LMFDB - Embedded newform 189.2.be.a.104.17

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			104.17
Character	$\chi$	$=$	189.104
Dual form			189.2.be.a.20.17

$q$-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} +(-1.60923 + 2.10009i) 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} +(2.05009 + 3.21327i) 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} +(4.10564 + 2.03561i) 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} +(4.53523 + 4.94272i) 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} +(4.77867 - 4.55503i) 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} +(-1.82075 - 6.75906i) 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} +(-0.952641 + 7.27350i) 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} +(2.09221 - 7.65654i) 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} +(8.92585 - 3.70418i) 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} +(-2.56342 + 4.93232i) 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} +(-0.138536 - 0.316683i) 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} +(-0.244303 - 0.0768495i) 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} +(-10.0472 - 0.865519i) 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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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	−0.634461	−	0.772955i	$-0.718778\pi$
$2$	0.492726	−	1.35375i	0.348410	−	0.957249i	0.982871	−	0.184294i	$-0.0589998\pi$
$3$	−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	−0.712797	−	0.701370i	$-0.752572\pi$
$5$	0.440273	−	2.49691i	0.196896	−	1.11665i	0.909693	−	0.415282i	$-0.136317\pi$
$6$	−2.46514	−	0.386507i	−1.00639	−	0.157791i
$7$	−1.60923	+	2.10009i	−0.608232	+	0.793759i
$7$	−1.60923	+	2.10009i	−0.608232	+	0.793759i
$8$	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	0.147215	−	0.989104i	$-0.452969\pi$
$11$	2.06906	−	0.364832i	0.623846	−	0.110001i	0.476631	+	0.879104i	$0.341858\pi$
$12$	−0.0631609	+	0.114365i	−0.0182330	+	0.0330142i
$13$	0.0331071	+	0.0909611i	0.00918227	+	0.0252281i	0.944199	−	0.329375i	$-0.106838\pi$
$13$	0.0331071	+	0.0909611i	0.00918227	+	0.0252281i	−0.935017	+	0.354603i	$0.884616\pi$
$14$	2.05009	+	3.21327i	0.547911	+	0.858783i
$15$	−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	−0.224831	+	0.974398i	$0.572183\pi$
$17$	−3.94280	+	6.82913i	−0.956269	+	1.65631i	−0.731438	+	0.681908i	$0.761150\pi$
$18$	0.164277	+	4.31878i	0.0387204	+	1.01795i
$19$	1.53773	−	0.887809i	0.352780	−	0.203677i	−0.313129	−	0.949711i	$-0.601377\pi$
$19$	1.53773	−	0.887809i	0.352780	−	0.203677i	0.665909	+	0.746033i	$0.268044\pi$
$20$	−0.146502	+	0.122930i	−0.0327588	+	0.0274879i
$21$	4.10564	+	2.03561i	0.895924	+	0.444207i
$22$	0.525589	−	2.98077i	0.112056	−	0.635501i
$23$	3.82906	−	4.56329i	0.798414	−	0.951513i	−0.201193	−	0.979552i	$-0.564482\pi$
$23$	3.82906	−	4.56329i	0.798414	−	0.951513i	0.999607	+	0.0280391i	$0.00892629\pi$
$24$	−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	−0.875040	−	0.484051i	$-0.839165\pi$
$29$	0.573096	−	1.57457i	0.106421	−	0.292390i	0.981461	+	0.191661i	$0.0613873\pi$
$30$	−2.05041	+	5.98506i	−0.374351	+	1.09272i
$31$	0.916092	−	1.09176i	0.164535	−	0.196085i	−0.677477	−	0.735544i	$-0.736927\pi$
$31$	0.916092	−	1.09176i	0.164535	−	0.196085i	0.842012	+	0.539459i	$0.181371\pi$
$32$	−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
$35$	4.53523	+	4.94272i	0.766594	+	0.835472i
$36$	0.215428	+	0.0692562i	0.0359047	+	0.0115427i
$37$	−1.88241	+	3.26042i	−0.309466	+	0.536010i	−0.978246	−	0.207450i	$-0.933483\pi$
$37$	−1.88241	+	3.26042i	−0.309466	+	0.536010i	0.668780	+	0.743460i	$0.266817\pi$
$38$	−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	$-0.541785\pi$
$41$	2.60026	−	0.946417i	0.406092	−	0.147806i	0.536987	+	0.843591i	$0.319563\pi$
$42$	4.77867	−	4.55503i	0.737366	−	0.702856i
$43$	1.03518	+	5.87080i	0.157864	+	0.895289i	0.956121	+	0.292973i	$0.0946445\pi$
$43$	1.03518	+	5.87080i	0.157864	+	0.895289i	−0.798257	+	0.602317i	$0.794244\pi$
$44$	−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	$-0.622585\pi$
$47$	3.23438	−	2.71396i	0.471782	−	0.395872i	0.847444	+	0.530885i	$0.178140\pi$
$48$	−6.69876	+	2.58338i	−0.966883	+	0.372879i
$49$	−1.82075	−	6.75906i	−0.260107	−	0.965580i
$50$	−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	$0.219174\pi$
$53$			9.25188i			1.27084i	−0.772165	+	0.635422i	$0.780826\pi$
$54$	7.28596	−	1.71797i	0.991493	−	0.233786i
$55$		−	5.32689i		−	0.718278i
$56$	−0.952641	+	7.27350i	−0.127302	+	0.971962i
$57$	−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	−0.779991	−	0.625791i	$-0.784776\pi$
$59$	1.28271	−	7.27458i	0.166994	−	0.947070i	0.946985	−	0.321279i	$-0.104113\pi$
$60$	0.257750	+	0.208059i	0.0332754	+	0.0268603i
$61$	7.80852	+	9.30583i	0.999778	+	1.19149i	0.981462	+	0.191657i	$0.0613861\pi$
$61$	7.80852	+	9.30583i	0.999778	+	1.19149i	0.0183160	+	0.999832i	$0.494169\pi$
$62$	−1.02659	−	1.77810i	−0.130377	−	0.225819i
$63$	2.09221	−	7.65654i	0.263594	−	0.964634i
$64$	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	−0.896558	−	0.442926i	$-0.853940\pi$
$67$	−10.6299	+	3.86898i	−1.29865	+	0.472671i	−0.402096	+	0.915597i	$0.631718\pi$
$68$	0.558931	−	0.203434i	0.0677804	−	0.0246700i
$69$	−9.03188	−	4.98809i	−1.08731	−	0.600496i
$70$	8.92585	−	3.70418i	1.06684	−	0.442735i
$71$	−11.9234	−	6.88396i	−1.41504	−	0.816976i	−0.419185	−	0.907901i	$-0.637684\pi$
$71$	−11.9234	−	6.88396i	−1.41504	−	0.816976i	−0.995858	+	0.0909251i	$0.971018\pi$
$72$	−5.10053	+	6.57043i	−0.601103	+	0.774333i
$73$	−12.0252	+	6.94274i	−1.40744	+	0.812587i	−0.995141	−	0.0984612i	$-0.968608\pi$
$73$	−12.0252	+	6.94274i	−1.40744	+	0.812587i	−0.412301	+	0.911048i	$0.635275\pi$
$74$	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
$77$	−2.56342	+	4.93232i	−0.292129	+	0.562090i
$78$	−0.0464565	−	0.237028i	−0.00526016	−	0.0268381i
$79$	−5.82433	−	2.11988i	−0.655288	−	0.238505i	−0.00708756	−	0.999975i	$-0.502256\pi$
$79$	−5.82433	−	2.11988i	−0.655288	−	0.238505i	−0.648201	+	0.761469i	$0.724478\pi$
$80$	−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	$-0.558049\pi$
$83$	−8.67692	−	3.15814i	−0.952416	−	0.346651i	−0.771057	+	0.636766i	$0.780272\pi$
$84$	−0.138536	−	0.316683i	−0.0151155	−	0.0345529i
$85$	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	0.978963	+	0.204037i	$0.0654062\pi$
$89$	6.28476	+	10.8855i	0.666183	+	1.15386i	−0.312781	+	0.949825i	$0.601260\pi$
$90$	10.8559	+	1.49126i	1.14432	+	0.157192i
$91$	−0.244303	−	0.0768495i	−0.0256100	−	0.00805602i
$92$	−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	$-0.839149\pi$
$97$	−15.0854	+	2.65997i	−1.53169	+	0.270079i	−0.656676	+	0.754172i	$0.728038\pi$
$98$	−10.0472	−	0.865519i	−1.01492	−	0.0874306i
$99$	−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	$-0.897591\pi$
$101$	−8.06029	+	6.76338i	−0.802028	+	0.672982i	0.146662	+	0.989187i	$0.453147\pi$
$102$	12.3590	−	15.3108i	1.22373	−	1.51600i
$103$	8.05199	+	1.41978i	0.793386	+	0.139895i	0.555630	−	0.831429i	$-0.312477\pi$
$103$	8.05199	+	1.41978i	0.793386	+	0.139895i	0.237756	+	0.971325i	$0.423588\pi$
$104$	0.205595	+	0.172514i	0.0201602	+	0.0169164i
$105$	6.89034	−	9.35519i	0.672429	−	0.912973i
$106$	12.5248	+	4.55864i	1.21651	+	0.442774i
$107$		−	8.64958i		−	0.836187i	−0.908404	−	0.418093i	$-0.862698\pi$
$107$		−	8.64958i		−	0.836187i	0.908404	−	0.418093i	$-0.137302\pi$
$108$	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
$112$	9.73130	+	5.05755i	0.919521	+	0.477893i
$113$	−9.10544	−	1.60554i	−0.856568	−	0.151036i	−0.271917	−	0.962321i	$-0.587658\pi$
$113$	−9.10544	−	1.60554i	−0.856568	−	0.151036i	−0.584651	+	0.811285i	$0.698769\pi$
$114$	−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
$119$	−7.99690	−	19.2699i	−0.733075	−	1.76647i
$120$	−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
$126$	−9.33419	−	6.60492i	−0.831555	−	0.588413i
$127$	9.01241	+	15.6100i	0.799722	+	1.38516i	0.919797	+	0.392394i	$0.128353\pi$
$127$	9.01241	+	15.6100i	0.799722	+	1.38516i	−0.120075	+	0.992765i	$0.538314\pi$
$128$	−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	$-0.256289\pi$
$131$	1.18288	+	0.992556i	0.103349	+	0.0867200i	−0.589649	+	0.807660i	$0.700734\pi$
$132$	−0.0889600	+	0.259671i	−0.00774298	+	0.0226015i
$133$	−0.610086	+	4.65806i	−0.0529011	+	0.403905i
$134$			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	−0.548718	−	0.836007i	$-0.684884\pi$
$137$	4.78721	−	13.1528i	0.408999	−	1.12372i	0.957718	−	0.287709i	$-0.0928937\pi$
$138$	−11.2029	+	9.76918i	−0.953654	+	0.831608i
$139$	11.1981	−	13.3454i	0.949810	−	1.13194i	−0.0413335	−	0.999145i	$-0.513161\pi$
$139$	11.1981	−	13.3454i	0.949810	−	1.13194i	0.991144	−	0.132794i	$-0.0423949\pi$
$140$	−0.0224079	−	0.505490i	−0.00189381	−	0.0427217i
$141$	−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
$147$	−10.8819	+	5.34644i	−0.897523	+	0.440967i
$148$	0.266850	−	0.0971254i	0.0219349	−	0.00798366i
$149$	1.16714	+	3.20670i	0.0956160	+	0.262703i	0.978275	−	0.207311i	$-0.0664712\pi$
$149$	1.16714	+	3.20670i	0.0956160	+	0.262703i	−0.882659	+	0.470014i	$0.844249\pi$
$150$	3.12002	+	1.72311i	0.254749	+	0.140692i
$151$	2.20278	+	12.4926i	0.179260	+	1.01663i	0.933111	+	0.359587i	$0.117083\pi$
$151$	2.20278	+	12.4926i	0.179260	+	1.01663i	−0.753852	+	0.657044i	$0.771806\pi$
$152$	2.46154	−	4.26352i	0.199658	−	0.345817i
$153$	3.21945	−	23.4367i	0.260277	−	1.89474i
$154$	5.41408	+	5.90053i	0.436279	+	0.475478i
$155$	−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	$-0.245300\pi$
$157$	14.4524	+	2.54834i	1.15343	+	0.203380i	0.435955	+	0.899969i	$0.356411\pi$
$158$	−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	$-0.960180\pi$
$167$	−0.221778	+	1.25777i	−0.0171617	+	0.0973290i	0.975024	+	0.222101i	$0.0712913\pi$
$168$	12.6802	−	0.803856i	0.978300	−	0.0620188i
$169$	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	−0.996497	−	0.0836300i	$-0.973349\pi$
$173$	−1.16666	−	6.61644i	−0.0886992	−	0.503038i	0.907798	−	0.419408i	$-0.137762\pi$
$174$	−2.02134	+	3.66002i	−0.153238	+	0.277466i
$175$	3.18598	−	2.03268i	0.240838	−	0.153656i
$176$	−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	0.395245	−	0.918576i	$-0.370660\pi$
$179$	−2.71116	−	1.56529i	−0.202642	−	0.116995i	−0.597887	+	0.801580i	$0.703993\pi$
$180$	0.267774	−	0.507413i	0.0199587	−	0.0378204i
$181$	−3.24378	+	1.87280i	−0.241108	+	0.139204i	−0.615686	−	0.787992i	$-0.711121\pi$
$181$	−3.24378	+	1.87280i	−0.241108	+	0.139204i	0.374578	+	0.927196i	$0.377788\pi$
$182$	−0.224410	+	0.292861i	−0.0166344	+	0.0217083i
$183$	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
$189$	−13.7109	−	1.00549i	−0.997322	−	0.0731384i
$190$	−6.48567			−0.470520
$191$	−0.477709	+	1.31249i	−0.0345658	+	0.0949687i	−0.955775	−	0.294099i	$-0.904981\pi$
$191$	−0.477709	+	1.31249i	−0.0345658	+	0.0949687i	0.921209	+	0.389068i	$0.127203\pi$
$192$	−12.5775	−	4.30890i	−0.907705	−	0.310968i
$193$	0.851514	+	0.714505i	0.0612933	+	0.0514312i	0.672920	−	0.739716i	$-0.265040\pi$
$193$	0.851514	+	0.714505i	0.0612933	+	0.0514312i	−0.611626	+	0.791147i	$0.709484\pi$
$194$	−3.83204	+	21.7326i	−0.275125	+	1.56031i
$195$	−0.152956	−	0.396619i	−0.0109534	−	0.0284025i
$196$	−0.222505	+	0.478830i	−0.0158932	+	0.0342022i
$197$	3.19302	−	1.84349i	0.227493	−	0.131343i	−0.381922	−	0.924195i	$-0.624738\pi$
$197$	3.19302	−	1.84349i	0.227493	−	0.131343i	0.609415	+	0.792851i	$0.291404\pi$
$198$	1.91553	+	8.87590i	0.136131	+	0.630783i
$199$	15.0783	+	8.70545i	1.06887	+	0.617113i	0.927873	−	0.372897i	$-0.121636\pi$
$199$	15.0783	+	8.70545i	1.06887	+	0.617113i	0.140998	+	0.990010i	$0.454969\pi$
$200$	−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
$203$	2.38449	+	3.73740i	0.167358	+	0.262314i
$204$	−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
$210$	−9.26957	−	13.9374i	−0.639661	−	0.961770i
$211$	−0.368145	+	2.08786i	−0.0253442	+	0.143734i	−0.994854	−	0.101318i	$-0.967694\pi$
$211$	−0.368145	+	2.08786i	−0.0253442	+	0.143734i	0.969510	+	0.245052i	$0.0788051\pi$
$212$	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	−0.963392	−	0.268096i	$-0.913605\pi$
$223$	−15.8310	−	18.8667i	−1.06012	−	1.26341i	−0.0967321	−	0.995310i	$-0.530839\pi$
$224$	0.831378	−	0.762838i	0.0555488	−	0.0509693i
$225$	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	$-0.0388431\pi$
$227$	0.274602	+	1.55735i	0.0182260	+	0.103365i	−0.974338	+	0.225091i	$0.927732\pi$
$228$	0.00440959	+	0.231937i	0.000292032	+	0.0153604i
$229$	−4.53395	−	12.4569i	−0.299612	−	0.823176i	−0.994565	−	0.104121i	$-0.966797\pi$
$229$	−4.53395	−	12.4569i	−0.299612	−	0.823176i	0.694953	−	0.719055i	$-0.255425\pi$
$230$	−20.4463	+	7.44186i	−1.34819	+	0.490702i
$231$	9.23749	+	2.71394i	0.607782	+	0.178564i
$232$	−0.806741	−	4.57526i	−0.0529651	−	0.300380i
$233$	−13.6803	−	7.89830i	−0.896223	−	0.517435i	−0.0202503	−	0.999795i	$-0.506446\pi$
$233$	−13.6803	−	7.89830i	−0.896223	−	0.517435i	−0.875973	+	0.482360i	$0.839780\pi$
$234$	−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
$238$	−30.0269	+	1.33107i	−1.94636	+	0.0862802i
$239$	−2.51826	+	3.00115i	−0.162893	+	0.194128i	−0.841317	−	0.540543i	$-0.818219\pi$
$239$	−2.51826	+	3.00115i	−0.162893	+	0.194128i	0.678424	+	0.734671i	$0.262663\pi$
$240$	3.50119	+	17.8636i	0.226001	+	1.15309i
$241$	8.25538	−	22.6815i	0.531776	−	1.46104i	−0.325180	−	0.945652i	$-0.605425\pi$
$241$	8.25538	−	22.6815i	0.531776	−	1.46104i	0.856956	−	0.515390i	$-0.172353\pi$
$242$			9.48784i			0.609901i
$243$	−12.8385	−	8.84153i	−0.823591	−	0.567184i
$244$		−	0.916303i		−	0.0586603i
$245$	−17.6784	+	1.57042i	−1.12943	+	0.100330i
$246$	−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	$-0.234319\pi$
$251$	−3.34189	−	5.78833i	−0.210938	−	0.365356i	−0.952008	+	0.306072i	$0.900985\pi$
$252$	−0.492118	+	0.340969i	−0.0310005	+	0.0214790i
$253$	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	$-0.841207\pi$
$257$	−19.9314	+	7.25443i	−1.24329	+	0.452519i	−0.365158	+	0.930945i	$0.618985\pi$
$258$	−0.282755	−	14.8724i	−0.0176036	−	0.925918i
$259$	−3.81795	−	9.19999i	−0.237236	−	0.571660i
$260$	−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	0.952240	−	0.305350i	$-0.0987736\pi$
$263$	7.88441	+	9.39628i	0.486174	+	0.579399i	−0.466066	+	0.884750i	$0.654329\pi$
$264$	−7.85091	−	6.33733i	−0.483190	−	0.390036i
$265$	23.1011	+	4.07335i	1.41909	+	0.250224i
$266$	6.00526	+	3.12105i	0.368206	+	0.191364i
$267$	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	$-0.628610\pi$
$269$	−12.8959			−0.786276			−0.393138	+	0.919480i	$0.628610\pi$
$270$	−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
$273$	−0.0492356	+	0.440847i	−0.00297987	+	0.0266813i
$274$	−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	−0.284267	−	0.958745i	$-0.591750\pi$
$277$	10.1616	−	8.52659i	0.610551	−	0.512313i	0.894817	+	0.446432i	$0.147306\pi$
$278$	−12.5488	−	21.7351i	−0.752624	−	1.30358i
$279$	−1.30856	+	4.07039i	−0.0783412	+	0.243688i
$280$	17.7419	+	5.58098i	1.06028	+	0.333527i
$281$	−13.8620	+	2.44425i	−0.826938	+	0.145811i	−0.571071	−	0.820901i	$-0.693472\pi$
$281$	−13.8620	+	2.44425i	−0.826938	+	0.145811i	−0.255867	+	0.966712i	$0.582361\pi$
$282$	−9.02214	+	5.44018i	−0.537261	+	0.323958i
$283$	2.86418	+	7.86927i	0.170258	+	0.467779i	0.995249	−	0.0973668i	$-0.0310420\pi$
$283$	2.86418	+	7.86927i	0.170258	+	0.467779i	−0.824991	+	0.565146i	$0.808820\pi$
$284$	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
$287$	−2.19686	+	6.98378i	−0.129676	+	0.412240i
$288$	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	$-0.454477\pi$
$293$	−13.8218	−	11.5979i	−0.807477	−	0.677554i	−0.950004	+	0.312237i	$0.898922\pi$
$294$	1.87597	+	17.3657i	0.109409	+	1.01279i
$295$	−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
$301$	−13.9951	−	7.27351i	−0.806662	−	0.419238i
$302$	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	$-0.345225\pi$
$307$	−1.13352	−	0.654438i	−0.0646934	−	0.0373507i	−0.531998	+	0.846746i	$0.678559\pi$
$308$	0.387262	−	0.160712i	0.0220663	−	0.00915740i
$309$	−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	$-0.367115\pi$
$311$	22.9897	−	8.36756i	1.30363	−	0.474481i	0.898176	+	0.439637i	$0.144893\pi$
$312$	0.224734	−	0.406922i	0.0127230	−	0.0230374i
$313$	0.0802239	−	0.0141456i	0.00453453	−	0.000799559i	−0.171380	−	0.985205i	$-0.554823\pi$
$313$	0.0802239	−	0.0141456i	0.00453453	−	0.000799559i	0.175915	+	0.984405i	$0.443712\pi$
$314$	10.5709	−	18.3093i	0.596550	−	1.03326i
$315$	−18.1966	−	8.59504i	−1.02526	−	0.484275i
$316$	0.233759	+	0.404882i	0.0131500	+	0.0227764i
$317$	8.06845	+	9.61560i	0.453169	+	0.540066i	0.943457	−	0.331495i	$-0.107553\pi$
$317$	8.06845	+	9.61560i	0.453169	+	0.540066i	−0.490288	+	0.871560i	$0.663108\pi$
$318$	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
$322$	22.5130	+	2.94863i	1.25460	+	0.164321i
$323$			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
$329$	0.494706	+	11.1599i	0.0272741	+	0.615264i
$330$	−2.05888	+	13.1315i	−0.113338	+	0.722866i
$331$	8.49272	−	7.12624i	0.466802	−	0.391693i	−0.378824	−	0.925469i	$-0.623672\pi$
$331$	8.49272	−	7.12624i	0.466802	−	0.391693i	0.845626	+	0.533775i	$0.179227\pi$
$332$	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
$336$	5.35452	−	18.2253i	0.292113	−	0.994269i
$337$	−0.468324	+	0.170456i	−0.0255113	+	0.00928534i	−0.354744	−	0.934963i	$-0.615432\pi$
$337$	−0.468324	+	0.170456i	−0.0255113	+	0.00928534i	0.329233	+	0.944249i	$0.393210\pi$
$338$	−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
$343$	17.1246	+	7.05315i	0.924643	+	0.380835i
$344$	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	0.424136	−	0.905599i	$-0.360578\pi$
$347$	23.1420	−	27.5795i	1.24233	−	1.48055i	0.818190	−	0.574948i	$-0.194978\pi$
$348$	0.143878	+	0.164993i	0.00771266	+	0.00884457i
$349$	−8.71674	+	23.9491i	−0.466597	+	1.28196i	0.453844	+	0.891081i	$0.350052\pi$
$349$	−8.71674	+	23.9491i	−0.466597	+	1.28196i	−0.920441	+	0.390882i	$0.872170\pi$
$350$	−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	$-0.252116\pi$
$353$	14.7098	+	5.35392i	0.782922	+	0.284960i	0.0805314	+	0.996752i	$0.474338\pi$
$354$	−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
$357$	−30.0892	+	20.0119i	−1.59249	+	1.05914i
$358$	−3.45488	+	2.89899i	−0.182596	+	0.153216i
$359$	−4.91929	+	2.84015i	−0.259630	+	0.149898i	−0.624166	−	0.781292i	$-0.714561\pi$
$359$	−4.91929	+	2.84015i	−0.259630	+	0.149898i	0.364536	+	0.931189i	$0.381228\pi$
$360$	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
$364$	0.0103903	+	0.0162855i	0.000544599	+	0.000853593i
$365$	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	$-0.719777\pi$
$367$	−18.6146	+	3.28226i	−0.971675	+	0.171332i	−0.334791	+	0.942292i	$0.608666\pi$
$368$	−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
$371$	−19.4298	−	14.8884i	−1.00874	−	0.772968i
$372$	0.0669971	+	0.173725i	0.00347364	+	0.00900721i
$373$	−2.60608	+	14.7798i	−0.134938	+	0.765269i	0.839966	+	0.542640i	$0.182575\pi$
$373$	−2.60608	+	14.7798i	−0.134938	+	0.765269i	−0.974903	+	0.222629i	$0.928536\pi$
$374$	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
$378$	−8.11690	+	18.0658i	−0.417488	+	0.929203i
$379$	−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	−0.861689	−	0.507438i	$-0.830593\pi$
$383$	2.37952	−	13.4949i	0.121588	−	0.689558i	0.983276	−	0.182121i	$-0.0582961\pi$
$384$	−12.9584	+	16.0533i	−0.661280	+	0.819217i
$385$	11.1869	+	8.57220i	0.570140	+	0.436880i
$386$	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	−0.523432	−	0.852068i	$-0.675348\pi$
$389$	−14.2770	+	2.51742i	−0.723872	+	0.127638i	−0.200440	+	0.979706i	$0.564237\pi$
$390$	−0.612290	+	0.0116409i	−0.0310045	+	0.000589458i
$391$	16.0661	+	44.1413i	0.812498	+	2.23232i
$392$	−13.7420	−	13.7054i	−0.694075	−	0.692226i
$393$	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	0.527931	−	0.849288i	$-0.322968\pi$
$397$	30.4332	−	17.5706i	1.52740	−	0.881845i	0.999470	−	0.0325575i	$-0.0103652\pi$
$398$	19.2145	−	16.1229i	0.963135	−	0.808167i
$399$	8.12060	−	0.514801i	0.406539	−	0.0257723i
$400$	−1.02816	+	5.83100i	−0.0514082	+	0.291550i
$401$	5.80377	−	6.91666i	0.289826	−	0.345402i	−0.601410	−	0.798940i	$-0.705394\pi$
$401$	5.80377	−	6.91666i	0.289826	−	0.345402i	0.891237	+	0.453539i	$0.149839\pi$
$402$	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	$-0.872273\pi$
$409$	−7.60537	+	9.06373i	−0.376062	+	0.448173i	0.544506	+	0.838757i	$0.316717\pi$
$410$	−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
$413$	13.2131	+	14.4003i	0.650174	+	0.708591i
$414$	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	$-0.770798\pi$
$419$	−18.4999	+	6.73342i	−0.903780	+	0.328949i	−0.152014	+	0.988378i	$0.548576\pi$
$420$	−0.851722	+	0.206484i	−0.0415598	+	0.0100754i
$421$	2.28747	+	12.9729i	0.111485	+	0.632260i	0.988431	+	0.151672i	$0.0484657\pi$
$421$	2.28747	+	12.9729i	0.111485	+	0.632260i	−0.876946	+	0.480588i	$0.840423\pi$
$422$	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
$427$	−32.1088	+	1.42335i	−1.55385	+	0.0688808i
$428$	−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	$-0.852290\pi$
$431$		−	18.5835i		−	0.895137i	0.894250	−	0.447568i	$-0.147710\pi$
$432$	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	$-0.214990\pi$
$434$	5.38618	+	0.705451i	0.258545	+	0.0338627i
$435$	−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	$-0.117877\pi$
$439$	8.67250	+	10.3355i	0.413916	+	0.493286i	−0.518295	+	0.855202i	$0.673433\pi$
$440$	−7.38468	−	12.7906i	−0.352051	−	0.609770i
$441$	12.7126	+	16.7150i	0.605360	+	0.795952i
$442$	−0.549830	+	0.952333i	−0.0261527	+	0.0452979i
$443$	8.97414	−	1.58238i	0.426374	−	0.0751813i	0.0436564	−	0.999047i	$-0.486099\pi$
$443$	8.97414	−	1.58238i	0.426374	−	0.0751813i	0.382718	+	0.923865i	$0.374988\pi$
$444$	−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
$448$	7.78430	+	18.7576i	0.367774	+	0.886212i
$449$	9.47386	+	5.46974i	0.447099	+	0.258133i	0.706604	−	0.707609i	$-0.250226\pi$
$449$	9.47386	+	5.46974i	0.447099	+	0.258133i	−0.259505	+	0.965742i	$0.583559\pi$
$450$	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
$455$	−0.299446	+	0.576169i	−0.0140383	+	0.0270112i
$456$	−8.06678	−	2.76358i	−0.377762	−	0.129416i
$457$	6.62792	+	2.41237i	0.310041	+	0.112846i	0.492355	−	0.870395i	$-0.336136\pi$
$457$	6.62792	+	2.41237i	0.310041	+	0.112846i	−0.182313	+	0.983240i	$0.558359\pi$
$458$	−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	$-0.224051\pi$
$461$	19.9750	+	7.27029i	0.930327	+	0.338611i	0.167988	+	0.985789i	$0.446273\pi$
$462$	8.22556	−	11.1681i	0.382688	−	0.519585i
$463$	−16.3752	−	13.7404i	−0.761019	−	0.638570i	0.177373	−	0.984144i	$-0.443240\pi$
$463$	−16.3752	−	13.7404i	−0.761019	−	0.638570i	−0.938392	+	0.345573i	$0.887684\pi$
$464$	−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	0.798792	+	0.601607i	$0.205473\pi$
$467$	19.8901	+	34.4506i	0.920403	+	1.59418i	0.121611	+	0.992578i	$0.461194\pi$
$468$	0.000832588		0.0218885i	3.84864e−5		0.00101179i
$469$	8.98083	−	28.5499i	0.414696	−	1.31831i
$470$	−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
$476$	−0.472219	+	1.50118i	−0.0216441	+	0.0688064i
$477$	−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	$-0.668014\pi$
$479$	5.68281	−	4.76844i	0.259654	−	0.217876i	0.763316	+	0.646025i	$0.223570\pi$
$480$	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
$483$	25.0098	−	10.9408i	1.13799	−	0.497822i
$484$	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
$490$	−6.58464	+	24.7060i	−0.297464	+	1.11610i
$491$	−36.4703	−	6.43071i	−1.64588	−	0.290214i	−0.727560	−	0.686044i	$-0.759346\pi$
$491$	−36.4703	−	6.43071i	−1.64588	−	0.290214i	−0.918324	+	0.395830i	$0.870457\pi$
$492$	−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
$497$	33.6444	−	13.9622i	1.50916	−	0.626292i
$498$	20.1692	+	11.1389i	0.903801	+	0.499148i
$499$	−7.60426	+	2.76772i	−0.340413	+	0.123900i	−0.506569	−	0.862199i	$-0.669087\pi$
$499$	−7.60426	+	2.76772i	−0.340413	+	0.123900i	0.166156	+	0.986099i	$0.446864\pi$
$500$	−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	$-0.677379\pi$
$503$	10.5540	−	18.2800i	0.470578	−	0.815065i	0.999434	+	0.0336470i	$0.0107122\pi$
$504$	−5.59057	−	21.2849i	−0.249024	−	0.948105i
$505$	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	$-0.335648\pi$
$509$	−6.24961	−	5.24405i	−0.277009	−	0.232438i	−0.770698	+	0.637200i	$0.780092\pi$
$510$	−32.7884	−	37.6003i	−1.45189	−	1.66497i
$511$	4.77092	−	36.4264i	0.211053	−	1.61141i
$512$		−	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
$518$	−14.3357	+	0.635489i	−0.629876	+	0.0279218i
$519$	−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	−0.987109	−	0.160047i	$-0.948835\pi$
$521$	−14.4293	−	24.9923i	−0.632160	−	1.09493i	0.354950	−	0.934885i	$-0.384498\pi$
$522$	6.89437	+	2.21641i	0.301758	+	0.0970098i
$523$	−4.15555	−	2.39921i	−0.181710	−	0.104910i	0.406386	−	0.913701i	$-0.366789\pi$
$523$	−4.15555	−	2.39921i	−0.181710	−	0.104910i	−0.588096	+	0.808791i	$0.700122\pi$
$524$	−0.0202253	−	0.114704i	−0.000883548	−	0.00501085i
$525$	−4.51634	−	4.73809i	−0.197109	−	0.206787i
$526$	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
$532$	0.261097	−	0.239572i	0.0113200	−	0.0103868i
$533$	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
$546$	0.572539	+	0.283870i	0.0245024	+	0.0121485i
$547$	−15.5394	+	13.0391i	−0.664418	+	0.557513i	−0.911407	−	0.411505i	$-0.865003\pi$
$547$	−15.5394	+	13.0391i	−0.664418	+	0.557513i	0.246989	+	0.969018i	$0.420559\pi$
$548$	−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
$553$	13.8246	−	8.82023i	0.587883	−	0.375074i
$554$	−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	0.460326	−	0.887750i	$-0.347733\pi$
$557$	−1.84854	−	1.06725i	−0.0783251	−	0.0452210i	−0.538651	+	0.842529i	$0.681066\pi$
$558$	4.86555	+	3.77705i	0.205975	+	0.159895i
$559$	−0.499743	+	0.288527i	−0.0211369	+	0.0122034i
$560$	16.9127	−	22.0715i	0.714691	−	0.932690i
$561$	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	$-0.337099\pi$
$563$	−6.73571	−	5.65193i	−0.283876	−	0.238200i	−0.773596	+	0.633680i	$0.781544\pi$
$564$	0.106096	+	0.541315i	0.00446743	+	0.0227935i
$565$	−8.01775	+	22.0286i	−0.337309	+	0.926750i
$566$	12.0643			0.507101
$567$	2.85857	+	23.6396i	0.120049	+	0.992768i
$568$	−38.1730			−1.60170
$569$	−12.2179	+	33.5684i	−0.512202	+	1.40726i	0.366736	+	0.930325i	$0.380475\pi$
$569$	−12.2179	+	33.5684i	−0.512202	+	1.40726i	−0.878937	+	0.476937i	$0.841747\pi$
$570$	2.16062	+	11.0238i	0.0904982	+	0.461735i
$571$	−5.96309	−	5.00363i	−0.249548	−	0.209395i	0.509430	−	0.860512i	$-0.329856\pi$
$571$	−5.96309	−	5.00363i	−0.249548	−	0.209395i	−0.758977	+	0.651117i	$0.774301\pi$
$572$	0.00266379	−	0.0151071i	0.000111379	−	0.000631661i
$573$	2.39000	+	0.374727i	0.0998438	+	0.0156544i
$574$	8.37187	+	6.41510i	0.349435	+	0.267761i
$575$	−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	$-0.197445\pi$
$577$	17.2269	+	9.94598i	0.717167	+	0.414056i	−0.0965422	+	0.995329i	$0.530778\pi$
$578$	−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
$581$	20.5956	−	13.1401i	0.854447	−	0.545144i
$582$	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	−0.394533	+	0.918882i	$0.629093\pi$
$587$	−33.1432	+	27.8104i	−1.36796	+	1.14786i	−0.973432	+	0.228977i	$0.926462\pi$
$588$	0.887998	+	0.218679i	0.0366204	+	0.00901816i
$589$	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	$-0.752325\pi$
$593$	−34.6890			−1.42451			−0.712253	+	0.701923i	$0.752325\pi$
$594$	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	0.891748	−	0.452532i	$-0.149479\pi$
$599$	38.5459	+	6.79668i	1.57494	+	0.277705i	0.683194	+	0.730237i	$0.260590\pi$
$600$	2.46822	+	6.40014i	0.100765	+	0.261285i
$601$	−5.30537	−	6.32270i	−0.216411	−	0.257908i	0.646907	−	0.762569i	$-0.276062\pi$
$601$	−5.30537	−	6.32270i	−0.216411	−	0.257908i	−0.863318	+	0.504660i	$0.831618\pi$
$602$	−16.7423	+	15.3620i	−0.682364	+	0.626109i
$603$	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	$-0.0557814\pi$
$607$	2.91471	+	8.00809i	0.118304	+	0.325038i	−0.866380	+	0.499385i	$0.833559\pi$
$608$	−0.711573	+	0.258992i	−0.0288581	+	0.0105035i
$609$	5.55814	−	5.29801i	0.225227	−	0.214686i
$610$	−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	0.987907	−	0.155049i	$-0.0495537\pi$
$613$	8.90517	+	15.4242i	0.359677	+	0.622978i	−0.628230	+	0.778028i	$0.716220\pi$
$614$	−1.44446	+	1.21205i	−0.0582938	+	0.0489143i
$615$	−11.3380	+	4.37249i	−0.457190	+	0.176316i
$616$	0.682529	+	15.3969i	0.0274999	+	0.620358i
$617$	0.725589	−	0.864723i	0.0292111	−	0.0348125i	−0.751241	−	0.660028i	$-0.770544\pi$
$617$	0.725589	−	0.864723i	0.0292111	−	0.0348125i	0.780452	+	0.625215i	$0.214989\pi$
$618$	−19.3005	−	6.61211i	−0.776380	−	0.265978i
$619$	11.5905	−	31.8445i	0.465860	−	1.27994i	−0.455155	−	0.890412i	$-0.650416\pi$
$619$	11.5905	−	31.8445i	0.465860	−	1.27994i	0.921015	−	0.389527i	$-0.127362\pi$
$620$			0.272559i			0.0109462i
$621$	30.7398	+	3.62876i	1.23355	+	0.145617i
$622$		−	35.2453i		−	1.41321i
$623$	−32.9742	−	4.31877i	−1.32108	−	0.173028i
$624$	−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
$630$	−20.6015	+	20.3987i	−0.820783	+	0.812702i
$631$	5.72941	−	9.92363i	0.228084	−	0.395054i	−0.729156	−	0.684347i	$-0.760087\pi$
$631$	5.72941	−	9.92363i	0.228084	−	0.395054i	0.957240	+	0.289294i	$0.0934205\pi$
$632$	−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
$637$	0.554532	−	0.389390i	0.0219713	−	0.0154282i
$638$	−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	0.972004	−	0.234963i	$-0.0754968\pi$
$641$	14.4774	+	17.2535i	0.571824	+	0.681474i	−0.400180	+	0.916437i	$0.631052\pi$
$642$	−3.34313	+	21.3224i	−0.131943	+	0.841528i
$643$	−2.47158	−	0.435807i	−0.0974698	−	0.0171866i	0.124701	−	0.992194i	$-0.460203\pi$
$643$	−2.47158	−	0.435807i	−0.0974698	−	0.0171866i	−0.222170	+	0.975008i	$0.571314\pi$
$644$	0.548227	−	1.05485i	0.0216032	−	0.0415670i
$645$	−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	$-0.373841\pi$
$647$	19.6391			0.772091			0.386045	+	0.922480i	$0.373841\pi$
$648$	6.72863	−	24.0291i	0.264326	−	0.943954i
$649$		−	15.5195i		−	0.609195i
$650$	−0.187180	−	0.0681279i	−0.00734180	−	0.00267220i
$651$	5.98353	−	2.61755i	0.234513	−	0.102590i
$652$	−0.0899383	−	0.0754672i	−0.00352225	−	0.00295552i
$653$	−11.3035	−	1.99311i	−0.442340	−	0.0779965i	−0.0519576	−	0.998649i	$-0.516546\pi$
$653$	−11.3035	−	1.99311i	−0.442340	−	0.0779965i	−0.390382	+	0.920653i	$0.627657\pi$
$654$	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
$658$	15.3515	+	4.82905i	0.598463	+	0.188256i
$659$	29.2489	−	5.15736i	1.13937	−	0.200902i	0.428042	−	0.903759i	$-0.359203\pi$
$659$	29.2489	−	5.15736i	1.13937	−	0.200902i	0.711332	+	0.702856i	$0.248092\pi$
$660$	0.609208	+	0.336451i	0.0237134	+	0.0130963i
$661$	3.15998	+	8.68198i	0.122909	+	0.337690i	0.985854	−	0.167609i	$-0.0536045\pi$
$661$	3.15998	+	8.68198i	0.122909	+	0.337690i	−0.862945	+	0.505299i	$0.831382\pi$
$662$	−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
$665$	11.3622	+	3.57415i	0.440605	+	0.138599i
$666$	−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
$672$	−1.57357	−	1.15897i	−0.0607017	−	0.0447084i
$673$	−0.574231	−	0.209003i	−0.0221350	−	0.00805648i	0.330929	−	0.943656i	$-0.392638\pi$
$673$	−0.574231	−	0.209003i	−0.0221350	−	0.00805648i	−0.353064	+	0.935599i	$0.614860\pi$
$674$			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	$-0.400197\pi$
$677$	−1.73677	−	0.632133i	−0.0667495	−	0.0242948i	−0.375179	+	0.926952i	$0.622419\pi$
$678$	21.8256	+	7.47718i	0.838207	+	0.287159i
$679$	18.6898	−	35.9612i	0.717247	−	1.38007i
$680$	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	−0.833830	−	0.552021i	$-0.813857\pi$
$683$	−20.1934	+	11.6587i	−0.772680	+	0.446107i	0.0611497	+	0.998129i	$0.480523\pi$
$684$	0.392757	−	0.0847617i	0.0150174	−	0.00324095i
$685$	−30.7336	−	17.7440i	−1.17427	−	0.677965i
$686$	17.9860	−	19.7073i	0.686708	−	0.752427i
$687$	−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	$-0.518877\pi$
$691$	5.95279	−	1.04964i	0.226455	−	0.0399301i	0.285724	+	0.958312i	$0.407766\pi$
$692$	−0.253385	+	0.438876i	−0.00963225	+	0.0166836i
$693$	1.53558	−	16.6052i	0.0583317	−	0.630779i
$694$	−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
$700$	−0.282646	−	0.0370194i	−0.0106830	−	0.00139920i
$701$		−	5.95954i		−	0.225089i	−0.993647	−	0.112544i	$-0.964100\pi$
$701$		−	5.95954i		−	0.225089i	0.993647	−	0.112544i	$-0.0359001\pi$
$702$	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
$707$	−1.23284	−	27.8112i	−0.0463658	−	1.04595i
$708$	0.750939	+	0.606165i	0.0282220	+	0.0227811i
$709$	19.8453	−	16.6521i	0.745304	−	0.625384i	−0.188952	−	0.981986i	$-0.560509\pi$
$709$	19.8453	−	16.6521i	0.745304	−	0.625384i	0.934256	+	0.356602i	$0.116065\pi$
$710$	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
$714$	12.2655	+	50.5937i	0.459025	+	1.89342i
$715$	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	0.240943	+	0.970539i	$0.422543\pi$
$719$	−19.3073	+	33.4412i	−0.720040	+	1.24715i	−0.960983	+	0.276607i	$0.910790\pi$
$720$	29.1966	−	11.9020i	1.08809	−	0.443563i
$721$	−15.9392	+	14.6251i	−0.593606	+	0.544669i
$722$	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	0.685916	+	0.727681i	$0.259402\pi$
$727$	−8.28491	+	22.7626i	−0.307270	+	0.844218i	−0.993186	+	0.116537i	$0.962821\pi$
$728$	−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	0.0509402	−	0.998702i	$-0.483778\pi$
$733$	27.7677	−	33.0923i	1.02562	−	1.22229i	0.974684	−	0.223589i	$-0.0717773\pi$
$734$	−4.72854	+	26.8169i	−0.174533	+	0.989828i
$735$	8.55858	+	29.5250i	0.315688	+	1.08905i
$736$	−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	−0.836020	−	0.548700i	$-0.815123\pi$
$739$	1.55436	−	2.69223i	0.0571780	−	0.0990352i	0.893198	+	0.449664i	$0.148456\pi$
$740$	−0.125027	−	0.709062i	−0.00459608	−	0.0260656i
$741$	0.143923	−	0.260599i	0.00528714	−	0.00957336i
$742$	−29.7288	+	18.9672i	−1.09138	+	0.696308i
$743$	−4.69492	−	12.8992i	−0.172240	−	0.473225i	0.823296	−	0.567613i	$-0.192133\pi$
$743$	−4.69492	−	12.8992i	−0.172240	−	0.473225i	−0.995536	+	0.0943876i	$0.969911\pi$
$744$	−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
$749$	18.1649	+	13.9192i	0.663731	+	0.508596i
$750$	−14.1927	+	17.5824i	−0.518244	+	0.642018i
$751$	−2.41618	+	13.7028i	−0.0881677	+	0.500024i	0.908460	+	0.417971i	$0.137259\pi$
$751$	−2.41618	+	13.7028i	−0.0881677	+	0.500024i	−0.996628	+	0.0820528i	$0.973852\pi$
$752$	−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
$756$	0.743492	+	0.722870i	0.0270405	+	0.0262905i
$757$	−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	0.864812	+	0.502095i	$0.167437\pi$
$761$	−3.29855	+	18.7070i	−0.119572	+	0.678128i	−0.984384	+	0.176032i	$0.943674\pi$
$762$	−16.1835	−	41.9640i	−0.586265	−	1.52020i
$763$	3.79178	−	4.94837i	0.137272	−	0.179143i
$764$	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	−0.969653	−	0.244485i	$-0.921381\pi$
$769$	−10.6489	−	29.2575i	−0.384008	−	1.05505i	0.585645	−	0.810568i	$-0.300841\pi$
$770$	17.1167	−	10.9206i	0.616845	−	0.393552i
$771$	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	$-0.852053\pi$
$773$	−1.63416	+	2.83045i	−0.0587768	+	0.101804i	0.835140	+	0.550038i	$0.185387\pi$
$774$	−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
$777$	−14.3654	+	9.55427i	−0.515357	+	0.342758i
$778$	−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	$-0.914746\pi$
$787$	−15.0442	+	17.9290i	−0.536269	+	0.639100i	0.428078	+	0.903742i	$0.359191\pi$
$788$	−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
$791$	18.0245	−	16.5386i	0.640878	−	0.588044i
$792$	−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	$-0.763910\pi$
$797$	−24.5022	+	8.91806i	−0.867912	+	0.315894i	−0.130590	+	0.991436i	$0.541687\pi$
$798$	3.30432	−	11.2470i	0.116972	−	0.398138i
$799$	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
$805$	39.9207	−	1.76965i	1.40702	−	0.0623719i
$806$	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	$-0.856322\pi$
$809$		−	24.8140i		−	0.872412i	0.899847	−	0.436206i	$-0.143678\pi$
$810$	−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	$0.842160\pi$
$812$	0.0434266	−	0.331566i	0.00152397	−	0.0116357i
$813$	−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
$819$	0.765715	−	0.0631760i	0.0267562	−	0.00220755i
$820$	−0.264600	+	0.458301i	−0.00924025	+	0.0160046i
$821$	18.1866	−	3.20679i	0.634716	−	0.111918i	0.152973	−	0.988230i	$-0.451115\pi$
$821$	18.1866	−	3.20679i	0.634716	−	0.111918i	0.481743	+	0.876313i	$0.340004\pi$
$822$	−16.8848	+	30.5731i	−0.588924	+	1.06636i
$823$	−14.9272	+	5.43305i	−0.520329	+	0.189384i	−0.588815	−	0.808268i	$-0.700405\pi$
$823$	−14.9272	+	5.43305i	−0.520329	+	0.189384i	0.0684859	+	0.997652i	$0.478183\pi$
$824$	21.3023	−	7.75339i	0.742099	−	0.270102i
$825$	0.0988057	+	5.19702i	0.00343997	+	0.180937i
$826$	26.0049	−	10.7919i	0.904825	−	0.375498i
$827$	6.41452	+	3.70343i	0.223055	+	0.128781i	0.607364	−	0.794424i	$-0.292227\pi$
$827$	6.41452	+	3.70343i	0.223055	+	0.128781i	−0.384309	+	0.923204i	$0.625560\pi$
$828$	1.14092	−	0.717876i	0.0396498	−	0.0249479i
$829$	−6.47519	+	3.73846i	−0.224893	+	0.129842i	−0.608214	−	0.793773i	$-0.708114\pi$
$829$	−6.47519	+	3.73846i	−0.224893	+	0.129842i	0.383321	+	0.923615i	$0.374780\pi$
$830$	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
$833$	53.3373	+	14.2155i	1.84803	+	0.492537i
$834$	−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	$-0.298519\pi$
$839$	15.2482	+	5.54991i	0.526428	+	0.191604i	−0.0651148	+	0.997878i	$0.520741\pi$
$840$	3.57560	−	32.0153i	0.123370	−	1.10463i
$841$	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
$847$	5.22859	−	16.6216i	0.179657	−	0.571125i
$848$	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	$-0.532585\pi$
$853$	4.14761	−	0.731336i	0.142012	−	0.0250405i	0.244202	+	0.969724i	$0.421474\pi$
$854$	−13.8940	+	44.1687i	−0.475442	+	1.51142i
$855$	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	$-0.504693\pi$
$857$	28.3201	−	23.7634i	0.967397	−	0.811742i	0.982140	+	0.188149i	$0.0602488\pi$
$858$	−0.182597	−	0.473477i	−0.00623375	−	0.0161642i
$859$	−15.3634	−	2.70898i	−0.524191	−	0.0924291i	−0.0947102	−	0.995505i	$-0.530192\pi$
$859$	−15.3634	−	2.70898i	−0.524191	−	0.0924291i	−0.429481	+	0.903076i	$0.641304\pi$
$860$	−0.873353	−	0.732830i	−0.0297811	−	0.0249893i
$861$	12.6023	+	1.40747i	0.429484	+	0.0479665i
$862$	−25.1575	−	9.15659i	−0.856868	−	0.311875i
$863$		−	29.1929i		−	0.993737i	−0.867826	−	0.496868i	$-0.834483\pi$
$863$		−	29.1929i		−	0.993737i	0.867826	−	0.496868i	$-0.165517\pi$
$864$	−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
$868$	0.131162	−	0.252370i	0.00445192	−	0.00856600i
$869$	−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
$875$	9.18336	+	22.1288i	0.310454	+	0.748091i
$876$	−0.0344834	−	1.81377i	−0.00116508	−	0.0612815i
$877$	42.4663	−	15.4565i	1.43399	−	0.521928i	0.495914	−	0.868371i	$-0.334833\pi$
$877$	42.4663	−	15.4565i	1.43399	−	0.521928i	0.938071	+	0.346443i	$0.112611\pi$
$878$	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	−0.448247	−	0.893910i	$-0.647951\pi$
$881$	16.3257	−	28.2769i	0.550025	−	0.952672i	0.998272	−	0.0587620i	$-0.0187153\pi$
$882$	28.8918	−	8.97377i	0.972837	−	0.302163i
$883$	16.0749	+	27.8425i	0.540963	+	0.936975i	0.998849	+	0.0479641i	$0.0152733\pi$
$883$	16.0749	+	27.8425i	0.540963	+	0.936975i	−0.457886	+	0.889011i	$0.651393\pi$
$884$	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	$-0.342502\pi$
$887$	−9.21436	−	7.73177i	−0.309388	−	0.259607i	−0.784239	+	0.620459i	$0.786946\pi$
$888$	17.7422	−	3.47739i	0.595388	−	0.116694i
$889$	−47.2853	−	6.19316i	−1.58590	−	0.207712i
$890$		−	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
$896$	31.4831	−	1.39562i	1.05178	−	0.0466243i
$897$	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
$903$	−7.70060	+	26.2106i	−0.256260	+	0.872235i
$904$	−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	−0.949269	−	0.314464i	$-0.898175\pi$
$907$	−4.96322	−	28.1478i	−0.164801	−	0.934633i	0.784468	−	0.620169i	$-0.212936\pi$
$908$	0.0596405	−	0.103300i	0.00197924	−	0.00342815i
$909$	14.7324	−	27.9170i	0.488644	−	0.925949i
$910$	0.632446	+	0.689270i	0.0209654	+	0.0228491i
$911$	−22.1361	−	26.3808i	−0.733403	−	0.874036i	0.262456	−	0.964944i	$-0.415467\pi$
$911$	−22.1361	−	26.3808i	−0.733403	−	0.874036i	−0.995859	+	0.0909082i	$0.971023\pi$
$912$	−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
$924$	−0.402175	−	0.604695i	−0.0132306	−	0.0198930i
$925$	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	0.999271	+	0.0381876i	$0.0121585\pi$
$929$	2.23489	+	12.6747i	0.0733243	+	0.415843i	−0.925946	+	0.377655i	$0.876730\pi$
$930$	4.65586	+	7.72140i	0.152672	+	0.253195i
$931$	−8.80057	−	8.77713i	−0.288427	−	0.287659i
$932$	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	$-0.644915\pi$
$937$	3.62026	−	2.09016i	0.118269	−	0.0682824i	0.557967	+	0.829863i	$0.311581\pi$
$938$	−34.2245	−	26.2251i	−1.11747	−	0.856281i
$939$	−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	$-0.167633\pi$
$941$	15.9401	+	13.3754i	0.519633	+	0.436024i	−0.344871	+	0.938650i	$0.612077\pi$
$942$	−34.6421	−	11.8680i	−1.12870	−	0.386679i
$943$	5.63777	−	15.4896i	0.183591	−	0.504412i
$944$	−30.6195			−0.996581
$945$	−8.54715	+	33.7922i	−0.278039	+	1.09926i
$946$	18.0436			0.586647
$947$	−12.6075	+	34.6388i	−0.409688	+	1.12561i	0.547667	+	0.836697i	$0.315516\pi$
$947$	−12.6075	+	34.6388i	−0.409688	+	1.12561i	−0.957355	+	0.288913i	$0.906706\pi$
$948$	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
$952$	−45.9156	−	35.1836i	−1.48813	−	1.14031i
$953$	20.4679	−	11.8171i	0.663020	−	0.382795i	−0.130407	−	0.991461i	$-0.541628\pi$
$953$	20.4679	−	11.8171i	0.663020	−	0.382795i	0.793427	+	0.608666i	$0.208295\pi$
$954$	−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
$959$	19.9182	+	31.2194i	0.643194	+	1.00813i
$960$	−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
$966$	−2.48810	−	39.2480i	−0.0800534	−	1.26278i
$967$	7.67106	−	43.5048i	0.246685	−	1.39902i	−0.569862	−	0.821740i	$-0.693004\pi$
$967$	7.67106	−	43.5048i	0.246685	−	1.39902i	0.816547	−	0.577279i	$-0.195885\pi$
$968$	−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	$-0.678193\pi$
$971$	−33.0944			−1.06205			−0.531025	+	0.847356i	$0.678193\pi$
$972$	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	−0.672695	−	0.739920i	$-0.734863\pi$
$977$	−48.6949	−	8.58623i	−1.55789	−	0.274698i	−0.885194	+	0.465222i	$0.845974\pi$
$978$	−3.83701	−	0.601603i	−0.122694	−	0.0192371i
$979$	16.9749	+	20.2299i	0.542521	+	0.646552i
$980$	1.09763	+	0.766391i	0.0350626	+	0.0244815i
$981$	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	−0.988679	−	0.150048i	$-0.952057\pi$
$983$	−3.47841	−	19.7270i	−0.110944	−	0.629194i	0.877735	−	0.479147i	$-0.159054\pi$
$984$	−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
$987$	18.8038	−	4.55862i	0.598530	−	0.145103i
$988$	−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	−0.722360	−	0.691517i	$-0.756943\pi$
$991$	−30.2226	−	52.3470i	−0.960051	−	1.66286i	−0.237691	−	0.971341i	$-0.576391\pi$
$992$	−0.465596	+	0.390682i	−0.0147827	+	0.0124042i
$993$	−14.9418	−	12.0612i	−0.474163	−	0.382749i
$994$	−2.32398	−	52.4258i	−0.0737123	−	1.66284i
$995$	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	0.548315	+	0.836272i	$0.315269\pi$
$997$	−12.9226	+	35.5046i	−0.409264	+	1.12444i	−0.957579	+	0.288171i	$0.906953\pi$
$998$			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.104.17	yes	132
3.2	odd	2		567.2.be.a.503.5		132
7.6	odd	2	inner	189.2.be.a.104.18	yes	132
21.20	even	2		567.2.be.a.503.6		132
27.7	even	9		567.2.be.a.62.6		132
27.20	odd	18	inner	189.2.be.a.20.18	yes	132
189.20	even	18	inner	189.2.be.a.20.17	✓	132
189.34	odd	18		567.2.be.a.62.5		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.17	✓	132	189.20	even	18	inner
189.2.be.a.20.18	yes	132	27.20	odd	18	inner
189.2.be.a.104.17	yes	132	1.1	even	1	trivial
189.2.be.a.104.18	yes	132	7.6	odd	2	inner
567.2.be.a.62.5		132	189.34	odd	18
567.2.be.a.62.6		132	27.7	even	9
567.2.be.a.503.5		132	3.2	odd	2
567.2.be.a.503.6		132	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
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} +(-1.60923 + 2.10009i) 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} +(2.05009 + 3.21327i) 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} +(4.10564 + 2.03561i) 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} +(4.53523 + 4.94272i) 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} +(4.77867 - 4.55503i) 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} +(-1.82075 - 6.75906i) 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} +(-0.952641 + 7.27350i) 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} +(2.09221 - 7.65654i) 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} +(8.92585 - 3.70418i) 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} +(-2.56342 + 4.93232i) 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} +(-0.138536 - 0.316683i) 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} +(-0.244303 - 0.0768495i) 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} +(-10.0472 - 0.865519i) 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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