LMFDB - Embedded newform 189.2.be.a.20.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(20,189)] 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("189.20"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.be (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			20.18
Character	$\chi$	$=$	189.20
Dual form			189.2.be.a.104.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.492726 + 1.35375i) q^{2} +(0.333137 - 1.69971i) q^{3} +(-0.0577819 + 0.0484848i) q^{4} +(-0.440273 - 2.49691i) q^{5} +(2.46514 - 0.386507i) q^{6} +(-2.34762 - 1.22011i) q^{7} +(2.40115 + 1.38630i) q^{8} +(-2.77804 - 1.13247i) q^{9} +(3.16327 - 1.82631i) q^{10} +(2.06906 + 0.364832i) q^{11} +(0.0631609 + 0.114365i) q^{12} +(-0.0331071 + 0.0909611i) q^{13} +(0.494989 - 3.77928i) q^{14} +(-4.39070 - 0.0834760i) q^{15} +(-0.719801 + 4.08219i) q^{16} +(3.94280 + 6.82913i) q^{17} +(0.164277 - 4.31878i) q^{18} +(-1.53773 - 0.887809i) q^{19} +(0.146502 + 0.122930i) q^{20} +(-2.85591 + 3.58382i) q^{21} +(0.525589 + 2.98077i) q^{22} +(3.82906 + 4.56329i) q^{23} +(3.15622 - 3.61943i) q^{24} +(-1.34226 + 0.488541i) q^{25} -0.139452 q^{26} +(-2.85034 + 4.34460i) q^{27} +(0.194807 - 0.0433240i) q^{28} +(0.573096 + 1.57457i) q^{29} +(-2.05041 - 5.98506i) q^{30} +(-0.916092 - 1.09176i) q^{31} +(-0.419987 + 0.0740550i) q^{32} +(1.30939 - 3.39527i) q^{33} +(-7.30224 + 8.70247i) q^{34} +(-2.01290 + 6.39899i) q^{35} +(0.215428 - 0.0692562i) q^{36} +(-1.88241 - 3.26042i) q^{37} +(0.444195 - 2.51916i) q^{38} +(0.143578 + 0.0865751i) q^{39} +(2.40431 - 6.60580i) q^{40} +(-2.60026 - 0.946417i) q^{41} +(-6.25879 - 2.10036i) q^{42} +(1.03518 - 5.87080i) q^{43} +(-0.137243 + 0.0792375i) q^{44} +(-1.60459 + 7.43511i) q^{45} +(-4.29090 + 7.43206i) q^{46} +(-3.23438 - 2.71396i) q^{47} +(6.69876 + 2.58338i) q^{48} +(4.02268 + 5.72870i) q^{49} +(-1.32273 - 1.57637i) q^{50} +(12.9210 - 4.42659i) q^{51} +(-0.00249724 - 0.00686110i) q^{52} -9.25188i q^{53} +(-7.28596 - 1.71797i) q^{54} -5.32689i q^{55} +(-3.94555 - 6.18417i) q^{56} +(-2.02129 + 2.31794i) q^{57} +(-1.84920 + 1.55166i) q^{58} +(-1.28271 - 7.27458i) q^{59} +(0.257750 - 0.208059i) q^{60} +(-7.80852 + 9.30583i) q^{61} +(1.02659 - 1.77810i) q^{62} +(5.14006 + 6.04813i) q^{63} +(3.83798 + 6.64757i) q^{64} +(0.241698 + 0.0426179i) q^{65} +(5.24153 + 0.0996521i) q^{66} +(-10.6299 - 3.86898i) q^{67} +(-0.558931 - 0.203434i) q^{68} +(9.03188 - 4.98809i) q^{69} +(-9.65446 + 0.427973i) q^{70} +(-11.9234 + 6.88396i) q^{71} +(-5.10053 - 6.57043i) q^{72} +(12.0252 + 6.94274i) q^{73} +(3.48630 - 4.15481i) q^{74} +(0.383224 + 2.44420i) q^{75} +(0.131898 - 0.0232572i) q^{76} +(-4.41225 - 3.38097i) q^{77} +(-0.0464565 + 0.237028i) q^{78} +(-5.82433 + 2.11988i) q^{79} +10.5098 q^{80} +(6.43501 + 6.29211i) q^{81} -3.98644i q^{82} +(8.67692 - 3.15814i) q^{83} +(-0.00874090 - 0.345548i) q^{84} +(15.3158 - 12.8515i) q^{85} +(8.45769 - 1.49132i) q^{86} +(2.86723 - 0.449552i) q^{87} +(4.46236 + 3.74436i) q^{88} +(-6.28476 + 10.8855i) q^{89} +(-10.8559 + 1.49126i) q^{90} +(0.188705 - 0.173148i) q^{91} +(-0.442501 - 0.0780248i) q^{92} +(-2.16085 + 1.19339i) q^{93} +(2.08038 - 5.71579i) q^{94} +(-1.53976 + 4.23045i) q^{95} +(-0.0140409 + 0.738527i) q^{96} +(15.0854 + 2.65997i) q^{97} +(-5.77318 + 8.26840i) q^{98} +(-5.33478 - 3.35668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	0.492726	+	1.35375i	0.348410	+	0.957249i	0.982871	+	0.184294i	$0.0589998\pi$
$2$	0.492726	+	1.35375i	0.348410	+	0.957249i	−0.634461	+	0.772955i	$0.718778\pi$
$3$	0.333137	−	1.69971i	0.192337	−	0.981329i
$3$	0.333137	−	1.69971i	0.192337	−	0.981329i
$4$	−0.0577819	+	0.0484848i	−0.0288910	+	0.0242424i
$5$	−0.440273	−	2.49691i	−0.196896	−	1.11665i	−0.909693	−	0.415282i	$-0.863683\pi$
$5$	−0.440273	−	2.49691i	−0.196896	−	1.11665i	0.712797	−	0.701370i	$-0.247428\pi$
$6$	2.46514	−	0.386507i	1.00639	−	0.157791i
$7$	−2.34762	−	1.22011i	−0.887319	−	0.461157i
$7$	−2.34762	−	1.22011i	−0.887319	−	0.461157i
$8$	2.40115	+	1.38630i	0.848933	+	0.490132i
$9$	−2.77804	−	1.13247i	−0.926013	−	0.377491i
$10$	3.16327	−	1.82631i	1.00031	−	0.577531i
$11$	2.06906	+	0.364832i	0.623846	+	0.110001i	0.476631	−	0.879104i	$-0.341858\pi$
$11$	2.06906	+	0.364832i	0.623846	+	0.110001i	0.147215	+	0.989104i	$0.452969\pi$
$12$	0.0631609	+	0.114365i	0.0182330	+	0.0330142i
$13$	−0.0331071	+	0.0909611i	−0.00918227	+	0.0252281i	−0.944199	−	0.329375i	$-0.893162\pi$
$13$	−0.0331071	+	0.0909611i	−0.00918227	+	0.0252281i	0.935017	+	0.354603i	$0.115384\pi$
$14$	0.494989	−	3.77928i	0.132291	−	1.01006i
$15$	−4.39070	−	0.0834760i	−1.13367	−	0.0215534i
$16$	−0.719801	+	4.08219i	−0.179950	+	1.02055i
$17$	3.94280	+	6.82913i	0.956269	+	1.65631i	0.731438	+	0.681908i	$0.238850\pi$
$17$	3.94280	+	6.82913i	0.956269	+	1.65631i	0.224831	+	0.974398i	$0.427817\pi$
$18$	0.164277	−	4.31878i	0.0387204	−	1.01795i
$19$	−1.53773	−	0.887809i	−0.352780	−	0.203677i	0.313129	−	0.949711i	$-0.398623\pi$
$19$	−1.53773	−	0.887809i	−0.352780	−	0.203677i	−0.665909	+	0.746033i	$0.731956\pi$
$20$	0.146502	+	0.122930i	0.0327588	+	0.0274879i
$21$	−2.85591	+	3.58382i	−0.623211	+	0.782054i
$22$	0.525589	+	2.98077i	0.112056	+	0.635501i
$23$	3.82906	+	4.56329i	0.798414	+	0.951513i	0.999607	−	0.0280391i	$-0.00892629\pi$
$23$	3.82906	+	4.56329i	0.798414	+	0.951513i	−0.201193	+	0.979552i	$0.564482\pi$
$24$	3.15622	−	3.61943i	0.644261	−	0.738813i
$25$	−1.34226	+	0.488541i	−0.268451	+	0.0977083i
$26$	−0.139452			−0.0273487
$27$	−2.85034	+	4.34460i	−0.548549	+	0.836118i
$28$	0.194807	−	0.0433240i	0.0368150	−	0.00818746i
$29$	0.573096	+	1.57457i	0.106421	+	0.292390i	0.981461	−	0.191661i	$-0.0613873\pi$
$29$	0.573096	+	1.57457i	0.106421	+	0.292390i	−0.875040	+	0.484051i	$0.839165\pi$
$30$	−2.05041	−	5.98506i	−0.374351	−	1.09272i
$31$	−0.916092	−	1.09176i	−0.164535	−	0.196085i	0.677477	−	0.735544i	$-0.263073\pi$
$31$	−0.916092	−	1.09176i	−0.164535	−	0.196085i	−0.842012	+	0.539459i	$0.818629\pi$
$32$	−0.419987	+	0.0740550i	−0.0742439	+	0.0130912i
$33$	1.30939	−	3.39527i	0.227936	−	0.591041i
$34$	−7.30224	+	8.70247i	−1.25232	+	1.49246i
$35$	−2.01290	+	6.39899i	−0.340243	+	1.08163i
$36$	0.215428	−	0.0692562i	0.0359047	−	0.0115427i
$37$	−1.88241	−	3.26042i	−0.309466	−	0.536010i	0.668780	−	0.743460i	$-0.266817\pi$
$37$	−1.88241	−	3.26042i	−0.309466	−	0.536010i	−0.978246	+	0.207450i	$0.933483\pi$
$38$	0.444195	−	2.51916i	0.0720580	−	0.408661i
$39$	0.143578	+	0.0865751i	0.0229910	+	0.0138631i
$40$	2.40431	−	6.60580i	0.380155	−	1.04447i
$41$	−2.60026	−	0.946417i	−0.406092	−	0.147806i	0.130894	−	0.991396i	$-0.458215\pi$
$41$	−2.60026	−	0.946417i	−0.406092	−	0.147806i	−0.536987	+	0.843591i	$0.680437\pi$
$42$	−6.25879	−	2.10036i	−0.965753	−	0.324092i
$43$	1.03518	−	5.87080i	0.157864	−	0.895289i	−0.798257	−	0.602317i	$-0.794244\pi$
$43$	1.03518	−	5.87080i	0.157864	−	0.895289i	0.956121	−	0.292973i	$-0.0946445\pi$
$44$	−0.137243	+	0.0792375i	−0.0206902	+	0.0119455i
$45$	−1.60459	+	7.43511i	−0.239198	+	1.10836i
$46$	−4.29090	+	7.43206i	−0.632659	+	1.09580i
$47$	−3.23438	−	2.71396i	−0.471782	−	0.395872i	0.375662	−	0.926757i	$-0.377415\pi$
$47$	−3.23438	−	2.71396i	−0.471782	−	0.395872i	−0.847444	+	0.530885i	$0.821860\pi$
$48$	6.69876	+	2.58338i	0.966883	+	0.372879i
$49$	4.02268	+	5.72870i	0.574668	+	0.818386i
$50$	−1.32273	−	1.57637i	−0.187062	−	0.222932i
$51$	12.9210	−	4.42659i	1.80931	−	0.619846i
$52$	−0.00249724	−	0.00686110i	−0.000346304	−	0.000951464i
$53$		−	9.25188i		−	1.27084i	−0.772165	−	0.635422i	$-0.780826\pi$
$53$		−	9.25188i		−	1.27084i	0.772165	−	0.635422i	$-0.219174\pi$
$54$	−7.28596	−	1.71797i	−0.991493	−	0.233786i
$55$		−	5.32689i		−	0.718278i
$56$	−3.94555	−	6.18417i	−0.527246	−	0.826395i
$57$	−2.02129	+	2.31794i	−0.267727	+	0.307018i
$58$	−1.84920	+	1.55166i	−0.242812	+	0.203743i
$59$	−1.28271	−	7.27458i	−0.166994	−	0.947070i	−0.946985	−	0.321279i	$-0.895887\pi$
$59$	−1.28271	−	7.27458i	−0.166994	−	0.947070i	0.779991	−	0.625791i	$-0.215224\pi$
$60$	0.257750	−	0.208059i	0.0332754	−	0.0268603i
$61$	−7.80852	+	9.30583i	−0.999778	+	1.19149i	−0.0183160	+	0.999832i	$0.505831\pi$
$61$	−7.80852	+	9.30583i	−0.999778	+	1.19149i	−0.981462	+	0.191657i	$0.938614\pi$
$62$	1.02659	−	1.77810i	0.130377	−	0.225819i
$63$	5.14006	+	6.04813i	0.647586	+	0.761992i
$64$	3.83798	+	6.64757i	0.479747	+	0.830947i
$65$	0.241698	+	0.0426179i	0.0299789	+	0.00528609i
$66$	5.24153	+	0.0996521i	0.645188	+	0.0122663i
$67$	−10.6299	−	3.86898i	−1.29865	−	0.472671i	−0.402096	−	0.915597i	$-0.631718\pi$
$67$	−10.6299	−	3.86898i	−1.29865	−	0.472671i	−0.896558	+	0.442926i	$0.853940\pi$
$68$	−0.558931	−	0.203434i	−0.0677804	−	0.0246700i
$69$	9.03188	−	4.98809i	1.08731	−	0.600496i
$70$	−9.65446	+	0.427973i	−1.15393	+	0.0511526i
$71$	−11.9234	+	6.88396i	−1.41504	+	0.816976i	−0.995858	−	0.0909251i	$-0.971018\pi$
$71$	−11.9234	+	6.88396i	−1.41504	+	0.816976i	−0.419185	+	0.907901i	$0.637684\pi$
$72$	−5.10053	−	6.57043i	−0.601103	−	0.774333i
$73$	12.0252	+	6.94274i	1.40744	+	0.812587i	0.995141	−	0.0984612i	$-0.0313920\pi$
$73$	12.0252	+	6.94274i	1.40744	+	0.812587i	0.412301	+	0.911048i	$0.364725\pi$
$74$	3.48630	−	4.15481i	0.405274	−	0.482987i
$75$	0.383224	+	2.44420i	0.0442510	+	0.282232i
$76$	0.131898	−	0.0232572i	0.0151298	−	0.00266779i
$77$	−4.41225	−	3.38097i	−0.502823	−	0.385297i
$78$	−0.0464565	+	0.237028i	−0.00526016	+	0.0268381i
$79$	−5.82433	+	2.11988i	−0.655288	+	0.238505i	−0.648201	−	0.761469i	$-0.724478\pi$
$79$	−5.82433	+	2.11988i	−0.655288	+	0.238505i	−0.00708756	+	0.999975i	$0.502256\pi$
$80$	10.5098			1.17503
$81$	6.43501	+	6.29211i	0.715001	+	0.699123i
$82$		−	3.98644i		−	0.440228i
$83$	8.67692	−	3.15814i	0.952416	−	0.346651i	0.181359	−	0.983417i	$-0.441951\pi$
$83$	8.67692	−	3.15814i	0.952416	−	0.346651i	0.771057	+	0.636766i	$0.219728\pi$
$84$	−0.00874090	−	0.345548i	−0.000953710	−	0.0377024i
$85$	15.3158	−	12.8515i	1.66123	−	1.39394i
$86$	8.45769	−	1.49132i	0.912016	−	0.160813i
$87$	2.86723	−	0.449552i	0.307400	−	0.0481970i
$88$	4.46236	+	3.74436i	0.475689	+	0.399150i
$89$	−6.28476	+	10.8855i	−0.666183	+	1.15386i	0.312781	+	0.949825i	$0.398740\pi$
$89$	−6.28476	+	10.8855i	−0.666183	+	1.15386i	−0.978963	+	0.204037i	$0.934594\pi$
$90$	−10.8559	+	1.49126i	−1.14432	+	0.157192i
$91$	0.188705	−	0.173148i	0.0197817	−	0.0181509i
$92$	−0.442501	−	0.0780248i	−0.0461339	−	0.00813465i
$93$	−2.16085	+	1.19339i	−0.224070	+	0.123749i
$94$	2.08038	−	5.71579i	0.214575	−	0.589539i
$95$	−1.53976	+	4.23045i	−0.157976	+	0.434035i
$96$	−0.0140409	+	0.738527i	−0.00143304	+	0.0753756i
$97$	15.0854	+	2.65997i	1.53169	+	0.270079i	0.875016	−	0.484094i	$-0.160851\pi$
$97$	15.0854	+	2.65997i	1.53169	+	0.270079i	0.656676	+	0.754172i	$0.271962\pi$
$98$	−5.77318	+	8.26840i	−0.583179	+	0.835235i
$99$	−5.33478	−	3.35668i	−0.536165	−	0.337359i
$100$	0.0538713	−	0.0933079i	0.00538713	−	0.00933079i
$101$	8.06029	+	6.76338i	0.802028	+	0.672982i	0.948691	−	0.316205i	$-0.102409\pi$
$101$	8.06029	+	6.76338i	0.802028	+	0.672982i	−0.146662	+	0.989187i	$0.546853\pi$
$102$	12.3590	+	15.3108i	1.22373	+	1.51600i
$103$	−8.05199	+	1.41978i	−0.793386	+	0.139895i	−0.555630	−	0.831429i	$-0.687523\pi$
$103$	−8.05199	+	1.41978i	−0.793386	+	0.139895i	−0.237756	+	0.971325i	$0.576412\pi$
$104$	−0.205595	+	0.172514i	−0.0201602	+	0.0169164i
$105$	10.2059	+	5.55309i	0.995990	+	0.541926i
$106$	12.5248	−	4.55864i	1.21651	−	0.442774i
$107$			8.64958i			0.836187i	0.908404	+	0.418093i	$0.137302\pi$
$107$			8.64958i			0.836187i	−0.908404	+	0.418093i	$0.862698\pi$
$108$	−0.0459486	−	0.389238i	−0.00442140	−	0.0374544i
$109$	−2.35627			−0.225690			−0.112845	−	0.993613i	$-0.535996\pi$
$109$	−2.35627			−0.225690			−0.112845	+	0.993613i	$0.535996\pi$
$110$	7.21130	−	2.62470i	0.687570	−	0.250255i
$111$	−6.16888	+	2.11338i	−0.585524	+	0.200593i
$112$	6.67053	−	8.70522i	0.630306	−	0.822566i
$113$	−9.10544	+	1.60554i	−0.856568	+	0.151036i	−0.584651	−	0.811285i	$-0.698769\pi$
$113$	−9.10544	+	1.60554i	−0.856568	+	0.151036i	−0.271917	+	0.962321i	$0.587658\pi$
$114$	−4.13386	−	1.59423i	−0.387171	−	0.149313i
$115$	9.70830	−	11.5699i	0.905304	−	1.07890i
$116$	−0.109457	−	0.0631952i	−0.0101629	−	0.00586753i
$117$	0.194984	−	0.215201i	0.0180263	−	0.0198953i
$118$	9.21597	−	5.32084i	0.848399	−	0.489823i
$119$	−0.923944	−	20.8429i	−0.0846978	−	1.91066i
$120$	−10.4270	−	6.28727i	−0.951849	−	0.573947i
$121$	−6.18870	−	2.25250i	−0.562609	−	0.204773i
$122$	−16.4453	−	5.98559i	−1.48888	−	0.541909i
$123$	−2.47488	+	4.10441i	−0.223152	+	0.370082i
$124$	0.105867	+	0.0186672i	0.00950715	+	0.00167637i
$125$	−4.52777	−	7.84233i	−0.404976	−	0.701439i
$126$	−5.65504	+	9.93844i	−0.503791	+	0.885387i
$127$	9.01241	−	15.6100i	0.799722	−	1.38516i	−0.120075	−	0.992765i	$-0.538314\pi$
$127$	9.01241	−	15.6100i	0.799722	−	1.38516i	0.919797	−	0.392394i	$-0.128353\pi$
$128$	−7.65636	+	9.12449i	−0.676733	+	0.806499i
$129$	−9.63382	−	3.71529i	−0.848210	−	0.327113i
$130$	0.0613968	+	0.348198i	0.00538485	+	0.0305390i
$131$	−1.18288	+	0.992556i	−0.103349	+	0.0867200i	−0.692998	−	0.720940i	$-0.743711\pi$
$131$	−1.18288	+	0.992556i	−0.103349	+	0.0867200i	0.589649	+	0.807660i	$0.299266\pi$
$132$	0.0889600	+	0.259671i	0.00774298	+	0.0226015i
$133$	2.52679	+	3.96044i	0.219101	+	0.343413i
$134$		−	16.2967i		−	1.40782i
$135$	12.1030	+	5.20425i	1.04166	+	0.447910i
$136$			21.8636i			1.87479i
$137$	4.78721	+	13.1528i	0.408999	+	1.12372i	0.957718	+	0.287709i	$0.0928937\pi$
$137$	4.78721	+	13.1528i	0.408999	+	1.12372i	−0.548718	+	0.836007i	$0.684884\pi$
$138$	11.2029	+	9.76918i	0.953654	+	0.831608i
$139$	−11.1981	−	13.3454i	−0.949810	−	1.13194i	−0.991144	−	0.132794i	$-0.957605\pi$
$139$	−11.1981	−	13.3454i	−0.949810	−	1.13194i	0.0413335	−	0.999145i	$-0.486839\pi$
$140$	−0.193944	−	0.467341i	−0.0163913	−	0.0394975i
$141$	−5.69044	+	4.59338i	−0.479222	+	0.386833i
$142$	−15.1941	−	12.7494i	−1.27506	−	1.06991i
$143$	−0.101686	+	0.176126i	−0.00850343	+	0.0147284i
$144$	6.62261	−	10.5253i	0.551884	−	0.877112i
$145$	3.67924	−	2.12421i	0.305544	−	0.176406i
$146$	−3.47364	+	19.7000i	−0.287481	+	1.63038i
$147$	11.0772	−	4.92895i	0.913636	−	0.406533i
$148$	0.266850	+	0.0971254i	0.0219349	+	0.00798366i
$149$	1.16714	−	3.20670i	0.0956160	−	0.262703i	−0.882659	−	0.470014i	$-0.844249\pi$
$149$	1.16714	−	3.20670i	0.0956160	−	0.262703i	0.978275	+	0.207311i	$0.0664712\pi$
$150$	−3.12002	+	1.72311i	−0.254749	+	0.140692i
$151$	2.20278	−	12.4926i	0.179260	−	1.01663i	−0.753852	−	0.657044i	$-0.771806\pi$
$151$	2.20278	−	12.4926i	0.179260	−	1.01663i	0.933111	−	0.359587i	$-0.117083\pi$
$152$	−2.46154	−	4.26352i	−0.199658	−	0.345817i
$153$	−3.21945	−	23.4367i	−0.260277	−	1.89474i
$154$	2.40297	−	7.63899i	0.193636	−	0.615567i
$155$	−2.32268	+	2.76807i	−0.186563	+	0.222337i
$156$	−0.0124938	+	0.00195890i	−0.00100031	+	0.000156837i
$157$	−14.4524	+	2.54834i	−1.15343	+	0.203380i	−0.717471	−	0.696589i	$-0.754700\pi$
$157$	−14.4524	+	2.54834i	−1.15343	+	0.203380i	−0.435955	+	0.899969i	$0.643589\pi$
$158$	−5.73960	−	6.84019i	−0.456618	−	0.544176i
$159$	−15.7255	−	3.08214i	−1.24712	−	0.244430i
$160$	0.369817	+	1.01607i	0.0292366	+	0.0803270i
$161$	−3.42148	−	15.3848i	−0.269651	−	1.21249i
$162$	−5.34727	+	11.8117i	−0.420121	+	0.928015i
$163$	1.55651			0.121915			0.0609577	−	0.998140i	$-0.480585\pi$
$163$	1.55651			0.121915			0.0609577	+	0.998140i	$0.480585\pi$
$164$	0.196135	−	0.0713873i	0.0153156	−	0.00557441i
$165$	−9.05418	−	1.77458i	−0.704867	−	0.138151i
$166$	8.55069	+	10.1903i	0.663662	+	0.790922i
$167$	0.221778	+	1.25777i	0.0171617	+	0.0973290i	0.992186	−	0.124772i	$-0.0398198\pi$
$167$	0.221778	+	1.25777i	0.0171617	+	0.0973290i	−0.975024	+	0.222101i	$0.928709\pi$
$168$	−11.8257	+	4.64612i	−0.912374	+	0.358456i
$169$	9.95140	+	8.35022i	0.765492	+	0.642324i
$170$	24.9442	+	14.4016i	1.91314	+	1.10455i
$171$	3.26646	+	4.20781i	0.249792	+	0.321779i
$172$	0.224830	+	0.389417i	0.0171431	+	0.0296928i
$173$	1.16666	−	6.61644i	0.0886992	−	0.503038i	−0.907798	−	0.419408i	$-0.862238\pi$
$173$	1.16666	−	6.61644i	0.0886992	−	0.503038i	0.996497	−	0.0836300i	$-0.0266514\pi$
$174$	2.02134	+	3.66002i	0.153238	+	0.277466i
$175$	3.74719	+	0.490785i	0.283261	+	0.0370998i
$176$	−2.97863	+	8.18371i	−0.224523	+	0.616871i
$177$	−12.7920	−	0.243202i	−0.961506	−	0.0182802i
$178$	−17.8330	−	3.14443i	−1.33664	−	0.235685i
$179$	−2.71116	+	1.56529i	−0.202642	+	0.116995i	−0.597887	−	0.801580i	$-0.703993\pi$
$179$	−2.71116	+	1.56529i	−0.202642	+	0.116995i	0.395245	+	0.918576i	$0.370660\pi$
$180$	−0.267774	−	0.507413i	−0.0199587	−	0.0378204i
$181$	3.24378	+	1.87280i	0.241108	+	0.139204i	0.615686	−	0.787992i	$-0.288879\pi$
$181$	3.24378	+	1.87280i	0.241108	+	0.139204i	−0.374578	+	0.927196i	$0.622212\pi$
$182$	0.327380	+	0.170146i	0.0242670	+	0.0126121i
$183$	13.2159	+	16.3723i	0.976949	+	1.21028i
$184$	2.86802	+	16.2654i	0.211433	+	1.19910i
$185$	−7.31221	+	6.13567i	−0.537604	+	0.451104i
$186$	−2.68026	−	2.33725i	−0.196526	−	0.171376i
$187$	5.66642	+	15.5684i	0.414369	+	1.13847i
$188$	0.318474			0.0232271
$189$	11.9924	−	6.72176i	0.872320	−	0.488936i
$190$	−6.48567			−0.470520
$191$	−0.477709	−	1.31249i	−0.0345658	−	0.0949687i	0.921209	−	0.389068i	$-0.127203\pi$
$191$	−0.477709	−	1.31249i	−0.0345658	−	0.0949687i	−0.955775	+	0.294099i	$0.904981\pi$
$192$	12.5775	−	4.30890i	0.907705	−	0.310968i
$193$	0.851514	−	0.714505i	0.0612933	−	0.0514312i	−0.611626	−	0.791147i	$-0.709484\pi$
$193$	0.851514	−	0.714505i	0.0612933	−	0.0514312i	0.672920	+	0.739716i	$0.265040\pi$
$194$	3.83204	+	21.7326i	0.275125	+	1.56031i
$195$	0.152956	−	0.396619i	0.0109534	−	0.0284025i
$196$	−0.510193	−	0.135977i	−0.0364424	−	0.00971263i
$197$	3.19302	+	1.84349i	0.227493	+	0.131343i	0.609415	−	0.792851i	$-0.291404\pi$
$197$	3.19302	+	1.84349i	0.227493	+	0.131343i	−0.381922	+	0.924195i	$0.624738\pi$
$198$	1.91553	−	8.87590i	0.136131	−	0.630783i
$199$	−15.0783	+	8.70545i	−1.06887	+	0.617113i	−0.927873	−	0.372897i	$-0.878364\pi$
$199$	−15.0783	+	8.70545i	−1.06887	+	0.617113i	−0.140998	+	0.990010i	$0.545031\pi$
$200$	−3.90022	−	0.687714i	−0.275787	−	0.0486287i
$201$	−10.1174	+	16.7789i	−0.713625	+	1.18350i
$202$	−5.18444	+	14.2441i	−0.364776	+	1.00221i
$203$	0.575728	−	4.39574i	0.0404082	−	0.308520i
$204$	−0.531980	+	0.882251i	−0.0372461	+	0.0617699i
$205$	−1.21830	+	6.90930i	−0.0850894	+	0.482566i
$206$	−5.88947	−	10.2009i	−0.410338	−	0.710727i
$207$	−5.46947	−	17.0133i	−0.380154	−	1.18251i
$208$	−0.347490	−	0.200624i	−0.0240941	−	0.0139107i
$209$	−2.85776	−	2.39795i	−0.197675	−	0.165869i
$210$	−2.48883	+	16.5524i	−0.171745	+	1.14222i
$211$	−0.368145	−	2.08786i	−0.0253442	−	0.143734i	0.969510	−	0.245052i	$-0.0788051\pi$
$211$	−0.368145	−	2.08786i	−0.0253442	−	0.143734i	−0.994854	+	0.101318i	$0.967694\pi$
$212$	0.448576	+	0.534591i	0.0308083	+	0.0367159i
$213$	7.72863	+	22.5596i	0.529557	+	1.54576i
$214$	−11.7094	+	4.26188i	−0.800439	+	0.291336i
$215$	−15.1146			−1.03081
$216$	−12.8670	+	6.48058i	−0.875490	+	0.440947i
$217$	0.818580	+	3.68076i	0.0555689	+	0.249866i
$218$	−1.16099	−	3.18981i	−0.0786325	−	0.216041i
$219$	15.8067	−	18.1265i	1.06812	−	1.22487i
$220$	0.258273	+	0.307798i	0.0174128	+	0.0207517i
$221$	−0.751719	+	0.132548i	−0.0505661	+	0.00891617i
$222$	−5.90056	−	7.30982i	−0.396020	−	0.490603i
$223$	15.8310	−	18.8667i	1.06012	−	1.26341i	0.0967321	−	0.995310i	$-0.469161\pi$
$223$	15.8310	−	18.8667i	1.06012	−	1.26341i	0.963392	−	0.268096i	$-0.0863946\pi$
$224$	1.07633	+	0.338576i	0.0719151	+	0.0226220i
$225$	4.28210	+	0.162882i	0.285473	+	0.0108588i
$226$	−6.65999	−	11.5354i	−0.443016	−	0.767326i
$227$	−0.274602	+	1.55735i	−0.0182260	+	0.103365i	−0.992564	−	0.121727i	$-0.961157\pi$
$227$	−0.274602	+	1.55735i	−0.0182260	+	0.103365i	0.974338	+	0.225091i	$0.0722680\pi$
$228$	0.00440959	−	0.231937i	0.000292032	−	0.0153604i
$229$	4.53395	−	12.4569i	0.299612	−	0.823176i	−0.694953	−	0.719055i	$-0.744575\pi$
$229$	4.53395	−	12.4569i	0.299612	−	0.823176i	0.994565	−	0.104121i	$-0.0332029\pi$
$230$	20.4463	+	7.44186i	1.34819	+	0.490702i
$231$	−7.21655	+	6.37323i	−0.474814	+	0.419328i
$232$	−0.806741	+	4.57526i	−0.0529651	+	0.300380i
$233$	−13.6803	+	7.89830i	−0.896223	+	0.517435i	−0.875973	−	0.482360i	$-0.839780\pi$
$233$	−13.6803	+	7.89830i	−0.896223	+	0.517435i	−0.0202503	+	0.999795i	$0.506446\pi$
$234$	0.387402	+	0.157925i	0.0253253	+	0.0103239i
$235$	−5.35251	+	9.27083i	−0.349160	+	0.604762i
$236$	0.426824	+	0.358148i	0.0277839	+	0.0233134i
$237$	1.66289	+	10.6059i	0.108016	+	0.688927i
$238$	27.7608	−	11.5206i	1.79947	−	0.746770i
$239$	−2.51826	−	3.00115i	−0.162893	−	0.194128i	0.678424	−	0.734671i	$-0.262663\pi$
$239$	−2.51826	−	3.00115i	−0.162893	−	0.194128i	−0.841317	+	0.540543i	$0.818219\pi$
$240$	3.50119	−	17.8636i	0.226001	−	1.15309i
$241$	−8.25538	−	22.6815i	−0.531776	−	1.46104i	−0.856956	−	0.515390i	$-0.827647\pi$
$241$	−8.25538	−	22.6815i	−0.531776	−	1.46104i	0.325180	−	0.945652i	$-0.394575\pi$
$242$		−	9.48784i		−	0.609901i
$243$	12.8385	−	8.84153i	0.823591	−	0.567184i
$244$		−	0.916303i		−	0.0586603i
$245$	12.5330	−	12.5665i	0.800703	−	0.802842i
$246$	−6.77579	−	1.32803i	−0.432009	−	0.0846720i
$247$	0.131666	−	0.110481i	0.00837770	−	0.00702973i
$248$	−0.686166	−	3.89144i	−0.0435716	−	0.247107i
$249$	−2.47733	−	15.8004i	−0.156994	−	1.00131i
$250$	8.38563	−	9.99361i	0.530354	−	0.632051i
$251$	3.34189	−	5.78833i	0.210938	−	0.365356i	−0.741070	−	0.671428i	$-0.765681\pi$
$251$	3.34189	−	5.78833i	0.210938	−	0.365356i	0.952008	+	0.306072i	$0.0990147\pi$
$252$	−0.590245	−	0.100258i	−0.0371819	−	0.00631565i
$253$	6.25773	+	10.8387i	0.393420	+	0.681424i
$254$	25.5727	+	4.50915i	1.60457	+	0.282929i
$255$	−16.7416	−	30.3138i	−1.04840	−	1.89832i
$256$	−1.69873	−	0.618288i	−0.106171	−	0.0386430i
$257$	19.9314	+	7.25443i	1.24329	+	0.452519i	0.878128	−	0.478426i	$-0.158793\pi$
$257$	19.9314	+	7.25443i	1.24329	+	0.452519i	0.365158	+	0.930945i	$0.381015\pi$
$258$	0.282755	−	14.8724i	0.0176036	−	0.925918i
$259$	0.441118	+	9.95098i	0.0274097	+	0.618324i
$260$	−0.0160321	+	0.00925613i	−0.000994268	+	0.000574041i
$261$	0.191073	−	5.02323i	0.0118271	−	0.310930i
$262$	−1.92651	−	1.11227i	−0.119020	−	0.0687165i
$263$	7.88441	−	9.39628i	0.486174	−	0.579399i	−0.466066	−	0.884750i	$-0.654329\pi$
$263$	7.88441	−	9.39628i	0.486174	−	0.579399i	0.952240	+	0.305350i	$0.0987736\pi$
$264$	7.85091	−	6.33733i	0.483190	−	0.390036i
$265$	−23.1011	+	4.07335i	−1.41909	+	0.250224i
$266$	−4.11644	+	5.37206i	−0.252395	+	0.329382i
$267$	16.4086	+	14.3086i	1.00419	+	0.875674i
$268$	0.801806	−	0.291833i	0.0489781	−	0.0178266i
$269$	12.8959			0.786276			0.393138	−	0.919480i	$-0.371390\pi$
$269$	12.8959			0.786276			0.393138	+	0.919480i	$0.371390\pi$
$270$	−1.08180	+	18.9488i	−0.0658365	+	1.15318i
$271$		−	15.7114i		−	0.954402i	−0.878794	−	0.477201i	$-0.841651\pi$
$271$		−	15.7114i		−	0.954402i	0.878794	−	0.477201i	$-0.158349\pi$
$272$	−30.7158	+	11.1797i	−1.86242	+	0.677866i
$273$	−0.231437	−	0.378427i	−0.0140072	−	0.0229034i
$274$	−15.4468	+	12.9614i	−0.933177	+	0.783028i
$275$	−2.95545	+	0.521125i	−0.178220	+	0.0314250i
$276$	−0.280033	+	0.726131i	−0.0168560	+	0.0437079i
$277$	10.1616	+	8.52659i	0.610551	+	0.512313i	0.894817	−	0.446432i	$-0.147306\pi$
$277$	10.1616	+	8.52659i	0.610551	+	0.512313i	−0.284267	+	0.958745i	$0.591750\pi$
$278$	12.5488	−	21.7351i	0.752624	−	1.30358i
$279$	1.30856	+	4.07039i	0.0783412	+	0.243688i
$280$	−13.7042	+	12.5744i	−0.818983	+	0.751465i
$281$	−13.8620	−	2.44425i	−0.826938	−	0.145811i	−0.255867	−	0.966712i	$-0.582361\pi$
$281$	−13.8620	−	2.44425i	−0.826938	−	0.145811i	−0.571071	+	0.820901i	$0.693472\pi$
$282$	−9.02214	−	5.44018i	−0.537261	−	0.323958i
$283$	−2.86418	+	7.86927i	−0.170258	+	0.467779i	−0.995249	−	0.0973668i	$-0.968958\pi$
$283$	−2.86418	+	7.86927i	−0.170258	+	0.467779i	0.824991	+	0.565146i	$0.191180\pi$
$284$	0.355188	−	0.975871i	0.0210765	−	0.0579073i
$285$	6.67760	+	4.02646i	0.395547	+	0.238507i
$286$	−0.288534	−	0.0508764i	−0.0170614	−	0.00300838i
$287$	4.94970	+	5.39443i	0.292172	+	0.318423i
$288$	1.25061	+	0.269896i	0.0736926	+	0.0159038i
$289$	−22.5913	+	39.1293i	−1.32890	+	2.30172i
$290$	4.68851	+	3.93413i	0.275319	+	0.231020i
$291$	9.54669	−	24.7547i	0.559637	−	1.45115i
$292$	−1.03146	+	0.181874i	−0.0603614	+	0.0106433i
$293$	13.8218	−	11.5979i	0.807477	−	0.677554i	−0.142527	−	0.989791i	$-0.545523\pi$
$293$	13.8218	−	11.5979i	0.807477	−	0.677554i	0.950004	+	0.312237i	$0.101078\pi$
$294$	12.1306	+	12.5672i	0.707473	+	0.732937i
$295$	−17.5992	+	6.40560i	−1.02467	+	0.372948i
$296$		−	10.4383i		−	0.606716i
$297$	−7.48259	+	7.94935i	−0.434184	+	0.461268i
$298$	4.91616			0.284785
$299$	−0.541851	+	0.197218i	−0.0313361	+	0.0114054i
$300$	−0.140650	−	0.122650i	−0.00812043	−	0.00708120i
$301$	−9.59323	+	12.5194i	−0.552944	+	0.721607i
$302$	17.9972	−	3.17340i	1.03563	−	0.182609i
$303$	14.1810	−	11.4470i	0.814676	−	0.657615i
$304$	4.73107	−	5.63827i	0.271345	−	0.323377i
$305$	26.6737	+	15.4001i	1.52733	+	0.881805i
$306$	30.1412	−	15.9062i	1.72306	−	0.909298i
$307$	1.13352	−	0.654438i	0.0646934	−	0.0373507i	−0.467304	−	0.884096i	$-0.654775\pi$
$307$	1.13352	−	0.654438i	0.0646934	−	0.0373507i	0.531998	+	0.846746i	$0.321441\pi$
$308$	0.418874	−	0.0185683i	0.0238676	−	0.00105803i
$309$	−0.269192	+	14.1590i	−0.0153138	+	0.805480i
$310$	−4.89173	−	1.78044i	−0.277832	−	0.101122i
$311$	−22.9897	−	8.36756i	−1.30363	−	0.474481i	−0.405450	−	0.914117i	$-0.632885\pi$
$311$	−22.9897	−	8.36756i	−1.30363	−	0.474481i	−0.898176	+	0.439637i	$0.855107\pi$
$312$	0.224734	+	0.406922i	0.0127230	+	0.0230374i
$313$	−0.0802239	−	0.0141456i	−0.00453453	−	0.000799559i	0.171380	−	0.985205i	$-0.445177\pi$
$313$	−0.0802239	−	0.0141456i	−0.00453453	−	0.000799559i	−0.175915	+	0.984405i	$0.556288\pi$
$314$	−10.5709	−	18.3093i	−0.596550	−	1.03326i
$315$	12.8386	−	15.4971i	0.723373	−	0.873162i
$316$	0.233759	−	0.404882i	0.0131500	−	0.0227764i
$317$	8.06845	−	9.61560i	0.453169	−	0.540066i	−0.490288	−	0.871560i	$-0.663108\pi$
$317$	8.06845	−	9.61560i	0.453169	−	0.540066i	0.943457	+	0.331495i	$0.107553\pi$
$318$	−3.57592	−	22.8071i	−0.200528	−	1.27896i
$319$	0.611320	+	3.46697i	0.0342273	+	0.194113i
$320$	14.9086	−	12.5098i	0.833418	−	0.699321i
$321$	14.7018	+	2.88149i	0.820575	+	0.160829i
$322$	19.1413	−	12.2123i	1.06670	−	0.680566i
$323$		−	14.0018i		−	0.779081i
$324$	−0.676899	−	0.0515701i	−0.0376055	−	0.00286500i
$325$		−	0.138267i		−	0.00766969i
$326$	0.766934	+	2.10713i	0.0424765	+	0.116703i
$327$	−0.784959	+	4.00498i	−0.0434084	+	0.221476i
$328$	−4.93158	−	5.87723i	−0.272301	−	0.324516i
$329$	4.28177	+	10.3176i	0.236062	+	0.568830i
$330$	−2.05888	−	13.1315i	−0.113338	−	0.722866i
$331$	8.49272	+	7.12624i	0.466802	+	0.391693i	0.845626	−	0.533775i	$-0.179227\pi$
$331$	8.49272	+	7.12624i	0.466802	+	0.391693i	−0.378824	+	0.925469i	$0.623672\pi$
$332$	−0.348247	+	0.603182i	−0.0191126	+	0.0331039i
$333$	1.53706	+	11.1894i	0.0842303	+	0.613173i
$334$	−1.59343	+	0.919969i	−0.0871888	+	0.0503385i
$335$	−4.98043	+	28.2454i	−0.272110	+	1.54321i
$336$	−12.5742	−	14.2380i	−0.685977	−	0.776747i
$337$	−0.468324	−	0.170456i	−0.0255113	−	0.00928534i	0.329233	−	0.944249i	$-0.393210\pi$
$337$	−0.468324	−	0.170456i	−0.0255113	−	0.00928534i	−0.354744	+	0.934963i	$0.615432\pi$
$338$	−6.40082	+	17.5861i	−0.348159	+	0.956559i
$339$	−0.304411	+	16.0115i	−0.0165333	+	0.869625i
$340$	−0.261875	+	1.48517i	−0.0142022	+	0.0805445i
$341$	−1.49714	−	2.59313i	−0.0810749	−	0.140426i
$342$	−4.08687	+	6.49528i	−0.220992	+	0.351224i
$343$	−2.45411	−	18.3569i	−0.132509	−	0.991182i
$344$	10.6243	−	12.6616i	0.572825	−	0.682667i
$345$	−16.4313	−	20.3557i	−0.884632	−	1.09591i
$346$	9.53187	−	1.68073i	0.512437	−	0.0903564i
$347$	23.1420	+	27.5795i	1.24233	+	1.48055i	0.818190	+	0.574948i	$0.194978\pi$
$347$	23.1420	+	27.5795i	1.24233	+	1.48055i	0.424136	+	0.905599i	$0.360578\pi$
$348$	−0.143878	+	0.164993i	−0.00771266	+	0.00884457i
$349$	8.71674	+	23.9491i	0.466597	+	1.28196i	0.920441	+	0.390882i	$0.127830\pi$
$349$	8.71674	+	23.9491i	0.466597	+	1.28196i	−0.453844	+	0.891081i	$0.649948\pi$
$350$	1.18193	+	5.31459i	0.0631771	+	0.284077i
$351$	−0.300823	−	0.403108i	−0.0160567	−	0.0215163i
$352$	−0.895997			−0.0477568
$353$	−14.7098	+	5.35392i	−0.782922	+	0.284960i	−0.702391	−	0.711792i	$-0.747884\pi$
$353$	−14.7098	+	5.35392i	−0.782922	+	0.284960i	−0.0805314	+	0.996752i	$0.525662\pi$
$354$	−5.97372	−	17.4371i	−0.317500	−	0.926769i
$355$	22.4382	+	26.7408i	1.19089	+	1.41925i
$356$	−0.164637	−	0.933701i	−0.00872573	−	0.0494861i
$357$	−35.7346	−	5.37308i	−1.89128	−	0.284374i
$358$	−3.45488	−	2.89899i	−0.182596	−	0.153216i
$359$	−4.91929	−	2.84015i	−0.259630	−	0.149898i	0.364536	−	0.931189i	$-0.381228\pi$
$359$	−4.91929	−	2.84015i	−0.259630	−	0.149898i	−0.624166	+	0.781292i	$0.714561\pi$
$360$	−14.1602	+	15.6283i	−0.746306	+	0.823686i
$361$	−7.92359	−	13.7241i	−0.417031	−	0.722319i
$362$	−0.937012	+	5.31406i	−0.0492482	+	0.279301i
$363$	−5.89029	+	9.76861i	−0.309160	+	0.512719i
$364$	−0.00250870	+	0.0191542i	−0.000131492	+	0.00100395i
$365$	12.0410	−	33.0825i	0.630257	−	1.73162i
$366$	−15.6523	+	25.9582i	−0.818158	+	1.35686i
$367$	18.6146	+	3.28226i	0.971675	+	0.171332i	0.636884	−	0.770960i	$-0.280223\pi$
$367$	18.6146	+	3.28226i	0.971675	+	0.171332i	0.334791	+	0.942292i	$0.391334\pi$
$368$	−21.3844	+	12.3463i	−1.11474	+	0.643595i
$369$	6.15183	+	5.57391i	0.320252	+	0.290166i
$370$	−11.9091	−	6.87573i	−0.619125	−	0.357452i
$371$	−11.2883	+	21.7199i	−0.586058	+	1.12764i
$372$	0.0669971	−	0.173725i	0.00347364	−	0.00900721i
$373$	−2.60608	−	14.7798i	−0.134938	−	0.765269i	−0.974903	−	0.222629i	$-0.928536\pi$
$373$	−2.60608	−	14.7798i	−0.134938	−	0.765269i	0.839966	−	0.542640i	$-0.182575\pi$
$374$	−18.2837	+	15.3419i	−0.945429	+	0.793309i
$375$	−14.8381	+	5.08334i	−0.766234	+	0.262502i
$376$	−4.00383	−	11.0004i	−0.206482	−	0.567304i
$377$	−0.162198			−0.00835363
$378$	15.0086	+	12.9228i	0.771958	+	0.664677i
$379$	−2.87213			−0.147532			−0.0737658	−	0.997276i	$-0.523502\pi$
$379$	−2.87213			−0.147532			−0.0737658	+	0.997276i	$0.523502\pi$
$380$	−0.116142	−	0.319099i	−0.00595798	−	0.0163694i
$381$	−23.5301	−	20.5187i	−1.20548	−	1.05121i
$382$	1.54141	−	1.29340i	0.0788656	−	0.0661761i
$383$	−2.37952	−	13.4949i	−0.121588	−	0.689558i	−0.983276	−	0.182121i	$-0.941704\pi$
$383$	−2.37952	−	13.4949i	−0.121588	−	0.689558i	0.861689	−	0.507438i	$-0.169407\pi$
$384$	12.9584	+	16.0533i	0.661280	+	0.819217i
$385$	−6.49938	+	12.5055i	−0.331239	+	0.637341i
$386$	1.38683	+	0.800685i	0.0705876	+	0.0407538i
$387$	−9.52430	+	15.1370i	−0.484147	+	0.769458i
$388$	−1.00063	+	0.577716i	−0.0507994	+	0.0293291i
$389$	−14.2770	−	2.51742i	−0.723872	−	0.127638i	−0.200440	−	0.979706i	$-0.564237\pi$
$389$	−14.2770	−	2.51742i	−0.723872	−	0.127638i	−0.523432	+	0.852068i	$0.675348\pi$
$390$	0.612290	+	0.0116409i	0.0310045	+	0.000589458i
$391$	−16.0661	+	44.1413i	−0.812498	+	2.23232i
$392$	1.71732	+	19.3321i	0.0867379	+	0.976419i
$393$	1.29300	+	2.34122i	0.0652231	+	0.118099i
$394$	−0.922349	+	5.23090i	−0.0464673	+	0.263529i
$395$	7.85745	+	13.6095i	0.395351	+	0.684768i
$396$	0.471002	−	0.0647005i	0.0236687	−	0.00325132i
$397$	−30.4332	−	17.5706i	−1.52740	−	0.881845i	−0.999470	−	0.0325575i	$-0.989635\pi$
$397$	−30.4332	−	17.5706i	−1.52740	−	0.881845i	−0.527931	−	0.849288i	$-0.677032\pi$
$398$	−19.2145	−	16.1229i	−0.963135	−	0.808167i
$399$	7.57337	−	2.97545i	0.379143	−	0.148959i
$400$	−1.02816	−	5.83100i	−0.0514082	−	0.291550i
$401$	5.80377	+	6.91666i	0.289826	+	0.345402i	0.891237	−	0.453539i	$-0.149839\pi$
$401$	5.80377	+	6.91666i	0.289826	+	0.345402i	−0.601410	+	0.798940i	$0.705394\pi$
$402$	−27.6997	−	5.42902i	−1.38153	−	0.270775i
$403$	0.129636	−	0.0471838i	0.00645765	−	0.00235039i
$404$	−0.793660			−0.0394861
$405$	12.8777	−	18.8379i	0.639897	−	0.936062i
$406$	6.23442	−	1.38650i	0.309409	−	0.0688108i
$407$	−2.70531	−	7.43278i	−0.134097	−	0.368429i
$408$	37.1619	+	7.28358i	1.83979	+	0.360591i
$409$	7.60537	+	9.06373i	0.376062	+	0.448173i	0.920567	−	0.390585i	$-0.127727\pi$
$409$	7.60537	+	9.06373i	0.376062	+	0.448173i	−0.544506	+	0.838757i	$0.683283\pi$
$410$	−9.95377	+	1.75512i	−0.491582	+	0.0866791i
$411$	23.9507	−	3.75522i	1.18140	−	0.185231i
$412$	0.396422	−	0.472437i	0.0195303	−	0.0232753i
$413$	−5.86446	+	18.6430i	−0.288571	+	0.917363i
$414$	20.3369	−	15.7872i	0.999504	−	0.775900i
$415$	−11.7058	−	20.2750i	−0.574615	−	0.995263i
$416$	0.00716844	−	0.0406542i	0.000351461	−	0.00199324i
$417$	−26.4138	+	14.5877i	−1.29349	+	0.714363i
$418$	1.83814	−	5.05024i	0.0899061	−	0.247015i
$419$	18.4999	+	6.73342i	0.903780	+	0.328949i	0.751767	−	0.659429i	$-0.229202\pi$
$419$	18.4999	+	6.73342i	0.903780	+	0.328949i	0.152014	+	0.988378i	$0.451424\pi$
$420$	−0.858955	+	0.173961i	−0.0419127	+	0.00848841i
$421$	2.28747	−	12.9729i	0.111485	−	0.632260i	−0.876946	−	0.480588i	$-0.840423\pi$
$421$	2.28747	−	12.9729i	0.111485	−	0.632260i	0.988431	−	0.151672i	$-0.0484657\pi$
$422$	2.64505	−	1.52712i	0.128759	−	0.0743390i
$423$	5.91173	+	11.2023i	0.287438	+	0.544676i
$424$	12.8259	−	22.2151i	0.622881	−	1.07886i
$425$	−8.62855	−	7.24022i	−0.418546	−	0.351202i
$426$	−26.7320	+	21.5784i	−1.29517	+	1.04548i
$427$	29.6856	−	12.3194i	1.43659	−	0.596176i
$428$	−0.419373	−	0.499790i	−0.0202712	−	0.0241583i
$429$	0.265488	+	0.231511i	0.0128179	+	0.0111775i
$430$	−7.44737	−	20.4615i	−0.359144	−	0.986741i
$431$			18.5835i			0.895137i	0.894250	+	0.447568i	$0.147710\pi$
$431$			18.5835i			0.895137i	−0.894250	+	0.447568i	$0.852290\pi$
$432$	−15.6838	−	14.7629i	−0.754588	−	0.710281i
$433$		−	26.0198i		−	1.25043i	−0.780451	−	0.625217i	$-0.785010\pi$
$433$		−	26.0198i		−	1.25043i	0.780451	−	0.625217i	$-0.214990\pi$
$434$	−4.57951	+	2.92176i	−0.219823	+	0.140249i
$435$	−2.38485	−	6.96130i	−0.114345	−	0.333769i
$436$	0.136150	−	0.114243i	0.00652039	−	0.00547126i
$437$	−1.83673	−	10.4166i	−0.0878625	−	0.498293i
$438$	32.3271	+	12.4670i	1.54465	+	0.595696i
$439$	−8.67250	+	10.3355i	−0.413916	+	0.493286i	−0.932211	−	0.361916i	$-0.882123\pi$
$439$	−8.67250	+	10.3355i	−0.413916	+	0.493286i	0.518295	+	0.855202i	$0.326567\pi$
$440$	7.38468	−	12.7906i	0.352051	−	0.609770i
$441$	−4.68756	−	20.4701i	−0.223217	−	0.974769i
$442$	−0.549830	−	0.952333i	−0.0261527	−	0.0452979i
$443$	8.97414	+	1.58238i	0.426374	+	0.0751813i	0.382718	−	0.923865i	$-0.374988\pi$
$443$	8.97414	+	1.58238i	0.426374	+	0.0751813i	0.0436564	+	0.999047i	$0.486099\pi$
$444$	0.253983	−	0.421212i	0.0120535	−	0.0199898i
$445$	29.9472	+	10.8999i	1.41963	+	0.516704i
$446$	33.3412	+	12.1352i	1.57875	+	0.574619i
$447$	−5.06164	−	3.05207i	−0.239407	−	0.144358i
$448$	−0.899381	−	20.2887i	−0.0424917	−	0.958553i
$449$	9.47386	−	5.46974i	0.447099	−	0.258133i	−0.259505	−	0.965742i	$-0.583559\pi$
$449$	9.47386	−	5.46974i	0.447099	−	0.258133i	0.706604	+	0.707609i	$0.250226\pi$
$450$	1.88940	+	5.87717i	0.0890672	+	0.277052i
$451$	−5.03482	−	2.90685i	−0.237080	−	0.136878i
$452$	0.448286	−	0.534247i	0.0210856	−	0.0251288i
$453$	−20.5000	−	7.90583i	−0.963172	−	0.371448i
$454$	−2.24357	+	0.395601i	−0.105296	+	0.0185665i
$455$	−0.515417	−	0.394948i	−0.0241631	−	0.0185154i
$456$	−8.06678	+	2.76358i	−0.377762	+	0.129416i
$457$	6.62792	−	2.41237i	0.310041	−	0.112846i	−0.182313	−	0.983240i	$-0.558359\pi$
$457$	6.62792	−	2.41237i	0.310041	−	0.112846i	0.492355	+	0.870395i	$0.336136\pi$
$458$	19.0976			0.892372
$459$	−40.9081	−	2.33549i	−1.90943	−	0.109011i
$460$			1.13924i			0.0531172i
$461$	−19.9750	+	7.27029i	−0.930327	+	0.338611i	−0.762339	−	0.647178i	$-0.775949\pi$
$461$	−19.9750	+	7.27029i	−0.930327	+	0.338611i	−0.167988	+	0.985789i	$0.553727\pi$
$462$	−12.1836	−	6.62918i	−0.566831	−	0.308417i
$463$	−16.3752	+	13.7404i	−0.761019	+	0.638570i	−0.938392	−	0.345573i	$-0.887684\pi$
$463$	−16.3752	+	13.7404i	−0.761019	+	0.638570i	0.177373	+	0.984144i	$0.443240\pi$
$464$	−6.84021	+	1.20611i	−0.317549	+	0.0559924i
$465$	3.93115	+	4.87004i	0.182303	+	0.225843i
$466$	−17.4330	−	14.6280i	−0.807567	−	0.677629i
$467$	−19.8901	+	34.4506i	−0.920403	+	1.59418i	−0.121611	+	0.992578i	$0.538806\pi$
$467$	−19.8901	+	34.4506i	−0.920403	+	1.59418i	−0.798792	+	0.601607i	$0.794527\pi$
$468$	−0.000832588		0.0218885i	−3.84864e−5		0.00101179i
$469$	20.2345	+	22.0526i	0.934344	+	1.01829i
$470$	−15.1877	−	2.67801i	−0.700558	−	0.123527i
$471$	−0.483168	+	25.4138i	−0.0222632	+	1.17101i
$472$	7.00481	−	19.2455i	0.322422	−	0.885848i
$473$	4.28371	−	11.7694i	0.196965	−	0.541158i
$474$	−13.5384	+	7.47695i	−0.621840	+	0.343428i
$475$	2.49776	+	0.440422i	0.114605	+	0.0202080i
$476$	1.06395	+	1.15954i	0.0487660	+	0.0531476i
$477$	−10.4775	+	25.7021i	−0.479732	+	1.17682i
$478$	2.82200	−	4.88785i	0.129075	−	0.223565i
$479$	−5.68281	−	4.76844i	−0.259654	−	0.217876i	0.503662	−	0.863901i	$-0.331986\pi$
$479$	−5.68281	−	4.76844i	−0.259654	−	0.217876i	−0.763316	+	0.646025i	$0.776430\pi$
$480$	1.85022	−	0.290094i	0.0844505	−	0.0132409i
$481$	0.358893	−	0.0632825i	0.0163641	−	0.00288543i
$482$	26.6375	−	22.3515i	1.21330	−	1.01808i
$483$	−27.2895	+	0.690307i	−1.24171	+	0.0314101i
$484$	0.466807	−	0.169904i	0.0212185	−	0.00772290i
$485$		−	38.8381i		−	1.76355i
$486$	18.2951	+	13.0237i	0.829884	+	0.590768i
$487$	21.2597			0.963370			0.481685	−	0.876345i	$-0.340025\pi$
$487$	21.2597			0.963370			0.481685	+	0.876345i	$0.340025\pi$
$488$	−31.6501	+	11.5197i	−1.43273	+	0.521472i
$489$	0.518531	−	2.64562i	0.0234488	−	0.119639i
$490$	23.1872	+	10.7748i	1.04749	+	0.486754i
$491$	−36.4703	+	6.43071i	−1.64588	+	0.290214i	−0.918324	−	0.395830i	$-0.870457\pi$
$491$	−36.4703	+	6.43071i	−1.64588	+	0.290214i	−0.727560	+	0.686044i	$0.759346\pi$
$492$	−0.0559980	−	0.357154i	−0.00252459	−	0.0161018i
$493$	−8.49333	+	10.1220i	−0.382520	+	0.455870i
$494$	0.214439	+	0.123806i	0.00964807	+	0.00557032i
$495$	−6.03256	+	14.7983i	−0.271143	+	0.665135i
$496$	5.11616	−	2.95382i	0.229722	−	0.132630i
$497$	36.3907	−	1.61317i	1.63235	−	0.0723604i
$498$	20.1692	−	11.1389i	0.903801	−	0.499148i
$499$	−7.60426	−	2.76772i	−0.340413	−	0.123900i	0.166156	−	0.986099i	$-0.446864\pi$
$499$	−7.60426	−	2.76772i	−0.340413	−	0.123900i	−0.506569	+	0.862199i	$0.669087\pi$
$500$	0.641857	+	0.233617i	0.0287047	+	0.0104477i
$501$	2.21173	+	0.0420494i	0.0988126	+	0.00187863i
$502$	9.48261	+	1.67204i	0.423229	+	0.0746268i
$503$	−10.5540	−	18.2800i	−0.470578	−	0.815065i	0.528856	−	0.848712i	$-0.322621\pi$
$503$	−10.5540	−	18.2800i	−0.470578	−	0.815065i	−0.999434	+	0.0336470i	$0.989288\pi$
$504$	3.95749	+	21.6481i	0.176281	+	0.964283i
$505$	13.3388	−	23.1035i	0.593570	−	1.02809i
$506$	−11.5896	+	13.8119i	−0.515220	+	0.614016i
$507$	17.5081	−	14.1327i	0.777564	−	0.627657i
$508$	0.236091	+	1.33894i	0.0104748	+	0.0594058i
$509$	6.24961	−	5.24405i	0.277009	−	0.232438i	−0.493689	−	0.869638i	$-0.664352\pi$
$509$	6.24961	−	5.24405i	0.277009	−	0.232438i	0.770698	+	0.637200i	$0.219908\pi$
$510$	32.7884	−	37.6003i	1.45189	−	1.66497i
$511$	−19.7597	−	30.9710i	−0.874119	−	1.37007i
$512$			21.2181i			0.937714i
$513$	8.24024	−	4.15026i	0.363815	−	0.183238i
$514$			30.5566i			1.34780i
$515$	7.09014	+	19.4800i	0.312429	+	0.858392i
$516$	0.736796	−	0.252417i	0.0324356	−	0.0111120i
$517$	−5.70199	−	6.79536i	−0.250773	−	0.298860i
$518$	−13.2538	+	5.50027i	−0.582340	+	0.241668i
$519$	−10.8574	−	4.18716i	−0.476586	−	0.183796i
$520$	0.521271	+	0.437398i	0.0228592	+	0.0191812i
$521$	14.4293	−	24.9923i	0.632160	−	1.09493i	−0.354950	−	0.934885i	$-0.615502\pi$
$521$	14.4293	−	24.9923i	0.632160	−	1.09493i	0.987109	−	0.160047i	$-0.0511646\pi$
$522$	6.89437	−	2.21641i	0.301758	−	0.0970098i
$523$	4.15555	−	2.39921i	0.181710	−	0.104910i	−0.406386	−	0.913701i	$-0.633211\pi$
$523$	4.15555	−	2.39921i	0.181710	−	0.104910i	0.588096	+	0.808791i	$0.299878\pi$
$524$	0.0202253	−	0.114704i	0.000883548	−	0.00501085i
$525$	2.08252	−	6.20564i	0.0908885	−	0.270836i
$526$	16.6051	+	6.04377i	0.724017	+	0.263521i
$527$	3.84377	−	10.5607i	0.167437	−	0.460030i
$528$	12.9177	+	7.78910i	0.562169	+	0.338977i
$529$	−2.16806	+	12.2957i	−0.0942633	+	0.534594i
$530$	−16.8968	−	29.2662i	−0.733951	−	1.27124i
$531$	−4.67486	+	21.6617i	−0.202872	+	0.940038i
$532$	−0.338024	−	0.106331i	−0.0146552	−	0.00461002i
$533$	0.172174	−	0.205189i	0.00745770	−	0.00888774i
$534$	−11.2855	+	29.2634i	−0.488369	+	1.26635i
$535$	21.5972	−	3.80818i	0.933730	−	0.164642i
$536$	−20.1605	−	24.0263i	−0.870799	−	1.03778i
$537$	1.75735	+	5.12965i	0.0758354	+	0.221361i
$538$	6.35414	+	17.4578i	0.273946	+	0.752661i
$539$	6.23316	+	13.3207i	0.268481	+	0.573761i
$540$	−0.951662	+	0.286100i	−0.0409530	+	0.0123118i
$541$	42.2221			1.81527			0.907635	−	0.419760i	$-0.137886\pi$
$541$	42.2221			1.81527			0.907635	+	0.419760i	$0.137886\pi$
$542$	21.2694	−	7.74144i	0.913600	−	0.332523i
$543$	4.26384	−	4.88959i	0.182979	−	0.209833i
$544$	−2.16165	−	2.57616i	−0.0926802	−	0.110452i
$545$	1.03740	+	5.88339i	0.0444373	+	0.252017i
$546$	0.398261	−	0.499770i	0.0170440	−	0.0213882i
$547$	−15.5394	−	13.0391i	−0.664418	−	0.557513i	0.246989	−	0.969018i	$-0.420559\pi$
$547$	−15.5394	−	13.0391i	−0.664418	−	0.557513i	−0.911407	+	0.411505i	$0.865003\pi$
$548$	−0.914324	−	0.527885i	−0.0390580	−	0.0225501i
$549$	32.2310	−	17.0090i	1.37558	−	0.725928i
$550$	−2.16170	−	3.74418i	−0.0921753	−	0.159652i
$551$	0.516649	−	2.93006i	0.0220100	−	0.124825i
$552$	28.6019	+	0.543779i	1.21738	+	0.0231448i
$553$	16.2598	+	2.12962i	0.691438	+	0.0905605i
$554$	−6.53602	+	17.9576i	−0.277689	+	0.762944i
$555$	7.99291	+	14.4727i	0.339280	+	0.614330i
$556$	1.29410	+	0.228184i	0.0548819	+	0.00967715i
$557$	−1.84854	+	1.06725i	−0.0783251	+	0.0452210i	−0.538651	−	0.842529i	$-0.681066\pi$
$557$	−1.84854	+	1.06725i	−0.0783251	+	0.0452210i	0.460326	+	0.887750i	$0.347733\pi$
$558$	−4.86555	+	3.77705i	−0.205975	+	0.159895i
$559$	0.499743	+	0.288527i	0.0211369	+	0.0122034i
$560$	−24.6730	−	12.8231i	−1.04263	−	0.541873i
$561$	28.3494	−	4.44488i	1.19691	−	0.187663i
$562$	−3.52127	−	19.9701i	−0.148536	−	0.842387i
$563$	6.73571	−	5.65193i	0.283876	−	0.238200i	−0.489719	−	0.871880i	$-0.662901\pi$
$563$	6.73571	−	5.65193i	0.283876	−	0.238200i	0.773596	+	0.633680i	$0.218456\pi$
$564$	0.106096	−	0.541315i	0.00446743	−	0.0227935i
$565$	8.01775	+	22.0286i	0.337309	+	0.926750i
$566$	−12.0643			−0.507101
$567$	−7.42994	−	22.6229i	−0.312028	−	0.950073i
$568$	−38.1730			−1.60170
$569$	−12.2179	−	33.5684i	−0.512202	−	1.40726i	−0.878937	−	0.476937i	$-0.841747\pi$
$569$	−12.2179	−	33.5684i	−0.512202	−	1.40726i	0.366736	−	0.930325i	$-0.380475\pi$
$570$	−2.16062	+	11.0238i	−0.0904982	+	0.461735i
$571$	−5.96309	+	5.00363i	−0.249548	+	0.209395i	−0.758977	−	0.651117i	$-0.774301\pi$
$571$	−5.96309	+	5.00363i	−0.249548	+	0.209395i	0.509430	+	0.860512i	$0.329856\pi$
$572$	−0.00266379	−	0.0151071i	−0.000111379	−	0.000631661i
$573$	−2.39000	+	0.374727i	−0.0998438	+	0.0156544i
$574$	−4.86388	+	9.35865i	−0.203014	+	0.390623i
$575$	−7.36893	−	4.25446i	−0.307306	−	0.177423i
$576$	−3.13386	−	22.8136i	−0.130577	−	0.950568i
$577$	−17.2269	+	9.94598i	−0.717167	+	0.414056i	−0.813709	−	0.581272i	$-0.802555\pi$
$577$	−17.2269	+	9.94598i	−0.717167	+	0.414056i	0.0965422	+	0.995329i	$0.469222\pi$
$578$	−64.1027	−	11.3030i	−2.66632	−	0.470145i
$579$	−0.930782	−	1.68536i	−0.0386820	−	0.0700410i
$580$	−0.109602	+	0.301128i	−0.00455096	+	0.0125037i
$581$	−24.2234	−	3.17264i	−1.00496	−	0.131623i
$582$	38.2157	+	0.726558i	1.58409	+	0.0301168i
$583$	3.37538	−	19.1427i	0.139794	−	0.792811i
$584$	19.2495	+	33.3411i	0.796549	+	1.37966i
$585$	−0.623183	−	0.392110i	−0.0257654	−	0.0162118i
$586$	22.5110	+	12.9967i	0.929921	+	0.536890i
$587$	33.1432	+	27.8104i	1.36796	+	1.14786i	0.973432	+	0.228977i	$0.0735379\pi$
$587$	33.1432	+	27.8104i	1.36796	+	1.14786i	0.394533	+	0.918882i	$0.370907\pi$
$588$	−0.401086	+	0.821883i	−0.0165405	+	0.0338939i
$589$	0.439431	+	2.49214i	0.0181065	+	0.102687i
$590$	−17.3432	−	20.6688i	−0.714009	−	0.850922i
$591$	4.19712	−	4.81308i	0.172646	−	0.197984i
$592$	14.6646	−	5.33749i	0.602713	−	0.219369i
$593$	34.6890			1.42451			0.712253	−	0.701923i	$-0.247675\pi$
$593$	34.6890			1.42451			0.712253	+	0.701923i	$0.247675\pi$
$594$	−14.4483	−	6.21273i	−0.592823	−	0.254912i
$595$	−51.6359	+	11.4835i	−2.11687	+	0.470779i
$596$	0.0880363	+	0.241878i	0.00360611	+	0.00990770i
$597$	9.77362	+	28.5288i	0.400008	+	1.16761i
$598$	−0.533969	−	0.636359i	−0.0218356	−	0.0260227i
$599$	38.5459	−	6.79668i	1.57494	−	0.277705i	0.683194	−	0.730237i	$-0.260590\pi$
$599$	38.5459	−	6.79668i	1.57494	−	0.277705i	0.891748	+	0.452532i	$0.149479\pi$
$600$	−2.46822	+	6.40014i	−0.100765	+	0.261285i
$601$	5.30537	−	6.32270i	0.216411	−	0.257908i	−0.646907	−	0.762569i	$-0.723938\pi$
$601$	5.30537	−	6.32270i	0.216411	−	0.257908i	0.863318	+	0.504660i	$0.168382\pi$
$602$	−21.6750	−	6.81823i	−0.883409	−	0.277890i
$603$	25.1489	+	22.7863i	1.02414	+	0.927930i
$604$	0.478419	+	0.828647i	0.0194666	+	0.0337172i
$605$	−2.89958	+	16.4443i	−0.117885	+	0.668557i
$606$	22.4838	+	13.5573i	0.913342	+	0.550728i
$607$	−2.91471	+	8.00809i	−0.118304	+	0.325038i	−0.984684	−	0.174347i	$-0.944219\pi$
$607$	−2.91471	+	8.00809i	−0.118304	+	0.325038i	0.866380	+	0.499385i	$0.166441\pi$
$608$	0.711573	+	0.258992i	0.0288581	+	0.0105035i
$609$	−7.27969	−	2.44295i	−0.294988	−	0.0989934i
$610$	−7.70507	+	43.6976i	−0.311969	+	1.76927i
$611$	0.353946	−	0.204351i	0.0143191	−	0.00826715i
$612$	1.32235	+	1.19812i	0.0534528	+	0.0484313i
$613$	8.90517	−	15.4242i	0.359677	−	0.622978i	−0.628230	−	0.778028i	$-0.716220\pi$
$613$	8.90517	−	15.4242i	0.359677	−	0.622978i	0.987907	+	0.155049i	$0.0495537\pi$
$614$	1.44446	+	1.21205i	0.0582938	+	0.0489143i
$615$	11.3380	+	4.37249i	0.457190	+	0.176316i
$616$	−5.90741	−	14.2349i	−0.238016	−	0.573541i
$617$	0.725589	+	0.864723i	0.0292111	+	0.0348125i	0.780452	−	0.625215i	$-0.214989\pi$
$617$	0.725589	+	0.864723i	0.0292111	+	0.0348125i	−0.751241	+	0.660028i	$0.770544\pi$
$618$	−19.3005	+	6.61211i	−0.776380	+	0.265978i
$619$	−11.5905	−	31.8445i	−0.465860	−	1.27994i	−0.921015	−	0.389527i	$-0.872638\pi$
$619$	−11.5905	−	31.8445i	−0.465860	−	1.27994i	0.455155	−	0.890412i	$-0.349584\pi$
$620$		−	0.272559i		−	0.0109462i
$621$	−30.7398	+	3.62876i	−1.23355	+	0.145617i
$622$		−	35.2453i		−	1.41321i
$623$	28.0357	−	17.8870i	1.12323	−	0.716629i
$624$	−0.456764	+	0.523798i	−0.0182852	+	0.0209687i
$625$	−23.0592	+	19.3490i	−0.922369	+	0.773959i
$626$	−0.0203787	−	0.115573i	−0.000814497	−	0.00461924i
$627$	−5.02784	+	4.05853i	−0.200793	+	0.162082i
$628$	0.711530	−	0.847969i	0.0283932	−	0.0338376i
$629$	14.8439	−	25.7104i	0.591865	−	1.02514i
$630$	27.3051	+	9.74449i	1.08786	+	0.388230i
$631$	5.72941	+	9.92363i	0.228084	+	0.395054i	0.957240	−	0.289294i	$-0.0934205\pi$
$631$	5.72941	+	9.92363i	0.228084	+	0.395054i	−0.729156	+	0.684347i	$0.760087\pi$
$632$	−16.9239	−	2.98413i	−0.673195	−	0.118702i
$633$	−3.67139	−	0.0698006i	−0.145925	−	0.00277432i
$634$	16.9927	+	6.18483i	0.674866	+	0.245631i
$635$	−42.9446	−	15.6305i	−1.70420	−	0.620279i
$636$	1.05809	−	0.584357i	0.0419559	−	0.0231713i
$637$	−0.654269	+	0.176246i	−0.0259231	+	0.00698313i
$638$	−4.39221	+	2.53584i	−0.173889	+	0.100395i
$639$	40.9195	−	5.62102i	1.61875	−	0.222364i
$640$	26.1539	+	15.1000i	1.03382	+	0.596879i
$641$	14.4774	−	17.2535i	0.571824	−	0.681474i	−0.400180	−	0.916437i	$-0.631052\pi$
$641$	14.4774	−	17.2535i	0.571824	−	0.681474i	0.972004	+	0.234963i	$0.0754968\pi$
$642$	3.34313	+	21.3224i	0.131943	+	0.841528i
$643$	2.47158	−	0.435807i	0.0974698	−	0.0171866i	−0.124701	−	0.992194i	$-0.539797\pi$
$643$	2.47158	−	0.435807i	0.0974698	−	0.0171866i	0.222170	+	0.975008i	$0.428686\pi$
$644$	0.943627	+	0.723071i	0.0371841	+	0.0284930i
$645$	−5.03524	+	25.6905i	−0.198262	+	1.01156i
$646$	18.9550	−	6.89906i	0.745774	−	0.271440i
$647$	−19.6391			−0.772091			−0.386045	−	0.922480i	$-0.626159\pi$
$647$	−19.6391			−0.772091			−0.386045	+	0.922480i	$0.626159\pi$
$648$	6.72863	+	24.0291i	0.264326	+	0.943954i
$649$		−	15.5195i		−	0.609195i
$650$	0.187180	−	0.0681279i	0.00734180	−	0.00267220i
$651$	6.52893	−	0.165154i	0.255889	−	0.00647290i
$652$	−0.0899383	+	0.0754672i	−0.00352225	+	0.00295552i
$653$	−11.3035	+	1.99311i	−0.442340	+	0.0779965i	−0.390382	−	0.920653i	$-0.627657\pi$
$653$	−11.3035	+	1.99311i	−0.442340	+	0.0779965i	−0.0519576	+	0.998649i	$0.516546\pi$
$654$	−5.80852	+	0.910715i	−0.227131	+	0.0356118i
$655$	2.99911	+	2.51655i	0.117185	+	0.0983299i
$656$	5.73513	−	9.93353i	0.223919	−	0.387839i
$657$	−25.5440	−	32.9054i	−0.996565	−	1.28376i
$658$	−11.8578	+	10.8802i	−0.462266	+	0.424156i
$659$	29.2489	+	5.15736i	1.13937	+	0.200902i	0.711332	−	0.702856i	$-0.248092\pi$
$659$	29.2489	+	5.15736i	1.13937	+	0.200902i	0.428042	+	0.903759i	$0.359203\pi$
$660$	0.609208	−	0.336451i	0.0237134	−	0.0130963i
$661$	−3.15998	+	8.68198i	−0.122909	+	0.337690i	−0.985854	−	0.167609i	$-0.946395\pi$
$661$	−3.15998	+	8.68198i	−0.122909	+	0.337690i	0.862945	+	0.505299i	$0.168618\pi$
$662$	−5.46259	+	15.0083i	−0.212310	+	0.583316i
$663$	−0.0251313	+	1.32186i	−0.000976018	+	0.0513369i
$664$	25.2127	+	4.44568i	0.978442	+	0.172526i
$665$	8.77638	−	8.05284i	0.340333	−	0.312276i
$666$	−14.3903	+	7.59409i	−0.557612	+	0.294265i
$667$	−4.99080	+	8.64432i	−0.193245	+	0.334710i
$668$	−0.0737974	−	0.0619234i	−0.00285531	−	0.00239589i
$669$	−26.7940	−	33.1934i	−1.03592	−	1.28333i
$670$	−40.6913	+	7.17498i	−1.57204	+	0.277194i
$671$	−19.5514	+	16.4056i	−0.754773	+	0.633329i
$672$	0.934045	−	1.71665i	0.0360316	−	0.0662213i
$673$	−0.574231	+	0.209003i	−0.0221350	+	0.00805648i	−0.353064	−	0.935599i	$-0.614860\pi$
$673$	−0.574231	+	0.209003i	−0.0221350	+	0.00805648i	0.330929	+	0.943656i	$0.392638\pi$
$674$		−	0.717984i		−	0.0276557i
$675$	1.70338	−	7.22407i	0.0655630	−	0.278055i
$676$	−0.979870			−0.0376873
$677$	1.73677	−	0.632133i	0.0667495	−	0.0242948i	−0.308430	−	0.951247i	$-0.599803\pi$
$677$	1.73677	−	0.632133i	0.0667495	−	0.0242948i	0.375179	+	0.926952i	$0.377581\pi$
$678$	−21.8256	+	7.47718i	−0.838207	+	0.287159i
$679$	−32.1695	−	24.6504i	−1.23455	−	0.945997i
$680$	54.5915	−	9.62596i	2.09349	−	0.369139i
$681$	2.55556	+	0.985553i	0.0979292	+	0.0377665i
$682$	2.77278	−	3.30447i	0.106175	−	0.126535i
$683$	−20.1934	−	11.6587i	−0.772680	−	0.446107i	0.0611497	−	0.998129i	$-0.480523\pi$
$683$	−20.1934	−	11.6587i	−0.772680	−	0.446107i	−0.833830	+	0.552021i	$0.813857\pi$
$684$	−0.392757	−	0.0847617i	−0.0150174	−	0.00324095i
$685$	30.7336	−	17.7440i	1.17427	−	0.677965i
$686$	23.6416	−	12.3672i	0.902640	−	0.472182i
$687$	−19.6627	−	11.8563i	−0.750180	−	0.452344i
$688$	23.2206	+	8.45162i	0.885279	+	0.322215i
$689$	0.841561	+	0.306303i	0.0320609	+	0.0116692i
$690$	19.4604	−	32.2737i	0.740846	−	1.22864i
$691$	−5.95279	−	1.04964i	−0.226455	−	0.0399301i	0.0592693	−	0.998242i	$-0.481123\pi$
$691$	−5.95279	−	1.04964i	−0.226455	−	0.0399301i	−0.285724	+	0.958312i	$0.592234\pi$
$692$	0.253385	+	0.438876i	0.00963225	+	0.0166836i
$693$	8.42855	+	14.3892i	0.320174	+	0.546601i
$694$	−25.9332	+	44.9177i	−0.984412	+	1.70505i
$695$	−28.3920	+	33.8362i	−1.07697	+	1.28348i
$696$	7.50786	+	2.89541i	0.284585	+	0.109750i
$697$	−3.78910	−	21.4890i	−0.143522	−	0.813955i
$698$	−28.1262	+	23.6007i	−1.06459	+	0.893298i
$699$	8.86744	+	25.8837i	0.335397	+	0.979012i
$700$	−0.240315	+	0.153323i	−0.00908306	+	0.00579507i
$701$			5.95954i			0.225089i	0.993647	+	0.112544i	$0.0359001\pi$
$701$			5.95954i			0.225089i	−0.993647	+	0.112544i	$0.964100\pi$
$702$	0.397485	−	0.605862i	0.0150021	−	0.0228668i
$703$			6.68487i			0.252125i
$704$	5.51577	+	15.1545i	0.207884	+	0.571155i
$705$	13.9746	+	12.1862i	0.526314	+	0.458958i
$706$	−14.4958	−	17.2754i	−0.545556	−	0.650168i
$707$	−10.6705	−	25.7123i	−0.401304	−	0.967010i
$708$	0.750939	−	0.606165i	0.0282220	−	0.0227811i
$709$	19.8453	+	16.6521i	0.745304	+	0.625384i	0.934256	−	0.356602i	$-0.116065\pi$
$709$	19.8453	+	16.6521i	0.745304	+	0.625384i	−0.188952	+	0.981986i	$0.560509\pi$
$710$	−25.1445	+	43.5516i	−0.943658	+	1.63446i
$711$	18.5809	+	0.706777i	0.696839	+	0.0265062i
$712$	−30.1812	+	17.4251i	−1.13109	+	0.653035i
$713$	1.47423	−	8.36079i	0.0552104	−	0.313114i
$714$	−10.3336	−	51.0234i	−0.386724	−	1.90950i
$715$	0.484540	+	0.176358i	0.0181208	+	0.00659542i
$716$	0.0807634	−	0.221896i	0.00301827	−	0.00829263i
$717$	−5.94001	+	3.28052i	−0.221834	+	0.122513i
$718$	1.42101	−	8.05893i	0.0530315	−	0.300757i
$719$	19.3073	+	33.4412i	0.720040	+	1.24715i	0.960983	+	0.276607i	$0.0892099\pi$
$719$	19.3073	+	33.4412i	0.720040	+	1.24715i	−0.240943	+	0.970539i	$0.577457\pi$
$720$	−29.1966	−	11.9020i	−1.08809	−	0.443563i
$721$	20.6353	+	6.49117i	0.768500	+	0.241744i
$722$	14.6748	−	17.4888i	0.546141	−	0.650866i
$723$	−41.3021	+	6.47573i	−1.53604	+	0.240835i
$724$	−0.278234	+	0.0490602i	−0.0103405	+	0.00182331i
$725$	−1.53848	−	1.83349i	−0.0571379	−	0.0680943i
$726$	−16.1266	−	3.16075i	−0.598514	−	0.117306i
$727$	8.28491	+	22.7626i	0.307270	+	0.844218i	0.993186	+	0.116537i	$0.0371794\pi$
$727$	8.28491	+	22.7626i	0.307270	+	0.844218i	−0.685916	+	0.727681i	$0.740598\pi$
$728$	0.693145	−	0.154152i	0.0256897	−	0.00571323i
$729$	−10.7511	−	24.7672i	−0.398188	−	0.917304i
$730$	50.7185			1.87718
$731$	44.1740	−	16.0780i	1.63383	−	0.594667i
$732$	−1.55745	−	0.305254i	−0.0575651	−	0.0112825i
$733$	−27.7677	−	33.0923i	−1.02562	−	1.22229i	−0.974684	−	0.223589i	$-0.928223\pi$
$733$	−27.7677	−	33.0923i	−1.02562	−	1.22229i	−0.0509402	−	0.998702i	$-0.516222\pi$
$734$	4.72854	+	26.8169i	0.174533	+	0.989828i
$735$	−17.1842	−	25.4888i	−0.633847	−	0.940169i
$736$	−1.94609	−	1.63296i	−0.0717338	−	0.0601918i
$737$	−20.5825	−	11.8833i	−0.758166	−	0.437727i
$738$	−4.51453	+	11.0745i	−0.166182	+	0.407657i
$739$	1.55436	+	2.69223i	0.0571780	+	0.0990352i	0.893198	−	0.449664i	$-0.148456\pi$
$739$	1.55436	+	2.69223i	0.0571780	+	0.0990352i	−0.836020	+	0.548700i	$0.815123\pi$
$740$	0.125027	−	0.709062i	0.00459608	−	0.0260656i
$741$	−0.143923	−	0.260599i	−0.00528714	−	0.00957336i
$742$	−34.9655	−	4.57957i	−1.28362	−	0.168121i
$743$	−4.69492	+	12.8992i	−0.172240	+	0.473225i	−0.995536	−	0.0943876i	$-0.969911\pi$
$743$	−4.69492	+	12.8992i	−0.172240	+	0.473225i	0.823296	+	0.567613i	$0.192133\pi$
$744$	−6.84292	−	0.130098i	−0.250874	−	0.00476961i
$745$	−8.52069	−	1.50243i	−0.312174	−	0.0550447i
$746$	18.7241	−	10.8104i	0.685539	−	0.395796i
$747$	−27.6813	−	1.05294i	−1.01281	−	0.0385249i
$748$	−1.08225	−	0.624834i	−0.0395708	−	0.0228462i
$749$	10.5534	−	20.3060i	0.385613	−	0.741964i
$750$	−14.1927	−	17.5824i	−0.518244	−	0.642018i
$751$	−2.41618	−	13.7028i	−0.0881677	−	0.500024i	−0.996628	−	0.0820528i	$-0.973852\pi$
$751$	−2.41618	−	13.7028i	−0.0881677	−	0.500024i	0.908460	−	0.417971i	$-0.137259\pi$
$752$	13.4070	−	11.2498i	0.488904	−	0.410239i
$753$	−8.72518	−	7.60856i	−0.317963	−	0.277271i
$754$	−0.0799193	−	0.219576i	−0.00291049	−	0.00799650i
$755$	−32.1627			−1.17052
$756$	−0.367042	+	0.969846i	−0.0133492	+	0.0352730i
$757$	−17.3160			−0.629361			−0.314681	−	0.949198i	$-0.601897\pi$
$757$	−17.3160			−0.629361			−0.314681	+	0.949198i	$0.601897\pi$
$758$	−1.41518	−	3.88816i	−0.0514015	−	0.141224i
$759$	20.5074	−	7.02557i	0.744370	−	0.255012i
$760$	−9.56187	+	8.02336i	−0.346845	+	0.291038i
$761$	3.29855	+	18.7070i	0.119572	+	0.678128i	0.984384	+	0.176032i	$0.0563263\pi$
$761$	3.29855	+	18.7070i	0.119572	+	0.678128i	−0.864812	+	0.502095i	$0.832563\pi$
$762$	16.1835	−	41.9640i	0.586265	−	1.52020i
$763$	5.53163	+	2.87490i	0.200259	+	0.104078i
$764$	0.0912389	+	0.0526768i	0.00330091	+	0.00190578i
$765$	−57.1019	+	18.3572i	−2.06452	+	0.663706i
$766$	17.0963	−	9.87058i	0.617716	−	0.356639i
$767$	0.704171	+	0.124164i	0.0254261	+	0.00448331i
$768$	−1.61682	+	2.68138i	−0.0583420	+	0.0967560i
$769$	10.6489	−	29.2575i	0.384008	−	1.05505i	−0.585645	−	0.810568i	$-0.699159\pi$
$769$	10.6489	−	29.2575i	0.384008	−	1.05505i	0.969653	−	0.244485i	$-0.0786190\pi$
$770$	−20.1318	−	2.63675i	−0.725501	−	0.0950219i
$771$	18.9703	−	31.4609i	0.683199	−	1.13304i
$772$	−0.0145595	+	0.0825710i	−0.000524007	+	0.00297179i
$773$	1.63416	+	2.83045i	0.0587768	+	0.101804i	0.893917	−	0.448233i	$-0.147947\pi$
$773$	1.63416	+	2.83045i	0.0587768	+	0.101804i	−0.835140	+	0.550038i	$0.814613\pi$
$774$	−25.1847	−	5.43516i	−0.905244	−	0.195363i
$775$	1.76300	+	1.01787i	0.0633287	+	0.0365629i
$776$	32.5348	+	27.2999i	1.16793	+	0.980010i
$777$	17.0608	+	2.56526i	0.612051	+	0.0920284i
$778$	−3.62668	−	20.5679i	−0.130023	−	0.737396i
$779$	3.15826	+	3.76387i	0.113156	+	0.134855i
$780$	0.0103919	+	0.0303335i	0.000372089	+	0.00108611i
$781$	−27.1817	+	9.89333i	−0.972637	+	0.354011i
$782$	−67.6726			−2.41997
$783$	−8.47439	−	1.99819i	−0.302850	−	0.0714095i
$784$	−26.2812	+	12.2978i	−0.938615	+	0.439208i
$785$	12.7260	+	34.9643i	0.454209	+	1.24793i
$786$	−2.53234	+	2.90398i	−0.0903254	+	0.103581i
$787$	15.0442	+	17.9290i	0.536269	+	0.639100i	0.964347	−	0.264641i	$-0.0852536\pi$
$787$	15.0442	+	17.9290i	0.536269	+	0.639100i	−0.428078	+	0.903742i	$0.640809\pi$
$788$	−0.273880	+	0.0482925i	−0.00975658	+	0.00172035i
$789$	−13.3444	−	16.5315i	−0.475072	−	0.588536i
$790$	−14.5523	+	17.3428i	−0.517749	+	0.617030i
$791$	23.3351	+	7.34042i	0.829700	+	0.260995i
$792$	−8.15621	−	15.4555i	−0.289818	−	0.549187i
$793$	−0.587951	−	1.01836i	−0.0208787	−	0.0361630i
$794$	8.79107	−	49.8566i	0.311983	−	1.76935i
$795$	−0.772310	+	40.6222i	−0.0273910	+	1.44072i
$796$	0.449170	−	1.23408i	0.0159204	−	0.0437410i
$797$	24.5022	+	8.91806i	0.867912	+	0.315894i	0.737321	−	0.675542i	$-0.236090\pi$
$797$	24.5022	+	8.91806i	0.867912	+	0.315894i	0.130590	+	0.991436i	$0.458313\pi$
$798$	7.75962	+	8.78640i	0.274688	+	0.311035i
$799$	5.78151	−	32.7886i	0.204535	−	1.15998i
$800$	0.527551	−	0.304582i	0.0186517	−	0.0107686i
$801$	29.7869	−	23.1231i	1.05247	−	0.817014i
$802$	−6.50379	+	11.2649i	−0.229657	+	0.397777i
$803$	22.3479	+	18.7521i	0.788642	+	0.661749i
$804$	−0.228922	−	1.46006i	−0.00807345	−	0.0514923i
$805$	−36.9080	+	15.3166i	−1.30084	+	0.539840i
$806$	0.127751	+	0.152247i	0.00449982	+	0.00536268i
$807$	4.29609	−	21.9193i	0.151230	−	0.771595i
$808$	9.97783	+	27.4139i	0.351019	+	0.964416i
$809$			24.8140i			0.872412i	0.899847	+	0.436206i	$0.143678\pi$
$809$			24.8140i			0.872412i	−0.899847	+	0.436206i	$0.856322\pi$
$810$	31.8470	+	8.15128i	1.11899	+	0.286407i
$811$			27.0995i			0.951593i	0.879555	+	0.475797i	$0.157840\pi$
$811$			27.0995i			0.951593i	−0.879555	+	0.475797i	$0.842160\pi$
$812$	0.179860	+	0.281908i	0.00631184	+	0.00989304i
$813$	−26.7049	−	5.23406i	−0.936583	−	0.183567i
$814$	8.72918	−	7.32465i	0.305958	−	0.256729i
$815$	−0.685289	−	3.88647i	−0.0240046	−	0.136137i
$816$	8.76961	+	55.9324i	0.306998	+	1.95803i
$817$	−6.80398	+	8.10867i	−0.238041	+	0.283687i
$818$	−8.52270	+	14.7617i	−0.297989	+	0.516132i
$819$	−0.720317	+	0.267309i	−0.0251699	+	0.00934053i
$820$	−0.264600	−	0.458301i	−0.00924025	−	0.0160046i
$821$	18.1866	+	3.20679i	0.634716	+	0.111918i	0.481743	−	0.876313i	$-0.340004\pi$
$821$	18.1866	+	3.20679i	0.634716	+	0.111918i	0.152973	+	0.988230i	$0.451115\pi$
$822$	16.8848	+	30.5731i	0.588924	+	1.06636i
$823$	−14.9272	−	5.43305i	−0.520329	−	0.189384i	0.0684859	−	0.997652i	$-0.478183\pi$
$823$	−14.9272	−	5.43305i	−0.520329	−	0.189384i	−0.588815	+	0.808268i	$0.700405\pi$
$824$	−21.3023	−	7.75339i	−0.742099	−	0.270102i
$825$	−0.0988057	+	5.19702i	−0.00343997	+	0.180937i
$826$	−28.1276	+	1.24687i	−0.978686	+	0.0433842i
$827$	6.41452	−	3.70343i	0.223055	−	0.128781i	−0.384309	−	0.923204i	$-0.625560\pi$
$827$	6.41452	−	3.70343i	0.223055	−	0.128781i	0.607364	+	0.794424i	$0.292227\pi$
$828$	1.14092	+	0.717876i	0.0396498	+	0.0249479i
$829$	6.47519	+	3.73846i	0.224893	+	0.129842i	0.608214	−	0.793773i	$-0.291886\pi$
$829$	6.47519	+	3.73846i	0.224893	+	0.129842i	−0.383321	+	0.923615i	$0.625220\pi$
$830$	21.6797	−	25.8368i	0.752512	−	0.896809i
$831$	17.8779	−	14.4313i	0.620179	−	0.500615i
$832$	−0.731735	+	0.129025i	−0.0253683	+	0.00447312i
$833$	−23.2614	+	50.0585i	−0.805961	+	1.73442i
$834$	−32.7629	−	28.5700i	−1.13449	−	0.989299i
$835$	3.04289	−	1.10752i	0.105304	−	0.0383274i
$836$	0.281391			0.00973211
$837$	7.35442	−	0.868171i	0.254206	−	0.0300084i
$838$			28.3621i			0.979752i
$839$	−15.2482	+	5.54991i	−0.526428	+	0.191604i	−0.591543	−	0.806274i	$-0.701481\pi$
$839$	−15.2482	+	5.54991i	−0.526428	+	0.191604i	0.0651148	+	0.997878i	$0.479259\pi$
$840$	16.8075	+	27.4822i	0.579914	+	0.948225i
$841$	20.0645	−	16.8361i	0.691878	−	0.580555i
$842$	18.6892	−	3.29541i	0.644073	−	0.113567i
$843$	−8.77246	+	22.7471i	−0.302139	+	0.783453i
$844$	0.122501	+	0.102791i	0.00421667	+	0.00353821i
$845$	16.4684	−	28.5241i	0.566530	−	0.981260i
$846$	−12.2523	+	13.5227i	−0.421244	+	0.464921i
$847$	11.7804	+	12.8389i	0.404781	+	0.441150i
$848$	37.7680	+	6.65951i	1.29696	+	0.228689i
$849$	12.4213	+	7.48982i	0.426299	+	0.257050i
$850$	5.54996	−	15.2484i	0.190362	−	0.523015i
$851$	7.67042	−	21.0743i	0.262939	−	0.722418i
$852$	−1.54037	−	0.928815i	−0.0527723	−	0.0318207i
$853$	−4.14761	−	0.731336i	−0.142012	−	0.0250405i	0.102190	−	0.994765i	$-0.467415\pi$
$853$	−4.14761	−	0.731336i	−0.142012	−	0.0250405i	−0.244202	+	0.969724i	$0.578526\pi$
$854$	31.3042	+	34.1169i	1.07121	+	1.16746i
$855$	9.06838	−	10.0086i	0.310132	−	0.342288i
$856$	−11.9909	+	20.7689i	−0.409842	+	0.709867i
$857$	−28.3201	−	23.7634i	−0.967397	−	0.811742i	0.0147437	−	0.999891i	$-0.495307\pi$
$857$	−28.3201	−	23.7634i	−0.967397	−	0.811742i	−0.982140	+	0.188149i	$0.939751\pi$
$858$	−0.182597	+	0.473477i	−0.00623375	+	0.0161642i
$859$	15.3634	−	2.70898i	0.524191	−	0.0924291i	0.0947102	−	0.995505i	$-0.469808\pi$
$859$	15.3634	−	2.70898i	0.524191	−	0.0924291i	0.429481	+	0.903076i	$0.358696\pi$
$860$	0.873353	−	0.732830i	0.0297811	−	0.0249893i
$861$	10.8179	−	6.61599i	0.368673	−	0.225472i
$862$	−25.1575	+	9.15659i	−0.856868	+	0.311875i
$863$			29.1929i			0.993737i	0.867826	+	0.496868i	$0.165517\pi$
$863$			29.1929i			0.993737i	−0.867826	+	0.496868i	$0.834483\pi$
$864$	0.875368	−	2.03576i	0.0297806	−	0.0692579i
$865$	−17.0343			−0.579183
$866$	35.2245	−	12.8207i	1.19698	−	0.435664i
$867$	58.9825	+	51.4341i	2.00315	+	1.74679i
$868$	−0.225760	−	0.172993i	−0.00766280	−	0.00587176i
$869$	−12.8243	+	2.26127i	−0.435035	+	0.0767084i
$870$	8.24881	−	6.65852i	0.279661	−	0.225745i
$871$	0.703854	−	0.838820i	0.0238492	−	0.0284223i
$872$	−5.65774	−	3.26650i	−0.191595	−	0.110618i
$873$	−38.8956	−	24.4733i	−1.31642	−	0.828297i
$874$	13.1965	−	7.61900i	0.446378	−	0.257717i
$875$	1.06102	+	23.9352i	0.0358692	+	0.809157i
$876$	−0.0344834	+	1.81377i	−0.00116508	+	0.0612815i
$877$	42.4663	+	15.4565i	1.43399	+	0.521928i	0.938071	−	0.346443i	$-0.112611\pi$
$877$	42.4663	+	15.4565i	1.43399	+	0.521928i	0.495914	+	0.868371i	$0.334833\pi$
$878$	−18.2649	−	6.64787i	−0.616410	−	0.224355i
$879$	−15.1085	−	27.3567i	−0.509596	−	0.922719i
$880$	21.7454	+	3.83430i	0.733037	+	0.129254i
$881$	−16.3257	−	28.2769i	−0.550025	−	0.952672i	−0.998272	−	0.0587620i	$-0.981285\pi$
$881$	−16.3257	−	28.2769i	−0.550025	−	0.952672i	0.448247	−	0.893910i	$-0.352049\pi$
$882$	25.4019	−	16.4320i	0.855325	−	0.553293i
$883$	16.0749	−	27.8425i	0.540963	−	0.936975i	−0.457886	−	0.889011i	$-0.651393\pi$
$883$	16.0749	−	27.8425i	0.540963	−	0.936975i	0.998849	−	0.0479641i	$-0.0152733\pi$
$884$	0.0370092	−	0.0441059i	0.00124475	−	0.00148344i
$885$	5.02472	+	32.0476i	0.168904	+	1.07727i
$886$	2.27964	+	12.9285i	0.0765858	+	0.434340i
$887$	9.21436	−	7.73177i	0.309388	−	0.259607i	−0.474851	−	0.880066i	$-0.657498\pi$
$887$	9.21436	−	7.73177i	0.309388	−	0.259607i	0.784239	+	0.620459i	$0.213054\pi$
$888$	−17.7422	−	3.47739i	−0.595388	−	0.116694i
$889$	−40.2036	+	25.6502i	−1.34838	+	0.860280i
$890$			45.9117i			1.53896i
$891$	11.0189	+	15.3665i	0.369147	+	0.514796i
$892$			1.85772i			0.0622010i
$893$	2.56412	+	7.04485i	0.0858049	+	0.235747i
$894$	1.63775	−	8.35605i	0.0547747	−	0.279468i
$895$	5.10204	+	6.08037i	0.170542	+	0.203244i
$896$	29.1071	−	12.0793i	0.972400	−	0.403541i
$897$	0.154703	+	0.986692i	0.00516537	+	0.0329447i
$898$	12.0727	+	10.1302i	0.402871	+	0.338049i
$899$	1.19404	−	2.06813i	0.0398233	−	0.0689760i
$900$	−0.255325	+	0.198205i	−0.00851085	+	0.00660684i
$901$	63.1822	−	36.4783i	2.10491	−	1.21527i
$902$	1.45438	−	8.24819i	0.0484255	−	0.274635i
$903$	18.0835	+	20.4764i	0.601782	+	0.681412i
$904$	−24.0892	−	8.76777i	−0.801197	−	0.291612i
$905$	3.24806	−	8.92397i	0.107969	−	0.296643i
$906$	0.601679	−	31.6473i	0.0199894	−	1.05141i
$907$	−4.96322	+	28.1478i	−0.164801	+	0.934633i	0.784468	+	0.620169i	$0.212936\pi$
$907$	−4.96322	+	28.1478i	−0.164801	+	0.934633i	−0.949269	+	0.314464i	$0.898175\pi$
$908$	−0.0596405	−	0.103300i	−0.00197924	−	0.00342815i
$909$	−14.7324	−	27.9170i	−0.488644	−	0.925949i
$910$	0.280703	−	0.892349i	0.00930520	−	0.0295811i
$911$	−22.1361	+	26.3808i	−0.733403	+	0.874036i	−0.995859	−	0.0909082i	$-0.971023\pi$
$911$	−22.1361	+	26.3808i	−0.733403	+	0.874036i	0.262456	+	0.964944i	$0.415467\pi$
$912$	−8.00734	−	9.91977i	−0.265149	−	0.328476i
$913$	19.1053	−	3.36878i	0.632293	−	0.111490i
$914$	6.53150	+	7.78394i	0.216043	+	0.257470i
$915$	35.0616	−	40.2073i	1.15910	−	1.32921i
$916$	0.341991	+	0.939612i	0.0112997	+	0.0310457i
$917$	3.98799	−	0.886906i	0.131695	−	0.0292882i
$918$	−16.9948	−	56.5303i	−0.560913	−	1.86578i
$919$	11.7323			0.387012			0.193506	−	0.981099i	$-0.438014\pi$
$919$	11.7323			0.387012			0.193506	+	0.981099i	$0.438014\pi$
$920$	39.3504	−	14.3224i	1.29735	−	0.472195i
$921$	−0.734739	−	2.14467i	−0.0242105	−	0.0706694i
$922$	−19.6844	−	23.4589i	−0.648271	−	0.772579i
$923$	−0.231424	−	1.31247i	−0.00761741	−	0.0432005i
$924$	0.107982	−	0.718151i	0.00355233	−	0.0236254i
$925$	4.11952	+	3.45669i	0.135449	+	0.113655i
$926$	−26.6696	−	15.3977i	−0.876417	−	0.506000i
$927$	23.9766	+	5.17445i	0.787496	+	0.169951i
$928$	−0.357298	−	0.618858i	−0.0117289	−	0.0203150i
$929$	−2.23489	+	12.6747i	−0.0733243	+	0.415843i	0.925946	+	0.377655i	$0.123270\pi$
$929$	−2.23489	+	12.6747i	−0.0733243	+	0.415843i	−0.999271	+	0.0381876i	$0.987842\pi$
$930$	−4.65586	+	7.72140i	−0.152672	+	0.253195i
$931$	−1.09980	−	12.3806i	−0.0360445	−	0.405757i
$932$	0.407524	−	1.11966i	0.0133489	−	0.0366758i
$933$	−21.8812	+	36.2883i	−0.716357	+	1.18803i
$934$	−56.4380	−	9.95155i	−1.84671	−	0.325625i
$935$	36.3780	−	21.0028i	1.18969	−	0.686867i
$936$	0.766518	−	0.246421i	0.0250544	−	0.00805454i
$937$	−3.62026	−	2.09016i	−0.118269	−	0.0682824i	0.439699	−	0.898145i	$-0.355085\pi$
$937$	−3.62026	−	2.09016i	−0.118269	−	0.0682824i	−0.557967	+	0.829863i	$0.688419\pi$
$938$	−19.8837	+	38.2585i	−0.649225	+	1.24918i
$939$	−0.0507691	+	0.131645i	−0.00165679	+	0.00429608i
$940$	−0.140216	−	0.795202i	−0.00457333	−	0.0259366i
$941$	−15.9401	+	13.3754i	−0.519633	+	0.436024i	−0.864504	−	0.502626i	$-0.832367\pi$
$941$	−15.9401	+	13.3754i	−0.519633	+	0.436024i	0.344871	+	0.938650i	$0.387923\pi$
$942$	−34.6421	+	11.8680i	−1.12870	+	0.386679i
$943$	−5.63777	−	15.4896i	−0.183591	−	0.504412i
$944$	30.6195			0.996581
$945$	−22.0636	−	26.9846i	−0.717728	−	0.877808i
$946$	18.0436			0.586647
$947$	−12.6075	−	34.6388i	−0.409688	−	1.12561i	−0.957355	−	0.288913i	$-0.906706\pi$
$947$	−12.6075	−	34.6388i	−0.409688	−	1.12561i	0.547667	−	0.836697i	$-0.315516\pi$
$948$	−0.610310	−	0.532204i	−0.0198219	−	0.0172852i
$949$	−1.02964	+	0.863970i	−0.0334235	+	0.0280456i
$950$	0.634488	+	3.59836i	0.0205855	+	0.116746i
$951$	−13.6559	−	16.9173i	−0.442821	−	0.548582i
$952$	26.6760	−	51.3276i	0.864573	−	1.66354i
$953$	20.4679	+	11.8171i	0.663020	+	0.382795i	0.793427	−	0.608666i	$-0.208295\pi$
$953$	20.4679	+	11.8171i	0.663020	+	0.382795i	−0.130407	+	0.991461i	$0.541628\pi$
$954$	−39.9568	−	1.51987i	−1.29365	−	0.0492076i
$955$	−3.06686	+	1.77065i	−0.0992412	+	0.0572969i
$956$	0.291020	+	0.0513147i	0.00941226	+	0.00165963i
$957$	6.09650	+	0.115907i	0.197072	+	0.00374673i
$958$	3.65523	−	10.0427i	0.118095	−	0.324464i
$959$	4.80920	−	36.7187i	0.155297	−	1.18571i
$960$	−16.2965	−	29.5079i	−0.525967	−	0.952362i
$961$	5.03039	−	28.5287i	0.162271	−	0.920282i
$962$	0.262505	+	0.454671i	0.00846349	+	0.0146592i
$963$	9.79542	−	24.0289i	0.315653	−	0.774320i
$964$	1.57672	+	0.910319i	0.0507827	+	0.0293194i
$965$	−2.15895	−	1.81158i	−0.0694991	−	0.0583167i
$966$	−14.3807	−	36.6031i	−0.462693	−	1.17769i
$967$	7.67106	+	43.5048i	0.246685	+	1.39902i	0.816547	+	0.577279i	$0.195885\pi$
$967$	7.67106	+	43.5048i	0.246685	+	1.39902i	−0.569862	+	0.821740i	$0.693004\pi$
$968$	−11.7373	−	13.9880i	−0.377252	−	0.449591i
$969$	−23.7990	−	4.66452i	−0.764535	−	0.149846i
$970$	52.5772	−	19.1365i	1.68815	−	0.614437i
$971$	33.0944			1.06205			0.531025	−	0.847356i	$-0.321807\pi$
$971$	33.0944			1.06205			0.531025	+	0.847356i	$0.321807\pi$
$972$	−0.313154	+	1.13335i	−0.0100444	+	0.0363523i
$973$	10.0061	+	44.9928i	0.320782	+	1.44240i
$974$	10.4752	+	28.7804i	0.335648	+	0.922184i
$975$	−0.235015	−	0.0460619i	−0.00752649	−	0.00147516i
$976$	−32.3676	−	38.5742i	−1.03606	−	1.23473i
$977$	−48.6949	+	8.58623i	−1.55789	+	0.274698i	−0.885194	−	0.465222i	$-0.845974\pi$
$977$	−48.6949	+	8.58623i	−1.55789	+	0.274698i	−0.672695	+	0.739920i	$0.734863\pi$
$978$	3.83701	−	0.601603i	0.122694	−	0.0192371i
$979$	−16.9749	+	20.2299i	−0.542521	+	0.646552i
$980$	−0.114898	+	1.33377i	−0.00367028	+	0.0426058i
$981$	6.54581	+	2.66841i	0.208991	+	0.0851958i
$982$	−26.6755	−	46.2033i	−0.851249	−	1.47441i
$983$	3.47841	−	19.7270i	0.110944	−	0.629194i	−0.877735	−	0.479147i	$-0.840946\pi$
$983$	3.47841	−	19.7270i	0.110944	−	0.629194i	0.988679	−	0.150048i	$-0.0479427\pi$
$984$	−11.6325	+	6.42435i	−0.370830	+	0.204801i
$985$	3.19723	−	8.78432i	0.101872	−	0.279892i
$986$	−17.8875	−	6.51053i	−0.569655	−	0.207337i
$987$	18.9634	−	3.84059i	0.603613	−	0.122247i
$988$	−0.00225127	+	0.0127676i	−7.16225e−5	+	0.000406191i
$989$	30.7540	−	17.7558i	0.977920	−	0.564602i
$990$	−23.0057	−	0.875085i	−0.731168	−	0.0278120i
$991$	−30.2226	+	52.3470i	−0.960051	+	1.66286i	−0.237691	+	0.971341i	$0.576391\pi$
$991$	−30.2226	+	52.3470i	−0.960051	+	1.66286i	−0.722360	+	0.691517i	$0.756943\pi$
$992$	0.465596	+	0.390682i	0.0147827	+	0.0124042i
$993$	14.9418	−	12.0612i	0.474163	−	0.382749i
$994$	20.1145	+	48.4693i	0.637993	+	1.53735i
$995$	28.3753	+	33.8163i	0.899556	+	1.07205i
$996$	0.909222	+	0.792863i	0.0288098	+	0.0251228i
$997$	12.9226	+	35.5046i	0.409264	+	1.12444i	0.957579	+	0.288171i	$0.0930471\pi$
$997$	12.9226	+	35.5046i	0.409264	+	1.12444i	−0.548315	+	0.836272i	$0.684731\pi$
$998$		−	11.6580i		−	0.369028i
$999$	19.5307	+	1.11503i	0.617925	+	0.0352780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.20.18	yes	132
3.2	odd	2		567.2.be.a.62.6		132
7.6	odd	2	inner	189.2.be.a.20.17	✓	132
21.20	even	2		567.2.be.a.62.5		132
27.4	even	9		567.2.be.a.503.5		132
27.23	odd	18	inner	189.2.be.a.104.17	yes	132
189.104	even	18	inner	189.2.be.a.104.18	yes	132
189.139	odd	18		567.2.be.a.503.6		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.17	✓	132	7.6	odd	2	inner
189.2.be.a.20.18	yes	132	1.1	even	1	trivial
189.2.be.a.104.17	yes	132	27.23	odd	18	inner
189.2.be.a.104.18	yes	132	189.104	even	18	inner
567.2.be.a.62.5		132	21.20	even	2
567.2.be.a.62.6		132	3.2	odd	2
567.2.be.a.503.5		132	27.4	even	9
567.2.be.a.503.6		132	189.139	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.492726 + 1.35375i) q^{2} +(0.333137 - 1.69971i) q^{3} +(-0.0577819 + 0.0484848i) q^{4} +(-0.440273 - 2.49691i) q^{5} +(2.46514 - 0.386507i) q^{6} +(-2.34762 - 1.22011i) q^{7} +(2.40115 + 1.38630i) q^{8} +(-2.77804 - 1.13247i) q^{9} +(3.16327 - 1.82631i) q^{10} +(2.06906 + 0.364832i) q^{11} +(0.0631609 + 0.114365i) q^{12} +(-0.0331071 + 0.0909611i) q^{13} +(0.494989 - 3.77928i) q^{14} +(-4.39070 - 0.0834760i) q^{15} +(-0.719801 + 4.08219i) q^{16} +(3.94280 + 6.82913i) q^{17} +(0.164277 - 4.31878i) q^{18} +(-1.53773 - 0.887809i) q^{19} +(0.146502 + 0.122930i) q^{20} +(-2.85591 + 3.58382i) q^{21} +(0.525589 + 2.98077i) q^{22} +(3.82906 + 4.56329i) q^{23} +(3.15622 - 3.61943i) q^{24} +(-1.34226 + 0.488541i) q^{25} -0.139452 q^{26} +(-2.85034 + 4.34460i) q^{27} +(0.194807 - 0.0433240i) q^{28} +(0.573096 + 1.57457i) q^{29} +(-2.05041 - 5.98506i) q^{30} +(-0.916092 - 1.09176i) q^{31} +(-0.419987 + 0.0740550i) q^{32} +(1.30939 - 3.39527i) q^{33} +(-7.30224 + 8.70247i) q^{34} +(-2.01290 + 6.39899i) q^{35} +(0.215428 - 0.0692562i) q^{36} +(-1.88241 - 3.26042i) q^{37} +(0.444195 - 2.51916i) q^{38} +(0.143578 + 0.0865751i) q^{39} +(2.40431 - 6.60580i) q^{40} +(-2.60026 - 0.946417i) q^{41} +(-6.25879 - 2.10036i) q^{42} +(1.03518 - 5.87080i) q^{43} +(-0.137243 + 0.0792375i) q^{44} +(-1.60459 + 7.43511i) q^{45} +(-4.29090 + 7.43206i) q^{46} +(-3.23438 - 2.71396i) q^{47} +(6.69876 + 2.58338i) q^{48} +(4.02268 + 5.72870i) q^{49} +(-1.32273 - 1.57637i) q^{50} +(12.9210 - 4.42659i) q^{51} +(-0.00249724 - 0.00686110i) q^{52} -9.25188i q^{53} +(-7.28596 - 1.71797i) q^{54} -5.32689i q^{55} +(-3.94555 - 6.18417i) q^{56} +(-2.02129 + 2.31794i) q^{57} +(-1.84920 + 1.55166i) q^{58} +(-1.28271 - 7.27458i) q^{59} +(0.257750 - 0.208059i) q^{60} +(-7.80852 + 9.30583i) q^{61} +(1.02659 - 1.77810i) q^{62} +(5.14006 + 6.04813i) q^{63} +(3.83798 + 6.64757i) q^{64} +(0.241698 + 0.0426179i) q^{65} +(5.24153 + 0.0996521i) q^{66} +(-10.6299 - 3.86898i) q^{67} +(-0.558931 - 0.203434i) q^{68} +(9.03188 - 4.98809i) q^{69} +(-9.65446 + 0.427973i) q^{70} +(-11.9234 + 6.88396i) q^{71} +(-5.10053 - 6.57043i) q^{72} +(12.0252 + 6.94274i) q^{73} +(3.48630 - 4.15481i) q^{74} +(0.383224 + 2.44420i) q^{75} +(0.131898 - 0.0232572i) q^{76} +(-4.41225 - 3.38097i) q^{77} +(-0.0464565 + 0.237028i) q^{78} +(-5.82433 + 2.11988i) q^{79} +10.5098 q^{80} +(6.43501 + 6.29211i) q^{81} -3.98644i q^{82} +(8.67692 - 3.15814i) q^{83} +(-0.00874090 - 0.345548i) q^{84} +(15.3158 - 12.8515i) q^{85} +(8.45769 - 1.49132i) q^{86} +(2.86723 - 0.449552i) q^{87} +(4.46236 + 3.74436i) q^{88} +(-6.28476 + 10.8855i) q^{89} +(-10.8559 + 1.49126i) q^{90} +(0.188705 - 0.173148i) q^{91} +(-0.442501 - 0.0780248i) q^{92} +(-2.16085 + 1.19339i) q^{93} +(2.08038 - 5.71579i) q^{94} +(-1.53976 + 4.23045i) q^{95} +(-0.0140409 + 0.738527i) q^{96} +(15.0854 + 2.65997i) q^{97} +(-5.77318 + 8.26840i) q^{98} +(-5.33478 - 3.35668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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