LMFDB - Embedded newform 252.2.bj.b.115.31

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,2,Mod(103,252)] 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("252.103"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.31
Character	$\chi$	$=$	252.115
Dual form			252.2.bj.b.103.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.937998 - 1.05838i) q^{2} +(1.65520 - 0.510207i) q^{3} +(-0.240318 - 1.98551i) q^{4} +(-3.41753 - 1.97311i) q^{5} +(1.01258 - 2.23040i) q^{6} +(0.174185 + 2.64001i) q^{7} +(-2.32683 - 1.60806i) q^{8} +(2.47938 - 1.68899i) q^{9} +(-5.29393 + 1.76626i) q^{10} +(4.23698 - 2.44622i) q^{11} +(-1.41080 - 3.16380i) q^{12} +(-1.13829 + 0.657191i) q^{13} +(2.95751 + 2.29197i) q^{14} +(-6.66340 - 1.52225i) q^{15} +(-3.88449 + 0.954307i) q^{16} +(1.67931 + 0.969547i) q^{17} +(0.538066 - 4.20838i) q^{18} +(1.49477 + 2.58902i) q^{19} +(-3.09634 + 7.25972i) q^{20} +(1.63526 + 4.28088i) q^{21} +(1.38526 - 6.77887i) q^{22} +(2.92226 + 1.68717i) q^{23} +(-4.67182 - 1.47449i) q^{24} +(5.28635 + 9.15623i) q^{25} +(-0.372157 + 1.82118i) q^{26} +(3.24213 - 4.06061i) q^{27} +(5.19991 - 0.980288i) q^{28} +(-1.32976 + 2.30322i) q^{29} +(-7.86137 + 5.62451i) q^{30} +0.886605 q^{31} +(-2.63363 + 5.00639i) q^{32} +(5.76497 - 6.21072i) q^{33} +(2.60133 - 0.867902i) q^{34} +(4.61376 - 9.36601i) q^{35} +(-3.94934 - 4.51693i) q^{36} +(0.237205 + 0.410852i) q^{37} +(4.14225 + 0.846467i) q^{38} +(-1.54879 + 1.66854i) q^{39} +(4.77915 + 10.0867i) q^{40} +(-8.79016 + 5.07500i) q^{41} +(6.06465 + 2.28473i) q^{42} +(-2.31047 - 1.33395i) q^{43} +(-5.87522 - 7.82469i) q^{44} +(-11.8059 + 0.880085i) q^{45} +(4.52673 - 1.51029i) q^{46} +2.46166 q^{47} +(-5.94272 + 3.56147i) q^{48} +(-6.93932 + 0.919699i) q^{49} +(14.6493 + 2.99358i) q^{50} +(3.27426 + 0.748002i) q^{51} +(1.57841 + 2.10215i) q^{52} +(6.34427 - 10.9886i) q^{53} +(-1.25654 - 7.24024i) q^{54} -19.3067 q^{55} +(3.83999 - 6.42296i) q^{56} +(3.79508 + 3.52270i) q^{57} +(1.19035 + 3.56781i) q^{58} -6.99484 q^{59} +(-1.42110 + 13.5961i) q^{60} -2.37140i q^{61} +(0.831634 - 0.938361i) q^{62} +(4.89082 + 6.25139i) q^{63} +(2.82830 + 7.48336i) q^{64} +5.18685 q^{65} +(-1.16574 - 11.9271i) q^{66} -1.39480i q^{67} +(1.52148 - 3.56728i) q^{68} +(5.69773 + 1.30164i) q^{69} +(-5.58506 - 13.6684i) q^{70} +2.15535i q^{71} +(-8.48509 - 0.0569854i) q^{72} +(3.96915 + 2.29159i) q^{73} +(0.657333 + 0.134326i) q^{74} +(13.4215 + 12.4583i) q^{75} +(4.78130 - 3.59007i) q^{76} +(7.19607 + 10.7596i) q^{77} +(0.313184 + 3.20430i) q^{78} +10.0544i q^{79} +(15.1583 + 4.40317i) q^{80} +(3.29463 - 8.37529i) q^{81} +(-2.87390 + 14.0636i) q^{82} +(1.29635 - 2.24535i) q^{83} +(8.10674 - 4.27560i) q^{84} +(-3.82605 - 6.62692i) q^{85} +(-3.57904 + 1.19410i) q^{86} +(-1.02591 + 4.49075i) q^{87} +(-13.7924 - 1.12136i) q^{88} +(-11.6706 + 6.73801i) q^{89} +(-10.1425 + 13.3206i) q^{90} +(-1.93326 - 2.89062i) q^{91} +(2.64761 - 6.20762i) q^{92} +(1.46751 - 0.452352i) q^{93} +(2.30903 - 2.60536i) q^{94} -11.7974i q^{95} +(-1.80489 + 9.63028i) q^{96} +(-1.88401 - 1.08773i) q^{97} +(-5.53568 + 8.20708i) q^{98} +(6.37343 - 13.2213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26}+ \cdots + 21 q^{98}+O(q^{100}) $ 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.937998	−	1.05838i	0.663265	−	0.748385i
$2$	0.937998	−	1.05838i	0.663265	−	0.748385i
$3$	1.65520	−	0.510207i	0.955630	−	0.294568i
$3$	1.65520	−	0.510207i	0.955630	−	0.294568i
$4$	−0.240318	−	1.98551i	−0.120159	−	0.992755i
$5$	−3.41753	−	1.97311i	−1.52837	−	0.882403i	−0.999431	−	0.0337413i	$-0.989258\pi$
$5$	−3.41753	−	1.97311i	−1.52837	−	0.882403i	−0.528936	−	0.848662i	$-0.677409\pi$
$6$	1.01258	−	2.23040i	0.413386	−	0.910556i
$7$	0.174185	+	2.64001i	0.0658356	+	0.997830i
$7$	0.174185	+	2.64001i	0.0658356	+	0.997830i
$8$	−2.32683	−	1.60806i	−0.822660	−	0.568534i
$9$	2.47938	−	1.68899i	0.826459	−	0.562997i
$10$	−5.29393	+	1.76626i	−1.67409	+	0.558539i
$11$	4.23698	−	2.44622i	1.27750	−	0.737563i	0.301109	−	0.953590i	$-0.402643\pi$
$11$	4.23698	−	2.44622i	1.27750	−	0.737563i	0.976388	+	0.216026i	$0.0693097\pi$
$12$	−1.41080	−	3.16380i	−0.407262	−	0.913312i
$13$	−1.13829	+	0.657191i	−0.315704	+	0.182272i	−0.649476	−	0.760382i	$-0.725012\pi$
$13$	−1.13829	+	0.657191i	−0.315704	+	0.182272i	0.333772	+	0.942654i	$0.391678\pi$
$14$	2.95751	+	2.29197i	0.790427	+	0.612556i
$15$	−6.66340	−	1.52225i	−1.72048	−	0.393043i
$16$	−3.88449	+	0.954307i	−0.971124	+	0.238577i
$17$	1.67931	+	0.969547i	0.407291	+	0.235150i	0.689625	−	0.724166i	$-0.257775\pi$
$17$	1.67931	+	0.969547i	0.407291	+	0.235150i	−0.282334	+	0.959316i	$0.591109\pi$
$18$	0.538066	−	4.20838i	0.126823	−	0.991925i
$19$	1.49477	+	2.58902i	0.342924	+	0.593962i	0.984974	−	0.172701i	$-0.0552493\pi$
$19$	1.49477	+	2.58902i	0.342924	+	0.593962i	−0.642050	+	0.766662i	$0.721916\pi$
$20$	−3.09634	+	7.25972i	−0.692363	+	1.62332i
$21$	1.63526	+	4.28088i	0.356844	+	0.934164i
$22$	1.38526	−	6.77887i	0.295338	−	1.44526i
$23$	2.92226	+	1.68717i	0.609333	+	0.351798i	0.772704	−	0.634766i	$-0.218904\pi$
$23$	2.92226	+	1.68717i	0.609333	+	0.351798i	−0.163372	+	0.986565i	$0.552237\pi$
$24$	−4.67182	−	1.47449i	−0.953631	−	0.300979i
$25$	5.28635	+	9.15623i	1.05727	+	1.83125i
$26$	−0.372157	+	1.82118i	−0.0729861	+	0.357163i
$27$	3.24213	−	4.06061i	0.623949	−	0.781465i
$28$	5.19991	−	0.980288i	0.982690	−	0.185257i
$29$	−1.32976	+	2.30322i	−0.246931	+	0.427697i	−0.962673	−	0.270668i	$-0.912755\pi$
$29$	−1.32976	+	2.30322i	−0.246931	+	0.427697i	0.715742	+	0.698365i	$0.246089\pi$
$30$	−7.86137	+	5.62451i	−1.43528	+	1.02689i
$31$	0.886605			0.159239			0.0796195	−	0.996825i	$-0.474629\pi$
$31$	0.886605			0.159239			0.0796195	+	0.996825i	$0.474629\pi$
$32$	−2.63363	+	5.00639i	−0.465565	+	0.885014i
$33$	5.76497	−	6.21072i	1.00355	−	1.08115i
$34$	2.60133	−	0.867902i	0.446125	−	0.148844i
$35$	4.61376	−	9.36601i	0.779868	−	1.58314i
$36$	−3.94934	−	4.51693i	−0.658224	−	0.752822i
$37$	0.237205	+	0.410852i	0.0389963	+	0.0675436i	0.884865	−	0.465848i	$-0.154251\pi$
$37$	0.237205	+	0.410852i	0.0389963	+	0.0675436i	−0.845869	+	0.533391i	$0.820917\pi$
$38$	4.14225	+	0.846467i	0.671961	+	0.137315i
$39$	−1.54879	+	1.66854i	−0.248005	+	0.267181i
$40$	4.77915	+	10.0867i	0.755649	+	1.59485i
$41$	−8.79016	+	5.07500i	−1.37279	+	0.792582i	−0.991279	−	0.131781i	$-0.957930\pi$
$41$	−8.79016	+	5.07500i	−1.37279	+	0.792582i	−0.381514	+	0.924363i	$0.624597\pi$
$42$	6.06465	+	2.28473i	0.935796	+	0.352542i
$43$	−2.31047	−	1.33395i	−0.352344	−	0.203426i	0.313373	−	0.949630i	$-0.398541\pi$
$43$	−2.31047	−	1.33395i	−0.352344	−	0.203426i	−0.665717	+	0.746204i	$0.731874\pi$
$44$	−5.87522	−	7.82469i	−0.885722	−	1.17962i
$45$	−11.8059	+	0.880085i	−1.75992	+	0.131195i
$46$	4.52673	−	1.51029i	0.667430	−	0.222680i
$47$	2.46166			0.359070			0.179535	−	0.983752i	$-0.442541\pi$
$47$	2.46166			0.359070			0.179535	+	0.983752i	$0.442541\pi$
$48$	−5.94272	+	3.56147i	−0.857758	+	0.514053i
$49$	−6.93932	+	0.919699i	−0.991331	+	0.131386i
$50$	14.6493	+	2.99358i	2.07173	+	0.423356i
$51$	3.27426	+	0.748002i	0.458488	+	0.104741i
$52$	1.57841	+	2.10215i	0.218886	+	0.291515i
$53$	6.34427	−	10.9886i	0.871453	−	1.50940i	0.0109585	−	0.999940i	$-0.496512\pi$
$53$	6.34427	−	10.9886i	0.871453	−	1.50940i	0.860494	−	0.509460i	$-0.170155\pi$
$54$	−1.25654	−	7.24024i	−0.170993	−	0.985272i
$55$	−19.3067			−2.60331
$56$	3.83999	−	6.42296i	0.513141	−	0.858305i
$57$	3.79508	+	3.52270i	0.502671	+	0.466594i
$58$	1.19035	+	3.56781i	0.156301	+	0.468476i
$59$	−6.99484			−0.910650			−0.455325	−	0.890325i	$-0.650477\pi$
$59$	−6.99484			−0.910650			−0.455325	+	0.890325i	$0.650477\pi$
$60$	−1.42110	+	13.5961i	−0.183464	+	1.75524i
$61$		−	2.37140i		−	0.303626i	−0.988409	−	0.151813i	$-0.951489\pi$
$61$		−	2.37140i		−	0.303626i	0.988409	−	0.151813i	$-0.0485112\pi$
$62$	0.831634	−	0.938361i	0.105618	−	0.119172i
$63$	4.89082	+	6.25139i	0.616186	+	0.787601i
$64$	2.82830	+	7.48336i	0.353538	+	0.935420i
$65$	5.18685			0.643349
$66$	−1.16574	−	11.9271i	−0.143493	−	1.46813i
$67$		−	1.39480i		−	0.170402i	−0.996364	−	0.0852008i	$-0.972847\pi$
$67$		−	1.39480i		−	0.170402i	0.996364	−	0.0852008i	$-0.0271532\pi$
$68$	1.52148	−	3.56728i	0.184506	−	0.432596i
$69$	5.69773	+	1.30164i	0.685925	+	0.156699i
$70$	−5.58506	−	13.6684i	−0.667542	−	1.63369i
$71$			2.15535i			0.255793i	0.991788	+	0.127896i	$0.0408225\pi$
$71$			2.15535i			0.255793i	−0.991788	+	0.127896i	$0.959177\pi$
$72$	−8.48509	−	0.0569854i	−0.999977	−	0.00671579i
$73$	3.96915	+	2.29159i	0.464554	+	0.268210i	0.713957	−	0.700189i	$-0.246901\pi$
$73$	3.96915	+	2.29159i	0.464554	+	0.268210i	−0.249403	+	0.968400i	$0.580234\pi$
$74$	0.657333	+	0.134326i	0.0764135	+	0.0156151i
$75$	13.4215	+	12.4583i	1.54979	+	1.43856i
$76$	4.78130	−	3.59007i	0.548453	−	0.411809i
$77$	7.19607	+	10.7596i	0.820068	+	1.22617i
$78$	0.313184	+	3.20430i	0.0354611	+	0.362815i
$79$			10.0544i			1.13121i	0.824675	+	0.565607i	$0.191358\pi$
$79$			10.0544i			1.13121i	−0.824675	+	0.565607i	$0.808642\pi$
$80$	15.1583	+	4.40317i	1.69475	+	0.492289i
$81$	3.29463	−	8.37529i	0.366070	−	0.930587i
$82$	−2.87390	+	14.0636i	−0.317369	+	1.55307i
$83$	1.29635	−	2.24535i	0.142293	−	0.246459i	−0.786067	−	0.618142i	$-0.787886\pi$
$83$	1.29635	−	2.24535i	0.142293	−	0.246459i	0.928360	+	0.371683i	$0.121219\pi$
$84$	8.10674	−	4.27560i	0.884518	−	0.466506i
$85$	−3.82605	−	6.62692i	−0.414994	−	0.718790i
$86$	−3.57904	+	1.19410i	−0.385938	+	0.128763i
$87$	−1.02591	+	4.49075i	−0.109989	+	0.481459i
$88$	−13.7924	−	1.12136i	−1.47028	−	0.119537i
$89$	−11.6706	+	6.73801i	−1.23708	+	0.714227i	−0.968496	−	0.249029i	$-0.919888\pi$
$89$	−11.6706	+	6.73801i	−1.23708	+	0.714227i	−0.268582	+	0.963257i	$0.586555\pi$
$90$	−10.1425	+	13.3206i	−1.06911	+	1.40412i
$91$	−1.93326	−	2.89062i	−0.202661	−	0.303019i
$92$	2.64761	−	6.20762i	0.276033	−	0.647190i
$93$	1.46751	−	0.452352i	0.152174	−	0.0469067i
$94$	2.30903	−	2.60536i	0.238158	−	0.268722i
$95$		−	11.7974i		−	1.21039i
$96$	−1.80489	+	9.63028i	−0.184211	+	0.982887i
$97$	−1.88401	−	1.08773i	−0.191292	−	0.110442i	0.401295	−	0.915949i	$-0.368560\pi$
$97$	−1.88401	−	1.08773i	−0.191292	−	0.110442i	−0.592587	+	0.805506i	$0.701893\pi$
$98$	−5.53568	+	8.20708i	−0.559188	+	0.829041i
$99$	6.37343	−	13.2213i	0.640553	−	1.32879i
$100$	16.9094	−	12.6965i	1.69094	−	1.26965i
$101$	−0.618126	+	0.356875i	−0.0615058	+	0.0355104i	−0.530438	−	0.847724i	$-0.677972\pi$
$101$	−0.618126	+	0.356875i	−0.0615058	+	0.0355104i	0.468932	+	0.883234i	$0.344639\pi$
$102$	3.86291	−	2.76377i	0.382486	−	0.273654i
$103$	−0.582342	+	1.00865i	−0.0573798	+	0.0993848i	−0.893288	−	0.449484i	$-0.851608\pi$
$103$	−0.582342	+	1.00865i	−0.0573798	+	0.0993848i	0.835909	+	0.548869i	$0.184941\pi$
$104$	3.70541	+	0.301260i	0.363345	+	0.0295409i
$105$	2.85809	−	17.8566i	0.278921	−	1.74263i
$106$	−5.67915	−	17.0219i	−0.551608	−	1.65331i
$107$	−10.5529	+	6.09270i	−1.02018	+	0.589004i	−0.914157	−	0.405360i	$-0.867146\pi$
$107$	−10.5529	+	6.09270i	−1.02018	+	0.589004i	−0.106027	+	0.994363i	$0.533813\pi$
$108$	−8.84153	−	5.46145i	−0.850776	−	0.525528i
$109$	−4.74875	+	8.22508i	−0.454848	+	0.787820i	−0.998679	−	0.0513747i	$-0.983640\pi$
$109$	−4.74875	+	8.22508i	−0.454848	+	0.787820i	0.543832	+	0.839194i	$0.316973\pi$
$110$	−18.1096	+	20.4337i	−1.72669	+	1.94828i
$111$	0.602242	+	0.559018i	0.0571622	+	0.0530596i
$112$	−3.19600	−	10.0889i	−0.301994	−	0.953310i
$113$	−6.24802	−	10.8219i	−0.587764	−	1.01804i	−0.994525	−	0.104502i	$-0.966675\pi$
$113$	−6.24802	−	10.8219i	−0.587764	−	1.01804i	0.406761	−	0.913535i	$-0.366658\pi$
$114$	7.28812	−	0.712332i	0.682595	−	0.0667160i
$115$	−6.65794	−	11.5319i	−0.620856	−	1.07535i
$116$	4.89263	+	2.08675i	0.454269	+	0.193750i
$117$	−1.71226	+	3.55198i	−0.158298	+	0.328381i
$118$	−6.56115	+	7.40317i	−0.604003	+	0.681517i
$119$	−2.26711	+	4.60227i	−0.207825	+	0.421889i
$120$	13.0567	+	14.2571i	1.19191	+	1.30149i
$121$	6.46799	−	11.2029i	0.587999	−	1.01844i
$122$	−2.50983	−	2.22437i	−0.227229	−	0.201385i
$123$	−11.9602	+	12.8849i	−1.07841	+	1.16180i
$124$	−0.213067	−	1.76036i	−0.0191340	−	0.158085i
$125$		−	21.9911i		−	1.96695i
$126$	11.2039	+	0.687465i	0.998123	+	0.0612443i
$127$		−	6.01418i		−	0.533672i	−0.963742	−	0.266836i	$-0.914022\pi$
$127$		−	6.01418i		−	0.533672i	0.963742	−	0.266836i	$-0.0859782\pi$
$128$	10.5732	+	4.02598i	0.934543	+	0.355850i
$129$	−4.50489	−	1.02914i	−0.396633	−	0.0906106i
$130$	4.86525	−	5.48963i	0.426711	−	0.481473i
$131$	0.999291	−	1.73082i	0.0873085	−	0.151223i	−0.819064	−	0.573702i	$-0.805507\pi$
$131$	0.999291	−	1.73082i	0.0873085	−	0.151223i	0.906373	+	0.422479i	$0.138840\pi$
$132$	−13.7169	−	9.95385i	−1.19390	−	0.866372i
$133$	−6.57467	+	4.39718i	−0.570097	+	0.381284i
$134$	−1.47622	−	1.30832i	−0.127526	−	0.113021i
$135$	−19.0921	+	7.48018i	−1.64319	+	0.643791i
$136$	−2.34837	−	4.95639i	−0.201371	−	0.425007i
$137$	−5.03081	−	8.71362i	−0.429811	−	0.744455i	0.567045	−	0.823687i	$-0.308087\pi$
$137$	−5.03081	−	8.71362i	−0.429811	−	0.744455i	−0.996856	+	0.0792320i	$0.974753\pi$
$138$	6.72208	−	4.80940i	0.572222	−	0.409403i
$139$	8.02010	+	13.8912i	0.680256	+	1.17824i	0.974903	+	0.222631i	$0.0714646\pi$
$139$	8.02010	+	13.8912i	0.680256	+	1.17824i	−0.294647	+	0.955606i	$0.595202\pi$
$140$	−19.7051	−	6.90984i	−1.66538	−	0.583988i
$141$	4.07454	−	1.25596i	0.343138	−	0.105771i
$142$	2.28117	+	2.02171i	0.191431	+	0.169658i
$143$	−3.21527	+	5.56901i	−0.268874	+	0.465704i
$144$	−8.01931	+	8.92696i	−0.668276	+	0.743913i
$145$	9.08903	−	5.24755i	0.754803	−	0.435785i
$146$	6.14842	−	2.05135i	0.508847	−	0.169771i
$147$	−11.0167	+	5.06278i	−0.908644	+	0.417571i
$148$	0.758745	−	0.569708i	0.0623684	−	0.0468297i
$149$	−4.84527	+	8.39226i	−0.396940	+	0.687521i	−0.993347	−	0.115162i	$-0.963261\pi$
$149$	−4.84527	+	8.39226i	−0.396940	+	0.687521i	0.596406	+	0.802683i	$0.296595\pi$
$150$	25.7749	−	2.51921i	2.10451	−	0.205692i
$151$	14.3307	−	8.27382i	1.16621	−	0.673314i	0.213428	−	0.976959i	$-0.431537\pi$
$151$	14.3307	−	8.27382i	1.16621	−	0.673314i	0.952785	+	0.303645i	$0.0982037\pi$
$152$	0.685211	−	8.42789i	0.0555779	−	0.683592i
$153$	5.80119	−	0.432456i	0.468998	−	0.0349620i
$154$	18.1376	+	2.47632i	1.46157	+	0.199548i
$155$	−3.03000	−	1.74937i	−0.243375	−	0.140513i
$156$	3.68511	+	2.67416i	0.295045	+	0.214104i
$157$			13.0987i			1.04539i	0.852519	+	0.522696i	$0.175074\pi$
$157$			13.0987i			1.04539i	−0.852519	+	0.522696i	$0.824926\pi$
$158$	10.6414	+	9.43106i	0.846583	+	0.750295i
$159$	4.89458	−	21.4252i	0.388165	−	1.69913i
$160$	18.8787	−	11.9131i	1.49249	−	0.941809i
$161$	−3.94512	+	8.00867i	−0.310919	+	0.631172i
$162$	−5.77385	−	11.3430i	−0.453636	−	0.891187i
$163$	6.95666	−	4.01643i	0.544888	−	0.314591i	−0.202170	−	0.979350i	$-0.564799\pi$
$163$	6.95666	−	4.01643i	0.544888	−	0.314591i	0.747057	+	0.664759i	$0.231466\pi$
$164$	12.1889	+	16.2333i	0.951793	+	1.26761i
$165$	−31.9564	+	9.85040i	−2.48780	+	0.766853i
$166$	−1.16044	−	3.47816i	−0.0900680	−	0.269957i
$167$	−4.83680	−	8.37758i	−0.374283	−	0.648277i	0.615937	−	0.787796i	$-0.288778\pi$
$167$	−4.83680	−	8.37758i	−0.374283	−	0.648277i	−0.990219	+	0.139519i	$0.955444\pi$
$168$	3.07892	−	12.5905i	0.237543	−	0.971377i
$169$	−5.63620	+	9.76219i	−0.433554	+	0.750937i
$170$	−10.6026	−	2.16664i	−0.813182	−	0.166173i
$171$	8.07893	+	3.89450i	0.617811	+	0.297820i
$172$	−2.09333	+	4.90804i	−0.159615	+	0.374234i
$173$		−	16.3879i		−	1.24595i	−0.782242	−	0.622974i	$-0.785924\pi$
$173$		−	16.3879i		−	1.24595i	0.782242	−	0.622974i	$-0.214076\pi$
$174$	3.79060	+	5.29811i	0.287364	+	0.401649i
$175$	−23.2517	+	15.5509i	−1.75767	+	1.17554i
$176$	−14.1241	+	13.5457i	−1.06464	+	1.02105i
$177$	−11.5779	+	3.56882i	−0.870245	+	0.268249i
$178$	−3.81563	+	18.6721i	−0.285994	+	1.39953i
$179$	16.0572	+	9.27065i	1.20017	+	0.692921i	0.960594	−	0.277955i	$-0.0896567\pi$
$179$	16.0572	+	9.27065i	1.20017	+	0.692921i	0.239581	+	0.970876i	$0.422990\pi$
$180$	4.58459	+	23.2293i	0.341715	+	1.73141i
$181$		−	23.0045i		−	1.70991i	−0.518700	−	0.854956i	$-0.673584\pi$
$181$		−	23.0045i		−	1.70991i	0.518700	−	0.854956i	$-0.326416\pi$
$182$	−4.87276	−	0.665278i	−0.361193	−	0.0493137i
$183$	−1.20990	−	3.92514i	−0.0894386	−	0.290154i
$184$	−4.08654	−	8.62491i	−0.301264	−	0.635837i
$185$		−	1.87213i		−	0.137642i
$186$	0.897762	−	1.97748i	0.0658271	−	0.144996i
$187$	9.48691			0.693751
$188$	−0.591581	−	4.88764i	−0.0431455	−	0.356468i
$189$	11.2848	+	7.85197i	0.820848	+	0.571147i
$190$	−12.4861	−	11.0660i	−0.905836	−	0.802808i
$191$		−	3.94412i		−	0.285386i	−0.989767	−	0.142693i	$-0.954424\pi$
$191$		−	3.94412i		−	0.285386i	0.989767	−	0.142693i	$-0.0455762\pi$
$192$	8.49947	+	10.9434i	0.613396	+	0.789775i
$193$	5.75001			0.413895			0.206947	−	0.978352i	$-0.433647\pi$
$193$	5.75001			0.413895			0.206947	+	0.978352i	$0.433647\pi$
$194$	−2.91842	+	0.973695i	−0.209530	+	0.0699073i
$195$	8.58527	−	2.64637i	0.614804	−	0.189510i
$196$	3.49371	+	13.5571i	0.249551	+	0.968362i
$197$	−16.6012			−1.18279			−0.591393	−	0.806384i	$-0.701422\pi$
$197$	−16.6012			−1.18279			−0.591393	+	0.806384i	$0.701422\pi$
$198$	−8.01486	−	19.1471i	−0.569591	−	1.36072i
$199$	6.23391	−	10.7974i	0.441910	−	0.765411i	−0.555921	−	0.831235i	$-0.687634\pi$
$199$	6.23391	−	10.7974i	0.441910	−	0.765411i	0.997831	+	0.0658244i	$0.0209677\pi$
$200$	2.42329	−	29.8058i	0.171352	−	2.10759i
$201$	−0.711636	−	2.30867i	−0.0501949	−	0.162841i
$202$	−0.202093	+	0.988957i	−0.0142192	+	0.0695828i
$203$	−6.31215	−	3.10941i	−0.443026	−	0.218238i
$204$	0.698302	−	6.68083i	0.0488909	−	0.467751i
$205$	40.0542			2.79751
$206$	0.521290	+	1.56244i	0.0363200	+	0.108861i
$207$	10.0950	−	0.752541i	0.701650	−	0.0523052i
$208$	3.79451	−	3.63913i	0.263102	−	0.252328i
$209$	12.6666	+	7.31308i	0.876169	+	0.505856i
$210$	−16.2181	−	19.7744i	−1.11916	−	1.36456i
$211$	19.4166	−	11.2102i	1.33669	−	0.771739i	0.350376	−	0.936609i	$-0.386054\pi$
$211$	19.4166	−	11.2102i	1.33669	−	0.771739i	0.986315	+	0.164870i	$0.0527205\pi$
$212$	−23.3426	−	9.95585i	−1.60318	−	0.683771i
$213$	1.09967	+	3.56754i	0.0753485	+	0.244444i
$214$	−3.45021	+	16.8838i	−0.235851	+	1.15416i
$215$	5.26408	+	9.11765i	0.359007	+	0.621819i
$216$	−14.0736	+	4.23483i	−0.957587	+	0.288144i
$217$	0.154433	+	2.34065i	0.0104836	+	0.158893i
$218$	4.25090	+	12.7411i	0.287907	+	0.862934i
$219$	7.73893	+	1.76795i	0.522948	+	0.119467i
$220$	4.63974	+	38.3336i	0.312811	+	2.58445i
$221$	−2.54871			−0.171445
$222$	1.15655	−	0.113040i	0.0776227	−	0.00758675i
$223$	4.48502	−	7.76829i	0.300339	−	0.520203i	−0.675873	−	0.737018i	$-0.736233\pi$
$223$	4.48502	−	7.76829i	0.300339	−	0.520203i	0.976213	+	0.216815i	$0.0695668\pi$
$224$	−13.6757	−	6.08079i	−0.913744	−	0.406290i
$225$	28.5716	+	13.7732i	1.90478	+	0.918210i
$226$	−17.3142	−	3.53816i	−1.15173	−	0.235355i
$227$	−3.89688	−	6.74960i	−0.258645	−	0.447987i	0.707234	−	0.706980i	$-0.249943\pi$
$227$	−3.89688	−	6.74960i	−0.258645	−	0.447987i	−0.965879	+	0.258993i	$0.916609\pi$
$228$	6.08233	−	8.38174i	0.402812	−	0.555094i
$229$	−5.88977	−	3.40046i	−0.389207	−	0.224709i	0.292610	−	0.956232i	$-0.405476\pi$
$229$	−5.88977	−	3.40046i	−0.389207	−	0.224709i	−0.681816	+	0.731523i	$0.738810\pi$
$230$	−18.4502	−	3.77029i	−1.21657	−	0.248606i
$231$	17.4005	+	14.1378i	1.14487	+	0.930197i
$232$	6.79785	−	3.22087i	0.446301	−	0.211460i
$233$	8.45700	+	14.6480i	0.554037	+	0.959619i	0.997978	+	0.0635635i	$0.0202466\pi$
$233$	8.45700	+	14.6480i	0.554037	+	0.959619i	−0.443941	+	0.896056i	$0.646420\pi$
$234$	2.15324	+	5.14396i	0.140761	+	0.336271i
$235$	−8.41279	−	4.85713i	−0.548790	−	0.316844i
$236$	1.68099	+	13.8883i	0.109423	+	0.904052i
$237$	5.12985	+	16.6421i	0.333220	+	1.08102i
$238$	2.74438	+	6.71637i	0.177892	+	0.435357i
$239$	−16.8495	+	9.72804i	−1.08990	+	0.629254i	−0.933550	−	0.358447i	$-0.883306\pi$
$239$	−16.8495	+	9.72804i	−1.08990	+	0.629254i	−0.156351	+	0.987702i	$0.549973\pi$
$240$	27.3366	−	0.445762i	1.76457	−	0.0287738i
$241$	−20.4013	+	11.7787i	−1.31417	+	0.758734i	−0.982783	−	0.184763i	$-0.940848\pi$
$241$	−20.4013	+	11.7787i	−1.31417	+	0.758734i	−0.331382	+	0.943497i	$0.607515\pi$
$242$	−5.78990	−	17.3539i	−0.372189	−	1.11555i
$243$	1.18014	−	15.5437i	0.0757058	−	0.997130i
$244$	−4.70843	+	0.569889i	−0.301426	+	0.0364834i
$245$	25.5300	+	10.5490i	1.63105	+	0.673948i
$246$	2.41849	+	24.7444i	0.154197	+	1.57765i
$247$	−3.40296	−	1.96470i	−0.216525	−	0.125011i
$248$	−2.06298	−	1.42571i	−0.130999	−	0.0905328i
$249$	1.00013	−	4.37791i	0.0633807	−	0.277439i
$250$	−23.2749	−	20.6276i	−1.47203	−	1.30461i
$251$	−4.53190			−0.286051			−0.143026	−	0.989719i	$-0.545683\pi$
$251$	−4.53190			−0.286051			−0.143026	+	0.989719i	$0.545683\pi$
$252$	11.2368	−	11.2131i	0.707854	−	0.706359i
$253$	16.5087			1.03789
$254$	−6.36526	−	5.64129i	−0.399392	−	0.353966i
$255$	−9.71399	−	9.01680i	−0.608313	−	0.564654i
$256$	14.1786	−	7.41400i	0.886162	−	0.463375i
$257$	20.6842	+	11.9420i	1.29025	+	0.744924i	0.978698	−	0.205306i	$-0.0658189\pi$
$257$	20.6842	+	11.9420i	1.29025	+	0.744924i	0.311549	+	0.950230i	$0.399152\pi$
$258$	−5.31479	+	3.80253i	−0.330885	+	0.236735i
$259$	−1.04334	+	0.697789i	−0.0648297	+	0.0433585i
$260$	−1.24649	−	10.2985i	−0.0773042	−	0.638688i
$261$	0.593127	+	7.95651i	0.0367136	+	0.492496i
$262$	−0.894528	−	2.68113i	−0.0552641	−	0.165641i
$263$	−23.5572	+	13.6008i	−1.45260	+	0.838660i	−0.998628	−	0.0523561i	$-0.983327\pi$
$263$	−23.5572	+	13.6008i	−1.45260	+	0.838660i	−0.453972	+	0.891016i	$0.649994\pi$
$264$	−23.4013	+	5.18091i	−1.44025	+	0.318863i
$265$	−43.3635	+	25.0359i	−2.66380	+	1.53794i
$266$	−1.51317	+	11.0830i	−0.0927781	+	0.679544i
$267$	−15.8794	+	17.1072i	−0.971801	+	1.04694i
$268$	−2.76938	+	0.335195i	−0.169167	+	0.0204753i
$269$	15.8637	+	9.15891i	0.967227	+	0.558429i	0.898390	−	0.439199i	$-0.144738\pi$
$269$	15.8637	+	9.15891i	0.967227	+	0.558429i	0.0688372	+	0.997628i	$0.478071\pi$
$270$	−9.99155	+	27.2231i	−0.608067	+	1.65674i
$271$	0.772505	+	1.33802i	0.0469264	+	0.0812788i	0.888535	−	0.458810i	$-0.151724\pi$
$271$	0.772505	+	1.33802i	0.0469264	+	0.0812788i	−0.841608	+	0.540089i	$0.818391\pi$
$272$	−7.44850	−	2.16363i	−0.451632	−	0.131189i
$273$	−4.67475	−	3.79819i	−0.282929	−	0.229877i
$274$	−13.9412	−	2.84887i	−0.842217	−	0.172107i
$275$	44.7963	+	25.8632i	2.70132	+	1.55961i
$276$	1.21516	−	11.6257i	0.0731438	−	0.699785i
$277$	−0.243046	−	0.420968i	−0.0146032	−	0.0252935i	0.858631	−	0.512593i	$-0.171315\pi$
$277$	−0.243046	−	0.420968i	−0.0146032	−	0.0252935i	−0.873235	+	0.487300i	$0.837982\pi$
$278$	22.2250	+	4.54166i	1.33296	+	0.272391i
$279$	2.19823	−	1.49747i	0.131604	−	0.0896510i
$280$	−25.7965	+	14.3739i	−1.54164	+	0.859007i
$281$	−13.1672	+	22.8062i	−0.785489	+	1.36051i	0.143218	+	0.989691i	$0.454255\pi$
$281$	−13.1672	+	22.8062i	−0.785489	+	1.36051i	−0.928707	+	0.370815i	$0.879078\pi$
$282$	2.49264	−	5.49048i	0.148434	−	0.326953i
$283$	−17.1770			−1.02107			−0.510533	−	0.859858i	$-0.670552\pi$
$283$	−17.1770			−1.02107			−0.510533	+	0.859858i	$0.670552\pi$
$284$	4.27947	−	0.517969i	0.253940	−	0.0307358i
$285$	−6.01912	−	19.5271i	−0.356542	−	1.15668i
$286$	2.87818	+	8.62668i	0.170191	+	0.510106i
$287$	−14.9292	−	22.3221i	−0.881241	−	1.31763i
$288$	1.92598	+	16.8609i	0.113489	+	0.993539i
$289$	−6.61996	−	11.4661i	−0.389409	−	0.674476i
$290$	2.97161	−	14.5418i	0.174499	−	0.853924i
$291$	−3.67337	−	0.839180i	−0.215337	−	0.0491936i
$292$	3.59612	−	8.43150i	0.210447	−	0.493416i
$293$	21.5170	−	12.4229i	1.25704	−	0.725751i	0.284540	−	0.958664i	$-0.408159\pi$
$293$	21.5170	−	12.4229i	1.25704	−	0.725751i	0.972498	+	0.232913i	$0.0748258\pi$
$294$	−4.97535	+	16.4087i	−0.290169	+	0.956976i
$295$	23.9051	+	13.8016i	1.39181	+	0.803561i
$296$	0.108736	−	1.33742i	0.00632016	−	0.0777361i
$297$	3.80369	−	25.1357i	0.220712	−	1.45852i
$298$	4.33730	+	13.0000i	0.251253	+	0.753072i
$299$	−4.43516			−0.256492
$300$	21.5105	−	29.6425i	1.24191	−	1.71141i
$301$	3.11920	−	6.33203i	0.179788	−	0.364972i
$302$	4.68534	−	22.9281i	0.269611	−	1.31936i
$303$	−0.841042	+	0.906072i	−0.0483166	+	0.0520525i
$304$	−8.27715	−	8.63056i	−0.474727	−	0.494997i
$305$	−4.67903	+	8.10432i	−0.267921	+	0.464052i
$306$	4.98380	−	6.54548i	0.284905	−	0.374180i
$307$	32.0881			1.83136			0.915682	−	0.401904i	$-0.131652\pi$
$307$	32.0881			1.83136			0.915682	+	0.401904i	$0.131652\pi$
$308$	19.6339	−	16.8736i	1.11874	−	0.961461i
$309$	−0.449274	+	1.96662i	−0.0255583	+	0.111877i
$310$	−4.69363	+	1.56597i	−0.266580	+	0.0889412i
$311$	13.0485			0.739915			0.369957	−	0.929049i	$-0.379372\pi$
$311$	13.0485			0.739915			0.369957	+	0.929049i	$0.379372\pi$
$312$	6.28689	−	1.39188i	0.355925	−	0.0787996i
$313$		−	13.3212i		−	0.752960i	−0.926425	−	0.376480i	$-0.877134\pi$
$313$		−	13.3212i		−	0.752960i	0.926425	−	0.376480i	$-0.122866\pi$
$314$	13.8634	+	12.2866i	0.782355	+	0.693371i
$315$	−4.37984	−	31.0145i	−0.246776	−	1.74747i
$316$	19.9632	−	2.41627i	1.12302	−	0.135926i
$317$	−19.6535			−1.10385			−0.551927	−	0.833893i	$-0.686107\pi$
$317$	−19.6535			−1.10385			−0.551927	+	0.833893i	$0.686107\pi$
$318$	−18.0848	−	25.2771i	−1.01415	−	1.41747i
$319$			13.0116i			0.728509i
$320$	5.09971	−	31.1552i	0.285083	−	1.74163i
$321$	−14.3586	+	15.4688i	−0.801417	+	0.863384i
$322$	4.77566	+	11.6875i	0.266137	+	0.651321i
$323$			5.79701i			0.322554i
$324$	−17.4210	−	4.52878i	−0.967832	−	0.251599i
$325$	−12.0348	−	6.94828i	−0.667569	−	0.385421i
$326$	2.27444	−	11.1302i	0.125970	−	0.616443i
$327$	−3.66364	+	16.0370i	−0.202600	+	0.886848i
$328$	28.6141	+	2.32641i	1.57995	+	0.128454i
$329$	0.428783	+	6.49880i	0.0236396	+	0.358291i
$330$	−19.5496	+	43.0616i	−1.07617	+	2.37046i
$331$		−	14.4064i		−	0.791847i	−0.918283	−	0.395924i	$-0.870425\pi$
$331$		−	14.4064i		−	0.791847i	0.918283	−	0.395924i	$-0.129575\pi$
$332$	−4.76969	−	2.03432i	−0.261771	−	0.111648i
$333$	1.28205	+	0.618019i	0.0702557	+	0.0338672i
$334$	−13.4035	−	2.73901i	−0.733409	−	0.149872i
$335$	−2.75209	+	4.76677i	−0.150363	+	0.260436i
$336$	−10.4374	−	15.0685i	−0.569409	−	0.822054i
$337$	−0.489878	−	0.848494i	−0.0266854	−	0.0462204i	0.852374	−	0.522932i	$-0.175162\pi$
$337$	−0.489878	−	0.848494i	−0.0266854	−	0.0462204i	−0.879060	+	0.476712i	$0.841829\pi$
$338$	5.04531	+	15.1221i	0.274429	+	0.822536i
$339$	−15.8631	−	14.7246i	−0.861567	−	0.799731i
$340$	−12.2383	+	9.18923i	−0.663717	+	0.498356i
$341$	3.75652	−	2.16883i	0.203427	−	0.117449i
$342$	11.6999	−	4.89750i	0.632657	−	0.264827i
$343$	−3.63674	−	18.1597i	−0.196365	−	0.980531i
$344$	3.23101	+	6.81926i	0.174204	+	0.367670i
$345$	−16.9039	−	15.6907i	−0.910074	−	0.844757i
$346$	−17.3445	−	15.3718i	−0.932448	−	0.826394i
$347$			27.4334i			1.47270i	0.676600	+	0.736351i	$0.263453\pi$
$347$			27.4334i			1.47270i	−0.676600	+	0.736351i	$0.736547\pi$
$348$	9.16296	+	0.957743i	0.491186	+	0.0513404i
$349$	13.0352	+	7.52589i	0.697760	+	0.402852i	0.806512	−	0.591217i	$-0.201352\pi$
$349$	13.0352	+	7.52589i	0.697760	+	0.402852i	−0.108753	+	0.994069i	$0.534686\pi$
$350$	−5.35140	+	39.1958i	−0.286045	+	2.09510i
$351$	−1.02188	+	6.75285i	−0.0545441	+	0.360440i
$352$	1.08809	+	27.6544i	0.0579955	+	1.47399i
$353$	16.0275	−	9.25348i	0.853058	−	0.492513i	−0.00862373	−	0.999963i	$-0.502745\pi$
$353$	16.0275	−	9.25348i	0.853058	−	0.492513i	0.861681	+	0.507450i	$0.169412\pi$
$354$	−7.08287	+	15.6013i	−0.376450	+	0.829198i
$355$	4.25275	−	7.36598i	0.225712	−	0.390945i
$356$	16.1830	+	21.5528i	0.857699	+	1.14229i
$357$	−1.40441	+	8.77437i	−0.0743292	+	0.464389i
$358$	24.8735	−	8.29874i	1.31461	−	0.438602i
$359$	−5.04854	+	2.91478i	−0.266452	+	0.153836i	−0.627274	−	0.778799i	$-0.715829\pi$
$359$	−5.04854	+	2.91478i	−0.266452	+	0.153836i	0.360822	+	0.932635i	$0.382496\pi$
$360$	28.8856	+	16.9368i	1.52241	+	0.892647i
$361$	5.03132	−	8.71450i	0.264806	−	0.458658i
$362$	−24.3474	−	21.5782i	−1.27967	−	1.13413i
$363$	4.99003	−	21.8430i	0.261909	−	1.14646i
$364$	−5.27475	+	4.53318i	−0.276472	+	0.237603i
$365$	−9.04313	−	15.6632i	−0.473339	−	0.819848i
$366$	−5.28915	−	2.40124i	−0.276469	−	0.125515i
$367$	0.903984	+	1.56575i	0.0471876	+	0.0817313i	0.888654	−	0.458577i	$-0.151641\pi$
$367$	0.903984	+	1.56575i	0.0471876	+	0.0817313i	−0.841467	+	0.540309i	$0.818307\pi$
$368$	−12.9616	−	3.76505i	−0.675668	−	0.196267i
$369$	−13.2225	+	27.4293i	−0.688336	+	1.42791i
$370$	−1.98142	−	1.75606i	−0.103009	−	0.0912930i
$371$	30.1151	+	14.8349i	1.56350	+	0.770190i
$372$	−1.25082	−	2.80504i	−0.0648519	−	0.145435i
$373$	2.97957	−	5.16077i	0.154276	−	0.267214i	−0.778519	−	0.627621i	$-0.784029\pi$
$373$	2.97957	−	5.16077i	0.154276	−	0.267214i	0.932795	+	0.360407i	$0.117362\pi$
$374$	8.89870	−	10.0407i	0.460141	−	0.519193i
$375$	−11.2200	−	36.3997i	−0.579400	−	1.87967i
$376$	−5.72787	−	3.95849i	−0.295392	−	0.204143i
$377$		−	3.49564i		−	0.180034i
$378$	18.8955	−	4.57842i	0.971877	−	0.235488i
$379$			16.5311i			0.849146i	0.905394	+	0.424573i	$0.139576\pi$
$379$			16.5311i			0.849146i	−0.905394	+	0.424573i	$0.860424\pi$
$380$	−23.4239	+	2.83513i	−1.20162	+	0.145439i
$381$	−3.06848	−	9.95467i	−0.157203	−	0.509993i
$382$	−4.17436	−	3.69957i	−0.213579	−	0.189287i
$383$	1.64900	−	2.85616i	0.0842601	−	0.145943i	−0.820816	−	0.571193i	$-0.806481\pi$
$383$	1.64900	−	2.85616i	0.0842601	−	0.145943i	0.905076	+	0.425250i	$0.139814\pi$
$384$	19.5548	+	1.26930i	0.997900	+	0.0647739i
$385$	−3.36293	−	50.9698i	−0.171391	−	2.59766i
$386$	5.39350	−	6.08567i	0.274522	−	0.309753i
$387$	−7.98157	+	0.594994i	−0.405726	+	0.0302453i
$388$	−1.70694	+	4.00211i	−0.0866567	+	0.203176i
$389$	−4.82441	−	8.35612i	−0.244607	−	0.423672i	0.717414	−	0.696647i	$-0.245326\pi$
$389$	−4.82441	−	8.35612i	−0.244607	−	0.423672i	−0.962021	+	0.272975i	$0.911992\pi$
$390$	5.25212	−	11.5687i	0.265952	−	0.585805i
$391$	3.27157	+	5.66653i	0.165451	+	0.286569i
$392$	17.6256	+	9.01884i	0.890225	+	0.455520i
$393$	0.770949	−	3.37470i	0.0388892	−	0.170231i
$394$	−15.5719	+	17.5703i	−0.784500	+	0.885178i
$395$	19.8386	−	34.3614i	0.998186	−	1.72891i
$396$	−27.7827	−	9.47718i	−1.39613	−	0.476246i
$397$	−3.22184	+	1.86013i	−0.161700	+	0.0933573i	−0.578666	−	0.815565i	$-0.696427\pi$
$397$	−3.22184	+	1.86013i	−0.161700	+	0.0933573i	0.416967	+	0.908922i	$0.363093\pi$
$398$	−5.58036	−	16.7258i	−0.279718	−	0.838389i
$399$	−8.63893	+	10.6327i	−0.432488	+	0.532299i
$400$	−29.2727	−	30.5225i	−1.46363	−	1.52613i
$401$	11.9860	−	20.7604i	0.598553	−	1.03672i	−0.394482	−	0.918904i	$-0.629076\pi$
$401$	11.9860	−	20.7604i	0.598553	−	1.03672i	0.993035	−	0.117821i	$-0.0375908\pi$
$402$	−3.11095	−	1.41235i	−0.155160	−	0.0704417i
$403$	−1.00921	+	0.582668i	−0.0502724	+	0.0290248i
$404$	0.857125	+	1.14153i	0.0426436	+	0.0567933i
$405$	−27.7849	+	22.1221i	−1.38064	+	1.09926i
$406$	−9.21171	+	3.76401i	−0.457169	+	0.186805i
$407$	2.01007	+	1.16051i	0.0996353	+	0.0575245i
$408$	−6.41582	−	7.00567i	−0.317630	−	0.346832i
$409$		−	22.1550i		−	1.09549i	−0.836644	−	0.547747i	$-0.815486\pi$
$409$		−	22.1550i		−	1.09549i	0.836644	−	0.547747i	$-0.184514\pi$
$410$	37.5708	−	42.3924i	1.85549	−	2.09361i
$411$	−12.7728	−	11.8560i	−0.630033	−	0.584815i
$412$	2.14262	+	0.913849i	0.105559	+	0.0450221i
$413$	−1.21839	−	18.4665i	−0.0599532	−	0.908675i
$414$	8.67261	−	11.3902i	0.426235	−	0.559796i
$415$	−8.86064	+	5.11570i	−0.434952	+	0.251120i
$416$	−0.292322	−	7.42952i	−0.0143323	−	0.364262i
$417$	20.3623	+	18.9008i	0.997144	+	0.925578i
$418$	19.6213	−	6.54639i	0.959707	−	0.320194i
$419$	−17.6835	−	30.6287i	−0.863895	−	1.49631i	−0.868140	−	0.496319i	$-0.834685\pi$
$419$	−17.6835	−	30.6287i	−0.863895	−	1.49631i	0.00424524	−	0.999991i	$-0.498649\pi$
$420$	−36.1413	−	1.38351i	−1.76351	−	0.0675082i
$421$	−15.4856	+	26.8219i	−0.754723	+	1.30722i	0.190788	+	0.981631i	$0.438896\pi$
$421$	−15.4856	+	26.8219i	−0.754723	+	1.30722i	−0.945512	+	0.325588i	$0.894438\pi$
$422$	6.34815	−	31.0651i	0.309023	−	1.51223i
$423$	6.10338	−	4.15772i	0.296756	−	0.202155i
$424$	−32.4324	+	15.3667i	−1.57505	+	0.746272i
$425$			20.5015i			0.994467i
$426$	4.80729	+	2.18247i	0.232914	+	0.105741i
$427$	6.26051	−	0.413061i	0.302967	−	0.0199894i
$428$	14.6332	+	19.4886i	0.707321	+	0.942019i
$429$	−2.48057	+	10.8583i	−0.119763	+	0.524242i
$430$	14.5876	+	2.98097i	0.703476	+	0.143755i
$431$	4.22345	+	2.43841i	0.203437	+	0.117454i	0.598257	−	0.801304i	$-0.295860\pi$
$431$	4.22345	+	2.43841i	0.203437	+	0.117454i	−0.394821	+	0.918758i	$0.629193\pi$
$432$	−8.71897	+	18.8674i	−0.419492	+	0.907759i
$433$		−	13.0744i		−	0.628314i	−0.949371	−	0.314157i	$-0.898278\pi$
$433$		−	13.0744i		−	0.628314i	0.949371	−	0.314157i	$-0.101722\pi$
$434$	2.62214	+	2.03207i	0.125867	+	0.0975427i
$435$	12.3668	−	13.3230i	0.592944	−	0.638791i
$436$	17.4722	+	7.45206i	0.836766	+	0.356889i
$437$			10.0877i			0.482560i
$438$	9.13026	−	6.53236i	0.436261	−	0.312128i
$439$	1.91733			0.0915094			0.0457547	−	0.998953i	$-0.485431\pi$
$439$	1.91733			0.0915094			0.0457547	+	0.998953i	$0.485431\pi$
$440$	44.9234	+	31.0463i	2.14164	+	1.48007i
$441$	−15.6518	+	14.0007i	−0.745325	+	0.666701i
$442$	−2.39069	+	2.69749i	−0.113713	+	0.128307i
$443$		−	21.2905i		−	1.01154i	−0.862668	−	0.505770i	$-0.831208\pi$
$443$		−	21.2905i		−	1.01154i	0.862668	−	0.505770i	$-0.168792\pi$
$444$	0.965206	−	1.33010i	0.0458066	−	0.0631237i
$445$	53.1794			2.52095
$446$	−4.01482	−	12.0335i	−0.190107	−	0.569802i
$447$	−3.73811	+	16.3630i	−0.176806	+	0.773942i
$448$	−19.2635	+	8.77023i	−0.910116	+	0.414355i
$449$	5.99969			0.283143			0.141572	−	0.989928i	$-0.454784\pi$
$449$	5.99969			0.283143			0.141572	+	0.989928i	$0.454784\pi$
$450$	41.3773	−	17.3203i	1.95055	−	0.816488i
$451$	−24.8291	+	43.0053i	−1.16916	+	2.02504i
$452$	−19.9854	+	15.0062i	−0.940036	+	0.705832i
$453$	19.4988	−	21.0064i	0.916133	−	0.986969i
$454$	−10.7989	−	2.20675i	−0.506817	−	0.103568i
$455$	0.903469	+	13.6933i	0.0423553	+	0.641953i
$456$	−3.16581	−	14.2995i	−0.148253	−	0.669633i
$457$	−25.3351			−1.18513			−0.592563	−	0.805524i	$-0.701884\pi$
$457$	−25.3351			−1.18513			−0.592563	+	0.805524i	$0.701884\pi$
$458$	−9.12356	+	3.04396i	−0.426316	+	0.142235i
$459$	9.38149	−	3.67561i	0.437890	−	0.171563i
$460$	−21.2966	+	15.9907i	−0.992961	+	0.745571i
$461$	−17.3693	−	10.0282i	−0.808970	−	0.467059i	0.0376278	−	0.999292i	$-0.488020\pi$
$461$	−17.3693	−	10.0282i	−0.808970	−	0.467059i	−0.846598	+	0.532233i	$0.821353\pi$
$462$	31.2848	−	5.15510i	1.45550	−	0.239837i
$463$	−33.2880	+	19.2188i	−1.54702	+	0.893175i	−0.548658	+	0.836047i	$0.684861\pi$
$463$	−33.2880	+	19.2188i	−1.54702	+	0.893175i	−0.998367	+	0.0571279i	$0.981806\pi$
$464$	2.96748	−	10.2158i	0.137762	−	0.474259i
$465$	−5.90780	−	1.34963i	−0.273968	−	0.0625877i
$466$	23.4357	+	4.78907i	1.08564	+	0.221850i
$467$	−16.3595	−	28.3355i	−0.757028	−	1.31121i	−0.944360	−	0.328914i	$-0.893317\pi$
$467$	−16.3595	−	28.3355i	−0.757028	−	1.31121i	0.187332	−	0.982297i	$-0.440016\pi$
$468$	7.46398	+	2.54610i	0.345022	+	0.117693i
$469$	3.68228	−	0.242952i	0.170032	−	0.0112185i
$470$	−13.0319	+	4.34792i	−0.601115	+	0.200554i
$471$	6.68306	+	21.6810i	0.307939	+	0.999008i
$472$	16.2758	+	11.2481i	0.749155	+	0.517736i
$473$	−13.0526			−0.600158
$474$	22.4254	+	10.1810i	1.03003	+	0.467628i
$475$	−15.8038	+	27.3729i	−0.725126	+	1.25596i
$476$	9.68267	+	3.39535i	0.443804	+	0.155626i
$477$	−2.82979	−	37.9603i	−0.129567	−	1.73808i
$478$	−5.50884	+	26.9579i	−0.251969	+	1.23303i
$479$	18.3983	+	31.8668i	0.840639	+	1.45603i	0.889355	+	0.457217i	$0.151154\pi$
$479$	18.3983	+	31.8668i	0.840639	+	1.45603i	−0.0487157	+	0.998813i	$0.515513\pi$
$480$	25.1699	−	29.3505i	1.14884	−	1.33966i
$481$	−0.540016	−	0.311778i	−0.0246226	−	0.0142159i
$482$	−6.67011	+	32.6407i	−0.303815	+	1.48674i
$483$	−2.44389	+	15.2688i	−0.111201	+	0.694754i
$484$	−23.7978	−	10.1500i	−1.08172	−	0.461363i
$485$	4.29243	+	7.43471i	0.194909	+	0.337593i
$486$	−15.3441	−	15.8290i	−0.696024	−	0.718019i
$487$	−3.93075	−	2.26942i	−0.178119	−	0.102837i	0.408289	−	0.912853i	$-0.366125\pi$
$487$	−3.93075	−	2.26942i	−0.178119	−	0.102837i	−0.586409	+	0.810015i	$0.699459\pi$
$488$	−3.81334	+	5.51784i	−0.172622	+	0.249781i
$489$	9.46546	−	10.1973i	0.428043	−	0.461139i
$490$	35.1119	−	17.1254i	1.58619	−	0.773648i
$491$	−10.6660	+	6.15804i	−0.481351	+	0.277908i	−0.720980	−	0.692956i	$-0.756308\pi$
$491$	−10.6660	+	6.15804i	−0.481351	+	0.277908i	0.239628	+	0.970865i	$0.422975\pi$
$492$	28.4574	+	20.6506i	1.28296	+	0.930999i
$493$	−4.46616	+	2.57854i	−0.201146	+	0.116132i
$494$	−5.27136	+	1.75872i	−0.237170	+	0.0791288i
$495$	−47.8685	+	32.6088i	−2.15153	+	1.46566i
$496$	−3.44401	+	0.846093i	−0.154641	+	0.0379907i
$497$	−5.69015	+	0.375429i	−0.255238	+	0.0168403i
$498$	−3.69535	−	5.16498i	−0.165593	−	0.231448i
$499$	−11.2164	−	6.47580i	−0.502115	−	0.289896i	0.227471	−	0.973785i	$-0.426954\pi$
$499$	−11.2164	−	6.47580i	−0.502115	−	0.289896i	−0.729587	+	0.683888i	$0.760288\pi$
$500$	−43.6636	+	5.28487i	−1.95270	+	0.236346i
$501$	−12.2802	−	11.3988i	−0.548638	−	0.509261i
$502$	−4.25092	+	4.79645i	−0.189728	+	0.214076i
$503$	20.4872			0.913480			0.456740	−	0.889600i	$-0.349017\pi$
$503$	20.4872			0.913480			0.456740	+	0.889600i	$0.349017\pi$
$504$	−1.32753	−	22.4107i	−0.0591329	−	0.998250i
$505$	2.81662			0.125338
$506$	15.4852	−	17.4724i	0.688399	−	0.776744i
$507$	−4.34831	+	19.0340i	−0.193115	+	0.845330i
$508$	−11.9412	+	1.44532i	−0.529806	+	0.0641255i
$509$	−24.6392	−	14.2255i	−1.09211	−	0.630533i	−0.157976	−	0.987443i	$-0.550497\pi$
$509$	−24.6392	−	14.2255i	−1.09211	−	0.630533i	−0.934139	+	0.356910i	$0.883830\pi$
$510$	−18.6549	+	1.82330i	−0.826051	+	0.0807372i
$511$	−5.35846	+	10.8778i	−0.237044	+	0.481204i
$512$	5.45270	−	21.9606i	0.240977	−	0.970531i
$513$	15.3593	+	2.32426i	0.678128	+	0.102618i
$514$	32.0409	−	10.6901i	1.41327	−	0.471519i
$515$	3.98034	−	2.29805i	0.175395	−	0.101264i
$516$	−0.960759	+	9.19182i	−0.0422951	+	0.404647i
$517$	10.4300	−	6.02176i	0.458710	−	0.264837i
$518$	−0.240124	+	1.75877i	−0.0105505	+	0.0772757i
$519$	−8.36122	−	27.1252i	−0.367017	−	1.19067i
$520$	−12.0689	−	8.34075i	−0.529257	−	0.365766i
$521$	32.0751	+	18.5186i	1.40524	+	0.811314i	0.994924	−	0.100630i	$-0.0320858\pi$
$521$	32.0751	+	18.5186i	1.40524	+	0.811314i	0.410314	+	0.911944i	$0.365419\pi$
$522$	8.97733	+	6.83544i	0.392927	+	0.299179i
$523$	2.33168	+	4.03859i	0.101957	+	0.176595i	0.912491	−	0.409097i	$-0.134156\pi$
$523$	2.33168	+	4.03859i	0.101957	+	0.176595i	−0.810534	+	0.585692i	$0.800823\pi$
$524$	−3.67671	−	1.56815i	−0.160618	−	0.0685051i
$525$	−30.5521	+	37.6031i	−1.33340	+	1.64113i
$526$	−7.70192	+	37.6899i	−0.335820	+	1.64336i
$527$	1.48888	+	0.859605i	0.0648566	+	0.0374450i
$528$	−16.4671	+	29.6271i	−0.716637	+	1.28935i
$529$	−5.80694	−	10.0579i	−0.252476	−	0.437301i
$530$	−14.1775	+	69.3785i	−0.615830	+	3.01361i
$531$	−17.3428	+	11.8142i	−0.752615	+	0.512693i
$532$	10.3107	+	11.9974i	0.447024	+	0.520151i
$533$	6.67049	−	11.5536i	0.288931	−	0.500443i
$534$	3.21099	+	32.8528i	0.138953	+	1.42168i
$535$	48.0864			2.07895
$536$	−2.24292	+	3.24546i	−0.0968792	+	0.140183i
$537$	31.3079	+	7.15227i	1.35104	+	0.308643i
$538$	24.5737	−	8.19871i	1.05945	−	0.353472i
$539$	−27.1520	+	20.8718i	−1.16952	+	0.899014i
$540$	19.4402	+	36.1100i	0.836571	+	1.55393i
$541$	11.6836	+	20.2366i	0.502318	+	0.870040i	0.999996	+	0.00267870i	$0.000852658\pi$
$541$	11.6836	+	20.2366i	0.502318	+	0.870040i	−0.497678	+	0.867362i	$0.665814\pi$
$542$	2.14074	+	0.437458i	0.0919524	+	0.0187904i
$543$	−11.7371	−	38.0771i	−0.503686	−	1.63404i
$544$	−9.27661	+	5.85383i	−0.397731	+	0.250981i
$545$	32.4580	−	18.7396i	1.39035	−	0.802718i
$546$	−8.40482	+	1.38495i	−0.359693	+	0.0592703i
$547$	21.8092	+	12.5915i	0.932493	+	0.538375i	0.887599	−	0.460617i	$-0.152372\pi$
$547$	21.8092	+	12.5915i	0.932493	+	0.538375i	0.0448939	+	0.998992i	$0.485705\pi$
$548$	−16.0920	+	12.0828i	−0.687415	+	0.516150i
$549$	−4.00526	−	5.87959i	−0.170940	−	0.250935i
$550$	69.3918	−	23.1517i	2.95888	−	0.987192i
$551$	−7.95077			−0.338714
$552$	−11.1645	−	12.1910i	−0.475194	−	0.518882i
$553$	−26.5439	+	1.75133i	−1.12876	+	0.0744742i
$554$	−0.673520	−	0.137633i	−0.0286151	−	0.00584749i
$555$	−0.955174	−	3.09875i	−0.0405449	−	0.131535i
$556$	25.6538	−	19.2623i	1.08796	−	0.816903i
$557$	−3.17042	+	5.49134i	−0.134335	+	0.232675i	−0.925343	−	0.379130i	$-0.876223\pi$
$557$	−3.17042	+	5.49134i	−0.134335	+	0.232675i	0.791008	+	0.611806i	$0.209557\pi$
$558$	0.477052	−	3.73117i	0.0201952	−	0.157953i
$559$	3.50664			0.148315
$560$	−8.98407	+	40.7852i	−0.379646	+	1.72349i
$561$	15.7027	−	4.84029i	0.662970	−	0.204357i
$562$	11.7868	+	35.3280i	0.497195	+	1.49022i
$563$	1.28515			0.0541628			0.0270814	−	0.999633i	$-0.491379\pi$
$563$	1.28515			0.0541628			0.0270814	+	0.999633i	$0.491379\pi$
$564$	−3.47290	−	7.78820i	−0.146235	−	0.327943i
$565$			49.3122i			2.07458i
$566$	−16.1120	+	18.1797i	−0.677237	+	0.764149i
$567$	22.6847	+	7.23900i	0.952669	+	0.304010i
$568$	3.46593	−	5.01514i	0.145427	−	0.210430i
$569$	−19.8770			−0.833286			−0.416643	−	0.909070i	$-0.636793\pi$
$569$	−19.8770			−0.833286			−0.416643	+	0.909070i	$0.636793\pi$
$570$	−26.3129	−	11.9459i	−1.10213	−	0.500358i
$571$		−	14.3467i		−	0.600391i	−0.953878	−	0.300196i	$-0.902948\pi$
$571$		−	14.3467i		−	0.600391i	0.953878	−	0.300196i	$-0.0970519\pi$
$572$	11.8300	+	5.04561i	0.494637	+	0.210968i
$573$	−2.01232	−	6.52830i	−0.0840657	−	0.272724i
$574$	−37.6287	−	5.13745i	−1.57059	−	0.214433i
$575$			35.6758i			1.48778i
$576$	19.6517	+	13.7771i	0.818823	+	0.574046i
$577$	10.9881	+	6.34398i	0.457440	+	0.264103i	0.710967	−	0.703225i	$-0.248257\pi$
$577$	10.9881	+	6.34398i	0.457440	+	0.264103i	−0.253527	+	0.967328i	$0.581591\pi$
$578$	−18.3449	−	3.74878i	−0.763049	−	0.155929i
$579$	9.51742	−	2.93370i	0.395531	−	0.121920i
$580$	−12.6033	−	16.7853i	−0.523324	−	0.696970i
$581$	6.15354	+	3.03128i	0.255292	+	0.125759i
$582$	−4.33379	+	3.10066i	−0.179641	+	0.128527i
$583$		−	62.0779i		−	2.57101i
$584$	−5.55054	−	11.7148i	−0.229683	−	0.484761i
$585$	12.8602	−	8.76053i	0.531702	−	0.362203i
$586$	7.03488	−	34.4257i	0.290608	−	1.42211i
$587$	−12.4489	+	21.5622i	−0.513823	+	0.889967i	0.486049	+	0.873932i	$0.338438\pi$
$587$	−12.4489	+	21.5622i	−0.513823	+	0.889967i	−0.999871	+	0.0160352i	$0.994896\pi$
$588$	12.6997	+	20.6571i	0.523727	+	0.851886i
$589$	1.32527	+	2.29544i	0.0546068	+	0.0945818i
$590$	37.0302	−	12.3547i	1.52451	−	0.508634i
$591$	−27.4783	+	8.47004i	−1.13031	+	0.348411i
$592$	−1.31350	−	1.36958i	−0.0539846	−	0.0562896i
$593$	−22.9565	+	13.2540i	−0.942712	+	0.544275i	−0.890809	−	0.454377i	$-0.849862\pi$
$593$	−22.9565	+	13.2540i	−0.942712	+	0.544275i	−0.0519027	+	0.998652i	$0.516529\pi$
$594$	−23.0352	−	27.6030i	−0.945144	−	1.13256i
$595$	16.8287	−	11.2551i	0.689909	−	0.461415i
$596$	17.8273	+	7.60352i	0.730235	+	0.311452i
$597$	4.80943	−	21.0525i	0.196837	−	0.861622i
$598$	−4.16017	+	4.69406i	−0.170122	+	0.191955i
$599$		−	24.6495i		−	1.00715i	−0.863951	−	0.503576i	$-0.832017\pi$
$599$		−	24.6495i		−	1.00715i	0.863951	−	0.503576i	$-0.167983\pi$
$600$	−11.1961	−	50.5709i	−0.457078	−	2.06455i
$601$	0.673377	+	0.388774i	0.0274676	+	0.0158584i	0.513671	−	0.857987i	$-0.328285\pi$
$601$	0.673377	+	0.388774i	0.0274676	+	0.0158584i	−0.486203	+	0.873846i	$0.661619\pi$
$602$	−3.77586	−	9.24072i	−0.153893	−	0.376624i
$603$	−2.35580	−	3.45823i	−0.0959356	−	0.140830i
$604$	−19.8717	−	26.4653i	−0.808566	−	1.07686i
$605$	−44.2091	+	25.5241i	−1.79736	+	1.03770i
$606$	0.170068	+	1.74003i	0.00690856	+	0.0706840i
$607$	21.0843	−	36.5192i	0.855787	−	1.48227i	−0.0201256	−	0.999797i	$-0.506407\pi$
$607$	21.0843	−	36.5192i	0.855787	−	1.48227i	0.875913	−	0.482469i	$-0.160260\pi$
$608$	−16.8983	+	0.664883i	−0.685318	+	0.0269646i
$609$	−12.0343	−	1.92619i	−0.487655	−	0.0780532i
$610$	4.18849	+	12.5540i	0.169587	+	0.508297i
$611$	−2.80208	+	1.61778i	−0.113360	+	0.0654483i
$612$	−2.25278	−	11.4144i	−0.0910630	−	0.461399i
$613$	4.18716	−	7.25237i	0.169118	−	0.292921i	−0.768992	−	0.639258i	$-0.779241\pi$
$613$	4.18716	−	7.25237i	0.169118	−	0.292921i	0.938110	+	0.346338i	$0.112575\pi$
$614$	30.0986	−	33.9612i	1.21468	−	1.37056i
$615$	66.2977	−	20.4359i	2.67338	−	0.824057i
$616$	0.557978	−	36.6074i	0.0224816	−	1.47496i
$617$	−8.84616	−	15.3220i	−0.356133	−	0.616840i	0.631178	−	0.775638i	$-0.282572\pi$
$617$	−8.84616	−	15.3220i	−0.356133	−	0.616840i	−0.987311	+	0.158797i	$0.949238\pi$
$618$	1.66001	+	2.32019i	0.0667754	+	0.0933318i
$619$	−14.1334	−	24.4797i	−0.568068	−	0.983922i	−0.996757	−	0.0804700i	$-0.974358\pi$
$619$	−14.1334	−	24.4797i	−0.568068	−	0.983922i	0.428689	−	0.903452i	$-0.358975\pi$
$620$	−2.74523	+	6.43650i	−0.110251	+	0.258496i
$621$	16.3253	−	6.39614i	0.655111	−	0.256668i
$622$	12.2395	−	13.8103i	0.490760	−	0.553741i
$623$	−19.8213	−	29.6368i	−0.794122	−	1.18737i
$624$	4.42397	−	7.95948i	0.177100	−	0.318634i
$625$	−16.9592	+	29.3743i	−0.678369	+	1.17497i
$626$	−14.0989	−	12.4953i	−0.563504	−	0.499412i
$627$	24.6970	+	5.64201i	0.986303	+	0.225320i
$628$	26.0076	−	3.14786i	1.03782	−	0.125613i
$629$			0.919927i			0.0366799i
$630$	−36.9332	−	24.4560i	−1.47146	−	0.974350i
$631$		−	21.2515i		−	0.846007i	−0.906128	−	0.423004i	$-0.860976\pi$
$631$		−	21.2515i		−	0.846007i	0.906128	−	0.423004i	$-0.139024\pi$
$632$	16.1681	−	23.3950i	0.643134	−	0.930604i
$633$	26.4188	−	28.4615i	1.05005	−	1.13124i
$634$	−18.4350	+	20.8008i	−0.732147	+	0.826107i
$635$	−11.8667	+	20.5537i	−0.470914	+	0.815647i
$636$	−43.7162	−	4.56936i	−1.73346	−	0.181187i
$637$	7.29452	−	5.60734i	0.289020	−	0.222171i
$638$	13.7711	+	12.2049i	0.545205	+	0.483195i
$639$	3.64036	+	5.34392i	0.144011	+	0.211402i
$640$	−28.1904	−	34.6209i	−1.11432	−	1.36851i
$641$	17.2510	+	29.8796i	0.681373	+	1.18017i	0.974562	+	0.224119i	$0.0719503\pi$
$641$	17.2510	+	29.8796i	0.681373	+	1.18017i	−0.293189	+	0.956055i	$0.594716\pi$
$642$	2.90347	+	29.7065i	0.114591	+	1.17242i
$643$	3.50574	+	6.07213i	0.138253	+	0.239461i	0.926835	−	0.375468i	$-0.122518\pi$
$643$	3.50574	+	6.07213i	0.138253	+	0.239461i	−0.788582	+	0.614929i	$0.789185\pi$
$644$	16.8494	+	5.90845i	0.663958	+	0.232826i
$645$	13.3650	+	12.4058i	0.526246	+	0.488477i
$646$	6.13541	+	5.43758i	0.241394	+	0.213939i
$647$	−0.330066	+	0.571691i	−0.0129762	+	0.0224755i	−0.872441	−	0.488720i	$-0.837464\pi$
$647$	−0.330066	+	0.571691i	−0.0129762	+	0.0224755i	0.859464	+	0.511196i	$0.170797\pi$
$648$	−21.1340	+	14.1899i	−0.830222	+	0.557434i
$649$	−29.6370	+	17.1109i	−1.16335	+	0.671662i
$650$	−18.6425	+	6.21984i	−0.731219	+	0.243962i
$651$	1.44983	+	3.79545i	0.0568234	+	0.148755i
$652$	−9.64647	−	12.8473i	−0.377785	−	0.503139i
$653$	−1.19024	+	2.06155i	−0.0465776	+	0.0806748i	−0.888374	−	0.459120i	$-0.848165\pi$
$653$	−1.19024	+	2.06155i	−0.0465776	+	0.0806748i	0.841797	+	0.539795i	$0.181498\pi$
$654$	13.5367	+	18.9202i	0.529326	+	0.739838i
$655$	−6.83022	+	3.94343i	−0.266879	+	0.154083i
$656$	29.3022	−	28.1023i	1.14406	−	1.09721i
$657$	13.7115	−	1.02214i	0.534937	−	0.0398774i
$658$	7.28037	+	5.64205i	0.283819	+	0.219950i
$659$	−4.53599	−	2.61885i	−0.176697	−	0.102016i	0.409043	−	0.912515i	$-0.365863\pi$
$659$	−4.53599	−	2.61885i	−0.176697	−	0.102016i	−0.585740	+	0.810499i	$0.699196\pi$
$660$	27.2378	+	61.0825i	1.06023	+	2.37763i
$661$		−	7.34107i		−	0.285535i	−0.989756	−	0.142767i	$-0.954400\pi$
$661$		−	7.34107i		−	0.285535i	0.989756	−	0.142767i	$-0.0456001\pi$
$662$	−15.2474	−	13.5132i	−0.592606	−	0.525204i
$663$	−4.21863	+	1.30037i	−0.163838	+	0.0505022i
$664$	−6.62704	+	3.13994i	−0.257179	+	0.121853i
$665$	31.1453	−	2.05493i	1.20776	−	0.0796867i
$666$	1.85665	−	0.777185i	0.0719438	−	0.0301153i
$667$	−7.77183	+	4.48707i	−0.300926	+	0.173740i
$668$	−15.4714	+	11.6168i	−0.598606	+	0.449467i
$669$	3.46018	−	15.1464i	0.133778	−	0.585592i
$670$	2.46357	+	7.38397i	0.0951760	+	0.285268i
$671$	−5.80096	−	10.0476i	−0.223943	−	0.387881i
$672$	−25.7384	−	3.08750i	−0.992882	−	0.119103i
$673$	6.21172	−	10.7590i	0.239444	−	0.414730i	−0.721111	−	0.692820i	$-0.756368\pi$
$673$	6.21172	−	10.7590i	0.239444	−	0.414730i	0.960555	+	0.278090i	$0.0897014\pi$
$674$	−1.35753	−	0.277411i	−0.0522901	−	0.0106855i
$675$	54.3189	+	8.21988i	2.09074	+	0.316383i
$676$	20.7374	+	8.84470i	0.797592	+	0.340181i
$677$		−	29.8294i		−	1.14644i	−0.819403	−	0.573218i	$-0.805695\pi$
$677$		−	29.8294i		−	1.14644i	0.819403	−	0.573218i	$-0.194305\pi$
$678$	−30.4637	+	2.97749i	−1.16995	+	0.114350i
$679$	2.54346	−	5.16326i	0.0976089	−	0.198148i
$680$	−1.75388	+	21.5722i	−0.0672583	+	0.827258i
$681$	−9.89382	−	9.18373i	−0.379132	−	0.351921i
$682$	1.22818	−	6.01017i	0.0470293	−	0.230141i
$683$	9.32990	+	5.38662i	0.356999	+	0.206113i	0.667763	−	0.744374i	$-0.267252\pi$
$683$	9.32990	+	5.38662i	0.356999	+	0.206113i	−0.310765	+	0.950487i	$0.600585\pi$
$684$	5.79106	−	16.9767i	0.221427	−	0.649121i
$685$			39.7054i			1.51707i
$686$	−22.6310	−	13.1847i	−0.864056	−	0.503395i
$687$	−11.4837	−	2.62344i	−0.438130	−	0.100091i
$688$	10.2480	+	2.97683i	0.390702	+	0.113491i
$689$			16.6776i			0.635365i
$690$	−32.4624	+	3.17283i	−1.23582	+	0.120788i
$691$	−47.3937			−1.80294			−0.901471	−	0.432840i	$-0.857512\pi$
$691$	−47.3937			−1.80294			−0.901471	+	0.432840i	$0.857512\pi$
$692$	−32.5383	+	3.93831i	−1.23692	+	0.149712i
$693$	36.0146	+	14.5230i	1.36808	+	0.551682i
$694$	29.0348	+	25.7325i	1.10215	+	0.976791i
$695$		−	63.2982i		−	2.40104i
$696$	9.60850	−	8.79950i	0.364209	−	0.333544i
$697$	−19.6818			−0.745502
$698$	20.1922	−	6.73689i	0.764287	−	0.254995i
$699$	21.4715	+	19.9305i	0.812128	+	0.753840i
$700$	36.4643	+	42.4294i	1.37822	+	1.60368i
$701$	−39.5982			−1.49560			−0.747801	−	0.663923i	$-0.768890\pi$
$701$	−39.5982			−1.49560			−0.747801	+	0.663923i	$0.768890\pi$
$702$	6.18852	+	7.41569i	0.233571	+	0.279887i
$703$	−0.709135	+	1.22826i	−0.0267455	+	0.0463246i
$704$	30.2894	+	24.7882i	1.14157	+	0.934240i
$705$	−16.4030	−	3.74726i	−0.617773	−	0.141130i
$706$	5.24011	−	25.6429i	0.197214	−	0.965082i
$707$	−1.04982	−	1.56970i	−0.0394826	−	0.0590345i
$708$	9.86829	+	22.1303i	0.370873	+	0.831708i
$709$	27.4992			1.03276			0.516378	−	0.856361i	$-0.327280\pi$
$709$	27.4992			1.03276			0.516378	+	0.856361i	$0.327280\pi$
$710$	−3.80690	−	11.4103i	−0.142870	−	0.428220i
$711$	16.9819	+	24.9288i	0.636870	+	0.934902i
$712$	37.9906	+	3.08874i	1.42376	+	0.115755i
$713$	2.59089	+	1.49585i	0.0970295	+	0.0560200i
$714$	7.96924	+	9.71673i	0.298241	+	0.363640i
$715$	21.9766	−	12.6882i	0.821877	−	0.474511i
$716$	14.5481	−	34.1097i	0.543689	−	1.27474i
$717$	−22.9259	+	24.6986i	−0.856184	+	0.922385i
$718$	−1.65060	+	8.07731i	−0.0615997	+	0.301443i
$719$	26.4956	+	45.8917i	0.988118	+	1.71147i	0.627164	+	0.778887i	$0.284216\pi$
$719$	26.4956	+	45.8917i	0.988118	+	1.71147i	0.360954	+	0.932584i	$0.382451\pi$
$720$	45.0202	−	14.6852i	1.67780	−	0.547284i
$721$	−2.76427	−	1.36170i	−0.102947	−	0.0507123i
$722$	−4.50385	−	13.4992i	−0.167616	−	0.502389i
$723$	−27.7587	+	29.9050i	−1.03236	+	1.11218i
$724$	−45.6757	+	5.52840i	−1.69752	+	0.205461i
$725$	−28.1184			−1.04429
$726$	−18.4375	−	25.7701i	−0.684280	−	0.956416i
$727$	−15.2977	+	26.4963i	−0.567359	+	0.982694i	0.429467	+	0.903082i	$0.358701\pi$
$727$	−15.2977	+	26.4963i	−0.567359	+	0.982694i	−0.996826	+	0.0796118i	$0.974632\pi$
$728$	−0.149904	+	9.83479i	−0.00555580	+	0.364502i
$729$	−5.97715	−	26.3301i	−0.221376	−	0.975189i
$730$	−25.0600	−	5.12099i	−0.927511	−	0.189536i
$731$	−2.58666	−	4.48023i	−0.0956711	−	0.165707i
$732$	−7.50263	+	3.34555i	−0.277305	+	0.123655i
$733$	−0.610768	−	0.352627i	−0.0225592	−	0.0130246i	0.488678	−	0.872464i	$-0.337479\pi$
$733$	−0.610768	−	0.352627i	−0.0225592	−	0.0130246i	−0.511237	+	0.859440i	$0.670813\pi$
$734$	2.50508	+	0.511913i	0.0924643	+	0.0188950i
$735$	47.6394	+	4.43505i	1.75721	+	0.163589i
$736$	−16.1428	+	10.1866i	−0.595030	+	0.375483i
$737$	−3.41198	−	5.90973i	−0.125682	−	0.217688i
$738$	16.6279	+	39.7231i	0.612080	+	1.46223i
$739$	−29.5374	−	17.0534i	−1.08655	−	0.627321i	−0.153896	−	0.988087i	$-0.549182\pi$
$739$	−29.5374	−	17.0534i	−1.08655	−	0.627321i	−0.932656	+	0.360766i	$0.882515\pi$
$740$	−3.71713	+	0.449907i	−0.136645	+	0.0165389i
$741$	−6.63498	−	1.51576i	−0.243742	−	0.0556828i
$742$	43.9488	−	17.9580i	1.61341	−	0.659258i
$743$	32.7970	−	18.9353i	1.20320	−	0.694670i	0.241938	−	0.970292i	$-0.422217\pi$
$743$	32.7970	−	18.9353i	1.20320	−	0.694670i	0.961266	+	0.275621i	$0.0888836\pi$
$744$	−4.14205	−	1.30729i	−0.151855	−	0.0479276i
$745$	33.1178	−	19.1205i	1.21334	−	0.700523i
$746$	−2.66720	−	7.99429i	−0.0976530	−	0.292692i
$747$	−0.578223	−	7.75659i	−0.0211561	−	0.283799i
$748$	−2.27987	−	18.8363i	−0.0833605	−	0.688725i
$749$	−17.9229	−	26.7984i	−0.654890	−	0.979194i
$750$	−49.0490	−	22.2679i	−1.79101	−	0.813108i
$751$	−15.6928	−	9.06026i	−0.572639	−	0.330613i	0.185563	−	0.982632i	$-0.440589\pi$
$751$	−15.6928	−	9.06026i	−0.572639	−	0.330613i	−0.758203	+	0.652019i	$0.773922\pi$
$752$	−9.56230	+	2.34918i	−0.348701	+	0.0856657i
$753$	−7.50120	+	2.31221i	−0.273359	+	0.0842615i
$754$	−3.69970	−	3.27890i	−0.134735	−	0.119411i
$755$	−65.3007			−2.37654
$756$	12.8782	−	24.2930i	0.468376	−	0.883529i
$757$	−30.0755			−1.09311			−0.546555	−	0.837423i	$-0.684061\pi$
$757$	−30.0755			−1.09311			−0.546555	+	0.837423i	$0.684061\pi$
$758$	17.4961	+	15.5061i	0.635488	+	0.563209i
$759$	27.3252	−	8.42286i	0.991843	−	0.305731i
$760$	−18.9709	+	27.4506i	−0.688147	+	0.995738i
$761$	19.2695	+	11.1252i	0.698518	+	0.403290i	0.806795	−	0.590831i	$-0.201200\pi$
$761$	19.2695	+	11.1252i	0.698518	+	0.403290i	−0.108277	+	0.994121i	$0.534533\pi$
$762$	−13.4140	−	6.08987i	−0.485938	−	0.220613i
$763$	−22.5415	−	11.1041i	−0.816056	−	0.401995i
$764$	−7.83108	+	0.947842i	−0.283318	+	0.0342917i
$765$	−20.6790	−	9.96847i	−0.747652	−	0.360411i
$766$	−1.47613	−	4.42434i	−0.0533346	−	0.159858i
$767$	7.96214	−	4.59694i	0.287496	−	0.165986i
$768$	19.6857	−	19.5057i	0.710348	−	0.703851i
$769$	9.46235	−	5.46309i	0.341221	−	0.197004i	−0.319591	−	0.947556i	$-0.603545\pi$
$769$	9.46235	−	5.46309i	0.341221	−	0.197004i	0.660812	+	0.750552i	$0.270212\pi$
$770$	−57.0997	−	44.2504i	−2.05773	−	1.59467i
$771$	40.3295	+	9.21324i	1.45243	+	0.331807i
$772$	−1.38183	−	11.4167i	−0.0497332	−	0.410896i
$773$	−10.6286	−	6.13643i	−0.382284	−	0.220712i	0.296527	−	0.955024i	$-0.404171\pi$
$773$	−10.6286	−	6.13643i	−0.382284	−	0.220712i	−0.678812	+	0.734312i	$0.737505\pi$
$774$	−6.85697	+	9.00560i	−0.246469	+	0.323700i
$775$	4.68690	+	8.11795i	0.168359	+	0.291605i
$776$	2.63463	+	5.56056i	0.0945777	+	0.199612i
$777$	−1.37091	+	1.68730i	−0.0491812	+	0.0605314i
$778$	−13.3692	−	2.73199i	−0.479309	−	0.0979467i
$779$	−26.2786	−	15.1719i	−0.941527	−	0.543591i
$780$	−7.31758	−	16.4102i	−0.262011	−	0.587578i
$781$	5.27246	+	9.13217i	0.188663	+	0.326775i
$782$	9.06605	+	1.85264i	0.324201	+	0.0662504i
$783$	5.04121	+	12.8670i	0.180158	+	0.459829i
$784$	26.0781	−	10.1948i	0.931360	−	0.364100i
$785$	25.8452	−	44.7653i	0.922456	−	1.59774i
$786$	−2.84856	−	3.98142i	−0.101605	−	0.142013i
$787$	2.27050			0.0809345			0.0404672	−	0.999181i	$-0.487115\pi$
$787$	2.27050			0.0809345			0.0404672	+	0.999181i	$0.487115\pi$
$788$	3.98956	+	32.9618i	0.142122	+	1.17422i
$789$	−32.0527	+	34.5311i	−1.14111	+	1.22934i
$790$	−17.7587	−	53.2276i	−0.631827	−	1.89375i
$791$	27.4816	−	18.3798i	0.977133	−	0.653512i
$792$	−36.0905	+	20.5150i	−1.28242	+	0.728967i
$793$	1.55846	+	2.69933i	0.0553425	+	0.0958560i
$794$	−1.05336	+	5.15472i	−0.0373825	+	0.182934i
$795$	−59.0018	+	63.5638i	−2.09258	+	2.25438i
$796$	−22.9365	−	9.78266i	−0.812964	−	0.346737i
$797$	4.92030	−	2.84074i	0.174286	−	0.100624i	−0.410319	−	0.911942i	$-0.634583\pi$
$797$	4.92030	−	2.84074i	0.174286	−	0.100624i	0.584605	+	0.811318i	$0.301249\pi$
$798$	3.15004	+	19.1167i	0.111510	+	0.676722i
$799$	4.13388	+	2.38669i	0.146246	+	0.0844352i
$800$	−59.7620	+	2.35140i	−2.11290	+	0.0831345i
$801$	−17.5553	+	36.4175i	−0.620287	+	1.28675i
$802$	−10.7294	−	32.1589i	−0.378869	−	1.13557i
$803$	22.4229			0.791289
$804$	−4.41287	+	1.96777i	−0.155630	+	0.0693980i
$805$	29.2846	−	19.5857i	1.03215	−	0.690306i
$806$	−0.329957	+	1.61467i	−0.0116222	+	0.0568742i
$807$	30.9305	+	7.06606i	1.08881	+	0.248737i
$808$	2.01215	+	0.163593i	0.0707872	+	0.00575519i
$809$	−8.28527	+	14.3505i	−0.291295	+	0.504537i	−0.974116	−	0.226048i	$-0.927419\pi$
$809$	−8.28527	+	14.3505i	−0.291295	+	0.504537i	0.682821	+	0.730585i	$0.260753\pi$
$810$	−2.64863	+	50.1574i	−0.0930635	+	1.76235i
$811$	10.2931			0.361438			0.180719	−	0.983535i	$-0.442158\pi$
$811$	10.2931			0.361438			0.180719	+	0.983535i	$0.442158\pi$
$812$	−4.65683	+	13.2801i	−0.163423	+	0.466040i
$813$	1.96132	+	1.82055i	0.0687864	+	0.0638495i
$814$	3.11370	−	1.03885i	0.109135	−	0.0364116i
$815$	−31.6995			−1.11038
$816$	−13.4327	+	0.219038i	−0.470237	+	0.00766788i
$817$		−	7.97581i		−	0.279038i
$818$	−23.4483	−	20.7814i	−0.819851	−	0.726603i
$819$	−9.67552	−	3.90168i	−0.338090	−	0.136336i
$820$	−9.62575	−	79.5280i	−0.336146	−	2.77724i
$821$	−0.101592			−0.00354560			−0.00177280	−	0.999998i	$-0.500564\pi$
$821$	−0.101592			−0.00354560			−0.00177280	+	0.999998i	$0.500564\pi$
$822$	−24.5290	+	2.39743i	−0.855546	+	0.0836199i
$823$			55.1859i			1.92366i	0.273650	+	0.961829i	$0.411769\pi$
$823$			55.1859i			1.92366i	−0.273650	+	0.961829i	$0.588231\pi$
$824$	2.97697	−	1.41051i	0.103708	−	0.0491374i
$825$	87.3424	+	19.9533i	3.04087	+	0.694685i
$826$	−20.6873	−	16.0320i	−0.719803	−	0.557824i
$827$		−	37.1634i		−	1.29230i	−0.763211	−	0.646149i	$-0.776378\pi$
$827$		−	37.1634i		−	1.29230i	0.763211	−	0.646149i	$-0.223622\pi$
$828$	−3.92018	−	19.8628i	−0.136236	−	0.690281i
$829$	33.4823	+	19.3310i	1.16289	+	0.671393i	0.951994	−	0.306116i	$-0.0990295\pi$
$829$	33.4823	+	19.3310i	1.16289	+	0.671393i	0.210893	+	0.977509i	$0.432363\pi$
$830$	−2.89694	+	14.1764i	−0.100554	+	0.492070i
$831$	−0.617071	−	0.572783i	−0.0214060	−	0.0198696i
$832$	−8.13742	−	6.65949i	−0.282114	−	0.230876i
$833$	−12.5449	−	5.18354i	−0.434656	−	0.179599i
$834$	39.1040	−	3.82197i	1.35406	−	0.132344i
$835$			38.1742i			1.32107i
$836$	11.4762	−	26.9072i	0.396912	−	0.930604i
$837$	2.87449	−	3.60016i	0.0993569	−	0.124440i
$838$	−49.0038	−	10.0139i	−1.69281	−	0.345924i
$839$	−2.58403	+	4.47567i	−0.0892106	+	0.154517i	−0.907178	−	0.420748i	$-0.861768\pi$
$839$	−2.58403	+	4.47567i	−0.0892106	+	0.154517i	0.817967	+	0.575265i	$0.195101\pi$
$840$	−35.3647	+	36.9533i	−1.22020	+	1.27501i
$841$	10.9635	+	18.9893i	0.378050	+	0.654802i
$842$	13.8621	+	41.5485i	0.477721	+	1.43186i
$843$	−10.1584	+	44.4669i	−0.349875	+	1.53152i
$844$	−26.9240	−	35.8578i	−0.926763	−	1.23427i
$845$	38.5238	−	22.2417i	1.32526	−	0.765138i
$846$	1.32454	−	10.3596i	0.0455385	−	0.356170i
$847$	30.7024	+	15.1242i	1.05495	+	0.519673i
$848$	−14.1578	+	48.7395i	−0.486180	+	1.67372i
$849$	−28.4313	+	8.76381i	−0.975761	+	0.300773i
$850$	21.6983	+	19.2303i	0.744244	+	0.659595i
$851$			1.60082i			0.0548754i
$852$	6.81910	−	3.04076i	0.233619	−	0.104175i
$853$	−30.1332	−	17.3974i	−1.03174	−	0.595675i	−0.114257	−	0.993451i	$-0.536449\pi$
$853$	−30.1332	−	17.3974i	−1.03174	−	0.595675i	−0.917483	+	0.397776i	$0.869782\pi$
$854$	5.43518	−	7.01342i	0.185988	−	0.239994i
$855$	−19.9257	−	29.2502i	−0.681445	−	1.00034i
$856$	34.3522	+	2.79293i	1.17413	+	0.0954602i
$857$	37.1025	−	21.4212i	1.26740	−	0.731733i	0.292903	−	0.956142i	$-0.405379\pi$
$857$	37.1025	−	21.4212i	1.26740	−	0.731733i	0.974495	+	0.224409i	$0.0720452\pi$
$858$	9.16537	+	12.8104i	0.312900	+	0.437340i
$859$	−15.9716	+	27.6637i	−0.544945	+	0.943873i	0.453665	+	0.891172i	$0.350116\pi$
$859$	−15.9716	+	27.6637i	−0.544945	+	0.943873i	−0.998610	+	0.0527008i	$0.983217\pi$
$860$	16.8381	−	12.6430i	0.574175	−	0.431123i
$861$	−36.0997	−	29.3306i	−1.23027	−	0.999586i
$862$	6.54235	−	2.18277i	0.222833	−	0.0743455i
$863$	30.0490	−	17.3488i	1.02288	−	0.590560i	0.107943	−	0.994157i	$-0.465574\pi$
$863$	30.0490	−	17.3488i	1.02288	−	0.590560i	0.914937	+	0.403597i	$0.132240\pi$
$864$	11.7904	+	26.9256i	0.401119	+	0.916026i
$865$	−32.3352	+	56.0061i	−1.09943	+	1.90427i
$866$	−13.8376	−	12.2637i	−0.470221	−	0.416739i
$867$	−16.8074	−	15.6011i	−0.570811	−	0.529843i
$868$	4.61026	−	0.869128i	0.156482	−	0.0295001i
$869$	24.5954	+	42.6005i	0.834342	+	1.44512i
$870$	−2.50072	−	25.5857i	−0.0847822	−	0.867437i
$871$	0.916648	+	1.58768i	0.0310594	+	0.0537965i
$872$	24.2760	−	11.5021i	0.822088	−	0.389511i
$873$	−6.50833	+	0.485170i	−0.220273	+	0.0164205i
$874$	10.6766	+	9.46225i	0.361141	+	0.320065i
$875$	58.0568	−	3.83052i	1.96268	−	0.129495i
$876$	1.65048	−	15.7906i	0.0557647	−	0.533514i
$877$	11.1213	−	19.2627i	0.375540	−	0.650455i	−0.614867	−	0.788631i	$-0.710790\pi$
$877$	11.1213	−	19.2627i	0.375540	−	0.650455i	0.990408	+	0.138175i	$0.0441238\pi$
$878$	1.79846	−	2.02926i	0.0606950	−	0.0684842i
$879$	29.2767	−	31.5404i	0.987480	−	1.06383i
$880$	74.9967	−	18.4245i	2.52814	−	0.621090i
$881$			20.4228i			0.688061i	0.938958	+	0.344031i	$0.111792\pi$
$881$			20.4228i			0.688061i	−0.938958	+	0.344031i	$0.888208\pi$
$882$	0.136631	+	29.6982i	0.00460062	+	0.999989i
$883$		−	11.6027i		−	0.390461i	−0.980757	−	0.195231i	$-0.937454\pi$
$883$		−	11.6027i		−	0.390461i	0.980757	−	0.195231i	$-0.0625456\pi$
$884$	0.612501	+	5.06049i	0.0206006	+	0.170203i
$885$	46.6094	+	10.6479i	1.56676	+	0.357925i
$886$	−22.5333	−	19.9704i	−0.757021	−	0.670919i
$887$	26.5399	−	45.9684i	0.891123	−	1.54347i	0.0525911	−	0.998616i	$-0.483252\pi$
$887$	26.5399	−	45.9684i	0.891123	−	1.54347i	0.838531	−	0.544853i	$-0.183415\pi$
$888$	−0.502382	−	2.26918i	−0.0168588	−	0.0761487i
$889$	15.8775	−	1.04758i	0.532514	−	0.0351346i
$890$	49.8822	−	56.2838i	1.67206	−	1.88664i
$891$	−6.52854	−	43.5453i	−0.218714	−	1.45882i
$892$	−16.5018	−	7.03819i	−0.552522	−	0.235656i
$893$	3.67962	+	6.37328i	0.123134	+	0.213274i
$894$	13.8118	+	19.3048i	0.461937	+	0.645648i
$895$	−36.5841	−	63.3655i	−1.22287	−	2.11808i
$896$	−8.78695	+	28.6145i	−0.293551	+	0.955943i
$897$	−7.34108	+	2.26285i	−0.245111	+	0.0755543i
$898$	5.62770	−	6.34993i	0.187799	−	0.211900i
$899$	−1.17898	+	2.04205i	−0.0393210	+	0.0681060i
$900$	20.4804	−	60.0392i	0.682681	−	2.00131i
$901$	21.3079	−	12.3021i	0.709870	−	0.409844i
$902$	22.2261	+	66.6175i	0.740049	+	2.21812i
$903$	1.93226	−	12.0722i	0.0643014	−	0.401738i
$904$	−2.86412	+	35.2279i	−0.0952593	+	1.17166i
$905$	−45.3905	+	78.6187i	−1.50883	+	2.61337i
$906$	−3.94288	−	40.3410i	−0.130993	−	1.34024i
$907$	47.3583	−	27.3424i	1.57251	−	0.907888i	0.576647	−	0.816993i	$-0.304361\pi$
$907$	47.3583	−	27.3424i	1.57251	−	0.907888i	0.995860	−	0.0908948i	$-0.0289727\pi$
$908$	−12.4649	+	9.35935i	−0.413662	+	0.310601i
$909$	−0.929808	+	1.92884i	−0.0308398	+	0.0639754i
$910$	15.3401	+	11.8881i	0.508521	+	0.394087i
$911$	−1.27865	−	0.738229i	−0.0423636	−	0.0244586i	0.478669	−	0.877996i	$-0.341120\pi$
$911$	−1.27865	−	0.738229i	−0.0423636	−	0.0244586i	−0.521032	+	0.853537i	$0.674453\pi$
$912$	−18.1037	−	10.0622i	−0.599474	−	0.333194i
$913$		−	12.6846i		−	0.419800i
$914$	−23.7643	+	26.8141i	−0.786053	+	0.886930i
$915$	−3.60985	+	15.8015i	−0.119338	+	0.522383i
$916$	−5.33623	+	12.5114i	−0.176314	+	0.413388i
$917$	4.74345	+	2.33666i	0.156643	+	0.0771632i
$918$	4.90965	−	13.3769i	0.162042	−	0.441502i
$919$	16.9505	−	9.78639i	0.559146	−	0.322823i	−0.193657	−	0.981069i	$-0.562035\pi$
$919$	16.9505	−	9.78639i	0.559146	−	0.322823i	0.752803	+	0.658246i	$0.228701\pi$
$920$	−3.05203	+	37.5391i	−0.100623	+	1.23763i
$921$	53.1122	−	16.3716i	1.75011	−	0.539461i
$922$	−26.9060	+	8.97685i	−0.886102	+	0.295637i
$923$	−1.41648	−	2.45341i	−0.0466239	−	0.0807549i
$924$	23.8890	−	37.9465i	0.785891	−	1.24835i
$925$	−2.50790	+	4.34381i	−0.0824592	+	0.142824i
$926$	−10.8833	+	53.2584i	−0.357649	+	1.75018i
$927$	0.259747	+	3.48438i	0.00853121	+	0.114442i
$928$	−8.02871	−	12.7232i	−0.263555	−	0.417658i
$929$			14.4455i			0.473942i	0.971517	+	0.236971i	$0.0761546\pi$
$929$			14.4455i			0.473942i	−0.971517	+	0.236971i	$0.923845\pi$
$930$	−6.96992	+	4.98672i	−0.228553	+	0.163521i
$931$	−12.7538	−	16.5913i	−0.417989	−	0.543758i
$932$	27.0513	−	20.3116i	0.886094	−	0.665329i
$933$	21.5980	−	6.65746i	0.707085	−	0.217955i
$934$	−45.3348	−	9.26415i	−1.48340	−	0.303132i
$935$	−32.4218	−	18.7187i	−1.06031	−	0.612168i
$936$	9.69592	−	5.51146i	0.316921	−	0.180148i
$937$		−	31.4809i		−	1.02844i	−0.857659	−	0.514218i	$-0.828082\pi$
$937$		−	31.4809i		−	1.02844i	0.857659	−	0.514218i	$-0.171918\pi$
$938$	3.19684	−	4.12513i	0.104381	−	0.134690i
$939$	−6.79658	−	22.0493i	−0.221798	−	0.719552i
$940$	−7.62213	+	17.8709i	−0.248606	+	0.582886i
$941$		−	40.3346i		−	1.31487i	−0.753511	−	0.657435i	$-0.771641\pi$
$941$		−	40.3346i		−	1.31487i	0.753511	−	0.657435i	$-0.228359\pi$
$942$	29.2153	+	13.2636i	0.951887	+	0.432150i
$943$	−34.2495			−1.11532
$944$	27.1714	−	6.67523i	0.884354	−	0.217260i
$945$	−23.0733	−	49.1005i	−0.750575	−	1.59724i
$946$	−12.2433	+	13.8145i	−0.398064	+	0.449149i
$947$			14.8597i			0.482876i	0.970416	+	0.241438i	$0.0776190\pi$
$947$			14.8597i			0.482876i	−0.970416	+	0.241438i	$0.922381\pi$
$948$	31.8103	−	14.1848i	1.03315	−	0.460700i
$949$	−6.02405			−0.195549
$950$	14.1469	+	42.4021i	0.458987	+	1.37571i
$951$	−32.5306	+	10.0274i	−1.05488	+	0.325160i
$952$	12.6759	−	7.06306i	0.410828	−	0.228915i
$953$	−11.8041			−0.382371			−0.191185	−	0.981554i	$-0.561233\pi$
$953$	−11.8041			−0.382371			−0.191185	+	0.981554i	$0.561233\pi$
$954$	−42.8306	−	32.6117i	−1.38669	−	1.05584i
$955$	−7.78219	+	13.4791i	−0.251826	+	0.436175i
$956$	23.3643	+	31.1169i	0.755657	+	1.00639i
$957$	6.63860	+	21.5368i	0.214596	+	0.696186i
$958$	50.9846	+	10.4187i	1.64724	+	0.336612i
$959$	22.1278	−	14.7992i	0.714543	−	0.477890i
$960$	−7.45455	−	54.1700i	−0.240595	−	1.74833i
$961$	−30.2139			−0.974643
$962$	−0.836512	+	0.279092i	−0.0269702	+	0.00899829i
$963$	−15.8740	+	32.9298i	−0.511534	+	1.06115i
$964$	28.2895	+	37.6764i	0.911145	+	1.21347i
$965$	−19.6508	−	11.3454i	−0.632583	−	0.365222i
$966$	13.8677	+	16.9087i	0.446187	+	0.544027i
$967$	2.41663	−	1.39524i	0.0777137	−	0.0448680i	−0.460640	−	0.887587i	$-0.652380\pi$
$967$	2.41663	−	1.39524i	0.0777137	−	0.0448680i	0.538353	+	0.842719i	$0.319047\pi$
$968$	−33.0648	+	15.6663i	−1.06274	+	0.503535i
$969$	2.95767	+	9.59521i	0.0950142	+	0.308242i
$970$	11.8950	+	2.43074i	0.381926	+	0.0780464i
$971$	26.2483	+	45.4633i	0.842347	+	1.45899i	0.887905	+	0.460026i	$0.152160\pi$
$971$	26.2483	+	45.4633i	0.842347	+	1.45899i	−0.0455582	+	0.998962i	$0.514507\pi$
$972$	−31.1458	+	1.39227i	−0.999002	+	0.0446569i
$973$	−35.2760	+	23.5928i	−1.13090	+	0.756350i
$974$	−6.08894	+	2.03150i	−0.195102	+	0.0650935i
$975$	−23.4650	−	5.36057i	−0.751482	−	0.171676i
$976$	2.26304	+	9.21167i	0.0724382	+	0.294858i
$977$	−10.2879			−0.329140			−0.164570	−	0.986365i	$-0.552624\pi$
$977$	−10.2879			−0.329140			−0.164570	+	0.986365i	$0.552624\pi$
$978$	−1.91403	−	19.5831i	−0.0612038	−	0.626198i
$979$	−32.9653	+	57.0976i	−1.05358	+	1.82485i
$980$	14.8097	−	53.2252i	0.473080	−	1.70022i
$981$	2.11813	+	28.4137i	0.0676266	+	0.907179i
$982$	−3.48721	+	17.0649i	−0.111281	+	0.544563i
$983$	16.4524	+	28.4963i	0.524749	+	0.908891i	0.999585	+	0.0288169i	$0.00917397\pi$
$983$	16.4524	+	28.4963i	0.524749	+	0.908891i	−0.474836	+	0.880074i	$0.657493\pi$
$984$	48.5491	−	10.7485i	1.54769	−	0.342648i
$985$	56.7351	+	32.7560i	1.80773	+	1.04369i
$986$	−1.46019	+	7.14554i	−0.0465019	+	0.227560i
$987$	4.02546	+	10.5381i	0.128132	+	0.335430i
$988$	−3.08314	+	7.22876i	−0.0980876	+	0.229978i
$989$	−4.50120	−	7.79630i	−0.143130	−	0.247908i
$990$	−10.3883	+	81.2499i	−0.330161	+	2.58229i
$991$	48.3716	+	27.9273i	1.53657	+	0.887141i	0.999036	+	0.0439007i	$0.0139785\pi$
$991$	48.3716	+	27.9273i	1.53657	+	0.887141i	0.537537	+	0.843240i	$0.319355\pi$
$992$	−2.33499	+	4.43869i	−0.0741361	+	0.140929i
$993$	−7.35024	−	23.8455i	−0.233253	−	0.756713i
$994$	−4.94000	+	6.37446i	−0.156687	+	0.202186i
$995$	−42.6092	+	24.6004i	−1.35080	+	0.779885i
$996$	−8.93272	−	0.933677i	−0.283044	−	0.0295847i
$997$	0.219422	−	0.126684i	0.00694917	−	0.00401211i	−0.496521	−	0.868024i	$-0.665390\pi$
$997$	0.219422	−	0.126684i	0.00694917	−	0.00401211i	0.503471	+	0.864012i	$0.332056\pi$
$998$	−17.3748	+	5.79689i	−0.549990	+	0.183497i
$999$	2.43736	+	0.368836i	0.0771147	+	0.0116695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bj.b.115.31	yes	84
3.2	odd	2		756.2.bj.b.451.12		84
4.3	odd	2	inner	252.2.bj.b.115.32	yes	84
7.5	odd	6		252.2.n.b.187.4	yes	84
9.4	even	3		252.2.n.b.31.25	yes	84
9.5	odd	6		756.2.n.b.199.18		84
12.11	even	2		756.2.bj.b.451.11		84
21.5	even	6		756.2.n.b.19.39		84
28.19	even	6		252.2.n.b.187.25	yes	84
36.23	even	6		756.2.n.b.199.39		84
36.31	odd	6		252.2.n.b.31.4	✓	84
63.5	even	6		756.2.bj.b.523.12		84
63.40	odd	6	inner	252.2.bj.b.103.31	yes	84
84.47	odd	6		756.2.n.b.19.18		84
252.103	even	6	inner	252.2.bj.b.103.32	yes	84
252.131	odd	6		756.2.bj.b.523.11		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.4	✓	84	36.31	odd	6
252.2.n.b.31.25	yes	84	9.4	even	3
252.2.n.b.187.4	yes	84	7.5	odd	6
252.2.n.b.187.25	yes	84	28.19	even	6
252.2.bj.b.103.31	yes	84	63.40	odd	6	inner
252.2.bj.b.103.32	yes	84	252.103	even	6	inner
252.2.bj.b.115.31	yes	84	1.1	even	1	trivial
252.2.bj.b.115.32	yes	84	4.3	odd	2	inner
756.2.n.b.19.18		84	84.47	odd	6
756.2.n.b.19.39		84	21.5	even	6
756.2.n.b.199.18		84	9.5	odd	6
756.2.n.b.199.39		84	36.23	even	6
756.2.bj.b.451.11		84	12.11	even	2
756.2.bj.b.451.12		84	3.2	odd	2
756.2.bj.b.523.11		84	252.131	odd	6
756.2.bj.b.523.12		84	63.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.937998 - 1.05838i) q^{2} +(1.65520 - 0.510207i) q^{3} +(-0.240318 - 1.98551i) q^{4} +(-3.41753 - 1.97311i) q^{5} +(1.01258 - 2.23040i) q^{6} +(0.174185 + 2.64001i) q^{7} +(-2.32683 - 1.60806i) q^{8} +(2.47938 - 1.68899i) q^{9} +(-5.29393 + 1.76626i) q^{10} +(4.23698 - 2.44622i) q^{11} +(-1.41080 - 3.16380i) q^{12} +(-1.13829 + 0.657191i) q^{13} +(2.95751 + 2.29197i) q^{14} +(-6.66340 - 1.52225i) q^{15} +(-3.88449 + 0.954307i) q^{16} +(1.67931 + 0.969547i) q^{17} +(0.538066 - 4.20838i) q^{18} +(1.49477 + 2.58902i) q^{19} +(-3.09634 + 7.25972i) q^{20} +(1.63526 + 4.28088i) q^{21} +(1.38526 - 6.77887i) q^{22} +(2.92226 + 1.68717i) q^{23} +(-4.67182 - 1.47449i) q^{24} +(5.28635 + 9.15623i) q^{25} +(-0.372157 + 1.82118i) q^{26} +(3.24213 - 4.06061i) q^{27} +(5.19991 - 0.980288i) q^{28} +(-1.32976 + 2.30322i) q^{29} +(-7.86137 + 5.62451i) q^{30} +0.886605 q^{31} +(-2.63363 + 5.00639i) q^{32} +(5.76497 - 6.21072i) q^{33} +(2.60133 - 0.867902i) q^{34} +(4.61376 - 9.36601i) q^{35} +(-3.94934 - 4.51693i) q^{36} +(0.237205 + 0.410852i) q^{37} +(4.14225 + 0.846467i) q^{38} +(-1.54879 + 1.66854i) q^{39} +(4.77915 + 10.0867i) q^{40} +(-8.79016 + 5.07500i) q^{41} +(6.06465 + 2.28473i) q^{42} +(-2.31047 - 1.33395i) q^{43} +(-5.87522 - 7.82469i) q^{44} +(-11.8059 + 0.880085i) q^{45} +(4.52673 - 1.51029i) q^{46} +2.46166 q^{47} +(-5.94272 + 3.56147i) q^{48} +(-6.93932 + 0.919699i) q^{49} +(14.6493 + 2.99358i) q^{50} +(3.27426 + 0.748002i) q^{51} +(1.57841 + 2.10215i) q^{52} +(6.34427 - 10.9886i) q^{53} +(-1.25654 - 7.24024i) q^{54} -19.3067 q^{55} +(3.83999 - 6.42296i) q^{56} +(3.79508 + 3.52270i) q^{57} +(1.19035 + 3.56781i) q^{58} -6.99484 q^{59} +(-1.42110 + 13.5961i) q^{60} -2.37140i q^{61} +(0.831634 - 0.938361i) q^{62} +(4.89082 + 6.25139i) q^{63} +(2.82830 + 7.48336i) q^{64} +5.18685 q^{65} +(-1.16574 - 11.9271i) q^{66} -1.39480i q^{67} +(1.52148 - 3.56728i) q^{68} +(5.69773 + 1.30164i) q^{69} +(-5.58506 - 13.6684i) q^{70} +2.15535i q^{71} +(-8.48509 - 0.0569854i) q^{72} +(3.96915 + 2.29159i) q^{73} +(0.657333 + 0.134326i) q^{74} +(13.4215 + 12.4583i) q^{75} +(4.78130 - 3.59007i) q^{76} +(7.19607 + 10.7596i) q^{77} +(0.313184 + 3.20430i) q^{78} +10.0544i q^{79} +(15.1583 + 4.40317i) q^{80} +(3.29463 - 8.37529i) q^{81} +(-2.87390 + 14.0636i) q^{82} +(1.29635 - 2.24535i) q^{83} +(8.10674 - 4.27560i) q^{84} +(-3.82605 - 6.62692i) q^{85} +(-3.57904 + 1.19410i) q^{86} +(-1.02591 + 4.49075i) q^{87} +(-13.7924 - 1.12136i) q^{88} +(-11.6706 + 6.73801i) q^{89} +(-10.1425 + 13.3206i) q^{90} +(-1.93326 - 2.89062i) q^{91} +(2.64761 - 6.20762i) q^{92} +(1.46751 - 0.452352i) q^{93} +(2.30903 - 2.60536i) q^{94} -11.7974i q^{95} +(-1.80489 + 9.63028i) q^{96} +(-1.88401 - 1.08773i) q^{97} +(-5.53568 + 8.20708i) q^{98} +(6.37343 - 13.2213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26}+ \cdots + 21 q^{98}+O(q^{100}) \) 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

Introduction

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