LMFDB - Embedded newform 156.3.l.c.47.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [156,3,Mod(47,156)] 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("156.47"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(156, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,-36,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.9
Character	$\chi$	$=$	156.47
Dual form			156.3.l.c.83.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.72150 + 1.01806i) q^{2} +(-1.28511 + 2.71081i) q^{3} +(1.92709 - 3.50518i) q^{4} +(-5.44277 + 5.44277i) q^{5} +(-0.547465 - 5.97497i) q^{6} +(-2.75895 - 2.75895i) q^{7} +(0.251018 + 7.99606i) q^{8} +(-5.69698 - 6.96738i) q^{9} +(3.82862 - 14.9108i) q^{10} +(7.22392 - 7.22392i) q^{11} +(7.02536 + 9.72853i) q^{12} +(-3.11329 + 12.6217i) q^{13} +(7.55830 + 1.94073i) q^{14} +(-7.75976 - 21.7489i) q^{15} +(-8.57262 - 13.5096i) q^{16} -10.4137 q^{17} +(16.9006 + 6.19442i) q^{18} +(15.8902 - 15.8902i) q^{19} +(8.58918 + 29.5666i) q^{20} +(11.0245 - 3.93343i) q^{21} +(-5.08153 + 19.7903i) q^{22} -31.2150i q^{23} +(-21.9984 - 9.59536i) q^{24} -34.2475i q^{25} +(-7.49017 - 24.8977i) q^{26} +(26.2085 - 6.48958i) q^{27} +(-14.9874 + 4.35387i) q^{28} -30.0673i q^{29} +(35.5001 + 29.5407i) q^{30} +(-27.4600 + 27.4600i) q^{31} +(28.5114 + 14.5293i) q^{32} +(10.2991 + 28.8662i) q^{33} +(17.9271 - 10.6018i) q^{34} +30.0326 q^{35} +(-35.4006 + 6.54218i) q^{36} +(-11.1224 + 11.1224i) q^{37} +(-11.1777 + 43.5321i) q^{38} +(-30.2141 - 24.6598i) q^{39} +(-44.8870 - 42.1545i) q^{40} +(-28.9702 + 28.9702i) q^{41} +(-14.9742 + 17.9951i) q^{42} -76.9839 q^{43} +(-11.4000 - 39.2423i) q^{44} +(68.9292 + 6.91448i) q^{45} +(31.7789 + 53.7365i) q^{46} +(-41.9769 + 41.9769i) q^{47} +(47.6388 - 5.87739i) q^{48} -33.7764i q^{49} +(34.8661 + 58.9569i) q^{50} +(13.3827 - 28.2294i) q^{51} +(38.2418 + 35.2359i) q^{52} +30.1801i q^{53} +(-38.5110 + 37.8537i) q^{54} +78.6362i q^{55} +(21.3682 - 22.7532i) q^{56} +(22.6546 + 63.4960i) q^{57} +(30.6104 + 51.7608i) q^{58} +(-2.76368 + 2.76368i) q^{59} +(-91.1876 - 14.7127i) q^{60} -35.8124 q^{61} +(19.3163 - 75.2284i) q^{62} +(-3.50496 + 34.9403i) q^{63} +(-63.8740 + 4.01430i) q^{64} +(-51.7521 - 85.6420i) q^{65} +(-47.1175 - 39.2079i) q^{66} +(56.2324 - 56.2324i) q^{67} +(-20.0681 + 36.5018i) q^{68} +(84.6180 + 40.1148i) q^{69} +(-51.7010 + 30.5751i) q^{70} +(-8.19412 - 8.19412i) q^{71} +(54.2816 - 47.3024i) q^{72} +(-20.8717 + 20.8717i) q^{73} +(7.82383 - 30.4704i) q^{74} +(92.8384 + 44.0118i) q^{75} +(-25.0762 - 86.3199i) q^{76} -39.8608 q^{77} +(77.1187 + 11.6919i) q^{78} -59.4245i q^{79} +(120.189 + 26.8710i) q^{80} +(-16.0888 + 79.3861i) q^{81} +(20.3785 - 79.3655i) q^{82} +(-4.56261 - 4.56261i) q^{83} +(7.45791 - 46.2231i) q^{84} +(56.6791 - 56.6791i) q^{85} +(132.527 - 78.3745i) q^{86} +(81.5068 + 38.6398i) q^{87} +(59.5762 + 55.9495i) q^{88} +(-29.4572 - 29.4572i) q^{89} +(-125.701 + 58.2711i) q^{90} +(43.4120 - 26.2332i) q^{91} +(-109.414 - 60.1543i) q^{92} +(-39.1498 - 109.728i) q^{93} +(29.5279 - 114.998i) q^{94} +172.973i q^{95} +(-76.0264 + 58.6172i) q^{96} +(-73.7534 - 73.7534i) q^{97} +(34.3866 + 58.1460i) q^{98} +(-91.4863 - 9.17725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 36 q^{6} - 64 q^{9} - 8 q^{13} + 80 q^{16} + 48 q^{18} + 8 q^{21} + 124 q^{24} - 8 q^{28} + 24 q^{33} + 64 q^{34} - 128 q^{37} - 136 q^{40} - 140 q^{42} - 160 q^{45} + 88 q^{46} - 108 q^{48} - 320 q^{52}+ \cdots + 336 q^{97}+O(q^{100}) $ 96 * q - 36 * q^6 - 64 * q^9 - 8 * q^13 + 80 * q^16 + 48 * q^18 + 8 * q^21 + 124 * q^24 - 8 * q^28 + 24 * q^33 + 64 * q^34 - 128 * q^37 - 136 * q^40 - 140 * q^42 - 160 * q^45 + 88 * q^46 - 108 * q^48 - 320 * q^52 - 216 * q^54 + 136 * q^57 + 280 * q^58 + 80 * q^60 - 464 * q^61 - 240 * q^66 - 120 * q^70 - 32 * q^72 + 288 * q^73 + 88 * q^76 - 296 * q^78 - 144 * q^81 + 204 * q^84 + 848 * q^85 - 392 * q^93 + 1384 * q^94 - 204 * q^96 + 336 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.72150	+	1.01806i	−0.860748	+	0.509032i
$2$	−1.72150	+	1.01806i	−0.860748	+	0.509032i
$3$	−1.28511	+	2.71081i	−0.428370	+	0.903603i
$3$	−1.28511	+	2.71081i	−0.428370	+	0.903603i
$4$	1.92709	−	3.50518i	0.481773	−	0.876296i
$5$	−5.44277	+	5.44277i	−1.08855	+	1.08855i	−0.0928763	+	0.995678i	$0.529606\pi$
$5$	−5.44277	+	5.44277i	−1.08855	+	1.08855i	−0.995678	+	0.0928763i	$0.970394\pi$
$6$	−0.547465	−	5.97497i	−0.0912442	−	0.995829i
$7$	−2.75895	−	2.75895i	−0.394135	−	0.394135i	0.482023	−	0.876158i	$-0.339902\pi$
$7$	−2.75895	−	2.75895i	−0.394135	−	0.394135i	−0.876158	+	0.482023i	$0.839902\pi$
$8$	0.251018	+	7.99606i	0.0313772	+	0.999508i
$9$	−5.69698	−	6.96738i	−0.632998	−	0.774153i
$10$	3.82862	−	14.9108i	0.382862	−	1.49108i
$11$	7.22392	−	7.22392i	0.656720	−	0.656720i	−0.297883	−	0.954602i	$-0.596280\pi$
$11$	7.22392	−	7.22392i	0.656720	−	0.656720i	0.954602	+	0.297883i	$0.0962804\pi$
$12$	7.02536	+	9.72853i	0.585447	+	0.810711i
$13$	−3.11329	+	12.6217i	−0.239484	+	0.970900i
$13$	−3.11329	+	12.6217i	−0.239484	+	0.970900i
$14$	7.55830	+	1.94073i	0.539878	+	0.138624i
$15$	−7.75976	−	21.7489i	−0.517317	−	1.44993i
$16$	−8.57262	−	13.5096i	−0.535789	−	0.844352i
$17$	−10.4137			−0.612568			−0.306284	−	0.951940i	$-0.599086\pi$
$17$	−10.4137			−0.612568			−0.306284	+	0.951940i	$0.599086\pi$
$18$	16.9006	+	6.19442i	0.938920	+	0.344135i
$19$	15.8902	−	15.8902i	0.836326	−	0.836326i	−0.152047	−	0.988373i	$-0.548587\pi$
$19$	15.8902	−	15.8902i	0.836326	−	0.836326i	0.988373	+	0.152047i	$0.0485866\pi$
$20$	8.58918	+	29.5666i	0.429459	+	1.47833i
$21$	11.0245	−	3.93343i	0.524978	−	0.187306i
$22$	−5.08153	+	19.7903i	−0.230979	+	0.899561i
$23$		−	31.2150i		−	1.35718i	−0.734519	−	0.678588i	$-0.762592\pi$
$23$		−	31.2150i		−	1.35718i	0.734519	−	0.678588i	$-0.237408\pi$
$24$	−21.9984	−	9.59536i	−0.916599	−	0.399807i
$25$		−	34.2475i		−	1.36990i
$26$	−7.49017	−	24.8977i	−0.288084	−	0.957605i
$27$	26.2085	−	6.48958i	0.970685	−	0.240355i
$28$	−14.9874	+	4.35387i	−0.535263	+	0.155495i
$29$		−	30.0673i		−	1.03680i	−0.855137	−	0.518402i	$-0.826527\pi$
$29$		−	30.0673i		−	1.03680i	0.855137	−	0.518402i	$-0.173473\pi$
$30$	35.5001	+	29.5407i	1.18334	+	0.984689i
$31$	−27.4600	+	27.4600i	−0.885808	+	0.885808i	−0.994117	−	0.108309i	$-0.965456\pi$
$31$	−27.4600	+	27.4600i	−0.885808	+	0.885808i	0.108309	+	0.994117i	$0.465456\pi$
$32$	28.5114	+	14.5293i	0.890981	+	0.454040i
$33$	10.2991	+	28.8662i	0.312095	+	0.874733i
$34$	17.9271	−	10.6018i	0.527267	−	0.311817i
$35$	30.0326			0.858075
$36$	−35.4006	+	6.54218i	−0.983349	+	0.181727i
$37$	−11.1224	+	11.1224i	−0.300605	+	0.300605i	−0.841250	−	0.540646i	$-0.818180\pi$
$37$	−11.1224	+	11.1224i	−0.300605	+	0.300605i	0.540646	+	0.841250i	$0.318180\pi$
$38$	−11.1777	+	43.5321i	−0.294149	+	1.14558i
$39$	−30.2141	−	24.6598i	−0.774721	−	0.632303i
$40$	−44.8870	−	42.1545i	−1.12217	−	1.05386i
$41$	−28.9702	+	28.9702i	−0.706590	+	0.706590i	−0.965816	−	0.259227i	$-0.916532\pi$
$41$	−28.9702	+	28.9702i	−0.706590	+	0.706590i	0.259227	+	0.965816i	$0.416532\pi$
$42$	−14.9742	+	17.9951i	−0.356529	+	0.428454i
$43$	−76.9839			−1.79032			−0.895162	−	0.445742i	$-0.852940\pi$
$43$	−76.9839			−1.79032			−0.895162	+	0.445742i	$0.852940\pi$
$44$	−11.4000	−	39.2423i	−0.259091	−	0.891871i
$45$	68.9292	+	6.91448i	1.53176	+	0.153655i
$46$	31.7789	+	53.7365i	0.690845	+	1.16819i
$47$	−41.9769	+	41.9769i	−0.893125	+	0.893125i	−0.994816	−	0.101691i	$-0.967575\pi$
$47$	−41.9769	+	41.9769i	−0.893125	+	0.893125i	0.101691	+	0.994816i	$0.467575\pi$
$48$	47.6388	−	5.87739i	0.992475	−	0.122446i
$49$		−	33.7764i		−	0.689315i
$50$	34.8661	+	58.9569i	0.697322	+	1.17914i
$51$	13.3827	−	28.2294i	0.262406	−	0.553519i
$52$	38.2418	+	35.2359i	0.735419	+	0.677613i
$53$			30.1801i			0.569435i	0.958611	+	0.284718i	$0.0918998\pi$
$53$			30.1801i			0.569435i	−0.958611	+	0.284718i	$0.908100\pi$
$54$	−38.5110	+	37.8537i	−0.713167	+	0.700995i
$55$			78.6362i			1.42975i
$56$	21.3682	−	22.7532i	0.381574	−	0.406308i
$57$	22.6546	+	63.4960i	0.397450	+	1.11396i
$58$	30.6104	+	51.7608i	0.527766	+	0.892427i
$59$	−2.76368	+	2.76368i	−0.0468421	+	0.0468421i	−0.730140	−	0.683298i	$-0.760545\pi$
$59$	−2.76368	+	2.76368i	−0.0468421	+	0.0468421i	0.683298	+	0.730140i	$0.260545\pi$
$60$	−91.1876	−	14.7127i	−1.51979	−	0.245212i
$61$	−35.8124			−0.587089			−0.293544	−	0.955945i	$-0.594835\pi$
$61$	−35.8124			−0.587089			−0.293544	+	0.955945i	$0.594835\pi$
$62$	19.3163	−	75.2284i	0.311553	−	1.21336i
$63$	−3.50496	+	34.9403i	−0.0556343	+	0.554608i
$64$	−63.8740	+	4.01430i	−0.998031	+	0.0627235i
$65$	−51.7521	−	85.6420i	−0.796186	−	1.31757i
$66$	−47.1175	−	39.2079i	−0.713902	−	0.594058i
$67$	56.2324	−	56.2324i	0.839290	−	0.839290i	−0.149475	−	0.988765i	$-0.547758\pi$
$67$	56.2324	−	56.2324i	0.839290	−	0.839290i	0.988765	+	0.149475i	$0.0477584\pi$
$68$	−20.0681	+	36.5018i	−0.295119	+	0.536791i
$69$	84.6180	+	40.1148i	1.22635	+	0.581373i
$70$	−51.7010	+	30.5751i	−0.738586	+	0.436787i
$71$	−8.19412	−	8.19412i	−0.115410	−	0.115410i	0.647043	−	0.762453i	$-0.276005\pi$
$71$	−8.19412	−	8.19412i	−0.115410	−	0.115410i	−0.762453	+	0.647043i	$0.776005\pi$
$72$	54.2816	−	47.3024i	0.753911	−	0.656977i
$73$	−20.8717	+	20.8717i	−0.285914	+	0.285914i	−0.835462	−	0.549548i	$-0.814800\pi$
$73$	−20.8717	+	20.8717i	−0.285914	+	0.285914i	0.549548	+	0.835462i	$0.314800\pi$
$74$	7.82383	−	30.4704i	0.105727	−	0.411762i
$75$	92.8384	+	44.0118i	1.23785	+	0.586824i
$76$	−25.0762	−	86.3199i	−0.329950	−	1.13579i
$77$	−39.8608			−0.517673
$78$	77.1187	+	11.6919i	0.988702	+	0.149896i
$79$		−	59.4245i		−	0.752209i	−0.926577	−	0.376104i	$-0.877263\pi$
$79$		−	59.4245i		−	0.752209i	0.926577	−	0.376104i	$-0.122737\pi$
$80$	120.189	+	26.8710i	1.50236	+	0.335887i
$81$	−16.0888	+	79.3861i	−0.198627	+	0.980075i
$82$	20.3785	−	79.3655i	0.248519	−	0.967872i
$83$	−4.56261	−	4.56261i	−0.0549712	−	0.0549712i	0.679087	−	0.734058i	$-0.262376\pi$
$83$	−4.56261	−	4.56261i	−0.0549712	−	0.0549712i	−0.734058	+	0.679087i	$0.762376\pi$
$84$	7.45791	−	46.2231i	0.0887846	−	0.550275i
$85$	56.6791	−	56.6791i	0.666813	−	0.666813i
$86$	132.527	−	78.3745i	1.54102	−	0.911331i
$87$	81.5068	+	38.6398i	0.936860	+	0.444136i
$88$	59.5762	+	55.9495i	0.677002	+	0.635790i
$89$	−29.4572	−	29.4572i	−0.330980	−	0.330980i	0.521979	−	0.852958i	$-0.325194\pi$
$89$	−29.4572	−	29.4572i	−0.330980	−	0.330980i	−0.852958	+	0.521979i	$0.825194\pi$
$90$	−125.701	+	58.2711i	−1.39667	+	0.647456i
$91$	43.4120	−	26.2332i	0.477055	−	0.288277i
$92$	−109.414	−	60.1543i	−1.18929	−	0.653851i
$93$	−39.1498	−	109.728i	−0.420965	−	1.17987i
$94$	29.5279	−	114.998i	0.314126	−	1.22338i
$95$			172.973i			1.82077i
$96$	−76.0264	+	58.6172i	−0.791942	+	0.610596i
$97$	−73.7534	−	73.7534i	−0.760344	−	0.760344i	0.216040	−	0.976384i	$-0.430686\pi$
$97$	−73.7534	−	73.7534i	−0.760344	−	0.760344i	−0.976384	+	0.216040i	$0.930686\pi$
$98$	34.3866	+	58.1460i	0.350883	+	0.593326i
$99$	−91.4863	−	9.17725i	−0.924104	−	0.0926995i
$100$	−120.044	−	65.9981i	−1.20044	−	0.659981i
$101$	−17.6895			−0.175144			−0.0875719	−	0.996158i	$-0.527911\pi$
$101$	−17.6895			−0.175144			−0.0875719	+	0.996158i	$0.527911\pi$
$102$	5.70111	+	62.2213i	0.0558933	+	0.610013i
$103$	−32.3819			−0.314388			−0.157194	−	0.987568i	$-0.550245\pi$
$103$	−32.3819			−0.314388			−0.157194	+	0.987568i	$0.550245\pi$
$104$	−101.705	−	21.7258i	−0.977937	−	0.208902i
$105$	−38.5952	+	81.4127i	−0.367574	+	0.775359i
$106$	−30.7252	−	51.9548i	−0.289861	−	0.490140i
$107$	−85.2271			−0.796515			−0.398258	−	0.917274i	$-0.630385\pi$
$107$	−85.2271			−0.796515			−0.398258	+	0.917274i	$0.630385\pi$
$108$	27.7590	−	104.372i	0.257028	−	0.966404i
$109$	128.706	+	128.706i	1.18079	+	1.18079i	0.979540	+	0.201248i	$0.0644998\pi$
$109$	128.706	+	128.706i	1.18079	+	1.18079i	0.201248	+	0.979540i	$0.435500\pi$
$110$	−80.0567	−	135.372i	−0.727788	−	1.23065i
$111$	−15.8572	−	44.4441i	−0.142857	−	0.400397i
$112$	−13.6209	+	60.9238i	−0.121616	+	0.543962i
$113$		−	98.8848i		−	0.875086i	−0.899197	−	0.437543i	$-0.855849\pi$
$113$		−	98.8848i		−	0.875086i	0.899197	−	0.437543i	$-0.144151\pi$
$114$	−103.643	−	86.2441i	−0.909147	−	0.756527i
$115$	169.896	+	169.896i	1.47736	+	1.47736i
$116$	−105.391	−	57.9425i	−0.908547	−	0.499505i
$117$	105.677	−	50.2141i	0.903219	−	0.429180i
$118$	1.94406	−	7.57127i	0.0164751	−	0.0641633i
$119$	28.7307	+	28.7307i	0.241435	+	0.241435i
$120$	171.958	−	67.5068i	1.43298	−	0.562557i
$121$			16.6301i			0.137438i
$122$	61.6509	−	36.4593i	0.505335	−	0.298847i
$123$	−41.3028	−	115.763i	−0.335795	−	0.941159i
$124$	43.3344	+	149.171i	0.349471	+	1.20299i
$125$	50.3320	+	50.3320i	0.402656	+	0.402656i
$126$	−29.5377	−	63.7178i	−0.234426	−	0.505697i
$127$	103.720			0.816694			0.408347	−	0.912827i	$-0.366105\pi$
$127$	103.720			0.816694			0.408347	+	0.912827i	$0.366105\pi$
$128$	105.872	−	71.9384i	0.827125	−	0.562019i
$129$	98.9328	−	208.689i	0.766921	−	1.61774i
$130$	176.280	+	94.7454i	1.35600	+	0.728810i
$131$	−56.1262			−0.428444			−0.214222	−	0.976785i	$-0.568722\pi$
$131$	−56.1262			−0.428444			−0.214222	+	0.976785i	$0.568722\pi$
$132$	121.029	+	19.5275i	0.916884	+	0.147936i
$133$	−87.6804			−0.659251
$134$	−39.5557	+	154.052i	−0.295192	+	1.14964i
$135$	−107.326	+	177.968i	−0.795004	+	1.31828i
$136$	−2.61401	−	83.2682i	−0.0192207	−	0.612266i
$137$	75.0074	+	75.0074i	0.547499	+	0.547499i	0.925717	−	0.378217i	$-0.123463\pi$
$137$	75.0074	+	75.0074i	0.547499	+	0.547499i	−0.378217	+	0.925717i	$0.623463\pi$
$138$	−186.509	+	17.0891i	−1.35151	+	0.123834i
$139$		−	173.052i		−	1.24498i	−0.782628	−	0.622490i	$-0.786121\pi$
$139$		−	173.052i		−	1.24498i	0.782628	−	0.622490i	$-0.213879\pi$
$140$	57.8757	−	105.270i	0.413398	−	0.751927i
$141$	−59.8464	−	167.736i	−0.424443	−	1.18962i
$142$	22.4483	+	5.76401i	0.158087	+	0.0405916i
$143$	68.6880	+	113.668i	0.480335	+	0.794883i
$144$	−45.2887	+	136.693i	−0.314505	+	0.949256i
$145$	163.650	+	163.650i	1.12862	+	1.12862i
$146$	14.6818	−	57.1793i	0.100560	−	0.391639i
$147$	91.5615	+	43.4064i	0.622867	+	0.295282i
$148$	17.5521	+	60.4198i	0.118595	+	0.408242i
$149$	−138.106	+	138.106i	−0.926884	+	0.926884i	−0.997503	−	0.0706197i	$-0.977502\pi$
$149$	−138.106	+	138.106i	−0.926884	+	0.926884i	0.0706197	+	0.997503i	$0.477502\pi$
$150$	−204.628	+	18.7493i	−1.36419	+	0.124995i
$151$	−106.560	−	106.560i	−0.705693	−	0.705693i	0.259933	−	0.965627i	$-0.416299\pi$
$151$	−106.560	−	106.560i	−0.705693	−	0.705693i	−0.965627	+	0.259933i	$0.916299\pi$
$152$	131.048	+	123.070i	0.862156	+	0.809673i
$153$	59.3264	+	72.5559i	0.387754	+	0.474222i
$154$	68.6202	−	40.5808i	0.445586	−	0.263512i
$155$		−	298.917i		−	1.92850i
$156$	−144.663	+	58.3842i	−0.927325	+	0.374258i
$157$	148.752			0.947467			0.473733	−	0.880668i	$-0.342906\pi$
$157$	148.752			0.947467			0.473733	+	0.880668i	$0.342906\pi$
$158$	60.4979	+	102.299i	0.382898	+	0.647462i
$159$	−81.8124	−	38.7847i	−0.514543	−	0.243929i
$160$	−234.261	+	76.1014i	−1.46413	+	0.475634i
$161$	−86.1206	+	86.1206i	−0.534911	+	0.534911i
$162$	−53.1233	−	153.042i	−0.327922	−	0.944705i
$163$	36.6617	+	36.6617i	0.224919	+	0.224919i	0.810566	−	0.585647i	$-0.199160\pi$
$163$	36.6617	+	36.6617i	0.224919	+	0.224919i	−0.585647	+	0.810566i	$0.699160\pi$
$164$	45.7175	+	157.374i	0.278766	+	0.959597i
$165$	−213.168	−	101.056i	−1.29193	−	0.612462i
$166$	12.4995	+	3.20949i	0.0752985	+	0.0193343i
$167$	67.0902	−	67.0902i	0.401738	−	0.401738i	−0.477107	−	0.878845i	$-0.658315\pi$
$167$	67.0902	−	67.0902i	0.401738	−	0.401738i	0.878845	+	0.477107i	$0.158315\pi$
$168$	34.2193	+	87.1655i	0.203686	+	0.518842i
$169$	−149.615	−	78.5902i	−0.885295	−	0.465031i
$170$	−39.8699	+	155.276i	−0.234529	+	0.913387i
$171$	−201.239	−	20.1869i	−1.17684	−	0.118052i
$172$	−148.355	+	269.843i	−0.862530	+	1.56885i
$173$	1.07602			0.00621977			0.00310988	−	0.999995i	$-0.499010\pi$
$173$	1.07602			0.00621977			0.00310988	+	0.999995i	$0.499010\pi$
$174$	−179.651	+	16.4608i	−1.03248	+	0.0946024i
$175$	−94.4870	+	94.4870i	−0.539926	+	0.539926i
$176$	−159.520	−	35.6645i	−0.906366	−	0.202639i
$177$	−3.94018	−	11.0435i	−0.0222609	−	0.0623924i
$178$	80.6997	+	20.7211i	0.453369	+	0.116411i
$179$			280.851i			1.56900i	0.620130	+	0.784499i	$0.287080\pi$
$179$			280.851i			1.56900i	−0.620130	+	0.784499i	$0.712920\pi$
$180$	157.070	−	228.285i	0.872609	−	1.26825i
$181$			311.872i			1.72305i	0.507715	+	0.861525i	$0.330490\pi$
$181$			311.872i			1.72305i	−0.507715	+	0.861525i	$0.669510\pi$
$182$	−48.0265	+	89.3565i	−0.263882	+	0.490970i
$183$	46.0229	−	97.0807i	0.251491	−	0.530495i
$184$	249.597	−	7.83552i	1.35651	−	0.0425844i
$185$		−	121.073i		−	0.654449i
$186$	179.106	+	149.040i	0.962938	+	0.801288i
$187$	−75.2274	+	75.2274i	−0.402286	+	0.402286i
$188$	66.2433	+	228.030i	0.352358	+	1.21293i
$189$	−90.2122	−	54.4034i	−0.477313	−	0.287849i
$190$	−176.098	−	297.773i	−0.926831	−	1.56723i
$191$	97.0718			0.508229			0.254115	−	0.967174i	$-0.418216\pi$
$191$	97.0718			0.508229			0.254115	+	0.967174i	$0.418216\pi$
$192$	71.2031	−	178.309i	0.370850	−	0.928693i
$193$	−118.585	+	118.585i	−0.614431	+	0.614431i	−0.944098	−	0.329666i	$-0.893064\pi$
$193$	−118.585	+	118.585i	−0.614431	+	0.614431i	0.329666	+	0.944098i	$0.393064\pi$
$194$	202.052	+	51.8805i	1.04150	+	0.267425i
$195$	298.666	−	30.2307i	1.53162	−	0.155029i
$196$	−118.393	−	65.0903i	−0.604044	−	0.332094i
$197$	−28.2416	+	28.2416i	−0.143358	+	0.143358i	−0.775144	−	0.631785i	$-0.782322\pi$
$197$	−28.2416	+	28.2416i	−0.143358	+	0.143358i	0.631785	+	0.775144i	$0.282322\pi$
$198$	166.836	−	77.3403i	0.842607	−	0.390607i
$199$	−95.0913			−0.477846			−0.238923	−	0.971039i	$-0.576794\pi$
$199$	−95.0913			−0.477846			−0.238923	+	0.971039i	$0.576794\pi$
$200$	273.845	−	8.59672i	1.36923	−	0.0429836i
$201$	80.1706	+	224.700i	0.398859	+	1.11791i
$202$	30.4524	−	18.0091i	0.150755	−	0.0891537i
$203$	−82.9541	+	82.9541i	−0.408641	+	0.408641i
$204$	−73.1597	−	101.310i	−0.358626	−	0.496616i
$205$		−	315.356i		−	1.53832i
$206$	55.7453	−	32.9669i	0.270608	−	0.160033i
$207$	−217.487	+	177.832i	−1.05066	+	0.859089i
$208$	197.204	−	66.1417i	0.948095	−	0.317989i
$209$		−	229.579i		−	1.09846i
$210$	−16.4418	−	179.444i	−0.0782944	−	0.854495i
$211$		−	83.2846i		−	0.394714i	−0.980332	−	0.197357i	$-0.936764\pi$
$211$		−	83.2846i		−	0.394714i	0.980332	−	0.197357i	$-0.0632358\pi$
$212$	105.787	+	58.1598i	0.498994	+	0.274339i
$213$	32.7431	−	11.6824i	0.153723	−	0.0548468i
$214$	146.718	−	86.7667i	0.685599	−	0.405452i
$215$	419.006	−	419.006i	1.94886	−	1.94886i
$216$	58.4699	+	207.936i	0.270694	+	0.962665i
$217$	151.522			0.698256
$218$	−352.598	−	90.5359i	−1.61742	−	0.415302i
$219$	−29.7568	−	83.4017i	−0.135876	−	0.380830i
$220$	275.634	+	151.539i	1.25288	+	0.688815i
$221$	32.4208	−	131.438i	0.146700	−	0.594742i
$222$	72.5449	+	60.3667i	0.326779	+	0.271922i
$223$	−260.917	+	260.917i	−1.17003	+	1.17003i	−0.187829	+	0.982202i	$0.560145\pi$
$223$	−260.917	+	260.917i	−1.17003	+	1.17003i	−0.982202	+	0.187829i	$0.939855\pi$
$224$	−38.5759	−	118.747i	−0.172214	−	0.530120i
$225$	−238.615	+	195.107i	−1.06051	+	0.867144i
$226$	100.671	+	170.230i	0.445447	+	0.753229i
$227$	−68.1176	−	68.1176i	−0.300077	−	0.300077i	0.540967	−	0.841044i	$-0.318059\pi$
$227$	−68.1176	−	68.1176i	−0.300077	−	0.300077i	−0.841044	+	0.540967i	$0.818059\pi$
$228$	266.223	+	42.9539i	1.16764	+	0.188394i
$229$	−153.346	+	153.346i	−0.669631	+	0.669631i	−0.957631	−	0.287999i	$-0.907010\pi$
$229$	−153.346	+	153.346i	−0.669631	+	0.669631i	0.287999	+	0.957631i	$0.407010\pi$
$230$	−465.441	−	119.510i	−2.02366	−	0.519611i
$231$	51.2255	−	108.055i	0.221756	−	0.467771i
$232$	240.420	−	7.54743i	1.03629	−	0.0325320i
$233$	316.762			1.35949			0.679746	−	0.733448i	$-0.262090\pi$
$233$	316.762			1.35949			0.679746	+	0.733448i	$0.262090\pi$
$234$	−130.801	+	194.029i	−0.558977	+	0.829183i
$235$		−	456.941i		−	1.94443i
$236$	4.36134	+	15.0131i	0.0184803	+	0.0636148i
$237$	161.089	+	76.3670i	0.679698	+	0.322224i
$238$	−78.7095	−	20.2101i	−0.330712	−	0.0849164i
$239$	−92.0182	−	92.0182i	−0.385013	−	0.385013i	0.487891	−	0.872905i	$-0.337766\pi$
$239$	−92.0182	−	92.0182i	−0.385013	−	0.385013i	−0.872905	+	0.487891i	$0.837766\pi$
$240$	−227.298	+	291.276i	−0.947074	+	1.21365i
$241$	277.003	−	277.003i	1.14939	−	1.14939i	0.162716	−	0.986673i	$-0.447974\pi$
$241$	277.003	−	277.003i	1.14939	−	1.14939i	0.986673	−	0.162716i	$-0.0520255\pi$
$242$	−16.9304	−	28.6286i	−0.0699605	−	0.118300i
$243$	−194.525	−	145.634i	−0.800513	−	0.599315i
$244$	−69.0139	+	125.529i	−0.282844	+	0.514464i
$245$	183.837	+	183.837i	0.750357	+	0.750357i
$246$	188.956	+	157.236i	0.768114	+	0.639170i
$247$	151.090	+	250.032i	0.611702	+	1.01228i
$248$	−226.465	−	212.679i	−0.913166	−	0.857578i
$249$	18.2318	−	6.50491i	0.0732202	−	0.0261242i
$250$	−137.887	−	35.4051i	−0.551549	−	0.141620i
$251$		−	298.102i		−	1.18766i	−0.804591	−	0.593829i	$-0.797616\pi$
$251$		−	298.102i		−	1.18766i	0.804591	−	0.593829i	$-0.202384\pi$
$252$	115.718	+	79.6187i	0.459197	+	0.315947i
$253$	−225.495	−	225.495i	−0.891284	−	0.891284i
$254$	−178.554	+	105.594i	−0.702967	+	0.415723i
$255$	80.8074	+	226.485i	0.316892	+	0.888178i
$256$	−109.020	+	231.626i	−0.425860	+	0.904789i
$257$	−54.4517			−0.211874			−0.105937	−	0.994373i	$-0.533784\pi$
$257$	−54.4517			−0.211874			−0.105937	+	0.994373i	$0.533784\pi$
$258$	42.1460	+	459.977i	0.163357	+	1.78285i
$259$	61.3720			0.236958
$260$	−399.922	+	16.3605i	−1.53816	+	0.0629249i
$261$	−209.490	+	171.293i	−0.802646	+	0.656295i
$262$	96.6210	−	57.1400i	0.368782	−	0.218092i
$263$	−522.069			−1.98505			−0.992526	−	0.122032i	$-0.961059\pi$
$263$	−522.069			−1.98505			−0.992526	+	0.122032i	$0.961059\pi$
$264$	−228.231	+	89.5984i	−0.864510	+	0.339388i
$265$	−164.263	−	164.263i	−0.619861	−	0.619861i
$266$	150.941	−	89.2642i	0.567449	−	0.335580i
$267$	117.709	−	41.9971i	0.440856	−	0.157292i
$268$	−88.7399	−	305.470i	−0.331119	−	1.13981i
$269$			393.339i			1.46223i	0.682255	+	0.731114i	$0.260999\pi$
$269$			393.339i			1.46223i	−0.682255	+	0.731114i	$0.739001\pi$
$270$	3.57750	−	415.636i	0.0132500	−	1.53939i
$271$	−200.463	−	200.463i	−0.739715	−	0.739715i	0.232808	−	0.972523i	$-0.425209\pi$
$271$	−200.463	−	200.463i	−0.739715	−	0.739715i	−0.972523	+	0.232808i	$0.925209\pi$
$272$	89.2724	+	140.685i	0.328207	+	0.517223i
$273$	15.3240	+	151.394i	0.0561317	+	0.554558i
$274$	−205.487	−	52.7626i	−0.749953	−	0.192564i
$275$	−247.401	−	247.401i	−0.899640	−	0.899640i
$276$	303.676	−	219.297i	1.10028	−	0.794554i
$277$		−	179.237i		−	0.647064i	−0.946217	−	0.323532i	$-0.895130\pi$
$277$		−	179.237i		−	0.647064i	0.946217	−	0.323532i	$-0.104870\pi$
$278$	176.178	+	297.909i	0.633734	+	1.07161i
$279$	347.764	+	34.8852i	1.24647	+	0.125037i
$280$	7.53871	+	240.143i	0.0269240	+	0.857652i
$281$	176.486	+	176.486i	0.628066	+	0.628066i	0.947581	−	0.319515i	$-0.103520\pi$
$281$	176.486	+	176.486i	0.628066	+	0.628066i	−0.319515	+	0.947581i	$0.603520\pi$
$282$	273.791	+	227.830i	0.970892	+	0.807907i
$283$	400.184			1.41408			0.707039	−	0.707174i	$-0.250030\pi$
$283$	400.184			1.41408			0.707039	+	0.707174i	$0.250030\pi$
$284$	−44.5127	+	12.9311i	−0.156735	+	0.0455319i
$285$	−468.898	−	222.290i	−1.64526	−	0.779964i
$286$	−233.968	−	125.751i	−0.818068	−	0.439688i
$287$	159.854			0.556984
$288$	−61.1978	−	281.423i	−0.212492	−	0.977163i
$289$	−180.556			−0.624760
$290$	−448.328	−	115.116i	−1.54596	−	0.396953i
$291$	294.713	−	105.150i	1.01276	−	0.361341i
$292$	32.9374	+	113.381i	0.112799	+	0.388291i
$293$	−286.353	−	286.353i	−0.977314	−	0.977314i	0.0224343	−	0.999748i	$-0.492858\pi$
$293$	−286.353	−	286.353i	−0.977314	−	0.977314i	−0.999748	+	0.0224343i	$0.992858\pi$
$294$	−201.813	+	18.4914i	−0.686439	+	0.0628960i
$295$		−	30.0842i		−	0.101980i
$296$	−91.7270	−	86.1432i	−0.309889	−	0.291024i
$297$	142.448	−	236.208i	0.479622	−	0.795314i
$298$	97.1479	−	378.349i	0.326000	−	1.26963i
$299$	393.987	+	97.1816i	1.31768	+	0.325022i
$300$	333.178	−	240.601i	1.11059	−	0.802003i
$301$	212.394	+	212.394i	0.705629	+	0.705629i
$302$	291.927	+	74.9575i	0.966644	+	0.248204i
$303$	22.7330	−	47.9529i	0.0750263	−	0.158260i
$304$	−350.891	−	78.4500i	−1.15425	−	0.258059i
$305$	194.919	−	194.919i	0.639078	−	0.639078i
$306$	−175.997	−	64.5066i	−0.575153	−	0.210806i
$307$	289.250	+	289.250i	0.942184	+	0.942184i	0.998418	−	0.0562339i	$-0.0179092\pi$
$307$	289.250	+	289.250i	0.942184	+	0.942184i	−0.0562339	+	0.998418i	$0.517909\pi$
$308$	−76.8155	+	139.719i	−0.249401	+	0.453634i
$309$	41.6144	−	87.7813i	0.134674	−	0.284082i
$310$	304.317	+	514.585i	0.981668	+	1.65995i
$311$			217.935i			0.700755i	0.936608	+	0.350378i	$0.113947\pi$
$311$			217.935i			0.700755i	−0.936608	+	0.350378i	$0.886053\pi$
$312$	189.597	−	247.784i	0.607684	−	0.794179i
$313$	−394.594			−1.26068			−0.630341	−	0.776318i	$-0.717085\pi$
$313$	−394.594			−1.26068			−0.630341	+	0.776318i	$0.717085\pi$
$314$	−256.076	+	151.439i	−0.815530	+	0.482291i
$315$	−171.095	−	209.249i	−0.543160	−	0.664282i
$316$	−208.294	−	114.517i	−0.659158	−	0.362394i
$317$	343.861	−	343.861i	1.08473	−	1.08473i	0.0886734	−	0.996061i	$-0.471737\pi$
$317$	343.861	−	343.861i	1.08473	−	1.08473i	0.996061	−	0.0886734i	$-0.0282627\pi$
$318$	180.325	−	16.5225i	0.567060	−	0.0519577i
$319$	−217.204	−	217.204i	−0.680890	−	0.680890i
$320$	325.802	−	369.500i	1.01813	−	1.15469i
$321$	109.526	−	231.035i	0.341203	−	0.719734i
$322$	60.5800	−	235.932i	0.188137	−	0.732710i
$323$	−165.475	+	165.475i	−0.512307	+	0.512307i
$324$	247.258	+	209.379i	0.763143	+	0.646230i
$325$	432.262	+	106.623i	1.33004	+	0.328069i
$326$	−100.437	−	25.7890i	−0.308089	−	0.0791075i
$327$	−514.299	+	183.496i	−1.57278	+	0.561150i
$328$	−238.919	−	224.375i	−0.728412	−	0.684071i
$329$	231.624			0.704024
$330$	469.849	−	43.0506i	1.42379	−	0.130456i
$331$	−35.0496	+	35.0496i	−0.105890	+	0.105890i	−0.758067	−	0.652177i	$-0.773856\pi$
$331$	−35.0496	+	35.0496i	−0.105890	+	0.105890i	0.652177	+	0.758067i	$0.273856\pi$
$332$	−24.7854	+	7.20021i	−0.0746547	+	0.0216874i
$333$	140.858	+	14.1298i	0.422996	+	0.0424319i
$334$	−47.1934	+	183.798i	−0.141298	+	0.550292i
$335$			612.121i			1.82723i
$336$	−147.648	−	115.218i	−0.439430	−	0.342909i
$337$			221.657i			0.657737i	0.944376	+	0.328869i	$0.106667\pi$
$337$			221.657i			0.657737i	−0.944376	+	0.328869i	$0.893333\pi$
$338$	337.571	−	17.0248i	0.998731	−	0.0503691i
$339$	268.058	+	127.078i	0.790731	+	0.374861i
$340$	−89.4448	−	307.897i	−0.263073	−	0.905579i
$341$			396.738i			1.16346i
$342$	366.984	−	170.123i	1.07305	−	0.497435i
$343$	−228.376	+	228.376i	−0.665818	+	0.665818i
$344$	−19.3243	−	615.568i	−0.0561753	−	1.78944i
$345$	−678.892	+	242.221i	−1.96780	+	0.702090i
$346$	−1.85236	+	1.09546i	−0.00535365	+	0.00316606i
$347$	214.860			0.619194			0.309597	−	0.950868i	$-0.399806\pi$
$347$	214.860			0.619194			0.309597	+	0.950868i	$0.399806\pi$
$348$	292.511	−	211.234i	0.840549	−	0.606994i
$349$	−179.091	+	179.091i	−0.513156	+	0.513156i	−0.915492	−	0.402336i	$-0.868198\pi$
$349$	−179.091	+	179.091i	−0.513156	+	0.513156i	0.402336	+	0.915492i	$0.368198\pi$
$350$	66.4652	−	258.853i	0.189900	−	0.739579i
$351$	0.314828	+	351.000i	0.000896945	+	1.00000i
$352$	310.922	−	101.006i	0.883302	−	0.286948i
$353$	−323.534	+	323.534i	−0.916527	+	0.916527i	−0.996775	−	0.0802475i	$-0.974429\pi$
$353$	−323.534	+	323.534i	−0.916527	+	0.916527i	0.0802475	+	0.996775i	$0.474429\pi$
$354$	18.0259	+	14.9999i	0.0509207	+	0.0423726i
$355$	89.1975			0.251260
$356$	−160.020	+	46.4861i	−0.449493	+	0.130579i
$357$	−114.806	+	40.9614i	−0.321585	+	0.114738i
$358$	−285.924	−	483.483i	−0.798670	−	1.35051i
$359$	−227.130	+	227.130i	−0.632675	+	0.632675i	−0.948738	−	0.316063i	$-0.897639\pi$
$359$	−227.130	+	227.130i	−0.632675	+	0.632675i	0.316063	+	0.948738i	$0.397639\pi$
$360$	−37.9862	+	552.898i	−0.105517	+	1.53583i
$361$		−	143.997i		−	0.398883i
$362$	−317.506	−	536.886i	−0.877087	−	1.48311i
$363$	−45.0809	−	21.3715i	−0.124190	−	0.0588745i
$364$	−8.29314	−	202.721i	−0.0227834	−	0.556925i
$365$		−	227.200i		−	0.622465i
$366$	19.6061	+	213.978i	0.0535685	+	0.584640i
$367$			249.013i			0.678510i	0.940694	+	0.339255i	$0.110175\pi$
$367$			249.013i			0.678510i	−0.940694	+	0.339255i	$0.889825\pi$
$368$	−421.704	+	267.595i	−1.14593	+	0.727160i
$369$	366.889	+	36.8036i	0.994278	+	0.0997389i
$370$	123.260	+	208.427i	0.333135	+	0.563315i
$371$	83.2652	−	83.2652i	0.224434	−	0.224434i
$372$	−460.063	−	74.2292i	−1.23673	−	0.199541i
$373$	183.251			0.491290			0.245645	−	0.969360i	$-0.421000\pi$
$373$	183.251			0.491290			0.245645	+	0.969360i	$0.421000\pi$
$374$	52.9173	−	206.090i	0.141490	−	0.551042i
$375$	−201.122	+	71.7582i	−0.536327	+	0.191355i
$376$	−346.187	−	325.113i	−0.920709	−	0.864661i
$377$	379.501	+	93.6084i	1.00663	+	0.248298i
$378$	210.686	+	1.81344i	0.557371	+	0.00479746i
$379$	147.153	−	147.153i	0.388266	−	0.388266i	−0.485803	−	0.874069i	$-0.661473\pi$
$379$	147.153	−	147.153i	0.388266	−	0.388266i	0.874069	+	0.485803i	$0.161473\pi$
$380$	606.303	+	333.336i	1.59554	+	0.877199i
$381$	−133.292	+	281.165i	−0.349847	+	0.737967i
$382$	−167.109	+	98.8252i	−0.437457	+	0.258705i
$383$	−291.092	−	291.092i	−0.760031	−	0.760031i	0.216297	−	0.976328i	$-0.430602\pi$
$383$	−291.092	−	291.092i	−0.760031	−	0.760031i	−0.976328	+	0.216297i	$0.930602\pi$
$384$	58.9541	+	379.448i	0.153526	+	0.988145i
$385$	216.953	−	216.953i	0.563515	−	0.563515i
$386$	83.4166	−	324.871i	0.216105	−	0.841635i
$387$	438.576	+	536.376i	1.13327	+	1.38598i
$388$	−400.649	+	116.389i	−1.03260	+	0.299973i
$389$	276.916			0.711866			0.355933	−	0.934511i	$-0.384163\pi$
$389$	276.916			0.711866			0.355933	+	0.934511i	$0.384163\pi$
$390$	−483.376	+	356.103i	−1.23943	+	0.913085i
$391$			325.063i			0.831362i
$392$	270.078	−	8.47848i	0.688976	−	0.0216288i
$393$	72.1284	−	152.147i	0.183533	−	0.387144i
$394$	19.8660	−	77.3695i	0.0504214	−	0.196369i
$395$	323.434	+	323.434i	0.818820	+	0.818820i
$396$	−208.471	+	302.991i	−0.526441	+	0.765128i
$397$	−231.663	+	231.663i	−0.583535	+	0.583535i	−0.935873	−	0.352338i	$-0.885387\pi$
$397$	−231.663	+	231.663i	−0.583535	+	0.583535i	0.352338	+	0.935873i	$0.385387\pi$
$398$	163.699	−	96.8090i	0.411305	−	0.243239i
$399$	112.679	−	237.685i	0.282403	−	0.595701i
$400$	−462.671	+	293.591i	−1.15668	+	0.733977i
$401$	78.9536	+	78.9536i	0.196892	+	0.196892i	0.798666	−	0.601774i	$-0.205539\pi$
$401$	78.9536	+	78.9536i	0.196892	+	0.196892i	−0.601774	+	0.798666i	$0.705539\pi$
$402$	−366.773	−	305.202i	−0.912370	−	0.759209i
$403$	−261.101	−	432.084i	−0.647894	−	1.07217i
$404$	−34.0893	+	62.0050i	−0.0843796	+	0.153478i
$405$	−344.513	−	519.648i	−0.850649	−	1.28308i
$406$	58.3526	−	227.258i	0.143726	−	0.559748i
$407$			160.694i			0.394826i
$408$	229.084	+	99.9228i	0.561480	+	0.244909i
$409$	178.035	+	178.035i	0.435294	+	0.435294i	0.890425	−	0.455130i	$-0.150407\pi$
$409$	178.035	+	178.035i	0.435294	+	0.435294i	−0.455130	+	0.890425i	$0.650407\pi$
$410$	321.052	+	542.884i	0.783055	+	1.32411i
$411$	−299.724	+	106.938i	−0.729255	+	0.260190i
$412$	−62.4030	+	113.505i	−0.151464	+	0.275497i
$413$	15.2497			0.0369242
$414$	193.359	−	527.552i	0.467051	−	1.27428i
$415$	49.6665			0.119678
$416$	−272.149	+	314.628i	−0.654204	+	0.756318i
$417$	469.112	+	222.391i	1.12497	+	0.533312i
$418$	233.726	+	395.219i	0.559153	+	0.945500i
$419$	461.725			1.10197			0.550985	−	0.834515i	$-0.314252\pi$
$419$	461.725			1.10197			0.550985	+	0.834515i	$0.314252\pi$
$420$	210.990	+	292.173i	0.502357	+	0.695651i
$421$	−164.828	−	164.828i	−0.391515	−	0.391515i	0.483712	−	0.875227i	$-0.339288\pi$
$421$	−164.828	−	164.828i	−0.391515	−	0.391515i	−0.875227	+	0.483712i	$0.839288\pi$
$422$	84.7891	+	143.374i	0.200922	+	0.339749i
$423$	531.610	+	53.3273i	1.25676	+	0.126069i
$424$	−241.322	+	7.57572i	−0.569155	+	0.0178673i
$425$			356.642i			0.839157i
$426$	−44.4737	+	53.4457i	−0.104398	+	0.125459i
$427$	98.8045	+	98.8045i	0.231392	+	0.231392i
$428$	−164.241	+	298.737i	−0.383740	+	0.697983i
$429$	−396.405	+	40.1237i	−0.924021	+	0.0935283i
$430$	−294.742	+	1147.89i	−0.685446	+	2.66951i
$431$	−105.807	−	105.807i	−0.245492	−	0.245492i	0.573626	−	0.819118i	$-0.305536\pi$
$431$	−105.807	−	105.807i	−0.245492	−	0.245492i	−0.819118	+	0.573626i	$0.805536\pi$
$432$	−312.347	−	298.434i	−0.723027	−	0.690820i
$433$		−	691.891i		−	1.59790i	−0.601397	−	0.798950i	$-0.705389\pi$
$433$		−	691.891i		−	1.59790i	0.601397	−	0.798950i	$-0.294611\pi$
$434$	−260.844	+	154.259i	−0.601022	+	0.355435i
$435$	−653.930	+	233.315i	−1.50329	+	0.536356i
$436$	699.166	−	203.110i	1.60359	−	0.465848i
$437$	−496.013	−	496.013i	−1.13504	−	1.13504i
$438$	136.134	+	113.281i	0.310809	+	0.258633i
$439$	118.062			0.268934			0.134467	−	0.990918i	$-0.457068\pi$
$439$	118.062			0.268934			0.134467	+	0.990918i	$0.457068\pi$
$440$	−628.780	+	19.7391i	−1.42905	+	0.0448615i
$441$	−235.333	+	192.424i	−0.533635	+	0.436335i
$442$	78.0001	+	259.276i	0.176471	+	0.586598i
$443$	−715.543			−1.61522			−0.807611	−	0.589716i	$-0.799240\pi$
$443$	−715.543			−1.61522			−0.807611	+	0.589716i	$0.799240\pi$
$444$	−186.343	−	30.0657i	−0.419691	−	0.0677155i
$445$	320.657			0.720578
$446$	183.537	−	714.797i	0.411518	−	1.60268i
$447$	−196.897	−	551.859i	−0.440486	−	1.23458i
$448$	187.300	+	165.150i	0.418081	+	0.368638i
$449$	41.8739	+	41.8739i	0.0932604	+	0.0932604i	0.752198	−	0.658937i	$-0.228994\pi$
$449$	41.8739	+	41.8739i	0.0932604	+	0.0932604i	−0.658937	+	0.752198i	$0.728994\pi$
$450$	212.143	−	578.802i	0.471430	−	1.28623i
$451$			418.556i			0.928063i
$452$	−346.609	−	190.560i	−0.766835	−	0.421593i
$453$	425.804	−	151.922i	0.939965	−	0.335369i
$454$	186.612	+	47.9161i	0.411040	+	0.105542i
$455$	−93.5004	+	379.063i	−0.205495	+	0.833105i
$456$	−502.031	+	197.087i	−1.10094	+	0.432207i
$457$	−81.6833	−	81.6833i	−0.178738	−	0.178738i	0.612067	−	0.790806i	$-0.290338\pi$
$457$	−81.6833	−	81.6833i	−0.178738	−	0.178738i	−0.790806	+	0.612067i	$0.790338\pi$
$458$	107.868	−	420.099i	0.235520	−	0.917247i
$459$	−272.926	+	67.5803i	−0.594611	+	0.147234i
$460$	922.924	−	268.112i	2.00636	−	0.582851i
$461$	97.4905	−	97.4905i	0.211476	−	0.211476i	−0.593418	−	0.804894i	$-0.702222\pi$
$461$	97.4905	−	97.4905i	0.211476	−	0.211476i	0.804894	+	0.593418i	$0.202222\pi$
$462$	21.8224	+	238.167i	0.0472346	+	0.515513i
$463$	−148.096	−	148.096i	−0.319862	−	0.319862i	0.528852	−	0.848714i	$-0.322623\pi$
$463$	−148.096	−	148.096i	−0.319862	−	0.319862i	−0.848714	+	0.528852i	$0.822623\pi$
$464$	−406.198	+	257.756i	−0.875428	+	0.555508i
$465$	810.308	+	384.142i	1.74260	+	0.826112i
$466$	−545.304	+	322.483i	−1.17018	+	0.692024i
$467$		−	612.990i		−	1.31261i	−0.754495	−	0.656306i	$-0.772118\pi$
$467$		−	612.990i		−	1.31261i	0.754495	−	0.656306i	$-0.227882\pi$
$468$	27.6390	−	467.183i	0.0590576	−	0.998255i
$469$	−310.285			−0.661588
$470$	465.195	+	786.622i	0.989776	+	1.67366i
$471$	−191.163	+	403.239i	−0.405866	+	0.856134i
$472$	−22.7923	−	21.4048i	−0.0482888	−	0.0453492i
$473$	−556.125	+	556.125i	−1.17574	+	1.17574i
$474$	−355.060	+	32.5328i	−0.749071	+	0.0686347i
$475$	−544.199	−	544.199i	−1.14568	−	1.14568i
$476$	156.073	−	45.3397i	0.327885	−	0.0952514i
$477$	210.276	−	171.935i	0.440830	−	0.360451i
$478$	252.089	+	64.7286i	0.527384	+	0.135415i
$479$	565.402	−	565.402i	1.18038	−	1.18038i	0.200735	−	0.979646i	$-0.435667\pi$
$479$	565.402	−	565.402i	1.18038	−	1.18038i	0.979646	−	0.200735i	$-0.0643330\pi$
$480$	94.7543	−	732.835i	0.197405	−	1.52674i
$481$	−105.756	−	175.010i	−0.219867	−	0.363847i
$482$	−194.853	+	758.865i	−0.404258	+	1.57441i
$483$	−122.782	−	344.131i	−0.254207	−	0.712487i
$484$	58.2914	+	32.0477i	0.120437	+	0.0662142i
$485$	802.845			1.65535
$486$	483.138	+	52.6689i	0.994110	+	0.108372i
$487$	123.462	−	123.462i	0.253514	−	0.253514i	−0.568895	−	0.822410i	$-0.692629\pi$
$487$	123.462	−	123.462i	0.253514	−	0.253514i	0.822410	+	0.568895i	$0.192629\pi$
$488$	−8.98955	−	286.358i	−0.0184212	−	0.586800i
$489$	−146.497	+	52.2686i	−0.299586	+	0.106889i
$490$	−503.633	−	129.317i	−1.02782	−	0.263912i
$491$			582.782i			1.18693i	0.804860	+	0.593464i	$0.202240\pi$
$491$			582.782i			1.18693i	−0.804860	+	0.593464i	$0.797760\pi$
$492$	−485.363	−	78.3114i	−0.986510	−	0.159169i
$493$			313.111i			0.635113i
$494$	−514.650	−	276.610i	−1.04180	−	0.559938i
$495$	547.889	−	447.989i	1.10685	−	0.905029i
$496$	606.380	+	135.570i	1.22254	+	0.273328i
$497$			45.2143i			0.0909744i
$498$	−24.7636	+	29.7593i	−0.0497261	+	0.0597577i
$499$	58.4515	−	58.4515i	0.117137	−	0.117137i	−0.646108	−	0.763246i	$-0.723605\pi$
$499$	58.4515	−	58.4515i	0.117137	−	0.117137i	0.763246	+	0.646108i	$0.223605\pi$
$500$	273.417	−	79.4284i	0.546834	−	0.158857i
$501$	95.6505	+	268.087i	0.190919	+	0.535104i
$502$	303.487	+	513.182i	0.604556	+	1.02227i
$503$	554.637			1.10266			0.551329	−	0.834288i	$-0.314121\pi$
$503$	554.637			1.10266			0.551329	+	0.834288i	$0.314121\pi$
$504$	−280.265	−	19.2552i	−0.556080	−	0.0382049i
$505$	96.2800	−	96.2800i	0.190653	−	0.190653i
$506$	617.756	+	158.620i	1.22086	+	0.313479i
$507$	405.315	−	304.580i	0.799437	−	0.600750i
$508$	199.878	−	363.558i	0.393461	−	0.715665i
$509$	−137.865	+	137.865i	−0.270855	+	0.270855i	−0.829444	−	0.558589i	$-0.811343\pi$
$509$	−137.865	+	137.865i	−0.270855	+	0.270855i	0.558589	+	0.829444i	$0.311343\pi$
$510$	−369.686	−	307.626i	−0.724875	−	0.603189i
$511$	115.168			0.225377
$512$	−48.1321	−	509.733i	−0.0940080	−	0.995571i
$513$	313.337	−	519.579i	0.610794	−	1.01282i
$514$	93.7384	−	55.4353i	0.182370	−	0.107851i
$515$	176.247	−	176.247i	0.342228	−	0.342228i
$516$	−540.839	−	748.940i	−1.04814	−	1.45143i
$517$			606.475i			1.17307i
$518$	−105.652	+	62.4806i	−0.203961	+	0.120619i
$519$	−1.38280	+	2.91688i	−0.00266436	+	0.00562020i
$520$	671.808	−	435.310i	1.29194	−	0.837135i
$521$		−	561.832i		−	1.07837i	−0.842186	−	0.539187i	$-0.818732\pi$
$521$		−	561.832i		−	1.07837i	0.842186	−	0.539187i	$-0.181268\pi$
$522$	186.250	−	508.155i	0.356800	−	0.973477i
$523$			457.062i			0.873924i	0.899480	+	0.436962i	$0.143946\pi$
$523$			457.062i			0.873924i	−0.899480	+	0.436962i	$0.856054\pi$
$524$	−108.160	+	196.733i	−0.206413	+	0.375444i
$525$	−134.710	−	377.562i	−0.256591	−	0.719167i
$526$	898.739	−	531.499i	1.70863	−	1.01045i
$527$	285.960	−	285.960i	0.542618	−	0.542618i
$528$	301.681	−	386.597i	0.571366	−	0.732190i
$529$	−445.379			−0.841925
$530$	450.009	+	115.548i	0.849073	+	0.218015i
$531$	35.0003	+	3.51098i	0.0659139	+	0.00661201i
$532$	−168.968	+	307.336i	−0.317610	+	0.577699i
$533$	−275.460	−	455.846i	−0.516811	−	0.855245i
$534$	−159.879	+	192.133i	−0.299399	+	0.359799i
$535$	463.872	−	463.872i	0.867050	−	0.867050i
$536$	463.753	+	435.523i	0.865212	+	0.812542i
$537$	−761.333	−	360.924i	−1.41775	−	0.672112i
$538$	−400.444	−	677.132i	−0.744320	−	1.25861i
$539$	−243.998	−	243.998i	−0.452687	−	0.452687i
$540$	416.985	+	719.157i	0.772194	+	1.33177i
$541$	333.836	−	333.836i	0.617071	−	0.617071i	−0.327708	−	0.944779i	$-0.606276\pi$
$541$	333.836	−	333.836i	0.617071	−	0.617071i	0.944779	+	0.327708i	$0.106276\pi$
$542$	549.180	+	141.012i	1.01325	+	0.260170i
$543$	−845.426	−	400.790i	−1.55695	−	0.738103i
$544$	−296.908	−	151.303i	−0.545787	−	0.278131i
$545$	−1401.03			−2.57070
$546$	−180.509	−	245.024i	−0.330603	−	0.448761i
$547$			790.697i			1.44551i	0.691102	+	0.722757i	$0.257126\pi$
$547$			790.697i			1.44551i	−0.691102	+	0.722757i	$0.742874\pi$
$548$	407.461	−	118.368i	0.743542	−	0.216001i
$549$	204.023	+	249.519i	0.371626	+	0.454497i
$550$	677.770	+	174.030i	1.23231	+	0.316418i
$551$	−477.776	−	477.776i	−0.867106	−	0.867106i
$552$	−299.520	+	686.681i	−0.542608	+	1.24399i
$553$	−163.949	+	163.949i	−0.296472	+	0.296472i
$554$	182.474	+	308.555i	0.329376	+	0.556959i
$555$	328.206	+	155.592i	0.591362	+	0.280346i
$556$	−606.580	−	333.488i	−1.09097	−	0.599798i
$557$	−62.7640	−	62.7640i	−0.112682	−	0.112682i	0.648518	−	0.761200i	$-0.275389\pi$
$557$	−62.7640	−	62.7640i	−0.112682	−	0.112682i	−0.761200	+	0.648518i	$0.775389\pi$
$558$	−634.190	+	293.991i	−1.13654	+	0.526866i
$559$	239.674	−	971.668i	0.428754	−	1.73823i
$560$	−257.458	−	405.730i	−0.459747	−	0.724517i
$561$	−107.252	−	300.603i	−0.191179	−	0.535834i
$562$	−483.495	−	124.146i	−0.860312	−	0.220901i
$563$			83.6121i			0.148512i	0.997239	+	0.0742558i	$0.0236581\pi$
$563$			83.6121i			0.148512i	−0.997239	+	0.0742558i	$0.976342\pi$
$564$	−703.276	−	113.471i	−1.24694	−	0.201189i
$565$	538.207	+	538.207i	0.952579	+	0.952579i
$566$	−688.915	+	407.413i	−1.21717	+	0.719811i
$567$	263.410	−	174.634i	0.464568	−	0.307996i
$568$	63.4638	−	67.5776i	0.111732	−	0.118975i
$569$	70.7650			0.124367			0.0621836	−	0.998065i	$-0.480194\pi$
$569$	70.7650			0.124367			0.0621836	+	0.998065i	$0.480194\pi$
$570$	1033.51	−	94.6969i	1.81318	−	0.166135i
$571$	382.309			0.669543			0.334772	−	0.942299i	$-0.391341\pi$
$571$	382.309			0.669543			0.334772	+	0.942299i	$0.391341\pi$
$572$	530.796	−	21.7144i	0.927966	−	0.0379623i
$573$	−124.748	+	263.143i	−0.217710	+	0.459238i
$574$	−275.188	+	162.742i	−0.479422	+	0.283522i
$575$	−1069.04			−1.85919
$576$	391.858	+	422.165i	0.680309	+	0.732925i
$577$	−569.733	−	569.733i	−0.987406	−	0.987406i	0.0125162	−	0.999922i	$-0.496016\pi$
$577$	−569.733	−	569.733i	−0.987406	−	0.987406i	−0.999922	+	0.0125162i	$0.996016\pi$
$578$	310.826	−	183.817i	0.537761	−	0.318023i
$579$	−169.067	−	473.857i	−0.291998	−	0.818406i
$580$	888.989	−	258.254i	1.53274	−	0.445265i
$581$			25.1760i			0.0433322i
$582$	−400.297	+	481.052i	−0.687795	+	0.826549i
$583$	218.018	+	218.018i	0.373959	+	0.373959i
$584$	−172.131	−	161.652i	−0.294744	−	0.276802i
$585$	−301.870	+	848.477i	−0.516016	+	1.45039i
$586$	784.481	+	201.430i	1.33870	+	0.343737i
$587$	−229.283	−	229.283i	−0.390601	−	0.390601i	0.484301	−	0.874902i	$-0.339074\pi$
$587$	−229.283	−	229.283i	−0.390601	−	0.390601i	−0.874902	+	0.484301i	$0.839074\pi$
$588$	328.595	−	237.292i	0.558835	−	0.403557i
$589$			872.691i			1.48165i
$590$	30.6276	+	51.7898i	0.0519112	+	0.0877793i
$591$	−40.2640	−	112.851i	−0.0681286	−	0.190949i
$592$	245.607	+	54.9112i	0.414877	+	0.0927554i
$593$	−352.879	−	352.879i	−0.595075	−	0.595075i	0.343923	−	0.938998i	$-0.388244\pi$
$593$	−352.879	−	352.879i	−0.595075	−	0.595075i	−0.938998	+	0.343923i	$0.888244\pi$
$594$	−4.74824	+	551.652i	−0.00799366	+	0.928708i
$595$	−312.749			−0.525629
$596$	217.943	+	750.228i	0.365677	+	1.25877i
$597$	122.203	−	257.774i	0.204695	−	0.431783i
$598$	−777.184	+	233.806i	−1.29964	+	0.390980i
$599$	1088.44			1.81710			0.908550	−	0.417776i	$-0.137190\pi$
$599$	1088.44			1.81710			0.908550	+	0.417776i	$0.137190\pi$
$600$	−328.617	+	753.390i	−0.547695	+	1.25565i
$601$	−28.1338			−0.0468116			−0.0234058	−	0.999726i	$-0.507451\pi$
$601$	−28.1338			−0.0468116			−0.0234058	+	0.999726i	$0.507451\pi$
$602$	−581.867	−	149.405i	−0.966557	−	0.248181i
$603$	−712.148	−	71.4376i	−1.18101	−	0.118470i
$604$	−578.862	+	168.161i	−0.958380	+	0.278412i
$605$	−90.5135	−	90.5135i	−0.149609	−	0.149609i
$606$	9.68439	+	105.694i	0.0159808	+	0.174413i
$607$		−	161.951i		−	0.266805i	−0.991062	−	0.133403i	$-0.957410\pi$
$607$		−	161.951i		−	0.266805i	0.991062	−	0.133403i	$-0.0425904\pi$
$608$	683.925	−	222.178i	1.12488	−	0.365425i
$609$	−118.268	−	331.478i	−0.194200	−	0.544299i
$610$	−137.112	+	533.991i	−0.224774	+	0.875396i
$611$	−399.133	−	660.506i	−0.653246	−	1.08102i
$612$	368.649	−	68.1280i	0.602368	−	0.111320i
$613$	703.654	+	703.654i	1.14789	+	1.14789i	0.986968	+	0.160917i	$0.0514453\pi$
$613$	703.654	+	703.654i	1.14789	+	1.14789i	0.160917	+	0.986968i	$0.448555\pi$
$614$	−792.419	−	203.468i	−1.29058	−	0.331381i
$615$	854.870	+	405.267i	1.39003	+	0.658971i
$616$	−10.0058	−	318.729i	−0.0162431	−	0.517418i
$617$	−770.124	+	770.124i	−1.24818	+	1.24818i	−0.291651	+	0.956525i	$0.594204\pi$
$617$	−770.124	+	770.124i	−1.24818	+	1.24818i	−0.956525	+	0.291651i	$0.905796\pi$
$618$	17.7280	+	193.481i	0.0286861	+	0.313076i
$619$	−164.734	−	164.734i	−0.266130	−	0.266130i	0.561409	−	0.827539i	$-0.310260\pi$
$619$	−164.734	−	164.734i	−0.266130	−	0.266130i	−0.827539	+	0.561409i	$0.810260\pi$
$620$	−1047.76	−	576.042i	−1.68994	−	0.929100i
$621$	−202.573	−	818.099i	−0.326204	−	1.31739i
$622$	−221.872	−	375.174i	−0.356707	−	0.603174i
$623$			162.542i			0.260901i
$624$	−74.1310	+	619.581i	−0.118800	+	0.992918i
$625$	308.297			0.493275
$626$	679.291	−	401.722i	1.08513	−	0.641728i
$627$	622.345	+	295.034i	0.992575	+	0.470549i
$628$	286.659	−	521.404i	0.456464	−	0.830261i
$629$	115.825	−	115.825i	0.184141	−	0.184141i
$630$	507.568	+	186.035i	0.805664	+	0.295293i
$631$	−202.194	−	202.194i	−0.320434	−	0.320434i	0.528499	−	0.848934i	$-0.322755\pi$
$631$	−202.194	−	202.194i	−0.320434	−	0.320434i	−0.848934	+	0.528499i	$0.822755\pi$
$632$	475.162	−	14.9166i	0.751838	−	0.0236022i
$633$	225.769	+	107.030i	0.356665	+	0.169084i
$634$	−241.883	+	942.027i	−0.381518	+	1.48585i
$635$	−564.525	+	564.525i	−0.889015	+	0.889015i
$636$	−293.608	+	212.026i	−0.461647	+	0.333374i
$637$	426.316	+	105.156i	0.669256	+	0.165080i
$638$	595.043	+	152.788i	0.932669	+	0.239480i
$639$	−10.4098	+	103.773i	−0.0162908	+	0.162400i
$640$	−184.693	+	967.781i	−0.288582	+	1.51216i
$641$	158.903			0.247898			0.123949	−	0.992289i	$-0.460444\pi$
$641$	158.903			0.247898			0.123949	+	0.992289i	$0.460444\pi$
$642$	46.6589	+	509.230i	0.0726774	+	0.793193i
$643$	−101.002	+	101.002i	−0.157079	+	0.157079i	−0.781271	−	0.624192i	$-0.785428\pi$
$643$	−101.002	+	101.002i	−0.157079	+	0.157079i	0.624192	+	0.781271i	$0.285428\pi$
$644$	135.906	+	467.831i	0.211034	+	0.726446i
$645$	597.376	+	1674.31i	0.926165	+	2.59583i
$646$	116.400	−	453.329i	0.180186	−	0.701747i
$647$		−	291.993i		−	0.451303i	−0.974208	−	0.225652i	$-0.927549\pi$
$647$		−	291.993i		−	0.451303i	0.974208	−	0.225652i	$-0.0724511\pi$
$648$	−638.815	−	108.720i	−0.985825	−	0.167777i
$649$			39.9292i			0.0615242i
$650$	−852.685	+	256.520i	−1.31182	+	0.394646i
$651$	−194.722	+	410.746i	−0.299112	+	0.630947i
$652$	199.157	−	57.8555i	0.305455	−	0.0887355i
$653$		−	380.358i		−	0.582478i	−0.956650	−	0.291239i	$-0.905932\pi$
$653$		−	380.358i		−	0.582478i	0.956650	−	0.291239i	$-0.0940675\pi$
$654$	698.552	−	839.476i	1.06812	−	1.28360i
$655$	305.482	−	305.482i	0.466385	−	0.466385i
$656$	639.727	+	143.026i	0.975193	+	0.218027i
$657$	264.327	+	26.5154i	0.402324	+	0.0403583i
$658$	−398.739	+	235.808i	−0.605987	+	0.358371i
$659$	460.463			0.698729			0.349365	−	0.936987i	$-0.386397\pi$
$659$	460.463			0.698729			0.349365	+	0.936987i	$0.386397\pi$
$660$	−765.015	+	552.448i	−1.15911	+	0.837042i
$661$	341.332	−	341.332i	0.516388	−	0.516388i	−0.400089	−	0.916476i	$-0.631021\pi$
$661$	341.332	−	341.332i	0.516388	−	0.516388i	0.916476	+	0.400089i	$0.131021\pi$
$662$	24.6550	−	96.0204i	0.0372432	−	0.145046i
$663$	314.639	+	256.799i	0.474569	+	0.387329i
$664$	35.3376	−	37.6282i	0.0532193	−	0.0566690i
$665$	477.224	−	477.224i	0.717630	−	0.717630i
$666$	−256.871	+	119.078i	−0.385692	+	0.178795i
$667$	−938.553			−1.40713
$668$	−105.874	−	364.453i	−0.158495	−	0.545588i
$669$	−371.989	−	1042.60i	−0.556037	−	1.55845i
$670$	−623.178	−	1053.76i	−0.930116	−	1.57278i
$671$	−258.706	+	258.706i	−0.385553	+	0.385553i
$672$	371.475	+	48.0311i	0.552790	+	0.0714748i
$673$			737.757i			1.09622i	0.836406	+	0.548110i	$0.184653\pi$
$673$			737.757i			1.09622i	−0.836406	+	0.548110i	$0.815347\pi$
$674$	−225.661	−	381.582i	−0.334809	−	0.566146i
$675$	−222.252	−	897.575i	−0.329262	−	1.32974i
$676$	−563.795	+	372.977i	−0.834016	+	0.551741i
$677$		−	667.189i		−	0.985508i	−0.870169	−	0.492754i	$-0.835990\pi$
$677$		−	667.189i		−	0.985508i	0.870169	−	0.492754i	$-0.164010\pi$
$678$	−590.834	+	54.1360i	−0.871436	+	0.0798466i
$679$			406.963i			0.599357i
$680$	467.437	+	438.982i	0.687408	+	0.645562i
$681$	272.192	−	97.1152i	0.399695	−	0.142607i
$682$	−403.905	−	682.983i	−0.592236	−	1.00144i
$683$	−872.580	+	872.580i	−1.27757	+	1.27757i	−0.335544	+	0.942024i	$0.608920\pi$
$683$	−872.580	+	872.580i	−1.27757	+	1.27757i	−0.942024	+	0.335544i	$0.891080\pi$
$684$	−458.565	+	666.478i	−0.670417	+	0.974384i
$685$	−816.496			−1.19196
$686$	160.647	−	625.649i	0.234179	−	0.912024i
$687$	−218.625	−	612.756i	−0.318231	−	0.891931i
$688$	659.954	+	1040.02i	0.959235	+	1.51166i
$689$	−380.924	−	93.9594i	−0.552865	−	0.136371i
$690$	922.113	−	1108.14i	1.33640	−	1.60600i
$691$	−273.184	+	273.184i	−0.395346	+	0.395346i	−0.876588	−	0.481242i	$-0.840186\pi$
$691$	−273.184	+	273.184i	−0.395346	+	0.395346i	0.481242	+	0.876588i	$0.340186\pi$
$692$	2.07359	−	3.77165i	0.00299652	−	0.00545035i
$693$	227.086	+	277.725i	0.327686	+	0.400758i
$694$	−369.881	+	218.742i	−0.532970	+	0.315190i
$695$	941.883	+	941.883i	1.35523	+	1.35523i
$696$	−288.507	+	661.433i	−0.414521	+	0.950334i
$697$	301.685	−	301.685i	0.432834	−	0.432834i
$698$	125.979	−	490.632i	0.180485	−	0.702911i
$699$	−407.074	+	858.680i	−0.582366	+	1.22844i
$700$	149.109	+	513.279i	0.213013	+	0.733256i
$701$	510.090			0.727660			0.363830	−	0.931465i	$-0.381469\pi$
$701$	510.090			0.727660			0.363830	+	0.931465i	$0.381469\pi$
$702$	−357.882	−	603.924i	−0.509804	−	0.860291i
$703$			353.473i			0.502807i
$704$	−432.421	+	490.419i	−0.614235	+	0.696618i
$705$	1238.68	+	587.220i	1.75699	+	0.832936i
$706$	227.584	−	886.341i	0.322357	−	1.25544i
$707$	48.8044	+	48.8044i	0.0690303	+	0.0690303i
$708$	−46.3024	−	7.47071i	−0.0653989	−	0.0105519i
$709$	389.393	−	389.393i	0.549215	−	0.549215i	−0.376999	−	0.926214i	$-0.623044\pi$
$709$	389.393	−	389.393i	0.549215	−	0.549215i	0.926214	+	0.376999i	$0.123044\pi$
$710$	−153.553	+	90.8087i	−0.216272	+	0.127900i
$711$	−414.033	+	338.540i	−0.582325	+	0.476147i
$712$	228.147	−	242.936i	0.320431	−	0.341202i
$713$	857.166	+	857.166i	1.20220	+	1.20220i
$714$	155.936	−	187.394i	0.218398	−	0.262457i
$715$	−992.523	−	244.818i	−1.38814	−	0.342402i
$716$	984.433	+	541.225i	1.37491	+	0.755901i
$717$	367.698	−	131.190i	0.512828	−	0.182971i
$718$	159.771	−	622.237i	0.222522	−	0.866626i
$719$		−	116.566i		−	0.162123i	−0.996709	−	0.0810613i	$-0.974169\pi$
$719$		−	116.566i		−	0.162123i	0.996709	−	0.0810613i	$-0.0258310\pi$
$720$	−497.492	−	990.483i	−0.690961	−	1.37567i
$721$	89.3400	+	89.3400i	0.123911	+	0.123911i
$722$	146.598	+	247.890i	0.203044	+	0.343337i
$723$	394.923	+	1106.88i	0.546228	+	1.53096i
$724$	1093.17	+	601.006i	1.50990	+	0.830119i
$725$	−1029.73			−1.42032
$726$	99.3641	−	9.10437i	0.136865	−	0.0125405i
$727$	145.407			0.200009			0.100004	−	0.994987i	$-0.468114\pi$
$727$	145.407			0.200009			0.100004	+	0.994987i	$0.468114\pi$
$728$	220.659	+	340.540i	0.303103	+	0.467775i
$729$	644.771	−	340.164i	0.884459	−	0.466618i
$730$	231.304	+	391.124i	0.316855	+	0.535786i
$731$	801.684			1.09669
$732$	−251.595	−	348.402i	−0.343709	−	0.475959i
$733$	507.751	+	507.751i	0.692703	+	0.692703i	0.962826	−	0.270123i	$-0.0870644\pi$
$733$	507.751	+	507.751i	0.692703	+	0.692703i	−0.270123	+	0.962826i	$0.587064\pi$
$734$	−253.511	−	428.675i	−0.345383	−	0.584026i
$735$	−734.599	+	262.097i	−0.999455	+	0.356594i
$736$	453.532	−	889.984i	0.616212	−	1.20922i
$737$		−	812.437i		−	1.10236i
$738$	−669.066	+	310.159i	−0.906593	+	0.420269i
$739$	583.034	+	583.034i	0.788950	+	0.788950i	0.981322	−	0.192372i	$-0.0616180\pi$
$739$	583.034	+	583.034i	0.788950	+	0.788950i	−0.192372	+	0.981322i	$0.561618\pi$
$740$	−424.383	−	233.319i	−0.573491	−	0.315296i
$741$	−871.958	+	88.2586i	−1.17673	+	0.119107i
$742$	−58.5714	+	228.110i	−0.0789372	+	0.307426i
$743$	−312.769	−	312.769i	−0.420954	−	0.420954i	0.464578	−	0.885532i	$-0.346206\pi$
$743$	−312.769	−	312.769i	−0.420954	−	0.420954i	−0.885532	+	0.464578i	$0.846206\pi$
$744$	867.566	−	340.588i	1.16608	−	0.457779i
$745$		−	1503.35i		−	2.01793i
$746$	−315.466	+	186.561i	−0.422877	+	0.250082i
$747$	−5.79633	+	57.7826i	−0.00775948	+	0.0773528i
$748$	118.716	+	408.656i	0.158711	+	0.546332i
$749$	235.137	+	235.137i	0.313935	+	0.313935i
$750$	273.177	−	328.287i	0.364236	−	0.437716i
$751$	−447.999			−0.596536			−0.298268	−	0.954482i	$-0.596409\pi$
$751$	−447.999			−0.596536			−0.298268	+	0.954482i	$0.596409\pi$
$752$	926.944	+	207.240i	1.23264	+	0.275585i
$753$	808.098	+	383.094i	1.07317	+	0.508757i
$754$	−748.608	+	225.209i	−0.992849	+	0.298686i
$755$	1159.96			1.53637
$756$	−364.541	+	211.370i	−0.482198	+	0.279590i
$757$	−1256.45			−1.65978			−0.829890	−	0.557927i	$-0.811597\pi$
$757$	−1256.45			−1.65978			−0.829890	+	0.557927i	$0.811597\pi$
$758$	−103.512	+	403.134i	−0.136559	+	0.531839i
$759$	901.059	−	321.488i	1.18717	−	0.423568i
$760$	−1383.11	+	43.4193i	−1.81988	+	0.0571307i
$761$	371.292	+	371.292i	0.487900	+	0.487900i	0.907643	−	0.419743i	$-0.137880\pi$
$761$	371.292	+	371.292i	0.487900	+	0.487900i	−0.419743	+	0.907643i	$0.637880\pi$
$762$	−56.7831	−	619.725i	−0.0745186	−	0.813287i
$763$		−	710.186i		−	0.930781i
$764$	187.066	−	340.254i	0.244851	−	0.445359i
$765$	−717.805	−	72.0051i	−0.938307	−	0.0941243i
$766$	797.463	+	204.763i	1.04107	+	0.267315i
$767$	−26.2782	−	43.4865i	−0.0342610	−	0.0566969i
$768$	−487.791	−	593.198i	−0.635144	−	0.772393i
$769$	−954.425	−	954.425i	−1.24112	−	1.24112i	−0.959535	−	0.281589i	$-0.909138\pi$
$769$	−954.425	−	954.425i	−1.24112	−	1.24112i	−0.281589	−	0.959535i	$-0.590862\pi$
$770$	−152.612	+	594.356i	−0.198197	+	0.771891i
$771$	69.9765	−	147.608i	0.0907607	−	0.191450i
$772$	187.138	+	644.188i	0.242407	+	0.834440i
$773$	−960.080	+	960.080i	−1.24202	+	1.24202i	−0.282855	+	0.959163i	$0.591282\pi$
$773$	−960.080	+	960.080i	−1.24202	+	1.24202i	−0.959163	+	0.282855i	$0.908718\pi$
$774$	−1301.07	−	476.871i	−1.68097	−	0.616112i
$775$	940.438	+	940.438i	1.21347	+	1.21347i
$776$	571.223	−	608.250i	0.736112	−	0.783827i
$777$	−78.8698	+	166.368i	−0.101506	+	0.214116i
$778$	−476.710	+	281.918i	−0.612737	+	0.362363i
$779$			920.683i			1.18188i
$780$	469.594	−	1105.14i	0.602043	−	1.41684i
$781$	−118.387			−0.151584
$782$	−330.934	−	559.594i	−0.423190	−	0.715593i
$783$	−195.124	−	788.019i	−0.249201	−	1.00641i
$784$	−456.307	+	289.553i	−0.582024	+	0.369327i
$785$	−809.624	+	809.624i	−1.03137	+	1.03137i
$786$	30.7271	+	335.352i	0.0390931	+	0.426657i
$787$	284.587	+	284.587i	0.361610	+	0.361610i	0.864406	−	0.502795i	$-0.167695\pi$
$787$	284.587	+	284.587i	0.361610	+	0.361610i	−0.502795	+	0.864406i	$0.667695\pi$
$788$	44.5678	+	153.416i	0.0565581	+	0.194691i
$789$	670.916	−	1415.23i	0.850337	−	1.79370i
$790$	−886.066	−	227.514i	−1.12160	−	0.287992i
$791$	−272.818	+	272.818i	−0.344902	+	0.344902i
$792$	50.4172	−	733.834i	0.0636581	−	0.926558i
$793$	111.495	−	452.014i	0.140599	−	0.570005i
$794$	162.959	−	634.655i	0.205238	−	0.799314i
$795$	656.382	−	234.190i	0.825638	−	0.294578i
$796$	−183.250	+	333.312i	−0.230213	+	0.418734i
$797$	−105.582			−0.132474			−0.0662372	−	0.997804i	$-0.521099\pi$
$797$	−105.582			−0.132474			−0.0662372	+	0.997804i	$0.521099\pi$
$798$	48.0020	+	523.888i	0.0601528	+	0.656501i
$799$	437.133	−	437.133i	0.547100	−	0.547100i
$800$	497.592	−	976.444i	0.621990	−	1.22055i
$801$	−37.4223	+	373.056i	−0.0467195	+	0.465738i
$802$	−216.298	−	55.5385i	−0.269698	−	0.0692500i
$803$			301.551i			0.375531i
$804$	942.112	+	152.006i	1.17178	+	0.189062i
$805$		−	937.469i		−	1.16456i
$806$	889.374	+	478.013i	1.10344	+	0.593068i
$807$	−1066.27	−	505.484i	−1.32127	−	0.626375i
$808$	−4.44038	−	141.446i	−0.00549552	−	0.175057i
$809$		−	877.283i		−	1.08440i	−0.840248	−	0.542202i	$-0.817591\pi$
$809$		−	877.283i		−	1.08440i	0.840248	−	0.542202i	$-0.182409\pi$
$810$	1122.11	+	543.835i	1.38532	+	0.671402i
$811$	519.759	−	519.759i	0.640886	−	0.640886i	−0.309887	−	0.950773i	$-0.600291\pi$
$811$	519.759	−	519.759i	0.640886	−	0.640886i	0.950773	+	0.309887i	$0.100291\pi$
$812$	130.909	+	450.630i	0.161218	+	0.554963i
$813$	801.033	−	285.800i	0.985281	−	0.351537i
$814$	−163.597	−	276.634i	−0.200979	−	0.339845i
$815$	−399.083			−0.489672
$816$	−496.094	+	61.2051i	−0.607959	+	0.0750062i
$817$	−1223.29	+	1223.29i	−1.49729	+	1.49729i
$818$	−487.738	−	125.236i	−0.596257	−	0.153100i
$819$	−430.094	−	153.018i	−0.525145	−	0.186835i
$820$	−1105.38	−	607.720i	−1.34803	−	0.741122i
$821$	−744.139	+	744.139i	−0.906382	+	0.906382i	−0.995978	−	0.0895965i	$-0.971442\pi$
$821$	−744.139	+	744.139i	−0.906382	+	0.906382i	0.0895965	+	0.995978i	$0.471442\pi$
$822$	407.103	−	489.231i	0.495259	−	0.595172i
$823$	1435.48			1.74421			0.872104	−	0.489320i	$-0.162755\pi$
$823$	1435.48			1.74421			0.872104	+	0.489320i	$0.162755\pi$
$824$	−8.12843	−	258.928i	−0.00986460	−	0.314233i
$825$	988.595	−	352.720i	1.19830	−	0.427539i
$826$	−26.2523	+	15.5252i	−0.0317824	+	0.0187956i
$827$	−365.654	+	365.654i	−0.442145	+	0.442145i	−0.892732	−	0.450587i	$-0.851215\pi$
$827$	−365.654	+	365.654i	−0.442145	+	0.442145i	0.450587	+	0.892732i	$0.351215\pi$
$828$	204.214	+	1105.03i	0.246636	+	1.33458i
$829$		−	25.9567i		−	0.0313108i	−0.999877	−	0.0156554i	$-0.995017\pi$
$829$		−	25.9567i		−	0.0313108i	0.999877	−	0.0156554i	$-0.00498348\pi$
$830$	−85.5006	+	50.5636i	−0.103013	+	0.0609201i
$831$	485.877	+	230.339i	0.584689	+	0.277183i
$832$	148.191	−	818.696i	0.178114	−	0.984010i
$833$			351.736i			0.422252i
$834$	−1033.98	+	94.7400i	−1.23979	+	0.113597i
$835$			730.314i			0.874627i
$836$	−804.716	−	442.420i	−0.962579	−	0.529210i
$837$	−541.482	+	897.891i	−0.646932	+	1.07275i
$838$	−794.858	+	470.066i	−0.948518	+	0.560937i
$839$	13.1071	−	13.1071i	0.0156223	−	0.0156223i	−0.699253	−	0.714875i	$-0.746484\pi$
$839$	13.1071	−	13.1071i	0.0156223	−	0.0156223i	0.714875	+	0.699253i	$0.246484\pi$
$840$	−660.669	−	288.174i	−0.786511	−	0.343064i
$841$	−63.0439			−0.0749630
$842$	451.555	+	115.945i	0.536289	+	0.137702i
$843$	−705.226	+	251.617i	−0.836567	+	0.298478i
$844$	−291.928	−	160.497i	−0.345886	−	0.190163i
$845$	1242.07	−	386.571i	1.46990	−	0.457480i
$846$	−969.455	+	449.410i	−1.14593	+	0.531218i
$847$	45.8814	−	45.8814i	0.0541693	−	0.0541693i
$848$	407.721	−	258.722i	0.480804	−	0.305097i
$849$	−514.281	+	1084.82i	−0.605749	+	1.27777i
$850$	−363.084	−	613.957i	−0.427157	−	0.722302i
$851$	347.185	+	347.185i	0.407973	+	0.407973i
$852$	22.1501	−	137.283i	0.0259978	−	0.161131i
$853$	605.976	−	605.976i	0.710405	−	0.710405i	−0.256215	−	0.966620i	$-0.582475\pi$
$853$	605.976	−	605.976i	0.710405	−	0.710405i	0.966620	+	0.256215i	$0.0824754\pi$
$854$	−270.681	−	69.5023i	−0.316957	−	0.0813844i
$855$	1205.17	−	985.426i	1.40956	−	1.15255i
$856$	−21.3935	−	681.481i	−0.0249924	−	0.796123i
$857$	860.293			1.00384			0.501921	−	0.864913i	$-0.332627\pi$
$857$	860.293			1.00384			0.501921	+	0.864913i	$0.332627\pi$
$858$	641.561	−	472.638i	0.747740	−	0.550860i
$859$		−	103.438i		−	0.120417i	−0.998186	−	0.0602083i	$-0.980824\pi$
$859$		−	103.438i		−	0.120417i	0.998186	−	0.0602083i	$-0.0191765\pi$
$860$	−661.229	−	2276.15i	−0.768871	−	2.64669i
$861$	−205.430	+	433.335i	−0.238595	+	0.503292i
$862$	289.864	+	74.4280i	0.336270	+	0.0863434i
$863$	−672.167	−	672.167i	−0.778873	−	0.778873i	0.200766	−	0.979639i	$-0.435657\pi$
$863$	−672.167	−	672.167i	−0.778873	−	0.778873i	−0.979639	+	0.200766i	$0.935657\pi$
$864$	841.530	+	195.764i	0.973993	+	0.226578i
$865$	−5.85653	+	5.85653i	−0.00677055	+	0.00677055i
$866$	704.389	+	1191.09i	0.813382	+	1.37539i
$867$	232.034	−	489.452i	0.267629	−	0.564536i
$868$	291.996	−	531.111i	0.336401	−	0.611879i
$869$	−429.278	−	429.278i	−0.493990	−	0.493990i
$870$	888.209	−	1067.39i	1.02093	−	1.22689i
$871$	534.681	+	884.817i	0.613870	+	1.01586i
$872$	−996.833	+	1061.45i	−1.14316	+	1.21726i
$873$	−93.6961	+	934.039i	−0.107327	+	1.06992i
$874$	1358.86	+	348.911i	1.55476	+	0.399212i
$875$		−	277.726i		−	0.317401i
$876$	−349.682	−	56.4198i	−0.399181	−	0.0644062i
$877$	113.938	+	113.938i	0.129918	+	0.129918i	0.769076	−	0.639158i	$-0.220717\pi$
$877$	113.938	+	113.938i	0.129918	+	0.129918i	−0.639158	+	0.769076i	$0.720717\pi$
$878$	−203.243	+	120.194i	−0.231484	+	0.136896i
$879$	1144.24	−	408.253i	1.30176	−	0.464452i
$880$	1062.35	−	674.119i	1.20721	−	0.766044i
$881$	1133.08			1.28613			0.643064	−	0.765813i	$-0.277663\pi$
$881$	1133.08			1.28613			0.643064	+	0.765813i	$0.277663\pi$
$882$	209.226	−	570.841i	0.237217	−	0.647212i
$883$	−1121.07			−1.26961			−0.634806	−	0.772671i	$-0.718920\pi$
$883$	−1121.07			−1.26961			−0.634806	+	0.772671i	$0.718920\pi$
$884$	−398.237	−	366.934i	−0.450494	−	0.415084i
$885$	81.5525	+	38.6615i	0.0921497	+	0.0436853i
$886$	1231.80	−	728.468i	1.39030	−	0.822199i
$887$	−1215.46			−1.37030			−0.685151	−	0.728401i	$-0.740264\pi$
$887$	−1215.46			−1.37030			−0.685151	+	0.728401i	$0.740264\pi$
$888$	351.397	−	137.951i	0.395718	−	0.155350i
$889$	−286.158	−	286.158i	−0.321888	−	0.321888i
$890$	−552.010	+	326.449i	−0.620236	+	0.366797i
$891$	457.254	+	689.703i	0.513192	+	0.774077i
$892$	411.750	+	1417.37i	0.461604	+	1.58898i
$893$			1334.04i			1.49389i
$894$	900.785	+	749.569i	1.00759	+	0.838444i
$895$	−1528.61	−	1528.61i	−1.70794	−	1.70794i
$896$	−490.569	−	93.6209i	−0.547510	−	0.104488i
$897$	−769.758	+	943.135i	−0.858147	+	1.05143i
$898$	−114.716	−	29.4555i	−0.127746	−	0.0328012i
$899$	825.650	+	825.650i	0.918410	+	0.918410i
$900$	224.053	+	1212.38i	0.248948	+	1.34709i
$901$		−	314.285i		−	0.348818i
$902$	−426.117	−	720.543i	−0.472413	−	0.798828i
$903$	−848.711	+	302.811i	−0.939879	+	0.335338i
$904$	790.689	−	24.8218i	0.874655	−	0.0274578i
$905$	−1697.45	−	1697.45i	−1.87563	−	1.87563i
$906$	−578.353	+	695.029i	−0.638359	+	0.767140i
$907$	−705.040			−0.777332			−0.388666	−	0.921379i	$-0.627064\pi$
$907$	−705.040			−0.777332			−0.388666	+	0.921379i	$0.627064\pi$
$908$	−370.034	+	107.496i	−0.407526	+	0.118387i
$909$	100.777	+	123.250i	0.110866	+	0.135588i
$910$	−224.950	−	747.744i	−0.247197	−	0.821697i
$911$	−1360.01			−1.49288			−0.746438	−	0.665455i	$-0.768238\pi$
$911$	−1360.01			−1.49288			−0.746438	+	0.665455i	$0.768238\pi$
$912$	663.597	−	850.383i	0.727628	−	0.932437i
$913$	−65.9199			−0.0722014
$914$	223.776	+	57.4587i	0.244832	+	0.0628651i
$915$	277.896	+	778.880i	0.303711	+	0.851235i
$916$	241.993	+	833.015i	0.264185	+	0.909405i
$917$	154.849	+	154.849i	0.168865	+	0.168865i
$918$	401.040	−	394.195i	0.436863	−	0.429407i
$919$			288.668i			0.314110i	0.987590	+	0.157055i	$0.0502001\pi$
$919$			288.668i			0.314110i	−0.987590	+	0.157055i	$0.949800\pi$
$920$	−1315.85	+	1401.15i	−1.43028	+	1.52299i
$921$	−1155.82	+	412.384i	−1.25496	+	0.447757i
$922$	−68.5780	+	267.081i	−0.0743796	+	0.289676i
$923$	128.935	−	77.9131i	0.139691	−	0.0844129i
$924$	−280.036	−	387.787i	−0.303070	−	0.419683i
$925$	380.913	+	380.913i	0.411798	+	0.411798i
$926$	405.718	+	104.176i	0.438141	+	0.112501i
$927$	184.479	+	225.617i	0.199007	+	0.243384i
$928$	436.857	−	857.261i	0.470751	−	0.923773i
$929$	−15.1256	+	15.1256i	−0.0162816	+	0.0162816i	−0.715201	−	0.698919i	$-0.753665\pi$
$929$	−15.1256	+	15.1256i	−0.0162816	+	0.0162816i	0.698919	+	0.715201i	$0.253665\pi$
$930$	−1786.02	+	163.647i	−1.92046	+	0.175964i
$931$	−536.714	−	536.714i	−0.576492	−	0.576492i
$932$	610.429	−	1110.31i	0.654967	−	1.19132i
$933$	−590.780	−	280.070i	−0.633205	−	0.300183i
$934$	624.063	+	1055.26i	0.668161	+	1.12983i
$935$		−	818.891i		−	0.875819i
$936$	428.042	+	832.392i	0.457310	+	0.889308i
$937$	908.180			0.969242			0.484621	−	0.874724i	$-0.338957\pi$
$937$	908.180			0.969242			0.484621	+	0.874724i	$0.338957\pi$
$938$	534.154	−	315.889i	0.569460	−	0.336769i
$939$	507.097	−	1069.67i	0.540039	−	1.13916i
$940$	−1601.66	−	880.568i	−1.70390	−	0.936774i
$941$	155.836	−	155.836i	0.165607	−	0.165607i	−0.619439	−	0.785045i	$-0.712640\pi$
$941$	155.836	−	155.836i	0.165607	−	0.165607i	0.785045	+	0.619439i	$0.212640\pi$
$942$	−81.4367	−	888.791i	−0.0864508	−	0.943514i
$943$	904.305	+	904.305i	0.958966	+	0.958966i
$944$	61.0283	+	13.6443i	0.0646487	+	0.0144537i
$945$	787.110	−	194.899i	0.832920	−	0.206243i
$946$	391.196	−	1523.54i	0.413527	−	1.61051i
$947$	347.766	−	347.766i	0.367230	−	0.367230i	−0.499236	−	0.866466i	$-0.666386\pi$
$947$	347.766	−	347.766i	0.367230	−	0.367230i	0.866466	+	0.499236i	$0.166386\pi$
$948$	578.113	−	417.478i	0.609824	−	0.440378i
$949$	−198.457	−	328.416i	−0.209122	−	0.346066i
$950$	1490.87	+	382.807i	1.56933	+	0.402955i
$951$	490.242	+	1374.04i	0.515502	+	1.44484i
$952$	−222.521	+	236.944i	−0.233740	+	0.248891i
$953$	855.448			0.897637			0.448818	−	0.893623i	$-0.351845\pi$
$953$	855.448			0.897637			0.448818	+	0.893623i	$0.351845\pi$
$954$	−186.948	+	510.060i	−0.195962	+	0.534654i
$955$	−528.339	+	528.339i	−0.553235	+	0.553235i
$956$	−499.868	+	145.213i	−0.522875	+	0.151897i
$957$	867.929	−	309.667i	0.906927	−	0.323581i
$958$	−397.722	+	1548.95i	−0.415159	+	1.61686i
$959$		−	413.883i		−	0.431577i
$960$	582.953	+	1358.04i	0.607243	+	1.41462i
$961$		−	547.109i		−	0.569312i
$962$	360.230	+	193.613i	0.374460	+	0.201261i
$963$	485.538	+	593.810i	0.504193	+	0.616625i
$964$	−437.135	−	1504.76i	−0.453460	−	1.56095i
$965$		−	1290.86i		−	1.33768i
$966$	561.716	+	467.420i	0.581487	+	0.483872i
$967$	128.444	−	128.444i	0.132827	−	0.132827i	−0.637567	−	0.770395i	$-0.720059\pi$
$967$	128.444	−	128.444i	0.132827	−	0.132827i	0.770395	+	0.637567i	$0.220059\pi$
$968$	−132.975	+	4.17443i	−0.137371	+	0.00431243i
$969$	−235.918	−	661.225i	−0.243465	−	0.682379i
$970$	−1382.09	+	817.347i	−1.42484	+	0.842626i
$971$	−214.511			−0.220918			−0.110459	−	0.993881i	$-0.535232\pi$
$971$	−214.511			−0.220918			−0.110459	+	0.993881i	$0.535232\pi$
$972$	−885.340	+	401.196i	−0.910843	+	0.412753i
$973$	−477.442	+	477.442i	−0.490690	+	0.490690i
$974$	−86.8468	+	338.230i	−0.0891651	+	0.347259i
$975$	−844.537	+	1034.76i	−0.866192	+	1.06129i
$976$	307.006	+	483.813i	0.314556	+	0.495710i
$977$	1135.10	−	1135.10i	1.16182	−	1.16182i	0.177739	−	0.984078i	$-0.443122\pi$
$977$	1135.10	−	1135.10i	1.16182	−	1.16182i	0.984078	−	0.177739i	$-0.0568784\pi$
$978$	198.982	−	239.124i	0.203458	−	0.244503i
$979$	−425.592			−0.434722
$980$	998.655	−	290.112i	1.01904	−	0.296033i
$981$	163.508	−	1629.98i	0.166675	−	1.66155i
$982$	−593.309	−	1003.26i	−0.604184	−	1.02165i
$983$	1008.71	−	1008.71i	1.02615	−	1.02615i	0.0265010	−	0.999649i	$-0.491563\pi$
$983$	1008.71	−	1008.71i	1.02615	−	1.02615i	0.999649	−	0.0265010i	$-0.00843653\pi$
$984$	915.276	−	359.318i	0.930159	−	0.365160i
$985$		−	307.425i		−	0.312107i
$986$	−318.767	−	539.019i	−0.323293	−	0.546672i
$987$	−297.662	+	627.888i	−0.301583	+	0.636158i
$988$	1167.57	−	47.7645i	1.18176	−	0.0483446i
$989$			2403.06i			2.42978i
$990$	−487.106	+	1329.00i	−0.492026	+	1.34242i
$991$		−	1656.57i		−	1.67162i	−0.549020	−	0.835809i	$-0.684999\pi$
$991$		−	1656.57i		−	1.67162i	0.549020	−	0.835809i	$-0.315001\pi$
$992$	−1181.90	+	383.949i	−1.19143	+	0.387046i
$993$	−49.9702	−	140.055i	−0.0503224	−	0.141043i
$994$	−46.0310	−	77.8362i	−0.0463089	−	0.0783060i
$995$	517.560	−	517.560i	0.520161	−	0.520161i
$996$	12.3335	−	76.4415i	0.0123831	−	0.0767485i
$997$	−215.724			−0.216373			−0.108187	−	0.994131i	$-0.534504\pi$
$997$	−215.724			−0.216373			−0.108187	+	0.994131i	$0.534504\pi$
$998$	−41.1166	+	160.131i	−0.0411990	+	0.160452i
$999$	−219.321	+	363.680i	−0.219541	+	0.364044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.l.c.47.9	✓	96
3.2	odd	2	inner	156.3.l.c.47.40	yes	96
4.3	odd	2	inner	156.3.l.c.47.16	yes	96
12.11	even	2	inner	156.3.l.c.47.33	yes	96
13.5	odd	4	inner	156.3.l.c.83.33	yes	96
39.5	even	4	inner	156.3.l.c.83.16	yes	96
52.31	even	4	inner	156.3.l.c.83.40	yes	96
156.83	odd	4	inner	156.3.l.c.83.9	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.l.c.47.9	✓	96	1.1	even	1	trivial
156.3.l.c.47.16	yes	96	4.3	odd	2	inner
156.3.l.c.47.33	yes	96	12.11	even	2	inner
156.3.l.c.47.40	yes	96	3.2	odd	2	inner
156.3.l.c.83.9	yes	96	156.83	odd	4	inner
156.3.l.c.83.16	yes	96	39.5	even	4	inner
156.3.l.c.83.33	yes	96	13.5	odd	4	inner
156.3.l.c.83.40	yes	96	52.31	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72150 + 1.01806i) q^{2} +(-1.28511 + 2.71081i) q^{3} +(1.92709 - 3.50518i) q^{4} +(-5.44277 + 5.44277i) q^{5} +(-0.547465 - 5.97497i) q^{6} +(-2.75895 - 2.75895i) q^{7} +(0.251018 + 7.99606i) q^{8} +(-5.69698 - 6.96738i) q^{9} +(3.82862 - 14.9108i) q^{10} +(7.22392 - 7.22392i) q^{11} +(7.02536 + 9.72853i) q^{12} +(-3.11329 + 12.6217i) q^{13} +(7.55830 + 1.94073i) q^{14} +(-7.75976 - 21.7489i) q^{15} +(-8.57262 - 13.5096i) q^{16} -10.4137 q^{17} +(16.9006 + 6.19442i) q^{18} +(15.8902 - 15.8902i) q^{19} +(8.58918 + 29.5666i) q^{20} +(11.0245 - 3.93343i) q^{21} +(-5.08153 + 19.7903i) q^{22} -31.2150i q^{23} +(-21.9984 - 9.59536i) q^{24} -34.2475i q^{25} +(-7.49017 - 24.8977i) q^{26} +(26.2085 - 6.48958i) q^{27} +(-14.9874 + 4.35387i) q^{28} -30.0673i q^{29} +(35.5001 + 29.5407i) q^{30} +(-27.4600 + 27.4600i) q^{31} +(28.5114 + 14.5293i) q^{32} +(10.2991 + 28.8662i) q^{33} +(17.9271 - 10.6018i) q^{34} +30.0326 q^{35} +(-35.4006 + 6.54218i) q^{36} +(-11.1224 + 11.1224i) q^{37} +(-11.1777 + 43.5321i) q^{38} +(-30.2141 - 24.6598i) q^{39} +(-44.8870 - 42.1545i) q^{40} +(-28.9702 + 28.9702i) q^{41} +(-14.9742 + 17.9951i) q^{42} -76.9839 q^{43} +(-11.4000 - 39.2423i) q^{44} +(68.9292 + 6.91448i) q^{45} +(31.7789 + 53.7365i) q^{46} +(-41.9769 + 41.9769i) q^{47} +(47.6388 - 5.87739i) q^{48} -33.7764i q^{49} +(34.8661 + 58.9569i) q^{50} +(13.3827 - 28.2294i) q^{51} +(38.2418 + 35.2359i) q^{52} +30.1801i q^{53} +(-38.5110 + 37.8537i) q^{54} +78.6362i q^{55} +(21.3682 - 22.7532i) q^{56} +(22.6546 + 63.4960i) q^{57} +(30.6104 + 51.7608i) q^{58} +(-2.76368 + 2.76368i) q^{59} +(-91.1876 - 14.7127i) q^{60} -35.8124 q^{61} +(19.3163 - 75.2284i) q^{62} +(-3.50496 + 34.9403i) q^{63} +(-63.8740 + 4.01430i) q^{64} +(-51.7521 - 85.6420i) q^{65} +(-47.1175 - 39.2079i) q^{66} +(56.2324 - 56.2324i) q^{67} +(-20.0681 + 36.5018i) q^{68} +(84.6180 + 40.1148i) q^{69} +(-51.7010 + 30.5751i) q^{70} +(-8.19412 - 8.19412i) q^{71} +(54.2816 - 47.3024i) q^{72} +(-20.8717 + 20.8717i) q^{73} +(7.82383 - 30.4704i) q^{74} +(92.8384 + 44.0118i) q^{75} +(-25.0762 - 86.3199i) q^{76} -39.8608 q^{77} +(77.1187 + 11.6919i) q^{78} -59.4245i q^{79} +(120.189 + 26.8710i) q^{80} +(-16.0888 + 79.3861i) q^{81} +(20.3785 - 79.3655i) q^{82} +(-4.56261 - 4.56261i) q^{83} +(7.45791 - 46.2231i) q^{84} +(56.6791 - 56.6791i) q^{85} +(132.527 - 78.3745i) q^{86} +(81.5068 + 38.6398i) q^{87} +(59.5762 + 55.9495i) q^{88} +(-29.4572 - 29.4572i) q^{89} +(-125.701 + 58.2711i) q^{90} +(43.4120 - 26.2332i) q^{91} +(-109.414 - 60.1543i) q^{92} +(-39.1498 - 109.728i) q^{93} +(29.5279 - 114.998i) q^{94} +172.973i q^{95} +(-76.0264 + 58.6172i) q^{96} +(-73.7534 - 73.7534i) q^{97} +(34.3866 + 58.1460i) q^{98} +(-91.4863 - 9.17725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 36 q^{6} - 64 q^{9} - 8 q^{13} + 80 q^{16} + 48 q^{18} + 8 q^{21} + 124 q^{24} - 8 q^{28} + 24 q^{33} + 64 q^{34} - 128 q^{37} - 136 q^{40} - 140 q^{42} - 160 q^{45} + 88 q^{46} - 108 q^{48} - 320 q^{52}+ \cdots + 336 q^{97}+O(q^{100}) \) 96 * q - 36 * q^6 - 64 * q^9 - 8 * q^13 + 80 * q^16 + 48 * q^18 + 8 * q^21 + 124 * q^24 - 8 * q^28 + 24 * q^33 + 64 * q^34 - 128 * q^37 - 136 * q^40 - 140 * q^42 - 160 * q^45 + 88 * q^46 - 108 * q^48 - 320 * q^52 - 216 * q^54 + 136 * q^57 + 280 * q^58 + 80 * q^60 - 464 * q^61 - 240 * q^66 - 120 * q^70 - 32 * q^72 + 288 * q^73 + 88 * q^76 - 296 * q^78 - 144 * q^81 + 204 * q^84 + 848 * q^85 - 392 * q^93 + 1384 * q^94 - 204 * q^96 + 336 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more