LMFDB - Embedded newform 820.2.k.c.83.13

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			83.13
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.896192 - 1.09400i) q^{2} +(1.47545 - 1.47545i) q^{3} +(-0.393681 + 1.96087i) q^{4} +(1.51870 - 1.64120i) q^{5} +(-2.93643 - 0.291859i) q^{6} +(2.76703 + 2.76703i) q^{7} +(2.49801 - 1.32663i) q^{8} -1.35390i q^{9} +(-3.15653 - 0.190630i) q^{10} +5.16144i q^{11} +(2.31231 + 3.47402i) q^{12} +(-4.63454 - 4.63454i) q^{13} +(0.547348 - 5.50693i) q^{14} +(-0.180745 - 4.66228i) q^{15} +(-3.69003 - 1.54392i) q^{16} +(2.01443 - 2.01443i) q^{17} +(-1.48117 + 1.21336i) q^{18} +2.80537 q^{19} +(2.62030 + 3.62409i) q^{20} +8.16523 q^{21} +(5.64663 - 4.62564i) q^{22} +(4.87516 - 4.87516i) q^{23} +(1.72832 - 5.64306i) q^{24} +(-0.387093 - 4.98499i) q^{25} +(-0.916761 + 9.22363i) q^{26} +(2.42873 + 2.42873i) q^{27} +(-6.51512 + 4.33646i) q^{28} +3.16774i q^{29} +(-4.93856 + 4.37603i) q^{30} -0.472710i q^{31} +(1.61793 + 5.42055i) q^{32} +(7.61544 + 7.61544i) q^{33} +(-4.00910 - 0.398475i) q^{34} +(8.74355 - 0.338965i) q^{35} +(2.65483 + 0.533006i) q^{36} +(0.798301 - 0.798301i) q^{37} +(-2.51415 - 3.06908i) q^{38} -13.6761 q^{39} +(1.61647 - 6.11449i) q^{40} +1.00000 q^{41} +(-7.31761 - 8.93278i) q^{42} +(4.45887 - 4.45887i) q^{43} +(-10.1209 - 2.03196i) q^{44} +(-2.22203 - 2.05617i) q^{45} +(-9.70251 - 0.964358i) q^{46} +(-4.64694 - 4.64694i) q^{47} +(-7.72242 + 3.16648i) q^{48} +8.31291i q^{49} +(-5.10668 + 4.89099i) q^{50} -5.94437i q^{51} +(10.9123 - 7.26320i) q^{52} +(3.62838 + 3.62838i) q^{53} +(0.480429 - 4.83365i) q^{54} +(8.47097 + 7.83868i) q^{55} +(10.5829 + 3.24125i) q^{56} +(4.13919 - 4.13919i) q^{57} +(3.46551 - 2.83890i) q^{58} -11.1651 q^{59} +(9.21328 + 1.48104i) q^{60} +0.219103 q^{61} +(-0.517146 + 0.423639i) q^{62} +(3.74629 - 3.74629i) q^{63} +(4.48012 - 6.62786i) q^{64} +(-14.6447 + 0.567738i) q^{65} +(1.50642 - 15.1562i) q^{66} +(1.42724 + 1.42724i) q^{67} +(3.15699 + 4.74307i) q^{68} -14.3861i q^{69} +(-8.20672 - 9.26168i) q^{70} +3.80715i q^{71} +(-1.79612 - 3.38206i) q^{72} +(-8.38424 - 8.38424i) q^{73} +(-1.58877 - 0.157912i) q^{74} +(-7.92624 - 6.78397i) q^{75} +(-1.10442 + 5.50098i) q^{76} +(-14.2819 + 14.2819i) q^{77} +(12.2564 + 14.9616i) q^{78} +3.21731 q^{79} +(-8.13793 + 3.71134i) q^{80} +11.2287 q^{81} +(-0.896192 - 1.09400i) q^{82} +(-7.88656 + 7.88656i) q^{83} +(-3.21450 + 16.0110i) q^{84} +(-0.246770 - 6.36539i) q^{85} +(-8.87401 - 0.882011i) q^{86} +(4.67384 + 4.67384i) q^{87} +(6.84731 + 12.8933i) q^{88} +13.1858i q^{89} +(-0.258095 + 4.27363i) q^{90} -25.6478i q^{91} +(7.64030 + 11.4788i) q^{92} +(-0.697460 - 0.697460i) q^{93} +(-0.919214 + 9.24831i) q^{94} +(4.26052 - 4.60419i) q^{95} +(10.3849 + 5.61057i) q^{96} +(-2.08198 + 2.08198i) q^{97} +(9.09434 - 7.44996i) q^{98} +6.98809 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 $

$2$	−0.896192	−	1.09400i	−0.633703	−	0.773576i
$2$	−0.896192	−	1.09400i	−0.633703	−	0.773576i
$3$	1.47545	−	1.47545i	0.851851	−	0.851851i	−0.138510	−	0.990361i	$-0.544231\pi$
$3$	1.47545	−	1.47545i	0.851851	−	0.851851i	0.990361	+	0.138510i	$0.0442313\pi$
$4$	−0.393681	+	1.96087i	−0.196841	+	0.980435i
$5$	1.51870	−	1.64120i	0.679184	−	0.733968i
$5$	1.51870	−	1.64120i	0.679184	−	0.733968i
$6$	−2.93643	−	0.291859i	−1.19879	−	0.119151i
$7$	2.76703	+	2.76703i	1.04584	+	1.04584i	0.998898	+	0.0469414i	$0.0149474\pi$
$7$	2.76703	+	2.76703i	1.04584	+	1.04584i	0.0469414	+	0.998898i	$0.485053\pi$
$8$	2.49801	−	1.32663i	0.883180	−	0.469034i
$9$		−	1.35390i		−	0.451301i
$10$	−3.15653	−	0.190630i	−0.998181	−	0.0602826i
$11$			5.16144i			1.55623i	0.628120	+	0.778116i	$0.283825\pi$
$11$			5.16144i			1.55623i	−0.628120	+	0.778116i	$0.716175\pi$
$12$	2.31231	+	3.47402i	0.667506	+	1.00286i
$13$	−4.63454	−	4.63454i	−1.28539	−	1.28539i	−0.937556	−	0.347834i	$-0.886917\pi$
$13$	−4.63454	−	4.63454i	−1.28539	−	1.28539i	−0.347834	−	0.937556i	$-0.613083\pi$
$14$	0.547348	−	5.50693i	0.146285	−	1.47179i
$15$	−0.180745	−	4.66228i	−0.0466681	−	1.20380i
$16$	−3.69003	−	1.54392i	−0.922508	−	0.385979i
$17$	2.01443	−	2.01443i	0.488570	−	0.488570i	−0.419285	−	0.907855i	$-0.637719\pi$
$17$	2.01443	−	2.01443i	0.488570	−	0.488570i	0.907855	+	0.419285i	$0.137719\pi$
$18$	−1.48117	+	1.21336i	−0.349116	+	0.285991i
$19$	2.80537			0.643597			0.321798	−	0.946808i	$-0.395713\pi$
$19$	2.80537			0.643597			0.321798	+	0.946808i	$0.395713\pi$
$20$	2.62030	+	3.62409i	0.585917	+	0.810371i
$21$	8.16523			1.78180
$22$	5.64663	−	4.62564i	1.20386	−	0.986189i
$23$	4.87516	−	4.87516i	1.01654	−	1.01654i	0.0166798	−	0.999861i	$-0.494690\pi$
$23$	4.87516	−	4.87516i	1.01654	−	1.01654i	0.999861	−	0.0166798i	$-0.00530959\pi$
$24$	1.72832	−	5.64306i	0.352791	−	1.15189i
$25$	−0.387093	−	4.98499i	−0.0774186	−	0.996999i
$26$	−0.916761	+	9.22363i	−0.179792	+	1.80890i
$27$	2.42873	+	2.42873i	0.467410	+	0.467410i
$28$	−6.51512	+	4.33646i	−1.23124	+	0.819514i
$29$			3.16774i			0.588234i	0.955769	+	0.294117i	$0.0950255\pi$
$29$			3.16774i			0.588234i	−0.955769	+	0.294117i	$0.904974\pi$
$30$	−4.93856	+	4.37603i	−0.901654	+	0.798950i
$31$		−	0.472710i		−	0.0849012i	−0.999099	−	0.0424506i	$-0.986483\pi$
$31$		−	0.472710i		−	0.0849012i	0.999099	−	0.0424506i	$-0.0135165\pi$
$32$	1.61793	+	5.42055i	0.286012	+	0.958226i
$33$	7.61544	+	7.61544i	1.32568	+	1.32568i
$34$	−4.00910	−	0.398475i	−0.687555	−	0.0683379i
$35$	8.74355	−	0.338965i	1.47793	−	0.0572956i
$36$	2.65483	+	0.533006i	0.442471	+	0.0888344i
$37$	0.798301	−	0.798301i	0.131240	−	0.131240i	−0.638435	−	0.769675i	$-0.720418\pi$
$37$	0.798301	−	0.798301i	0.131240	−	0.131240i	0.769675	+	0.638435i	$0.220418\pi$
$38$	−2.51415	−	3.06908i	−0.407849	−	0.497871i
$39$	−13.6761			−2.18992
$40$	1.61647	−	6.11449i	0.255586	−	0.966786i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−7.31761	−	8.93278i	−1.12913	−	1.37836i
$43$	4.45887	−	4.45887i	0.679971	−	0.679971i	−0.280023	−	0.959993i	$-0.590342\pi$
$43$	4.45887	−	4.45887i	0.679971	−	0.679971i	0.959993	+	0.280023i	$0.0903420\pi$
$44$	−10.1209	−	2.03196i	−1.52579	−	0.306330i
$45$	−2.22203	−	2.05617i	−0.331240	−	0.306516i
$46$	−9.70251	−	0.964358i	−1.43056	−	0.142187i
$47$	−4.64694	−	4.64694i	−0.677826	−	0.677826i	0.281682	−	0.959508i	$-0.409108\pi$
$47$	−4.64694	−	4.64694i	−0.677826	−	0.677826i	−0.959508	+	0.281682i	$0.909108\pi$
$48$	−7.72242	+	3.16648i	−1.11464	+	0.457042i
$49$			8.31291i			1.18756i
$50$	−5.10668	+	4.89099i	−0.722194	+	0.691690i
$51$		−	5.94437i		−	0.832378i
$52$	10.9123	−	7.26320i	1.51326	−	1.00722i
$53$	3.62838	+	3.62838i	0.498397	+	0.498397i	0.910939	−	0.412542i	$-0.135359\pi$
$53$	3.62838	+	3.62838i	0.498397	+	0.498397i	−0.412542	+	0.910939i	$0.635359\pi$
$54$	0.480429	−	4.83365i	0.0653781	−	0.657776i
$55$	8.47097	+	7.83868i	1.14223	+	1.05697i
$56$	10.5829	+	3.24125i	1.41420	+	0.433131i
$57$	4.13919	−	4.13919i	0.548249	−	0.548249i
$58$	3.46551	−	2.83890i	0.455044	−	0.372766i
$59$	−11.1651			−1.45358			−0.726788	−	0.686862i	$-0.758988\pi$
$59$	−11.1651			−1.45358			−0.726788	+	0.686862i	$0.758988\pi$
$60$	9.21328	+	1.48104i	1.18943	+	0.191201i
$61$	0.219103			0.0280533			0.0140266	−	0.999902i	$-0.495535\pi$
$61$	0.219103			0.0280533			0.0140266	+	0.999902i	$0.495535\pi$
$62$	−0.517146	+	0.423639i	−0.0656776	+	0.0538022i
$63$	3.74629	−	3.74629i	0.471988	−	0.471988i
$64$	4.48012	−	6.62786i	0.560015	−	0.828483i
$65$	−14.6447	+	0.567738i	−1.81645	+	0.0704192i
$66$	1.50642	−	15.1562i	0.185427	−	1.86560i
$67$	1.42724	+	1.42724i	0.174366	+	0.174366i	0.788894	−	0.614529i	$-0.210654\pi$
$67$	1.42724	+	1.42724i	0.174366	+	0.174366i	−0.614529	+	0.788894i	$0.710654\pi$
$68$	3.15699	+	4.74307i	0.382841	+	0.575182i
$69$		−	14.3861i		−	1.73188i
$70$	−8.20672	−	9.26168i	−0.980891	−	1.10698i
$71$			3.80715i			0.451825i	0.974148	+	0.225913i	$0.0725364\pi$
$71$			3.80715i			0.451825i	−0.974148	+	0.225913i	$0.927464\pi$
$72$	−1.79612	−	3.38206i	−0.211675	−	0.398580i
$73$	−8.38424	−	8.38424i	−0.981301	−	0.981301i	0.0185274	−	0.999828i	$-0.494102\pi$
$73$	−8.38424	−	8.38424i	−0.981301	−	0.981301i	−0.999828	+	0.0185274i	$0.994102\pi$
$74$	−1.58877	−	0.157912i	−0.184691	−	0.0183569i
$75$	−7.92624	−	6.78397i	−0.915244	−	0.783345i
$76$	−1.10442	+	5.50098i	−0.126686	+	0.631005i
$77$	−14.2819	+	14.2819i	−1.62757	+	1.62757i
$78$	12.2564	+	14.9616i	1.38776	+	1.69407i
$79$	3.21731			0.361975			0.180988	−	0.983485i	$-0.442071\pi$
$79$	3.21731			0.361975			0.180988	+	0.983485i	$0.442071\pi$
$80$	−8.13793	+	3.71134i	−0.909849	+	0.414940i
$81$	11.2287			1.24763
$82$	−0.896192	−	1.09400i	−0.0989678	−	0.120812i
$83$	−7.88656	+	7.88656i	−0.865663	+	0.865663i	−0.991989	−	0.126326i	$-0.959681\pi$
$83$	−7.88656	+	7.88656i	−0.865663	+	0.865663i	0.126326	+	0.991989i	$0.459681\pi$
$84$	−3.21450	+	16.0110i	−0.350730	+	1.74694i
$85$	−0.246770	−	6.36539i	−0.0267660	−	0.690424i
$86$	−8.87401	−	0.882011i	−0.956909	−	0.0951097i
$87$	4.67384	+	4.67384i	0.501088	+	0.501088i
$88$	6.84731	+	12.8933i	0.729926	+	1.37443i
$89$			13.1858i			1.39769i	0.715274	+	0.698844i	$0.246302\pi$
$89$			13.1858i			1.39769i	−0.715274	+	0.698844i	$0.753698\pi$
$90$	−0.258095	+	4.27363i	−0.0272056	+	0.450480i
$91$		−	25.6478i		−	2.68862i
$92$	7.64030	+	11.4788i	0.796556	+	1.19675i
$93$	−0.697460	−	0.697460i	−0.0723232	−	0.0723232i
$94$	−0.919214	+	9.24831i	−0.0948097	+	0.953890i
$95$	4.26052	−	4.60419i	0.437121	−	0.472380i
$96$	10.3849	+	5.61057i	1.05991	+	0.572627i
$97$	−2.08198	+	2.08198i	−0.211393	+	0.211393i	−0.804859	−	0.593466i	$-0.797759\pi$
$97$	−2.08198	+	2.08198i	−0.211393	+	0.211393i	0.593466	+	0.804859i	$0.297759\pi$
$98$	9.09434	−	7.44996i	0.918667	−	0.752560i
$99$	6.98809			0.702329
$100$	9.92732	+	1.20346i	0.992732	+	0.120346i
$101$	−2.54261			−0.252999			−0.126499	−	0.991967i	$-0.540374\pi$
$101$	−2.54261			−0.252999			−0.126499	+	0.991967i	$0.540374\pi$
$102$	−6.50315	+	5.32729i	−0.643908	+	0.527481i
$103$	−12.6502	+	12.6502i	−1.24646	+	1.24646i	−0.289190	+	0.957272i	$0.593386\pi$
$103$	−12.6502	+	12.6502i	−1.24646	+	1.24646i	−0.957272	+	0.289190i	$0.906614\pi$
$104$	−17.7254	−	5.42882i	−1.73812	−	0.532340i
$105$	12.4005	−	13.4008i	1.21017	−	1.30778i
$106$	0.717732	−	7.22118i	0.0697123	−	0.701383i
$107$	2.76820	+	2.76820i	0.267612	+	0.267612i	0.828137	−	0.560525i	$-0.189401\pi$
$107$	2.76820	+	2.76820i	0.267612	+	0.267612i	−0.560525	+	0.828137i	$0.689401\pi$
$108$	−5.71858	+	3.80629i	−0.550271	+	0.366260i
$109$		−	18.1472i		−	1.73819i	−0.494649	−	0.869093i	$-0.664703\pi$
$109$		−	18.1472i		−	1.73819i	0.494649	−	0.869093i	$-0.335297\pi$
$110$	0.983927	−	16.2922i	0.0938138	−	1.55340i
$111$		−	2.35571i		−	0.223594i
$112$	−5.93836	−	14.4825i	−0.561122	−	1.36847i
$113$	−1.72248	−	1.72248i	−0.162037	−	0.162037i	0.621432	−	0.783468i	$-0.286551\pi$
$113$	−1.72248	−	1.72248i	−0.162037	−	0.162037i	−0.783468	+	0.621432i	$0.786551\pi$
$114$	−8.23778	−	0.818775i	−0.771539	−	0.0766853i
$115$	−0.597214	−	15.4050i	−0.0556905	−	1.43653i
$116$	−6.21152	−	1.24708i	−0.576725	−	0.115788i
$117$	−6.27472	+	6.27472i	−0.580098	+	0.580098i
$118$	10.0061	+	12.2147i	0.921136	+	1.12445i
$119$	11.1480			1.02193
$120$	−6.63661	−	11.4066i	−0.605837	−	1.04128i
$121$	−15.6405			−1.42186
$122$	−0.196358	−	0.239699i	−0.0177774	−	0.0217013i
$123$	1.47545	−	1.47545i	0.133037	−	0.133037i
$124$	0.926923	+	0.186097i	0.0832402	+	0.0167120i
$125$	−8.76926	−	6.93542i	−0.784347	−	0.620323i
$126$	−7.45584	−	0.741056i	−0.664219	−	0.0660185i
$127$	9.58498	+	9.58498i	0.850530	+	0.850530i	0.990198	−	0.139669i	$-0.0446037\pi$
$127$	9.58498	+	9.58498i	0.850530	+	0.850530i	−0.139669	+	0.990198i	$0.544604\pi$
$128$	−11.2659	+	1.03858i	−0.995778	+	0.0917980i
$129$		−	13.1577i		−	1.15847i
$130$	13.7456	+	15.5125i	1.20557	+	1.36054i
$131$			7.56540i			0.660992i	0.943807	+	0.330496i	$0.107216\pi$
$131$			7.56540i			0.660992i	−0.943807	+	0.330496i	$0.892784\pi$
$132$	−17.9310	+	11.9348i	−1.56069	+	1.03879i
$133$	7.76255	+	7.76255i	0.673099	+	0.673099i
$134$	0.282324	−	2.84049i	0.0243891	−	0.245381i
$135$	7.67456	−	0.297523i	0.660521	−	0.0256067i
$136$	2.35966	−	7.70445i	0.202340	−	0.660651i
$137$	−9.68003	+	9.68003i	−0.827021	+	0.827021i	−0.987104	−	0.160083i	$-0.948824\pi$
$137$	−9.68003	+	9.68003i	−0.827021	+	0.827021i	0.160083	+	0.987104i	$0.448824\pi$
$138$	−15.7384	+	12.8927i	−1.33974	+	1.09750i
$139$	−13.8908			−1.17820			−0.589099	−	0.808061i	$-0.700517\pi$
$139$	−13.8908			−1.17820			−0.589099	+	0.808061i	$0.700517\pi$
$140$	−2.77751	+	17.2784i	−0.234742	+	1.46029i
$141$	−13.7127			−1.15481
$142$	4.16503	−	3.41193i	0.349521	−	0.286323i
$143$	23.9209	−	23.9209i	2.00037	−	2.00037i
$144$	−2.09031	+	4.99594i	−0.174193	+	0.416328i
$145$	5.19890	+	4.81085i	0.431745	+	0.399519i
$146$	−1.65849	+	16.6863i	−0.137258	+	1.38096i
$147$	12.2653	+	12.2653i	1.01162	+	1.01162i
$148$	1.25109	+	1.87964i	0.102839	+	0.154506i
$149$		−	1.41999i		−	0.116330i	−0.998307	−	0.0581650i	$-0.981475\pi$
$149$		−	1.41999i		−	0.116330i	0.998307	−	0.0581650i	$-0.0185249\pi$
$150$	−0.318247	+	14.7511i	−0.0259847	+	1.20442i
$151$		−	12.6577i		−	1.03007i	−0.857169	−	0.515036i	$-0.827779\pi$
$151$		−	12.6577i		−	1.03007i	0.857169	−	0.515036i	$-0.172221\pi$
$152$	7.00785	−	3.72169i	0.568412	−	0.301869i
$153$	−2.72734	−	2.72734i	−0.220492	−	0.220492i
$154$	28.4237	+	2.82510i	2.29044	+	0.227653i
$155$	−0.775813	−	0.717905i	−0.0623148	−	0.0576635i
$156$	5.38401	−	26.8170i	0.431066	−	2.14708i
$157$	−12.4304	+	12.4304i	−0.992058	+	0.992058i	−0.999969	−	0.00791080i	$-0.997482\pi$
$157$	−12.4304	+	12.4304i	−0.992058	+	0.992058i	0.00791080	+	0.999969i	$0.497482\pi$
$158$	−2.88332	−	3.51974i	−0.229385	−	0.280015i
$159$	10.7070			0.849120
$160$	11.3534	+	5.57685i	0.897562	+	0.440888i
$161$	26.9794			2.12628
$162$	−10.0630	−	12.2842i	−0.790626	−	0.965136i
$163$	−9.09289	+	9.09289i	−0.712210	+	0.712210i	−0.966997	−	0.254787i	$-0.917995\pi$
$163$	−9.09289	+	9.09289i	−0.712210	+	0.712210i	0.254787	+	0.966997i	$0.417995\pi$
$164$	−0.393681	+	1.96087i	−0.0307413	+	0.153118i
$165$	24.0641	−	0.932903i	1.87339	−	0.0726264i
$166$	15.6958	+	1.56005i	1.21823	+	0.121083i
$167$	8.92057	+	8.92057i	0.690295	+	0.690295i	0.962297	−	0.272002i	$-0.0876858\pi$
$167$	8.92057	+	8.92057i	0.690295	+	0.690295i	−0.272002	+	0.962297i	$0.587686\pi$
$168$	20.3968	−	10.8322i	1.57365	−	0.835724i
$169$			29.9579i			2.30445i
$170$	−6.74260	+	5.97458i	−0.517134	+	0.458229i
$171$		−	3.79820i		−	0.290456i
$172$	6.98789	+	10.4986i	0.532822	+	0.800513i
$173$	−9.26438	−	9.26438i	−0.704358	−	0.704358i	0.260985	−	0.965343i	$-0.415953\pi$
$173$	−9.26438	−	9.26438i	−0.704358	−	0.704358i	−0.965343	+	0.260985i	$0.915953\pi$
$174$	0.924534	−	9.30184i	0.0700888	−	0.705171i
$175$	12.7225	−	14.8647i	0.961733	−	1.12367i
$176$	7.96883	−	19.0459i	0.600673	−	1.43564i
$177$	−16.4736	+	16.4736i	−1.23823	+	1.23823i
$178$	14.4253	−	11.8170i	1.08122	−	0.885720i
$179$	−14.7559			−1.10291			−0.551455	−	0.834205i	$-0.685927\pi$
$179$	−14.7559			−1.10291			−0.551455	+	0.834205i	$0.685927\pi$
$180$	4.90666	−	3.54763i	0.365721	−	0.264425i
$181$	8.01452			0.595714			0.297857	−	0.954610i	$-0.403728\pi$
$181$	8.01452			0.595714			0.297857	+	0.954610i	$0.403728\pi$
$182$	−28.0588	+	22.9854i	−2.07985	+	1.70379i
$183$	0.323275	−	0.323275i	0.0238972	−	0.0238972i
$184$	5.71068	−	18.6457i	0.420997	−	1.37458i
$185$	−0.0977930	−	2.52255i	−0.00718988	−	0.185462i
$186$	−0.137965	+	1.38808i	−0.0101161	+	0.101779i
$187$	10.3973	+	10.3973i	0.760329	+	0.760329i
$188$	10.9415	−	7.28264i	0.797988	−	0.531141i
$189$			13.4408i			0.977671i
$190$	−8.85524	−	0.534789i	−0.642426	−	0.0387977i
$191$			13.7652i			0.996013i	0.867173	+	0.498007i	$0.165934\pi$
$191$			13.7652i			0.996013i	−0.867173	+	0.498007i	$0.834066\pi$
$192$	−3.16889	−	16.3893i	−0.228695	−	1.18279i
$193$	−4.16959	−	4.16959i	−0.300134	−	0.300134i	0.540932	−	0.841066i	$-0.318072\pi$
$193$	−4.16959	−	4.16959i	−0.300134	−	0.300134i	−0.841066	+	0.540932i	$0.818072\pi$
$194$	4.14354	+	0.411837i	0.297489	+	0.0295682i
$195$	−20.7698	+	22.4452i	−1.48736	+	1.60733i
$196$	−16.3005	−	3.27264i	−1.16432	−	0.233760i
$197$	−3.76308	+	3.76308i	−0.268108	+	0.268108i	−0.828338	−	0.560229i	$-0.810713\pi$
$197$	−3.76308	+	3.76308i	−0.268108	+	0.268108i	0.560229	+	0.828338i	$0.310713\pi$
$198$	−6.26266	−	7.64498i	−0.445068	−	0.543305i
$199$	12.4473			0.882368			0.441184	−	0.897417i	$-0.354559\pi$
$199$	12.4473			0.882368			0.441184	+	0.897417i	$0.354559\pi$
$200$	−7.58019	−	11.9390i	−0.536001	−	0.844218i
$201$	4.21165			0.297067
$202$	2.27866	+	2.78162i	0.160326	+	0.195714i
$203$	−8.76522	+	8.76522i	−0.615198	+	0.615198i
$204$	11.6561	+	2.34019i	0.816093	+	0.163846i
$205$	1.51870	−	1.64120i	0.106071	−	0.114627i
$206$	25.1764	+	2.50234i	1.75412	+	0.174347i
$207$	−6.60049	−	6.60049i	−0.458766	−	0.458766i
$208$	9.94625	+	24.2569i	0.689648	+	1.68192i
$209$			14.4798i			1.00159i
$210$	−25.7738	−	1.55654i	−1.77856	−	0.107411i
$211$			10.6591i			0.733805i	0.930259	+	0.366902i	$0.119582\pi$
$211$			10.6591i			0.733805i	−0.930259	+	0.366902i	$0.880418\pi$
$212$	−8.54322	+	5.68636i	−0.586750	+	0.390541i
$213$	5.61725	+	5.61725i	0.384888	+	0.384888i
$214$	0.547579	−	5.50925i	0.0374317	−	0.376605i
$215$	−0.546218	−	14.0896i	−0.0372517	−	0.960902i
$216$	9.28903	+	2.84498i	0.632038	+	0.193576i
$217$	1.30800	−	1.30800i	0.0887930	−	0.0887930i
$218$	−19.8531	+	16.2634i	−1.34462	+	1.10149i
$219$	−24.7410			−1.67184
$220$	−18.7055	+	13.5245i	−1.26113	+	0.911824i
$221$	−18.6719			−1.25601
$222$	−2.57715	+	2.11116i	−0.172967	+	0.141692i
$223$	7.75189	−	7.75189i	0.519105	−	0.519105i	−0.398196	−	0.917301i	$-0.630363\pi$
$223$	7.75189	−	7.75189i	0.519105	−	0.519105i	0.917301	+	0.398196i	$0.130363\pi$
$224$	−10.5220	+	19.4757i	−0.703028	+	1.30127i
$225$	−6.74920	+	0.524086i	−0.449946	+	0.0349391i
$226$	−0.340724	+	3.42806i	−0.0226646	+	0.228031i
$227$	0.729773	+	0.729773i	0.0484367	+	0.0484367i	0.730910	−	0.682474i	$-0.239096\pi$
$227$	0.729773	+	0.729773i	0.0484367	+	0.0484367i	−0.682474	+	0.730910i	$0.739096\pi$
$228$	6.48689	+	9.74593i	0.429605	+	0.645440i
$229$		−	19.3441i		−	1.27830i	−0.769083	−	0.639148i	$-0.779287\pi$
$229$		−	19.3441i		−	1.27830i	0.769083	−	0.639148i	$-0.220713\pi$
$230$	−16.3179	+	14.4592i	−1.07597	+	0.953412i
$231$			42.1443i			2.77289i
$232$	4.20241	+	7.91304i	0.275902	+	0.519517i
$233$	3.30122	+	3.30122i	0.216270	+	0.216270i	0.806925	−	0.590655i	$-0.201130\pi$
$233$	3.30122	+	3.30122i	0.216270	+	0.216270i	−0.590655	+	0.806925i	$0.701130\pi$
$234$	12.4879	+	1.24120i	0.816359	+	0.0811401i
$235$	−14.6839	+	0.569257i	−0.957871	+	0.0371342i
$236$	4.39550	−	21.8934i	0.286123	−	1.42514i
$237$	4.74697	−	4.74697i	0.308349	−	0.308349i
$238$	−9.99070	−	12.1959i	−0.647601	−	0.790542i
$239$	−2.32731			−0.150541			−0.0752707	−	0.997163i	$-0.523982\pi$
$239$	−2.32731			−0.150541			−0.0752707	+	0.997163i	$0.523982\pi$
$240$	−6.53122	+	17.4830i	−0.421588	+	1.12852i
$241$	11.9852			0.772037			0.386019	−	0.922491i	$-0.373850\pi$
$241$	11.9852			0.772037			0.386019	+	0.922491i	$0.373850\pi$
$242$	14.0168	+	17.1107i	0.901037	+	1.09992i
$243$	9.28111	−	9.28111i	0.595384	−	0.595384i
$244$	−0.0862567	+	0.429633i	−0.00552202	+	0.0275044i
$245$	13.6432	+	12.6248i	0.871630	+	0.806571i
$246$	−2.93643	−	0.291859i	−0.187220	−	0.0186083i
$247$	−13.0016	−	13.0016i	−0.827273	−	0.827273i
$248$	−0.627110	−	1.18083i	−0.0398215	−	0.0749831i
$249$			23.2725i			1.47483i
$250$	0.271577	+	15.8091i	0.0171761	+	0.999852i
$251$		−	5.36487i		−	0.338628i	−0.985562	−	0.169314i	$-0.945845\pi$
$251$		−	5.36487i		−	0.338628i	0.985562	−	0.169314i	$-0.0541552\pi$
$252$	5.87115	+	8.82083i	0.369847	+	0.555660i
$253$	25.1628	+	25.1628i	1.58197	+	1.58197i
$254$	1.89601	−	19.0760i	0.118966	−	1.19693i
$255$	−9.75591	−	9.02772i	−0.610939	−	0.565338i
$256$	11.2326	+	11.3942i	0.702040	+	0.712137i
$257$	21.1536	−	21.1536i	1.31952	−	1.31952i	0.405369	−	0.914153i	$-0.367143\pi$
$257$	21.1536	−	21.1536i	1.31952	−	1.31952i	0.914153	−	0.405369i	$-0.132857\pi$
$258$	−14.3945	+	11.7918i	−0.896163	+	0.734125i
$259$	4.41785			0.274512
$260$	4.65208	−	28.9399i	0.288510	−	1.79477i
$261$	4.28881			0.265471
$262$	8.27656	−	6.78005i	0.511328	−	0.418873i
$263$	−7.76480	+	7.76480i	−0.478798	+	0.478798i	−0.904747	−	0.425949i	$-0.859940\pi$
$263$	−7.76480	+	7.76480i	−0.478798	+	0.478798i	0.425949	+	0.904747i	$0.359940\pi$
$264$	29.1263	+	8.92060i	1.79260	+	0.549025i
$265$	11.4653	−	0.444482i	0.704310	−	0.0273043i
$266$	1.53551	−	15.4490i	0.0941485	−	0.947238i
$267$	19.4549	+	19.4549i	1.19062	+	1.19062i
$268$	−3.36052	+	2.23676i	−0.205277	+	0.136632i
$269$		−	24.0498i		−	1.46634i	−0.680046	−	0.733170i	$-0.738040\pi$
$269$		−	24.0498i		−	1.46634i	0.680046	−	0.733170i	$-0.261960\pi$
$270$	−7.20337	−	8.12935i	−0.438383	−	0.494737i
$271$			6.58939i			0.400277i	0.979768	+	0.200138i	$0.0641392\pi$
$271$			6.58939i			0.400277i	−0.979768	+	0.200138i	$0.935861\pi$
$272$	−10.5434	+	4.32319i	−0.639287	+	0.262132i
$273$	−37.8421	−	37.8421i	−2.29031	−	2.29031i
$274$	19.2651	+	1.91481i	1.16385	+	0.115678i
$275$	25.7297	−	1.99796i	1.55156	−	0.120481i
$276$	28.2093	+	5.66354i	1.69800	+	0.340905i
$277$	3.55240	−	3.55240i	0.213443	−	0.213443i	−0.592285	−	0.805728i	$-0.701774\pi$
$277$	3.55240	−	3.55240i	0.213443	−	0.213443i	0.805728	+	0.592285i	$0.201774\pi$
$278$	12.4488	+	15.1965i	0.746628	+	0.911427i
$279$	−0.640003			−0.0383160
$280$	21.3918	−	12.4462i	1.27840	−	0.743801i
$281$	−6.44099			−0.384237			−0.192119	−	0.981372i	$-0.561536\pi$
$281$	−6.44099			−0.384237			−0.192119	+	0.981372i	$0.561536\pi$
$282$	12.2892	+	15.0017i	0.731809	+	0.893336i
$283$	4.65107	−	4.65107i	0.276477	−	0.276477i	−0.555224	−	0.831701i	$-0.687367\pi$
$283$	4.65107	−	4.65107i	0.276477	−	0.276477i	0.831701	+	0.555224i	$0.187367\pi$
$284$	−7.46532	−	1.49880i	−0.442985	−	0.0889375i
$285$	−0.507056	−	13.0794i	−0.0300354	−	0.774759i
$286$	−47.6072	−	4.73181i	−2.81507	−	0.279798i
$287$	2.76703	+	2.76703i	0.163333	+	0.163333i
$288$	7.33889	−	2.19051i	0.432448	−	0.129077i
$289$			8.88417i			0.522598i
$290$	0.603867	−	9.99905i	0.0354603	−	0.587164i
$291$			6.14370i			0.360150i
$292$	19.7411	−	13.1397i	1.15526	−	0.768942i
$293$	2.71277	+	2.71277i	0.158482	+	0.158482i	0.781894	−	0.623412i	$-0.214254\pi$
$293$	2.71277	+	2.71277i	0.158482	+	0.158482i	−0.623412	+	0.781894i	$0.714254\pi$
$294$	2.42620	−	24.4103i	0.141499	−	1.42364i
$295$	−16.9565	+	18.3242i	−0.987245	+	1.06688i
$296$	0.935116	−	3.05321i	0.0543525	−	0.177464i
$297$	−12.5358	+	12.5358i	−0.727399	+	0.727399i
$298$	−1.55347	+	1.27258i	−0.0899901	+	0.0737186i
$299$	−45.1882			−2.61330
$300$	16.4229	−	12.8716i	0.948177	−	0.743143i
$301$	24.6756			1.42228
$302$	−13.8476	+	11.3438i	−0.796839	+	0.652760i
$303$	−3.75149	+	3.75149i	−0.215517	+	0.215517i
$304$	−10.3519	−	4.33126i	−0.593723	−	0.248415i
$305$	0.332752	−	0.359592i	0.0190533	−	0.0205902i
$306$	−0.539496	+	5.42793i	−0.0308409	+	0.310294i
$307$	−23.1966	−	23.1966i	−1.32390	−	1.32390i	−0.910591	−	0.413309i	$-0.864373\pi$
$307$	−23.1966	−	23.1966i	−1.32390	−	1.32390i	−0.413309	−	0.910591i	$-0.635627\pi$
$308$	−22.3824	−	33.6274i	−1.27535	−	1.91610i
$309$			37.3295i			2.12360i
$310$	−0.0901129	+	1.49212i	−0.00511807	+	0.0847468i
$311$			33.4135i			1.89470i	0.320195	+	0.947352i	$0.396251\pi$
$311$			33.4135i			1.89470i	−0.320195	+	0.947352i	$0.603749\pi$
$312$	−34.1629	+	18.1430i	−1.93410	+	1.02715i
$313$	5.34074	+	5.34074i	0.301876	+	0.301876i	0.841748	−	0.539871i	$-0.181527\pi$
$313$	5.34074	+	5.34074i	0.301876	+	0.301876i	−0.539871	+	0.841748i	$0.681527\pi$
$314$	24.7390	+	2.45887i	1.39610	+	0.138762i
$315$	−0.458926	−	11.8379i	−0.0258575	−	0.666991i
$316$	−1.26659	+	6.30872i	−0.0712514	+	0.354893i
$317$	16.4824	−	16.4824i	0.925745	−	0.925745i	−0.0716827	−	0.997427i	$-0.522837\pi$
$317$	16.4824	−	16.4824i	0.925745	−	0.925745i	0.997427	+	0.0716827i	$0.0228369\pi$
$318$	−9.59551	−	11.7135i	−0.538090	−	0.656859i
$319$	−16.3501			−0.915429
$320$	−4.07370	−	17.4185i	−0.227727	−	0.973725i
$321$	8.16868			0.455931
$322$	−24.1787	−	29.5155i	−1.34743	−	1.64484i
$323$	5.65122	−	5.65122i	0.314442	−	0.314442i
$324$	−4.42051	+	22.0179i	−0.245584	+	1.22322i
$325$	−21.3092	+	24.8971i	−1.18202	+	1.38105i
$326$	18.0966	+	1.79867i	1.00228	+	0.0996191i
$327$	−26.7753	−	26.7753i	−1.48068	−	1.48068i
$328$	2.49801	−	1.32663i	0.137930	−	0.0732508i
$329$		−	25.7164i		−	1.41779i
$330$	−22.5866	−	25.4901i	−1.24335	−	1.40318i
$331$		−	17.9582i		−	0.987073i	−0.869725	−	0.493536i	$-0.835704\pi$
$331$		−	17.9582i		−	0.987073i	0.869725	−	0.493536i	$-0.164296\pi$
$332$	−12.3597	−	18.5693i	−0.678329	−	1.01912i
$333$	−1.08082	−	1.08082i	−0.0592287	−	0.0592287i
$334$	1.76458	−	17.7537i	0.0965537	−	0.971437i
$335$	4.50996	−	0.174839i	0.246405	−	0.00955250i
$336$	−30.1299	−	12.6064i	−1.64372	−	0.687737i
$337$	7.07477	−	7.07477i	0.385387	−	0.385387i	−0.487651	−	0.873039i	$-0.662146\pi$
$337$	7.07477	−	7.07477i	0.385387	−	0.385387i	0.873039	+	0.487651i	$0.162146\pi$
$338$	32.7740	−	26.8480i	1.78267	−	1.46034i
$339$	−5.08285			−0.276063
$340$	12.5789	+	2.02205i	0.682185	+	0.109661i
$341$	2.43986			0.132126
$342$	−4.15524	+	3.40392i	−0.224690	+	0.184063i
$343$	−3.63287	+	3.63287i	−0.196156	+	0.196156i
$344$	5.22304	−	17.0536i	0.281607	−	0.919466i
$345$	−23.6105	−	21.8482i	−1.27115	−	1.17627i
$346$	−1.83259	+	18.4379i	−0.0985208	+	0.991228i
$347$	−1.01264	−	1.01264i	−0.0543616	−	0.0543616i	0.679403	−	0.733765i	$-0.262239\pi$
$347$	−1.01264	−	1.01264i	−0.0543616	−	0.0543616i	−0.733765	+	0.679403i	$0.762239\pi$
$348$	−11.0048	+	7.32479i	−0.589919	+	0.392650i
$349$			18.2163i			0.975094i	0.873097	+	0.487547i	$0.162108\pi$
$349$			18.2163i			0.975094i	−0.873097	+	0.487547i	$0.837892\pi$
$350$	−27.6639	−	0.596834i	−1.47870	−	0.0319021i
$351$		−	22.5121i		−	1.20161i
$352$	−27.9778	+	8.35083i	−1.49122	+	0.445101i
$353$	24.9501	+	24.9501i	1.32796	+	1.32796i	0.907146	+	0.420817i	$0.138256\pi$
$353$	24.9501	+	24.9501i	1.32796	+	1.32796i	0.420817	+	0.907146i	$0.361744\pi$
$354$	32.7856	+	3.25865i	1.74254	+	0.173195i
$355$	6.24830	+	5.78192i	0.331625	+	0.306872i
$356$	−25.8556	−	5.19099i	−1.37034	−	0.275122i
$357$	16.4482	−	16.4482i	0.870534	−	0.870534i
$358$	13.2241	+	16.1430i	0.698917	+	0.853184i
$359$	19.3556			1.02155			0.510775	−	0.859714i	$-0.329359\pi$
$359$	19.3556			1.02155			0.510775	+	0.859714i	$0.329359\pi$
$360$	−8.27843	−	2.18854i	−0.436312	−	0.115346i
$361$	−11.1299			−0.585783
$362$	−7.18254	−	8.76790i	−0.377506	−	0.460831i
$363$	−23.0767	+	23.0767i	−1.21121	+	1.21121i
$364$	50.2921	+	10.0971i	2.63602	+	0.529230i
$365$	−26.4934	+	1.02708i	−1.38673	+	0.0537599i
$366$	−0.643381	−	0.0639473i	−0.0336300	−	0.00334258i
$367$	−24.3061	−	24.3061i	−1.26877	−	1.26877i	−0.946724	−	0.322046i	$-0.895629\pi$
$367$	−24.3061	−	24.3061i	−1.26877	−	1.26877i	−0.322046	−	0.946724i	$-0.604371\pi$
$368$	−25.5163	+	10.4626i	−1.33013	+	0.545403i
$369$		−	1.35390i		−	0.0704814i
$370$	−2.67204	+	2.36768i	−0.138913	+	0.123090i
$371$			20.0797i			1.04249i
$372$	1.64221	−	1.09305i	0.0851444	−	0.0566721i
$373$	−25.4251	−	25.4251i	−1.31646	−	1.31646i	−0.916556	−	0.399907i	$-0.869042\pi$
$373$	−25.4251	−	25.4251i	−1.31646	−	1.31646i	−0.399907	−	0.916556i	$-0.630958\pi$
$374$	2.05670	−	20.6927i	0.106350	−	1.06999i
$375$	−23.1715	+	2.70575i	−1.19657	+	0.139724i
$376$	−17.7729	−	5.44335i	−0.916566	−	0.280719i
$377$	14.6810	−	14.6810i	0.756110	−	0.756110i
$378$	14.7042	−	12.0455i	0.756303	−	0.619553i
$379$	−9.35180			−0.480370			−0.240185	−	0.970727i	$-0.577208\pi$
$379$	−9.35180			−0.480370			−0.240185	+	0.970727i	$0.577208\pi$
$380$	7.35093	+	10.1669i	0.377095	+	0.521552i
$381$	28.2843			1.44905
$382$	15.0591	−	12.3362i	0.770492	−	0.631177i
$383$	7.82588	−	7.82588i	0.399884	−	0.399884i	−0.478308	−	0.878192i	$-0.658750\pi$
$383$	7.82588	−	7.82588i	0.399884	−	0.399884i	0.878192	+	0.478308i	$0.158750\pi$
$384$	−15.0900	+	18.1547i	−0.770056	+	0.926453i
$385$	1.74955	+	45.1293i	0.0891652	+	2.30000i
$386$	−0.824790	+	8.29830i	−0.0419807	+	0.422372i
$387$	−6.03687	−	6.03687i	−0.306871	−	0.306871i
$388$	−3.26285	−	4.90212i	−0.165646	−	0.248868i
$389$		−	3.87545i		−	0.196493i	−0.995162	−	0.0982466i	$-0.968677\pi$
$389$		−	3.87545i		−	0.196493i	0.995162	−	0.0982466i	$-0.0313234\pi$
$390$	43.1688	+	2.60707i	2.18594	+	0.132014i
$391$		−	19.6413i		−	0.993303i
$392$	11.0281	+	20.7657i	0.557005	+	1.04883i
$393$	11.1624	+	11.1624i	0.563067	+	0.563067i
$394$	7.48925	+	0.744376i	0.377303	+	0.0375011i
$395$	4.88613	−	5.28025i	0.245848	−	0.265678i
$396$	−2.75108	+	13.7027i	−0.138247	+	0.688588i
$397$	8.75247	−	8.75247i	0.439274	−	0.439274i	−0.452494	−	0.891768i	$-0.649466\pi$
$397$	8.75247	−	8.75247i	0.439274	−	0.439274i	0.891768	+	0.452494i	$0.149466\pi$
$398$	−11.1552	−	13.6174i	−0.559159	−	0.682579i
$399$	22.9065			1.14676
$400$	−6.26803	+	18.9924i	−0.313401	+	0.949621i
$401$	−30.7408			−1.53512			−0.767561	−	0.640976i	$-0.778530\pi$
$401$	−30.7408			−1.53512			−0.767561	+	0.640976i	$0.778530\pi$
$402$	−3.77445	−	4.60756i	−0.188252	−	0.229804i
$403$	−2.19079	+	2.19079i	−0.109131	+	0.109131i
$404$	1.00098	−	4.98572i	0.0498005	−	0.248049i
$405$	17.0530	−	18.4285i	0.847369	−	0.915720i
$406$	17.4445	+	1.73385i	0.865756	+	0.0860497i
$407$	4.12038	+	4.12038i	0.204240	+	0.204240i
$408$	−7.88596	−	14.8491i	−0.390413	−	0.735140i
$409$		−	33.0543i		−	1.63443i	−0.576334	−	0.817215i	$-0.695517\pi$
$409$		−	33.0543i		−	1.63443i	0.576334	−	0.817215i	$-0.304483\pi$
$410$	−3.15653	−	0.190630i	−0.155890	−	0.00941456i
$411$			28.5648i			1.40900i
$412$	−19.8253	−	29.7856i	−0.976721	−	1.46743i
$413$	−30.8942	−	30.8942i	−1.52021	−	1.52021i
$414$	−1.30565	+	13.1363i	−0.0641690	+	0.645612i
$415$	0.966115	+	24.9208i	0.0474247	+	1.22331i
$416$	17.6234	−	32.6201i	0.864058	−	1.59933i
$417$	−20.4951	+	20.4951i	−1.00365	+	1.00365i
$418$	15.8409	−	12.9766i	0.774803	−	0.634708i
$419$	5.31819			0.259811			0.129905	−	0.991526i	$-0.458533\pi$
$419$	5.31819			0.259811			0.129905	+	0.991526i	$0.458533\pi$
$420$	21.3954	+	29.5915i	1.04399	+	1.44392i
$421$	−14.2970			−0.696793			−0.348396	−	0.937347i	$-0.613274\pi$
$421$	−14.2970			−0.696793			−0.348396	+	0.937347i	$0.613274\pi$
$422$	11.6611	−	9.55262i	0.567654	−	0.465015i
$423$	−6.29150	+	6.29150i	−0.305903	+	0.305903i
$424$	13.8773	+	4.25023i	0.673939	+	0.206409i
$425$	−10.8217	−	9.26213i	−0.524928	−	0.449279i
$426$	1.11115	−	11.1794i	0.0538355	−	0.541645i
$427$	0.606265	+	0.606265i	0.0293392	+	0.0293392i
$428$	−6.51787	+	4.33829i	−0.315053	+	0.209699i
$429$		−	70.5881i		−	3.40803i
$430$	−14.9245	+	13.2245i	−0.719725	+	0.637744i
$431$		−	13.3608i		−	0.643567i	−0.946813	−	0.321784i	$-0.895718\pi$
$431$		−	13.3608i		−	0.643567i	0.946813	−	0.321784i	$-0.104282\pi$
$432$	−5.21234	−	12.7119i	−0.250779	−	0.611600i
$433$	19.4410	+	19.4410i	0.934275	+	0.934275i	0.997969	−	0.0636946i	$-0.0202884\pi$
$433$	19.4410	+	19.4410i	0.934275	+	0.934275i	−0.0636946	+	0.997969i	$0.520288\pi$
$434$	−2.60318	−	0.258737i	−0.124957	−	0.0124198i
$435$	14.7689	−	0.572552i	0.708113	−	0.0274517i
$436$	35.5843	+	7.14421i	1.70418	+	0.342146i
$437$	13.6766	−	13.6766i	0.654242	−	0.654242i
$438$	22.1727	+	27.0668i	1.05945	+	1.29330i
$439$	21.0213			1.00329			0.501646	−	0.865073i	$-0.332728\pi$
$439$	21.0213			1.00329			0.501646	+	0.865073i	$0.332728\pi$
$440$	31.5596	+	8.34330i	1.50454	+	0.397751i
$441$	11.2549			0.535946
$442$	16.7336	+	20.4271i	0.795935	+	0.971617i
$443$	−14.7645	+	14.7645i	−0.701482	+	0.701482i	−0.964729	−	0.263247i	$-0.915207\pi$
$443$	−14.7645	+	14.7645i	−0.701482	+	0.701482i	0.263247	+	0.964729i	$0.415207\pi$
$444$	4.61923	+	0.927397i	0.219219	+	0.0440123i
$445$	21.6405	+	20.0252i	1.02586	+	0.949288i
$446$	−15.4278	−	1.53341i	−0.730526	−	0.0726089i
$447$	−2.09512	−	2.09512i	−0.0990958	−	0.0990958i
$448$	30.7361	−	5.94287i	1.45214	−	0.280774i
$449$			9.10729i			0.429800i	0.976636	+	0.214900i	$0.0689425\pi$
$449$			9.10729i			0.429800i	−0.976636	+	0.214900i	$0.931058\pi$
$450$	6.62192	+	6.91395i	0.312160	+	0.325927i
$451$			5.16144i			0.243043i
$452$	4.05566	−	2.69945i	0.190762	−	0.126971i
$453$	−18.6759	−	18.6759i	−0.877468	−	0.877468i
$454$	0.144357	−	1.45239i	0.00677500	−	0.0681640i
$455$	−42.0933	−	38.9514i	−1.97336	−	1.82607i
$456$	4.84857	−	15.8309i	0.227055	−	0.741350i
$457$	−6.88978	+	6.88978i	−0.322290	+	0.322290i	−0.849645	−	0.527355i	$-0.823184\pi$
$457$	−6.88978	+	6.88978i	−0.322290	+	0.322290i	0.527355	+	0.849645i	$0.323184\pi$
$458$	−21.1625	+	17.3361i	−0.988860	+	0.810061i
$459$	9.78501			0.456725
$460$	30.4424	+	4.89361i	1.41938	+	0.228166i
$461$	−25.5632			−1.19060			−0.595298	−	0.803505i	$-0.702966\pi$
$461$	−25.5632			−1.19060			−0.595298	+	0.803505i	$0.702966\pi$
$462$	46.1060	−	37.7694i	2.14504	−	1.75719i
$463$	7.12636	−	7.12636i	0.331190	−	0.331190i	−0.521848	−	0.853038i	$-0.674757\pi$
$463$	7.12636	−	7.12636i	0.331190	−	0.331190i	0.853038	+	0.521848i	$0.174757\pi$
$464$	4.89072	−	11.6890i	0.227046	−	0.542650i
$465$	−2.20391	+	0.0854398i	−0.102204	+	0.00396218i
$466$	0.653016	−	6.57006i	0.0302504	−	0.304352i
$467$	18.5947	+	18.5947i	0.860461	+	0.860461i	0.991392	−	0.130931i	$-0.0417966\pi$
$467$	18.5947	+	18.5947i	0.860461	+	0.860461i	−0.130931	+	0.991392i	$0.541797\pi$
$468$	−9.83367	−	14.7741i	−0.454561	−	0.682935i
$469$			7.89846i			0.364717i
$470$	13.7823	+	15.5540i	0.635732	+	0.717454i
$471$			36.6810i			1.69017i
$472$	−27.8906	+	14.8120i	−1.28377	+	0.681776i
$473$	23.0142	+	23.0142i	1.05819	+	1.05819i
$474$	−9.44739	−	0.939001i	−0.433933	−	0.0431298i
$475$	−1.08594	−	13.9848i	−0.0498263	−	0.641665i
$476$	−4.38874	+	21.8597i	−0.201158	+	1.00194i
$477$	4.91248	−	4.91248i	0.224927	−	0.224927i
$478$	2.08572	+	2.54609i	0.0953986	+	0.116455i
$479$	−19.1887			−0.876753			−0.438377	−	0.898791i	$-0.644446\pi$
$479$	−19.1887			−0.876753			−0.438377	+	0.898791i	$0.644446\pi$
$480$	24.9797	−	8.52296i	1.14016	−	0.389018i
$481$	−7.39951			−0.337389
$482$	−10.7411	−	13.1119i	−0.489242	−	0.597230i
$483$	39.8068	−	39.8068i	1.81127	−	1.81127i
$484$	6.15736	−	30.6689i	0.279880	−	1.39404i
$485$	0.255045	+	6.57884i	0.0115810	+	0.298730i
$486$	−18.4712	−	1.83590i	−0.837871	−	0.0832782i
$487$	3.48393	+	3.48393i	0.157872	+	0.157872i	0.781623	−	0.623751i	$-0.214392\pi$
$487$	3.48393	+	3.48393i	0.157872	+	0.157872i	−0.623751	+	0.781623i	$0.714392\pi$
$488$	0.547322	−	0.290668i	0.0247761	−	0.0131579i
$489$			26.8322i			1.21339i
$490$	1.58469	−	26.2399i	0.0715892	−	1.18540i
$491$			17.3707i			0.783928i	0.919981	+	0.391964i	$0.128204\pi$
$491$			17.3707i			0.783928i	−0.919981	+	0.391964i	$0.871796\pi$
$492$	2.31231	+	3.47402i	0.104247	+	0.156621i
$493$	6.38117	+	6.38117i	0.287394	+	0.287394i
$494$	−2.57186	+	25.8757i	−0.115713	+	1.16420i
$495$	10.6128	−	11.4689i	0.477011	−	0.515487i
$496$	−0.729825	+	1.74431i	−0.0327701	+	0.0783220i
$497$	−10.5345	+	10.5345i	−0.472536	+	0.472536i
$498$	25.4601	−	20.8566i	1.14089	−	0.934605i
$499$	−23.0608			−1.03234			−0.516172	−	0.856485i	$-0.672644\pi$
$499$	−23.0608			−1.03234			−0.516172	+	0.856485i	$0.672644\pi$
$500$	17.0518	−	14.4650i	0.762578	−	0.646897i
$501$	26.3237			1.17606
$502$	−5.86918	+	4.80795i	−0.261954	+	0.214589i
$503$	20.1778	−	20.1778i	0.899684	−	0.899684i	−0.0957236	−	0.995408i	$-0.530516\pi$
$503$	20.1778	−	20.1778i	0.899684	−	0.899684i	0.995408	+	0.0957236i	$0.0305165\pi$
$504$	4.38834	−	14.3282i	0.195472	−	0.638229i
$505$	−3.86146	+	4.17293i	−0.171833	+	0.185693i
$506$	4.97747	−	50.0789i	0.221276	−	2.22628i
$507$	44.2014	+	44.2014i	1.96305	+	1.96305i
$508$	−22.5683	+	15.0215i	−1.00131	+	0.666471i
$509$		−	28.8845i		−	1.28028i	−0.768258	−	0.640140i	$-0.778876\pi$
$509$		−	28.8845i		−	1.28028i	0.768258	−	0.640140i	$-0.221124\pi$
$510$	−1.13318	+	18.7636i	−0.0501779	+	0.830864i
$511$		−	46.3989i		−	2.05257i
$512$	2.39868	−	22.4999i	0.106007	−	0.994365i
$513$	6.81350	+	6.81350i	0.300824	+	0.300824i
$514$	−42.0997	−	4.18440i	−1.85694	−	0.184566i
$515$	1.54967	+	39.9734i	0.0682866	+	1.76144i
$516$	25.8005	+	5.17993i	1.13580	+	0.228034i
$517$	23.9849	−	23.9849i	1.05485	−	1.05485i
$518$	−3.95924	−	4.83313i	−0.173959	−	0.212356i
$519$	−27.3382			−1.20002
$520$	−35.8294	+	20.8463i	−1.57122	+	0.914170i
$521$	−19.2622			−0.843894			−0.421947	−	0.906621i	$-0.638653\pi$
$521$	−19.2622			−0.843894			−0.421947	+	0.906621i	$0.638653\pi$
$522$	−3.84359	−	4.69196i	−0.168230	−	0.205362i
$523$	27.1330	−	27.1330i	1.18644	−	1.18644i	0.208398	−	0.978044i	$-0.433175\pi$
$523$	27.1330	−	27.1330i	1.18644	−	1.18644i	0.978044	−	0.208398i	$-0.0668251\pi$
$524$	−14.8348	−	2.97836i	−0.648060	−	0.130110i
$525$	−3.16070	−	40.7036i	−0.137944	−	1.77645i
$526$	15.4535	+	1.53596i	0.673803	+	0.0669710i
$527$	−0.952239	−	0.952239i	−0.0414802	−	0.0414802i
$528$	−16.3436	−	39.8588i	−0.711264	−	1.73463i
$529$		−	24.5343i		−	1.06671i
$530$	−10.7614	−	12.1448i	−0.467446	−	0.527535i
$531$			15.1165i			0.656000i
$532$	−18.2773	+	12.1654i	−0.792423	+	0.527437i
$533$	−4.63454	−	4.63454i	−0.200744	−	0.200744i
$534$	3.84839	−	38.7191i	0.166536	−	1.67554i
$535$	8.74724	−	0.339108i	0.378176	−	0.0146609i
$536$	5.45869	+	1.67185i	0.235780	+	0.0722129i
$537$	−21.7716	+	21.7716i	−0.939515	+	0.939515i
$538$	−26.3105	+	21.5532i	−1.13433	+	0.929224i
$539$	−42.9066			−1.84812
$540$	−2.43793	+	15.1660i	−0.104912	+	0.652639i
$541$	−17.7922			−0.764948			−0.382474	−	0.923966i	$-0.624928\pi$
$541$	−17.7922			−0.764948			−0.382474	+	0.923966i	$0.624928\pi$
$542$	7.20880	−	5.90535i	0.309645	−	0.253657i
$543$	11.8250	−	11.8250i	0.507460	−	0.507460i
$544$	14.1785	+	7.66010i	0.607897	+	0.328424i
$545$	−29.7832	−	27.5602i	−1.27577	−	1.18055i
$546$	−7.48556	+	75.3130i	−0.320352	+	3.22310i
$547$	2.45787	+	2.45787i	0.105091	+	0.105091i	0.757697	−	0.652606i	$-0.226324\pi$
$547$	2.45787	+	2.45787i	0.105091	+	0.105091i	−0.652606	+	0.757697i	$0.726324\pi$
$548$	−15.1704	−	22.7921i	−0.648049	−	0.973632i
$549$		−	0.296644i		−	0.0126605i
$550$	−25.2445	−	26.3578i	−1.07643	−	1.12390i
$551$			8.88668i			0.378585i
$552$	−19.0850	−	35.9366i	−0.812312	−	1.52956i
$553$	8.90238	+	8.90238i	0.378568	+	0.378568i
$554$	−7.06997	−	0.702702i	−0.300374	−	0.0298550i
$555$	−3.86619	−	3.57761i	−0.164111	−	0.151861i
$556$	5.46853	−	27.2380i	0.231917	−	1.15515i
$557$	−16.7540	+	16.7540i	−0.709889	+	0.709889i	−0.966512	−	0.256623i	$-0.917390\pi$
$557$	−16.7540	+	16.7540i	−0.709889	+	0.709889i	0.256623	+	0.966512i	$0.417390\pi$
$558$	0.573566	+	0.700165i	0.0242810	+	0.0296403i
$559$	−41.3296			−1.74806
$560$	−32.7873	−	12.2485i	−1.38552	−	0.517594i
$561$	30.6815			1.29537
$562$	5.77236	+	7.04646i	0.243493	+	0.297237i
$563$	−26.5154	+	26.5154i	−1.11749	+	1.11749i	−0.125383	+	0.992108i	$0.540016\pi$
$563$	−26.5154	+	26.5154i	−1.11749	+	1.11749i	−0.992108	+	0.125383i	$0.959984\pi$
$564$	5.39841	−	26.8887i	0.227314	−	1.13222i
$565$	−5.44286	+	0.211006i	−0.228983	+	0.00887708i
$566$	−9.25652	−	0.920030i	−0.389081	−	0.0386718i
$567$	31.0700	+	31.0700i	1.30482	+	1.30482i
$568$	5.05067	+	9.51029i	0.211921	+	0.399043i
$569$			35.4293i			1.48527i	0.669694	+	0.742637i	$0.266425\pi$
$569$			35.4293i			1.48527i	−0.669694	+	0.742637i	$0.733575\pi$
$570$	−13.8545	+	12.2764i	−0.580301	+	0.514202i
$571$		−	27.3582i		−	1.14491i	−0.819937	−	0.572453i	$-0.805992\pi$
$571$		−	27.3582i		−	1.14491i	0.819937	−	0.572453i	$-0.194008\pi$
$572$	37.4886	+	56.3230i	1.56748	+	2.35498i
$573$	20.3098	+	20.3098i	0.848455	+	0.848455i
$574$	0.547348	−	5.50693i	0.0228459	−	0.229855i
$575$	−26.1898	−	22.4155i	−1.09219	−	0.934791i
$576$	−8.97348	−	6.06564i	−0.373895	−	0.252735i
$577$	−25.7833	+	25.7833i	−1.07337	+	1.07337i	−0.0762883	+	0.997086i	$0.524307\pi$
$577$	−25.7833	+	25.7833i	−1.07337	+	1.07337i	−0.997086	+	0.0762883i	$0.975693\pi$
$578$	9.71931	−	7.96192i	0.404270	−	0.331172i
$579$	−12.3041			−0.511339
$580$	−11.4802	+	8.30043i	−0.476688	+	0.344657i
$581$	−43.6447			−1.81069
$582$	6.72122	−	5.50593i	0.278604	−	0.228228i
$583$	−18.7277	+	18.7277i	−0.775621	+	0.775621i
$584$	−32.0667	−	9.82116i	−1.32693	−	0.406402i
$585$	0.768662	+	19.8275i	0.0317802	+	0.819766i
$586$	0.536614	−	5.39894i	0.0221673	−	0.223028i
$587$	3.77789	+	3.77789i	0.155930	+	0.155930i	0.780761	−	0.624830i	$-0.214832\pi$
$587$	3.77789	+	3.77789i	0.155930	+	0.155930i	−0.624830	+	0.780761i	$0.714832\pi$
$588$	−28.8792	+	19.2220i	−1.19096	+	0.792703i
$589$		−	1.32613i		−	0.0546422i
$590$	35.2430	+	2.12841i	1.45093	+	0.0876254i
$591$			11.1045i			0.456776i
$592$	−4.17826	+	1.71324i	−0.171726	+	0.0704139i
$593$	7.64940	+	7.64940i	0.314123	+	0.314123i	0.846505	−	0.532381i	$-0.178703\pi$
$593$	7.64940	+	7.64940i	0.314123	+	0.314123i	−0.532381	+	0.846505i	$0.678703\pi$
$594$	24.9486	+	2.47971i	1.02365	+	0.101744i
$595$	16.9304	−	18.2961i	0.694079	−	0.750065i
$596$	2.78441	+	0.559023i	0.114054	+	0.0228985i
$597$	18.3654	−	18.3654i	0.751646	−	0.751646i
$598$	40.4973	+	49.4360i	1.65606	+	2.02159i
$599$	41.9169			1.71268			0.856339	−	0.516415i	$-0.172734\pi$
$599$	41.9169			1.71268			0.856339	+	0.516415i	$0.172734\pi$
$600$	−28.7996	−	6.43126i	−1.17574	−	0.262555i
$601$	25.5216			1.04105			0.520525	−	0.853847i	$-0.325736\pi$
$601$	25.5216			1.04105			0.520525	+	0.853847i	$0.325736\pi$
$602$	−22.1141	−	26.9952i	−0.901303	−	1.10024i
$603$	1.93235	−	1.93235i	0.0786914	−	0.0786914i
$604$	24.8202	+	4.98311i	1.00992	+	0.202760i
$605$	−23.7532	+	25.6692i	−0.965704	+	1.04360i
$606$	7.46619	+	0.742084i	0.303293	+	0.0301451i
$607$	−1.52889	−	1.52889i	−0.0620559	−	0.0620559i	0.675398	−	0.737454i	$-0.263972\pi$
$607$	−1.52889	−	1.52889i	−0.0620559	−	0.0620559i	−0.737454	+	0.675398i	$0.763972\pi$
$608$	4.53889	+	15.2067i	0.184076	+	0.616711i
$609$			25.8653i			1.04811i
$610$	−0.691604	−	0.0417677i	−0.0280022	−	0.00169112i
$611$			43.0729i			1.74254i
$612$	6.42166	−	4.27425i	0.259580	−	0.172776i
$613$	−19.8046	−	19.8046i	−0.799901	−	0.799901i	0.183179	−	0.983080i	$-0.441361\pi$
$613$	−19.8046	−	19.8046i	−0.799901	−	0.799901i	−0.983080	+	0.183179i	$0.941361\pi$
$614$	−4.58853	+	46.1657i	−0.185178	+	1.86310i
$615$	−0.180745	−	4.66228i	−0.00728833	−	0.188001i
$616$	−16.7295	+	54.6230i	−0.674052	+	2.20082i
$617$	−24.8092	+	24.8092i	−0.998780	+	0.998780i	−0.999999	−	0.00121975i	$-0.999612\pi$
$617$	−24.8092	+	24.8092i	−0.998780	+	0.998780i	0.00121975	+	0.999999i	$0.499612\pi$
$618$	40.8385	−	33.4544i	1.64277	−	1.34573i
$619$	−22.1097			−0.888665			−0.444332	−	0.895862i	$-0.646559\pi$
$619$	−22.1097			−0.888665			−0.444332	+	0.895862i	$0.646559\pi$
$620$	1.71314	−	1.23864i	0.0688015	−	0.0497451i
$621$	23.6809			0.950283
$622$	36.5544	−	29.9449i	1.46570	−	1.20068i
$623$	−36.4854	+	36.4854i	−1.46176	+	1.46176i
$624$	50.4651	+	21.1147i	2.02022	+	0.845264i
$625$	−24.7003	+	3.85931i	−0.988013	+	0.154372i
$626$	1.05645	−	10.6291i	0.0422244	−	0.424824i
$627$	21.3642	+	21.3642i	0.853202	+	0.853202i
$628$	−19.4809	−	29.2681i	−0.777371	−	1.16793i
$629$		−	3.21624i		−	0.128240i
$630$	−12.5394	+	11.1111i	−0.499582	+	0.442677i
$631$			22.7713i			0.906510i	0.891381	+	0.453255i	$0.149737\pi$
$631$			22.7713i			0.906510i	−0.891381	+	0.453255i	$0.850263\pi$
$632$	8.03687	−	4.26817i	0.319689	−	0.169779i
$633$	15.7270	+	15.7270i	0.625093	+	0.625093i
$634$	−32.8032	−	3.26040i	−1.30278	−	0.129487i
$635$	30.2876	−	1.17417i	1.20193	−	0.0465957i
$636$	−4.21514	+	20.9950i	−0.167141	+	0.832507i
$637$	38.5265	−	38.5265i	1.52648	−	1.52648i
$638$	14.6528	+	17.8870i	0.580110	+	0.708154i
$639$	5.15450			0.203909
$640$	−15.4051	+	20.0670i	−0.608939	+	0.793217i
$641$	−18.0005			−0.710979			−0.355489	−	0.934680i	$-0.615686\pi$
$641$	−18.0005			−0.710979			−0.355489	+	0.934680i	$0.615686\pi$
$642$	−7.32070	−	8.93655i	−0.288925	−	0.352697i
$643$	7.70880	−	7.70880i	0.304005	−	0.304005i	−0.538573	−	0.842579i	$-0.681037\pi$
$643$	7.70880	−	7.70880i	0.304005	−	0.304005i	0.842579	+	0.538573i	$0.181037\pi$
$644$	−10.6213	+	52.9032i	−0.418538	+	2.08468i
$645$	−21.5944	−	19.9826i	−0.850278	−	0.786813i
$646$	−11.2470	−	1.11787i	−0.442508	−	0.0439820i
$647$	−13.3371	−	13.3371i	−0.524336	−	0.524336i	0.394542	−	0.918878i	$-0.370903\pi$
$647$	−13.3371	−	13.3371i	−0.524336	−	0.524336i	−0.918878	+	0.394542i	$0.870903\pi$
$648$	28.0493	−	14.8962i	1.10188	−	0.585180i
$649$		−	57.6281i		−	2.26210i
$650$	46.3346	+	0.999646i	1.81739	+	0.0392093i
$651$		−	3.85978i		−	0.151277i
$652$	−14.2503	−	21.4097i	−0.558084	−	0.838468i
$653$	−1.46778	−	1.46778i	−0.0574388	−	0.0574388i	0.677804	−	0.735243i	$-0.262932\pi$
$653$	−1.46778	−	1.46778i	−0.0574388	−	0.0574388i	−0.735243	+	0.677804i	$0.762932\pi$
$654$	−5.29643	+	53.2880i	−0.207107	+	2.08372i
$655$	12.4164	+	11.4896i	0.485147	+	0.448935i
$656$	−3.69003	−	1.54392i	−0.144071	−	0.0602798i
$657$	−11.3514	+	11.3514i	−0.442862	+	0.442862i
$658$	−28.1338	+	23.0469i	−1.09677	+	0.898460i
$659$	37.0340			1.44264			0.721320	−	0.692602i	$-0.243536\pi$
$659$	37.0340			1.44264			0.721320	+	0.692602i	$0.243536\pi$
$660$	−7.64427	+	47.5538i	−0.297553	+	1.85103i
$661$	25.7704			1.00235			0.501177	−	0.865345i	$-0.332901\pi$
$661$	25.7704			1.00235			0.501177	+	0.865345i	$0.332901\pi$
$662$	−19.6463	+	16.0940i	−0.763576	+	0.625511i
$663$	−27.5494	+	27.5494i	−1.06993	+	1.06993i
$664$	−9.23819	+	30.1633i	−0.358511	+	1.17056i
$665$	24.5289	−	0.950924i	0.951191	−	0.0368752i
$666$	−0.213798	+	2.15104i	−0.00828450	+	0.0833513i
$667$	15.4432	+	15.4432i	0.597964	+	0.597964i
$668$	−21.0040	+	13.9802i	−0.812667	+	0.540911i
$669$		−	22.8750i		−	0.884400i
$670$	−4.23306	−	4.77721i	−0.163537	−	0.184560i
$671$			1.13089i			0.0436574i
$672$	13.2107	+	44.2600i	0.509615	+	1.70737i
$673$	19.9874	+	19.9874i	0.770458	+	0.770458i	0.978187	−	0.207728i	$-0.0666070\pi$
$673$	19.9874	+	19.9874i	0.770458	+	0.770458i	−0.207728	+	0.978187i	$0.566607\pi$
$674$	−14.0802	−	1.39946i	−0.542348	−	0.0539054i
$675$	11.1671	−	13.0474i	0.429821	−	0.502193i
$676$	−58.7436	−	11.7939i	−2.25937	−	0.453610i
$677$	23.9716	−	23.9716i	0.921304	−	0.921304i	−0.0758177	−	0.997122i	$-0.524157\pi$
$677$	23.9716	−	23.9716i	0.921304	−	0.921304i	0.997122	+	0.0758177i	$0.0241567\pi$
$678$	4.55521	+	5.56065i	0.174942	+	0.213556i
$679$	−11.5218			−0.442165
$680$	−9.06094	−	15.5735i	−0.347471	−	0.597215i
$681$	2.15349			0.0825218
$682$	−2.18659	−	2.66922i	−0.0837287	−	0.102210i
$683$	−3.64212	+	3.64212i	−0.139362	+	0.139362i	−0.773346	−	0.633984i	$-0.781418\pi$
$683$	−3.64212	+	3.64212i	−0.139362	+	0.139362i	0.633984	+	0.773346i	$0.281418\pi$
$684$	7.44778	+	1.49528i	0.284773	+	0.0571735i
$685$	1.18582	+	30.5880i	0.0453078	+	1.16871i
$686$	7.23011	+	0.718619i	0.276047	+	0.0274370i
$687$	−28.5413	−	28.5413i	−1.08892	−	1.08892i
$688$	−23.3375	+	9.56923i	−0.889733	+	0.364824i
$689$		−	33.6318i		−	1.28127i
$690$	−2.74243	+	45.4101i	−0.104402	+	1.72873i
$691$		−	8.33510i		−	0.317082i	−0.987352	−	0.158541i	$-0.949321\pi$
$691$		−	8.33510i		−	0.317082i	0.987352	−	0.158541i	$-0.0506790\pi$
$692$	21.8135	−	14.5190i	0.829224	−	0.551931i
$693$	19.3362	+	19.3362i	0.734523	+	0.734523i
$694$	−0.200312	+	2.01536i	−0.00760372	+	0.0765019i
$695$	−21.0959	+	22.7976i	−0.800214	+	0.864761i
$696$	17.8757	+	5.47485i	0.677578	+	0.207524i
$697$	2.01443	−	2.01443i	0.0763018	−	0.0763018i
$698$	19.9286	−	16.3253i	0.754310	−	0.617920i
$699$	9.74156			0.368460
$700$	24.1392	+	30.7992i	0.912375	+	1.16410i
$701$	7.73940			0.292313			0.146157	−	0.989261i	$-0.453310\pi$
$701$	7.73940			0.292313			0.146157	+	0.989261i	$0.453310\pi$
$702$	−24.6283	+	20.1752i	−0.929536	+	0.761463i
$703$	2.23953	−	2.23953i	0.0844656	−	0.0844656i
$704$	34.2093	+	23.1239i	1.28931	+	0.871513i
$705$	−20.8254	+	22.5052i	−0.784331	+	0.847596i
$706$	4.93540	−	49.6556i	0.185746	−	1.86881i
$707$	−7.03547	−	7.03547i	−0.264596	−	0.264596i
$708$	−25.8172	−	38.7879i	−0.970271	−	1.45774i
$709$			17.2164i			0.646576i	0.946301	+	0.323288i	$0.104788\pi$
$709$			17.2164i			0.646576i	−0.946301	+	0.323288i	$0.895212\pi$
$710$	0.725758	−	12.0174i	0.0272372	−	0.451003i
$711$		−	4.35592i		−	0.163360i
$712$	17.4926	+	32.9382i	0.655563	+	1.23441i
$713$	−2.30454	−	2.30454i	−0.0863055	−	0.0863055i
$714$	−32.7352	−	3.25364i	−1.22508	−	0.121764i
$715$	−2.93034	−	75.5877i	−0.109589	−	2.82682i
$716$	5.80913	−	28.9345i	0.217097	−	1.08133i
$717$	−3.43383	+	3.43383i	−0.128239	+	0.128239i
$718$	−17.3463	−	21.1751i	−0.647359	−	0.790247i
$719$	−18.6378			−0.695073			−0.347536	−	0.937667i	$-0.612982\pi$
$719$	−18.6378			−0.695073			−0.347536	+	0.937667i	$0.612982\pi$
$720$	5.02479	+	11.0180i	0.187263	+	0.410615i
$721$	−70.0070			−2.60720
$722$	9.97451	+	12.1761i	0.371213	+	0.453148i
$723$	17.6836	−	17.6836i	0.657661	−	0.657661i
$724$	−3.15517	+	15.7154i	−0.117261	+	0.584060i
$725$	15.7911	−	1.22621i	0.586469	−	0.0455402i
$726$	45.9271	+	4.56482i	1.70452	+	0.169416i
$727$	4.07066	+	4.07066i	0.150972	+	0.150972i	0.778552	−	0.627580i	$-0.215954\pi$
$727$	4.07066	+	4.07066i	0.150972	+	0.150972i	−0.627580	+	0.778552i	$0.715954\pi$
$728$	−34.0251	−	64.0685i	−1.26105	−	2.37454i
$729$			6.29834i			0.233272i
$730$	24.8668	+	28.0634i	0.920361	+	1.03867i
$731$		−	17.9641i		−	0.664427i
$732$	0.506634	+	0.761169i	0.0187257	+	0.0281336i
$733$	2.69579	+	2.69579i	0.0995714	+	0.0995714i	0.755138	−	0.655566i	$-0.227570\pi$
$733$	2.69579	+	2.69579i	0.0995714	+	0.0995714i	−0.655566	+	0.755138i	$0.727570\pi$
$734$	−4.80801	+	48.3739i	−0.177467	+	1.78551i
$735$	38.7571	−	1.50251i	1.42958	−	0.0554211i
$736$	34.3137	+	18.5384i	1.26482	+	0.683333i
$737$	−7.36664	+	7.36664i	−0.271354	+	0.271354i
$738$	−1.48117	+	1.21336i	−0.0545227	+	0.0446643i
$739$	−14.3841			−0.529126			−0.264563	−	0.964368i	$-0.585228\pi$
$739$	−14.3841			−0.529126			−0.264563	+	0.964368i	$0.585228\pi$
$740$	4.98490	+	0.801323i	0.183249	+	0.0294572i
$741$	−38.3664			−1.40943
$742$	21.9672	−	17.9952i	0.806442	−	0.660626i
$743$	21.4698	−	21.4698i	0.787652	−	0.787652i	−0.193456	−	0.981109i	$-0.561970\pi$
$743$	21.4698	−	21.4698i	0.787652	−	0.787652i	0.981109	+	0.193456i	$0.0619698\pi$
$744$	−2.66753	−	0.816993i	−0.0977965	−	0.0299524i
$745$	−2.33049	−	2.15654i	−0.0853825	−	0.0790094i
$746$	−5.02936	+	50.6009i	−0.184138	+	1.85263i
$747$	10.6776	+	10.6776i	0.390674	+	0.390674i
$748$	−24.4811	+	16.2946i	−0.895117	+	0.595790i
$749$			15.3194i			0.559758i
$750$	23.7262	+	22.9248i	0.866357	+	0.837094i
$751$			29.4342i			1.07407i	0.843560	+	0.537035i	$0.180456\pi$
$751$			29.4342i			1.07407i	−0.843560	+	0.537035i	$0.819544\pi$
$752$	9.97286	+	24.3218i	0.363673	+	0.886926i
$753$	−7.91560	−	7.91560i	−0.288460	−	0.288460i
$754$	−29.2180	−	2.90406i	−1.06406	−	0.105760i
$755$	−20.7739	−	19.2233i	−0.756040	−	0.699608i
$756$	−26.3556	−	5.29138i	−0.958544	−	0.192445i
$757$	9.67924	−	9.67924i	0.351798	−	0.351798i	−0.508980	−	0.860778i	$-0.669977\pi$
$757$	9.67924	−	9.67924i	0.351798	−	0.351798i	0.860778	+	0.508980i	$0.169977\pi$
$758$	8.38100	+	10.2309i	0.304412	+	0.371603i
$759$	74.2530			2.69521
$760$	4.53479	−	17.1534i	0.164494	−	0.622221i
$761$	19.4258			0.704183			0.352092	−	0.935966i	$-0.385471\pi$
$761$	19.4258			0.704183			0.352092	+	0.935966i	$0.385471\pi$
$762$	−25.3482	−	30.9431i	−0.918267	−	1.12095i
$763$	50.2138	−	50.2138i	1.81786	−	1.81786i
$764$	−26.9917	−	5.41909i	−0.976527	−	0.196056i
$765$	−8.61812	+	0.334103i	−0.311589	+	0.0120795i
$766$	−15.5750	−	1.54804i	−0.562748	−	0.0559330i
$767$	51.7452	+	51.7452i	1.86841	+	1.86841i
$768$	33.3848	+	0.238365i	1.20467	+	0.00860124i
$769$		−	26.4031i		−	0.952122i	−0.879412	−	0.476061i	$-0.842064\pi$
$769$		−	26.4031i		−	0.952122i	0.879412	−	0.476061i	$-0.157936\pi$
$770$	47.8036	−	42.3585i	1.72272	−	1.52649i
$771$		−	62.4220i		−	2.24807i
$772$	9.81753	−	6.53455i	0.353341	−	0.235183i
$773$	8.12280	+	8.12280i	0.292157	+	0.292157i	0.837932	−	0.545775i	$-0.183765\pi$
$773$	8.12280	+	8.12280i	0.292157	+	0.292157i	−0.545775	+	0.837932i	$0.683765\pi$
$774$	−1.19416	+	12.0145i	−0.0429231	+	0.431854i
$775$	−2.35646	+	0.182983i	−0.0846464	+	0.00657293i
$776$	−2.43879	+	7.96281i	−0.0875475	+	0.285848i
$777$	6.51831	−	6.51831i	0.233843	−	0.233843i
$778$	−4.23975	+	3.47315i	−0.152002	+	0.124518i
$779$	2.80537			0.100513
$780$	−35.8354	−	49.5632i	−1.28311	−	1.77465i
$781$	−19.6504			−0.703145
$782$	−21.4876	+	17.6024i	−0.768396	+	0.629459i
$783$	−7.69359	+	7.69359i	−0.274946	+	0.274946i
$784$	12.8344	−	30.6749i	0.458373	−	1.09553i
$785$	1.52275	+	39.2790i	0.0543492	+	1.40193i
$786$	2.20803	−	22.2153i	0.0787580	−	0.792392i
$787$	−16.3323	−	16.3323i	−0.582185	−	0.582185i	0.353318	−	0.935503i	$-0.385053\pi$
$787$	−16.3323	−	16.3323i	−0.582185	−	0.582185i	−0.935503	+	0.353318i	$0.885053\pi$
$788$	−5.89746	−	8.86036i	−0.210088	−	0.315637i
$789$			22.9131i			0.815730i
$790$	−10.1555	−	0.613316i	−0.361317	−	0.0218208i
$791$		−	9.53229i		−	0.338929i
$792$	17.4563	−	9.27059i	0.620283	−	0.329416i
$793$	−1.01544	−	1.01544i	−0.0360594	−	0.0360594i
$794$	−17.4191	−	1.73133i	−0.618181	−	0.0614426i
$795$	16.2607	−	17.5723i	0.576708	−	0.623227i
$796$	−4.90028	+	24.4076i	−0.173686	+	0.865105i
$797$	18.4862	−	18.4862i	0.654816	−	0.654816i	−0.299333	−	0.954149i	$-0.596764\pi$
$797$	18.4862	−	18.4862i	0.654816	−	0.654816i	0.954149	+	0.299333i	$0.0967640\pi$
$798$	−20.5286	−	25.0598i	−0.726705	−	0.887106i
$799$	−18.7218			−0.662331
$800$	26.3951	−	10.1636i	0.933208	−	0.359338i
$801$	17.8522			0.630778
$802$	27.5497	+	33.6305i	0.972812	+	1.18753i
$803$	43.2747	−	43.2747i	1.52713	−	1.52713i
$804$	−1.65805	+	8.25851i	−0.0584749	+	0.291255i
$805$	40.9737	−	44.2787i	1.44413	−	1.56062i
$806$	4.36010	+	0.433362i	0.153578	+	0.0152645i
$807$	−35.4842	−	35.4842i	−1.24910	−	1.24910i
$808$	−6.35146	+	3.37309i	−0.223444	+	0.118665i
$809$			34.7772i			1.22270i	0.791360	+	0.611350i	$0.209373\pi$
$809$			34.7772i			1.22270i	−0.791360	+	0.611350i	$0.790627\pi$
$810$	−35.4435	−	2.14052i	−1.24536	−	0.0752103i
$811$			9.58144i			0.336450i	0.985749	+	0.168225i	$0.0538035\pi$
$811$			9.58144i			0.336450i	−0.985749	+	0.168225i	$0.946196\pi$
$812$	−13.7368	−	20.6382i	−0.482066	−	0.724258i
$813$	9.72231	+	9.72231i	0.340976	+	0.340976i
$814$	0.815055	−	8.20036i	0.0285677	−	0.287422i
$815$	1.11389	+	28.7327i	0.0390180	+	1.00646i
$816$	−9.17761	+	21.9349i	−0.321281	+	0.767875i
$817$	12.5088	−	12.5088i	0.437627	−	0.437627i
$818$	−36.1615	+	29.6230i	−1.26436	+	1.03574i
$819$	−34.7247			−1.21338
$820$	2.62030	+	3.62409i	0.0915049	+	0.126559i
$821$	12.8259			0.447626			0.223813	−	0.974632i	$-0.428150\pi$
$821$	12.8259			0.447626			0.223813	+	0.974632i	$0.428150\pi$
$822$	31.2499	−	25.5995i	1.08997	−	0.892886i
$823$	−20.7141	+	20.7141i	−0.722047	+	0.722047i	−0.969022	−	0.246975i	$-0.920563\pi$
$823$	−20.7141	+	20.7141i	−0.722047	+	0.722047i	0.246975	+	0.969022i	$0.420563\pi$
$824$	−14.8182	+	48.3825i	−0.516218	+	1.68548i
$825$	35.0151	−	40.9108i	1.21907	−	1.42433i
$826$	−6.11121	+	61.4855i	−0.212636	+	2.13936i
$827$	−25.4825	−	25.4825i	−0.886114	−	0.886114i	0.108034	−	0.994147i	$-0.465545\pi$
$827$	−25.4825	−	25.4825i	−0.886114	−	0.886114i	−0.994147	+	0.108034i	$0.965545\pi$
$828$	15.5412	−	10.3442i	0.540094	−	0.359486i
$829$			30.8680i			1.07209i	0.844189	+	0.536045i	$0.180082\pi$
$829$			30.8680i			1.07209i	−0.844189	+	0.536045i	$0.819918\pi$
$830$	26.3976	−	23.3907i	0.916273	−	0.811904i
$831$		−	10.4828i		−	0.363644i
$832$	−51.4804	+	9.95381i	−1.78476	+	0.345086i
$833$	16.7457	+	16.7457i	0.580206	+	0.580206i
$834$	40.7893	+	4.05415i	1.41242	+	0.140384i
$835$	28.1882	−	1.09278i	0.975491	−	0.0378173i
$836$	−28.3930	−	5.70041i	−0.981991	−	0.197153i
$837$	1.14809	−	1.14809i	0.0396837	−	0.0396837i
$838$	−4.76612	−	5.81811i	−0.164643	−	0.200983i
$839$	36.0577			1.24485			0.622424	−	0.782680i	$-0.286148\pi$
$839$	36.0577			1.24485			0.622424	+	0.782680i	$0.286148\pi$
$840$	13.1988	−	49.9262i	0.455403	−	1.72262i
$841$	18.9654			0.653981
$842$	12.8128	+	15.6409i	0.441560	+	0.539022i
$843$	−9.50336	+	9.50336i	−0.327313	+	0.327313i
$844$	−20.9012	−	4.19630i	−0.719448	−	0.144443i
$845$	49.1670	+	45.4971i	1.69140	+	1.56515i
$846$	12.5213	+	1.24453i	0.430492	+	0.0427877i
$847$	−43.2776	−	43.2776i	−1.48704	−	1.48704i
$848$	−7.78692	−	18.9908i	−0.267404	−	0.652145i
$849$		−	13.7248i		−	0.471035i
$850$	−0.434501	+	20.1396i	−0.0149033	+	0.690782i
$851$		−	7.78369i		−	0.266821i
$852$	−13.2261	+	8.80330i	−0.453119	+	0.301596i
$853$	−0.104364	−	0.104364i	−0.00357336	−	0.00357336i	0.705318	−	0.708891i	$-0.250804\pi$
$853$	−0.104364	−	0.104364i	−0.00357336	−	0.00357336i	−0.708891	+	0.705318i	$0.750804\pi$
$854$	0.119926	−	1.20658i	0.00410377	−	0.0412884i
$855$	−6.23362	−	5.76833i	−0.213185	−	0.197273i
$856$	10.5874	+	3.24262i	0.361869	+	0.110831i
$857$	25.0673	−	25.0673i	0.856281	−	0.856281i	−0.134616	−	0.990898i	$-0.542980\pi$
$857$	25.0673	−	25.0673i	0.856281	−	0.856281i	0.990898	+	0.134616i	$0.0429802\pi$
$858$	−77.2236	+	63.2605i	−2.63637	+	2.15968i
$859$	45.3441			1.54712			0.773560	−	0.633723i	$-0.218474\pi$
$859$	45.3441			1.54712			0.773560	+	0.633723i	$0.218474\pi$
$860$	27.8429	+	4.47575i	0.949435	+	0.152622i
$861$	8.16523			0.278270
$862$	−14.6167	+	11.9738i	−0.497848	+	0.407830i
$863$	32.0908	−	32.0908i	1.09238	−	1.09238i	0.0971115	−	0.995274i	$-0.469040\pi$
$863$	32.0908	−	32.0908i	1.09238	−	1.09238i	0.995274	−	0.0971115i	$-0.0309603\pi$
$864$	−9.23555	+	17.0946i	−0.314200	+	0.581569i
$865$	−29.2745	+	1.13490i	−0.995365	+	0.0385877i
$866$	3.84564	−	38.6914i	0.130680	−	1.31479i
$867$	13.1082	+	13.1082i	0.445176	+	0.445176i
$868$	2.04989	+	3.07976i	0.0695778	+	0.104534i
$869$			16.6059i			0.563318i
$870$	−13.8621	−	15.6441i	−0.469970	−	0.530383i
$871$		−	13.2292i		−	0.448256i
$872$	−24.0746	−	45.3319i	−0.815268	−	1.53513i
$873$	2.81879	+	2.81879i	0.0954017	+	0.0954017i
$874$	−27.2192	−	2.70538i	−0.920702	−	0.0915110i
$875$	−5.07430	−	43.4553i	−0.171543	−	1.46906i
$876$	9.74009	−	48.5140i	0.329087	−	1.63914i
$877$	36.0607	−	36.0607i	1.21768	−	1.21768i	0.249244	−	0.968441i	$-0.419818\pi$
$877$	36.0607	−	36.0607i	1.21768	−	1.21768i	0.968441	−	0.249244i	$-0.0801822\pi$
$878$	−18.8391	−	22.9973i	−0.635789	−	0.776123i
$879$	8.00511			0.270006
$880$	−19.1559	−	42.0035i	−0.645744	−	1.41594i
$881$	−8.35118			−0.281358			−0.140679	−	0.990055i	$-0.544929\pi$
$881$	−8.35118			−0.281358			−0.140679	+	0.990055i	$0.544929\pi$
$882$	−10.0865	−	12.3129i	−0.339631	−	0.414595i
$883$	−29.6377	+	29.6377i	−0.997388	+	0.997388i	−0.999997	−	0.00260899i	$-0.999170\pi$
$883$	−29.6377	+	29.6377i	−0.997388	+	0.997388i	0.00260899	+	0.999997i	$0.499170\pi$
$884$	7.35077	−	36.6131i	0.247233	−	1.23143i
$885$	2.01804	+	52.0549i	0.0678356	+	1.74981i
$886$	29.3842	+	2.92057i	0.987181	+	0.0981185i
$887$	−1.87526	−	1.87526i	−0.0629652	−	0.0629652i	0.674923	−	0.737888i	$-0.264177\pi$
$887$	−1.87526	−	1.87526i	−0.0629652	−	0.0629652i	−0.737888	+	0.674923i	$0.764177\pi$
$888$	−3.12514	−	5.88458i	−0.104873	−	0.197474i
$889$			53.0439i			1.77903i
$890$	2.51361	−	41.6212i	0.0842564	−	1.39515i
$891$			57.9560i			1.94160i
$892$	12.1487	+	18.2522i	0.406768	+	0.611130i
$893$	−13.0364	−	13.0364i	−0.436247	−	0.436247i
$894$	−0.414437	+	4.16970i	−0.0138608	+	0.139455i
$895$	−22.4098	+	24.2175i	−0.749078	+	0.809500i
$896$	−34.0470	−	28.2994i	−1.13743	−	0.945417i
$897$	−66.6729	+	66.6729i	−2.22614	+	2.22614i
$898$	9.96339	−	8.16187i	0.332483	−	0.272365i
$899$	1.49742			0.0499418
$900$	1.62937	−	13.4406i	0.0543122	−	0.448021i
$901$	14.6182			0.487003
$902$	5.64663	−	4.62564i	0.188012	−	0.154017i
$903$	36.4077	−	36.4077i	1.21157	−	1.21157i
$904$	−6.58785	−	2.01768i	−0.219109	−	0.0671070i
$905$	12.1717	−	13.1534i	0.404600	−	0.437235i
$906$	−3.69428	+	37.1686i	−0.122734	+	1.23484i
$907$	1.64793	+	1.64793i	0.0547186	+	0.0547186i	0.733937	−	0.679218i	$-0.237681\pi$
$907$	1.64793	+	1.64793i	0.0547186	+	0.0547186i	−0.679218	+	0.733937i	$0.737681\pi$
$908$	−1.71829	+	1.14369i	−0.0570234	+	0.0379548i
$909$			3.44244i			0.114179i
$910$	−4.88925	+	80.9580i	−0.162077	+	2.68373i
$911$			41.1643i			1.36384i	0.731429	+	0.681918i	$0.238854\pi$
$911$			41.1643i			1.36384i	−0.731429	+	0.681918i	$0.761146\pi$
$912$	−21.6643	+	8.88316i	−0.717376	+	0.294151i
$913$	−40.7060	−	40.7060i	−1.34717	−	1.34717i
$914$	13.7120	+	1.36287i	0.453553	+	0.0450798i
$915$	−0.0396017	−	1.02152i	−0.00130919	−	0.0337704i
$916$	37.9314	+	7.61543i	1.25329	+	0.251621i
$917$	−20.9337	+	20.9337i	−0.691291	+	0.691291i
$918$	−8.76924	−	10.7048i	−0.289428	−	0.353312i
$919$	26.9931			0.890421			0.445210	−	0.895426i	$-0.353129\pi$
$919$	26.9931			0.890421			0.445210	+	0.895426i	$0.353129\pi$
$920$	−21.9286	−	37.6897i	−0.722964	−	1.24259i
$921$	−68.4508			−2.25553
$922$	22.9095	+	27.9662i	0.754485	+	0.921017i
$923$	17.6444	−	17.6444i	0.580771	−	0.580771i
$924$	−82.6396	−	16.5914i	−2.71864	−	0.545818i
$925$	−4.28854	−	3.67051i	−0.141006	−	0.120686i
$926$	−14.1828	−	1.40967i	−0.466077	−	0.0463246i
$927$	17.1271	+	17.1271i	0.562529	+	0.562529i
$928$	−17.1709	+	5.12516i	−0.563661	+	0.168242i
$929$			18.9464i			0.621610i	0.950474	+	0.310805i	$0.100599\pi$
$929$			18.9464i			0.621610i	−0.950474	+	0.310805i	$0.899401\pi$
$930$	2.06859	+	2.33451i	0.0678318	+	0.0765515i
$931$			23.3208i			0.764309i
$932$	−7.77289	+	5.17363i	−0.254609	+	0.169468i
$933$	49.2999	+	49.2999i	1.61401	+	1.61401i
$934$	3.67823	−	37.0071i	0.120355	−	1.21091i
$935$	32.8546	−	1.27369i	1.07446	−	0.0416541i
$936$	−7.35010	+	23.9985i	−0.240245	+	0.784416i
$937$	9.19528	−	9.19528i	0.300397	−	0.300397i	−0.540772	−	0.841169i	$-0.681868\pi$
$937$	9.19528	−	9.19528i	0.300397	−	0.300397i	0.841169	+	0.540772i	$0.181868\pi$
$938$	8.64093	−	7.07853i	0.282136	−	0.231122i
$939$	15.7600			0.514307
$940$	4.66453	−	29.0173i	0.152140	−	0.946440i
$941$	−37.8616			−1.23425			−0.617127	−	0.786864i	$-0.711704\pi$
$941$	−37.8616			−1.23425			−0.617127	+	0.786864i	$0.711704\pi$
$942$	40.1291	−	32.8732i	1.30748	−	1.07107i
$943$	4.87516	−	4.87516i	0.158757	−	0.158757i
$944$	41.1997	+	17.2380i	1.34093	+	0.561050i
$945$	22.0590	+	20.4125i	0.717580	+	0.664019i
$946$	4.55245	−	45.8027i	0.148013	−	1.48917i
$947$	35.2315	+	35.2315i	1.14487	+	1.14487i	0.987547	+	0.157323i	$0.0502863\pi$
$947$	35.2315	+	35.2315i	1.14487	+	1.14487i	0.157323	+	0.987547i	$0.449714\pi$
$948$	7.43941	+	11.1770i	0.241621	+	0.363012i
$949$			77.7142i			2.52271i
$950$	−14.3262	+	13.7211i	−0.464802	+	0.445170i
$951$		−	48.6379i		−	1.57719i
$952$	27.8477	−	14.7892i	0.902550	−	0.479320i
$953$	−41.1900	−	41.1900i	−1.33427	−	1.33427i	−0.901505	−	0.432769i	$-0.857537\pi$
$953$	−41.1900	−	41.1900i	−1.33427	−	1.33427i	−0.432769	−	0.901505i	$-0.642463\pi$
$954$	−9.77678	−	0.971740i	−0.316535	−	0.0314612i
$955$	22.5914	+	20.9052i	0.731042	+	0.676476i
$956$	0.916220	−	4.56356i	0.0296327	−	0.147596i
$957$	−24.1237	+	24.1237i	−0.779809	+	0.779809i
$958$	17.1967	+	20.9925i	0.555601	+	0.678236i
$959$	−53.5699			−1.72986
$960$	−31.7107	−	19.6896i	−1.02346	−	0.635479i
$961$	30.7765			0.992792
$962$	6.63138	+	8.09508i	0.213804	+	0.260996i
$963$	3.74787	−	3.74787i	0.120773	−	0.120773i
$964$	−4.71837	+	23.5015i	−0.151968	+	0.756933i
$965$	−13.1755	+	0.510781i	−0.424135	+	0.0164426i
$966$	−79.2232	−	7.87420i	−2.54896	−	0.253348i
$967$	−12.4773	−	12.4773i	−0.401242	−	0.401242i	0.477429	−	0.878670i	$-0.341569\pi$
$967$	−12.4773	−	12.4773i	−0.401242	−	0.401242i	−0.878670	+	0.477429i	$0.841569\pi$
$968$	−39.0700	+	20.7491i	−1.25576	+	0.666900i
$969$		−	16.6762i		−	0.535716i
$970$	6.96870	−	6.17493i	0.223752	−	0.198265i
$971$			31.9289i			1.02465i	0.858793	+	0.512323i	$0.171215\pi$
$971$			31.9289i			1.02465i	−0.858793	+	0.512323i	$0.828785\pi$
$972$	14.5453	+	21.8529i	0.466540	+	0.700931i
$973$	−38.4362	−	38.4362i	−1.23221	−	1.23221i
$974$	0.689157	−	6.93369i	0.0220820	−	0.222170i
$975$	5.29390	+	68.1751i	0.169541	+	2.18335i
$976$	−0.808497	−	0.338277i	−0.0258793	−	0.0108280i
$977$	5.97477	−	5.97477i	0.191150	−	0.191150i	−0.605043	−	0.796193i	$-0.706844\pi$
$977$	5.97477	−	5.97477i	0.191150	−	0.191150i	0.796193	+	0.605043i	$0.206844\pi$
$978$	29.3545	−	24.0468i	0.938653	−	0.768932i
$979$	−68.0576			−2.17513
$980$	−30.1267	+	21.7823i	−0.962363	+	0.695811i
$981$	−24.5695			−0.784445
$982$	19.0036	−	15.5675i	0.606428	−	0.496778i
$983$	−14.0475	+	14.0475i	−0.448046	+	0.448046i	−0.894705	−	0.446658i	$-0.852614\pi$
$983$	−14.0475	+	14.0475i	−0.448046	+	0.448046i	0.446658	+	0.894705i	$0.352614\pi$
$984$	1.72832	−	5.64306i	0.0550967	−	0.179894i
$985$	0.460982	+	11.8910i	0.0146881	+	0.378878i
$986$	1.26226	−	12.6998i	0.0401987	−	0.404443i
$987$	−37.9433	−	37.9433i	−1.20775	−	1.20775i
$988$	30.6130	−	20.3760i	0.973929	−	0.648247i
$989$		−	43.4754i		−	1.38244i
$990$	−22.0581	−	1.33214i	−0.701052	−	0.0423382i
$991$		−	6.77267i		−	0.215141i	−0.994197	−	0.107570i	$-0.965693\pi$
$991$		−	6.77267i		−	0.215141i	0.994197	−	0.107570i	$-0.0343071\pi$
$992$	2.56235	−	0.764810i	0.0813546	−	0.0242827i
$993$	−26.4964	−	26.4964i	−0.840839	−	0.840839i
$994$	20.9657	+	2.08383i	0.664991	+	0.0660952i
$995$	18.9038	−	20.4286i	0.599290	−	0.647630i
$996$	−45.6343	−	9.16193i	−1.44598	−	0.290307i
$997$	−31.7502	+	31.7502i	−1.00554	+	1.00554i	−0.00555505	+	0.999985i	$0.501768\pi$
$997$	−31.7502	+	31.7502i	−1.00554	+	1.00554i	−0.999985	+	0.00555505i	$0.998232\pi$
$998$	20.6669	+	25.2286i	0.654200	+	0.798597i
$999$	3.87772			0.122686

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.k.c.83.13	✓	108
4.3	odd	2	inner	820.2.k.c.83.40	yes	108
5.2	odd	4	inner	820.2.k.c.247.40	yes	108
20.7	even	4	inner	820.2.k.c.247.13	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.13	✓	108	1.1	even	1	trivial
820.2.k.c.83.40	yes	108	4.3	odd	2	inner
820.2.k.c.247.13	yes	108	20.7	even	4	inner
820.2.k.c.247.40	yes	108	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.896192 - 1.09400i) q^{2} +(1.47545 - 1.47545i) q^{3} +(-0.393681 + 1.96087i) q^{4} +(1.51870 - 1.64120i) q^{5} +(-2.93643 - 0.291859i) q^{6} +(2.76703 + 2.76703i) q^{7} +(2.49801 - 1.32663i) q^{8} -1.35390i q^{9} +(-3.15653 - 0.190630i) q^{10} +5.16144i q^{11} +(2.31231 + 3.47402i) q^{12} +(-4.63454 - 4.63454i) q^{13} +(0.547348 - 5.50693i) q^{14} +(-0.180745 - 4.66228i) q^{15} +(-3.69003 - 1.54392i) q^{16} +(2.01443 - 2.01443i) q^{17} +(-1.48117 + 1.21336i) q^{18} +2.80537 q^{19} +(2.62030 + 3.62409i) q^{20} +8.16523 q^{21} +(5.64663 - 4.62564i) q^{22} +(4.87516 - 4.87516i) q^{23} +(1.72832 - 5.64306i) q^{24} +(-0.387093 - 4.98499i) q^{25} +(-0.916761 + 9.22363i) q^{26} +(2.42873 + 2.42873i) q^{27} +(-6.51512 + 4.33646i) q^{28} +3.16774i q^{29} +(-4.93856 + 4.37603i) q^{30} -0.472710i q^{31} +(1.61793 + 5.42055i) q^{32} +(7.61544 + 7.61544i) q^{33} +(-4.00910 - 0.398475i) q^{34} +(8.74355 - 0.338965i) q^{35} +(2.65483 + 0.533006i) q^{36} +(0.798301 - 0.798301i) q^{37} +(-2.51415 - 3.06908i) q^{38} -13.6761 q^{39} +(1.61647 - 6.11449i) q^{40} +1.00000 q^{41} +(-7.31761 - 8.93278i) q^{42} +(4.45887 - 4.45887i) q^{43} +(-10.1209 - 2.03196i) q^{44} +(-2.22203 - 2.05617i) q^{45} +(-9.70251 - 0.964358i) q^{46} +(-4.64694 - 4.64694i) q^{47} +(-7.72242 + 3.16648i) q^{48} +8.31291i q^{49} +(-5.10668 + 4.89099i) q^{50} -5.94437i q^{51} +(10.9123 - 7.26320i) q^{52} +(3.62838 + 3.62838i) q^{53} +(0.480429 - 4.83365i) q^{54} +(8.47097 + 7.83868i) q^{55} +(10.5829 + 3.24125i) q^{56} +(4.13919 - 4.13919i) q^{57} +(3.46551 - 2.83890i) q^{58} -11.1651 q^{59} +(9.21328 + 1.48104i) q^{60} +0.219103 q^{61} +(-0.517146 + 0.423639i) q^{62} +(3.74629 - 3.74629i) q^{63} +(4.48012 - 6.62786i) q^{64} +(-14.6447 + 0.567738i) q^{65} +(1.50642 - 15.1562i) q^{66} +(1.42724 + 1.42724i) q^{67} +(3.15699 + 4.74307i) q^{68} -14.3861i q^{69} +(-8.20672 - 9.26168i) q^{70} +3.80715i q^{71} +(-1.79612 - 3.38206i) q^{72} +(-8.38424 - 8.38424i) q^{73} +(-1.58877 - 0.157912i) q^{74} +(-7.92624 - 6.78397i) q^{75} +(-1.10442 + 5.50098i) q^{76} +(-14.2819 + 14.2819i) q^{77} +(12.2564 + 14.9616i) q^{78} +3.21731 q^{79} +(-8.13793 + 3.71134i) q^{80} +11.2287 q^{81} +(-0.896192 - 1.09400i) q^{82} +(-7.88656 + 7.88656i) q^{83} +(-3.21450 + 16.0110i) q^{84} +(-0.246770 - 6.36539i) q^{85} +(-8.87401 - 0.882011i) q^{86} +(4.67384 + 4.67384i) q^{87} +(6.84731 + 12.8933i) q^{88} +13.1858i q^{89} +(-0.258095 + 4.27363i) q^{90} -25.6478i q^{91} +(7.64030 + 11.4788i) q^{92} +(-0.697460 - 0.697460i) q^{93} +(-0.919214 + 9.24831i) q^{94} +(4.26052 - 4.60419i) q^{95} +(10.3849 + 5.61057i) q^{96} +(-2.08198 + 2.08198i) q^{97} +(9.09434 - 7.44996i) q^{98} +6.98809 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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