LMFDB - Embedded newform 820.2.k.c.83.19

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			83.19
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.412299 + 1.35278i) 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} +(2.19345 - 1.78572i) q^{8} +2.18571i q^{9} +(3.14852 - 0.294630i) q^{10} -4.03380i q^{11} +(1.77100 - 0.347446i) 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} +(-2.95678 - 0.901167i) q^{18} +2.15426 q^{19} +(-0.899565 + 4.38073i) q^{20} -2.48810 q^{21} +(5.45684 + 1.66313i) 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} +(-1.06164 - 5.41138i) q^{28} +3.18989i q^{29} +(-1.82101 + 2.19700i) q^{30} -6.99289i q^{31} +(-5.63313 + 0.517535i) 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} +(-0.888200 + 2.91424i) q^{38} +2.64388 q^{39} +(-5.55526 - 3.02308i) q^{40} +1.00000 q^{41} +(1.02584 - 3.36585i) 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} +(-3.32747 - 1.39878i) q^{48} +0.602521i q^{49} +(-3.28061 - 6.26399i) q^{50} -7.32647i q^{51} +(1.12811 + 5.75019i) 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} +(-4.31521 - 1.31519i) q^{58} -10.6374 q^{59} +(-2.22126 - 3.36924i) q^{60} -15.0668 q^{61} +(9.45982 + 2.88316i) 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} +(15.9344 - 3.12611i) q^{68} -7.20602i q^{69} +(6.71305 + 5.56418i) q^{70} -1.40844i q^{71} +(3.90306 + 4.79424i) 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} +(-1.09007 + 3.57659i) q^{78} +6.18073 q^{79} +(6.37999 - 6.26863i) q^{80} -2.33447 q^{81} +(-0.412299 + 1.35278i) 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} +(-7.20324 - 8.84794i) q^{88} +10.6842i q^{89} +(0.643976 + 6.88176i) q^{90} -8.07852i q^{91} +(15.6724 - 3.07471i) 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} +(-0.815078 - 0.248419i) 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 $

$2$	−0.412299	+	1.35278i	−0.291540	+	0.956559i
$2$	−0.412299	+	1.35278i	−0.291540	+	0.956559i
$3$	−0.638078	+	0.638078i	−0.368395	+	0.368395i	−0.866892	−	0.498497i	$-0.833886\pi$
$3$	−0.638078	+	0.638078i	−0.368395	+	0.368395i	0.498497	+	0.866892i	$0.333886\pi$
$4$	−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	$-0.0755314\pi$
$7$	1.94968	+	1.94968i	0.736911	+	0.736911i	−0.235068	+	0.971979i	$0.575531\pi$
$8$	2.19345	−	1.78572i	0.775501	−	0.631347i
$9$			2.18571i			0.728571i
$10$	3.14852	−	0.294630i	0.995650	−	0.0931701i
$11$		−	4.03380i		−	1.21624i	−0.793846	−	0.608119i	$-0.791924\pi$
$11$		−	4.03380i		−	1.21624i	0.793846	−	0.608119i	$-0.208076\pi$
$12$	1.77100	−	0.347446i	0.511243	−	0.100299i
$13$	−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	$0.805971\pi$
$18$	−2.95678	−	0.901167i	−0.696921	−	0.212407i
$19$	2.15426			0.494221			0.247111	−	0.968987i	$-0.420519\pi$
$19$	2.15426			0.494221			0.247111	+	0.968987i	$0.420519\pi$
$20$	−0.899565	+	4.38073i	−0.201149	+	0.979561i
$21$	−2.48810			−0.542948
$22$	5.45684	+	1.66313i	1.16340	+	0.354582i
$23$	−5.64666	+	5.64666i	−1.17741	+	1.17741i	−0.197007	+	0.980402i	$0.563122\pi$
$23$	−5.64666	+	5.64666i	−1.17741	+	1.17741i	−0.980402	+	0.197007i	$0.936878\pi$
$24$	−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
$28$	−1.06164	−	5.41138i	−0.200631	−	1.02265i
$29$			3.18989i			0.592347i	0.955134	+	0.296174i	$0.0957107\pi$
$29$			3.18989i			0.592347i	−0.955134	+	0.296174i	$0.904289\pi$
$30$	−1.82101	+	2.19700i	−0.332469	+	0.401116i
$31$		−	6.99289i		−	1.25596i	−0.778230	−	0.627980i	$-0.783882\pi$
$31$		−	6.99289i		−	1.25596i	0.778230	−	0.627980i	$-0.216118\pi$
$32$	−5.63313	+	0.517535i	−0.995806	+	0.0914882i
$33$	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	$0.266828\pi$
$38$	−0.888200	+	2.91424i	−0.144085	+	0.472751i
$39$	2.64388			0.423360
$40$	−5.55526	−	3.02308i	−0.878364	−	0.477991i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	1.02584	−	3.36585i	0.158291	−	0.519362i
$43$	−0.276275	+	0.276275i	−0.0421315	+	0.0421315i	−0.727859	−	0.685727i	$-0.759484\pi$
$43$	−0.276275	+	0.276275i	−0.0421315	+	0.0421315i	0.685727	+	0.727859i	$0.259484\pi$
$44$	−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	$-0.416584\pi$
$47$	−4.84550	−	4.84550i	−0.706789	−	0.706789i	−0.965859	+	0.259069i	$0.916584\pi$
$48$	−3.32747	−	1.39878i	−0.480278	−	0.201897i
$49$			0.602521i			0.0860745i
$50$	−3.28061	−	6.26399i	−0.463948	−	0.885862i
$51$		−	7.32647i		−	1.02591i
$52$	1.12811	+	5.75019i	0.156441	+	0.797408i
$53$	−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
$58$	−4.31521	−	1.31519i	−0.566615	−	0.172693i
$59$	−10.6374			−1.38488			−0.692439	−	0.721477i	$-0.743464\pi$
$59$	−10.6374			−1.38488			−0.692439	+	0.721477i	$0.743464\pi$
$60$	−2.22126	−	3.36924i	−0.286763	−	0.434967i
$61$	−15.0668			−1.92911			−0.964555	−	0.263882i	$-0.914997\pi$
$61$	−15.0668			−1.92911			−0.964555	+	0.263882i	$0.914997\pi$
$62$	9.45982	+	2.88316i	1.20140	+	0.366162i
$63$	−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	$-0.200446\pi$
$67$	1.79484	+	1.79484i	0.219275	+	0.219275i	−0.588918	+	0.808193i	$0.700446\pi$
$68$	15.9344	−	3.12611i	1.93233	−	0.379096i
$69$		−	7.20602i		−	0.867503i
$70$	6.71305	+	5.56418i	0.802363	+	0.665047i
$71$		−	1.40844i		−	0.167151i	−0.996501	−	0.0835754i	$-0.973366\pi$
$71$		−	1.40844i		−	0.167151i	0.996501	−	0.0835754i	$-0.0266339\pi$
$72$	3.90306	+	4.79424i	0.459980	+	0.565007i
$73$	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
$78$	−1.09007	+	3.57659i	−0.123426	+	0.404969i
$79$	6.18073			0.695387			0.347693	−	0.937608i	$-0.386965\pi$
$79$	6.18073			0.695387			0.347693	+	0.937608i	$0.386965\pi$
$80$	6.37999	−	6.26863i	0.713305	−	0.700854i
$81$	−2.33447			−0.259386
$82$	−0.412299	+	1.35278i	−0.0455308	+	0.149389i
$83$	3.37057	−	3.37057i	0.369968	−	0.369968i	−0.497498	−	0.867465i	$-0.665748\pi$
$83$	3.37057	−	3.37057i	0.369968	−	0.369968i	0.867465	+	0.497498i	$0.165748\pi$
$84$	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
$88$	−7.20324	−	8.84794i	−0.767867	−	0.943193i
$89$			10.6842i			1.13252i	0.824227	+	0.566259i	$0.191610\pi$
$89$			10.6842i			1.13252i	−0.824227	+	0.566259i	$0.808390\pi$
$90$	0.643976	+	6.88176i	0.0678810	+	0.725401i
$91$		−	8.07852i		−	0.846859i
$92$	15.6724	−	3.07471i	1.63396	−	0.320561i
$93$	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	$0.997766\pi$
$98$	−0.815078	−	0.248419i	−0.0823353	−	0.0250941i
$99$	8.81673			0.886115
$100$	9.82639	−	1.85530i	0.982639	−	0.185530i
$101$	−18.9280			−1.88340			−0.941701	−	0.336451i	$-0.890773\pi$
$101$	−18.9280			−1.88340			−0.941701	+	0.336451i	$0.890773\pi$
$102$	9.91109	+	3.02070i	0.981344	+	0.299094i
$103$	5.33609	−	5.33609i	0.525781	−	0.525781i	−0.393531	−	0.919312i	$-0.628746\pi$
$103$	5.33609	−	5.33609i	0.525781	−	0.525781i	0.919312	+	0.393531i	$0.128746\pi$
$104$	−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	$-0.0929806\pi$
$107$	6.92710	+	6.92710i	0.669669	+	0.669669i	−0.287971	+	0.957639i	$0.592981\pi$
$108$	1.80176	+	9.18389i	0.173374	+	0.883720i
$109$		−	0.514746i		−	0.0493037i	−0.999696	−	0.0246519i	$-0.992152\pi$
$109$		−	0.514746i		−	0.0493037i	0.999696	−	0.0246519i	$-0.00784773\pi$
$110$	−1.18848	−	12.7005i	−0.113317	−	1.21095i
$111$		−	0.580103i		−	0.0550610i
$112$	−4.27405	+	10.1672i	−0.403859	+	0.960714i
$113$	−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
$118$	4.38581	−	14.3901i	0.403747	−	1.32472i
$119$	−22.3864			−2.05216
$120$	5.47366	−	1.61573i	0.499674	−	0.147495i
$121$	−5.27158			−0.479234
$122$	6.21204	−	20.3821i	0.562412	−	1.84531i
$123$	−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	$0.0520635\pi$
$127$	12.9541	+	12.9541i	1.14949	+	1.14949i	0.162834	+	0.986653i	$0.447937\pi$
$128$	9.92841	+	5.42463i	0.877556	+	0.479474i
$129$		−	0.352570i		−	0.0310421i
$130$	−7.13336	−	5.91256i	−0.625637	−	0.518566i
$131$			2.79439i			0.244147i	0.992521	+	0.122073i	$0.0389543\pi$
$131$			2.79439i			0.244147i	−0.992521	+	0.122073i	$0.961046\pi$
$132$	−1.40153	−	7.14386i	−0.121987	−	0.621793i
$133$	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	$0.316572\pi$
$138$	9.74815	+	2.97104i	0.829817	+	0.252911i
$139$	−11.0434			−0.936688			−0.468344	−	0.883546i	$-0.655149\pi$
$139$	−11.0434			−0.936688			−0.468344	+	0.883546i	$0.655149\pi$
$140$	−10.2949	+	6.78716i	−0.870077	+	0.573620i
$141$	6.18362			0.520755
$142$	1.90530	+	0.580698i	0.159890	+	0.0487311i
$143$	−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
$148$	1.26167	−	0.247522i	0.103709	−	0.0203462i
$149$			4.60185i			0.376998i	0.982073	+	0.188499i	$0.0603622\pi$
$149$			4.60185i			0.376998i	−0.982073	+	0.188499i	$0.939638\pi$
$150$	6.09020	+	1.90363i	0.497263	+	0.155431i
$151$		−	5.42095i		−	0.441151i	−0.975370	−	0.220575i	$-0.929207\pi$
$151$		−	5.42095i		−	0.441151i	0.975370	−	0.220575i	$-0.0707935\pi$
$152$	4.72526	−	3.84690i	0.383269	−	0.312025i
$153$	−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	$0.336787\pi$
$158$	−2.54831	+	8.36116i	−0.202733	+	0.665178i
$159$	2.22850			0.176732
$160$	5.84960	+	11.2153i	0.462451	+	0.886645i
$161$	−22.0184			−1.73529
$162$	0.962501	−	3.15802i	0.0756212	−	0.248118i
$163$	−7.02755	+	7.02755i	−0.550440	+	0.550440i	−0.926568	−	0.376128i	$-0.877255\pi$
$163$	−7.02755	+	7.02755i	−0.550440	+	0.550440i	0.376128	+	0.926568i	$0.377255\pi$
$164$	−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	$-0.235400\pi$
$167$	0.837985	+	0.837985i	0.0648452	+	0.0648452i	−0.673940	+	0.738786i	$0.735400\pi$
$168$	−5.45752	+	4.44304i	−0.421057	+	0.342788i
$169$		−	4.41567i		−	0.339667i
$170$	−16.3843	+	19.7673i	−1.25662	+	1.51608i
$171$			4.70859i			0.360075i
$172$	0.766806	−	0.150437i	0.0584684	−	0.0114707i
$173$	−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
$178$	−14.4533	−	4.40507i	−1.08332	−	0.330174i
$179$	7.71084			0.576335			0.288168	−	0.957580i	$-0.406954\pi$
$179$	7.71084			0.576335			0.288168	+	0.957580i	$0.406954\pi$
$180$	−9.57501	−	1.96619i	−0.713679	−	0.146551i
$181$	20.6235			1.53293			0.766465	−	0.642286i	$-0.222014\pi$
$181$	20.6235			1.53293			0.766465	+	0.642286i	$0.222014\pi$
$182$	10.9285	+	3.33077i	0.810071	+	0.246893i
$183$	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
$188$	2.63847	+	13.4488i	0.192430	+	0.980853i
$189$		−	12.9026i		−	0.938524i
$190$	6.78273	−	0.634709i	0.492071	−	0.0460466i
$191$		−	5.27951i		−	0.382012i	−0.981589	−	0.191006i	$-0.938825\pi$
$191$		−	5.27951i		−	0.382012i	0.981589	−	0.191006i	$-0.0611750\pi$
$192$	3.96332	+	6.03379i	0.286028	+	0.435451i
$193$	−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	$0.375818\pi$
$198$	−3.63513	+	11.9271i	−0.258338	+	0.847621i
$199$	18.8123			1.33357			0.666783	−	0.745252i	$-0.267671\pi$
$199$	18.8123			1.33357			0.666783	+	0.745252i	$0.267671\pi$
$200$	−1.54161	+	14.0579i	−0.109008	+	0.994041i
$201$	−2.29050			−0.161559
$202$	7.80398	−	25.6053i	0.549086	−	1.80158i
$203$	−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
$208$	4.54165	−	10.8038i	0.314907	−	0.749111i
$209$		−	8.68986i		−	0.601090i
$210$	−7.83384	+	0.733068i	−0.540586	+	0.0505865i
$211$			5.08959i			0.350382i	0.984535	+	0.175191i	$0.0560542\pi$
$211$			5.08959i			0.350382i	−0.984535	+	0.175191i	$0.943946\pi$
$212$	0.950872	+	4.84677i	0.0653061	+	0.332878i
$213$	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
$218$	0.696337	+	0.212229i	0.0471619	+	0.0143740i
$219$	−3.26394			−0.220556
$220$	17.6710	+	3.62867i	1.19138	+	0.244645i
$221$	23.7881			1.60016
$222$	0.784751	+	0.239176i	0.0526691	+	0.0160525i
$223$	13.8751	−	13.8751i	0.929144	−	0.929144i	−0.0685064	−	0.997651i	$-0.521823\pi$
$223$	13.8751	−	13.8751i	0.929144	−	0.929144i	0.997651	+	0.0685064i	$0.0218234\pi$
$224$	−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	$-0.199598\pi$
$227$	3.35974	+	3.35974i	0.222994	+	0.222994i	−0.586764	+	0.809758i	$0.699598\pi$
$228$	3.81519	−	0.748489i	0.252667	−	0.0495699i
$229$		−	16.2935i		−	1.07670i	−0.842720	−	0.538352i	$-0.819047\pi$
$229$		−	16.2935i		−	1.07670i	0.842720	−	0.538352i	$-0.180953\pi$
$230$	−16.1150	+	19.4423i	−1.06259	+	1.28199i
$231$			10.0365i			0.660354i
$232$	5.69624	+	6.99685i	0.373976	+	0.459366i
$233$	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
$238$	9.22990	−	30.2839i	0.598286	−	1.96301i
$239$	−26.5804			−1.71934			−0.859671	−	0.510848i	$-0.829331\pi$
$239$	−26.5804			−1.71934			−0.859671	+	0.510848i	$0.829331\pi$
$240$	−0.0710610	+	8.07081i	−0.00458697	+	0.520969i
$241$	29.6040			1.90696			0.953481	−	0.301454i	$-0.0974720\pi$
$241$	29.6040			1.90696			0.953481	+	0.301454i	$0.0974720\pi$
$242$	2.17347	−	7.13128i	0.139716	−	0.458416i
$243$	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
$248$	−12.4873	−	15.3385i	−0.792946	−	0.973998i
$249$			4.30137i			0.272588i
$250$	−10.1764	+	12.1013i	−0.643612	+	0.765352i
$251$		−	23.4221i		−	1.47839i	−0.673492	−	0.739195i	$-0.735206\pi$
$251$		−	23.4221i		−	1.47839i	0.673492	−	0.739195i	$-0.264794\pi$
$252$	11.8277	−	2.32044i	0.745076	−	0.146174i
$253$	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	$0.499253\pi$
$258$	0.476949	+	0.145364i	0.0296936	+	0.00905000i
$259$	−1.77254			−0.110140
$260$	10.9395	−	7.21211i	0.678437	−	0.447276i
$261$	−6.97218			−0.431567
$262$	−3.78019	−	1.15212i	−0.233541	−	0.0711785i
$263$	6.85597	−	6.85597i	0.422757	−	0.422757i	−0.463395	−	0.886152i	$-0.653369\pi$
$263$	6.85597	−	6.85597i	0.422757	−	0.422757i	0.886152	+	0.463395i	$0.153369\pi$
$264$	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
$268$	−0.977325	−	4.98161i	−0.0596996	−	0.304300i
$269$		−	1.00339i		−	0.0611777i	−0.999532	−	0.0305888i	$-0.990262\pi$
$269$		−	1.00339i		−	0.0611777i	0.999532	−	0.0305888i	$-0.00973824\pi$
$270$	−11.3930	−	9.44322i	−0.693357	−	0.574696i
$271$			27.6326i			1.67856i	0.543697	+	0.839281i	$0.317024\pi$
$271$			27.6326i			1.67856i	−0.543697	+	0.839281i	$0.682976\pi$
$272$	−29.9385	−	12.5854i	−1.81529	−	0.763100i
$273$	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	$0.197858\pi$
$278$	4.55318	−	14.9392i	0.273082	−	0.895997i
$279$	15.2844			0.915055
$280$	−4.93695	−	16.7251i	−0.295039	−	0.999513i
$281$	13.3028			0.793579			0.396790	−	0.917910i	$-0.370124\pi$
$281$	13.3028			0.793579			0.396790	+	0.917910i	$0.370124\pi$
$282$	−2.54950	+	8.36507i	−0.151821	+	0.498133i
$283$	−22.5760	+	22.5760i	−1.34201	+	1.34201i	−0.447945	+	0.894061i	$0.647844\pi$
$283$	−22.5760	+	22.5760i	−1.34201	+	1.34201i	−0.894061	+	0.447945i	$0.852156\pi$
$284$	−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
$288$	−1.13118	−	12.3124i	−0.0666556	−	0.725515i
$289$		−	48.9191i		−	2.87759i
$290$	0.939836	+	10.0434i	0.0551891	+	0.589771i
$291$		−	12.6566i		−	0.741941i
$292$	−1.39268	−	7.09875i	−0.0815004	−	0.415423i
$293$	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
$298$	−6.22528	−	1.89734i	−0.360621	−	0.109910i
$299$	23.3970			1.35308
$300$	−5.08618	+	7.45383i	−0.293651	+	0.430347i
$301$	−1.07730			−0.0620944
$302$	7.33334	+	2.23505i	0.421986	+	0.128613i
$303$	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	$-0.183576\pi$
$307$	5.13335	+	5.13335i	0.292976	+	0.292976i	−0.545279	+	0.838255i	$0.683576\pi$
$308$	−21.8284	+	4.28245i	−1.24379	+	0.244015i
$309$			6.80969i			0.387390i
$310$	−2.06031	−	22.0173i	−0.117018	−	1.25050i
$311$		−	24.6338i		−	1.39685i	−0.715681	−	0.698427i	$-0.753884\pi$
$311$		−	24.6338i		−	1.39685i	0.715681	−	0.698427i	$-0.246116\pi$
$312$	5.79922	−	4.72123i	0.328316	−	0.267287i
$313$	−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	$-0.185875\pi$
$318$	−0.918809	+	3.01467i	−0.0515243	+	0.169054i
$319$	12.8674			0.720435
$320$	−17.5836	+	3.28916i	−0.982951	+	0.183870i
$321$	−8.84007			−0.493405
$322$	9.07816	−	29.7860i	0.505906	−	1.65991i
$323$	−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
$328$	2.19345	−	1.78572i	0.121113	−	0.0985998i
$329$		−	18.8944i		−	1.04168i
$330$	8.86227	+	7.34559i	0.487852	+	0.404361i
$331$			18.5469i			1.01943i	0.860344	+	0.509714i	$0.170249\pi$
$331$			18.5469i			1.01943i	−0.860344	+	0.509714i	$0.829751\pi$
$332$	−9.35507	+	1.83534i	−0.513426	+	0.100727i
$333$	−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	$0.393291\pi$
$338$	5.97342	+	1.82058i	0.324911	+	0.0990264i
$339$	6.74399			0.366283
$340$	−19.9855	−	30.3144i	−1.08387	−	1.64403i
$341$	−28.2079			−1.52755
$342$	−6.36968	−	1.94135i	−0.344433	−	0.104976i
$343$	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	$-0.448279\pi$
$347$	−15.3691	−	15.3691i	−0.825057	−	0.825057i	−0.986828	+	0.161771i	$0.948279\pi$
$348$	1.10831	+	5.64929i	0.0594119	+	0.302834i
$349$			18.7053i			1.00127i	0.865658	+	0.500637i	$0.166901\pi$
$349$			18.7053i			1.00127i	−0.865658	+	0.500637i	$0.833099\pi$
$350$	5.81665	−	18.6089i	0.310913	−	0.994690i
$351$			13.7104i			0.731808i
$352$	2.08764	+	22.7229i	0.111271	+	1.21114i
$353$	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
$358$	−3.17917	+	10.4311i	−0.168025	+	0.551299i
$359$	24.2558			1.28017			0.640086	−	0.768303i	$-0.278899\pi$
$359$	24.2558			1.28017			0.640086	+	0.768303i	$0.278899\pi$
$360$	6.60759	−	12.1422i	0.348251	−	0.639951i
$361$	−14.3592			−0.755746
$362$	−8.50304	+	27.8990i	−0.446910	+	1.46634i
$363$	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	$-0.122958\pi$
$367$	10.5282	+	10.5282i	0.549568	+	0.549568i	−0.376748	+	0.926316i	$0.622958\pi$
$368$	−29.4463	−	12.3785i	−1.53499	−	0.645272i
$369$			2.18571i			0.113784i
$370$	−1.29730	+	1.56516i	−0.0674432	+	0.0813686i
$371$		−	6.80930i		−	0.353521i
$372$	−2.42965	−	12.3844i	−0.125972	−	0.642101i
$373$	−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
$378$	17.4543	+	5.31972i	0.897753	+	0.273617i
$379$	−2.32598			−0.119478			−0.0597388	−	0.998214i	$-0.519027\pi$
$379$	−2.32598			−0.119478			−0.0597388	+	0.998214i	$0.519027\pi$
$380$	−1.93790	+	9.43723i	−0.0994120	+	0.484119i
$381$	−16.5314			−0.846930
$382$	7.14200	+	2.17674i	0.365417	+	0.111372i
$383$	9.19034	−	9.19034i	0.469604	−	0.469604i	−0.432182	−	0.901786i	$-0.642256\pi$
$383$	9.19034	−	9.19034i	0.469604	−	0.469604i	0.901786	+	0.432182i	$0.142256\pi$
$384$	−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
$388$	27.5268	−	5.40039i	1.39746	−	0.274163i
$389$			6.16642i			0.312650i	0.987706	+	0.156325i	$0.0499647\pi$
$389$			6.16642i			0.312650i	−0.987706	+	0.156325i	$0.950035\pi$
$390$	8.32433	−	0.778966i	0.421519	−	0.0394445i
$391$		−	64.8354i		−	3.27887i
$392$	1.07593	+	1.32160i	0.0543428	+	0.0667508i
$393$	−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	$0.222269\pi$
$398$	−7.75628	+	25.4488i	−0.388787	+	1.27563i
$399$	−5.36001			−0.268336
$400$	−18.3816	−	7.88150i	−0.919078	−	0.394075i
$401$	−14.4100			−0.719602			−0.359801	−	0.933029i	$-0.617155\pi$
$401$	−14.4100			−0.719602			−0.359801	+	0.933029i	$0.617155\pi$
$402$	0.944370	−	3.09854i	0.0471009	−	0.154541i
$403$	−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
$408$	−13.0830	−	16.0702i	−0.647705	−	0.795595i
$409$			15.6654i			0.774607i	0.921952	+	0.387303i	$0.126593\pi$
$409$			15.6654i			0.774607i	−0.921952	+	0.387303i	$0.873407\pi$
$410$	3.14852	−	0.294630i	0.155494	−	0.0145507i
$411$		−	4.38578i		−	0.216335i
$412$	−14.8104	+	2.90561i	−0.729657	+	0.143149i
$413$	−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
$418$	11.7555	+	3.58282i	0.574978	+	0.175242i
$419$	23.6142			1.15363			0.576816	−	0.816874i	$-0.304295\pi$
$419$	23.6142			1.15363			0.576816	+	0.816874i	$0.304295\pi$
$420$	2.23821	−	10.8997i	0.109213	−	0.531851i
$421$	4.64972			0.226613			0.113307	−	0.993560i	$-0.463856\pi$
$421$	4.64972			0.226613			0.113307	+	0.993560i	$0.463856\pi$
$422$	−6.88508	−	2.09843i	−0.335161	−	0.102150i
$423$	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
$428$	−3.77194	−	19.2263i	−0.182324	−	0.929338i
$429$		−	10.6649i		−	0.514907i
$430$	−0.788459	+	0.951257i	−0.0380229	+	0.0458737i
$431$			22.4427i			1.08102i	0.841336	+	0.540512i	$0.181770\pi$
$431$			22.4427i			1.08102i	−0.841336	+	0.540512i	$0.818230\pi$
$432$	7.25367	−	17.2553i	0.348992	−	0.830195i
$433$	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
$438$	1.34572	−	4.41538i	0.0643009	−	0.210975i
$439$	−21.0685			−1.00554			−0.502771	−	0.864419i	$-0.667686\pi$
$439$	−21.0685			−1.00554			−0.502771	+	0.864419i	$0.667686\pi$
$440$	−12.1945	+	22.4089i	−0.581351	+	1.06830i
$441$	−1.31694			−0.0627113
$442$	−9.80780	+	32.1800i	−0.466509	+	1.53064i
$443$	6.83015	−	6.83015i	0.324510	−	0.324510i	−0.525984	−	0.850494i	$-0.676303\pi$
$443$	6.83015	−	6.83015i	0.324510	−	0.324510i	0.850494	+	0.525984i	$0.176303\pi$
$444$	−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
$448$	18.4365	−	12.1101i	0.871045	−	0.572149i
$449$		−	8.48929i		−	0.400634i	−0.979731	−	0.200317i	$-0.935803\pi$
$449$		−	8.48929i		−	0.400634i	0.979731	−	0.200317i	$-0.0641973\pi$
$450$	13.6913	−	7.17046i	0.645413	−	0.338019i
$451$		−	4.03380i		−	0.189944i
$452$	2.87757	+	14.6675i	0.135350	+	0.689902i
$453$	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	$0.0545125\pi$
$458$	22.0415	+	6.71779i	1.02993	+	0.313902i
$459$	37.9930			1.77336
$460$	−19.6569	−	29.8160i	−0.916509	−	1.39018i
$461$	8.43314			0.392771			0.196385	−	0.980527i	$-0.437080\pi$
$461$	8.43314			0.392771			0.196385	+	0.980527i	$0.437080\pi$
$462$	−13.5772	−	4.13805i	−0.631667	−	0.192519i
$463$	−6.01329	+	6.01329i	−0.279461	+	0.279461i	−0.832894	−	0.553433i	$-0.813318\pi$
$463$	−6.01329	+	6.01329i	−0.279461	+	0.279461i	0.553433	+	0.832894i	$0.313318\pi$
$464$	−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	$-0.302559\pi$
$467$	−5.02338	−	5.02338i	−0.232454	−	0.232454i	−0.813716	+	0.581262i	$0.802559\pi$
$468$	−12.5683	+	2.46572i	−0.580968	+	0.113978i
$469$			6.99873i			0.323172i
$470$	−16.6838	−	13.8285i	−0.769567	−	0.637863i
$471$		−	6.08947i		−	0.280588i
$472$	−23.3327	+	18.9955i	−1.07397	+	0.874338i
$473$	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
$478$	10.9591	−	35.9574i	0.501256	−	1.64465i
$479$	5.87249			0.268321			0.134161	−	0.990960i	$-0.457166\pi$
$479$	5.87249			0.268321			0.134161	+	0.990960i	$0.457166\pi$
$480$	−10.8887	−	3.42372i	−0.497000	−	0.156271i
$481$	1.88352			0.0858810
$482$	−12.2057	+	40.0477i	−0.555955	+	1.82412i
$483$	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	$-0.358975\pi$
$487$	−10.4771	−	10.4771i	−0.474761	−	0.474761i	−0.903451	+	0.428690i	$0.858975\pi$
$488$	−33.0483	+	26.9051i	−1.49603	+	1.21794i
$489$		−	8.96826i		−	0.405559i
$490$	0.177521	+	1.89705i	0.00801956	+	0.0857000i
$491$			39.0056i			1.76030i	0.474695	+	0.880150i	$0.342558\pi$
$491$			39.0056i			1.76030i	−0.474695	+	0.880150i	$0.657442\pi$
$492$	1.77100	−	0.347446i	0.0798428	−	0.0156641i
$493$	−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
$498$	−5.81880	−	1.77345i	−0.260747	−	0.0794703i
$499$	−23.5208			−1.05293			−0.526467	−	0.850196i	$-0.676484\pi$
$499$	−23.5208			−1.05293			−0.526467	+	0.850196i	$0.676484\pi$
$500$	−12.1746	−	18.7558i	−0.544466	−	0.838783i
$501$	−1.06940			−0.0477773
$502$	31.6849	+	9.65691i	1.41417	+	0.431009i
$503$	−5.23281	+	5.23281i	−0.233319	+	0.233319i	−0.814077	−	0.580757i	$-0.802757\pi$
$503$	−5.23281	+	5.23281i	−0.233319	+	0.233319i	0.580757	+	0.814077i	$0.302757\pi$
$504$	−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
$508$	−7.05374	−	35.9542i	−0.312959	−	1.59521i
$509$		−	7.83938i		−	0.347474i	−0.984792	−	0.173737i	$-0.944416\pi$
$509$		−	7.83938i		−	0.347474i	0.984792	−	0.173737i	$-0.0555843\pi$
$510$	−2.15860	−	23.0676i	−0.0955842	−	1.02145i
$511$			9.97313i			0.441185i
$512$	−10.4302	−	20.0801i	−0.460953	−	0.887425i
$513$	−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
$518$	0.730815	−	2.39785i	0.0321102	−	0.105355i
$519$	5.75513			0.252622
$520$	5.24606	+	17.7722i	0.230055	+	0.779364i
$521$	−31.1058			−1.36277			−0.681385	−	0.731925i	$-0.738622\pi$
$521$	−31.1058			−1.36277			−0.681385	+	0.731925i	$0.738622\pi$
$522$	2.87462	−	9.43181i	0.125819	−	0.412819i
$523$	29.1213	−	29.1213i	1.27338	−	1.27338i	0.329083	−	0.944301i	$-0.393261\pi$
$523$	29.1213	−	29.1213i	1.27338	−	1.27338i	0.944301	−	0.329083i	$-0.106739\pi$
$524$	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
$528$	−5.64241	+	13.4223i	−0.245554	+	0.584133i
$529$		−	40.7695i		−	1.77259i
$530$	−6.01264	−	4.98364i	−0.261172	−	0.216475i
$531$		−	23.2504i		−	1.00898i
$532$	−2.28705	−	11.6575i	−0.0991561	−	0.505417i
$533$	−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
$538$	1.35736	+	0.413696i	0.0585200	+	0.0178357i
$539$	2.43045			0.104687
$540$	17.4719	−	11.5188i	0.751872	−	0.495690i
$541$	14.8901			0.640175			0.320088	−	0.947388i	$-0.396288\pi$
$541$	14.8901			0.640175			0.320088	+	0.947388i	$0.396288\pi$
$542$	−37.3808	−	11.3929i	−1.60564	−	0.489368i
$543$	−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	$-0.265928\pi$
$547$	−1.65436	−	1.65436i	−0.0707353	−	0.0707353i	−0.741589	+	0.670854i	$0.765928\pi$
$548$	9.53866	−	1.87136i	0.407471	−	0.0799404i
$549$		−	32.9318i		−	1.40549i
$550$	−25.2677	+	13.2333i	−1.07742	+	0.564271i
$551$			6.87185i			0.292751i
$552$	−12.8679	−	15.8060i	−0.547695	−	0.672749i
$553$	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	$0.175175\pi$
$558$	−6.30176	+	20.6764i	−0.266775	+	0.875304i
$559$	1.14475			0.0484177
$560$	24.6608	+	0.217131i	1.04211	+	0.00917544i
$561$	−29.5535			−1.24775
$562$	−5.48474	+	17.9958i	−0.231360	+	0.759105i
$563$	−28.9612	+	28.9612i	−1.22057	+	1.22057i	−0.253142	+	0.967429i	$0.581464\pi$
$563$	−28.9612	+	28.9612i	−1.22057	+	1.22057i	−0.967429	+	0.253142i	$0.918536\pi$
$564$	−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
$568$	−2.51507	−	3.08933i	−0.105530	−	0.129626i
$569$			13.7813i			0.577743i	0.957368	+	0.288872i	$0.0932801\pi$
$569$			13.7813i			0.577743i	−0.957368	+	0.288872i	$0.906720\pi$
$570$	−3.92292	+	4.73291i	−0.164313	+	0.198240i
$571$			16.6485i			0.696719i	0.937361	+	0.348359i	$0.113261\pi$
$571$			16.6485i			0.696719i	−0.937361	+	0.348359i	$0.886739\pi$
$572$	23.1951	−	4.55058i	0.969838	−	0.190269i
$573$	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	$0.960970\pi$
$578$	66.1767	+	20.1693i	2.75259	+	0.838933i
$579$	2.13038			0.0885357
$580$	−13.9740	−	2.86951i	−0.580240	−	0.119150i
$581$	13.1431			0.545266
$582$	17.1215	+	5.21830i	0.709710	+	0.216305i
$583$	−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	$-0.436665\pi$
$587$	−18.9611	−	18.9611i	−0.782608	−	0.782608i	−0.980270	+	0.197662i	$0.936665\pi$
$588$	0.209344	+	1.06706i	0.00863319	+	0.0440050i
$589$		−	15.0645i		−	0.620721i
$590$	−33.4922	+	3.13411i	−1.37885	+	0.129029i
$591$		−	9.75388i		−	0.401221i
$592$	−2.37050	−	0.996498i	−0.0974271	−	0.0409558i
$593$	−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
$598$	−9.64655	+	31.6509i	−0.394477	+	1.29430i
$599$	−2.11193			−0.0862912			−0.0431456	−	0.999069i	$-0.513738\pi$
$599$	−2.11193			−0.0862912			−0.0431456	+	0.999069i	$0.513738\pi$
$600$	−7.98635	−	9.95368i	−0.326041	−	0.406357i
$601$	13.4953			0.550486			0.275243	−	0.961375i	$-0.411242\pi$
$601$	13.4953			0.550486			0.275243	+	0.961375i	$0.411242\pi$
$602$	0.444169	−	1.45734i	0.0181030	−	0.0593969i
$603$	−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	$-0.975673\pi$
$607$	−26.4465	−	26.4465i	−1.07343	−	1.07343i	−0.0763504	−	0.997081i	$-0.524327\pi$
$608$	−12.1352	+	1.11491i	−0.492148	+	0.0452154i
$609$		−	7.93676i		−	0.321614i
$610$	−47.4383	+	4.43914i	−1.92072	+	0.179735i
$611$			20.0774i			0.812244i
$612$	6.83277	+	34.8279i	0.276198	+	1.40784i
$613$	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	$0.941382\pi$
$618$	−9.21201	−	2.80763i	−0.370561	−	0.112940i
$619$	−17.1316			−0.688578			−0.344289	−	0.938864i	$-0.611880\pi$
$619$	−17.1316			−0.688578			−0.344289	+	0.938864i	$0.611880\pi$
$620$	30.6339	+	6.29055i	1.23029	+	0.252635i
$621$	37.3683			1.49954
$622$	33.3241	+	10.1565i	1.33617	+	0.407238i
$623$	−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
$628$	13.2440	−	2.59830i	0.528494	−	0.103683i
$629$		−	5.21942i		−	0.208112i
$630$	−12.1617	+	14.6728i	−0.484534	+	0.584578i
$631$			30.8174i			1.22682i	0.789765	+	0.613410i	$0.210203\pi$
$631$			30.8174i			1.22682i	−0.789765	+	0.613410i	$0.789797\pi$
$632$	13.5571	−	11.0370i	0.539273	−	0.439030i
$633$	−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
$638$	−5.30521	+	17.4067i	−0.210035	+	0.689139i
$639$	3.07844			0.121781
$640$	2.80019	−	25.1428i	0.110687	−	0.993855i
$641$	−29.7451			−1.17486			−0.587431	−	0.809274i	$-0.699861\pi$
$641$	−29.7451			−1.17486			−0.587431	+	0.809274i	$0.699861\pi$
$642$	3.64476	−	11.9587i	0.143847	−	0.471971i
$643$	24.9951	−	24.9951i	0.985711	−	0.985711i	−0.0141887	−	0.999899i	$-0.504517\pi$
$643$	24.9951	−	24.9951i	0.985711	−	0.985711i	0.999899	+	0.0141887i	$0.00451657\pi$
$644$	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	$-0.142777\pi$
$647$	11.8895	+	11.8895i	0.467423	+	0.467423i	−0.433656	+	0.901079i	$0.642777\pi$
$648$	−5.12054	+	4.16871i	−0.201154	+	0.163762i
$649$			42.9094i			1.68434i
$650$	−6.18084	+	19.7741i	−0.242432	+	0.775603i
$651$			17.3990i			0.681921i
$652$	19.5051	−	3.82664i	0.763878	−	0.149863i
$653$	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
$658$	25.5599	+	7.79014i	0.996429	+	0.303691i
$659$	16.9620			0.660746			0.330373	−	0.943850i	$-0.392825\pi$
$659$	16.9620			0.660746			0.330373	+	0.943850i	$0.392825\pi$
$660$	−13.5909	+	8.96011i	−0.529024	+	0.348772i
$661$	−28.0409			−1.09066			−0.545332	−	0.838220i	$-0.683596\pi$
$661$	−28.0409			−1.09066			−0.545332	+	0.838220i	$0.683596\pi$
$662$	−25.0898	−	7.64686i	−0.975143	−	0.297204i
$663$	−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
$668$	−0.456299	−	2.32584i	−0.0176547	−	0.0899896i
$669$			17.7068i			0.684584i
$670$	6.17991	+	5.12228i	0.238751	+	0.197891i
$671$			60.7767i			2.34626i
$672$	14.0158	−	1.28768i	0.540671	−	0.0496733i
$673$	−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	$0.172638\pi$
$678$	−2.78054	+	9.12312i	−0.106786	+	0.350371i
$679$	−38.6728			−1.48413
$680$	49.2487	−	14.5374i	1.88860	−	0.557482i
$681$	−4.28756			−0.164300
$682$	11.6301	−	38.1591i	0.445340	−	1.46119i
$683$	−26.8090	+	26.8090i	−1.02582	+	1.02582i	−0.0261603	+	0.999658i	$0.508328\pi$
$683$	−26.8090	+	26.8090i	−1.02582	+	1.02582i	−0.999658	+	0.0261603i	$0.991672\pi$
$684$	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
$688$	−1.44072	−	0.605643i	−0.0549271	−	0.0230899i
$689$			7.23564i			0.275656i
$690$	−2.12311	−	22.6883i	−0.0808253	−	0.863729i
$691$		−	9.60561i		−	0.365415i	−0.983167	−	0.182707i	$-0.941514\pi$
$691$		−	9.60561i		−	0.365415i	0.983167	−	0.182707i	$-0.0584861\pi$
$692$	2.45564	+	12.5169i	0.0933494	+	0.475819i
$693$	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
$698$	−25.3042	−	7.71219i	−0.957777	−	0.291911i
$699$	−4.34200			−0.164229
$700$	22.7756	+	15.5411i	0.860836	+	0.587398i
$701$	32.9276			1.24366			0.621830	−	0.783152i	$-0.286390\pi$
$701$	32.9276			1.24366			0.621830	+	0.783152i	$0.286390\pi$
$702$	−18.5472	−	5.65280i	−0.700017	−	0.213351i
$703$	−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
$708$	−18.8389	+	3.69594i	−0.708009	+	0.138902i
$709$			18.8092i			0.706395i	0.935549	+	0.353197i	$0.114906\pi$
$709$			18.8092i			0.706395i	−0.935549	+	0.353197i	$0.885094\pi$
$710$	−0.414967	−	4.43450i	−0.0155735	−	0.166424i
$711$			13.5093i			0.506638i
$712$	19.0789	+	23.4352i	0.715012	+	0.878269i
$713$	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
$718$	−10.0006	+	32.8127i	−0.373221	+	1.22456i
$719$	18.6102			0.694043			0.347022	−	0.937857i	$-0.387193\pi$
$719$	18.6102			0.694043			0.347022	+	0.937857i	$0.387193\pi$
$720$	13.7014	+	13.9448i	0.510621	+	0.519693i
$721$	20.8074			0.774907
$722$	5.92027	−	19.4248i	0.220330	−	0.722915i
$723$	−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	$-0.935362\pi$
$727$	−31.8467	−	31.8467i	−1.18113	−	1.18113i	−0.201675	−	0.979453i	$-0.564638\pi$
$728$	−14.4260	−	17.7198i	−0.534662	−	0.656740i
$729$			7.56551i			0.280204i
$730$	8.80631	+	7.29920i	0.325936	+	0.270156i
$731$		−	3.17221i		−	0.117329i
$732$	−26.6833	+	5.23491i	−0.986244	+	0.193488i
$733$	−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
$738$	−2.95678	−	0.901167i	−0.108841	−	0.0331724i
$739$	−22.7425			−0.836596			−0.418298	−	0.908310i	$-0.637373\pi$
$739$	−22.7425			−0.836596			−0.418298	+	0.908310i	$0.637373\pi$
$740$	−1.58243	−	2.40027i	−0.0581714	−	0.0882355i
$741$	5.69561			0.209233
$742$	9.21147	+	2.80747i	0.338164	+	0.103065i
$743$	37.9417	−	37.9417i	1.39194	−	1.39194i	0.570983	−	0.820962i	$-0.306562\pi$
$743$	37.9417	−	37.9417i	1.39194	−	1.39194i	0.820962	−	0.570983i	$-0.193438\pi$
$744$	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
$748$	−12.6101	−	64.2761i	−0.461071	−	2.35017i
$749$			27.0113i			0.986972i
$750$	−1.22823	−	14.2149i	−0.0448485	−	0.519055i
$751$			35.3710i			1.29071i	0.763884	+	0.645353i	$0.223290\pi$
$751$			35.3710i			1.29071i	−0.763884	+	0.645353i	$0.776710\pi$
$752$	10.6222	−	25.2684i	0.387352	−	0.921445i
$753$	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	$0.283453\pi$
$758$	0.959001	−	3.14654i	0.0348325	−	0.114287i
$759$	−29.0677			−1.05509
$760$	−11.9675	−	6.51251i	−0.434106	−	0.236233i
$761$	−37.2819			−1.35147			−0.675734	−	0.737145i	$-0.736173\pi$
$761$	−37.2819			−1.35147			−0.675734	+	0.737145i	$0.736173\pi$
$762$	6.81589	−	22.3633i	0.246914	−	0.810139i
$763$	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
$768$	0.151504	−	14.4373i	0.00546695	−	0.520960i
$769$		−	41.6703i		−	1.50267i	−0.659921	−	0.751335i	$-0.729410\pi$
$769$		−	41.6703i		−	1.50267i	0.659921	−	0.751335i	$-0.270590\pi$
$770$	22.4448	−	27.0791i	0.808856	−	0.975864i
$771$		−	20.4103i		−	0.735060i
$772$	0.909006	+	4.63338i	0.0327159	+	0.166759i
$773$	−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
$778$	−8.34180	−	2.54241i	−0.299068	−	0.0911498i
$779$	2.15426			0.0771844
$780$	−2.37834	+	11.5821i	−0.0851584	+	0.414707i
$781$	−5.68136			−0.203295
$782$	87.7079	+	26.7316i	3.13643	+	0.955919i
$783$	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	$-0.481330\pi$
$787$	−26.3608	−	26.3608i	−0.939660	−	0.939660i	−0.998280	+	0.0586202i	$0.981330\pi$
$788$	21.2137	−	4.16185i	0.755708	−	0.148260i
$789$			8.74930i			0.311483i
$790$	19.4602	−	1.82103i	0.692362	−	0.0647893i
$791$		−	20.6066i		−	0.732687i
$792$	19.3390	−	15.7442i	0.687183	−	0.559446i
$793$	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	$0.182890\pi$
$798$	2.20993	−	7.25091i	0.0782307	−	0.256679i
$799$	55.6365			1.96828
$800$	18.2406	−	21.6166i	0.644904	−	0.764264i
$801$	−23.3525			−0.825120
$802$	5.94124	−	19.4936i	0.209793	−	0.688342i
$803$	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
$808$	−41.5175	+	33.8000i	−1.46058	+	1.18908i
$809$		−	5.63303i		−	0.198047i	−0.995085	−	0.0990234i	$-0.968428\pi$
$809$		−	5.63303i		−	0.198047i	0.995085	−	0.0990234i	$-0.0315719\pi$
$810$	−7.35013	+	0.687804i	−0.258257	+	0.0241670i
$811$		−	43.8944i		−	1.54134i	−0.637234	−	0.770670i	$-0.719922\pi$
$811$		−	43.8944i		−	1.54134i	0.637234	−	0.770670i	$-0.280078\pi$
$812$	17.2617	−	3.38651i	0.605767	−	0.118843i
$813$	−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
$818$	−21.1919	−	6.45885i	−0.740957	−	0.225829i
$819$	17.6573			0.616997
$820$	−0.899565	+	4.38073i	−0.0314142	+	0.152982i
$821$	−10.5431			−0.367957			−0.183979	−	0.982930i	$-0.558898\pi$
$821$	−10.5431			−0.367957			−0.183979	+	0.982930i	$0.558898\pi$
$822$	5.93299	+	1.80826i	0.206937	+	0.0630702i
$823$	−28.2777	+	28.2777i	−0.985698	+	0.985698i	−0.999899	−	0.0142009i	$-0.995480\pi$
$823$	−28.2777	+	28.2777i	−0.985698	+	0.985698i	0.0142009	+	0.999899i	$0.495480\pi$
$824$	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	$-0.254373\pi$
$827$	−0.558699	−	0.558699i	−0.0194279	−	0.0194279i	−0.716754	+	0.697326i	$0.754373\pi$
$828$	6.72044	+	34.2553i	0.233551	+	1.19046i
$829$		−	1.98019i		−	0.0687750i	−0.999409	−	0.0343875i	$-0.989052\pi$
$829$		−	1.98019i		−	0.0687750i	0.999409	−	0.0343875i	$-0.0109480\pi$
$830$	9.61923	−	11.6054i	0.333888	−	0.402828i
$831$			4.89840i			0.169924i
$832$	−19.5909	+	12.8683i	−0.679192	+	0.446130i
$833$	−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
$838$	−9.73614	+	31.9448i	−0.336329	+	1.10352i
$839$	−52.0647			−1.79747			−0.898737	−	0.438489i	$-0.855514\pi$
$839$	−52.0647			−1.79747			−0.898737	+	0.438489i	$0.855514\pi$
$840$	13.8221	+	7.52174i	0.476906	+	0.259525i
$841$	18.8246			0.649125
$842$	−1.91708	+	6.29004i	−0.0660668	+	0.216769i
$843$	−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
$848$	3.82811	−	9.10643i	0.131458	−	0.312716i
$849$		−	28.8106i		−	0.988776i
$850$	54.7960	+	17.1277i	1.87949	+	0.587476i
$851$		−	5.13361i		−	0.175978i
$852$	−0.489356	−	2.49434i	−0.0167651	−	0.0854547i
$853$	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	$0.482363\pi$
$858$	14.4273	+	4.39713i	0.492538	+	0.150116i
$859$	−27.8302			−0.949553			−0.474776	−	0.880106i	$-0.657471\pi$
$859$	−27.8302			−0.949553			−0.474776	+	0.880106i	$0.657471\pi$
$860$	−0.961759	−	1.45881i	−0.0327957	−	0.0497451i
$861$	−2.48810			−0.0847942
$862$	−30.3599	−	9.25309i	−1.03406	−	0.315162i
$863$	8.13263	−	8.13263i	0.276838	−	0.276838i	−0.555007	−	0.831845i	$-0.687285\pi$
$863$	8.13263	−	8.13263i	0.276838	−	0.276838i	0.831845	+	0.555007i	$0.187285\pi$
$864$	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
$868$	−37.8411	+	7.42392i	−1.28441	+	0.251984i
$869$		−	24.9319i		−	0.845756i
$870$	−7.00819	−	5.80881i	−0.237600	−	0.196937i
$871$		−	7.43693i		−	0.251991i
$872$	−0.919191	−	1.12907i	−0.0311277	−	0.0382351i
$873$	−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	$0.412144\pi$
$878$	8.68651	−	28.5010i	0.293156	−	0.961861i
$879$	−6.66232			−0.224714
$880$	−25.2864	−	25.7356i	−0.852405	−	0.867549i
$881$	44.0279			1.48334			0.741669	−	0.670766i	$-0.234034\pi$
$881$	44.0279			1.48334			0.741669	+	0.670766i	$0.234034\pi$
$882$	0.542972	−	1.78152i	0.0182828	−	0.0599871i
$883$	0.939158	−	0.939158i	0.0316052	−	0.0316052i	−0.691128	−	0.722733i	$-0.742886\pi$
$883$	0.939158	−	0.939158i	0.0316052	−	0.0316052i	0.722733	+	0.691128i	$0.242886\pi$
$884$	−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	$-0.320952\pi$
$887$	−9.31080	−	9.31080i	−0.312626	−	0.312626i	−0.845926	+	0.533300i	$0.820952\pi$
$888$	−1.03590	−	1.27243i	−0.0347626	−	0.0426998i
$889$			50.5126i			1.69414i
$890$	3.14787	+	33.6393i	0.105517	+	1.12759i
$891$			9.41680i			0.315475i
$892$	−38.5105	+	7.55525i	−1.28943	+	0.252969i
$893$	−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
$898$	11.4841	+	3.50013i	0.383230	+	0.116801i
$899$	22.3065			0.743964
$900$	4.05514	+	21.4776i	0.135171	+	0.715922i
$901$	20.0507			0.667985
$902$	5.45684	+	1.66313i	0.181693	+	0.0553763i
$903$	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	$-0.388463\pi$
$907$	−17.9482	−	17.9482i	−0.595959	−	0.595959i	−0.939235	+	0.343276i	$0.888463\pi$
$908$	−1.82945	−	9.32503i	−0.0607123	−	0.309462i
$909$		−	41.3711i		−	1.37219i
$910$	−2.38017	−	25.4354i	−0.0789020	−	0.843176i
$911$			1.18779i			0.0393532i	0.999806	+	0.0196766i	$0.00626366\pi$
$911$			1.18779i			0.0393532i	−0.999806	+	0.0196766i	$0.993736\pi$
$912$	−7.16822	−	3.01334i	−0.237364	−	0.0997815i
$913$	−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
$918$	−15.6645	+	51.3961i	−0.517005	+	1.69632i
$919$	56.6966			1.87025			0.935125	−	0.354319i	$-0.115287\pi$
$919$	56.6966			1.87025			0.935125	+	0.354319i	$0.115287\pi$
$920$	48.4390	−	14.2984i	1.59699	−	0.471403i
$921$	−6.55097			−0.215862
$922$	−3.47698	+	11.4082i	−0.114508	+	0.375708i
$923$	−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
$928$	−1.65088	−	17.9691i	−0.0541928	−	0.589863i
$929$			8.73875i			0.286709i	0.989671	+	0.143355i	$0.0457889\pi$
$929$			8.73875i			0.286709i	−0.989671	+	0.143355i	$0.954211\pi$
$930$	15.3634	+	12.7341i	0.503785	+	0.417567i
$931$			1.29799i			0.0425398i
$932$	−1.85267	−	9.44342i	−0.0606863	−	0.309330i
$933$	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	$0.415530\pi$
$938$	−9.46774	−	2.88557i	−0.309133	−	0.0942173i
$939$	5.91686			0.193089
$940$	25.5857	−	16.8680i	0.834513	−	0.550173i
$941$	31.6452			1.03160			0.515802	−	0.856708i	$-0.327494\pi$
$941$	31.6452			1.03160			0.515802	+	0.856708i	$0.327494\pi$
$942$	8.23771	+	2.51069i	0.268399	+	0.0818026i
$943$	−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	$-0.233173\pi$
$947$	2.29952	+	2.29952i	0.0747244	+	0.0747244i	−0.668757	+	0.743481i	$0.733173\pi$
$948$	10.9461	−	2.14747i	0.355512	−	0.0697466i
$949$		−	10.5976i		−	0.344011i
$950$	−7.06728	−	13.4943i	−0.229293	−	0.437812i
$951$			31.4830i			1.02091i
$952$	−49.1034	+	39.9758i	−1.59145	+	1.29562i
$953$	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
$958$	−2.42123	+	7.94418i	−0.0782262	+	0.256665i
$959$	−13.4010			−0.432741
$960$	9.12095	−	13.3184i	0.294377	−	0.429850i
$961$	−17.9004			−0.577434
$962$	−0.776573	+	2.54798i	−0.0250377	+	0.0821502i
$963$	−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	$-0.0734355\pi$
$967$	23.1621	+	23.1621i	0.744842	+	0.744842i	−0.228663	+	0.973506i	$0.573436\pi$
$968$	−11.5629	+	9.41355i	−0.371647	+	0.302563i
$969$		−	15.7831i		−	0.507027i
$970$	−28.3041	+	34.1482i	−0.908790	+	1.09643i
$971$		−	45.2890i		−	1.45339i	−0.686958	−	0.726697i	$-0.741054\pi$
$971$		−	45.2890i		−	1.45339i	0.686958	−	0.726697i	$-0.258946\pi$
$972$	−31.6860	+	6.21637i	−1.01633	+	0.199390i
$973$	−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	$0.441268\pi$
$978$	12.1321	+	3.69761i	0.387941	+	0.118236i
$979$	43.0978			1.37741
$980$	−2.63948	−	0.542007i	−0.0843152	−	0.0173138i
$981$	1.12509			0.0359213
$982$	−52.7660	−	16.0820i	−1.68383	−	0.513197i
$983$	12.5294	−	12.5294i	0.399627	−	0.399627i	−0.478474	−	0.878102i	$-0.658810\pi$
$983$	12.5294	−	12.5294i	0.399627	−	0.399627i	0.878102	+	0.478474i	$0.158810\pi$
$984$	−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
$988$	2.43024	+	12.3874i	0.0773163	+	0.394096i
$989$		−	3.12006i		−	0.0992121i
$990$	27.7597	−	2.59767i	0.882261	−	0.0825594i
$991$		−	3.28857i		−	0.104465i	−0.998635	−	0.0522325i	$-0.983366\pi$
$991$		−	3.28857i		−	0.104465i	0.998635	−	0.0522325i	$-0.0166337\pi$
$992$	3.61906	+	39.3918i	0.114905	+	1.25069i
$993$	−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	$0.146679\pi$
$998$	9.69759	−	31.8184i	0.306972	−	1.00719i
$999$	3.00825			0.0951768

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.7	✓	108	4.3	odd	2	inner
820.2.k.c.83.19	yes	108	1.1	even	1	trivial
820.2.k.c.247.7	yes	108	5.2	odd	4	inner
820.2.k.c.247.19	yes	108	20.7	even	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+(-0.412299 + 1.35278i) 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} +(2.19345 - 1.78572i) q^{8} +2.18571i q^{9} +(3.14852 - 0.294630i) q^{10} -4.03380i q^{11} +(1.77100 - 0.347446i) 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} +(-2.95678 - 0.901167i) q^{18} +2.15426 q^{19} +(-0.899565 + 4.38073i) q^{20} -2.48810 q^{21} +(5.45684 + 1.66313i) 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} +(-1.06164 - 5.41138i) q^{28} +3.18989i q^{29} +(-1.82101 + 2.19700i) q^{30} -6.99289i q^{31} +(-5.63313 + 0.517535i) 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} +(-0.888200 + 2.91424i) q^{38} +2.64388 q^{39} +(-5.55526 - 3.02308i) q^{40} +1.00000 q^{41} +(1.02584 - 3.36585i) 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} +(-3.32747 - 1.39878i) q^{48} +0.602521i q^{49} +(-3.28061 - 6.26399i) q^{50} -7.32647i q^{51} +(1.12811 + 5.75019i) 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} +(-4.31521 - 1.31519i) q^{58} -10.6374 q^{59} +(-2.22126 - 3.36924i) q^{60} -15.0668 q^{61} +(9.45982 + 2.88316i) 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} +(15.9344 - 3.12611i) q^{68} -7.20602i q^{69} +(6.71305 + 5.56418i) q^{70} -1.40844i q^{71} +(3.90306 + 4.79424i) 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} +(-1.09007 + 3.57659i) q^{78} +6.18073 q^{79} +(6.37999 - 6.26863i) q^{80} -2.33447 q^{81} +(-0.412299 + 1.35278i) 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} +(-7.20324 - 8.84794i) q^{88} +10.6842i q^{89} +(0.643976 + 6.88176i) q^{90} -8.07852i q^{91} +(15.6724 - 3.07471i) 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} +(-0.815078 - 0.248419i) 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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