LMFDB - Embedded newform 81.2.g.a.76.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,2,Mod(4,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			76.5
Character	$\chi$	$=$	81.76
Dual form			81.2.g.a.16.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.308722 - 0.0731685i) q^{2} +(-0.589070 + 1.62880i) q^{3} +(-1.69731 + 0.852421i) q^{4} +(1.26676 + 1.70155i) q^{5} +(-0.0626820 + 0.545949i) q^{6} +(2.12510 - 1.39770i) q^{7} +(-0.947719 + 0.795231i) q^{8} +(-2.30599 - 1.91896i) q^{9} +(0.515577 + 0.432621i) q^{10} +(3.03935 + 0.355249i) q^{11} +(-0.388591 - 3.26672i) q^{12} +(-1.58287 - 5.28715i) q^{13} +(0.553798 - 0.586992i) q^{14} +(-3.51771 + 1.06097i) q^{15} +(2.03401 - 2.73216i) q^{16} +(-0.745021 + 4.22522i) q^{17} +(-0.852318 - 0.423699i) q^{18} +(-0.0105922 - 0.0600713i) q^{19} +(-3.60052 - 1.80825i) q^{20} +(1.02475 + 4.28471i) q^{21} +(0.964308 - 0.112711i) q^{22} +(3.57659 + 2.35236i) q^{23} +(-0.737001 - 2.01209i) q^{24} +(0.143411 - 0.479026i) q^{25} +(-0.875520 - 1.51644i) q^{26} +(4.48399 - 2.62561i) q^{27} +(-2.41553 + 4.18381i) q^{28} +(-7.32825 - 7.76750i) q^{29} +(-1.00836 + 0.584929i) q^{30} +(-0.268252 + 4.60570i) q^{31} +(1.40807 - 3.26426i) q^{32} +(-2.36902 + 4.74124i) q^{33} +(0.0791488 + 1.35893i) q^{34} +(5.07026 + 1.84542i) q^{35} +(5.54974 + 1.29139i) q^{36} +(-3.30730 + 1.20376i) q^{37} +(-0.00766537 - 0.0177703i) q^{38} +(9.54414 + 0.536322i) q^{39} +(-2.55366 - 0.605229i) q^{40} +(2.45211 + 0.581160i) q^{41} +(0.629868 + 1.24781i) q^{42} +(-0.307278 - 0.712352i) q^{43} +(-5.46154 + 1.98784i) q^{44} +(0.344070 - 6.35463i) q^{45} +(1.27629 + 0.464532i) q^{46} +(0.264358 + 4.53885i) q^{47} +(3.25196 + 4.92244i) q^{48} +(-0.210070 + 0.486996i) q^{49} +(0.00922453 - 0.158379i) q^{50} +(-6.44318 - 3.70244i) q^{51} +(7.19350 + 7.62466i) q^{52} +(0.986349 - 1.70841i) q^{53} +(1.19220 - 1.13867i) q^{54} +(3.24565 + 5.62164i) q^{55} +(-0.902505 + 3.01458i) q^{56} +(0.104084 + 0.0181336i) q^{57} +(-2.83073 - 1.86180i) q^{58} +(-7.16462 + 0.837424i) q^{59} +(5.06624 - 4.79935i) q^{60} +(-10.4367 - 5.24152i) q^{61} +(0.254177 + 1.44151i) q^{62} +(-7.58260 - 0.854890i) q^{63} +(-0.987085 + 5.59804i) q^{64} +(6.99126 - 9.39089i) q^{65} +(-0.384461 + 1.63706i) q^{66} +(0.832392 - 0.882284i) q^{67} +(-2.33714 - 7.80658i) q^{68} +(-5.93839 + 4.43985i) q^{69} +(1.70033 + 0.198740i) q^{70} +(-10.9300 - 9.17137i) q^{71} +(3.71145 - 0.0151639i) q^{72} +(7.44218 - 6.24473i) q^{73} +(-0.932958 + 0.613616i) q^{74} +(0.695759 + 0.515768i) q^{75} +(0.0691843 + 0.0929306i) q^{76} +(6.95546 - 3.49317i) q^{77} +(2.98573 - 0.532756i) q^{78} +(1.56773 - 0.371558i) q^{79} +7.22552 q^{80} +(1.63521 + 8.85020i) q^{81} +0.799542 q^{82} +(3.21323 - 0.761549i) q^{83} +(-5.39169 - 6.39897i) q^{84} +(-8.13321 + 4.08465i) q^{85} +(-0.146985 - 0.197436i) q^{86} +(16.9686 - 7.36068i) q^{87} +(-3.16296 + 2.08031i) q^{88} +(-10.7606 + 9.02919i) q^{89} +(-0.358737 - 1.98699i) q^{90} +(-10.7536 - 9.02336i) q^{91} +(-8.07578 - 0.943923i) q^{92} +(-7.34376 - 3.15001i) q^{93} +(0.413714 + 1.38190i) q^{94} +(0.0887968 - 0.0941191i) q^{95} +(4.48739 + 4.21634i) q^{96} +(4.19394 - 5.63344i) q^{97} +(-0.0292204 + 0.165717i) q^{98} +(-6.32702 - 6.65159i) 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{25}{27}\right)$

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 $

$2$	0.308722	−	0.0731685i	0.218300	−	0.0517379i	−0.120011	−	0.992773i	$-0.538293\pi$
$2$	0.308722	−	0.0731685i	0.218300	−	0.0517379i	0.338310	+	0.941035i	$0.390145\pi$
$3$	−0.589070	+	1.62880i	−0.340100	+	0.940389i
$3$	−0.589070	+	1.62880i	−0.340100	+	0.940389i
$4$	−1.69731	+	0.852421i	−0.848655	+	0.426210i
$5$	1.26676	+	1.70155i	0.566512	+	0.760958i	0.989399	−	0.145225i	$-0.0463905\pi$
$5$	1.26676	+	1.70155i	0.566512	+	0.760958i	−0.422886	+	0.906183i	$0.638983\pi$
$6$	−0.0626820	+	0.545949i	−0.0255898	+	0.222883i
$7$	2.12510	−	1.39770i	0.803213	−	0.528282i	−0.0802542	−	0.996774i	$-0.525573\pi$
$7$	2.12510	−	1.39770i	0.803213	−	0.528282i	0.883467	+	0.468493i	$0.155203\pi$
$8$	−0.947719	+	0.795231i	−0.335069	+	0.281157i
$9$	−2.30599	−	1.91896i	−0.768664	−	0.639652i
$10$	0.515577	+	0.432621i	0.163040	+	0.136807i
$11$	3.03935	+	0.355249i	0.916399	+	0.107112i	0.561201	−	0.827679i	$-0.310339\pi$
$11$	3.03935	+	0.355249i	0.916399	+	0.107112i	0.355198	+	0.934791i	$0.384413\pi$
$12$	−0.388591	−	3.26672i	−0.112176	−	0.943020i
$13$	−1.58287	−	5.28715i	−0.439009	−	1.46639i	−0.836082	−	0.548605i	$-0.815159\pi$
$13$	−1.58287	−	5.28715i	−0.439009	−	1.46639i	0.397073	−	0.917787i	$-0.370026\pi$
$14$	0.553798	−	0.586992i	0.148009	−	0.156880i
$15$	−3.51771	+	1.06097i	−0.908268	+	0.273940i
$16$	2.03401	−	2.73216i	0.508504	−	0.683039i
$17$	−0.745021	+	4.22522i	−0.180694	+	1.02477i	0.750670	+	0.660678i	$0.229731\pi$
$17$	−0.745021	+	4.22522i	−0.180694	+	1.02477i	−0.931364	+	0.364090i	$0.881380\pi$
$18$	−0.852318	−	0.423699i	−0.200893	−	0.0998667i
$19$	−0.0105922	−	0.0600713i	−0.00243002	−	0.0137813i	0.983569	−	0.180535i	$-0.0577828\pi$
$19$	−0.0105922	−	0.0600713i	−0.00243002	−	0.0137813i	−0.985999	+	0.166753i	$0.946672\pi$
$20$	−3.60052	−	1.80825i	−0.805102	−	0.404337i
$21$	1.02475	+	4.28471i	0.223618	+	0.935001i
$22$	0.964308	−	0.112711i	0.205591	−	0.0240302i
$23$	3.57659	+	2.35236i	0.745770	+	0.490501i	0.864629	−	0.502410i	$-0.167553\pi$
$23$	3.57659	+	2.35236i	0.745770	+	0.490501i	−0.118859	+	0.992911i	$0.537924\pi$
$24$	−0.737001	−	2.01209i	−0.150440	−	0.410717i
$25$	0.143411	−	0.479026i	0.0286822	−	0.0958052i
$26$	−0.875520	−	1.51644i	−0.171704	−	0.297399i
$27$	4.48399	−	2.62561i	0.862945	−	0.505298i
$28$	−2.41553	+	4.18381i	−0.456491	+	0.790666i
$29$	−7.32825	−	7.76750i	−1.36082	−	1.44239i	−0.775026	−	0.631930i	$-0.782263\pi$
$29$	−7.32825	−	7.76750i	−1.36082	−	1.44239i	−0.585797	−	0.810458i	$-0.699218\pi$
$30$	−1.00836	+	0.584929i	−0.184101	+	0.106793i
$31$	−0.268252	+	4.60570i	−0.0481794	+	0.827208i	0.884509	+	0.466524i	$0.154494\pi$
$31$	−0.268252	+	4.60570i	−0.0481794	+	0.827208i	−0.932688	+	0.360684i	$0.882543\pi$
$32$	1.40807	−	3.26426i	0.248913	−	0.577046i
$33$	−2.36902	+	4.74124i	−0.412394	+	0.825343i
$34$	0.0791488	+	1.35893i	0.0135739	+	0.233055i
$35$	5.07026	+	1.84542i	0.857030	+	0.311933i
$36$	5.54974	+	1.29139i	0.924957	+	0.215231i
$37$	−3.30730	+	1.20376i	−0.543716	+	0.197896i	−0.599252	−	0.800560i	$-0.704535\pi$
$37$	−3.30730	+	1.20376i	−0.543716	+	0.197896i	0.0555362	+	0.998457i	$0.482313\pi$
$38$	−0.00766537	−	0.0177703i	−0.00124349	−	0.00288273i
$39$	9.54414	+	0.536322i	1.52829	+	0.0858803i
$40$	−2.55366	−	0.605229i	−0.403769	−	0.0956951i
$41$	2.45211	+	0.581160i	0.382955	+	0.0907619i	0.417584	−	0.908638i	$-0.362877\pi$
$41$	2.45211	+	0.581160i	0.382955	+	0.0907619i	−0.0346293	+	0.999400i	$0.511025\pi$
$42$	0.629868	+	1.24781i	0.0971907	+	0.192541i
$43$	−0.307278	−	0.712352i	−0.0468595	−	0.108633i	0.893178	−	0.449702i	$-0.148470\pi$
$43$	−0.307278	−	0.712352i	−0.0468595	−	0.108633i	−0.940038	+	0.341070i	$0.889211\pi$
$44$	−5.46154	+	1.98784i	−0.823359	+	0.299678i
$45$	0.344070	−	6.35463i	0.0512909	−	0.947292i
$46$	1.27629	+	0.464532i	0.188179	+	0.0684915i
$47$	0.264358	+	4.53885i	0.0385606	+	0.662060i	0.961107	+	0.276175i	$0.0890668\pi$
$47$	0.264358	+	4.53885i	0.0385606	+	0.662060i	−0.922547	+	0.385885i	$0.873896\pi$
$48$	3.25196	+	4.92244i	0.469381	+	0.710493i
$49$	−0.210070	+	0.486996i	−0.0300100	+	0.0695709i
$50$	0.00922453	−	0.158379i	0.00130455	−	0.0223982i
$51$	−6.44318	−	3.70244i	−0.902226	−	0.518446i
$52$	7.19350	+	7.62466i	0.997559	+	1.05735i
$53$	0.986349	−	1.70841i	0.135485	−	0.234668i	−0.790297	−	0.612724i	$-0.790074\pi$
$53$	0.986349	−	1.70841i	0.135485	−	0.234668i	0.925783	+	0.378056i	$0.123407\pi$
$54$	1.19220	−	1.13867i	0.162237	−	0.154953i
$55$	3.24565	+	5.62164i	0.437644	+	0.758021i
$56$	−0.902505	+	3.01458i	−0.120602	+	0.402840i
$57$	0.104084	+	0.0181336i	0.0137862	+	0.00240186i
$58$	−2.83073	−	1.86180i	−0.371693	−	0.244466i
$59$	−7.16462	+	0.837424i	−0.932754	+	0.109023i	−0.568876	−	0.822423i	$-0.692622\pi$
$59$	−7.16462	+	0.837424i	−0.932754	+	0.109023i	−0.363878	+	0.931447i	$0.618548\pi$
$60$	5.06624	−	4.79935i	0.654049	−	0.619594i
$61$	−10.4367	−	5.24152i	−1.33629	−	0.671108i	−0.370109	−	0.928988i	$-0.620680\pi$
$61$	−10.4367	−	5.24152i	−1.33629	−	0.671108i	−0.966177	+	0.257880i	$0.916976\pi$
$62$	0.254177	+	1.44151i	0.0322805	+	0.183072i
$63$	−7.58260	−	0.854890i	−0.955318	−	0.107706i
$64$	−0.987085	+	5.59804i	−0.123386	+	0.699755i
$65$	6.99126	−	9.39089i	0.867159	−	1.16480i
$66$	−0.384461	+	1.63706i	−0.0473238	+	0.201508i
$67$	0.832392	−	0.882284i	0.101693	−	0.107788i	−0.674528	−	0.738249i	$-0.735653\pi$
$67$	0.832392	−	0.882284i	0.101693	−	0.107788i	0.776221	+	0.630461i	$0.217134\pi$
$68$	−2.33714	−	7.80658i	−0.283420	−	0.946687i
$69$	−5.93839	+	4.43985i	−0.714898	+	0.534495i
$70$	1.70033	+	0.198740i	0.203228	+	0.0237540i
$71$	−10.9300	−	9.17137i	−1.29715	−	1.08844i	−0.990629	−	0.136579i	$-0.956389\pi$
$71$	−10.9300	−	9.17137i	−1.29715	−	1.08844i	−0.306525	−	0.951863i	$-0.599166\pi$
$72$	3.71145	−	0.0151639i	0.437398	−	0.00178708i
$73$	7.44218	−	6.24473i	0.871042	−	0.730891i	−0.0932755	−	0.995640i	$-0.529734\pi$
$73$	7.44218	−	6.24473i	0.871042	−	0.730891i	0.964317	+	0.264750i	$0.0852893\pi$
$74$	−0.932958	+	0.613616i	−0.108454	+	0.0713315i
$75$	0.695759	+	0.515768i	0.0803393	+	0.0595557i
$76$	0.0691843	+	0.0929306i	0.00793598	+	0.0106599i
$77$	6.95546	−	3.49317i	0.792649	−	0.398083i
$78$	2.98573	−	0.532756i	0.338067	−	0.0603228i
$79$	1.56773	−	0.371558i	0.176383	−	0.0418036i	−0.141475	−	0.989942i	$-0.545185\pi$
$79$	1.56773	−	0.371558i	0.176383	−	0.0418036i	0.317858	+	0.948138i	$0.397036\pi$
$80$	7.22552			0.807838
$81$	1.63521	+	8.85020i	0.181690	+	0.983356i
$82$	0.799542			0.0882947
$83$	3.21323	−	0.761549i	0.352698	−	0.0835909i	−0.0504480	−	0.998727i	$-0.516065\pi$
$83$	3.21323	−	0.761549i	0.352698	−	0.0835909i	0.403146	+	0.915136i	$0.367917\pi$
$84$	−5.39169	−	6.39897i	−0.588282	−	0.698185i
$85$	−8.13321	+	4.08465i	−0.882170	+	0.443043i
$86$	−0.146985	−	0.197436i	−0.0158498	−	0.0212900i
$87$	16.9686	−	7.36068i	1.81922	−	0.789147i
$88$	−3.16296	+	2.08031i	−0.337172	+	0.221762i
$89$	−10.7606	+	9.02919i	−1.14062	+	0.957092i	−0.999459	−	0.0328946i	$-0.989527\pi$
$89$	−10.7606	+	9.02919i	−1.14062	+	0.957092i	−0.141159	+	0.989987i	$0.545083\pi$
$90$	−0.358737	−	1.98699i	−0.0378142	−	0.209447i
$91$	−10.7536	−	9.02336i	−1.12729	−	0.945905i
$92$	−8.07578	−	0.943923i	−0.841958	−	0.0984108i
$93$	−7.34376	−	3.15001i	−0.761512	−	0.326641i
$94$	0.413714	+	1.38190i	0.0426714	+	0.142532i
$95$	0.0887968	−	0.0941191i	0.00911036	−	0.00965642i
$96$	4.48739	+	4.21634i	0.457992	+	0.430328i
$97$	4.19394	−	5.63344i	0.425830	−	0.571989i	−0.536491	−	0.843906i	$-0.680250\pi$
$97$	4.19394	−	5.63344i	0.425830	−	0.571989i	0.962321	+	0.271917i	$0.0876577\pi$
$98$	−0.0292204	+	0.165717i	−0.00295170	+	0.0167399i
$99$	−6.32702	−	6.65159i	−0.635889	−	0.668510i
$100$	0.164919	+	0.935301i	0.0164919	+	0.0935301i
$101$	9.69929	+	4.87117i	0.965115	+	0.484699i	0.860298	−	0.509792i	$-0.170278\pi$
$101$	9.69929	+	4.87117i	0.965115	+	0.484699i	0.104818	+	0.994491i	$0.466574\pi$
$102$	−2.26006	−	0.671589i	−0.223779	−	0.0664972i
$103$	12.3527	−	1.44382i	1.21714	−	0.142264i	0.516824	−	0.856092i	$-0.327114\pi$
$103$	12.3527	−	1.44382i	1.21714	−	0.142264i	0.700321	+	0.713828i	$0.253040\pi$
$104$	5.70462	+	3.75199i	0.559384	+	0.367913i
$105$	−5.99257	+	7.17137i	−0.584815	+	0.699854i
$106$	0.179506	−	0.599593i	0.0174352	−	0.0582376i
$107$	−2.48915	−	4.31134i	−0.240636	−	0.416793i	0.720260	−	0.693704i	$-0.244023\pi$
$107$	−2.48915	−	4.31134i	−0.240636	−	0.416793i	−0.960896	+	0.276911i	$0.910689\pi$
$108$	−5.37260	+	8.27871i	−0.516979	+	0.796620i
$109$	−0.180626	+	0.312853i	−0.0173008	+	0.0299659i	−0.874546	−	0.484942i	$-0.838841\pi$
$109$	−0.180626	+	0.312853i	−0.0173008	+	0.0299659i	0.857245	+	0.514908i	$0.172174\pi$
$110$	1.41333	+	1.49804i	0.134756	+	0.142833i
$111$	−0.0124532	−	6.09603i	−0.00118201	−	0.578609i
$112$	0.503750	−	8.64906i	0.0475999	−	0.817259i
$113$	−7.81938	+	18.1274i	−0.735585	+	1.70528i	−0.0270186	+	0.999635i	$0.508601\pi$
$113$	−7.81938	+	18.1274i	−0.735585	+	1.70528i	−0.708567	+	0.705644i	$0.750658\pi$
$114$	0.0334598	−	0.00201740i	0.00313380	−	0.000188947i
$115$	0.528013	+	9.06563i	0.0492375	+	0.845375i
$116$	19.0595	+	6.93709i	1.76963	+	0.644092i
$117$	−6.49573	+	15.2296i	−0.600531	+	1.40798i
$118$	−2.15060	+	0.782756i	−0.197979	+	0.0720585i
$119$	4.32236	+	10.0203i	0.396230	+	0.918564i
$120$	2.49008	−	3.80289i	0.227312	−	0.347154i
$121$	−1.59204	−	0.377320i	−0.144731	−	0.0343018i
$122$	−3.60556	−	0.854534i	−0.326432	−	0.0773659i
$123$	−2.39106	+	3.65165i	−0.215594	+	0.329258i
$124$	−3.47069	−	8.04596i	−0.311677	−	0.722549i
$125$	10.9637	−	3.99045i	0.980620	−	0.356916i
$126$	−2.40347	+	0.290884i	−0.214118	+	0.0259140i
$127$	13.5556	+	4.93382i	1.20286	+	0.437806i	0.864222	−	0.503111i	$-0.167811\pi$
$127$	13.5556	+	4.93382i	1.20286	+	0.437806i	0.338639	+	0.940916i	$0.390033\pi$
$128$	0.518275	+	8.89844i	0.0458095	+	0.786519i
$129$	1.34129	−	0.0808708i	0.118094	−	0.00712028i
$130$	1.47124	−	3.41072i	0.129036	−	0.299140i
$131$	−0.177620	+	3.04963i	−0.0155188	+	0.266447i	0.981620	+	0.190848i	$0.0611238\pi$
$131$	−0.177620	+	3.04963i	−0.0155188	+	0.266447i	−0.997138	+	0.0755987i	$0.975913\pi$
$132$	−0.0205648	−	10.0667i	−0.00178993	−	0.876198i
$133$	−0.106471	−	0.112853i	−0.00923223	−	0.00978559i
$134$	0.192422	−	0.333285i	0.0166228	−	0.0287915i
$135$	10.1478	+	4.30374i	0.873380	+	0.370407i
$136$	−2.65396	−	4.59679i	−0.227575	−	0.394171i
$137$	−0.747117	+	2.49555i	−0.0638306	+	0.213209i	−0.983955	−	0.178417i	$-0.942902\pi$
$137$	−0.747117	+	2.49555i	−0.0638306	+	0.213209i	0.920124	+	0.391626i	$0.128087\pi$
$138$	−1.50846	+	1.80518i	−0.128408	+	0.153667i
$139$	15.8610	+	10.4319i	1.34531	+	0.884823i	0.998587	−	0.0531448i	$-0.0169245\pi$
$139$	15.8610	+	10.4319i	1.34531	+	0.884823i	0.346722	+	0.937968i	$0.387295\pi$
$140$	−10.1789	+	1.18974i	−0.860272	+	0.100551i
$141$	−7.54862	−	2.24312i	−0.635708	−	0.188904i
$142$	−4.04539	−	2.03167i	−0.339482	−	0.170494i
$143$	−2.93264	−	16.6318i	−0.245240	−	1.39082i
$144$	−9.93331	+	2.39714i	−0.827776	+	0.199762i
$145$	3.93367	−	22.3090i	0.326674	−	1.85266i
$146$	1.84065	−	2.47242i	0.152333	−	0.204619i
$147$	−0.669475	−	0.629037i	−0.0552174	−	0.0518821i
$148$	4.58740	−	4.86236i	0.377082	−	0.399683i
$149$	−1.17521	−	3.92548i	−0.0962772	−	0.321588i	0.896260	−	0.443529i	$-0.146274\pi$
$149$	−1.17521	−	3.92548i	−0.0962772	−	0.321588i	−0.992537	+	0.121940i	$0.961088\pi$
$150$	0.252534	+	0.108321i	0.0206193	+	0.00884440i
$151$	−9.87403	−	1.15411i	−0.803537	−	0.0939200i	−0.295597	−	0.955313i	$-0.595519\pi$
$151$	−9.87403	−	1.15411i	−0.803537	−	0.0939200i	−0.507940	+	0.861393i	$0.669593\pi$
$152$	0.0578090	+	0.0485075i	0.00468893	+	0.00393448i
$153$	9.82603	−	8.31367i	0.794388	−	0.672120i
$154$	1.89172	−	1.58734i	0.152439	−	0.127911i
$155$	−8.17666	+	5.37787i	−0.656765	+	0.431961i
$156$	−16.6565	+	7.22532i	−1.33359	+	0.578489i
$157$	6.89692	+	9.26417i	0.550434	+	0.739361i	0.987072	−	0.160276i	$-0.0512384\pi$
$157$	6.89692	+	9.26417i	0.550434	+	0.739361i	−0.436638	+	0.899637i	$0.643831\pi$
$158$	0.456806	−	0.229417i	0.0363415	−	0.0182514i
$159$	2.20163	+	2.61294i	0.174600	+	0.207220i
$160$	7.33800	−	1.73914i	0.580120	−	0.137491i
$161$	10.8885			0.858135
$162$	1.15238	+	2.61261i	0.0905395	+	0.205266i
$163$	−14.1333			−1.10700			−0.553502	−	0.832848i	$-0.686709\pi$
$163$	−14.1333			−1.10700			−0.553502	+	0.832848i	$0.686709\pi$
$164$	−4.65738	+	1.10382i	−0.363680	+	0.0861938i
$165$	−11.0685	+	1.97499i	−0.861678	+	0.153753i
$166$	0.936274	−	0.470214i	0.0726689	−	0.0364957i
$167$	−4.00307	−	5.37705i	−0.309767	−	0.416089i	0.619790	−	0.784768i	$-0.287218\pi$
$167$	−4.00307	−	5.37705i	−0.309767	−	0.416089i	−0.929557	+	0.368679i	$0.879810\pi$
$168$	−4.37851	−	3.24580i	−0.337809	−	0.250419i
$169$	−14.5872	+	9.59412i	−1.12209	+	0.738009i
$170$	−2.21203	+	1.85612i	−0.169655	+	0.142358i
$171$	−0.0908488	+	0.158850i	−0.00694738	+	0.0121476i
$172$	1.12877	+	0.947150i	0.0860679	+	0.0722195i
$173$	14.6888	+	1.71687i	1.11677	+	0.130531i	0.654394	−	0.756154i	$-0.272924\pi$
$173$	14.6888	+	1.71687i	1.11677	+	0.130531i	0.462374	+	0.886685i	$0.346998\pi$
$174$	4.70000	−	3.51397i	0.356306	−	0.266393i
$175$	−0.364772	−	1.21842i	−0.0275742	−	0.0921042i
$176$	7.15268	−	7.58140i	0.539154	−	0.571470i
$177$	2.85647	−	12.1631i	0.214705	−	0.914231i
$178$	−2.66137	+	3.57485i	−0.199478	+	0.267946i
$179$	−0.110050	+	0.624125i	−0.00822552	+	0.0466493i	−0.988644	−	0.150275i	$-0.951984\pi$
$179$	−0.110050	+	0.624125i	−0.00822552	+	0.0466493i	0.980419	+	0.196924i	$0.0630953\pi$
$180$	4.83283	+	11.0791i	0.360218	+	0.825785i
$181$	−2.42311	−	13.7421i	−0.180108	−	1.02145i	−0.932081	−	0.362251i	$-0.882008\pi$
$181$	−2.42311	−	13.7421i	−0.180108	−	1.02145i	0.751972	−	0.659195i	$-0.229103\pi$
$182$	−3.98011	−	1.99888i	−0.295025	−	0.148167i
$183$	14.6854	−	13.9117i	1.08557	−	1.02839i
$184$	−5.26027	+	0.614837i	−0.387792	+	0.0453264i
$185$	−6.23781	−	4.10267i	−0.458613	−	0.301634i
$186$	−2.49766	−	0.435146i	−0.183137	−	0.0319065i
$187$	−3.76539	+	12.5773i	−0.275352	+	0.919741i
$188$	−4.31771	−	7.47849i	−0.314901	−	0.545425i
$189$	5.85913	−	11.8470i	0.426189	−	0.861740i
$190$	0.0205270	−	0.0355538i	0.00148918	−	0.00257934i
$191$	−5.82843	−	6.17777i	−0.421730	−	0.447008i	0.481319	−	0.876546i	$-0.340158\pi$
$191$	−5.82843	−	6.17777i	−0.421730	−	0.447008i	−0.903049	+	0.429538i	$0.858677\pi$
$192$	−8.53664	−	4.90540i	−0.616079	−	0.354017i
$193$	−0.770479	+	13.2286i	−0.0554603	+	0.952217i	0.849732	+	0.527215i	$0.176764\pi$
$193$	−0.770479	+	13.2286i	−0.0554603	+	0.952217i	−0.905192	+	0.425002i	$0.860273\pi$
$194$	0.882572	−	2.04603i	0.0633650	−	0.146897i
$195$	11.1776	+	16.9193i	0.800442	+	1.21161i
$196$	−0.0585725	−	1.00565i	−0.00418375	−	0.0718322i
$197$	7.09307	+	2.58167i	0.505360	+	0.183936i	0.582103	−	0.813115i	$-0.302230\pi$
$197$	7.09307	+	2.58167i	0.505360	+	0.183936i	−0.0767431	+	0.997051i	$0.524452\pi$
$198$	−2.43998	−	1.59055i	−0.173402	−	0.113036i
$199$	1.98595	−	0.722827i	0.140780	−	0.0512399i	−0.270669	−	0.962672i	$-0.587245\pi$
$199$	1.98595	−	0.722827i	0.140780	−	0.0512399i	0.411449	+	0.911433i	$0.365023\pi$
$200$	0.245023	+	0.568027i	0.0173257	+	0.0401656i
$201$	0.946728	+	1.87553i	0.0667771	+	0.132290i
$202$	3.35080	+	0.794155i	0.235762	+	0.0558765i
$203$	−26.4299	−	6.26401i	−1.85502	−	0.439647i
$204$	14.0921	+	0.791890i	0.986645	+	0.0554434i
$205$	2.11736	+	4.90858i	0.147883	+	0.342830i
$206$	3.70790	−	1.34957i	0.258342	−	0.0940287i
$207$	−3.73351	−	12.2878i	−0.259497	−	0.854064i
$208$	−17.6649	−	6.42950i	−1.22484	−	0.445805i
$209$	−0.0108531	−	0.186341i	−0.000750725	−	0.0128895i
$210$	−1.32532	+	2.65243i	−0.0914558	+	0.183035i
$211$	0.260017	−	0.602788i	0.0179003	−	0.0414976i	−0.909031	−	0.416727i	$-0.863177\pi$
$211$	0.260017	−	0.602788i	0.0179003	−	0.0414976i	0.926932	+	0.375230i	$0.122436\pi$
$212$	−0.217858	+	3.74048i	−0.0149626	+	0.256897i
$213$	21.3769	−	12.4003i	1.46472	−	0.849651i
$214$	−1.08391	−	1.14888i	−0.0740947	−	0.0785357i
$215$	0.822857	−	1.42523i	0.0561184	−	0.0971998i
$216$	−2.16160	+	6.05415i	−0.147079	+	0.411932i
$217$	5.86733	+	10.1625i	0.398301	+	0.689877i
$218$	−0.0328722	+	0.109801i	−0.00222639	+	0.00743665i
$219$	5.78747	+	15.8004i	0.391081	+	1.06769i
$220$	−10.3009	−	6.77500i	−0.694485	−	0.456770i
$221$	23.5187	−	2.74894i	1.58204	−	0.184914i
$222$	−0.449882	−	1.88107i	−0.0301941	−	0.126249i
$223$	20.1166	+	10.1029i	1.34711	+	0.676542i	0.968499	−	0.249016i	$-0.0801073\pi$
$223$	20.1166	+	10.1029i	1.34711	+	0.676542i	0.378606	+	0.925558i	$0.376404\pi$
$224$	−1.57018	−	8.90495i	−0.104912	−	0.594987i
$225$	−1.24993	+	0.829431i	−0.0833290	+	0.0552954i
$226$	−1.08766	+	6.16845i	−0.0723503	+	0.410319i
$227$	−8.00706	+	10.7553i	−0.531447	+	0.713857i	−0.984057	−	0.177851i	$-0.943085\pi$
$227$	−8.00706	+	10.7553i	−0.531447	+	0.713857i	0.452610	+	0.891708i	$0.350493\pi$
$228$	−0.192120	+	0.0579449i	−0.0127235	+	0.00383749i
$229$	−4.27075	+	4.52673i	−0.282219	+	0.299135i	−0.852940	−	0.522010i	$-0.825183\pi$
$229$	−4.27075	+	4.52673i	−0.282219	+	0.299135i	0.570720	+	0.821144i	$0.306664\pi$
$230$	0.826328	+	2.76013i	0.0544865	+	0.181997i
$231$	1.59242	+	13.3868i	0.104773	+	0.880786i
$232$	13.1221	+	1.53375i	0.861507	+	0.100696i
$233$	−9.49107	−	7.96396i	−0.621781	−	0.521736i	0.276582	−	0.960990i	$-0.410798\pi$
$233$	−9.49107	−	7.96396i	−0.621781	−	0.521736i	−0.898363	+	0.439254i	$0.855243\pi$
$234$	−0.891050	+	5.17700i	−0.0582498	+	0.338431i
$235$	−7.38822	+	6.19946i	−0.481955	+	0.404408i
$236$	11.4467	−	7.52864i	0.745119	−	0.490073i
$237$	−0.318307	+	2.77239i	−0.0206762	+	0.180086i
$238$	2.06758	+	2.77724i	0.134021	+	0.180022i
$239$	−8.78624	+	4.41262i	−0.568335	+	0.285428i	−0.709671	−	0.704533i	$-0.751156\pi$
$239$	−8.78624	+	4.41262i	−0.568335	+	0.285428i	0.141336	+	0.989962i	$0.454860\pi$
$240$	−4.25634	+	11.7689i	−0.274745	+	0.759682i
$241$	−16.8698	+	3.99822i	−1.08668	+	0.257548i	−0.734654	−	0.678441i	$-0.762656\pi$
$241$	−16.8698	+	3.99822i	−1.08668	+	0.257548i	−0.352027	+	0.935990i	$0.614508\pi$
$242$	−0.519105			−0.0333693
$243$	−15.3785	−	2.54996i	−0.986530	−	0.163580i
$244$	22.1823			1.42008
$245$	−1.09476	+	0.259463i	−0.0699416	+	0.0165765i
$246$	−0.470987	+	1.30230i	−0.0300290	+	0.0830314i
$247$	−0.300840	+	0.151088i	−0.0191420	+	0.00961347i
$248$	−3.40837	−	4.57823i	−0.216432	−	0.290718i
$249$	−0.652404	+	5.68232i	−0.0413444	+	0.360102i
$250$	3.09275	−	2.03413i	0.195603	−	0.128650i
$251$	−19.1764	+	16.0909i	−1.21040	+	1.01565i	−0.211132	+	0.977458i	$0.567715\pi$
$251$	−19.1764	+	16.0909i	−1.21040	+	1.01565i	−0.999270	+	0.0381908i	$0.987841\pi$
$252$	13.5987	−	5.01255i	0.856640	−	0.315761i
$253$	10.0348	+	8.42023i	0.630885	+	0.529375i
$254$	4.54590	+	0.531340i	0.285235	+	0.0333392i
$255$	−1.86206	−	15.6535i	−0.116607	−	0.980262i
$256$	−2.44952	−	8.18196i	−0.153095	−	0.511373i
$257$	−1.65416	+	1.75330i	−0.103183	+	0.109368i	−0.776907	−	0.629616i	$-0.783212\pi$
$257$	−1.65416	+	1.75330i	−0.103183	+	0.109368i	0.673723	+	0.738984i	$0.264694\pi$
$258$	0.408168	−	0.123107i	0.0254114	−	0.00766429i
$259$	−5.34585	+	7.18072i	−0.332175	+	0.446188i
$260$	−3.86134	+	21.8987i	−0.239470	+	1.35810i
$261$	1.99341	+	31.9744i	0.123389	+	1.97917i
$262$	0.168301	+	0.954483i	0.0103977	+	0.0589682i
$263$	−3.50552	−	1.76054i	−0.216160	−	0.108559i	0.337425	−	0.941352i	$-0.390444\pi$
$263$	−3.50552	−	1.76054i	−0.216160	−	0.108559i	−0.553585	+	0.832793i	$0.686740\pi$
$264$	−1.52521	−	6.37728i	−0.0938701	−	0.392494i
$265$	4.15641	−	0.485815i	0.255327	−	0.0298434i
$266$	−0.0411273	−	0.0270499i	−0.00252168	−	0.00165853i
$267$	−8.36803	−	22.8457i	−0.512115	−	1.39813i
$268$	−0.660749	+	2.20706i	−0.0403617	+	0.134817i
$269$	−5.54513	−	9.60445i	−0.338093	−	0.585594i	0.645981	−	0.763353i	$-0.276448\pi$
$269$	−5.54513	−	9.60445i	−0.338093	−	0.585594i	−0.984074	+	0.177760i	$0.943115\pi$
$270$	3.44773	+	0.586166i	0.209822	+	0.0356729i
$271$	−0.397309	+	0.688159i	−0.0241348	+	0.0418027i	−0.877841	−	0.478953i	$-0.841016\pi$
$271$	−0.397309	+	0.688159i	−0.0241348	+	0.0418027i	0.853706	+	0.520756i	$0.174350\pi$
$272$	10.0286	+	10.6297i	0.608072	+	0.644519i
$273$	21.0319	−	12.2001i	1.27291	−	0.738385i
$274$	−0.0480564	+	0.825096i	−0.00290319	+	0.0498459i
$275$	0.606050	−	1.40498i	0.0365462	−	0.0847236i
$276$	6.29466	−	12.5978i	0.378894	−	0.758299i
$277$	−1.69712	−	29.1384i	−0.101970	−	1.75076i	−0.530913	−	0.847426i	$-0.678151\pi$
$277$	−1.69712	−	29.1384i	−0.101970	−	1.75076i	0.428943	−	0.903332i	$-0.358886\pi$
$278$	5.65991	+	2.06004i	0.339459	+	0.123553i
$279$	9.45673	−	10.1059i	0.566160	−	0.605027i
$280$	−6.27272	+	2.28308i	−0.374867	+	0.136440i
$281$	−10.9274	−	25.3326i	−0.651875	−	1.51122i	−0.847643	−	0.530566i	$-0.821979\pi$
$281$	−10.9274	−	25.3326i	−0.651875	−	1.51122i	0.195768	−	0.980650i	$-0.437280\pi$
$282$	−2.49455	−	0.140178i	−0.148548	−	0.00834750i
$283$	−4.97091	−	1.17813i	−0.295490	−	0.0700324i	0.0801970	−	0.996779i	$-0.474445\pi$
$283$	−4.97091	−	1.17813i	−0.295490	−	0.0700324i	−0.375687	+	0.926747i	$0.622593\pi$
$284$	26.3695	+	6.24968i	1.56474	+	0.370850i
$285$	0.100994	+	0.200075i	0.00598236	+	0.0118514i
$286$	−2.12230	−	4.92004i	−0.125494	−	0.290928i
$287$	6.02327	−	2.19229i	0.355542	−	0.129407i
$288$	−9.51097	+	4.82535i	−0.560439	+	0.284336i
$289$	−1.32268	−	0.481415i	−0.0778046	−	0.0283185i
$290$	−0.417902	−	7.17510i	−0.0245400	−	0.421336i
$291$	6.70523	+	10.1496i	0.393068	+	0.594979i
$292$	−7.30855	+	16.9431i	−0.427700	+	0.991521i
$293$	0.136260	−	2.33949i	0.00796037	−	0.136674i	−0.991986	−	0.126346i	$-0.959675\pi$
$293$	0.136260	−	2.33949i	0.00796037	−	0.136674i	0.999947	−	0.0103287i	$-0.00328778\pi$
$294$	−0.252707	−	0.145213i	−0.0147382	−	0.00846900i
$295$	−10.5008	−	11.1302i	−0.611379	−	0.648024i
$296$	2.17712	−	3.77089i	0.126543	−	0.219178i
$297$	14.5612	−	6.38720i	0.844925	−	0.370623i
$298$	−0.650036	−	1.12590i	−0.0376556	−	0.0652214i
$299$	6.77601	−	22.6334i	0.391867	−	1.30893i
$300$	−1.62057	−	0.282338i	−0.0935636	−	0.0163008i
$301$	−1.64865	−	1.08434i	−0.0950268	−	0.0625001i
$302$	−3.13278	+	0.366169i	−0.180271	+	0.0210707i
$303$	−13.6477	+	12.9288i	−0.784041	+	0.742738i
$304$	−0.185669	−	0.0932464i	−0.0106488	−	0.00534805i
$305$	−4.30210	−	24.3984i	−0.246337	−	1.39705i
$306$	2.42522	−	3.28557i	0.138640	−	0.187824i
$307$	−2.80743	+	15.9217i	−0.160228	+	0.908700i	0.793620	+	0.608413i	$0.208194\pi$
$307$	−2.80743	+	15.9217i	−0.160228	+	0.908700i	−0.953849	+	0.300287i	$0.902918\pi$
$308$	−8.82793	+	11.8580i	−0.503018	+	0.675670i
$309$	−4.92489	+	20.9706i	−0.280167	+	1.19297i
$310$	−2.13082	+	2.25854i	−0.121023	+	0.128277i
$311$	6.07993	+	20.3084i	0.344761	+	1.15158i	0.938023	+	0.346572i	$0.112655\pi$
$311$	6.07993	+	20.3084i	0.344761	+	1.15158i	−0.593262	+	0.805009i	$0.702160\pi$
$312$	−9.47167	+	7.08151i	−0.536228	+	0.400912i
$313$	5.37482	+	0.628227i	0.303803	+	0.0355095i	0.266629	−	0.963799i	$-0.414090\pi$
$313$	5.37482	+	0.628227i	0.303803	+	0.0355095i	0.0371743	+	0.999309i	$0.488164\pi$
$314$	2.80708	+	2.35542i	0.158413	+	0.132924i
$315$	−8.15069	−	13.9851i	−0.459239	−	0.787974i
$316$	−2.34420	+	1.96701i	−0.131871	+	0.110653i
$317$	−7.29158	+	4.79574i	−0.409536	+	0.269356i	−0.737517	−	0.675328i	$-0.764002\pi$
$317$	−7.29158	+	4.79574i	−0.409536	+	0.269356i	0.327982	+	0.944684i	$0.393632\pi$
$318$	0.870876	+	0.645582i	0.0488363	+	0.0362025i
$319$	−19.5137	−	26.2115i	−1.09256	−	1.46756i
$320$	−10.7758	+	5.41179i	−0.602384	+	0.302528i
$321$	8.48861	−	1.51466i	0.473788	−	0.0845399i
$322$	3.36153	−	0.796696i	0.187330	−	0.0443981i
$323$	0.261706			0.0145617
$324$	−10.3195	−	13.6277i	−0.573308	−	0.757092i
$325$	−2.75968			−0.153080
$326$	−4.36325	+	1.03411i	−0.241658	+	0.0572741i
$327$	−0.403175	−	0.478496i	−0.0222956	−	0.0264609i
$328$	−2.78607	+	1.39921i	−0.153835	+	0.0772587i
$329$	6.90575	+	9.27603i	0.380726	+	0.511404i
$330$	−3.27257	+	1.41958i	−0.180149	+	0.0781456i
$331$	16.4178	−	10.7982i	0.902405	−	0.593521i	−0.0112834	−	0.999936i	$-0.503592\pi$
$331$	16.4178	−	10.7982i	0.902405	−	0.593521i	0.913689	+	0.406415i	$0.133221\pi$
$332$	−4.80468	+	4.03161i	−0.263691	+	0.221263i
$333$	9.93656	+	3.57070i	0.544520	+	0.195673i
$334$	−1.62927	−	1.36712i	−0.0891495	−	0.0748053i
$335$	2.55569	+	0.298718i	0.139632	+	0.0163207i
$336$	13.7909	+	5.91541i	0.752353	+	0.322712i
$337$	2.10672	+	7.03692i	0.114760	+	0.383326i	0.996001	−	0.0893418i	$-0.0284764\pi$
$337$	2.10672	+	7.03692i	0.114760	+	0.383326i	−0.881241	+	0.472667i	$0.843291\pi$
$338$	−3.80139	+	4.02924i	−0.206768	+	0.219162i
$339$	−24.9197	−	23.4145i	−1.35345	−	1.27170i
$340$	10.3227	−	13.8658i	0.559829	−	0.751980i
$341$	−2.45148	+	13.9030i	−0.132755	+	0.752892i
$342$	−0.0164242	+	0.0556878i	−0.000888120	+	0.00301125i
$343$	3.32603	+	18.8629i	0.179589	+	1.01850i
$344$	0.857698	+	0.430752i	0.0462440	+	0.0232246i
$345$	−15.0772	−	4.48027i	−0.811727	−	0.241209i
$346$	4.66038	−	0.544720i	0.250543	−	0.0292843i
$347$	−15.2213	−	10.0112i	−0.817124	−	0.537431i	0.0707630	−	0.997493i	$-0.477457\pi$
$347$	−15.2213	−	10.0112i	−0.817124	−	0.537431i	−0.887887	+	0.460063i	$0.847827\pi$
$348$	−22.5265	+	26.9577i	−1.20755	+	1.44508i
$349$	4.62046	−	15.4334i	0.247328	−	0.826132i	−0.740697	−	0.671839i	$-0.765505\pi$
$349$	4.62046	−	15.4334i	0.247328	−	0.826132i	0.988025	−	0.154293i	$-0.0493101\pi$
$350$	−0.201764	−	0.349465i	−0.0107847	−	0.0186797i
$351$	−20.9795	−	19.5516i	−1.11981	−	1.04359i
$352$	5.43923	−	9.42103i	0.289912	−	0.502142i
$353$	11.7923	+	12.4991i	0.627641	+	0.665260i	0.960682	−	0.277652i	$-0.0895562\pi$
$353$	11.7923	+	12.4991i	0.627641	+	0.665260i	−0.333041	+	0.942912i	$0.608075\pi$
$354$	−0.00809784	−	3.96401i	−0.000430395	−	0.210685i
$355$	1.75988	−	30.2159i	0.0934046	−	1.60370i
$356$	10.5673	−	24.4979i	0.560068	−	1.29838i
$357$	−18.8673	+	1.13758i	−0.998565	+	0.0602069i
$358$	0.0116914	+	0.200733i	0.000617909	+	0.0106091i
$359$	26.7193	+	9.72505i	1.41019	+	0.513268i	0.931187	−	0.364543i	$-0.118775\pi$
$359$	26.7193	+	9.72505i	1.41019	+	0.513268i	0.479007	+	0.877811i	$0.340997\pi$
$360$	4.72732	+	6.29602i	0.249151	+	0.331829i
$361$	17.8507	−	6.49711i	0.939509	−	0.341953i
$362$	−1.75356	−	4.06521i	−0.0921651	−	0.213663i
$363$	1.55240	−	2.37084i	0.0814799	−	0.124437i
$364$	25.9439	+	6.14882i	1.35983	+	0.322286i
$365$	20.0532	+	4.75270i	1.04963	+	0.248768i
$366$	3.51580	−	5.36937i	0.183774	−	0.280661i
$367$	4.11015	+	9.52840i	0.214548	+	0.497379i	0.991171	−	0.132587i	$-0.0423283\pi$
$367$	4.11015	+	9.52840i	0.214548	+	0.497379i	−0.776623	+	0.629965i	$0.783069\pi$
$368$	13.7018	−	4.98706i	0.714258	−	0.259969i
$369$	−4.53932	−	6.04564i	−0.236308	−	0.314723i
$370$	−2.22594	−	0.810174i	−0.115721	−	0.0421190i
$371$	−0.291750	−	5.00916i	−0.0151469	−	0.260063i
$372$	15.1498	−	0.913430i	0.785478	−	0.0473592i
$373$	5.89862	−	13.6745i	0.305419	−	0.708040i	−0.694516	−	0.719477i	$-0.744381\pi$
$373$	5.89862	−	13.6745i	0.305419	−	0.708040i	0.999935	+	0.0114370i	$0.00364061\pi$
$374$	−0.242199	+	4.15839i	−0.0125238	+	0.215025i
$375$	0.0412823	+	20.2083i	0.00213181	+	1.04355i
$376$	−3.85997	−	4.09133i	−0.199063	−	0.210994i
$377$	−29.4683	+	51.0405i	−1.51769	+	2.62872i
$378$	0.942019	−	4.08612i	0.0484522	−	0.210168i
$379$	−5.81217	−	10.0670i	−0.298551	−	0.517106i	0.677253	−	0.735750i	$-0.263170\pi$
$379$	−5.81217	−	10.0670i	−0.298551	−	0.517106i	−0.975805	+	0.218644i	$0.929837\pi$
$380$	−0.0704866	+	0.235442i	−0.00361589	+	0.0120779i
$381$	−16.0214	+	19.1730i	−0.820800	+	0.982260i
$382$	−2.25138	−	1.48076i	−0.115191	−	0.0757622i
$383$	28.3232	−	3.31050i	1.44725	−	0.169159i	0.644101	−	0.764941i	$-0.277232\pi$
$383$	28.3232	−	3.31050i	1.44725	−	0.169159i	0.803146	+	0.595782i	$0.203158\pi$
$384$	−14.7991	−	4.39764i	−0.755214	−	0.224416i
$385$	14.7547	+	7.41010i	0.751970	+	0.377653i
$386$	0.730054	+	4.14034i	0.0371588	+	0.210738i
$387$	−0.658390	+	2.23233i	−0.0334679	+	0.113476i
$388$	−2.31635	+	13.1367i	−0.117595	+	0.666915i
$389$	1.83350	−	2.46281i	0.0929619	−	0.124870i	−0.753209	−	0.657782i	$-0.771495\pi$
$389$	1.83350	−	2.46281i	0.0929619	−	0.124870i	0.846171	+	0.532912i	$0.178902\pi$
$390$	4.68872	+	4.40551i	0.237422	+	0.223082i
$391$	−12.6039	+	13.3593i	−0.637405	+	0.675610i
$392$	−0.188187	−	0.628590i	−0.00950490	−	0.0317486i
$393$	−4.86261	−	2.08575i	−0.245286	−	0.105212i
$394$	2.37868	+	0.278028i	0.119836	+	0.0140069i
$395$	2.61816	+	2.19690i	0.131734	+	0.110538i
$396$	16.4089	+	5.89652i	0.824576	+	0.296312i
$397$	−8.05095	+	6.75555i	−0.404065	+	0.339051i	−0.822063	−	0.569397i	$-0.807177\pi$
$397$	−8.05095	+	6.75555i	−0.404065	+	0.339051i	0.417997	+	0.908448i	$0.362732\pi$
$398$	0.560219	−	0.368462i	0.0280812	−	0.0184693i
$399$	0.246534	−	0.106942i	0.0123421	−	0.00535381i
$400$	−1.01707	−	1.36617i	−0.0508537	−	0.0683083i
$401$	23.6797	−	11.8924i	1.18251	−	0.593878i	0.254730	−	0.967012i	$-0.418013\pi$
$401$	23.6797	−	11.8924i	1.18251	−	0.593878i	0.927777	+	0.373134i	$0.121717\pi$
$402$	0.429506	+	0.509746i	0.0214218	+	0.0254238i
$403$	24.7756	−	5.87194i	1.23416	−	0.292502i
$404$	−20.6150			−1.02563
$405$	−12.9877	+	13.9935i	−0.645363	+	0.695341i
$406$	−8.61783			−0.427696
$407$	−10.4797	+	2.48373i	−0.519458	+	0.123114i
$408$	9.05063	−	1.61494i	0.448073	−	0.0799514i
$409$	23.5494	−	11.8270i	1.16444	−	0.584806i	0.241750	−	0.970338i	$-0.422278\pi$
$409$	23.5494	−	11.8270i	1.16444	−	0.584806i	0.922694	+	0.385532i	$0.125982\pi$
$410$	1.01283	+	1.36046i	0.0500200	+	0.0671886i
$411$	−3.62465	−	2.68696i	−0.178791	−	0.132538i
$412$	−19.7356	+	12.9803i	−0.972301	+	0.639493i
$413$	−14.0551	+	11.7936i	−0.691605	+	0.580326i
$414$	−2.05170	−	3.52035i	−0.100836	−	0.173016i
$415$	5.36621	+	4.50278i	0.263417	+	0.221033i
$416$	−19.4874	−	2.27775i	−0.955450	−	0.111676i
$417$	−26.3347	+	19.6892i	−1.28962	+	0.964186i
$418$	−0.0169849	−	0.0567334i	−0.000830757	−	0.00277492i
$419$	−5.37434	+	5.69647i	−0.262554	+	0.278291i	−0.845217	−	0.534423i	$-0.820529\pi$
$419$	−5.37434	+	5.69647i	−0.262554	+	0.278291i	0.582664	+	0.812713i	$0.302011\pi$
$420$	4.05822	−	17.2802i	0.198021	−	0.843188i
$421$	−19.0206	+	25.5491i	−0.927008	+	1.24519i	0.0422420	+	0.999107i	$0.486550\pi$
$421$	−19.0206	+	25.5491i	−0.927008	+	1.24519i	−0.969250	+	0.246080i	$0.920857\pi$
$422$	0.0361680	−	0.205119i	0.00176063	−	0.00998504i
$423$	8.10026	−	10.9739i	0.393848	−	0.533567i
$424$	0.423796	+	2.40347i	0.0205813	+	0.116723i
$425$	1.91715	+	0.962827i	0.0929953	+	0.0467040i
$426$	5.69221	−	5.39235i	0.275789	−	0.261260i
$427$	−29.5052	+	3.44866i	−1.42786	+	0.166892i
$428$	7.89994	+	5.19587i	0.381858	+	0.251152i
$429$	28.8175	+	5.02062i	1.39132	+	0.242398i
$430$	0.149752	−	0.500207i	0.00722169	−	0.0241221i
$431$	16.6567	+	28.8502i	0.802324	+	1.38967i	0.918083	+	0.396389i	$0.129737\pi$
$431$	16.6567	+	28.8502i	0.802324	+	1.38967i	−0.115759	+	0.993277i	$0.536930\pi$
$432$	1.94694	−	17.5915i	0.0936724	−	0.846371i
$433$	2.75793	−	4.77688i	0.132538	−	0.229562i	−0.792116	−	0.610370i	$-0.791021\pi$
$433$	2.75793	−	4.77688i	0.132538	−	0.229562i	0.924654	+	0.380808i	$0.124354\pi$
$434$	2.55495	+	2.70809i	0.122642	+	0.129993i
$435$	34.0197	+	19.5487i	1.63112	+	0.937290i
$436$	0.0398954	−	0.684978i	0.00191064	−	0.0328045i
$437$	0.103425	−	0.239767i	0.00494751	−	0.0114696i
$438$	2.94281	+	4.45448i	0.140613	+	0.212843i
$439$	0.192462	+	3.30445i	0.00918572	+	0.157713i	0.999782	+	0.0208932i	$0.00665100\pi$
$439$	0.192462	+	3.30445i	0.00918572	+	0.157713i	−0.990596	+	0.136820i	$0.956312\pi$
$440$	−7.54647	−	2.74669i	−0.359764	−	0.130943i
$441$	1.41894	−	0.719895i	0.0675688	−	0.0342807i
$442$	7.05960	−	2.56948i	0.335791	−	0.122218i
$443$	6.80697	+	15.7803i	0.323409	+	0.749747i	0.999911	+	0.0133061i	$0.00423559\pi$
$443$	6.80697	+	15.7803i	0.323409	+	0.749747i	−0.676502	+	0.736440i	$0.736505\pi$
$444$	5.21752	+	10.3362i	0.247612	+	0.490536i
$445$	−28.9947	−	6.87187i	−1.37448	−	0.325758i
$446$	6.94965	+	1.64710i	0.329075	+	0.0779923i
$447$	7.08612	+	0.398196i	0.335162	+	0.0188340i
$448$	5.72673	+	13.2761i	0.270563	+	0.627235i
$449$	16.5392	−	6.01977i	0.780532	−	0.284090i	0.0791375	−	0.996864i	$-0.474783\pi$
$449$	16.5392	−	6.01977i	0.780532	−	0.284090i	0.701394	+	0.712773i	$0.252561\pi$
$450$	−0.325194	+	0.347519i	−0.0153298	+	0.0163822i
$451$	7.24636	+	2.63746i	0.341218	+	0.124193i
$452$	−2.18023	−	37.4331i	−0.102550	−	1.76071i
$453$	7.69631	−	15.4030i	0.361604	−	0.723695i
$454$	−1.68500	+	3.90628i	−0.0790811	+	0.183331i
$455$	1.73148	−	29.7283i	0.0811728	−	1.39368i
$456$	−0.113063	+	0.0655851i	−0.00529464	+	0.00307130i
$457$	−12.2662	−	13.0015i	−0.573791	−	0.608183i	0.373862	−	0.927484i	$-0.378033\pi$
$457$	−12.2662	−	13.0015i	−0.573791	−	0.608183i	−0.947653	+	0.319301i	$0.896552\pi$
$458$	−0.987261	+	1.70999i	−0.0461317	+	0.0799024i
$459$	7.75310	+	20.9020i	0.361884	+	0.975622i
$460$	−8.62394	−	14.9371i	−0.402093	−	0.696446i
$461$	1.44181	−	4.81599i	0.0671520	−	0.224303i	−0.917826	−	0.396983i	$-0.870057\pi$
$461$	1.44181	−	4.81599i	0.0671520	−	0.224303i	0.984978	+	0.172679i	$0.0552425\pi$
$462$	1.47111	+	4.01629i	0.0684421	+	0.186855i
$463$	−14.3747	−	9.45440i	−0.668050	−	0.439383i	0.169657	−	0.985503i	$-0.445734\pi$
$463$	−14.3747	−	9.45440i	−0.668050	−	0.439383i	−0.837707	+	0.546120i	$0.816104\pi$
$464$	−36.1278	+	4.22273i	−1.67719	+	0.196035i
$465$	−3.94287	−	16.4861i	−0.182846	−	0.764525i
$466$	−3.51282	−	1.76420i	−0.162728	−	0.0817251i
$467$	−6.50441	−	36.8883i	−0.300988	−	1.70699i	−0.641812	−	0.766862i	$-0.721817\pi$
$467$	−6.50441	−	36.8883i	−0.300988	−	1.70699i	0.340824	−	0.940127i	$-0.389294\pi$
$468$	−1.95675	−	31.3864i	−0.0904509	−	1.45084i
$469$	0.535748	−	3.03838i	0.0247385	−	0.140299i
$470$	−1.82730	+	2.45449i	−0.0842872	+	0.113217i
$471$	−19.1523	+	5.77647i	−0.882490	+	0.266166i
$472$	6.12410	−	6.49117i	0.281885	−	0.298780i
$473$	−0.680865	−	2.27425i	−0.0313062	−	0.104570i
$474$	0.104584	+	0.879189i	0.00480368	+	0.0403825i
$475$	−0.0302947	−	0.00354095i	−0.00139002	−	0.000162470i
$476$	−15.8779	−	13.3232i	−0.727764	−	0.610666i
$477$	−5.55287	+	2.04681i	−0.254249	+	0.0937171i
$478$	−2.38964	+	2.00515i	−0.109300	+	0.0917134i
$479$	2.85966	−	1.88083i	0.130661	−	0.0859371i	−0.482496	−	0.875898i	$-0.660270\pi$
$479$	2.85966	−	1.88083i	0.130661	−	0.0859371i	0.613157	+	0.789961i	$0.289899\pi$
$480$	−1.48988	+	12.9766i	−0.0680036	+	0.592299i
$481$	11.5995	+	15.5808i	0.528890	+	0.710423i
$482$	−4.91555	+	2.46868i	−0.223897	+	0.112445i
$483$	−6.41410	+	17.7352i	−0.291852	+	0.806981i
$484$	3.02381	−	0.716657i	0.137446	−	0.0325753i
$485$	14.8983			0.676498
$486$	−4.93425	+	0.337990i	−0.223822	+	0.0153315i
$487$	−5.43342			−0.246212			−0.123106	−	0.992394i	$-0.539285\pi$
$487$	−5.43342			−0.246212			−0.123106	+	0.992394i	$0.539285\pi$
$488$	14.0593	−	3.33212i	0.636435	−	0.150838i
$489$	8.32549	−	23.0203i	0.376492	−	1.04101i
$490$	−0.318992	+	0.160204i	−0.0144106	+	0.00723726i
$491$	2.37303	+	3.18753i	0.107093	+	0.143851i	0.852439	−	0.522827i	$-0.175123\pi$
$491$	2.37303	+	3.18753i	0.107093	+	0.143851i	−0.745345	+	0.666679i	$0.767715\pi$
$492$	0.945620	−	8.23617i	0.0426318	−	0.371315i
$493$	38.2791	−	25.1766i	1.72400	−	1.13390i
$494$	−0.0818212	+	0.0686561i	−0.00368131	+	0.00308898i
$495$	3.30323	−	19.1917i	0.148469	−	0.862604i
$496$	12.0379	+	10.1010i	0.540516	+	0.453547i
$497$	−36.0462	−	4.21320i	−1.61689	−	0.188988i
$498$	0.214355	+	1.80199i	0.00960549	+	0.0807493i
$499$	6.15378	+	20.5551i	0.275481	+	0.920171i	0.978017	+	0.208523i	$0.0668656\pi$
$499$	6.15378	+	20.5551i	0.275481	+	0.920171i	−0.702537	+	0.711648i	$0.747949\pi$
$500$	−15.2072	+	16.1187i	−0.680086	+	0.720849i
$501$	11.1162	−	3.35274i	0.496637	−	0.149790i
$502$	−4.74283	+	6.37072i	−0.211683	+	0.284339i
$503$	4.28340	−	24.2924i	0.190987	−	1.08314i	−0.727031	−	0.686605i	$-0.759100\pi$
$503$	4.28340	−	24.2924i	0.190987	−	1.08314i	0.918018	−	0.396538i	$-0.129789\pi$
$504$	7.86601	−	5.21972i	0.350380	−	0.232505i
$505$	3.99812	+	22.6745i	0.177914	+	1.00900i
$506$	3.71407	+	1.86528i	0.165111	+	0.0829217i
$507$	−7.03407	−	29.4112i	−0.312394	−	1.30620i
$508$	−27.2137	+	3.18082i	−1.20741	+	0.141126i
$509$	6.13825	+	4.03719i	0.272073	+	0.178945i	0.678213	−	0.734866i	$-0.262755\pi$
$509$	6.13825	+	4.03719i	0.272073	+	0.178945i	−0.406139	+	0.913811i	$0.633125\pi$
$510$	−1.72020	−	4.69635i	−0.0761719	−	0.207958i
$511$	7.08712	−	23.6726i	0.313516	−	1.04722i
$512$	−10.2684	−	17.7854i	−0.453804	−	0.786011i
$513$	−0.205219	−	0.241548i	−0.00906064	−	0.0106646i
$514$	−0.382388	+	0.662316i	−0.0168664	+	0.0292135i
$515$	18.1046	+	19.1898i	0.797784	+	0.845602i
$516$	−2.20765	+	1.28060i	−0.0971862	+	0.0563755i
$517$	−0.808947	+	13.8891i	−0.0355774	+	0.610841i
$518$	−1.12498	+	2.60799i	−0.0494287	+	0.114589i
$519$	−11.4492	+	22.9138i	−0.502563	+	1.00580i
$520$	0.842175	+	14.4596i	0.0369318	+	0.634095i
$521$	−25.5909	−	9.31432i	−1.12116	−	0.408068i	−0.286082	−	0.958205i	$-0.592353\pi$
$521$	−25.5909	−	9.31432i	−1.12116	−	0.408068i	−0.835074	+	0.550137i	$0.814575\pi$
$522$	2.95493	+	9.72535i	0.129334	+	0.425667i
$523$	−14.3006	+	5.20499i	−0.625321	+	0.227598i	−0.635193	−	0.772353i	$-0.719080\pi$
$523$	−14.3006	+	5.20499i	−0.625321	+	0.227598i	0.00987267	+	0.999951i	$0.496857\pi$
$524$	−2.29809	−	5.32757i	−0.100392	−	0.232736i
$525$	2.19945	+	0.123595i	0.0959918	+	0.00539415i
$526$	−1.21105	−	0.287024i	−0.0528042	−	0.0125148i
$527$	−19.2603	−	4.56477i	−0.838990	−	0.198844i
$528$	8.13517	+	16.1163i	0.354038	+	0.701371i
$529$	−1.85144	−	4.29212i	−0.0804975	−	0.186614i
$530$	1.24763	−	0.454101i	0.0541936	−	0.0197249i
$531$	18.1285	+	11.8175i	0.786712	+	0.512836i
$532$	0.276913	+	0.100788i	0.0120057	+	0.00436972i
$533$	−0.808684	−	13.8846i	−0.0350280	−	0.601407i
$534$	−4.25498	−	6.44069i	−0.184131	−	0.278716i
$535$	4.18282	−	9.69687i	0.180839	−	0.419232i
$536$	−0.0872544	+	1.49810i	−0.00376882	+	0.0647081i
$537$	−0.951748	−	0.546903i	−0.0410710	−	0.0236006i
$538$	−2.41465	−	2.55938i	−0.104103	−	0.110343i
$539$	−0.811481	+	1.40553i	−0.0349530	+	0.0605403i
$540$	−20.8925	+	1.34537i	−0.899069	+	0.0578955i
$541$	−8.31159	−	14.3961i	−0.357343	−	0.618937i	0.630173	−	0.776455i	$-0.282984\pi$
$541$	−8.31159	−	14.3961i	−0.357343	−	0.618937i	−0.987516	+	0.157518i	$0.949651\pi$
$542$	−0.0723064	+	0.241520i	−0.00310583	+	0.0103742i
$543$	23.8106	+	4.14832i	1.02181	+	0.178021i
$544$	12.7432	+	8.38133i	0.546360	+	0.359347i
$545$	−0.761146	+	0.0889653i	−0.0326039	+	0.00381085i
$546$	5.60035	−	5.30532i	0.239673	−	0.227047i
$547$	10.0828	+	5.06375i	0.431108	+	0.216510i	0.651101	−	0.758991i	$-0.274307\pi$
$547$	10.0828	+	5.06375i	0.431108	+	0.216510i	−0.219994	+	0.975501i	$0.570604\pi$
$548$	−0.859166	−	4.87257i	−0.0367018	−	0.208146i
$549$	14.0088	+	32.1145i	0.597879	+	1.37062i
$550$	0.0843006	−	0.478093i	0.00359459	−	0.0203859i
$551$	−0.388981	+	0.522493i	−0.0165712	+	0.0222589i
$552$	2.09722	−	8.93012i	0.0892636	−	0.380091i
$553$	2.81225	−	2.98082i	0.119589	−	0.126757i
$554$	−2.65595	−	8.87150i	−0.112841	−	0.376914i
$555$	10.3569	−	7.74340i	0.439628	−	0.328689i
$556$	−35.8133	−	4.18598i	−1.51882	−	0.177525i
$557$	22.3339	+	18.7404i	0.946318	+	0.794055i	0.978674	−	0.205421i	$-0.0658565\pi$
$557$	22.3339	+	18.7404i	0.946318	+	0.794055i	−0.0323557	+	0.999476i	$0.510301\pi$
$558$	2.18006	−	3.81186i	0.0922895	−	0.161369i
$559$	−3.27993	+	2.75219i	−0.138726	+	0.116405i
$560$	15.3550	−	10.0991i	0.648866	−	0.426766i
$561$	−18.2678	−	13.5420i	−0.771267	−	0.571742i
$562$	−5.22709	−	7.02119i	−0.220491	−	0.296171i
$563$	−19.1827	+	9.63393i	−0.808456	+	0.406022i	−0.804487	−	0.593970i	$-0.797560\pi$
$563$	−19.1827	+	9.63393i	−0.808456	+	0.406022i	−0.00396900	+	0.999992i	$0.501263\pi$
$564$	14.7244	−	2.62734i	0.620010	−	0.110631i
$565$	−40.7500	+	9.65792i	−1.71436	+	0.406312i
$566$	−1.62083			−0.0681286
$567$	15.8449	+	16.5221i	0.665424	+	0.693861i
$568$	17.6519			0.740659
$569$	−2.60889	+	0.618318i	−0.109370	+	0.0259212i	−0.284937	−	0.958546i	$-0.591973\pi$
$569$	−2.60889	+	0.618318i	−0.109370	+	0.0259212i	0.175566	+	0.984468i	$0.443824\pi$
$570$	0.0458183	+	0.0543781i	0.00191912	+	0.00227765i
$571$	−2.53863	+	1.27495i	−0.106239	+	0.0533550i	−0.501125	−	0.865375i	$-0.667080\pi$
$571$	−2.53863	+	1.27495i	−0.106239	+	0.0533550i	0.394886	+	0.918730i	$0.370784\pi$
$572$	19.1549	+	25.7295i	0.800907	+	1.07581i
$573$	13.4957	−	5.85421i	0.563792	−	0.244563i
$574$	1.69911	−	1.11752i	0.0709194	−	0.0466444i
$575$	1.63976	−	1.37592i	0.0683828	−	0.0573800i
$576$	13.0186	−	11.0149i	0.542442	−	0.458953i
$577$	4.53692	+	3.80692i	0.188874	+	0.158484i	0.732322	−	0.680959i	$-0.238437\pi$
$577$	4.53692	+	3.80692i	0.188874	+	0.158484i	−0.543447	+	0.839443i	$0.682881\pi$
$578$	−0.443564	−	0.0518452i	−0.0184498	−	0.00215648i
$579$	−21.0929	−	9.04754i	−0.876593	−	0.376003i
$580$	12.3400	+	41.2184i	0.512389	+	1.71150i
$581$	5.76402	−	6.10951i	0.239132	−	0.253465i
$582$	2.81268	+	2.64279i	0.116590	+	0.109547i
$583$	3.60477	−	4.84205i	0.149294	−	0.200537i
$584$	−2.08710	+	11.8365i	−0.0863646	+	0.489798i
$585$	−34.1425	+	8.23940i	−1.41162	+	0.340657i
$586$	−0.129110	−	0.732221i	−0.00533350	−	0.0302478i
$587$	−10.0693	−	5.05698i	−0.415603	−	0.208724i	0.228695	−	0.973498i	$-0.426554\pi$
$587$	−10.0693	−	5.05698i	−0.415603	−	0.208724i	−0.644298	+	0.764774i	$0.722850\pi$
$588$	1.67251	+	0.496996i	0.0689732	+	0.0204958i
$589$	0.279512	−	0.0326703i	0.0115171	−	0.00134615i
$590$	−4.05620	−	2.66781i	−0.166991	−	0.109832i
$591$	−8.38334	+	10.0324i	−0.344844	+	0.412679i
$592$	−3.43824	+	11.4845i	−0.141311	+	0.472010i
$593$	4.74627	+	8.22078i	0.194906	+	0.337587i	0.946870	−	0.321617i	$-0.104226\pi$
$593$	4.74627	+	8.22078i	0.194906	+	0.337587i	−0.751964	+	0.659205i	$0.770893\pi$
$594$	4.02802	−	3.03729i	0.165271	−	0.124622i
$595$	−11.5748	+	20.0481i	−0.474519	+	0.821892i
$596$	5.34086	+	5.66098i	0.218770	+	0.231883i
$597$	0.00747786	+	3.66052i	0.000306048	+	0.149815i
$598$	0.435849	−	7.48324i	0.0178232	−	0.306012i
$599$	9.88250	−	22.9102i	0.403788	−	0.936086i	−0.588079	−	0.808804i	$-0.700115\pi$
$599$	9.88250	−	22.9102i	0.403788	−	0.936086i	0.991867	−	0.127282i	$-0.0406253\pi$
$600$	−1.06954	+	0.0644861i	−0.0436637	+	0.00263263i
$601$	0.667915	+	11.4676i	0.0272448	+	0.467775i	0.984146	+	0.177361i	$0.0567560\pi$
$601$	0.667915	+	11.4676i	0.0272448	+	0.467775i	−0.956901	+	0.290414i	$0.906207\pi$
$602$	−0.588315	−	0.214129i	−0.0239779	−	0.00872725i
$603$	−3.61255	+	0.437216i	−0.147115	+	0.0178048i
$604$	17.7431	−	6.45795i	0.721955	−	0.262770i
$605$	−1.37470	−	3.18691i	−0.0558894	−	0.129566i
$606$	−3.26738	+	4.98998i	−0.132728	+	0.202704i
$607$	38.7799	+	9.19101i	1.57403	+	0.373052i	0.922631	−	0.385684i	$-0.126035\pi$
$607$	38.7799	+	9.19101i	1.57403	+	0.373052i	0.651398	+	0.758736i	$0.274183\pi$
$608$	−0.211003	−	0.0500086i	−0.00855730	−	0.00202812i
$609$	25.7719	−	39.3592i	1.04433	−	1.59491i
$610$	−3.11335	−	7.21755i	−0.126056	−	0.292230i
$611$	23.5792	−	8.58211i	0.953911	−	0.347195i
$612$	−9.59108	+	22.4868i	−0.387696	+	0.908975i
$613$	−16.9065	−	6.15347i	−0.682848	−	0.248536i	−0.0227782	−	0.999741i	$-0.507251\pi$
$613$	−16.9065	−	6.15347i	−0.682848	−	0.248536i	−0.660070	+	0.751204i	$0.729473\pi$
$614$	0.298253	+	5.12080i	0.0120365	+	0.206659i
$615$	−9.24238	+	0.557254i	−0.372689	+	0.0224707i
$616$	−3.81395	+	8.84174i	−0.153669	+	0.356244i
$617$	−1.06681	+	18.3164i	−0.0429481	+	0.737390i	0.906256	+	0.422729i	$0.138928\pi$
$617$	−1.06681	+	18.3164i	−0.0429481	+	0.737390i	−0.949204	+	0.314661i	$0.898109\pi$
$618$	0.0139616	+	6.83442i	0.000561620	+	0.274921i
$619$	30.8377	+	32.6860i	1.23947	+	1.31376i	0.932113	+	0.362168i	$0.117963\pi$
$619$	30.8377	+	32.6860i	1.23947	+	1.31376i	0.307358	+	0.951594i	$0.400555\pi$
$620$	9.29411	−	16.0979i	0.373260	−	0.646506i
$621$	22.2138	+	1.15725i	0.891408	+	0.0464389i
$622$	3.36294	+	5.82478i	0.134842	+	0.233553i
$623$	−10.2472	+	34.2280i	−0.410545	+	1.37132i
$624$	20.8782	−	24.9852i	0.835799	−	1.00021i
$625$	18.5894	+	12.2265i	0.743578	+	0.489059i
$626$	1.70529	−	0.199320i	0.0681572	−	0.00796644i
$627$	0.309905	+	0.0920902i	0.0123764	+	0.00367773i
$628$	−19.6032	−	9.84509i	−0.782252	−	0.392862i
$629$	−2.62214	−	14.8709i	−0.104552	−	0.592941i
$630$	−3.53957	−	3.72115i	−0.141020	−	0.148254i
$631$	5.90645	−	33.4972i	0.235132	−	1.33350i	−0.607203	−	0.794547i	$-0.707708\pi$
$631$	5.90645	−	33.4972i	0.235132	−	1.33350i	0.842335	−	0.538954i	$-0.181180\pi$
$632$	−1.19029	+	1.59884i	−0.0473473	+	0.0635984i
$633$	0.828654	+	0.778601i	0.0329360	+	0.0309466i
$634$	−1.90017	+	2.01407i	−0.0754655	+	0.0799888i
$635$	8.77648	+	29.3155i	0.348284	+	1.16335i
$636$	−5.96417	−	2.55825i	−0.236495	−	0.101441i
$637$	2.90734	+	0.339819i	0.115193	+	0.0134641i
$638$	−7.94218	−	6.66428i	−0.314434	−	0.263841i
$639$	7.60507	+	42.1233i	0.300852	+	1.66637i
$640$	−14.4847	+	12.1541i	−0.572556	+	0.480432i
$641$	0.262859	−	0.172885i	0.0103823	−	0.00682856i	−0.544307	−	0.838886i	$-0.683207\pi$
$641$	0.262859	−	0.172885i	0.0103823	−	0.00682856i	0.554690	+	0.832057i	$0.312837\pi$
$642$	2.50980	−	1.08871i	0.0990538	−	0.0429678i
$643$	−19.7861	−	26.5774i	−0.780289	−	1.04811i	−0.997407	−	0.0719649i	$-0.977073\pi$
$643$	−19.7861	−	26.5774i	−0.780289	−	1.04811i	0.217118	−	0.976145i	$-0.430334\pi$
$644$	−18.4812	+	9.28160i	−0.728260	+	0.365746i
$645$	1.83670	+	2.17983i	0.0723199	+	0.0858307i
$646$	0.0807945	−	0.0191486i	0.00317882	−	0.000753393i
$647$	14.0510			0.552403			0.276201	−	0.961100i	$-0.410924\pi$
$647$	14.0510			0.552403			0.276201	+	0.961100i	$0.410924\pi$
$648$	−8.58767	−	7.08714i	−0.337356	−	0.278409i
$649$	−22.0733			−0.866453
$650$	−0.851975	+	0.201922i	−0.0334172	+	0.00792003i
$651$	−20.0090	+	3.57029i	−0.784215	+	0.139931i
$652$	23.9885	−	12.0475i	0.939463	−	0.471816i
$653$	−26.8202	−	36.0258i	−1.04956	−	1.40980i	−0.907555	−	0.419934i	$-0.862053\pi$
$653$	−26.8202	−	36.0258i	−1.04956	−	1.40980i	−0.142002	−	0.989866i	$-0.545354\pi$
$654$	−0.159480	−	0.118223i	−0.00623615	−	0.00462288i
$655$	−5.41411	+	3.56091i	−0.211547	+	0.139136i
$656$	6.57544	−	5.51745i	0.256728	−	0.215420i
$657$	−29.1450	+	0.119078i	−1.13705	+	0.00464566i
$658$	2.81067	+	2.35843i	0.109571	+	0.0919413i
$659$	33.2933	+	3.89143i	1.29692	+	0.151589i	0.736398	−	0.676549i	$-0.236525\pi$
$659$	33.2933	+	3.89143i	1.29692	+	0.151589i	0.560525	+	0.828137i	$0.310599\pi$
$660$	17.1031	−	12.7871i	0.665736	−	0.497739i
$661$	−4.65404	−	15.5456i	−0.181021	−	0.604653i	−0.999544	−	0.0301797i	$-0.990392\pi$
$661$	−4.65404	−	15.5456i	−0.181021	−	0.604653i	0.818523	−	0.574473i	$-0.194793\pi$
$662$	4.27846	−	4.53490i	0.166287	−	0.176254i
$663$	−9.37667	+	39.9266i	−0.364160	+	1.55062i
$664$	−2.43963	+	3.27699i	−0.0946761	+	0.127172i
$665$	0.0571518	−	0.324124i	0.00221625	−	0.0125690i
$666$	3.32890	+	0.375312i	0.128992	+	0.0145431i
$667$	−7.93821	−	45.0198i	−0.307369	−	1.74317i
$668$	11.3780	+	5.71422i	0.440226	+	0.221090i
$669$	−28.3057	+	26.8146i	−1.09436	+	1.03671i
$670$	0.810856	−	0.0947755i	0.0313261	−	0.00366150i
$671$	−29.8588	−	19.6385i	−1.15269	−	0.758135i
$672$	15.4293	+	2.68812i	0.595200	+	0.103697i
$673$	−0.564176	+	1.88448i	−0.0217474	+	0.0726413i	−0.968174	−	0.250276i	$-0.919479\pi$
$673$	−0.564176	+	1.88448i	−0.0217474	+	0.0726413i	0.946427	+	0.322918i	$0.104664\pi$
$674$	1.16527	+	2.01831i	0.0448846	+	0.0777424i
$675$	−0.614679	−	2.52449i	−0.0236590	−	0.0971676i
$676$	16.5807	−	28.7186i	0.637719	−	1.10456i
$677$	−14.0812	−	14.9252i	−0.541186	−	0.573624i	0.397847	−	0.917452i	$-0.369758\pi$
$677$	−14.0812	−	14.9252i	−0.541186	−	0.573624i	−0.939032	+	0.343828i	$0.888276\pi$
$678$	−9.40647	−	5.40524i	−0.361253	−	0.207587i
$679$	1.03868	−	17.8335i	0.0398610	−	0.684387i
$680$	4.45976	−	10.3389i	0.171024	−	0.396478i
$681$	−12.8016	−	19.3776i	−0.490559	−	0.742550i
$682$	0.260438	+	4.47155i	0.00997269	+	0.171225i
$683$	20.1405	+	7.33055i	0.770656	+	0.280496i	0.697271	−	0.716808i	$-0.254398\pi$
$683$	20.1405	+	7.33055i	0.770656	+	0.280496i	0.0733852	+	0.997304i	$0.476620\pi$
$684$	0.0187914	−	0.347059i	0.000718508	−	0.0132701i
$685$	−5.19273	+	1.89000i	−0.198404	+	0.0722131i
$686$	2.40699	+	5.58002i	0.0918992	+	0.213046i
$687$	−4.85738	−	9.62277i	−0.185321	−	0.367132i
$688$	−2.57126	−	0.609401i	−0.0980285	−	0.0232332i
$689$	−10.5939	−	2.51079i	−0.403594	−	0.0956536i
$690$	−4.98247	−	0.279984i	−0.189679	−	0.0106588i
$691$	10.9955	+	25.4903i	0.418287	+	0.969698i	0.988914	+	0.148489i	$0.0474409\pi$
$691$	10.9955	+	25.4903i	0.418287	+	0.969698i	−0.570627	+	0.821209i	$0.693300\pi$
$692$	−26.3949	+	9.60696i	−1.00338	+	0.365202i
$693$	−22.7425	−	5.29203i	−0.863916	−	0.201027i
$694$	−5.43167	−	1.97696i	−0.206183	−	0.0750446i
$695$	2.34156	+	40.2030i	0.0888204	+	1.52499i
$696$	−10.2280	+	20.4698i	−0.387691	+	0.775905i
$697$	−4.28240	+	9.92772i	−0.162208	+	0.376039i
$698$	0.297199	−	5.10271i	0.0112492	−	0.193141i
$699$	18.5626	−	10.7678i	0.702103	−	0.407274i
$700$	1.65774	+	1.75710i	0.0626567	+	0.0664123i
$701$	−0.354873	+	0.614659i	−0.0134034	+	0.0232153i	−0.872649	−	0.488347i	$-0.837600\pi$
$701$	−0.354873	+	0.614659i	−0.0134034	+	0.0232153i	0.859246	+	0.511563i	$0.170933\pi$
$702$	−7.90741	−	4.50096i	−0.298446	−	0.169878i
$703$	0.107343	+	0.185923i	0.00404851	+	0.00701223i
$704$	−4.98880	+	16.6638i	−0.188022	+	0.628039i
$705$	−5.74551	−	15.6859i	−0.216388	−	0.590764i
$706$	4.55508	+	2.99593i	0.171433	+	0.112753i
$707$	27.4204	−	3.20499i	1.03125	−	0.120536i
$708$	5.51973	+	23.0794i	0.207444	+	0.867376i
$709$	−18.0431	−	9.06158i	−0.677623	−	0.340315i	0.0764804	−	0.997071i	$-0.475632\pi$
$709$	−18.0431	−	9.06158i	−0.677623	−	0.340315i	−0.754103	+	0.656756i	$0.771928\pi$
$710$	−1.66754	−	9.45710i	−0.0625817	−	0.354919i
$711$	−4.32818	−	2.15159i	−0.162319	−	0.0806910i
$712$	3.01771	−	17.1143i	0.113093	−	0.641385i
$713$	−11.7937	+	15.8417i	−0.441677	+	0.593275i
$714$	−5.74153	+	1.73169i	−0.214871	+	0.0648068i
$715$	24.5850	−	26.0586i	0.919427	−	0.974536i
$716$	−0.345228	−	1.15314i	−0.0129018	−	0.0430949i
$717$	−2.01157	−	16.9104i	−0.0751233	−	0.631530i
$718$	8.96042	+	1.04732i	0.334400	+	0.0390857i
$719$	12.8502	+	10.7826i	0.479231	+	0.402123i	0.850148	−	0.526543i	$-0.176512\pi$
$719$	12.8502	+	10.7826i	0.479231	+	0.402123i	−0.370917	+	0.928666i	$0.620957\pi$
$720$	−16.6620	−	13.8655i	−0.620956	−	0.516735i
$721$	24.2326	−	20.3336i	0.902471	−	0.757263i
$722$	5.03551	−	3.31191i	0.187402	−	0.123256i
$723$	3.42520	−	29.8329i	0.127385	−	1.10950i
$724$	15.8269	+	21.2592i	0.588201	+	0.790090i
$725$	−4.77178	+	2.39648i	−0.177220	+	0.0890030i
$726$	0.305789	−	0.845519i	0.0113489	−	0.0313802i
$727$	−21.6038	+	5.12018i	−0.801239	+	0.189897i	−0.610782	−	0.791799i	$-0.709145\pi$
$727$	−21.6038	+	5.12018i	−0.801239	+	0.189897i	−0.190456	+	0.981696i	$0.560997\pi$
$728$	17.3671			0.643666
$729$	13.2124	−	23.5464i	0.489348	−	0.872089i
$730$	6.53862			0.242005
$731$	3.23877	−	0.767603i	0.119790	−	0.0283908i
$732$	−13.0670	+	36.1306i	−0.482969	+	1.33543i
$733$	3.48042	−	1.74793i	0.128552	−	0.0645613i	−0.383361	−	0.923599i	$-0.625233\pi$
$733$	3.48042	−	1.74793i	0.128552	−	0.0645613i	0.511913	+	0.859037i	$0.328937\pi$
$734$	1.96607	+	2.64090i	0.0725691	+	0.0974772i
$735$	0.222276	−	1.93599i	0.00819879	−	0.0714099i
$736$	12.7148	−	8.36265i	0.468673	−	0.308251i
$737$	2.84336	−	2.38586i	0.104737	−	0.0878844i
$738$	−1.84374	−	1.53429i	−0.0678690	−	0.0564779i
$739$	−15.2233	−	12.7738i	−0.559997	−	0.469894i	0.318312	−	0.947986i	$-0.396884\pi$
$739$	−15.2233	−	12.7738i	−0.559997	−	0.469894i	−0.878310	+	0.478092i	$0.841328\pi$
$740$	14.0847	+	1.64626i	0.517764	+	0.0605179i
$741$	−0.0688759	−	0.579010i	−0.00253022	−	0.0212705i
$742$	−0.456583	−	1.52509i	−0.0167617	−	0.0559879i
$743$	−4.26737	+	4.52315i	−0.156555	+	0.165938i	−0.800903	−	0.598793i	$-0.795647\pi$
$743$	−4.26737	+	4.52315i	−0.156555	+	0.165938i	0.644349	+	0.764732i	$0.277129\pi$
$744$	9.46480	−	2.85466i	0.346996	−	0.104657i
$745$	5.19071	−	6.97233i	0.190173	−	0.255447i
$746$	0.820489	−	4.65322i	0.0300402	−	0.170367i
$747$	−8.87106	−	4.40992i	−0.324575	−	0.161351i
$748$	−4.33010	−	24.5572i	−0.158324	−	0.897901i
$749$	−11.3157	−	5.68295i	−0.413466	−	0.207650i
$750$	1.49136	+	6.23573i	0.0544566	+	0.227697i
$751$	16.0055	−	1.87077i	0.584047	−	0.0682653i	0.181062	−	0.983472i	$-0.442047\pi$
$751$	16.0055	−	1.87077i	0.584047	−	0.0682653i	0.402985	+	0.915206i	$0.367973\pi$
$752$	12.9386	+	8.50983i	0.471821	+	0.310321i
$753$	−14.9127	−	40.7132i	−0.543447	−	1.48367i
$754$	−5.36295	+	17.9135i	−0.195307	+	0.652371i
$755$	−10.5442	−	18.2632i	−0.383744	−	0.664665i
$756$	0.153842	+	25.1024i	0.00559519	+	0.912966i
$757$	17.7618	−	30.7643i	0.645563	−	1.11815i	−0.338608	−	0.940928i	$-0.609956\pi$
$757$	17.7618	−	30.7643i	0.645563	−	1.11815i	0.984171	−	0.177221i	$-0.0567106\pi$
$758$	−2.53093	−	2.68263i	−0.0919276	−	0.0974376i
$759$	−19.6261	+	11.3847i	−0.712383	+	0.413237i
$760$	−0.00930802	+	0.159812i	−0.000337637	+	0.00579701i
$761$	−8.06167	+	18.6891i	−0.292235	+	0.677478i	−0.999568	−	0.0294034i	$-0.990639\pi$
$761$	−8.06167	+	18.6891i	−0.292235	+	0.677478i	0.707332	+	0.706881i	$0.249899\pi$
$762$	−3.54330	+	7.09138i	−0.128360	+	0.256893i
$763$	0.0534270	+	0.917306i	0.00193419	+	0.0332087i
$764$	15.1587	+	5.51732i	0.548423	+	0.199610i
$765$	26.5934	+	6.18810i	0.961486	+	0.223731i
$766$	8.50177	−	3.09439i	0.307181	−	0.111805i
$767$	15.7682	+	36.5549i	0.569358	+	1.31992i
$768$	14.7697	+	0.829968i	0.532957	+	0.0299489i
$769$	−18.1188	−	4.29422i	−0.653379	−	0.154854i	−0.109460	−	0.993991i	$-0.534912\pi$
$769$	−18.1188	−	4.29422i	−0.653379	−	0.154854i	−0.543919	+	0.839138i	$0.683060\pi$
$770$	5.09729	+	1.20808i	0.183694	+	0.0435362i
$771$	−1.88137	−	3.72711i	−0.0677559	−	0.134229i
$772$	−9.96861	−	23.1098i	−0.358778	−	0.831741i
$773$	3.69733	−	1.34572i	0.132984	−	0.0484021i	−0.274671	−	0.961538i	$-0.588569\pi$
$773$	3.69733	−	1.34572i	0.132984	−	0.0484021i	0.407655	+	0.913136i	$0.366347\pi$
$774$	−0.0399233	+	0.737344i	−0.00143501	+	0.0265033i
$775$	2.16778	+	0.789007i	0.0778689	+	0.0283420i
$776$	0.505207	+	8.67407i	0.0181359	+	0.311381i
$777$	−8.54689	−	12.9373i	−0.306618	−	0.464122i
$778$	0.385840	−	0.894479i	0.0138330	−	0.0320686i
$779$	0.00893786	−	0.153457i	0.000320232	−	0.00549817i
$780$	−33.3941	−	19.1893i	−1.19570	−	0.687085i
$781$	−29.9620	−	31.7579i	−1.07213	−	1.13639i
$782$	−2.91361	+	5.04653i	−0.104191	+	0.180463i
$783$	−53.2542	−	15.5883i	−1.90315	−	0.557080i
$784$	0.903265	+	1.56450i	0.0322595	+	0.0558750i
$785$	−7.02675	+	23.4710i	−0.250795	+	0.837715i
$786$	−1.65381	−	0.288128i	−0.0589893	−	0.0102772i
$787$	−6.16322	−	4.05361i	−0.219695	−	0.144496i	0.434891	−	0.900483i	$-0.356787\pi$
$787$	−6.16322	−	4.05361i	−0.219695	−	0.144496i	−0.654586	+	0.755987i	$0.727157\pi$
$788$	−14.2398	+	1.66439i	−0.507272	+	0.0592916i
$789$	4.93257	−	4.67272i	0.175604	−	0.166353i
$790$	0.969029	+	0.486664i	0.0344765	+	0.0173147i
$791$	8.71966	+	49.4517i	0.310035	+	1.75830i
$792$	11.2858	+	1.27240i	0.401023	+	0.0452128i
$793$	−11.1927	+	63.4772i	−0.397466	+	2.25414i
$794$	−1.99121	+	2.67466i	−0.0706655	+	0.0949202i
$795$	−1.65712	+	7.05616i	−0.0587721	+	0.250256i
$796$	−2.75462	+	2.91973i	−0.0976350	+	0.103487i
$797$	−4.28696	−	14.3194i	−0.151852	−	0.507221i	0.847884	−	0.530181i	$-0.177876\pi$
$797$	−4.28696	−	14.3194i	−0.151852	−	0.507221i	−0.999736	+	0.0229603i	$0.992691\pi$
$798$	0.0682857	−	0.0510540i	0.00241729	−	0.00180729i
$799$	−19.3746	−	2.26457i	−0.685425	−	0.0801146i
$800$	−1.36173	−	1.14263i	−0.0481446	−	0.0403981i
$801$	42.1404	−	0.172173i	1.48896	−	0.00608344i
$802$	6.44030	−	5.40405i	0.227415	−	0.190824i
$803$	24.8379	−	16.3361i	0.876509	−	0.576489i
$804$	−3.20563	−	2.37634i	−0.113054	−	0.0838071i
$805$	13.7931	+	18.5274i	0.486144	+	0.653005i
$806$	7.21915	−	3.62559i	0.254284	−	0.127706i
$807$	18.9102	−	3.37423i	0.665671	−	0.118778i
$808$	−13.0659	+	3.09668i	−0.459657	+	0.108941i
$809$	−28.6228			−1.00633			−0.503163	−	0.864192i	$-0.667830\pi$
$809$	−28.6228			−1.00633			−0.503163	+	0.864192i	$0.667830\pi$
$810$	−2.98571	+	5.27039i	−0.104907	+	0.185182i
$811$	15.2720			0.536273			0.268136	−	0.963381i	$-0.413592\pi$
$811$	15.2720			0.536273			0.268136	+	0.963381i	$0.413592\pi$
$812$	50.1993	−	11.8975i	1.76165	−	0.417519i
$813$	−0.886832	−	1.05251i	−0.0311025	−	0.0369132i
$814$	−3.05358	+	1.53356i	−0.107028	+	0.0537514i
$815$	−17.9035	−	24.0485i	−0.627131	−	0.842383i
$816$	−23.2212	+	10.0730i	−0.812904	+	0.352624i
$817$	−0.0395371	+	0.0260040i	−0.00138323	+	0.000909764i
$818$	6.40487	−	5.37433i	0.223941	−	0.187909i
$819$	7.48233	+	41.4435i	0.261454	+	1.44815i
$820$	−7.77799	−	6.52651i	−0.271619	−	0.227915i
$821$	3.09149	+	0.361343i	0.107894	+	0.0126110i	0.169868	−	0.985467i	$-0.445666\pi$
$821$	3.09149	+	0.361343i	0.107894	+	0.0126110i	−0.0619747	+	0.998078i	$0.519740\pi$
$822$	−1.31561	−	0.564314i	−0.0458871	−	0.0196827i
$823$	−11.0490	−	36.9063i	−0.385145	−	1.28647i	−0.902496	−	0.430699i	$-0.858267\pi$
$823$	−11.0490	−	36.9063i	−0.385145	−	1.28647i	0.517351	−	0.855773i	$-0.326918\pi$
$824$	−10.5587	+	11.1916i	−0.367829	+	0.389876i
$825$	1.93143	+	1.81477i	0.0672438	+	0.0631821i
$826$	−3.47619	+	4.66934i	−0.120952	+	0.162467i
$827$	−1.37656	+	7.80687i	−0.0478677	+	0.271471i	−0.999343	−	0.0362552i	$-0.988457\pi$
$827$	−1.37656	+	7.80687i	−0.0478677	+	0.271471i	0.951475	+	0.307727i	$0.0995682\pi$
$828$	16.8113	+	17.6738i	0.584234	+	0.614205i
$829$	5.51283	+	31.2648i	0.191469	+	1.08587i	0.917359	+	0.398061i	$0.130317\pi$
$829$	5.51283	+	31.2648i	0.191469	+	1.08587i	−0.725890	+	0.687811i	$0.758572\pi$
$830$	1.98613	+	0.997472i	0.0689396	+	0.0346227i
$831$	48.4604	+	14.4003i	1.68107	+	0.499541i
$832$	31.1601	−	3.64209i	1.08028	−	0.126267i
$833$	−1.90116	−	1.25041i	−0.0658713	−	0.0433243i
$834$	−6.68949	+	8.00537i	−0.231638	+	0.277203i
$835$	4.07842	−	13.6229i	0.141140	−	0.471439i
$836$	0.177262	+	0.307026i	0.00613073	+	0.0106187i
$837$	10.8899	+	21.3563i	0.376411	+	0.738180i
$838$	−1.24238	+	2.15186i	−0.0429172	+	0.0743347i
$839$	−31.0641	−	32.9260i	−1.07245	−	1.13673i	−0.990134	−	0.140127i	$-0.955249\pi$
$839$	−31.0641	−	32.9260i	−1.07245	−	1.13673i	−0.0823188	−	0.996606i	$-0.526233\pi$
$840$	−0.0236192	−	11.5619i	−0.000814938	−	0.398924i
$841$	−4.94448	+	84.8934i	−0.170499	+	2.92736i
$842$	−4.00269	+	9.27928i	−0.137942	+	0.319785i
$843$	47.6988	−	2.87592i	1.64283	−	0.0990521i
$844$	0.0724991	+	1.24476i	0.00249552	+	0.0428465i
$845$	−34.8033	−	12.6674i	−1.19727	−	0.435771i
$846$	1.69779	−	3.98055i	0.0583712	−	0.136854i
$847$	−3.91062	+	1.42335i	−0.134370	+	0.0489069i
$848$	−2.66139	−	6.16978i	−0.0913923	−	0.211871i
$849$	4.84715	−	7.40263i	0.166354	−	0.254058i
$850$	0.662314	+	0.156971i	0.0227172	+	0.00538407i
$851$	−14.6605	−	3.47460i	−0.502556	−	0.119108i
$852$	−25.7130	+	39.2692i	−0.880912	+	1.34534i
$853$	18.4697	+	42.8176i	0.632390	+	1.46605i	0.869186	+	0.494486i	$0.164644\pi$
$853$	18.4697	+	42.8176i	0.632390	+	1.46605i	−0.236796	+	0.971559i	$0.576097\pi$
$854$	−8.85657	+	3.22353i	−0.303066	+	0.110307i
$855$	−0.385375	+	0.0466407i	−0.0131796	+	0.00159508i
$856$	5.78753	+	2.10649i	0.197814	+	0.0719983i
$857$	0.396939	+	6.81518i	0.0135592	+	0.232802i	0.998278	+	0.0586529i	$0.0186805\pi$
$857$	0.396939	+	6.81518i	0.0135592	+	0.232802i	−0.984719	+	0.174149i	$0.944282\pi$
$858$	9.26395	−	0.558555i	0.316266	−	0.0190687i
$859$	4.35181	−	10.0886i	0.148482	−	0.344219i	−0.827701	−	0.561169i	$-0.810352\pi$
$859$	4.35181	−	10.0886i	0.148482	−	0.344219i	0.976183	+	0.216950i	$0.0696109\pi$
$860$	−0.181747	+	3.12048i	−0.00619752	+	0.106407i
$861$	0.0226799	+	11.1021i	0.000772928	+	0.378359i
$862$	7.25321	+	7.68796i	0.247045	+	0.261853i
$863$	27.8142	−	48.1756i	0.946807	−	1.63992i	0.194715	−	0.980860i	$-0.437622\pi$
$863$	27.8142	−	48.1756i	0.946807	−	1.63992i	0.752092	−	0.659058i	$-0.229045\pi$
$864$	−2.25691	−	18.3340i	−0.0767816	−	0.623734i
$865$	15.6858	+	27.1686i	0.533334	+	0.923761i
$866$	0.501918	−	1.67652i	0.0170559	−	0.0569705i
$867$	1.56328	−	1.87079i	0.0530918	−	0.0635355i
$868$	−18.6214	−	12.2475i	−0.632052	−	0.415707i
$869$	4.89687	−	0.572362i	0.166115	−	0.0194161i
$870$	11.9330	+	3.54596i	0.404566	+	0.120219i
$871$	−5.98233	−	3.00444i	−0.202704	−	0.101802i
$872$	−0.0776079	−	0.440136i	−0.00262814	−	0.0149049i
$873$	−20.4815	+	4.94268i	−0.693195	+	0.167284i
$874$	0.0143863	−	0.0815889i	0.000486625	−	0.00275979i
$875$	17.7215	−	23.8040i	0.599094	−	0.804723i
$876$	−23.2917	−	21.8849i	−0.786955	−	0.739421i
$877$	−16.9320	+	17.9469i	−0.571754	+	0.606024i	−0.947131	−	0.320848i	$-0.896032\pi$
$877$	−16.9320	+	17.9469i	−0.571754	+	0.606024i	0.375376	+	0.926873i	$0.377514\pi$
$878$	0.301199	+	1.00607i	0.0101650	+	0.0339534i
$879$	3.73029	+	1.60006i	0.125820	+	0.0539687i
$880$	21.9609	+	2.56686i	0.740302	+	0.0865289i
$881$	−13.2241	−	11.0964i	−0.445532	−	0.373846i	0.392243	−	0.919862i	$-0.371699\pi$
$881$	−13.2241	−	11.0964i	−0.445532	−	0.373846i	−0.837775	+	0.546016i	$0.816144\pi$
$882$	0.385386	−	0.326070i	0.0129766	−	0.0109793i
$883$	−24.0818	+	20.2071i	−0.810419	+	0.680022i	−0.950708	−	0.310089i	$-0.899641\pi$
$883$	−24.0818	+	20.2071i	−0.810419	+	0.680022i	0.140289	+	0.990111i	$0.455197\pi$
$884$	−37.5752	+	24.7136i	−1.26379	+	0.831208i
$885$	24.3145	−	10.5472i	0.817325	−	0.354542i
$886$	3.25609	+	4.37368i	0.109390	+	0.146937i
$887$	39.5207	−	19.8480i	1.32697	−	0.666431i	0.362841	−	0.931851i	$-0.381807\pi$
$887$	39.5207	−	19.8480i	1.32697	−	0.666431i	0.964133	+	0.265420i	$0.0855105\pi$
$888$	4.85955	+	5.76742i	0.163076	+	0.193542i
$889$	35.7029	−	8.46175i	1.19744	−	0.283798i
$890$	−9.45412			−0.316903
$891$	1.82594	+	27.4798i	0.0611712	+	0.920608i
$892$	−42.7560			−1.43158
$893$	0.269855	−	0.0639567i	0.00903034	−	0.00214023i
$894$	2.21678	−	0.395549i	0.0741401	−	0.0132291i
$895$	−1.20139	+	0.603360i	−0.0401580	+	0.0201681i
$896$	13.5388	+	18.1857i	0.452298	+	0.607542i
$897$	32.8739	+	24.3695i	1.09763	+	0.813673i
$898$	4.66555	−	3.06858i	0.155692	−	0.102400i
$899$	37.7406	−	31.6681i	1.25872	−	1.05619i
$900$	1.41450	−	2.47327i	0.0471501	−	0.0824424i
$901$	6.48355	+	5.44034i	0.215998	+	0.181244i
$902$	2.43009	+	0.284037i	0.0809132	+	0.00945739i
$903$	2.73734	−	2.04658i	0.0910930	−	0.0681059i
$904$	−7.00486	−	23.3979i	−0.232978	−	0.778201i
$905$	20.3135	−	21.5311i	0.675244	−	0.715716i
$906$	1.24901	−	5.31837i	0.0414955	−	0.176691i
$907$	8.82678	−	11.8564i	0.293088	−	0.393686i	−0.631051	−	0.775741i	$-0.717376\pi$
$907$	8.82678	−	11.8564i	0.293088	−	0.393686i	0.924139	+	0.382055i	$0.124784\pi$
$908$	4.42237	−	25.0805i	0.146762	−	0.832327i
$909$	−13.0189	−	29.8454i	−0.431811	−	0.989909i
$910$	−1.64063	−	9.30447i	−0.0543863	−	0.308440i
$911$	−34.6323	−	17.3930i	−1.14742	−	0.576256i	−0.229613	−	0.973282i	$-0.573746\pi$
$911$	−34.6323	−	17.3930i	−1.14742	−	0.576256i	−0.917807	+	0.397026i	$0.870042\pi$
$912$	0.261252	−	0.247489i	0.00865092	−	0.00819519i
$913$	10.0367	−	1.17312i	0.332165	−	0.0388246i
$914$	−4.73816	−	3.11634i	−0.156724	−	0.103079i
$915$	42.2744	+	7.36511i	1.39755	+	0.243483i
$916$	3.39011	−	11.3237i	0.112012	−	0.374147i
$917$	3.88500	+	6.72903i	0.128294	+	0.222212i
$918$	3.92292	+	5.88563i	0.129476	+	0.194255i
$919$	−20.8939	+	36.1894i	−0.689228	+	1.19378i	0.282860	+	0.959161i	$0.408717\pi$
$919$	−20.8939	+	36.1894i	−0.689228	+	1.19378i	−0.972088	+	0.234616i	$0.924617\pi$
$920$	−7.70968	−	8.17178i	−0.254181	−	0.269416i
$921$	−24.2795	−	13.9518i	−0.800038	−	0.459726i
$922$	0.0927409	−	1.59230i	0.00305426	−	0.0524396i
$923$	−31.1896	+	72.3057i	−1.02662	+	2.37997i
$924$	−14.1140	−	21.3641i	−0.464317	−	0.702828i
$925$	0.102328	+	1.75691i	0.00336454	+	0.0577669i
$926$	−5.12956	−	1.86701i	−0.168568	−	0.0613536i
$927$	−31.2558	−	20.3748i	−1.02657	−	0.669196i
$928$	−35.6738	+	12.9842i	−1.17105	+	0.426227i
$929$	−10.5455	−	24.4472i	−0.345986	−	0.802085i	−0.998999	−	0.0447384i	$-0.985755\pi$
$929$	−10.5455	−	24.4472i	−0.345986	−	0.802085i	0.653013	−	0.757347i	$-0.273505\pi$
$930$	−2.42351	−	4.80113i	−0.0794701	−	0.157435i
$931$	0.0314796	+	0.00746080i	0.00103170	+	0.000244518i
$932$	22.8979	+	5.42691i	0.750047	+	0.177764i
$933$	−36.6598	−	2.06006i	−1.20019	−	0.0674432i
$934$	−4.70712	−	10.9123i	−0.154022	−	0.357062i
$935$	−26.1707	+	9.52537i	−0.855875	+	0.311513i
$936$	−5.95491	−	19.5990i	−0.194642	−	0.640613i
$937$	10.5874	+	3.85350i	0.345875	+	0.125888i	0.509116	−	0.860698i	$-0.329972\pi$
$937$	10.5874	+	3.85350i	0.345875	+	0.125888i	−0.163241	+	0.986586i	$0.552195\pi$
$938$	−0.0569163	−	0.977214i	−0.00185838	−	0.0319072i
$939$	−4.18941	+	8.38446i	−0.136716	+	0.273616i
$940$	7.25556	−	16.8203i	0.236650	−	0.548617i
$941$	−1.02973	+	17.6798i	−0.0335683	+	0.576346i	0.939027	+	0.343842i	$0.111729\pi$
$941$	−1.02973	+	17.6798i	−0.0335683	+	0.576346i	−0.972596	+	0.232503i	$0.925308\pi$
$942$	−5.49007	+	3.18467i	−0.178876	+	0.103762i
$943$	7.40308	+	7.84681i	0.241078	+	0.255527i
$944$	−12.2850	+	21.2782i	−0.399842	+	0.692546i
$945$	27.5804	−	5.03763i	0.897189	−	0.163874i
$946$	−0.376601	−	0.652293i	−0.0122444	−	0.0212079i
$947$	17.0425	−	56.9257i	0.553805	−	1.84984i	0.0273661	−	0.999625i	$-0.491288\pi$
$947$	17.0425	−	56.9257i	0.553805	−	1.84984i	0.526439	−	0.850213i	$-0.323527\pi$
$948$	−1.82298	−	4.97694i	−0.0592077	−	0.161644i
$949$	−44.7969	−	29.4634i	−1.45417	−	0.956421i
$950$	−0.00961174	+	0.00112345i	−0.000311846	+	3.64496e-5i
$951$	−3.51607	−	14.7016i	−0.114016	−	0.476731i
$952$	−12.0649	−	6.05920i	−0.391025	−	0.196380i
$953$	9.46496	+	53.6784i	0.306600	+	1.73881i	0.615876	+	0.787843i	$0.288802\pi$
$953$	9.46496	+	53.6784i	0.306600	+	1.73881i	−0.309277	+	0.950972i	$0.600087\pi$
$954$	−1.56453	+	1.03819i	−0.0506536	+	0.0336127i
$955$	3.12859	−	17.7431i	0.101239	−	0.574155i
$956$	11.1516	−	14.9792i	0.360667	−	0.484460i
$957$	54.1883	−	16.3436i	1.75166	−	0.528314i
$958$	0.745222	−	0.789889i	0.0240770	−	0.0255202i
$959$	1.90033	+	6.34754i	0.0613648	+	0.204973i
$960$	−2.46706	−	20.7395i	−0.0796240	−	0.669365i
$961$	9.64987	+	1.12791i	0.311286	+	0.0363841i
$962$	4.72103	+	3.96142i	0.152212	+	0.127721i
$963$	−2.53331	+	14.7185i	−0.0816347	+	0.474297i
$964$	25.2252	−	21.1664i	0.812448	−	0.681725i
$965$	−23.4852	+	15.4465i	−0.756016	+	0.497240i
$966$	−0.682514	+	5.94457i	−0.0219595	+	0.191263i
$967$	16.9232	+	22.7318i	0.544213	+	0.731004i	0.986116	−	0.166058i	$-0.0531040\pi$
$967$	16.9232	+	22.7318i	0.544213	+	0.731004i	−0.441903	+	0.897063i	$0.645697\pi$
$968$	1.80886	−	0.908444i	0.0581390	−	0.0291985i
$969$	−0.154163	+	0.426267i	−0.00495244	+	0.0136937i
$970$	4.59944	−	1.09009i	0.147679	−	0.0350006i
$971$	−34.6038			−1.11049			−0.555244	−	0.831687i	$-0.687375\pi$
$971$	−34.6038			−1.11049			−0.555244	+	0.831687i	$0.687375\pi$
$972$	28.2757	−	8.78086i	0.906943	−	0.281646i
$973$	48.2868			1.54801
$974$	−1.67742	+	0.397555i	−0.0537479	+	0.0127385i
$975$	1.62565	−	4.49498i	0.0520624	−	0.143954i
$976$	−35.5491	+	17.8534i	−1.13790	+	0.571475i
$977$	−7.92451	−	10.6445i	−0.253528	−	0.340547i	0.657078	−	0.753822i	$-0.271792\pi$
$977$	−7.92451	−	10.6445i	−0.253528	−	0.340547i	−0.910606	+	0.413276i	$0.864385\pi$
$978$	0.885902	−	7.71604i	0.0283280	−	0.246732i
$979$	−35.9128	+	23.6202i	−1.14778	+	0.754905i
$980$	1.63697	−	1.37358i	0.0522912	−	0.0438775i
$981$	1.01687	−	0.374824i	0.0324663	−	0.0119672i
$982$	0.965832	+	0.810430i	0.0308209	+	0.0258618i
$983$	−35.7584	−	4.17956i	−1.14052	−	0.133307i	−0.475207	−	0.879874i	$-0.657627\pi$
$983$	−35.7584	−	4.17956i	−1.14052	−	0.133307i	−0.665310	+	0.746567i	$0.731701\pi$
$984$	−0.637856	−	5.36218i	−0.0203341	−	0.170940i
$985$	4.59237	+	15.3396i	0.146325	+	0.488760i
$986$	9.97548	−	10.5734i	0.317684	−	0.336725i
$987$	−19.1768	+	5.78387i	−0.610404	+	0.184102i
$988$	0.381829	−	0.512885i	0.0121476	−	0.0163170i
$989$	0.576698	−	3.27062i	0.0183379	−	0.104000i
$990$	−0.384450	−	6.16660i	−0.0122186	−	0.195988i
$991$	9.06181	+	51.3921i	0.287858	+	1.63252i	0.694895	+	0.719111i	$0.255451\pi$
$991$	9.06181	+	51.3921i	0.287858	+	1.63252i	−0.407037	+	0.913412i	$0.633438\pi$
$992$	14.6565	+	7.36077i	0.465344	+	0.233705i
$993$	7.91684	+	33.1023i	0.251233	+	1.05047i
$994$	−11.4365	+	1.33674i	−0.362745	+	0.0423988i
$995$	3.74565	+	2.46355i	0.118745	+	0.0780999i
$996$	−3.73640	−	10.2008i	−0.118392	−	0.323224i
$997$	−5.17685	+	17.2919i	−0.163952	+	0.547639i	−0.999999	−	0.00101867i	$-0.999676\pi$
$997$	−5.17685	+	17.2919i	−0.163952	+	0.547639i	0.836047	+	0.548658i	$0.184861\pi$
$998$	3.40379	+	5.89554i	0.107745	+	0.186620i
$999$	−11.6693	+	14.0813i	−0.369200	+	0.445512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.76.5	yes	144
3.2	odd	2		243.2.g.a.118.4		144
9.2	odd	6		729.2.g.a.109.5		144
9.4	even	3		729.2.g.c.352.4		144
9.5	odd	6		729.2.g.b.352.5		144
9.7	even	3		729.2.g.d.109.4		144
81.4	even	27		6561.2.a.c.1.42		72
81.11	odd	54		729.2.g.b.379.5		144
81.16	even	27	inner	81.2.g.a.16.5	✓	144
81.38	odd	54		729.2.g.a.622.5		144
81.43	even	27		729.2.g.d.622.4		144
81.65	odd	54		243.2.g.a.208.4		144
81.70	even	27		729.2.g.c.379.4		144
81.77	odd	54		6561.2.a.d.1.31		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.5	✓	144	81.16	even	27	inner
81.2.g.a.76.5	yes	144	1.1	even	1	trivial
243.2.g.a.118.4		144	3.2	odd	2
243.2.g.a.208.4		144	81.65	odd	54
729.2.g.a.109.5		144	9.2	odd	6
729.2.g.a.622.5		144	81.38	odd	54
729.2.g.b.352.5		144	9.5	odd	6
729.2.g.b.379.5		144	81.11	odd	54
729.2.g.c.352.4		144	9.4	even	3
729.2.g.c.379.4		144	81.70	even	27
729.2.g.d.109.4		144	9.7	even	3
729.2.g.d.622.4		144	81.43	even	27
6561.2.a.c.1.42		72	81.4	even	27
6561.2.a.d.1.31		72	81.77	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.308722 - 0.0731685i) q^{2} +(-0.589070 + 1.62880i) q^{3} +(-1.69731 + 0.852421i) q^{4} +(1.26676 + 1.70155i) q^{5} +(-0.0626820 + 0.545949i) q^{6} +(2.12510 - 1.39770i) q^{7} +(-0.947719 + 0.795231i) q^{8} +(-2.30599 - 1.91896i) q^{9} +(0.515577 + 0.432621i) q^{10} +(3.03935 + 0.355249i) q^{11} +(-0.388591 - 3.26672i) q^{12} +(-1.58287 - 5.28715i) q^{13} +(0.553798 - 0.586992i) q^{14} +(-3.51771 + 1.06097i) q^{15} +(2.03401 - 2.73216i) q^{16} +(-0.745021 + 4.22522i) q^{17} +(-0.852318 - 0.423699i) q^{18} +(-0.0105922 - 0.0600713i) q^{19} +(-3.60052 - 1.80825i) q^{20} +(1.02475 + 4.28471i) q^{21} +(0.964308 - 0.112711i) q^{22} +(3.57659 + 2.35236i) q^{23} +(-0.737001 - 2.01209i) q^{24} +(0.143411 - 0.479026i) q^{25} +(-0.875520 - 1.51644i) q^{26} +(4.48399 - 2.62561i) q^{27} +(-2.41553 + 4.18381i) q^{28} +(-7.32825 - 7.76750i) q^{29} +(-1.00836 + 0.584929i) q^{30} +(-0.268252 + 4.60570i) q^{31} +(1.40807 - 3.26426i) q^{32} +(-2.36902 + 4.74124i) q^{33} +(0.0791488 + 1.35893i) q^{34} +(5.07026 + 1.84542i) q^{35} +(5.54974 + 1.29139i) q^{36} +(-3.30730 + 1.20376i) q^{37} +(-0.00766537 - 0.0177703i) q^{38} +(9.54414 + 0.536322i) q^{39} +(-2.55366 - 0.605229i) q^{40} +(2.45211 + 0.581160i) q^{41} +(0.629868 + 1.24781i) q^{42} +(-0.307278 - 0.712352i) q^{43} +(-5.46154 + 1.98784i) q^{44} +(0.344070 - 6.35463i) q^{45} +(1.27629 + 0.464532i) q^{46} +(0.264358 + 4.53885i) q^{47} +(3.25196 + 4.92244i) q^{48} +(-0.210070 + 0.486996i) q^{49} +(0.00922453 - 0.158379i) q^{50} +(-6.44318 - 3.70244i) q^{51} +(7.19350 + 7.62466i) q^{52} +(0.986349 - 1.70841i) q^{53} +(1.19220 - 1.13867i) q^{54} +(3.24565 + 5.62164i) q^{55} +(-0.902505 + 3.01458i) q^{56} +(0.104084 + 0.0181336i) q^{57} +(-2.83073 - 1.86180i) q^{58} +(-7.16462 + 0.837424i) q^{59} +(5.06624 - 4.79935i) q^{60} +(-10.4367 - 5.24152i) q^{61} +(0.254177 + 1.44151i) q^{62} +(-7.58260 - 0.854890i) q^{63} +(-0.987085 + 5.59804i) q^{64} +(6.99126 - 9.39089i) q^{65} +(-0.384461 + 1.63706i) q^{66} +(0.832392 - 0.882284i) q^{67} +(-2.33714 - 7.80658i) q^{68} +(-5.93839 + 4.43985i) q^{69} +(1.70033 + 0.198740i) q^{70} +(-10.9300 - 9.17137i) q^{71} +(3.71145 - 0.0151639i) q^{72} +(7.44218 - 6.24473i) q^{73} +(-0.932958 + 0.613616i) q^{74} +(0.695759 + 0.515768i) q^{75} +(0.0691843 + 0.0929306i) q^{76} +(6.95546 - 3.49317i) q^{77} +(2.98573 - 0.532756i) q^{78} +(1.56773 - 0.371558i) q^{79} +7.22552 q^{80} +(1.63521 + 8.85020i) q^{81} +0.799542 q^{82} +(3.21323 - 0.761549i) q^{83} +(-5.39169 - 6.39897i) q^{84} +(-8.13321 + 4.08465i) q^{85} +(-0.146985 - 0.197436i) q^{86} +(16.9686 - 7.36068i) q^{87} +(-3.16296 + 2.08031i) q^{88} +(-10.7606 + 9.02919i) q^{89} +(-0.358737 - 1.98699i) q^{90} +(-10.7536 - 9.02336i) q^{91} +(-8.07578 - 0.943923i) q^{92} +(-7.34376 - 3.15001i) q^{93} +(0.413714 + 1.38190i) q^{94} +(0.0887968 - 0.0941191i) q^{95} +(4.48739 + 4.21634i) q^{96} +(4.19394 - 5.63344i) q^{97} +(-0.0292204 + 0.165717i) q^{98} +(-6.32702 - 6.65159i) 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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