.596932\pi$
$348$	5.40788	+	15.1820i	0.289893	+	0.813843i
$349$	14.3802	−	3.40817i	0.769755	−	0.182435i	0.173069	−	0.984910i	$-0.444632\pi$
$349$	14.3802	−	3.40817i	0.769755	−	0.182435i	0.596686	+	0.802475i	$0.296484\pi$
$350$	12.0141	+	20.8091i	0.642182	+	1.11229i
$351$	10.6796	−	2.95866i	0.570037	−	0.157922i
$352$	−5.62541	+	9.74350i	−0.299836	+	0.519330i
$353$	−1.98881	+	6.64309i	−0.105854	+	0.353576i	−0.994463	−	0.105089i	$-0.966487\pi$
$353$	−1.98881	+	6.64309i	−0.105854	+	0.353576i	0.888609	+	0.458665i	$0.151672\pi$
$354$	5.98611	+	3.51118i	0.318158	+	0.186617i
$355$	4.21820	+	2.77435i	0.223879	+	0.147247i
$356$	10.4560	+	14.0448i	0.554167	+	0.744375i
$357$	16.5326	−	0.848895i	0.875000	−	0.0449283i
$358$	−45.2250	+	29.7450i	−2.39022	+	1.57207i
$359$	28.2850	+	10.2949i	1.49283	+	0.543344i	0.954192	−	0.299195i	$-0.0967182\pi$
$359$	28.2850	+	10.2949i	1.49283	+	0.543344i	0.538634	+	0.842540i	$0.318940\pi$
$360$	−13.7406	−	18.9967i	−0.724194	−	1.00122i
$361$	−29.5849	+	10.7680i	−1.55710	+	0.566738i
$362$	9.46619	−	12.7153i	0.497532	−	0.668301i
$363$	19.7716	+	1.28803i	1.03774	+	0.0676042i
$364$	19.7278	−	20.9102i	1.03402	−	1.09599i
$365$	10.7929	−	11.4399i	0.564929	−	0.598789i
$366$	5.00533	+	0.326076i	0.261633	+	0.0170443i
$367$	−13.7405	+	18.4567i	−0.717247	+	0.963430i	0.282744	+	0.959195i	$0.408755\pi$
$367$	−13.7405	+	18.4567i	−0.717247	+	0.963430i	−0.999991	+	0.00423434i	$0.998652\pi$
$368$	15.3522	−	5.58774i	0.800288	−	0.291281i
$369$	7.44615	+	10.2945i	0.387631	+	0.535911i
$370$	−22.1715	−	8.06976i	−1.15264	−	0.419527i
$371$	−25.7607	+	16.9431i	−1.33743	+	0.879641i
$372$	27.5255	−	1.41334i	1.42713	−	0.0732784i
$373$	−18.8164	−	25.2748i	−0.974276	−	1.30868i	−0.951079	−	0.308949i	$-0.900023\pi$
$373$	−18.8164	−	25.2748i	−0.974276	−	1.30868i	−0.0231970	−	0.999731i	$-0.507385\pi$
$374$	−29.5846	−	19.4581i	−1.52978	−	1.00615i
$375$	16.8628	+	9.89094i	0.870789	+	0.510766i
$376$	−9.21276	+	30.7728i	−0.475112	+	1.58698i
$377$	−2.34830	+	4.06738i	−0.120944	+	0.209481i
$378$	−29.4919	−	28.9970i	−1.51690	−	1.49145i
$379$	9.45804	+	16.3818i	0.485827	+	0.841477i	0.999867	−	0.0162889i	$-0.00518516\pi$
$379$	9.45804	+	16.3818i	0.485827	+	0.841477i	−0.514040	+	0.857766i	$0.671852\pi$
$380$	−41.1180	+	9.74514i	−2.10931	+	0.499915i
$381$	−5.94697	−	16.6955i	−0.304673	−	0.855336i
$382$	−30.7713	+	15.4539i	−1.57440	+	0.790692i
$383$	11.8079	−	27.3739i	0.603358	−	1.39874i	−0.293302	−	0.956020i	$-0.594754\pi$
$383$	11.8079	−	27.3739i	0.603358	−	1.39874i	0.896659	−	0.442721i	$-0.145987\pi$
$384$	28.0227	+	8.59983i	1.43003	+	0.438858i
$385$	1.23679	+	21.2349i	0.0630327	+	1.08223i
$386$	−1.63631	−	9.27997i	−0.0832859	−	0.472338i
$387$	1.61049	+	1.75474i	0.0818656	+	0.0891987i
$388$	9.23585	−	52.3791i	0.468879	−	2.65915i
$389$	−5.79263	−	0.677061i	−0.293698	−	0.0343283i	−0.0320318	−	0.999487i	$-0.510198\pi$
$389$	−5.79263	−	0.677061i	−0.293698	−	0.0343283i	−0.261666	+	0.965159i	$0.584272\pi$
$390$	3.07850	−	12.6024i	0.155886	−	0.638149i
$391$	2.59845	+	8.67943i	0.131409	+	0.438938i
$392$	−17.1646	−	4.06808i	−0.866942	−	0.205469i
$393$	1.62866	+	14.8169i	0.0821549	+	0.747416i
$394$	−5.45197	−	12.6391i	−0.274666	−	0.636748i
$395$	−5.05517	−	4.24179i	−0.254353	−	0.213428i
$396$	9.61267	+	59.2714i	0.483055	+	2.97850i
$397$	4.50462	−	3.77983i	0.226081	−	0.189704i	−0.522710	−	0.852510i	$-0.675079\pi$
$397$	4.50462	−	3.77983i	0.226081	−	0.189704i	0.748791	+	0.662806i	$0.230635\pi$
$398$	37.8463	+	19.0071i	1.89706	+	0.952742i
$399$	−36.1551	+	15.3018i	−1.81002	+	0.766047i
$400$	16.1986	−	1.89335i	0.809931	−	0.0946674i
$401$	−0.623901	+	10.7120i	−0.0311561	+	0.534930i	0.946234	+	0.323484i	$0.104854\pi$
$401$	−0.623901	+	10.7120i	−0.0311561	+	0.534930i	−0.977390	+	0.211446i	$0.932183\pi$
$402$	25.4880	−	4.31373i	1.27123	−	0.215149i
$403$	5.51187	+	5.84225i	0.274566	+	0.291023i
$404$	−19.0349			−0.947023
$405$	−12.2416	−	3.25934i	−0.608289	−	0.161958i
$406$	17.5285			0.869924
$407$	21.8396	+	23.1486i	1.08255	+	1.14743i
$408$	10.0401	−	27.0057i	0.497059	−	1.33698i
$409$	−0.193574	+	3.32353i	−0.00957161	+	0.164338i	0.990135	+	0.140117i	$0.0447478\pi$
$409$	−0.193574	+	3.32353i	−0.00957161	+	0.164338i	−0.999707	+	0.0242216i	$0.992289\pi$
$410$	14.7727	−	1.72669i	0.729573	−	0.0852749i
$411$	−1.47708	−	1.11552i	−0.0728592	−	0.0550243i
$412$	52.7115	+	26.4727i	2.59691	+	1.30422i
$413$	3.92444	−	3.29300i	0.193109	−	0.162038i
$414$	11.5863	−	19.4454i	0.569434	−	0.955692i
$415$	−16.1303	−	13.5349i	−0.791805	−	0.664403i
$416$	−2.00629	−	4.65111i	−0.0983665	−	0.228039i
$417$	11.8098	+	5.19087i	0.578331	+	0.254198i
$418$	81.7133	+	19.3664i	3.99673	+	0.947242i
$419$	−0.820143	−	2.73947i	−0.0400666	−	0.133832i	0.935616	−	0.353019i	$-0.114845\pi$
$419$	−0.820143	−	2.73947i	−0.0400666	−	0.133832i	−0.975683	+	0.219187i	$0.929660\pi$
$420$	−31.5457	+	9.20830i	−1.53927	+	0.449319i
$421$	6.24383	+	0.729799i	0.304306	+	0.0355682i	0.266875	−	0.963731i	$-0.414009\pi$
$421$	6.24383	+	0.729799i	0.304306	+	0.0355682i	0.0374302	+	0.999299i	$0.488083\pi$
$422$	−8.36498	+	47.4401i	−0.407201	+	2.30935i
$423$	6.65472	+	16.0300i	0.323564	+	0.779405i
$424$	9.31841	+	52.8473i	0.452542	+	2.56649i
$425$	0.525874	+	9.02891i	0.0255086	+	0.437967i
$426$	11.3479	−	10.5597i	0.549808	−	0.511617i
$427$	1.46659	−	3.39993i	0.0709731	−	0.164534i
$428$	17.1967	−	8.63649i	0.831233	−	0.417461i
$429$	−11.3396	+	13.3269i	−0.547483	+	0.643427i
$430$	2.71305	−	0.643004i	0.130835	−	0.0310084i
$431$	−8.66111	−	15.0015i	−0.417191	−	0.722596i	0.578465	−	0.815707i	$-0.303652\pi$
$431$	−8.66111	−	15.0015i	−0.417191	−	0.722596i	−0.995656	+	0.0931115i	$0.970319\pi$
$432$	−26.0002	+	10.5848i	−1.25094	+	0.509261i
$433$	−6.83316	+	11.8354i	−0.328381	+	0.568772i	−0.982191	−	0.187887i	$-0.939836\pi$
$433$	−6.83316	+	11.8354i	−0.328381	+	0.568772i	0.653810	+	0.756659i	$0.273170\pi$
$434$	8.59739	−	28.7173i	0.412688	−	1.37847i
$435$	4.66790	−	2.65238i	0.223808	−	0.127172i
$436$	−25.1969	−	16.5723i	−1.20671	−	0.793668i
$437$	−12.8308	−	17.2348i	−0.613781	−	0.824451i
$438$	−26.2565	−	40.5252i	−1.25458	−	1.93637i
$439$	31.1535	−	20.4900i	1.48688	−	0.977934i	0.492696	−	0.870202i	$-0.336012\pi$
$439$	31.1535	−	20.4900i	1.48688	−	0.977934i	0.994180	−	0.107732i	$-0.0343588\pi$
$440$	34.7876	+	12.6617i	1.65843	+	0.603621i
$441$	−8.57556	+	4.16013i	−0.408360	+	0.198102i
$442$	14.9809	−	5.45261i	0.712570	−	0.259354i
$443$	−2.66634	+	3.58151i	−0.126682	+	0.170163i	−0.860939	−	0.508708i	$-0.830123\pi$
$443$	−2.66634	+	3.58151i	−0.126682	+	0.170163i	0.734257	+	0.678871i	$0.237531\pi$
$444$	−27.2999	+	40.8922i	−1.29559	+	1.94066i
$445$	4.00280	−	4.24272i	0.189751	−	0.201124i
$446$	−25.9160	+	27.4693i	−1.22716	+	1.30071i
$447$	1.87180	+	3.79184i	0.0885330	+	0.179348i
$448$	9.29471	−	12.4850i	0.439134	−	0.589859i
$449$	−3.44438	+	1.25365i	−0.162550	+	0.0591635i	−0.422014	−	0.906589i	$-0.638677\pi$
$449$	−3.44438	+	1.25365i	−0.162550	+	0.0591635i	0.259463	+	0.965753i	$0.416454\pi$
$450$	15.7309	−	16.2209i	0.741559	−	0.764662i
$451$	−18.8517	−	6.86146i	−0.887693	−	0.323094i
$452$	−27.6402	+	18.1793i	−1.30009	+	0.855080i
$453$	16.8450	−	32.9739i	0.791448	−	1.54925i
$454$	−9.38905	−	12.6117i	−0.440650	−	0.591896i
$455$	−8.00114	−	5.26243i	−0.375099	−	0.246707i
$456$	−0.469830	+	68.3269i	−0.0220018	+	3.19970i
$457$	5.26887	−	17.5993i	0.246467	−	0.823259i	−0.741813	−	0.670607i	$-0.766034\pi$
$457$	5.26887	−	17.5993i	0.246467	−	0.823259i	0.988280	−	0.152651i	$-0.0487812\pi$
$458$	11.6227	−	20.1311i	0.543092	−	0.940664i
$459$	−5.02157	−	14.7355i	−0.234387	−	0.687795i
$460$	−8.99256	−	15.5756i	−0.419280	−	0.726215i
$461$	−11.7380	+	2.78196i	−0.546694	+	0.129569i	−0.494676	−	0.869077i	$-0.664713\pi$
$461$	−11.7380	+	2.78196i	−0.546694	+	0.129569i	−0.0520176	+	0.998646i	$0.516565\pi$
$462$	64.2351	+	11.7824i	2.98849	+	0.548165i
$463$	2.46047	−	1.23569i	0.114348	−	0.0574275i	−0.390706	−	0.920516i	$-0.627769\pi$
$463$	2.46047	−	1.23569i	0.114348	−	0.0574275i	0.505053	+	0.863088i	$0.331473\pi$
$464$	4.71226	−	10.9242i	0.218761	−	0.507145i
$465$	−2.05594	−	8.94846i	−0.0953420	−	0.414975i
$466$	−3.05322	−	52.4217i	−0.141438	−	2.42839i
$467$	5.46587	+	30.9985i	0.252930	+	1.43444i	0.801330	+	0.598223i	$0.204126\pi$
$467$	5.46587	+	30.9985i	0.252930	+	1.43444i	−0.548399	+	0.836216i	$0.684763\pi$
$468$	−23.9893	−	12.4639i	−1.10891	−	0.576144i
$469$	3.31368	−	18.7928i	0.153011	−	0.867771i
$470$	20.1809	+	2.35881i	0.930874	+	0.108804i
$471$	−8.08760	−	7.73605i	−0.372657	−	0.356459i
$472$	−2.55718	−	8.54159i	−0.117704	−	0.393158i
$473$	−3.65944	−	0.867304i	−0.168261	−	0.0398787i
$474$	−16.3344	+	11.9868i	−0.750264	+	0.550573i
$475$	−8.49548	−	19.6947i	−0.389799	−	0.903656i
$476$	−30.9360	−	25.9584i	−1.41795	−	1.18980i
$477$	21.9532	+	18.9414i	1.00517	+	0.867269i
$478$	31.3458	−	26.3023i	1.43372	−	1.20304i
$479$	2.49117	+	1.25111i	0.113825	+	0.0571648i	0.504800	−	0.863236i	$-0.331566\pi$
$479$	2.49117	+	1.25111i	0.113825	+	0.0571648i	−0.390976	+	0.920401i	$0.627862\pi$
$480$	−0.711753	+	5.74648i	−0.0324869	+	0.262290i
$481$	−14.2314	+	1.66341i	−0.648895	+	0.0758450i
$482$	0.239701	−	4.11551i	0.0109181	−	0.187456i
$483$	−10.6524	−	12.8737i	−0.484700	−	0.585776i
$484$	−33.1691	−	35.1572i	−1.50769	−	1.59806i
$485$	−17.7181			−0.804538
$486$	−18.6400	+	34.1364i	−0.845528	+	1.54846i
$487$	−31.6987			−1.43640			−0.718202	−	0.695835i	$-0.755035\pi$
$487$	−31.6987			−1.43640			−0.718202	+	0.695835i	$0.755035\pi$
$488$	−4.42238	−	4.68745i	−0.200192	−	0.212191i
$489$	7.16664	+	8.66112i	0.324087	+	0.391670i
$490$	−0.648772	+	11.1390i	−0.0293085	+	0.503208i
$491$	34.9560	−	4.08577i	1.57754	−	0.184388i	0.718217	−	0.695819i	$-0.244959\pi$
$491$	34.9560	−	4.08577i	1.57754	−	0.184388i	0.859324	+	0.511431i	$0.170884\pi$
$492$	3.80977	−	30.7589i	0.171758	−	1.38672i
$493$	5.89592	+	2.96104i	0.265539	+	0.133359i
$494$	−28.9628	+	24.3027i	−1.30310	+	1.09343i
$495$	18.8889	−	6.58227i	0.848993	−	0.295851i
$496$	−15.5862	−	13.0783i	−0.699839	−	0.587235i
$497$	−4.53226	−	10.5070i	−0.203300	−	0.471302i
$498$	−52.1206	+	38.2482i	−2.33558	+	1.71394i
$499$	−7.77433	−	1.84255i	−0.348027	−	0.0824838i	0.0528848	−	0.998601i	$-0.483158\pi$
$499$	−7.77433	−	1.84255i	−0.348027	−	0.0824838i	−0.400912	+	0.916117i	$0.631307\pi$
$500$	−13.6778	−	45.6870i	−0.611689	−	2.04318i
$501$	−4.88593	−	4.67355i	−0.218287	−	0.208799i
$502$	−53.8144	−	6.29000i	−2.40185	−	0.280736i
$503$	−2.70376	+	15.3338i	−0.120555	+	0.683700i	0.863294	+	0.504701i	$0.168397\pi$
$503$	−2.70376	+	15.3338i	−0.120555	+	0.683700i	−0.983849	+	0.178999i	$0.942714\pi$
$504$	2.35988	+	53.0850i	0.105117	+	2.36459i
$505$	1.10111	+	6.24473i	0.0489989	+	0.277887i
$506$	2.07819	+	35.6812i	0.0923868	+	1.58622i
$507$	3.27785	+	14.2668i	0.145574	+	0.633611i
$508$	−17.1244	+	39.6989i	−0.759774	+	1.76136i
$509$	−15.4415	+	7.75504i	−0.684435	+	0.343736i	−0.756804	−	0.653642i	$-0.773240\pi$
$509$	−15.4415	+	7.75504i	−0.684435	+	0.343736i	0.0723693	+	0.997378i	$0.476944\pi$
$510$	−17.9252	−	3.28793i	−0.793739	−	0.145592i
$511$	−34.6849	+	8.22048i	−1.53437	+	0.363653i
$512$	−23.5802	−	40.8420i	−1.04211	−	1.80498i
$513$	23.1430	+	28.7655i	1.02179	+	1.27003i
$514$	7.67834	−	13.2993i	0.338677	−	0.586606i
$515$	5.63561	−	18.8243i	0.248335	−	0.829496i
$516$	0.0399515	−	5.81011i	0.00175877	−	0.255776i
$517$	−22.8973	−	15.0598i	−1.00702	−	0.662329i
$518$	31.9333	+	42.8939i	1.40307	+	1.88465i
$519$	12.8681	−	25.1891i	0.564846	−	1.10568i
$520$	−13.9253	+	9.15885i	−0.610667	+	0.401642i
$521$	−33.0219	−	12.0190i	−1.44672	−	0.526562i	−0.505045	−	0.863093i	$-0.668524\pi$
$521$	−33.0219	−	12.0190i	−1.44672	−	0.526562i	−0.941672	+	0.336531i	$0.890746\pi$
$522$	−4.50996	−	15.8547i	−0.197395	−	0.693940i
$523$	2.55225	−	0.928943i	0.111602	−	0.0406198i	−0.285616	−	0.958344i	$-0.592198\pi$
$523$	2.55225	−	0.928943i	0.111602	−	0.0406198i	0.397218	+	0.917724i	$0.369976\pi$
$524$	21.7146	−	29.1678i	0.948607	−	1.27420i
$525$	−7.38342	−	14.9572i	−0.322239	−	0.652784i
$526$	43.7128	−	46.3328i	1.90597	−	2.02021i
$527$	7.74298	−	8.20708i	0.337290	−	0.357506i
$528$	24.6117	−	36.8656i	1.07109	−	1.60437i
$529$	−8.27369	+	11.1135i	−0.359726	+	0.483195i
$530$	31.8961	−	11.6092i	1.38548	−	0.504273i
$531$	−3.98828	−	2.70243i	−0.173076	−	0.117275i
$532$	89.9974	+	32.7564i	3.90188	+	1.42017i
$533$	7.54627	−	4.96326i	0.326865	−	0.214983i
$534$	−9.73778	−	15.0297i	−0.421395	−	0.650397i
$535$	−3.82812	−	5.14206i	−0.165504	−	0.222311i
$536$	−27.7482	−	18.2503i	−1.19854	−	0.788291i
$537$	32.6709	−	18.5642i	1.40985	−	0.801104i
$538$	−11.7239	+	39.1605i	−0.505452	+	1.68833i
$539$	7.52504	−	13.0337i	0.324126	−	0.561403i
$540$	16.4455	+	26.1642i	0.707702	+	1.12593i
$541$	19.9581	+	34.5684i	0.858065	+	1.48621i	0.873772	+	0.486336i	$0.161667\pi$
$541$	19.9581	+	34.5684i	0.858065	+	1.48621i	−0.0157071	+	0.999877i	$0.505000\pi$
$542$	66.2135	−	15.6929i	2.84412	−	0.674068i
$543$	−7.13129	+	8.38102i	−0.306033	+	0.359664i
$544$	−6.35886	+	3.19354i	−0.272634	+	0.136922i
$545$	−3.97924	+	9.22493i	−0.170452	+	0.395152i
$546$	−21.5249	+	20.0297i	−0.921179	+	0.857193i
$547$	0.540346	+	9.27738i	0.0231035	+	0.396672i	0.989960	+	0.141350i	$0.0451444\pi$
$547$	0.540346	+	9.27738i	0.0231035	+	0.396672i	−0.966856	+	0.255322i	$0.917819\pi$
$548$	0.784096	+	4.44683i	0.0334949	+	0.189959i
$549$	−3.45261	−	0.451762i	−0.147354	−	0.0192807i
$550$	−6.19562	+	35.1371i	−0.264182	+	1.49825i
$551$	−15.5411	−	1.81649i	−0.662071	−	0.0773850i
$552$	−27.9165	+	8.14890i	−1.18820	+	0.346840i
$553$	4.28954	+	14.3281i	0.182410	+	0.609292i
$554$	55.6045	+	13.1785i	2.36241	+	0.559901i
$555$	14.9946	+	6.59069i	0.636485	+	0.279759i
$556$	−12.4646	−	28.8962i	−0.528617	−	1.22547i
$557$	28.8895	+	24.2411i	1.22409	+	1.02713i	0.998601	+	0.0528835i	$0.0168412\pi$
$557$	28.8895	+	24.2411i	1.22409	+	1.02713i	0.225485	+	0.974247i	$0.427603\pi$
$558$	−28.1871	−	0.387659i	−1.19326	−	0.0164109i
$559$	1.29707	−	1.08837i	0.0548602	−	0.0460332i
$560$	21.6787	+	10.8875i	0.916093	+	0.460079i
$561$	19.6159	+	14.8142i	0.828184	+	0.625457i
$562$	74.3141	−	8.68607i	3.13475	−	0.366400i
$563$	2.31955	−	39.8251i	0.0977572	−	1.67843i	−0.491806	−	0.870705i	$-0.663663\pi$
$563$	2.31955	−	39.8251i	0.0977572	−	1.67843i	0.589564	−	0.807722i	$-0.299300\pi$
$564$	14.7546	−	39.6866i	0.621279	−	1.67111i
$565$	7.56291	+	8.01622i	0.318174	+	0.337245i
$566$	−38.7153			−1.62732
$567$	19.1212	+	21.4179i	0.803015	+	0.899467i
$568$	−19.9153			−0.835626
$569$	−21.4166	−	22.7003i	−0.897831	−	0.951646i	0.101234	−	0.994863i	$-0.467721\pi$
$569$	−21.4166	−	22.7003i	−0.897831	−	0.951646i	−0.999066	+	0.0432171i	$0.986239\pi$
$570$	42.6138	−	7.21220i	1.78490	−	0.302086i
$571$	1.25067	−	21.4732i	0.0523390	−	0.898627i	−0.865311	−	0.501236i	$-0.832879\pi$
$571$	1.25067	−	21.4732i	0.0523390	−	0.898627i	0.917650	−	0.397390i	$-0.130084\pi$
$572$	42.3982	−	4.95563i	1.77276	−	0.207205i
$573$	22.0135	−	9.31669i	0.919626	−	0.389210i
$574$	−30.1239	−	15.1288i	−1.25735	−	0.631464i
$575$	6.99316	−	5.86796i	0.291635	−	0.244711i
$576$	−13.6842	−	5.19485i	−0.570176	−	0.216452i
$577$	1.05985	+	0.889324i	0.0441223	+	0.0370230i	0.664582	−	0.747215i	$-0.268610\pi$
$577$	1.05985	+	0.889324i	0.0441223	+	0.0370230i	−0.620460	+	0.784238i	$0.713054\pi$
$578$	7.92966	+	18.3830i	0.329831	+	0.764633i
$579$	0.714726	+	6.50232i	0.0297030	+	0.270227i
$580$	−12.7441	−	3.02040i	−0.529170	−	0.125415i
$581$	13.6873	+	45.7187i	0.567844	+	1.89673i
$582$	−12.9089	+	52.8451i	−0.535092	+	2.19050i
$583$	−45.4740	−	5.31515i	−1.88334	−	0.220131i
$584$	−10.7729	+	61.0961i	−0.445785	+	2.52817i
$585$	−2.70128	+	8.59109i	−0.111684	+	0.355198i
$586$	3.33572	+	18.9178i	0.137797	+	0.781488i
$587$	0.466073	+	8.00217i	0.0192369	+	0.330285i	0.994173	+	0.107799i	$0.0343802\pi$
$587$	0.466073	+	8.00217i	0.0192369	+	0.330285i	−0.974936	+	0.222486i	$0.928583\pi$
$588$	22.2283	+	6.82161i	0.916680	+	0.281318i
$589$	−10.5986	+	24.5703i	−0.436707	+	1.01240i
$590$	−5.03985	+	2.53111i	−0.207487	+	0.104204i
$591$	3.20634	+	9.00145i	0.131891	+	0.370270i
$592$	35.3175	−	8.37039i	1.45154	−	0.344021i
$593$	−10.7066	−	18.5444i	−0.439668	−	0.761527i	0.557996	−	0.829844i	$-0.311571\pi$
$593$	−10.7066	−	18.5444i	−0.439668	−	0.761527i	−0.997664	+	0.0683166i	$0.978237\pi$
$594$	−5.86999	−	61.1327i	−0.240849	−	2.50831i
$595$	−6.72652	+	11.6507i	−0.275761	+	0.477631i
$596$	2.95859	−	9.88237i	0.121188	−	0.404798i
$597$	−25.3594	−	14.8747i	−1.03789	−	0.608779i
$598$	−13.4444	−	8.84252i	−0.549782	−	0.361598i
$599$	−13.8938	−	18.6626i	−0.567684	−	0.762531i	0.421876	−	0.906653i	$-0.361372\pi$
$599$	−13.8938	−	18.6626i	−0.567684	−	0.762531i	−0.989560	+	0.144122i	$0.953964\pi$
$600$	−28.9925	+	1.48867i	−1.18361	+	0.0607745i
$601$	26.3770	−	17.3485i	1.07594	−	0.707658i	0.117537	−	0.993069i	$-0.462500\pi$
$601$	26.3770	−	17.3485i	1.07594	−	0.707658i	0.958405	+	0.285410i	$0.0921298\pi$
$602$	−5.93821	−	2.16133i	−0.242023	−	0.0880893i
$603$	−17.8509	+	1.83801i	−0.726943	+	0.0748494i
$604$	−84.8800	+	30.8938i	−3.45372	+	1.25705i
$605$	−9.61519	+	12.9154i	−0.390913	+	0.525087i
$606$	19.4274	+	1.26561i	0.789185	+	0.0514120i
$607$	3.23033	−	3.42395i	0.131115	−	0.138974i	−0.658489	−	0.752590i	$-0.728804\pi$
$607$	3.23033	−	3.42395i	0.131115	−	0.138974i	0.789605	+	0.613616i	$0.210286\pi$
$608$	11.5806	−	12.2747i	0.469656	−	0.497806i
$609$	−12.1424	−	0.791026i	−0.492036	−	0.0320540i
$610$	−2.43416	+	3.26965i	−0.0985563	+	0.132384i
$611$	11.5946	−	4.22010i	0.469069	−	0.170727i
$612$	−15.5200	+	34.6608i	−0.627357	+	1.40108i
$613$	41.2145	+	15.0009i	1.66464	+	0.605879i	0.991082	−	0.133255i	$-0.0425429\pi$
$613$	41.2145	+	15.0009i	1.66464	+	0.605879i	0.673558	+	0.739134i	$0.264765\pi$
$614$	27.4251	−	18.0378i	1.10679	−	0.727946i
$615$	−10.3114	+	0.529454i	−0.415795	+	0.0213496i
$616$	−50.1041	−	67.3015i	−2.01875	−	2.71166i
$617$	14.8817	+	9.78784i	0.599114	+	0.394044i	0.812531	−	0.582918i	$-0.198089\pi$
$617$	14.8817	+	9.78784i	0.599114	+	0.394044i	−0.213417	+	0.976961i	$0.568459\pi$
$618$	−52.0383	−	30.5233i	−2.09329	−	1.22783i
$619$	−1.60750	+	5.36943i	−0.0646109	+	0.215816i	−0.984198	−	0.177070i	$-0.943338\pi$
$619$	−1.60750	+	5.36943i	−0.0646109	+	0.215816i	0.919587	+	0.392886i	$0.128523\pi$
$620$	−11.1991	+	19.3975i	−0.449768	+	0.779021i
$621$	−8.90364	+	12.9475i	−0.357291	+	0.519565i
$622$	−6.83702	−	11.8421i	−0.274139	−	0.474823i
$623$	−12.8637	+	3.04874i	−0.515372	+	0.122145i
$624$	6.69646	+	18.7996i	0.268073	+	0.752586i
$625$	−0.708810	+	0.355978i	−0.0283524	+	0.0142391i
$626$	−23.8959	+	55.3970i	−0.955074	+	2.21411i
$627$	−55.7309	−	17.1032i	−2.22568	−	0.683035i
$628$	1.58747	+	27.2558i	0.0633470	+	1.08763i
$629$	3.49521	+	19.8223i	0.139363	+	0.790367i
$630$	32.8085	−	7.30074i	1.30712	−	0.290868i
$631$	−2.84022	+	16.1077i	−0.113067	+	0.641237i	0.874622	+	0.484806i	$0.161110\pi$
$631$	−2.84022	+	16.1077i	−0.113067	+	0.641237i	−0.987689	+	0.156431i	$0.950001\pi$
$632$	25.8544	+	3.02195i	1.02843	+	0.120207i
$633$	7.93551	−	32.4855i	0.315408	−	1.29118i
$634$	7.40308	+	24.7280i	0.294014	+	0.982075i
$635$	14.0145	+	3.32150i	0.556149	+	0.131810i
$636$	−7.72833	−	70.3096i	−0.306448	−	2.78796i
$637$	2.68379	+	6.22172i	0.106336	+	0.246514i
$638$	19.9384	+	16.7303i	0.789369	+	0.662360i
$639$	−8.33752	+	6.80284i	−0.329827	+	0.269116i
$640$	−18.2480	+	15.3119i	−0.721314	+	0.605255i
$641$	20.8476	+	10.4700i	0.823429	+	0.413541i	0.810044	−	0.586369i	$-0.199443\pi$
$641$	20.8476	+	10.4700i	0.823429	+	0.413541i	0.0133847	+	0.999910i	$0.495739\pi$
$642$	−18.1255	+	7.67119i	−0.715357	+	0.302758i
$643$	14.4953	−	1.69426i	0.571638	−	0.0668149i	0.174637	−	0.984633i	$-0.444125\pi$
$643$	14.4953	−	1.69426i	0.571638	−	0.0668149i	0.397002	+	0.917818i	$0.370051\pi$
$644$	−2.37012	+	40.6933i	−0.0933957	+	1.60354i
$645$	−1.90841	+	0.322991i	−0.0751438	+	0.0127177i
$646$	36.4479	+	38.6325i	1.43402	+	1.51998i
$647$	1.33592			0.0525205			0.0262602	−	0.999655i	$-0.491640\pi$
$647$	1.33592			0.0525205			0.0262602	+	0.999655i	$0.491640\pi$
$648$	47.4087	−	15.7929i	1.86239	−	0.620405i
$649$	7.60705			0.298603
$650$	−11.0235	−	11.6842i	−0.432377	−	0.458292i
$651$	−7.25159	+	19.5052i	−0.284212	+	0.764470i
$652$	1.59455	−	27.3774i	0.0624475	−	1.07218i
$653$	−16.3676	+	1.91310i	−0.640514	+	0.0748654i	−0.430150	−	0.902758i	$-0.641539\pi$
$653$	−16.3676	+	1.91310i	−0.640514	+	0.0748654i	−0.210365	+	0.977623i	$0.567465\pi$
$654$	24.6146	+	18.5893i	0.962507	+	0.726900i
$655$	−10.8251	−	5.43657i	−0.422972	−	0.212424i
$656$	−17.5271	+	14.7069i	−0.684316	+	0.574210i
$657$	16.3597	+	29.2578i	0.638252	+	1.14145i
$658$	−35.2765	−	29.6005i	−1.37522	−	1.15395i
$659$	−17.8283	−	41.3307i	−0.694493	−	1.61002i	−0.788929	−	0.614484i	$-0.789364\pi$
$659$	−17.8283	−	41.3307i	−0.694493	−	1.61002i	0.0944361	−	0.995531i	$-0.469895\pi$
$660$	−44.6719	−	19.6350i	−1.73885	−	0.764290i
$661$	24.2010	+	5.73574i	0.941310	+	0.223094i	0.672499	−	0.740098i	$-0.265221\pi$
$661$	24.2010	+	5.73574i	0.941310	+	0.223094i	0.268811	+	0.963193i	$0.413369\pi$
$662$	−22.0144	−	73.5332i	−0.855614	−	2.85795i
$663$	−10.6237	+	3.10110i	−0.412591	+	0.120437i
$664$	82.4975	+	9.64257i	3.20152	+	0.374204i
$665$	5.54020	−	31.4200i	0.214840	−	1.21842i
$666$	30.5817	−	39.9203i	1.18502	−	1.54688i
$667$	−1.15641	−	6.55832i	−0.0447764	−	0.253939i
$668$	0.959034	+	16.4660i	0.0371061	+	0.637087i
$669$	19.1923	−	17.8592i	0.742017	−	0.690475i
$670$	−8.32066	+	19.2895i	−0.321455	+	0.745217i
$671$	4.91333	−	2.46757i	0.189677	−	0.0952594i
$672$	8.50461	−	9.99501i	0.328072	−	0.385566i
$673$	1.92706	−	0.456722i	0.0742827	−	0.0176053i	−0.193306	−	0.981138i	$-0.561921\pi$
$673$	1.92706	−	0.456722i	0.0742827	−	0.0176053i	0.267589	+	0.963533i	$0.413773\pi$
$674$	−41.0936	−	71.1762i	−1.58287	−	2.74161i
$675$	−11.6292	+	10.5267i	−0.447607	+	0.405175i
$676$	17.8551	−	30.9260i	0.686735	−	1.18946i
$677$	−8.17155	+	27.2949i	−0.314058	+	1.04903i	0.644613	+	0.764509i	$0.277019\pi$
$677$	−8.17155	+	27.2949i	−0.314058	+	1.04903i	−0.958671	+	0.284518i	$0.908167\pi$
$678$	29.4189	−	16.7163i	1.12983	−	0.641987i
$679$	33.5508	+	22.0667i	1.28756	+	0.846842i
$680$	13.9818	+	18.7809i	0.536179	+	0.720214i
$681$	5.93489	+	9.16014i	0.227426	+	0.351017i
$682$	37.1891	−	24.4596i	1.42404	−	0.936608i
$683$	27.6811	+	10.0751i	1.05919	+	0.385512i	0.812123	−	0.583487i	$-0.198312\pi$
$683$	27.6811	+	10.0751i	1.05919	+	0.385512i	0.247064	+	0.968999i	$0.420534\pi$
$684$	6.47273	−	89.8314i	0.247491	−	3.43479i
$685$	1.41350	−	0.514472i	0.0540071	−	0.0196570i
$686$	−18.1707	+	24.4075i	−0.693762	+	0.931884i
$687$	−8.95981	+	13.4208i	−0.341838	+	0.512036i
$688$	−2.94340	+	3.11982i	−0.112216	+	0.118942i
$689$	14.1454	−	14.9932i	0.538895	−	0.571196i
$690$	8.14239	+	16.4947i	0.309976	+	0.627941i
$691$	29.0246	−	38.9868i	1.10415	−	1.48313i	0.246320	−	0.969189i	$-0.420779\pi$
$691$	29.0246	−	38.9868i	1.10415	−	1.48313i	0.857827	−	0.513938i	$-0.171814\pi$
$692$	−64.8408	+	23.6001i	−2.46488	+	0.897141i
$693$	−43.9656	−	11.0607i	−1.67011	−	0.420163i
$694$	−60.8034	−	22.1306i	−2.30807	−	0.840067i
$695$	−8.75884	+	5.76078i	−0.332242	+	0.218519i
$696$	−9.63445	+	18.8593i	−0.365193	+	0.714860i
$697$	−7.57688	−	10.1775i	−0.286995	−	0.385501i
$698$	30.8072	+	20.2622i	1.16607	+	0.766936i
$699$	−0.250649	+	36.4517i	−0.00948041	+	1.37873i
$700$	−11.6703	+	38.9816i	−0.441097	+	1.47337i
$701$	3.03784	−	5.26170i	0.114738	−	0.198732i	−0.802937	−	0.596064i	$-0.796731\pi$
$701$	3.03784	−	5.26170i	0.114738	−	0.198732i	0.917675	+	0.397332i	$0.130064\pi$
$702$	23.6553	+	14.3159i	0.892810	+	0.540320i
$703$	−23.8675	−	41.3397i	−0.900179	−	1.55916i
$704$	22.4891	−	5.33001i	0.847589	−	0.200882i
$705$	−13.8734	−	2.54473i	−0.522501	−	0.0958400i
$706$	−15.4614	+	7.76500i	−0.581897	+	0.292240i
$707$	5.69232	−	13.1963i	0.214082	−	0.496297i
$708$	2.63161	+	11.4540i	0.0989018	+	0.430469i
$709$	1.26191	+	21.6661i	0.0473919	+	0.813688i	0.935341	+	0.353747i	$0.115092\pi$
$709$	1.26191	+	21.6661i	0.0473919	+	0.813688i	−0.887949	+	0.459941i	$0.847871\pi$
$710$	2.18745	+	12.4056i	0.0820934	+	0.465575i
$711$	11.8562	−	7.56644i	0.444642	−	0.283764i
$712$	−3.99536	+	22.6588i	−0.149733	+	0.849175i
$713$	−11.3118	−	1.32216i	−0.423632	−	0.0495155i
$714$	29.8479	+	28.5505i	1.11703	+	1.06848i
$715$	−4.07839	−	13.6228i	−0.152523	−	0.509462i
$716$	−89.1966	−	21.1400i	−3.33343	−	0.790038i
$717$	−22.9010	+	16.8057i	−0.855254	+	0.627619i
$718$	29.7463	+	68.9597i	1.11012	+	2.57355i
$719$	−11.8323	−	9.92847i	−0.441270	−	0.370269i	0.394915	−	0.918718i	$-0.370774\pi$
$719$	−11.8323	−	9.92847i	−0.441270	−	0.370269i	−0.836184	+	0.548449i	$0.815219\pi$
$720$	4.27002	−	22.4099i	0.159134	−	0.835167i
$721$	−34.1158	+	28.6266i	−1.27054	+	1.06611i
$722$	−70.1977	−	35.2546i	−2.61249	−	1.31204i
$723$	−0.351772	+	2.84010i	−0.0130825	+	0.105624i
$724$	26.6634	−	3.11651i	0.990938	−	0.115824i
$725$	0.386539	−	6.63661i	0.0143557	−	0.246478i
$726$	31.5155	+	38.0876i	1.16965	+	1.41356i
$727$	17.6753	+	18.7348i	0.655542	+	0.694833i	0.966812	−	0.255488i	$-0.0822361\pi$
$727$	17.6753	+	18.7348i	0.655542	+	0.694833i	−0.311271	+	0.950321i	$0.600755\pi$
$728$	37.7756			1.40006
$729$	14.4529	−	22.8060i	0.535294	−	0.844666i
$730$	39.2412			1.45238
$731$	−1.63228	−	1.73012i	−0.0603721	−	0.0639907i
$732$	5.41518	+	6.54443i	0.200151	+	0.241889i
$733$	−1.69715	+	29.1389i	−0.0626857	+	1.07627i	0.809507	+	0.587110i	$0.199734\pi$
$733$	−1.69715	+	29.1389i	−0.0626857	+	1.07627i	−0.872193	+	0.489162i	$0.837303\pi$
$734$	−57.0224	+	6.66496i	−2.10473	+	0.246008i
$735$	0.952102	−	7.68698i	0.0351188	−	0.283539i
$736$	6.41842	+	3.22345i	0.236586	+	0.118818i
$737$	21.7063	−	18.2138i	0.799563	−	0.670913i
$738$	−5.93346	+	31.1399i	−0.218414	+	1.14628i
$739$	15.6599	+	13.1402i	0.576058	+	0.483370i	0.883650	−	0.468148i	$-0.155079\pi$
$739$	15.6599	+	13.1402i	0.576058	+	0.483370i	−0.307592	+	0.951518i	$0.599523\pi$
$740$	−15.8259	−	36.6886i	−0.581772	−	1.34870i
$741$	21.1600	−	15.5281i	0.777332	−	0.570437i
$742$	−74.8566	−	17.7413i	−2.74807	−	0.651305i
$743$	6.73922	+	22.5106i	0.247238	+	0.825832i	0.988052	+	0.154122i	$0.0492549\pi$
$743$	6.73922	+	22.5106i	0.247238	+	0.825832i	−0.740814	+	0.671710i	$0.765560\pi$
$744$	26.1721	+	25.0345i	0.959515	+	0.917808i
$745$	−3.41322	−	0.398948i	−0.125051	−	0.0146163i
$746$	13.6520	−	77.4244i	0.499836	−	2.83471i
$747$	37.8313	−	24.1434i	1.38418	−	0.883360i
$748$	−10.4129	−	59.0546i	−0.380734	−	2.15925i
$749$	0.844797	+	14.5046i	0.0308682	+	0.529987i
$750$	10.9221	+	47.5385i	0.398820	+	1.73586i
$751$	13.9011	−	32.2264i	0.507259	−	1.17596i	−0.451637	−	0.892202i	$-0.649160\pi$
$751$	13.9011	−	32.2264i	0.507259	−	1.17596i	0.958896	−	0.283757i	$-0.0915810\pi$
$752$	−27.9314	+	14.0277i	−1.01855	+	0.511537i
$753$	36.9947	+	6.78578i	1.34816	+	0.247288i
$754$	−11.4024	+	2.70242i	−0.415251	+	0.0984163i
$755$	15.0453	+	26.0592i	0.547554	+	0.948391i
$756$	1.44472	−	70.0259i	0.0525439	−	2.54682i
$757$	−23.1445	+	40.0875i	−0.841202	+	1.45701i	0.0476764	+	0.998863i	$0.484818\pi$
$757$	−23.1445	+	40.0875i	−0.841202	+	1.45701i	−0.888879	+	0.458142i	$0.848515\pi$
$758$	−13.5361	+	45.2139i	−0.491655	+	1.64224i
$759$	0.170606	−	24.8110i	0.00619259	−	0.900583i
$760$	−46.3926	−	30.5129i	−1.68284	−	1.10682i
$761$	4.23035	+	5.68235i	0.153350	+	0.205985i	0.872159	−	0.489223i	$-0.162720\pi$
$761$	4.23035	+	5.68235i	0.153350	+	0.205985i	−0.718809	+	0.695208i	$0.755312\pi$
$762$	20.1171	−	39.3790i	0.728766	−	1.42655i
$763$	19.0241	−	12.5123i	0.688717	−	0.452976i
$764$	−54.7961	−	19.9441i	−1.98245	−	0.721554i
$765$	12.2688	+	3.08656i	0.443581	+	0.111595i
$766$	69.8968	−	25.4404i	2.52547	−	0.919198i
$767$	−2.04519	+	2.74716i	−0.0738474	+	0.0991943i
$768$	24.8921	+	50.4257i	0.898215	+	1.81958i
$769$	29.7305	−	31.5125i	1.07211	−	1.13637i	0.0819197	−	0.996639i	$-0.473895\pi$
$769$	29.7305	−	31.5125i	1.07211	−	1.13637i	0.990190	−	0.139731i	$-0.0446236\pi$
$770$	−36.4202	+	38.6031i	−1.31249	+	1.39116i
$771$	−5.91915	+	8.86624i	−0.213173	+	0.319310i
$772$	9.52931	−	12.8001i	0.342967	−	0.460685i
$773$	33.8164	−	12.3082i	1.21629	−	0.442694i	0.347409	−	0.937714i	$-0.387062\pi$
$773$	33.8164	−	12.3082i	1.21629	−	0.442694i	0.868881	+	0.495020i	$0.164839\pi$
$774$	−0.427083	+	5.92726i	−0.0153512	+	0.213051i
$775$	−10.6833	−	3.88841i	−0.383756	−	0.139676i
$776$	58.3924	−	38.4053i	2.09617	−	1.37867i
$777$	−20.1853	−	31.1548i	−0.724143	−	1.11767i
$778$	−8.68943	−	11.6719i	−0.311531	−	0.418459i
$779$	25.1406	+	16.5352i	0.900755	+	0.592436i
$780$	19.1011	−	10.8536i	0.683928	−	0.388620i
$781$	4.87314	−	16.2774i	0.174375	−	0.582452i
$782$	−11.3026	+	19.5768i	−0.404182	+	0.700063i
$783$	2.40867	+	11.1865i	0.0860789	+	0.399771i
$784$	−8.58220	−	14.8648i	−0.306507	−	0.530886i
$785$	8.84990	−	2.09747i	0.315867	−	0.0748618i
$786$	−24.1017	+	28.3254i	−0.859679	+	1.01034i
$787$	18.7666	−	9.42494i	0.668957	−	0.335963i	−0.0816980	−	0.996657i	$-0.526034\pi$
$787$	18.7666	−	9.42494i	0.668957	−	0.335963i	0.750655	+	0.660694i	$0.229738\pi$
$788$	9.23273	−	21.4039i	0.328902	−	0.762481i
$789$	−32.3719	+	30.1233i	−1.15247	+	1.07242i
$790$	−0.957355	−	16.4371i	−0.0340611	−	0.584807i
$791$	−4.33738	−	24.5985i	−0.154219	−	0.874622i
$792$	−47.9834	+	62.6359i	−1.70502	+	2.22567i
$793$	−0.429848	+	2.43779i	−0.0152643	+	0.0865683i
$794$	14.5726	+	1.70330i	0.517163	+	0.0604477i
$795$	−22.6192	+	6.60261i	−0.802219	+	0.234170i
$796$	20.5696	+	68.7072i	0.729070	+	2.43526i
$797$	−41.0669	−	9.73304i	−1.45467	−	0.344762i	−0.574139	−	0.818758i	$-0.694663\pi$
$797$	−41.0669	−	9.73304i	−1.45467	−	0.344762i	−0.880527	+	0.473996i	$0.842811\pi$
$798$	−89.6752	−	39.4157i	−3.17447	−	1.39530i
$799$	−6.86535	−	15.9157i	−0.242879	−	0.563056i
$800$	5.49242	+	4.60868i	0.194186	+	0.162942i
$801$	6.06735	+	10.8509i	0.214379	+	0.383397i
$802$	−20.5087	+	17.2089i	−0.724188	+	0.607666i
$803$	−47.2998	−	23.7549i	−1.66917	−	0.838291i
$804$	34.9339	+	26.3826i	1.23202	+	0.930442i
$805$	13.4872	−	1.57643i	0.475363	−	0.0555619i
$806$	−1.16523	+	20.0063i	−0.0410436	+	0.704692i
$807$	9.88866	−	26.5984i	0.348097	−	0.936307i
$808$	−17.1648	−	18.1936i	−0.603855	−	0.640048i
$809$	15.1427			0.532390			0.266195	−	0.963919i	$-0.414233\pi$
$809$	15.1427			0.532390			0.266195	+	0.963919i	$0.414233\pi$
$810$	−15.0450	−	27.7971i	−0.528627	−	0.976692i
$811$	30.4862			1.07051			0.535257	−	0.844689i	$-0.320215\pi$
$811$	30.4862			1.07051			0.535257	+	0.844689i	$0.320215\pi$
$812$	20.3703	+	21.5913i	0.714858	+	0.757706i
$813$	−46.5760	+	7.88278i	−1.63349	+	0.276461i
$814$	−4.61698	+	79.2704i	−0.161825	+	2.77843i
$815$	−9.07386	+	1.06058i	−0.317844	+	0.0371506i
$816$	25.8177	−	10.9267i	0.903799	−	0.382512i
$817$	5.04094	+	2.53165i	0.176360	+	0.0885714i
$818$	−6.36311	+	5.33928i	−0.222481	+	0.186684i
$819$	15.8147	−	12.9037i	0.552611	−	0.450892i
$820$	19.2947	+	16.1902i	0.673800	+	0.565386i
$821$	−17.6031	−	40.8085i	−0.614352	−	1.42423i	−0.886844	−	0.462070i	$-0.847107\pi$
$821$	−17.6031	−	40.8085i	−0.614352	−	1.42423i	0.272492	−	0.962158i	$-0.412152\pi$
$822$	−0.504599	−	4.59066i	−0.0175999	−	0.160118i
$823$	−23.0619	−	5.46577i	−0.803888	−	0.190525i	−0.191923	−	0.981410i	$-0.561472\pi$
$823$	−23.0619	−	5.46577i	−0.803888	−	0.190525i	−0.611965	+	0.790885i	$0.709621\pi$
$824$	22.2300	+	74.2535i	0.774420	+	2.58674i
$825$	5.87754	−	24.0608i	0.204630	−	0.837689i
$826$	12.6957	+	1.48392i	0.441740	+	0.0516320i
$827$	0.904516	−	5.12977i	0.0314531	−	0.178379i	−0.965034	−	0.262124i	$-0.915577\pi$
$827$	0.904516	−	5.12977i	0.0314531	−	0.178379i	0.996487	+	0.0837448i	$0.0266881\pi$
$828$	37.4173	−	8.32632i	1.30034	−	0.289360i
$829$	1.35636	+	7.69231i	0.0471084	+	0.267165i	0.999260	−	0.0384608i	$-0.0122455\pi$
$829$	1.35636	+	7.69231i	0.0471084	+	0.267165i	−0.952152	+	0.305626i	$0.901134\pi$
$830$	−3.05477	−	52.4484i	−0.106033	−	1.82051i
$831$	−37.9239	−	11.6384i	−1.31557	−	0.403732i
$832$	−4.12143	+	9.55455i	−0.142885	+	0.331245i
$833$	8.50616	−	4.27195i	0.294721	−	0.148014i
$834$	10.8003	+	30.3208i	0.373985	+	1.04992i
$835$	5.34646	−	1.26713i	0.185022	−	0.0438510i
$836$	71.1060	+	123.159i	2.45925	+	4.25955i
$837$	19.5084	+	1.54057i	0.674310	+	0.0532499i
$838$	3.56743	−	6.17897i	0.123235	−	0.213449i
$839$	8.63105	−	28.8297i	0.297977	−	0.995312i	−0.669597	−	0.742725i	$-0.733533\pi$
$839$	8.63105	−	28.8297i	0.297977	−	0.995312i	0.967574	−	0.252588i	$-0.0812816\pi$
$840$	−37.2477	−	21.8478i	−1.28517	−	0.753822i
$841$	20.1774	+	13.2709i	0.695772	+	0.457616i
$842$	9.36628	+	12.5811i	0.322783	+	0.433573i
$843$	−51.8713	+	2.66341i	−1.78654	+	0.0917328i
$844$	−68.1571	+	44.8277i	−2.34607	+	1.54303i
$845$	−11.1787	−	4.06870i	−0.384557	−	0.139967i
$846$	−17.6975	+	39.5239i	−0.608453	+	1.35886i
$847$	34.2925	−	12.4814i	1.17830	−	0.428867i
$848$	−31.1810	+	41.8833i	−1.07076	+	1.43828i
$849$	26.8191	+	1.74715i	0.920428	+	0.0599619i
$850$	−15.4856	+	16.4138i	−0.531151	+	0.562987i
$851$	13.9421	−	14.7778i	0.477929	−	0.506575i
$852$	26.1949	+	1.70649i	0.897424	+	0.0584632i
$853$	3.32810	−	4.47042i	0.113952	−	0.153064i	−0.741488	−	0.670966i	$-0.765879\pi$
$853$	3.32810	−	4.47042i	0.113952	−	0.153064i	0.855440	+	0.517902i	$0.173287\pi$
$854$	8.68141	−	3.15978i	0.297072	−	0.108125i
$855$	−29.8451	+	3.07300i	−1.02068	+	0.105094i
$856$	23.7619	+	8.64862i	0.812165	+	0.295604i
$857$	−14.6309	+	9.62290i	−0.499782	+	0.328712i	−0.774245	−	0.632886i	$-0.781870\pi$
$857$	−14.6309	+	9.62290i	−0.499782	+	0.328712i	0.274463	+	0.961598i	$0.411500\pi$
$858$	−43.6019	+	2.23881i	−1.48854	+	0.0764317i
$859$	−20.0517	−	26.9341i	−0.684154	−	0.918978i	0.315396	−	0.948960i	$-0.397863\pi$
$859$	−20.0517	−	26.9341i	−0.684154	−	0.918978i	−0.999550	+	0.0299816i	$0.990455\pi$
$860$	3.94495	+	2.59463i	0.134522	+	0.0884763i
$861$	20.1849	+	11.8395i	0.687899	+	0.403490i
$862$	12.3956	−	41.4042i	0.422196	−	1.41023i
$863$	−5.63576	+	9.76143i	−0.191844	+	0.332283i	−0.945861	−	0.324571i	$-0.894780\pi$
$863$	−5.63576	+	9.76143i	−0.191844	+	0.332283i	0.754018	+	0.656854i	$0.228113\pi$
$864$	−11.2288	−	5.12085i	−0.382010	−	0.174215i
$865$	11.4933	+	19.9069i	0.390782	+	0.676855i
$866$	−33.1791	+	7.86359i	−1.12747	+	0.267216i
$867$	−4.66349	−	13.0922i	−0.158380	−	0.444636i
$868$	45.3647	−	22.7830i	1.53978	−	0.773306i
$869$	−8.79634	+	20.3922i	−0.298395	+	0.691758i
$870$	12.8061	+	3.93003i	0.434166	+	0.133240i
$871$	0.741772	+	12.7357i	0.0251340	+	0.431534i
$872$	−6.88157	−	39.0273i	−0.233039	−	1.32163i
$873$	11.3271	−	36.0246i	0.383366	−	1.21925i
$874$	9.30925	−	52.7954i	0.314890	−	1.78583i
$875$	35.7636	+	4.18016i	1.20903	+	0.141315i
$876$	19.4049	−	79.4377i	0.655632	−	2.68395i
$877$	−10.5547	−	35.2552i	−0.356408	−	1.19049i	−0.928824	−	0.370522i	$-0.879179\pi$
$877$	−10.5547	−	35.2552i	−0.356408	−	1.19049i	0.572416	−	0.819963i	$-0.306006\pi$
$878$	90.5273	+	21.4554i	3.05515	+	0.724083i
$879$	−1.45702	−	13.2554i	−0.0491439	−	0.447093i
$880$	14.2676	+	33.0759i	0.480959	+	1.11499i
$881$	−10.8033	−	9.06508i	−0.363974	−	0.305410i	0.442398	−	0.896819i	$-0.354128\pi$
$881$	−10.8033	−	9.06508i	−0.363974	−	0.305410i	−0.806372	+	0.591408i	$0.798572\pi$
$882$	−22.2331	−	8.44021i	−0.748628	−	0.284197i
$883$	−26.7963	+	22.4847i	−0.901767	+	0.756672i	−0.970535	−	0.240961i	$-0.922538\pi$
$883$	−26.7963	+	22.4847i	−0.901767	+	0.756672i	0.0687683	+	0.997633i	$0.478093\pi$
$884$	24.1262	+	12.1166i	0.811451	+	0.407526i
$885$	3.60546	−	1.52592i	0.121196	−	0.0512934i
$886$	−11.0652	+	1.29334i	−0.371742	+	0.0434504i
$887$	−2.54514	+	43.6983i	−0.0854573	+	1.46725i	0.634336	+	0.773057i	$0.281273\pi$
$887$	−2.54514	+	43.6983i	−0.0854573	+	1.46725i	−0.719794	+	0.694188i	$0.755764\pi$
$888$	−63.7025	+	10.7814i	−2.13772	+	0.361799i
$889$	−22.4010	−	23.7436i	−0.751304	−	0.796336i
$890$	14.5535			0.487833
$891$	1.30749	+	42.6131i	0.0438027	+	1.42759i
$892$	−63.9539			−2.14134
$893$	28.2092	+	29.9000i	0.943986	+	1.00057i
$894$	−3.67666	+	9.88943i	−0.122966	+	0.330752i
$895$	−1.77557	+	30.4853i	−0.0593507	+	1.01901i
$896$	53.6240	−	6.26775i	1.79145	−	0.209391i
$897$	8.91423	+	6.73216i	0.297638	+	0.224780i
$898$	−8.17267	−	4.10447i	−0.272726	−	0.136968i
$899$	−6.35325	+	5.33101i	−0.211893	+	0.177799i
$900$	38.2619	+	0.526218i	1.27540	+	0.0175406i
$901$	−22.1820	−	18.6129i	−0.738988	−	0.620085i
$902$	−19.8257	−	45.9610i	−0.660122	−	1.53034i
$903$	4.01601	+	1.76519i	0.133644	+	0.0587418i
$904$	−42.3004	−	10.0254i	−1.40689	−	0.333439i
$905$	−2.56482	−	8.56710i	−0.0852576	−	0.284780i
$906$	88.6844	−	25.8873i	2.94634	−	0.860046i
$907$	16.6087	+	1.94128i	0.551482	+	0.0644590i	0.387270	−	0.921966i	$-0.373418\pi$
$907$	16.6087	+	1.94128i	0.551482	+	0.0644590i	0.164212	+	0.986425i	$0.447492\pi$
$908$	4.62359	−	26.2217i	0.153439	−	0.870196i
$909$	−13.4008	−	1.75344i	−0.444475	−	0.0581581i
$910$	−4.14918	−	23.5311i	−0.137544	−	0.780050i
$911$	1.11002	+	19.0583i	0.0367765	+	0.631429i	0.965459	+	0.260554i	$0.0839052\pi$
$911$	1.11002	+	19.0583i	0.0367765	+	0.631429i	−0.928683	+	0.370875i	$0.879058\pi$
$912$	−48.6728	+	45.2919i	−1.61172	+	1.49976i
$913$	−28.0678	+	65.0685i	−0.928908	+	2.15345i
$914$	40.9612	−	20.5715i	1.35488	−	0.680444i
$915$	1.83376	−	2.15512i	0.0606222	−	0.0712460i
$916$	38.3042	−	9.07825i	1.26561	−	0.299954i
$917$	13.7274	+	23.7765i	0.453319	+	0.785171i
$918$	18.1446	−	34.3436i	0.598860	−	1.13351i
$919$	−2.23912	+	3.87828i	−0.0738619	+	0.127933i	−0.900591	−	0.434668i	$-0.856866\pi$
$919$	−2.23912	+	3.87828i	−0.0738619	+	0.127933i	0.826729	+	0.562600i	$0.190199\pi$
$920$	6.77809	−	22.6404i	0.223467	−	0.746432i
$921$	−19.8121	+	11.2576i	−0.652831	+	0.370951i
$922$	−25.1467	−	16.5393i	−0.828164	−	0.544692i
$923$	4.56816	+	6.13610i	0.150363	+	0.201972i
$924$	60.1360	+	92.8163i	1.97833	+	3.05343i
$925$	16.9446	−	11.1447i	0.557136	−	0.366434i
$926$	6.45541	+	2.34958i	0.212138	+	0.0772119i
$927$	34.6708	+	23.4927i	1.13874	+	0.771601i
$928$	4.91493	−	1.78889i	0.161340	−	0.0587231i
$929$	−24.3387	+	32.6925i	−0.798526	+	1.07261i	0.197210	+	0.980361i	$0.436812\pi$
$929$	−24.3387	+	32.6925i	−0.798526	+	1.07261i	−0.995736	+	0.0922458i	$0.970595\pi$
$930$	12.7198	−	19.0528i	0.417098	−	0.624767i
$931$	−15.4912	+	16.4197i	−0.507704	+	0.538135i
$932$	61.0240	−	64.6817i	1.99891	−	2.11872i
$933$	4.20177	+	8.51184i	0.137560	+	0.278665i
$934$	−46.8985	+	62.9956i	−1.53456	+	2.06128i
$935$	−18.7715	+	6.83227i	−0.613894	+	0.223439i
$936$	−9.71939	−	34.1683i	−0.317688	−	1.11683i
$937$	−25.7954	−	9.38877i	−0.842700	−	0.306718i	−0.115640	−	0.993291i	$-0.536892\pi$
$937$	−25.7954	−	9.38877i	−0.842700	−	0.306718i	−0.727060	+	0.686574i	$0.759114\pi$
$938$	39.7796	−	26.1634i	1.29885	−	0.854266i
$939$	19.0533	−	37.2965i	0.621780	−	1.21713i
$940$	20.5472	+	27.5997i	0.670176	+	0.900203i
$941$	2.11164	+	1.38885i	0.0688375	+	0.0452751i	0.583461	−	0.812141i	$-0.301698\pi$
$941$	2.11164	+	1.38885i	0.0688375	+	0.0452751i	−0.514624	+	0.857416i	$0.672068\pi$
$942$	0.192007	−	27.9234i	0.00625592	−	0.909794i
$943$	−3.67311	+	12.2690i	−0.119613	+	0.399535i
$944$	4.33786	−	7.51340i	0.141185	−	0.244540i
$945$	−23.0567	+	3.57683i	−0.750036	+	0.116354i
$946$	−4.69172	−	8.12630i	−0.152541	−	0.264209i
$947$	−12.4238	+	2.94449i	−0.403718	+	0.0956829i	−0.427458	−	0.904035i	$-0.640591\pi$
$947$	−12.4238	+	2.94449i	−0.403718	+	0.0956829i	0.0237399	+	0.999718i	$0.492443\pi$
$948$	−33.7478	−	6.19022i	−1.09608	−	0.201049i
$949$	21.2954	−	10.6950i	0.691279	−	0.347173i
$950$	21.1967	−	49.1394i	0.687711	−	1.59429i
$951$	−4.01238	−	17.4638i	−0.130110	−	0.566303i
$952$	−3.08554	−	52.9766i	−0.100003	−	1.71698i
$953$	1.62376	+	9.20879i	0.0525987	+	0.298302i	0.999747	−	0.0224940i	$-0.00716067\pi$
$953$	1.62376	+	9.20879i	0.0525987	+	0.298302i	−0.947148	+	0.320796i	$0.896050\pi$
$954$	3.21288	+	72.2732i	0.104021	+	2.33993i
$955$	−3.37322	+	19.1305i	−0.109155	+	0.619048i
$956$	68.8265	+	8.04467i	2.22601	+	0.260183i
$957$	−13.0568	−	12.4893i	−0.422068	−	0.403722i
$958$	1.99484	+	6.66324i	0.0644504	+	0.215279i
$959$	−3.31732	−	0.786220i	−0.107122	−	0.0253884i
$960$	9.58981	−	7.03738i	0.309510	−	0.227131i
$961$	−6.66071	−	15.4413i	−0.214862	−	0.498105i
$962$	−27.3859	−	22.9795i	−0.882958	−	0.740890i
$963$	12.9022	−	4.49606i	0.415767	−	0.144884i
$964$	5.34797	−	4.48748i	0.172247	−	0.144532i
$965$	−4.75053	−	2.38580i	−0.152925	−	0.0768018i
$966$	5.12465	−	41.3749i	0.164883	−	1.33121i
$967$	2.13167	−	0.249157i	0.0685500	−	0.00801235i	−0.0817488	−	0.996653i	$-0.526051\pi$
$967$	2.13167	−	0.249157i	0.0685500	−	0.00801235i	0.150299	+	0.988641i	$0.451976\pi$
$968$	3.69299	−	63.4062i	0.118697	−	2.03795i
$969$	−23.5050	−	28.4066i	−0.755089	−	0.912550i
$970$	−30.3371	−	32.1555i	−0.974066	−	1.03245i
$971$	−18.8603			−0.605255			−0.302627	−	0.953109i	$-0.597864\pi$
$971$	−18.8603			−0.605255			−0.302627	+	0.953109i	$0.597864\pi$
$972$	−63.7108	+	16.7104i	−2.04352	+	0.535987i
$973$	23.7603			0.761719
$974$	−54.2748	−	57.5279i	−1.73908	−	1.84331i
$975$	7.10896	+	8.59142i	0.227669	+	0.275146i
$976$	0.364601	−	6.25996i	0.0116706	−	0.200376i
$977$	−59.7085	+	6.97892i	−1.91024	+	0.223276i	−0.986975	−	0.160876i	$-0.948568\pi$
$977$	−59.7085	+	6.97892i	−1.91024	+	0.223276i	−0.923270	+	0.384151i	$0.874494\pi$
$978$	−3.44773	+	27.8359i	−0.110246	+	0.890095i
$979$	−17.5422	−	8.81001i	−0.560650	−	0.281569i
$980$	−14.4748	+	12.1458i	−0.462380	+	0.387983i
$981$	−16.2123	−	13.9881i	−0.517618	−	0.446606i
$982$	67.2670	+	56.4437i	2.14657	+	1.80119i
$983$	12.7239	+	29.4973i	0.405829	+	0.940817i	0.991481	+	0.130254i	$0.0415793\pi$
$983$	12.7239	+	29.4973i	0.405829	+	0.940817i	−0.585652	+	0.810563i	$0.699161\pi$
$984$	32.8349	−	24.0955i	1.04674	−	0.768138i
$985$	−7.55598	−	1.79080i	−0.240754	−	0.0570597i
$986$	4.72125	+	15.7701i	0.150355	+	0.502221i
$987$	23.1011	+	22.0970i	0.735317	+	0.703355i
$988$	−63.5941	−	7.43309i	−2.02320	−	0.236478i
$989$	−0.416905	+	2.36439i	−0.0132568	+	0.0751831i
$990$	44.2875	+	23.0100i	1.40755	+	0.731307i
$991$	−2.05455	−	11.6519i	−0.0652648	−	0.370135i	−0.999895	−	0.0145131i	$-0.995380\pi$
$991$	−2.05455	−	11.6519i	−0.0652648	−	0.370135i	0.934630	−	0.355622i	$-0.115731\pi$
$992$	−0.520093	−	8.92965i	−0.0165130	−	0.283517i
$993$	11.9315	+	51.9318i	0.378636	+	1.64801i
$994$	11.3082	−	26.2154i	0.358675	−	0.831503i
$995$	21.3507	−	10.7227i	0.676861	−	0.339933i
$996$	−107.684	−	19.7520i	−3.41211	−	0.625867i
$997$	−41.3358	+	9.79677i	−1.30912	+	0.310267i	−0.825198	−	0.564844i	$-0.808936\pi$
$997$	−41.3358	+	9.79677i	−1.30912	+	0.310267i	−0.483922	+	0.875111i	$0.660788\pi$
$998$	−9.96735	−	17.2640i	−0.315511	−	0.546481i
$999$	−22.9862	+	26.2737i	−0.727252	+	0.831263i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.22.8	✓	144
3.2	odd	2		243.2.g.a.199.1		144
9.2	odd	6		729.2.g.a.352.1		144
9.4	even	3		729.2.g.c.595.1		144
9.5	odd	6		729.2.g.b.595.8		144
9.7	even	3		729.2.g.d.352.8		144
81.11	odd	54		243.2.g.a.127.1		144
81.16	even	27		729.2.g.d.379.8		144
81.31	even	27		6561.2.a.c.1.6		72
81.38	odd	54		729.2.g.b.136.8		144
81.43	even	27		729.2.g.c.136.1		144
81.50	odd	54		6561.2.a.d.1.67		72
81.65	odd	54		729.2.g.a.379.1		144
81.70	even	27	inner	81.2.g.a.70.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.8	✓	144	1.1	even	1	trivial
81.2.g.a.70.8	yes	144	81.70	even	27	inner
243.2.g.a.127.1		144	81.11	odd	54
243.2.g.a.199.1		144	3.2	odd	2
729.2.g.a.352.1		144	9.2	odd	6
729.2.g.a.379.1		144	81.65	odd	54
729.2.g.b.136.8		144	81.38	odd	54
729.2.g.b.595.8		144	9.5	odd	6
729.2.g.c.136.1		144	81.43	even	27
729.2.g.c.595.1		144	9.4	even	3
729.2.g.d.352.8		144	9.7	even	3
729.2.g.d.379.8		144	81.16	even	27
6561.2.a.c.1.6		72	81.31	even	27
6561.2.a.d.1.67		72	81.50	odd	54

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71221 + 1.81484i) q^{2} +(-1.10419 - 1.33445i) q^{3} +(-0.245679 + 4.21814i) q^{4} +(1.39804 - 0.163408i) q^{5} +(0.531205 - 4.28879i) q^{6} +(-2.85083 - 1.43174i) q^{7} +(-4.25325 + 3.56890i) q^{8} +(-0.561524 + 2.94698i) q^{9} +(2.69030 + 2.25743i) q^{10} +(-1.87624 - 4.34961i) q^{11} +(5.90018 - 4.32979i) q^{12} +(2.07522 + 0.491837i) q^{13} +(-2.28284 - 7.62523i) q^{14} +(-1.76177 - 1.68519i) q^{15} +(-5.36597 - 0.627192i) q^{16} +(0.520249 - 2.95048i) q^{17} +(-6.30973 + 4.02677i) q^{18} +(1.23380 + 6.99724i) q^{19} +(0.345808 + 5.93730i) q^{20} +(1.23727 + 5.38521i) q^{21} +(4.68131 - 10.8525i) q^{22} +(-2.70239 + 1.35719i) q^{23} +(9.45892 + 1.73501i) q^{24} +(-2.93740 + 0.696176i) q^{25} +(2.66061 + 4.60832i) q^{26} +(4.55263 - 2.50470i) q^{27} +(6.73968 - 11.6735i) q^{28} +(-0.631591 + 2.10966i) q^{29} +(0.0418260 - 6.08272i) q^{30} +(3.14652 + 2.06950i) q^{31} +(-1.41830 - 1.90511i) q^{32} +(-3.73262 + 7.30654i) q^{33} +(6.24541 - 4.10767i) q^{34} +(-4.21955 - 1.53579i) q^{35} +(-12.2928 - 3.09260i) q^{36} +(-6.31317 + 2.29781i) q^{37} +(-10.5863 + 14.2199i) q^{38} +(-1.63511 - 3.31237i) q^{39} +(-5.36304 + 5.68449i) q^{40} +(2.90628 - 3.08048i) q^{41} +(-7.65481 + 11.4661i) q^{42} +(0.474097 - 0.636822i) q^{43} +(18.8082 - 6.84563i) q^{44} +(-0.303475 + 4.21177i) q^{45} +(-7.09015 - 2.58060i) q^{46} +(4.83370 - 3.17917i) q^{47} +(5.08810 + 7.85317i) q^{48} +(1.89725 + 2.54844i) q^{49} +(-6.29289 - 4.13890i) q^{50} +(-4.51172 + 2.56364i) q^{51} +(-2.58448 + 8.63275i) q^{52} +(4.83254 - 8.37020i) q^{53} +(12.3407 + 3.97371i) q^{54} +(-3.33382 - 5.77435i) q^{55} +(17.2350 - 4.08478i) q^{56} +(7.97512 - 9.37273i) q^{57} +(-4.91010 + 2.46595i) q^{58} +(-0.636054 + 1.47454i) q^{59} +(7.54120 - 7.01737i) q^{60} +(0.0674875 + 1.15872i) q^{61} +(1.63170 + 9.25383i) q^{62} +(5.82012 - 7.59739i) q^{63} +(-0.847235 + 4.80491i) q^{64} +(2.98162 + 0.348502i) q^{65} +(-19.6512 + 5.73625i) q^{66} +(1.71558 + 5.73045i) q^{67} +(12.3177 + 2.91935i) q^{68} +(4.79507 + 2.10761i) q^{69} +(-4.43754 - 10.2874i) q^{70} +(2.74773 + 2.30562i) q^{71} +(-8.12917 - 14.5383i) q^{72} +(8.55952 - 7.18229i) q^{73} +(-14.9796 - 7.52304i) q^{74} +(4.17246 + 3.15111i) q^{75} +(-29.8185 + 3.48528i) q^{76} +(-0.878675 + 15.0863i) q^{77} +(3.21175 - 8.63892i) q^{78} +(-3.21730 - 3.41014i) q^{79} -7.60435 q^{80} +(-8.36938 - 3.30960i) q^{81} +10.5667 q^{82} +(-10.2659 - 10.8812i) q^{83} +(-23.0196 + 3.89596i) q^{84} +(0.245199 - 4.20991i) q^{85} +(1.96748 - 0.229966i) q^{86} +(3.51264 - 1.48664i) q^{87} +(23.5034 + 11.8038i) q^{88} +(3.17449 - 2.66371i) q^{89} +(-8.16328 + 6.66067i) q^{90} +(-5.21193 - 4.37333i) q^{91} +(-5.06091 - 11.7325i) q^{92} +(-0.712713 - 6.48400i) q^{93} +(14.0460 + 3.32896i) q^{94} +(2.86831 + 9.58083i) q^{95} +(-0.976202 + 3.99627i) q^{96} +(-12.5027 - 1.46135i) q^{97} +(-1.37652 + 7.80666i) q^{98} +(13.8718 - 3.08682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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