LMFDB - Embedded newform 504.2.cz.b.187.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(187,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 5]))

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

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

chi := DirichletCharacter("504.187");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			187.1
Character	$\chi$	$=$	504.187
Dual form			504.2.cz.b.283.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41404 - 0.0223915i) q^{2} +(-0.178596 - 1.72282i) q^{3} +(1.99900 + 0.0633248i) q^{4} -2.54012 q^{5} +(0.213965 + 2.44013i) q^{6} +(-2.62252 + 0.349814i) q^{7} +(-2.82524 - 0.134304i) q^{8} +(-2.93621 + 0.615378i) q^{9} +O(q^{10})$	\(q+(-1.41404 - 0.0223915i) q^{2} +(-0.178596 - 1.72282i) q^{3} +(1.99900 + 0.0633248i) q^{4} -2.54012 q^{5} +(0.213965 + 2.44013i) q^{6} +(-2.62252 + 0.349814i) q^{7} +(-2.82524 - 0.134304i) q^{8} +(-2.93621 + 0.615378i) q^{9} +(3.59182 + 0.0568771i) q^{10} +1.41036 q^{11} +(-0.247917 - 3.45522i) q^{12} +(2.50251 + 4.33447i) q^{13} +(3.71618 - 0.435927i) q^{14} +(0.453657 + 4.37617i) q^{15} +(3.99198 + 0.253172i) q^{16} +(0.532316 - 0.307333i) q^{17} +(4.16568 - 0.804421i) q^{18} +(4.46624 + 2.57858i) q^{19} +(-5.07770 - 0.160853i) q^{20} +(1.07104 + 4.45566i) q^{21} +(-1.99431 - 0.0315802i) q^{22} -1.73822i q^{23} +(0.273196 + 4.89136i) q^{24} +1.45222 q^{25} +(-3.44158 - 6.18513i) q^{26} +(1.58458 + 4.94865i) q^{27} +(-5.26457 + 0.533206i) q^{28} +(-0.122038 - 0.0704587i) q^{29} +(-0.543498 - 6.19822i) q^{30} +(4.58909 - 7.94854i) q^{31} +(-5.63914 - 0.447381i) q^{32} +(-0.251886 - 2.42980i) q^{33} +(-0.759596 + 0.422661i) q^{34} +(6.66153 - 0.888569i) q^{35} +(-5.90844 + 1.04421i) q^{36} +(3.09619 + 1.78759i) q^{37} +(-6.25768 - 3.74622i) q^{38} +(7.02056 - 5.08548i) q^{39} +(7.17644 + 0.341149i) q^{40} +(-3.36519 + 1.94289i) q^{41} +(-1.41472 - 6.32444i) q^{42} +(-3.27077 + 5.66515i) q^{43} +(2.81931 + 0.0893110i) q^{44} +(7.45832 - 1.56314i) q^{45} +(-0.0389213 + 2.45790i) q^{46} +(4.09821 + 7.09831i) q^{47} +(-0.276784 - 6.92267i) q^{48} +(6.75526 - 1.83479i) q^{49} +(-2.05349 - 0.0325173i) q^{50} +(-0.624549 - 0.862196i) q^{51} +(4.72802 + 8.82306i) q^{52} +(-8.52661 + 4.92284i) q^{53} +(-2.12985 - 7.03305i) q^{54} -3.58249 q^{55} +(7.45623 - 0.636091i) q^{56} +(3.64478 - 8.15504i) q^{57} +(0.170989 + 0.102364i) q^{58} +(13.0145 + 7.51395i) q^{59} +(0.629738 + 8.77668i) q^{60} +(1.10736 + 1.91800i) q^{61} +(-6.66712 + 11.1368i) q^{62} +(7.48500 - 2.64097i) q^{63} +(7.96392 + 0.758882i) q^{64} +(-6.35667 - 11.0101i) q^{65} +(0.301769 + 3.44147i) q^{66} +(1.79489 - 3.10885i) q^{67} +(1.08356 - 0.580649i) q^{68} +(-2.99463 + 0.310439i) q^{69} +(-9.43954 + 1.10731i) q^{70} +5.96077i q^{71} +(8.37813 - 1.34425i) q^{72} +(-13.2909 + 7.67352i) q^{73} +(-4.33810 - 2.59704i) q^{74} +(-0.259361 - 2.50191i) q^{75} +(8.76471 + 5.43741i) q^{76} +(-3.69871 + 0.493364i) q^{77} +(-10.0412 + 7.03386i) q^{78} +(-10.0112 + 5.77995i) q^{79} +(-10.1401 - 0.643088i) q^{80} +(8.24262 - 3.61376i) q^{81} +(4.80200 - 2.67197i) q^{82} +(9.82635 + 5.67325i) q^{83} +(1.85885 + 8.97467i) q^{84} +(-1.35215 + 0.780663i) q^{85} +(4.75184 - 7.93748i) q^{86} +(-0.0995920 + 0.222833i) q^{87} +(-3.98461 - 0.189418i) q^{88} +(15.6471 + 9.03384i) q^{89} +(-10.5813 + 2.04333i) q^{90} +(-8.07913 - 10.4918i) q^{91} +(0.110072 - 3.47469i) q^{92} +(-14.5135 - 6.48659i) q^{93} +(-5.63608 - 10.1290i) q^{94} +(-11.3448 - 6.54992i) q^{95} +(0.236373 + 9.79511i) q^{96} +(-3.11892 - 1.80071i) q^{97} +(-9.59327 + 2.44320i) q^{98} +(-4.14112 + 0.867907i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.41404	−	0.0223915i	−0.999875	−	0.0158332i
$2$	−1.41404	−	0.0223915i	−0.999875	−	0.0158332i
$3$	−0.178596	−	1.72282i	−0.103113	−	0.994670i
$3$	−0.178596	−	1.72282i	−0.103113	−	0.994670i
$4$	1.99900	+	0.0633248i	0.999499	+	0.0316624i
$5$	−2.54012			−1.13598			−0.567988	−	0.823037i	$-0.692278\pi$
$5$	−2.54012			−1.13598			−0.567988	+	0.823037i	$0.692278\pi$
$6$	0.213965	+	2.44013i	0.0873510	+	0.996178i
$7$	−2.62252	+	0.349814i	−0.991221	+	0.132217i
$7$	−2.62252	+	0.349814i	−0.991221	+	0.132217i
$8$	−2.82524	−	0.134304i	−0.998872	−	0.0474837i
$9$	−2.93621	+	0.615378i	−0.978736	+	0.205126i
$10$	3.59182	+	0.0568771i	1.13583	+	0.0179861i
$11$	1.41036			0.425241			0.212620	−	0.977135i	$-0.431800\pi$
$11$	1.41036			0.425241			0.212620	+	0.977135i	$0.431800\pi$
$12$	−0.247917	−	3.45522i	−0.0715674	−	0.997436i
$13$	2.50251	+	4.33447i	0.694070	+	1.20216i	0.970493	+	0.241129i	$0.0775176\pi$
$13$	2.50251	+	4.33447i	0.694070	+	1.20216i	−0.276423	+	0.961036i	$0.589149\pi$
$14$	3.71618	−	0.435927i	0.993190	−	0.116506i
$15$	0.453657	+	4.37617i	0.117134	+	1.12992i
$16$	3.99198	+	0.253172i	0.997995	+	0.0632930i
$17$	0.532316	−	0.307333i	0.129106	−	0.0745392i	−0.434056	−	0.900886i	$-0.642918\pi$
$17$	0.532316	−	0.307333i	0.129106	−	0.0745392i	0.563162	+	0.826347i	$0.309585\pi$
$18$	4.16568	−	0.804421i	0.981861	−	0.189604i
$19$	4.46624	+	2.57858i	1.02463	+	0.591568i	0.915440	−	0.402454i	$-0.131843\pi$
$19$	4.46624	+	2.57858i	1.02463	+	0.591568i	0.109185	+	0.994021i	$0.465176\pi$
$20$	−5.07770	−	0.160853i	−1.13541	−	0.0359677i
$21$	1.07104	+	4.45566i	0.233720	+	0.972304i
$22$	−1.99431	−	0.0315802i	−0.425187	−	0.00673291i
$23$		−	1.73822i		−	0.362443i	−0.983442	−	0.181222i	$-0.941995\pi$
$23$		−	1.73822i		−	0.362443i	0.983442	−	0.181222i	$-0.0580051\pi$
$24$	0.273196	+	4.89136i	0.0557658	+	0.998444i
$25$	1.45222			0.290443
$26$	−3.44158	−	6.18513i	−0.674949	−	1.21300i
$27$	1.58458	+	4.94865i	0.304953	+	0.952367i
$28$	−5.26457	+	0.533206i	−0.994910	+	0.100766i
$29$	−0.122038	−	0.0704587i	−0.0226619	−	0.0130839i	0.488626	−	0.872493i	$-0.337498\pi$
$29$	−0.122038	−	0.0704587i	−0.0226619	−	0.0130839i	−0.511288	+	0.859409i	$0.670832\pi$
$30$	−0.543498	−	6.19822i	−0.0992287	−	1.13163i
$31$	4.58909	−	7.94854i	0.824225	−	1.42760i	−0.0782855	−	0.996931i	$-0.524945\pi$
$31$	4.58909	−	7.94854i	0.824225	−	1.42760i	0.902510	−	0.430668i	$-0.141722\pi$
$32$	−5.63914	−	0.447381i	−0.996868	−	0.0790865i
$33$	−0.251886	−	2.42980i	−0.0438477	−	0.422974i
$34$	−0.759596	+	0.422661i	−0.130270	+	0.0724857i
$35$	6.66153	−	0.888569i	1.12600	−	0.150196i
$36$	−5.90844	+	1.04421i	−0.984740	+	0.174034i
$37$	3.09619	+	1.78759i	0.509011	+	0.293878i	0.732427	−	0.680846i	$-0.238388\pi$
$37$	3.09619	+	1.78759i	0.509011	+	0.293878i	−0.223416	+	0.974723i	$0.571721\pi$
$38$	−6.25768	−	3.74622i	−1.01513	−	0.607717i
$39$	7.02056	−	5.08548i	1.12419	−	0.814329i
$40$	7.17644	+	0.341149i	1.13470	+	0.0539403i
$41$	−3.36519	+	1.94289i	−0.525554	+	0.303429i	−0.739204	−	0.673481i	$-0.764798\pi$
$41$	−3.36519	+	1.94289i	−0.525554	+	0.303429i	0.213650	+	0.976910i	$0.431465\pi$
$42$	−1.41472	−	6.32444i	−0.218296	−	0.975883i
$43$	−3.27077	+	5.66515i	−0.498788	+	0.863927i	−0.999999	−	0.00139869i	$-0.999555\pi$
$43$	−3.27077	+	5.66515i	−0.498788	+	0.863927i	0.501211	+	0.865325i	$0.332888\pi$
$44$	2.81931	+	0.0893110i	0.425027	+	0.0134641i
$45$	7.45832	−	1.56314i	1.11182	−	0.233019i
$46$	−0.0389213	+	2.45790i	−0.00573863	+	0.362398i
$47$	4.09821	+	7.09831i	0.597785	+	1.03539i	0.993147	+	0.116869i	$0.0372858\pi$
$47$	4.09821	+	7.09831i	0.597785	+	1.03539i	−0.395362	+	0.918525i	$0.629381\pi$
$48$	−0.276784	−	6.92267i	−0.0399503	−	0.999202i
$49$	6.75526	−	1.83479i	0.965037	−	0.262113i
$50$	−2.05349	−	0.0325173i	−0.290407	−	0.00459864i
$51$	−0.624549	−	0.862196i	−0.0874543	−	0.120732i
$52$	4.72802	+	8.82306i	0.655659	+	1.22354i
$53$	−8.52661	+	4.92284i	−1.17122	+	0.676204i	−0.953967	−	0.299911i	$-0.903043\pi$
$53$	−8.52661	+	4.92284i	−1.17122	+	0.676204i	−0.217253	+	0.976115i	$0.569710\pi$
$54$	−2.12985	−	7.03305i	−0.289836	−	0.957076i
$55$	−3.58249			−0.483063
$56$	7.45623	−	0.636091i	0.996381	−	0.0850012i
$57$	3.64478	−	8.15504i	0.482763	−	1.08016i
$58$	0.170989	+	0.102364i	0.0224519	+	0.0134410i
$59$	13.0145	+	7.51395i	1.69435	+	0.978233i	0.950930	+	0.309407i	$0.100131\pi$
$59$	13.0145	+	7.51395i	1.69435	+	0.978233i	0.743419	+	0.668826i	$0.233203\pi$
$60$	0.629738	+	8.77668i	0.0812989	+	1.13306i
$61$	1.10736	+	1.91800i	0.141783	+	0.245575i	0.928168	−	0.372161i	$-0.121383\pi$
$61$	1.10736	+	1.91800i	0.141783	+	0.245575i	−0.786385	+	0.617737i	$0.788050\pi$
$62$	−6.66712	+	11.1368i	−0.846725	+	1.41437i
$63$	7.48500	−	2.64097i	0.943022	−	0.332731i
$64$	7.96392	+	0.758882i	0.995491	+	0.0948602i
$65$	−6.35667	−	11.0101i	−0.788448	−	1.36563i
$66$	0.301769	+	3.44147i	0.0371452	+	0.423615i
$67$	1.79489	−	3.10885i	0.219281	−	0.379806i	−0.735307	−	0.677734i	$-0.762962\pi$
$67$	1.79489	−	3.10885i	0.219281	−	0.379806i	0.954588	+	0.297928i	$0.0962955\pi$
$68$	1.08356	−	0.580649i	0.131401	−	0.0704140i
$69$	−2.99463	+	0.310439i	−0.360511	+	0.0373725i
$70$	−9.43954	+	1.10731i	−1.12824	+	0.132349i
$71$			5.96077i			0.707413i	0.935356	+	0.353707i	$0.115079\pi$
$71$			5.96077i			0.707413i	−0.935356	+	0.353707i	$0.884921\pi$
$72$	8.37813	−	1.34425i	0.987372	−	0.158421i
$73$	−13.2909	+	7.67352i	−1.55559	+	0.898118i	−0.557915	+	0.829898i	$0.688398\pi$
$73$	−13.2909	+	7.67352i	−1.55559	+	0.898118i	−0.997670	+	0.0682194i	$0.978268\pi$
$74$	−4.33810	−	2.59704i	−0.504294	−	0.301900i
$75$	−0.259361	−	2.50191i	−0.0299484	−	0.288895i
$76$	8.76471	+	5.43741i	1.00538	+	0.623713i
$77$	−3.69871	+	0.493364i	−0.421507	+	0.0562241i
$78$	−10.0412	+	7.03386i	−1.13694	+	0.796427i
$79$	−10.0112	+	5.77995i	−1.12634	+	0.650295i	−0.943013	−	0.332756i	$-0.892021\pi$
$79$	−10.0112	+	5.77995i	−1.12634	+	0.650295i	−0.183331	+	0.983051i	$0.558688\pi$
$80$	−10.1401	−	0.643088i	−1.13370	−	0.0718994i
$81$	8.24262	−	3.61376i	0.915847	−	0.401528i
$82$	4.80200	−	2.67197i	0.530292	−	0.295070i
$83$	9.82635	+	5.67325i	1.07858	+	0.622720i	0.930514	−	0.366257i	$-0.119361\pi$
$83$	9.82635	+	5.67325i	1.07858	+	0.622720i	0.148069	+	0.988977i	$0.452694\pi$
$84$	1.85885	+	8.97467i	0.202817	+	0.979217i
$85$	−1.35215	+	0.780663i	−0.146661	+	0.0846748i
$86$	4.75184	−	7.93748i	0.512404	−	0.855921i
$87$	−0.0995920	+	0.222833i	−0.0106774	+	0.0238902i
$88$	−3.98461	−	0.189418i	−0.424761	−	0.0201920i
$89$	15.6471	+	9.03384i	1.65859	+	0.957585i	0.973368	+	0.229247i	$0.0736263\pi$
$89$	15.6471	+	9.03384i	1.65859	+	0.957585i	0.685218	+	0.728338i	$0.259707\pi$
$90$	−10.5813	+	2.04333i	−1.11537	+	0.215386i
$91$	−8.07913	−	10.4918i	−0.846923	−	1.09984i
$92$	0.110072	−	3.47469i	0.0114758	−	0.362262i
$93$	−14.5135	−	6.48659i	−1.50498	−	0.672628i
$94$	−5.63608	−	10.1290i	−0.581317	−	1.04473i
$95$	−11.3448	−	6.54992i	−1.16395	−	0.672007i
$96$	0.236373	+	9.79511i	0.0241247	+	0.999709i
$97$	−3.11892	−	1.80071i	−0.316678	−	0.182834i	0.333233	−	0.942845i	$-0.391860\pi$
$97$	−3.11892	−	1.80071i	−0.316678	−	0.182834i	−0.649911	+	0.760010i	$0.725194\pi$
$98$	−9.59327	+	2.44320i	−0.969066	+	0.246800i
$99$	−4.14112	+	0.867907i	−0.416198	+	0.0872280i
$100$	2.90298	+	0.0919613i	0.290298	+	0.00919613i
$101$	−9.24826			−0.920236			−0.460118	−	0.887858i	$-0.652193\pi$
$101$	−9.24826			−0.920236			−0.460118	+	0.887858i	$0.652193\pi$
$102$	0.863828	+	1.23316i	0.0855318	+	0.122101i
$103$	10.8077			1.06492			0.532459	−	0.846456i	$-0.321268\pi$
$103$	10.8077			1.06492			0.532459	+	0.846456i	$0.321268\pi$
$104$	−6.48803	−	12.5820i	−0.636204	−	1.23377i
$105$	−2.72057	−	11.3179i	−0.265500	−	1.10451i
$106$	12.1672	−	6.77015i	1.18178	−	0.657575i
$107$	1.05884	−	1.83397i	0.102362	−	0.177297i	−0.810295	−	0.586022i	$-0.800693\pi$
$107$	1.05884	−	1.83397i	0.102362	−	0.177297i	0.912657	+	0.408725i	$0.134027\pi$
$108$	2.85420	+	9.99267i	0.274646	+	0.961545i
$109$	1.95711	−	1.12994i	0.187457	−	0.108228i	−0.403334	−	0.915053i	$-0.632149\pi$
$109$	1.95711	−	1.12994i	0.187457	−	0.108228i	0.590792	+	0.806824i	$0.298816\pi$
$110$	5.06578	+	0.0802174i	0.483003	+	0.00764843i
$111$	2.52672	−	5.65343i	0.239826	−	0.536600i
$112$	−10.5576	+	0.732499i	−0.997602	+	0.0692146i
$113$	−5.90397	−	10.2260i	−0.555399	−	0.961978i	−0.997872	−	0.0651970i	$-0.979232\pi$
$113$	−5.90397	−	10.2260i	−0.555399	−	0.961978i	0.442474	−	0.896781i	$-0.354101\pi$
$114$	−5.33645	+	11.4499i	−0.499804	+	1.07238i
$115$			4.41528i			0.411727i
$116$	−0.239492	−	0.148575i	−0.0222363	−	0.0137948i
$117$	−10.0152	−	11.1869i	−0.925906	−	1.03423i
$118$	−18.2348	−	10.9164i	−1.67865	−	1.00494i
$119$	−1.28850	+	0.992199i	−0.118117	+	0.0909548i
$120$	−0.693950	−	12.4246i	−0.0633487	−	1.13421i
$121$	−9.01087			−0.819170
$122$	−1.52290	−	2.73692i	−0.137877	−	0.247789i
$123$	3.94826	+	5.45061i	0.356003	+	0.491465i
$124$	9.67692	−	15.5985i	0.869013	−	1.40079i
$125$	9.01180			0.806040
$126$	−10.6432	+	3.56683i	−0.948172	+	0.317758i
$127$			16.7577i			1.48701i	0.668731	+	0.743504i	$0.266838\pi$
$127$			16.7577i			1.48701i	−0.668731	+	0.743504i	$0.733162\pi$
$128$	−11.2443	−	1.25141i	−0.993864	−	0.110610i
$129$	10.3442	+	4.62317i	0.910753	+	0.407048i
$130$	8.74203	+	15.7110i	0.766726	+	1.37794i
$131$		−	1.46575i		−	0.128063i	−0.997948	−	0.0640317i	$-0.979604\pi$
$131$		−	1.46575i		−	0.128063i	0.997948	−	0.0640317i	$-0.0203959\pi$
$132$	−0.349653	−	4.87311i	−0.0304334	−	0.424150i
$133$	−12.6148	−	5.20005i	−1.09385	−	0.450901i
$134$	−2.60766	+	4.35583i	−0.225267	+	0.376287i
$135$	−4.02503	−	12.5702i	−0.346419	−	1.08187i
$136$	−1.54520	+	0.796796i	−0.132499	+	0.0683247i
$137$	−11.4392			−0.977318			−0.488659	−	0.872475i	$-0.662514\pi$
$137$	−11.4392			−0.977318			−0.488659	+	0.872475i	$0.662514\pi$
$138$	4.24147	−	0.371918i	0.361058	−	0.0316598i
$139$	−11.4218	+	6.59436i	−0.968781	+	0.559326i	−0.898864	−	0.438227i	$-0.855607\pi$
$139$	−11.4218	+	6.59436i	−0.968781	+	0.559326i	−0.0699166	+	0.997553i	$0.522273\pi$
$140$	13.3726	−	1.35441i	1.13019	−	0.114468i
$141$	11.4972	−	8.32820i	0.968236	−	0.701361i
$142$	0.133471	−	8.42875i	0.0112006	−	0.707325i
$143$	3.52944	+	6.11317i	0.295147	+	0.511209i
$144$	−11.8771	+	1.71321i	−0.989756	+	0.142768i
$145$	0.309992	+	0.178974i	0.0257434	+	0.0148630i
$146$	18.9657	−	10.5530i	1.56961	−	0.873375i
$147$	−4.36747	−	11.3104i	−0.360223	−	0.932866i
$148$	6.07608	+	3.76945i	0.499451	+	0.309847i
$149$			7.23332i			0.592576i	0.955099	+	0.296288i	$0.0957489\pi$
$149$			7.23332i			0.592576i	−0.955099	+	0.296288i	$0.904251\pi$
$150$	0.310724	+	3.54359i	0.0253705	+	0.289333i
$151$		−	9.89914i		−	0.805581i	−0.915292	−	0.402790i	$-0.868040\pi$
$151$		−	9.89914i		−	0.805581i	0.915292	−	0.402790i	$-0.131960\pi$
$152$	−12.2719	−	7.88494i	−0.995380	−	0.639553i
$153$	−1.37386	+	1.22997i	−0.111070	+	0.0994371i
$154$	5.24116	−	0.614815i	0.422345	−	0.0495432i
$155$	−11.6568	+	20.1902i	−0.936300	+	1.62172i
$156$	14.3561	−	9.72129i	1.14941	−	0.778326i
$157$	2.31059	−	4.00205i	0.184405	−	0.319398i	−0.758971	−	0.651124i	$-0.774298\pi$
$157$	2.31059	−	4.00205i	0.184405	−	0.319398i	0.943376	+	0.331726i	$0.107631\pi$
$158$	14.2856	−	7.94889i	1.13650	−	0.632380i
$159$	10.0040	+	13.8106i	0.793367	+	1.09525i
$160$	14.3241	+	1.13640i	1.13242	+	0.0898405i
$161$	0.608052	+	4.55852i	0.0479212	+	0.359261i
$162$	−11.7363	+	4.92542i	−0.922089	+	0.386977i
$163$	2.54012	−	4.39962i	0.198958	−	0.344605i	−0.749233	−	0.662306i	$-0.769578\pi$
$163$	2.54012	−	4.39962i	0.198958	−	0.344605i	0.948191	+	0.317702i	$0.102911\pi$
$164$	−6.85003	+	3.67074i	−0.534898	+	0.286636i
$165$	0.639821	+	6.17199i	0.0498100	+	0.480489i
$166$	−13.7678	−	8.24220i	−1.06859	−	0.639719i
$167$	−5.30722	−	9.19238i	−0.410685	−	0.711327i	0.584280	−	0.811552i	$-0.301377\pi$
$167$	−5.30722	−	9.19238i	−0.410685	−	0.711327i	−0.994965	+	0.100225i	$0.968044\pi$
$168$	−2.42752	−	12.7321i	−0.187288	−	0.982305i
$169$	−6.02507	+	10.4357i	−0.463467	+	0.802748i
$170$	1.92947	−	1.07361i	0.147983	−	0.0823421i
$171$	−14.7006	−	4.82283i	−1.12418	−	0.368811i
$172$	−6.89701	+	11.1175i	−0.525892	+	0.847701i
$173$	−1.19030	−	2.06165i	−0.0904966	−	0.156745i	0.817224	−	0.576321i	$-0.195512\pi$
$173$	−1.19030	−	2.06165i	−0.0904966	−	0.156745i	−0.907720	+	0.419576i	$0.862179\pi$
$174$	0.145816	−	0.312864i	0.0110543	−	0.0237182i
$175$	−3.80847	+	0.508005i	−0.287894	+	0.0384016i
$176$	5.63014	+	0.357065i	0.424388	+	0.0269148i
$177$	10.6208	−	23.7637i	0.798310	−	1.78619i
$178$	−21.9232	−	13.1245i	−1.64322	−	0.983726i
$179$	3.74108	+	6.47974i	0.279621	+	0.484318i	0.971291	−	0.237896i	$-0.0764577\pi$
$179$	3.74108	+	6.47974i	0.279621	+	0.484318i	−0.691669	+	0.722214i	$0.743124\pi$
$180$	15.0081	−	2.65241i	1.11864	−	0.197699i
$181$	0.360500			0.0267957			0.0133979	−	0.999910i	$-0.495735\pi$
$181$	0.360500			0.0267957			0.0133979	+	0.999910i	$0.495735\pi$
$182$	11.1893	+	15.0167i	0.829403	+	1.11311i
$183$	3.10660	−	2.25033i	0.229647	−	0.166349i
$184$	−0.233450	+	4.91087i	−0.0172101	+	0.362034i
$185$	−7.86470	−	4.54069i	−0.578224	−	0.333838i
$186$	20.3773	+	9.49725i	1.49414	+	0.696372i
$187$	0.750759	−	0.433451i	0.0549010	−	0.0316971i
$188$	7.74281	+	14.4490i	0.564703	+	1.05380i
$189$	−5.88671	−	12.4236i	−0.428195	−	0.903686i
$190$	15.8953	+	9.51585i	1.15316	+	0.690352i
$191$	−0.126623	+	0.0731058i	−0.00916211	+	0.00528975i	−0.504574	−	0.863368i	$-0.668350\pi$
$191$	−0.126623	+	0.0731058i	−0.00916211	+	0.00528975i	0.495412	+	0.868658i	$0.335017\pi$
$192$	−0.114913	−	13.8559i	−0.00829314	−	0.999966i
$193$	−0.0245404	+	0.0425053i	−0.00176646	+	0.00305960i	−0.866907	−	0.498469i	$-0.833896\pi$
$193$	−0.0245404	+	0.0425053i	−0.00176646	+	0.00305960i	0.865141	+	0.501529i	$0.167229\pi$
$194$	4.36994	+	2.61610i	0.313743	+	0.187825i
$195$	−17.8331	+	12.9177i	−1.27705	+	0.925059i
$196$	13.6199	−	3.23996i	0.972853	−	0.231426i
$197$			11.1576i			0.794950i	0.917613	+	0.397475i	$0.130113\pi$
$197$			11.1576i			0.794950i	−0.917613	+	0.397475i	$0.869887\pi$
$198$	5.87513	−	1.13453i	0.417527	−	0.0806273i
$199$	−8.16411	−	14.1406i	−0.578738	−	1.00240i	−0.995624	−	0.0934453i	$-0.970212\pi$
$199$	−8.16411	−	14.1406i	−0.578738	−	1.00240i	0.416886	−	0.908959i	$-0.363121\pi$
$200$	−4.10286	−	0.195039i	−0.290116	−	0.0137913i
$201$	−5.67654	−	2.53705i	−0.400392	−	0.178950i
$202$	13.0774	+	0.207082i	0.920121	+	0.0145703i
$203$	0.344695	+	0.142089i	0.0241929	+	0.00997270i
$204$	−1.19387	−	1.76308i	−0.0835878	−	0.123440i
$205$	8.54799	−	4.93518i	0.597017	−	0.344688i
$206$	−15.2825	−	0.242001i	−1.06478	−	0.0168610i
$207$	1.06966	+	5.10376i	0.0743466	+	0.354736i
$208$	8.89258	+	17.9367i	0.616590	+	1.24368i
$209$	6.29902	+	3.63674i	0.435712	+	0.251559i
$210$	3.59356	+	16.0649i	0.247979	+	1.10858i
$211$	10.9705	+	19.0015i	0.755242	+	1.30812i	0.945254	+	0.326335i	$0.105814\pi$
$211$	10.9705	+	19.0015i	0.755242	+	1.30812i	−0.190013	+	0.981782i	$0.560853\pi$
$212$	−17.3564	+	9.30080i	−1.19204	+	0.638782i
$213$	10.2693	−	1.06457i	0.703643	−	0.0729433i
$214$	−1.53831	+	2.56959i	−0.105157	+	0.175654i
$215$	8.30816	−	14.3902i	0.566612	−	0.981401i
$216$	−3.81219	−	14.1939i	−0.259387	−	0.965773i
$217$	−9.25449	+	22.4505i	−0.628236	+	1.52404i
$218$	−2.79273	+	1.55395i	−0.189147	+	0.105247i
$219$	15.5938	+	21.5274i	1.05373	+	1.45469i
$220$	−7.16140	−	0.226861i	−0.482821	−	0.0152949i
$221$	2.66425	+	1.53820i	0.179217	+	0.103471i
$222$	−3.69946	+	7.93758i	−0.248292	+	0.532736i
$223$	3.38619	−	5.86505i	0.226756	−	0.392753i	−0.730089	−	0.683352i	$-0.760521\pi$
$223$	3.38619	−	5.86505i	0.226756	−	0.392753i	0.956845	+	0.290600i	$0.0938547\pi$
$224$	14.9453	−	0.799379i	0.998573	−	0.0534108i
$225$	−4.26401	+	0.893663i	−0.284267	+	0.0595775i
$226$	8.11945	+	14.5921i	0.540098	+	0.970652i
$227$			15.7111i			1.04278i	0.853317	+	0.521392i	$0.174587\pi$
$227$			15.7111i			1.04278i	−0.853317	+	0.521392i	$0.825413\pi$
$228$	7.80232	−	16.0711i	0.516721	−	1.06433i
$229$	3.20788			0.211982			0.105991	−	0.994367i	$-0.466198\pi$
$229$	3.20788			0.211982			0.105991	+	0.994367i	$0.466198\pi$
$230$	0.0988648	−	6.24337i	0.00651895	−	0.411676i
$231$	1.51055	+	6.28410i	0.0993871	+	0.413463i
$232$	0.335324	+	0.215453i	0.0220151	+	0.0141452i
$233$	10.6422	−	18.4328i	0.697191	−	1.20757i	−0.272246	−	0.962228i	$-0.587766\pi$
$233$	10.6422	−	18.4328i	0.697191	−	1.20757i	0.969437	−	0.245342i	$-0.0789002\pi$
$234$	13.9114	+	16.0429i	0.909415	+	1.04876i
$235$	−10.4100	−	18.0306i	−0.679070	−	1.17618i
$236$	25.5402	+	15.8445i	1.66253	+	1.03139i
$237$	11.7458	+	16.2151i	0.762969	+	1.05329i
$238$	1.84421	−	1.37415i	0.119542	−	0.0890732i
$239$	10.9723	−	6.33484i	0.709736	−	0.409766i	−0.101227	−	0.994863i	$-0.532277\pi$
$239$	10.9723	−	6.33484i	0.709736	−	0.409766i	0.810963	+	0.585097i	$0.198944\pi$
$240$	0.703064	+	17.5844i	0.0453826	+	1.13507i
$241$			5.85187i			0.376952i	0.982078	+	0.188476i	$0.0603548\pi$
$241$			5.85187i			0.376952i	−0.982078	+	0.188476i	$0.939645\pi$
$242$	12.7417	+	0.201767i	0.819068	+	0.0129701i
$243$	−7.69795	−	13.5551i	−0.493824	−	0.869562i
$244$	2.09215	+	3.90421i	0.133936	+	0.249941i
$245$	−17.1592	+	4.66059i	−1.09626	+	0.297754i
$246$	−5.46094	−	7.79577i	−0.348177	−	0.497040i
$247$			25.8117i			1.64236i
$248$	−14.0328	+	21.8402i	−0.891083	+	1.38685i
$249$	8.01902	−	17.9422i	0.508185	−	1.13704i
$250$	−12.7430	−	0.201788i	−0.805939	−	0.0127622i
$251$		−	15.8454i		−	1.00015i	−0.865982	−	0.500076i	$-0.833306\pi$
$251$		−	15.8454i		−	1.00015i	0.865982	−	0.500076i	$-0.166694\pi$
$252$	15.1297	−	4.80530i	0.953084	−	0.302706i
$253$		−	2.45152i		−	0.154126i
$254$	0.375231	−	23.6961i	0.0235441	−	1.48682i
$255$	1.58643	+	2.19008i	0.0993460	+	0.137148i
$256$	15.8718	+	2.02132i	0.991988	+	0.126332i
$257$			20.2608i			1.26383i	0.775037	+	0.631916i	$0.217731\pi$
$257$			20.2608i			1.26383i	−0.775037	+	0.631916i	$0.782269\pi$
$258$	−14.5235	−	6.76896i	−0.904194	−	0.421417i
$259$	−8.74516	−	3.60490i	−0.543398	−	0.223998i
$260$	−12.0098	−	22.4116i	−0.744813	−	1.38991i
$261$	0.401688	+	0.131782i	0.0248638	+	0.00815708i
$262$	−0.0328204	+	2.07263i	−0.00202765	+	0.128047i
$263$		−	22.1801i		−	1.36769i	−0.729629	−	0.683843i	$-0.760307\pi$
$263$		−	22.1801i		−	1.36769i	0.729629	−	0.683843i	$-0.239693\pi$
$264$	0.385305	+	6.89859i	0.0237139	+	0.424579i
$265$	21.6586	−	12.5046i	1.33048	−	0.768152i
$266$	17.7214	+	7.63552i	1.08657	+	0.468164i
$267$	12.7692	−	28.5705i	0.781460	−	1.74848i
$268$	3.78486	−	6.10092i	0.231197	−	0.372673i
$269$	8.92867	+	15.4649i	0.544391	+	0.942913i	0.998645	+	0.0520405i	$0.0165725\pi$
$269$	8.92867	+	15.4649i	0.544391	+	0.942913i	−0.454254	+	0.890872i	$0.650094\pi$
$270$	5.41007	+	17.8648i	0.329247	+	1.08722i
$271$	7.58398	−	13.1358i	0.460694	−	0.797945i	−0.538302	−	0.842752i	$-0.680934\pi$
$271$	7.58398	−	13.1358i	0.460694	−	0.797945i	0.998996	+	0.0448070i	$0.0142673\pi$
$272$	2.20280	−	1.09210i	0.133565	−	0.0662182i
$273$	−16.6326	+	15.7927i	−1.00665	+	0.955817i
$274$	16.1755	+	0.256141i	0.977196	+	0.0154741i
$275$	2.04815			0.123508
$276$	−6.00592	+	0.430933i	−0.361514	+	0.0259391i
$277$		−	15.3762i		−	0.923867i	−0.886915	−	0.461934i	$-0.847156\pi$
$277$		−	15.3762i		−	0.923867i	0.886915	−	0.461934i	$-0.152844\pi$
$278$	16.2984	−	9.06891i	0.977515	−	0.543917i
$279$	−8.58316	+	26.1626i	−0.513860	+	1.56631i
$280$	−18.9397	+	1.61575i	−1.13187	+	0.0965594i
$281$	−3.50216	+	6.06591i	−0.208921	+	0.361862i	−0.951375	−	0.308035i	$-0.900329\pi$
$281$	−3.50216	+	6.06591i	−0.208921	+	0.361862i	0.742454	+	0.669897i	$0.233662\pi$
$282$	−16.4439	+	11.5189i	−0.979220	+	0.685943i
$283$	−13.5148	−	7.80276i	−0.803370	−	0.463826i	0.0412781	−	0.999148i	$-0.486857\pi$
$283$	−13.5148	−	7.80276i	−0.803370	−	0.463826i	−0.844648	+	0.535322i	$0.820190\pi$
$284$	−0.377464	+	11.9156i	−0.0223984	+	0.707059i
$285$	−9.25818	+	20.7148i	−0.548407	+	1.22704i
$286$	−4.85388	−	8.72328i	−0.287016	−	0.515818i
$287$	8.14564	−	6.27247i	0.480822	−	0.370252i
$288$	16.8330	−	2.15660i	0.991893	−	0.127079i
$289$	−8.31109	+	14.3952i	−0.488888	+	0.846779i
$290$	−0.434332	−	0.260016i	−0.0255048	−	0.0152687i
$291$	−2.54526	+	5.69493i	−0.149206	+	0.333843i
$292$	−27.0544	+	14.4977i	−1.58324	+	0.848414i
$293$	16.5346	+	28.6387i	0.965959	+	1.67309i	0.707015	+	0.707199i	$0.250041\pi$
$293$	16.5346	+	28.6387i	0.965959	+	1.67309i	0.258944	+	0.965892i	$0.416625\pi$
$294$	5.92251	+	16.0911i	0.345408	+	0.938453i
$295$	−33.0585	−	19.0863i	−1.92474	−	1.11125i
$296$	−8.50739	−	5.46619i	−0.494482	−	0.317716i
$297$	2.23484	+	6.97939i	0.129678	+	0.404985i
$298$	0.161965	−	10.2282i	0.00938237	−	0.592502i
$299$	7.53424	−	4.34990i	0.435717	−	0.251561i
$300$	−0.360029	−	5.01773i	−0.0207863	−	0.289699i
$301$	6.59593	−	16.0011i	0.380183	−	0.922290i
$302$	−0.221657	+	13.9977i	−0.0127549	+	0.805480i
$303$	1.65171	+	15.9331i	0.0948880	+	0.915331i
$304$	17.1763	+	11.4244i	0.985129	+	0.655233i
$305$	−2.81283	−	4.87196i	−0.161062	−	0.278968i
$306$	1.97023	−	1.70846i	0.112631	−	0.0976660i
$307$		−	24.0331i		−	1.37164i	−0.727771	−	0.685820i	$-0.759444\pi$
$307$		−	24.0331i		−	1.37164i	0.727771	−	0.685820i	$-0.240556\pi$
$308$	−7.42496	+	0.752014i	−0.423076	+	0.0428500i
$309$	−1.93022	−	18.6198i	−0.109806	−	1.05924i
$310$	16.9353	−	28.2887i	0.961860	−	1.60669i
$311$	7.72985	−	13.3885i	0.438319	−	0.759192i	−0.559241	−	0.829005i	$-0.688907\pi$
$311$	7.72985	−	13.3885i	0.438319	−	0.759192i	0.997560	+	0.0698139i	$0.0222405\pi$
$312$	−20.5177	+	13.4248i	−1.16159	+	0.760030i
$313$	−17.0443	+	9.84051i	−0.963398	+	0.556218i	−0.897217	−	0.441589i	$-0.854415\pi$
$313$	−17.0443	+	9.84051i	−0.963398	+	0.556218i	−0.0661810	+	0.997808i	$0.521081\pi$
$314$	−3.35686	+	5.60731i	−0.189439	+	0.316439i
$315$	−19.0128	+	6.70838i	−1.07125	+	0.377975i
$316$	−20.3783	+	10.9201i	−1.14637	+	0.614306i
$317$	10.2316	−	5.90720i	0.574662	−	0.331781i	−0.184347	−	0.982861i	$-0.559017\pi$
$317$	10.2316	−	5.90720i	0.574662	−	0.331781i	0.759009	+	0.651080i	$0.225684\pi$
$318$	−13.8368	−	19.7527i	−0.775927	−	1.10768i
$319$	−0.172118	−	0.0993724i	−0.00963676	−	0.00556379i
$320$	−20.2293	−	1.92765i	−1.13085	−	0.107759i
$321$	−3.34870	−	1.49665i	−0.186906	−	0.0835351i
$322$	−0.757735	−	6.45952i	−0.0422269	−	0.359975i
$323$	3.16993			0.176380
$324$	16.7058	−	6.70193i	0.928101	−	0.372329i
$325$	3.63418	+	6.29459i	0.201588	+	0.349161i
$326$	−3.69034	+	6.16435i	−0.204389	+	0.341412i
$327$	−2.29621	−	3.16994i	−0.126981	−	0.175298i
$328$	9.76839	−	5.03717i	0.539369	−	0.278131i
$329$	−13.2307	−	17.1819i	−0.729434	−	0.947267i
$330$	−0.766530	−	8.74174i	−0.0421961	−	0.481217i
$331$	−16.9311	−	29.3255i	−0.930617	−	1.61188i	−0.782269	−	0.622940i	$-0.785938\pi$
$331$	−16.9311	−	29.3255i	−0.930617	−	1.61188i	−0.148347	−	0.988935i	$-0.547395\pi$
$332$	19.2836	+	11.9631i	1.05832	+	0.656558i
$333$	−10.1911	−	3.34340i	−0.558469	−	0.183217i
$334$	7.29877	+	13.1172i	0.399371	+	0.717741i
$335$	−4.55925	+	7.89685i	−0.249098	+	0.431451i
$336$	3.14752	+	18.0580i	0.171711	+	0.985147i
$337$	−0.620110	−	1.07406i	−0.0337795	−	0.0585079i	0.848641	−	0.528969i	$-0.177421\pi$
$337$	−0.620110	−	1.07406i	−0.0337795	−	0.0585079i	−0.882421	+	0.470461i	$0.844088\pi$
$338$	8.75333	−	14.6216i	0.476119	−	0.795309i
$339$	−16.5631	+	11.9978i	−0.899582	+	0.651630i
$340$	−2.75238	+	1.47492i	−0.149268	+	0.0799887i
$341$	6.47228	−	11.2103i	0.350494	−	0.607073i
$342$	20.6792	+	7.14882i	1.11820	+	0.386564i
$343$	−17.0740	+	7.17486i	−0.921909	+	0.387406i
$344$	10.0016	−	15.5661i	0.539248	−	0.839268i
$345$	7.60673	−	0.788554i	0.409533	−	0.0424543i
$346$	1.63696	+	2.94191i	0.0880035	+	0.158158i
$347$	3.37864	−	5.85198i	0.181375	−	0.314151i	−0.760974	−	0.648782i	$-0.775279\pi$
$347$	3.37864	−	5.85198i	0.181375	−	0.314151i	0.942349	+	0.334632i	$0.108612\pi$
$348$	−0.213195	+	0.439136i	−0.0114285	+	0.0235402i
$349$	4.81681	−	8.34297i	0.257838	−	0.446589i	−0.707824	−	0.706388i	$-0.750323\pi$
$349$	4.81681	−	8.34297i	0.257838	−	0.446589i	0.965663	+	0.259800i	$0.0836565\pi$
$350$	5.39669	−	0.633060i	0.288465	−	0.0338385i
$351$	−17.4843	+	19.2523i	−0.933244	+	1.02761i
$352$	−7.95323	−	0.630970i	−0.423909	−	0.0336308i
$353$			10.3238i			0.549480i	0.961519	+	0.274740i	$0.0885918\pi$
$353$			10.3238i			0.549480i	−0.961519	+	0.274740i	$0.911408\pi$
$354$	−15.5503	+	33.3649i	−0.826491	+	1.77332i
$355$		−	15.1411i		−	0.803605i
$356$	30.7064	+	19.0495i	1.62744	+	1.00962i
$357$	1.93950	+	2.04265i	0.102649	+	0.108109i
$358$	−5.14493	−	9.24635i	−0.271918	−	0.488685i
$359$	21.2296	+	12.2569i	1.12045	+	0.646894i	0.941517	−	0.336966i	$-0.109401\pi$
$359$	21.2296	+	12.2569i	1.12045	+	0.646894i	0.178937	+	0.983861i	$0.442734\pi$
$360$	−21.2815	+	3.41455i	−1.12163	+	0.179962i
$361$	3.79819	+	6.57866i	0.199905	+	0.346245i
$362$	−0.509760	−	0.00807213i	−0.0267924	−	0.000424262i
$363$	1.60931	+	15.5241i	0.0844669	+	0.814804i
$364$	−15.4858	−	21.4847i	−0.811675	−	1.12611i
$365$	33.7606	−	19.4917i	1.76711	−	1.02024i
$366$	−4.44324	+	3.11249i	−0.232252	+	0.162692i
$367$	21.4918			1.12186			0.560930	−	0.827863i	$-0.310444\pi$
$367$	21.4918			1.12186			0.560930	+	0.827863i	$0.310444\pi$
$368$	0.440068	−	6.93893i	0.0229401	−	0.361717i
$369$	8.68527	−	7.77560i	0.452137	−	0.404781i
$370$	11.0193	+	6.59680i	0.572866	+	0.342951i
$371$	20.6392	−	15.8930i	1.07153	−	0.825123i
$372$	−28.6016	−	13.8857i	−1.48293	−	0.719942i
$373$			1.23074i			0.0637254i	0.999492	+	0.0318627i	$0.0101439\pi$
$373$			1.23074i			0.0637254i	−0.999492	+	0.0318627i	$0.989856\pi$
$374$	−1.07131	+	0.596105i	−0.0553959	+	0.0308239i
$375$	−1.60948	−	15.5257i	−0.0831129	−	0.801743i
$376$	−10.6251	−	20.6048i	−0.547947	−	1.06261i
$377$		−	0.705293i		−	0.0363244i
$378$	8.04583	+	17.6993i	0.413833	+	0.910353i
$379$	28.1628			1.44662			0.723312	−	0.690521i	$-0.242619\pi$
$379$	28.1628			1.44662			0.723312	+	0.690521i	$0.242619\pi$
$380$	−22.2634	−	13.8117i	−1.14209	−	0.708524i
$381$	28.8705	−	2.99287i	1.47908	−	0.153329i
$382$	0.180686	−	0.100539i	0.00924471	−	0.00514402i
$383$	−6.08440			−0.310898			−0.155449	−	0.987844i	$-0.549682\pi$
$383$	−6.08440			−0.310898			−0.155449	+	0.987844i	$0.549682\pi$
$384$	−0.147764	+	19.5954i	−0.00754053	+	0.999972i
$385$	9.39518	−	1.25321i	0.478823	−	0.0638693i
$386$	0.0356528	−	0.0595545i	0.00181468	−	0.00303125i
$387$	6.11746	−	18.6468i	0.310968	−	0.947870i
$388$	−6.12068	−	3.79711i	−0.310730	−	0.192769i
$389$		−	5.77012i		−	0.292557i	−0.989243	−	0.146278i	$-0.953270\pi$
$389$		−	5.77012i		−	0.292557i	0.989243	−	0.146278i	$-0.0467295\pi$
$390$	25.5059	−	17.8668i	1.29154	−	0.904723i
$391$	−0.534211	−	0.925281i	−0.0270162	−	0.0467935i
$392$	−19.3316	+	4.27645i	−0.976395	+	0.215994i
$393$	−2.52523	+	0.261778i	−0.127381	+	0.0132050i
$394$	0.249836	−	15.7773i	0.0125866	−	0.794850i
$395$	25.4296	−	14.6818i	1.27950	−	0.738720i
$396$	−8.33304	+	1.47271i	−0.418751	+	0.0740064i
$397$	−11.2253	+	19.4428i	−0.563383	+	0.975808i	0.433815	+	0.901002i	$0.357167\pi$
$397$	−11.2253	+	19.4428i	−0.563383	+	0.975808i	−0.997198	+	0.0748063i	$0.976166\pi$
$398$	11.2277	+	20.1782i	0.562794	+	1.01144i
$399$	−6.70577	+	22.6618i	−0.335708	+	1.13451i
$400$	5.79722	+	0.367661i	0.289861	+	0.0183830i
$401$	−8.79279			−0.439091			−0.219545	−	0.975602i	$-0.570457\pi$
$401$	−8.79279			−0.439091			−0.219545	+	0.975602i	$0.570457\pi$
$402$	7.97003	+	3.71458i	0.397509	+	0.185267i
$403$	45.9369			2.28828
$404$	−18.4872	−	0.585644i	−0.919775	−	0.0291369i
$405$	−20.9373	+	9.17938i	−1.04038	+	0.456127i
$406$	−0.484230	−	0.208637i	−0.0240319	−	0.0103545i
$407$	4.36676	+	2.52115i	0.216452	+	0.124969i
$408$	1.64870	+	2.51979i	0.0816229	+	0.124748i
$409$	10.5803	+	6.10854i	0.523162	+	0.302048i	0.738227	−	0.674552i	$-0.235663\pi$
$409$	10.5803	+	6.10854i	0.523162	+	0.302048i	−0.215065	+	0.976600i	$0.568996\pi$
$410$	−12.1977	+	6.78712i	−0.602400	+	0.335192i
$411$	2.04300	+	19.7077i	0.100774	+	0.972109i
$412$	21.6046	+	0.684397i	1.06438	+	0.0337178i
$413$	−36.7594	−	15.1528i	−1.80881	−	0.745623i
$414$	−1.39826	−	7.24086i	−0.0687207	−	0.355869i
$415$	−24.9601	−	14.4107i	−1.22524	−	0.707395i
$416$	−12.1728	−	25.5622i	−0.596821	−	1.25329i
$417$	13.4008	+	18.4999i	0.656238	+	0.905943i
$418$	−8.82561	−	5.28353i	−0.431675	−	0.258426i
$419$	−20.4770	+	11.8224i	−1.00037	+	0.577561i	−0.908357	−	0.418197i	$-0.862662\pi$
$419$	−20.4770	+	11.8224i	−1.00037	+	0.577561i	−0.0920093	+	0.995758i	$0.529329\pi$
$420$	−4.72170	−	22.7967i	−0.230396	−	1.11237i
$421$	3.30988	+	1.91096i	0.161313	+	0.0931344i	0.578484	−	0.815694i	$-0.303645\pi$
$421$	3.30988	+	1.91096i	0.161313	+	0.0931344i	−0.417170	+	0.908828i	$0.636978\pi$
$422$	−15.0872	−	27.1144i	−0.734435	−	1.31991i
$423$	−16.4013	−	18.3201i	−0.797460	−	0.890756i
$424$	24.7509	−	12.7630i	1.20201	−	0.619828i
$425$	0.773039	−	0.446314i	0.0374979	−	0.0216494i
$426$	−14.5450	+	1.27540i	−0.704709	+	0.0617932i
$427$	−3.57502	−	4.64264i	−0.173007	−	0.224673i
$428$	2.23276	−	3.59905i	0.107925	−	0.173967i
$429$	9.90154	−	7.17238i	0.478051	−	0.346286i
$430$	−12.0703	+	20.1622i	−0.582080	+	0.972306i
$431$	−24.5274	+	14.1609i	−1.18144	+	0.682105i	−0.956348	−	0.292232i	$-0.905602\pi$
$431$	−24.5274	+	14.1609i	−1.18144	+	0.682105i	−0.225094	+	0.974337i	$0.572269\pi$
$432$	5.07276	+	20.1561i	0.244063	+	0.969759i
$433$		−	0.836983i		−	0.0402228i	−0.999798	−	0.0201114i	$-0.993598\pi$
$433$		−	0.836983i		−	0.0402228i	0.999798	−	0.0201114i	$-0.00640209\pi$
$434$	13.5889	−	31.5387i	0.652287	−	1.51390i
$435$	0.252976	−	0.566023i	0.0121293	−	0.0271387i
$436$	3.98381	−	2.13481i	0.190790	−	0.102239i
$437$	4.48214	−	7.76329i	0.214410	−	0.371369i
$438$	−21.5682	−	30.7897i	−1.03057	−	1.47119i
$439$	12.1884	+	21.1110i	0.581721	+	1.00757i	0.995275	+	0.0970914i	$0.0309539\pi$
$439$	12.1884	+	21.1110i	0.581721	+	1.00757i	−0.413554	+	0.910480i	$0.635713\pi$
$440$	10.1214	+	0.481144i	0.482519	+	0.0229376i
$441$	−18.7058	+	9.54436i	−0.890750	+	0.454493i
$442$	−3.73290	−	2.23473i	−0.177556	−	0.106295i
$443$	1.91530	+	3.31739i	0.0909985	+	0.157614i	0.907932	−	0.419118i	$-0.137661\pi$
$443$	1.91530	+	3.31739i	0.0909985	+	0.157614i	−0.816933	+	0.576733i	$0.804327\pi$
$444$	5.40891	−	11.1412i	0.256695	−	0.528738i
$445$	−39.7455	−	22.9471i	−1.88412	−	1.08779i
$446$	−4.91952	+	8.21757i	−0.232946	+	0.389113i
$447$	12.4617	−	1.29184i	0.589418	−	0.0611021i
$448$	−21.1510	+	0.795704i	−0.999293	+	0.0375935i
$449$	−28.3303			−1.33699			−0.668495	−	0.743717i	$-0.733061\pi$
$449$	−28.3303			−1.33699			−0.668495	+	0.743717i	$0.733061\pi$
$450$	6.04947	−	1.16819i	0.285175	−	0.0550692i
$451$	−4.74614	+	2.74018i	−0.223487	+	0.129030i
$452$	−11.1545	−	20.8156i	−0.524661	−	0.979081i
$453$	−17.0544	+	1.76795i	−0.801287	+	0.0830656i
$454$	0.351796	−	22.2161i	0.0165106	−	1.04265i
$455$	20.5220	+	26.6505i	0.962085	+	1.24940i
$456$	−11.3926	+	22.5504i	−0.533508	+	1.05602i
$457$	14.1521	+	24.5121i	0.662007	+	1.14663i	0.980088	+	0.198566i	$0.0636284\pi$
$457$	14.1521	+	24.5121i	0.662007	+	1.14663i	−0.318081	+	0.948064i	$0.603038\pi$
$458$	−4.53605	−	0.0718292i	−0.211956	−	0.00335636i
$459$	2.36438	+	2.14725i	0.110360	+	0.100225i
$460$	−0.279597	+	8.82614i	−0.0130363	+	0.411521i
$461$	−10.8891	+	18.8604i	−0.507154	+	0.878416i	0.492812	+	0.870136i	$0.335969\pi$
$461$	−10.8891	+	18.8604i	−0.507154	+	0.878416i	−0.999966	+	0.00828044i	$0.997364\pi$
$462$	−1.99527	−	8.91976i	−0.0928282	−	0.414985i
$463$	−8.46040	+	4.88461i	−0.393188	+	0.227007i	−0.683541	−	0.729913i	$-0.739561\pi$
$463$	−8.46040	+	4.88461i	−0.393188	+	0.227007i	0.290353	+	0.956920i	$0.406227\pi$
$464$	−0.469335	−	0.312166i	−0.0217883	−	0.0144920i
$465$	36.8660	+	16.4767i	1.70962	+	0.764090i
$466$	−15.4611	+	25.8263i	−0.716223	+	1.19638i
$467$	−11.5689	−	6.67934i	−0.535347	−	0.309083i	0.207844	−	0.978162i	$-0.433355\pi$
$467$	−11.5689	−	6.67934i	−0.535347	−	0.309083i	−0.743191	+	0.669079i	$0.766689\pi$
$468$	−19.3120	−	22.9968i	−0.892696	−	1.06303i
$469$	−3.61963	+	8.78090i	−0.167139	+	0.405465i
$470$	14.3163	+	25.7290i	0.660362	+	1.18679i
$471$	−7.30747	−	3.26597i	−0.336710	−	0.150488i
$472$	−35.7600	−	22.9766i	−1.64599	−	1.05758i
$473$	−4.61298	+	7.98991i	−0.212105	+	0.367377i
$474$	−16.2458	−	23.1918i	−0.746197	−	1.06523i
$475$	6.48595	+	3.74466i	0.297596	+	0.171817i
$476$	−2.63854	+	1.90181i	−0.120937	+	0.0871693i
$477$	22.0065	−	19.7016i	1.00761	−	0.902073i
$478$	−15.6570	+	8.71200i	−0.716135	+	0.398478i
$479$	4.90258			0.224005			0.112002	−	0.993708i	$-0.464274\pi$
$479$	4.90258			0.224005			0.112002	+	0.993708i	$0.464274\pi$
$480$	−0.600417	−	24.8808i	−0.0274051	−	1.13565i
$481$			17.8938i			0.815886i
$482$	0.131032	−	8.27476i	0.00596836	−	0.376905i
$483$	7.74490	−	1.86170i	0.352405	−	0.0847102i
$484$	−18.0127	−	0.570612i	−0.818760	−	0.0259369i
$485$	7.92243	+	4.57402i	0.359739	+	0.207695i
$486$	10.5817	+	19.3398i	0.479994	+	0.877272i
$487$	3.30660	−	1.90906i	0.149836	−	0.0865079i	−0.423208	−	0.906033i	$-0.639096\pi$
$487$	3.30660	−	1.90906i	0.149836	−	0.0865079i	0.573044	+	0.819525i	$0.305763\pi$
$488$	−2.87096	−	5.56754i	−0.129962	−	0.252031i
$489$	−8.03340	−	3.59041i	−0.363283	−	0.162364i
$490$	24.3681	−	6.20602i	1.10084	−	0.280359i
$491$	−11.4881	−	19.8980i	−0.518450	−	0.897982i	−0.999770	−	0.0214373i	$-0.993176\pi$
$491$	−11.4881	−	19.8980i	−0.518450	−	0.897982i	0.481320	−	0.876545i	$-0.340158\pi$
$492$	7.54740	+	11.1458i	0.340263	+	0.502491i
$493$	−0.0866171			−0.00390104
$494$	0.577962	−	36.4986i	0.0260037	−	1.64215i
$495$	10.5189	−	2.20459i	0.472791	−	0.0990889i
$496$	20.3319	−	30.5686i	0.912929	−	1.37257i
$497$	−2.08516	−	15.6323i	−0.0935321	−	0.701203i
$498$	−11.7409	+	25.1914i	−0.526124	+	1.12885i
$499$	−25.0764			−1.12258			−0.561288	−	0.827621i	$-0.689694\pi$
$499$	−25.0764			−1.12258			−0.561288	+	0.827621i	$0.689694\pi$
$500$	18.0146	+	0.570670i	0.805636	+	0.0255212i
$501$	−14.8889	+	10.7851i	−0.665189	+	0.481843i
$502$	−0.354802	+	22.4059i	−0.0158356	+	1.00003i
$503$	−33.4672			−1.49223			−0.746115	−	0.665817i	$-0.768083\pi$
$503$	−33.4672			−1.49223			−0.746115	+	0.665817i	$0.768083\pi$
$504$	−21.5016	+	6.45610i	−0.957757	+	0.287577i
$505$	23.4917			1.04537
$506$	−0.0548932	+	3.46653i	−0.00244030	+	0.154106i
$507$	19.0549	+	8.51631i	0.846258	+	0.378223i
$508$	−1.06118	+	33.4987i	−0.0470823	+	1.48626i
$509$	−23.9527			−1.06169			−0.530843	−	0.847470i	$-0.678125\pi$
$509$	−23.9527			−1.06169			−0.530843	+	0.847470i	$0.678125\pi$
$510$	−2.19423	−	3.13238i	−0.0971621	−	0.138704i
$511$	32.1715	−	24.7733i	1.42318	−	1.09591i
$512$	−22.3981	−	3.21361i	−0.989863	−	0.142023i
$513$	−5.68338	+	26.1878i	−0.250927	+	1.15622i
$514$	0.453669	−	28.6495i	0.0200105	−	1.26367i
$515$	−27.4529			−1.20972
$516$	20.3852	+	9.89675i	0.897408	+	0.435680i
$517$	5.77997	+	10.0112i	0.254203	+	0.440292i
$518$	12.2853	+	5.29328i	0.539783	+	0.232573i
$519$	−3.33927	+	2.41887i	−0.146578	+	0.106177i
$520$	16.4804	+	31.9598i	0.722713	+	1.40153i
$521$	10.2377	−	5.91074i	0.448522	−	0.258954i	−0.258684	−	0.965962i	$-0.583289\pi$
$521$	10.2377	−	5.91074i	0.448522	−	0.258954i	0.707206	+	0.707008i	$0.249956\pi$
$522$	−0.565050	−	0.195339i	−0.0247316	−	0.00854974i
$523$	20.9812	+	12.1135i	0.917444	+	0.529686i	0.882819	−	0.469714i	$-0.155643\pi$
$523$	20.9812	+	12.1135i	0.917444	+	0.529686i	0.0346252	+	0.999400i	$0.488976\pi$
$524$	0.0928185	−	2.93004i	0.00405480	−	0.127999i
$525$	1.55538	+	6.47058i	0.0678824	+	0.282399i
$526$	−0.496647	+	31.3635i	−0.0216548	+	1.36751i
$527$		−	5.64151i		−	0.245748i
$528$	−0.390366	−	9.76348i	−0.0169885	−	0.424901i
$529$	19.9786			0.868635
$530$	−30.9061	+	17.1970i	−1.34247	+	0.746990i
$531$	−42.8373	−	14.0536i	−1.85898	−	0.609876i
$532$	−24.8877	−	11.1937i	−1.07902	−	0.485309i
$533$	−16.8428	−	9.72420i	−0.729543	−	0.421202i
$534$	−18.6958	+	40.1138i	−0.809046	+	1.73589i
$535$	−2.68959	+	4.65851i	−0.116281	+	0.201405i
$536$	−5.48853	+	8.54217i	−0.237068	+	0.368965i
$537$	10.4953	−	7.60246i	0.452904	−	0.328070i
$538$	−12.2792	−	22.0679i	−0.529393	−	0.951414i
$539$	9.52737	−	2.58772i	0.410373	−	0.111461i
$540$	−7.25002	−	25.3826i	−0.311991	−	1.09229i
$541$	33.8843	+	19.5631i	1.45680	+	0.841084i	0.998852	−	0.0478943i	$-0.0152511\pi$
$541$	33.8843	+	19.5631i	1.45680	+	0.841084i	0.457949	+	0.888979i	$0.348584\pi$
$542$	−11.0181	+	18.4047i	−0.473270	+	0.790551i
$543$	−0.0643840	−	0.621076i	−0.00276298	−	0.0266529i
$544$	−3.13930	+	1.49494i	−0.134596	+	0.0640952i
$545$	−4.97130	+	2.87018i	−0.212947	+	0.122945i
$546$	23.8727	−	21.9590i	1.02166	−	0.939758i
$547$	6.59201	−	11.4177i	0.281854	−	0.488186i	−0.689987	−	0.723821i	$-0.742384\pi$
$547$	6.59201	−	11.4177i	0.281854	−	0.488186i	0.971841	+	0.235636i	$0.0757173\pi$
$548$	−22.8670	−	0.724386i	−0.976828	−	0.0309442i
$549$	−4.43174	−	4.95021i	−0.189142	−	0.211270i
$550$	−2.89616	−	0.0458612i	−0.123493	−	0.00195553i
$551$	−0.363367	−	0.629371i	−0.0154800	−	0.0268121i
$552$	8.50224	−	0.474873i	0.361879	−	0.0202119i
$553$	24.2326	−	18.6601i	1.03048	−	0.793508i
$554$	−0.344296	+	21.7425i	−0.0146278	+	0.923751i
$555$	−6.41817	+	14.3604i	−0.272436	+	0.609565i
$556$	−23.2497	+	12.4588i	−0.986005	+	0.528372i
$557$	28.9929	−	16.7390i	1.22847	−	0.709256i	0.261758	−	0.965133i	$-0.415698\pi$
$557$	28.9929	−	16.7390i	1.22847	−	0.709256i	0.966709	+	0.255877i	$0.0823643\pi$
$558$	12.7227	−	36.8026i	0.538595	−	1.55798i
$559$	−32.7405			−1.38478
$560$	26.8176	−	1.86064i	1.13325	−	0.0786262i
$561$	−0.880840	−	1.21601i	−0.0371891	−	0.0513399i
$562$	5.08800	−	8.49900i	0.214624	−	0.358509i
$563$	−13.7603	−	7.94452i	−0.579928	−	0.334822i	0.181177	−	0.983451i	$-0.442009\pi$
$563$	−13.7603	−	7.94452i	−0.579928	−	0.334822i	−0.761105	+	0.648629i	$0.775343\pi$
$564$	23.5102	−	15.9200i	0.989958	−	0.670353i
$565$	14.9968	+	25.9752i	0.630920	+	1.09279i
$566$	18.9357	+	11.3360i	0.795926	+	0.476488i
$567$	−20.3523	+	12.3605i	−0.854717	+	0.519094i
$568$	0.800556	−	16.8406i	0.0335906	−	0.706615i
$569$	15.7709	+	27.3160i	0.661149	+	1.14514i	0.980314	+	0.197445i	$0.0632644\pi$
$569$	15.7709	+	27.3160i	0.661149	+	1.14514i	−0.319164	+	0.947699i	$0.603402\pi$
$570$	13.5552	−	29.0842i	0.567766	−	1.21820i
$571$	−20.0445	+	34.7181i	−0.838837	+	1.45291i	0.0520304	+	0.998645i	$0.483431\pi$
$571$	−20.0445	+	34.7181i	−0.838837	+	1.45291i	−0.890868	+	0.454263i	$0.849903\pi$
$572$	6.66823	+	12.4437i	0.278813	+	0.520298i
$573$	0.148562	+	0.205092i	0.00620628	+	0.00856783i
$574$	−11.6587	+	8.68711i	−0.486624	+	0.362593i
$575$		−	2.52427i		−	0.105269i
$576$	−23.8507	+	2.67259i	−0.993780	+	0.111358i
$577$	28.0924	−	16.2191i	1.16950	−	0.675212i	0.215939	−	0.976407i	$-0.430719\pi$
$577$	28.0924	−	16.2191i	1.16950	−	0.675212i	0.953563	+	0.301195i	$0.0973855\pi$
$578$	12.0745	−	20.1693i	0.502234	−	0.838932i
$579$	0.0776117	+	0.0346874i	0.00322543	+	0.00144156i
$580$	0.608339	+	0.377398i	0.0252599	+	0.0156706i
$581$	−27.7544	−	11.4408i	−1.15145	−	0.474646i
$582$	3.72661	−	7.99584i	0.154473	−	0.331438i
$583$	−12.0256	+	6.94300i	−0.498050	+	0.287549i
$584$	38.5806	−	19.8945i	1.59648	−	0.823240i
$585$	25.4398	+	28.4161i	1.05181	+	1.17486i
$586$	−22.7392	−	40.8664i	−0.939348	−	1.68818i
$587$	36.8537	+	21.2775i	1.52112	+	0.878216i	0.999689	+	0.0249199i	$0.00793307\pi$
$587$	36.8537	+	21.2775i	1.52112	+	0.878216i	0.521426	+	0.853297i	$0.325400\pi$
$588$	−8.01434	−	22.8860i	−0.330506	−	0.943804i
$589$	40.9919	−	23.6667i	1.68904	−	0.975170i
$590$	46.3186	+	27.7290i	1.90691	+	1.14159i
$591$	19.2226	−	1.99272i	0.790712	−	0.0819694i
$592$	11.9074	+	7.91988i	0.489390	+	0.325505i
$593$	−5.70449	−	3.29349i	−0.234255	−	0.135247i	0.378278	−	0.925692i	$-0.376516\pi$
$593$	−5.70449	−	3.29349i	−0.234255	−	0.135247i	−0.612534	+	0.790445i	$0.709850\pi$
$594$	−3.00386	−	9.91915i	−0.123250	−	0.406988i
$595$	3.27295	−	2.52031i	0.134178	−	0.103322i
$596$	−0.458048	+	14.4594i	−0.0187624	+	0.592279i
$597$	−22.9037	+	16.5907i	−0.937386	+	0.679014i
$598$	−10.7511	+	5.98221i	−0.439645	+	0.244631i
$599$	−1.41231	−	0.815399i	−0.0577056	−	0.0333163i	0.470870	−	0.882203i	$-0.343940\pi$
$599$	−1.41231	−	0.815399i	−0.0577056	−	0.0333163i	−0.528575	+	0.848886i	$0.677274\pi$
$600$	0.396739	+	7.10331i	0.0161968	+	0.289991i
$601$	−30.9682	−	17.8795i	−1.26322	−	0.729319i	−0.289522	−	0.957171i	$-0.593496\pi$
$601$	−30.9682	−	17.8795i	−1.26322	−	0.729319i	−0.973696	+	0.227853i	$0.926830\pi$
$602$	−9.68518	+	22.4785i	−0.394739	+	0.916155i
$603$	−3.35706	+	10.2328i	−0.136710	+	0.416710i
$604$	0.626861	−	19.7884i	0.0255066	−	0.805177i
$605$	22.8887			0.930559
$606$	−1.97881	−	22.5669i	−0.0803835	−	0.916719i
$607$	7.07331			0.287097			0.143548	−	0.989643i	$-0.454149\pi$
$607$	7.07331			0.287097			0.143548	+	0.989643i	$0.454149\pi$
$608$	−24.0321	−	16.5391i	−0.974631	−	0.670749i
$609$	0.183232	−	0.619224i	0.00742495	−	0.0250922i
$610$	3.86835	+	6.95212i	0.156625	+	0.281483i
$611$	−20.5116	+	35.5271i	−0.829810	+	1.43727i
$612$	−2.82424	+	2.37170i	−0.114163	+	0.0958705i
$613$	26.3960	−	15.2397i	1.06613	−	0.615528i	0.139005	−	0.990292i	$-0.455610\pi$
$613$	26.3960	−	15.2397i	1.06613	−	0.615528i	0.927120	+	0.374764i	$0.122276\pi$
$614$	−0.538136	+	33.9836i	−0.0217174	+	1.37147i
$615$	−10.0291	−	13.8452i	−0.404411	−	0.558293i
$616$	10.5160	−	0.897119i	0.423702	−	0.0361459i
$617$	3.38333	+	5.86010i	0.136208	+	0.235919i	0.926058	−	0.377381i	$-0.123175\pi$
$617$	3.38333	+	5.86010i	0.136208	+	0.235919i	−0.789850	+	0.613300i	$0.789842\pi$
$618$	2.31248	+	26.3722i	0.0930216	+	1.06085i
$619$		−	6.84296i		−	0.275042i	−0.990499	−	0.137521i	$-0.956087\pi$
$619$		−	6.84296i		−	0.275042i	0.990499	−	0.137521i	$-0.0439134\pi$
$620$	−24.5805	+	39.6221i	−0.987178	+	1.59126i
$621$	8.60182	−	2.75435i	0.345179	−	0.110528i
$622$	−11.2301	+	18.7587i	−0.450285	+	0.752156i
$623$	−44.1950	−	18.2179i	−1.77063	−	0.729885i
$624$	29.3134	−	18.5237i	1.17348	−	0.741543i
$625$	−30.1522			−1.20609
$626$	24.3215	−	13.5332i	0.972084	−	0.540895i
$627$	5.14046	−	11.5016i	0.205290	−	0.459329i
$628$	4.87228	−	7.85377i	0.194425	−	0.313400i
$629$	2.19754			0.0876216
$630$	27.0350	−	9.06017i	1.07710	−	0.360966i
$631$			28.6466i			1.14040i	0.821505	+	0.570202i	$0.193135\pi$
$631$			28.6466i			1.14040i	−0.821505	+	0.570202i	$0.806865\pi$
$632$	29.0602	−	14.9852i	1.15595	−	0.596079i
$633$	30.7768	−	22.2938i	1.22327	−	0.886099i
$634$	−14.6001	+	8.12389i	−0.579843	+	0.322641i
$635$		−	42.5667i		−	1.68921i
$636$	19.1234	+	28.2409i	0.758291	+	1.11982i
$637$	24.8579	+	24.6889i	0.984906	+	0.978209i
$638$	0.241156	+	0.144370i	0.00954746	+	0.00571567i
$639$	−3.66813	−	17.5021i	−0.145109	−	0.692371i
$640$	28.5619	+	3.17873i	1.12901	+	0.125651i
$641$	17.1170			0.676081			0.338041	−	0.941132i	$-0.390236\pi$
$641$	17.1170			0.676081			0.338041	+	0.941132i	$0.390236\pi$
$642$	4.70168	+	2.19131i	0.185560	+	0.0864840i
$643$	13.5864	−	7.84409i	0.535794	−	0.309341i	−0.207579	−	0.978218i	$-0.566558\pi$
$643$	13.5864	−	7.84409i	0.535794	−	0.309341i	0.743373	+	0.668878i	$0.233225\pi$
$644$	0.926827	+	9.15096i	0.0365221	+	0.360598i
$645$	−26.2754	−	11.7434i	−1.03459	−	0.462397i
$646$	−4.48240	−	0.0709796i	−0.176358	−	0.00279265i
$647$	4.09924	+	7.10010i	0.161158	+	0.279134i	0.935284	−	0.353898i	$-0.115144\pi$
$647$	4.09924	+	7.10010i	0.161158	+	0.279134i	−0.774126	+	0.633031i	$0.781811\pi$
$648$	−23.7727	+	9.10270i	−0.933880	+	0.357588i
$649$	18.3552	+	10.5974i	0.720506	+	0.415984i
$650$	−4.99792	−	8.98215i	−0.196034	−	0.352309i
$651$	40.3310	+	11.9342i	1.58070	+	0.467739i
$652$	5.35630	−	8.63398i	0.209769	−	0.338133i
$653$		−	11.7560i		−	0.460050i	−0.973185	−	0.230025i	$-0.926119\pi$
$653$		−	11.7560i		−	0.460050i	0.973185	−	0.230025i	$-0.0738807\pi$
$654$	3.17595	+	4.53383i	0.124189	+	0.177287i
$655$			3.72319i			0.145477i
$656$	−13.9256	+	6.90401i	−0.543705	+	0.269556i
$657$	34.3028	−	30.7100i	1.33828	−	1.19811i
$658$	18.3240	+	24.5920i	0.714344	+	0.958698i
$659$	−6.63452	+	11.4913i	−0.258444	+	0.447638i	−0.965825	−	0.259194i	$-0.916543\pi$
$659$	−6.63452	+	11.4913i	−0.258444	+	0.447638i	0.707381	+	0.706832i	$0.249876\pi$
$660$	0.888160	+	12.3783i	0.0345716	+	0.481825i
$661$	−24.9568	+	43.2265i	−0.970708	+	1.68131i	−0.277279	+	0.960789i	$0.589433\pi$
$661$	−24.9568	+	43.2265i	−0.970708	+	1.68131i	−0.693429	+	0.720525i	$0.743901\pi$
$662$	23.2845	+	41.8464i	0.904979	+	1.62641i
$663$	2.17422	−	4.86473i	0.0844398	−	0.188931i
$664$	−26.9998	−	17.3480i	−1.04780	−	0.673232i
$665$	32.0432	+	13.2087i	1.24258	+	0.512213i
$666$	14.3357	+	4.95588i	0.555498	+	0.192036i
$667$	−0.122473	+	0.212129i	−0.00474216	+	0.00821365i
$668$	−10.0270	−	18.7116i	−0.387957	−	0.723974i
$669$	−10.7092	−	4.78631i	−0.414041	−	0.185049i
$670$	6.62377	−	11.0643i	0.255898	−	0.427453i
$671$	1.56178	+	2.70508i	0.0602919	+	0.104429i
$672$	−4.04636	−	25.6052i	−0.156092	−	0.987743i
$673$	22.3150	−	38.6507i	0.860180	−	1.48988i	−0.0115741	−	0.999933i	$-0.503684\pi$
$673$	22.3150	−	38.6507i	0.860180	−	1.48988i	0.871754	−	0.489943i	$-0.162982\pi$
$674$	0.852808	+	1.53265i	0.0328489	+	0.0590354i
$675$	2.30116	+	7.18651i	0.0885715	+	0.276609i
$676$	−12.7049	+	20.4794i	−0.488651	+	0.787671i
$677$	2.99508	+	5.18763i	0.115110	+	0.199377i	0.917824	−	0.396988i	$-0.129945\pi$
$677$	2.99508	+	5.18763i	0.115110	+	0.199377i	−0.802714	+	0.596365i	$0.796611\pi$
$678$	23.6894	−	16.5944i	0.909787	−	0.637305i
$679$	8.80935	+	3.63136i	0.338072	+	0.139359i
$680$	3.92498	−	2.02396i	0.150516	−	0.0776153i
$681$	27.0674	−	2.80595i	1.03723	−	0.107524i
$682$	−9.40306	+	15.7069i	−0.360062	+	0.601448i
$683$	−17.8106	−	30.8489i	−0.681504	−	1.18040i	−0.974522	−	0.224292i	$-0.927993\pi$
$683$	−17.8106	−	30.8489i	−0.681504	−	1.18040i	0.293018	−	0.956107i	$-0.405340\pi$
$684$	−29.0811	−	10.5717i	−1.11194	−	0.404220i
$685$	29.0570			1.11021
$686$	24.3039	−	9.76320i	0.927928	−	0.372761i
$687$	−0.572915	−	5.52659i	−0.0218581	−	0.210852i
$688$	−14.4911	+	21.7871i	−0.552469	+	0.830625i
$689$	−42.6758	−	24.6389i	−1.62582	−	0.938666i
$690$	−10.7738	+	0.944717i	−0.410153	+	0.0359648i
$691$	−11.8528	+	6.84322i	−0.450902	+	0.260328i	−0.708211	−	0.706001i	$-0.750497\pi$
$691$	−11.8528	+	6.84322i	−0.450902	+	0.260328i	0.257309	+	0.966329i	$0.417164\pi$
$692$	−2.24885	−	4.19662i	−0.0854883	−	0.159531i
$693$	10.5566	−	3.72473i	0.401011	−	0.141491i
$694$	−4.90856	+	8.19926i	−0.186326	+	0.311240i
$695$	29.0127	−	16.7505i	1.10051	−	0.635381i
$696$	0.311298	−	0.616181i	0.0117997	−	0.0233563i
$697$	−1.19423	+	2.06847i	−0.0452347	+	0.0783487i
$698$	−6.99796	+	11.6894i	−0.264877	+	0.442450i
$699$	−33.6569	−	15.0425i	−1.27302	−	0.568959i
$700$	−7.64530	+	0.774330i	−0.288965	+	0.0292669i
$701$			44.5521i			1.68271i	0.540483	+	0.841355i	$0.318242\pi$
$701$			44.5521i			1.68271i	−0.540483	+	0.841355i	$0.681758\pi$
$702$	25.1545	−	26.8320i	0.949397	−	1.01271i
$703$	9.21889	+	15.9676i	0.347697	+	0.602229i
$704$	11.2320	+	1.07030i	0.423323	+	0.0403384i
$705$	−29.2042	+	21.1546i	−1.09989	+	0.796730i
$706$	0.231165	−	14.5982i	0.00870002	−	0.549411i
$707$	24.2538	−	3.23517i	0.912157	−	0.121671i
$708$	22.7358	−	46.8309i	0.854464	−	1.76001i
$709$	−44.8614	+	25.9007i	−1.68480	+	0.972722i	−0.726415	+	0.687256i	$0.758815\pi$
$709$	−44.8614	+	25.9007i	−1.68480	+	0.972722i	−0.958389	+	0.285466i	$0.907852\pi$
$710$	−0.339031	+	21.4100i	−0.0127236	+	0.803504i
$711$	25.8380	−	23.1318i	0.969000	−	0.867509i
$712$	−42.9934	−	27.6242i	−1.61125	−	1.03526i
$713$	−13.8163	−	7.97683i	−0.517424	−	0.298735i
$714$	−2.69679	−	2.93181i	−0.100925	−	0.109720i
$715$	−8.96521	−	15.5282i	−0.335280	−	0.580722i
$716$	7.06808	+	13.1899i	0.264146	+	0.492929i
$717$	−12.8734	−	17.7718i	−0.480765	−	0.663701i
$718$	−29.7449	−	17.8071i	−1.11007	−	0.664554i
$719$	21.3012	−	36.8947i	0.794399	−	1.37594i	−0.128821	−	0.991668i	$-0.541119\pi$
$719$	21.3012	−	36.8947i	0.794399	−	1.37594i	0.923220	−	0.384272i	$-0.125547\pi$
$720$	30.1692	−	4.35177i	1.12434	−	0.162181i
$721$	−28.3435	+	3.78069i	−1.05557	+	0.140800i
$722$	−5.22347	−	9.38751i	−0.194397	−	0.349367i
$723$	10.0817	−	1.04512i	0.374943	−	0.0388686i
$724$	0.720638	+	0.0228286i	0.0267823	+	0.000848417i
$725$	−0.177226	−	0.102321i	−0.00658200	−	0.00380012i
$726$	−1.92801	−	21.9877i	−0.0715553	−	0.816039i
$727$	−10.0198	+	17.3548i	−0.371613	+	0.643653i	−0.989814	−	0.142368i	$-0.954528\pi$
$727$	−10.0198	+	17.3548i	−0.371613	+	0.643653i	0.618201	+	0.786020i	$0.287862\pi$
$728$	21.4164	+	30.7270i	0.793744	+	1.13882i
$729$	−21.9782	+	15.6831i	−0.814008	+	0.580854i
$730$	−48.1751	+	26.8060i	−1.78304	+	0.992134i
$731$			4.02086i			0.148717i
$732$	6.35259	−	4.30168i	0.234799	−	0.158995i
$733$	25.6889			0.948840			0.474420	−	0.880299i	$-0.342658\pi$
$733$	25.6889			0.948840			0.474420	+	0.880299i	$0.342658\pi$
$734$	−30.3901	−	0.481233i	−1.12172	−	0.0177626i
$735$	11.0939	+	28.7298i	0.409205	+	1.05971i
$736$	−0.777645	+	9.80204i	−0.0286644	+	0.361308i
$737$	2.53145	−	4.38460i	0.0932473	−	0.161509i
$738$	−12.4554	+	10.8005i	−0.458490	+	0.397572i
$739$	−14.1006	−	24.4230i	−0.518700	−	0.898414i	−0.999764	−	0.0217289i	$-0.993083\pi$
$739$	−14.1006	−	24.4230i	−0.518700	−	0.898414i	0.481064	−	0.876685i	$-0.340250\pi$
$740$	−15.4340	−	9.57485i	−0.567364	−	0.351979i
$741$	44.4688	−	4.60987i	1.63360	−	0.169348i
$742$	−29.5404	+	22.0111i	−1.08446	+	0.808054i
$743$	1.54957	−	0.894647i	0.0568484	−	0.0328214i	−0.471306	−	0.881970i	$-0.656217\pi$
$743$	1.54957	−	0.894647i	0.0568484	−	0.0328214i	0.528155	+	0.849148i	$0.322884\pi$
$744$	40.1328	+	20.2754i	1.47134	+	0.743331i
$745$		−	18.3735i		−	0.673153i
$746$	0.0275582	−	1.74031i	0.00100898	−	0.0637174i
$747$	−32.3434	−	10.6109i	−1.18338	−	0.388233i
$748$	1.52821	−	0.818926i	0.0558770	−	0.0299429i
$749$	−2.13529	+	5.18003i	−0.0780220	+	0.189274i
$750$	1.92821	+	21.9899i	0.0704084	+	0.802959i
$751$			13.9014i			0.507271i	0.967300	+	0.253635i	$0.0816263\pi$
$751$			13.9014i			0.507271i	−0.967300	+	0.253635i	$0.918374\pi$
$752$	14.5629	+	29.3739i	0.531054	+	1.07115i
$753$	−27.2987	+	2.82993i	−0.994820	+	0.103128i
$754$	−0.0157926	+	0.997310i	−0.000575132	+	0.0363199i
$755$			25.1450i			0.915121i
$756$	−10.9808	−	25.2076i	−0.399367	−	0.916791i
$757$		−	15.5570i		−	0.565427i	−0.959204	−	0.282714i	$-0.908765\pi$
$757$		−	15.5570i		−	0.565427i	0.959204	−	0.282714i	$-0.0912346\pi$
$758$	−39.8232	−	0.630606i	−1.44644	−	0.0229047i
$759$	−4.22352	+	0.437832i	−0.153304	+	0.0158923i
$760$	31.1720	+	20.0287i	1.13073	+	0.726518i
$761$		−	14.8193i		−	0.537201i	−0.963252	−	0.268600i	$-0.913439\pi$
$761$		−	14.8193i		−	0.537201i	0.963252	−	0.268600i	$-0.0865611\pi$
$762$	−40.8910	+	3.58558i	−1.48132	+	0.129892i
$763$	−4.73730	+	3.64791i	−0.171502	+	0.132063i
$764$	−0.257748	+	0.138120i	−0.00932500	+	0.00499700i
$765$	3.48978	−	3.12427i	0.126173	−	0.112958i
$766$	8.60357	+	0.136239i	0.310859	+	0.00492251i
$767$			75.2148i			2.71585i
$768$	0.647713	−	27.7052i	0.0233723	−	0.999727i
$769$	33.3827	−	19.2735i	1.20381	−	0.695021i	0.242411	−	0.970174i	$-0.422062\pi$
$769$	33.3827	−	19.2735i	1.20381	−	0.695021i	0.961401	+	0.275152i	$0.0887283\pi$
$770$	−13.3132	+	1.56171i	−0.479774	+	0.0562800i
$771$	34.9056	−	3.61850i	1.25709	−	0.130317i
$772$	−0.0517479	+	0.0834139i	−0.00186245	+	0.00300213i
$773$	−17.2528	−	29.8828i	−0.620541	−	1.07481i	−0.989385	−	0.145318i	$-0.953580\pi$
$773$	−17.2528	−	29.8828i	−0.620541	−	1.07481i	0.368844	−	0.929491i	$-0.379754\pi$
$774$	−9.06784	+	26.2303i	−0.325937	+	0.942828i
$775$	6.66435	−	11.5430i	0.239391	−	0.414637i
$776$	8.56984	+	5.50631i	0.307639	+	0.197665i
$777$	−4.64873	+	15.7101i	−0.166772	+	0.563598i
$778$	−0.129202	+	8.15916i	−0.00463211	+	0.292520i
$779$	−20.0396			−0.717995
$780$	−36.4663	+	24.6933i	−1.30570	+	0.884160i
$781$			8.40685i			0.300821i
$782$	0.734676	+	1.32034i	0.0262719	+	0.0472154i
$783$	0.155296	−	0.715571i	0.00554983	−	0.0255724i
$784$	27.4314	−	5.61420i	0.979692	−	0.200507i
$785$	−5.86917	+	10.1657i	−0.209480	+	0.362829i
$786$	3.57662	−	0.313621i	0.127574	−	0.0111865i
$787$	−27.3529	−	15.7922i	−0.975024	−	0.562930i	−0.0742600	−	0.997239i	$-0.523659\pi$
$787$	−27.3529	−	15.7922i	−0.975024	−	0.562930i	−0.900764	+	0.434308i	$0.856993\pi$
$788$	−0.706556	+	22.3041i	−0.0251700	+	0.794551i
$789$	−38.2124	+	3.96129i	−1.36040	+	0.141026i
$790$	−36.2871	+	20.1912i	−1.29104	+	0.718369i
$791$	19.0605	+	24.7526i	0.677713	+	0.880100i
$792$	11.8162	−	1.89587i	0.419871	−	0.0673670i
$793$	−5.54235	+	9.59963i	−0.196815	+	0.340893i
$794$	16.3084	−	27.2415i	0.578763	−	0.966766i
$795$	−25.4113	−	35.0806i	−0.901247	−	1.24418i
$796$	−15.4246	−	28.7841i	−0.546710	−	1.02023i
$797$	−13.3860	−	23.1853i	−0.474157	−	0.821265i	0.525405	−	0.850852i	$-0.323914\pi$
$797$	−13.3860	−	23.1853i	−0.474157	−	0.821265i	−0.999562	+	0.0295878i	$0.990581\pi$
$798$	9.98963	−	31.8944i	0.353629	−	1.12905i
$799$	4.36309	+	2.51903i	0.154355	+	0.0891169i
$800$	−8.18925	−	0.649694i	−0.289534	−	0.0229702i
$801$	−51.5023	−	16.8964i	−1.81974	−	0.597003i
$802$	12.4333	+	0.196884i	0.439036	+	0.00695221i
$803$	−18.7450	+	10.8225i	−0.661498	+	0.381916i
$804$	−11.1867	−	5.43102i	−0.394526	−	0.191537i
$805$	−1.54453	−	11.5792i	−0.0544374	−	0.408113i
$806$	−64.9564	−	1.02860i	−2.28799	−	0.0362307i
$807$	25.0486	−	18.1445i	0.881753	−	0.638715i
$808$	26.1285	+	1.24208i	0.919198	+	0.0436962i
$809$	−17.0375	−	29.5098i	−0.599005	−	1.03751i	−0.992968	−	0.118381i	$-0.962229\pi$
$809$	−17.0375	−	29.5098i	−0.599005	−	1.03751i	0.393963	−	0.919126i	$-0.371104\pi$
$810$	29.8116	−	12.5112i	1.04747	−	0.439597i
$811$		−	4.85432i		−	0.170458i	−0.996361	−	0.0852291i	$-0.972838\pi$
$811$		−	4.85432i		−	0.170458i	0.996361	−	0.0852291i	$-0.0271622\pi$
$812$	0.680047	+	0.305863i	0.0238650	+	0.0107337i
$813$	−23.9851	−	10.7198i	−0.841195	−	0.375960i
$814$	−6.11830	−	3.66277i	−0.214446	−	0.128380i
$815$	−6.45222	+	11.1756i	−0.226011	+	0.391463i
$816$	−2.27490	−	3.59999i	−0.0796375	−	0.126025i
$817$	−29.2161	+	16.8679i	−1.02214	+	0.590134i
$818$	−14.8241	−	8.87460i	−0.518314	−	0.310293i
$819$	30.1785	+	25.8345i	1.05452	+	0.902729i
$820$	17.3999	−	9.32412i	0.607632	−	0.325612i
$821$	31.0954	−	17.9529i	1.08524	−	0.626562i	0.152933	−	0.988237i	$-0.451128\pi$
$821$	31.0954	−	17.9529i	1.08524	−	0.626562i	0.932304	+	0.361675i	$0.117795\pi$
$822$	−2.44760	−	27.9131i	−0.0853697	−	0.973583i
$823$	30.4518	+	17.5814i	1.06148	+	0.612848i	0.925842	−	0.377910i	$-0.123357\pi$
$823$	30.4518	+	17.5814i	1.06148	+	0.612848i	0.135642	+	0.990758i	$0.456690\pi$
$824$	−30.5344	−	1.45152i	−1.06372	−	0.0505662i
$825$	−0.365793	−	3.52860i	−0.0127353	−	0.122850i
$826$	51.6399	+	22.2498i	1.79678	+	0.774169i
$827$	9.34617			0.324998			0.162499	−	0.986709i	$-0.448045\pi$
$827$	9.34617			0.324998			0.162499	+	0.986709i	$0.448045\pi$
$828$	1.81506	+	10.2701i	0.0630775	+	0.356912i
$829$	−22.9500	−	39.7505i	−0.797085	−	1.38059i	−0.921507	−	0.388362i	$-0.873041\pi$
$829$	−22.9500	−	39.7505i	−0.797085	−	1.38059i	0.124422	−	0.992229i	$-0.460292\pi$
$830$	34.9718	+	20.9362i	1.21389	+	0.726706i
$831$	−26.4904	+	2.74614i	−0.918943	+	0.0952624i
$832$	16.6404	+	36.4185i	0.576903	+	1.26258i
$833$	3.03204	−	3.05280i	0.105054	−	0.105773i
$834$	−18.5349	−	26.4596i	−0.641812	−	0.916220i
$835$	13.4810	+	23.3497i	0.466529	+	0.808051i
$836$	12.3614	+	7.66872i	0.427529	+	0.265228i
$837$	46.6063	+	10.1147i	1.61095	+	0.349614i
$838$	29.2199	−	16.2588i	1.00939	−	0.561650i
$839$	16.6752	−	28.8823i	0.575692	−	0.997128i	−0.420274	−	0.907397i	$-0.638066\pi$
$839$	16.6752	−	28.8823i	0.575692	−	0.997128i	0.995966	−	0.0897308i	$-0.0286007\pi$
$840$	6.16621	+	32.3412i	0.212754	+	1.11588i
$841$	−14.4901	−	25.0975i	−0.499658	−	0.865432i
$842$	−4.63750	−	2.77628i	−0.159819	−	0.0956768i
$843$	11.0759	+	4.95023i	0.381476	+	0.170495i
$844$	20.7268	+	38.6786i	0.713445	+	1.33137i
$845$	15.3044	−	26.5080i	0.526487	−	0.911903i
$846$	22.7819	+	26.2726i	0.783257	+	0.903271i
$847$	23.6312	−	3.15213i	0.811979	−	0.108308i
$848$	−35.2844	+	17.4932i	−1.21167	+	0.600718i
$849$	−11.0290	+	24.6771i	−0.378516	+	0.846914i
$850$	−1.10310	+	0.613795i	−0.0378360	+	0.0210530i
$851$	3.10721	−	5.38185i	0.106514	−	0.184488i
$852$	20.5958	−	1.47777i	0.705599	−	0.0506277i
$853$	−13.2523	+	22.9536i	−0.453749	+	0.785916i	−0.998615	−	0.0526066i	$-0.983247\pi$
$853$	−13.2523	+	22.9536i	−0.453749	+	0.785916i	0.544866	+	0.838523i	$0.316580\pi$
$854$	4.95126	+	6.64491i	0.169428	+	0.227384i
$855$	37.3413	+	12.2506i	1.27705	+	0.418961i
$856$	−3.23779	+	5.03920i	−0.110666	+	0.172236i
$857$			35.6784i			1.21875i	0.792881	+	0.609376i	$0.208580\pi$
$857$			35.6784i			1.21875i	−0.792881	+	0.609376i	$0.791420\pi$
$858$	−14.1617	+	9.92029i	−0.483474	+	0.338673i
$859$			50.2378i			1.71409i	0.515239	+	0.857047i	$0.327703\pi$
$859$			50.2378i			1.71409i	−0.515239	+	0.857047i	$0.672297\pi$
$860$	17.5192	−	28.2398i	0.597401	−	0.962968i
$861$	−12.2611	−	12.9132i	−0.417857	−	0.440081i
$862$	34.9997	−	19.4748i	1.19209	−	0.663314i
$863$	−32.8472	−	18.9643i	−1.11813	−	0.645554i	−0.177208	−	0.984173i	$-0.556707\pi$
$863$	−32.8472	−	18.9643i	−1.11813	−	0.645554i	−0.940923	+	0.338620i	$0.890040\pi$
$864$	−6.72174	−	28.6150i	−0.228678	−	0.973502i
$865$	3.02350	+	5.23685i	0.102802	+	0.178058i
$866$	−0.0187413	+	1.18352i	−0.000636855	+	0.0402178i
$867$	26.2847	+	11.7476i	0.892675	+	0.398968i
$868$	−19.9214	+	44.2925i	−0.676176	+	1.50339i
$869$	−14.1194	+	8.15183i	−0.478967	+	0.276532i
$870$	−0.370391	+	0.794713i	−0.0125574	+	0.0269433i
$871$	17.9669			0.608786
$872$	−5.68106	+	2.92950i	−0.192385	+	0.0992052i
$873$	10.2659	+	3.36794i	0.347448	+	0.113987i
$874$	−6.51174	+	10.8772i	−0.220263	+	0.367927i
$875$	−23.6337	+	3.15245i	−0.798963	+	0.106572i
$876$	29.8087	+	44.0207i	1.00714	+	1.48732i
$877$			7.74844i			0.261646i	0.991406	+	0.130823i	$0.0417620\pi$
$877$			7.74844i			0.261646i	−0.991406	+	0.130823i	$0.958238\pi$
$878$	−16.7622	−	30.1246i	−0.565695	−	1.01666i
$879$	46.3863	−	33.6008i	1.56457	−	1.13333i
$880$	−14.3012	−	0.906988i	−0.482095	−	0.0305746i
$881$			3.97978i			0.134082i	0.997750	+	0.0670411i	$0.0213559\pi$
$881$			3.97978i			0.134082i	−0.997750	+	0.0670411i	$0.978644\pi$
$882$	26.6643	−	13.0772i	0.897835	−	0.440333i
$883$	34.0519			1.14594			0.572970	−	0.819577i	$-0.305791\pi$
$883$	34.0519			1.14594			0.572970	+	0.819577i	$0.305791\pi$
$884$	5.22842	+	3.24358i	0.175851	+	0.109093i
$885$	−26.9782	+	60.3626i	−0.906861	+	2.02907i
$886$	−2.63402	−	4.73380i	−0.0884916	−	0.159035i
$887$	2.29476			0.0770504			0.0385252	−	0.999258i	$-0.487734\pi$
$887$	2.29476			0.0770504			0.0385252	+	0.999258i	$0.487734\pi$
$888$	−7.89786	+	15.6329i	−0.265035	+	0.524607i
$889$	−5.86208	−	43.9476i	−0.196608	−	1.47395i
$890$	55.6877	+	33.3379i	1.86666	+	1.11749i
$891$	11.6251	−	5.09671i	0.389455	−	0.170746i
$892$	7.14038	−	11.5098i	0.239078	−	0.385376i
$893$			42.2703i			1.41452i
$894$	−17.6502	+	1.54768i	−0.590311	+	0.0517621i
$895$	−9.50279	−	16.4593i	−0.317643	−	0.550174i
$896$	29.9262	−	0.651551i	0.999763	−	0.0217668i
$897$	−8.83967	−	12.2033i	−0.295148	−	0.407455i
$898$	40.0601	+	0.634358i	1.33682	+	0.0211688i
$899$	−1.12009	+	0.646683i	−0.0373570	+	0.0215681i
$900$	−8.58033	+	1.51641i	−0.286011	+	0.0505471i
$901$	−3.02590	+	5.24102i	−0.100807	+	0.174604i
$902$	6.77257	−	3.76845i	0.225502	−	0.125476i
$903$	−28.7451	−	8.50585i	−0.956576	−	0.283057i
$904$	15.3067	+	29.6837i	0.509094	+	0.987266i
$905$	−0.915713			−0.0304393
$906$	24.1552	−	2.11807i	0.802501	−	0.0703683i
$907$	59.8569			1.98752			0.993759	−	0.111551i	$-0.0355819\pi$
$907$	59.8569			1.98752			0.993759	+	0.111551i	$0.0355819\pi$
$908$	−0.994905	+	31.4065i	−0.0330171	+	1.04226i
$909$	27.1548	−	5.69118i	0.900668	−	0.188765i
$910$	−28.4221	−	38.1443i	−0.942183	−	1.26447i
$911$	−22.0979	−	12.7582i	−0.732137	−	0.422699i	0.0870666	−	0.996202i	$-0.472251\pi$
$911$	−22.0979	−	12.7582i	−0.732137	−	0.422699i	−0.819203	+	0.573503i	$0.805584\pi$
$912$	16.6145	−	31.6320i	0.550161	−	1.04744i
$913$	13.8587	+	8.00134i	0.458657	+	0.264806i
$914$	−19.4627	−	34.9779i	−0.643769	−	1.15697i
$915$	−7.89115	+	5.71611i	−0.260873	+	0.188969i
$916$	6.41254	+	0.203138i	0.211876	+	0.00671187i
$917$	0.512741	+	3.84397i	0.0169322	+	0.126939i
$918$	−3.29524	−	3.08923i	−0.108759	−	0.101960i
$919$	7.85360	+	4.53428i	0.259066	+	0.149572i	0.623909	−	0.781497i	$-0.285544\pi$
$919$	7.85360	+	4.53428i	0.259066	+	0.149572i	−0.364842	+	0.931069i	$0.618877\pi$
$920$	0.592990	−	12.4742i	0.0195503	−	0.411263i
$921$	−41.4046	+	4.29222i	−1.36433	+	0.141433i
$922$	15.8198	−	26.4255i	0.520998	−	0.870276i
$923$	−25.8368	+	14.9169i	−0.850427	+	0.490994i
$924$	2.62165	+	12.6575i	0.0862461	+	0.416403i
$925$	4.49634	+	2.59596i	0.147839	+	0.0853548i
$926$	12.0727	−	6.71758i	0.396733	−	0.220753i
$927$	−31.7337	+	6.65084i	−1.04227	+	0.218442i
$928$	0.656667	+	0.451924i	0.0215562	+	0.0148351i
$929$	7.56286	−	4.36642i	0.248129	−	0.143258i	−0.370778	−	0.928722i	$-0.620909\pi$
$929$	7.56286	−	4.36642i	0.248129	−	0.143258i	0.618907	+	0.785464i	$0.287576\pi$
$930$	−51.7609	−	24.1242i	−1.69731	−	0.791063i
$931$	34.9018	+	9.22440i	1.14386	+	0.302318i
$932$	22.4409	−	36.1731i	0.735076	−	1.18489i
$933$	−24.4465	−	10.9260i	−0.800341	−	0.357701i
$934$	16.2094	+	9.70387i	0.530386	+	0.317520i
$935$	−1.90702	+	1.10102i	−0.0623662	+	0.0360072i
$936$	26.7929	+	32.9507i	0.875753	+	1.07703i
$937$			23.0937i			0.754438i	0.926124	+	0.377219i	$0.123120\pi$
$937$			23.0937i			0.754438i	−0.926124	+	0.377219i	$0.876880\pi$
$938$	5.31491	−	12.3355i	0.173538	−	0.402767i
$939$	19.9974	+	27.6067i	0.652592	+	0.900910i
$940$	−19.6677	−	36.7023i	−0.641489	−	1.19710i
$941$	11.9012	−	20.6135i	0.387967	−	0.671979i	−0.604209	−	0.796826i	$-0.706511\pi$
$941$	11.9012	−	20.6135i	0.387967	−	0.671979i	0.992176	+	0.124847i	$0.0398440\pi$
$942$	10.2599	+	4.78182i	0.334286	+	0.155800i
$943$	3.37717	+	5.84943i	0.109976	+	0.190484i
$944$	50.0515	+	33.2905i	1.62904	+	1.08351i
$945$	14.9529	+	31.5575i	0.486419	+	1.02657i
$946$	6.70183	−	11.1947i	0.217895	−	0.363972i
$947$	−8.88842	−	15.3952i	−0.288835	−	0.500277i	0.684697	−	0.728828i	$-0.259935\pi$
$947$	−8.88842	−	15.3952i	−0.288835	−	0.500277i	−0.973532	+	0.228551i	$0.926601\pi$
$948$	22.4529	+	33.1578i	0.729237	+	1.07692i
$949$	−66.5212	−	38.4060i	−2.15937	−	1.24671i
$950$	−9.08752	−	5.44032i	−0.294838	−	0.176507i
$951$	−12.0044	−	16.5721i	−0.389268	−	0.537388i
$952$	3.77358	−	2.63015i	0.122302	−	0.0852435i
$953$	−35.9175			−1.16348			−0.581742	−	0.813374i	$-0.697629\pi$
$953$	−35.9175			−1.16348			−0.581742	+	0.813374i	$0.697629\pi$
$954$	−31.5591	+	27.3660i	−1.02176	+	0.886006i
$955$	0.321637	−	0.185697i	0.0104079	−	0.00600903i
$956$	22.3347	−	11.9685i	0.722355	−	0.387089i
$957$	−0.140461	+	0.314276i	−0.00454046	+	0.0101591i
$958$	−6.93243	−	0.109776i	−0.223977	−	0.00354671i
$959$	29.9996	−	4.00159i	0.968738	−	0.129218i
$960$	0.291893	+	35.1957i	0.00942082	+	1.13594i
$961$	−26.6195	−	46.1063i	−0.858693	−	1.48730i
$962$	0.400669	−	25.3025i	0.0129181	−	0.815784i
$963$	−1.98040	+	6.03651i	−0.0638174	+	0.194524i
$964$	−0.370569	+	11.6979i	−0.0119352	+	0.376763i
$965$	0.0623357	−	0.107969i	0.00200666	−	0.00347563i
$966$	−10.9933	+	2.45909i	−0.353702	+	0.0791199i
$967$	−40.2132	+	23.2171i	−1.29317	+	0.746613i	−0.979215	−	0.202825i	$-0.934988\pi$
$967$	−40.2132	+	23.2171i	−1.29317	+	0.746613i	−0.313956	+	0.949438i	$0.601654\pi$
$968$	25.4579	+	1.21020i	0.818246	+	0.0388972i
$969$	−0.566139	−	5.46122i	−0.0181870	−	0.175440i
$970$	−11.1002	−	6.64522i	−0.356405	−	0.213365i
$971$	0.534455	+	0.308568i	0.0171515	+	0.00990240i	0.508551	−	0.861032i	$-0.330181\pi$
$971$	0.534455	+	0.308568i	0.0171515	+	0.00990240i	−0.491400	+	0.870934i	$0.663515\pi$
$972$	−14.5298	−	27.5841i	−0.466044	−	0.884762i
$973$	27.6470	−	21.2893i	0.886323	−	0.682505i
$974$	−4.71839	+	2.62545i	−0.151187	+	0.0841247i
$975$	10.1954	−	7.38522i	0.326513	−	0.236516i
$976$	3.93497	+	7.93699i	0.125955	+	0.254057i
$977$	13.1089	−	22.7053i	0.419392	−	0.726408i	−0.576487	−	0.817107i	$-0.695577\pi$
$977$	13.1089	−	22.7053i	0.419392	−	0.726408i	0.995878	+	0.0906988i	$0.0289101\pi$
$978$	11.2791	+	5.25685i	0.360667	+	0.168096i
$979$	22.0681	+	12.7410i	0.705298	+	0.407204i
$980$	−34.5963	+	8.22990i	−1.10514	+	0.262894i
$981$	−5.05114	+	4.52210i	−0.161271	+	0.144379i
$982$	15.7990	+	28.3937i	0.504167	+	0.906079i
$983$	12.1980			0.389054			0.194527	−	0.980897i	$-0.437683\pi$
$983$	12.1980			0.389054			0.194527	+	0.980897i	$0.437683\pi$
$984$	−10.4227	−	15.9295i	−0.332265	−	0.507815i
$985$		−	28.3418i		−	0.903044i
$986$	0.122480	+	0.00193949i	0.00390055	+	6.17659e-5i
$987$	−27.2383	+	25.8628i	−0.867004	+	0.823221i
$988$	−1.63452	+	51.5975i	−0.0520010	+	1.64153i
$989$	9.84725	+	5.68531i	0.313124	+	0.180782i
$990$	−14.9235	+	2.88184i	−0.474301	+	0.0915907i
$991$	−1.86047	+	1.07414i	−0.0590997	+	0.0341212i	−0.529259	−	0.848460i	$-0.677530\pi$
$991$	−1.86047	+	1.07414i	−0.0590997	+	0.0341212i	0.470159	+	0.882582i	$0.344197\pi$
$992$	−29.4345	+	42.7698i	−0.934547	+	1.35794i
$993$	−47.4987	+	34.4066i	−1.50733	+	1.09186i
$994$	2.59846	+	22.1513i	0.0824181	+	0.702596i
$995$	20.7378	+	35.9190i	0.657433	+	1.13871i
$996$	17.1662	−	35.3587i	0.543932	−	1.12038i
$997$	−23.3822			−0.740522			−0.370261	−	0.928928i	$-0.620732\pi$
$997$	−23.3822			−0.740522			−0.370261	+	0.928928i	$0.620732\pi$
$998$	35.4590	+	0.561499i	1.12243	+	0.0177739i
$999$	−3.93997	+	18.1545i	−0.124655	+	0.574384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cz.b.187.1	yes	180
7.3	odd	6		504.2.bf.b.115.61	✓	180
8.3	odd	2	inner	504.2.cz.b.187.59	yes	180
9.4	even	3		504.2.bf.b.355.61	yes	180
56.3	even	6		504.2.bf.b.115.62	yes	180
63.31	odd	6	inner	504.2.cz.b.283.59	yes	180
72.67	odd	6		504.2.bf.b.355.62	yes	180
504.283	even	6	inner	504.2.cz.b.283.1	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.61	✓	180	7.3	odd	6
504.2.bf.b.115.62	yes	180	56.3	even	6
504.2.bf.b.355.61	yes	180	9.4	even	3
504.2.bf.b.355.62	yes	180	72.67	odd	6
504.2.cz.b.187.1	yes	180	1.1	even	1	trivial
504.2.cz.b.187.59	yes	180	8.3	odd	2	inner
504.2.cz.b.283.1	yes	180	504.283	even	6	inner
504.2.cz.b.283.59	yes	180	63.31	odd	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41404 - 0.0223915i) q^{2} +(-0.178596 - 1.72282i) q^{3} +(1.99900 + 0.0633248i) q^{4} -2.54012 q^{5} +(0.213965 + 2.44013i) q^{6} +(-2.62252 + 0.349814i) q^{7} +(-2.82524 - 0.134304i) q^{8} +(-2.93621 + 0.615378i) q^{9} +O(q^{10})\)	\(q+(-1.41404 - 0.0223915i) q^{2} +(-0.178596 - 1.72282i) q^{3} +(1.99900 + 0.0633248i) q^{4} -2.54012 q^{5} +(0.213965 + 2.44013i) q^{6} +(-2.62252 + 0.349814i) q^{7} +(-2.82524 - 0.134304i) q^{8} +(-2.93621 + 0.615378i) q^{9} +(3.59182 + 0.0568771i) q^{10} +1.41036 q^{11} +(-0.247917 - 3.45522i) q^{12} +(2.50251 + 4.33447i) q^{13} +(3.71618 - 0.435927i) q^{14} +(0.453657 + 4.37617i) q^{15} +(3.99198 + 0.253172i) q^{16} +(0.532316 - 0.307333i) q^{17} +(4.16568 - 0.804421i) q^{18} +(4.46624 + 2.57858i) q^{19} +(-5.07770 - 0.160853i) q^{20} +(1.07104 + 4.45566i) q^{21} +(-1.99431 - 0.0315802i) q^{22} -1.73822i q^{23} +(0.273196 + 4.89136i) q^{24} +1.45222 q^{25} +(-3.44158 - 6.18513i) q^{26} +(1.58458 + 4.94865i) q^{27} +(-5.26457 + 0.533206i) q^{28} +(-0.122038 - 0.0704587i) q^{29} +(-0.543498 - 6.19822i) q^{30} +(4.58909 - 7.94854i) q^{31} +(-5.63914 - 0.447381i) q^{32} +(-0.251886 - 2.42980i) q^{33} +(-0.759596 + 0.422661i) q^{34} +(6.66153 - 0.888569i) q^{35} +(-5.90844 + 1.04421i) q^{36} +(3.09619 + 1.78759i) q^{37} +(-6.25768 - 3.74622i) q^{38} +(7.02056 - 5.08548i) q^{39} +(7.17644 + 0.341149i) q^{40} +(-3.36519 + 1.94289i) q^{41} +(-1.41472 - 6.32444i) q^{42} +(-3.27077 + 5.66515i) q^{43} +(2.81931 + 0.0893110i) q^{44} +(7.45832 - 1.56314i) q^{45} +(-0.0389213 + 2.45790i) q^{46} +(4.09821 + 7.09831i) q^{47} +(-0.276784 - 6.92267i) q^{48} +(6.75526 - 1.83479i) q^{49} +(-2.05349 - 0.0325173i) q^{50} +(-0.624549 - 0.862196i) q^{51} +(4.72802 + 8.82306i) q^{52} +(-8.52661 + 4.92284i) q^{53} +(-2.12985 - 7.03305i) q^{54} -3.58249 q^{55} +(7.45623 - 0.636091i) q^{56} +(3.64478 - 8.15504i) q^{57} +(0.170989 + 0.102364i) q^{58} +(13.0145 + 7.51395i) q^{59} +(0.629738 + 8.77668i) q^{60} +(1.10736 + 1.91800i) q^{61} +(-6.66712 + 11.1368i) q^{62} +(7.48500 - 2.64097i) q^{63} +(7.96392 + 0.758882i) q^{64} +(-6.35667 - 11.0101i) q^{65} +(0.301769 + 3.44147i) q^{66} +(1.79489 - 3.10885i) q^{67} +(1.08356 - 0.580649i) q^{68} +(-2.99463 + 0.310439i) q^{69} +(-9.43954 + 1.10731i) q^{70} +5.96077i q^{71} +(8.37813 - 1.34425i) q^{72} +(-13.2909 + 7.67352i) q^{73} +(-4.33810 - 2.59704i) q^{74} +(-0.259361 - 2.50191i) q^{75} +(8.76471 + 5.43741i) q^{76} +(-3.69871 + 0.493364i) q^{77} +(-10.0412 + 7.03386i) q^{78} +(-10.0112 + 5.77995i) q^{79} +(-10.1401 - 0.643088i) q^{80} +(8.24262 - 3.61376i) q^{81} +(4.80200 - 2.67197i) q^{82} +(9.82635 + 5.67325i) q^{83} +(1.85885 + 8.97467i) q^{84} +(-1.35215 + 0.780663i) q^{85} +(4.75184 - 7.93748i) q^{86} +(-0.0995920 + 0.222833i) q^{87} +(-3.98461 - 0.189418i) q^{88} +(15.6471 + 9.03384i) q^{89} +(-10.5813 + 2.04333i) q^{90} +(-8.07913 - 10.4918i) q^{91} +(0.110072 - 3.47469i) q^{92} +(-14.5135 - 6.48659i) q^{93} +(-5.63608 - 10.1290i) q^{94} +(-11.3448 - 6.54992i) q^{95} +(0.236373 + 9.79511i) q^{96} +(-3.11892 - 1.80071i) q^{97} +(-9.59327 + 2.44320i) q^{98} +(-4.14112 + 0.867907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

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