LMFDB - Embedded newform 1001.2.i.d.716.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(144,1001)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1001.144");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.99302524233$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			716.22
Character	$\chi$	$=$	1001.716
Dual form			1001.2.i.d.144.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07970 - 1.87010i) q^{2} +(0.921233 + 1.59562i) q^{3} +(-1.33151 - 2.30625i) q^{4} +(0.721922 - 1.25041i) q^{5} +3.97863 q^{6} +(1.85361 - 1.88789i) q^{7} -1.43174 q^{8} +(-0.197342 + 0.341806i) q^{9} +O(q^{10})$	\(q+(1.07970 - 1.87010i) q^{2} +(0.921233 + 1.59562i) q^{3} +(-1.33151 - 2.30625i) q^{4} +(0.721922 - 1.25041i) q^{5} +3.97863 q^{6} +(1.85361 - 1.88789i) q^{7} -1.43174 q^{8} +(-0.197342 + 0.341806i) q^{9} +(-1.55892 - 2.70013i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(2.45327 - 4.24918i) q^{12} -1.00000 q^{13} +(-1.52919 - 5.50479i) q^{14} +2.66024 q^{15} +(1.11717 - 1.93500i) q^{16} +(-1.16139 - 2.01159i) q^{17} +(0.426141 + 0.738098i) q^{18} +(-2.92300 + 5.06279i) q^{19} -3.84499 q^{20} +(4.71997 + 1.21848i) q^{21} -2.15940 q^{22} +(-2.78727 + 4.82770i) q^{23} +(-1.31896 - 2.28451i) q^{24} +(1.45766 + 2.52473i) q^{25} +(-1.07970 + 1.87010i) q^{26} +4.80021 q^{27} +(-6.82204 - 1.76114i) q^{28} +3.21224 q^{29} +(2.87226 - 4.97490i) q^{30} +(-3.52714 - 6.10919i) q^{31} +(-3.84417 - 6.65830i) q^{32} +(0.921233 - 1.59562i) q^{33} -5.01584 q^{34} +(-1.02247 - 3.68068i) q^{35} +1.05105 q^{36} +(1.97724 - 3.42469i) q^{37} +(6.31194 + 10.9326i) q^{38} +(-0.921233 - 1.59562i) q^{39} +(-1.03360 + 1.79025i) q^{40} -2.86690 q^{41} +(7.37483 - 7.51121i) q^{42} +9.67635 q^{43} +(-1.33151 + 2.30625i) q^{44} +(0.284931 + 0.493515i) q^{45} +(6.01885 + 10.4249i) q^{46} +(-4.03101 + 6.98191i) q^{47} +4.11672 q^{48} +(-0.128254 - 6.99882i) q^{49} +6.29534 q^{50} +(2.13983 - 3.70629i) q^{51} +(1.33151 + 2.30625i) q^{52} +(-0.0397446 - 0.0688396i) q^{53} +(5.18279 - 8.97686i) q^{54} -1.44384 q^{55} +(-2.65388 + 2.70296i) q^{56} -10.7711 q^{57} +(3.46826 - 6.00720i) q^{58} +(2.63830 + 4.56967i) q^{59} +(-3.54214 - 6.13516i) q^{60} +(-1.78855 + 3.09786i) q^{61} -15.2331 q^{62} +(0.279497 + 1.00614i) q^{63} -12.1335 q^{64} +(-0.721922 + 1.25041i) q^{65} +(-1.98931 - 3.44559i) q^{66} +(-5.84833 - 10.1296i) q^{67} +(-3.09282 + 5.35692i) q^{68} -10.2709 q^{69} +(-7.98719 - 2.06192i) q^{70} +12.6096 q^{71} +(0.282542 - 0.489377i) q^{72} +(4.50196 + 7.79762i) q^{73} +(-4.26967 - 7.39528i) q^{74} +(-2.68568 + 4.65174i) q^{75} +15.5680 q^{76} +(-2.56177 - 0.661329i) q^{77} -3.97863 q^{78} +(-6.50049 + 11.2592i) q^{79} +(-1.61303 - 2.79385i) q^{80} +(5.01414 + 8.68474i) q^{81} +(-3.09540 + 5.36139i) q^{82} -10.4249 q^{83} +(-3.47459 - 12.5078i) q^{84} -3.35375 q^{85} +(10.4476 - 18.0957i) q^{86} +(2.95922 + 5.12552i) q^{87} +(0.715869 + 1.23992i) q^{88} +(0.730504 - 1.26527i) q^{89} +1.23056 q^{90} +(-1.85361 + 1.88789i) q^{91} +14.8452 q^{92} +(6.49865 - 11.2560i) q^{93} +(8.70457 + 15.0768i) q^{94} +(4.22036 + 7.30988i) q^{95} +(7.08275 - 12.2677i) q^{96} +2.90071 q^{97} +(-13.2270 - 7.31680i) q^{98} +0.394684 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) $ 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1001\mathbb{Z}\right)^\times$.

$n$	$365$	$430$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.07970	−	1.87010i	0.763465	−	1.32236i	−0.177590	−	0.984105i	$-0.556830\pi$
$2$	1.07970	−	1.87010i	0.763465	−	1.32236i	0.941055	−	0.338255i	$-0.109837\pi$
$3$	0.921233	+	1.59562i	0.531874	+	0.921233i	0.999308	+	0.0372051i	$0.0118455\pi$
$3$	0.921233	+	1.59562i	0.531874	+	0.921233i	−0.467433	+	0.884028i	$0.654821\pi$
$4$	−1.33151	−	2.30625i	−0.665756	−	1.15312i
$5$	0.721922	−	1.25041i	0.322854	−	0.559199i	−0.658222	−	0.752824i	$-0.728691\pi$
$5$	0.721922	−	1.25041i	0.322854	−	0.559199i	0.981076	+	0.193625i	$0.0620245\pi$
$6$	3.97863			1.62427
$7$	1.85361	−	1.88789i	0.700599	−	0.713555i
$7$	1.85361	−	1.88789i	0.700599	−	0.713555i
$8$	−1.43174			−0.506196
$9$	−0.197342	+	0.341806i	−0.0657806	+	0.113935i
$10$	−1.55892	−	2.70013i	−0.492974	−	0.853857i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	2.45327	−	4.24918i	0.708197	−	1.22663i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−1.52919	−	5.50479i	−0.408694	−	1.47122i
$15$	2.66024			0.686870
$16$	1.11717	−	1.93500i	0.279294	−	0.483751i
$17$	−1.16139	−	2.01159i	−0.281679	−	0.487883i	0.690119	−	0.723696i	$-0.257558\pi$
$17$	−1.16139	−	2.01159i	−0.281679	−	0.487883i	−0.971799	+	0.235813i	$0.924225\pi$
$18$	0.426141	+	0.738098i	0.100442	+	0.173971i
$19$	−2.92300	+	5.06279i	−0.670583	+	1.16148i	0.307157	+	0.951659i	$0.400622\pi$
$19$	−2.92300	+	5.06279i	−0.670583	+	1.16148i	−0.977739	+	0.209824i	$0.932711\pi$
$20$	−3.84499			−0.859767
$21$	4.71997	+	1.21848i	1.02998	+	0.265893i
$22$	−2.15940			−0.460386
$23$	−2.78727	+	4.82770i	−0.581187	+	1.00664i	0.414153	+	0.910207i	$0.364078\pi$
$23$	−2.78727	+	4.82770i	−0.581187	+	1.00664i	−0.995339	+	0.0964371i	$0.969255\pi$
$24$	−1.31896	−	2.28451i	−0.269232	−	0.466324i
$25$	1.45766	+	2.52473i	0.291531	+	0.504947i
$26$	−1.07970	+	1.87010i	−0.211747	+	0.366756i
$27$	4.80021			0.923801
$28$	−6.82204	−	1.76114i	−1.28925	−	0.332823i
$29$	3.21224			0.596497			0.298249	−	0.954488i	$-0.403598\pi$
$29$	3.21224			0.596497			0.298249	+	0.954488i	$0.403598\pi$
$30$	2.87226	−	4.97490i	0.524401	−	0.908289i
$31$	−3.52714	−	6.10919i	−0.633494	−	1.09724i	−0.986832	−	0.161748i	$-0.948287\pi$
$31$	−3.52714	−	6.10919i	−0.633494	−	1.09724i	0.353338	−	0.935496i	$-0.385046\pi$
$32$	−3.84417	−	6.65830i	−0.679560	−	1.17703i
$33$	0.921233	−	1.59562i	0.160366	−	0.277762i
$34$	−5.01584			−0.860209
$35$	−1.02247	−	3.68068i	−0.172828	−	0.622148i
$36$	1.05105			0.175175
$37$	1.97724	−	3.42469i	0.325057	−	0.563015i	−0.656467	−	0.754355i	$-0.727950\pi$
$37$	1.97724	−	3.42469i	0.325057	−	0.563015i	0.981524	+	0.191340i	$0.0612833\pi$
$38$	6.31194	+	10.9326i	1.02393	+	1.77350i
$39$	−0.921233	−	1.59562i	−0.147515	−	0.255504i
$40$	−1.03360	+	1.79025i	−0.163427	+	0.283064i
$41$	−2.86690			−0.447735			−0.223867	−	0.974620i	$-0.571868\pi$
$41$	−2.86690			−0.447735			−0.223867	+	0.974620i	$0.571868\pi$
$42$	7.37483	−	7.51121i	1.13796	−	1.15901i
$43$	9.67635			1.47563			0.737815	−	0.675003i	$-0.235858\pi$
$43$	9.67635			1.47563			0.737815	+	0.675003i	$0.235858\pi$
$44$	−1.33151	+	2.30625i	−0.200733	+	0.347680i
$45$	0.284931	+	0.493515i	0.0424750	+	0.0735689i
$46$	6.01885	+	10.4249i	0.887431	+	1.53707i
$47$	−4.03101	+	6.98191i	−0.587983	+	1.01842i	0.406513	+	0.913645i	$0.366744\pi$
$47$	−4.03101	+	6.98191i	−0.587983	+	1.01842i	−0.994496	+	0.104772i	$0.966589\pi$
$48$	4.11672			0.594197
$49$	−0.128254	−	6.99882i	−0.0183221	−	0.999832i
$50$	6.29534			0.890295
$51$	2.13983	−	3.70629i	0.299636	−	0.518985i
$52$	1.33151	+	2.30625i	0.184648	+	0.319819i
$53$	−0.0397446	−	0.0688396i	−0.00545934	−	0.00945585i	0.863283	−	0.504720i	$-0.168404\pi$
$53$	−0.0397446	−	0.0688396i	−0.00545934	−	0.00945585i	−0.868742	+	0.495265i	$0.835071\pi$
$54$	5.18279	−	8.97686i	0.705289	−	1.22160i
$55$	−1.44384			−0.194688
$56$	−2.65388	+	2.70296i	−0.354640	+	0.361198i
$57$	−10.7711			−1.42666
$58$	3.46826	−	6.00720i	0.455404	−	0.788784i
$59$	2.63830	+	4.56967i	0.343478	+	0.594921i	0.985076	−	0.172120i	$-0.0550617\pi$
$59$	2.63830	+	4.56967i	0.343478	+	0.594921i	−0.641598	+	0.767041i	$0.721728\pi$
$60$	−3.54214	−	6.13516i	−0.457288	−	0.792046i
$61$	−1.78855	+	3.09786i	−0.229000	+	0.396640i	−0.957512	−	0.288393i	$-0.906879\pi$
$61$	−1.78855	+	3.09786i	−0.229000	+	0.396640i	0.728512	+	0.685033i	$0.240212\pi$
$62$	−15.2331			−1.93460
$63$	0.279497	+	1.00614i	0.0352134	+	0.126761i
$64$	−12.1335			−1.51669
$65$	−0.721922	+	1.25041i	−0.0895435	+	0.155094i
$66$	−1.98931	−	3.44559i	−0.244868	−	0.424123i
$67$	−5.84833	−	10.1296i	−0.714488	−	1.23753i	−0.963157	−	0.268941i	$-0.913326\pi$
$67$	−5.84833	−	10.1296i	−0.714488	−	1.23753i	0.248669	−	0.968589i	$-0.420007\pi$
$68$	−3.09282	+	5.35692i	−0.375060	+	0.649622i
$69$	−10.2709			−1.23647
$70$	−7.98719	−	2.06192i	−0.954651	−	0.246447i
$71$	12.6096			1.49649			0.748244	−	0.663424i	$-0.230897\pi$
$71$	12.6096			1.49649			0.748244	+	0.663424i	$0.230897\pi$
$72$	0.282542	−	0.489377i	0.0332979	−	0.0576736i
$73$	4.50196	+	7.79762i	0.526915	+	0.912643i	0.999508	+	0.0313623i	$0.00998456\pi$
$73$	4.50196	+	7.79762i	0.526915	+	0.912643i	−0.472594	+	0.881281i	$0.656682\pi$
$74$	−4.26967	−	7.39528i	−0.496339	−	0.859684i
$75$	−2.68568	+	4.65174i	−0.310116	+	0.537137i
$76$	15.5680			1.78578
$77$	−2.56177	−	0.661329i	−0.291940	−	0.0753655i
$78$	−3.97863			−0.450491
$79$	−6.50049	+	11.2592i	−0.731362	+	1.26676i	0.224939	+	0.974373i	$0.427782\pi$
$79$	−6.50049	+	11.2592i	−0.731362	+	1.26676i	−0.956301	+	0.292383i	$0.905552\pi$
$80$	−1.61303	−	2.79385i	−0.180342	−	0.312361i
$81$	5.01414	+	8.68474i	0.557126	+	0.964971i
$82$	−3.09540	+	5.36139i	−0.341830	+	0.592066i
$83$	−10.4249			−1.14428			−0.572140	−	0.820156i	$-0.693887\pi$
$83$	−10.4249			−1.14428			−0.572140	+	0.820156i	$0.693887\pi$
$84$	−3.47459	−	12.5078i	−0.379108	−	1.36472i
$85$	−3.35375			−0.363765
$86$	10.4476	−	18.0957i	1.12659	−	1.95131i
$87$	2.95922	+	5.12552i	0.317262	+	0.549513i
$88$	0.715869	+	1.23992i	0.0763119	+	0.132176i
$89$	0.730504	−	1.26527i	0.0774332	−	0.134118i	−0.824709	−	0.565558i	$-0.808661\pi$
$89$	0.730504	−	1.26527i	0.0774332	−	0.134118i	0.902142	+	0.431440i	$0.141994\pi$
$90$	1.23056			0.129713
$91$	−1.85361	+	1.88789i	−0.194311	+	0.197905i
$92$	14.8452			1.54771
$93$	6.49865	−	11.2560i	0.673878	−	1.16719i
$94$	8.70457	+	15.0768i	0.897808	+	1.55505i
$95$	4.22036	+	7.30988i	0.433000	+	0.749978i
$96$	7.08275	−	12.2677i	0.722881	−	1.25207i
$97$	2.90071			0.294523			0.147261	−	0.989098i	$-0.452954\pi$
$97$	2.90071			0.294523			0.147261	+	0.989098i	$0.452954\pi$
$98$	−13.2270	−	7.31680i	−1.33613	−	0.739108i
$99$	0.394684			0.0396672
$100$	3.88177	−	6.72343i	0.388177	−	0.672343i
$101$	5.96906	+	10.3387i	0.593944	+	1.02874i	0.993695	+	0.112117i	$0.0357632\pi$
$101$	5.96906	+	10.3387i	0.593944	+	1.02874i	−0.399751	+	0.916624i	$0.630903\pi$
$102$	−4.62076	−	8.00339i	−0.457523	−	0.792453i
$103$	−6.52583	+	11.3031i	−0.643009	+	1.11372i	0.341748	+	0.939792i	$0.388981\pi$
$103$	−6.52583	+	11.3031i	−0.643009	+	1.11372i	−0.984757	+	0.173933i	$0.944352\pi$
$104$	1.43174			0.140393
$105$	4.93104	−	5.02223i	0.481220	−	0.490120i
$106$	−0.171649			−0.0166720
$107$	−3.72951	+	6.45970i	−0.360545	+	0.624483i	−0.988051	−	0.154130i	$-0.950743\pi$
$107$	−3.72951	+	6.45970i	−0.360545	+	0.624483i	0.627505	+	0.778612i	$0.284076\pi$
$108$	−6.39154	−	11.0705i	−0.615026	−	1.06526i
$109$	−9.30032	−	16.1086i	−0.890810	−	1.54293i	−0.838907	−	0.544275i	$-0.816805\pi$
$109$	−9.30032	−	16.1086i	−0.890810	−	1.54293i	−0.0519028	−	0.998652i	$-0.516529\pi$
$110$	−1.55892	+	2.70013i	−0.148637	+	0.257447i
$111$	7.28601			0.691557
$112$	−1.58227	−	5.69585i	−0.149510	−	0.538207i
$113$	13.1888			1.24070			0.620348	−	0.784327i	$-0.286992\pi$
$113$	13.1888			1.24070			0.620348	+	0.784327i	$0.286992\pi$
$114$	−11.6295	+	20.1430i	−1.08921	+	1.88656i
$115$	4.02439	+	6.97045i	0.375276	+	0.649998i
$116$	−4.27713	−	7.40821i	−0.397122	−	0.687835i
$117$	0.197342	−	0.341806i	0.0182443	−	0.0316000i
$118$	11.3943			1.04893
$119$	−5.95044	−	1.53613i	−0.545476	−	0.140817i
$120$	−3.80876			−0.347691
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	3.86220	+	6.68952i	0.349667	+	0.605641i
$123$	−2.64109	−	4.57449i	−0.238139	−	0.412468i
$124$	−9.39287	+	16.2689i	−0.843505	+	1.46099i
$125$	11.4285			1.02219
$126$	2.18335	+	0.563639i	0.194508	+	0.0502129i
$127$	2.14552			0.190384			0.0951920	−	0.995459i	$-0.469654\pi$
$127$	2.14552			0.190384			0.0951920	+	0.995459i	$0.469654\pi$
$128$	−5.41225	+	9.37430i	−0.478380	+	0.828579i
$129$	8.91418	+	15.4398i	0.784850	+	1.35940i
$130$	1.55892	+	2.70013i	0.136727	+	0.236817i
$131$	3.98066	−	6.89471i	0.347792	−	0.602393i	−0.638065	−	0.769982i	$-0.720265\pi$
$131$	3.98066	−	6.89471i	0.347792	−	0.602393i	0.985857	+	0.167589i	$0.0535982\pi$
$132$	−4.90653			−0.427059
$133$	4.13988	+	14.9027i	0.358973	+	1.29223i
$134$	−25.2578			−2.18194
$135$	3.46538	−	6.00221i	0.298252	−	0.516588i
$136$	1.66281	+	2.88007i	0.142585	+	0.246964i
$137$	7.58275	+	13.1337i	0.647838	+	1.12209i	0.983638	+	0.180155i	$0.0576598\pi$
$137$	7.58275	+	13.1337i	0.647838	+	1.12209i	−0.335801	+	0.941933i	$0.609007\pi$
$138$	−11.0895	+	19.2076i	−0.944003	+	1.63506i
$139$	−16.6647			−1.41348			−0.706742	−	0.707471i	$-0.749836\pi$
$139$	−16.6647			−1.41348			−0.706742	+	0.707471i	$0.749836\pi$
$140$	−7.12712	+	7.25892i	−0.602352	+	0.613491i
$141$	−14.8540			−1.25093
$142$	13.6146	−	23.5812i	1.14251	−	1.97889i
$143$	0.500000	+	0.866025i	0.0418121	+	0.0724207i
$144$	0.440931	+	0.763715i	0.0367442	+	0.0636429i
$145$	2.31899	−	4.01660i	0.192581	−	0.333560i
$146$	19.4431			1.60912
$147$	11.0493	−	6.65220i	0.911334	−	0.548664i
$148$	−10.5309			−0.865634
$149$	−4.20840	+	7.28916i	−0.344765	+	0.597151i	−0.985311	−	0.170769i	$-0.945375\pi$
$149$	−4.20840	+	7.28916i	−0.344765	+	0.597151i	0.640546	+	0.767920i	$0.278708\pi$
$150$	5.79947	+	10.0450i	0.473525	+	0.820169i
$151$	0.744596	+	1.28968i	0.0605943	+	0.104952i	0.894731	−	0.446605i	$-0.147367\pi$
$151$	0.744596	+	1.28968i	0.0605943	+	0.104952i	−0.834137	+	0.551557i	$0.814034\pi$
$152$	4.18497	−	7.24858i	0.339446	−	0.587938i
$153$	0.916767			0.0741162
$154$	−4.00269	+	4.07672i	−0.322546	+	0.328511i
$155$	−10.1853			−0.818103
$156$	−2.45327	+	4.24918i	−0.196419	+	0.340207i
$157$	5.51780	+	9.55712i	0.440369	+	0.762741i	0.997717	−	0.0675380i	$-0.0215144\pi$
$157$	5.51780	+	9.55712i	0.440369	+	0.762741i	−0.557348	+	0.830279i	$0.688181\pi$
$158$	14.0372	+	24.3131i	1.11674	+	1.93425i
$159$	0.0732280	−	0.126835i	0.00580736	−	0.0100586i
$160$	−11.1008			−0.877593
$161$	3.94764	+	14.2107i	0.311118	+	1.11996i
$162$	21.6551			1.70139
$163$	−4.15468	+	7.19612i	−0.325420	+	0.563643i	−0.981597	−	0.190963i	$-0.938839\pi$
$163$	−4.15468	+	7.19612i	−0.325420	+	0.563643i	0.656178	+	0.754607i	$0.272172\pi$
$164$	3.81731	+	6.61178i	0.298082	+	0.516293i
$165$	−1.33012	−	2.30383i	−0.103550	−	0.179353i
$166$	−11.2558	+	19.4956i	−0.873617	+	1.51315i
$167$	−8.66399			−0.670439			−0.335220	−	0.942140i	$-0.608811\pi$
$167$	−8.66399			−0.670439			−0.335220	+	0.942140i	$0.608811\pi$
$168$	−6.75775	−	1.74454i	−0.521372	−	0.134594i
$169$	1.00000			0.0769231
$170$	−3.62105	+	6.27183i	−0.277721	+	0.481028i
$171$	−1.15366	−	1.99820i	−0.0882227	−	0.152806i
$172$	−12.8842	−	22.3161i	−0.982410	−	1.70158i
$173$	−5.32297	+	9.21965i	−0.404698	+	0.700957i	−0.994286	−	0.106747i	$-0.965957\pi$
$173$	−5.32297	+	9.21965i	−0.404698	+	0.700957i	0.589588	+	0.807704i	$0.299290\pi$
$174$	12.7803			0.968872
$175$	7.46835	+	1.92798i	0.564554	+	0.145742i
$176$	−2.23435			−0.168420
$177$	−4.86098	+	8.41947i	−0.365374	+	0.632846i
$178$	−1.57745	−	2.73223i	−0.118235	−	0.204789i
$179$	−0.566201	−	0.980688i	−0.0423198	−	0.0733001i	0.844090	−	0.536202i	$-0.180142\pi$
$179$	−0.566201	−	0.980688i	−0.0423198	−	0.0733001i	−0.886409	+	0.462902i	$0.846808\pi$
$180$	0.758779	−	1.31424i	0.0565560	−	0.0979579i
$181$	−15.1958			−1.12950			−0.564749	−	0.825263i	$-0.691027\pi$
$181$	−15.1958			−1.12950			−0.564749	+	0.825263i	$0.691027\pi$
$182$	1.52919	+	5.50479i	0.113351	+	0.408042i
$183$	−6.59068			−0.487197
$184$	3.99064	−	6.91200i	0.294194	−	0.509559i
$185$	−2.85483	−	4.94471i	−0.209891	−	0.363543i
$186$	−14.0332	−	24.3062i	−1.02896	−	1.78222i
$187$	−1.16139	+	2.01159i	−0.0849295	+	0.147102i
$188$	21.4693			1.56581
$189$	8.89772	−	9.06226i	0.647214	−	0.659183i
$190$	18.2269			1.32232
$191$	−10.6392	+	18.4276i	−0.769826	+	1.33338i	0.167831	+	0.985816i	$0.446324\pi$
$191$	−10.6392	+	18.4276i	−0.769826	+	1.33338i	−0.937657	+	0.347562i	$0.887010\pi$
$192$	−11.1778	−	19.3605i	−0.806689	−	1.39723i
$193$	−7.95423	−	13.7771i	−0.572558	−	0.991700i	−0.996302	−	0.0859181i	$-0.972618\pi$
$193$	−7.95423	−	13.7771i	−0.572558	−	0.991700i	0.423744	−	0.905782i	$-0.360716\pi$
$194$	3.13191	−	5.42462i	0.224858	−	0.389465i
$195$	−2.66024			−0.190503
$196$	−15.9702	+	9.61481i	−1.14073	+	0.686772i
$197$	−21.6318			−1.54120			−0.770599	−	0.637320i	$-0.780043\pi$
$197$	−21.6318			−1.54120			−0.770599	+	0.637320i	$0.780043\pi$
$198$	0.426141	−	0.738098i	0.0302845	−	0.0524543i
$199$	4.11217	+	7.12248i	0.291504	+	0.504899i	0.974165	−	0.225835i	$-0.0725111\pi$
$199$	4.11217	+	7.12248i	0.291504	+	0.504899i	−0.682662	+	0.730734i	$0.739178\pi$
$200$	−2.08698	−	3.61476i	−0.147572	−	0.255602i
$201$	10.7754	−	18.6635i	0.760035	−	1.31642i
$202$	25.7792			1.81382
$203$	5.95423	−	6.06435i	0.417905	−	0.425634i
$204$	−11.3968			−0.797938
$205$	−2.06968	+	3.58479i	−0.144553	+	0.250373i
$206$	14.0919	+	24.4079i	0.981830	+	1.70058i
$207$	−1.10009	−	1.90541i	−0.0764617	−	0.132435i
$208$	−1.11717	+	1.93500i	−0.0774621	+	0.134168i
$209$	5.84600			0.404376
$210$	−4.06801	−	14.6440i	−0.280720	−	1.01054i
$211$	6.27907			0.432269			0.216135	−	0.976364i	$-0.430655\pi$
$211$	6.27907			0.432269			0.216135	+	0.976364i	$0.430655\pi$
$212$	−0.105841	+	0.183322i	−0.00726917	+	0.0125906i
$213$	11.6164	+	20.1202i	0.795943	+	1.37861i
$214$	8.05352	+	13.9491i	0.550527	+	0.953541i
$215$	6.98558	−	12.0994i	0.476412	−	0.825171i
$216$	−6.87264			−0.467624
$217$	−18.0714	−	4.66521i	−1.22677	−	0.316695i
$218$	−40.1663			−2.72041
$219$	−8.29471	+	14.3669i	−0.560505	+	0.970823i
$220$	1.92250	+	3.32986i	0.129615	+	0.224499i
$221$	1.16139	+	2.01159i	0.0781238	+	0.135314i
$222$	7.86672	−	13.6256i	0.527980	−	0.914487i
$223$	14.1242			0.945827			0.472913	−	0.881109i	$-0.343202\pi$
$223$	14.1242			0.945827			0.472913	+	0.881109i	$0.343202\pi$
$224$	−19.6957	−	5.08452i	−1.31598	−	0.339724i
$225$	−1.15063			−0.0767084
$226$	14.2399	−	24.6643i	0.947227	−	1.64064i
$227$	5.99175	+	10.3780i	0.397686	+	0.688813i	0.993440	−	0.114354i	$-0.0364799\pi$
$227$	5.99175	+	10.3780i	0.397686	+	0.688813i	−0.595754	+	0.803167i	$0.703147\pi$
$228$	14.3418	+	24.8407i	0.949809	+	1.64512i
$229$	13.8080	−	23.9162i	0.912461	−	1.58043i	0.101884	−	0.994796i	$-0.467513\pi$
$229$	13.8080	−	23.9162i	0.912461	−	1.58043i	0.810577	−	0.585632i	$-0.199154\pi$
$230$	17.3806			1.14604
$231$	−1.30475	−	4.69685i	−0.0858464	−	0.309030i
$232$	−4.59908			−0.301944
$233$	13.7597	−	23.8325i	0.901429	−	1.56132i	0.0757896	−	0.997124i	$-0.475852\pi$
$233$	13.7597	−	23.8325i	0.901429	−	1.56132i	0.825640	−	0.564198i	$-0.190814\pi$
$234$	−0.426141	−	0.738098i	−0.0278577	−	0.0482510i
$235$	5.82015	+	10.0808i	0.379665	+	0.657599i
$236$	7.02586	−	12.1692i	0.457345	−	0.792144i
$237$	−23.9539			−1.55597
$238$	−9.29741	+	9.46935i	−0.602662	+	0.613807i
$239$	−14.3899			−0.930805			−0.465403	−	0.885099i	$-0.654090\pi$
$239$	−14.3899			−0.930805			−0.465403	+	0.885099i	$0.654090\pi$
$240$	2.97195	−	5.14757i	0.191839	−	0.332274i
$241$	1.59769	+	2.76728i	0.102916	+	0.178256i	0.912885	−	0.408217i	$-0.133849\pi$
$241$	1.59769	+	2.76728i	0.102916	+	0.178256i	−0.809969	+	0.586473i	$0.800516\pi$
$242$	1.07970	+	1.87010i	0.0694059	+	0.120214i
$243$	−2.03807	+	3.53004i	−0.130742	+	0.226452i
$244$	9.52590			0.609833
$245$	−8.84396	−	4.89224i	−0.565020	−	0.312554i
$246$	−11.4063			−0.727242
$247$	2.92300	−	5.06279i	0.185986	−	0.322137i
$248$	5.04994	+	8.74676i	0.320672	+	0.555420i
$249$	−9.60375	−	16.6342i	−0.608613	−	1.05415i
$250$	12.3394	−	21.3724i	0.780409	−	1.35171i
$251$	8.88571			0.560861			0.280430	−	0.959874i	$-0.409523\pi$
$251$	8.88571			0.560861			0.280430	+	0.959874i	$0.409523\pi$
$252$	1.94824	−	1.98427i	0.122728	−	0.124997i
$253$	5.57455			0.350469
$254$	2.31652	−	4.01233i	0.145351	−	0.251756i
$255$	−3.08958	−	5.35131i	−0.193477	−	0.335112i
$256$	−0.446288	−	0.772994i	−0.0278930	−	0.0483121i
$257$	9.49970	−	16.4540i	0.592575	−	1.02637i	−0.401309	−	0.915943i	$-0.631445\pi$
$257$	9.49970	−	16.4540i	0.592575	−	1.02637i	0.993884	−	0.110428i	$-0.0352220\pi$
$258$	38.4986			2.39682
$259$	−2.80039	−	10.0809i	−0.174008	−	0.626394i
$260$	3.84499			0.238456
$261$	−0.633909	+	1.09796i	−0.0392380	+	0.0679622i
$262$	−8.59585	−	14.8885i	−0.531054	−	0.919812i
$263$	0.0497494	+	0.0861685i	0.00306768	+	0.00531337i	0.867555	−	0.497341i	$-0.165690\pi$
$263$	0.0497494	+	0.0861685i	0.00306768	+	0.00531337i	−0.864487	+	0.502654i	$0.832357\pi$
$264$	−1.31896	+	2.28451i	−0.0811766	+	0.140602i
$265$	−0.114770			−0.00705026
$266$	32.3394	+	8.34854i	1.98286	+	0.511882i
$267$	2.69186			0.164739
$268$	−15.5743	+	26.9754i	−0.951349	+	1.64779i
$269$	5.59759	+	9.69531i	0.341291	+	0.591133i	0.984673	−	0.174412i	$-0.0558025\pi$
$269$	5.59759	+	9.69531i	0.341291	+	0.591133i	−0.643382	+	0.765545i	$0.722469\pi$
$270$	−7.48315	−	12.9612i	−0.455410	−	0.788793i
$271$	−0.243193	+	0.421222i	−0.0147729	+	0.0255874i	−0.873317	−	0.487152i	$-0.838036\pi$
$271$	−0.243193	+	0.421222i	−0.0147729	+	0.0255874i	0.858544	+	0.512739i	$0.171369\pi$
$272$	−5.18992			−0.314685
$273$	−4.71997	−	1.21848i	−0.285665	−	0.0737456i
$274$	32.7484			1.97840
$275$	1.45766	−	2.52473i	0.0879000	−	0.152247i
$276$	13.6758	+	23.6873i	0.823189	+	1.42581i
$277$	−14.9682	−	25.9256i	−0.899350	−	1.55772i	−0.828326	−	0.560246i	$-0.810707\pi$
$277$	−14.9682	−	25.9256i	−0.899350	−	1.55772i	−0.0710240	−	0.997475i	$-0.522627\pi$
$278$	−17.9930	+	31.1647i	−1.07915	+	1.86913i
$279$	2.78421			0.166687
$280$	1.46390	+	5.26976i	0.0874849	+	0.314929i
$281$	−15.8356			−0.944674			−0.472337	−	0.881418i	$-0.656589\pi$
$281$	−15.8356			−0.944674			−0.472337	+	0.881418i	$0.656589\pi$
$282$	−16.0379	+	27.7784i	−0.955042	+	1.65418i
$283$	−2.36901	−	4.10324i	−0.140823	−	0.243912i	0.786984	−	0.616974i	$-0.211641\pi$
$283$	−2.36901	−	4.10324i	−0.140823	−	0.243912i	−0.927807	+	0.373061i	$0.878308\pi$
$284$	−16.7899	−	29.0809i	−0.996296	−	1.72563i
$285$	−7.77587	+	13.4682i	−0.460603	+	0.797788i
$286$	2.15940			0.127688
$287$	−5.31412	+	5.41239i	−0.313683	+	0.319483i
$288$	3.03446			0.178807
$289$	5.80233	−	10.0499i	0.341313	−	0.591172i
$290$	−5.00762	−	8.67346i	−0.294058	−	0.509323i
$291$	2.67223	+	4.62845i	0.156649	+	0.271324i
$292$	11.9888	−	20.7653i	0.701593	−	1.21519i
$293$	−20.5267			−1.19918			−0.599591	−	0.800307i	$-0.704670\pi$
$293$	−20.5267			−1.19918			−0.599591	+	0.800307i	$0.704670\pi$
$294$	−0.510277	−	27.8457i	−0.0297599	−	1.62400i
$295$	7.61860			0.443572
$296$	−2.83089	+	4.90325i	−0.164542	+	0.284996i
$297$	−2.40010	−	4.15710i	−0.139268	−	0.241220i
$298$	9.08763	+	15.7402i	0.526432	+	0.911808i
$299$	2.78727	−	4.82770i	0.161192	−	0.279193i
$300$	14.3041			0.825846
$301$	17.9362	−	18.2679i	1.03383	−	1.05294i
$302$	3.21577			0.185047
$303$	−10.9978	+	19.0487i	−0.631807	+	1.09432i
$304$	6.53101	+	11.3120i	0.374579	+	0.648790i
$305$	2.58239	+	4.47282i	0.147867	+	0.256113i
$306$	0.989835	−	1.71444i	0.0565851	−	0.0980083i
$307$	23.2216			1.32533			0.662663	−	0.748918i	$-0.269426\pi$
$307$	23.2216			1.32533			0.662663	+	0.748918i	$0.269426\pi$
$308$	1.88583	+	6.78863i	0.107455	+	0.386818i
$309$	−24.0473			−1.36800
$310$	−10.9971	+	19.0475i	−0.624593	+	1.08183i
$311$	−0.116391	−	0.201596i	−0.00659995	−	0.0114315i	0.862707	−	0.505705i	$-0.168768\pi$
$311$	−0.116391	−	0.201596i	−0.00659995	−	0.0114315i	−0.869307	+	0.494273i	$0.835434\pi$
$312$	1.31896	+	2.28451i	0.0746716	+	0.129335i
$313$	8.02658	−	13.9024i	0.453689	−	0.785813i	−0.544922	−	0.838486i	$-0.683441\pi$
$313$	8.02658	−	13.9024i	0.453689	−	0.785813i	0.998612	+	0.0526735i	$0.0167743\pi$
$314$	23.8303			1.34482
$315$	1.45985	+	0.376867i	0.0822534	+	0.0212340i
$316$	34.6219			1.94763
$317$	−14.2758	+	24.7265i	−0.801811	+	1.38878i	0.116612	+	0.993178i	$0.462797\pi$
$317$	−14.2758	+	24.7265i	−0.801811	+	1.38878i	−0.918423	+	0.395600i	$0.870537\pi$
$318$	−0.158129	−	0.273887i	−0.00886743	−	0.0153588i
$319$	−1.60612	−	2.78188i	−0.0899253	−	0.155755i
$320$	−8.75946	+	15.1718i	−0.489669	+	0.848132i
$321$	−13.7430			−0.767059
$322$	30.8378	+	7.96088i	1.71852	+	0.443642i
$323$	13.5790			0.755557
$324$	13.3528	−	23.1277i	0.741821	−	1.28487i
$325$	−1.45766	−	2.52473i	−0.0808562	−	0.140047i
$326$	8.97163	+	15.5393i	0.496893	+	0.860643i
$327$	17.1355	−	29.6796i	0.947597	−	1.64129i
$328$	4.10465			0.226641
$329$	5.70916	+	20.5518i	0.314756	+	1.13306i
$330$	−5.74452			−0.316226
$331$	8.85433	−	15.3361i	0.486678	−	0.842951i	−0.513205	−	0.858266i	$-0.671542\pi$
$331$	8.85433	−	15.3361i	0.486678	−	0.842951i	0.999883	+	0.0153152i	$0.00487517\pi$
$332$	13.8809	+	24.0424i	0.761811	+	1.31950i
$333$	0.780386	+	1.35167i	0.0427649	+	0.0740710i
$334$	−9.35452	+	16.2025i	−0.511857	+	0.886562i
$335$	−16.8882			−0.922700
$336$	7.63079	−	7.77190i	0.416294	−	0.423992i
$337$	4.00567			0.218203			0.109102	−	0.994031i	$-0.465203\pi$
$337$	4.00567			0.218203			0.109102	+	0.994031i	$0.465203\pi$
$338$	1.07970	−	1.87010i	0.0587280	−	0.101720i
$339$	12.1499	+	21.0443i	0.659894	+	1.14297i
$340$	4.46555	+	7.73456i	0.242179	+	0.419466i
$341$	−3.52714	+	6.10919i	−0.191006	+	0.330831i
$342$	−4.98244			−0.269420
$343$	−13.4507	−	12.7310i	−0.726272	−	0.687408i
$344$	−13.8540			−0.746957
$345$	−7.41480	+	12.8428i	−0.399200	+	0.691434i
$346$	11.4944	+	19.9090i	0.617945	+	1.07031i
$347$	11.9305	+	20.6642i	0.640462	+	1.10931i	0.985330	+	0.170661i	$0.0545903\pi$
$347$	11.9305	+	20.6642i	0.640462	+	1.10931i	−0.344868	+	0.938651i	$0.612076\pi$
$348$	7.88047	−	13.6494i	0.422438	−	0.731683i
$349$	19.4955			1.04357			0.521784	−	0.853077i	$-0.325267\pi$
$349$	19.4955			1.04357			0.521784	+	0.853077i	$0.325267\pi$
$350$	11.6691	−	11.8849i	0.623740	−	0.635275i
$351$	−4.80021			−0.256216
$352$	−3.84417	+	6.65830i	−0.204895	+	0.354888i
$353$	−11.7743	−	20.3938i	−0.626685	−	1.08545i	−0.988212	−	0.153089i	$-0.951078\pi$
$353$	−11.7743	−	20.3938i	−0.626685	−	1.08545i	0.361528	−	0.932361i	$-0.382255\pi$
$354$	10.4968	+	18.1810i	0.557900	+	0.966311i
$355$	9.10317	−	15.7672i	0.483146	−	0.836834i
$356$	−3.89070			−0.206207
$357$	−3.03066	−	10.9098i	−0.160400	−	0.577407i
$358$	−2.44531			−0.129239
$359$	10.6452	−	18.4380i	0.561831	−	0.973119i	−0.435506	−	0.900186i	$-0.643431\pi$
$359$	10.6452	−	18.4380i	0.561831	−	0.973119i	0.997337	−	0.0729335i	$-0.0232361\pi$
$360$	−0.407947	−	0.706584i	−0.0215007	−	0.0372403i
$361$	−7.58788	−	13.1426i	−0.399362	−	0.691715i
$362$	−16.4070	+	28.4177i	−0.862331	+	1.49360i
$363$	−1.84247			−0.0967044
$364$	6.82204	+	1.76114i	0.357572	+	0.0923086i
$365$	13.0003			0.680465
$366$	−7.11597	+	12.3252i	−0.371958	+	0.644250i
$367$	−15.1306	−	26.2070i	−0.789811	−	1.36799i	−0.926083	−	0.377321i	$-0.876845\pi$
$367$	−15.1306	−	26.2070i	−0.789811	−	1.36799i	0.136272	−	0.990671i	$-0.456488\pi$
$368$	6.22774	+	10.7868i	0.324644	+	0.562299i
$369$	0.565760	−	0.979925i	0.0294523	−	0.0510128i
$370$	−12.3295			−0.640979
$371$	−0.203633	−	0.0525685i	−0.0105721	−	0.00272922i
$372$	−34.6121			−1.79455
$373$	−8.45805	+	14.6498i	−0.437941	+	0.758537i	−0.997531	−	0.0702335i	$-0.977626\pi$
$373$	−8.45805	+	14.6498i	−0.437941	+	0.758537i	0.559589	+	0.828770i	$0.310959\pi$
$374$	2.50792	+	4.34384i	0.129681	+	0.224615i
$375$	10.5283	+	18.2356i	0.543679	+	0.941680i
$376$	5.77135	−	9.99626i	0.297634	−	0.515518i
$377$	−3.21224			−0.165439
$378$	−7.34044	−	26.4242i	−0.377552	−	1.35911i
$379$	−5.36365			−0.275512			−0.137756	−	0.990466i	$-0.543989\pi$
$379$	−5.36365			−0.275512			−0.137756	+	0.990466i	$0.543989\pi$
$380$	11.2389	−	19.4664i	0.576545	−	0.998605i
$381$	1.97652	+	3.42344i	0.101260	+	0.175388i
$382$	22.9743	+	39.7927i	1.17547	+	2.03597i
$383$	−5.84948	+	10.1316i	−0.298894	+	0.517700i	−0.975883	−	0.218293i	$-0.929951\pi$
$383$	−5.84948	+	10.1316i	−0.298894	+	0.517700i	0.676989	+	0.735993i	$0.263285\pi$
$384$	−19.9438			−1.01775
$385$	−2.67633	+	2.72582i	−0.136398	+	0.138921i
$386$	−34.3528			−1.74851
$387$	−1.90955	+	3.30744i	−0.0970679	+	0.168127i
$388$	−3.86234	−	6.68976i	−0.196080	−	0.339621i
$389$	2.28909	+	3.96481i	0.116061	+	0.201024i	0.918204	−	0.396109i	$-0.129640\pi$
$389$	2.28909	+	3.96481i	0.116061	+	0.201024i	−0.802142	+	0.597133i	$0.796306\pi$
$390$	−2.87226	+	4.97490i	−0.145443	+	0.251914i
$391$	12.9485			0.654833
$392$	0.183627	+	10.0205i	0.00927454	+	0.506111i
$393$	14.6685			0.739926
$394$	−23.3558	+	40.4535i	−1.17665	+	2.03802i
$395$	9.38570	+	16.2565i	0.472246	+	0.817953i
$396$	−0.525526	−	0.910238i	−0.0264087	−	0.0457412i
$397$	−14.7157	+	25.4883i	−0.738560	+	1.27922i	0.214584	+	0.976706i	$0.431160\pi$
$397$	−14.7157	+	25.4883i	−0.738560	+	1.27922i	−0.953144	+	0.302517i	$0.902173\pi$
$398$	17.7596			0.890211
$399$	−19.9654	+	20.3346i	−0.999518	+	1.01800i
$400$	6.51383			0.325691
$401$	15.0253	−	26.0246i	0.750329	−	1.29961i	−0.197334	−	0.980336i	$-0.563228\pi$
$401$	15.0253	−	26.0246i	0.750329	−	1.29961i	0.947663	−	0.319272i	$-0.103438\pi$
$402$	−23.2684	−	40.3020i	−1.16052	−	2.01008i
$403$	3.52714	+	6.10919i	0.175700	+	0.304321i
$404$	15.8958	−	27.5323i	0.790843	−	1.36978i
$405$	14.4793			0.719481
$406$	−4.91213	−	17.6827i	−0.243785	−	0.877577i
$407$	−3.95449			−0.196017
$408$	−3.06367	+	5.30644i	−0.151674	+	0.262708i
$409$	−19.5426	−	33.8488i	−0.966321	−	1.67372i	−0.706023	−	0.708189i	$-0.749512\pi$
$409$	−19.5426	−	33.8488i	−0.966321	−	1.67372i	−0.260298	−	0.965528i	$-0.583821\pi$
$410$	4.46928	+	7.74101i	0.220722	+	0.382301i
$411$	−13.9710	+	24.1984i	−0.689136	+	1.19362i
$412$	34.7569			1.71235
$413$	13.5174	+	3.48957i	0.665149	+	0.171711i
$414$	−4.75108			−0.233503
$415$	−7.52596	+	13.0353i	−0.369435	+	0.639880i
$416$	3.84417	+	6.65830i	0.188476	+	0.326450i
$417$	−15.3521	−	26.5906i	−0.751796	−	1.30215i
$418$	6.31194	−	10.9326i	0.308727	−	0.534731i
$419$	−38.9585			−1.90325			−0.951623	−	0.307267i	$-0.900586\pi$
$419$	−38.9585			−1.90325			−0.951623	+	0.307267i	$0.900586\pi$
$420$	−18.1483	−	4.68504i	−0.885544	−	0.228606i
$421$	−12.0576			−0.587651			−0.293826	−	0.955859i	$-0.594929\pi$
$421$	−12.0576			−0.587651			−0.293826	+	0.955859i	$0.594929\pi$
$422$	6.77953	−	11.7425i	0.330022	−	0.571615i
$423$	−1.59097	−	2.75565i	−0.0773558	−	0.133984i
$424$	0.0569038	+	0.0985602i	0.00276349	+	0.00478651i
$425$	3.38583	−	5.86442i	0.164237	−	0.284466i
$426$	50.1690			2.43070
$427$	2.53314	+	9.11880i	0.122587	+	0.441290i
$428$	19.8635			0.960141
$429$	−0.921233	+	1.59562i	−0.0444776	+	0.0770374i
$430$	−15.0847	−	26.1274i	−0.727448	−	1.25998i
$431$	6.45584	+	11.1818i	0.310967	+	0.538610i	0.978572	−	0.205905i	$-0.0660139\pi$
$431$	6.45584	+	11.1818i	0.310967	+	0.538610i	−0.667605	+	0.744516i	$0.732681\pi$
$432$	5.36267	−	9.28842i	0.258012	−	0.446889i
$433$	2.53061			0.121613			0.0608066	−	0.998150i	$-0.480633\pi$
$433$	2.53061			0.121613			0.0608066	+	0.998150i	$0.480633\pi$
$434$	−28.2362	+	28.7583i	−1.35538	+	1.38044i
$435$	8.54531			0.409716
$436$	−24.7670	+	42.8977i	−1.18612	+	2.05443i
$437$	−16.2944	−	28.2227i	−0.779467	−	1.35008i
$438$	17.9116	+	31.0239i	0.855851	+	1.48238i
$439$	7.10268	−	12.3022i	0.338993	−	0.587152i	−0.645251	−	0.763971i	$-0.723247\pi$
$439$	7.10268	−	12.3022i	0.338993	−	0.587152i	0.984244	+	0.176818i	$0.0565805\pi$
$440$	2.06721			0.0985502
$441$	2.41755	+	1.33732i	0.115122	+	0.0636821i
$442$	5.01584			0.238579
$443$	4.96368	−	8.59734i	0.235831	−	0.408472i	−0.723683	−	0.690133i	$-0.757552\pi$
$443$	4.96368	−	8.59734i	0.235831	−	0.408472i	0.959514	+	0.281661i	$0.0908853\pi$
$444$	−9.70141	−	16.8033i	−0.460409	−	0.797451i
$445$	−1.05473	−	1.82685i	−0.0499992	−	0.0866011i
$446$	15.2499	−	26.4137i	0.722105	−	1.25072i
$447$	−15.5077			−0.733488
$448$	−22.4908	+	22.9068i	−1.06259	+	1.08224i
$449$	−5.22614			−0.246637			−0.123318	−	0.992367i	$-0.539354\pi$
$449$	−5.22614			−0.246637			−0.123318	+	0.992367i	$0.539354\pi$
$450$	−1.24233	+	2.15179i	−0.0585642	+	0.101436i
$451$	1.43345	+	2.48281i	0.0674986	+	0.116911i
$452$	−17.5610	−	30.4166i	−0.826000	−	1.43067i
$453$	−1.37189	+	2.37619i	−0.0644571	+	0.111643i
$454$	25.8772			1.21448
$455$	1.02247	+	3.68068i	0.0479339	+	0.172553i
$456$	15.4213			0.722170
$457$	7.52018	−	13.0253i	0.351779	−	0.609300i	−0.634782	−	0.772691i	$-0.718910\pi$
$457$	7.52018	−	13.0253i	0.351779	−	0.609300i	0.986561	+	0.163392i	$0.0522434\pi$
$458$	−29.8171	−	51.6448i	−1.39326	−	2.41320i
$459$	−5.57493	−	9.65607i	−0.260216	−	0.450707i
$460$	10.7170	−	18.5625i	0.499685	−	0.865480i
$461$	9.30260			0.433265			0.216633	−	0.976253i	$-0.430493\pi$
$461$	9.30260			0.433265			0.216633	+	0.976253i	$0.430493\pi$
$462$	−10.1923	−	2.63118i	−0.474190	−	0.122414i
$463$	31.8860			1.48187			0.740934	−	0.671578i	$-0.234383\pi$
$463$	31.8860			1.48187			0.740934	+	0.671578i	$0.234383\pi$
$464$	3.58863	−	6.21569i	0.166598	−	0.288556i
$465$	−9.38304	−	16.2519i	−0.435128	−	0.753664i
$466$	−29.7128	−	51.4641i	−1.37642	−	2.38403i
$467$	−11.5503	+	20.0057i	−0.534483	+	0.925752i	0.464705	+	0.885465i	$0.346160\pi$
$467$	−11.5503	+	20.0057i	−0.534483	+	0.925752i	−0.999188	+	0.0402863i	$0.987173\pi$
$468$	−1.05105			−0.0485849
$469$	−29.9641	−	7.73535i	−1.38361	−	0.357185i
$470$	25.1361			1.15944
$471$	−10.1664	+	17.6087i	−0.468442	+	0.811365i
$472$	−3.77736	−	6.54257i	−0.173867	−	0.301146i
$473$	−4.83818	−	8.37997i	−0.222460	−	0.385311i
$474$	−25.8630	+	44.7961i	−1.18793	+	2.05755i
$475$	−17.0429			−0.781983
$476$	4.38039	+	15.7686i	0.200775	+	0.722750i
$477$	0.0313731			0.00143647
$478$	−15.5368	+	26.9105i	−0.710637	+	1.23086i
$479$	−11.9786	−	20.7476i	−0.547318	−	0.947983i	−0.998457	−	0.0555293i	$-0.982315\pi$
$479$	−11.9786	−	20.7476i	−0.547318	−	0.947983i	0.451139	−	0.892454i	$-0.351018\pi$
$480$	−10.2264	−	17.7126i	−0.466769	−	0.808468i
$481$	−1.97724	+	3.42469i	−0.0901545	+	0.156152i
$482$	6.90011			0.314292
$483$	−19.0383	+	19.3904i	−0.866272	+	0.882292i
$484$	2.66302			0.121047
$485$	2.09409	−	3.62707i	0.0950877	−	0.164697i
$486$	4.40102	+	7.62278i	0.199634	+	0.345777i
$487$	6.14803	+	10.6487i	0.278594	+	0.482539i	0.971036	−	0.238935i	$-0.0767983\pi$
$487$	6.14803	+	10.6487i	0.278594	+	0.482539i	−0.692442	+	0.721474i	$0.743465\pi$
$488$	2.56073	−	4.43532i	0.115919	−	0.200777i
$489$	−15.3097			−0.692329
$490$	−18.6978	+	11.2569i	−0.844681	+	0.508536i
$491$	−18.1711			−0.820050			−0.410025	−	0.912074i	$-0.634480\pi$
$491$	−18.1711			−0.820050			−0.410025	+	0.912074i	$0.634480\pi$
$492$	−7.03327	+	12.1820i	−0.317084	+	0.549206i
$493$	−3.73067	−	6.46171i	−0.168021	−	0.291021i
$494$	−6.31194	−	10.9326i	−0.283988	−	0.491881i
$495$	0.284931	−	0.493515i	0.0128067	−	0.0221819i
$496$	−15.7618			−0.707723
$497$	23.3733	−	23.8056i	1.04844	−	1.06783i
$498$	−41.4767			−1.85862
$499$	14.0128	−	24.2709i	0.627300	−	1.08652i	−0.360791	−	0.932647i	$-0.617493\pi$
$499$	14.0128	−	24.2709i	0.627300	−	1.08652i	0.988091	−	0.153869i	$-0.0491734\pi$
$500$	−15.2172	−	26.3569i	−0.680532	−	1.17872i
$501$	−7.98155	−	13.8245i	−0.356590	−	0.617631i
$502$	9.59392	−	16.6172i	0.428197	−	0.741660i
$503$	−1.10511			−0.0492744			−0.0246372	−	0.999696i	$-0.507843\pi$
$503$	−1.10511			−0.0492744			−0.0246372	+	0.999696i	$0.507843\pi$
$504$	−0.400167	−	1.44052i	−0.0178248	−	0.0641659i
$505$	17.2368			0.767027
$506$	6.01885	−	10.4249i	0.267570	−	0.463446i
$507$	0.921233	+	1.59562i	0.0409134	+	0.0708641i
$508$	−2.85678	−	4.94809i	−0.126749	−	0.219536i
$509$	−10.1994	+	17.6658i	−0.452078	+	0.783023i	−0.998515	−	0.0544779i	$-0.982651\pi$
$509$	−10.1994	+	17.6658i	−0.452078	+	0.783023i	0.546437	+	0.837500i	$0.315984\pi$
$510$	−13.3433			−0.590852
$511$	23.0659	+	5.95456i	1.02038	+	0.263414i
$512$	−23.5764			−1.04194
$513$	−14.0310	+	24.3024i	−0.619485	+	1.07298i
$514$	−20.5137	−	35.5308i	−0.904820	−	1.56719i
$515$	9.42229	+	16.3199i	0.415196	+	0.719140i
$516$	23.7387	−	41.1166i	1.04504	−	1.81006i
$517$	8.06202			0.354567
$518$	−21.8758	−	5.64731i	−0.961166	−	0.248129i
$519$	−19.6148			−0.860994
$520$	1.03360	−	1.79025i	0.0453265	−	0.0785078i
$521$	3.19900	+	5.54082i	0.140151	+	0.242748i	0.927553	−	0.373691i	$-0.121908\pi$
$521$	3.19900	+	5.54082i	0.140151	+	0.242748i	−0.787403	+	0.616439i	$0.788575\pi$
$522$	1.36887	+	2.37094i	0.0599136	+	0.103773i
$523$	−11.9200	+	20.6461i	−0.521225	+	0.902789i	0.478470	+	0.878104i	$0.341192\pi$
$523$	−11.9200	+	20.6461i	−0.521225	+	0.902789i	−0.999695	+	0.0246849i	$0.992142\pi$
$524$	−21.2012			−0.926178
$525$	3.80376	+	13.6928i	0.166010	+	0.597602i
$526$	0.214858			0.00936825
$527$	−8.19281	+	14.1904i	−0.356884	+	0.618142i
$528$	−2.05836	−	3.56518i	−0.0895785	−	0.155155i
$529$	−4.03778	−	6.99364i	−0.175556	−	0.304071i
$530$	−0.123917	+	0.214631i	−0.00538263	+	0.00932298i
$531$	−2.08259			−0.0903767
$532$	28.8571	−	29.3908i	1.25111	−	1.27425i
$533$	2.86690			0.124179
$534$	2.90640	−	5.03404i	0.125772	−	0.217844i
$535$	5.38483	+	9.32680i	0.232807	+	0.403233i
$536$	8.37328	+	14.5029i	0.361671	+	0.626432i
$537$	1.04321	−	1.80689i	0.0450177	−	0.0779729i
$538$	24.1749			1.04225
$539$	−5.99703	+	3.61048i	−0.258310	+	0.155515i
$540$	−18.4568			−0.794253
$541$	13.3679	−	23.1539i	0.574732	−	0.995466i	−0.421338	−	0.906904i	$-0.638439\pi$
$541$	13.3679	−	23.1539i	0.574732	−	0.995466i	0.996071	−	0.0885622i	$-0.0282272\pi$
$542$	0.525151	+	0.909588i	0.0225572	+	0.0390702i
$543$	−13.9989	−	24.2468i	−0.600751	−	1.04053i
$544$	−8.92919	+	15.4658i	−0.382836	+	0.663091i
$545$	−26.8565			−1.15040
$546$	−7.37483	+	7.51121i	−0.315614	+	0.321450i
$547$	25.7256			1.09995			0.549973	−	0.835183i	$-0.314638\pi$
$547$	25.7256			1.09995			0.549973	+	0.835183i	$0.314638\pi$
$548$	20.1930	−	34.9754i	0.862604	−	1.49407i
$549$	−0.705911	−	1.22267i	−0.0301276	−	0.0521825i
$550$	−3.14767	−	5.45192i	−0.134217	−	0.232471i
$551$	−9.38937	+	16.2629i	−0.400001	+	0.692821i
$552$	14.7053			0.625897
$553$	9.20671	+	33.1423i	0.391509	+	1.40936i
$554$	−64.6447			−2.74649
$555$	5.25993	−	9.11047i	0.223272	−	0.386718i
$556$	22.1893	+	38.4330i	0.941036	+	1.62992i
$557$	−21.6041	−	37.4194i	−0.915395	−	1.58551i	−0.806322	−	0.591476i	$-0.798545\pi$
$557$	−21.6041	−	37.4194i	−0.915395	−	1.58551i	−0.109073	−	0.994034i	$-0.534788\pi$
$558$	3.00612	−	5.20675i	0.127259	−	0.220420i
$559$	−9.67635			−0.409266
$560$	−8.26440	−	2.13348i	−0.349234	−	0.0901562i
$561$	−4.27966			−0.180687
$562$	−17.0977	+	29.6142i	−0.721225	+	1.24920i
$563$	18.7891	+	32.5437i	0.791868	+	1.37155i	0.924809	+	0.380431i	$0.124224\pi$
$563$	18.7891	+	32.5437i	0.791868	+	1.37155i	−0.132942	+	0.991124i	$0.542442\pi$
$564$	19.7783	+	34.2570i	0.832816	+	1.44248i
$565$	9.52127	−	16.4913i	0.400563	−	0.693795i
$566$	−10.2313			−0.430053
$567$	25.6901	+	6.63199i	1.07888	+	0.278517i
$568$	−18.0537			−0.757515
$569$	0.898636	−	1.55648i	0.0376728	−	0.0652512i	−0.846574	−	0.532271i	$-0.821339\pi$
$569$	0.898636	−	1.55648i	0.0376728	−	0.0652512i	0.884247	+	0.467019i	$0.154672\pi$
$570$	16.7913	+	29.0833i	0.703308	+	1.21817i
$571$	−15.1069	−	26.1659i	−0.632204	−	1.09501i	−0.987100	−	0.160104i	$-0.948817\pi$
$571$	−15.1069	−	26.1659i	−0.632204	−	1.09501i	0.354896	−	0.934906i	$-0.384516\pi$
$572$	1.33151	−	2.30625i	0.0556733	−	0.0964290i
$573$	−39.2048			−1.63780
$574$	4.38404	+	15.7817i	0.182986	+	0.658715i
$575$	−16.2515			−0.677736
$576$	2.39445	−	4.14732i	0.0997689	−	0.172805i
$577$	4.30069	+	7.44901i	0.179040	+	0.310106i	0.941552	−	0.336868i	$-0.109368\pi$
$577$	4.30069	+	7.44901i	0.179040	+	0.310106i	−0.762512	+	0.646974i	$0.776034\pi$
$578$	−12.5296	−	21.7018i	−0.521161	−	0.902678i
$579$	14.6554	−	25.3839i	0.609058	−	1.05492i
$580$	−12.3510			−0.512849
$581$	−19.3237	+	19.6810i	−0.801681	+	0.816507i
$582$	11.5409			0.478384
$583$	−0.0397446	+	0.0688396i	−0.00164605	+	0.00285105i
$584$	−6.44562	−	11.1641i	−0.266722	−	0.461976i
$585$	−0.284931	−	0.493515i	−0.0117805	−	0.0204043i
$586$	−22.1627	+	38.3869i	−0.915533	+	1.58575i
$587$	13.8780			0.572807			0.286404	−	0.958109i	$-0.407540\pi$
$587$	13.8780			0.572807			0.286404	+	0.958109i	$0.407540\pi$
$588$	−30.0539	−	16.6250i	−1.23940	−	0.685604i
$589$	41.2394			1.69924
$590$	8.22581	−	14.2475i	0.338651	−	0.586561i
$591$	−19.9279	−	34.5161i	−0.819724	−	1.41980i
$592$	−4.41785	−	7.65195i	−0.181573	−	0.314493i
$593$	−18.9396	+	32.8043i	−0.777756	+	1.34711i	0.155477	+	0.987840i	$0.450309\pi$
$593$	−18.9396	+	32.8043i	−0.777756	+	1.34711i	−0.933233	+	0.359273i	$0.883025\pi$
$594$	−10.3656			−0.425305
$595$	−6.21654	+	6.33150i	−0.254853	+	0.259566i
$596$	22.4141			0.918119
$597$	−7.57653	+	13.1229i	−0.310087	+	0.537086i
$598$	−6.01885	−	10.4249i	−0.246129	−	0.426308i
$599$	2.94197	+	5.09565i	0.120206	+	0.208203i	0.919849	−	0.392273i	$-0.128311\pi$
$599$	2.94197	+	5.09565i	0.120206	+	0.208203i	−0.799643	+	0.600476i	$0.794978\pi$
$600$	3.84519	−	6.66007i	0.156979	−	0.271896i
$601$	−10.1736			−0.414990			−0.207495	−	0.978236i	$-0.566531\pi$
$601$	−10.1736			−0.414990			−0.207495	+	0.978236i	$0.566531\pi$
$602$	−14.7970	−	53.2663i	−0.603081	−	2.17097i
$603$	4.61649			0.187998
$604$	1.98288	−	3.43444i	0.0806821	−	0.139745i
$605$	0.721922	+	1.25041i	0.0293503	+	0.0508362i
$606$	23.7487	+	41.1339i	0.964724	+	1.67095i
$607$	10.9471	−	18.9610i	0.444330	−	0.769602i	−0.553676	−	0.832732i	$-0.686775\pi$
$607$	10.9471	−	18.9610i	0.444330	−	0.769602i	0.998005	+	0.0631308i	$0.0201085\pi$
$608$	44.9460			1.82280
$609$	15.1617	+	3.91404i	0.614381	+	0.158605i
$610$	11.1528			0.451565
$611$	4.03101	−	6.98191i	0.163077	−	0.282458i
$612$	−1.22069	−	2.11429i	−0.0493433	−	0.0854651i
$613$	−17.5129	−	30.3332i	−0.707339	−	1.22515i	−0.965841	−	0.259136i	$-0.916562\pi$
$613$	−17.5129	−	30.3332i	−0.707339	−	1.22515i	0.258502	−	0.966011i	$-0.416771\pi$
$614$	25.0724	−	43.4267i	1.01184	−	1.75256i
$615$	−7.62663			−0.307536
$616$	3.66778	+	0.946850i	0.147779	+	0.0381497i
$617$	18.9358			0.762326			0.381163	−	0.924508i	$-0.375524\pi$
$617$	18.9358			0.762326			0.381163	+	0.924508i	$0.375524\pi$
$618$	−25.9639	+	44.9707i	−1.04442	+	1.80899i
$619$	−0.0807235	−	0.139817i	−0.00324455	−	0.00561973i	0.864399	−	0.502807i	$-0.167699\pi$
$619$	−0.0807235	−	0.139817i	−0.00324455	−	0.00561973i	−0.867643	+	0.497188i	$0.834366\pi$
$620$	13.5618	+	23.4898i	0.544657	+	0.943374i
$621$	−13.3795	+	23.1740i	−0.536900	+	0.929939i
$622$	−0.502672			−0.0201553
$623$	−1.03462	−	3.72443i	−0.0414512	−	0.149216i
$624$	−4.11672			−0.164801
$625$	0.962198	−	1.66658i	0.0384879	−	0.0666630i
$626$	−17.3326	−	30.0210i	−0.692751	−	1.19988i
$627$	5.38553	+	9.32802i	0.215077	+	0.372525i
$628$	14.6940	−	25.4508i	0.586356	−	1.01560i
$629$	−9.18543			−0.366247
$630$	2.28098	−	2.32317i	0.0908766	−	0.0925572i
$631$	33.5120			1.33409			0.667046	−	0.745016i	$-0.267558\pi$
$631$	33.5120			1.33409			0.667046	+	0.745016i	$0.267558\pi$
$632$	9.30699	−	16.1202i	0.370212	−	0.641226i
$633$	5.78449	+	10.0190i	0.229913	+	0.398221i
$634$	30.8273	+	53.3945i	1.22431	+	2.12056i
$635$	1.54890	−	2.68277i	0.0614661	−	0.106462i
$636$	−0.390016			−0.0154651
$637$	0.128254	+	6.99882i	0.00508162	+	0.277304i
$638$	−6.93651			−0.274619
$639$	−2.48841	+	4.31005i	−0.0984399	+	0.170503i
$640$	7.81445	+	13.5350i	0.308893	+	0.535019i
$641$	−7.00943	−	12.1407i	−0.276856	−	0.479528i	0.693746	−	0.720220i	$-0.255959\pi$
$641$	−7.00943	−	12.1407i	−0.276856	−	0.479528i	−0.970602	+	0.240692i	$0.922626\pi$
$642$	−14.8383	+	25.7008i	−0.585622	+	1.01433i
$643$	9.35554			0.368947			0.184473	−	0.982838i	$-0.440942\pi$
$643$	9.35554			0.368947			0.184473	+	0.982838i	$0.440942\pi$
$644$	27.5171	−	28.0260i	1.08433	−	1.10438i
$645$	25.7414			1.01357
$646$	14.6613	−	25.3941i	0.576841	−	0.999118i
$647$	−19.8272	−	34.3416i	−0.779486	−	1.35011i	−0.932238	−	0.361845i	$-0.882147\pi$
$647$	−19.8272	−	34.3416i	−0.779486	−	1.35011i	0.152752	−	0.988265i	$-0.451186\pi$
$648$	−7.17893	−	12.4343i	−0.282015	−	0.488464i
$649$	2.63830	−	4.56967i	0.103562	−	0.179375i
$650$	−6.29534			−0.246923
$651$	−9.20410	−	33.1329i	−0.360737	−	1.29858i
$652$	22.1280			0.866600
$653$	−1.00763	+	1.74526i	−0.0394315	+	0.0682973i	−0.885068	−	0.465462i	$-0.845888\pi$
$653$	−1.00763	+	1.74526i	−0.0394315	+	0.0682973i	0.845636	+	0.533760i	$0.179221\pi$
$654$	−37.0025	−	64.0903i	−1.44691	−	2.50613i
$655$	−5.74746	−	9.95489i	−0.224572	−	0.388970i
$656$	−3.20283	+	5.54746i	−0.125050	+	0.216592i
$657$	−3.55370			−0.138643
$658$	44.5982	+	11.5132i	1.73862	+	0.448830i
$659$	30.3622			1.18274			0.591371	−	0.806399i	$-0.298587\pi$
$659$	30.3622			1.18274			0.591371	+	0.806399i	$0.298587\pi$
$660$	−3.54214	+	6.13516i	−0.137877	+	0.238811i
$661$	15.3827	+	26.6437i	0.598319	+	1.03632i	0.993069	+	0.117531i	$0.0374979\pi$
$661$	15.3827	+	26.6437i	0.598319	+	1.03632i	−0.394750	+	0.918789i	$0.629169\pi$
$662$	−19.1201	−	33.1169i	−0.743123	−	1.28713i
$663$	−2.13983	+	3.70629i	−0.0831041	+	0.143941i
$664$	14.9257			0.579229
$665$	21.6232	+	5.58210i	0.838510	+	0.216464i
$666$	3.37034			0.130598
$667$	−8.95338	+	15.5077i	−0.346676	+	0.600461i
$668$	11.5362	+	19.9813i	0.446349	+	0.773099i
$669$	13.0117	+	22.5369i	0.503061	+	0.871327i
$670$	−18.2342	+	31.5825i	−0.704448	+	1.22014i
$671$	3.57710			0.138092
$672$	−10.0314	−	36.1110i	−0.386969	−	1.39301i
$673$	−25.4985			−0.982896			−0.491448	−	0.870907i	$-0.663532\pi$
$673$	−25.4985			−0.982896			−0.491448	+	0.870907i	$0.663532\pi$
$674$	4.32493	−	7.49101i	0.166590	−	0.288543i
$675$	6.99705	+	12.1193i	0.269317	+	0.466470i
$676$	−1.33151	−	2.30625i	−0.0512120	−	0.0887018i
$677$	−0.420408	+	0.728169i	−0.0161576	+	0.0279858i	−0.873991	−	0.485942i	$-0.838477\pi$
$677$	−0.420408	+	0.728169i	−0.0161576	+	0.0279858i	0.857834	+	0.513928i	$0.171810\pi$
$678$	52.4732			2.01522
$679$	5.37679	−	5.47623i	0.206342	−	0.210158i
$680$	4.80168			0.184136
$681$	−11.0396	+	19.1211i	−0.423038	+	0.732724i
$682$	7.61653	+	13.1922i	0.291652	+	0.505156i
$683$	2.12887	+	3.68732i	0.0814591	+	0.141091i	0.903877	−	0.427793i	$-0.140709\pi$
$683$	2.12887	+	3.68732i	0.0814591	+	0.141091i	−0.822418	+	0.568884i	$0.807375\pi$
$684$	−3.07223	+	5.32126i	−0.117470	+	0.203463i
$685$	21.8966			0.836627
$686$	−38.3310	+	11.4086i	−1.46348	+	0.435581i
$687$	50.8817			1.94126
$688$	10.8102	−	18.7238i	0.412134	−	0.713838i
$689$	0.0397446	+	0.0688396i	0.00151415	+	0.00262258i
$690$	16.0116	+	27.7328i	0.609549	+	1.05577i
$691$	−16.1398	+	27.9550i	−0.613987	+	1.06346i	0.376574	+	0.926387i	$0.377102\pi$
$691$	−16.1398	+	27.9550i	−0.613987	+	1.06346i	−0.990561	+	0.137071i	$0.956231\pi$
$692$	28.3504			1.07772
$693$	0.731590	−	0.745120i	0.0277908	−	0.0283048i
$694$	51.5254			1.95588
$695$	−12.0306	+	20.8377i	−0.456349	+	0.790419i
$696$	−4.23682	−	7.33839i	−0.160596	−	0.278161i
$697$	3.32960	+	5.76704i	0.126118	+	0.218442i
$698$	21.0493	−	36.4584i	0.796728	−	1.37997i
$699$	50.7037			1.91779
$700$	−5.49779	−	19.7910i	−0.207797	−	0.748029i
$701$	−26.9652			−1.01846			−0.509231	−	0.860630i	$-0.670070\pi$
$701$	−26.9652			−1.01846			−0.509231	+	0.860630i	$0.670070\pi$
$702$	−5.18279	+	8.97686i	−0.195612	+	0.338810i
$703$	11.5590	+	20.0207i	0.435955	+	0.755096i
$704$	6.06676	+	10.5079i	0.228650	+	0.396033i
$705$	−10.7234	+	18.5735i	−0.403868	+	0.699520i
$706$	−50.8511			−1.91381
$707$	30.5827	+	7.89503i	1.15018	+	0.296923i
$708$	25.8898			0.973000
$709$	−6.52265	+	11.2976i	−0.244963	+	0.424289i	−0.962121	−	0.272622i	$-0.912109\pi$
$709$	−6.52265	+	11.2976i	−0.244963	+	0.424289i	0.717158	+	0.696911i	$0.245443\pi$
$710$	−19.6574	−	34.0477i	−0.737730	−	1.27779i
$711$	−2.56564	−	4.44381i	−0.0962189	−	0.166656i
$712$	−1.04589	+	1.81153i	−0.0391964	+	0.0678901i
$713$	39.3245			1.47271
$714$	−23.6746	−	6.11168i	−0.885999	−	0.228724i
$715$	1.44384			0.0539967
$716$	−1.50781	+	2.61160i	−0.0563494	+	0.0976000i
$717$	−13.2565	−	22.9609i	−0.495071	−	0.857489i
$718$	−22.9872	−	39.8150i	−0.857876	−	1.48588i
$719$	12.0483	−	20.8683i	0.449326	−	0.778255i	−0.549017	−	0.835811i	$-0.684998\pi$
$719$	12.0483	−	20.8683i	0.449326	−	0.778255i	0.998342	+	0.0575566i	$0.0183310\pi$
$720$	1.27327			0.0474520
$721$	9.24260	+	33.2715i	0.344212	+	1.23910i
$722$	−32.7706			−1.21959
$723$	−2.94369	+	5.09862i	−0.109477	+	0.189620i
$724$	20.2334	+	35.0453i	0.751970	+	1.30245i
$725$	4.68233	+	8.11004i	0.173898	+	0.301199i
$726$	−1.98931	+	3.44559i	−0.0738304	+	0.127878i
$727$	7.35228			0.272681			0.136341	−	0.990662i	$-0.456466\pi$
$727$	7.35228			0.272681			0.136341	+	0.990662i	$0.456466\pi$
$728$	2.65388	−	2.70296i	0.0983595	−	0.100178i
$729$	22.5747			0.836099
$730$	14.0364	−	24.3118i	0.519511	−	0.899819i
$731$	−11.2381	−	19.4649i	−0.415655	−	0.719935i
$732$	8.77557	+	15.1997i	0.324355	+	0.561799i
$733$	22.5771	−	39.1047i	0.833904	−	1.44436i	−0.0610161	−	0.998137i	$-0.519434\pi$
$733$	22.5771	−	39.1047i	0.833904	−	1.44436i	0.894920	−	0.446227i	$-0.147233\pi$
$734$	−65.3461			−2.41197
$735$	−0.341187	−	18.6185i	−0.0125849	−	0.686755i
$736$	42.8590			1.57980
$737$	−5.84833	+	10.1296i	−0.215426	+	0.373129i
$738$	−1.22170	−	2.11605i	−0.0449715	−	0.0778930i
$739$	−11.7188	−	20.2976i	−0.431084	−	0.746659i	0.565883	−	0.824486i	$-0.308535\pi$
$739$	−11.7188	−	20.2976i	−0.431084	−	0.746659i	−0.996967	+	0.0778261i	$0.975202\pi$
$740$	−7.60249	+	13.1679i	−0.279473	+	0.484061i
$741$	10.7711			0.395685
$742$	−0.318171	+	0.324055i	−0.0116804	+	0.0118964i
$743$	6.59453			0.241930			0.120965	−	0.992657i	$-0.461401\pi$
$743$	6.59453			0.241930			0.120965	+	0.992657i	$0.461401\pi$
$744$	−9.30435	+	16.1156i	−0.341114	+	0.590827i
$745$	6.07628	+	10.5244i	0.222618	+	0.385585i
$746$	18.2643	+	31.6348i	0.668705	+	1.15823i
$747$	2.05727	−	3.56329i	0.0752714	−	0.130374i
$748$	6.18564			0.226169
$749$	5.28214	+	19.0147i	0.193005	+	0.694781i
$750$	45.4697			1.66032
$751$	3.40233	−	5.89301i	0.124153	−	0.215039i	−0.797249	−	0.603651i	$-0.793712\pi$
$751$	3.40233	−	5.89301i	0.124153	−	0.215039i	0.921401	+	0.388612i	$0.127045\pi$
$752$	9.00668	+	15.6000i	0.328440	+	0.568875i
$753$	8.18581	+	14.1782i	0.298308	+	0.516684i
$754$	−3.46826	+	6.00720i	−0.126306	+	0.218769i
$755$	2.15016			0.0782524
$756$	−32.7472	−	8.45382i	−1.19101	−	0.307462i
$757$	−35.0924			−1.27546			−0.637728	−	0.770261i	$-0.720126\pi$
$757$	−35.0924			−1.27546			−0.637728	+	0.770261i	$0.720126\pi$
$758$	−5.79115	+	10.0306i	−0.210344	+	0.364326i
$759$	5.13546	+	8.89487i	0.186405	+	0.322863i
$760$	−6.04245	−	10.4658i	−0.219183	−	0.379635i
$761$	−2.11276	+	3.65940i	−0.0765874	+	0.132653i	−0.901775	−	0.432205i	$-0.857736\pi$
$761$	−2.11276	+	3.65940i	−0.0765874	+	0.132653i	0.825188	+	0.564858i	$0.191069\pi$
$762$	8.53622			0.309235
$763$	−47.6505	−	12.3012i	−1.72506	−	0.445332i
$764$	56.6649			2.05007
$765$	0.661835	−	1.14633i	0.0239287	−	0.0414457i
$766$	12.6314	+	21.8782i	0.456391	+	0.790492i
$767$	−2.63830	−	4.56967i	−0.0952636	−	0.165001i
$768$	0.822271	−	1.42422i	0.0296712	−	0.0513919i
$769$	44.2512			1.59574			0.797869	−	0.602831i	$-0.205961\pi$
$769$	44.2512			1.59574			0.797869	+	0.602831i	$0.205961\pi$
$770$	2.20792	+	7.94807i	0.0795678	+	0.286428i
$771$	35.0058			1.26070
$772$	−21.1823	+	36.6889i	−0.762368	+	1.32046i
$773$	−21.0976	−	36.5421i	−0.758828	−	1.31433i	−0.943449	−	0.331519i	$-0.892439\pi$
$773$	−21.0976	−	36.5421i	−0.758828	−	1.31433i	0.184620	−	0.982810i	$-0.440894\pi$
$774$	4.12349	+	7.14210i	0.148216	+	0.256717i
$775$	10.2827	−	17.8102i	0.369366	−	0.639761i
$776$	−4.15306			−0.149086
$777$	13.5054	−	13.7552i	0.484504	−	0.493464i
$778$	9.88612			0.354435
$779$	8.37996	−	14.5145i	0.300243	−	0.520036i
$780$	3.54214	+	6.13516i	0.126829	+	0.219674i
$781$	−6.30481	−	10.9203i	−0.225604	−	0.390758i
$782$	13.9805	−	24.2149i	0.499942	−	0.865925i
$783$	15.4194			0.551044
$784$	−13.6860	−	7.57074i	−0.488787	−	0.270384i
$785$	15.9337			0.568698
$786$	15.8376	−	27.4315i	0.564907	−	0.978448i
$787$	−9.43300	−	16.3384i	−0.336250	−	0.582403i	0.647474	−	0.762088i	$-0.275825\pi$
$787$	−9.43300	−	16.3384i	−0.336250	−	0.582403i	−0.983724	+	0.179685i	$0.942492\pi$
$788$	28.8029	+	49.8882i	1.02606	+	1.77719i
$789$	−0.0916616	+	0.158763i	−0.00326324	+	0.00565210i
$790$	40.5350			1.44217
$791$	24.4468	−	24.8989i	0.869230	−	0.885305i
$792$	−0.565084			−0.0200794
$793$	1.78855	−	3.09786i	0.0635132	−	0.110008i
$794$	31.7771	+	55.0396i	1.12773	+	1.95328i
$795$	−0.105730	−	0.183130i	−0.00374985	−	0.00649494i
$796$	10.9508	−	18.9673i	0.388141	−	0.672279i
$797$	−2.21969			−0.0786253			−0.0393126	−	0.999227i	$-0.512517\pi$
$797$	−2.21969			−0.0786253			−0.0393126	+	0.999227i	$0.512517\pi$
$798$	16.4710	+	59.2925i	0.583068	+	2.09893i
$799$	18.7264			0.662491
$800$	11.2070	−	19.4110i	0.396226	−	0.686283i
$801$	0.288318	+	0.499381i	0.0101872	+	0.0176448i
$802$	−32.4458	−	56.1977i	−1.14570	−	1.98441i
$803$	4.50196	−	7.79762i	0.158871	−	0.275172i
$804$	−57.3901			−2.02399
$805$	20.6191	+	5.32289i	0.726727	+	0.187607i
$806$	15.2331			0.536562
$807$	−10.3134	+	17.8633i	−0.363048	+	0.628817i
$808$	−8.54613	−	14.8023i	−0.300652	−	0.520744i
$809$	−2.56521	−	4.44307i	−0.0901880	−	0.156210i	0.817402	−	0.576067i	$-0.195413\pi$
$809$	−2.56521	−	4.44307i	−0.0901880	−	0.156210i	−0.907590	+	0.419857i	$0.862080\pi$
$810$	15.6333	−	27.0777i	0.549298	−	0.951412i
$811$	14.4576			0.507675			0.253838	−	0.967247i	$-0.418307\pi$
$811$	14.4576			0.507675			0.253838	+	0.967247i	$0.418307\pi$
$812$	−21.9140	−	5.65718i	−0.769031	−	0.198528i
$813$	−0.896149			−0.0314293
$814$	−4.26967	+	7.39528i	−0.149652	+	0.259204i
$815$	5.99871	+	10.3901i	0.210126	+	0.363948i
$816$	−4.78113	−	8.28116i	−0.167373	−	0.289899i
$817$	−28.2840	+	48.9893i	−0.989532	+	1.71392i
$818$	−84.4009			−2.95101
$819$	−0.279497	−	1.00614i	−0.00976643	−	0.0351572i
$820$	11.0232			0.384947
$821$	−26.1917	+	45.3654i	−0.914097	+	1.58326i	−0.105879	+	0.994379i	$0.533766\pi$
$821$	−26.1917	+	45.3654i	−0.914097	+	1.58326i	−0.808218	+	0.588883i	$0.799568\pi$
$822$	30.1689	+	52.2541i	1.05226	+	1.82257i
$823$	13.1224	+	22.7286i	0.457417	+	0.792269i	0.998824	−	0.0484918i	$-0.0154415\pi$
$823$	13.1224	+	22.7286i	0.457417	+	0.792269i	−0.541407	+	0.840761i	$0.682108\pi$
$824$	9.34328	−	16.1830i	0.325488	−	0.563763i
$825$	5.37137			0.187007
$826$	21.1206	−	21.5112i	0.734881	−	0.748471i
$827$	−5.05300			−0.175710			−0.0878550	−	0.996133i	$-0.528001\pi$
$827$	−5.05300			−0.175710			−0.0878550	+	0.996133i	$0.528001\pi$
$828$	−2.92957	+	5.07417i	−0.101810	+	0.176339i
$829$	−7.97604	−	13.8149i	−0.277019	−	0.479811i	0.693623	−	0.720338i	$-0.256013\pi$
$829$	−7.97604	−	13.8149i	−0.277019	−	0.479811i	−0.970643	+	0.240527i	$0.922680\pi$
$830$	16.2516	+	28.1486i	0.564100	+	0.977051i
$831$	27.5784	−	47.7671i	0.956683	−	1.65702i
$832$	12.1335			0.420654
$833$	−13.9298	+	8.38639i	−0.482640	+	0.290571i
$834$	−66.3028			−2.29588
$835$	−6.25473	+	10.8335i	−0.216454	+	0.374909i
$836$	−7.78402	−	13.4823i	−0.269216	−	0.466296i
$837$	−16.9310	−	29.3254i	−0.585222	−	1.01363i
$838$	−42.0636	+	72.8562i	−1.45306	+	2.51678i
$839$	−54.0718			−1.86676			−0.933382	−	0.358883i	$-0.883158\pi$
$839$	−54.0718			−1.86676			−0.933382	+	0.358883i	$0.883158\pi$
$840$	−7.05996	+	7.19052i	−0.243592	+	0.248096i
$841$	−18.6815			−0.644191
$842$	−13.0186	+	22.5489i	−0.448651	+	0.777086i
$843$	−14.5883	−	25.2677i	−0.502448	−	0.870265i
$844$	−8.36066	−	14.4811i	−0.287786	−	0.498460i
$845$	0.721922	−	1.25041i	0.0248349	−	0.0430153i
$846$	−6.87111			−0.236234
$847$	0.708155	+	2.54922i	0.0243325	+	0.0875922i
$848$	−0.177607			−0.00609903
$849$	4.36482	−	7.56009i	0.149800	−	0.259461i
$850$	−7.31136	−	12.6637i	−0.250778	−	0.434360i
$851$	11.0222	+	19.0911i	0.377837	+	0.654433i
$852$	30.9348	−	53.5806i	1.05981	−	1.83564i
$853$	−31.6029			−1.08206			−0.541031	−	0.841003i	$-0.681966\pi$
$853$	−31.6029			−1.08206			−0.541031	+	0.841003i	$0.681966\pi$
$854$	19.7881	+	5.10837i	0.677135	+	0.174805i
$855$	−3.33142			−0.113932
$856$	5.33968	−	9.24859i	0.182506	−	0.316110i
$857$	0.704582	+	1.22037i	0.0240680	+	0.0416871i	0.877809	−	0.479012i	$-0.159005\pi$
$857$	0.704582	+	1.22037i	0.0240680	+	0.0416871i	−0.853741	+	0.520699i	$0.825671\pi$
$858$	1.98931	+	3.44559i	0.0679141	+	0.117631i
$859$	4.18833	−	7.25440i	0.142904	−	0.247517i	−0.785685	−	0.618627i	$-0.787689\pi$
$859$	4.18833	−	7.25440i	0.142904	−	0.247517i	0.928589	+	0.371110i	$0.121023\pi$
$860$	−37.2055			−1.26870
$861$	−13.5317	−	3.49325i	−0.461159	−	0.119050i
$862$	27.8815			0.949649
$863$	14.1718	−	24.5463i	0.482414	−	0.835566i	−0.517382	−	0.855755i	$-0.673093\pi$
$863$	14.1718	−	24.5463i	0.482414	−	0.835566i	0.999796	+	0.0201886i	$0.00642668\pi$
$864$	−18.4528	−	31.9612i	−0.627777	−	1.08734i
$865$	7.68554	+	13.3117i	0.261316	+	0.452613i
$866$	2.73230	−	4.73248i	0.0928474	−	0.160816i
$867$	21.3812			0.726143
$868$	13.3032	+	47.8890i	0.451541	+	1.62546i
$869$	13.0010			0.441028
$870$	9.22638	−	15.9806i	0.312804	−	0.541792i
$871$	5.84833	+	10.1296i	0.198163	+	0.343229i
$872$	13.3156	+	23.0633i	0.450924	+	0.781023i
$873$	−0.572432	+	0.991482i	−0.0193739	+	0.0335566i
$874$	−70.3724			−2.38038
$875$	21.1840	−	21.5757i	0.716148	−	0.729392i
$876$	44.1780			1.49264
$877$	4.99186	−	8.64615i	0.168563	−	0.291960i	−0.769352	−	0.638825i	$-0.779421\pi$
$877$	4.99186	−	8.64615i	0.168563	−	0.291960i	0.937915	+	0.346866i	$0.112754\pi$
$878$	−15.3376	−	26.5654i	−0.517618	−	0.896540i
$879$	−18.9099	−	32.7529i	−0.637814	−	1.10473i
$880$	−1.61303	+	2.79385i	−0.0543751	+	0.0941805i
$881$	29.4855			0.993392			0.496696	−	0.867925i	$-0.334546\pi$
$881$	29.4855			0.993392			0.496696	+	0.867925i	$0.334546\pi$
$882$	5.11116	−	3.07715i	0.172102	−	0.103613i
$883$	44.4101			1.49452			0.747259	−	0.664533i	$-0.231369\pi$
$883$	44.4101			1.49452			0.747259	+	0.664533i	$0.231369\pi$
$884$	3.09282	−	5.35692i	0.104023	−	0.180173i
$885$	7.01851	+	12.1564i	0.235925	+	0.408633i
$886$	−10.7186	−	18.5651i	−0.360098	−	0.623708i
$887$	−12.7551	+	22.0925i	−0.428275	+	0.741794i	−0.996720	−	0.0809274i	$-0.974212\pi$
$887$	−12.7551	+	22.0925i	−0.428275	+	0.741794i	0.568445	+	0.822721i	$0.307545\pi$
$888$	−10.4317			−0.350063
$889$	3.97695	−	4.05050i	0.133383	−	0.135849i
$890$	−4.55519			−0.152690
$891$	5.01414	−	8.68474i	0.167980	−	0.290950i
$892$	−18.8066	−	32.5739i	−0.629690	−	1.09066i
$893$	−23.5653	−	40.8163i	−0.788582	−	1.36586i
$894$	−16.7437	+	29.0009i	−0.559992	+	0.969934i
$895$	−1.63501			−0.0546524
$896$	7.66543	+	27.5940i	0.256084	+	0.921852i
$897$	10.2709			0.342936
$898$	−5.64268	+	9.77340i	−0.188299	+	0.326143i
$899$	−11.3300	−	19.6242i	−0.377877	−	0.654503i
$900$	1.53207	+	2.65363i	0.0510691	+	0.0884543i
$901$	−0.0923182	+	0.159900i	−0.00307557	+	0.00532704i
$902$	6.19080			0.206131
$903$	45.6721	+	11.7904i	1.51987	+	0.392360i
$904$	−18.8829			−0.628034
$905$	−10.9702	+	19.0010i	−0.364662	+	0.631613i
$906$	2.96247	+	5.13115i	0.0984215	+	0.170471i
$907$	2.12432	+	3.67943i	0.0705370	+	0.122174i	0.899137	−	0.437668i	$-0.144195\pi$
$907$	2.12432	+	3.67943i	0.0705370	+	0.122174i	−0.828600	+	0.559841i	$0.810862\pi$
$908$	15.9562	−	27.6369i	0.529524	−	0.917163i
$909$	−4.71178			−0.156280
$910$	7.98719	+	2.06192i	0.264773	+	0.0683520i
$911$	8.87326			0.293984			0.146992	−	0.989138i	$-0.453041\pi$
$911$	8.87326			0.293984			0.146992	+	0.989138i	$0.453041\pi$
$912$	−12.0332	+	20.8421i	−0.398458	+	0.690149i
$913$	5.21244	+	9.02821i	0.172507	+	0.298790i
$914$	−16.2391	−	28.1270i	−0.537142	−	0.930357i
$915$	−4.75796	+	8.24103i	−0.157293	+	0.272440i
$916$	−73.5423			−2.42991
$917$	−5.63785	−	20.2951i	−0.186178	−	0.670205i
$918$	−24.0771			−0.794661
$919$	−21.2048	+	36.7278i	−0.699482	+	1.21154i	0.269165	+	0.963094i	$0.413252\pi$
$919$	−21.2048	+	36.7278i	−0.699482	+	1.21154i	−0.968646	+	0.248444i	$0.920081\pi$
$920$	−5.76187	−	9.97985i	−0.189963	−	0.329026i
$921$	21.3925	+	37.0529i	0.704907	+	1.22094i
$922$	10.0440	−	17.3968i	0.330783	−	0.572933i
$923$	−12.6096			−0.415051
$924$	−9.09480	+	9.26299i	−0.299197	+	0.304730i
$925$	11.5286			0.379057
$926$	34.4274	−	59.6300i	1.13135	−	1.95956i
$927$	−2.57564	−	4.46114i	−0.0845951	−	0.146523i
$928$	−12.3484	−	21.3880i	−0.405355	−	0.702096i
$929$	−4.51971	+	7.82836i	−0.148287	+	0.256840i	−0.930594	−	0.366052i	$-0.880709\pi$
$929$	−4.51971	+	7.82836i	−0.148287	+	0.256840i	0.782308	+	0.622892i	$0.214043\pi$
$930$	−40.5235			−1.32882
$931$	35.8084	+	19.8083i	1.17357	+	0.649189i
$932$	−73.2850			−2.40053
$933$	0.214447	−	0.371434i	0.00702069	−	0.0121602i
$934$	24.9417	+	43.2003i	0.816118	+	1.41356i
$935$	1.67687	+	2.90443i	0.0548396	+	0.0949850i
$936$	−0.282542	+	0.489377i	−0.00923517	+	0.0159958i
$937$	−33.3368			−1.08907			−0.544533	−	0.838739i	$-0.683293\pi$
$937$	−33.3368			−1.08907			−0.544533	+	0.838739i	$0.683293\pi$
$938$	−46.8182	+	47.6840i	−1.52867	+	1.55694i
$939$	29.5774			0.965223
$940$	15.4992	−	26.8454i	0.505528	−	0.875601i
$941$	−4.03595	−	6.99047i	−0.131568	−	0.227883i	0.792713	−	0.609595i	$-0.208668\pi$
$941$	−4.03595	−	6.99047i	−0.131568	−	0.227883i	−0.924281	+	0.381712i	$0.875335\pi$
$942$	21.9533	+	38.0242i	0.715277	+	1.23890i
$943$	7.99084	−	13.8405i	0.260217	−	0.450710i
$944$	11.7898			0.383725
$945$	−4.90805	−	17.6680i	−0.159659	−	0.574741i
$946$	−20.8952			−0.679360
$947$	−8.77279	+	15.1949i	−0.285077	+	0.493769i	−0.972628	−	0.232368i	$-0.925353\pi$
$947$	−8.77279	+	15.1949i	−0.285077	+	0.493769i	0.687550	+	0.726137i	$0.258686\pi$
$948$	31.8949	+	55.2435i	1.03590	+	1.79423i
$949$	−4.50196	−	7.79762i	−0.146140	−	0.253122i
$950$	−18.4013	+	31.8719i	−0.597016	+	1.03406i
$951$	−52.6055			−1.70585
$952$	8.51947	+	2.19933i	0.276117	+	0.0712807i
$953$	28.1480			0.911802			0.455901	−	0.890031i	$-0.349317\pi$
$953$	28.1480			0.911802			0.455901	+	0.890031i	$0.349317\pi$
$954$	0.0338736	−	0.0586707i	0.00109670	−	0.00189954i
$955$	15.3614	+	26.6067i	0.497082	+	0.860971i
$956$	19.1603	+	33.1867i	0.619689	+	1.07333i
$957$	2.95922	−	5.12552i	0.0956580	−	0.165684i
$958$	−51.7335			−1.67143
$959$	38.8504	+	10.0294i	1.25455	+	0.323866i
$960$	−32.2780			−1.04177
$961$	−9.38150	+	16.2492i	−0.302629	+	0.524169i
$962$	4.26967	+	7.39528i	0.137660	+	0.238433i
$963$	−1.47198	−	2.54954i	−0.0474338	−	0.0821578i
$964$	4.25469	−	7.36933i	0.137034	−	0.237350i
$965$	−22.9694			−0.739410
$966$	15.7062	+	56.5393i	0.505339	+	1.81912i
$967$	20.3638			0.654854			0.327427	−	0.944876i	$-0.393818\pi$
$967$	20.3638			0.654854			0.327427	+	0.944876i	$0.393818\pi$
$968$	0.715869	−	1.23992i	0.0230089	−	0.0398526i
$969$	12.5095	+	21.6670i	0.401861	+	0.696045i
$970$	−4.52199	−	7.83231i	−0.145192	−	0.251480i
$971$	6.17359	−	10.6930i	0.198120	−	0.343154i	−0.749799	−	0.661666i	$-0.769850\pi$
$971$	6.17359	−	10.6930i	0.198120	−	0.343154i	0.947919	+	0.318512i	$0.103183\pi$
$972$	10.8549			0.348170
$973$	−30.8899	+	31.4612i	−0.990286	+	1.00860i
$974$	26.5522			0.850786
$975$	2.68568	−	4.65174i	0.0860107	−	0.148975i
$976$	3.99624	+	6.92170i	0.127917	+	0.221558i
$977$	−4.22549	−	7.31876i	−0.135185	−	0.234148i	0.790483	−	0.612484i	$-0.209830\pi$
$977$	−4.22549	−	7.31876i	−0.135185	−	0.234148i	−0.925668	+	0.378336i	$0.876496\pi$
$978$	−16.5299	+	28.6307i	−0.528569	+	0.915508i
$979$	−1.46101			−0.0466940
$980$	0.493137	+	26.9104i	0.0157527	+	0.859622i
$981$	7.34138			0.234392
$982$	−19.6194	+	33.9817i	−0.626079	+	1.08440i
$983$	10.4009	+	18.0149i	0.331737	+	0.574585i	0.982852	−	0.184394i	$-0.0590321\pi$
$983$	10.4009	+	18.0149i	0.331737	+	0.574585i	−0.651116	+	0.758978i	$0.725699\pi$
$984$	3.78134	+	6.54947i	0.120545	+	0.208790i
$985$	−15.6165	+	27.0485i	−0.497581	+	0.861836i
$986$	−16.1121			−0.513112
$987$	−27.5335	+	28.0427i	−0.876402	+	0.892609i
$988$	−15.5680			−0.495286
$989$	−26.9706	+	46.7145i	−0.857616	+	1.48544i
$990$	−0.615281	−	1.06570i	−0.0195549	−	0.0338701i
$991$	0.309290	+	0.535706i	0.00982492	+	0.0170173i	0.870896	−	0.491467i	$-0.163539\pi$
$991$	0.309290	+	0.535706i	0.00982492	+	0.0170173i	−0.861071	+	0.508484i	$0.830206\pi$
$992$	−27.1179	+	46.9695i	−0.860994	+	1.49128i
$993$	32.6276			1.03541
$994$	−19.2825	−	69.4134i	−0.611605	−	2.20166i
$995$	11.8747			0.376452
$996$	−25.5750	+	44.2972i	−0.810375	+	1.40361i
$997$	−9.09400	−	15.7513i	−0.288010	−	0.498848i	0.685325	−	0.728238i	$-0.259660\pi$
$997$	−9.09400	−	15.7513i	−0.288010	−	0.498848i	−0.973335	+	0.229390i	$0.926327\pi$
$998$	−30.2593	−	52.4107i	−0.957843	−	1.65903i
$999$	9.49118	−	16.4392i	0.300288	−	0.520113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.i.d.716.22	yes	50
7.2	even	3		7007.2.a.bh.1.4		25
7.4	even	3	inner	1001.2.i.d.144.22	✓	50
7.5	odd	6		7007.2.a.bi.1.4		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.d.144.22	✓	50	7.4	even	3	inner
1001.2.i.d.716.22	yes	50	1.1	even	1	trivial
7007.2.a.bh.1.4		25	7.2	even	3
7007.2.a.bi.1.4		25	7.5	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07970 - 1.87010i) q^{2} +(0.921233 + 1.59562i) q^{3} +(-1.33151 - 2.30625i) q^{4} +(0.721922 - 1.25041i) q^{5} +3.97863 q^{6} +(1.85361 - 1.88789i) q^{7} -1.43174 q^{8} +(-0.197342 + 0.341806i) q^{9} +O(q^{10})\)	\(q+(1.07970 - 1.87010i) q^{2} +(0.921233 + 1.59562i) q^{3} +(-1.33151 - 2.30625i) q^{4} +(0.721922 - 1.25041i) q^{5} +3.97863 q^{6} +(1.85361 - 1.88789i) q^{7} -1.43174 q^{8} +(-0.197342 + 0.341806i) q^{9} +(-1.55892 - 2.70013i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(2.45327 - 4.24918i) q^{12} -1.00000 q^{13} +(-1.52919 - 5.50479i) q^{14} +2.66024 q^{15} +(1.11717 - 1.93500i) q^{16} +(-1.16139 - 2.01159i) q^{17} +(0.426141 + 0.738098i) q^{18} +(-2.92300 + 5.06279i) q^{19} -3.84499 q^{20} +(4.71997 + 1.21848i) q^{21} -2.15940 q^{22} +(-2.78727 + 4.82770i) q^{23} +(-1.31896 - 2.28451i) q^{24} +(1.45766 + 2.52473i) q^{25} +(-1.07970 + 1.87010i) q^{26} +4.80021 q^{27} +(-6.82204 - 1.76114i) q^{28} +3.21224 q^{29} +(2.87226 - 4.97490i) q^{30} +(-3.52714 - 6.10919i) q^{31} +(-3.84417 - 6.65830i) q^{32} +(0.921233 - 1.59562i) q^{33} -5.01584 q^{34} +(-1.02247 - 3.68068i) q^{35} +1.05105 q^{36} +(1.97724 - 3.42469i) q^{37} +(6.31194 + 10.9326i) q^{38} +(-0.921233 - 1.59562i) q^{39} +(-1.03360 + 1.79025i) q^{40} -2.86690 q^{41} +(7.37483 - 7.51121i) q^{42} +9.67635 q^{43} +(-1.33151 + 2.30625i) q^{44} +(0.284931 + 0.493515i) q^{45} +(6.01885 + 10.4249i) q^{46} +(-4.03101 + 6.98191i) q^{47} +4.11672 q^{48} +(-0.128254 - 6.99882i) q^{49} +6.29534 q^{50} +(2.13983 - 3.70629i) q^{51} +(1.33151 + 2.30625i) q^{52} +(-0.0397446 - 0.0688396i) q^{53} +(5.18279 - 8.97686i) q^{54} -1.44384 q^{55} +(-2.65388 + 2.70296i) q^{56} -10.7711 q^{57} +(3.46826 - 6.00720i) q^{58} +(2.63830 + 4.56967i) q^{59} +(-3.54214 - 6.13516i) q^{60} +(-1.78855 + 3.09786i) q^{61} -15.2331 q^{62} +(0.279497 + 1.00614i) q^{63} -12.1335 q^{64} +(-0.721922 + 1.25041i) q^{65} +(-1.98931 - 3.44559i) q^{66} +(-5.84833 - 10.1296i) q^{67} +(-3.09282 + 5.35692i) q^{68} -10.2709 q^{69} +(-7.98719 - 2.06192i) q^{70} +12.6096 q^{71} +(0.282542 - 0.489377i) q^{72} +(4.50196 + 7.79762i) q^{73} +(-4.26967 - 7.39528i) q^{74} +(-2.68568 + 4.65174i) q^{75} +15.5680 q^{76} +(-2.56177 - 0.661329i) q^{77} -3.97863 q^{78} +(-6.50049 + 11.2592i) q^{79} +(-1.61303 - 2.79385i) q^{80} +(5.01414 + 8.68474i) q^{81} +(-3.09540 + 5.36139i) q^{82} -10.4249 q^{83} +(-3.47459 - 12.5078i) q^{84} -3.35375 q^{85} +(10.4476 - 18.0957i) q^{86} +(2.95922 + 5.12552i) q^{87} +(0.715869 + 1.23992i) q^{88} +(0.730504 - 1.26527i) q^{89} +1.23056 q^{90} +(-1.85361 + 1.88789i) q^{91} +14.8452 q^{92} +(6.49865 - 11.2560i) q^{93} +(8.70457 + 15.0768i) q^{94} +(4.22036 + 7.30988i) q^{95} +(7.08275 - 12.2677i) q^{96} +2.90071 q^{97} +(-13.2270 - 7.31680i) q^{98} +0.394684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

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