LMFDB - Embedded newform 820.2.k.c.247.7

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			247.7
Character	$\chi$	$=$	820.247
Dual form			820.2.k.c.83.7

$q$-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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

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

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	0.866892	−	0.498497i	$-0.166114\pi$
$3$	0.638078	+	0.638078i	0.368395	+	0.368395i	−0.498497	+	0.866892i	$0.666114\pi$
$4$	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	−0.971979	−	0.235068i	$-0.924469\pi$
$7$	−1.94968	+	1.94968i	−0.736911	+	0.736911i	0.235068	+	0.971979i	$0.424469\pi$
$8$	−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	$-0.791924\pi$
$11$		−	4.03380i		−	1.21624i	0.793846	−	0.608119i	$-0.208076\pi$
$12$	0.347446	+	1.77100i	0.100299	+	0.511243i
$13$	−2.07175	+	2.07175i	−0.574601	+	0.574601i	−0.933411	−	0.358810i	$-0.883183\pi$
$13$	−2.07175	+	2.07175i	−0.574601	+	0.574601i	0.358810	+	0.933411i	$0.383183\pi$
$14$	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	−0.819899	−	0.572508i	$-0.805971\pi$
$17$	−5.74104	−	5.74104i	−1.39241	−	1.39241i	−0.572508	−	0.819899i	$-0.694029\pi$
$18$	−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	0.980402	+	0.197007i	$0.0631222\pi$
$23$	5.64666	+	5.64666i	1.17741	+	1.17741i	0.197007	+	0.980402i	$0.436878\pi$
$24$	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	$-0.904289\pi$
$29$		−	3.18989i		−	0.592347i	0.955134	−	0.296174i	$-0.0957107\pi$
$30$	2.83920	−	0.286077i	0.518364	−	0.0522302i
$31$		−	6.99289i		−	1.25596i	−0.778230	−	0.627980i	$-0.783882\pi$
$31$		−	6.99289i		−	1.25596i	0.778230	−	0.627980i	$-0.216118\pi$
$32$	−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	0.668753	−	0.743484i	$-0.266828\pi$
$37$	−0.454571	−	0.454571i	−0.0747309	−	0.0747309i	−0.743484	+	0.668753i	$0.766828\pi$
$38$	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	0.727859	−	0.685727i	$-0.240516\pi$
$43$	0.276275	+	0.276275i	0.0421315	+	0.0421315i	−0.685727	+	0.727859i	$0.740516\pi$
$44$	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	−0.259069	−	0.965859i	$-0.583416\pi$
$47$	4.84550	−	4.84550i	0.706789	−	0.706789i	0.965859	+	0.259069i	$0.0834158\pi$
$48$	−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	−0.816795	−	0.576928i	$-0.804251\pi$
$53$	−1.74626	+	1.74626i	−0.239867	+	0.239867i	0.576928	+	0.816795i	$0.304251\pi$
$54$	−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	−0.808193	−	0.588918i	$-0.799554\pi$
$67$	−1.79484	+	1.79484i	−0.219275	+	0.219275i	0.588918	+	0.808193i	$0.299554\pi$
$68$	−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	$-0.973366\pi$
$71$		−	1.40844i		−	0.167151i	0.996501	−	0.0835754i	$-0.0266339\pi$
$72$	−4.79424	+	3.90306i	−0.565007	+	0.459980i
$73$	2.55763	−	2.55763i	0.299348	−	0.299348i	−0.541410	−	0.840758i	$-0.682109\pi$
$73$	2.55763	−	2.55763i	0.299348	−	0.299348i	0.840758	+	0.541410i	$0.182109\pi$
$74$	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	0.497498	−	0.867465i	$-0.334252\pi$
$83$	−3.37057	−	3.37057i	−0.369968	−	0.369968i	−0.867465	+	0.497498i	$0.834252\pi$
$84$	−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	$-0.808390\pi$
$89$		−	10.6842i		−	1.13252i	0.824227	−	0.566259i	$-0.191610\pi$
$90$	−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	−0.999975	−	0.00701685i	$-0.997766\pi$
$97$	−9.91772	−	9.91772i	−1.00699	−	1.00699i	−0.00701685	−	0.999975i	$-0.502234\pi$
$98$	−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	0.393531	−	0.919312i	$-0.371254\pi$
$103$	−5.33609	−	5.33609i	−0.525781	−	0.525781i	−0.919312	+	0.393531i	$0.871254\pi$
$104$	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	−0.957639	−	0.287971i	$-0.907019\pi$
$107$	−6.92710	+	6.92710i	−0.669669	+	0.669669i	0.287971	+	0.957639i	$0.407019\pi$
$108$	9.18389	−	1.80176i	0.883720	−	0.173374i
$109$			0.514746i			0.0493037i	0.999696	+	0.0246519i	$0.00784773\pi$
$109$			0.514746i			0.0493037i	−0.999696	+	0.0246519i	$0.992152\pi$
$110$	−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	−0.910545	−	0.413411i	$-0.864337\pi$
$113$	−5.28461	+	5.28461i	−0.497134	+	0.497134i	0.413411	+	0.910545i	$0.364337\pi$
$114$	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	−0.162834	+	0.986653i	$0.552063\pi$
$127$	−12.9541	+	12.9541i	−1.14949	+	1.14949i	−0.986653	+	0.162834i	$0.947937\pi$
$128$	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	$0.0389543\pi$
$131$			2.79439i			0.244147i	−0.992521	+	0.122073i	$0.961046\pi$
$132$	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	0.544890	−	0.838508i	$-0.316572\pi$
$137$	−3.43671	−	3.43671i	−0.293618	−	0.293618i	−0.838508	+	0.544890i	$0.816572\pi$
$138$	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	$-0.939638\pi$
$149$		−	4.60185i		−	0.376998i	0.982073	−	0.188499i	$-0.0603622\pi$
$150$	−1.81678	+	6.11668i	−0.148339	+	0.499425i
$151$		−	5.42095i		−	0.441151i	−0.975370	−	0.220575i	$-0.929207\pi$
$151$		−	5.42095i		−	0.441151i	0.975370	−	0.220575i	$-0.0707935\pi$
$152$	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	0.490574	−	0.871399i	$-0.336787\pi$
$157$	−4.77173	−	4.77173i	−0.380825	−	0.380825i	−0.871399	+	0.490574i	$0.836787\pi$
$158$	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	0.926568	−	0.376128i	$-0.122745\pi$
$163$	7.02755	+	7.02755i	0.550440	+	0.550440i	−0.376128	+	0.926568i	$0.622745\pi$
$164$	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	−0.738786	−	0.673940i	$-0.764600\pi$
$167$	−0.837985	+	0.837985i	−0.0648452	+	0.0648452i	0.673940	+	0.738786i	$0.264600\pi$
$168$	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	−0.857445	−	0.514576i	$-0.827949\pi$
$173$	−4.50974	+	4.50974i	−0.342869	+	0.342869i	0.514576	+	0.857445i	$0.327949\pi$
$174$	−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	$-0.938825\pi$
$191$		−	5.27951i		−	0.382012i	0.981589	−	0.191006i	$-0.0611750\pi$
$192$	−6.03379	+	3.96332i	−0.435451	+	0.286028i
$193$	−1.66937	+	1.66937i	−0.120164	+	0.120164i	−0.764632	−	0.644468i	$-0.777079\pi$
$193$	−1.66937	+	1.66937i	−0.120164	+	0.120164i	0.644468	+	0.764632i	$0.277079\pi$
$194$	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	0.380307	−	0.924860i	$-0.375818\pi$
$197$	−7.64317	−	7.64317i	−0.544553	−	0.544553i	−0.924860	+	0.380307i	$0.875818\pi$
$198$	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	$0.0560542\pi$
$211$			5.08959i			0.350382i	−0.984535	+	0.175191i	$0.943946\pi$
$212$	−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	0.0685064	−	0.997651i	$-0.478177\pi$
$223$	−13.8751	−	13.8751i	−0.929144	−	0.929144i	−0.997651	+	0.0685064i	$0.978177\pi$
$224$	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	−0.809758	−	0.586764i	$-0.800402\pi$
$227$	−3.35974	+	3.35974i	−0.222994	+	0.222994i	0.586764	+	0.809758i	$0.300402\pi$
$228$	−0.748489	−	3.81519i	−0.0495699	−	0.252667i
$229$			16.2935i			1.07670i	0.842720	+	0.538352i	$0.180953\pi$
$229$			16.2935i			1.07670i	−0.842720	+	0.538352i	$0.819047\pi$
$230$	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	−0.586819	−	0.809718i	$-0.699620\pi$
$233$	3.40240	−	3.40240i	0.222899	−	0.222899i	0.809718	+	0.586819i	$0.199620\pi$
$234$	−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	$-0.735206\pi$
$251$		−	23.4221i		−	1.47839i	0.673492	−	0.739195i	$-0.264794\pi$
$252$	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	0.00234525	−	0.999997i	$-0.499253\pi$
$257$	−15.9936	−	15.9936i	−0.997652	−	0.997652i	−0.999997	+	0.00234525i	$0.999253\pi$
$258$	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	0.463395	−	0.886152i	$-0.346631\pi$
$263$	−6.85597	−	6.85597i	−0.422757	−	0.422757i	−0.886152	+	0.463395i	$0.846631\pi$
$264$	−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	$0.00973824\pi$
$269$			1.00339i			0.0611777i	−0.999532	+	0.0305888i	$0.990262\pi$
$270$	−1.48351	−	14.7233i	−0.0902836	−	0.896029i
$271$			27.6326i			1.67856i	0.543697	+	0.839281i	$0.317024\pi$
$271$			27.6326i			1.67856i	−0.543697	+	0.839281i	$0.682976\pi$
$272$	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	0.812954	−	0.582327i	$-0.197858\pi$
$277$	3.83840	+	3.83840i	0.230627	+	0.230627i	−0.582327	+	0.812954i	$0.697858\pi$
$278$	−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	0.894061	+	0.447945i	$0.147844\pi$
$283$	22.5760	+	22.5760i	1.34201	+	1.34201i	0.447945	+	0.894061i	$0.352156\pi$
$284$	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	−0.537972	−	0.842963i	$-0.680809\pi$
$293$	5.22061	−	5.22061i	0.304991	−	0.304991i	0.842963	+	0.537972i	$0.180809\pi$
$294$	−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	−0.838255	−	0.545279i	$-0.816424\pi$
$307$	−5.13335	+	5.13335i	−0.292976	+	0.292976i	0.545279	+	0.838255i	$0.316424\pi$
$308$	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	$-0.753884\pi$
$311$		−	24.6338i		−	1.39685i	0.715681	−	0.698427i	$-0.246116\pi$
$312$	4.72123	+	5.79922i	0.267287	+	0.328316i
$313$	−4.63647	+	4.63647i	−0.262069	+	0.262069i	−0.825894	−	0.563825i	$-0.809329\pi$
$313$	−4.63647	+	4.63647i	−0.262069	+	0.262069i	0.563825	+	0.825894i	$0.309329\pi$
$314$	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	0.834295	+	0.551318i	$0.185875\pi$
$317$	24.6701	+	24.6701i	1.38561	+	1.38561i	0.551318	+	0.834295i	$0.314125\pi$
$318$	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	$0.170249\pi$
$331$			18.5469i			1.01943i	−0.860344	+	0.509714i	$0.829751\pi$
$332$	−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	0.328992	−	0.944333i	$-0.393291\pi$
$337$	−11.2961	−	11.2961i	−0.615340	−	0.615340i	−0.944333	+	0.328992i	$0.893291\pi$
$338$	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	−0.161771	−	0.986828i	$-0.551721\pi$
$347$	15.3691	−	15.3691i	0.825057	−	0.825057i	0.986828	+	0.161771i	$0.0517207\pi$
$348$	5.64929	−	1.10831i	0.302834	−	0.0594119i
$349$		−	18.7053i		−	1.00127i	−0.865658	−	0.500637i	$-0.833099\pi$
$349$		−	18.7053i		−	1.00127i	0.865658	−	0.500637i	$-0.166901\pi$
$350$	−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	−0.630849	−	0.775906i	$-0.717293\pi$
$353$	2.72537	−	2.72537i	0.145057	−	0.145057i	0.775906	+	0.630849i	$0.217293\pi$
$354$	−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	−0.926316	−	0.376748i	$-0.877042\pi$
$367$	−10.5282	+	10.5282i	−0.549568	+	0.549568i	0.376748	+	0.926316i	$0.377042\pi$
$368$	−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	−0.861013	−	0.508583i	$-0.830170\pi$
$373$	−6.80656	+	6.80656i	−0.352430	+	0.352430i	0.508583	+	0.861013i	$0.330170\pi$
$374$	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	0.432182	−	0.901786i	$-0.357744\pi$
$383$	−9.19034	−	9.19034i	−0.469604	−	0.469604i	−0.901786	+	0.432182i	$0.857744\pi$
$384$	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	$-0.950035\pi$
$389$		−	6.16642i		−	0.312650i	0.987706	−	0.156325i	$-0.0499647\pi$
$390$	−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	0.765951	−	0.642899i	$-0.222269\pi$
$397$	2.45178	+	2.45178i	0.123051	+	0.123051i	−0.642899	+	0.765951i	$0.722269\pi$
$398$	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	$-0.873407\pi$
$409$		−	15.6654i		−	0.774607i	0.921952	−	0.387303i	$-0.126593\pi$
$410$	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	$0.181770\pi$
$431$			22.4427i			1.08102i	−0.841336	+	0.540512i	$0.818230\pi$
$432$	17.2553	+	7.25367i	0.830195	+	0.348992i
$433$	18.2325	−	18.2325i	0.876198	−	0.876198i	−0.116941	−	0.993139i	$-0.537309\pi$
$433$	18.2325	−	18.2325i	0.876198	−	0.876198i	0.993139	+	0.116941i	$0.0373087\pi$
$434$	−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	0.525984	−	0.850494i	$-0.323697\pi$
$443$	−6.83015	−	6.83015i	−0.324510	−	0.324510i	−0.850494	+	0.525984i	$0.823697\pi$
$444$	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	$0.0641973\pi$
$449$			8.48929i			0.400634i	−0.979731	+	0.200317i	$0.935803\pi$
$450$	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	0.985371	−	0.170420i	$-0.0545125\pi$
$457$	17.4217	+	17.4217i	0.814951	+	0.814951i	−0.170420	+	0.985371i	$0.554513\pi$
$458$	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	0.832894	−	0.553433i	$-0.186682\pi$
$463$	6.01329	+	6.01329i	0.279461	+	0.279461i	−0.553433	+	0.832894i	$0.686682\pi$
$464$	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	−0.581262	−	0.813716i	$-0.697441\pi$
$467$	5.02338	−	5.02338i	0.232454	−	0.232454i	0.813716	+	0.581262i	$0.197441\pi$
$468$	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	−0.428690	−	0.903451i	$-0.641025\pi$
$487$	10.4771	−	10.4771i	0.474761	−	0.474761i	0.903451	+	0.428690i	$0.141025\pi$
$488$	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	$0.342558\pi$
$491$			39.0056i			1.76030i	−0.474695	+	0.880150i	$0.657442\pi$
$492$	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	0.814077	−	0.580757i	$-0.197243\pi$
$503$	5.23281	+	5.23281i	0.233319	+	0.233319i	−0.580757	+	0.814077i	$0.697243\pi$
$504$	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	$0.0555843\pi$
$509$			7.83938i			0.347474i	−0.984792	+	0.173737i	$0.944416\pi$
$510$	−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	−0.944301	−	0.329083i	$-0.893261\pi$
$523$	−29.1213	−	29.1213i	−1.27338	−	1.27338i	−0.329083	−	0.944301i	$-0.606739\pi$
$524$	−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	−0.670854	−	0.741589i	$-0.734072\pi$
$547$	1.65436	−	1.65436i	0.0707353	−	0.0707353i	0.741589	+	0.670854i	$0.234072\pi$
$548$	−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	0.852353	−	0.522967i	$-0.175175\pi$
$557$	7.77377	+	7.77377i	0.329385	+	0.329385i	−0.522967	+	0.852353i	$0.675175\pi$
$558$	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	0.967429	+	0.253142i	$0.0814639\pi$
$563$	28.9612	+	28.9612i	1.22057	+	1.22057i	0.253142	+	0.967429i	$0.418536\pi$
$564$	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	$-0.906720\pi$
$569$		−	13.7813i		−	0.577743i	0.957368	−	0.288872i	$-0.0932801\pi$
$570$	−6.11637	+	0.616283i	−0.256186	+	0.0258133i
$571$			16.6485i			0.696719i	0.937361	+	0.348359i	$0.113261\pi$
$571$			16.6485i			0.696719i	−0.937361	+	0.348359i	$0.886739\pi$
$572$	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	−0.992492	−	0.122310i	$-0.960970\pi$
$577$	−26.7785	−	26.7785i	−1.11480	−	1.11480i	−0.122310	−	0.992492i	$-0.539030\pi$
$578$	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	−0.197662	−	0.980270i	$-0.563335\pi$
$587$	18.9611	−	18.9611i	0.782608	−	0.782608i	0.980270	+	0.197662i	$0.0633349\pi$
$588$	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	−0.933172	−	0.359430i	$-0.882971\pi$
$593$	−13.9715	+	13.9715i	−0.573742	+	0.573742i	0.359430	+	0.933172i	$0.382971\pi$
$594$	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	0.0763504	−	0.997081i	$-0.475673\pi$
$607$	26.4465	−	26.4465i	1.07343	−	1.07343i	0.997081	−	0.0763504i	$-0.0243268\pi$
$608$	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	0.0936743	−	0.995603i	$-0.470139\pi$
$613$	26.9692	−	26.9692i	1.08928	−	1.08928i	0.995603	−	0.0936743i	$-0.0298612\pi$
$614$	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	−0.983091	−	0.183115i	$-0.941382\pi$
$617$	−28.9680	−	28.9680i	−1.16621	−	1.16621i	−0.183115	−	0.983091i	$-0.558618\pi$
$618$	−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	$0.210203\pi$
$631$			30.8174i			1.22682i	−0.789765	+	0.613410i	$0.789797\pi$
$632$	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	0.0141887	−	0.999899i	$-0.495483\pi$
$643$	−24.9951	−	24.9951i	−0.985711	−	0.985711i	−0.999899	+	0.0141887i	$0.995483\pi$
$644$	−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	−0.901079	−	0.433656i	$-0.857223\pi$
$647$	−11.8895	+	11.8895i	−0.467423	+	0.467423i	0.433656	+	0.901079i	$0.357223\pi$
$648$	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	0.145992	−	0.989286i	$-0.453363\pi$
$653$	29.0107	−	29.0107i	1.13528	−	1.13528i	0.989286	−	0.145992i	$-0.0466372\pi$
$654$	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	−0.999988	−	0.00484872i	$-0.998457\pi$
$673$	−25.8162	+	25.8162i	−0.995140	+	0.995140i	0.00484872	+	0.999988i	$0.498457\pi$
$674$	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	0.856494	−	0.516156i	$-0.172638\pi$
$677$	8.85534	+	8.85534i	0.340338	+	0.340338i	−0.516156	+	0.856494i	$0.672638\pi$
$678$	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	0.999658	+	0.0261603i	$0.00832803\pi$
$683$	26.8090	+	26.8090i	1.02582	+	1.02582i	0.0261603	+	0.999658i	$0.491672\pi$
$684$	−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	$-0.941514\pi$
$691$		−	9.60561i		−	0.365415i	0.983167	−	0.182707i	$-0.0584861\pi$
$692$	−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	$-0.885094\pi$
$709$		−	18.8092i		−	0.706395i	0.935549	−	0.353197i	$-0.114906\pi$
$710$	−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	0.201675	−	0.979453i	$-0.435362\pi$
$727$	31.8467	−	31.8467i	1.18113	−	1.18113i	0.979453	−	0.201675i	$-0.0646384\pi$
$728$	−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	−0.920347	−	0.391102i	$-0.872094\pi$
$733$	−14.3288	+	14.3288i	−0.529246	+	0.529246i	0.391102	+	0.920347i	$0.372094\pi$
$734$	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	−0.820962	−	0.570983i	$-0.806562\pi$
$743$	−37.9417	−	37.9417i	−1.39194	−	1.39194i	−0.570983	−	0.820962i	$-0.693438\pi$
$744$	−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	$0.223290\pi$
$751$			35.3710i			1.29071i	−0.763884	+	0.645353i	$0.776710\pi$
$752$	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	0.629029	−	0.777382i	$-0.283453\pi$
$757$	−4.08174	−	4.08174i	−0.148353	−	0.148353i	−0.777382	+	0.629029i	$0.783453\pi$
$758$	−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	$0.270590\pi$
$769$			41.6703i			1.50267i	−0.659921	+	0.751335i	$0.729410\pi$
$770$	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	−0.999083	−	0.0428046i	$-0.986371\pi$
$773$	−26.5873	+	26.5873i	−0.956279	+	0.956279i	0.0428046	+	0.999083i	$0.486371\pi$
$774$	−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	−0.0586202	−	0.998280i	$-0.518670\pi$
$787$	26.3608	−	26.3608i	0.939660	−	0.939660i	0.998280	+	0.0586202i	$0.0186701\pi$
$788$	−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	0.839429	−	0.543469i	$-0.182890\pi$
$797$	8.35530	+	8.35530i	0.295960	+	0.295960i	−0.543469	+	0.839429i	$0.682890\pi$
$798$	−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	$0.0315719\pi$
$809$			5.63303i			0.198047i	−0.995085	+	0.0990234i	$0.968428\pi$
$810$	−4.67042	+	5.71706i	−0.164102	+	0.200877i
$811$		−	43.8944i		−	1.54134i	−0.637234	−	0.770670i	$-0.719922\pi$
$811$		−	43.8944i		−	1.54134i	0.637234	−	0.770670i	$-0.280078\pi$
$812$	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	0.999899	−	0.0142009i	$-0.00452044\pi$
$823$	28.2777	+	28.2777i	0.985698	+	0.985698i	−0.0142009	+	0.999899i	$0.504520\pi$
$824$	−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	−0.697326	−	0.716754i	$-0.745627\pi$
$827$	0.558699	−	0.558699i	0.0194279	−	0.0194279i	0.716754	+	0.697326i	$0.245627\pi$
$828$	34.2553	−	6.72044i	1.19046	−	0.233551i
$829$			1.98019i			0.0687750i	0.999409	+	0.0343875i	$0.0109480\pi$
$829$			1.98019i			0.0687750i	−0.999409	+	0.0343875i	$0.989052\pi$
$830$	−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	−0.262637	−	0.964895i	$-0.584592\pi$
$853$	20.5102	−	20.5102i	0.702257	−	0.702257i	0.964895	+	0.262637i	$0.0845923\pi$
$854$	−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	0.0553807	−	0.998465i	$-0.482363\pi$
$857$	−27.6084	−	27.6084i	−0.943085	−	0.943085i	−0.998465	+	0.0553807i	$0.982363\pi$
$858$	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	0.555007	−	0.831845i	$-0.312715\pi$
$863$	−8.13263	−	8.13263i	−0.276838	−	0.276838i	−0.831845	+	0.555007i	$0.812715\pi$
$864$	−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	0.272516	−	0.962151i	$-0.412144\pi$
$877$	−20.4230	−	20.4230i	−0.689636	−	0.689636i	−0.962151	+	0.272516i	$0.912144\pi$
$878$	−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	0.691128	−	0.722733i	$-0.257114\pi$
$883$	−0.939158	−	0.939158i	−0.0316052	−	0.0316052i	−0.722733	+	0.691128i	$0.757114\pi$
$884$	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	−0.533300	−	0.845926i	$-0.679048\pi$
$887$	9.31080	−	9.31080i	0.312626	−	0.312626i	0.845926	+	0.533300i	$0.179048\pi$
$888$	−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	−0.343276	−	0.939235i	$-0.611537\pi$
$907$	17.9482	−	17.9482i	0.595959	−	0.595959i	0.939235	+	0.343276i	$0.111537\pi$
$908$	−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	$0.00626366\pi$
$911$			1.18779i			0.0393532i	−0.999806	+	0.0196766i	$0.993736\pi$
$912$	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	$-0.954211\pi$
$929$		−	8.73875i		−	0.286709i	0.989671	−	0.143355i	$-0.0457889\pi$
$930$	−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	0.262267	−	0.964995i	$-0.415530\pi$
$937$	−21.5108	−	21.5108i	−0.702728	−	0.702728i	−0.964995	+	0.262267i	$0.915530\pi$
$938$	−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	−0.743481	−	0.668757i	$-0.766827\pi$
$947$	−2.29952	+	2.29952i	−0.0747244	+	0.0747244i	0.668757	+	0.743481i	$0.266827\pi$
$948$	−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	0.269243	−	0.963072i	$-0.413227\pi$
$953$	38.0424	−	38.0424i	1.23231	−	1.23231i	0.963072	−	0.269243i	$-0.0867733\pi$
$954$	−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	−0.973506	−	0.228663i	$-0.926564\pi$
$967$	−23.1621	+	23.1621i	−0.744842	+	0.744842i	0.228663	+	0.973506i	$0.426564\pi$
$968$	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	$-0.741054\pi$
$971$		−	45.2890i		−	1.45339i	0.686958	−	0.726697i	$-0.258946\pi$
$972$	−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	0.183468	−	0.983026i	$-0.441268\pi$
$977$	−24.9918	−	24.9918i	−0.799558	−	0.799558i	−0.983026	+	0.183468i	$0.941268\pi$
$978$	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	0.478474	−	0.878102i	$-0.341190\pi$
$983$	−12.5294	−	12.5294i	−0.399627	−	0.399627i	−0.878102	+	0.478474i	$0.841190\pi$
$984$	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	$-0.983366\pi$
$991$		−	3.28857i		−	0.104465i	0.998635	−	0.0522325i	$-0.0166337\pi$
$992$	−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	0.895695	−	0.444669i	$-0.146679\pi$
$997$	14.2413	+	14.2413i	0.451026	+	0.451026i	−0.444669	+	0.895695i	$0.646679\pi$
$998$	−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.247.7	yes	108
4.3	odd	2	inner	820.2.k.c.247.19	yes	108
5.3	odd	4	inner	820.2.k.c.83.19	yes	108
20.3	even	4	inner	820.2.k.c.83.7	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.7	✓	108	20.3	even	4	inner
820.2.k.c.83.19	yes	108	5.3	odd	4	inner
820.2.k.c.247.7	yes	108	1.1	even	1	trivial
820.2.k.c.247.19	yes	108	4.3	odd	2	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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