LMFDB - Embedded newform 798.2.bo.d.169.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(43,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 16])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.43"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bo (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,9,0,6,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 18x^{10} + 153x^{8} - 773x^{6} + 2448x^{4} - 4608x^{2} + 4096 $ x^12 - 18x^10 + 153x^8 - 773x^6 + 2448x^4 - 4608*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.1
Root			$1.89389 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	798.169
Dual form			798.2.bo.d.85.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.733478 + 0.266964i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.135541 - 0.768692i) q^{10} +(0.793785 - 1.37488i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.19946 + 1.84557i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(-0.733478 - 0.266964i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.02799 + 5.83005i) q^{17} -1.00000 q^{18} +(1.92019 + 3.91316i) q^{19} +0.780550 q^{20} +(-0.173648 + 0.984808i) q^{21} +(1.21615 + 1.02047i) q^{22} +(-2.61196 - 0.950677i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-3.36350 + 2.82231i) q^{25} +(-1.43560 - 2.48653i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-0.173648 - 0.984808i) q^{28} +(-0.185461 - 1.05180i) q^{29} +(0.390275 - 0.675977i) q^{30} +(2.58705 + 4.48090i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(1.49183 - 0.542981i) q^{33} +(-5.56297 - 2.02475i) q^{34} +(-0.597936 - 0.501728i) q^{35} +(0.173648 - 0.984808i) q^{36} -1.91948 q^{37} +(-4.18715 + 1.21151i) q^{38} -2.87120 q^{39} +(-0.135541 + 0.768692i) q^{40} +(-0.199173 - 0.167126i) q^{41} +(-0.939693 - 0.342020i) q^{42} +(-0.784669 + 0.285596i) q^{43} +(-1.21615 + 1.02047i) q^{44} +(-0.390275 - 0.675977i) q^{45} +(1.38980 - 2.40720i) q^{46} +(-1.30902 - 7.42384i) q^{47} +(0.173648 + 0.984808i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.19537 - 3.80249i) q^{50} +(-4.53497 + 3.80529i) q^{51} +(2.69804 - 0.982007i) q^{52} +(-5.94373 - 2.16334i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(-0.215181 + 1.22035i) q^{55} +1.00000 q^{56} +(-1.04438 + 4.23193i) q^{57} +1.06803 q^{58} +(-0.906187 + 5.13924i) q^{59} +(0.597936 + 0.501728i) q^{60} +(6.35895 + 2.31447i) q^{61} +(-4.86206 + 1.76964i) q^{62} +(-0.766044 + 0.642788i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.12056 - 1.94086i) q^{65} +(0.275679 + 1.56345i) q^{66} +(1.35802 + 7.70172i) q^{67} +(2.95999 - 5.12686i) q^{68} +(-1.38980 - 2.40720i) q^{69} +(0.597936 - 0.501728i) q^{70} +(2.22532 - 0.809951i) q^{71} +(0.939693 + 0.342020i) q^{72} +(6.81014 + 5.71438i) q^{73} +(0.333314 - 1.89032i) q^{74} -4.39074 q^{75} +(-0.466011 - 4.33392i) q^{76} +1.58757 q^{77} +(0.498578 - 2.82758i) q^{78} +(3.35911 + 2.81863i) q^{79} +(-0.733478 - 0.266964i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(0.199173 - 0.167126i) q^{82} +(-5.55161 - 9.61567i) q^{83} +(0.500000 - 0.866025i) q^{84} +(-0.802402 - 4.55065i) q^{85} +(-0.145001 - 0.822341i) q^{86} +(0.534013 - 0.924938i) q^{87} +(-0.793785 - 1.37488i) q^{88} +(5.22893 - 4.38759i) q^{89} +(0.733478 - 0.266964i) q^{90} +(-2.69804 - 0.982007i) q^{91} +(2.12929 + 1.78669i) q^{92} +(-0.898472 + 5.09549i) q^{93} +7.53836 q^{94} +(-2.45309 - 2.35760i) q^{95} -1.00000 q^{96} +(1.76622 - 10.0167i) q^{97} +(-0.766044 - 0.642788i) q^{98} +(1.49183 + 0.542981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 9 q^{5} + 6 q^{7} + 6 q^{8} + 9 q^{10} + 3 q^{11} - 6 q^{12} - 9 q^{13} + 9 q^{15} + 15 q^{17} - 12 q^{18} + 9 q^{19} - 15 q^{22} + 3 q^{23} + 3 q^{25} + 3 q^{26} - 6 q^{27} + 3 q^{29} + 6 q^{31}+ \cdots - 12 q^{99}+O(q^{100}) $ 12 * q + 9 * q^5 + 6 * q^7 + 6 * q^8 + 9 * q^10 + 3 * q^11 - 6 * q^12 - 9 * q^13 + 9 * q^15 + 15 * q^17 - 12 * q^18 + 9 * q^19 - 15 * q^22 + 3 * q^23 + 3 * q^25 + 3 * q^26 - 6 * q^27 + 3 * q^29 + 6 * q^31 - 12 * q^33 - 6 * q^34 - 9 * q^38 + 6 * q^39 + 9 * q^40 - 27 * q^41 + 6 * q^43 + 15 * q^44 - 15 * q^46 - 6 * q^47 - 6 * q^49 - 21 * q^51 + 9 * q^52 - 9 * q^53 - 9 * q^55 + 12 * q^56 - 18 * q^57 + 12 * q^58 - 24 * q^59 - 15 * q^61 - 24 * q^62 - 6 * q^64 - 24 * q^65 + 3 * q^66 + 33 * q^67 - 6 * q^68 + 15 * q^69 - 33 * q^71 + 33 * q^73 + 12 * q^74 + 9 * q^76 + 6 * q^77 + 33 * q^79 + 9 * q^80 + 27 * q^82 - 36 * q^83 + 6 * q^84 + 15 * q^85 - 6 * q^86 + 6 * q^87 - 3 * q^88 - 6 * q^89 - 9 * q^90 - 9 * q^91 + 3 * q^92 - 21 * q^93 - 18 * q^94 - 18 * q^95 - 12 * q^96 + 21 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$1$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−0.733478	+	0.266964i	−0.328021	+	0.119390i	−0.500781	−	0.865574i	$-0.666954\pi$
$5$	−0.733478	+	0.266964i	−0.328021	+	0.119390i	0.172760	+	0.984964i	$0.444732\pi$
$6$	−0.766044	+	0.642788i	−0.312736	+	0.262417i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	−0.135541	−	0.768692i	−0.0428619	−	0.243082i
$11$	0.793785	−	1.37488i	0.239335	−	0.414541i	−0.721189	−	0.692739i	$-0.756404\pi$
$11$	0.793785	−	1.37488i	0.239335	−	0.414541i	0.960524	+	0.278198i	$0.0897372\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−2.19946	+	1.84557i	−0.610022	+	0.511869i	−0.894649	−	0.446769i	$-0.852575\pi$
$13$	−2.19946	+	1.84557i	−0.610022	+	0.511869i	0.284628	+	0.958638i	$0.408130\pi$
$14$	−0.939693	+	0.342020i	−0.251143	+	0.0914087i
$15$	−0.733478	−	0.266964i	−0.189383	−	0.0689298i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−1.02799	+	5.83005i	−0.249325	+	1.41399i	0.560904	+	0.827881i	$0.310454\pi$
$17$	−1.02799	+	5.83005i	−0.249325	+	1.41399i	−0.810229	+	0.586113i	$0.800657\pi$
$18$	−1.00000			−0.235702
$19$	1.92019	+	3.91316i	0.440523	+	0.897741i
$19$	1.92019	+	3.91316i	0.440523	+	0.897741i
$20$	0.780550			0.174536
$21$	−0.173648	+	0.984808i	−0.0378931	+	0.214903i
$22$	1.21615	+	1.02047i	0.259284	+	0.217565i
$23$	−2.61196	−	0.950677i	−0.544632	−	0.198230i	0.0550278	−	0.998485i	$-0.482475\pi$
$23$	−2.61196	−	0.950677i	−0.544632	−	0.198230i	−0.599660	+	0.800255i	$0.704697\pi$
$24$	0.939693	−	0.342020i	0.191814	−	0.0698146i
$25$	−3.36350	+	2.82231i	−0.672701	+	0.564463i
$26$	−1.43560	−	2.48653i	−0.281544	−	0.487649i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	−0.173648	−	0.984808i	−0.0328164	−	0.186111i
$29$	−0.185461	−	1.05180i	−0.0344392	−	0.195314i	0.962734	−	0.270449i	$-0.0871723\pi$
$29$	−0.185461	−	1.05180i	−0.0344392	−	0.195314i	−0.997173	+	0.0751351i	$0.976061\pi$
$30$	0.390275	−	0.675977i	0.0712542	−	0.123416i
$31$	2.58705	+	4.48090i	0.464647	+	0.804793i	0.999186	−	0.0403516i	$-0.0128478\pi$
$31$	2.58705	+	4.48090i	0.464647	+	0.804793i	−0.534538	+	0.845144i	$0.679514\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	1.49183	−	0.542981i	0.259694	−	0.0945208i
$34$	−5.56297	−	2.02475i	−0.954041	−	0.347243i
$35$	−0.597936	−	0.501728i	−0.101070	−	0.0848075i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$	−1.91948			−0.315560			−0.157780	−	0.987474i	$-0.550434\pi$
$37$	−1.91948			−0.315560			−0.157780	+	0.987474i	$0.550434\pi$
$38$	−4.18715	+	1.21151i	−0.679246	+	0.196533i
$39$	−2.87120			−0.459759
$40$	−0.135541	+	0.768692i	−0.0214309	+	0.121541i
$41$	−0.199173	−	0.167126i	−0.0311056	−	0.0261007i	0.627102	−	0.778937i	$-0.284241\pi$
$41$	−0.199173	−	0.167126i	−0.0311056	−	0.0261007i	−0.658208	+	0.752836i	$0.728685\pi$
$42$	−0.939693	−	0.342020i	−0.144998	−	0.0527749i
$43$	−0.784669	+	0.285596i	−0.119661	+	0.0435530i	−0.401157	−	0.916009i	$-0.631392\pi$
$43$	−0.784669	+	0.285596i	−0.119661	+	0.0435530i	0.281496	+	0.959562i	$0.409169\pi$
$44$	−1.21615	+	1.02047i	−0.183341	+	0.153842i
$45$	−0.390275	−	0.675977i	−0.0581788	−	0.100769i
$46$	1.38980	−	2.40720i	0.204914	−	0.354922i
$47$	−1.30902	−	7.42384i	−0.190941	−	1.08288i	−0.918082	−	0.396391i	$-0.870263\pi$
$47$	−1.30902	−	7.42384i	−0.190941	−	1.08288i	0.727141	−	0.686488i	$-0.240848\pi$
$48$	0.173648	+	0.984808i	0.0250640	+	0.142145i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−2.19537	−	3.80249i	−0.310472	−	0.537754i
$51$	−4.53497	+	3.80529i	−0.635023	+	0.532848i
$52$	2.69804	−	0.982007i	0.374151	−	0.136180i
$53$	−5.94373	−	2.16334i	−0.816434	−	0.297158i	−0.100155	−	0.994972i	$-0.531934\pi$
$53$	−5.94373	−	2.16334i	−0.816434	−	0.297158i	−0.716279	+	0.697814i	$0.754156\pi$
$54$	−0.766044	−	0.642788i	−0.104245	−	0.0874723i
$55$	−0.215181	+	1.22035i	−0.0290150	+	0.164552i
$56$	1.00000			0.133631
$57$	−1.04438	+	4.23193i	−0.138331	+	0.560533i
$58$	1.06803			0.140239
$59$	−0.906187	+	5.13924i	−0.117976	+	0.669073i	0.867258	+	0.497858i	$0.165880\pi$
$59$	−0.906187	+	5.13924i	−0.117976	+	0.669073i	−0.985234	+	0.171214i	$0.945231\pi$
$60$	0.597936	+	0.501728i	0.0771932	+	0.0647728i
$61$	6.35895	+	2.31447i	0.814180	+	0.296337i	0.715349	−	0.698767i	$-0.246268\pi$
$61$	6.35895	+	2.31447i	0.814180	+	0.296337i	0.0988304	+	0.995104i	$0.468490\pi$
$62$	−4.86206	+	1.76964i	−0.617482	+	0.224745i
$63$	−0.766044	+	0.642788i	−0.0965125	+	0.0809836i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.12056	−	1.94086i	0.138988	−	0.240734i
$66$	0.275679	+	1.56345i	0.0339337	+	0.192448i
$67$	1.35802	+	7.70172i	0.165909	+	0.940914i	0.948123	+	0.317905i	$0.102979\pi$
$67$	1.35802	+	7.70172i	0.165909	+	0.940914i	−0.782214	+	0.623010i	$0.785910\pi$
$68$	2.95999	−	5.12686i	0.358952	−	0.621723i
$69$	−1.38980	−	2.40720i	−0.167312	−	0.289793i
$70$	0.597936	−	0.501728i	0.0714671	−	0.0599680i
$71$	2.22532	−	0.809951i	0.264097	−	0.0961234i	−0.206578	−	0.978430i	$-0.566233\pi$
$71$	2.22532	−	0.809951i	0.264097	−	0.0961234i	0.470675	+	0.882307i	$0.344010\pi$
$72$	0.939693	+	0.342020i	0.110744	+	0.0403075i
$73$	6.81014	+	5.71438i	0.797066	+	0.668818i	0.947483	−	0.319805i	$-0.103617\pi$
$73$	6.81014	+	5.71438i	0.797066	+	0.668818i	−0.150417	+	0.988623i	$0.548062\pi$
$74$	0.333314	−	1.89032i	0.0387469	−	0.219745i
$75$	−4.39074			−0.506999
$76$	−0.466011	−	4.33392i	−0.0534552	−	0.497134i
$77$	1.58757			0.180920
$78$	0.498578	−	2.82758i	0.0564529	−	0.320160i
$79$	3.35911	+	2.81863i	0.377929	+	0.317120i	0.811889	−	0.583812i	$-0.198439\pi$
$79$	3.35911	+	2.81863i	0.377929	+	0.317120i	−0.433960	+	0.900932i	$0.642884\pi$
$80$	−0.733478	−	0.266964i	−0.0820053	−	0.0298475i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	0.199173	−	0.167126i	0.0219950	−	0.0184560i
$83$	−5.55161	−	9.61567i	−0.609369	−	1.05546i	−0.991345	−	0.131285i	$-0.958090\pi$
$83$	−5.55161	−	9.61567i	−0.609369	−	1.05546i	0.381976	−	0.924172i	$-0.375244\pi$
$84$	0.500000	−	0.866025i	0.0545545	−	0.0944911i
$85$	−0.802402	−	4.55065i	−0.0870327	−	0.493587i
$86$	−0.145001	−	0.822341i	−0.0156359	−	0.0886753i
$87$	0.534013	−	0.924938i	0.0572522	−	0.0991637i
$88$	−0.793785	−	1.37488i	−0.0846178	−	0.146562i
$89$	5.22893	−	4.38759i	0.554265	−	0.465084i	−0.322117	−	0.946700i	$-0.604394\pi$
$89$	5.22893	−	4.38759i	0.554265	−	0.465084i	0.876382	+	0.481616i	$0.159950\pi$
$90$	0.733478	−	0.266964i	0.0773153	−	0.0281405i
$91$	−2.69804	−	0.982007i	−0.282832	−	0.102942i
$92$	2.12929	+	1.78669i	0.221994	+	0.186275i
$93$	−0.898472	+	5.09549i	−0.0931672	+	0.528377i
$94$	7.53836			0.777523
$95$	−2.45309	−	2.35760i	−0.251682	−	0.241884i
$96$	−1.00000			−0.102062
$97$	1.76622	−	10.0167i	0.179332	−	1.01704i	−0.753692	−	0.657228i	$-0.771729\pi$
$97$	1.76622	−	10.0167i	0.179332	−	1.01704i	0.933024	−	0.359815i	$-0.117160\pi$
$98$	−0.766044	−	0.642788i	−0.0773822	−	0.0649314i
$99$	1.49183	+	0.542981i	0.149934	+	0.0545716i
$100$	4.12595	−	1.50172i	0.412595	−	0.150172i
$101$	10.1796	−	8.54167i	1.01291	−	0.849928i	0.0241857	−	0.999707i	$-0.492301\pi$
$101$	10.1796	−	8.54167i	1.01291	−	0.849928i	0.988719	+	0.149779i	$0.0478562\pi$
$102$	−2.95999	−	5.12686i	−0.293083	−	0.507635i
$103$	−2.85773	+	4.94974i	−0.281581	+	0.487712i	−0.971774	−	0.235913i	$-0.924192\pi$
$103$	−2.85773	+	4.94974i	−0.281581	+	0.487712i	0.690194	+	0.723625i	$0.257525\pi$
$104$	0.498578	+	2.82758i	0.0488896	+	0.277267i
$105$	−0.135541	−	0.768692i	−0.0132275	−	0.0750167i
$106$	3.16259	−	5.47777i	0.307178	−	0.532048i
$107$	−0.0407792	−	0.0706317i	−0.00394228	−	0.00682822i	0.864048	−	0.503410i	$-0.167922\pi$
$107$	−0.0407792	−	0.0706317i	−0.00394228	−	0.00682822i	−0.867990	+	0.496582i	$0.834588\pi$
$108$	0.766044	−	0.642788i	0.0737127	−	0.0618523i
$109$	−1.95078	+	0.710024i	−0.186850	+	0.0680080i	−0.433751	−	0.901033i	$-0.642810\pi$
$109$	−1.95078	+	0.710024i	−0.186850	+	0.0680080i	0.246900	+	0.969041i	$0.420588\pi$
$110$	−1.16445	−	0.423824i	−0.111026	−	0.0404100i
$111$	−1.47041	−	1.23382i	−0.139565	−	0.117109i
$112$	−0.173648	+	0.984808i	−0.0164082	+	0.0930556i
$113$	−1.25721			−0.118268			−0.0591340	−	0.998250i	$-0.518834\pi$
$113$	−1.25721			−0.118268			−0.0591340	+	0.998250i	$0.518834\pi$
$114$	−3.98629	−	1.76338i	−0.373350	−	0.165156i
$115$	2.16961			0.202318
$116$	−0.185461	+	1.05180i	−0.0172196	+	0.0976572i
$117$	−2.19946	−	1.84557i	−0.203341	−	0.170623i
$118$	−4.90381	−	1.78484i	−0.451432	−	0.164308i
$119$	−5.56297	+	2.02475i	−0.509956	+	0.185609i
$120$	−0.597936	+	0.501728i	−0.0545839	+	0.0458013i
$121$	4.23981	+	7.34357i	0.385437	+	0.667597i
$122$	−3.38352	+	5.86044i	−0.306330	+	0.530579i
$123$	−0.0451489	−	0.256052i	−0.00407094	−	0.0230874i
$124$	−0.898472	−	5.09549i	−0.0806851	−	0.457588i
$125$	3.66497	−	6.34792i	0.327805	−	0.567775i
$126$	−0.500000	−	0.866025i	−0.0445435	−	0.0771517i
$127$	4.96514	−	4.16625i	0.440585	−	0.369695i	−0.395343	−	0.918534i	$-0.629374\pi$
$127$	4.96514	−	4.16625i	0.440585	−	0.369695i	0.835928	+	0.548839i	$0.184930\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−0.784669	−	0.285596i	−0.0690862	−	0.0251453i
$130$	1.71679	+	1.44056i	0.150573	+	0.126346i
$131$	−3.25468	+	18.4582i	−0.284363	+	1.61270i	0.423191	+	0.906040i	$0.360910\pi$
$131$	−3.25468	+	18.4582i	−0.284363	+	1.61270i	−0.707554	+	0.706660i	$0.750201\pi$
$132$	−1.58757			−0.138180
$133$	−2.42880	+	3.61952i	−0.210604	+	0.313852i
$134$	−7.82053			−0.675591
$135$	0.135541	−	0.768692i	0.0116655	−	0.0661585i
$136$	4.53497	+	3.80529i	0.388871	+	0.326301i
$137$	−4.11553	−	1.49793i	−0.351614	−	0.127977i	0.160174	−	0.987089i	$-0.448794\pi$
$137$	−4.11553	−	1.49793i	−0.351614	−	0.127977i	−0.511788	+	0.859112i	$0.671017\pi$
$138$	2.61196	−	0.950677i	0.222345	−	0.0809270i
$139$	0.460504	−	0.386408i	0.0390594	−	0.0327747i	−0.623049	−	0.782183i	$-0.714106\pi$
$139$	0.460504	−	0.386408i	0.0390594	−	0.0327747i	0.662108	+	0.749408i	$0.269662\pi$
$140$	0.390275	+	0.675977i	0.0329843	+	0.0571304i
$141$	3.76918	−	6.52842i	0.317422	−	0.549792i
$142$	0.411223	+	2.33216i	0.0345090	+	0.195710i
$143$	0.791528	+	4.48898i	0.0661909	+	0.375387i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.416824	+	0.721960i	0.0346154	+	0.0599555i
$146$	−6.81014	+	5.71438i	−0.563611	+	0.472926i
$147$	−0.939693	+	0.342020i	−0.0775045	+	0.0282093i
$148$	1.80372	+	0.656500i	0.148265	+	0.0539640i
$149$	15.0186	+	12.6021i	1.23037	+	1.03240i	0.998215	+	0.0597234i	$0.0190219\pi$
$149$	15.0186	+	12.6021i	1.23037	+	1.03240i	0.232154	+	0.972679i	$0.425423\pi$
$150$	0.762444	−	4.32404i	0.0622533	−	0.353056i
$151$	14.8027			1.20463			0.602314	−	0.798259i	$-0.294245\pi$
$151$	14.8027			1.20463			0.602314	+	0.798259i	$0.294245\pi$
$152$	4.34900	+	0.293645i	0.352750	+	0.0238178i
$153$	−5.91999			−0.478603
$154$	−0.275679	+	1.56345i	−0.0222148	+	0.125986i
$155$	−3.09378	−	2.59599i	−0.248498	−	0.208515i
$156$	2.69804	+	0.982007i	0.216016	+	0.0786235i
$157$	13.0050	−	4.73344i	1.03791	−	0.377770i	0.233825	−	0.972279i	$-0.424876\pi$
$157$	13.0050	−	4.73344i	1.03791	−	0.377770i	0.804089	+	0.594509i	$0.202654\pi$
$158$	−3.35911	+	2.81863i	−0.267236	+	0.224238i
$159$	−3.16259	−	5.47777i	−0.250810	−	0.434415i
$160$	0.390275	−	0.675977i	0.0308540	−	0.0534406i
$161$	−0.482671	−	2.73737i	−0.0380398	−	0.215735i
$162$	−0.173648	−	0.984808i	−0.0136431	−	0.0773738i
$163$	5.41154	−	9.37307i	0.423865	−	0.734155i	−0.572449	−	0.819940i	$-0.694006\pi$
$163$	5.41154	−	9.37307i	0.423865	−	0.734155i	0.996314	+	0.0857850i	$0.0273398\pi$
$164$	0.130001	+	0.225168i	0.0101514	+	0.0175827i
$165$	−0.949266	+	0.796528i	−0.0739002	+	0.0620097i
$166$	10.4336	−	3.79753i	0.809806	−	0.294745i
$167$	5.29178	+	1.92605i	0.409490	+	0.149042i	0.538548	−	0.842595i	$-0.318973\pi$
$167$	5.29178	+	1.92605i	0.409490	+	0.149042i	−0.129058	+	0.991637i	$0.541195\pi$
$168$	0.766044	+	0.642788i	0.0591016	+	0.0495921i
$169$	−0.825910	+	4.68397i	−0.0635316	+	0.360305i
$170$	4.62085			0.354403
$171$	−3.52028	+	2.57054i	−0.269202	+	0.196574i
$172$	0.835027			0.0636702
$173$	3.04184	−	17.2511i	0.231267	−	1.31158i	−0.619068	−	0.785337i	$-0.712490\pi$
$173$	3.04184	−	17.2511i	0.231267	−	1.31158i	0.850335	−	0.526242i	$-0.176399\pi$
$174$	0.818155	+	0.686514i	0.0620242	+	0.0520445i
$175$	−4.12595	−	1.50172i	−0.311892	−	0.113520i
$176$	1.49183	−	0.542981i	0.112451	−	0.0409287i
$177$	−3.99762	+	3.35440i	−0.300480	+	0.252132i
$178$	3.41294	+	5.91139i	0.255811	+	0.443077i
$179$	−5.69539	+	9.86470i	−0.425693	+	0.737322i	−0.996485	−	0.0837727i	$-0.973303\pi$
$179$	−5.69539	+	9.86470i	−0.425693	+	0.737322i	0.570792	+	0.821095i	$0.306636\pi$
$180$	0.135541	+	0.768692i	0.0101026	+	0.0572949i
$181$	−1.17719	−	6.67615i	−0.0874995	−	0.496234i	−0.996789	−	0.0800706i	$-0.974485\pi$
$181$	−1.17719	−	6.67615i	−0.0874995	−	0.496234i	0.909290	−	0.416164i	$-0.136626\pi$
$182$	1.43560	−	2.48653i	0.106414	−	0.184314i
$183$	3.38352	+	5.86044i	0.250117	+	0.433216i
$184$	−2.12929	+	1.78669i	−0.156974	+	0.131716i
$185$	1.40789	−	0.512431i	0.103510	−	0.0376747i
$186$	−4.86206	−	1.76964i	−0.356503	−	0.129757i
$187$	7.19959	+	6.04117i	0.526486	+	0.441774i
$188$	−1.30902	+	7.42384i	−0.0954703	+	0.541439i
$189$	−1.00000			−0.0727393
$190$	2.74775	−	2.00643i	0.199343	−	0.145562i
$191$	0.728650			0.0527233			0.0263616	−	0.999652i	$-0.491608\pi$
$191$	0.728650			0.0527233			0.0263616	+	0.999652i	$0.491608\pi$
$192$	0.173648	−	0.984808i	0.0125320	−	0.0710724i
$193$	2.53275	+	2.12523i	0.182311	+	0.152977i	0.729376	−	0.684113i	$-0.239811\pi$
$193$	2.53275	+	2.12523i	0.182311	+	0.152977i	−0.547065	+	0.837090i	$0.684255\pi$
$194$	9.55783	+	3.47877i	0.686212	+	0.249761i
$195$	2.10596	−	0.766506i	0.150811	−	0.0548906i
$196$	0.766044	−	0.642788i	0.0547175	−	0.0459134i
$197$	−10.3809	−	17.9803i	−0.739609	−	1.28104i	−0.952671	−	0.304002i	$-0.901677\pi$
$197$	−10.3809	−	17.9803i	−0.739609	−	1.28104i	0.213062	−	0.977039i	$-0.431656\pi$
$198$	−0.793785	+	1.37488i	−0.0564118	+	0.0977082i
$199$	3.65788	+	20.7449i	0.259300	+	1.47057i	0.784788	+	0.619764i	$0.212772\pi$
$199$	3.65788	+	20.7449i	0.259300	+	1.47057i	−0.525488	+	0.850801i	$0.676117\pi$
$200$	0.762444	+	4.32404i	0.0539129	+	0.305756i
$201$	−3.91026	+	6.77278i	−0.275809	+	0.477715i
$202$	6.64424	+	11.5082i	0.467487	+	0.809712i
$203$	0.818155	−	0.686514i	0.0574232	−	0.0481838i
$204$	5.56297	−	2.02475i	0.389486	−	0.141761i
$205$	0.190706	+	0.0694112i	0.0133195	+	0.00484789i
$206$	−4.37830	−	3.67383i	−0.305051	−	0.255968i
$207$	0.482671	−	2.73737i	0.0335480	−	0.190260i
$208$	−2.87120			−0.199082
$209$	6.90434	+	0.466182i	0.477583	+	0.0322465i
$210$	0.780550			0.0538631
$211$	4.21965	−	23.9308i	0.290492	−	1.64746i	−0.394486	−	0.918902i	$-0.629077\pi$
$211$	4.21965	−	23.9308i	0.290492	−	1.64746i	0.684979	−	0.728563i	$-0.259811\pi$
$212$	4.84537	+	4.06575i	0.332782	+	0.279237i
$213$	2.22532	+	0.809951i	0.152476	+	0.0554969i
$214$	0.0766399	−	0.0278946i	0.00523899	−	0.00190684i
$215$	0.499293	−	0.418957i	0.0340515	−	0.0285726i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	−2.58705	+	4.48090i	−0.175620	+	0.304183i
$218$	−0.360489	−	2.04443i	−0.0244154	−	0.138467i
$219$	1.54373	+	8.75494i	0.104316	+	0.591604i
$220$	0.619589	−	1.07316i	0.0417727	−	0.0723524i
$221$	−8.49872	−	14.7202i	−0.571686	−	0.990189i
$222$	1.47041	−	1.23382i	0.0986871	−	0.0828083i
$223$	15.9435	−	5.80296i	1.06766	−	0.388595i	0.252357	−	0.967634i	$-0.418794\pi$
$223$	15.9435	−	5.80296i	1.06766	−	0.388595i	0.815300	+	0.579039i	$0.196572\pi$
$224$	−0.939693	−	0.342020i	−0.0627859	−	0.0228522i
$225$	−3.36350	−	2.82231i	−0.224234	−	0.188154i
$226$	0.218312	−	1.23811i	0.0145219	−	0.0823576i
$227$	23.4540			1.55670			0.778348	−	0.627833i	$-0.216058\pi$
$227$	23.4540			1.55670			0.778348	+	0.627833i	$0.216058\pi$
$228$	2.42880	−	3.61952i	0.160851	−	0.239709i
$229$	3.36222			0.222182			0.111091	−	0.993810i	$-0.464566\pi$
$229$	3.36222			0.222182			0.111091	+	0.993810i	$0.464566\pi$
$230$	−0.376749	+	2.13665i	−0.0248421	+	0.140887i
$231$	1.21615	+	1.02047i	0.0800167	+	0.0671420i
$232$	−1.00362	−	0.365286i	−0.0658906	−	0.0239822i
$233$	3.75562	−	1.36693i	0.246039	−	0.0895508i	−0.216057	−	0.976381i	$-0.569320\pi$
$233$	3.75562	−	1.36693i	0.246039	−	0.0895508i	0.462096	+	0.886830i	$0.347098\pi$
$234$	2.19946	−	1.84557i	0.143783	−	0.120649i
$235$	2.94204	+	5.09576i	0.191917	+	0.332411i
$236$	2.60926	−	4.51938i	0.169849	−	0.294186i
$237$	0.761448	+	4.31839i	0.0494614	+	0.280509i
$238$	−1.02799	−	5.83005i	−0.0666350	−	0.377906i
$239$	−12.2290	+	21.1812i	−0.791025	+	1.37010i	0.134308	+	0.990940i	$0.457119\pi$
$239$	−12.2290	+	21.1812i	−0.791025	+	1.37010i	−0.925333	+	0.379156i	$0.876214\pi$
$240$	−0.390275	−	0.675977i	−0.0251922	−	0.0436341i
$241$	5.61168	−	4.70876i	0.361480	−	0.303318i	−0.443900	−	0.896076i	$-0.646406\pi$
$241$	5.61168	−	4.70876i	0.361480	−	0.303318i	0.805380	+	0.592758i	$0.201961\pi$
$242$	−7.96824	+	2.90020i	−0.512218	+	0.186432i
$243$	−0.939693	−	0.342020i	−0.0602813	−	0.0219406i
$244$	−5.18386	−	4.34978i	−0.331863	−	0.278466i
$245$	0.135541	−	0.768692i	0.00865941	−	0.0491099i
$246$	0.260002			0.0165771
$247$	−11.4454	−	5.06301i	−0.728254	−	0.322152i
$248$	5.17409			0.328555
$249$	1.92805	−	10.9345i	0.122185	−	0.692948i
$250$	5.61507	+	4.71160i	0.355128	+	0.297988i
$251$	10.0048	+	3.64145i	0.631498	+	0.229846i	0.637883	−	0.770133i	$-0.279810\pi$
$251$	10.0048	+	3.64145i	0.631498	+	0.229846i	−0.00638522	+	0.999980i	$0.502032\pi$
$252$	0.939693	−	0.342020i	0.0591951	−	0.0215452i
$253$	−3.38040	+	2.83649i	−0.212524	+	0.178329i
$254$	3.24077	+	5.61317i	0.203344	+	0.352202i
$255$	2.31042	−	4.00177i	0.144684	−	0.250601i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−1.71950	−	9.75178i	−0.107260	−	0.608299i	−0.990294	−	0.138990i	$-0.955614\pi$
$257$	−1.71950	−	9.75178i	−0.107260	−	0.608299i	0.883034	−	0.469309i	$-0.155497\pi$
$258$	0.417513	−	0.723155i	0.0259933	−	0.0450216i
$259$	−0.959739	−	1.66232i	−0.0596353	−	0.103291i
$260$	−1.71679	+	1.44056i	−0.106471	+	0.0893398i
$261$	1.00362	−	0.365286i	0.0621223	−	0.0226107i
$262$	−17.6126	−	6.41046i	−1.08811	−	0.396040i
$263$	−9.97471	−	8.36978i	−0.615067	−	0.516103i	0.281181	−	0.959655i	$-0.409274\pi$
$263$	−9.97471	−	8.36978i	−0.615067	−	0.516103i	−0.896249	+	0.443552i	$0.853718\pi$
$264$	0.275679	−	1.56345i	0.0169668	−	0.0962238i
$265$	4.93713			0.303285
$266$	−3.14277	−	3.02043i	−0.192696	−	0.185194i
$267$	6.82588			0.417737
$268$	1.35802	−	7.70172i	0.0829543	−	0.470457i
$269$	21.2042	+	17.7924i	1.29284	+	1.08482i	0.991335	+	0.131357i	$0.0419334\pi$
$269$	21.2042	+	17.7924i	1.29284	+	1.08482i	0.301505	+	0.953465i	$0.402511\pi$
$270$	0.733478	+	0.266964i	0.0446380	+	0.0162469i
$271$	2.48263	−	0.903602i	0.150809	−	0.0548899i	−0.265513	−	0.964107i	$-0.585541\pi$
$271$	2.48263	−	0.903602i	0.150809	−	0.0548899i	0.416322	+	0.909217i	$0.363319\pi$
$272$	−4.53497	+	3.80529i	−0.274973	+	0.230730i
$273$	−1.43560	−	2.48653i	−0.0868864	−	0.150492i
$274$	2.18983	−	3.79290i	0.132292	−	0.229137i
$275$	1.21043	+	6.86471i	0.0729919	+	0.413957i
$276$	0.482671	+	2.73737i	0.0290534	+	0.164770i
$277$	7.08684	−	12.2748i	0.425807	−	0.737519i	−0.570689	−	0.821167i	$-0.693324\pi$
$277$	7.08684	−	12.2748i	0.425807	−	0.737519i	0.996495	+	0.0836476i	$0.0266570\pi$
$278$	0.300572	+	0.520607i	0.0180271	+	0.0312239i
$279$	−3.96358	+	3.32584i	−0.237294	+	0.199113i
$280$	−0.733478	+	0.266964i	−0.0438337	+	0.0159541i
$281$	−13.7786	−	5.01500i	−0.821962	−	0.299170i	−0.103407	−	0.994639i	$-0.532974\pi$
$281$	−13.7786	−	5.01500i	−0.821962	−	0.299170i	−0.718556	+	0.695469i	$0.755197\pi$
$282$	5.77472	+	4.84557i	0.343880	+	0.288549i
$283$	−4.14626	+	23.5146i	−0.246469	+	1.39780i	0.570586	+	0.821238i	$0.306716\pi$
$283$	−4.14626	+	23.5146i	−0.246469	+	1.39780i	−0.817055	+	0.576560i	$0.804395\pi$
$284$	−2.36814			−0.140523
$285$	−0.363745	−	3.38284i	−0.0215464	−	0.200382i
$286$	−4.55823			−0.269534
$287$	0.0451489	−	0.256052i	0.00266506	−	0.0151143i
$288$	−0.766044	−	0.642788i	−0.0451396	−	0.0378766i
$289$	−16.9579	−	6.17218i	−0.997524	−	0.363069i
$290$	−0.783373	+	0.285124i	−0.0460012	+	0.0167431i
$291$	7.79162	−	6.53794i	0.456753	−	0.383261i
$292$	−4.44500	−	7.69897i	−0.260124	−	0.450548i
$293$	9.73190	−	16.8561i	0.568543	−	0.984746i	−0.428167	−	0.903700i	$-0.640840\pi$
$293$	9.73190	−	16.8561i	0.568543	−	0.984746i	0.996710	−	0.0810464i	$-0.0258262\pi$
$294$	−0.173648	−	0.984808i	−0.0101274	−	0.0574352i
$295$	−0.707325	−	4.01144i	−0.0411821	−	0.233555i
$296$	−0.959739	+	1.66232i	−0.0557837	+	0.0966202i
$297$	0.793785	+	1.37488i	0.0460601	+	0.0797784i
$298$	−15.0186	+	12.6021i	−0.870002	+	0.730019i
$299$	7.49946	−	2.72958i	0.433705	−	0.157856i
$300$	4.12595	+	1.50172i	0.238212	+	0.0867020i
$301$	−0.639668	−	0.536745i	−0.0368698	−	0.0309375i
$302$	−2.57047	+	14.5778i	−0.147914	+	0.838860i
$303$	13.2885			0.763404
$304$	−1.04438	+	4.23193i	−0.0598993	+	0.242718i
$305$	−5.28202			−0.302448
$306$	1.02799	−	5.83005i	0.0587666	−	0.333282i
$307$	−19.2538	−	16.1559i	−1.09887	−	0.922063i	−0.101523	−	0.994833i	$-0.532372\pi$
$307$	−19.2538	−	16.1559i	−1.09887	−	0.922063i	−0.997349	+	0.0727699i	$0.976816\pi$
$308$	−1.49183	−	0.542981i	−0.0850048	−	0.0309392i
$309$	−5.37078	+	1.95480i	−0.305533	+	0.111205i
$310$	3.09378	−	2.59599i	0.175715	−	0.147442i
$311$	−6.51118	−	11.2777i	−0.369215	−	0.639500i	0.620228	−	0.784422i	$-0.287040\pi$
$311$	−6.51118	−	11.2777i	−0.369215	−	0.639500i	−0.989443	+	0.144922i	$0.953707\pi$
$312$	−1.43560	+	2.48653i	−0.0812748	+	0.140772i
$313$	−0.600614	−	3.40625i	−0.0339487	−	0.192533i	0.963117	−	0.269083i	$-0.0867206\pi$
$313$	−0.600614	−	3.40625i	−0.0339487	−	0.192533i	−0.997066	+	0.0765502i	$0.975609\pi$
$314$	2.40323	+	13.6294i	0.135622	+	0.769152i
$315$	0.390275	−	0.675977i	0.0219895	−	0.0380870i
$316$	−2.19250	−	3.79753i	−0.123338	−	0.213628i
$317$	5.61174	−	4.70881i	0.315186	−	0.264473i	−0.471445	−	0.881895i	$-0.656268\pi$
$317$	5.61174	−	4.70881i	0.315186	−	0.264473i	0.786632	+	0.617422i	$0.211823\pi$
$318$	5.94373	−	2.16334i	0.333308	−	0.121314i
$319$	−1.59331	−	0.579918i	−0.0892083	−	0.0324692i
$320$	0.597936	+	0.501728i	0.0334257	+	0.0280475i
$321$	0.0141625	−	0.0803194i	0.000790473	−	0.00448299i
$322$	2.77959			0.154901
$323$	−24.7879	+	7.17211i	−1.37923	+	0.399067i
$324$	1.00000			0.0555556
$325$	2.18913	−	12.4152i	0.121431	−	0.688669i
$326$	8.29097	+	6.95695i	0.459194	+	0.385310i
$327$	−1.95078	−	0.710024i	−0.107878	−	0.0392644i
$328$	−0.244322	+	0.0889260i	−0.0134904	+	0.00491012i
$329$	5.77472	−	4.84557i	0.318371	−	0.267145i
$330$	−0.619589	−	1.07316i	−0.0341073	−	0.0590755i
$331$	−10.7027	+	18.5377i	−0.588275	+	1.01892i	0.406183	+	0.913792i	$0.366859\pi$
$331$	−10.7027	+	18.5377i	−0.588275	+	1.01892i	−0.994458	+	0.105131i	$0.966474\pi$
$332$	1.92805	+	10.9345i	0.105816	+	0.600111i
$333$	−0.333314	−	1.89032i	−0.0182655	−	0.103589i
$334$	−2.81570	+	4.87693i	−0.154068	+	0.266854i
$335$	−3.05216	−	5.28649i	−0.166757	−	0.288832i
$336$	−0.766044	+	0.642788i	−0.0417912	+	0.0350669i
$337$	−15.1711	+	5.52183i	−0.826423	+	0.300794i	−0.720390	−	0.693569i	$-0.756037\pi$
$337$	−15.1711	+	5.52183i	−0.826423	+	0.300794i	−0.106033	+	0.994363i	$0.533815\pi$
$338$	−4.46939	−	1.62673i	−0.243103	−	0.0884822i
$339$	−0.963076	−	0.808117i	−0.0523071	−	0.0438909i
$340$	−0.802402	+	4.55065i	−0.0435163	+	0.246793i
$341$	8.21423			0.444826
$342$	−1.92019	−	3.91316i	−0.103832	−	0.211600i
$343$	−1.00000			−0.0539949
$344$	−0.145001	+	0.822341i	−0.00781793	+	0.0443377i
$345$	1.66202	+	1.39460i	0.0894802	+	0.0750828i
$346$	16.4608	+	5.99125i	0.884940	+	0.322092i
$347$	4.16625	−	1.51639i	0.223656	−	0.0814042i	−0.227762	−	0.973717i	$-0.573141\pi$
$347$	4.16625	−	1.51639i	0.223656	−	0.0814042i	0.451418	+	0.892313i	$0.350918\pi$
$348$	−0.818155	+	0.686514i	−0.0438577	+	0.0368010i
$349$	−8.74412	−	15.1453i	−0.468062	−	0.810707i	0.531272	−	0.847202i	$-0.321714\pi$
$349$	−8.74412	−	15.1453i	−0.468062	−	0.810707i	−0.999334	+	0.0364940i	$0.988381\pi$
$350$	2.19537	−	3.80249i	0.117347	−	0.203252i
$351$	−0.498578	−	2.82758i	−0.0266121	−	0.150925i
$352$	0.275679	+	1.56345i	0.0146937	+	0.0833322i
$353$	−5.90895	+	10.2346i	−0.314502	+	0.544733i	−0.979331	−	0.202262i	$-0.935171\pi$
$353$	−5.90895	+	10.2346i	−0.314502	+	0.544733i	0.664830	+	0.746995i	$0.268504\pi$
$354$	−2.60926	−	4.51938i	−0.138681	−	0.240202i
$355$	−1.41600	+	1.18816i	−0.0751532	+	0.0630610i
$356$	−6.41423	+	2.33459i	−0.339954	+	0.123733i
$357$	−5.56297	−	2.02475i	−0.294423	−	0.107161i
$358$	−8.72584	−	7.32185i	−0.461175	−	0.386972i
$359$	−4.89230	+	27.7456i	−0.258206	+	1.46436i	0.529503	+	0.848308i	$0.322379\pi$
$359$	−4.89230	+	27.7456i	−0.258206	+	1.46436i	−0.787708	+	0.616048i	$0.788733\pi$
$360$	−0.780550			−0.0411386
$361$	−11.6257	+	15.0281i	−0.611879	+	0.790951i
$362$	6.77914			0.356304
$363$	−1.47247	+	8.35080i	−0.0772847	+	0.438303i
$364$	2.19946	+	1.84557i	0.115283	+	0.0967341i
$365$	−6.52062	−	2.37331i	−0.341305	−	0.124225i
$366$	−6.35895	+	2.31447i	−0.332387	+	0.120979i
$367$	−13.3950	+	11.2397i	−0.699213	+	0.586710i	−0.921550	−	0.388260i	$-0.873076\pi$
$367$	−13.3950	+	11.2397i	−0.699213	+	0.586710i	0.222336	+	0.974970i	$0.428632\pi$
$368$	−1.38980	−	2.40720i	−0.0724482	−	0.125484i
$369$	0.130001	−	0.225168i	0.00676759	−	0.0117218i
$370$	0.260168	+	1.47549i	0.0135255	+	0.0767069i
$371$	−1.09836	−	6.22909i	−0.0570238	−	0.323398i
$372$	2.58705	−	4.48090i	0.134132	−	0.232324i
$373$	−17.9160	−	31.0314i	−0.927654	−	1.60674i	−0.787236	−	0.616652i	$-0.788489\pi$
$373$	−17.9160	−	31.0314i	−0.927654	−	1.60674i	−0.140419	−	0.990092i	$-0.544845\pi$
$374$	−7.19959	+	6.04117i	−0.372282	+	0.312381i
$375$	6.88790	−	2.50699i	0.355689	−	0.129460i
$376$	−7.08375	−	2.57827i	−0.365316	−	0.132964i
$377$	2.34909	+	1.97112i	0.120984	+	0.101518i
$378$	0.173648	−	0.984808i	0.00893150	−	0.0506530i
$379$	−26.4928			−1.36084			−0.680422	−	0.732820i	$-0.738204\pi$
$379$	−26.4928			−1.36084			−0.680422	+	0.732820i	$0.738204\pi$
$380$	1.49881	+	3.05442i	0.0768872	+	0.156689i
$381$	6.48153			0.332059
$382$	−0.126529	+	0.717580i	−0.00647378	+	0.0367146i
$383$	2.70089	+	2.26632i	0.138009	+	0.115803i	0.709179	−	0.705028i	$-0.249066\pi$
$383$	2.70089	+	2.26632i	0.138009	+	0.115803i	−0.571170	+	0.820832i	$0.693510\pi$
$384$	0.939693	+	0.342020i	0.0479535	+	0.0174536i
$385$	−1.16445	+	0.423824i	−0.0593457	+	0.0216001i
$386$	−2.53275	+	2.12523i	−0.128913	+	0.108171i
$387$	−0.417513	−	0.723155i	−0.0212234	−	0.0367600i
$388$	−5.08562	+	8.80855i	−0.258183	+	0.447186i
$389$	−1.98526	−	11.2590i	−0.100657	−	0.570853i	−0.992866	−	0.119232i	$-0.961957\pi$
$389$	−1.98526	−	11.2590i	−0.100657	−	0.570853i	0.892210	−	0.451622i	$-0.149154\pi$
$390$	0.389165	+	2.20707i	0.0197062	+	0.111759i
$391$	8.22758	−	14.2506i	0.416087	−	0.720683i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$	−14.3579	+	12.0477i	−0.724262	+	0.607728i
$394$	19.5097	−	7.10096i	0.982886	−	0.357741i
$395$	−3.21630	−	1.17064i	−0.161830	−	0.0589012i
$396$	−1.21615	−	1.02047i	−0.0611138	−	0.0512806i
$397$	−5.22009	+	29.6046i	−0.261989	+	1.48581i	0.515485	+	0.856899i	$0.327612\pi$
$397$	−5.22009	+	29.6046i	−0.261989	+	1.48581i	−0.777474	+	0.628915i	$0.783499\pi$
$398$	−21.0649			−1.05589
$399$	−4.18715	+	1.21151i	−0.209620	+	0.0606513i
$400$	−4.39074			−0.219537
$401$	3.24643	−	18.4114i	0.162119	−	0.919421i	−0.789867	−	0.613278i	$-0.789850\pi$
$401$	3.24643	−	18.4114i	0.162119	−	0.919421i	0.951986	−	0.306143i	$-0.0990385\pi$
$402$	−5.99087	−	5.02694i	−0.298798	−	0.250721i
$403$	−13.9599	−	5.08100i	−0.695393	−	0.253102i
$404$	−12.4871	+	4.54493i	−0.621256	+	0.226119i
$405$	0.597936	−	0.501728i	0.0297117	−	0.0249311i
$406$	0.534013	+	0.924938i	0.0265026	+	0.0459039i
$407$	−1.52365	+	2.63904i	−0.0755246	+	0.130813i
$408$	1.02799	+	5.83005i	0.0508933	+	0.288630i
$409$	1.28619	+	7.29434i	0.0635979	+	0.360682i	0.999954	+	0.00962915i	$0.00306510\pi$
$409$	1.28619	+	7.29434i	0.0635979	+	0.360682i	−0.936356	+	0.351053i	$0.885824\pi$
$410$	−0.101472	+	0.175755i	−0.00501137	+	0.00867994i
$411$	−2.18983	−	3.79290i	−0.108016	−	0.187090i
$412$	4.37830	−	3.67383i	0.215703	−	0.180997i
$413$	−4.90381	+	1.78484i	−0.241301	+	0.0878263i
$414$	2.61196	+	0.950677i	0.128371	+	0.0467232i
$415$	6.63902	+	5.57080i	0.325897	+	0.273460i
$416$	0.498578	−	2.82758i	0.0244448	−	0.138633i
$417$	0.601145			0.0294382
$418$	−1.65803	+	6.71849i	−0.0810967	+	0.328612i
$419$	30.5420			1.49208			0.746038	−	0.665903i	$-0.231954\pi$
$419$	30.5420			1.49208			0.746038	+	0.665903i	$0.231954\pi$
$420$	−0.135541	+	0.768692i	−0.00661373	+	0.0375083i
$421$	−11.0839	−	9.30050i	−0.540196	−	0.453278i	0.331409	−	0.943487i	$-0.392476\pi$
$421$	−11.0839	−	9.30050i	−0.540196	−	0.453278i	−0.871605	+	0.490209i	$0.836921\pi$
$422$	22.8345	+	8.31108i	1.11157	+	0.404577i
$423$	7.08375	−	2.57827i	0.344424	−	0.125360i
$424$	−4.84537	+	4.06575i	−0.235312	+	0.197450i
$425$	−12.9966	−	22.5107i	−0.630426	−	1.09193i
$426$	−1.18407	+	2.05087i	−0.0573683	+	0.0993648i
$427$	1.17509	+	6.66424i	0.0568664	+	0.322505i
$428$	0.0141625	+	0.0803194i	0.000684569	+	0.00388239i
$429$	−2.27911	+	3.94754i	−0.110037	+	0.190589i
$430$	0.325890	+	0.564459i	0.0157158	+	0.0272206i
$431$	−4.64156	+	3.89473i	−0.223576	+	0.187603i	−0.747695	−	0.664043i	$-0.768839\pi$
$431$	−4.64156	+	3.89473i	−0.223576	+	0.187603i	0.524119	+	0.851645i	$0.324395\pi$
$432$	−0.939693	+	0.342020i	−0.0452110	+	0.0164555i
$433$	−28.8443	−	10.4985i	−1.38617	−	0.504524i	−0.462126	−	0.886814i	$-0.652913\pi$
$433$	−28.8443	−	10.4985i	−1.38617	−	0.504524i	−0.924042	+	0.382290i	$0.875136\pi$
$434$	−3.96358	−	3.32584i	−0.190258	−	0.159646i
$435$	−0.144761	+	0.820983i	−0.00694078	+	0.0393631i
$436$	2.07597			0.0994211
$437$	−1.29532	−	12.0465i	−0.0619637	−	0.576264i
$438$	−8.89000			−0.424781
$439$	−5.72285	+	32.4559i	−0.273137	+	1.54903i	0.471682	+	0.881769i	$0.343647\pi$
$439$	−5.72285	+	32.4559i	−0.273137	+	1.54903i	−0.744819	+	0.667266i	$0.767464\pi$
$440$	0.949266	+	0.796528i	0.0452545	+	0.0379730i
$441$	−0.939693	−	0.342020i	−0.0447473	−	0.0162867i
$442$	15.9724	−	5.81347i	0.759728	−	0.276519i
$443$	−3.02720	+	2.54013i	−0.143827	+	0.120685i	−0.711862	−	0.702319i	$-0.752148\pi$
$443$	−3.02720	+	2.54013i	−0.143827	+	0.120685i	0.568036	+	0.823004i	$0.307704\pi$
$444$	0.959739	+	1.66232i	0.0455472	+	0.0788900i
$445$	−2.66397	+	4.61414i	−0.126284	+	0.218731i
$446$	2.94624	+	16.7090i	0.139509	+	0.791192i
$447$	3.40443	+	19.3075i	0.161024	+	0.913213i
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	0.667755	+	1.15659i	0.0315133	+	0.0545826i	0.881352	−	0.472460i	$-0.156634\pi$
$449$	0.667755	+	1.15659i	0.0315133	+	0.0545826i	−0.849839	+	0.527043i	$0.823301\pi$
$450$	3.36350	−	2.82231i	0.158557	−	0.133045i
$451$	−0.387878	+	0.141176i	−0.0182645	+	0.00664773i
$452$	1.18139	+	0.429990i	0.0555678	+	0.0202250i
$453$	11.3395	+	9.51501i	0.532778	+	0.447054i
$454$	−4.07274	+	23.0977i	−0.191143	+	1.08403i
$455$	2.24111			0.105065
$456$	3.14277	+	3.02043i	0.147174	+	0.141444i
$457$	16.7969			0.785726			0.392863	−	0.919597i	$-0.371485\pi$
$457$	16.7969			0.785726			0.392863	+	0.919597i	$0.371485\pi$
$458$	−0.583844	+	3.31114i	−0.0272812	+	0.154719i
$459$	−4.53497	−	3.80529i	−0.211674	−	0.177616i
$460$	−2.03877	−	0.742052i	−0.0950581	−	0.0345983i
$461$	25.7024	−	9.35492i	1.19708	−	0.435702i	0.334877	−	0.942262i	$-0.391305\pi$
$461$	25.7024	−	9.35492i	1.19708	−	0.435702i	0.862205	+	0.506560i	$0.169083\pi$
$462$	−1.21615	+	1.02047i	−0.0565804	+	0.0474766i
$463$	−7.22492	−	12.5139i	−0.335770	−	0.581571i	0.647862	−	0.761758i	$-0.275663\pi$
$463$	−7.22492	−	12.5139i	−0.335770	−	0.581571i	−0.983633	+	0.180186i	$0.942330\pi$
$464$	0.534013	−	0.924938i	0.0247909	−	0.0429391i
$465$	−0.701303	−	3.97728i	−0.0325221	−	0.184442i
$466$	0.694011	+	3.93593i	0.0321494	+	0.182328i
$467$	−15.0439	+	26.0567i	−0.696147	+	1.20576i	0.273646	+	0.961831i	$0.411770\pi$
$467$	−15.0439	+	26.0567i	−0.696147	+	1.20576i	−0.969793	+	0.243931i	$0.921563\pi$
$468$	1.43560	+	2.48653i	0.0663606	+	0.114940i
$469$	−5.99087	+	5.02694i	−0.276633	+	0.232122i
$470$	−5.52922	+	2.01247i	−0.255044	+	0.0928284i
$471$	13.0050	+	4.73344i	0.599240	+	0.218105i
$472$	3.99762	+	3.35440i	0.184005	+	0.154399i
$473$	−0.230199	+	1.30552i	−0.0105846	+	0.0600280i
$474$	−4.38501			−0.201410
$475$	−17.5028	−	7.74255i	−0.803082	−	0.355252i
$476$	5.91999			0.271342
$477$	1.09836	−	6.22909i	0.0502903	−	0.285210i
$478$	−18.7358	−	15.7212i	−0.856957	−	0.719073i
$479$	−24.4633	−	8.90390i	−1.11775	−	0.406830i	−0.283923	−	0.958847i	$-0.591636\pi$
$479$	−24.4633	−	8.90390i	−1.11775	−	0.406830i	−0.833832	+	0.552018i	$0.813858\pi$
$480$	0.733478	−	0.266964i	0.0334785	−	0.0121852i
$481$	4.22182	−	3.54253i	0.192499	−	0.161525i
$482$	3.66276	+	6.34409i	0.166834	+	0.288966i
$483$	1.38980	−	2.40720i	0.0632380	−	0.109531i
$484$	−1.47247	−	8.35080i	−0.0669305	−	0.379582i
$485$	1.37862	+	7.81855i	0.0625999	+	0.355022i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−18.9094	−	32.7521i	−0.856867	−	1.48414i	−0.874902	−	0.484301i	$-0.839074\pi$
$487$	−18.9094	−	32.7521i	−0.856867	−	1.48414i	0.0180343	−	0.999837i	$-0.494259\pi$
$488$	5.18386	−	4.34978i	0.234662	−	0.196905i
$489$	10.1704	−	3.70171i	0.459920	−	0.167397i
$490$	0.733478	+	0.266964i	0.0331351	+	0.0120602i
$491$	0.573546	+	0.481262i	0.0258838	+	0.0217191i	0.655638	−	0.755076i	$-0.272400\pi$
$491$	0.573546	+	0.481262i	0.0258838	+	0.0217191i	−0.629754	+	0.776795i	$0.716844\pi$
$492$	−0.0451489	+	0.256052i	−0.00203547	+	0.0115437i
$493$	6.32270			0.284760
$494$	6.97357	−	10.3924i	0.313756	−	0.467574i
$495$	−1.23918			−0.0556969
$496$	−0.898472	+	5.09549i	−0.0403426	+	0.228794i
$497$	1.81410	+	1.52221i	0.0813734	+	0.0682804i
$498$	10.4336	+	3.79753i	0.467542	+	0.170171i
$499$	8.37311	−	3.04756i	0.374832	−	0.136428i	−0.147733	−	0.989027i	$-0.547198\pi$
$499$	8.37311	−	3.04756i	0.374832	−	0.136428i	0.522565	+	0.852600i	$0.324975\pi$
$500$	−5.61507	+	4.71160i	−0.251113	+	0.210709i
$501$	2.81570	+	4.87693i	0.125796	+	0.217885i
$502$	−5.32345	+	9.22048i	−0.237597	+	0.411530i
$503$	3.02210	+	17.1392i	0.134749	+	0.764198i	0.975034	+	0.222054i	$0.0712761\pi$
$503$	3.02210	+	17.1392i	0.134749	+	0.764198i	−0.840286	+	0.542144i	$0.817613\pi$
$504$	0.173648	+	0.984808i	0.00773490	+	0.0438668i
$505$	−5.18617	+	8.98271i	−0.230781	+	0.399725i
$506$	−2.20640	−	3.82160i	−0.0980864	−	0.169891i
$507$	−3.64348	+	3.05724i	−0.161813	+	0.135777i
$508$	−6.09065	+	2.21682i	−0.270229	+	0.0983553i
$509$	−4.42069	−	1.60900i	−0.195944	−	0.0713177i	0.242184	−	0.970230i	$-0.422136\pi$
$509$	−4.42069	−	1.60900i	−0.195944	−	0.0713177i	−0.438128	+	0.898913i	$0.644358\pi$
$510$	3.53977	+	2.97022i	0.156744	+	0.131524i
$511$	−1.54373	+	8.75494i	−0.0682907	+	0.387296i
$512$	−1.00000			−0.0441942
$513$	−4.34900	−	0.293645i	−0.192013	−	0.0129648i
$514$	9.90221			0.436768
$515$	0.774681	−	4.39343i	0.0341365	−	0.193598i
$516$	0.639668	+	0.536745i	0.0281598	+	0.0236289i
$517$	−11.2459	−	4.09319i	−0.494596	−	0.180018i
$518$	1.80372	−	0.656500i	0.0792509	−	0.0288450i
$519$	13.4190	−	11.2599i	0.589028	−	0.494254i
$520$	−1.12056	−	1.94086i	−0.0491397	−	0.0851124i
$521$	6.52037	−	11.2936i	0.285662	−	0.494782i	−0.687107	−	0.726556i	$-0.741120\pi$
$521$	6.52037	−	11.2936i	0.285662	−	0.494782i	0.972770	+	0.231774i	$0.0744530\pi$
$522$	0.185461	+	1.05180i	0.00811740	+	0.0460360i
$523$	0.391954	+	2.22288i	0.0171390	+	0.0971999i	0.992177	−	0.124837i	$-0.0398407\pi$
$523$	0.391954	+	2.22288i	0.0171390	+	0.0971999i	−0.975038	+	0.222037i	$0.928730\pi$
$524$	9.37147	−	16.2319i	0.409395	−	0.709092i
$525$	−2.19537	−	3.80249i	−0.0958138	−	0.165954i
$526$	9.97471	−	8.36978i	0.434918	−	0.364940i
$527$	−28.7833	+	10.4763i	−1.25382	+	0.456353i
$528$	1.49183	+	0.542981i	0.0649235	+	0.0236302i
$529$	−11.7005	−	9.81784i	−0.508715	−	0.426863i
$530$	−0.857323	+	4.86212i	−0.0372397	+	0.211197i
$531$	−5.21852			−0.226465
$532$	3.52028	−	2.57054i	0.152623	−	0.111447i
$533$	0.746517			0.0323353
$534$	−1.18530	+	6.72218i	−0.0512930	+	0.290897i
$535$	0.0487668	+	0.0409202i	0.00210837	+	0.00176913i
$536$	7.34889	+	2.67478i	0.317424	+	0.115533i
$537$	−10.7038	+	3.89587i	−0.461904	+	0.168119i
$538$	−21.2042	+	17.7924i	−0.914176	+	0.767085i
$539$	0.793785	+	1.37488i	0.0341907	+	0.0592201i
$540$	−0.390275	+	0.675977i	−0.0167948	+	0.0290894i
$541$	−7.53564	−	42.7367i	−0.323982	−	1.83740i	−0.516732	−	0.856147i	$-0.672852\pi$
$541$	−7.53564	−	42.7367i	−0.323982	−	1.83740i	0.192750	−	0.981248i	$-0.438260\pi$
$542$	0.458771	+	2.60182i	0.0197059	+	0.111758i
$543$	3.38957	−	5.87091i	0.145460	−	0.251945i
$544$	−2.95999	−	5.12686i	−0.126909	−	0.219812i
$545$	1.24130	−	1.04157i	0.0531714	−	0.0446161i
$546$	2.69804	−	0.982007i	0.115466	−	0.0420260i
$547$	7.79298	+	2.83641i	0.333204	+	0.121276i	0.503204	−	0.864168i	$-0.332155\pi$
$547$	7.79298	+	2.83641i	0.333204	+	0.121276i	−0.170000	+	0.985444i	$0.554377\pi$
$548$	3.35501	+	2.81519i	0.143319	+	0.120259i
$549$	−1.17509	+	6.66424i	−0.0501514	+	0.284423i
$550$	−6.97061			−0.297228
$551$	3.75975	−	2.74540i	0.160171	−	0.116958i
$552$	−2.77959			−0.118307
$553$	−0.761448	+	4.31839i	−0.0323801	+	0.183637i
$554$	10.8577	+	9.11066i	0.461298	+	0.387075i
$555$	1.40789	+	0.512431i	0.0597618	+	0.0217515i
$556$	−0.564891	+	0.205604i	−0.0239567	+	0.00871954i
$557$	2.75532	−	2.31199i	0.116747	−	0.0979621i	−0.582545	−	0.812798i	$-0.697943\pi$
$557$	2.75532	−	2.31199i	0.116747	−	0.0979621i	0.699292	+	0.714836i	$0.253499\pi$
$558$	−2.58705	−	4.48090i	−0.109518	−	0.189691i
$559$	1.19876	−	2.07632i	0.0507023	−	0.0878189i
$560$	−0.135541	−	0.768692i	−0.00572766	−	0.0324832i
$561$	1.63201	+	9.25561i	0.0689037	+	0.390772i
$562$	7.33144	−	12.6984i	0.309258	−	0.535651i
$563$	−1.31378	−	2.27553i	−0.0553691	−	0.0959022i	0.837012	−	0.547184i	$-0.184300\pi$
$563$	−1.31378	−	2.27553i	−0.0553691	−	0.0959022i	−0.892381	+	0.451282i	$0.850967\pi$
$564$	−5.77472	+	4.84557i	−0.243160	+	0.204035i
$565$	0.922133	−	0.335629i	0.0387944	−	0.0141200i
$566$	−22.4374	−	8.16653i	−0.943113	−	0.343265i
$567$	−0.766044	−	0.642788i	−0.0321708	−	0.0269945i
$568$	0.411223	−	2.33216i	0.0172545	−	0.0978552i
$569$	−6.04517			−0.253427			−0.126713	−	0.991939i	$-0.540443\pi$
$569$	−6.04517			−0.253427			−0.126713	+	0.991939i	$0.540443\pi$
$570$	3.39461	+	0.229205i	0.142185	+	0.00960034i
$571$	45.3237			1.89674			0.948370	−	0.317168i	$-0.102732\pi$
$571$	45.3237			1.89674			0.948370	+	0.317168i	$0.102732\pi$
$572$	0.791528	−	4.48898i	0.0330954	−	0.187694i
$573$	0.558178	+	0.468367i	0.0233182	+	0.0195663i
$574$	0.244322	+	0.0889260i	0.0101978	+	0.00371170i
$575$	11.4685	−	4.17418i	0.478268	−	0.174075i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	7.56422	+	13.1016i	0.314902	+	0.545427i	0.979417	−	0.201848i	$-0.0646949\pi$
$577$	7.56422	+	13.1016i	0.314902	+	0.545427i	−0.664514	+	0.747276i	$0.731362\pi$
$578$	9.02312	−	15.6285i	0.375312	−	0.650060i
$579$	0.574127	+	3.25604i	0.0238599	+	0.135316i
$580$	−0.144761	−	0.820983i	−0.00601089	−	0.0340895i
$581$	5.55161	−	9.61567i	0.230320	−	0.398925i
$582$	5.08562	+	8.80855i	0.210806	+	0.365126i
$583$	−7.69237	+	6.45466i	−0.318585	+	0.267325i
$584$	8.35387	−	3.04056i	0.345686	−	0.125819i
$585$	2.10596	+	0.766506i	0.0870707	+	0.0316911i
$586$	14.9101	+	12.5111i	0.615932	+	0.516828i
$587$	−2.22739	+	12.6322i	−0.0919343	+	0.521385i	0.903709	+	0.428146i	$0.140833\pi$
$587$	−2.22739	+	12.6322i	−0.0919343	+	0.521385i	−0.995644	+	0.0932390i	$0.970278\pi$
$588$	1.00000			0.0412393
$589$	−12.5668	+	18.7277i	−0.517808	+	0.771663i
$590$	4.07332			0.167696
$591$	3.60525	−	20.4464i	0.148300	−	0.841052i
$592$	−1.47041	−	1.23382i	−0.0604333	−	0.0507095i
$593$	37.5322	+	13.6606i	1.54126	+	0.560974i	0.966348	−	0.257238i	$-0.0828124\pi$
$593$	37.5322	+	13.6606i	1.54126	+	0.560974i	0.574916	+	0.818212i	$0.305035\pi$
$594$	−1.49183	+	0.542981i	−0.0612104	+	0.0222788i
$595$	3.53977	−	2.97022i	0.145117	−	0.121767i
$596$	−9.80268	−	16.9787i	−0.401533	−	0.695476i
$597$	−10.5325	+	18.2427i	−0.431065	+	0.746626i
$598$	1.38584	+	7.85952i	0.0566714	+	0.321400i
$599$	−3.07578	−	17.4436i	−0.125673	−	0.712727i	−0.980906	−	0.194483i	$-0.937697\pi$
$599$	−3.07578	−	17.4436i	−0.125673	−	0.712727i	0.855233	−	0.518244i	$-0.173414\pi$
$600$	−2.19537	+	3.80249i	−0.0896256	+	0.155236i
$601$	−1.40927	−	2.44092i	−0.0574852	−	0.0995673i	0.835851	−	0.548957i	$-0.184975\pi$
$601$	−1.40927	−	2.44092i	−0.0574852	−	0.0995673i	−0.893336	+	0.449390i	$0.851642\pi$
$602$	0.639668	−	0.536745i	0.0260709	−	0.0218761i
$603$	−7.34889	+	2.67478i	−0.299270	+	0.108925i
$604$	−13.9100	−	5.06283i	−0.565990	−	0.206004i
$605$	−5.07027	−	4.25447i	−0.206136	−	0.172969i
$606$	−2.30752	+	13.0866i	−0.0937367	+	0.531607i
$607$	−19.3696			−0.786189			−0.393095	−	0.919498i	$-0.628595\pi$
$607$	−19.3696			−0.786189			−0.393095	+	0.919498i	$0.628595\pi$
$608$	−3.98629	−	1.76338i	−0.161665	−	0.0715145i
$609$	1.06803			0.0432786
$610$	0.917214	−	5.20178i	0.0371369	−	0.210614i
$611$	16.5804	+	13.9126i	0.670770	+	0.562843i
$612$	5.56297	+	2.02475i	0.224870	+	0.0818459i
$613$	29.7954	−	10.8446i	1.20342	−	0.438010i	0.339006	−	0.940784i	$-0.389909\pi$
$613$	29.7954	−	10.8446i	1.20342	−	0.438010i	0.864418	+	0.502774i	$0.167687\pi$
$614$	19.2538	−	16.1559i	0.777020	−	0.651997i
$615$	0.101472	+	0.175755i	0.00409176	+	0.00708714i
$616$	0.793785	−	1.37488i	0.0319825	−	0.0553953i
$617$	8.17398	+	46.3570i	0.329072	+	1.86626i	0.479359	+	0.877619i	$0.340869\pi$
$617$	8.17398	+	46.3570i	0.329072	+	1.86626i	−0.150287	+	0.988642i	$0.548020\pi$
$618$	−0.992480	−	5.62863i	−0.0399234	−	0.226417i
$619$	8.16699	−	14.1456i	0.328259	−	0.568562i	−0.653907	−	0.756575i	$-0.726871\pi$
$619$	8.16699	−	14.1456i	0.328259	−	0.568562i	0.982167	+	0.188013i	$0.0602047\pi$
$620$	2.01932	+	3.49757i	0.0810979	+	0.140466i
$621$	2.12929	−	1.78669i	0.0854456	−	0.0716974i
$622$	12.2370	−	4.45391i	0.490660	−	0.178586i
$623$	6.41423	+	2.33459i	0.256981	+	0.0935333i
$624$	−2.19946	−	1.84557i	−0.0880491	−	0.0738819i
$625$	2.81871	−	15.9857i	0.112748	−	0.639428i
$626$	3.45880			0.138241
$627$	4.98937	+	4.79514i	0.199256	+	0.191499i
$628$	−13.8397			−0.552262
$629$	1.97321	−	11.1906i	0.0786771	−	0.446200i
$630$	0.597936	+	0.501728i	0.0238224	+	0.0199893i
$631$	17.0322	+	6.19920i	0.678040	+	0.246786i	0.658006	−	0.753013i	$-0.271400\pi$
$631$	17.0322	+	6.19920i	0.678040	+	0.246786i	0.0200341	+	0.999799i	$0.493623\pi$
$632$	4.12056	−	1.49976i	0.163907	−	0.0596573i
$633$	18.6149	−	15.6197i	0.739874	−	0.620828i
$634$	3.66280	+	6.34416i	0.145468	+	0.251959i
$635$	−2.52958	+	4.38137i	−0.100383	+	0.173869i
$636$	1.09836	+	6.22909i	0.0435527	+	0.247000i
$637$	−0.498578	−	2.82758i	−0.0197544	−	0.112033i
$638$	0.847783	−	1.46840i	0.0335640	−	0.0581346i
$639$	1.18407	+	2.05087i	0.0468410	+	0.0811310i
$640$	−0.597936	+	0.501728i	−0.0236355	+	0.0198325i
$641$	16.4986	−	6.00502i	0.651657	−	0.237184i	0.00502702	−	0.999987i	$-0.498400\pi$
$641$	16.4986	−	6.00502i	0.651657	−	0.237184i	0.646630	+	0.762803i	$0.276178\pi$
$642$	0.0766399	+	0.0278946i	0.00302474	+	0.00110091i
$643$	31.4975	+	26.4295i	1.24214	+	1.04228i	0.997354	+	0.0727025i	$0.0231624\pi$
$643$	31.4975	+	26.4295i	1.24214	+	1.04228i	0.244787	+	0.969577i	$0.421282\pi$
$644$	−0.482671	+	2.73737i	−0.0190199	+	0.107867i
$645$	0.651781			0.0256638
$646$	−2.75878	−	25.6567i	−0.108543	−	1.00945i
$647$	−6.81556			−0.267947			−0.133974	−	0.990985i	$-0.542774\pi$
$647$	−6.81556			−0.267947			−0.133974	+	0.990985i	$0.542774\pi$
$648$	−0.173648	+	0.984808i	−0.00682154	+	0.0386869i
$649$	6.34650	+	5.32535i	0.249122	+	0.209038i
$650$	11.8464	+	4.31174i	0.464654	+	0.169120i
$651$	−4.86206	+	1.76964i	−0.190559	+	0.0693578i
$652$	−8.29097	+	6.95695i	−0.324699	+	0.272455i
$653$	7.75131	+	13.4257i	0.303332	+	0.525387i	0.976889	−	0.213749i	$-0.0685675\pi$
$653$	7.75131	+	13.4257i	0.303332	+	0.525387i	−0.673556	+	0.739136i	$0.735234\pi$
$654$	1.03799	−	1.79785i	0.0405885	−	0.0703013i
$655$	−2.54044	−	14.4076i	−0.0992632	−	0.562950i
$656$	−0.0451489	−	0.256052i	−0.00176277	−	0.00999716i
$657$	−4.44500	+	7.69897i	−0.173416	+	0.300365i
$658$	3.76918	+	6.52842i	0.146938	+	0.254504i
$659$	11.4732	−	9.62719i	0.446934	−	0.375022i	−0.391363	−	0.920236i	$-0.627996\pi$
$659$	11.4732	−	9.62719i	0.446934	−	0.375022i	0.838297	+	0.545215i	$0.183552\pi$
$660$	1.16445	−	0.423824i	0.0453260	−	0.0164973i
$661$	5.36645	+	1.95323i	0.208731	+	0.0759718i	0.444270	−	0.895893i	$-0.353463\pi$
$661$	5.36645	+	1.95323i	0.208731	+	0.0759718i	−0.235539	+	0.971865i	$0.575685\pi$
$662$	−16.3975	−	13.7592i	−0.637308	−	0.534765i
$663$	2.95158	−	16.7392i	0.114630	−	0.650097i
$664$	−11.1032			−0.430889
$665$	0.815191	−	3.30324i	0.0316117	−	0.128094i
$666$	1.91948			0.0743782
$667$	−0.515506	+	2.92358i	−0.0199605	+	0.113201i
$668$	−4.31390	−	3.61979i	−0.166910	−	0.140054i
$669$	15.9435	+	5.80296i	0.616412	+	0.224356i
$670$	5.73618	−	2.08780i	0.221608	−	0.0806587i
$671$	8.22974	−	6.90557i	0.317706	−	0.266587i
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	−24.2014	+	41.9180i	−0.932894	+	1.61582i	−0.154547	+	0.987985i	$0.549392\pi$
$673$	−24.2014	+	41.9180i	−0.932894	+	1.61582i	−0.778347	+	0.627834i	$0.783942\pi$
$674$	−2.80351	−	15.8995i	−0.107987	−	0.612425i
$675$	−0.762444	−	4.32404i	−0.0293465	−	0.166432i
$676$	2.37811	−	4.11901i	0.0914659	−	0.158424i
$677$	−17.3402	−	30.0341i	−0.666437	−	1.15430i	−0.978894	−	0.204371i	$-0.934485\pi$
$677$	−17.3402	−	30.0341i	−0.666437	−	1.15430i	0.312457	−	0.949932i	$-0.398848\pi$
$678$	0.963076	−	0.808117i	0.0369867	−	0.0310355i
$679$	9.55783	−	3.47877i	0.366796	−	0.133503i
$680$	−4.34218	−	1.58042i	−0.166515	−	0.0606065i
$681$	17.9668	+	15.0759i	0.688490	+	0.577711i
$682$	−1.42639	+	8.08944i	−0.0546192	+	0.309761i
$683$	−0.661766			−0.0253218			−0.0126609	−	0.999920i	$-0.504030\pi$
$683$	−0.661766			−0.0253218			−0.0126609	+	0.999920i	$0.504030\pi$
$684$	4.18715	−	1.21151i	0.160100	−	0.0463232i
$685$	3.41855			0.130616
$686$	0.173648	−	0.984808i	0.00662992	−	0.0376001i
$687$	2.57561	+	2.16119i	0.0982657	+	0.0824547i
$688$	−0.784669	−	0.285596i	−0.0299152	−	0.0108882i
$689$	17.0656	−	6.21138i	0.650148	−	0.236635i
$690$	−1.66202	+	1.39460i	−0.0632720	+	0.0530915i
$691$	21.6688	+	37.5315i	0.824321	+	1.42777i	0.902437	+	0.430822i	$0.141776\pi$
$691$	21.6688	+	37.5315i	0.824321	+	1.42777i	−0.0781153	+	0.996944i	$0.524890\pi$
$692$	−8.75863	+	15.1704i	−0.332953	+	0.576691i
$693$	0.275679	+	1.56345i	0.0104722	+	0.0593906i
$694$	0.769893	+	4.36628i	0.0292247	+	0.165742i
$695$	−0.234612	+	0.406360i	−0.00889934	+	0.0154141i
$696$	−0.534013	−	0.924938i	−0.0202417	−	0.0350597i
$697$	1.17910	−	0.989385i	0.0446617	−	0.0374756i
$698$	16.4336	−	5.98133i	0.622020	−	0.226397i
$699$	3.75562	+	1.36693i	0.142051	+	0.0517022i
$700$	3.36350	+	2.82231i	0.127128	+	0.106673i
$701$	−1.12315	+	6.36971i	−0.0424208	+	0.240580i	−0.998644	−	0.0520577i	$-0.983422\pi$
$701$	−1.12315	+	6.36971i	−0.0424208	+	0.240580i	0.956223	+	0.292638i	$0.0945331\pi$
$702$	2.87120			0.108366
$703$	−3.68577	−	7.51123i	−0.139011	−	0.283291i
$704$	−1.58757			−0.0598338
$705$	−1.02176	+	5.79468i	−0.0384817	+	0.218240i
$706$	−9.05304	−	7.59640i	−0.340716	−	0.285894i
$707$	12.4871	+	4.54493i	0.469625	+	0.170930i
$708$	4.90381	−	1.78484i	0.184296	−	0.0670784i
$709$	6.45803	−	5.41893i	0.242536	−	0.203512i	−0.513414	−	0.858141i	$-0.671620\pi$
$709$	6.45803	−	5.41893i	0.242536	−	0.203512i	0.755950	+	0.654629i	$0.227175\pi$
$710$	−0.924225	−	1.60081i	−0.0346856	−	0.0600771i
$711$	−2.19250	+	3.79753i	−0.0822253	+	0.142418i
$712$	−1.18530	−	6.72218i	−0.0444211	−	0.251924i
$713$	−2.49739	−	14.1634i	−0.0935279	−	0.530423i
$714$	2.95999	−	5.12686i	0.110775	−	0.191868i
$715$	−1.77896	−	3.08125i	−0.0665294	−	0.115232i
$716$	8.72584	−	7.32185i	0.326100	−	0.273630i
$717$	−22.9829	+	8.36510i	−0.858313	+	0.312400i
$718$	−26.4745	−	9.63594i	−0.988021	−	0.359610i
$719$	−0.135147	−	0.113402i	−0.00504012	−	0.00422916i	0.640264	−	0.768155i	$-0.278825\pi$
$719$	−0.135147	−	0.113402i	−0.00504012	−	0.00422916i	−0.645304	+	0.763926i	$0.723269\pi$
$720$	0.135541	−	0.768692i	0.00505132	−	0.0286475i
$721$	−5.71546			−0.212855
$722$	−12.7810	−	14.0587i	−0.475659	−	0.523210i
$723$	7.32553			0.272439
$724$	−1.17719	+	6.67615i	−0.0437497	+	0.248117i
$725$	3.59231	+	3.01430i	0.133415	+	0.111948i
$726$	−7.96824	−	2.90020i	−0.295729	−	0.107637i
$727$	−0.901959	+	0.328286i	−0.0334518	+	0.0121755i	−0.358692	−	0.933456i	$-0.616777\pi$
$727$	−0.901959	+	0.328286i	−0.0334518	+	0.0121755i	0.325240	+	0.945631i	$0.394555\pi$
$728$	−2.19946	+	1.84557i	−0.0815176	+	0.0684014i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	3.46955	−	6.00943i	0.128414	−	0.222419i
$731$	−0.858403	−	4.86825i	−0.0317492	−	0.180059i
$732$	−1.17509	−	6.66424i	−0.0434324	−	0.246317i
$733$	−13.4886	+	23.3629i	−0.498212	+	0.862928i	−0.999998	−	0.00206366i	$-0.999343\pi$
$733$	−13.4886	+	23.3629i	−0.498212	+	0.862928i	0.501786	+	0.864992i	$0.332676\pi$
$734$	−8.74296	−	15.1433i	−0.322709	−	0.558948i
$735$	0.597936	−	0.501728i	0.0220552	−	0.0185065i
$736$	2.61196	−	0.950677i	0.0962783	−	0.0350424i
$737$	11.6669	+	4.24640i	0.429755	+	0.156418i
$738$	0.199173	+	0.167126i	0.00733167	+	0.00615200i
$739$	−8.08057	+	45.8272i	−0.297249	+	1.68578i	0.360672	+	0.932693i	$0.382548\pi$
$739$	−8.08057	+	45.8272i	−0.297249	+	1.68578i	−0.657920	+	0.753088i	$0.728564\pi$
$740$	−1.49825			−0.0550767
$741$	−5.51326	−	11.2355i	−0.202535	−	0.412745i
$742$	6.32518			0.232205
$743$	−0.736056	+	4.17438i	−0.0270033	+	0.153143i	−0.995328	−	0.0965509i	$-0.969219\pi$
$743$	−0.736056	+	4.17438i	−0.0270033	+	0.153143i	0.968325	+	0.249694i	$0.0803301\pi$
$744$	3.96358	+	3.32584i	0.145312	+	0.121931i
$745$	−14.3801	−	5.23392i	−0.526846	−	0.191756i
$746$	33.6710	−	12.2553i	1.23278	−	0.448697i
$747$	8.50556	−	7.13701i	0.311202	−	0.261130i
$748$	−4.69920	−	8.13925i	−0.171820	−	0.297600i
$749$	0.0407792	−	0.0706317i	0.00149004	−	0.00258083i
$750$	1.27283	+	7.21859i	0.0464773	+	0.263586i
$751$	−8.68924	−	49.2791i	−0.317075	−	1.79822i	−0.560343	−	0.828261i	$-0.689331\pi$
$751$	−8.68924	−	49.2791i	−0.317075	−	1.79822i	0.243268	−	0.969959i	$-0.421781\pi$
$752$	3.76918	−	6.52842i	0.137448	−	0.238067i
$753$	5.32345	+	9.22048i	0.193997	+	0.336013i
$754$	−2.34909	+	1.97112i	−0.0855486	+	0.0717838i
$755$	−10.8575	+	3.95179i	−0.395144	+	0.143821i
$756$	0.939693	+	0.342020i	0.0341763	+	0.0124392i
$757$	4.93409	+	4.14020i	0.179333	+	0.150478i	0.728035	−	0.685540i	$-0.240434\pi$
$757$	4.93409	+	4.14020i	0.179333	+	0.150478i	−0.548703	+	0.836018i	$0.684878\pi$
$758$	4.60043	−	26.0903i	0.167095	−	0.947643i
$759$	−4.41280			−0.160174
$760$	−3.26828	+	0.945643i	−0.118553	+	0.0343021i
$761$	−33.4665			−1.21316			−0.606580	−	0.795022i	$-0.707459\pi$
$761$	−33.4665			−1.21316			−0.606580	+	0.795022i	$0.707459\pi$
$762$	−1.12551	+	6.38307i	−0.0407728	+	0.231234i
$763$	−1.59029	−	1.33441i	−0.0575723	−	0.0483089i
$764$	−0.684707	−	0.249213i	−0.0247718	−	0.00901621i
$765$	4.34218	−	1.58042i	0.156992	−	0.0571403i
$766$	−2.70089	+	2.26632i	−0.0975872	+	0.0818854i
$767$	−7.49171	−	12.9760i	−0.270510	−	0.468537i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	0.318945	+	1.80883i	0.0115015	+	0.0652281i	0.990018	−	0.140939i	$-0.0450121\pi$
$769$	0.318945	+	1.80883i	0.0115015	+	0.0652281i	−0.978517	+	0.206167i	$0.933901\pi$
$770$	−0.215181	−	1.22035i	−0.00775459	−	0.0439784i
$771$	4.95111	−	8.57557i	0.178310	−	0.308842i
$772$	−1.65313	−	2.86331i	−0.0594975	−	0.103053i
$773$	20.4715	−	17.1776i	0.736307	−	0.617835i	−0.195536	−	0.980697i	$-0.562645\pi$
$773$	20.4715	−	17.1776i	0.736307	−	0.617835i	0.931843	+	0.362861i	$0.118200\pi$
$774$	0.784669	−	0.285596i	0.0282043	−	0.0102655i
$775$	−21.3480	−	7.77005i	−0.766844	−	0.279108i
$776$	−7.79162	−	6.53794i	−0.279703	−	0.234698i
$777$	0.333314	−	1.89032i	0.0119576	−	0.0678147i
$778$	11.4327			0.409881
$779$	0.271541	−	1.10031i	0.00972896	−	0.0394228i
$780$	−2.24111			−0.0802448
$781$	0.652845	−	3.70247i	0.0233606	−	0.132485i
$782$	12.6054	+	10.5772i	0.450768	+	0.378239i
$783$	1.00362	+	0.365286i	0.0358663	+	0.0130543i
$784$	−0.939693	+	0.342020i	−0.0335605	+	0.0122150i
$785$	−8.27523	+	6.94375i	−0.295356	+	0.247833i
$786$	−9.37147	−	16.2319i	−0.334269	−	0.578971i
$787$	−3.98441	+	6.90121i	−0.142029	+	0.246001i	−0.928261	−	0.371931i	$-0.878696\pi$
$787$	−3.98441	+	6.90121i	−0.142029	+	0.246001i	0.786232	+	0.617932i	$0.212029\pi$
$788$	3.60525	+	20.4464i	0.128432	+	0.728373i
$789$	−2.26108	−	12.8232i	−0.0804967	−	0.456520i
$790$	1.71136	−	2.96416i	0.0608874	−	0.105460i
$791$	−0.628603	−	1.08877i	−0.0223506	−	0.0387123i
$792$	1.21615	−	1.02047i	0.0432140	−	0.0362608i
$793$	−18.2578	+	6.64529i	−0.648353	+	0.235981i
$794$	−28.2484	−	10.2816i	−1.00250	−	0.364880i
$795$	3.78206	+	3.17352i	0.134136	+	0.112553i
$796$	3.65788	−	20.7449i	0.129650	−	0.735283i
$797$	−14.4987			−0.513569			−0.256785	−	0.966469i	$-0.582663\pi$
$797$	−14.4987			−0.513569			−0.256785	+	0.966469i	$0.582663\pi$
$798$	−0.466011	−	4.33392i	−0.0164966	−	0.153419i
$799$	44.6270			1.57879
$800$	0.762444	−	4.32404i	0.0269565	−	0.152878i
$801$	5.22893	+	4.38759i	0.184755	+	0.155028i
$802$	17.5679	+	6.39421i	0.620346	+	0.225787i
$803$	13.2623	−	4.82710i	0.468018	−	0.170345i
$804$	5.99087	−	5.02694i	0.211282	−	0.177286i
$805$	1.08481	+	1.87894i	0.0382344	+	0.0662240i
$806$	7.42792	−	12.8655i	0.261637	−	0.453169i
$807$	4.80659	+	27.2595i	0.169200	+	0.959581i
$808$	−2.30752	−	13.0866i	−0.0811783	−	0.460385i
$809$	−16.4939	+	28.5683i	−0.579895	+	1.00441i	0.415596	+	0.909549i	$0.363573\pi$
$809$	−16.4939	+	28.5683i	−0.579895	+	1.00441i	−0.995491	+	0.0948584i	$0.969760\pi$
$810$	0.390275	+	0.675977i	0.0137129	+	0.0237514i
$811$	19.4546	−	16.3244i	0.683144	−	0.573226i	−0.233779	−	0.972290i	$-0.575109\pi$
$811$	19.4546	−	16.3244i	0.683144	−	0.573226i	0.916923	+	0.399064i	$0.130665\pi$
$812$	−1.00362	+	0.365286i	−0.0352200	+	0.0128190i
$813$	2.48263	+	0.903602i	0.0870695	+	0.0316907i
$814$	−2.33437	−	1.95877i	−0.0818196	−	0.0686548i
$815$	−1.46697	+	8.31962i	−0.0513859	+	0.291424i
$816$	−5.91999			−0.207241
$817$	−2.62430	−	2.52214i	−0.0918126	−	0.0882384i
$818$	−7.40687			−0.258975
$819$	0.498578	−	2.82758i	0.0174217	−	0.0988035i
$820$	−0.155465	−	0.130450i	−0.00542906	−	0.00455553i
$821$	28.1783	+	10.2560i	0.983428	+	0.357938i	0.783172	−	0.621805i	$-0.213600\pi$
$821$	28.1783	+	10.2560i	0.983428	+	0.357938i	0.200256	+	0.979744i	$0.435823\pi$
$822$	4.11553	−	1.49793i	0.143546	−	0.0522464i
$823$	12.4210	−	10.4225i	0.432970	−	0.363305i	−0.400101	−	0.916471i	$-0.631025\pi$
$823$	12.4210	−	10.4225i	0.432970	−	0.363305i	0.833071	+	0.553166i	$0.186581\pi$
$824$	2.85773	+	4.94974i	0.0995538	+	0.172432i
$825$	−3.48530	+	6.03672i	−0.121343	+	0.210172i
$826$	−0.906187	−	5.13924i	−0.0315303	−	0.178817i
$827$	5.77989	+	32.7794i	0.200987	+	1.13985i	0.903631	+	0.428311i	$0.140891\pi$
$827$	5.77989	+	32.7794i	0.200987	+	1.13985i	−0.702645	+	0.711541i	$0.747998\pi$
$828$	−1.38980	+	2.40720i	−0.0482988	+	0.0836560i
$829$	23.2565	+	40.2814i	0.807730	+	1.39903i	0.914433	+	0.404738i	$0.132637\pi$
$829$	23.2565	+	40.2814i	0.807730	+	1.39903i	−0.106702	+	0.994291i	$0.534029\pi$
$830$	−6.63902	+	5.57080i	−0.230444	+	0.193365i
$831$	13.3189	−	4.84768i	0.462027	−	0.168164i
$832$	2.69804	+	0.982007i	0.0935378	+	0.0340450i
$833$	−4.53497	−	3.80529i	−0.157127	−	0.131846i
$834$	−0.104388	+	0.592012i	−0.00361465	+	0.0204997i
$835$	−4.39559			−0.152116
$836$	−6.32851	−	2.79949i	−0.218876	−	0.0968224i
$837$	−5.17409			−0.178843
$838$	−5.30357	+	30.0780i	−0.183209	+	1.03903i
$839$	12.6797	+	10.6396i	0.437753	+	0.367318i	0.834868	−	0.550451i	$-0.185544\pi$
$839$	12.6797	+	10.6396i	0.437753	+	0.367318i	−0.397115	+	0.917769i	$0.629989\pi$
$840$	−0.733478	−	0.266964i	−0.0253074	−	0.00921113i
$841$	26.1792	−	9.52845i	0.902731	−	0.328567i
$842$	11.0839	−	9.30050i	0.381976	−	0.320516i
$843$	−7.33144	−	12.6984i	−0.252508	−	0.437357i
$844$	−12.1500	+	21.0444i	−0.418220	+	0.724378i
$845$	−0.644665	−	3.65607i	−0.0221771	−	0.125773i
$846$	1.30902	+	7.42384i	0.0450051	+	0.255237i
$847$	−4.23981	+	7.34357i	−0.145682	+	0.252328i
$848$	−3.16259	−	5.47777i	−0.108604	−	0.188107i
$849$	−18.2911	+	15.3481i	−0.627749	+	0.526744i
$850$	24.4255	−	8.89017i	0.837789	−	0.304930i
$851$	5.01361	+	1.82480i	0.171864	+	0.0625535i
$852$	−1.81410	−	1.52221i	−0.0621500	−	0.0521500i
$853$	−3.21007	+	18.2052i	−0.109911	+	0.623334i	0.879234	+	0.476390i	$0.158055\pi$
$853$	−3.21007	+	18.2052i	−0.109911	+	0.623334i	−0.989145	+	0.146944i	$0.953056\pi$
$854$	−6.76705			−0.231564
$855$	1.89580	−	2.82522i	0.0648351	−	0.0966204i
$856$	−0.0815585			−0.00278761
$857$	5.56425	−	31.5564i	0.190071	−	1.07795i	−0.729194	−	0.684307i	$-0.760105\pi$
$857$	5.56425	−	31.5564i	0.190071	−	1.07795i	0.919265	−	0.393640i	$-0.128784\pi$
$858$	−3.49180	−	2.92997i	−0.119208	−	0.100028i
$859$	−30.8285	−	11.2207i	−1.05185	−	0.382844i	−0.242492	−	0.970153i	$-0.577965\pi$
$859$	−30.8285	−	11.2207i	−1.05185	−	0.382844i	−0.809363	+	0.587309i	$0.800187\pi$
$860$	−0.612473	+	0.222922i	−0.0208852	+	0.00760158i
$861$	0.199173	−	0.167126i	0.00678781	−	0.00569564i
$862$	−3.02956	−	5.24735i	−0.103187	−	0.178726i
$863$	−17.4714	+	30.2613i	−0.594733	+	1.03011i	0.398851	+	0.917016i	$0.369409\pi$
$863$	−17.4714	+	30.2613i	−0.594733	+	1.03011i	−0.993584	+	0.113093i	$0.963924\pi$
$864$	−0.173648	−	0.984808i	−0.00590763	−	0.0335038i
$865$	2.37431	+	13.4654i	0.0807289	+	0.457836i
$866$	15.3477	−	26.5830i	0.521537	−	0.903329i
$867$	−9.02312	−	15.6285i	−0.306441	−	0.530772i
$868$	3.96358	−	3.32584i	0.134533	−	0.112886i
$869$	6.54167	−	2.38097i	0.221911	−	0.0807690i
$870$	−0.783373	−	0.285124i	−0.0265588	−	0.00966662i
$871$	−17.2010	−	14.4333i	−0.582833	−	0.489055i
$872$	−0.360489	+	2.04443i	−0.0122077	+	0.0692333i
$873$	10.1712			0.344244
$874$	12.0884	+	0.816215i	0.408898	+	0.0276089i
$875$	7.32995			0.247797
$876$	1.54373	−	8.75494i	0.0521579	−	0.295802i
$877$	−2.11587	−	1.77542i	−0.0714478	−	0.0599518i	0.606364	−	0.795187i	$-0.292627\pi$
$877$	−2.11587	−	1.77542i	−0.0714478	−	0.0599518i	−0.677812	+	0.735235i	$0.737072\pi$
$878$	−30.9690	−	11.2718i	−1.04515	−	0.380405i
$879$	18.2900	−	6.65701i	0.616906	−	0.224535i
$880$	−0.949266	+	0.796528i	−0.0319997	+	0.0268510i
$881$	15.1768	+	26.2869i	0.511318	+	0.885629i	0.999914	+	0.0131190i	$0.00417601\pi$
$881$	15.1768	+	26.2869i	0.511318	+	0.885629i	−0.488596	+	0.872510i	$0.662491\pi$
$882$	0.500000	−	0.866025i	0.0168359	−	0.0291606i
$883$	−4.94439	−	28.0411i	−0.166392	−	0.943657i	−0.947617	−	0.319407i	$-0.896516\pi$
$883$	−4.94439	−	28.0411i	−0.166392	−	0.943657i	0.781225	−	0.624249i	$-0.214595\pi$
$884$	2.95158	+	16.7392i	0.0992722	+	0.563001i
$885$	2.03666	−	3.52760i	0.0684616	−	0.118579i
$886$	−1.97587	−	3.42230i	−0.0663806	−	0.114974i
$887$	−33.1083	+	27.7811i	−1.11167	+	0.932799i	−0.998154	−	0.0607371i	$-0.980655\pi$
$887$	−33.1083	+	27.7811i	−1.11167	+	0.932799i	−0.113513	+	0.993536i	$0.536210\pi$
$888$	−1.80372	+	0.656500i	−0.0605288	+	0.0220307i
$889$	6.09065	+	2.21682i	0.204274	+	0.0743496i
$890$	−4.08144	−	3.42474i	−0.136810	−	0.114797i
$891$	−0.275679	+	1.56345i	−0.00923558	+	0.0523776i
$892$	−16.9667			−0.568088
$893$	26.5371	−	19.3776i	0.888031	−	0.648448i
$894$	−19.6054			−0.655701
$895$	1.54392	−	8.75600i	0.0516075	−	0.292681i
$896$	0.766044	+	0.642788i	0.0255917	+	0.0214740i
$897$	7.49946	+	2.72958i	0.250400	+	0.0911381i
$898$	−1.25497	+	0.456771i	−0.0418788	+	0.0152427i
$899$	4.23321	−	3.55209i	0.141186	−	0.118469i
$900$	2.19537	+	3.80249i	0.0731790	+	0.126750i
$901$	18.7225	−	32.4283i	0.623737	−	1.08034i
$902$	−0.0716770	−	0.406501i	−0.00238658	−	0.0135350i
$903$	−0.145001	−	0.822341i	−0.00482533	−	0.0273658i
$904$	−0.628603	+	1.08877i	−0.0209070	+	0.0362121i
$905$	2.64573	+	4.58254i	0.0879471	+	0.152329i
$906$	−11.3395	+	9.51501i	−0.376731	+	0.316115i
$907$	41.5739	−	15.1317i	1.38044	−	0.502439i	0.458128	−	0.888886i	$-0.348520\pi$
$907$	41.5739	−	15.1317i	1.38044	−	0.502439i	0.922311	+	0.386448i	$0.126298\pi$
$908$	−22.0396	−	8.02174i	−0.731408	−	0.266211i
$909$	10.1796	+	8.54167i	0.337635	+	0.283309i
$910$	−0.389165	+	2.20707i	−0.0129007	+	0.0731635i
$911$	40.3921			1.33825			0.669125	−	0.743150i	$-0.266669\pi$
$911$	40.3921			1.33825			0.669125	+	0.743150i	$0.266669\pi$
$912$	−3.52028	+	2.57054i	−0.116568	+	0.0851189i
$913$	−17.6271			−0.583373
$914$	−2.91675	+	16.5417i	−0.0964776	+	0.547152i
$915$	−4.04626	−	3.39522i	−0.133765	−	0.112242i
$916$	−3.15945	−	1.14995i	−0.104391	−	0.0379953i
$917$	−17.6126	+	6.41046i	−0.581619	+	0.211692i
$918$	4.53497	−	3.80529i	0.149676	−	0.125593i
$919$	−15.8501	−	27.4532i	−0.522848	−	0.905598i	−0.999647	−	0.0265861i	$-0.991536\pi$
$919$	−15.8501	−	27.4532i	−0.522848	−	0.905598i	0.476799	−	0.879012i	$-0.341797\pi$
$920$	1.08481	−	1.87894i	0.0357650	−	0.0619468i
$921$	−4.36448	−	24.7522i	−0.143815	−	0.815613i
$922$	4.74962	+	26.9364i	0.156420	+	0.887104i
$923$	−3.39969	+	5.88844i	−0.111902	+	0.193820i
$924$	−0.793785	−	1.37488i	−0.0261136	−	0.0452301i
$925$	6.45617	−	5.41737i	0.212277	−	0.178122i
$926$	13.5784	−	4.94213i	0.446214	−	0.162409i
$927$	−5.37078	−	1.95480i	−0.176400	−	0.0642042i
$928$	0.818155	+	0.686514i	0.0268573	+	0.0225359i
$929$	−9.75681	+	55.3336i	−0.320111	+	1.81544i	0.221903	+	0.975069i	$0.428773\pi$
$929$	−9.75681	+	55.3336i	−0.320111	+	1.81544i	−0.542014	+	0.840369i	$0.682338\pi$
$930$	4.03864			0.132432
$931$	−4.34900	−	0.293645i	−0.142533	−	0.00962384i
$932$	−3.99665			−0.130915
$933$	2.26131	−	12.8245i	0.0740320	−	0.419856i
$934$	−23.0485	−	19.3400i	−0.754171	−	0.632825i
$935$	−6.89351	−	2.50903i	−0.225442	−	0.0820541i
$936$	−2.69804	+	0.982007i	−0.0881883	+	0.0320979i
$937$	−0.133545	+	0.112057i	−0.00436272	+	0.00366075i	−0.644966	−	0.764211i	$-0.723129\pi$
$937$	−0.133545	+	0.112057i	−0.00436272	+	0.00366075i	0.640604	+	0.767872i	$0.278684\pi$
$938$	−3.91026	−	6.77278i	−0.127675	−	0.221139i
$939$	1.72940	−	2.99541i	0.0564368	−	0.0977514i
$940$	−1.02176	−	5.79468i	−0.0333261	−	0.189002i
$941$	−4.68242	−	26.5553i	−0.152642	−	0.865678i	−0.960910	−	0.276862i	$-0.910705\pi$
$941$	−4.68242	−	26.5553i	−0.152642	−	0.865678i	0.808267	−	0.588816i	$-0.200406\pi$
$942$	−6.91983	+	11.9855i	−0.225460	+	0.390509i
$943$	0.361350	+	0.625877i	0.0117672	+	0.0203814i
$944$	−3.99762	+	3.35440i	−0.130112	+	0.109177i
$945$	0.733478	−	0.266964i	0.0238600	−	0.00868434i
$946$	−1.24572	−	0.453404i	−0.0405017	−	0.0147414i
$947$	−18.4541	−	15.4849i	−0.599679	−	0.503190i	0.291664	−	0.956521i	$-0.405791\pi$
$947$	−18.4541	−	15.4849i	−0.599679	−	0.503190i	−0.891342	+	0.453331i	$0.850236\pi$
$948$	0.761448	−	4.31839i	0.0247307	−	0.140255i
$949$	−25.5249			−0.828575
$950$	10.6642	−	15.8924i	0.345994	−	0.515617i
$951$	7.32560			0.237549
$952$	−1.02799	+	5.83005i	−0.0333175	+	0.188953i
$953$	20.1716	+	16.9260i	0.653424	+	0.548288i	0.908108	−	0.418737i	$-0.137527\pi$
$953$	20.1716	+	16.9260i	0.653424	+	0.548288i	−0.254684	+	0.967024i	$0.581971\pi$
$954$	5.94373	+	2.16334i	0.192435	+	0.0700407i
$955$	−0.534449	+	0.194523i	−0.0172943	+	0.00629463i
$956$	18.7358	−	15.7212i	0.605960	−	0.508461i
$957$	−0.847783	−	1.46840i	−0.0274049	−	0.0474667i
$958$	13.0166	−	22.5455i	0.420548	−	0.728411i
$959$	−0.760520	−	4.31312i	−0.0245585	−	0.139278i
$960$	0.135541	+	0.768692i	0.00437457	+	0.0248094i
$961$	2.11438	−	3.66222i	0.0682059	−	0.118136i
$962$	2.75560	+	4.77284i	0.0888441	+	0.153882i
$963$	0.0624774	−	0.0524248i	0.00201331	−	0.00168936i
$964$	−6.88374	+	2.50548i	−0.221710	+	0.0806960i
$965$	−2.42507	−	0.882654i	−0.0780658	−	0.0284136i
$966$	2.12929	+	1.78669i	0.0685089	+	0.0574858i
$967$	1.76027	−	9.98296i	0.0566063	−	0.321030i	−0.943335	−	0.331841i	$-0.892330\pi$
$967$	1.76027	−	9.98296i	0.0566063	−	0.321030i	0.999942	+	0.0108109i	$0.00344128\pi$
$968$	8.47962			0.272545
$969$	−23.5988	−	10.4392i	−0.758102	−	0.335355i
$970$	−7.93916			−0.254911
$971$	−0.0343278	+	0.194683i	−0.00110163	+	0.00624766i	−0.985354	−	0.170523i	$-0.945454\pi$
$971$	−0.0343278	+	0.194683i	−0.00110163	+	0.00624766i	0.984252	+	0.176771i	$0.0565652\pi$
$972$	0.766044	+	0.642788i	0.0245709	+	0.0206174i
$973$	0.564891	+	0.205604i	0.0181096	+	0.00659135i
$974$	35.5381	−	12.9348i	1.13871	−	0.414458i
$975$	9.65728	−	8.10342i	0.309280	−	0.259517i
$976$	3.38352	+	5.86044i	0.108304	+	0.187588i
$977$	−27.3831	+	47.4289i	−0.876062	+	1.51738i	−0.0204346	+	0.999791i	$0.506505\pi$
$977$	−27.3831	+	47.4289i	−0.876062	+	1.51738i	−0.855627	+	0.517593i	$0.826828\pi$
$978$	1.87941	+	10.6587i	0.0600969	+	0.340826i
$979$	−1.88175	−	10.6719i	−0.0601410	−	0.341076i
$980$	−0.390275	+	0.675977i	−0.0124669	+	0.0215933i
$981$	−1.03799	−	1.79785i	−0.0331404	−	0.0574008i
$982$	−0.573546	+	0.481262i	−0.0183026	+	0.0153577i
$983$	−16.5846	+	6.03629i	−0.528966	+	0.192528i	−0.592676	−	0.805441i	$-0.701929\pi$
$983$	−16.5846	+	6.03629i	−0.528966	+	0.192528i	0.0637107	+	0.997968i	$0.479707\pi$
$984$	−0.244322	−	0.0889260i	−0.00778870	−	0.00283486i
$985$	12.4142	+	10.4168i	0.395551	+	0.331906i
$986$	−1.09793	+	6.22664i	−0.0349651	+	0.198297i
$987$	7.53836			0.239949
$988$	9.02352	+	8.67224i	0.287076	+	0.275901i
$989$	2.32104			0.0738047
$990$	0.215181	−	1.22035i	0.00683890	−	0.0387853i
$991$	12.2944	+	10.3162i	0.390545	+	0.327706i	0.816825	−	0.576885i	$-0.195732\pi$
$991$	12.2944	+	10.3162i	0.390545	+	0.327706i	−0.426280	+	0.904591i	$0.640176\pi$
$992$	−4.86206	−	1.76964i	−0.154370	−	0.0561863i
$993$	−20.1145	+	7.32110i	−0.638316	+	0.232328i
$994$	−1.81410	+	1.52221i	−0.0575397	+	0.0482815i
$995$	−8.22111	−	14.2394i	−0.260627	−	0.451419i
$996$	−5.55161	+	9.61567i	−0.175910	+	0.304684i
$997$	−1.49094	−	8.45553i	−0.0472185	−	0.267789i	0.952054	−	0.305930i	$-0.0989675\pi$
$997$	−1.49094	−	8.45553i	−0.0472185	−	0.267789i	−0.999272	+	0.0381410i	$0.987856\pi$
$998$	1.54729	+	8.77510i	0.0489785	+	0.277771i
$999$	0.959739	−	1.66232i	0.0303648	−	0.0525934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bo.d.169.1	yes	12
19.9	even	9	inner	798.2.bo.d.85.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bo.d.85.1	✓	12	19.9	even	9	inner
798.2.bo.d.169.1	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.733478 + 0.266964i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.135541 - 0.768692i) q^{10} +(0.793785 - 1.37488i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.19946 + 1.84557i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(-0.733478 - 0.266964i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.02799 + 5.83005i) q^{17} -1.00000 q^{18} +(1.92019 + 3.91316i) q^{19} +0.780550 q^{20} +(-0.173648 + 0.984808i) q^{21} +(1.21615 + 1.02047i) q^{22} +(-2.61196 - 0.950677i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-3.36350 + 2.82231i) q^{25} +(-1.43560 - 2.48653i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-0.173648 - 0.984808i) q^{28} +(-0.185461 - 1.05180i) q^{29} +(0.390275 - 0.675977i) q^{30} +(2.58705 + 4.48090i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(1.49183 - 0.542981i) q^{33} +(-5.56297 - 2.02475i) q^{34} +(-0.597936 - 0.501728i) q^{35} +(0.173648 - 0.984808i) q^{36} -1.91948 q^{37} +(-4.18715 + 1.21151i) q^{38} -2.87120 q^{39} +(-0.135541 + 0.768692i) q^{40} +(-0.199173 - 0.167126i) q^{41} +(-0.939693 - 0.342020i) q^{42} +(-0.784669 + 0.285596i) q^{43} +(-1.21615 + 1.02047i) q^{44} +(-0.390275 - 0.675977i) q^{45} +(1.38980 - 2.40720i) q^{46} +(-1.30902 - 7.42384i) q^{47} +(0.173648 + 0.984808i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.19537 - 3.80249i) q^{50} +(-4.53497 + 3.80529i) q^{51} +(2.69804 - 0.982007i) q^{52} +(-5.94373 - 2.16334i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(-0.215181 + 1.22035i) q^{55} +1.00000 q^{56} +(-1.04438 + 4.23193i) q^{57} +1.06803 q^{58} +(-0.906187 + 5.13924i) q^{59} +(0.597936 + 0.501728i) q^{60} +(6.35895 + 2.31447i) q^{61} +(-4.86206 + 1.76964i) q^{62} +(-0.766044 + 0.642788i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.12056 - 1.94086i) q^{65} +(0.275679 + 1.56345i) q^{66} +(1.35802 + 7.70172i) q^{67} +(2.95999 - 5.12686i) q^{68} +(-1.38980 - 2.40720i) q^{69} +(0.597936 - 0.501728i) q^{70} +(2.22532 - 0.809951i) q^{71} +(0.939693 + 0.342020i) q^{72} +(6.81014 + 5.71438i) q^{73} +(0.333314 - 1.89032i) q^{74} -4.39074 q^{75} +(-0.466011 - 4.33392i) q^{76} +1.58757 q^{77} +(0.498578 - 2.82758i) q^{78} +(3.35911 + 2.81863i) q^{79} +(-0.733478 - 0.266964i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(0.199173 - 0.167126i) q^{82} +(-5.55161 - 9.61567i) q^{83} +(0.500000 - 0.866025i) q^{84} +(-0.802402 - 4.55065i) q^{85} +(-0.145001 - 0.822341i) q^{86} +(0.534013 - 0.924938i) q^{87} +(-0.793785 - 1.37488i) q^{88} +(5.22893 - 4.38759i) q^{89} +(0.733478 - 0.266964i) q^{90} +(-2.69804 - 0.982007i) q^{91} +(2.12929 + 1.78669i) q^{92} +(-0.898472 + 5.09549i) q^{93} +7.53836 q^{94} +(-2.45309 - 2.35760i) q^{95} -1.00000 q^{96} +(1.76622 - 10.0167i) q^{97} +(-0.766044 - 0.642788i) q^{98} +(1.49183 + 0.542981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 9 q^{5} + 6 q^{7} + 6 q^{8} + 9 q^{10} + 3 q^{11} - 6 q^{12} - 9 q^{13} + 9 q^{15} + 15 q^{17} - 12 q^{18} + 9 q^{19} - 15 q^{22} + 3 q^{23} + 3 q^{25} + 3 q^{26} - 6 q^{27} + 3 q^{29} + 6 q^{31}+ \cdots - 12 q^{99}+O(q^{100}) \) 12 * q + 9 * q^5 + 6 * q^7 + 6 * q^8 + 9 * q^10 + 3 * q^11 - 6 * q^12 - 9 * q^13 + 9 * q^15 + 15 * q^17 - 12 * q^18 + 9 * q^19 - 15 * q^22 + 3 * q^23 + 3 * q^25 + 3 * q^26 - 6 * q^27 + 3 * q^29 + 6 * q^31 - 12 * q^33 - 6 * q^34 - 9 * q^38 + 6 * q^39 + 9 * q^40 - 27 * q^41 + 6 * q^43 + 15 * q^44 - 15 * q^46 - 6 * q^47 - 6 * q^49 - 21 * q^51 + 9 * q^52 - 9 * q^53 - 9 * q^55 + 12 * q^56 - 18 * q^57 + 12 * q^58 - 24 * q^59 - 15 * q^61 - 24 * q^62 - 6 * q^64 - 24 * q^65 + 3 * q^66 + 33 * q^67 - 6 * q^68 + 15 * q^69 - 33 * q^71 + 33 * q^73 + 12 * q^74 + 9 * q^76 + 6 * q^77 + 33 * q^79 + 9 * q^80 + 27 * q^82 - 36 * q^83 + 6 * q^84 + 15 * q^85 - 6 * q^86 + 6 * q^87 - 3 * q^88 - 6 * q^89 - 9 * q^90 - 9 * q^91 + 3 * q^92 - 21 * q^93 - 18 * q^94 - 18 * q^95 - 12 * q^96 + 21 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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