LMFDB - Embedded newform 820.2.k.c.83.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(83,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.83"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [108] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.7
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35278 + 0.412299i) q^{2} +(0.638078 - 0.638078i) q^{3} +(1.66002 - 1.11550i) q^{4} +(-0.848351 - 2.06889i) q^{5} +(-0.600099 + 1.12626i) q^{6} +(-1.94968 - 1.94968i) q^{7} +(-1.78572 + 2.19345i) q^{8} +2.18571i q^{9} +(2.00063 + 2.44897i) q^{10} +4.03380i q^{11} +(0.347446 - 1.77100i) q^{12} +(-2.07175 - 2.07175i) q^{13} +(3.44134 + 1.83364i) q^{14} +(-1.86143 - 0.778799i) q^{15} +(1.51132 - 3.70350i) q^{16} +(-5.74104 + 5.74104i) q^{17} +(-0.901167 - 2.95678i) q^{18} -2.15426 q^{19} +(-3.71612 - 2.48806i) q^{20} -2.48810 q^{21} +(-1.66313 - 5.45684i) q^{22} +(5.64666 - 5.64666i) q^{23} +(0.260164 + 2.53902i) q^{24} +(-3.56060 + 3.51029i) q^{25} +(3.65681 + 1.94844i) q^{26} +(3.30889 + 3.30889i) q^{27} +(-5.41138 - 1.06164i) q^{28} +3.18989i q^{29} +(2.83920 + 0.286077i) q^{30} +6.99289i q^{31} +(-0.517535 + 5.63313i) q^{32} +(2.57388 + 2.57388i) q^{33} +(5.39933 - 10.1334i) q^{34} +(-2.37966 + 5.68769i) q^{35} +(2.43816 + 3.62832i) q^{36} +(-0.454571 + 0.454571i) q^{37} +(2.91424 - 0.888200i) q^{38} -2.64388 q^{39} +(6.05291 + 1.83364i) q^{40} +1.00000 q^{41} +(3.36585 - 1.02584i) q^{42} +(0.276275 - 0.276275i) q^{43} +(4.49971 + 6.69619i) q^{44} +(4.52199 - 1.85425i) q^{45} +(-5.31056 + 9.96679i) q^{46} +(4.84550 + 4.84550i) q^{47} +(-1.39878 - 3.32747i) q^{48} +0.602521i q^{49} +(3.36941 - 6.21668i) q^{50} +7.32647i q^{51} +(-5.75019 - 1.12811i) q^{52} +(-1.74626 - 1.74626i) q^{53} +(-5.84045 - 3.11194i) q^{54} +(8.34549 - 3.42208i) q^{55} +(7.75811 - 0.794944i) q^{56} +(-1.37459 + 1.37459i) q^{57} +(-1.31519 - 4.31521i) q^{58} +10.6374 q^{59} +(-3.95875 + 0.783601i) q^{60} -15.0668 q^{61} +(-2.88316 - 9.45982i) q^{62} +(4.26144 - 4.26144i) q^{63} +(-1.62243 - 7.83376i) q^{64} +(-2.52865 + 6.04380i) q^{65} +(-4.54310 - 2.42068i) q^{66} +(-1.79484 - 1.79484i) q^{67} +(-3.12611 + 15.9344i) q^{68} -7.20602i q^{69} +(0.874122 - 8.67532i) q^{70} +1.40844i q^{71} +(-4.79424 - 3.90306i) q^{72} +(2.55763 + 2.55763i) q^{73} +(0.427514 - 0.802352i) q^{74} +(-0.0321033 + 4.51178i) q^{75} +(-3.57611 + 2.40307i) q^{76} +(7.86464 - 7.86464i) q^{77} +(3.57659 - 1.09007i) q^{78} -6.18073 q^{79} +(-8.94426 + 0.0151081i) q^{80} -2.33447 q^{81} +(-1.35278 + 0.412299i) q^{82} +(-3.37057 + 3.37057i) q^{83} +(-4.13029 + 2.77547i) q^{84} +(16.7480 + 7.00716i) q^{85} +(-0.259831 + 0.487647i) q^{86} +(2.03540 + 2.03540i) q^{87} +(-8.84794 - 7.20324i) q^{88} +10.6842i q^{89} +(-5.35275 + 4.37281i) q^{90} +8.07852i q^{91} +(3.07471 - 15.6724i) q^{92} +(4.46201 + 4.46201i) q^{93} +(-8.55269 - 4.55710i) q^{94} +(1.82757 + 4.45692i) q^{95} +(3.26415 + 3.92461i) q^{96} +(-9.91772 + 9.91772i) q^{97} +(-0.248419 - 0.815078i) q^{98} -8.81673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) $ 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.35278	+	0.412299i	−0.956559	+	0.291540i
$2$	−1.35278	+	0.412299i	−0.956559	+	0.291540i
$3$	0.638078	−	0.638078i	0.368395	−	0.368395i	−0.498497	−	0.866892i	$-0.666114\pi$
$3$	0.638078	−	0.638078i	0.368395	−	0.368395i	0.866892	+	0.498497i	$0.166114\pi$
$4$	1.66002	−	1.11550i	0.830009	−	0.557750i
$5$	−0.848351	−	2.06889i	−0.379394	−	0.925235i
$5$	−0.848351	−	2.06889i	−0.379394	−	0.925235i
$6$	−0.600099	+	1.12626i	−0.244990	+	0.459793i
$7$	−1.94968	−	1.94968i	−0.736911	−	0.736911i	0.235068	−	0.971979i	$-0.424469\pi$
$7$	−1.94968	−	1.94968i	−0.736911	−	0.736911i	−0.971979	+	0.235068i	$0.924469\pi$
$8$	−1.78572	+	2.19345i	−0.631347	+	0.775501i
$9$			2.18571i			0.728571i
$10$	2.00063	+	2.44897i	0.632656	+	0.774433i
$11$			4.03380i			1.21624i	0.793846	+	0.608119i	$0.208076\pi$
$11$			4.03380i			1.21624i	−0.793846	+	0.608119i	$0.791924\pi$
$12$	0.347446	−	1.77100i	0.100299	−	0.511243i
$13$	−2.07175	−	2.07175i	−0.574601	−	0.574601i	0.358810	−	0.933411i	$-0.383183\pi$
$13$	−2.07175	−	2.07175i	−0.574601	−	0.574601i	−0.933411	+	0.358810i	$0.883183\pi$
$14$	3.44134	+	1.83364i	0.919737	+	0.490060i
$15$	−1.86143	−	0.778799i	−0.480619	−	0.201085i
$16$	1.51132	−	3.70350i	0.377831	−	0.925875i
$17$	−5.74104	+	5.74104i	−1.39241	+	1.39241i	−0.572508	+	0.819899i	$0.694029\pi$
$17$	−5.74104	+	5.74104i	−1.39241	+	1.39241i	−0.819899	+	0.572508i	$0.805971\pi$
$18$	−0.901167	−	2.95678i	−0.212407	−	0.696921i
$19$	−2.15426			−0.494221			−0.247111	−	0.968987i	$-0.579481\pi$
$19$	−2.15426			−0.494221			−0.247111	+	0.968987i	$0.579481\pi$
$20$	−3.71612	−	2.48806i	−0.830950	−	0.556347i
$21$	−2.48810			−0.542948
$22$	−1.66313	−	5.45684i	−0.354582	−	1.16340i
$23$	5.64666	−	5.64666i	1.17741	−	1.17741i	0.197007	−	0.980402i	$-0.436878\pi$
$23$	5.64666	−	5.64666i	1.17741	−	1.17741i	0.980402	−	0.197007i	$-0.0631222\pi$
$24$	0.260164	+	2.53902i	0.0531057	+	0.518275i
$25$	−3.56060	+	3.51029i	−0.712120	+	0.702058i
$26$	3.65681	+	1.94844i	0.717159	+	0.382121i
$27$	3.30889	+	3.30889i	0.636796	+	0.636796i
$28$	−5.41138	−	1.06164i	−1.02265	−	0.200631i
$29$			3.18989i			0.592347i	0.955134	+	0.296174i	$0.0957107\pi$
$29$			3.18989i			0.592347i	−0.955134	+	0.296174i	$0.904289\pi$
$30$	2.83920	+	0.286077i	0.518364	+	0.0522302i
$31$			6.99289i			1.25596i	0.778230	+	0.627980i	$0.216118\pi$
$31$			6.99289i			1.25596i	−0.778230	+	0.627980i	$0.783882\pi$
$32$	−0.517535	+	5.63313i	−0.0914882	+	0.995806i
$33$	2.57388	+	2.57388i	0.448056	+	0.448056i
$34$	5.39933	−	10.1334i	0.925977	−	1.73786i
$35$	−2.37966	+	5.68769i	−0.402236	+	0.961395i
$36$	2.43816	+	3.62832i	0.406360	+	0.604720i
$37$	−0.454571	+	0.454571i	−0.0747309	+	0.0747309i	−0.743484	−	0.668753i	$-0.766828\pi$
$37$	−0.454571	+	0.454571i	−0.0747309	+	0.0747309i	0.668753	+	0.743484i	$0.266828\pi$
$38$	2.91424	−	0.888200i	0.472751	−	0.144085i
$39$	−2.64388			−0.423360
$40$	6.05291	+	1.83364i	0.957050	+	0.289923i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	3.36585	−	1.02584i	0.519362	−	0.158291i
$43$	0.276275	−	0.276275i	0.0421315	−	0.0421315i	−0.685727	−	0.727859i	$-0.740516\pi$
$43$	0.276275	−	0.276275i	0.0421315	−	0.0421315i	0.727859	+	0.685727i	$0.240516\pi$
$44$	4.49971	+	6.69619i	0.678356	+	1.00949i
$45$	4.52199	−	1.85425i	0.674099	−	0.276415i
$46$	−5.31056	+	9.96679i	−0.783000	+	1.46952i
$47$	4.84550	+	4.84550i	0.706789	+	0.706789i	0.965859	−	0.259069i	$-0.0834158\pi$
$47$	4.84550	+	4.84550i	0.706789	+	0.706789i	−0.259069	+	0.965859i	$0.583416\pi$
$48$	−1.39878	−	3.32747i	−0.201897	−	0.480278i
$49$			0.602521i			0.0860745i
$50$	3.36941	−	6.21668i	0.476507	−	0.879171i
$51$			7.32647i			1.02591i
$52$	−5.75019	−	1.12811i	−0.797408	−	0.156441i
$53$	−1.74626	−	1.74626i	−0.239867	−	0.239867i	0.576928	−	0.816795i	$-0.304251\pi$
$53$	−1.74626	−	1.74626i	−0.239867	−	0.239867i	−0.816795	+	0.576928i	$0.804251\pi$
$54$	−5.84045	−	3.11194i	−0.794785	−	0.423482i
$55$	8.34549	−	3.42208i	1.12531	−	0.461434i
$56$	7.75811	−	0.794944i	1.03672	−	0.106229i
$57$	−1.37459	+	1.37459i	−0.182068	+	0.182068i
$58$	−1.31519	−	4.31521i	−0.172693	−	0.566615i
$59$	10.6374			1.38488			0.692439	−	0.721477i	$-0.256536\pi$
$59$	10.6374			1.38488			0.692439	+	0.721477i	$0.256536\pi$
$60$	−3.95875	+	0.783601i	−0.511073	+	0.101162i
$61$	−15.0668			−1.92911			−0.964555	−	0.263882i	$-0.914997\pi$
$61$	−15.0668			−1.92911			−0.964555	+	0.263882i	$0.914997\pi$
$62$	−2.88316	−	9.45982i	−0.366162	−	1.20140i
$63$	4.26144	−	4.26144i	0.536891	−	0.536891i
$64$	−1.62243	−	7.83376i	−0.202803	−	0.979220i
$65$	−2.52865	+	6.04380i	−0.313641	+	0.749642i
$66$	−4.54310	−	2.42068i	−0.559218	−	0.297966i
$67$	−1.79484	−	1.79484i	−0.219275	−	0.219275i	0.588918	−	0.808193i	$-0.299554\pi$
$67$	−1.79484	−	1.79484i	−0.219275	−	0.219275i	−0.808193	+	0.588918i	$0.799554\pi$
$68$	−3.12611	+	15.9344i	−0.379096	+	1.93233i
$69$		−	7.20602i		−	0.867503i
$70$	0.874122	−	8.67532i	0.104478	−	1.03690i
$71$			1.40844i			0.167151i	0.996501	+	0.0835754i	$0.0266339\pi$
$71$			1.40844i			0.167151i	−0.996501	+	0.0835754i	$0.973366\pi$
$72$	−4.79424	−	3.90306i	−0.565007	−	0.459980i
$73$	2.55763	+	2.55763i	0.299348	+	0.299348i	0.840758	−	0.541410i	$-0.182109\pi$
$73$	2.55763	+	2.55763i	0.299348	+	0.299348i	−0.541410	+	0.840758i	$0.682109\pi$
$74$	0.427514	−	0.802352i	0.0496975	−	0.0932716i
$75$	−0.0321033	+	4.51178i	−0.00370697	+	0.520976i
$76$	−3.57611	+	2.40307i	−0.410208	+	0.275652i
$77$	7.86464	−	7.86464i	0.896259	−	0.896259i
$78$	3.57659	−	1.09007i	0.404969	−	0.123426i
$79$	−6.18073			−0.695387			−0.347693	−	0.937608i	$-0.613035\pi$
$79$	−6.18073			−0.695387			−0.347693	+	0.937608i	$0.613035\pi$
$80$	−8.94426	+	0.0151081i	−0.999999	+	0.00168914i
$81$	−2.33447			−0.259386
$82$	−1.35278	+	0.412299i	−0.149389	+	0.0455308i
$83$	−3.37057	+	3.37057i	−0.369968	+	0.369968i	−0.867465	−	0.497498i	$-0.834252\pi$
$83$	−3.37057	+	3.37057i	−0.369968	+	0.369968i	0.497498	+	0.867465i	$0.334252\pi$
$84$	−4.13029	+	2.77547i	−0.450652	+	0.302829i
$85$	16.7480	+	7.00716i	1.81658	+	0.760033i
$86$	−0.259831	+	0.487647i	−0.0280183	+	0.0525843i
$87$	2.03540	+	2.03540i	0.218218	+	0.218218i
$88$	−8.84794	−	7.20324i	−0.943193	−	0.767867i
$89$			10.6842i			1.13252i	0.824227	+	0.566259i	$0.191610\pi$
$89$			10.6842i			1.13252i	−0.824227	+	0.566259i	$0.808390\pi$
$90$	−5.35275	+	4.37281i	−0.564229	+	0.460934i
$91$			8.07852i			0.846859i
$92$	3.07471	−	15.6724i	0.320561	−	1.63396i
$93$	4.46201	+	4.46201i	0.462689	+	0.462689i
$94$	−8.55269	−	4.55710i	−0.882143	−	0.470028i
$95$	1.82757	+	4.45692i	0.187505	+	0.457271i
$96$	3.26415	+	3.92461i	0.333146	+	0.400554i
$97$	−9.91772	+	9.91772i	−1.00699	+	1.00699i	−0.00701685	+	0.999975i	$0.502234\pi$
$97$	−9.91772	+	9.91772i	−1.00699	+	1.00699i	−0.999975	+	0.00701685i	$0.997766\pi$
$98$	−0.248419	−	0.815078i	−0.0250941	−	0.0823353i
$99$	−8.81673			−0.886115
$100$	−1.99494	+	9.79899i	−0.199494	+	0.979899i
$101$	−18.9280			−1.88340			−0.941701	−	0.336451i	$-0.890773\pi$
$101$	−18.9280			−1.88340			−0.941701	+	0.336451i	$0.890773\pi$
$102$	−3.02070	−	9.91109i	−0.299094	−	0.981344i
$103$	−5.33609	+	5.33609i	−0.525781	+	0.525781i	−0.919312	−	0.393531i	$-0.871254\pi$
$103$	−5.33609	+	5.33609i	−0.525781	+	0.525781i	0.393531	+	0.919312i	$0.371254\pi$
$104$	8.24385	−	0.844716i	0.808376	−	0.0828313i
$105$	2.11078	+	5.14760i	0.205991	+	0.502355i
$106$	3.08228	+	1.64232i	0.299378	+	0.159516i
$107$	−6.92710	−	6.92710i	−0.669669	−	0.669669i	0.287971	−	0.957639i	$-0.407019\pi$
$107$	−6.92710	−	6.92710i	−0.669669	−	0.669669i	−0.957639	+	0.287971i	$0.907019\pi$
$108$	9.18389	+	1.80176i	0.883720	+	0.173374i
$109$		−	0.514746i		−	0.0493037i	−0.999696	−	0.0246519i	$-0.992152\pi$
$109$		−	0.514746i		−	0.0493037i	0.999696	−	0.0246519i	$-0.00784773\pi$
$110$	−9.87868	+	8.07016i	−0.941895	+	0.769460i
$111$			0.580103i			0.0550610i
$112$	−10.1672	+	4.27405i	−0.960714	+	0.403859i
$113$	−5.28461	−	5.28461i	−0.497134	−	0.497134i	0.413411	−	0.910545i	$-0.364337\pi$
$113$	−5.28461	−	5.28461i	−0.497134	−	0.497134i	−0.910545	+	0.413411i	$0.864337\pi$
$114$	1.29277	−	2.42625i	0.121079	−	0.227239i
$115$	−16.4727	−	6.89196i	−1.53608	−	0.642678i
$116$	3.55832	+	5.29527i	0.330382	+	0.491654i
$117$	4.52826	−	4.52826i	0.418638	−	0.418638i
$118$	−14.3901	+	4.38581i	−1.32472	+	0.403747i
$119$	22.3864			2.05216
$120$	5.03224	−	2.69223i	0.459378	−	0.245766i
$121$	−5.27158			−0.479234
$122$	20.3821	−	6.21204i	1.84531	−	0.562412i
$123$	0.638078	−	0.638078i	0.0575336	−	0.0575336i
$124$	7.80056	+	11.6083i	0.700511	+	1.04246i
$125$	10.2830	+	4.38853i	0.919743	+	0.392522i
$126$	−4.00780	+	7.52178i	−0.357043	+	0.670093i
$127$	−12.9541	−	12.9541i	−1.14949	−	1.14949i	−0.986653	−	0.162834i	$-0.947937\pi$
$127$	−12.9541	−	12.9541i	−1.14949	−	1.14949i	−0.162834	−	0.986653i	$-0.552063\pi$
$128$	5.42463	+	9.92841i	0.479474	+	0.877556i
$129$		−	0.352570i		−	0.0310421i
$130$	0.928852	−	9.21849i	0.0814657	−	0.808515i
$131$		−	2.79439i		−	0.244147i	−0.992521	−	0.122073i	$-0.961046\pi$
$131$		−	2.79439i		−	0.244147i	0.992521	−	0.122073i	$-0.0389543\pi$
$132$	7.14386	+	1.40153i	0.621793	+	0.121987i
$133$	4.20012	+	4.20012i	0.364197	+	0.364197i
$134$	3.16803	+	1.68801i	0.273676	+	0.145822i
$135$	4.03863	−	9.65283i	0.347590	−	0.830783i
$136$	−2.34080	−	22.8446i	−0.200722	−	1.95890i
$137$	−3.43671	+	3.43671i	−0.293618	+	0.293618i	−0.838508	−	0.544890i	$-0.816572\pi$
$137$	−3.43671	+	3.43671i	−0.293618	+	0.293618i	0.544890	+	0.838508i	$0.316572\pi$
$138$	2.97104	+	9.74815i	0.252911	+	0.829817i
$139$	11.0434			0.936688			0.468344	−	0.883546i	$-0.344851\pi$
$139$	11.0434			0.936688			0.468344	+	0.883546i	$0.344851\pi$
$140$	2.39433	+	12.0962i	0.202358	+	1.02231i
$141$	6.18362			0.520755
$142$	−0.580698	−	1.90530i	−0.0487311	−	0.159890i
$143$	8.35705	−	8.35705i	0.698852	−	0.698852i
$144$	8.09478	+	3.30332i	0.674565	+	0.275276i
$145$	6.59952	−	2.70615i	0.548061	−	0.224733i
$146$	−4.51442	−	2.40540i	−0.373616	−	0.199072i
$147$	0.384456	+	0.384456i	0.0317094	+	0.0317094i
$148$	−0.247522	+	1.26167i	−0.0203462	+	0.103709i
$149$			4.60185i			0.376998i	0.982073	+	0.188499i	$0.0603622\pi$
$149$			4.60185i			0.376998i	−0.982073	+	0.188499i	$0.939638\pi$
$150$	−1.81678	−	6.11668i	−0.148339	−	0.499425i
$151$			5.42095i			0.441151i	0.975370	+	0.220575i	$0.0707935\pi$
$151$			5.42095i			0.441151i	−0.975370	+	0.220575i	$0.929207\pi$
$152$	3.84690	−	4.72526i	0.312025	−	0.383269i
$153$	−12.5483	−	12.5483i	−1.01447	−	1.01447i
$154$	−7.39653	+	13.8817i	−0.596029	+	1.11862i
$155$	14.4675	−	5.93242i	1.16206	−	0.476504i
$156$	−4.38890	+	2.94925i	−0.351393	+	0.236129i
$157$	−4.77173	+	4.77173i	−0.380825	+	0.380825i	−0.871399	−	0.490574i	$-0.836787\pi$
$157$	−4.77173	+	4.77173i	−0.380825	+	0.380825i	0.490574	+	0.871399i	$0.336787\pi$
$158$	8.36116	−	2.54831i	0.665178	−	0.202733i
$159$	−2.22850			−0.176732
$160$	12.0934	−	3.70815i	0.956065	−	0.293155i
$161$	−22.0184			−1.73529
$162$	3.15802	−	0.962501i	0.248118	−	0.0756212i
$163$	7.02755	−	7.02755i	0.550440	−	0.550440i	−0.376128	−	0.926568i	$-0.622745\pi$
$163$	7.02755	−	7.02755i	0.550440	−	0.550440i	0.926568	+	0.376128i	$0.122745\pi$
$164$	1.66002	−	1.11550i	0.129626	−	0.0871059i
$165$	3.14152	−	7.50864i	0.244567	−	0.584547i
$166$	3.16995	−	5.94931i	0.246036	−	0.461756i
$167$	−0.837985	−	0.837985i	−0.0648452	−	0.0648452i	0.673940	−	0.738786i	$-0.264600\pi$
$167$	−0.837985	−	0.837985i	−0.0648452	−	0.0648452i	−0.738786	+	0.673940i	$0.764600\pi$
$168$	4.44304	−	5.45752i	0.342788	−	0.421057i
$169$		−	4.41567i		−	0.339667i
$170$	−25.5454	−	2.57394i	−1.95924	−	0.197412i
$171$		−	4.70859i		−	0.360075i
$172$	0.150437	−	0.766806i	0.0114707	−	0.0584684i
$173$	−4.50974	−	4.50974i	−0.342869	−	0.342869i	0.514576	−	0.857445i	$-0.327949\pi$
$173$	−4.50974	−	4.50974i	−0.342869	−	0.342869i	−0.857445	+	0.514576i	$0.827949\pi$
$174$	−3.59264	−	1.91425i	−0.272357	−	0.145119i
$175$	13.7860	+	0.0980934i	1.04212	+	0.00741517i
$176$	14.9392	+	6.09638i	1.12608	+	0.459532i
$177$	6.78752	−	6.78752i	0.510182	−	0.510182i
$178$	−4.40507	−	14.4533i	−0.330174	−	1.08332i
$179$	−7.71084			−0.576335			−0.288168	−	0.957580i	$-0.593046\pi$
$179$	−7.71084			−0.576335			−0.288168	+	0.957580i	$0.593046\pi$
$180$	5.43818	−	8.12237i	0.405338	−	0.605406i
$181$	20.6235			1.53293			0.766465	−	0.642286i	$-0.222014\pi$
$181$	20.6235			1.53293			0.766465	+	0.642286i	$0.222014\pi$
$182$	−3.33077	−	10.9285i	−0.246893	−	0.810071i
$183$	−9.61382	+	9.61382i	−0.710674	+	0.710674i
$184$	2.30231	+	22.4690i	0.169729	+	1.65644i
$185$	1.32609	+	0.554820i	0.0974962	+	0.0407912i
$186$	−7.87579	−	4.19643i	−0.577481	−	0.307697i
$187$	−23.1582	−	23.1582i	−1.69350	−	1.69350i
$188$	13.4488	+	2.63847i	0.980853	+	0.192430i
$189$		−	12.9026i		−	0.938524i
$190$	−4.30988	−	5.27572i	−0.312672	−	0.382741i
$191$			5.27951i			0.382012i	0.981589	+	0.191006i	$0.0611750\pi$
$191$			5.27951i			0.382012i	−0.981589	+	0.191006i	$0.938825\pi$
$192$	−6.03379	−	3.96332i	−0.435451	−	0.286028i
$193$	−1.66937	−	1.66937i	−0.120164	−	0.120164i	0.644468	−	0.764632i	$-0.277079\pi$
$193$	−1.66937	−	1.66937i	−0.120164	−	0.120164i	−0.764632	+	0.644468i	$0.777079\pi$
$194$	9.32741	−	17.5056i	0.669669	−	1.25683i
$195$	2.24294	+	5.46990i	0.160620	+	0.391708i
$196$	0.672112	+	1.00020i	0.0480080	+	0.0714426i
$197$	−7.64317	+	7.64317i	−0.544553	+	0.544553i	−0.924860	−	0.380307i	$-0.875818\pi$
$197$	−7.64317	+	7.64317i	−0.544553	+	0.544553i	0.380307	+	0.924860i	$0.375818\pi$
$198$	11.9271	−	3.63513i	0.847621	−	0.258338i
$199$	−18.8123			−1.33357			−0.666783	−	0.745252i	$-0.732329\pi$
$199$	−18.8123			−1.33357			−0.666783	+	0.745252i	$0.732329\pi$
$200$	−1.34141	−	14.0784i	−0.0948517	−	0.995491i
$201$	−2.29050			−0.161559
$202$	25.6053	−	7.80398i	1.80158	−	0.549086i
$203$	6.21927	−	6.21927i	0.436507	−	0.436507i
$204$	8.17267	+	12.1621i	0.572201	+	0.851516i
$205$	−0.848351	−	2.06889i	−0.0592514	−	0.144497i
$206$	5.01848	−	9.41862i	0.349654	−	0.656226i
$207$	12.3420	+	12.3420i	0.857826	+	0.857826i
$208$	−10.8038	+	4.54165i	−0.749111	+	0.314907i
$209$		−	8.68986i		−	0.601090i
$210$	−4.97777	−	6.09329i	−0.343499	−	0.420477i
$211$		−	5.08959i		−	0.350382i	−0.984535	−	0.175191i	$-0.943946\pi$
$211$		−	5.08959i		−	0.350382i	0.984535	−	0.175191i	$-0.0560542\pi$
$212$	−4.84677	−	0.950872i	−0.332878	−	0.0653061i
$213$	0.898694	+	0.898694i	0.0615775	+	0.0615775i
$214$	12.2269	+	6.51480i	0.835812	+	0.445342i
$215$	−0.805960	−	0.337204i	−0.0549660	−	0.0229971i
$216$	−13.1666	+	1.34913i	−0.895875	+	0.0917970i
$217$	13.6339	−	13.6339i	0.925530	−	0.925530i
$218$	0.212229	+	0.696337i	0.0143740	+	0.0471619i
$219$	3.26394			0.220556
$220$	10.0363	−	14.9901i	0.676650	−	1.01063i
$221$	23.7881			1.60016
$222$	−0.239176	−	0.784751i	−0.0160525	−	0.0526691i
$223$	−13.8751	+	13.8751i	−0.929144	+	0.929144i	−0.997651	−	0.0685064i	$-0.978177\pi$
$223$	−13.8751	+	13.8751i	−0.929144	+	0.929144i	0.0685064	+	0.997651i	$0.478177\pi$
$224$	11.9918	−	9.97378i	0.801239	−	0.666402i
$225$	−7.67248	−	7.78245i	−0.511499	−	0.518830i
$226$	9.32775	+	4.97006i	0.620472	+	0.330604i
$227$	−3.35974	−	3.35974i	−0.222994	−	0.222994i	0.586764	−	0.809758i	$-0.300402\pi$
$227$	−3.35974	−	3.35974i	−0.222994	−	0.222994i	−0.809758	+	0.586764i	$0.800402\pi$
$228$	−0.748489	+	3.81519i	−0.0495699	+	0.252667i
$229$		−	16.2935i		−	1.07670i	−0.842720	−	0.538352i	$-0.819047\pi$
$229$		−	16.2935i		−	1.07670i	0.842720	−	0.538352i	$-0.180953\pi$
$230$	25.1254	+	2.53163i	1.65672	+	0.166930i
$231$		−	10.0365i		−	0.660354i
$232$	−6.99685	−	5.69624i	−0.459366	−	0.373976i
$233$	3.40240	+	3.40240i	0.222899	+	0.222899i	0.809718	−	0.586819i	$-0.199620\pi$
$233$	3.40240	+	3.40240i	0.222899	+	0.222899i	−0.586819	+	0.809718i	$0.699620\pi$
$234$	−4.25873	+	7.99273i	−0.278402	+	0.522501i
$235$	5.91412	−	14.1355i	0.385795	−	0.922098i
$236$	17.6584	−	11.8661i	1.14946	−	0.772415i
$237$	−3.94379	+	3.94379i	−0.256177	+	0.256177i
$238$	−30.2839	+	9.22990i	−1.96301	+	0.598286i
$239$	26.5804			1.71934			0.859671	−	0.510848i	$-0.170669\pi$
$239$	26.5804			1.71934			0.859671	+	0.510848i	$0.170669\pi$
$240$	−5.69750	+	5.71678i	−0.367772	+	0.369017i
$241$	29.6040			1.90696			0.953481	−	0.301454i	$-0.0974720\pi$
$241$	29.6040			1.90696			0.953481	+	0.301454i	$0.0974720\pi$
$242$	7.13128	−	2.17347i	0.458416	−	0.139716i
$243$	−11.4162	+	11.4162i	−0.732353	+	0.732353i
$244$	−25.0112	+	16.8070i	−1.60118	+	1.07596i
$245$	1.24655	−	0.511150i	0.0796391	−	0.0326561i
$246$	−0.600099	+	1.12626i	−0.0382609	+	0.0718076i
$247$	4.46310	+	4.46310i	0.283980	+	0.283980i
$248$	−15.3385	−	12.4873i	−0.973998	−	0.792946i
$249$			4.30137i			0.272588i
$250$	−15.7201	−	1.69702i	−0.994224	−	0.107329i
$251$			23.4221i			1.47839i	0.673492	+	0.739195i	$0.264794\pi$
$251$			23.4221i			1.47839i	−0.673492	+	0.739195i	$0.735206\pi$
$252$	2.32044	−	11.8277i	0.146174	−	0.745076i
$253$	22.7775	+	22.7775i	1.43201	+	1.43201i
$254$	22.8649	+	12.1830i	1.43467	+	0.764431i
$255$	15.1576	−	6.21542i	0.949209	−	0.389225i
$256$	−11.4318	−	11.1944i	−0.714488	−	0.699648i
$257$	−15.9936	+	15.9936i	−0.997652	+	0.997652i	−0.999997	−	0.00234525i	$-0.999253\pi$
$257$	−15.9936	+	15.9936i	−0.997652	+	0.997652i	0.00234525	+	0.999997i	$0.499253\pi$
$258$	0.145364	+	0.476949i	0.00905000	+	0.0296936i
$259$	1.77254			0.110140
$260$	2.54425	+	12.8535i	0.157787	+	0.797143i
$261$	−6.97218			−0.431567
$262$	1.15212	+	3.78019i	0.0711785	+	0.233541i
$263$	−6.85597	+	6.85597i	−0.422757	+	0.422757i	−0.886152	−	0.463395i	$-0.846631\pi$
$263$	−6.85597	+	6.85597i	−0.422757	+	0.422757i	0.463395	+	0.886152i	$0.346631\pi$
$264$	−10.2419	+	1.04945i	−0.630346	+	0.0645892i
$265$	−2.13137	+	5.09426i	−0.130929	+	0.312938i
$266$	−7.41354	−	3.95013i	−0.454553	−	0.242198i
$267$	6.81733	+	6.81733i	0.417214	+	0.417214i
$268$	−4.98161	−	0.977325i	−0.304300	−	0.0596996i
$269$		−	1.00339i		−	0.0611777i	−0.999532	−	0.0305888i	$-0.990262\pi$
$269$		−	1.00339i		−	0.0611777i	0.999532	−	0.0305888i	$-0.00973824\pi$
$270$	−1.48351	+	14.7233i	−0.0902836	+	0.896029i
$271$		−	27.6326i		−	1.67856i	−0.543697	−	0.839281i	$-0.682976\pi$
$271$		−	27.6326i		−	1.67856i	0.543697	−	0.839281i	$-0.317024\pi$
$272$	12.5854	+	29.9385i	0.763100	+	1.81529i
$273$	5.15473	+	5.15473i	0.311979	+	0.311979i
$274$	3.23216	−	6.06606i	0.195262	−	0.366464i
$275$	−14.1598	−	14.3628i	−0.853869	−	0.866107i
$276$	−8.03831	−	11.9621i	−0.483849	−	0.720035i
$277$	3.83840	−	3.83840i	0.230627	−	0.230627i	−0.582327	−	0.812954i	$-0.697858\pi$
$277$	3.83840	−	3.83840i	0.230627	−	0.230627i	0.812954	+	0.582327i	$0.197858\pi$
$278$	−14.9392	+	4.55318i	−0.895997	+	0.273082i
$279$	−15.2844			−0.915055
$280$	−8.22625	−	15.3763i	−0.491612	−	0.918908i
$281$	13.3028			0.793579			0.396790	−	0.917910i	$-0.370124\pi$
$281$	13.3028			0.793579			0.396790	+	0.917910i	$0.370124\pi$
$282$	−8.36507	+	2.54950i	−0.498133	+	0.151821i
$283$	22.5760	−	22.5760i	1.34201	−	1.34201i	0.447945	−	0.894061i	$-0.352156\pi$
$283$	22.5760	−	22.5760i	1.34201	−	1.34201i	0.894061	−	0.447945i	$-0.147844\pi$
$284$	1.57111	+	2.33803i	0.0932283	+	0.138737i
$285$	4.01000	+	1.67773i	0.237532	+	0.0993804i
$286$	−7.85963	+	14.7508i	−0.464750	+	0.872236i
$287$	−1.94968	−	1.94968i	−0.115086	−	0.115086i
$288$	−12.3124	−	1.13118i	−0.725515	−	0.0666556i
$289$		−	48.9191i		−	2.87759i
$290$	−7.81195	+	6.38179i	−0.458734	+	0.374752i
$291$			12.6566i			0.741941i
$292$	7.09875	+	1.39268i	0.415423	+	0.0815004i
$293$	5.22061	+	5.22061i	0.304991	+	0.304991i	0.842963	−	0.537972i	$-0.180809\pi$
$293$	5.22061	+	5.22061i	0.304991	+	0.304991i	−0.537972	+	0.842963i	$0.680809\pi$
$294$	−0.678594	−	0.361573i	−0.0395764	−	0.0210873i
$295$	−9.02429	−	22.0077i	−0.525414	−	1.28134i
$296$	−0.185342	−	1.80881i	−0.0107728	−	0.105135i
$297$	−13.3474	+	13.3474i	−0.774496	+	0.774496i
$298$	−1.89734	−	6.22528i	−0.109910	−	0.360621i
$299$	−23.3970			−1.35308
$300$	4.97960	+	7.52545i	0.287497	+	0.434482i
$301$	−1.07730			−0.0620944
$302$	−2.23505	−	7.33334i	−0.128613	−	0.421986i
$303$	−12.0775	+	12.0775i	−0.693836	+	0.693836i
$304$	−3.25578	+	7.97830i	−0.186732	+	0.457587i
$305$	12.7820	+	31.1716i	0.731893	+	1.78488i
$306$	22.1487	+	11.8014i	1.26615	+	0.674640i
$307$	−5.13335	−	5.13335i	−0.292976	−	0.292976i	0.545279	−	0.838255i	$-0.316424\pi$
$307$	−5.13335	−	5.13335i	−0.292976	−	0.292976i	−0.838255	+	0.545279i	$0.816424\pi$
$308$	4.28245	−	21.8284i	0.244015	−	1.24379i
$309$			6.80969i			0.387390i
$310$	−17.1254	+	13.9902i	−0.972657	+	0.794590i
$311$			24.6338i			1.39685i	0.715681	+	0.698427i	$0.246116\pi$
$311$			24.6338i			1.39685i	−0.715681	+	0.698427i	$0.753884\pi$
$312$	4.72123	−	5.79922i	0.267287	−	0.328316i
$313$	−4.63647	−	4.63647i	−0.262069	−	0.262069i	0.563825	−	0.825894i	$-0.309329\pi$
$313$	−4.63647	−	4.63647i	−0.262069	−	0.262069i	−0.825894	+	0.563825i	$0.809329\pi$
$314$	4.48771	−	8.42247i	0.253256	−	0.475308i
$315$	−12.4317	−	5.20125i	−0.700444	−	0.293057i
$316$	−10.2601	+	6.89460i	−0.577178	+	0.387852i
$317$	24.6701	−	24.6701i	1.38561	−	1.38561i	0.551318	−	0.834295i	$-0.314125\pi$
$317$	24.6701	−	24.6701i	1.38561	−	1.38561i	0.834295	−	0.551318i	$-0.185875\pi$
$318$	3.01467	−	0.918809i	0.169054	−	0.0515243i
$319$	−12.8674			−0.720435
$320$	−14.8308	+	10.0024i	−0.829066	+	0.559151i
$321$	−8.84007			−0.493405
$322$	29.7860	−	9.07816i	1.65991	−	0.505906i
$323$	12.3677	−	12.3677i	0.688157	−	0.688157i
$324$	−3.87527	+	2.60410i	−0.215293	+	0.144672i
$325$	14.6491	+	0.104235i	0.812588	+	0.00578193i
$326$	−6.60926	+	12.4042i	−0.366053	+	0.687003i
$327$	−0.328448	−	0.328448i	−0.0181632	−	0.0181632i
$328$	−1.78572	+	2.19345i	−0.0985998	+	0.121113i
$329$		−	18.8944i		−	1.04168i
$330$	−1.15398	+	11.4528i	−0.0635243	+	0.630454i
$331$		−	18.5469i		−	1.01943i	−0.860344	−	0.509714i	$-0.829751\pi$
$331$		−	18.5469i		−	1.01943i	0.860344	−	0.509714i	$-0.170249\pi$
$332$	−1.83534	+	9.35507i	−0.100727	+	0.513426i
$333$	−0.993560	−	0.993560i	−0.0544468	−	0.0544468i
$334$	1.47911	+	0.788108i	0.0809332	+	0.0431233i
$335$	−2.19067	+	5.23598i	−0.119689	+	0.286072i
$336$	−3.76032	+	9.21468i	−0.205142	+	0.502702i
$337$	−11.2961	+	11.2961i	−0.615340	+	0.615340i	−0.944333	−	0.328992i	$-0.893291\pi$
$337$	−11.2961	+	11.2961i	−0.615340	+	0.615340i	0.328992	+	0.944333i	$0.393291\pi$
$338$	1.82058	+	5.97342i	0.0990264	+	0.324911i
$339$	−6.74399			−0.366283
$340$	35.6185	−	7.05036i	1.93168	−	0.382360i
$341$	−28.2079			−1.52755
$342$	1.94135	+	6.36968i	0.104976	+	0.344433i
$343$	−12.4731	+	12.4731i	−0.673481	+	0.673481i
$344$	0.112646	+	1.09934i	0.00607345	+	0.0592727i
$345$	−14.9085	+	6.11323i	−0.802644	+	0.329126i
$346$	7.96004	+	4.24131i	0.427934	+	0.228014i
$347$	15.3691	+	15.3691i	0.825057	+	0.825057i	0.986828	−	0.161771i	$-0.0517207\pi$
$347$	15.3691	+	15.3691i	0.825057	+	0.825057i	−0.161771	+	0.986828i	$0.551721\pi$
$348$	5.64929	+	1.10831i	0.302834	+	0.0594119i
$349$			18.7053i			1.00127i	0.865658	+	0.500637i	$0.166901\pi$
$349$			18.7053i			1.00127i	−0.865658	+	0.500637i	$0.833099\pi$
$350$	−18.6898	+	5.55125i	−0.999013	+	0.296727i
$351$		−	13.7104i		−	0.731808i
$352$	−22.7229	−	2.08764i	−1.21114	−	0.111271i
$353$	2.72537	+	2.72537i	0.145057	+	0.145057i	0.775906	−	0.630849i	$-0.217293\pi$
$353$	2.72537	+	2.72537i	0.145057	+	0.145057i	−0.630849	+	0.775906i	$0.717293\pi$
$354$	−6.38352	+	11.9805i	−0.339281	+	0.636757i
$355$	2.91390	−	1.19485i	0.154654	−	0.0634160i
$356$	11.9182	+	17.7359i	0.631662	+	0.940001i
$357$	14.2843	−	14.2843i	0.756005	−	0.756005i
$358$	10.4311	−	3.17917i	0.551299	−	0.168025i
$359$	−24.2558			−1.28017			−0.640086	−	0.768303i	$-0.721101\pi$
$359$	−24.2558			−1.28017			−0.640086	+	0.768303i	$0.721101\pi$
$360$	−4.00780	+	13.2299i	−0.211230	+	0.697278i
$361$	−14.3592			−0.755746
$362$	−27.8990	+	8.50304i	−1.46634	+	0.446910i
$363$	−3.36368	+	3.36368i	−0.176547	+	0.176547i
$364$	9.01159	+	13.4105i	0.472335	+	0.702901i
$365$	3.12168	−	7.46122i	0.163396	−	0.390538i
$366$	9.04160	−	16.9691i	0.472612	−	0.886991i
$367$	−10.5282	−	10.5282i	−0.549568	−	0.549568i	0.376748	−	0.926316i	$-0.377042\pi$
$367$	−10.5282	−	10.5282i	−0.549568	−	0.549568i	−0.926316	+	0.376748i	$0.877042\pi$
$368$	−12.3785	−	29.4463i	−0.645272	−	1.53499i
$369$			2.18571i			0.113784i
$370$	−2.02266	−	0.203803i	−0.105153	−	0.0105952i
$371$			6.80930i			0.353521i
$372$	12.3844	+	2.42965i	0.642101	+	0.125972i
$373$	−6.80656	−	6.80656i	−0.352430	−	0.352430i	0.508583	−	0.861013i	$-0.330170\pi$
$373$	−6.80656	−	6.80656i	−0.352430	−	0.352430i	−0.861013	+	0.508583i	$0.830170\pi$
$374$	40.8761	+	21.7798i	2.11365	+	1.12621i
$375$	9.36161	−	3.76116i	0.483431	−	0.194225i
$376$	−19.2811	+	1.97566i	−0.994345	+	0.101887i
$377$	6.60866	−	6.60866i	0.340364	−	0.340364i
$378$	5.31972	+	17.4543i	0.273617	+	0.897753i
$379$	2.32598			0.119478			0.0597388	−	0.998214i	$-0.480973\pi$
$379$	2.32598			0.119478			0.0597388	+	0.998214i	$0.480973\pi$
$380$	8.00549	+	5.35992i	0.410673	+	0.274958i
$381$	−16.5314			−0.846930
$382$	−2.17674	−	7.14200i	−0.111372	−	0.365417i
$383$	−9.19034	+	9.19034i	−0.469604	+	0.469604i	−0.901786	−	0.432182i	$-0.857744\pi$
$383$	−9.19034	+	9.19034i	−0.469604	+	0.469604i	0.432182	+	0.901786i	$0.357744\pi$
$384$	9.79645	+	2.87376i	0.499923	+	0.146651i
$385$	−22.9430	−	9.59908i	−1.16929	−	0.489215i
$386$	2.94657	+	1.57001i	0.149977	+	0.0799115i
$387$	0.603858	+	0.603858i	0.0306958	+	0.0306958i
$388$	−5.40039	+	27.5268i	−0.274163	+	1.39746i
$389$			6.16642i			0.312650i	0.987706	+	0.156325i	$0.0499647\pi$
$389$			6.16642i			0.312650i	−0.987706	+	0.156325i	$0.950035\pi$
$390$	−5.28944	−	6.47480i	−0.267841	−	0.327864i
$391$			64.8354i			3.27887i
$392$	−1.32160	−	1.07593i	−0.0667508	−	0.0543428i
$393$	−1.78304	−	1.78304i	−0.0899424	−	0.0899424i
$394$	7.18824	−	13.4908i	0.362138	−	0.679656i
$395$	5.24343	+	12.7873i	0.263826	+	0.643396i
$396$	−14.6359	+	9.83506i	−0.735484	+	0.494230i
$397$	2.45178	−	2.45178i	0.123051	−	0.123051i	−0.642899	−	0.765951i	$-0.722269\pi$
$397$	2.45178	−	2.45178i	0.123051	−	0.123051i	0.765951	+	0.642899i	$0.222269\pi$
$398$	25.4488	−	7.75628i	1.27563	−	0.388787i
$399$	5.36001			0.268336
$400$	7.61913	+	18.4919i	0.380956	+	0.924593i
$401$	−14.4100			−0.719602			−0.359801	−	0.933029i	$-0.617155\pi$
$401$	−14.4100			−0.719602			−0.359801	+	0.933029i	$0.617155\pi$
$402$	3.09854	−	0.944370i	0.154541	−	0.0471009i
$403$	14.4875	−	14.4875i	0.721676	−	0.721676i
$404$	−31.4208	+	21.1141i	−1.56324	+	1.05047i
$405$	1.98045	+	4.82976i	0.0984094	+	0.239993i
$406$	−5.84909	+	10.9775i	−0.290286	+	0.544804i
$407$	−1.83365	−	1.83365i	−0.0908906	−	0.0908906i
$408$	−16.0702	−	13.0830i	−0.795595	−	0.647705i
$409$			15.6654i			0.774607i	0.921952	+	0.387303i	$0.126593\pi$
$409$			15.6654i			0.774607i	−0.921952	+	0.387303i	$0.873407\pi$
$410$	2.00063	+	2.44897i	0.0988042	+	0.120946i
$411$			4.38578i			0.216335i
$412$	−2.90561	+	14.8104i	−0.143149	+	0.729657i
$413$	−20.7396	−	20.7396i	−1.02053	−	1.02053i
$414$	−21.7845	−	11.6074i	−1.07065	−	0.570471i
$415$	9.83275	+	4.11390i	0.482671	+	0.201944i
$416$	12.7427	−	10.5983i	0.624761	−	0.519622i
$417$	7.04654	−	7.04654i	0.345071	−	0.345071i
$418$	3.58282	+	11.7555i	0.175242	+	0.574978i
$419$	−23.6142			−1.15363			−0.576816	−	0.816874i	$-0.695705\pi$
$419$	−23.6142			−1.15363			−0.576816	+	0.816874i	$0.695705\pi$
$420$	9.24609	+	6.19054i	0.451163	+	0.302067i
$421$	4.64972			0.226613			0.113307	−	0.993560i	$-0.463856\pi$
$421$	4.64972			0.226613			0.113307	+	0.993560i	$0.463856\pi$
$422$	2.09843	+	6.88508i	0.102150	+	0.335161i
$423$	−10.5909	+	10.5909i	−0.514946	+	0.514946i
$424$	6.94865	−	0.712002i	0.337456	−	0.0345779i
$425$	0.288846	−	40.5943i	0.0140111	−	1.96911i
$426$	−1.58626	−	0.845202i	−0.0768547	−	0.0409502i
$427$	29.3755	+	29.3755i	1.42158	+	1.42158i
$428$	−19.2263	−	3.77194i	−0.929338	−	0.182324i
$429$		−	10.6649i		−	0.514907i
$430$	1.22931	+	0.123865i	0.0592828	+	0.00597332i
$431$		−	22.4427i		−	1.08102i	−0.841336	−	0.540512i	$-0.818230\pi$
$431$		−	22.4427i		−	1.08102i	0.841336	−	0.540512i	$-0.181770\pi$
$432$	17.2553	−	7.25367i	0.830195	−	0.348992i
$433$	18.2325	+	18.2325i	0.876198	+	0.876198i	0.993139	−	0.116941i	$-0.0373087\pi$
$433$	18.2325	+	18.2325i	0.876198	+	0.876198i	−0.116941	+	0.993139i	$0.537309\pi$
$434$	−12.8224	+	24.0649i	−0.615495	+	1.15515i
$435$	2.48428	−	5.93775i	0.119112	−	0.284693i
$436$	−0.574199	−	0.854488i	−0.0274991	−	0.0409226i
$437$	−12.1644	+	12.1644i	−0.581900	+	0.581900i
$438$	−4.41538	+	1.34572i	−0.210975	+	0.0643009i
$439$	21.0685			1.00554			0.502771	−	0.864419i	$-0.332314\pi$
$439$	21.0685			1.00554			0.502771	+	0.864419i	$0.332314\pi$
$440$	−7.39653	+	24.4163i	−0.352616	+	1.16400i
$441$	−1.31694			−0.0627113
$442$	−32.1800	+	9.80780i	−1.53064	+	0.466509i
$443$	−6.83015	+	6.83015i	−0.324510	+	0.324510i	−0.850494	−	0.525984i	$-0.823697\pi$
$443$	−6.83015	+	6.83015i	−0.324510	+	0.324510i	0.525984	+	0.850494i	$0.323697\pi$
$444$	0.647105	+	0.962982i	0.0307102	+	0.0457011i
$445$	22.1043	−	9.06392i	1.04785	−	0.429671i
$446$	13.0492	−	24.4906i	0.617899	−	1.15966i
$447$	2.93634	+	2.93634i	0.138884	+	0.138884i
$448$	−12.1101	+	18.4365i	−0.572149	+	0.871045i
$449$		−	8.48929i		−	0.400634i	−0.979731	−	0.200317i	$-0.935803\pi$
$449$		−	8.48929i		−	0.400634i	0.979731	−	0.200317i	$-0.0641973\pi$
$450$	13.5879	+	7.36457i	0.640538	+	0.347169i
$451$			4.03380i			0.189944i
$452$	−14.6675	−	2.87757i	−0.689902	−	0.135350i
$453$	3.45899	+	3.45899i	0.162518	+	0.162518i
$454$	5.93021	+	3.15977i	0.278318	+	0.148295i
$455$	16.7136	−	6.85342i	0.783544	−	0.321294i
$456$	−0.560460	−	5.46971i	−0.0262460	−	0.256143i
$457$	17.4217	−	17.4217i	0.814951	−	0.814951i	−0.170420	−	0.985371i	$-0.554513\pi$
$457$	17.4217	−	17.4217i	0.814951	−	0.814951i	0.985371	+	0.170420i	$0.0545125\pi$
$458$	6.71779	+	22.0415i	0.313902	+	1.02993i
$459$	−37.9930			−1.77336
$460$	−35.0329	+	6.93445i	−1.63342	+	0.323321i
$461$	8.43314			0.392771			0.196385	−	0.980527i	$-0.437080\pi$
$461$	8.43314			0.392771			0.196385	+	0.980527i	$0.437080\pi$
$462$	4.13805	+	13.5772i	0.192519	+	0.631667i
$463$	6.01329	−	6.01329i	0.279461	−	0.279461i	−0.553433	−	0.832894i	$-0.686682\pi$
$463$	6.01329	−	6.01329i	0.279461	−	0.279461i	0.832894	+	0.553433i	$0.186682\pi$
$464$	11.8137	+	4.82095i	0.548439	+	0.223807i
$465$	5.44605	−	13.0168i	0.252555	−	0.603637i
$466$	−6.00550	−	3.19989i	−0.278199	−	0.148232i
$467$	5.02338	+	5.02338i	0.232454	+	0.232454i	0.813716	−	0.581262i	$-0.197441\pi$
$467$	5.02338	+	5.02338i	0.232454	+	0.232454i	−0.581262	+	0.813716i	$0.697441\pi$
$468$	2.46572	−	12.5683i	0.113978	−	0.580968i
$469$			6.99873i			0.323172i
$470$	−2.17244	+	21.5606i	−0.100207	+	0.994516i
$471$			6.08947i			0.280588i
$472$	−18.9955	+	23.3327i	−0.874338	+	1.07397i
$473$	1.11444	+	1.11444i	0.0512420	+	0.0512420i
$474$	3.70905	−	6.96110i	0.170363	−	0.319734i
$475$	7.67046	−	7.56207i	0.351945	−	0.346972i
$476$	37.1619	−	24.9720i	1.70331	−	1.14459i
$477$	3.81682	−	3.81682i	0.174760	−	0.174760i
$478$	−35.9574	+	10.9591i	−1.64465	+	0.501256i
$479$	−5.87249			−0.268321			−0.134161	−	0.990960i	$-0.542834\pi$
$479$	−5.87249			−0.268321			−0.134161	+	0.990960i	$0.542834\pi$
$480$	5.35043	−	10.0826i	0.244213	−	0.460206i
$481$	1.88352			0.0858810
$482$	−40.0477	+	12.2057i	−1.82412	+	0.555955i
$483$	−14.0494	+	14.0494i	−0.639272	+	0.639272i
$484$	−8.75092	+	5.88044i	−0.397769	+	0.267293i
$485$	28.9324	+	12.1050i	1.31375	+	0.549658i
$486$	10.7367	−	20.1506i	0.487029	−	0.914048i
$487$	10.4771	+	10.4771i	0.474761	+	0.474761i	0.903451	−	0.428690i	$-0.141025\pi$
$487$	10.4771	+	10.4771i	0.474761	+	0.474761i	−0.428690	+	0.903451i	$0.641025\pi$
$488$	26.9051	−	33.0483i	1.21794	−	1.49603i
$489$		−	8.96826i		−	0.405559i
$490$	−1.47556	+	1.20542i	−0.0666589	+	0.0544555i
$491$		−	39.0056i		−	1.76030i	−0.474695	−	0.880150i	$-0.657442\pi$
$491$		−	39.0056i		−	1.76030i	0.474695	−	0.880150i	$-0.342558\pi$
$492$	0.347446	−	1.77100i	0.0156641	−	0.0798428i
$493$	−18.3133	−	18.3133i	−0.824789	−	0.824789i
$494$	−7.87771	−	4.19745i	−0.354435	−	0.188852i
$495$	7.47969	+	18.2408i	0.336187	+	0.819865i
$496$	25.8981	+	10.5685i	1.16286	+	0.474540i
$497$	2.74601	−	2.74601i	0.123175	−	0.123175i
$498$	−1.77345	−	5.81880i	−0.0794703	−	0.260747i
$499$	23.5208			1.05293			0.526467	−	0.850196i	$-0.323516\pi$
$499$	23.5208			1.05293			0.526467	+	0.850196i	$0.323516\pi$
$500$	21.9654	−	4.18568i	0.982324	−	0.187189i
$501$	−1.06940			−0.0477773
$502$	−9.65691	−	31.6849i	−0.431009	−	1.41417i
$503$	5.23281	−	5.23281i	0.233319	−	0.233319i	−0.580757	−	0.814077i	$-0.697243\pi$
$503$	5.23281	−	5.23281i	0.233319	−	0.233319i	0.814077	+	0.580757i	$0.197243\pi$
$504$	1.73752	+	16.9570i	0.0773952	+	0.755324i
$505$	16.0576	+	39.1598i	0.714552	+	1.74259i
$506$	−40.2041	−	21.4218i	−1.78729	−	0.952314i
$507$	−2.81754	−	2.81754i	−0.125132	−	0.125132i
$508$	−35.9542	−	7.05374i	−1.59521	−	0.312959i
$509$		−	7.83938i		−	0.347474i	−0.984792	−	0.173737i	$-0.944416\pi$
$509$		−	7.83938i		−	0.347474i	0.984792	−	0.173737i	$-0.0555843\pi$
$510$	−17.9423	+	14.6576i	−0.794500	+	0.649048i
$511$		−	9.97313i		−	0.441185i
$512$	20.0801	+	10.4302i	0.887425	+	0.460953i
$513$	−7.12821	−	7.12821i	−0.314718	−	0.314718i
$514$	15.0416	−	28.2299i	0.663458	−	1.24517i
$515$	15.5667	+	6.51290i	0.685949	+	0.286993i
$516$	−0.393292	−	0.585273i	−0.0173137	−	0.0257652i
$517$	−19.5458	+	19.5458i	−0.859624	+	0.859624i
$518$	−2.39785	+	0.730815i	−0.105355	+	0.0321102i
$519$	−5.75513			−0.252622
$520$	−8.74131	−	16.3390i	−0.383332	−	0.716512i
$521$	−31.1058			−1.36277			−0.681385	−	0.731925i	$-0.738622\pi$
$521$	−31.1058			−1.36277			−0.681385	+	0.731925i	$0.738622\pi$
$522$	9.43181	−	2.87462i	0.412819	−	0.125819i
$523$	−29.1213	+	29.1213i	−1.27338	+	1.27338i	−0.329083	+	0.944301i	$0.606739\pi$
$523$	−29.1213	+	29.1213i	−1.27338	+	1.27338i	−0.944301	+	0.329083i	$0.893261\pi$
$524$	−3.11714	−	4.63874i	−0.136173	−	0.202644i
$525$	8.85913	−	8.73395i	0.386644	−	0.381181i
$526$	6.44790	−	12.1013i	0.281142	−	0.527643i
$527$	−40.1464	−	40.1464i	−1.74881	−	1.74881i
$528$	13.4223	−	5.64241i	0.584133	−	0.245554i
$529$		−	40.7695i		−	1.77259i
$530$	0.782919	−	7.77016i	0.0340078	−	0.337514i
$531$			23.2504i			1.00898i
$532$	11.6575	+	2.28705i	0.505417	+	0.0991561i
$533$	−2.07175	−	2.07175i	−0.0897376	−	0.0897376i
$534$	−12.0331	−	6.41156i	−0.520724	−	0.277455i
$535$	−8.45479	+	20.2080i	−0.365533	+	0.873669i
$536$	7.14196	−	0.731810i	0.308486	−	0.0316094i
$537$	−4.92012	+	4.92012i	−0.212319	+	0.212319i
$538$	0.413696	+	1.35736i	0.0178357	+	0.0585200i
$539$	−2.43045			−0.104687
$540$	−4.06353	−	20.5290i	−0.174866	−	0.883426i
$541$	14.8901			0.640175			0.320088	−	0.947388i	$-0.396288\pi$
$541$	14.8901			0.640175			0.320088	+	0.947388i	$0.396288\pi$
$542$	11.3929	+	37.3808i	0.489368	+	1.60564i
$543$	13.1594	−	13.1594i	0.564724	−	0.564724i
$544$	−29.3688	−	35.3112i	−1.25918	−	1.51396i
$545$	−1.06495	+	0.436685i	−0.0456175	+	0.0187056i
$546$	−9.09850	−	4.84792i	−0.389380	−	0.207472i
$547$	1.65436	+	1.65436i	0.0707353	+	0.0707353i	0.741589	−	0.670854i	$-0.234072\pi$
$547$	1.65436	+	1.65436i	0.0707353	+	0.0707353i	−0.670854	+	0.741589i	$0.734072\pi$
$548$	−1.87136	+	9.53866i	−0.0799404	+	0.407471i
$549$		−	32.9318i		−	1.40549i
$550$	25.0769	+	13.5916i	1.06928	+	0.579546i
$551$		−	6.87185i		−	0.292751i
$552$	15.8060	+	12.8679i	0.672749	+	0.547695i
$553$	12.0505	+	12.0505i	0.512438	+	0.512438i
$554$	−3.60993	+	6.77507i	−0.153371	+	0.287845i
$555$	1.20017	−	0.492131i	0.0509443	−	0.0208898i
$556$	18.3322	−	12.3189i	0.777459	−	0.522437i
$557$	7.77377	−	7.77377i	0.329385	−	0.329385i	−0.522967	−	0.852353i	$-0.675175\pi$
$557$	7.77377	−	7.77377i	0.329385	−	0.329385i	0.852353	+	0.522967i	$0.175175\pi$
$558$	20.6764	−	6.30176i	0.875304	−	0.266775i
$559$	−1.14475			−0.0484177
$560$	17.4679	+	17.4090i	0.738154	+	0.735665i
$561$	−29.5535			−1.24775
$562$	−17.9958	+	5.48474i	−0.759105	+	0.231360i
$563$	28.9612	−	28.9612i	1.22057	−	1.22057i	0.253142	−	0.967429i	$-0.418536\pi$
$563$	28.9612	−	28.9612i	1.22057	−	1.22057i	0.967429	−	0.253142i	$-0.0814639\pi$
$564$	10.2649	−	6.89783i	0.432232	−	0.290451i
$565$	−6.45006	+	15.4165i	−0.271356	+	0.648576i
$566$	−21.2323	+	39.8485i	−0.892460	+	1.67496i
$567$	4.55148	+	4.55148i	0.191144	+	0.191144i
$568$	−3.08933	−	2.51507i	−0.129626	−	0.105530i
$569$			13.7813i			0.577743i	0.957368	+	0.288872i	$0.0932801\pi$
$569$			13.7813i			0.577743i	−0.957368	+	0.288872i	$0.906720\pi$
$570$	−6.11637	−	0.616283i	−0.256186	−	0.0258133i
$571$		−	16.6485i		−	0.696719i	−0.937361	−	0.348359i	$-0.886739\pi$
$571$		−	16.6485i		−	0.696719i	0.937361	−	0.348359i	$-0.113261\pi$
$572$	4.55058	−	23.1951i	0.190269	−	0.969838i
$573$	3.36874	+	3.36874i	0.140731	+	0.140731i
$574$	3.44134	+	1.83364i	0.143639	+	0.0765345i
$575$	−0.284097	+	39.9269i	−0.0118477	+	1.66507i
$576$	17.1223	−	3.54615i	0.713431	−	0.147756i
$577$	−26.7785	+	26.7785i	−1.11480	+	1.11480i	−0.122310	+	0.992492i	$0.539030\pi$
$577$	−26.7785	+	26.7785i	−1.11480	+	1.11480i	−0.992492	+	0.122310i	$0.960970\pi$
$578$	20.1693	+	66.1767i	0.838933	+	2.75259i
$579$	−2.13038			−0.0885357
$580$	7.93663	−	11.8540i	0.329551	−	0.492211i
$581$	13.1431			0.545266
$582$	−5.21830	−	17.1215i	−0.216305	−	0.709710i
$583$	7.04407	−	7.04407i	0.291735	−	0.291735i
$584$	−10.1772	+	1.04282i	−0.421137	+	0.0431523i
$585$	−13.2100	−	5.52691i	−0.546167	−	0.228510i
$586$	−9.21478	−	4.90987i	−0.380659	−	0.202825i
$587$	18.9611	+	18.9611i	0.782608	+	0.782608i	0.980270	−	0.197662i	$-0.0633349\pi$
$587$	18.9611	+	18.9611i	0.782608	+	0.782608i	−0.197662	+	0.980270i	$0.563335\pi$
$588$	1.06706	+	0.209344i	0.0440050	+	0.00863319i
$589$		−	15.0645i		−	0.620721i
$590$	21.2816	+	26.0508i	0.876150	+	1.07250i
$591$			9.75388i			0.401221i
$592$	0.996498	+	2.37050i	0.0409558	+	0.0974271i
$593$	−13.9715	−	13.9715i	−0.573742	−	0.573742i	0.359430	−	0.933172i	$-0.382971\pi$
$593$	−13.9715	−	13.9715i	−0.573742	−	0.573742i	−0.933172	+	0.359430i	$0.882971\pi$
$594$	12.5530	−	23.5592i	0.515055	−	0.966647i
$595$	−18.9915	−	46.3150i	−0.778577	−	1.89873i
$596$	5.13335	+	7.63915i	0.210270	+	0.312912i
$597$	−12.0037	+	12.0037i	−0.491279	+	0.491279i
$598$	31.6509	−	9.64655i	1.29430	−	0.394477i
$599$	2.11193			0.0862912			0.0431456	−	0.999069i	$-0.486262\pi$
$599$	2.11193			0.0862912			0.0431456	+	0.999069i	$0.486262\pi$
$600$	−9.83903	−	8.12719i	−0.401677	−	0.331791i
$601$	13.4953			0.550486			0.275243	−	0.961375i	$-0.411242\pi$
$601$	13.4953			0.550486			0.275243	+	0.961375i	$0.411242\pi$
$602$	1.45734	−	0.444169i	0.0593969	−	0.0181030i
$603$	3.92300	−	3.92300i	0.159757	−	0.159757i
$604$	6.04706	+	8.99887i	0.246052	+	0.366159i
$605$	4.47215	+	10.9063i	0.181819	+	0.443405i
$606$	11.3587	−	21.3178i	0.461414	−	0.865975i
$607$	26.4465	+	26.4465i	1.07343	+	1.07343i	0.997081	+	0.0763504i	$0.0243268\pi$
$607$	26.4465	+	26.4465i	1.07343	+	1.07343i	0.0763504	+	0.997081i	$0.475673\pi$
$608$	1.11491	−	12.1352i	0.0452154	−	0.492148i
$609$		−	7.93676i		−	0.321614i
$610$	−30.1432	−	36.8983i	−1.22046	−	1.49397i
$611$		−	20.0774i		−	0.812244i
$612$	−34.8279	−	6.83277i	−1.40784	−	0.276198i
$613$	26.9692	+	26.9692i	1.08928	+	1.08928i	0.995603	+	0.0936743i	$0.0298612\pi$
$613$	26.9692	+	26.9692i	1.08928	+	1.08928i	0.0936743	+	0.995603i	$0.470139\pi$
$614$	9.06077	+	4.82781i	0.365663	+	0.194835i
$615$	−1.86143	−	0.778799i	−0.0750600	−	0.0314042i
$616$	3.20665	+	31.2947i	0.129200	+	1.26090i
$617$	−28.9680	+	28.9680i	−1.16621	+	1.16621i	−0.183115	+	0.983091i	$0.558618\pi$
$617$	−28.9680	+	28.9680i	−1.16621	+	1.16621i	−0.983091	+	0.183115i	$0.941382\pi$
$618$	−2.80763	−	9.21201i	−0.112940	−	0.370561i
$619$	17.1316			0.688578			0.344289	−	0.938864i	$-0.388120\pi$
$619$	17.1316			0.688578			0.344289	+	0.938864i	$0.388120\pi$
$620$	17.3987	−	25.9864i	0.698749	−	1.04364i
$621$	37.3683			1.49954
$622$	−10.1565	−	33.3241i	−0.407238	−	1.33617i
$623$	20.8307	−	20.8307i	0.834565	−	0.834565i
$624$	−3.99576	+	9.79162i	−0.159958	+	0.391978i
$625$	0.355754	−	24.9975i	0.0142302	−	0.999899i
$626$	8.18372	+	4.36050i	0.327087	+	0.174281i
$627$	−5.54481	−	5.54481i	−0.221439	−	0.221439i
$628$	−2.59830	+	13.2440i	−0.103683	+	0.528494i
$629$		−	5.21942i		−	0.208112i
$630$	18.9617	+	1.91058i	0.755454	+	0.0761193i
$631$		−	30.8174i		−	1.22682i	−0.789765	−	0.613410i	$-0.789797\pi$
$631$		−	30.8174i		−	1.22682i	0.789765	−	0.613410i	$-0.210203\pi$
$632$	11.0370	−	13.5571i	0.439030	−	0.539273i
$633$	−3.24755	−	3.24755i	−0.129079	−	0.129079i
$634$	−23.2018	+	43.5447i	−0.921459	+	1.72938i
$635$	−15.8109	+	37.7901i	−0.627437	+	1.49965i
$636$	−3.69935	+	2.48589i	−0.146689	+	0.0985720i
$637$	1.24828	−	1.24828i	0.0494585	−	0.0494585i
$638$	17.4067	−	5.30521i	0.689139	−	0.210035i
$639$	−3.07844			−0.121781
$640$	15.9388	−	19.6457i	0.630036	−	0.776566i
$641$	−29.7451			−1.17486			−0.587431	−	0.809274i	$-0.699861\pi$
$641$	−29.7451			−1.17486			−0.587431	+	0.809274i	$0.699861\pi$
$642$	11.9587	−	3.64476i	0.471971	−	0.143847i
$643$	−24.9951	+	24.9951i	−0.985711	+	0.985711i	−0.999899	−	0.0141887i	$-0.995483\pi$
$643$	−24.9951	+	24.9951i	−0.985711	+	0.985711i	0.0141887	+	0.999899i	$0.495483\pi$
$644$	−36.5509	+	24.5615i	−1.44031	+	0.967858i
$645$	−0.729429	+	0.299103i	−0.0287212	+	0.0117772i
$646$	−11.6316	+	21.8299i	−0.457637	+	0.858887i
$647$	−11.8895	−	11.8895i	−0.467423	−	0.467423i	0.433656	−	0.901079i	$-0.357223\pi$
$647$	−11.8895	−	11.8895i	−0.467423	−	0.467423i	−0.901079	+	0.433656i	$0.857223\pi$
$648$	4.16871	−	5.12054i	0.163762	−	0.201154i
$649$			42.9094i			1.68434i
$650$	−19.8600	+	5.89882i	−0.778974	+	0.231371i
$651$		−	17.3990i		−	0.681921i
$652$	3.82664	−	19.5051i	0.149863	−	0.763878i
$653$	29.0107	+	29.0107i	1.13528	+	1.13528i	0.989286	+	0.145992i	$0.0466372\pi$
$653$	29.0107	+	29.0107i	1.13528	+	1.13528i	0.145992	+	0.989286i	$0.453363\pi$
$654$	0.579737	+	0.308899i	0.0226695	+	0.0120789i
$655$	−5.78128	+	2.37062i	−0.225893	+	0.0926279i
$656$	1.51132	−	3.70350i	0.0590073	−	0.144597i
$657$	−5.59024	+	5.59024i	−0.218096	+	0.218096i
$658$	7.79014	+	25.5599i	0.303691	+	0.996429i
$659$	−16.9620			−0.660746			−0.330373	−	0.943850i	$-0.607175\pi$
$659$	−16.9620			−0.660746			−0.330373	+	0.943850i	$0.607175\pi$
$660$	−3.16089	−	15.9688i	−0.123038	−	0.621586i
$661$	−28.0409			−1.09066			−0.545332	−	0.838220i	$-0.683596\pi$
$661$	−28.0409			−1.09066			−0.545332	+	0.838220i	$0.683596\pi$
$662$	7.64686	+	25.0898i	0.297204	+	0.975143i
$663$	15.1786	−	15.1786i	0.589490	−	0.589490i
$664$	−1.37428	−	13.4120i	−0.0533325	−	0.520488i
$665$	5.12641	−	12.2528i	0.198793	−	0.475142i
$666$	1.75371	+	0.934423i	0.0679549	+	0.0362081i
$667$	18.0122	+	18.0122i	0.697435	+	0.697435i
$668$	−2.32584	−	0.456299i	−0.0899896	−	0.0176547i
$669$			17.7068i			0.684584i
$670$	0.804700	−	7.98633i	0.0310883	−	0.308539i
$671$		−	60.7767i		−	2.34626i
$672$	1.28768	−	14.0158i	0.0496733	−	0.540671i
$673$	−25.8162	−	25.8162i	−0.995140	−	0.995140i	0.00484872	−	0.999988i	$-0.498457\pi$
$673$	−25.8162	−	25.8162i	−0.995140	−	0.995140i	−0.999988	+	0.00484872i	$0.998457\pi$
$674$	10.6238	−	19.9386i	0.409213	−	0.768005i
$675$	−23.3968	−	0.166479i	−0.900543	−	0.00640777i
$676$	−4.92568	−	7.33009i	−0.189449	−	0.281927i
$677$	8.85534	−	8.85534i	0.340338	−	0.340338i	−0.516156	−	0.856494i	$-0.672638\pi$
$677$	8.85534	−	8.85534i	0.340338	−	0.340338i	0.856494	+	0.516156i	$0.172638\pi$
$678$	9.12312	−	2.78054i	0.350371	−	0.106786i
$679$	38.6728			1.48413
$680$	−45.2770	+	24.2230i	−1.73629	+	0.928911i
$681$	−4.28756			−0.164300
$682$	38.1591	−	11.6301i	1.46119	−	0.445340i
$683$	26.8090	−	26.8090i	1.02582	−	1.02582i	0.0261603	−	0.999658i	$-0.491672\pi$
$683$	26.8090	−	26.8090i	1.02582	−	1.02582i	0.999658	−	0.0261603i	$-0.00832803\pi$
$684$	−5.25243	−	7.81635i	−0.200832	−	0.298866i
$685$	10.0257	+	4.19464i	0.383063	+	0.160269i
$686$	11.7306	−	22.0159i	0.447878	−	0.840571i
$687$	−10.3965	−	10.3965i	−0.396652	−	0.396652i
$688$	−0.605643	−	1.44072i	−0.0230899	−	0.0549271i
$689$			7.23564i			0.275656i
$690$	17.6473	−	14.4166i	0.671823	−	0.548830i
$691$			9.60561i			0.365415i	0.983167	+	0.182707i	$0.0584861\pi$
$691$			9.60561i			0.365415i	−0.983167	+	0.182707i	$0.941514\pi$
$692$	−12.5169	−	2.45564i	−0.475819	−	0.0933494i
$693$	17.1898	+	17.1898i	0.652988	+	0.652988i
$694$	−27.1277	−	14.4543i	−1.02975	−	0.548679i
$695$	−9.36867	−	22.8475i	−0.355374	−	0.866656i
$696$	−8.09919	+	0.829893i	−0.306999	+	0.0314570i
$697$	−5.74104	+	5.74104i	−0.217457	+	0.217457i
$698$	−7.71219	−	25.3042i	−0.291911	−	0.957777i
$699$	4.34200			0.164229
$700$	22.9944	−	15.2154i	0.869107	−	0.575089i
$701$	32.9276			1.24366			0.621830	−	0.783152i	$-0.286390\pi$
$701$	32.9276			1.24366			0.621830	+	0.783152i	$0.286390\pi$
$702$	5.65280	+	18.5472i	0.213351	+	0.700017i
$703$	0.979263	−	0.979263i	0.0369336	−	0.0369336i
$704$	31.5998	−	6.54455i	1.19096	−	0.246657i
$705$	−5.24588	−	12.7932i	−0.197571	−	0.481821i
$706$	−4.81049	−	2.56315i	−0.181045	−	0.0964655i
$707$	36.9035	+	36.9035i	1.38790	+	1.38790i
$708$	3.69594	−	18.8389i	0.138902	−	0.708009i
$709$			18.8092i			0.706395i	0.935549	+	0.353197i	$0.114906\pi$
$709$			18.8092i			0.706395i	−0.935549	+	0.353197i	$0.885094\pi$
$710$	−3.44923	+	2.81777i	−0.129447	+	0.105749i
$711$		−	13.5093i		−	0.506638i
$712$	−23.4352	−	19.0789i	−0.878269	−	0.715012i
$713$	39.4864	+	39.4864i	1.47878	+	1.47878i
$714$	−13.4341	+	25.2129i	−0.502758	+	0.943568i
$715$	−24.3795	−	10.2001i	−0.911742	−	0.381462i
$716$	−12.8001	+	8.60144i	−0.478364	+	0.321451i
$717$	16.9604	−	16.9604i	0.633397	−	0.633397i
$718$	32.8127	−	10.0006i	1.22456	−	0.373221i
$719$	−18.6102			−0.694043			−0.347022	−	0.937857i	$-0.612807\pi$
$719$	−18.6102			−0.694043			−0.347022	+	0.937857i	$0.612807\pi$
$720$	−0.0330219	−	19.5496i	−0.00123065	−	0.728570i
$721$	20.8074			0.774907
$722$	19.4248	−	5.92027i	0.722915	−	0.220330i
$723$	18.8897	−	18.8897i	0.702515	−	0.702515i
$724$	34.2354	−	23.0055i	1.27235	−	0.854992i
$725$	−11.1974	−	11.3579i	−0.415862	−	0.421822i
$726$	3.16347	−	5.93716i	0.117407	−	0.220349i
$727$	31.8467	+	31.8467i	1.18113	+	1.18113i	0.979453	+	0.201675i	$0.0646384\pi$
$727$	31.8467	+	31.8467i	1.18113	+	1.18113i	0.201675	+	0.979453i	$0.435362\pi$
$728$	−17.7198	−	14.4260i	−0.656740	−	0.534662i
$729$			7.56551i			0.280204i
$730$	−1.14669	+	11.3804i	−0.0424409	+	0.421209i
$731$			3.17221i			0.117329i
$732$	−5.23491	+	26.6833i	−0.193488	+	0.986244i
$733$	−14.3288	−	14.3288i	−0.529246	−	0.529246i	0.391102	−	0.920347i	$-0.372094\pi$
$733$	−14.3288	−	14.3288i	−0.529246	−	0.529246i	−0.920347	+	0.391102i	$0.872094\pi$
$734$	18.5831	+	9.90156i	0.685915	+	0.365473i
$735$	0.469243	−	1.12155i	0.0173083	−	0.0413690i
$736$	28.8860	+	34.7307i	1.06475	+	1.28019i
$737$	7.24003	−	7.24003i	0.266690	−	0.266690i
$738$	−0.901167	−	2.95678i	−0.0331724	−	0.108841i
$739$	22.7425			0.836596			0.418298	−	0.908310i	$-0.362627\pi$
$739$	22.7425			0.836596			0.418298	+	0.908310i	$0.362627\pi$
$740$	2.82024	−	0.558242i	0.103674	−	0.0205214i
$741$	5.69561			0.209233
$742$	−2.80747	−	9.21147i	−0.103065	−	0.338164i
$743$	−37.9417	+	37.9417i	−1.39194	+	1.39194i	−0.570983	+	0.820962i	$0.693438\pi$
$743$	−37.9417	+	37.9417i	−1.39194	+	1.39194i	−0.820962	+	0.570983i	$0.806562\pi$
$744$	−17.7551	+	1.81930i	−0.650933	+	0.0666986i
$745$	9.52071	−	3.90398i	0.348812	−	0.143031i
$746$	12.0141	+	6.40142i	0.439868	+	0.234373i
$747$	−7.36709	−	7.36709i	−0.269548	−	0.269548i
$748$	−64.2761	−	12.6101i	−2.35017	−	0.461071i
$749$			27.0113i			0.986972i
$750$	−11.1135	+	8.94780i	−0.405806	+	0.326727i
$751$		−	35.3710i		−	1.29071i	−0.763884	−	0.645353i	$-0.776710\pi$
$751$		−	35.3710i		−	1.29071i	0.763884	−	0.645353i	$-0.223290\pi$
$752$	25.2684	−	10.6222i	0.921445	−	0.387352i
$753$	14.9451	+	14.9451i	0.544631	+	0.544631i
$754$	−6.21531	+	11.6648i	−0.226348	+	0.424807i
$755$	11.2153	−	4.59887i	0.408168	−	0.167370i
$756$	−14.3928	−	21.4185i	−0.523461	−	0.778984i
$757$	−4.08174	+	4.08174i	−0.148353	+	0.148353i	−0.777382	−	0.629029i	$-0.783453\pi$
$757$	−4.08174	+	4.08174i	−0.148353	+	0.148353i	0.629029	+	0.777382i	$0.283453\pi$
$758$	−3.14654	+	0.959001i	−0.114287	+	0.0348325i
$759$	29.0677			1.05509
$760$	−13.0395	−	3.95013i	−0.472994	−	0.143286i
$761$	−37.2819			−1.35147			−0.675734	−	0.737145i	$-0.736173\pi$
$761$	−37.2819			−1.35147			−0.675734	+	0.737145i	$0.736173\pi$
$762$	22.3633	−	6.81589i	0.810139	−	0.246914i
$763$	−1.00359	+	1.00359i	−0.0363324	+	0.0363324i
$764$	5.88929	+	8.76408i	0.213067	+	0.317073i
$765$	−15.3156	+	36.6063i	−0.553738	+	1.32350i
$766$	8.64332	−	16.2217i	0.312296	−	0.586112i
$767$	−22.0382	−	22.0382i	−0.795752	−	0.795752i
$768$	−14.4373	+	0.151504i	−0.520960	+	0.00546695i
$769$		−	41.6703i		−	1.50267i	−0.659921	−	0.751335i	$-0.729410\pi$
$769$		−	41.6703i		−	1.50267i	0.659921	−	0.751335i	$-0.270590\pi$
$770$	34.9945	+	3.52604i	1.26112	+	0.127070i
$771$			20.4103i			0.735060i
$772$	−4.63338	−	0.909006i	−0.166759	−	0.0327159i
$773$	−26.5873	−	26.5873i	−0.956279	−	0.956279i	0.0428046	−	0.999083i	$-0.486371\pi$
$773$	−26.5873	−	26.5873i	−0.956279	−	0.956279i	−0.999083	+	0.0428046i	$0.986371\pi$
$774$	−1.06586	−	0.567915i	−0.0383114	−	0.0204133i
$775$	−24.5470	−	24.8989i	−0.881756	−	0.894394i
$776$	−4.04375	−	39.4643i	−0.145162	−	1.41668i
$777$	1.13102	−	1.13102i	0.0405750	−	0.0405750i
$778$	−2.54241	−	8.34180i	−0.0911498	−	0.299068i
$779$	−2.15426			−0.0771844
$780$	9.82499	+	6.57814i	0.351791	+	0.235535i
$781$	−5.68136			−0.203295
$782$	−26.7316	−	87.7079i	−0.955919	−	3.13643i
$783$	−10.5550	+	10.5550i	−0.377205	+	0.377205i
$784$	2.23144	+	0.910604i	0.0796942	+	0.0325216i
$785$	13.9203	+	5.82407i	0.496836	+	0.207870i
$786$	3.14720	+	1.67691i	0.112257	+	0.0598134i
$787$	26.3608	+	26.3608i	0.939660	+	0.939660i	0.998280	−	0.0586202i	$-0.0186701\pi$
$787$	26.3608	+	26.3608i	0.939660	+	0.939660i	−0.0586202	+	0.998280i	$0.518670\pi$
$788$	−4.16185	+	21.2137i	−0.148260	+	0.755708i
$789$			8.74930i			0.311483i
$790$	−12.3654	−	15.1365i	−0.439940	−	0.538531i
$791$			20.6066i			0.732687i
$792$	15.7442	−	19.3390i	0.559446	−	0.687183i
$793$	31.2148	+	31.2148i	1.10847	+	1.10847i
$794$	−2.30585	+	4.32758i	−0.0818314	+	0.153580i
$795$	1.89055	+	4.61052i	0.0670509	+	0.163518i
$796$	−31.2287	+	20.9851i	−1.10687	+	0.743796i
$797$	8.35530	−	8.35530i	0.295960	−	0.295960i	−0.543469	−	0.839429i	$-0.682890\pi$
$797$	8.35530	−	8.35530i	0.295960	−	0.295960i	0.839429	+	0.543469i	$0.182890\pi$
$798$	−7.25091	+	2.20993i	−0.256679	+	0.0782307i
$799$	−55.6365			−1.96828
$800$	−17.9312	−	21.8740i	−0.633963	−	0.773364i
$801$	−23.3525			−0.825120
$802$	19.4936	−	5.94124i	0.688342	−	0.209793i
$803$	−10.3170	+	10.3170i	−0.364078	+	0.364078i
$804$	−3.80227	+	2.55505i	−0.134096	+	0.0901096i
$805$	18.6793	+	45.5536i	0.658359	+	1.60555i
$806$	−13.6252	+	25.5716i	−0.479928	+	0.900722i
$807$	−0.640240	−	0.640240i	−0.0225375	−	0.0225375i
$808$	33.8000	−	41.5175i	1.18908	−	1.46058i
$809$		−	5.63303i		−	0.198047i	−0.995085	−	0.0990234i	$-0.968428\pi$
$809$		−	5.63303i		−	0.198047i	0.995085	−	0.0990234i	$-0.0315719\pi$
$810$	−4.67042	−	5.71706i	−0.164102	−	0.200877i
$811$			43.8944i			1.54134i	0.637234	+	0.770670i	$0.280078\pi$
$811$			43.8944i			1.54134i	−0.637234	+	0.770670i	$0.719922\pi$
$812$	3.38651	−	17.2617i	0.118843	−	0.605767i
$813$	−17.6318	−	17.6318i	−0.618374	−	0.618374i
$814$	3.23653	+	1.72451i	0.113440	+	0.0604440i
$815$	−20.5010	−	8.57739i	−0.718120	−	0.300453i
$816$	27.1336	+	11.0727i	0.949865	+	0.387621i
$817$	−0.595168	+	0.595168i	−0.0208223	+	0.0208223i
$818$	−6.45885	−	21.1919i	−0.225829	−	0.740957i
$819$	−17.6573			−0.616997
$820$	−3.71612	−	2.48806i	−0.129773	−	0.0868868i
$821$	−10.5431			−0.367957			−0.183979	−	0.982930i	$-0.558898\pi$
$821$	−10.5431			−0.367957			−0.183979	+	0.982930i	$0.558898\pi$
$822$	−1.80826	−	5.93299i	−0.0630702	−	0.206937i
$823$	28.2777	−	28.2777i	0.985698	−	0.985698i	−0.0142009	−	0.999899i	$-0.504520\pi$
$823$	28.2777	−	28.2777i	0.985698	−	0.985698i	0.999899	+	0.0142009i	$0.00452044\pi$
$824$	−2.17569	−	21.2332i	−0.0757936	−	0.739694i
$825$	−18.1996	−	0.129499i	−0.633630	−	0.00450856i
$826$	36.6071	+	19.5052i	1.27372	+	0.678672i
$827$	0.558699	+	0.558699i	0.0194279	+	0.0194279i	0.716754	−	0.697326i	$-0.245627\pi$
$827$	0.558699	+	0.558699i	0.0194279	+	0.0194279i	−0.697326	+	0.716754i	$0.745627\pi$
$828$	34.2553	+	6.72044i	1.19046	+	0.233551i
$829$		−	1.98019i		−	0.0687750i	−0.999409	−	0.0343875i	$-0.989052\pi$
$829$		−	1.98019i		−	0.0687750i	0.999409	−	0.0343875i	$-0.0109480\pi$
$830$	−14.9977	−	1.51116i	−0.520577	−	0.0524532i
$831$		−	4.89840i		−	0.169924i
$832$	−12.8683	+	19.5909i	−0.446130	+	0.679192i
$833$	−3.45910	−	3.45910i	−0.119851	−	0.119851i
$834$	−6.62713	+	12.4377i	−0.229479	+	0.430682i
$835$	−1.02279	+	2.44460i	−0.0353952	+	0.0845990i
$836$	−9.69353	−	14.4253i	−0.335258	−	0.498911i
$837$	−23.1387	+	23.1387i	−0.799790	+	0.799790i
$838$	31.9448	−	9.73614i	1.10352	−	0.336329i
$839$	52.0647			1.79747			0.898737	−	0.438489i	$-0.144486\pi$
$839$	52.0647			1.79747			0.898737	+	0.438489i	$0.144486\pi$
$840$	−15.0603	−	4.56227i	−0.519628	−	0.157413i
$841$	18.8246			0.649125
$842$	−6.29004	+	1.91708i	−0.216769	+	0.0660668i
$843$	8.48824	−	8.48824i	0.292351	−	0.292351i
$844$	−5.67743	−	8.44881i	−0.195425	−	0.290820i
$845$	−9.13553	+	3.74604i	−0.314272	+	0.128868i
$846$	9.96050	−	18.6937i	0.342449	−	0.642703i
$847$	10.2779	+	10.2779i	0.353153	+	0.353153i
$848$	−9.10643	+	3.82811i	−0.312716	+	0.131458i
$849$		−	28.8106i		−	0.988776i
$850$	16.3462	+	55.0341i	0.560671	+	1.88766i
$851$			5.13361i			0.175978i
$852$	2.49434	+	0.489356i	0.0854547	+	0.0167651i
$853$	20.5102	+	20.5102i	0.702257	+	0.702257i	0.964895	−	0.262637i	$-0.0845923\pi$
$853$	20.5102	+	20.5102i	0.702257	+	0.702257i	−0.262637	+	0.964895i	$0.584592\pi$
$854$	−51.8501	−	27.6271i	−1.77427	−	0.945379i
$855$	−9.74155	+	3.99454i	−0.333154	+	0.136610i
$856$	27.5641	−	2.82439i	0.942121	−	0.0965356i
$857$	−27.6084	+	27.6084i	−0.943085	+	0.943085i	−0.998465	−	0.0553807i	$-0.982363\pi$
$857$	−27.6084	+	27.6084i	−0.943085	+	0.943085i	0.0553807	+	0.998465i	$0.482363\pi$
$858$	4.39713	+	14.4273i	0.150116	+	0.492538i
$859$	27.8302			0.949553			0.474776	−	0.880106i	$-0.342529\pi$
$859$	27.8302			0.949553			0.474776	+	0.880106i	$0.342529\pi$
$860$	−1.71406	+	0.339283i	−0.0584490	+	0.0115695i
$861$	−2.48810			−0.0847942
$862$	9.25309	+	30.3599i	0.315162	+	1.03406i
$863$	−8.13263	+	8.13263i	−0.276838	+	0.276838i	−0.831845	−	0.555007i	$-0.812715\pi$
$863$	−8.13263	+	8.13263i	−0.276838	+	0.276838i	0.555007	+	0.831845i	$0.312715\pi$
$864$	−20.3519	+	16.9269i	−0.692385	+	0.575866i
$865$	−5.50430	+	13.1560i	−0.187152	+	0.447317i
$866$	−32.1818	−	17.1473i	−1.09358	−	0.582689i
$867$	−31.2142	−	31.2142i	−1.06009	−	1.06009i
$868$	7.42392	−	37.8411i	0.251984	−	1.28441i
$869$		−	24.9319i		−	0.845756i
$870$	−0.912552	+	9.05672i	−0.0309384	+	0.307052i
$871$			7.43693i			0.251991i
$872$	1.12907	+	0.919191i	0.0382351	+	0.0311277i
$873$	−21.6773	−	21.6773i	−0.733665	−	0.733665i
$874$	11.4403	−	21.4710i	0.386975	−	0.726269i
$875$	−11.4924	−	28.6049i	−0.388514	−	0.967022i
$876$	5.41820	−	3.64092i	0.183064	−	0.123015i
$877$	−20.4230	+	20.4230i	−0.689636	+	0.689636i	−0.962151	−	0.272516i	$-0.912144\pi$
$877$	−20.4230	+	20.4230i	−0.689636	+	0.689636i	0.272516	+	0.962151i	$0.412144\pi$
$878$	−28.5010	+	8.68651i	−0.961861	+	0.293156i
$879$	6.66232			0.224714
$880$	−0.0609431	−	36.0794i	−0.00205439	−	1.21624i
$881$	44.0279			1.48334			0.741669	−	0.670766i	$-0.234034\pi$
$881$	44.0279			1.48334			0.741669	+	0.670766i	$0.234034\pi$
$882$	1.78152	−	0.542972i	0.0599871	−	0.0182828i
$883$	−0.939158	+	0.939158i	−0.0316052	+	0.0316052i	−0.722733	−	0.691128i	$-0.757114\pi$
$883$	−0.939158	+	0.939158i	−0.0316052	+	0.0316052i	0.691128	+	0.722733i	$0.257114\pi$
$884$	39.4886	−	26.5356i	1.32815	−	0.892487i
$885$	−19.8008	−	8.28443i	−0.665598	−	0.278478i
$886$	6.42361	−	12.0557i	0.215805	−	0.405020i
$887$	9.31080	+	9.31080i	0.312626	+	0.312626i	0.845926	−	0.533300i	$-0.179048\pi$
$887$	9.31080	+	9.31080i	0.312626	+	0.312626i	−0.533300	+	0.845926i	$0.679048\pi$
$888$	−1.27243	−	1.03590i	−0.0426998	−	0.0347626i
$889$			50.5126i			1.69414i
$890$	−26.1652	+	21.3751i	−0.877060	+	0.716494i
$891$		−	9.41680i		−	0.315475i
$892$	−7.55525	+	38.5105i	−0.252969	+	1.28943i
$893$	−10.4385	−	10.4385i	−0.349310	−	0.349310i
$894$	−5.18287	−	2.76156i	−0.173341	−	0.0923605i
$895$	6.54150	+	15.9529i	0.218658	+	0.533246i
$896$	8.78093	−	29.9336i	0.293350	−	1.00001i
$897$	−14.9291	+	14.9291i	−0.498468	+	0.498468i
$898$	3.50013	+	11.4841i	0.116801	+	0.383230i
$899$	−22.3065			−0.743964
$900$	−21.4178	−	4.36036i	−0.713926	−	0.145345i
$901$	20.0507			0.667985
$902$	−1.66313	−	5.45684i	−0.0553763	−	0.181693i
$903$	−0.687400	+	0.687400i	−0.0228752	+	0.0228752i
$904$	21.0283	−	2.15469i	0.699392	−	0.0716641i
$905$	−17.4959	−	42.6677i	−0.581585	−	1.41832i
$906$	−6.10539	−	3.25311i	−0.202838	−	0.108077i
$907$	17.9482	+	17.9482i	0.595959	+	0.595959i	0.939235	−	0.343276i	$-0.111537\pi$
$907$	17.9482	+	17.9482i	0.595959	+	0.595959i	−0.343276	+	0.939235i	$0.611537\pi$
$908$	−9.32503	−	1.82945i	−0.309462	−	0.0607123i
$909$		−	41.3711i		−	1.37219i
$910$	−19.7841	+	16.1622i	−0.655836	+	0.535770i
$911$		−	1.18779i		−	0.0393532i	−0.999806	−	0.0196766i	$-0.993736\pi$
$911$		−	1.18779i		−	0.0393532i	0.999806	−	0.0196766i	$-0.00626366\pi$
$912$	3.01334	+	7.16822i	0.0997815	+	0.237364i
$913$	−13.5962	−	13.5962i	−0.449969	−	0.449969i
$914$	−16.3847	+	30.7506i	−0.541958	+	1.01714i
$915$	28.0458	+	11.7340i	0.927166	+	0.387915i
$916$	−18.1754	−	27.0475i	−0.600531	−	0.893673i
$917$	−5.44817	+	5.44817i	−0.179914	+	0.179914i
$918$	51.3961	−	15.6645i	1.69632	−	0.517005i
$919$	−56.6966			−1.87025			−0.935125	−	0.354319i	$-0.884713\pi$
$919$	−56.6966			−1.87025			−0.935125	+	0.354319i	$0.884713\pi$
$920$	44.5326	−	23.8248i	1.46820	−	0.785481i
$921$	−6.55097			−0.215862
$922$	−11.4082	+	3.47698i	−0.375708	+	0.114508i
$923$	2.91794	−	2.91794i	0.0960450	−	0.0960450i
$924$	−11.1957	−	16.6608i	−0.368312	−	0.548100i
$925$	0.0228706	−	3.21422i	0.000751980	−	0.105683i
$926$	−5.65537	+	10.6139i	−0.185847	+	0.348795i
$927$	−11.6632	−	11.6632i	−0.383069	−	0.383069i
$928$	−17.9691	−	1.65088i	−0.589863	−	0.0541928i
$929$			8.73875i			0.286709i	0.989671	+	0.143355i	$0.0457889\pi$
$929$			8.73875i			0.286709i	−0.989671	+	0.143355i	$0.954211\pi$
$930$	−2.00050	+	19.8542i	−0.0655990	+	0.651044i
$931$		−	1.29799i		−	0.0425398i
$932$	9.44342	+	1.85267i	0.309330	+	0.0606863i
$933$	15.7183	+	15.7183i	0.514594	+	0.514594i
$934$	−8.86666	−	4.72438i	−0.290126	−	0.154587i
$935$	−28.2655	+	67.5581i	−0.924381	+	2.20939i
$936$	1.84631	+	18.0187i	0.0603484	+	0.588959i
$937$	−21.5108	+	21.5108i	−0.702728	+	0.702728i	−0.964995	−	0.262267i	$-0.915530\pi$
$937$	−21.5108	+	21.5108i	−0.702728	+	0.702728i	0.262267	+	0.964995i	$0.415530\pi$
$938$	−2.88557	−	9.46774i	−0.0942173	−	0.309133i
$939$	−5.91686			−0.193089
$940$	−5.95059	−	30.0624i	−0.194087	−	0.980527i
$941$	31.6452			1.03160			0.515802	−	0.856708i	$-0.327494\pi$
$941$	31.6452			1.03160			0.515802	+	0.856708i	$0.327494\pi$
$942$	−2.51069	−	8.23771i	−0.0818026	−	0.268399i
$943$	5.64666	−	5.64666i	0.183880	−	0.183880i
$944$	16.0766	−	39.3958i	0.523249	−	1.28222i
$945$	−26.6940	+	10.9459i	−0.868355	+	0.356071i
$946$	−1.96707	−	1.04811i	−0.0639550	−	0.0340769i
$947$	−2.29952	−	2.29952i	−0.0747244	−	0.0747244i	0.668757	−	0.743481i	$-0.266827\pi$
$947$	−2.29952	−	2.29952i	−0.0747244	−	0.0747244i	−0.743481	+	0.668757i	$0.766827\pi$
$948$	−2.14747	+	10.9461i	−0.0697466	+	0.355512i
$949$		−	10.5976i		−	0.344011i
$950$	−7.25859	+	13.3923i	−0.235500	+	0.434505i
$951$		−	31.4830i		−	1.02091i
$952$	−39.9758	+	49.1034i	−1.29562	+	1.59145i
$953$	38.0424	+	38.0424i	1.23231	+	1.23231i	0.963072	+	0.269243i	$0.0867733\pi$
$953$	38.0424	+	38.0424i	1.23231	+	1.23231i	0.269243	+	0.963072i	$0.413227\pi$
$954$	−3.58964	+	6.73698i	−0.116219	+	0.218118i
$955$	10.9227	−	4.47888i	0.353451	−	0.144933i
$956$	44.1239	−	29.6504i	1.42707	−	0.958962i
$957$	−8.21040	+	8.21040i	−0.265405	+	0.265405i
$958$	7.94418	−	2.42123i	0.256665	−	0.0782262i
$959$	13.4010			0.432741
$960$	−3.08089	+	15.8455i	−0.0994353	+	0.511412i
$961$	−17.9004			−0.577434
$962$	−2.54798	+	0.776573i	−0.0821502	+	0.0250377i
$963$	15.1407	−	15.1407i	0.487901	−	0.487901i
$964$	49.1432	−	33.0232i	1.58280	−	1.06361i
$965$	−2.03753	+	4.86996i	−0.0655905	+	0.156770i
$966$	13.2132	−	24.7984i	0.425128	−	0.797874i
$967$	−23.1621	−	23.1621i	−0.744842	−	0.744842i	0.228663	−	0.973506i	$-0.426564\pi$
$967$	−23.1621	−	23.1621i	−0.744842	−	0.744842i	−0.973506	+	0.228663i	$0.926564\pi$
$968$	9.41355	−	11.5629i	0.302563	−	0.371647i
$969$		−	15.7831i		−	0.507027i
$970$	−44.1300	−	4.44652i	−1.41693	−	0.142769i
$971$			45.2890i			1.45339i	0.686958	+	0.726697i	$0.258946\pi$
$971$			45.2890i			1.45339i	−0.686958	+	0.726697i	$0.741054\pi$
$972$	−6.21637	+	31.6860i	−0.199390	+	1.01633i
$973$	−21.5311	−	21.5311i	−0.690255	−	0.690255i
$974$	−18.4928	−	9.85346i	−0.592549	−	0.315725i
$975$	9.41381	−	9.28079i	0.301483	−	0.297223i
$976$	−22.7709	+	55.8000i	−0.728877	+	1.78611i
$977$	−24.9918	+	24.9918i	−0.799558	+	0.799558i	−0.983026	−	0.183468i	$-0.941268\pi$
$977$	−24.9918	+	24.9918i	−0.799558	+	0.799558i	0.183468	+	0.983026i	$0.441268\pi$
$978$	3.69761	+	12.1321i	0.118236	+	0.387941i
$979$	−43.0978			−1.37741
$980$	1.49911	−	2.23904i	0.0478872	−	0.0715236i
$981$	1.12509			0.0359213
$982$	16.0820	+	52.7660i	0.513197	+	1.68383i
$983$	−12.5294	+	12.5294i	−0.399627	+	0.399627i	−0.878102	−	0.478474i	$-0.841190\pi$
$983$	−12.5294	+	12.5294i	−0.399627	+	0.399627i	0.478474	+	0.878102i	$0.341190\pi$
$984$	0.260164	+	2.53902i	0.00829372	+	0.0809410i
$985$	22.2969	+	9.32877i	0.710440	+	0.297239i
$986$	32.3244	+	17.2233i	1.02942	+	0.548500i
$987$	−12.0561	−	12.0561i	−0.383750	−	0.383750i
$988$	12.3874	+	2.43024i	0.394096	+	0.0773163i
$989$		−	3.12006i		−	0.0992121i
$990$	−17.6390	−	21.5919i	−0.560606	−	0.686237i
$991$			3.28857i			0.104465i	0.998635	+	0.0522325i	$0.0166337\pi$
$991$			3.28857i			0.104465i	−0.998635	+	0.0522325i	$0.983366\pi$
$992$	−39.3918	−	3.61906i	−1.25069	−	0.114905i
$993$	−11.8344	−	11.8344i	−0.375552	−	0.375552i
$994$	−2.58256	+	4.84691i	−0.0819138	+	0.153735i
$995$	15.9594	+	38.9205i	0.505947	+	1.23386i
$996$	4.79818	+	7.14036i	0.152036	+	0.226251i
$997$	14.2413	−	14.2413i	0.451026	−	0.451026i	−0.444669	−	0.895695i	$-0.646679\pi$
$997$	14.2413	−	14.2413i	0.451026	−	0.451026i	0.895695	+	0.444669i	$0.146679\pi$
$998$	−31.8184	+	9.69759i	−1.00719	+	0.306972i
$999$	−3.00825			−0.0951768

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.k.c.83.7	✓	108
4.3	odd	2	inner	820.2.k.c.83.19	yes	108
5.2	odd	4	inner	820.2.k.c.247.19	yes	108
20.7	even	4	inner	820.2.k.c.247.7	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.7	✓	108	1.1	even	1	trivial
820.2.k.c.83.19	yes	108	4.3	odd	2	inner
820.2.k.c.247.7	yes	108	20.7	even	4	inner
820.2.k.c.247.19	yes	108	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35278 + 0.412299i) q^{2} +(0.638078 - 0.638078i) q^{3} +(1.66002 - 1.11550i) q^{4} +(-0.848351 - 2.06889i) q^{5} +(-0.600099 + 1.12626i) q^{6} +(-1.94968 - 1.94968i) q^{7} +(-1.78572 + 2.19345i) q^{8} +2.18571i q^{9} +(2.00063 + 2.44897i) q^{10} +4.03380i q^{11} +(0.347446 - 1.77100i) q^{12} +(-2.07175 - 2.07175i) q^{13} +(3.44134 + 1.83364i) q^{14} +(-1.86143 - 0.778799i) q^{15} +(1.51132 - 3.70350i) q^{16} +(-5.74104 + 5.74104i) q^{17} +(-0.901167 - 2.95678i) q^{18} -2.15426 q^{19} +(-3.71612 - 2.48806i) q^{20} -2.48810 q^{21} +(-1.66313 - 5.45684i) q^{22} +(5.64666 - 5.64666i) q^{23} +(0.260164 + 2.53902i) q^{24} +(-3.56060 + 3.51029i) q^{25} +(3.65681 + 1.94844i) q^{26} +(3.30889 + 3.30889i) q^{27} +(-5.41138 - 1.06164i) q^{28} +3.18989i q^{29} +(2.83920 + 0.286077i) q^{30} +6.99289i q^{31} +(-0.517535 + 5.63313i) q^{32} +(2.57388 + 2.57388i) q^{33} +(5.39933 - 10.1334i) q^{34} +(-2.37966 + 5.68769i) q^{35} +(2.43816 + 3.62832i) q^{36} +(-0.454571 + 0.454571i) q^{37} +(2.91424 - 0.888200i) q^{38} -2.64388 q^{39} +(6.05291 + 1.83364i) q^{40} +1.00000 q^{41} +(3.36585 - 1.02584i) q^{42} +(0.276275 - 0.276275i) q^{43} +(4.49971 + 6.69619i) q^{44} +(4.52199 - 1.85425i) q^{45} +(-5.31056 + 9.96679i) q^{46} +(4.84550 + 4.84550i) q^{47} +(-1.39878 - 3.32747i) q^{48} +0.602521i q^{49} +(3.36941 - 6.21668i) q^{50} +7.32647i q^{51} +(-5.75019 - 1.12811i) q^{52} +(-1.74626 - 1.74626i) q^{53} +(-5.84045 - 3.11194i) q^{54} +(8.34549 - 3.42208i) q^{55} +(7.75811 - 0.794944i) q^{56} +(-1.37459 + 1.37459i) q^{57} +(-1.31519 - 4.31521i) q^{58} +10.6374 q^{59} +(-3.95875 + 0.783601i) q^{60} -15.0668 q^{61} +(-2.88316 - 9.45982i) q^{62} +(4.26144 - 4.26144i) q^{63} +(-1.62243 - 7.83376i) q^{64} +(-2.52865 + 6.04380i) q^{65} +(-4.54310 - 2.42068i) q^{66} +(-1.79484 - 1.79484i) q^{67} +(-3.12611 + 15.9344i) q^{68} -7.20602i q^{69} +(0.874122 - 8.67532i) q^{70} +1.40844i q^{71} +(-4.79424 - 3.90306i) q^{72} +(2.55763 + 2.55763i) q^{73} +(0.427514 - 0.802352i) q^{74} +(-0.0321033 + 4.51178i) q^{75} +(-3.57611 + 2.40307i) q^{76} +(7.86464 - 7.86464i) q^{77} +(3.57659 - 1.09007i) q^{78} -6.18073 q^{79} +(-8.94426 + 0.0151081i) q^{80} -2.33447 q^{81} +(-1.35278 + 0.412299i) q^{82} +(-3.37057 + 3.37057i) q^{83} +(-4.13029 + 2.77547i) q^{84} +(16.7480 + 7.00716i) q^{85} +(-0.259831 + 0.487647i) q^{86} +(2.03540 + 2.03540i) q^{87} +(-8.84794 - 7.20324i) q^{88} +10.6842i q^{89} +(-5.35275 + 4.37281i) q^{90} +8.07852i q^{91} +(3.07471 - 15.6724i) q^{92} +(4.46201 + 4.46201i) q^{93} +(-8.55269 - 4.55710i) q^{94} +(1.82757 + 4.45692i) q^{95} +(3.26415 + 3.92461i) q^{96} +(-9.91772 + 9.91772i) q^{97} +(-0.248419 - 0.815078i) q^{98} -8.81673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) \) 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Introduction

L-functions

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