LMFDB - Embedded newform 136.2.s.c.107.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [136,2,Mod(3,136)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("136.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(136, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 8, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.s (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [112,-8,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			107.13
Character	$\chi$	$=$	136.107
Dual form			136.2.s.c.75.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36819 + 0.357863i) q^{2} +(0.921778 + 1.37954i) q^{3} +(1.74387 + 0.979245i) q^{4} +(-3.91277 - 0.778297i) q^{5} +(0.767479 + 2.21734i) q^{6} +(1.72342 - 0.342810i) q^{7} +(2.03550 + 1.96386i) q^{8} +(0.0945986 - 0.228381i) q^{9} +(-5.07487 - 2.46509i) q^{10} +(-2.25700 - 1.50808i) q^{11} +(0.256553 + 3.30838i) q^{12} +(1.43844 - 1.43844i) q^{13} +(2.48064 + 0.147720i) q^{14} +(-2.53301 - 6.11523i) q^{15} +(2.08216 + 3.41535i) q^{16} +(-3.43525 + 2.28014i) q^{17} +(0.211158 - 0.278615i) q^{18} +(-2.12471 - 5.12951i) q^{19} +(-6.06121 - 5.18881i) q^{20} +(2.06153 + 2.06153i) q^{21} +(-2.54831 - 2.87103i) q^{22} +(1.05741 + 0.706536i) q^{23} +(-0.832933 + 4.61829i) q^{24} +(10.0846 + 4.17717i) q^{25} +(2.48282 - 1.45329i) q^{26} +(5.28409 - 1.05107i) q^{27} +(3.34111 + 1.08984i) q^{28} +(-1.64434 + 8.26664i) q^{29} +(-1.27722 - 9.27324i) q^{30} +(-3.07326 - 4.59945i) q^{31} +(1.62655 + 5.41796i) q^{32} -4.50373i q^{33} +(-5.51604 + 1.89031i) q^{34} -7.01015 q^{35} +(0.388609 - 0.305632i) q^{36} +(-3.15531 + 2.10831i) q^{37} +(-1.07134 - 7.77849i) q^{38} +(3.31031 + 0.658462i) q^{39} +(-6.43598 - 9.26833i) q^{40} +(-0.810929 - 4.07682i) q^{41} +(2.08281 + 3.55830i) q^{42} +(-2.93119 + 7.07653i) q^{43} +(-2.45913 - 4.84005i) q^{44} +(-0.547891 + 0.819977i) q^{45} +(1.19389 + 1.34508i) q^{46} +(-2.10492 + 2.10492i) q^{47} +(-2.79232 + 6.02061i) q^{48} +(-3.61450 + 1.49717i) q^{49} +(12.3027 + 9.32405i) q^{50} +(-6.31208 - 2.63728i) q^{51} +(3.91704 - 1.09987i) q^{52} +(5.83351 - 2.41632i) q^{53} +(7.60576 + 0.452917i) q^{54} +(7.65738 + 7.65738i) q^{55} +(4.18126 + 2.68676i) q^{56} +(5.11785 - 7.65940i) q^{57} +(-5.20808 + 10.7219i) q^{58} +(3.89198 + 1.61211i) q^{59} +(1.57107 - 13.1446i) q^{60} +(0.411419 + 2.06835i) q^{61} +(-2.55882 - 7.39271i) q^{62} +(0.0847419 - 0.426026i) q^{63} +(0.286541 + 7.99487i) q^{64} +(-6.74782 + 4.50875i) q^{65} +(1.61172 - 6.16195i) q^{66} -0.474710i q^{67} +(-8.22345 + 0.612312i) q^{68} +2.11000i q^{69} +(-9.59119 - 2.50867i) q^{70} +(9.48983 - 6.34090i) q^{71} +(0.641064 - 0.279093i) q^{72} +(-1.48381 + 7.45963i) q^{73} +(-5.07155 + 1.75540i) q^{74} +(3.53318 + 17.7625i) q^{75} +(1.31783 - 11.0258i) q^{76} +(-4.40675 - 1.82533i) q^{77} +(4.29348 + 2.08553i) q^{78} +(-0.405234 + 0.606476i) q^{79} +(-5.48883 - 14.9840i) q^{80} +(5.79637 + 5.79637i) q^{81} +(0.349437 - 5.86805i) q^{82} +(14.3632 - 5.94945i) q^{83} +(1.57629 + 5.61378i) q^{84} +(15.2160 - 6.24801i) q^{85} +(-6.54285 + 8.63305i) q^{86} +(-12.9199 + 5.35158i) q^{87} +(-1.63248 - 7.50212i) q^{88} +(-5.56406 + 5.56406i) q^{89} +(-1.04306 + 0.925811i) q^{90} +(1.98593 - 2.97215i) q^{91} +(1.15210 + 2.26757i) q^{92} +(3.51226 - 8.47935i) q^{93} +(-3.63319 + 2.12665i) q^{94} +(4.32122 + 21.7242i) q^{95} +(-5.97497 + 7.23805i) q^{96} +(-2.52059 - 0.501377i) q^{97} +(-5.48109 + 0.754920i) q^{98} +(-0.557926 + 0.372794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 8 q^{20} - 8 q^{22} - 56 q^{24} - 16 q^{25} - 40 q^{26}+ \cdots + 48 q^{99}+O(q^{100}) $ 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 - 8 * q^10 - 16 * q^11 + 24 * q^12 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 8 * q^20 - 8 * q^22 - 56 * q^24 - 16 * q^25 - 40 * q^26 + 32 * q^27 + 40 * q^28 - 72 * q^30 + 32 * q^32 - 72 * q^34 - 32 * q^35 + 56 * q^36 + 48 * q^38 + 56 * q^40 - 16 * q^41 - 56 * q^42 - 96 * q^43 + 24 * q^44 - 24 * q^46 + 16 * q^48 - 16 * q^49 - 16 * q^51 - 16 * q^52 - 24 * q^54 + 32 * q^56 + 32 * q^57 + 48 * q^58 - 16 * q^59 + 96 * q^60 + 48 * q^62 + 40 * q^64 + 64 * q^65 - 16 * q^66 + 80 * q^68 + 64 * q^70 + 96 * q^72 - 96 * q^73 + 40 * q^74 - 16 * q^75 + 48 * q^76 + 96 * q^78 + 8 * q^80 - 96 * q^81 + 32 * q^82 + 128 * q^83 + 64 * q^86 - 72 * q^88 - 16 * q^89 + 152 * q^90 - 16 * q^91 - 120 * q^92 + 88 * q^94 - 160 * q^96 - 16 * q^97 + 128 * q^98 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{16}\right)$

Coefficient data

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

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

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

$2$	1.36819	+	0.357863i	0.967454	+	0.253047i
$2$	1.36819	+	0.357863i	0.967454	+	0.253047i
$3$	0.921778	+	1.37954i	0.532189	+	0.796477i	0.995990	−	0.0894623i	$-0.0285148\pi$
$3$	0.921778	+	1.37954i	0.532189	+	0.796477i	−0.463801	+	0.885939i	$0.653515\pi$
$4$	1.74387	+	0.979245i	0.871934	+	0.489623i
$5$	−3.91277	−	0.778297i	−1.74984	−	0.348065i	−0.786757	−	0.617263i	$-0.788241\pi$
$5$	−3.91277	−	0.778297i	−1.74984	−	0.348065i	−0.963085	+	0.269198i	$0.913241\pi$
$6$	0.767479	+	2.21734i	0.313322	+	0.905224i
$7$	1.72342	−	0.342810i	0.651392	−	0.129570i	0.141677	−	0.989913i	$-0.454751\pi$
$7$	1.72342	−	0.342810i	0.651392	−	0.129570i	0.509715	+	0.860343i	$0.329751\pi$
$8$	2.03550	+	1.96386i	0.719659	+	0.694328i
$9$	0.0945986	−	0.228381i	0.0315329	−	0.0761271i
$10$	−5.07487	−	2.46509i	−1.60481	−	0.779529i
$11$	−2.25700	−	1.50808i	−0.680511	−	0.454703i	0.166666	−	0.986013i	$-0.446700\pi$
$11$	−2.25700	−	1.50808i	−0.680511	−	0.454703i	−0.847177	+	0.531310i	$0.821700\pi$
$12$	0.256553	+	3.30838i	0.0740606	+	0.955047i
$13$	1.43844	−	1.43844i	0.398952	−	0.398952i	−0.478911	−	0.877863i	$-0.658968\pi$
$13$	1.43844	−	1.43844i	0.398952	−	0.398952i	0.877863	+	0.478911i	$0.158968\pi$
$14$	2.48064	+	0.147720i	0.662979	+	0.0394799i
$15$	−2.53301	−	6.11523i	−0.654021	−	1.57895i
$16$	2.08216	+	3.41535i	0.520539	+	0.853838i
$17$	−3.43525	+	2.28014i	−0.833171	+	0.553015i
$17$	−3.43525	+	2.28014i	−0.833171	+	0.553015i
$18$	0.211158	−	0.278615i	0.0497703	−	0.0656702i
$19$	−2.12471	−	5.12951i	−0.487443	−	1.17679i	−0.956002	−	0.293359i	$-0.905227\pi$
$19$	−2.12471	−	5.12951i	−0.487443	−	1.17679i	0.468559	−	0.883432i	$-0.344773\pi$
$20$	−6.06121	−	5.18881i	−1.35533	−	1.16025i
$21$	2.06153	+	2.06153i	0.449863	+	0.449863i
$22$	−2.54831	−	2.87103i	−0.543302	−	0.612106i
$23$	1.05741	+	0.706536i	0.220484	+	0.147323i	0.660907	−	0.750467i	$-0.270172\pi$
$23$	1.05741	+	0.706536i	0.220484	+	0.147323i	−0.440423	+	0.897790i	$0.645172\pi$
$24$	−0.832933	+	4.61829i	−0.170022	+	0.942705i
$25$	10.0846	+	4.17717i	2.01692	+	0.835435i
$26$	2.48282	−	1.45329i	0.486921	−	0.285014i
$27$	5.28409	−	1.05107i	1.01692	−	0.202279i
$28$	3.34111	+	1.08984i	0.631411	+	0.205960i
$29$	−1.64434	+	8.26664i	−0.305346	+	1.53508i	0.457921	+	0.888993i	$0.348594\pi$
$29$	−1.64434	+	8.26664i	−0.305346	+	1.53508i	−0.763267	+	0.646083i	$0.776406\pi$
$30$	−1.27722	−	9.27324i	−0.233187	−	1.69305i
$31$	−3.07326	−	4.59945i	−0.551973	−	0.826086i	0.445635	−	0.895215i	$-0.352978\pi$
$31$	−3.07326	−	4.59945i	−0.551973	−	0.826086i	−0.997608	+	0.0691289i	$0.977978\pi$
$32$	1.62655	+	5.41796i	0.287537	+	0.957770i
$33$		−	4.50373i		−	0.783999i
$34$	−5.51604	+	1.89031i	−0.945994	+	0.324186i
$35$	−7.01015			−1.18493
$36$	0.388609	−	0.305632i	0.0647682	−	0.0509386i
$37$	−3.15531	+	2.10831i	−0.518731	+	0.346605i	−0.787214	−	0.616680i	$-0.788477\pi$
$37$	−3.15531	+	2.10831i	−0.518731	+	0.346605i	0.268484	+	0.963284i	$0.413477\pi$
$38$	−1.07134	−	7.77849i	−0.173795	−	1.26184i
$39$	3.31031	+	0.658462i	0.530074	+	0.105438i
$40$	−6.43598	−	9.26833i	−1.01762	−	1.46545i
$41$	−0.810929	−	4.07682i	−0.126646	−	0.636692i	−0.991006	−	0.133818i	$-0.957276\pi$
$41$	−0.810929	−	4.07682i	−0.126646	−	0.636692i	0.864360	−	0.502874i	$-0.167724\pi$
$42$	2.08281	+	3.55830i	0.321385	+	0.549058i
$43$	−2.93119	+	7.07653i	−0.447003	+	1.07916i	0.526436	+	0.850215i	$0.323528\pi$
$43$	−2.93119	+	7.07653i	−0.447003	+	1.07916i	−0.973439	+	0.228946i	$0.926472\pi$
$44$	−2.45913	−	4.84005i	−0.370728	−	0.729665i
$45$	−0.547891	+	0.819977i	−0.0816747	+	0.122235i
$46$	1.19389	+	1.34508i	0.176029	+	0.198321i
$47$	−2.10492	+	2.10492i	−0.307034	+	0.307034i	−0.843758	−	0.536724i	$-0.819662\pi$
$47$	−2.10492	+	2.10492i	−0.307034	+	0.307034i	0.536724	+	0.843758i	$0.319662\pi$
$48$	−2.79232	+	6.02061i	−0.403037	+	0.869000i
$49$	−3.61450	+	1.49717i	−0.516357	+	0.213882i
$50$	12.3027	+	9.32405i	1.73987	+	1.31862i
$51$	−6.31208	−	2.63728i	−0.883868	−	0.369293i
$52$	3.91704	−	1.09987i	0.543196	−	0.152524i
$53$	5.83351	−	2.41632i	0.801295	−	0.331907i	0.0558197	−	0.998441i	$-0.482223\pi$
$53$	5.83351	−	2.41632i	0.801295	−	0.331907i	0.745475	+	0.666534i	$0.232223\pi$
$54$	7.60576	+	0.452917i	1.03501	+	0.0616342i
$55$	7.65738	+	7.65738i	1.03252	+	1.03252i
$56$	4.18126	+	2.68676i	0.558744	+	0.359033i
$57$	5.11785	−	7.65940i	0.677875	−	1.01451i
$58$	−5.20808	+	10.7219i	−0.683854	+	1.40785i
$59$	3.89198	+	1.61211i	0.506693	+	0.209879i	0.621360	−	0.783525i	$-0.286580\pi$
$59$	3.89198	+	1.61211i	0.506693	+	0.209879i	−0.114668	+	0.993404i	$0.536580\pi$
$60$	1.57107	−	13.1446i	0.202824	−	1.69696i
$61$	0.411419	+	2.06835i	0.0526769	+	0.264824i	0.998144	−	0.0608920i	$-0.0193945\pi$
$61$	0.411419	+	2.06835i	0.0526769	+	0.264824i	−0.945468	+	0.325716i	$0.894395\pi$
$62$	−2.55882	−	7.39271i	−0.324970	−	0.938875i
$63$	0.0847419	−	0.426026i	0.0106765	−	0.0536743i
$64$	0.286541	+	7.99487i	0.0358177	+	0.999358i
$65$	−6.74782	+	4.50875i	−0.836964	+	0.559242i
$66$	1.61172	−	6.16195i	0.198389	−	0.758483i
$67$		−	0.474710i		−	0.0579951i	−0.999579	−	0.0289975i	$-0.990769\pi$
$67$		−	0.474710i		−	0.0579951i	0.999579	−	0.0289975i	$-0.00923149\pi$
$68$	−8.22345	+	0.612312i	−0.997239	+	0.0742537i
$69$			2.11000i			0.254014i
$70$	−9.59119	−	2.50867i	−1.14637	−	0.299843i
$71$	9.48983	−	6.34090i	1.12624	−	0.752526i	0.154358	−	0.988015i	$-0.450669\pi$
$71$	9.48983	−	6.34090i	1.12624	−	0.752526i	0.971877	+	0.235489i	$0.0756690\pi$
$72$	0.641064	−	0.279093i	0.0755501	−	0.0328914i
$73$	−1.48381	+	7.45963i	−0.173667	+	0.873084i	0.791444	+	0.611242i	$0.209330\pi$
$73$	−1.48381	+	7.45963i	−0.173667	+	0.873084i	−0.965111	+	0.261842i	$0.915670\pi$
$74$	−5.07155	+	1.75540i	−0.589555	+	0.204061i
$75$	3.53318	+	17.7625i	0.407977	+	2.05104i
$76$	1.31783	−	11.0258i	0.151165	−	1.26475i
$77$	−4.40675	−	1.82533i	−0.502195	−	0.208016i
$78$	4.29348	+	2.08553i	0.486141	+	0.236140i
$79$	−0.405234	+	0.606476i	−0.0455924	+	0.0682339i	−0.853566	−	0.520985i	$-0.825565\pi$
$79$	−0.405234	+	0.606476i	−0.0455924	+	0.0682339i	0.807973	+	0.589219i	$0.200565\pi$
$80$	−5.48883	−	14.9840i	−0.613670	−	1.67526i
$81$	5.79637	+	5.79637i	0.644041	+	0.644041i
$82$	0.349437	−	5.86805i	0.0385889	−	0.648017i
$83$	14.3632	−	5.94945i	1.57657	−	0.653037i	0.588705	−	0.808348i	$-0.299638\pi$
$83$	14.3632	−	5.94945i	1.57657	−	0.653037i	0.987866	+	0.155311i	$0.0496379\pi$
$84$	1.57629	+	5.61378i	0.171988	+	0.612514i
$85$	15.2160	−	6.24801i	1.65040	−	0.677692i
$86$	−6.54285	+	8.63305i	−0.705533	+	0.930925i
$87$	−12.9199	+	5.35158i	−1.38515	+	0.573750i
$88$	−1.63248	−	7.50212i	−0.174023	−	0.799729i
$89$	−5.56406	+	5.56406i	−0.589789	+	0.589789i	−0.937574	−	0.347785i	$-0.886934\pi$
$89$	−5.56406	+	5.56406i	−0.589789	+	0.589789i	0.347785	+	0.937574i	$0.386934\pi$
$90$	−1.04306	+	0.925811i	−0.109948	+	0.0975891i
$91$	1.98593	−	2.97215i	0.208182	−	0.311566i
$92$	1.15210	+	2.26757i	0.120115	+	0.236410i
$93$	3.51226	−	8.47935i	0.364205	−	0.879268i
$94$	−3.63319	+	2.12665i	−0.374735	+	0.219347i
$95$	4.32122	+	21.7242i	0.443348	+	2.22886i
$96$	−5.97497	+	7.23805i	−0.609818	+	0.738731i
$97$	−2.52059	−	0.501377i	−0.255927	−	0.0509071i	0.0654591	−	0.997855i	$-0.479149\pi$
$97$	−2.52059	−	0.501377i	−0.255927	−	0.0509071i	−0.321386	+	0.946948i	$0.604149\pi$
$98$	−5.48109	+	0.754920i	−0.553673	+	0.0762584i
$99$	−0.557926	+	0.372794i	−0.0560737	+	0.0374672i
$100$	13.4957	+	17.1597i	1.34957	+	1.71597i
$101$	−12.5095			−1.24474			−0.622370	−	0.782724i	$-0.713830\pi$
$101$	−12.5095			−1.24474			−0.622370	+	0.782724i	$0.713830\pi$
$102$	−7.69232	−	5.86715i	−0.761654	−	0.580934i
$103$		−	0.883647i		−	0.0870683i	−0.999052	−	0.0435341i	$-0.986138\pi$
$103$		−	0.883647i		−	0.0870683i	0.999052	−	0.0435341i	$-0.0138617\pi$
$104$	5.75284	−	0.103060i	0.564113	−	0.0101058i
$105$	−6.46180	−	9.67077i	−0.630607	−	0.943771i
$106$	8.84604	−	1.21838i	0.859204	−	0.118340i
$107$	3.40001	−	17.0930i	0.328691	−	1.65244i	−0.364142	−	0.931343i	$-0.618638\pi$
$107$	3.40001	−	17.0930i	0.328691	−	1.65244i	0.692833	−	0.721098i	$-0.256362\pi$
$108$	10.2440	+	3.34149i	0.985731	+	0.321535i
$109$	16.2497	−	3.23227i	1.55644	−	0.309596i	0.659486	−	0.751716i	$-0.270774\pi$
$109$	16.2497	−	3.23227i	1.55644	−	0.309596i	0.896955	+	0.442121i	$0.145774\pi$
$110$	7.73643	+	13.2170i	0.737640	+	1.26019i
$111$	−5.81700	−	2.40948i	−0.552125	−	0.228698i
$112$	4.75925	+	5.17230i	0.449707	+	0.488737i
$113$	−3.17941	−	2.12441i	−0.299093	−	0.199848i	0.396964	−	0.917834i	$-0.370064\pi$
$113$	−3.17941	−	2.12441i	−0.299093	−	0.199848i	−0.696057	+	0.717986i	$0.745064\pi$
$114$	9.74318	−	8.64800i	0.912533	−	0.809960i
$115$	−3.58748	−	3.58748i	−0.334535	−	0.334535i
$116$	−10.9626	+	12.8057i	−1.01785	+	1.18898i
$117$	−0.192439	−	0.464588i	−0.0177910	−	0.0429512i
$118$	4.74804	+	3.59846i	0.437093	+	0.331265i
$119$	−5.13873	+	5.10728i	−0.471067	+	0.468184i
$120$	6.85348	−	17.4220i	0.625634	−	1.59041i
$121$	−1.38977	−	3.35521i	−0.126343	−	0.305019i
$122$	−0.177285	+	2.97711i	−0.0160506	+	0.269535i
$123$	4.87663	−	4.87663i	0.439711	−	0.439711i
$124$	−0.855362	−	11.0303i	−0.0768138	−	0.990551i
$125$	−19.6221	−	13.1111i	−1.75506	−	1.17269i
$126$	0.268402	−	0.552558i	0.0239111	−	0.0492258i
$127$	4.56457	−	11.0198i	0.405040	−	0.977852i	−0.581384	−	0.813630i	$-0.697488\pi$
$127$	4.56457	−	11.0198i	0.405040	−	0.977852i	0.986423	−	0.164223i	$-0.0525116\pi$
$128$	−2.46902	+	11.0410i	−0.218233	+	0.975897i
$129$	−12.4643	+	2.47929i	−1.09742	+	0.218290i
$130$	−10.8458	+	3.75402i	−0.951239	+	0.329249i
$131$	−8.64991	−	1.72057i	−0.755746	−	0.150327i	−0.197843	−	0.980234i	$-0.563394\pi$
$131$	−8.64991	−	1.72057i	−0.755746	−	0.150327i	−0.557903	+	0.829906i	$0.688394\pi$
$132$	4.41026	−	7.85392i	0.383864	−	0.683596i
$133$	−5.42022	−	8.11194i	−0.469993	−	0.703394i
$134$	0.169881	−	0.649492i	0.0146755	−	0.0561075i
$135$	−21.4934			−1.84986
$136$	−11.4703	−	2.10511i	−0.983573	−	0.180511i
$137$	2.20919			0.188744			0.0943718	−	0.995537i	$-0.469916\pi$
$137$	2.20919			0.188744			0.0943718	+	0.995537i	$0.469916\pi$
$138$	−0.755090	+	2.88688i	−0.0642776	+	0.245747i
$139$	10.7069	+	16.0240i	0.908147	+	1.35914i	0.933164	+	0.359452i	$0.117036\pi$
$139$	10.7069	+	16.0240i	0.908147	+	1.35914i	−0.0250163	+	0.999687i	$0.507964\pi$
$140$	−12.2248	−	6.86466i	−1.03318	−	0.580169i
$141$	−4.84408	−	0.963548i	−0.407946	−	0.0811454i
$142$	15.2530	−	5.27948i	1.28001	−	0.443044i
$143$	−5.41585	+	1.07728i	−0.452896	+	0.0900866i
$144$	0.976972	−	0.152438i	0.0814143	−	0.0127032i
$145$	12.8678	−	31.0656i	1.06861	−	2.57986i
$146$	−4.69966	+	9.67517i	−0.388946	+	0.800723i
$147$	−5.39717	−	3.60627i	−0.445151	−	0.297441i
$148$	−7.56701	+	0.586795i	−0.622005	+	0.0482343i
$149$	−0.306372	+	0.306372i	−0.0250990	+	0.0250990i	−0.719545	−	0.694446i	$-0.755650\pi$
$149$	−0.306372	+	0.306372i	−0.0250990	+	0.0250990i	0.694446	+	0.719545i	$0.255650\pi$
$150$	−1.52248	+	25.5668i	−0.124310	+	2.08752i
$151$	−7.80521	−	18.8434i	−0.635179	−	1.53346i	−0.833032	−	0.553225i	$-0.813397\pi$
$151$	−7.80521	−	18.8434i	−0.635179	−	1.53346i	0.197853	−	0.980232i	$-0.436603\pi$
$152$	5.74876	−	14.6138i	0.466286	−	1.18533i
$153$	0.195771	+	1.00025i	0.0158272	+	0.0808651i
$154$	−5.37603	−	4.07441i	−0.433213	−	0.328325i
$155$	8.44519	+	20.3885i	0.678334	+	1.63764i
$156$	5.12795	+	4.38988i	0.410565	+	0.351471i
$157$	1.99680	+	1.99680i	0.159362	+	0.159362i	0.782284	−	0.622922i	$-0.214055\pi$
$157$	1.99680	+	1.99680i	0.159362	+	0.159362i	−0.622922	+	0.782284i	$0.714055\pi$
$158$	−0.771471	+	0.684754i	−0.0613749	+	0.0544761i
$159$	8.71061	+	5.82024i	0.690796	+	0.461575i
$160$	−2.14753	−	22.4652i	−0.169777	−	1.77603i
$161$	2.06456	+	0.855170i	0.162710	+	0.0673968i
$162$	5.85621	+	10.0048i	0.460107	+	0.786052i
$163$	−11.6113	+	2.30962i	−0.909464	+	0.180904i	−0.627587	−	0.778547i	$-0.715957\pi$
$163$	−11.6113	+	2.30962i	−0.909464	+	0.180904i	−0.281878	+	0.959450i	$0.590957\pi$
$164$	2.57805	−	7.90353i	0.201312	−	0.617162i
$165$	−3.50524	+	17.6221i	−0.272883	+	1.37187i
$166$	21.7807	−	2.99989i	1.69051	−	0.232837i
$167$	4.20835	+	6.29824i	0.325652	+	0.487373i	0.957784	−	0.287488i	$-0.0928201\pi$
$167$	4.20835	+	6.29824i	0.325652	+	0.487373i	−0.632132	+	0.774860i	$0.717820\pi$
$168$	0.147702	+	8.24480i	0.0113955	+	0.636100i
$169$			8.86177i			0.681675i
$170$	23.0542	−	3.10322i	1.76818	−	0.238006i
$171$	−1.37248			−0.104956
$172$	−12.0413	+	9.47018i	−0.918139	+	0.722094i
$173$	9.61075	−	6.42170i	0.730692	−	0.488233i	−0.133719	−	0.991019i	$-0.542692\pi$
$173$	9.61075	−	6.42170i	0.730692	−	0.488233i	0.864410	+	0.502787i	$0.167692\pi$
$174$	−19.5919	+	2.69843i	−1.48526	+	0.204567i
$175$	18.8120	+	3.74193i	1.42205	+	0.282864i
$176$	0.451192	−	10.8485i	0.0340099	−	0.817737i
$177$	1.36357	+	6.85514i	0.102492	+	0.515264i
$178$	−9.60384	+	5.62151i	−0.719839	+	0.421350i
$179$	3.08040	−	7.43674i	0.230240	−	0.555848i	−0.765966	−	0.642881i	$-0.777739\pi$
$179$	3.08040	−	7.43674i	0.230240	−	0.555848i	0.996205	+	0.0870337i	$0.0277388\pi$
$180$	−1.75841	+	0.893412i	−0.131064	+	0.0665910i
$181$	0.209700	−	0.313838i	0.0155869	−	0.0233274i	−0.823594	−	0.567179i	$-0.808035\pi$
$181$	0.209700	−	0.313838i	0.0155869	−	0.0233274i	0.839181	+	0.543852i	$0.183035\pi$
$182$	3.78074	−	3.35577i	0.280247	−	0.248746i
$183$	−2.47412	+	2.47412i	−0.182893	+	0.182893i
$184$	0.764817	+	3.51475i	0.0563831	+	0.259111i
$185$	13.9869	−	5.79356i	1.02834	−	0.425951i
$186$	7.83987	−	10.3444i	0.574847	−	0.758490i
$187$	11.1920	+	0.0343542i	0.818440	+	0.00251223i
$188$	−5.73193	+	1.60947i	−0.418044	+	0.117383i
$189$	8.74639	−	3.62287i	0.636207	−	0.263525i
$190$	−1.86206	+	31.2692i	−0.135088	+	2.26851i
$191$	−9.71409	−	9.71409i	−0.702887	−	0.702887i	0.262142	−	0.965029i	$-0.415571\pi$
$191$	−9.71409	−	9.71409i	−0.702887	−	0.702887i	−0.965029	+	0.262142i	$0.915571\pi$
$192$	−10.7651	+	7.76479i	−0.776904	+	0.560375i
$193$	−5.42709	+	8.12221i	−0.390650	+	0.584650i	−0.973713	−	0.227777i	$-0.926854\pi$
$193$	−5.42709	+	8.12221i	−0.390650	+	0.584650i	0.583063	+	0.812427i	$0.301854\pi$
$194$	−3.26922	−	1.58800i	−0.234716	−	0.114012i
$195$	−12.4400	−	5.15281i	−0.890846	−	0.369001i
$196$	−7.76931	−	0.928605i	−0.554950	−	0.0663289i
$197$	−3.67141	−	18.4574i	−0.261577	−	1.31504i	−0.858532	−	0.512761i	$-0.828623\pi$
$197$	−3.67141	−	18.4574i	−0.261577	−	1.31504i	0.596955	−	0.802275i	$-0.296377\pi$
$198$	−0.896756	+	0.310391i	−0.0637297	+	0.0220586i
$199$	−1.48032	+	7.44206i	−0.104937	+	0.527553i	0.892180	+	0.451679i	$0.149175\pi$
$199$	−1.48032	+	7.44206i	−0.104937	+	0.527553i	−0.997117	+	0.0758743i	$0.975825\pi$
$200$	12.3238	+	28.3073i	0.871427	+	2.00163i
$201$	0.654881	−	0.437577i	0.0461917	−	0.0308643i
$202$	−17.1153	−	4.47667i	−1.20423	−	0.314978i
$203$			14.8106i			1.03950i
$204$	−8.42490	−	10.7801i	−0.589861	−	0.754761i
$205$			16.5828i			1.15819i
$206$	0.316224	−	1.20899i	0.0220324	−	0.0842346i
$207$	0.261389	−	0.174654i	0.0181678	−	0.0121393i
$208$	7.90785	+	1.91772i	0.548310	+	0.132970i
$209$	−2.94023	+	14.7816i	−0.203380	+	1.02246i
$210$	−5.38014	−	15.5439i	−0.371265	−	1.07263i
$211$	−0.296827	−	1.49225i	−0.0204344	−	0.102731i	0.969222	−	0.246188i	$-0.0791780\pi$
$211$	−0.296827	−	1.49225i	−0.0204344	−	0.102731i	−0.989657	+	0.143457i	$0.954178\pi$
$212$	12.5390	+	1.49870i	0.861185	+	0.102931i
$213$	17.4950	+	7.24668i	1.19874	+	0.496534i
$214$	10.7688	−	22.1697i	0.736139	−	1.51549i
$215$	16.9767	−	25.4075i	1.15780	−	1.73277i
$216$	12.8199	+	8.23773i	0.872286	+	0.560507i
$217$	−6.87325	−	6.87325i	−0.466587	−	0.466587i
$218$	23.3894	+	1.39282i	1.58413	+	0.0943336i
$219$	−11.6586	+	4.82915i	−0.787815	+	0.326324i
$220$	5.85501	+	20.8519i	0.394745	+	1.40584i
$221$	−1.66156	+	8.22126i	−0.111769	+	0.553022i
$222$	−7.09648	−	5.37831i	−0.476285	−	0.360968i
$223$	5.90153	−	2.44449i	0.395195	−	0.163695i	−0.176231	−	0.984349i	$-0.556390\pi$
$223$	5.90153	−	2.44449i	0.395195	−	0.163695i	0.571426	+	0.820654i	$0.306390\pi$
$224$	4.66057	+	8.77983i	0.311397	+	0.586627i
$225$	1.90798	−	1.90798i	0.127198	−	0.127198i
$226$	−3.58977	−	4.04438i	−0.238788	−	0.269028i
$227$	7.11025	−	10.6412i	0.471924	−	0.706284i	−0.516788	−	0.856113i	$-0.672872\pi$
$227$	7.11025	−	10.6412i	0.471924	−	0.706284i	0.988712	+	0.149829i	$0.0478724\pi$
$228$	16.4253	−	8.34536i	1.08779	−	0.552685i
$229$	−9.46723	+	22.8559i	−0.625612	+	1.51036i	0.219412	+	0.975632i	$0.429586\pi$
$229$	−9.46723	+	22.8559i	−0.625612	+	1.51036i	−0.845024	+	0.534729i	$0.820414\pi$
$230$	−3.62452	−	6.19217i	−0.238994	−	0.408300i
$231$	−1.54392	−	7.76183i	−0.101583	−	0.510691i
$232$	−19.5815	+	13.5975i	−1.28559	+	0.892721i
$233$	−1.74882	−	0.347862i	−0.114569	−	0.0227892i	0.137473	−	0.990506i	$-0.456102\pi$
$233$	−1.74882	−	0.347862i	−0.114569	−	0.0227892i	−0.252042	+	0.967716i	$0.581102\pi$
$234$	−0.0970333	−	0.704510i	−0.00634327	−	0.0460552i
$235$	9.87431	−	6.59780i	0.644129	−	0.430393i
$236$	5.20845	+	6.62251i	0.339041	+	0.431089i
$237$	−1.21019			−0.0786105
$238$	−8.85845	+	5.14875i	−0.574208	+	0.333744i
$239$			25.4829i			1.64835i	0.566335	+	0.824175i	$0.308361\pi$
$239$			25.4829i			1.64835i	−0.566335	+	0.824175i	$0.691639\pi$
$240$	15.6115	−	21.3840i	1.00772	−	1.38033i
$241$	10.4034	+	15.5698i	0.670141	+	1.00294i	0.998298	+	0.0583139i	$0.0185724\pi$
$241$	10.4034	+	15.5698i	0.670141	+	1.00294i	−0.328157	+	0.944623i	$0.606428\pi$
$242$	−0.700764	−	5.08789i	−0.0450468	−	0.327062i
$243$	0.499866	−	2.51300i	0.0320664	−	0.161209i
$244$	−1.30796	+	4.00980i	−0.0837333	+	0.256701i
$245$	15.3079	−	3.04493i	0.977987	−	0.194534i
$246$	8.41730	−	4.92698i	0.536668	−	0.314132i
$247$	−10.4348	−	4.32223i	−0.663950	−	0.275017i
$248$	2.77704	−	15.3976i	0.176342	−	0.977750i
$249$	21.4472	+	14.3306i	1.35916	+	0.908163i
$250$	−22.1548	−	24.9604i	−1.40119	−	1.57864i
$251$	−4.97402	−	4.97402i	−0.313957	−	0.313957i	0.532483	−	0.846440i	$-0.321259\pi$
$251$	−4.97402	−	4.97402i	−0.313957	−	0.313957i	−0.846440	+	0.532483i	$0.821259\pi$
$252$	0.564963	−	0.659951i	0.0355893	−	0.0415730i
$253$	−1.32105	−	3.18930i	−0.0830539	−	0.200510i
$254$	10.1888	−	13.4437i	0.639300	−	0.843533i
$255$	22.6451	+	15.2317i	1.41809	+	0.953848i
$256$	−7.32925	+	14.2226i	−0.458078	+	0.888912i
$257$	−2.37545	−	5.73484i	−0.148176	−	0.357729i	0.832312	−	0.554308i	$-0.187017\pi$
$257$	−2.37545	−	5.73484i	−0.148176	−	0.357729i	−0.980488	+	0.196578i	$0.937017\pi$
$258$	−17.9407	−	1.06835i	−1.11694	−	0.0665127i
$259$	−4.71518	+	4.71518i	−0.292987	+	0.292987i
$260$	−16.1825	+	1.25490i	−1.00360	+	0.0778253i
$261$	1.73239	+	1.15755i	0.107232	+	0.0716505i
$262$	−11.2190	−	5.44954i	−0.693110	−	0.336674i
$263$	−2.91136	+	7.02865i	−0.179522	+	0.433405i	−0.987867	−	0.155305i	$-0.950364\pi$
$263$	−2.91136	+	7.02865i	−0.179522	+	0.433405i	0.808344	+	0.588710i	$0.200364\pi$
$264$	8.84468	−	9.16736i	0.544353	−	0.564212i
$265$	−24.7058	+	4.91429i	−1.51766	+	0.301882i
$266$	−4.51292	−	13.0383i	−0.276705	−	0.799432i
$267$	−12.8047	−	2.54701i	−0.783633	−	0.155874i
$268$	0.464858	−	0.827832i	0.0283957	−	0.0505679i
$269$	0.468100	+	0.700560i	0.0285405	+	0.0427139i	0.845466	−	0.534030i	$-0.179323\pi$
$269$	0.468100	+	0.700560i	0.0285405	+	0.0427139i	−0.816925	+	0.576744i	$0.804323\pi$
$270$	−29.4070	−	7.69170i	−1.78966	−	0.468102i
$271$	0.495347			0.0300902			0.0150451	−	0.999887i	$-0.495211\pi$
$271$	0.495347			0.0300902			0.0150451	+	0.999887i	$0.495211\pi$
$272$	−14.9402	−	6.98498i	−0.905884	−	0.423527i
$273$	5.93079			0.358947
$274$	3.02258	+	0.790586i	0.182601	+	0.0477610i
$275$	−16.4614	−	24.6362i	−0.992660	−	1.48562i
$276$	−2.06621	+	3.67957i	−0.124371	+	0.221484i
$277$	−7.81295	−	1.55409i	−0.469434	−	0.0933763i	−0.0452959	−	0.998974i	$-0.514423\pi$
$277$	−7.81295	−	1.55409i	−0.469434	−	0.0933763i	−0.424139	+	0.905597i	$0.639423\pi$
$278$	8.91464	+	25.7554i	0.534665	+	1.54471i
$279$	−1.34115	+	0.266772i	−0.0802928	+	0.0159712i
$280$	−14.2692	−	13.7669i	−0.852746	−	0.822731i
$281$	−7.93869	+	19.1657i	−0.473583	+	1.14333i	0.488986	+	0.872292i	$0.337367\pi$
$281$	−7.93869	+	19.1657i	−0.473583	+	1.14333i	−0.962569	+	0.271038i	$0.912633\pi$
$282$	−6.28279	−	3.05183i	−0.374135	−	0.181734i
$283$	3.88907	+	2.59860i	0.231181	+	0.154470i	0.665766	−	0.746160i	$-0.268105\pi$
$283$	3.88907	+	2.59860i	0.231181	+	0.154470i	−0.434585	+	0.900631i	$0.643105\pi$
$284$	22.7583	−	1.76483i	1.35046	−	0.104723i
$285$	−25.9862	+	25.9862i	−1.53929	+	1.53929i
$286$	−7.79541	−	0.464210i	−0.460952	−	0.0274493i
$287$	−2.79514	−	6.74808i	−0.164992	−	0.398326i
$288$	1.39123	+	0.141058i	0.0819791	+	0.00831191i
$289$	6.60191	−	15.6657i	0.388348	−	0.921513i
$290$	28.7228	−	37.8987i	1.68666	−	2.22549i
$291$	−1.63176	−	3.93941i	−0.0956553	−	0.230932i
$292$	−9.89239	+	11.5556i	−0.578908	+	0.676241i
$293$	−14.3466	−	14.3466i	−0.838135	−	0.838135i	0.150478	−	0.988613i	$-0.451919\pi$
$293$	−14.3466	−	14.3466i	−0.838135	−	0.838135i	−0.988613	+	0.150478i	$0.951919\pi$
$294$	−6.09379	−	6.86550i	−0.355397	−	0.400404i
$295$	−13.9737	−	9.33693i	−0.813580	−	0.543617i
$296$	−10.5631	−	1.90510i	−0.613966	−	0.110732i
$297$	−13.5113	−	5.59656i	−0.784005	−	0.324745i
$298$	−0.528814	+	0.309535i	−0.0306334	+	0.0179309i
$299$	2.53733	−	0.504706i	0.146737	−	0.0291879i
$300$	−11.2324	+	34.4353i	−0.648506	+	1.98812i
$301$	−2.62578	+	13.2007i	−0.151347	+	0.760875i
$302$	−3.93562	−	28.5745i	−0.226469	−	1.64428i
$303$	−11.5310	−	17.2573i	−0.662436	−	0.991406i
$304$	13.0951	−	17.9371i	0.751056	−	1.02876i
$305$		−	8.41316i		−	0.481736i
$306$	−0.0900986	+	1.43858i	−0.00515060	+	0.0822383i
$307$	−10.3982			−0.593455			−0.296727	−	0.954962i	$-0.595895\pi$
$307$	−10.3982			−0.593455			−0.296727	+	0.954962i	$0.595895\pi$
$308$	−5.89734	−	7.49843i	−0.336032	−	0.427263i
$309$	1.21902	−	0.814526i	0.0693479	−	0.0463368i
$310$	4.25832	+	30.9175i	0.241856	+	1.75599i
$311$	32.5176	+	6.46816i	1.84391	+	0.366776i	0.988505	−	0.151191i	$-0.0483109\pi$
$311$	32.5176	+	6.46816i	1.84391	+	0.366776i	0.855401	+	0.517967i	$0.173311\pi$
$312$	5.44502	+	7.84127i	0.308264	+	0.443925i
$313$	−4.09832	−	20.6037i	−0.231651	−	1.16459i	−0.905049	−	0.425307i	$-0.860166\pi$
$313$	−4.09832	−	20.6037i	−0.231651	−	1.16459i	0.673398	−	0.739280i	$-0.264834\pi$
$314$	2.01741	+	3.44657i	0.113849	+	0.194501i
$315$	−0.663151	+	1.60099i	−0.0373643	+	0.0902054i
$316$	−1.30056	+	0.660791i	−0.0731624	+	0.0371724i
$317$	−4.02641	+	6.02595i	−0.226146	+	0.338451i	−0.927139	−	0.374716i	$-0.877740\pi$
$317$	−4.02641	+	6.02595i	−0.226146	+	0.338451i	0.700994	+	0.713167i	$0.252740\pi$
$318$	9.83489	+	11.0804i	0.551513	+	0.621357i
$319$	16.1780	−	16.1780i	0.905795	−	0.905795i
$320$	5.10121	−	31.5051i	0.285167	−	1.76119i
$321$	26.7145	−	11.0655i	1.49106	−	0.617616i
$322$	2.51867	+	1.90886i	0.140360	+	0.106377i
$323$	18.9949	+	12.7765i	1.05691	+	0.710905i
$324$	4.43204	+	15.7842i	0.246224	+	0.876898i
$325$	20.5147	−	8.49747i	1.13795	−	0.471355i
$326$	−16.7129	−	0.995240i	−0.925642	−	0.0551212i
$327$	19.4377	+	19.4377i	1.07491	+	1.07491i
$328$	6.35563	−	9.89092i	0.350931	−	0.546135i
$329$	−2.90607	+	4.34925i	−0.160217	+	0.239782i
$330$	−11.1021	+	22.8559i	−0.611150	+	1.25817i
$331$	13.2900	+	5.50492i	0.730487	+	0.302578i	0.716752	−	0.697328i	$-0.245628\pi$
$331$	13.2900	+	5.50492i	0.730487	+	0.302578i	0.0137350	+	0.999906i	$0.495628\pi$
$332$	30.8736	+	3.69008i	1.69441	+	0.202519i
$333$	0.183011	+	0.920059i	0.0100289	+	0.0504189i
$334$	3.50390	+	10.1232i	0.191725	+	0.553916i
$335$	−0.369466	+	1.85743i	−0.0201861	+	0.101482i
$336$	−2.74842	+	11.3333i	−0.149939	+	0.618281i
$337$	4.56567	−	3.05068i	0.248708	−	0.166181i	−0.424968	−	0.905208i	$-0.639715\pi$
$337$	4.56567	−	3.05068i	0.248708	−	0.166181i	0.673675	+	0.739027i	$0.264715\pi$
$338$	−3.17130	+	12.1246i	−0.172496	+	0.659489i
$339$		−	6.34435i		−	0.344578i
$340$	32.6530	+	4.00446i	1.77086	+	0.217172i
$341$			15.0157i			0.813145i
$342$	−1.87781	−	0.491159i	−0.101540	−	0.0265589i
$343$	−15.9434	+	10.6530i	−0.860861	+	0.575209i
$344$	−19.8637	+	8.64785i	−1.07098	+	0.466261i
$345$	1.64221	−	8.25594i	0.0884135	−	0.444485i
$346$	15.4474	−	5.34675i	0.830456	−	0.287443i
$347$	0.457262	+	2.29881i	0.0245471	+	0.123407i	0.991116	−	0.133000i	$-0.0424612\pi$
$347$	0.457262	+	2.29881i	0.0245471	+	0.123407i	−0.966569	+	0.256407i	$0.917461\pi$
$348$	−27.7711	−	3.31926i	−1.48868	−	0.177931i
$349$	−2.99685	−	1.24134i	−0.160418	−	0.0664472i	0.301030	−	0.953615i	$-0.402670\pi$
$349$	−2.99685	−	1.24134i	−0.160418	−	0.0664472i	−0.461447	+	0.887168i	$0.652670\pi$
$350$	24.3992	+	11.8518i	1.30419	+	0.633503i
$351$	6.08895	−	9.11276i	0.325004	−	0.486403i
$352$	4.49959	−	14.6813i	0.239829	−	0.782517i
$353$	9.74006	+	9.74006i	0.518411	+	0.518411i	0.917090	−	0.398679i	$-0.130531\pi$
$353$	9.74006	+	9.74006i	0.518411	+	0.518411i	−0.398679	+	0.917090i	$0.630531\pi$
$354$	−0.587577	+	9.86709i	−0.0312294	+	0.524430i
$355$	−42.0666	+	17.4245i	−2.23266	+	0.924799i
$356$	−15.1516	+	4.25441i	−0.803032	+	0.225483i
$357$	−11.7825	−	2.38130i	−0.623594	−	0.126032i
$358$	6.87589	−	9.07248i	0.363402	−	0.479496i
$359$	−0.00216710		0.000897642i	−0.000114375		4.73758e-5i	−0.382741	−	0.923856i	$-0.625020\pi$
$359$	−0.00216710		0.000897642i	−0.000114375		4.73758e-5i	0.382626	+	0.923903i	$0.375020\pi$
$360$	−2.72555	+	0.593086i	−0.143649	+	0.0312584i
$361$	−8.36248	+	8.36248i	−0.440130	+	0.440130i
$362$	0.399219	−	0.354345i	0.0209825	−	0.0186240i
$363$	3.34757	−	5.01000i	0.175702	−	0.262957i
$364$	6.37367	−	3.23833i	0.334071	−	0.169735i
$365$	11.6116	−	28.0329i	0.607780	−	1.46731i
$366$	−4.27046	+	2.49967i	−0.223221	+	0.130660i
$367$	0.489357	+	2.46017i	0.0255442	+	0.128420i	0.991453	−	0.130462i	$-0.0416461\pi$
$367$	0.489357	+	2.46017i	0.0255442	+	0.128420i	−0.965909	+	0.258882i	$0.916646\pi$
$368$	−0.211384	+	5.08253i	−0.0110191	+	0.264945i
$369$	−1.00778	−	0.200460i	−0.0524630	−	0.0104355i
$370$	21.2100	−	2.92129i	1.10265	−	0.151871i
$371$	9.22526	−	6.16412i	0.478952	−	0.320025i
$372$	14.4283	−	11.3475i	0.748072	−	0.588341i
$373$	−14.0865			−0.729370			−0.364685	−	0.931131i	$-0.618823\pi$
$373$	−14.0865			−0.729370			−0.364685	+	0.931131i	$0.618823\pi$
$374$	15.3004	+	4.05220i	0.791167	+	0.209534i
$375$		−	39.1550i		−	2.02196i
$376$	−8.41832	+	0.150811i	−0.434142	+	0.00777747i
$377$	9.52580	+	14.2564i	0.490603	+	0.734240i
$378$	13.2632	−	1.82676i	0.682185	−	0.0939585i
$379$	−2.62326	+	13.1880i	−0.134748	+	0.677424i	0.853068	+	0.521799i	$0.174739\pi$
$379$	−2.62326	+	13.1880i	−0.134748	+	0.677424i	−0.987816	+	0.155625i	$0.950261\pi$
$380$	−13.7377	+	42.1158i	−0.704730	+	2.16049i
$381$	19.4098	−	3.86085i	0.994394	−	0.197797i
$382$	−9.81438	−	16.7670i	−0.502147	−	0.857874i
$383$	−32.2120	−	13.3426i	−1.64595	−	0.681777i	−0.649076	−	0.760724i	$-0.724844\pi$
$383$	−32.2120	−	13.3426i	−1.64595	−	0.681777i	−0.996879	+	0.0789472i	$0.974844\pi$
$384$	−17.5074	+	6.77125i	−0.893420	+	0.345544i
$385$	15.8219	+	10.5719i	0.806359	+	0.538792i
$386$	−10.3319	+	9.17055i	−0.525880	+	0.466769i
$387$	1.33886	+	1.33886i	0.0680581	+	0.0680581i
$388$	−3.90461	−	3.34261i	−0.198227	−	0.169695i
$389$	7.40045	+	17.8663i	0.375218	+	0.905856i	0.992848	+	0.119387i	$0.0380929\pi$
$389$	7.40045	+	17.8663i	0.375218	+	0.905856i	−0.617630	+	0.786469i	$0.711907\pi$
$390$	−15.1762	−	11.5018i	−0.768478	−	0.582417i
$391$	−5.24346	−	0.0160949i	−0.265173	−	0.000813956i
$392$	−10.2975	−	4.05085i	−0.520105	−	0.204599i
$393$	−5.59970	−	13.5189i	−0.282467	−	0.681937i
$394$	1.58205	−	26.5670i	0.0797023	−	1.33843i
$395$	2.05760	−	2.05760i	0.103529	−	0.103529i
$396$	−1.33801	+	0.103758i	−0.0672374	+	0.00521403i
$397$	11.2307	+	7.50410i	0.563652	+	0.376620i	0.804509	−	0.593940i	$-0.202429\pi$
$397$	11.2307	+	7.50410i	0.563652	+	0.376620i	−0.240857	+	0.970561i	$0.577429\pi$
$398$	−4.68858	+	9.65237i	−0.235017	+	0.483830i
$399$	6.19449	−	14.9548i	0.310112	−	0.748677i
$400$	6.73118	+	43.1399i	0.336559	+	2.15700i
$401$	38.5529	−	7.66865i	1.92524	−	0.382954i	0.925247	−	0.379366i	$-0.123858\pi$
$401$	38.5529	−	7.66865i	1.92524	−	0.382954i	0.999994	−	0.00358817i	$-0.00114215\pi$
$402$	1.05259	−	0.364330i	0.0524985	−	0.0181711i
$403$	−11.0367	−	2.19535i	−0.549779	−	0.109358i
$404$	−21.8149	−	12.2498i	−1.08533	−	0.609453i
$405$	−18.1685	−	27.1911i	−0.902801	−	1.35114i
$406$	−5.30016	+	20.2637i	−0.263042	+	1.00567i
$407$	10.3010			0.510604
$408$	−7.66903	−	17.7642i	−0.379673	−	0.879459i
$409$	11.9403			0.590408			0.295204	−	0.955434i	$-0.404612\pi$
$409$	11.9403			0.590408			0.295204	+	0.955434i	$0.404612\pi$
$410$	−5.93435	+	22.6883i	−0.293077	+	1.12050i
$411$	2.03638	+	3.04766i	0.100447	+	0.150330i
$412$	0.865307	−	1.54096i	0.0426306	−	0.0759178i
$413$	7.26017	+	1.44414i	0.357249	+	0.0710613i
$414$	0.420131	−	0.145419i	0.0206483	−	0.00714693i
$415$	−60.8304	+	12.0999i	−2.98605	+	0.593962i
$416$	10.1331	+	5.45372i	0.496817	+	0.267391i
$417$	−12.2364	+	29.5412i	−0.599217	+	1.44664i
$418$	−9.31255	+	19.1717i	−0.455492	+	0.937719i
$419$	−8.58305	−	5.73501i	−0.419309	−	0.280174i	0.327964	−	0.944690i	$-0.393637\pi$
$419$	−8.58305	−	5.73501i	−0.419309	−	0.280174i	−0.747273	+	0.664517i	$0.768637\pi$
$420$	−1.79848	−	23.1922i	−0.0877567	−	1.13167i
$421$	−19.1617	+	19.1617i	−0.933883	+	0.933883i	−0.997946	−	0.0640632i	$-0.979594\pi$
$421$	−19.1617	+	19.1617i	−0.933883	+	0.933883i	0.0640632	+	0.997946i	$0.479594\pi$
$422$	0.127906	−	2.14790i	0.00622634	−	0.104558i
$423$	0.281602	+	0.679847i	0.0136919	+	0.0330553i
$424$	16.6194	+	6.53775i	0.807111	+	0.317501i
$425$	−44.1676	+	8.64464i	−2.14245	+	0.419327i
$426$	21.3432	+	16.1756i	1.03408	+	0.783712i
$427$	1.41810	+	3.42359i	0.0686266	+	0.165679i
$428$	22.6674	−	26.4785i	1.09567	−	1.27989i
$429$	−6.47836	−	6.47836i	−0.312778	−	0.312778i
$430$	32.3197	−	28.6868i	1.55859	−	1.38340i
$431$	−1.10864	−	0.740767i	−0.0534011	−	0.0356815i	0.528583	−	0.848882i	$-0.322723\pi$
$431$	−1.10864	−	0.740767i	−0.0534011	−	0.0356815i	−0.581984	+	0.813200i	$0.697723\pi$
$432$	14.5921	+	15.8585i	0.702062	+	0.762994i
$433$	−27.7088	−	11.4773i	−1.33160	−	0.551566i	−0.400488	−	0.916302i	$-0.631159\pi$
$433$	−27.7088	−	11.4773i	−1.33160	−	0.551566i	−0.931111	+	0.364736i	$0.881159\pi$
$434$	−6.94421	−	11.8636i	−0.333333	−	0.569469i
$435$	54.7175	−	10.8840i	2.62350	−	0.521847i
$436$	31.5026	+	10.2758i	1.50870	+	0.492122i
$437$	1.37750	−	6.92516i	0.0658948	−	0.331276i
$438$	−17.6793	+	2.43500i	−0.844750	+	0.116349i
$439$	18.7585	+	28.0741i	0.895296	+	1.33990i	0.940096	+	0.340909i	$0.110735\pi$
$439$	18.7585	+	28.0741i	0.895296	+	1.33990i	−0.0448004	+	0.998996i	$0.514265\pi$
$440$	0.548627	+	30.6246i	0.0261548	+	1.45997i
$441$			0.967114i			0.0460530i
$442$	−5.21541	+	10.6536i	−0.248072	+	0.506740i
$443$	26.4412			1.25626			0.628130	−	0.778108i	$-0.283821\pi$
$443$	26.4412			1.25626			0.628130	+	0.778108i	$0.283821\pi$
$444$	−7.78461	−	9.89809i	−0.369441	−	0.469743i
$445$	26.1014	−	17.4404i	1.23732	−	0.826753i
$446$	8.94918	−	1.23259i	0.423756	−	0.0583646i
$447$	−0.705060	−	0.140245i	−0.0333482	−	0.00663337i
$448$	3.23455	+	13.6803i	0.152818	+	0.646333i
$449$	−4.71747	−	23.7163i	−0.222631	−	1.11924i	−0.916774	−	0.399406i	$-0.869216\pi$
$449$	−4.71747	−	23.7163i	−0.222631	−	1.11924i	0.694143	−	0.719837i	$-0.255784\pi$
$450$	3.29326	−	1.92767i	0.155246	−	0.0908714i
$451$	−4.31790	+	10.4243i	−0.203322	+	0.490862i
$452$	−3.46415	−	6.81812i	−0.162940	−	0.320697i
$453$	18.8006	−	28.1370i	0.883328	−	1.32199i
$454$	13.5363	−	12.0147i	0.635288	−	0.563879i
$455$	−10.0837	+	10.0837i	−0.472731	+	0.472731i
$456$	25.4593	−	5.54001i	1.19224	−	0.259435i
$457$	−3.16113	+	1.30938i	−0.147871	+	0.0612504i	−0.455392	−	0.890291i	$-0.650501\pi$
$457$	−3.16113	+	1.30938i	−0.147871	+	0.0612504i	0.307520	+	0.951542i	$0.400501\pi$
$458$	−21.1322	+	27.8832i	−0.987443	+	1.30290i
$459$	−15.7556	+	15.6592i	−0.735408	+	0.730907i
$460$	−2.74307	−	9.76913i	−0.127897	−	0.455488i
$461$	−20.0966	+	8.32428i	−0.935992	+	0.387700i	−0.797948	−	0.602726i	$-0.794081\pi$
$461$	−20.0966	+	8.32428i	−0.935992	+	0.387700i	−0.138043	+	0.990426i	$0.544081\pi$
$462$	0.665292	−	11.1721i	0.0309522	−	0.519775i
$463$	−18.4645	−	18.4645i	−0.858120	−	0.858120i	0.132996	−	0.991117i	$-0.457540\pi$
$463$	−18.4645	−	18.4645i	−0.858120	−	0.858120i	−0.991117	+	0.132996i	$0.957540\pi$
$464$	−31.6572	+	11.5965i	−1.46965	+	0.538352i
$465$	−20.3421	+	30.4441i	−0.943343	+	1.41181i
$466$	−2.26823	−	1.10178i	−0.105074	−	0.0510389i
$467$	10.3991	+	4.30747i	0.481215	+	0.199326i	0.610085	−	0.792336i	$-0.291135\pi$
$467$	10.3991	+	4.30747i	0.481215	+	0.199326i	−0.128870	+	0.991661i	$0.541135\pi$
$468$	0.119358	−	0.998625i	0.00551732	−	0.0461615i
$469$	−0.162735	−	0.818125i	−0.00751441	−	0.0377775i
$470$	15.8710	−	5.49338i	0.732075	−	0.253391i
$471$	−0.914054	+	4.59526i	−0.0421174	+	0.211739i
$472$	4.75618	+	10.9247i	0.218921	+	0.502852i
$473$	17.2877	−	11.5513i	0.794888	−	0.531127i
$474$	−1.65577	−	0.433083i	−0.0760520	−	0.0198921i
$475$		−	60.6043i		−	2.78072i
$476$	−13.9626	+	3.87435i	−0.639973	+	0.177580i
$477$		−	1.56085i		−	0.0714662i
$478$	−9.11937	+	34.8653i	−0.417110	+	1.59470i
$479$	−13.6004	+	9.08748i	−0.621417	+	0.415217i	−0.826030	−	0.563625i	$-0.809406\pi$
$479$	−13.6004	+	9.08748i	−0.621417	+	0.415217i	0.204614	+	0.978843i	$0.434406\pi$
$480$	29.0120	−	23.6705i	1.32421	−	1.08041i
$481$	−1.50605	+	7.57142i	−0.0686700	+	0.345227i
$482$	8.66194	+	25.0253i	0.394540	+	1.13987i
$483$	0.723329	+	3.63642i	0.0329126	+	0.165463i
$484$	0.861990	−	7.21197i	0.0391814	−	0.327817i
$485$	9.47226	+	3.92354i	0.430113	+	0.178159i
$486$	1.58322	−	3.25936i	0.0718162	−	0.147848i
$487$	11.2391	−	16.8204i	0.509290	−	0.762207i	−0.484342	−	0.874879i	$-0.660941\pi$
$487$	11.2391	−	16.8204i	0.509290	−	0.762207i	0.993632	+	0.112672i	$0.0359410\pi$
$488$	−3.22449	+	5.01809i	−0.145966	+	0.227158i
$489$	−13.8892	−	13.8892i	−0.628092	−	0.628092i
$490$	22.0338	+	1.31209i	0.995384	+	0.0592743i
$491$	−19.3271	+	8.00557i	−0.872222	+	0.361286i	−0.773475	−	0.633826i	$-0.781483\pi$
$491$	−19.3271	+	8.00557i	−0.872222	+	0.361286i	−0.0987466	+	0.995113i	$0.531483\pi$
$492$	13.2796	−	3.72878i	0.598691	−	0.168107i
$493$	−13.2004	−	32.1473i	−0.594516	−	1.44784i
$494$	−12.7300	−	9.64784i	−0.572748	−	0.434077i
$495$	2.47318	−	1.02442i	0.111161	−	0.0460445i
$496$	9.30974	−	20.0730i	0.418020	−	0.901306i
$497$	14.1812	−	14.1812i	0.636116	−	0.636116i
$498$	24.2154	+	27.2821i	1.08512	+	1.22254i
$499$	5.07487	−	7.59508i	0.227182	−	0.340002i	−0.700314	−	0.713835i	$-0.746957\pi$
$499$	5.07487	−	7.59508i	0.227182	−	0.340002i	0.927496	+	0.373833i	$0.121957\pi$
$500$	−21.3794	−	42.0789i	−0.956118	−	1.88183i
$501$	−4.80950	+	11.6112i	−0.214873	+	0.518749i
$502$	−5.02537	−	8.58540i	−0.224293	−	0.383185i
$503$	4.29208	+	21.5777i	0.191374	+	0.962103i	0.950397	+	0.311039i	$0.100677\pi$
$503$	4.29208	+	21.5777i	0.191374	+	0.962103i	−0.759023	+	0.651064i	$0.774323\pi$
$504$	1.00915	−	0.700757i	0.0449510	−	0.0312142i
$505$	48.9466	+	9.73609i	2.17810	+	0.433250i
$506$	−0.666114	−	4.83632i	−0.0296124	−	0.215000i
$507$	−12.2252	+	8.16859i	−0.542938	+	0.362780i
$508$	18.7511	−	14.7473i	0.831947	−	0.654306i
$509$	−7.32849			−0.324830			−0.162415	−	0.986723i	$-0.551928\pi$
$509$	−7.32849			−0.324830			−0.162415	+	0.986723i	$0.551928\pi$
$510$	25.5319	+	28.9437i	1.13057	+	1.28165i
$511$			13.3648i			0.591222i
$512$	−15.1175	+	16.8363i	−0.668106	+	0.744066i
$513$	−16.6187	−	24.8716i	−0.733732	−	1.09811i
$514$	−1.19777	−	8.69641i	−0.0528314	−	0.383582i
$515$	−0.687740	+	3.45750i	−0.0303054	+	0.152356i
$516$	−24.1639	−	7.88200i	−1.06375	−	0.346986i
$517$	7.92519	−	1.57642i	0.348549	−	0.0693308i
$518$	−8.13864	+	4.76386i	−0.357591	+	0.209312i
$519$	17.7180	+	7.33902i	0.777732	+	0.322147i
$520$	−22.5897	−	4.07418i	−0.990626	−	0.178664i
$521$	−21.4087	−	14.3048i	−0.937932	−	0.626706i	−0.0101977	−	0.999948i	$-0.503246\pi$
$521$	−21.4087	−	14.3048i	−0.937932	−	0.626706i	−0.927734	+	0.373242i	$0.878246\pi$
$522$	1.95599	+	2.20370i	0.0856116	+	0.0964534i
$523$	3.54456	+	3.54456i	0.154993	+	0.154993i	0.780344	−	0.625351i	$-0.215044\pi$
$523$	3.54456	+	3.54456i	0.154993	+	0.154993i	−0.625351	+	0.780344i	$0.715044\pi$
$524$	−13.3994	−	11.4708i	−0.585357	−	0.501106i
$525$	12.1783	+	29.4011i	0.531505	+	1.28317i
$526$	−6.49857	+	8.57463i	−0.283351	+	0.373872i
$527$	21.0448	+	8.79282i	0.916726	+	0.383021i
$528$	15.3818	−	9.37748i	0.669408	−	0.408102i
$529$	−8.18281	−	19.7550i	−0.355774	−	0.858915i
$530$	−35.5608	−	2.11761i	−1.54466	−	0.0919833i
$531$	0.736352	−	0.736352i	0.0319550	−	0.0319550i
$532$	−1.50858	−	19.4539i	−0.0654053	−	0.843433i
$533$	−7.03074	−	4.69779i	−0.304535	−	0.203484i
$534$	−16.6077	−	8.06709i	−0.718685	−	0.349097i
$535$	−26.6069	+	64.2346i	−1.15031	+	2.77711i
$536$	0.932262	−	0.966273i	0.0402676	−	0.0417367i
$537$	13.0987	−	2.60549i	0.565251	−	0.112435i
$538$	0.389743	+	1.12601i	0.0168030	+	0.0485459i
$539$	10.4158	+	2.07183i	0.448639	+	0.0892399i
$540$	−37.4818	−	21.0474i	−1.61296	−	0.905734i
$541$	−18.1292	−	27.1323i	−0.779436	−	1.16651i	−0.982302	−	0.187303i	$-0.940026\pi$
$541$	−18.1292	−	27.1323i	−0.779436	−	1.16651i	0.202866	−	0.979207i	$-0.434974\pi$
$542$	0.677728	+	0.177266i	0.0291109	+	0.00761424i
$543$	0.626248			0.0268749
$544$	−17.9413	−	14.9033i	−0.769229	−	0.638974i
$545$	−66.0971			−2.83129
$546$	8.11442	+	2.12241i	0.347265	+	0.0908306i
$547$	12.9644	+	19.4026i	0.554318	+	0.829596i	0.997773	−	0.0667009i	$-0.0212473\pi$
$547$	12.9644	+	19.4026i	0.554318	+	0.829596i	−0.443455	+	0.896297i	$0.646247\pi$
$548$	3.85253	+	2.16334i	0.164572	+	0.0924132i
$549$	0.511291	+	0.101702i	0.0218214	+	0.00434054i
$550$	−13.7059	−	39.5979i	−0.584421	−	1.68846i
$551$	45.8976	−	9.12960i	1.95530	−	0.388934i
$552$	−4.14374	+	4.29491i	−0.176369	+	0.182804i
$553$	−0.490483	+	1.18413i	−0.0208575	+	0.0503544i
$554$	−10.1334	−	4.92225i	−0.430528	−	0.209126i
$555$	20.8853	+	13.9551i	0.886530	+	0.592361i
$556$	2.97999	+	38.4285i	0.126380	+	1.62973i
$557$	13.8015	−	13.8015i	0.584786	−	0.584786i	−0.351428	−	0.936215i	$-0.614304\pi$
$557$	13.8015	−	13.8015i	0.584786	−	0.584786i	0.936215	+	0.351428i	$0.114304\pi$
$558$	−1.93042	−	0.114955i	−0.0817211	−	0.00486643i
$559$	5.96282	+	14.3955i	0.252201	+	0.608866i
$560$	−14.5962	−	23.9421i	−0.616803	−	1.01174i
$561$	10.2691	+	15.4715i	0.433564	+	0.653206i
$562$	−17.7203	+	23.3813i	−0.747485	+	0.986280i
$563$	11.3315	+	27.3567i	0.477567	+	1.15295i	0.960747	+	0.277428i	$0.0894818\pi$
$563$	11.3315	+	27.3567i	0.477567	+	1.15295i	−0.483180	+	0.875521i	$0.660518\pi$
$564$	−7.50390	−	6.42385i	−0.315971	−	0.270493i
$565$	10.7869	+	10.7869i	0.453806	+	0.453806i
$566$	4.39104	+	4.94712i	0.184569	+	0.207943i
$567$	11.9766	+	8.00253i	0.502971	+	0.336075i
$568$	31.7692	+	5.72973i	1.33301	+	0.240414i
$569$	−8.65964	−	3.58694i	−0.363031	−	0.150372i	0.193709	−	0.981059i	$-0.437948\pi$
$569$	−8.65964	−	3.58694i	−0.363031	−	0.150372i	−0.556740	+	0.830687i	$0.687948\pi$
$570$	−44.8535	+	26.2545i	−1.87871	+	1.09968i
$571$	−12.2859	+	2.44381i	−0.514147	+	0.102270i	−0.445343	−	0.895360i	$-0.646918\pi$
$571$	−12.2859	+	2.44381i	−0.514147	+	0.102270i	−0.0688038	+	0.997630i	$0.521918\pi$
$572$	−10.4994	−	3.42481i	−0.439004	−	0.143199i
$573$	4.44673	−	22.3552i	0.185765	−	0.933902i
$574$	−1.40940	−	10.2329i	−0.0588270	−	0.427113i
$575$	7.71218	+	11.5421i	0.321620	+	0.481338i
$576$	1.85298	+	0.690863i	0.0772077	+	0.0287860i
$577$		−	5.73217i		−	0.238633i	−0.992856	−	0.119317i	$-0.961930\pi$
$577$		−	5.73217i		−	0.238633i	0.992856	−	0.119317i	$-0.0380704\pi$
$578$	14.6388	−	19.0710i	0.608895	−	0.793251i
$579$	−16.2075			−0.673560
$580$	52.8606	−	41.5736i	2.19492	−	1.72625i
$581$	22.7144	−	15.1773i	0.942351	−	0.629659i
$582$	−0.822781	−	5.97379i	−0.0341054	−	0.247622i
$583$	−16.8102	−	3.34376i	−0.696209	−	0.138485i
$584$	−17.6700	+	12.2701i	−0.731188	+	0.507741i
$585$	0.391380	+	1.96760i	0.0161816	+	0.0813502i
$586$	−14.4947	−	24.7629i	−0.598769	−	1.02294i
$587$	1.26920	−	3.06413i	0.0523856	−	0.126470i	−0.895520	−	0.445021i	$-0.853196\pi$
$587$	1.26920	−	3.06413i	0.0523856	−	0.126470i	0.947906	+	0.318551i	$0.103196\pi$
$588$	−5.88053	−	11.5740i	−0.242509	−	0.477305i
$589$	−17.0632	+	25.5368i	−0.703075	+	1.05223i
$590$	−15.7773	−	17.7753i	−0.649541	−	0.731799i
$591$	22.0785	−	22.0785i	0.908187	−	0.908187i
$592$	−13.7705	−	6.38667i	−0.565964	−	0.262490i
$593$	12.2414	−	5.07054i	0.502693	−	0.208222i	−0.116903	−	0.993143i	$-0.537297\pi$
$593$	12.2414	−	5.07054i	0.502693	−	0.208222i	0.619596	+	0.784921i	$0.287297\pi$
$594$	−16.4832	−	12.4923i	−0.676312	−	0.512566i
$595$	24.0816	−	15.9841i	0.987251	−	0.655285i
$596$	−0.834287	+	0.234260i	−0.0341737	+	0.00959565i
$597$	−11.6311	+	4.81777i	−0.476030	+	0.197178i
$598$	3.65215	+	0.217483i	0.149348	+	0.00889353i
$599$	4.43417	+	4.43417i	0.181175	+	0.181175i	0.791868	−	0.610693i	$-0.209109\pi$
$599$	4.43417	+	4.43417i	0.181175	+	0.181175i	−0.610693	+	0.791868i	$0.709109\pi$
$600$	−27.6912	+	43.0943i	−1.13049	+	1.75932i
$601$	4.36634	−	6.53469i	0.178107	−	0.266556i	−0.731665	−	0.681664i	$-0.761256\pi$
$601$	4.36634	−	6.53469i	0.178107	−	0.266556i	0.909772	+	0.415109i	$0.136256\pi$
$602$	−8.31658	+	17.1213i	−0.338959	+	0.697813i
$603$	−0.108415	−	0.0449069i	−0.00441500	−	0.00182875i
$604$	4.84109	−	40.5037i	0.196981	−	1.64807i
$605$	2.82650	+	14.2098i	0.114914	+	0.577710i
$606$	−9.60076	−	27.7377i	−0.390004	−	1.12677i
$607$	2.60650	−	13.1038i	0.105795	−	0.531866i	−0.891147	−	0.453715i	$-0.850098\pi$
$607$	2.60650	−	13.1038i	0.105795	−	0.531866i	0.996942	−	0.0781510i	$-0.0249016\pi$
$608$	24.3356	−	19.8550i	0.986937	−	0.805229i
$609$	−20.4318	+	13.6521i	−0.827938	+	0.553210i
$610$	3.01075	−	11.5108i	0.121902	−	0.466057i
$611$			6.05561i			0.244984i
$612$	−0.638086	+	1.93601i	−0.0257931	+	0.0782584i
$613$			2.78252i			0.112385i	0.998420	+	0.0561924i	$0.0178960\pi$
$613$			2.78252i			0.112385i	−0.998420	+	0.0561924i	$0.982104\pi$
$614$	−14.2266	−	3.72111i	−0.574140	−	0.150172i
$615$	−22.8766	+	15.2856i	−0.922472	+	0.616376i
$616$	−5.38525	−	12.3697i	−0.216978	−	0.498389i
$617$	−3.33870	+	16.7848i	−0.134411	+	0.675730i	0.853548	+	0.521014i	$0.174446\pi$
$617$	−3.33870	+	16.7848i	−0.134411	+	0.675730i	−0.987959	+	0.154716i	$0.950554\pi$
$618$	1.95934	−	0.678181i	0.0788163	−	0.0272804i
$619$	−6.44112	−	32.3817i	−0.258891	−	1.30153i	−0.863233	−	0.504806i	$-0.831564\pi$
$619$	−6.44112	−	32.3817i	−0.258891	−	1.30153i	0.604342	−	0.796725i	$-0.293436\pi$
$620$	−5.23803	+	43.8248i	−0.210364	+	1.76004i
$621$	6.33005	+	2.62199i	0.254016	+	0.105217i
$622$	42.1755	+	20.4865i	1.69108	+	0.821433i
$623$	−7.68181	+	11.4966i	−0.307765	+	0.460603i
$624$	4.64371	+	12.6769i	0.185897	+	0.507482i
$625$	27.9804	+	27.9804i	1.11922	+	1.11922i
$626$	1.76601	−	29.6563i	0.0705839	−	1.18530i
$627$	−23.1020	+	9.56915i	−0.922604	+	0.382155i
$628$	1.52680	+	5.43751i	0.0609259	+	0.216980i
$629$	6.03205	−	14.4372i	0.240514	−	0.575647i
$630$	−1.48025	+	1.95313i	−0.0589745	+	0.0778147i
$631$	−19.1037	+	7.91302i	−0.760507	+	0.315012i	−0.729021	−	0.684492i	$-0.760024\pi$
$631$	−19.1037	+	7.91302i	−0.760507	+	0.315012i	−0.0314865	+	0.999504i	$0.510024\pi$
$632$	−2.01589	+	0.438662i	−0.0801876	+	0.0174490i
$633$	1.78501	−	1.78501i	0.0709476	−	0.0709476i
$634$	−7.66534	+	6.80372i	−0.304429	+	0.270210i
$635$	−26.4368	+	39.5654i	−1.04911	+	1.57011i
$636$	9.49072	+	18.6796i	0.376331	+	0.740693i
$637$	−3.04565	+	7.35284i	−0.120673	+	0.291330i
$638$	27.9240	−	16.3450i	1.10552	−	0.647106i
$639$	−0.550418	−	2.76714i	−0.0217742	−	0.109466i
$640$	18.2539	−	41.2793i	0.721548	−	1.63171i
$641$	−8.54254	−	1.69922i	−0.337410	−	0.0671150i	0.0234775	−	0.999724i	$-0.492526\pi$
$641$	−8.54254	−	1.69922i	−0.337410	−	0.0671150i	−0.360888	+	0.932609i	$0.617526\pi$
$642$	40.5103	−	5.57956i	1.59882	−	0.220208i
$643$	19.0459	−	12.7260i	0.751095	−	0.501866i	−0.120125	−	0.992759i	$-0.538329\pi$
$643$	19.0459	−	12.7260i	0.751095	−	0.501866i	0.871220	+	0.490893i	$0.163329\pi$
$644$	2.76290	+	3.51302i	0.108874	+	0.138432i
$645$	50.6993			1.99628
$646$	21.4164	+	24.2783i	0.842617	+	0.955215i
$647$		−	44.2598i		−	1.74003i	−0.493024	−	0.870016i	$-0.664109\pi$
$647$		−	44.2598i		−	1.74003i	0.493024	−	0.870016i	$-0.335891\pi$
$648$	0.415291	+	23.1817i	0.0163142	+	0.910665i
$649$	−6.35301	−	9.50795i	−0.249377	−	0.373220i
$650$	31.1089	−	4.28468i	1.22019	−	0.168059i
$651$	3.14630	−	15.8175i	0.123313	−	0.619938i
$652$	−22.5102	−	7.34259i	−0.881568	−	0.287558i
$653$	−11.9296	+	2.37294i	−0.466841	+	0.0928604i	−0.422905	−	0.906174i	$-0.638990\pi$
$653$	−11.9296	+	2.37294i	−0.466841	+	0.0928604i	−0.0439355	+	0.999034i	$0.513990\pi$
$654$	19.6384	+	33.5504i	0.767921	+	1.31192i
$655$	32.5059	+	13.4644i	1.27011	+	0.526098i
$656$	12.2353	−	11.2582i	0.477707	−	0.439558i
$657$	1.56327	+	1.04455i	0.0609891	+	0.0407516i
$658$	−5.53248	+	4.91061i	−0.215679	+	0.191435i
$659$	−26.0905	−	26.0905i	−1.01634	−	1.01634i	−0.999864	−	0.0164765i	$-0.994755\pi$
$659$	−26.0905	−	26.0905i	−1.01634	−	1.01634i	−0.0164765	−	0.999864i	$-0.505245\pi$
$660$	−23.3690	+	27.2981i	−0.909637	+	1.06258i
$661$	−4.70510	−	11.3591i	−0.183007	−	0.441818i	0.805577	−	0.592492i	$-0.201856\pi$
$661$	−4.70510	−	11.3591i	−0.183007	−	0.441818i	−0.988584	+	0.150674i	$0.951856\pi$
$662$	16.2133	+	12.2878i	0.630146	+	0.477578i
$663$	−12.8731	+	5.28599i	−0.499951	+	0.205291i
$664$	40.9203	+	16.0972i	1.58801	+	0.624693i
$665$	14.8946	+	35.9587i	0.577586	+	1.39442i
$666$	−0.0788613	+	1.32430i	−0.00305581	+	0.0513158i
$667$	−7.57941	+	7.57941i	−0.293476	+	0.293476i
$668$	1.17129	+	15.1043i	0.0453185	+	0.584404i
$669$	8.81217	+	5.88810i	0.340698	+	0.227647i
$670$	−1.17020	+	2.40909i	−0.0452088	+	0.0930713i
$671$	2.19065	−	5.28871i	0.0845693	−	0.204168i
$672$	−7.81611	+	14.5225i	−0.301513	+	0.560217i
$673$	−31.4502	+	6.25584i	−1.21232	+	0.241145i	−0.759529	−	0.650473i	$-0.774571\pi$
$673$	−31.4502	+	6.25584i	−1.21232	+	0.241145i	−0.452788	+	0.891618i	$0.649571\pi$
$674$	7.33841	−	2.54002i	0.282665	−	0.0978379i
$675$	57.6784	+	11.4729i	2.22004	+	0.441594i
$676$	−8.67785	+	15.4538i	−0.333763	+	0.594376i
$677$	25.6042	+	38.3193i	0.984047	+	1.47273i	0.878168	+	0.478352i	$0.158766\pi$
$677$	25.6042	+	38.3193i	0.984047	+	1.47273i	0.105879	+	0.994379i	$0.466234\pi$
$678$	2.27041	−	8.68026i	0.0871944	−	0.333363i
$679$	−4.51592			−0.173305
$680$	43.2423	+	17.1641i	1.65827	+	0.658214i
$681$	21.2341			0.813692
$682$	−5.37355	+	20.5442i	−0.205764	+	0.786680i
$683$	−17.8349	−	26.6918i	−0.682433	−	1.02133i	−0.997388	−	0.0722266i	$-0.976990\pi$
$683$	−17.8349	−	26.6918i	−0.682433	−	1.02133i	0.314955	−	0.949107i	$-0.398010\pi$
$684$	−2.39343	−	1.34400i	−0.0915149	−	0.0513889i
$685$	−8.64404	−	1.71941i	−0.330272	−	0.0656951i
$686$	−25.6258	+	8.86978i	−0.978398	+	0.338650i
$687$	−40.2573	+	8.00767i	−1.53591	+	0.305512i
$688$	−30.2720	+	4.72339i	−1.15411	+	0.180077i
$689$	4.91543	−	11.8669i	0.187263	−	0.452093i
$690$	5.20134	−	10.7080i	0.198012	−	0.407646i
$691$	−21.0814	−	14.0862i	−0.801975	−	0.535863i	0.0857066	−	0.996320i	$-0.472685\pi$
$691$	−21.0814	−	14.0862i	−0.801975	−	0.535863i	−0.887682	+	0.460458i	$0.847685\pi$
$692$	23.0483	−	1.78732i	0.876165	−	0.0679435i
$693$	−0.833744	+	0.833744i	−0.0316713	+	0.0316713i
$694$	−0.197039	+	3.30884i	−0.00747950	+	0.125602i
$695$	−29.4221	−	71.0313i	−1.11605	−	2.69437i
$696$	−36.8081	−	14.4796i	−1.39521	−	0.548847i
$697$	12.0815	+	12.1559i	0.457618	+	0.460436i
$698$	−3.65603	−	2.77084i	−0.138383	−	0.104878i
$699$	−1.13214	−	2.73322i	−0.0428213	−	0.103380i
$700$	29.1413	+	24.9470i	1.10144	+	0.942907i
$701$	13.1199	+	13.1199i	0.495533	+	0.495533i	0.910044	−	0.414511i	$-0.136048\pi$
$701$	13.1199	+	13.1199i	0.495533	+	0.495533i	−0.414511	+	0.910044i	$0.636048\pi$
$702$	11.5919	−	10.2889i	0.437510	−	0.388331i
$703$	17.5188	+	11.7057i	0.660733	+	0.441488i
$704$	11.4102	−	18.4765i	0.430037	−	0.696361i
$705$	18.2038	+	7.54028i	0.685596	+	0.283983i
$706$	9.84061	+	16.8118i	0.370356	+	0.632721i
$707$	−21.5591	+	4.28837i	−0.810813	+	0.161281i
$708$	−4.33498	+	13.2897i	−0.162918	+	0.499459i
$709$	0.00545205	−	0.0274093i	0.000204756	−	0.00102938i	−0.980683	−	0.195605i	$-0.937333\pi$
$709$	0.00545205	−	0.0274093i	0.000204756	−	0.00102938i	0.980888	+	0.194576i	$0.0623330\pi$
$710$	−63.7905	+	8.78598i	−2.39402	+	0.329732i
$711$	0.100173	+	0.149920i	0.00375679	+	0.00562243i
$712$	−22.2527	+	0.398647i	−0.833954	+	0.0149399i
$713$		−	7.03485i		−	0.263457i
$714$	−15.2684	−	7.47456i	−0.571407	−	0.279728i
$715$	22.0294			0.823852
$716$	12.6542	−	9.95223i	0.472910	−	0.371932i
$717$	−35.1546	+	23.4896i	−1.31287	+	0.877234i
$718$	−0.00328623		0.000452618i	−0.000122641		1.68916e-5i
$719$	−50.0003	−	9.94567i	−1.86469	−	0.370911i	−0.871796	−	0.489870i	$-0.837044\pi$
$719$	−50.0003	−	9.94567i	−1.86469	−	0.370911i	−0.992899	+	0.118959i	$0.962044\pi$
$720$	−3.94130	−	0.163920i	−0.146884	−	0.00610893i
$721$	−0.302923	−	1.52290i	−0.0112814	−	0.0567156i
$722$	−14.4340	+	8.44881i	−0.537180	+	0.314432i
$723$	−11.8895	+	28.7037i	−0.442175	+	1.06750i
$724$	0.673013	−	0.341945i	0.0250123	−	0.0127083i
$725$	−51.1136	+	76.4970i	−1.89831	+	2.84103i
$726$	6.37300	−	5.65664i	0.236524	−	0.209938i
$727$	26.1689	−	26.1689i	0.970549	−	0.970549i	−0.0290292	−	0.999579i	$-0.509242\pi$
$727$	26.1689	−	26.1689i	0.970549	−	0.970549i	0.999579	+	0.0290292i	$0.00924158\pi$
$728$	9.87924	−	2.14975i	0.366149	−	0.0796749i
$729$	26.6475	−	11.0378i	0.986944	−	0.408806i
$730$	25.9188	−	34.1989i	0.959298	−	1.26576i
$731$	−6.06609	−	30.9932i	−0.224363	−	1.14632i
$732$	−6.73732	+	1.89177i	−0.249019	+	0.0699220i
$733$	27.7420	−	11.4911i	1.02467	−	0.424434i	0.193887	−	0.981024i	$-0.437891\pi$
$733$	27.7420	−	11.4911i	1.02467	−	0.424434i	0.830787	+	0.556590i	$0.187891\pi$
$734$	−0.210869	+	3.54109i	−0.00778332	+	0.130704i
$735$	18.3111	+	18.3111i	0.675416	+	0.675416i
$736$	−2.10806	+	6.87820i	−0.0777041	+	0.253534i
$737$	−0.715900	+	1.07142i	−0.0263705	+	0.0394663i
$738$	−1.30710	−	0.634914i	−0.0481149	−	0.0233715i
$739$	5.46559	+	2.26392i	0.201055	+	0.0832797i	0.480939	−	0.876754i	$-0.340296\pi$
$739$	5.46559	+	2.26392i	0.201055	+	0.0832797i	−0.279884	+	0.960034i	$0.590296\pi$
$740$	30.0646	+	3.59339i	1.10520	+	0.132096i
$741$	−3.65588	−	18.3793i	−0.134302	−	0.675182i
$742$	14.8278	−	5.13229i	0.544345	−	0.188412i
$743$	−1.93989	+	9.75248i	−0.0711677	+	0.357784i	−0.999916	−	0.0129257i	$-0.995886\pi$
$743$	−1.93989	+	9.75248i	−0.0711677	+	0.357784i	0.928749	+	0.370710i	$0.120886\pi$
$744$	23.8014	−	10.3622i	0.872603	−	0.379895i
$745$	1.43721	−	0.960315i	0.0526554	−	0.0351832i
$746$	−19.2729	−	5.04102i	−0.705632	−	0.184565i
$747$		−	3.84311i		−	0.140612i
$748$	19.4837	+	11.0196i	0.712396	+	0.402917i
$749$		−	30.6240i		−	1.11898i
$750$	14.0121	−	53.5713i	0.511650	−	1.95615i
$751$	35.8721	−	23.9690i	1.30899	−	0.874641i	0.311846	−	0.950133i	$-0.399053\pi$
$751$	35.8721	−	23.9690i	1.30899	−	0.874641i	0.997146	+	0.0754921i	$0.0240528\pi$
$752$	−11.5718	−	2.80627i	−0.421980	−	0.102334i
$753$	2.27691	−	11.4468i	0.0829751	−	0.417144i
$754$	7.93125	+	22.9143i	0.288839	+	0.834489i
$755$	15.8741	+	79.8047i	0.577719	+	2.90439i
$756$	18.8002	+	2.24705i	0.683758	+	0.0817243i
$757$	−11.6970	−	4.84507i	−0.425136	−	0.176097i	0.159848	−	0.987142i	$-0.448899\pi$
$757$	−11.6970	−	4.84507i	−0.425136	−	0.176097i	−0.584985	+	0.811044i	$0.698899\pi$
$758$	−8.30862	+	17.1049i	−0.301783	+	0.621279i
$759$	3.18205	−	4.76227i	0.115501	−	0.172860i
$760$	−33.8674	+	52.7060i	−1.22850	+	1.91185i
$761$	14.9604	+	14.9604i	0.542315	+	0.542315i	0.924207	−	0.381892i	$-0.124727\pi$
$761$	14.9604	+	14.9604i	0.542315	+	0.542315i	−0.381892	+	0.924207i	$0.624727\pi$
$762$	27.9379	+	1.66368i	1.01208	+	0.0602687i
$763$	26.8971	−	11.1411i	0.973739	−	0.403336i
$764$	−7.42762	−	26.4526i	−0.268722	−	0.957021i
$765$	0.0124810	−	4.06609i	0.000451251	−	0.147010i
$766$	−39.2971	−	29.7827i	−1.41986	−	1.07609i
$767$	7.91731	−	3.27946i	0.285878	−	0.118414i
$768$	−26.3766	+	2.99910i	−0.951782	+	0.108221i
$769$	5.62268	−	5.62268i	0.202759	−	0.202759i	−0.598422	−	0.801181i	$-0.704205\pi$
$769$	5.62268	−	5.62268i	0.202759	−	0.202759i	0.801181	+	0.598422i	$0.204205\pi$
$770$	17.8640	+	20.1263i	0.643776	+	0.725303i
$771$	5.72179	−	8.56327i	0.206065	−	0.308399i
$772$	−17.4178	+	8.84962i	−0.626879	+	0.318505i
$773$	16.6372	−	40.1658i	0.598399	−	1.44466i	−0.276813	−	0.960924i	$-0.589278\pi$
$773$	16.6372	−	40.1658i	0.598399	−	1.44466i	0.875212	−	0.483740i	$-0.160722\pi$
$774$	1.35268	+	2.31094i	0.0486212	+	0.0830650i
$775$	−11.7798	−	59.2211i	−0.423143	−	2.12728i
$776$	−4.14604	−	5.97063i	−0.148834	−	0.214333i
$777$	−10.8511	−	2.15842i	−0.389282	−	0.0774331i
$778$	3.73153	+	27.0927i	0.133782	+	0.971321i
$779$	−19.1891	+	12.8217i	−0.687521	+	0.459387i
$780$	−16.6478	−	21.1676i	−0.596088	−	0.757923i
$781$	−30.9811			−1.10859
$782$	−7.16827	−	1.89846i	−0.256337	−	0.0678887i
$783$			45.4100i			1.62282i
$784$	−12.6393	−	9.22742i	−0.451404	−	0.329551i
$785$	−6.25890	−	9.36710i	−0.223390	−	0.334326i
$786$	−2.82354	−	20.5003i	−0.100712	−	0.731220i
$787$	−5.54976	+	27.9005i	−0.197827	+	0.994546i	0.746462	+	0.665429i	$0.231751\pi$
$787$	−5.54976	+	27.9005i	−0.197827	+	0.994546i	−0.944289	+	0.329117i	$0.893249\pi$
$788$	11.6719	−	35.7825i	0.415793	−	1.27470i
$789$	−12.3799	+	2.46252i	−0.440737	+	0.0876680i
$790$	3.55153	−	2.07885i	0.126358	−	0.0739621i
$791$	−6.20773	−	2.57132i	−0.220721	−	0.0914258i
$792$	−1.86777	−	0.336863i	−0.0663685	−	0.0119699i
$793$	3.56700	+	2.38339i	0.126668	+	0.0846367i
$794$	12.6802	+	14.2861i	0.450005	+	0.506993i
$795$	−29.5527	−	29.5527i	−1.04813	−	1.04813i
$796$	−9.86908	+	11.5284i	−0.349800	+	0.408612i
$797$	16.1567	+	39.0057i	0.572299	+	1.38165i	0.899593	+	0.436729i	$0.143863\pi$
$797$	16.1567	+	39.0057i	0.572299	+	1.38165i	−0.327295	+	0.944922i	$0.606137\pi$
$798$	13.8270	−	18.2442i	0.489470	−	0.645838i
$799$	2.43142	−	12.0304i	0.0860173	−	0.425606i
$800$	−6.22866	+	61.4323i	−0.220216	+	2.17196i
$801$	0.744375	+	1.79708i	0.0263012	+	0.0634967i
$802$	55.4919	+	3.30450i	1.95949	+	0.116686i
$803$	14.5987	−	14.5987i	0.515176	−	0.515176i
$804$	1.57052	−	0.121788i	0.0553880	−	0.00429515i
$805$	−7.41257	−	4.95292i	−0.261259	−	0.174568i
$806$	−14.3147	−	6.95328i	−0.504214	−	0.244919i
$807$	−0.534966	+	1.29152i	−0.0188317	+	0.0454638i
$808$	−25.4631	−	24.5668i	−0.895787	−	0.864257i
$809$	20.4694	−	4.07161i	0.719664	−	0.143150i	0.178346	−	0.983968i	$-0.442925\pi$
$809$	20.4694	−	4.07161i	0.719664	−	0.143150i	0.541318	+	0.840818i	$0.317925\pi$
$810$	−15.1272	−	43.7043i	−0.531517	−	1.53561i
$811$	−19.7791	−	3.93431i	−0.694538	−	0.138152i	−0.164817	−	0.986324i	$-0.552703\pi$
$811$	−19.7791	−	3.93431i	−0.694538	−	0.138152i	−0.529721	+	0.848172i	$0.677703\pi$
$812$	−14.5032	+	25.8277i	−0.508963	+	0.906376i
$813$	0.456601	+	0.683351i	0.0160137	+	0.0239662i
$814$	14.0938	+	3.68636i	0.493986	+	0.129207i
$815$	47.2297			1.65438
$816$	−4.13551	−	27.0492i	−0.144772	−	0.946912i
$817$	42.5271			1.48784
$818$	16.3365	+	4.27297i	0.571192	+	0.149401i
$819$	−0.490918	−	0.734711i	−0.0171541	−	0.0256729i
$820$	−16.2386	+	28.9182i	−0.567077	+	1.00987i
$821$	−39.9253	−	7.94163i	−1.39340	−	0.277165i	−0.559387	−	0.828907i	$-0.688963\pi$
$821$	−39.9253	−	7.94163i	−1.39340	−	0.277165i	−0.834015	+	0.551742i	$0.813963\pi$
$822$	1.69551	+	4.89851i	0.0591376	+	0.170855i
$823$	−1.01321	+	0.201541i	−0.0353184	+	0.00702527i	−0.212718	−	0.977114i	$-0.568232\pi$
$823$	−1.01321	+	0.201541i	−0.0353184	+	0.00702527i	0.177399	+	0.984139i	$0.443232\pi$
$824$	1.73535	−	1.79867i	0.0604539	−	0.0626595i
$825$	18.8129	−	45.4183i	0.654980	−	1.58126i
$826$	9.41646	+	4.57399i	0.327641	+	0.159149i
$827$	−32.4708	−	21.6963i	−1.12912	−	0.754454i	−0.156690	−	0.987648i	$-0.550082\pi$
$827$	−32.4708	−	21.6963i	−1.12912	−	0.754454i	−0.972430	+	0.233194i	$0.925082\pi$
$828$	0.626857	−	0.0486106i	0.0217848	−	0.00168933i
$829$	−10.1880	+	10.1880i	−0.353845	+	0.353845i	−0.861538	−	0.507693i	$-0.830498\pi$
$829$	−10.1880	+	10.1880i	−0.353845	+	0.353845i	0.507693	+	0.861538i	$0.330498\pi$
$830$	−87.5575	−	5.21398i	−3.03917	−	0.180980i
$831$	−5.05787	−	12.2108i	−0.175456	−	0.423588i
$832$	11.9123	+	11.0880i	0.412986	+	0.384406i
$833$	9.00294	−	13.3847i	0.311933	−	0.463753i
$834$	−27.3133	+	36.0389i	−0.945782	+	1.24792i
$835$	−11.5644	−	27.9189i	−0.400202	−	0.966173i
$836$	−19.6021	+	22.8979i	−0.677954	+	0.791940i
$837$	−21.0737	−	21.0737i	−0.728414	−	0.728414i
$838$	−9.69087	−	10.9181i	−0.334765	−	0.377160i
$839$	−5.81558	−	3.88585i	−0.200776	−	0.134154i	0.451118	−	0.892464i	$-0.351025\pi$
$839$	−5.81558	−	3.88585i	−0.200776	−	0.134154i	−0.651894	+	0.758310i	$0.726025\pi$
$840$	5.83898	−	32.3749i	0.201464	−	1.11704i
$841$	−38.8410	−	16.0885i	−1.33934	−	0.554774i
$842$	−33.0740	+	19.3595i	−1.13980	+	0.667172i
$843$	−33.7575	+	6.71479i	−1.16267	+	0.231270i
$844$	0.943650	−	2.89295i	0.0324818	−	0.0995795i
$845$	6.89709	−	34.6740i	0.237267	−	1.19282i
$846$	0.141992	+	1.03093i	0.00488179	+	0.0354442i
$847$	−3.54536	−	5.30600i	−0.121820	−	0.182316i
$848$	20.3989	+	14.8923i	0.700500	+	0.511405i
$849$			7.76046i			0.266338i
$850$	−63.5232	−	3.97847i	−2.17883	−	0.136460i
$851$	−4.82605			−0.165435
$852$	23.4128	+	29.7692i	0.802108	+	1.01988i
$853$	−24.7676	+	16.5492i	−0.848026	+	0.566633i	−0.901915	−	0.431914i	$-0.857838\pi$
$853$	−24.7676	+	16.5492i	−0.848026	+	0.566633i	0.0538885	+	0.998547i	$0.482838\pi$
$854$	0.715047	+	5.19159i	0.0244684	+	0.177653i
$855$	5.37019	+	1.06820i	0.183657	+	0.0365316i
$856$	40.4889	−	28.1157i	1.38388	−	0.960975i
$857$	−1.68953	−	8.49385i	−0.0577133	−	0.290145i	0.941140	−	0.338017i	$-0.109756\pi$
$857$	−1.68953	−	8.49385i	−0.0577133	−	0.290145i	−0.998853	+	0.0478721i	$0.984756\pi$
$858$	−6.54524	−	11.1820i	−0.223451	−	0.381746i
$859$	5.35005	−	12.9162i	0.182541	−	0.440694i	−0.805948	−	0.591987i	$-0.798344\pi$
$859$	5.35005	−	12.9162i	0.182541	−	0.440694i	0.988489	+	0.151293i	$0.0483437\pi$
$860$	54.4853	−	27.6829i	1.85793	−	0.943979i
$861$	6.73273	−	10.0762i	0.229451	−	0.343397i
$862$	−1.25173	−	1.41025i	−0.0426340	−	0.0480332i
$863$	21.9763	−	21.9763i	0.748081	−	0.748081i	−0.226038	−	0.974119i	$-0.572577\pi$
$863$	21.9763	−	21.9763i	0.748081	−	0.748081i	0.974119	+	0.226038i	$0.0725772\pi$
$864$	14.2895	+	26.9194i	0.486139	+	0.915816i
$865$	−42.6026	+	17.6466i	−1.44853	+	0.600001i
$866$	−33.8035	−	25.6191i	−1.14869	−	0.870572i
$867$	27.6970	−	5.33272i	0.940638	−	0.181109i
$868$	−5.25545	−	18.7166i	−0.178382	−	0.635284i
$869$	1.82923	−	0.757691i	0.0620523	−	0.0257029i
$870$	78.7587	+	4.69002i	2.67017	+	0.159007i
$871$	−0.682843	−	0.682843i	−0.0231372	−	0.0231372i
$872$	39.4241	+	25.3328i	1.33507	+	0.857878i
$873$	−0.352950	+	0.528226i	−0.0119455	+	0.0178778i
$874$	4.36293	−	8.98196i	0.147578	−	0.303819i
$875$	−38.3118	−	15.8693i	−1.29518	−	0.536479i
$876$	−25.0600	−	2.99523i	−0.846699	−	0.101199i
$877$	0.471143	+	2.36860i	0.0159094	+	0.0799818i	0.987924	−	0.154937i	$-0.0495175\pi$
$877$	0.471143	+	2.36860i	0.0159094	+	0.0799818i	−0.972015	+	0.234919i	$0.924518\pi$
$878$	15.6185	+	45.1236i	0.527099	+	1.52285i
$879$	6.56729	−	33.0160i	0.221509	−	1.11360i
$880$	−10.2088	+	42.0965i	−0.344138	+	1.41907i
$881$	−30.2718	+	20.2270i	−1.01988	+	0.681464i	−0.948758	−	0.316003i	$-0.897659\pi$
$881$	−30.2718	+	20.2270i	−1.01988	+	0.681464i	−0.0711250	+	0.997467i	$0.522659\pi$
$882$	−0.346094	+	1.32319i	−0.0116536	+	0.0445542i
$883$			45.6924i			1.53767i	0.639446	+	0.768836i	$0.279164\pi$
$883$			45.6924i			1.53767i	−0.639446	+	0.768836i	$0.720836\pi$
$884$	−10.9482	+	12.7097i	−0.368227	+	0.427474i
$885$		−	27.8838i		−	0.937305i
$886$	36.1765	+	9.46232i	1.21537	+	0.317893i
$887$	−11.7069	+	7.82227i	−0.393078	+	0.262646i	−0.736365	−	0.676584i	$-0.763459\pi$
$887$	−11.7069	+	7.82227i	−0.393078	+	0.262646i	0.343288	+	0.939230i	$0.388459\pi$
$888$	−7.10865	−	16.3283i	−0.238551	−	0.547940i
$889$	4.08896	−	20.5566i	0.137139	−	0.689446i
$890$	41.9528	−	14.5210i	1.40626	−	0.486744i
$891$	−4.34102	−	21.8238i	−0.145430	−	0.731124i
$892$	12.6852	+	1.51617i	0.424733	+	0.0507651i
$893$	15.2696	+	6.32486i	0.510976	+	0.211653i
$894$	−0.914465	−	0.444196i	−0.0305843	−	0.0148561i
$895$	−17.8409	+	26.7007i	−0.596354	+	0.892507i
$896$	−0.470197	+	19.8747i	−0.0157082	+	0.663968i
$897$	3.03511	+	3.03511i	0.101340	+	0.101340i
$898$	2.03281	−	34.1366i	0.0678356	−	1.13915i
$899$	43.0755	−	17.8424i	1.43665	−	0.595079i
$900$	5.19564	−	1.45888i	0.173188	−	0.0486294i
$901$	−14.5300	+	21.6019i	−0.484066	+	0.719664i
$902$	−9.63816	+	12.7172i	−0.320916	+	0.423437i
$903$	−20.6312	+	8.54574i	−0.686564	+	0.284384i
$904$	−2.29965	−	10.5681i	−0.0764853	−	0.351491i
$905$	−1.06477	+	1.06477i	−0.0353940	+	0.0353940i
$906$	35.7919	−	31.7687i	1.18911	−	1.05544i
$907$	0.670220	−	1.00305i	0.0222543	−	0.0333059i	−0.820176	−	0.572112i	$-0.806124\pi$
$907$	0.670220	−	1.00305i	0.0222543	−	0.0333059i	0.842430	+	0.538806i	$0.181124\pi$
$908$	22.8197	−	11.5943i	0.757300	−	0.384769i
$909$	−1.18338	+	2.85693i	−0.0392502	+	0.0947584i
$910$	−17.4049	+	10.1878i	−0.576968	+	0.337722i
$911$	4.49473	+	22.5965i	0.148917	+	0.748656i	0.981000	+	0.194006i	$0.0621480\pi$
$911$	4.49473	+	22.5965i	0.148917	+	0.748656i	−0.832084	+	0.554650i	$0.812852\pi$
$912$	36.8157	+	1.53117i	1.21909	+	0.0507022i
$913$	−41.3901	−	8.23300i	−1.36981	−	0.272473i
$914$	−4.79360	+	0.660230i	−0.158558	+	0.0218385i
$915$	11.6063	−	7.75506i	0.383692	−	0.256374i
$916$	−38.8912	+	30.5870i	−1.28500	+	1.01062i
$917$	−15.4973			−0.511765
$918$	−27.1604	+	15.7863i	−0.896427	+	0.521026i
$919$		−	21.8485i		−	0.720717i	−0.932814	−	0.360358i	$-0.882654\pi$
$919$		−	21.8485i		−	0.720717i	0.932814	−	0.360358i	$-0.117346\pi$
$920$	−0.257032	−	14.3476i	−0.00847409	−	0.473028i
$921$	−9.58480	−	14.3447i	−0.315830	−	0.472673i
$922$	−30.4748	+	4.19735i	−1.00364	+	0.138232i
$923$	4.52955	−	22.7716i	0.149092	−	0.749536i
$924$	4.90833	−	15.0475i	0.161472	−	0.495026i
$925$	−40.6268	+	8.08118i	−1.33580	+	0.265708i
$926$	−18.6552	−	31.8707i	−0.613047	−	1.04734i
$927$	−0.201808	−	0.0835918i	−0.00662826	−	0.00274551i
$928$	−47.4629	+	4.53717i	−1.55805	+	0.148940i
$929$	44.3386	+	29.6261i	1.45470	+	0.972000i	0.996539	+	0.0831312i	$0.0264921\pi$
$929$	44.3386	+	29.6261i	1.45470	+	0.972000i	0.458162	+	0.888869i	$0.348508\pi$
$930$	−38.7266	+	34.3736i	−1.26990	+	1.12715i
$931$	15.3595	+	15.3595i	0.503389	+	0.503389i
$932$	−2.70907	−	2.31915i	−0.0887386	−	0.0759663i
$933$	21.0510	+	50.8215i	0.689178	+	1.66382i
$934$	12.6865	+	9.61488i	0.415114	+	0.314608i
$935$	−43.7649	−	8.84512i	−1.43127	−	0.289266i
$936$	0.520674	−	1.32359i	0.0170188	−	0.0432629i
$937$	12.1271	+	29.2774i	0.396175	+	0.956451i	0.988564	+	0.150799i	$0.0481847\pi$
$937$	12.1271	+	29.2774i	0.396175	+	0.956451i	−0.592389	+	0.805652i	$0.701815\pi$
$938$	0.0701242	−	1.17758i	0.00228964	−	0.0384495i
$939$	24.6458	−	24.6458i	0.804285	−	0.804285i
$940$	23.6804	−	1.83633i	0.772368	−	0.0598945i
$941$	12.7817	+	8.54045i	0.416671	+	0.278411i	0.746183	−	0.665741i	$-0.231884\pi$
$941$	12.7817	+	8.54045i	0.416671	+	0.278411i	−0.329512	+	0.944151i	$0.606884\pi$
$942$	−2.89507	+	5.96007i	−0.0943265	+	0.194190i
$943$	2.02294	−	4.88380i	0.0658759	−	0.159038i
$944$	2.59779	+	16.6491i	0.0845508	+	0.541883i
$945$	−37.0423	+	7.36816i	−1.20498	+	0.239686i
$946$	27.7865	−	9.61766i	0.903418	−	0.312697i
$947$	−5.57771	−	1.10948i	−0.181251	−	0.0360531i	0.103630	−	0.994616i	$-0.466954\pi$
$947$	−5.57771	−	1.10948i	−0.181251	−	0.0360531i	−0.284881	+	0.958563i	$0.591954\pi$
$948$	−2.11042	−	1.18508i	−0.0685432	−	0.0384895i
$949$	8.59587	+	12.8646i	0.279034	+	0.417604i
$950$	21.6880	−	82.9180i	0.703652	−	2.69022i
$951$	−12.0245			−0.389921
$952$	−20.4899	+	0.304156i	−0.664080	+	0.00985776i
$953$	50.4072			1.63285			0.816425	−	0.577451i	$-0.195952\pi$
$953$	50.4072			1.63285			0.816425	+	0.577451i	$0.195952\pi$
$954$	0.558568	−	2.13553i	0.0180843	−	0.0691403i
$955$	30.4485	+	45.5694i	0.985290	+	1.47459i
$956$	−24.9540	+	44.4388i	−0.807070	+	1.43725i
$957$	37.2307	+	7.40565i	1.20350	+	0.239391i
$958$	−21.8599	+	7.56630i	−0.706262	+	0.244456i
$959$	3.80736	−	0.757331i	0.122946	−	0.0244555i
$960$	48.1646	−	22.0033i	1.55451	−	0.710155i
$961$	0.153126	−	0.369678i	0.00493954	−	0.0119251i
$962$	−4.77009	+	9.82016i	−0.153794	+	0.316615i
$963$	−3.58208	−	2.39347i	−0.115431	−	0.0771285i
$964$	2.89552	+	37.3391i	0.0932583	+	1.20261i
$965$	27.5564	−	27.5564i	0.887072	−	0.887072i
$966$	−0.311690	+	5.23415i	−0.0100284	+	0.168406i
$967$	20.5670	+	49.6531i	0.661389	+	1.59674i	0.795628	+	0.605786i	$0.207141\pi$
$967$	20.5670	+	49.6531i	0.661389	+	1.59674i	−0.134238	+	0.990949i	$0.542859\pi$
$968$	3.76026	−	9.55884i	0.120859	−	0.307233i
$969$	−0.116585	+	37.9814i	−0.00374525	+	1.22014i
$970$	11.5557	+	8.75790i	0.371032	+	0.281199i
$971$	−6.40801	−	15.4703i	−0.205643	−	0.496466i	0.787085	−	0.616844i	$-0.211589\pi$
$971$	−6.40801	−	15.4703i	−0.205643	−	0.496466i	−0.992728	+	0.120378i	$0.961589\pi$
$972$	3.33254	−	3.89285i	0.106891	−	0.124863i
$973$	23.9457	+	23.9457i	0.767663	+	0.767663i
$974$	21.3965	−	18.9915i	0.685589	−	0.608525i
$975$	30.6326	+	20.4681i	0.981029	+	0.655502i
$976$	−6.20748	+	5.71176i	−0.198697	+	0.182829i
$977$	51.9957	+	21.5373i	1.66349	+	0.689040i	0.998336	−	0.0576654i	$-0.0183657\pi$
$977$	51.9957	+	21.5373i	1.66349	+	0.689040i	0.665155	+	0.746706i	$0.268366\pi$
$978$	−14.0326	−	23.9735i	−0.448714	−	0.766587i
$979$	20.9491	−	4.16704i	0.669537	−	0.133179i
$980$	29.6767	+	9.68024i	0.947989	+	0.309224i
$981$	0.799012	−	4.01690i	0.0255105	−	0.128250i
$982$	−29.3080	+	4.03665i	−0.935257	+	0.128815i
$983$	20.2455	+	30.2995i	0.645731	+	0.966404i	0.999517	+	0.0310779i	$0.00989398\pi$
$983$	20.2455	+	30.2995i	0.645731	+	0.966404i	−0.353786	+	0.935326i	$0.615106\pi$
$984$	19.5034	−	0.349395i	0.621745	−	0.0111383i
$985$			75.0769i			2.39215i
$986$	−6.55628	−	48.7074i	−0.208794	−	1.55116i
$987$	−8.67871			−0.276246
$988$	−13.9644	−	17.7556i	−0.444266	−	0.564882i
$989$	−8.09928	+	5.41177i	−0.257542	+	0.172084i
$990$	3.75037	−	0.516545i	0.119195	−	0.0164169i
$991$	8.06621	+	1.60447i	0.256232	+	0.0509677i	0.321535	−	0.946898i	$-0.395801\pi$
$991$	8.06621	+	1.60447i	0.256232	+	0.0509677i	−0.0653029	+	0.997865i	$0.520801\pi$
$992$	19.9209	−	24.1320i	0.632488	−	0.766193i
$993$	4.65623	+	23.4085i	0.147761	+	0.742845i
$994$	24.4775	−	14.3277i	0.776380	−	0.454446i
$995$	11.5843	−	27.9669i	0.367246	−	0.886610i
$996$	23.3680	+	45.9927i	0.740443	+	1.45734i
$997$	15.0804	−	22.5694i	0.477601	−	0.714780i	−0.511942	−	0.859020i	$-0.671074\pi$
$997$	15.0804	−	22.5694i	0.477601	−	0.714780i	0.989543	+	0.144240i	$0.0460737\pi$
$998$	9.66136	−	8.57538i	0.305825	−	0.271449i
$999$	−14.4570	+	14.4570i	−0.457399	+	0.457399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.s.c.107.13	yes	112
4.3	odd	2		544.2.cc.c.175.3		112
8.3	odd	2	inner	136.2.s.c.107.6	yes	112
8.5	even	2		544.2.cc.c.175.4		112
17.7	odd	16	inner	136.2.s.c.75.6	✓	112
68.7	even	16		544.2.cc.c.143.4		112
136.75	even	16	inner	136.2.s.c.75.13	yes	112
136.109	odd	16		544.2.cc.c.143.3		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.s.c.75.6	✓	112	17.7	odd	16	inner
136.2.s.c.75.13	yes	112	136.75	even	16	inner
136.2.s.c.107.6	yes	112	8.3	odd	2	inner
136.2.s.c.107.13	yes	112	1.1	even	1	trivial
544.2.cc.c.143.3		112	136.109	odd	16
544.2.cc.c.143.4		112	68.7	even	16
544.2.cc.c.175.3		112	4.3	odd	2
544.2.cc.c.175.4		112	8.5	even	2

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36819 + 0.357863i) q^{2} +(0.921778 + 1.37954i) q^{3} +(1.74387 + 0.979245i) q^{4} +(-3.91277 - 0.778297i) q^{5} +(0.767479 + 2.21734i) q^{6} +(1.72342 - 0.342810i) q^{7} +(2.03550 + 1.96386i) q^{8} +(0.0945986 - 0.228381i) q^{9} +(-5.07487 - 2.46509i) q^{10} +(-2.25700 - 1.50808i) q^{11} +(0.256553 + 3.30838i) q^{12} +(1.43844 - 1.43844i) q^{13} +(2.48064 + 0.147720i) q^{14} +(-2.53301 - 6.11523i) q^{15} +(2.08216 + 3.41535i) q^{16} +(-3.43525 + 2.28014i) q^{17} +(0.211158 - 0.278615i) q^{18} +(-2.12471 - 5.12951i) q^{19} +(-6.06121 - 5.18881i) q^{20} +(2.06153 + 2.06153i) q^{21} +(-2.54831 - 2.87103i) q^{22} +(1.05741 + 0.706536i) q^{23} +(-0.832933 + 4.61829i) q^{24} +(10.0846 + 4.17717i) q^{25} +(2.48282 - 1.45329i) q^{26} +(5.28409 - 1.05107i) q^{27} +(3.34111 + 1.08984i) q^{28} +(-1.64434 + 8.26664i) q^{29} +(-1.27722 - 9.27324i) q^{30} +(-3.07326 - 4.59945i) q^{31} +(1.62655 + 5.41796i) q^{32} -4.50373i q^{33} +(-5.51604 + 1.89031i) q^{34} -7.01015 q^{35} +(0.388609 - 0.305632i) q^{36} +(-3.15531 + 2.10831i) q^{37} +(-1.07134 - 7.77849i) q^{38} +(3.31031 + 0.658462i) q^{39} +(-6.43598 - 9.26833i) q^{40} +(-0.810929 - 4.07682i) q^{41} +(2.08281 + 3.55830i) q^{42} +(-2.93119 + 7.07653i) q^{43} +(-2.45913 - 4.84005i) q^{44} +(-0.547891 + 0.819977i) q^{45} +(1.19389 + 1.34508i) q^{46} +(-2.10492 + 2.10492i) q^{47} +(-2.79232 + 6.02061i) q^{48} +(-3.61450 + 1.49717i) q^{49} +(12.3027 + 9.32405i) q^{50} +(-6.31208 - 2.63728i) q^{51} +(3.91704 - 1.09987i) q^{52} +(5.83351 - 2.41632i) q^{53} +(7.60576 + 0.452917i) q^{54} +(7.65738 + 7.65738i) q^{55} +(4.18126 + 2.68676i) q^{56} +(5.11785 - 7.65940i) q^{57} +(-5.20808 + 10.7219i) q^{58} +(3.89198 + 1.61211i) q^{59} +(1.57107 - 13.1446i) q^{60} +(0.411419 + 2.06835i) q^{61} +(-2.55882 - 7.39271i) q^{62} +(0.0847419 - 0.426026i) q^{63} +(0.286541 + 7.99487i) q^{64} +(-6.74782 + 4.50875i) q^{65} +(1.61172 - 6.16195i) q^{66} -0.474710i q^{67} +(-8.22345 + 0.612312i) q^{68} +2.11000i q^{69} +(-9.59119 - 2.50867i) q^{70} +(9.48983 - 6.34090i) q^{71} +(0.641064 - 0.279093i) q^{72} +(-1.48381 + 7.45963i) q^{73} +(-5.07155 + 1.75540i) q^{74} +(3.53318 + 17.7625i) q^{75} +(1.31783 - 11.0258i) q^{76} +(-4.40675 - 1.82533i) q^{77} +(4.29348 + 2.08553i) q^{78} +(-0.405234 + 0.606476i) q^{79} +(-5.48883 - 14.9840i) q^{80} +(5.79637 + 5.79637i) q^{81} +(0.349437 - 5.86805i) q^{82} +(14.3632 - 5.94945i) q^{83} +(1.57629 + 5.61378i) q^{84} +(15.2160 - 6.24801i) q^{85} +(-6.54285 + 8.63305i) q^{86} +(-12.9199 + 5.35158i) q^{87} +(-1.63248 - 7.50212i) q^{88} +(-5.56406 + 5.56406i) q^{89} +(-1.04306 + 0.925811i) q^{90} +(1.98593 - 2.97215i) q^{91} +(1.15210 + 2.26757i) q^{92} +(3.51226 - 8.47935i) q^{93} +(-3.63319 + 2.12665i) q^{94} +(4.32122 + 21.7242i) q^{95} +(-5.97497 + 7.23805i) q^{96} +(-2.52059 - 0.501377i) q^{97} +(-5.48109 + 0.754920i) q^{98} +(-0.557926 + 0.372794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 8 q^{20} - 8 q^{22} - 56 q^{24} - 16 q^{25} - 40 q^{26}+ \cdots + 48 q^{99}+O(q^{100}) \) 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 - 8 * q^10 - 16 * q^11 + 24 * q^12 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 8 * q^20 - 8 * q^22 - 56 * q^24 - 16 * q^25 - 40 * q^26 + 32 * q^27 + 40 * q^28 - 72 * q^30 + 32 * q^32 - 72 * q^34 - 32 * q^35 + 56 * q^36 + 48 * q^38 + 56 * q^40 - 16 * q^41 - 56 * q^42 - 96 * q^43 + 24 * q^44 - 24 * q^46 + 16 * q^48 - 16 * q^49 - 16 * q^51 - 16 * q^52 - 24 * q^54 + 32 * q^56 + 32 * q^57 + 48 * q^58 - 16 * q^59 + 96 * q^60 + 48 * q^62 + 40 * q^64 + 64 * q^65 - 16 * q^66 + 80 * q^68 + 64 * q^70 + 96 * q^72 - 96 * q^73 + 40 * q^74 - 16 * q^75 + 48 * q^76 + 96 * q^78 + 8 * q^80 - 96 * q^81 + 32 * q^82 + 128 * q^83 + 64 * q^86 - 72 * q^88 - 16 * q^89 + 152 * q^90 - 16 * q^91 - 120 * q^92 + 88 * q^94 - 160 * q^96 - 16 * q^97 + 128 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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