LMFDB - Embedded newform 81.2.g.a.22.3

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			22.3
Character	$\chi$	$=$	81.22
Dual form			81.2.g.a.70.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.802450 - 0.850548i) q^{2} +(1.71504 - 0.242123i) q^{3} +(0.0367849 - 0.631572i) q^{4} +(-0.890819 + 0.104122i) q^{5} +(-1.58218 - 1.26443i) q^{6} +(0.770065 + 0.386741i) q^{7} +(-2.35823 + 1.97879i) q^{8} +(2.88275 - 0.830504i) q^{9} +(0.803399 + 0.674132i) q^{10} +(-0.624164 - 1.44697i) q^{11} +(-0.0898306 - 1.09208i) q^{12} +(-0.701936 - 0.166362i) q^{13} +(-0.288997 - 0.965318i) q^{14} +(-1.50258 + 0.394262i) q^{15} +(2.31869 + 0.271016i) q^{16} +(-0.865512 + 4.90856i) q^{17} +(-3.01965 - 1.78548i) q^{18} +(1.32212 + 7.49811i) q^{19} +(0.0329918 + 0.566447i) q^{20} +(1.41434 + 0.476828i) q^{21} +(-0.729860 + 1.69201i) q^{22} +(1.78064 - 0.894269i) q^{23} +(-3.56536 + 3.96470i) q^{24} +(-4.08251 + 0.967572i) q^{25} +(0.421770 + 0.730527i) q^{26} +(4.74296 - 2.12233i) q^{27} +(0.272582 - 0.472126i) q^{28} +(0.676408 - 2.25936i) q^{29} +(1.54109 + 0.961644i) q^{30} +(-7.93694 - 5.22021i) q^{31} +(2.04653 + 2.74896i) q^{32} +(-1.42081 - 2.33050i) q^{33} +(4.86950 - 3.20272i) q^{34} +(-0.726257 - 0.264336i) q^{35} +(-0.418482 - 1.85122i) q^{36} +(0.249308 - 0.0907406i) q^{37} +(5.31656 - 7.14138i) q^{38} +(-1.24413 - 0.115363i) q^{39} +(1.89472 - 2.00829i) q^{40} +(6.68585 - 7.08659i) q^{41} +(-0.729369 - 1.58559i) q^{42} +(1.78455 - 2.39707i) q^{43} +(-0.936828 + 0.340978i) q^{44} +(-2.48154 + 1.03999i) q^{45} +(-2.18949 - 0.796909i) q^{46} +(-6.28485 + 4.13361i) q^{47} +(4.04228 - 0.0966047i) q^{48} +(-3.73668 - 5.01923i) q^{49} +(4.09897 + 2.69594i) q^{50} +(-0.295914 + 8.62796i) q^{51} +(-0.130890 + 0.437203i) q^{52} +(5.30779 - 9.19335i) q^{53} +(-5.61114 - 2.33105i) q^{54} +(0.706679 + 1.22400i) q^{55} +(-2.58128 + 0.611774i) q^{56} +(4.08296 + 12.5395i) q^{57} +(-2.46448 + 1.23771i) q^{58} +(-3.55686 + 8.24573i) q^{59} +(0.193732 + 0.963493i) q^{60} +(-0.534338 - 9.17423i) q^{61} +(1.92897 + 10.9397i) q^{62} +(2.54110 + 0.475337i) q^{63} +(1.50664 - 8.54460i) q^{64} +(0.642620 + 0.0751115i) q^{65} +(-0.842068 + 3.07858i) q^{66} +(3.28408 + 10.9696i) q^{67} +(3.06827 + 0.727194i) q^{68} +(2.83734 - 1.96484i) q^{69} +(0.357955 + 0.829833i) q^{70} +(-7.34178 - 6.16048i) q^{71} +(-5.15481 + 7.66290i) q^{72} +(-4.91737 + 4.12616i) q^{73} +(-0.277236 - 0.139233i) q^{74} +(-6.76741 + 2.64790i) q^{75} +(4.78423 - 0.559196i) q^{76} +(0.0789579 - 1.35565i) q^{77} +(0.900232 + 1.15077i) q^{78} +(-1.46027 - 1.54779i) q^{79} -2.09376 q^{80} +(7.62052 - 4.78828i) q^{81} -11.3925 q^{82} +(-1.68900 - 1.79023i) q^{83} +(0.353177 - 0.875714i) q^{84} +(0.259926 - 4.46276i) q^{85} +(-3.47084 + 0.405683i) q^{86} +(0.613026 - 4.03868i) q^{87} +(4.33519 + 2.17721i) q^{88} +(6.94724 - 5.82943i) q^{89} +(2.87587 + 1.27613i) q^{90} +(-0.476197 - 0.399577i) q^{91} +(-0.499295 - 1.15750i) q^{92} +(-14.8761 - 7.03117i) q^{93} +(8.55911 + 2.02855i) q^{94} +(-1.95849 - 6.54180i) q^{95} +(4.17548 + 4.21908i) q^{96} +(8.70918 + 1.01796i) q^{97} +(-1.27060 + 7.20591i) q^{98} +(-3.00103 - 3.65290i) 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 $

$2$	−0.802450	−	0.850548i	−0.567418	−	0.601428i	0.378593	−	0.925563i	$-0.376408\pi$
$2$	−0.802450	−	0.850548i	−0.567418	−	0.601428i	−0.946011	+	0.324135i	$0.894927\pi$
$3$	1.71504	−	0.242123i	0.990181	−	0.139790i
$3$	1.71504	−	0.242123i	0.990181	−	0.139790i
$4$	0.0367849	−	0.631572i	0.0183924	−	0.315786i
$5$	−0.890819	+	0.104122i	−0.398386	+	0.0465647i	−0.312928	−	0.949777i	$-0.601310\pi$
$5$	−0.890819	+	0.104122i	−0.398386	+	0.0465647i	−0.0854589	+	0.996342i	$0.527236\pi$
$6$	−1.58218	−	1.26443i	−0.645920	−	0.516203i
$7$	0.770065	+	0.386741i	0.291057	+	0.146174i	0.588337	−	0.808616i	$-0.299783\pi$
$7$	0.770065	+	0.386741i	0.291057	+	0.146174i	−0.297279	+	0.954791i	$0.596079\pi$
$8$	−2.35823	+	1.97879i	−0.833762	+	0.699609i
$9$	2.88275	−	0.830504i	0.960918	−	0.276835i
$10$	0.803399	+	0.674132i	0.254057	+	0.213179i
$11$	−0.624164	−	1.44697i	−0.188192	−	0.436279i	0.797832	−	0.602880i	$-0.205980\pi$
$11$	−0.624164	−	1.44697i	−0.188192	−	0.436279i	−0.986024	+	0.166601i	$0.946721\pi$
$12$	−0.0898306	−	1.09208i	−0.0259319	−	0.315256i
$13$	−0.701936	−	0.166362i	−0.194682	−	0.0461405i	0.132118	−	0.991234i	$-0.457822\pi$
$13$	−0.701936	−	0.166362i	−0.194682	−	0.0461405i	−0.326800	+	0.945094i	$0.605970\pi$
$14$	−0.288997	−	0.965318i	−0.0772378	−	0.257992i
$15$	−1.50258	+	0.394262i	−0.387966	+	0.101798i
$16$	2.31869	+	0.271016i	0.579673	+	0.0677541i
$17$	−0.865512	+	4.90856i	−0.209917	+	1.19050i	0.679594	+	0.733588i	$0.262156\pi$
$17$	−0.865512	+	4.90856i	−0.209917	+	1.19050i	−0.889512	+	0.456913i	$0.848955\pi$
$18$	−3.01965	−	1.78548i	−0.711738	−	0.420842i
$19$	1.32212	+	7.49811i	0.303315	+	1.72018i	0.631333	+	0.775512i	$0.282508\pi$
$19$	1.32212	+	7.49811i	0.303315	+	1.72018i	−0.328018	+	0.944671i	$0.606381\pi$
$20$	0.0329918	+	0.566447i	0.00737718	+	0.126661i
$21$	1.41434	+	0.476828i	0.308633	+	0.104052i
$22$	−0.729860	+	1.69201i	−0.155607	+	0.360737i
$23$	1.78064	−	0.894269i	0.371288	−	0.186468i	−0.253364	−	0.967371i	$-0.581537\pi$
$23$	1.78064	−	0.894269i	0.371288	−	0.186468i	0.624652	+	0.780903i	$0.285241\pi$
$24$	−3.56536	+	3.96470i	−0.727777	+	0.809291i
$25$	−4.08251	+	0.967572i	−0.816501	+	0.193514i
$26$	0.421770	+	0.730527i	0.0827159	+	0.143268i
$27$	4.74296	−	2.12233i	0.912784	−	0.408443i
$28$	0.272582	−	0.472126i	0.0515131	−	0.0892233i
$29$	0.676408	−	2.25936i	0.125606	−	0.419553i	−0.871936	−	0.489619i	$-0.837136\pi$
$29$	0.676408	−	2.25936i	0.125606	−	0.419553i	0.997542	+	0.0700662i	$0.0223210\pi$
$30$	1.54109	+	0.961644i	0.281363	+	0.175571i
$31$	−7.93694	−	5.22021i	−1.42552	−	0.937577i	−0.999459	−	0.0328811i	$-0.989532\pi$
$31$	−7.93694	−	5.22021i	−1.42552	−	0.937577i	−0.426058	−	0.904696i	$-0.640098\pi$
$32$	2.04653	+	2.74896i	0.361779	+	0.485953i
$33$	−1.42081	−	2.33050i	−0.247332	−	0.405688i
$34$	4.86950	−	3.20272i	0.835112	−	0.549262i
$35$	−0.726257	−	0.264336i	−0.122760	−	0.0446809i
$36$	−0.418482	−	1.85122i	−0.0697469	−	0.308536i
$37$	0.249308	−	0.0907406i	0.0409859	−	0.0149177i	−0.321446	−	0.946928i	$-0.604169\pi$
$37$	0.249308	−	0.0907406i	0.0409859	−	0.0149177i	0.362432	+	0.932010i	$0.381947\pi$
$38$	5.31656	−	7.14138i	0.862460	−	1.15849i
$39$	−1.24413	−	0.115363i	−0.199220	−	0.0184728i
$40$	1.89472	−	2.00829i	0.299582	−	0.317539i
$41$	6.68585	−	7.08659i	1.04415	−	1.10674i	0.0500022	−	0.998749i	$-0.484077\pi$
$41$	6.68585	−	7.08659i	1.04415	−	1.10674i	0.994152	−	0.107990i	$-0.0344413\pi$
$42$	−0.729369	−	1.58559i	−0.112544	−	0.244662i
$43$	1.78455	−	2.39707i	0.272142	−	0.365550i	−0.644951	−	0.764224i	$-0.723122\pi$
$43$	1.78455	−	2.39707i	0.272142	−	0.365550i	0.917093	+	0.398674i	$0.130530\pi$
$44$	−0.936828	+	0.340978i	−0.141232	+	0.0514043i
$45$	−2.48154	+	1.03999i	−0.369926	+	0.155032i
$46$	−2.18949	−	0.796909i	−0.322823	−	0.117498i
$47$	−6.28485	+	4.13361i	−0.916740	+	0.602949i	−0.917797	−	0.397050i	$-0.870034\pi$
$47$	−6.28485	+	4.13361i	−0.916740	+	0.602949i	0.00105704	+	0.999999i	$0.499664\pi$
$48$	4.04228	−	0.0966047i	0.583453	−	0.0139437i
$49$	−3.73668	−	5.01923i	−0.533811	−	0.717033i
$50$	4.09897	+	2.69594i	0.579683	+	0.381263i
$51$	−0.295914	+	8.62796i	−0.0414362	+	1.20816i
$52$	−0.130890	+	0.437203i	−0.0181512	+	0.0606292i
$53$	5.30779	−	9.19335i	0.729080	−	1.26280i	−0.228192	−	0.973616i	$-0.573281\pi$
$53$	5.30779	−	9.19335i	0.729080	−	1.26280i	0.957272	−	0.289188i	$-0.0933853\pi$
$54$	−5.61114	−	2.33105i	−0.763579	−	0.317216i
$55$	0.706679	+	1.22400i	0.0952885	+	0.165045i
$56$	−2.58128	+	0.611774i	−0.344937	+	0.0817517i
$57$	4.08296	+	12.5395i	0.540801	+	1.66089i
$58$	−2.46448	+	1.23771i	−0.323602	+	0.162519i
$59$	−3.55686	+	8.24573i	−0.463064	+	1.07350i	0.513464	+	0.858111i	$0.328362\pi$
$59$	−3.55686	+	8.24573i	−0.463064	+	1.07350i	−0.976528	+	0.215392i	$0.930897\pi$
$60$	0.193732	+	0.963493i	0.0250107	+	0.124386i
$61$	−0.534338	−	9.17423i	−0.0684150	−	1.17464i	−0.841471	−	0.540302i	$-0.818310\pi$
$61$	−0.534338	−	9.17423i	−0.0684150	−	1.17464i	0.773056	−	0.634338i	$-0.218727\pi$
$62$	1.92897	+	10.9397i	0.244979	+	1.38934i
$63$	2.54110	+	0.475337i	0.320148	+	0.0598868i
$64$	1.50664	−	8.54460i	0.188331	−	1.06808i
$65$	0.642620	+	0.0751115i	0.0797072	+	0.00931643i
$66$	−0.842068	+	3.07858i	−0.103651	+	0.378947i
$67$	3.28408	+	10.9696i	0.401215	+	1.34015i	0.885255	+	0.465105i	$0.153983\pi$
$67$	3.28408	+	10.9696i	0.401215	+	1.34015i	−0.484041	+	0.875046i	$0.660831\pi$
$68$	3.06827	+	0.727194i	0.372083	+	0.0881852i
$69$	2.83734	−	1.96484i	0.341576	−	0.236539i
$70$	0.357955	+	0.829833i	0.0427838	+	0.0991840i
$71$	−7.34178	−	6.16048i	−0.871309	−	0.731115i	0.0930645	−	0.995660i	$-0.470334\pi$
$71$	−7.34178	−	6.16048i	−0.871309	−	0.731115i	−0.964373	+	0.264545i	$0.914778\pi$
$72$	−5.15481	+	7.66290i	−0.607500	+	0.903081i
$73$	−4.91737	+	4.12616i	−0.575535	+	0.482931i	−0.883477	−	0.468474i	$-0.844804\pi$
$73$	−4.91737	+	4.12616i	−0.575535	+	0.482931i	0.307943	+	0.951405i	$0.400360\pi$
$74$	−0.277236	−	0.139233i	−0.0322281	−	0.0161855i
$75$	−6.76741	+	2.64790i	−0.781433	+	0.305753i
$76$	4.78423	−	0.559196i	0.548789	−	0.0641442i
$77$	0.0789579	−	1.35565i	0.00899809	−	0.154491i
$78$	0.900232	+	1.15077i	0.101931	+	0.130299i
$79$	−1.46027	−	1.54779i	−0.164293	−	0.174140i	0.639997	−	0.768377i	$-0.278936\pi$
$79$	−1.46027	−	1.54779i	−0.164293	−	0.174140i	−0.804290	+	0.594237i	$0.797454\pi$
$80$	−2.09376			−0.234089
$81$	7.62052	−	4.78828i	0.846725	−	0.532031i
$82$	−11.3925			−1.25810
$83$	−1.68900	−	1.79023i	−0.185391	−	0.196503i	0.628012	−	0.778204i	$-0.283869\pi$
$83$	−1.68900	−	1.79023i	−0.185391	−	0.196503i	−0.813403	+	0.581701i	$0.802388\pi$
$84$	0.353177	−	0.875714i	0.0385348	−	0.0955483i
$85$	0.259926	−	4.46276i	0.0281930	−	0.484054i
$86$	−3.47084	+	0.405683i	−0.374270	+	0.0437459i
$87$	0.613026	−	4.03868i	0.0657233	−	0.432992i
$88$	4.33519	+	2.17721i	0.462132	+	0.232092i
$89$	6.94724	−	5.82943i	0.736406	−	0.617918i	−0.195464	−	0.980711i	$-0.562621\pi$
$89$	6.94724	−	5.82943i	0.736406	−	0.617918i	0.931870	+	0.362793i	$0.118177\pi$
$90$	2.87587	+	1.27613i	0.303143	+	0.134516i
$91$	−0.476197	−	0.399577i	−0.0499191	−	0.0418871i
$92$	−0.499295	−	1.15750i	−0.0520551	−	0.120677i
$93$	−14.8761	−	7.03117i	−1.54258	−	0.729098i
$94$	8.55911	+	2.02855i	0.882805	+	0.209229i
$95$	−1.95849	−	6.54180i	−0.200936	−	0.671174i
$96$	4.17548	+	4.21908i	0.426158	+	0.430608i
$97$	8.70918	+	1.01796i	0.884283	+	0.103358i	0.546097	−	0.837722i	$-0.316113\pi$
$97$	8.70918	+	1.01796i	0.884283	+	0.103358i	0.338185	+	0.941080i	$0.390187\pi$
$98$	−1.27060	+	7.20591i	−0.128350	+	0.727906i
$99$	−3.00103	−	3.65290i	−0.301615	−	0.367130i
$100$	0.460917	+	2.61399i	0.0460917	+	0.261399i
$101$	0.688452	+	11.8203i	0.0685035	+	1.17616i	0.840962	+	0.541094i	$0.181990\pi$
$101$	0.688452	+	11.8203i	0.0685035	+	1.17616i	−0.772458	+	0.635065i	$0.780973\pi$
$102$	7.57595	−	6.67182i	0.750131	−	0.660609i
$103$	−7.69739	+	17.8445i	−0.758446	+	1.75828i	−0.114199	+	0.993458i	$0.536430\pi$
$103$	−7.69739	+	17.8445i	−0.758446	+	1.75828i	−0.644247	+	0.764818i	$0.722829\pi$
$104$	1.98452	−	0.996666i	0.194599	−	0.0977311i
$105$	−1.30957	−	0.277504i	−0.127800	−	0.0270816i
$106$	−12.0786	+	2.86269i	−1.17318	+	0.278049i
$107$	−1.02359	−	1.77291i	−0.0989542	−	0.171394i	0.812298	−	0.583243i	$-0.198216\pi$
$107$	−1.02359	−	1.77291i	−0.0989542	−	0.171394i	−0.911252	+	0.411849i	$0.864883\pi$
$108$	−1.16594	−	3.07359i	−0.112192	−	0.295757i
$109$	1.38758	−	2.40336i	0.132906	−	0.230200i	−0.791889	−	0.610664i	$-0.790902\pi$
$109$	1.38758	−	2.40336i	0.132906	−	0.230200i	0.924796	+	0.380464i	$0.124236\pi$
$110$	0.473999	−	1.58327i	0.0451940	−	0.150958i
$111$	0.405603	−	0.215987i	0.0384982	−	0.0205006i
$112$	1.68073	+	1.10544i	0.158814	+	0.104454i
$113$	−0.899617	−	1.20839i	−0.0846288	−	0.113676i	0.757792	−	0.652496i	$-0.226278\pi$
$113$	−0.899617	−	1.20839i	−0.0846288	−	0.113676i	−0.842421	+	0.538819i	$0.818871\pi$
$114$	7.38904	−	13.5350i	0.692047	−	1.26767i
$115$	−1.49311	+	0.982035i	−0.139233	+	0.0915752i
$116$	−1.40207	−	0.510311i	−0.130179	−	0.0473812i
$117$	−2.16167	+	0.103381i	−0.199847	+	0.00955755i
$118$	9.86760	−	3.59151i	0.908386	−	0.330625i
$119$	−2.56484	+	3.44518i	−0.235119	+	0.315820i
$120$	2.76328	−	3.90306i	0.252252	−	0.356299i
$121$	5.84450	−	6.19481i	0.531319	−	0.563165i
$122$	−7.37434	+	7.81634i	−0.667641	+	0.707658i
$123$	9.75070	−	13.7726i	0.879191	−	1.24183i
$124$	−3.58890	+	4.82073i	−0.322293	+	0.432914i
$125$	7.75000	−	2.82077i	0.693182	−	0.252297i
$126$	−1.63481	−	2.54276i	−0.145640	−	0.226527i
$127$	11.5920	+	4.21916i	1.02863	+	0.374390i	0.800558	−	0.599255i	$-0.204536\pi$
$127$	11.5920	+	4.21916i	1.02863	+	0.374390i	0.228070	+	0.973645i	$0.426759\pi$
$128$	−2.74998	+	1.80869i	−0.243066	+	0.159867i
$129$	2.48020	−	4.54316i	0.218369	−	0.400003i
$130$	−0.451785	−	0.606852i	−0.0396241	−	0.0532244i
$131$	2.15501	+	1.41738i	0.188285	+	0.123837i	0.640152	−	0.768249i	$-0.278872\pi$
$131$	2.15501	+	1.41738i	0.188285	+	0.123837i	−0.451867	+	0.892085i	$0.649242\pi$
$132$	−1.52414	+	0.811620i	−0.132660	+	0.0706424i
$133$	−1.88171	+	6.28535i	−0.163165	+	0.545009i
$134$	6.69486	−	11.5958i	0.578348	−	1.00173i
$135$	−4.00414	+	2.38446i	−0.344622	+	0.205222i
$136$	−7.67195	−	13.2882i	−0.657864	−	1.13945i
$137$	−1.60140	+	0.379539i	−0.136817	+	0.0324262i	−0.298454	−	0.954424i	$-0.596471\pi$
$137$	−1.60140	+	0.379539i	−0.136817	+	0.0324262i	0.161637	+	0.986850i	$0.448323\pi$
$138$	−3.94802	−	0.836608i	−0.336078	−	0.0712168i
$139$	11.2701	−	5.66008i	0.955921	−	0.480082i	0.0987493	−	0.995112i	$-0.468516\pi$
$139$	11.2701	−	5.66008i	0.955921	−	0.480082i	0.857172	+	0.515031i	$0.172220\pi$
$140$	−0.193663	+	0.448960i	−0.0163675	+	0.0379441i
$141$	−9.77795	+	8.61104i	−0.823452	+	0.725180i
$142$	0.651628	+	11.1880i	0.0546834	+	0.938877i
$143$	0.197402	+	1.11952i	0.0165076	+	0.0936190i
$144$	6.90930	−	1.14441i	0.575775	−	0.0953677i
$145$	−0.367309	+	2.08311i	−0.0305033	+	0.172993i
$146$	7.45544	+	0.871416i	0.617017	+	0.0721189i
$147$	−7.62384	−	7.70346i	−0.628804	−	0.635371i
$148$	−0.0481385	−	0.160794i	−0.00395696	−	0.0132172i
$149$	−14.8032	−	3.50841i	−1.21272	−	0.287420i	−0.425997	−	0.904725i	$-0.640077\pi$
$149$	−14.8032	−	3.50841i	−1.21272	−	0.287420i	−0.786724	+	0.617304i	$0.788225\pi$
$150$	7.68267	+	3.63120i	0.627288	+	0.296486i
$151$	3.46501	+	8.03280i	0.281979	+	0.653700i	0.999063	−	0.0432866i	$-0.0137829\pi$
$151$	3.46501	+	8.03280i	0.281979	+	0.653700i	−0.717084	+	0.696987i	$0.754524\pi$
$152$	−17.9551	−	15.0661i	−1.45635	−	1.22202i
$153$	1.58153	+	14.8690i	0.127859	+	1.20209i
$154$	−1.21641	+	1.02069i	−0.0980210	+	0.0822494i
$155$	7.61392	+	3.82385i	0.611565	+	0.307139i
$156$	−0.118625	+	0.781515i	−0.00949762	+	0.0625713i
$157$	6.31011	−	0.737546i	0.503601	−	0.0588626i	0.139500	−	0.990222i	$-0.455450\pi$
$157$	6.31011	−	0.737546i	0.503601	−	0.0588626i	0.364101	+	0.931359i	$0.381376\pi$
$158$	−0.144680	+	2.48405i	−0.0115101	+	0.197621i
$159$	6.87716	−	17.0521i	0.545394	−	1.35232i
$160$	−2.10931	−	2.23574i	−0.166756	−	0.176751i
$161$	1.71706			0.135323
$162$	−10.1877	−	2.63926i	−0.800425	−	0.207360i
$163$	7.25447			0.568214			0.284107	−	0.958793i	$-0.408303\pi$
$163$	7.25447			0.568214			0.284107	+	0.958793i	$0.408303\pi$
$164$	−4.22975	−	4.48327i	−0.330288	−	0.350085i
$165$	1.50834	+	1.92812i	0.117424	+	0.150104i
$166$	−0.167342	+	2.87314i	−0.0129882	+	0.222999i
$167$	−17.7966	+	2.08012i	−1.37714	+	0.160964i	−0.772237	−	0.635335i	$-0.780862\pi$
$167$	−17.7966	+	2.08012i	−1.37714	+	0.160964i	−0.604903	+	0.796300i	$0.706788\pi$
$168$	−4.27888	+	1.67421i	−0.330122	+	0.129168i
$169$	−11.1522	−	5.60084i	−0.857861	−	0.430834i
$170$	−4.00437	+	3.36006i	−0.307121	+	0.257705i
$171$	10.0386	+	20.5172i	0.767667	+	1.56899i
$172$	−1.44828	−	1.21525i	−0.110430	−	0.0926619i
$173$	8.27627	+	19.1865i	0.629233	+	1.45873i	0.872425	+	0.488748i	$0.162546\pi$
$173$	8.27627	+	19.1865i	0.629233	+	1.45873i	−0.243192	+	0.969978i	$0.578195\pi$
$174$	−3.92701	+	2.71943i	−0.297706	+	0.206160i
$175$	−3.51800	−	0.833781i	−0.265936	−	0.0630279i
$176$	−1.05509	−	3.52425i	−0.0795305	−	0.265650i
$177$	−4.10369	+	15.0030i	−0.308452	+	1.12769i
$178$	−10.5330	−	1.23113i	−0.789483	−	0.0922774i
$179$	−3.07341	+	17.4302i	−0.229717	+	1.30279i	0.623742	+	0.781630i	$0.285612\pi$
$179$	−3.07341	+	17.4302i	−0.229717	+	1.30279i	−0.853459	+	0.521160i	$0.825499\pi$
$180$	0.565543	+	1.60553i	0.0421531	+	0.119669i
$181$	−2.14079	−	12.1411i	−0.159124	−	0.902437i	−0.954918	−	0.296870i	$-0.904057\pi$
$181$	−2.14079	−	12.1411i	−0.159124	−	0.902437i	0.795794	−	0.605567i	$-0.207054\pi$
$182$	0.0422654	+	0.725669i	0.00313292	+	0.0537902i
$183$	−3.13771	−	15.6048i	−0.231946	−	1.15354i
$184$	−2.42958	+	5.63240i	−0.179111	+	0.415226i
$185$	−0.212640	+	0.106792i	−0.0156336	+	0.00785149i
$186$	5.95702	+	18.2950i	0.436790	+	1.34146i
$187$	7.64278	−	1.81137i	0.558896	−	0.132461i
$188$	2.37949	+	4.12139i	0.173542	+	0.300583i
$189$	4.47319	+	0.199965i	0.325376	+	0.0145453i
$190$	−3.99252	+	6.91525i	−0.289648	+	0.501685i
$191$	0.289040	−	0.965461i	0.0209142	−	0.0698583i	−0.946895	−	0.321542i	$-0.895799\pi$
$191$	0.289040	−	0.965461i	0.0209142	−	0.0698583i	0.967810	+	0.251683i	$0.0809842\pi$
$192$	0.515113	−	15.0192i	0.0371751	−	1.08391i
$193$	−1.73329	−	1.14001i	−0.124765	−	0.0820594i	0.485592	−	0.874185i	$-0.338604\pi$
$193$	−1.73329	−	1.14001i	−0.124765	−	0.0820594i	−0.610358	+	0.792126i	$0.708974\pi$
$194$	−6.12286	−	8.22443i	−0.439596	−	0.590480i
$195$	1.12031	−	0.0267737i	0.0802269	−	0.00191731i
$196$	−3.30746	+	2.17535i	−0.236247	+	0.155382i
$197$	11.8230	+	4.30320i	0.842350	+	0.306591i	0.726918	−	0.686725i	$-0.240952\pi$
$197$	11.8230	+	4.30320i	0.842350	+	0.306591i	0.115433	+	0.993315i	$0.463174\pi$
$198$	−0.698788	+	5.48379i	−0.0496607	+	0.389716i
$199$	5.11877	−	1.86308i	0.362860	−	0.132070i	−0.154155	−	0.988047i	$-0.549265\pi$
$199$	5.11877	−	1.86308i	0.362860	−	0.132070i	0.517015	+	0.855977i	$0.327043\pi$
$200$	7.71288	−	10.3602i	0.545383	−	0.732577i
$201$	8.28835	+	18.0182i	0.584615	+	1.27091i
$202$	9.50125	−	10.0707i	0.668505	−	0.708574i
$203$	1.39467	−	1.47826i	0.0978864	−	0.103754i
$204$	5.43829	+	0.504269i	0.380757	+	0.0353059i
$205$	−5.21801	+	7.00901i	−0.364442	+	0.489530i
$206$	21.3544	−	7.77237i	1.48783	−	0.541527i
$207$	4.39044	−	4.05678i	0.305156	−	0.281966i
$208$	−1.58249	−	0.575978i	−0.109726	−	0.0399369i
$209$	10.0243	−	6.59312i	0.693399	−	0.456055i
$210$	0.814830	+	1.33653i	0.0562286	+	0.0922294i
$211$	−6.19411	−	8.32013i	−0.426420	−	0.572782i	0.536044	−	0.844190i	$-0.319918\pi$
$211$	−6.19411	−	8.32013i	−0.426420	−	0.572782i	−0.962464	+	0.271408i	$0.912511\pi$
$212$	−5.61102	−	3.69043i	−0.385366	−	0.253459i
$213$	−14.0831	−	8.78789i	−0.964956	−	0.602136i
$214$	−0.686564	+	2.29328i	−0.0469326	+	0.156766i
$215$	−1.34013	+	2.32117i	−0.0913959	+	0.158302i
$216$	−6.98536	+	14.3903i	−0.475293	+	0.979136i
$217$	−4.09309	−	7.08945i	−0.277857	−	0.481263i
$218$	−3.15764	+	0.748374i	−0.213862	+	0.0506863i
$219$	−7.43447	+	8.26716i	−0.502375	+	0.558643i
$220$	0.799041	−	0.401294i	0.0538714	−	0.0270552i
$221$	1.42413	−	3.30151i	0.0957974	−	0.222083i
$222$	−0.509184	−	0.171666i	−0.0341742	−	0.0115215i
$223$	−1.26869	−	21.7826i	−0.0849578	−	1.45867i	−0.724161	−	0.689631i	$-0.757773\pi$
$223$	−1.26869	−	21.7826i	−0.0849578	−	1.45867i	0.639203	−	0.769038i	$-0.279264\pi$
$224$	0.512822	+	2.90836i	0.0342644	+	0.194323i
$225$	−10.9653	+	6.17981i	−0.731019	+	0.411987i
$226$	−0.305900	+	1.73484i	−0.0203481	+	0.115400i
$227$	6.66993	+	0.779603i	0.442699	+	0.0517441i	0.334523	−	0.942388i	$-0.391425\pi$
$227$	6.66993	+	0.779603i	0.442699	+	0.0517441i	0.108176	+	0.994132i	$0.465499\pi$
$228$	8.06977	−	2.11742i	0.534433	−	0.140230i
$229$	−0.306696	−	1.02444i	−0.0202671	−	0.0676967i	0.947258	−	0.320473i	$-0.103842\pi$
$229$	−0.306696	−	1.02444i	−0.0202671	−	0.0676967i	−0.967525	+	0.252776i	$0.918657\pi$
$230$	2.03341	+	0.481928i	0.134079	+	0.0317774i
$231$	−0.192819	−	2.34412i	−0.0126866	−	0.154232i
$232$	2.87568	+	6.66658i	0.188798	+	0.437682i
$233$	−10.4737	−	8.78848i	−0.686155	−	0.575753i	0.231642	−	0.972801i	$-0.425590\pi$
$233$	−10.4737	−	8.78848i	−0.686155	−	0.575753i	−0.917798	+	0.397048i	$0.870035\pi$
$234$	1.82256	+	1.75565i	0.119145	+	0.114770i
$235$	5.16827	−	4.33669i	0.337141	−	0.282895i
$236$	5.07694	+	2.54973i	0.330480	+	0.165974i
$237$	−2.87918	−	2.30097i	−0.187023	−	0.149464i
$238$	4.98845	−	0.583067i	0.323353	−	0.0377946i
$239$	−0.583089	+	10.0113i	−0.0377169	+	0.647574i	0.925483	+	0.378789i	$0.123659\pi$
$239$	−0.583089	+	10.0113i	−0.0377169	+	0.647574i	−0.963200	+	0.268785i	$0.913378\pi$
$240$	−3.59088	+	0.506947i	−0.231791	+	0.0327233i
$241$	1.80957	+	1.91803i	0.116564	+	0.123551i	0.783028	−	0.621987i	$-0.213674\pi$
$241$	1.80957	+	1.91803i	0.116564	+	0.123551i	−0.666463	+	0.745538i	$0.732193\pi$
$242$	−9.95891			−0.640183
$243$	11.9102	−	10.0572i	0.764039	−	0.645171i
$244$	−5.81384			−0.372193
$245$	3.85132	+	4.08216i	0.246052	+	0.260799i
$246$	−19.5387	+	2.75840i	−1.24574	+	0.175869i
$247$	0.319357	−	5.48314i	0.0203202	−	0.348884i
$248$	29.0469	−	3.39509i	1.84448	−	0.215589i
$249$	−3.33016	−	2.66138i	−0.211040	−	0.168658i
$250$	−8.61819	−	4.32822i	−0.545062	−	0.273741i
$251$	20.1642	−	16.9197i	1.27275	−	1.06796i	0.278550	−	0.960422i	$-0.410146\pi$
$251$	20.1642	−	16.9197i	1.27275	−	1.06796i	0.994200	−	0.107543i	$-0.0342983\pi$
$252$	0.393684	−	1.58740i	0.0247997	−	0.0999969i
$253$	−2.40539	−	2.01836i	−0.151226	−	0.126893i
$254$	−5.71344	−	13.2453i	−0.358493	−	0.831081i
$255$	−0.634753	−	7.71676i	−0.0397498	−	0.483243i
$256$	−13.1400	−	3.11423i	−0.821249	−	0.194640i
$257$	−1.32701	−	4.43254i	−0.0827769	−	0.276494i	0.906573	−	0.422048i	$-0.138689\pi$
$257$	−1.32701	−	4.43254i	−0.0827769	−	0.276494i	−0.989350	+	0.145554i	$0.953504\pi$
$258$	−5.85441	+	1.53613i	−0.364480	+	0.0956356i
$259$	0.227076	+	0.0265414i	0.0141098	+	0.00164920i
$260$	0.0710770	−	0.403098i	0.00440801	−	0.0249991i
$261$	0.0735086	−	7.07494i	0.00455007	−	0.437928i
$262$	−0.523747	−	2.97032i	−0.0323572	−	0.183507i
$263$	−1.14772	−	19.7056i	−0.0707714	−	1.21510i	−0.827537	−	0.561412i	$-0.810258\pi$
$263$	−1.14772	−	19.7056i	−0.0707714	−	1.21510i	0.756765	−	0.653687i	$-0.226779\pi$
$264$	7.96219	+	2.68437i	0.490039	+	0.165211i
$265$	−3.77105	+	8.74227i	−0.231654	+	0.537034i
$266$	6.85597	−	3.44320i	0.420366	−	0.211116i
$267$	10.5034	−	11.6798i	0.642797	−	0.714793i
$268$	7.04890	−	1.67062i	0.430580	−	0.102049i
$269$	13.3460	+	23.1160i	0.813721	+	1.40941i	0.910243	+	0.414075i	$0.135895\pi$
$269$	13.3460	+	23.1160i	0.813721	+	1.40941i	−0.0965222	+	0.995331i	$0.530772\pi$
$270$	5.24122	+	1.49230i	0.318971	+	0.0908186i
$271$	−1.67728	+	2.90514i	−0.101888	+	0.176475i	−0.912462	−	0.409161i	$-0.865822\pi$
$271$	−1.67728	+	2.90514i	−0.101888	+	0.176475i	0.810575	+	0.585635i	$0.199155\pi$
$272$	−3.33716	+	11.1469i	−0.202345	+	0.675879i
$273$	−0.913447	−	0.569994i	−0.0552843	−	0.0344976i
$274$	1.60786	+	1.05751i	0.0971345	+	0.0638864i
$275$	3.94820	+	5.30336i	0.238086	+	0.319805i
$276$	−1.13657	−	1.86426i	−0.0684134	−	0.112216i
$277$	−1.11197	+	0.731356i	−0.0668120	+	0.0439430i	−0.582476	−	0.812848i	$-0.697916\pi$
$277$	−1.11197	+	0.731356i	−0.0668120	+	0.0439430i	0.515664	+	0.856791i	$0.327545\pi$
$278$	−13.8579	−	5.04386i	−0.831141	−	0.302511i
$279$	−27.2156	−	8.45691i	−1.62936	−	0.506302i
$280$	2.23575	−	0.813747i	0.133612	−	0.0486307i
$281$	−15.1609	+	20.3646i	−0.904422	+	1.21485i	0.0716557	+	0.997429i	$0.477172\pi$
$281$	−15.1609	+	20.3646i	−0.904422	+	1.21485i	−0.976078	+	0.217421i	$0.930236\pi$
$282$	15.1704	+	1.40669i	0.903385	+	0.0837670i
$283$	−10.4476	+	11.0738i	−0.621043	+	0.658267i	−0.959169	−	0.282834i	$-0.908725\pi$
$283$	−10.4476	+	11.0738i	−0.621043	+	0.658267i	0.338126	+	0.941101i	$0.390207\pi$
$284$	−4.16086	+	4.41025i	−0.246901	+	0.261700i
$285$	−4.94281	−	10.7453i	−0.292787	−	0.636495i
$286$	0.793800	−	1.06626i	0.0469384	−	0.0630492i
$287$	7.88922	−	2.87144i	0.465686	−	0.169496i
$288$	8.18266	+	6.22493i	0.482168	+	0.366808i
$289$	−7.37010	−	2.68250i	−0.433535	−	0.157794i
$290$	2.06653	−	1.35918i	0.121351	−	0.0798138i
$291$	15.1831	−	0.362854i	0.890049	−	0.0212709i
$292$	2.42508	+	3.25745i	0.141917	+	0.190628i
$293$	12.3390	+	8.11551i	0.720854	+	0.474113i	0.856173	−	0.516689i	$-0.172836\pi$
$293$	12.3390	+	8.11551i	0.720854	+	0.474113i	−0.135319	+	0.990802i	$0.543206\pi$
$294$	−0.434410	+	12.6661i	−0.0253353	+	0.738701i
$295$	2.30996	−	7.71581i	0.134491	−	0.449232i
$296$	−0.408369	+	0.707316i	−0.0237360	+	0.0411119i
$297$	−6.03135	−	5.53826i	−0.349974	−	0.321363i
$298$	8.89472	+	15.4061i	0.515257	+	0.892452i
$299$	−1.39866	+	0.331489i	−0.0808868	+	0.0191705i
$300$	1.42340	+	4.37151i	0.0821801	+	0.252389i
$301$	2.30127	−	1.15574i	0.132643	−	0.0666158i
$302$	4.05178	−	9.39308i	0.233154	−	0.540511i
$303$	4.04269	+	20.1056i	0.232246	+	1.15504i
$304$	1.03348	+	17.7441i	0.0592740	+	1.01770i
$305$	1.43124	+	8.11694i	0.0819523	+	0.464775i
$306$	11.3777	−	13.2768i	0.650419	−	0.758983i
$307$	−2.90763	+	16.4900i	−0.165947	+	0.941134i	0.782135	+	0.623109i	$0.214131\pi$
$307$	−2.90763	+	16.4900i	−0.165947	+	0.941134i	−0.948082	+	0.318025i	$0.896980\pi$
$308$	−0.853289	−	0.0997352i	−0.0486207	−	0.00568294i
$309$	−8.88078	+	32.4679i	−0.505210	+	1.84703i
$310$	−2.85742	−	9.54445i	−0.162291	−	0.542088i
$311$	6.41370	+	1.52008i	0.363688	+	0.0861956i	0.408397	−	0.912804i	$-0.366088\pi$
$311$	6.41370	+	1.52008i	0.363688	+	0.0861956i	−0.0447091	+	0.999000i	$0.514236\pi$
$312$	3.16223	−	2.18983i	0.179026	−	0.123974i
$313$	−0.551979	−	1.27963i	−0.0311997	−	0.0723290i	0.901904	−	0.431937i	$-0.142170\pi$
$313$	−0.551979	−	1.27963i	−0.0311997	−	0.0723290i	−0.933103	+	0.359608i	$0.882910\pi$
$314$	−5.69087	−	4.77520i	−0.321154	−	0.269480i
$315$	−2.31315	−	0.158856i	−0.130331	−	0.00895049i
$316$	−1.03126	+	0.865328i	−0.0580128	+	0.0486785i
$317$	−18.0816	−	9.08091i	−1.01556	−	0.510035i	−0.138476	−	0.990366i	$-0.544220\pi$
$317$	−18.0816	−	9.08091i	−1.01556	−	0.510035i	−0.877087	+	0.480331i	$0.840517\pi$
$318$	−20.0222	+	7.83415i	−1.12279	+	0.439317i
$319$	−3.69143	+	0.431466i	−0.206680	+	0.0241575i
$320$	−0.452468	+	7.76857i	−0.0252937	+	0.434276i
$321$	−2.18476	−	2.79278i	−0.121942	−	0.155878i
$322$	−1.37785	−	1.46044i	−0.0767847	−	0.0813870i
$323$	−37.9492			−2.11155
$324$	−2.74382	−	4.98905i	−0.152435	−	0.277169i
$325$	3.02663			0.167887
$326$	−5.82135	−	6.17027i	−0.322415	−	0.341740i
$327$	1.79785	−	4.45784i	0.0994215	−	0.246519i
$328$	−1.74391	+	29.9417i	−0.0962912	+	1.65326i
$329$	−6.43839	+	0.752539i	−0.354960	+	0.0414888i
$330$	0.429583	−	2.83014i	0.0236478	−	0.155794i
$331$	8.84083	+	4.44003i	0.485936	+	0.244046i	0.674860	−	0.737945i	$-0.264204\pi$
$331$	8.84083	+	4.44003i	0.485936	+	0.244046i	−0.188924	+	0.981992i	$0.560500\pi$
$332$	−1.19279	+	1.00087i	−0.0654629	+	0.0549299i
$333$	0.643332	−	0.468634i	0.0352544	−	0.0256810i
$334$	16.0501	+	13.4676i	0.878222	+	0.736916i
$335$	−4.06770	−	9.42999i	−0.222242	−	0.515215i
$336$	3.15018	+	1.48893i	0.171857	+	0.0812275i
$337$	−6.62108	−	1.56922i	−0.360673	−	0.0854811i	0.0462840	−	0.998928i	$-0.485262\pi$
$337$	−6.62108	−	1.56922i	−0.360673	−	0.0854811i	−0.406957	+	0.913447i	$0.633410\pi$
$338$	4.18530	+	13.9799i	0.227650	+	0.760404i
$339$	−1.83546	−	1.85463i	−0.0996886	−	0.100730i
$340$	−2.80899	−	0.328324i	−0.152339	−	0.0178059i
$341$	−2.59956	+	14.7428i	−0.140774	+	0.798368i
$342$	9.39538	−	25.0023i	0.508044	−	1.35197i
$343$	−1.98380	−	11.2507i	−0.107115	−	0.607480i
$344$	0.534914	+	9.18411i	0.0288406	+	0.495174i
$345$	−2.32298	+	2.04575i	−0.125065	+	0.110139i
$346$	9.67778	−	22.4356i	0.520281	−	1.20615i
$347$	−10.2220	+	5.13370i	−0.548747	+	0.275591i	−0.701496	−	0.712674i	$-0.747484\pi$
$347$	−10.2220	+	5.13370i	−0.548747	+	0.275591i	0.152748	+	0.988265i	$0.451188\pi$
$348$	−2.52817	−	0.535733i	−0.135524	−	0.0287183i
$349$	24.6115	−	5.83304i	1.31743	−	0.312236i	0.488975	−	0.872298i	$-0.337371\pi$
$349$	24.6115	−	5.83304i	1.31743	−	0.312236i	0.828451	+	0.560062i	$0.189223\pi$
$350$	2.11385	+	3.66129i	0.112990	+	0.195704i
$351$	−3.68233	+	0.700694i	−0.196548	+	0.0374003i
$352$	2.70031	−	4.67708i	0.143927	−	0.249289i
$353$	2.51245	−	8.39217i	0.133724	−	0.446670i	−0.864731	−	0.502236i	$-0.832511\pi$
$353$	2.51245	−	8.39217i	0.133724	−	0.446670i	0.998455	+	0.0555656i	$0.0176962\pi$
$354$	16.0538	−	8.54877i	0.853248	−	0.454362i
$355$	7.18164	+	4.72344i	0.381162	+	0.250694i
$356$	−3.42615	−	4.60212i	−0.181586	−	0.243912i
$357$	−3.56466	+	6.52965i	−0.188662	+	0.345586i
$358$	17.2914	−	11.3728i	0.913880	−	0.601069i
$359$	−25.5680	−	9.30599i	−1.34943	−	0.491151i	−0.436658	−	0.899628i	$-0.643838\pi$
$359$	−25.5680	−	9.30599i	−1.34943	−	0.491151i	−0.912769	+	0.408476i	$0.866060\pi$
$360$	3.79413	−	7.36298i	0.199968	−	0.388063i
$361$	−36.6194	+	13.3284i	−1.92734	+	0.701494i
$362$	−8.60866	+	11.5634i	−0.452461	+	0.607761i
$363$	8.52367	−	12.0395i	0.447377	−	0.631908i
$364$	−0.269879	+	0.286055i	−0.0141455	+	0.0149933i
$365$	3.95086	−	4.18767i	0.206798	−	0.219193i
$366$	−10.7548	+	15.1909i	−0.562162	+	0.794039i
$367$	14.5927	−	19.6014i	0.761733	−	1.02318i	−0.236932	−	0.971526i	$-0.576142\pi$
$367$	14.5927	−	19.6014i	0.761733	−	1.02318i	0.998665	−	0.0516582i	$-0.0164506\pi$
$368$	4.37111	−	1.59095i	0.227860	−	0.0829342i
$369$	13.3882	−	25.9815i	0.696962	−	1.35254i
$370$	0.261465	+	0.0951653i	0.0135929	+	0.00494741i
$371$	7.64279	−	5.02674i	0.396794	−	0.260976i
$372$	−4.98791	+	9.13671i	−0.258611	+	0.473717i
$373$	0.830672	+	1.11579i	0.0430106	+	0.0577732i	0.823108	−	0.567885i	$-0.192238\pi$
$373$	0.830672	+	1.11579i	0.0430106	+	0.0577732i	−0.780098	+	0.625658i	$0.784831\pi$
$374$	−7.67361	−	5.04701i	−0.396793	−	0.260975i
$375$	12.6086	−	6.71420i	0.651107	−	0.346720i
$376$	6.64159	−	22.1844i	0.342514	−	1.14408i
$377$	−0.850667	+	1.47340i	−0.0438116	+	0.0758839i
$378$	−3.41943	−	3.96512i	−0.175876	−	0.203944i
$379$	13.1685	+	22.8085i	0.676419	+	1.17159i	0.976052	+	0.217537i	$0.0698023\pi$
$379$	13.1685	+	22.8085i	0.676419	+	1.17159i	−0.299633	+	0.954054i	$0.596864\pi$
$380$	−4.20366	+	0.996285i	−0.215643	+	0.0511084i
$381$	20.9024	+	4.42934i	1.07086	+	0.226922i
$382$	−1.05311	+	0.528892i	−0.0538818	+	0.0270605i
$383$	3.25821	−	7.55338i	0.166487	−	0.385959i	−0.814465	−	0.580213i	$-0.802969\pi$
$383$	3.25821	−	7.55338i	0.166487	−	0.385959i	0.980951	+	0.194254i	$0.0622285\pi$
$384$	−4.27841	+	3.76782i	−0.218332	+	0.192276i
$385$	0.0708160	+	1.21586i	0.00360912	+	0.0619662i
$386$	0.421253	+	2.38905i	0.0214412	+	0.121599i
$387$	3.15365	−	8.39224i	0.160309	−	0.426602i
$388$	0.963279	−	5.46303i	0.0489031	−	0.277343i
$389$	−31.1427	−	3.64006i	−1.57900	−	0.184559i	−0.719057	−	0.694951i	$-0.755426\pi$
$389$	−31.1427	−	3.64006i	−1.57900	−	0.184559i	−0.859942	+	0.510392i	$0.829500\pi$
$390$	−0.921764	−	0.931390i	−0.0466753	−	0.0471628i
$391$	2.84841	+	9.51436i	0.144050	+	0.481162i
$392$	18.7440	+	4.44241i	0.946714	+	0.224375i
$393$	4.03913	+	1.90908i	0.203747	+	0.0963005i
$394$	−5.82725	−	13.5091i	−0.293573	−	0.680578i
$395$	1.46199	+	1.22676i	0.0735608	+	0.0617249i
$396$	−2.41746	+	1.76099i	−0.121482	+	0.0884933i
$397$	9.17064	−	7.69508i	0.460261	−	0.386205i	−0.382966	−	0.923762i	$-0.625097\pi$
$397$	9.17064	−	7.69508i	0.460261	−	0.386205i	0.843227	+	0.537557i	$0.180653\pi$
$398$	−5.69219	−	2.85873i	−0.285324	−	0.143295i
$399$	−1.70539	+	11.2353i	−0.0853761	+	0.562466i
$400$	−9.72831	+	1.13708i	−0.486416	+	0.0568538i
$401$	2.02272	−	34.7288i	0.101010	−	1.73427i	−0.444161	−	0.895947i	$-0.646498\pi$
$401$	2.02272	−	34.7288i	0.101010	−	1.73427i	0.545170	−	0.838325i	$-0.316465\pi$
$402$	8.67435	−	21.5083i	0.432637	−	1.07274i
$403$	4.70278	+	4.98466i	0.234262	+	0.248303i
$404$	7.49067			0.372675
$405$	−6.28995	+	5.05895i	−0.312550	+	0.251381i
$406$	−2.37648			−0.117943
$407$	−0.286908	−	0.304105i	−0.0142215	−	0.0150739i
$408$	−16.3751	−	20.9323i	−0.810689	−	1.03630i
$409$	0.186231	−	3.19746i	0.00920853	−	0.158104i	−0.990569	−	0.137014i	$-0.956249\pi$
$409$	0.186231	−	3.19746i	0.00920853	−	0.158104i	0.999778	−	0.0210899i	$-0.00671362\pi$
$410$	10.1487	−	1.18621i	0.501208	−	0.0585828i
$411$	−2.65458	+	1.03866i	−0.130941	+	0.0512335i
$412$	10.9870	+	5.51786i	0.541289	+	0.271846i
$413$	−5.92798	+	4.97417i	−0.291697	+	0.244763i
$414$	−6.97359	−	0.478911i	−0.342733	−	0.0235372i
$415$	1.69099	+	1.41891i	0.0830076	+	0.0696516i
$416$	−0.979209	−	2.27006i	−0.0480097	−	0.111299i
$417$	17.9584	−	12.4360i	0.879424	−	0.608996i
$418$	−13.6518	−	3.23554i	−0.667731	−	0.158255i
$419$	8.97203	+	29.9687i	0.438312	+	1.46407i	0.837114	+	0.547028i	$0.184241\pi$
$419$	8.97203	+	29.9687i	0.438312	+	1.46407i	−0.398802	+	0.917037i	$0.630574\pi$
$420$	−0.223436	+	0.816877i	−0.0109026	+	0.0398595i
$421$	14.0435	+	1.64144i	0.684436	+	0.0799991i	0.451203	−	0.892422i	$-0.350995\pi$
$421$	14.0435	+	1.64144i	0.684436	+	0.0799991i	0.233234	+	0.972421i	$0.425069\pi$
$422$	−2.10620	+	11.9449i	−0.102528	+	0.581468i
$423$	−14.6847	+	17.1358i	−0.713994	+	0.833170i
$424$	5.67475	+	32.1831i	0.275590	+	1.56295i
$425$	−1.21593	−	20.8767i	−0.0589812	−	1.01267i
$426$	3.82645	+	19.0302i	0.185392	+	0.922014i
$427$	3.13658	−	7.27141i	0.151790	−	0.351888i
$428$	−1.15737	+	0.581255i	−0.0559437	+	0.0280960i
$429$	0.609614	+	1.87223i	0.0294325	+	0.0903922i
$430$	3.04965	−	0.722780i	0.147067	−	0.0348555i
$431$	3.38702	+	5.86650i	0.163147	+	0.282579i	0.935996	−	0.352011i	$-0.114502\pi$
$431$	3.38702	+	5.86650i	0.163147	+	0.282579i	−0.772849	+	0.634590i	$0.781169\pi$
$432$	11.5727	−	3.63562i	0.556790	−	0.174919i
$433$	4.54088	−	7.86503i	0.218221	−	0.377969i	−0.736043	−	0.676934i	$-0.763308\pi$
$433$	4.54088	−	7.86503i	0.218221	−	0.377969i	0.954264	+	0.298965i	$0.0966415\pi$
$434$	−2.74541	+	9.17030i	−0.131784	+	0.440188i
$435$	−0.125581	+	3.66156i	−0.00602114	+	0.175558i
$436$	−1.46685	−	0.964765i	−0.0702496	−	0.0462039i
$437$	9.05953	+	12.1691i	0.433376	+	0.582125i
$438$	12.9974	−	0.310619i	0.621040	−	0.0148420i
$439$	−24.6971	+	16.2435i	−1.17873	+	0.775260i	−0.978854	−	0.204562i	$-0.934423\pi$
$439$	−24.6971	+	16.2435i	−1.17873	+	0.775260i	−0.199872	+	0.979822i	$0.564053\pi$
$440$	−4.08856	−	1.48812i	−0.194915	−	0.0709431i
$441$	−14.9404	−	11.3659i	−0.711448	−	0.541232i
$442$	−3.95088	+	1.43800i	−0.187924	+	0.0683989i
$443$	7.55647	−	10.1501i	0.359019	−	0.482246i	−0.585514	−	0.810662i	$-0.699107\pi$
$443$	7.55647	−	10.1501i	0.359019	−	0.482246i	0.944533	+	0.328416i	$0.106515\pi$
$444$	−0.121492	−	0.264113i	−0.00576573	−	0.0125342i
$445$	−5.58176	+	5.91632i	−0.264601	+	0.280461i
$446$	−17.5091	+	18.5585i	−0.829078	+	0.878771i
$447$	−26.2375	−	2.43289i	−1.24099	−	0.115072i
$448$	4.46477	−	5.99722i	0.210940	−	0.283342i
$449$	34.0362	−	12.3882i	1.60627	−	0.584634i	0.625571	−	0.780167i	$-0.284866\pi$
$449$	34.0362	−	12.3882i	1.60627	−	0.584634i	0.980697	+	0.195534i	$0.0626439\pi$
$450$	14.0553	+	4.36751i	0.662574	+	0.205886i
$451$	−14.4272	−	5.25106i	−0.679349	−	0.247263i
$452$	−0.796281	+	0.523722i	−0.0374539	+	0.0246338i
$453$	7.88758	+	12.9377i	0.370591	+	0.607864i
$454$	−4.68920	−	6.29869i	−0.220075	−	0.295612i
$455$	0.465811	+	0.306368i	0.0218375	+	0.0143628i
$456$	−34.4416	−	21.4917i	−1.61287	−	1.00644i
$457$	−10.0766	+	33.6580i	−0.471361	+	1.57446i	0.310227	+	0.950662i	$0.399595\pi$
$457$	−10.0766	+	33.6580i	−0.471361	+	1.57446i	−0.781589	+	0.623794i	$0.785590\pi$
$458$	−0.625224	+	1.08292i	−0.0292148	+	0.0506015i
$459$	6.31251	+	25.1180i	0.294643	+	1.17241i
$460$	0.565302	+	0.979131i	0.0263573	+	0.0456522i
$461$	35.0948	−	8.31761i	1.63453	−	0.387390i	0.692099	−	0.721802i	$-0.256686\pi$
$461$	35.0948	−	8.31761i	1.63453	−	0.387390i	0.942427	+	0.334413i	$0.108538\pi$
$462$	−1.83906	+	2.04505i	−0.0855609	+	0.0951441i
$463$	−16.3490	+	8.21076i	−0.759800	+	0.381586i	−0.786125	−	0.618067i	$-0.787916\pi$
$463$	−16.3490	+	8.21076i	−0.759800	+	0.381586i	0.0263247	+	0.999653i	$0.491620\pi$
$464$	2.18071	−	5.05545i	0.101237	−	0.234693i
$465$	13.9840	+	4.71457i	0.648495	+	0.218633i
$466$	0.929605	+	15.9607i	0.0430631	+	0.739365i
$467$	−4.40516	−	24.9829i	−0.203846	−	1.15607i	−0.899245	−	0.437446i	$-0.855883\pi$
$467$	−4.40516	−	24.9829i	−0.203846	−	1.15607i	0.695398	−	0.718625i	$-0.255228\pi$
$468$	−0.0142245	+	1.36905i	−0.000657526	+	0.0632846i
$469$	−1.71344	+	9.71740i	−0.0791193	+	0.448708i
$470$	−7.83584	−	0.915878i	−0.361440	−	0.0422463i
$471$	10.6435	−	2.79275i	0.490428	−	0.128683i
$472$	−7.92869	−	26.4837i	−0.364948	−	1.21901i
$473$	−4.58235	−	1.08604i	−0.210697	−	0.0499361i
$474$	0.353315	+	4.29529i	0.0162283	+	0.197289i
$475$	−12.6525	−	29.3318i	−0.580537	−	1.34584i
$476$	2.08153	+	1.74661i	0.0954070	+	0.0800560i
$477$	7.66591	−	30.9103i	0.350998	−	1.41529i
$478$	8.98295	−	7.53759i	0.410870	−	0.344761i
$479$	4.03943	+	2.02868i	0.184566	+	0.0926927i	0.538683	−	0.842509i	$-0.318922\pi$
$479$	4.03943	+	2.02868i	0.184566	+	0.0926927i	−0.354117	+	0.935201i	$0.615218\pi$
$480$	−4.15889	−	3.32368i	−0.189827	−	0.151705i
$481$	−0.190094	+	0.0222188i	−0.00866753	+	0.00101309i
$482$	0.179287	−	3.07824i	0.00816631	−	0.140210i
$483$	2.94483	−	0.415739i	0.133994	−	0.0189168i
$484$	−3.69748	−	3.91910i	−0.168067	−	0.178141i
$485$	−7.86429			−0.357099
$486$	−18.1115	−	2.05976i	−0.821553	−	0.0934328i
$487$	16.6868			0.756152			0.378076	−	0.925774i	$-0.376586\pi$
$487$	16.6868			0.756152			0.378076	+	0.925774i	$0.376586\pi$
$488$	19.4140	+	20.5776i	0.878830	+	0.931506i
$489$	12.4417	−	1.75648i	0.562634	−	0.0794306i
$490$	0.381579	−	6.55146i	0.0172380	−	0.295965i
$491$	11.8165	−	1.38115i	0.533273	−	0.0623306i	0.154805	−	0.987945i	$-0.450525\pi$
$491$	11.8165	−	1.38115i	0.533273	−	0.0623306i	0.378468	+	0.925614i	$0.376451\pi$
$492$	−8.33972	−	6.66489i	−0.375983	−	0.300477i
$493$	10.5048	+	5.27570i	0.473111	+	0.237605i
$494$	−4.91994	+	4.12832i	−0.221359	+	0.185742i
$495$	3.05372	+	2.94160i	0.137255	+	0.132215i
$496$	−16.9886	−	14.2551i	−0.762810	−	0.640073i
$497$	−3.27114	−	7.58334i	−0.146730	−	0.340159i
$498$	0.408657	+	4.96809i	0.0183124	+	0.222625i
$499$	8.88243	+	2.10518i	0.397632	+	0.0942406i	0.424567	−	0.905397i	$-0.360426\pi$
$499$	8.88243	+	2.10518i	0.397632	+	0.0942406i	−0.0269345	+	0.999637i	$0.508575\pi$
$500$	−1.49644	−	4.99845i	−0.0669227	−	0.223537i
$501$	−30.0182	+	7.87646i	−1.34112	+	0.351894i
$502$	−30.5718	−	3.57333i	−1.36449	−	0.159485i
$503$	−6.04218	+	34.2669i	−0.269407	+	1.52789i	0.486777	+	0.873526i	$0.338172\pi$
$503$	−6.04218	+	34.2669i	−0.269407	+	1.52789i	−0.756184	+	0.654359i	$0.772939\pi$
$504$	−6.93310	+	3.90735i	−0.308825	+	0.174047i
$505$	−1.84403	−	10.4580i	−0.0820584	−	0.465376i
$506$	0.213493	+	3.66554i	0.00949093	+	0.162953i
$507$	−20.4826	−	6.90548i	−0.909664	−	0.306683i
$508$	3.09112	−	7.16601i	0.137146	−	0.317940i
$509$	−7.90093	+	3.96800i	−0.350203	+	0.175878i	−0.615201	−	0.788371i	$-0.710925\pi$
$509$	−7.90093	+	3.96800i	−0.350203	+	0.175878i	0.264998	+	0.964249i	$0.414629\pi$
$510$	−6.05412	+	6.73221i	−0.268081	+	0.298107i
$511$	−5.38245	+	1.27567i	−0.238106	+	0.0564321i
$512$	11.1868	+	19.3762i	0.494394	+	0.856315i
$513$	22.1842	+	32.7573i	0.979458	+	1.44627i
$514$	−2.70522	+	4.68558i	−0.119322	+	0.206672i
$515$	4.99897	−	16.6977i	0.220281	−	0.735790i
$516$	−2.77810	−	1.73354i	−0.122299	−	0.0763151i
$517$	9.90401	+	6.51397i	0.435578	+	0.286484i
$518$	−0.159643	−	0.214437i	−0.00701430	−	0.00942184i
$519$	18.8397	+	30.9019i	0.826970	+	1.35644i
$520$	−1.66408	+	1.09448i	−0.0729747	+	0.0479962i
$521$	6.97035	+	2.53700i	0.305377	+	0.111148i	0.490163	−	0.871631i	$-0.336937\pi$
$521$	6.97035	+	2.53700i	0.305377	+	0.111148i	−0.184787	+	0.982779i	$0.559159\pi$
$522$	−6.07656	+	5.61477i	−0.265964	+	0.245752i
$523$	0.210186	−	0.0765015i	0.00919080	−	0.00334518i	−0.337421	−	0.941354i	$-0.609554\pi$
$523$	0.210186	−	0.0765015i	0.00919080	−	0.00334518i	0.346611	+	0.938009i	$0.387332\pi$
$524$	0.974447	−	1.30891i	0.0425689	−	0.0571800i
$525$	−6.23540	−	0.578181i	−0.272135	−	0.0252339i
$526$	−15.8395	+	16.7889i	−0.690637	+	0.732033i
$527$	32.4932	−	34.4408i	1.41543	−	1.50027i
$528$	−2.66283	−	5.78878i	−0.115885	−	0.251924i
$529$	−11.3637	+	15.2641i	−0.494074	+	0.663657i
$530$	10.4618	−	3.80778i	0.454431	−	0.165400i
$531$	−3.40544	+	26.7244i	−0.147783	+	1.15974i
$532$	3.90043	+	1.41964i	0.169105	+	0.0615493i
$533$	−5.87197	+	3.86206i	−0.254343	+	0.167284i
$534$	−18.3627	+	0.438842i	−0.794631	+	0.0189905i
$535$	1.09643	+	1.47276i	0.0474029	+	0.0636731i
$536$	−29.4512	−	19.3704i	−1.27210	−	0.836673i
$537$	−1.05078	+	30.6376i	−0.0453445	+	1.32211i
$538$	8.95172	−	29.9008i	0.385936	−	1.28912i
$539$	−4.93040	+	8.53970i	−0.212367	+	0.367831i
$540$	1.35867	+	2.61662i	0.0584677	+	0.112601i
$541$	1.21436	+	2.10334i	0.0522095	+	0.0904295i	0.890949	−	0.454103i	$-0.150040\pi$
$541$	1.21436	+	2.10334i	0.0522095	+	0.0904295i	−0.838740	+	0.544533i	$0.816707\pi$
$542$	3.81690	−	0.904621i	0.163950	−	0.0388568i
$543$	−6.61119	−	20.3041i	−0.283713	−	0.871332i
$544$	−15.2648	+	7.66625i	−0.654471	+	0.328688i
$545$	−0.985842	+	2.28544i	−0.0422288	+	0.0978974i
$546$	0.248189	+	1.23432i	0.0106215	+	0.0528241i
$547$	1.00181	+	17.2004i	0.0428342	+	0.735436i	0.949535	+	0.313661i	$0.101556\pi$
$547$	1.00181	+	17.2004i	0.0428342	+	0.735436i	−0.906701	+	0.421775i	$0.861407\pi$
$548$	0.180799	+	1.02536i	0.00772335	+	0.0438013i
$549$	−9.15960	−	26.0033i	−0.390922	−	1.10979i
$550$	1.34252	−	7.61382i	0.0572453	−	0.324654i
$551$	17.8352	+	2.08464i	0.759806	+	0.0888086i
$552$	−2.80310	+	10.2481i	−0.119308	+	0.436187i
$553$	−0.525905	−	1.75665i	−0.0223638	−	0.0747002i
$554$	1.51436	+	0.358909i	0.0643389	+	0.0152486i
$555$	−0.338830	+	0.234638i	−0.0143825	+	0.00995982i
$556$	−3.16018	−	7.32611i	−0.134021	−	0.310696i
$557$	−1.47916	−	1.24117i	−0.0626742	−	0.0525899i	0.610912	−	0.791698i	$-0.290803\pi$
$557$	−1.47916	−	1.24117i	−0.0626742	−	0.0525899i	−0.673587	+	0.739108i	$0.735247\pi$
$558$	14.6462	+	29.9344i	0.620023	+	1.26723i
$559$	−1.65142	+	1.38571i	−0.0698477	+	0.0586092i
$560$	−1.61233	−	0.809742i	−0.0681333	−	0.0342178i
$561$	12.6691	−	4.95708i	0.534891	−	0.209288i
$562$	29.4869	−	3.44653i	1.24383	−	0.145383i
$563$	−0.504208	+	8.65691i	−0.0212498	+	0.364845i	0.970875	+	0.239589i	$0.0770125\pi$
$563$	−0.504208	+	8.65691i	−0.0212498	+	0.364845i	−0.992124	+	0.125257i	$0.960025\pi$
$564$	5.07881	+	6.49224i	0.213856	+	0.273373i
$565$	0.927216	+	0.982792i	0.0390083	+	0.0413463i
$566$	17.8024			0.748291
$567$	7.72013	−	0.740114i	0.324215	−	0.0310819i
$568$	29.5040			1.23796
$569$	17.0230	+	18.0433i	0.713640	+	0.756414i	0.978135	−	0.207973i	$-0.0666867\pi$
$569$	17.0230	+	18.0433i	0.713640	+	0.756414i	−0.264495	+	0.964387i	$0.585205\pi$
$570$	−5.17301	+	12.8266i	−0.216673	+	0.537249i
$571$	0.615393	−	10.5659i	0.0257534	−	0.442169i	−0.960643	−	0.277786i	$-0.910400\pi$
$571$	0.615393	−	10.5659i	0.0257534	−	0.442169i	0.986397	−	0.164383i	$-0.0525634\pi$
$572$	0.714319	−	0.0834919i	0.0298672	−	0.00349097i
$573$	0.261956	−	1.72579i	0.0109434	−	0.0720960i
$574$	−8.77300	−	4.40597i	−0.366178	−	0.183901i
$575$	−6.40419	+	5.37375i	−0.267073	+	0.224101i
$576$	−2.75305	−	25.8833i	−0.114710	−	1.07847i
$577$	−8.88197	−	7.45286i	−0.369761	−	0.310267i	0.438906	−	0.898533i	$-0.355366\pi$
$577$	−8.88197	−	7.45286i	−0.369761	−	0.310267i	−0.808667	+	0.588267i	$0.799811\pi$
$578$	3.63255	+	8.42119i	0.151094	+	0.350275i
$579$	−3.24870	−	1.53549i	−0.135011	−	0.0638127i
$580$	1.30212	+	0.308609i	0.0540677	+	0.0128143i
$581$	−0.608281	−	2.03180i	−0.0252358	−	0.0842933i
$582$	−12.4923	−	12.6228i	−0.517823	−	0.523231i
$583$	−16.6155	−	1.94207i	−0.688143	−	0.0804323i
$584$	3.43149	−	19.4609i	0.141996	−	0.805299i
$585$	1.91489	−	0.317171i	0.0791711	−	0.0131134i
$586$	−2.99883	−	17.0072i	−0.123881	−	0.702562i
$587$	−0.382447	−	6.56636i	−0.0157853	−	0.271023i	−0.996961	−	0.0779046i	$-0.975177\pi$
$587$	−0.382447	−	6.56636i	−0.0157853	−	0.271023i	0.981176	−	0.193118i	$-0.0618600\pi$
$588$	−5.14573	+	4.53163i	−0.212207	+	0.186881i
$589$	28.6481	−	66.4138i	1.18042	−	2.73653i
$590$	−8.41629	+	4.22682i	−0.346493	+	0.174015i
$591$	21.3188	+	4.51757i	0.876938	+	0.185828i
$592$	0.602661	−	0.142833i	0.0247692	−	0.00587041i
$593$	−18.3087	−	31.7117i	−0.751850	−	1.30224i	−0.946925	−	0.321454i	$-0.895828\pi$
$593$	−18.3087	−	31.7117i	−0.751850	−	1.30224i	0.195075	−	0.980788i	$-0.437505\pi$
$594$	0.129301	+	9.57413i	0.00530527	+	0.392831i
$595$	1.92609	−	3.33609i	0.0789622	−	0.136766i
$596$	−2.76035	+	9.22020i	−0.113068	+	0.377674i
$597$	8.32782	−	4.43464i	0.340835	−	0.181498i
$598$	1.40431	+	0.923626i	0.0574263	+	0.0377699i
$599$	−4.90880	−	6.59366i	−0.200568	−	0.269410i	0.690447	−	0.723383i	$-0.257414\pi$
$599$	−4.90880	−	6.59366i	−0.200568	−	0.269410i	−0.891016	+	0.453973i	$0.850006\pi$
$600$	10.7195	−	19.6357i	0.437621	−	0.801623i
$601$	−17.4724	+	11.4918i	−0.712716	+	0.468761i	−0.853375	−	0.521298i	$-0.825448\pi$
$601$	−17.4724	+	11.4918i	−0.712716	+	0.468761i	0.140659	+	0.990058i	$0.455078\pi$
$602$	−2.82967	−	1.02991i	−0.115329	−	0.0419762i
$603$	18.5775	+	28.8952i	0.756535	+	1.17670i
$604$	5.20075	−	1.89292i	0.211616	−	0.0770218i
$605$	−4.56138	+	6.12700i	−0.185447	+	0.249098i
$606$	13.8567	−	19.5722i	0.562890	−	0.795067i
$607$	−12.2627	+	12.9977i	−0.497729	+	0.527562i	−0.926723	−	0.375745i	$-0.877387\pi$
$607$	−12.2627	+	12.9977i	−0.497729	+	0.527562i	0.428994	+	0.903307i	$0.358868\pi$
$608$	−17.9063	+	18.9795i	−0.726195	+	0.769722i
$609$	2.03399	−	2.87296i	0.0824216	−	0.116418i
$610$	5.75535	−	7.73078i	0.233027	−	0.313010i
$611$	5.09924	−	1.85597i	0.206293	−	0.0750846i
$612$	9.44901	−	0.451894i	0.381954	−	0.0182667i
$613$	−22.2961	−	8.11512i	−0.900532	−	0.327767i	−0.150066	−	0.988676i	$-0.547949\pi$
$613$	−22.2961	−	8.11512i	−0.900532	−	0.327767i	−0.750466	+	0.660909i	$0.770171\pi$
$614$	16.3588	−	10.7593i	0.660186	−	0.434211i
$615$	−7.25208	+	13.2842i	−0.292432	+	0.535669i
$616$	2.49636	+	3.35319i	0.100581	+	0.135104i
$617$	−18.6402	−	12.2599i	−0.750427	−	0.493563i	0.115764	−	0.993277i	$-0.463068\pi$
$617$	−18.6402	−	12.2599i	−0.750427	−	0.493563i	−0.866191	+	0.499713i	$0.833439\pi$
$618$	34.7419	−	18.5004i	1.39752	−	0.744193i
$619$	−2.19296	+	7.32498i	−0.0881424	+	0.294416i	−0.990683	−	0.136189i	$-0.956515\pi$
$619$	−2.19296	+	7.32498i	−0.0881424	+	0.294416i	0.902541	+	0.430605i	$0.141700\pi$
$620$	2.69512	−	4.66808i	0.108238	−	0.187475i
$621$	6.54755	−	8.02059i	0.262744	−	0.321855i
$622$	−3.85378	−	6.67495i	−0.154523	−	0.267641i
$623$	7.60431	−	1.80225i	0.304660	−	0.0722058i
$624$	−2.85349	−	0.604671i	−0.114231	−	0.0242062i
$625$	12.1365	−	6.09517i	0.485459	−	0.243807i
$626$	−0.645451	+	1.49632i	−0.0257974	+	0.0598052i
$627$	15.5959	−	13.7346i	0.622838	−	0.548508i
$628$	−0.233697	−	4.01242i	−0.00932552	−	0.160113i
$629$	0.229627	+	1.30228i	0.00915583	+	0.0519253i
$630$	1.72108	+	2.09492i	0.0685693	+	0.0834636i
$631$	4.21635	−	23.9121i	0.167850	−	0.951926i	−0.778227	−	0.627983i	$-0.783881\pi$
$631$	4.21635	−	23.9121i	0.167850	−	0.951926i	0.946077	−	0.323942i	$-0.105008\pi$
$632$	6.50641	+	0.760490i	0.258811	+	0.0302507i
$633$	−12.6377	−	12.7697i	−0.502302	−	0.507548i
$634$	6.78582	+	22.6662i	0.269499	+	0.900191i
$635$	−10.7657	−	2.55152i	−0.427225	−	0.101254i
$636$	−10.5167	−	4.97068i	−0.417014	−	0.197100i
$637$	1.78790	+	4.14482i	0.0708392	+	0.164224i
$638$	3.32917	+	2.79350i	0.131803	+	0.110596i
$639$	−26.2808	−	11.6618i	−1.03965	−	0.461333i
$640$	2.26141	−	1.89755i	0.0893901	−	0.0750072i
$641$	−26.1043	−	13.1101i	−1.03106	−	0.517817i	−0.148940	−	0.988846i	$-0.547586\pi$
$641$	−26.1043	−	13.1101i	−1.03106	−	0.517817i	−0.882117	+	0.471030i	$0.843882\pi$
$642$	−0.622230	+	4.09932i	−0.0245575	+	0.161787i
$643$	−26.6380	+	3.11354i	−1.05050	+	0.122786i	−0.623782	−	0.781598i	$-0.714405\pi$
$643$	−26.6380	+	3.11354i	−1.05050	+	0.122786i	−0.426719	+	0.904384i	$0.640331\pi$
$644$	0.0631617	−	1.08444i	0.00248892	−	0.0427331i
$645$	−1.73637	+	4.30538i	−0.0683694	+	0.169524i
$646$	30.4524	+	32.2776i	1.19813	+	1.26995i
$647$	−8.71687			−0.342696			−0.171348	−	0.985211i	$-0.554812\pi$
$647$	−8.71687			−0.342696			−0.171348	+	0.985211i	$0.554812\pi$
$648$	−8.49597	+	26.3713i	−0.333753	+	1.03596i
$649$	14.1514			0.555492
$650$	−2.42872	−	2.57429i	−0.0952621	−	0.100972i
$651$	−8.73636	−	11.1677i	−0.342405	−	0.437696i
$652$	0.266855	−	4.58172i	0.0104508	−	0.179434i
$653$	−0.945989	+	0.110570i	−0.0370194	+	0.00432695i	−0.134582	−	0.990902i	$-0.542969\pi$
$653$	−0.945989	+	0.110570i	−0.0370194	+	0.00432695i	0.0975631	+	0.995229i	$0.468895\pi$
$654$	−5.23429	+	2.04803i	−0.204677	+	0.0800844i
$655$	−2.06731	−	1.03824i	−0.0807764	−	0.0405674i
$656$	17.4230	−	14.6196i	0.680255	−	0.570801i
$657$	−10.7488	+	15.9786i	−0.419349	+	0.623385i
$658$	5.80655	+	4.87228i	0.226363	+	0.189941i
$659$	−1.91261	−	4.43392i	−0.0745046	−	0.172721i	0.876894	−	0.480685i	$-0.159612\pi$
$659$	−1.91261	−	4.43392i	−0.0745046	−	0.172721i	−0.951398	+	0.307964i	$0.900353\pi$
$660$	1.27323	−	0.881703i	0.0495604	−	0.0343202i
$661$	32.4674	+	7.69492i	1.26284	+	0.299298i	0.806886	−	0.590708i	$-0.201151\pi$
$661$	32.4674	+	7.69492i	1.26284	+	0.299298i	0.455950	+	0.890005i	$0.349300\pi$
$662$	−3.31787	−	11.0824i	−0.128953	−	0.430732i
$663$	1.64308	−	6.00705i	0.0638118	−	0.233294i
$664$	7.52555	+	0.879610i	0.292048	+	0.0341355i
$665$	1.02182	−	5.79504i	0.0396245	−	0.224722i
$666$	−0.914837	−	0.171129i	−0.0354492	−	0.00663112i
$667$	−0.816039	−	4.62799i	−0.0315972	−	0.179196i
$668$	0.659101	+	11.3163i	0.0255014	+	0.437842i
$669$	−7.44993	−	37.0509i	−0.288031	−	1.43247i
$670$	−4.75653	+	11.0269i	−0.183761	+	0.426005i
$671$	−12.9414	+	6.49939i	−0.499596	+	0.250906i
$672$	1.58369	+	4.86380i	0.0610923	+	0.187625i
$673$	−35.6848	+	8.45746i	−1.37555	+	0.326011i	−0.850909	−	0.525313i	$-0.823948\pi$
$673$	−35.6848	+	8.45746i	−1.37555	+	0.326011i	−0.524640	+	0.851324i	$0.675800\pi$
$674$	3.97839	+	6.89077i	0.153242	+	0.265423i
$675$	−17.3097	+	13.2536i	−0.666250	+	0.510131i
$676$	−3.94757	+	6.83738i	−0.151829	+	0.262976i
$677$	−13.4963	+	45.0807i	−0.518705	+	1.73259i	0.149639	+	0.988741i	$0.452189\pi$
$677$	−13.4963	+	45.0807i	−0.518705	+	1.73259i	−0.668343	+	0.743853i	$0.732996\pi$
$678$	−0.104585	+	3.04940i	−0.00401658	+	0.117111i
$679$	6.31295	+	4.15209i	0.242269	+	0.159343i
$680$	8.21791	+	11.0386i	0.315143	+	0.423310i
$681$	11.6280	−	0.277892i	0.445585	−	0.0106488i
$682$	14.6255	−	9.61933i	0.560039	−	0.368343i
$683$	−31.5034	−	11.4663i	−1.20544	−	0.438745i	−0.340322	−	0.940309i	$-0.610536\pi$
$683$	−31.5034	−	11.4663i	−1.20544	−	0.438745i	−0.865121	+	0.501564i	$0.832758\pi$
$684$	13.3273	−	5.58535i	0.509583	−	0.213561i
$685$	1.38704	−	0.504842i	0.0529961	−	0.0192890i
$686$	−7.97735	+	10.7154i	−0.304577	+	0.409117i
$687$	−0.774038	−	1.68270i	−0.0295314	−	0.0641989i
$688$	4.78748	−	5.07443i	0.182521	−	0.193461i
$689$	−5.25515	+	5.57013i	−0.200205	+	0.212205i
$690$	3.60408	+	0.334191i	0.137205	+	0.0127224i
$691$	−12.9081	+	17.3386i	−0.491047	+	0.659590i	−0.976712	−	0.214555i	$-0.931170\pi$
$691$	−12.9081	+	17.3386i	−0.491047	+	0.659590i	0.485665	+	0.874145i	$0.338577\pi$
$692$	12.4221	−	4.52128i	0.472218	−	0.171873i
$693$	−0.898261	−	3.97359i	−0.0341221	−	0.150944i
$694$	12.5691	+	4.57479i	0.477118	+	0.173657i
$695$	−9.45032	+	6.21557i	−0.358471	+	0.235770i
$696$	6.54605	+	10.7372i	0.248127	+	0.406993i
$697$	28.9983	+	38.9514i	1.09839	+	1.47539i
$698$	−24.7108	−	16.2526i	−0.935318	−	0.615169i
$699$	−20.0908	−	12.5367i	−0.759903	−	0.474182i
$700$	−0.656002	+	2.19120i	−0.0247945	+	0.0828195i
$701$	9.11796	−	15.7928i	0.344381	−	0.596485i	−0.640860	−	0.767658i	$-0.721422\pi$
$701$	9.11796	−	15.7928i	0.344381	−	0.596485i	0.985241	+	0.171173i	$0.0547555\pi$
$702$	3.55086	+	2.56973i	0.134019	+	0.0969881i
$703$	1.01000	+	1.74937i	0.0380928	+	0.0659786i
$704$	−13.3042	+	3.15316i	−0.501421	+	0.118839i
$705$	7.81379	−	8.68898i	0.294284	−	0.327246i
$706$	−9.15406	+	4.59734i	−0.344517	+	0.173023i
$707$	−4.04123	+	9.36863i	−0.151986	+	0.352343i
$708$	9.32452	+	3.14366i	0.350437	+	0.118146i
$709$	0.0330904	+	0.568140i	0.00124274	+	0.0213369i	0.998873	−	0.0474730i	$-0.0151168\pi$
$709$	0.0330904	+	0.568140i	0.00124274	+	0.0213369i	−0.997630	+	0.0688100i	$0.978080\pi$
$710$	−1.74540	−	9.89865i	−0.0655037	−	0.371490i
$711$	−5.49504	−	3.24914i	−0.206080	−	0.121852i
$712$	−4.84799	+	27.4943i	−0.181686	+	1.03039i
$713$	−18.8011	−	2.19753i	−0.704106	−	0.0822981i
$714$	8.41424	−	2.20781i	0.314895	−	0.0826251i
$715$	−0.292416	−	0.976736i	−0.0109357	−	0.0365279i
$716$	10.8953	+	2.58224i	0.407178	+	0.0965030i
$717$	1.42393	+	17.3109i	0.0531778	+	0.646488i
$718$	12.6019	+	29.2144i	0.470297	+	1.09027i
$719$	23.3247	+	19.5718i	0.869865	+	0.729903i	0.964070	−	0.265649i	$-0.0855864\pi$
$719$	23.3247	+	19.5718i	0.869865	+	0.729903i	−0.0942046	+	0.995553i	$0.530031\pi$
$720$	−6.03578	+	1.73887i	−0.224940	+	0.0648040i
$721$	−12.8287	+	10.7646i	−0.477766	+	0.400894i
$722$	40.7217	+	20.4512i	1.51551	+	0.761115i
$723$	3.56788	+	2.85136i	0.132691	+	0.106043i
$724$	−7.74670	+	0.905459i	−0.287904	+	0.0336511i
$725$	−0.575347	+	9.87833i	−0.0213679	+	0.366872i
$726$	−17.0800	+	2.41128i	−0.633897	+	0.0894911i
$727$	−9.17610	−	9.72610i	−0.340323	−	0.360721i	0.534496	−	0.845171i	$-0.320501\pi$
$727$	−9.17610	−	9.72610i	−0.340323	−	0.360721i	−0.874819	+	0.484450i	$0.839020\pi$
$728$	1.91367			0.0709252
$729$	17.9914	−	20.1323i	0.666348	−	0.745641i
$730$	−6.73219			−0.249169
$731$	10.2216	+	10.8343i	0.378060	+	0.400720i
$732$	−9.97099	+	1.40767i	−0.368539	+	0.0520289i
$733$	−1.09798	+	18.8516i	−0.0405549	+	0.696300i	0.915356	+	0.402644i	$0.131909\pi$
$733$	−1.09798	+	18.8516i	−0.0405549	+	0.696300i	−0.955911	+	0.293656i	$0.905128\pi$
$734$	−28.3818	+	3.31736i	−1.04759	+	0.122446i
$735$	7.59356	+	6.06859i	0.280093	+	0.223843i
$736$	6.10243	+	3.06476i	0.224939	+	0.112968i
$737$	13.8229	−	11.5988i	0.509174	−	0.427248i
$738$	−32.8419	+	9.46155i	−1.20893	+	0.348285i
$739$	−33.6731	−	28.2551i	−1.23869	−	1.03938i	−0.997626	−	0.0688708i	$-0.978060\pi$
$739$	−33.6731	−	28.2551i	−1.23869	−	1.03938i	−0.241060	−	0.970510i	$-0.577495\pi$
$740$	0.0596248	+	0.138226i	0.00219185	+	0.00508128i
$741$	−0.779886	−	9.48115i	−0.0286498	−	0.348299i
$742$	−10.4084	−	2.46685i	−0.382106	−	0.0905608i
$743$	11.3533	+	37.9226i	0.416512	+	1.39125i	0.866931	+	0.498429i	$0.166090\pi$
$743$	11.3533	+	37.9226i	0.416512	+	1.39125i	−0.450419	+	0.892817i	$0.648725\pi$
$744$	48.9946	−	12.8557i	1.79623	−	0.471311i
$745$	13.5522	+	1.58403i	0.496515	+	0.0580343i
$746$	0.282456	−	1.60189i	0.0103415	−	0.0586493i
$747$	−6.35576	−	3.75808i	−0.232545	−	0.137501i
$748$	−0.862874	−	4.89360i	−0.0315498	−	0.178928i
$749$	−0.102574	−	1.76112i	−0.00374796	−	0.0643500i
$750$	−15.8285	−	5.33642i	−0.577977	−	0.194859i
$751$	−1.94881	+	4.51785i	−0.0711131	+	0.164859i	−0.950065	−	0.312051i	$-0.898984\pi$
$751$	−1.94881	+	4.51785i	−0.0711131	+	0.164859i	0.878952	+	0.476910i	$0.158243\pi$
$752$	−15.6929	+	7.88128i	−0.572262	+	0.287401i
$753$	30.4858	−	33.9003i	1.11096	−	1.23540i
$754$	1.93581	−	0.458796i	0.0704982	−	0.0167084i
$755$	−3.92309	−	6.79499i	−0.142776	−	0.247295i
$756$	0.290838	−	2.81778i	0.0105777	−	0.102482i
$757$	6.52378	−	11.2995i	0.237111	−	0.410688i	−0.722773	−	0.691085i	$-0.757133\pi$
$757$	6.52378	−	11.2995i	0.237111	−	0.410688i	0.959884	+	0.280397i	$0.0904662\pi$
$758$	8.83264	−	29.5031i	0.320816	−	1.07160i
$759$	−4.61405	−	2.87918i	−0.167479	−	0.104508i
$760$	17.5634	+	11.5516i	0.637092	+	0.419022i
$761$	−4.61642	−	6.20092i	−0.167345	−	0.224783i	0.710538	−	0.703659i	$-0.248452\pi$
$761$	−4.61642	−	6.20092i	−0.167345	−	0.224783i	−0.877883	+	0.478876i	$0.841044\pi$
$762$	−13.0058	−	21.3328i	−0.471150	−	0.772807i
$763$	1.99801	−	1.31411i	0.0723328	−	0.0475740i
$764$	−0.599126	−	0.218064i	−0.0216756	−	0.00788928i
$765$	−2.95704	−	13.0809i	−0.106912	−	0.472941i
$766$	−9.03906	+	3.28995i	−0.326594	+	0.118871i
$767$	3.86847	−	5.19625i	0.139682	−	0.187626i
$768$	−23.2897	−	2.15955i	−0.840394	−	0.0779261i
$769$	3.91268	−	4.14720i	0.141095	−	0.149552i	−0.652972	−	0.757382i	$-0.726478\pi$
$769$	3.91268	−	4.14720i	0.141095	−	0.149552i	0.794067	+	0.607830i	$0.207960\pi$
$770$	0.977324	−	1.03590i	0.0352203	−	0.0373314i
$771$	−3.34911	−	7.28069i	−0.120615	−	0.262208i
$772$	−0.783754	+	1.05276i	−0.0282079	+	0.0378898i
$773$	−41.6056	+	15.1432i	−1.49645	+	0.544663i	−0.955138	−	0.296160i	$-0.904294\pi$
$773$	−41.6056	+	15.1432i	−1.49645	+	0.544663i	−0.541310	+	0.840823i	$0.682071\pi$
$774$	−9.66864	+	4.05203i	−0.347532	+	0.145647i
$775$	37.4535	+	13.6320i	1.34537	+	0.489675i
$776$	−22.5526	+	14.8331i	−0.809591	+	0.532476i
$777$	0.395872	−	0.00946078i	0.0142018	−	0.000339404i
$778$	21.8944	+	29.4093i	0.784954	+	1.05438i
$779$	61.9755	+	40.7619i	2.22050	+	1.46045i
$780$	0.0243008	−	0.708540i	0.000870110	−	0.0253698i
$781$	−4.33159	+	14.4685i	−0.154996	+	0.517724i
$782$	5.80671	−	10.0575i	0.207647	−	0.359656i
$783$	−1.58694	−	12.1516i	−0.0567125	−	0.434264i
$784$	−7.30392	−	12.6508i	−0.260854	−	0.451813i
$785$	−5.54437	+	1.31404i	−0.197887	+	0.0469001i
$786$	−1.61743	−	4.96741i	−0.0576919	−	0.177182i
$787$	12.3624	−	6.20865i	0.440674	−	0.221315i	−0.214606	−	0.976701i	$-0.568847\pi$
$787$	12.3624	−	6.20865i	0.440674	−	0.221315i	0.655280	+	0.755386i	$0.272551\pi$
$788$	3.15269	−	7.30875i	0.112310	−	0.260364i
$789$	−6.73957	−	33.5181i	−0.239935	−	1.19327i
$790$	−0.129761	−	2.22791i	−0.00461668	−	0.0792653i
$791$	−0.225427	−	1.27846i	−0.00801527	−	0.0454569i
$792$	14.3055	+	2.67597i	0.508322	+	0.0950866i
$793$	−1.15117	+	6.52861i	−0.0408793	+	0.231838i
$794$	−13.9040	−	1.62515i	−0.493435	−	0.0576743i
$795$	−4.35081	+	15.9064i	−0.154307	+	0.564143i
$796$	−0.988376	−	3.30140i	−0.0350320	−	0.117015i
$797$	−26.4560	−	6.27018i	−0.937118	−	0.222101i	−0.266442	−	0.963851i	$-0.585848\pi$
$797$	−26.4560	−	6.27018i	−0.937118	−	0.222101i	−0.670677	+	0.741750i	$0.733996\pi$
$798$	10.9246	−	7.56522i	0.386727	−	0.267806i
$799$	−14.8505	−	34.4273i	−0.525372	−	1.21795i
$800$	−11.0148	−	9.24250i	−0.389432	−	0.326772i
$801$	15.1858	−	22.5745i	0.536564	−	0.797631i
$802$	−31.1616	+	26.1477i	−1.10035	+	0.923307i
$803$	9.03970	+	4.53991i	0.319004	+	0.160210i
$804$	11.6847	−	4.57189i	0.412087	−	0.161238i
$805$	−1.52959	+	0.178783i	−0.0539108	+	0.00630127i
$806$	0.465940	−	7.99988i	0.0164120	−	0.281784i
$807$	28.4859	+	36.4135i	1.00275	+	1.28182i
$808$	−25.0134	−	26.5126i	−0.879968	−	0.932711i
$809$	15.5491			0.546677			0.273338	−	0.961918i	$-0.411872\pi$
$809$	15.5491			0.546677			0.273338	+	0.961918i	$0.411872\pi$
$810$	9.35025	+	1.29034i	0.328534	+	0.0453379i
$811$	−36.9597			−1.29783			−0.648916	−	0.760860i	$-0.724777\pi$
$811$	−36.9597			−1.29783			−0.648916	+	0.760860i	$0.724777\pi$
$812$	−0.882326	−	0.935210i	−0.0309636	−	0.0328195i
$813$	−2.17321	+	5.38855i	−0.0762179	+	0.188985i
$814$	−0.0284261	+	0.488058i	−0.000996336	+	0.0171064i
$815$	−6.46242	+	0.755348i	−0.226369	+	0.0264587i
$816$	−3.02445	+	19.9254i	−0.105877	+	0.697529i
$817$	20.3329	+	10.2116i	0.711357	+	0.357257i
$818$	−2.86903	+	2.40741i	−0.100313	+	0.0841729i
$819$	−1.70461	−	0.756398i	−0.0595639	−	0.0264307i
$820$	4.23475	+	3.55338i	0.147884	+	0.124089i
$821$	12.5281	+	29.0435i	0.437235	+	1.01362i	0.984295	+	0.176531i	$0.0564877\pi$
$821$	12.5281	+	29.0435i	0.437235	+	1.01362i	−0.547060	+	0.837093i	$0.684253\pi$
$822$	3.01360	+	1.42437i	0.105111	+	0.0496806i
$823$	21.0598	+	4.99127i	0.734100	+	0.173985i	0.580629	−	0.814168i	$-0.302807\pi$
$823$	21.0598	+	4.99127i	0.734100	+	0.173985i	0.153471	+	0.988153i	$0.450955\pi$
$824$	−17.1584	−	57.3132i	−0.597742	−	1.99660i
$825$	8.05541	+	8.13954i	0.280453	+	0.283382i
$826$	8.98768	+	1.05051i	0.312721	+	0.0365519i
$827$	7.85906	−	44.5709i	0.273286	−	1.54988i	−0.471067	−	0.882097i	$-0.656131\pi$
$827$	7.85906	−	44.5709i	0.273286	−	1.54988i	0.744353	−	0.667786i	$-0.232758\pi$
$828$	−2.40065	−	2.92211i	−0.0834283	−	0.101550i
$829$	−4.77128	−	27.0593i	−0.165713	−	0.939807i	−0.948326	−	0.317298i	$-0.897225\pi$
$829$	−4.77128	−	27.0593i	−0.165713	−	0.939807i	0.782613	−	0.622509i	$-0.213887\pi$
$830$	−0.150086	−	2.57688i	−0.00520956	−	0.0894447i
$831$	−1.73001	+	1.52354i	−0.0600132	+	0.0528511i
$832$	−2.47906	+	5.74712i	−0.0859461	+	0.199245i
$833$	27.8713	−	13.9975i	0.965685	−	0.484985i
$834$	−24.9881	−	5.29512i	−0.865268	−	0.183355i
$835$	15.6369	−	3.70602i	0.541138	−	0.128252i
$836$	−3.79528	−	6.57363i	−0.131263	−	0.227354i
$837$	−48.7236	−	7.91442i	−1.68414	−	0.273562i
$838$	18.2902	−	31.6795i	0.631824	−	1.09435i
$839$	3.63681	−	12.1478i	0.125557	−	0.419388i	−0.871980	−	0.489542i	$-0.837164\pi$
$839$	3.63681	−	12.1478i	0.125557	−	0.419388i	0.997536	+	0.0701540i	$0.0223491\pi$
$840$	3.63738	−	1.93694i	0.125502	−	0.0668307i
$841$	19.5820	+	12.8793i	0.675240	+	0.444112i
$842$	−9.87305	−	13.2618i	−0.340248	−	0.457032i
$843$	−21.0708	+	38.5970i	−0.725718	+	1.32935i
$844$	−5.48261	+	3.60597i	−0.188719	+	0.124123i
$845$	10.5178	+	3.82815i	0.361822	+	0.131692i
$846$	26.3585	−	1.26058i	0.906225	−	0.0433397i
$847$	6.89644	−	2.51010i	0.236964	−	0.0862480i
$848$	14.7987	−	19.8781i	0.508189	−	0.682616i
$849$	−15.2368	+	21.5216i	−0.522926	+	0.738619i
$850$	−16.7809	+	17.7867i	−0.575580	+	0.610079i
$851$	0.362780	−	0.384524i	0.0124359	−	0.0131813i
$852$	−6.06823	+	8.57121i	−0.207894	+	0.293645i
$853$	16.7408	−	22.4868i	0.573195	−	0.769935i	−0.417108	−	0.908857i	$-0.636956\pi$
$853$	16.7408	−	22.4868i	0.573195	−	0.769935i	0.990303	+	0.138922i	$0.0443637\pi$
$854$	−8.70162	+	3.16713i	−0.297763	+	0.108377i
$855$	−11.0788	−	17.2318i	−0.378888	−	0.589317i
$856$	5.92209	+	2.15546i	0.202413	+	0.0736722i
$857$	−6.26833	+	4.12275i	−0.214122	+	0.140830i	−0.652040	−	0.758185i	$-0.726087\pi$
$857$	−6.26833	+	4.12275i	−0.214122	+	0.140830i	0.437918	+	0.899015i	$0.355716\pi$
$858$	1.10324	−	2.02088i	0.0376639	−	0.0689916i
$859$	−13.2282	−	17.7686i	−0.451342	−	0.606257i	0.516970	−	0.856004i	$-0.327060\pi$
$859$	−13.2282	−	17.7686i	−0.451342	−	0.606257i	−0.968311	+	0.249747i	$0.919653\pi$
$860$	1.41669	+	0.931770i	0.0483087	+	0.0317731i
$861$	12.8351	−	6.83481i	0.437419	−	0.232930i
$862$	2.27182	−	7.58840i	0.0773784	−	0.258462i
$863$	−1.60358	+	2.77749i	−0.0545866	+	0.0945467i	−0.892027	−	0.451981i	$-0.850717\pi$
$863$	−1.60358	+	2.77749i	−0.0545866	+	0.0945467i	0.837441	+	0.546528i	$0.184051\pi$
$864$	15.5408	+	8.69482i	0.528710	+	0.295804i
$865$	−9.37040	−	16.2300i	−0.318603	−	0.551837i
$866$	−10.3334	+	2.44906i	−0.351143	+	0.0832225i
$867$	−13.2895	−	2.81613i	−0.451336	−	0.0956407i
$868$	−4.62806	+	2.32430i	−0.157087	+	0.0788918i
$869$	−1.32817	+	3.07904i	−0.0450551	+	0.104449i
$870$	3.21511	−	2.83141i	0.109002	−	0.0959938i
$871$	−0.480293	−	8.24631i	−0.0162741	−	0.279415i
$872$	1.48351	+	8.41343i	0.0502381	+	0.284915i
$873$	25.9518	−	4.29849i	0.878336	−	0.145482i
$874$	3.08054	−	17.4706i	0.104201	−	0.590953i
$875$	7.05892	+	0.825069i	0.238635	+	0.0278924i
$876$	4.94783	+	4.99951i	0.167172	+	0.168918i
$877$	−12.0732	−	40.3274i	−0.407684	−	1.36176i	−0.877746	−	0.479127i	$-0.840953\pi$
$877$	−12.0732	−	40.3274i	−0.407684	−	1.36176i	0.470061	−	0.882634i	$-0.344232\pi$
$878$	33.6340	+	7.97141i	1.13509	+	0.269022i
$879$	23.1270	+	10.9309i	0.780053	+	0.368690i
$880$	1.30685	+	3.02961i	0.0440538	+	0.102128i
$881$	3.90353	+	3.27545i	0.131513	+	0.110353i	0.706172	−	0.708041i	$-0.250421\pi$
$881$	3.90353	+	3.27545i	0.131513	+	0.110353i	−0.574658	+	0.818393i	$0.694865\pi$
$882$	2.32172	+	21.8281i	0.0781765	+	0.734990i
$883$	18.9650	−	15.9136i	0.638224	−	0.535534i	−0.265248	−	0.964180i	$-0.585454\pi$
$883$	18.9650	−	15.9136i	0.638224	−	0.535534i	0.903472	+	0.428647i	$0.141009\pi$
$884$	−2.03275	−	1.02089i	−0.0683689	−	0.0343362i
$885$	2.09351	−	13.7922i	0.0703725	−	0.463621i
$886$	−14.6968	+	1.71781i	−0.493750	+	0.0577111i
$887$	0.0307371	−	0.527736i	0.00103205	−	0.0177196i	−0.997753	−	0.0670024i	$-0.978656\pi$
$887$	0.0307371	−	0.527736i	0.00103205	−	0.0177196i	0.998785	+	0.0492827i	$0.0156935\pi$
$888$	−0.529113	+	1.31195i	−0.0177559	+	0.0440263i
$889$	7.29491	+	7.73215i	0.244663	+	0.259328i
$890$	9.51120			0.318816
$891$	−11.6850	−	8.03803i	−0.391461	−	0.269284i
$892$	−13.8039			−0.462190
$893$	−39.3036	−	41.6594i	−1.31524	−	1.39408i
$894$	18.9850	+	24.2685i	0.634954	+	0.811661i
$895$	0.922990	−	15.8471i	0.0308521	−	0.529711i
$896$	−2.81716	+	0.329279i	−0.0941147	+	0.0110004i
$897$	−2.31851	+	0.907168i	−0.0774128	+	0.0302895i
$898$	−37.8491	−	19.0085i	−1.26304	−	0.634323i
$899$	−17.1630	+	14.4014i	−0.572417	+	0.480315i
$900$	3.49964	+	7.15269i	0.116655	+	0.238423i
$901$	40.5322	+	34.0106i	1.35032	+	1.13306i
$902$	7.11081	+	16.4847i	0.236764	+	0.548881i
$903$	3.66695	−	2.53934i	0.122028	−	0.0845038i
$904$	4.51267	+	1.06952i	0.150089	+	0.0355718i
$905$	3.17121	+	10.5926i	0.105415	+	0.352109i
$906$	4.67470	−	17.0906i	0.155306	−	0.567797i
$907$	11.7526	+	1.37369i	0.390240	+	0.0456125i	0.308951	−	0.951078i	$-0.400022\pi$
$907$	11.7526	+	1.37369i	0.390240	+	0.0456125i	0.0812894	+	0.996691i	$0.474096\pi$
$908$	0.737728	−	4.18386i	0.0244824	−	0.138846i
$909$	11.8014	+	33.5031i	0.391428	+	1.11123i
$910$	−0.113209	−	0.642039i	−0.00375284	−	0.0212834i
$911$	2.17424	+	37.3303i	0.0720358	+	1.23681i	0.819725	+	0.572758i	$0.194126\pi$
$911$	2.17424	+	37.3303i	0.0720358	+	1.23681i	−0.747689	+	0.664049i	$0.768837\pi$
$912$	6.06873	+	30.1817i	0.200956	+	0.999417i
$913$	−1.53621	+	3.56133i	−0.0508411	+	0.117863i
$914$	36.7137	−	18.4383i	1.21438	−	0.609885i
$915$	4.41993	+	13.5744i	0.146119	+	0.448755i
$916$	−0.658288	+	0.156017i	−0.0217504	+	0.00515495i
$917$	1.11134	+	1.92491i	0.0366998	+	0.0635660i
$918$	16.2986	−	25.5251i	0.537934	−	0.842453i
$919$	−19.8571	+	34.3934i	−0.655024	+	1.13453i	0.326864	+	0.945071i	$0.394008\pi$
$919$	−19.8571	+	34.3934i	−0.655024	+	1.13453i	−0.981888	+	0.189463i	$0.939325\pi$
$920$	1.57786	−	5.27043i	0.0520206	−	0.173761i
$921$	−0.994103	+	28.9851i	−0.0327568	+	0.955091i
$922$	−35.2363	−	23.1753i	−1.16045	−	0.763238i
$923$	4.12859	+	5.54566i	0.135894	+	0.182538i
$924$	−1.48758	+	0.0355509i	−0.0489377	+	0.00116954i
$925$	−0.930003	+	0.611672i	−0.0305783	+	0.0201117i
$926$	20.1029	+	7.31684i	0.660621	+	0.240446i
$927$	−7.36969	+	57.8341i	−0.242052	+	1.89952i
$928$	7.59519	−	2.76442i	0.249324	−	0.0907467i
$929$	7.98907	−	10.7312i	0.262113	−	0.352079i	−0.651511	−	0.758639i	$-0.725865\pi$
$929$	7.98907	−	10.7312i	0.262113	−	0.352079i	0.913624	+	0.406560i	$0.133272\pi$
$930$	−7.21154	−	15.6773i	−0.236476	−	0.514079i
$931$	32.6944	−	34.6540i	1.07152	−	1.13574i
$932$	−5.93583	+	6.29162i	−0.194435	+	0.206089i
$933$	11.3678	+	1.05409i	0.372166	+	0.0345093i
$934$	−17.7142	+	23.7943i	−0.579627	+	0.778574i
$935$	−6.61974	+	2.40939i	−0.216488	+	0.0787954i
$936$	4.89316	−	4.52130i	0.159938	−	0.147783i
$937$	−24.5052	−	8.91915i	−0.800548	−	0.291376i	−0.0908347	−	0.995866i	$-0.528953\pi$
$937$	−24.5052	−	8.91915i	−0.800548	−	0.291376i	−0.709714	+	0.704490i	$0.751176\pi$
$938$	9.64007	−	6.34037i	0.314759	−	0.207020i
$939$	−1.25650	−	2.06098i	−0.0410042	−	0.0672574i
$940$	−2.54882	−	3.42366i	−0.0831333	−	0.111667i
$941$	10.9374	+	7.19363i	0.356549	+	0.234506i	0.715128	−	0.698994i	$-0.246368\pi$
$941$	10.9374	+	7.19363i	0.356549	+	0.234506i	−0.358579	+	0.933499i	$0.616739\pi$
$942$	−10.9163	−	6.81179i	−0.355671	−	0.221940i
$943$	5.56775	−	18.5976i	0.181311	−	0.605620i
$944$	−10.4820	+	18.1554i	−0.341160	+	0.590907i
$945$	−4.00562	+	0.287624i	−0.130303	+	0.00935640i
$946$	2.75338	+	4.76900i	0.0895202	+	0.155054i
$947$	−21.2869	+	5.04508i	−0.691730	+	0.163943i	−0.561421	−	0.827530i	$-0.689745\pi$
$947$	−21.2869	+	5.04508i	−0.691730	+	0.163943i	−0.130309	+	0.991473i	$0.541597\pi$
$948$	−1.55914	+	1.73377i	−0.0506384	+	0.0563102i
$949$	4.13812	−	2.07824i	0.134329	−	0.0674625i
$950$	−14.7951	+	34.2989i	−0.480016	+	1.11280i
$951$	−33.2094	−	11.1962i	−1.07689	−	0.363061i
$952$	−0.768804	−	13.1998i	−0.0249171	−	0.427810i
$953$	2.23323	+	12.6653i	0.0723415	+	0.410269i	0.999377	+	0.0352952i	$0.0112371\pi$
$953$	2.23323	+	12.6653i	0.0723415	+	0.410269i	−0.927035	+	0.374974i	$0.877652\pi$
$954$	−32.4422	+	18.2838i	−1.05035	+	0.591959i
$955$	−0.156957	+	0.890146i	−0.00507900	+	0.0288045i
$956$	6.30138	+	0.736525i	0.203801	+	0.0238209i
$957$	−6.22649	+	1.63376i	−0.201274	+	0.0528121i
$958$	−1.51595	−	5.06364i	−0.0489783	−	0.163599i
$959$	−1.37997	−	0.327058i	−0.0445615	−	0.0105613i
$960$	1.10495	+	13.4330i	0.0356621	+	0.433548i
$961$	23.4660	+	54.4003i	0.756968	+	1.75485i
$962$	0.171439	+	0.143854i	0.00552741	+	0.00463805i
$963$	−4.42317	−	4.26076i	−0.142535	−	0.137301i
$964$	1.27794	−	1.07232i	0.0411596	−	0.0345370i
$965$	1.66275	+	0.835065i	0.0535258	+	0.0268817i
$966$	−2.71668	−	2.17111i	−0.0874079	−	0.0698542i
$967$	−53.9418	+	6.30489i	−1.73465	+	0.202752i	−0.923899	−	0.382638i	$-0.875016\pi$
$967$	−53.9418	+	6.30489i	−1.73465	+	0.202752i	−0.810752	+	0.585389i	$0.800942\pi$
$968$	−1.52446	+	26.1739i	−0.0489978	+	0.841260i
$969$	−65.0846	+	9.18839i	−2.09082	+	0.295174i
$970$	6.31070	+	6.68896i	0.202624	+	0.214769i
$971$	1.23845			0.0397437			0.0198718	−	0.999803i	$-0.493674\pi$
$971$	1.23845			0.0397437			0.0198718	+	0.999803i	$0.493674\pi$
$972$	−5.91374	−	7.89209i	−0.189683	−	0.253139i
$973$	10.8677			0.348403
$974$	−13.3904	−	14.1929i	−0.429055	−	0.454771i
$975$	5.19080	−	0.732817i	0.166238	−	0.0234689i
$976$	1.24740	−	21.4170i	0.0399283	−	0.685543i
$977$	32.6141	−	3.81204i	1.04342	−	0.121958i	0.422920	−	0.906167i	$-0.361005\pi$
$977$	32.6141	−	3.81204i	1.04342	−	0.121958i	0.620497	+	0.784209i	$0.286931\pi$
$978$	−11.4778	−	9.17280i	−0.367021	−	0.293314i
$979$	−12.7712	−	6.41396i	−0.408171	−	0.204991i
$980$	2.71985	−	2.28222i	0.0868823	−	0.0729029i
$981$	2.00405	−	8.08069i	0.0639845	−	0.257997i
$982$	−10.6569	−	8.94222i	−0.340076	−	0.285358i
$983$	−8.51171	−	19.7324i	−0.271481	−	0.629365i	0.726869	−	0.686776i	$-0.240975\pi$
$983$	−8.51171	−	19.7324i	−0.271481	−	0.629365i	−0.998351	+	0.0574112i	$0.981715\pi$
$984$	4.25872	+	51.7736i	0.135763	+	1.65048i
$985$	−10.9802	−	2.60235i	−0.349857	−	0.0829177i
$986$	−3.94233	−	13.1683i	−0.125549	−	0.419364i
$987$	−10.8599	+	2.84952i	−0.345675	+	0.0907013i
$988$	−3.45125	−	0.403393i	−0.109799	−	0.0128337i
$989$	1.03401	−	5.86418i	0.0328797	−	0.186470i
$990$	0.0515117	−	4.95782i	0.00163715	−	0.157570i
$991$	3.69428	+	20.9513i	0.117353	+	0.665540i	0.985558	+	0.169336i	$0.0541622\pi$
$991$	3.69428	+	20.9513i	0.117353	+	0.665540i	−0.868206	+	0.496204i	$0.834727\pi$
$992$	−1.89301	−	32.5017i	−0.0601030	−	1.03193i
$993$	16.2374	+	5.47428i	0.515280	+	0.173721i
$994$	−3.82507	+	8.86751i	−0.121324	+	0.281260i
$995$	−4.36591	+	2.19264i	−0.138409	+	0.0695114i
$996$	−1.80335	+	2.00534i	−0.0571414	+	0.0635416i
$997$	−36.1745	+	8.57352i	−1.14566	+	0.271526i	−0.759248	−	0.650801i	$-0.774433\pi$
$997$	−36.1745	+	8.57352i	−1.14566	+	0.271526i	−0.386410	+	0.922327i	$0.626285\pi$
$998$	−5.33716	−	9.24423i	−0.168945	−	0.292621i
$999$	0.989876	−	0.959493i	0.0313183	−	0.0303570i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.22.3	✓	144
3.2	odd	2		243.2.g.a.199.6		144
9.2	odd	6		729.2.g.a.352.6		144
9.4	even	3		729.2.g.c.595.6		144
9.5	odd	6		729.2.g.b.595.3		144
9.7	even	3		729.2.g.d.352.3		144
81.11	odd	54		243.2.g.a.127.6		144
81.16	even	27		729.2.g.d.379.3		144
81.31	even	27		6561.2.a.c.1.51		72
81.38	odd	54		729.2.g.b.136.3		144
81.43	even	27		729.2.g.c.136.6		144
81.50	odd	54		6561.2.a.d.1.22		72
81.65	odd	54		729.2.g.a.379.6		144
81.70	even	27	inner	81.2.g.a.70.3	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.3	✓	144	1.1	even	1	trivial
81.2.g.a.70.3	yes	144	81.70	even	27	inner
243.2.g.a.127.6		144	81.11	odd	54
243.2.g.a.199.6		144	3.2	odd	2
729.2.g.a.352.6		144	9.2	odd	6
729.2.g.a.379.6		144	81.65	odd	54
729.2.g.b.136.3		144	81.38	odd	54
729.2.g.b.595.3		144	9.5	odd	6
729.2.g.c.136.6		144	81.43	even	27
729.2.g.c.595.6		144	9.4	even	3
729.2.g.d.352.3		144	9.7	even	3
729.2.g.d.379.3		144	81.16	even	27
6561.2.a.c.1.51		72	81.31	even	27
6561.2.a.d.1.22		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.802450 - 0.850548i) q^{2} +(1.71504 - 0.242123i) q^{3} +(0.0367849 - 0.631572i) q^{4} +(-0.890819 + 0.104122i) q^{5} +(-1.58218 - 1.26443i) q^{6} +(0.770065 + 0.386741i) q^{7} +(-2.35823 + 1.97879i) q^{8} +(2.88275 - 0.830504i) q^{9} +(0.803399 + 0.674132i) q^{10} +(-0.624164 - 1.44697i) q^{11} +(-0.0898306 - 1.09208i) q^{12} +(-0.701936 - 0.166362i) q^{13} +(-0.288997 - 0.965318i) q^{14} +(-1.50258 + 0.394262i) q^{15} +(2.31869 + 0.271016i) q^{16} +(-0.865512 + 4.90856i) q^{17} +(-3.01965 - 1.78548i) q^{18} +(1.32212 + 7.49811i) q^{19} +(0.0329918 + 0.566447i) q^{20} +(1.41434 + 0.476828i) q^{21} +(-0.729860 + 1.69201i) q^{22} +(1.78064 - 0.894269i) q^{23} +(-3.56536 + 3.96470i) q^{24} +(-4.08251 + 0.967572i) q^{25} +(0.421770 + 0.730527i) q^{26} +(4.74296 - 2.12233i) q^{27} +(0.272582 - 0.472126i) q^{28} +(0.676408 - 2.25936i) q^{29} +(1.54109 + 0.961644i) q^{30} +(-7.93694 - 5.22021i) q^{31} +(2.04653 + 2.74896i) q^{32} +(-1.42081 - 2.33050i) q^{33} +(4.86950 - 3.20272i) q^{34} +(-0.726257 - 0.264336i) q^{35} +(-0.418482 - 1.85122i) q^{36} +(0.249308 - 0.0907406i) q^{37} +(5.31656 - 7.14138i) q^{38} +(-1.24413 - 0.115363i) q^{39} +(1.89472 - 2.00829i) q^{40} +(6.68585 - 7.08659i) q^{41} +(-0.729369 - 1.58559i) q^{42} +(1.78455 - 2.39707i) q^{43} +(-0.936828 + 0.340978i) q^{44} +(-2.48154 + 1.03999i) q^{45} +(-2.18949 - 0.796909i) q^{46} +(-6.28485 + 4.13361i) q^{47} +(4.04228 - 0.0966047i) q^{48} +(-3.73668 - 5.01923i) q^{49} +(4.09897 + 2.69594i) q^{50} +(-0.295914 + 8.62796i) q^{51} +(-0.130890 + 0.437203i) q^{52} +(5.30779 - 9.19335i) q^{53} +(-5.61114 - 2.33105i) q^{54} +(0.706679 + 1.22400i) q^{55} +(-2.58128 + 0.611774i) q^{56} +(4.08296 + 12.5395i) q^{57} +(-2.46448 + 1.23771i) q^{58} +(-3.55686 + 8.24573i) q^{59} +(0.193732 + 0.963493i) q^{60} +(-0.534338 - 9.17423i) q^{61} +(1.92897 + 10.9397i) q^{62} +(2.54110 + 0.475337i) q^{63} +(1.50664 - 8.54460i) q^{64} +(0.642620 + 0.0751115i) q^{65} +(-0.842068 + 3.07858i) q^{66} +(3.28408 + 10.9696i) q^{67} +(3.06827 + 0.727194i) q^{68} +(2.83734 - 1.96484i) q^{69} +(0.357955 + 0.829833i) q^{70} +(-7.34178 - 6.16048i) q^{71} +(-5.15481 + 7.66290i) q^{72} +(-4.91737 + 4.12616i) q^{73} +(-0.277236 - 0.139233i) q^{74} +(-6.76741 + 2.64790i) q^{75} +(4.78423 - 0.559196i) q^{76} +(0.0789579 - 1.35565i) q^{77} +(0.900232 + 1.15077i) q^{78} +(-1.46027 - 1.54779i) q^{79} -2.09376 q^{80} +(7.62052 - 4.78828i) q^{81} -11.3925 q^{82} +(-1.68900 - 1.79023i) q^{83} +(0.353177 - 0.875714i) q^{84} +(0.259926 - 4.46276i) q^{85} +(-3.47084 + 0.405683i) q^{86} +(0.613026 - 4.03868i) q^{87} +(4.33519 + 2.17721i) q^{88} +(6.94724 - 5.82943i) q^{89} +(2.87587 + 1.27613i) q^{90} +(-0.476197 - 0.399577i) q^{91} +(-0.499295 - 1.15750i) q^{92} +(-14.8761 - 7.03117i) q^{93} +(8.55911 + 2.02855i) q^{94} +(-1.95849 - 6.54180i) q^{95} +(4.17548 + 4.21908i) q^{96} +(8.70918 + 1.01796i) q^{97} +(-1.27060 + 7.20591i) q^{98} +(-3.00103 - 3.65290i) 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

Properties

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