LMFDB - Embedded newform 189.2.be.a.104.15

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			104.15
Character	$\chi$	$=$	189.104
Dual form			189.2.be.a.20.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.471430 - 1.29524i) q^{2} +(-1.37746 + 1.05005i) q^{3} +(0.0766803 + 0.0643424i) q^{4} +(0.459149 - 2.60396i) q^{5} +(0.710690 + 2.27917i) q^{6} +(1.90985 + 1.83097i) q^{7} +(2.50689 - 1.44736i) q^{8} +(0.794802 - 2.89280i) q^{9} +(-3.15631 - 1.82230i) q^{10} +(-0.681802 + 0.120220i) q^{11} +(-0.173187 - 0.00811128i) q^{12} +(-0.171823 - 0.472079i) q^{13} +(3.27192 - 1.61055i) q^{14} +(2.10182 + 4.06899i) q^{15} +(-0.658089 - 3.73221i) q^{16} +(2.42375 - 4.19806i) q^{17} +(-3.37219 - 2.39321i) q^{18} +(1.03438 - 0.597199i) q^{19} +(0.202753 - 0.170130i) q^{20} +(-4.55336 - 0.516662i) q^{21} +(-0.165708 + 0.939774i) q^{22} +(-4.74912 + 5.65978i) q^{23} +(-1.93336 + 4.62603i) q^{24} +(-1.87135 - 0.681115i) q^{25} -0.692459 q^{26} +(1.94277 + 4.81930i) q^{27} +(0.0286387 + 0.263284i) q^{28} +(-2.19806 + 6.03911i) q^{29} +(6.26119 - 0.804131i) q^{30} +(-5.17613 + 6.16868i) q^{31} +(0.557110 + 0.0982336i) q^{32} +(0.812919 - 0.881523i) q^{33} +(-4.29488 - 5.11844i) q^{34} +(5.64470 - 4.13250i) q^{35} +(0.247075 - 0.170681i) q^{36} +(-3.71414 + 6.43307i) q^{37} +(-0.285881 - 1.62131i) q^{38} +(0.732384 + 0.469849i) q^{39} +(-2.61782 - 7.19241i) q^{40} +(-3.25278 + 1.18391i) q^{41} +(-2.81579 + 5.65413i) q^{42} +(-1.81376 - 10.2863i) q^{43} +(-0.0600160 - 0.0346503i) q^{44} +(-7.16781 - 3.39786i) q^{45} +(5.09191 + 8.81945i) q^{46} +(2.93133 - 2.45968i) q^{47} +(4.82549 + 4.44995i) q^{48} +(0.295069 + 6.99378i) q^{49} +(-1.76442 + 2.10275i) q^{50} +(1.06954 + 8.32773i) q^{51} +(0.0171993 - 0.0472546i) q^{52} -10.3394i q^{53} +(7.15804 - 0.244393i) q^{54} +1.83059i q^{55} +(7.43787 + 1.82582i) q^{56} +(-0.797730 + 1.90876i) q^{57} +(6.78588 + 5.69403i) q^{58} +(-1.13100 + 6.41423i) q^{59} +(-0.100640 + 0.447248i) q^{60} +(-2.36159 - 2.81444i) q^{61} +(5.54975 + 9.61245i) q^{62} +(6.81459 - 4.06956i) q^{63} +(4.17966 - 7.23938i) q^{64} +(-1.30817 + 0.230665i) q^{65} +(-0.758552 - 1.46850i) q^{66} +(-3.24000 + 1.17926i) q^{67} +(0.455968 - 0.165959i) q^{68} +(0.598694 - 12.7829i) q^{69} +(-2.69151 - 9.25944i) q^{70} +(0.286623 + 0.165482i) q^{71} +(-2.19443 - 8.40230i) q^{72} +(-3.13921 + 1.81243i) q^{73} +(6.58144 + 7.84345i) q^{74} +(3.29291 - 1.02679i) q^{75} +(0.117742 + 0.0207610i) q^{76} +(-1.52226 - 1.01876i) q^{77} +(0.953836 - 0.727115i) q^{78} +(9.71572 + 3.53623i) q^{79} -10.0207 q^{80} +(-7.73658 - 4.59840i) q^{81} +4.77127i q^{82} +(-12.8972 - 4.69419i) q^{83} +(-0.315910 - 0.332592i) q^{84} +(-9.81874 - 8.23890i) q^{85} +(-14.1784 - 2.50003i) q^{86} +(-3.31361 - 10.6267i) q^{87} +(-1.53520 + 1.28819i) q^{88} +(4.84538 + 8.39244i) q^{89} +(-7.78018 + 7.68221i) q^{90} +(0.536208 - 1.21620i) q^{91} +(-0.728328 + 0.128424i) q^{92} +(0.652525 - 13.9323i) q^{93} +(-1.80397 - 4.95636i) q^{94} +(-1.08015 - 2.96769i) q^{95} +(-0.870548 + 0.449679i) q^{96} +(3.19371 - 0.563137i) q^{97} +(9.19775 + 2.91489i) q^{98} +(-0.194125 + 2.06787i) 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 $

$2$	0.471430	−	1.29524i	0.333351	−	0.915875i	−0.653882	−	0.756596i	$-0.726861\pi$
$2$	0.471430	−	1.29524i	0.333351	−	0.915875i	0.987234	−	0.159279i	$-0.0509169\pi$
$3$	−1.37746	+	1.05005i	−0.795278	+	0.606245i
$3$	−1.37746	+	1.05005i	−0.795278	+	0.606245i
$4$	0.0766803	+	0.0643424i	0.0383402	+	0.0321712i
$5$	0.459149	−	2.60396i	0.205338	−	1.16453i	−0.691570	−	0.722310i	$-0.743081\pi$
$5$	0.459149	−	2.60396i	0.205338	−	1.16453i	0.896907	−	0.442218i	$-0.145808\pi$
$6$	0.710690	+	2.27917i	0.290138	+	0.930468i
$7$	1.90985	+	1.83097i	0.721856	+	0.692043i
$7$	1.90985	+	1.83097i	0.721856	+	0.692043i
$8$	2.50689	−	1.44736i	0.886321	−	0.511718i
$9$	0.794802	−	2.89280i	0.264934	−	0.964267i
$10$	−3.15631	−	1.82230i	−0.998113	−	0.576261i
$11$	−0.681802	+	0.120220i	−0.205571	+	0.0362477i	−0.275485	−	0.961305i	$-0.588839\pi$
$11$	−0.681802	+	0.120220i	−0.205571	+	0.0362477i	0.0699143	+	0.997553i	$0.477727\pi$
$12$	−0.173187	−	0.00811128i	−0.0499947	−	0.00234153i
$13$	−0.171823	−	0.472079i	−0.0476550	−	0.130931i	0.913582	−	0.406655i	$-0.133305\pi$
$13$	−0.171823	−	0.472079i	−0.0476550	−	0.130931i	−0.961237	+	0.275724i	$0.911083\pi$
$14$	3.27192	−	1.61055i	0.874457	−	0.430437i
$15$	2.10182	+	4.06899i	0.542689	+	1.05061i
$16$	−0.658089	−	3.73221i	−0.164522	−	0.933052i
$17$	2.42375	−	4.19806i	0.587846	−	1.01818i	−0.406668	−	0.913576i	$-0.633309\pi$
$17$	2.42375	−	4.19806i	0.587846	−	1.01818i	0.994514	−	0.104604i	$-0.0333574\pi$
$18$	−3.37219	−	2.39321i	−0.794832	−	0.564086i
$19$	1.03438	−	0.597199i	0.237303	−	0.137007i	−0.376634	−	0.926362i	$-0.622918\pi$
$19$	1.03438	−	0.597199i	0.237303	−	0.137007i	0.613936	+	0.789355i	$0.289585\pi$
$20$	0.202753	−	0.170130i	0.0453370	−	0.0380422i
$21$	−4.55336	−	0.516662i	−0.993624	−	0.112745i
$22$	−0.165708	+	0.939774i	−0.0353290	+	0.200361i
$23$	−4.74912	+	5.65978i	−0.990259	+	1.18014i	−0.00662300	+	0.999978i	$0.502108\pi$
$23$	−4.74912	+	5.65978i	−0.990259	+	1.18014i	−0.983636	+	0.180167i	$0.942336\pi$
$24$	−1.93336	+	4.62603i	−0.394645	+	0.944285i
$25$	−1.87135	−	0.681115i	−0.374270	−	0.136223i
$26$	−0.692459			−0.135802
$27$	1.94277	+	4.81930i	0.373886	+	0.927475i
$28$	0.0286387	+	0.263284i	0.00541221	+	0.0497560i
$29$	−2.19806	+	6.03911i	−0.408169	+	1.12143i	0.549984	+	0.835175i	$0.314634\pi$
$29$	−2.19806	+	6.03911i	−0.408169	+	1.12143i	−0.958152	+	0.286259i	$0.907588\pi$
$30$	6.26119	−	0.804131i	1.14313	−	0.146814i
$31$	−5.17613	+	6.16868i	−0.929661	+	1.10793i	0.0642712	+	0.997932i	$0.479528\pi$
$31$	−5.17613	+	6.16868i	−0.929661	+	1.10793i	−0.993932	+	0.109994i	$0.964917\pi$
$32$	0.557110	+	0.0982336i	0.0984841	+	0.0173654i
$33$	0.812919	−	0.881523i	0.141511	−	0.153453i
$34$	−4.29488	−	5.11844i	−0.736566	−	0.877806i
$35$	5.64470	−	4.13250i	0.954128	−	0.698519i
$36$	0.247075	−	0.170681i	0.0411792	−	0.0284469i
$37$	−3.71414	+	6.43307i	−0.610600	+	1.05759i	0.380539	+	0.924765i	$0.375738\pi$
$37$	−3.71414	+	6.43307i	−0.610600	+	1.05759i	−0.991139	+	0.132826i	$0.957595\pi$
$38$	−0.285881	−	1.62131i	−0.0463759	−	0.263011i
$39$	0.732384	+	0.469849i	0.117275	+	0.0752360i
$40$	−2.61782	−	7.19241i	−0.413914	−	1.13722i
$41$	−3.25278	+	1.18391i	−0.507998	+	0.184896i	−0.583288	−	0.812265i	$-0.698234\pi$
$41$	−3.25278	+	1.18391i	−0.507998	+	0.184896i	0.0752897	+	0.997162i	$0.476012\pi$
$42$	−2.81579	+	5.65413i	−0.434486	+	0.872452i
$43$	−1.81376	−	10.2863i	−0.276596	−	1.56865i	−0.733846	−	0.679315i	$-0.762277\pi$
$43$	−1.81376	−	10.2863i	−0.276596	−	1.56865i	0.457250	−	0.889338i	$-0.348834\pi$
$44$	−0.0600160	−	0.0346503i	−0.00904776	−	0.00522373i
$45$	−7.16781	−	3.39786i	−1.06851	−	0.506523i
$46$	5.09191	+	8.81945i	0.750761	+	1.30036i
$47$	2.93133	−	2.45968i	0.427579	−	0.358781i	−0.403458	−	0.914998i	$-0.632192\pi$
$47$	2.93133	−	2.45968i	0.427579	−	0.358781i	0.831037	+	0.556217i	$0.187748\pi$
$48$	4.82549	+	4.44995i	0.696499	+	0.642295i
$49$	0.295069	+	6.99378i	0.0421527	+	0.999111i
$50$	−1.76442	+	2.10275i	−0.249527	+	0.297374i
$51$	1.06954	+	8.32773i	0.149765	+	1.16611i
$52$	0.0171993	−	0.0472546i	0.00238511	−	0.00655304i
$53$		−	10.3394i		−	1.42022i	−0.704090	−	0.710111i	$-0.748645\pi$
$53$		−	10.3394i		−	1.42022i	0.704090	−	0.710111i	$-0.251355\pi$
$54$	7.15804	−	0.244393i	0.974086	−	0.0332577i
$55$			1.83059i			0.246836i
$56$	7.43787	+	1.82582i	0.993927	+	0.243986i
$57$	−0.797730	+	1.90876i	−0.105662	+	0.252822i
$58$	6.78588	+	5.69403i	0.891030	+	0.747663i
$59$	−1.13100	+	6.41423i	−0.147244	+	0.835061i	0.818294	+	0.574799i	$0.194920\pi$
$59$	−1.13100	+	6.41423i	−0.147244	+	0.835061i	−0.965538	+	0.260262i	$0.916191\pi$
$60$	−0.100640	+	0.447248i	−0.0129926	+	0.0577395i
$61$	−2.36159	−	2.81444i	−0.302371	−	0.360352i	0.593369	−	0.804931i	$-0.297798\pi$
$61$	−2.36159	−	2.81444i	−0.302371	−	0.360352i	−0.895739	+	0.444579i	$0.853353\pi$
$62$	5.54975	+	9.61245i	0.704819	+	1.22078i
$63$	6.81459	−	4.06956i	0.858558	−	0.512716i
$64$	4.17966	−	7.23938i	0.522457	−	0.904922i
$65$	−1.30817	+	0.230665i	−0.162258	+	0.0286105i
$66$	−0.758552	−	1.46850i	−0.0933712	−	0.180760i
$67$	−3.24000	+	1.17926i	−0.395829	+	0.144070i	−0.532263	−	0.846579i	$-0.678658\pi$
$67$	−3.24000	+	1.17926i	−0.395829	+	0.144070i	0.136434	+	0.990649i	$0.456436\pi$
$68$	0.455968	−	0.165959i	0.0552942	−	0.0201254i
$69$	0.598694	−	12.7829i	0.0720743	−	1.53888i
$70$	−2.69151	−	9.25944i	−0.321697	−	1.10671i
$71$	0.286623	+	0.165482i	0.0340159	+	0.0196391i	0.516912	−	0.856039i	$-0.327082\pi$
$71$	0.286623	+	0.165482i	0.0340159	+	0.0196391i	−0.482896	+	0.875678i	$0.660415\pi$
$72$	−2.19443	−	8.40230i	−0.258616	−	0.990221i
$73$	−3.13921	+	1.81243i	−0.367417	+	0.212128i	−0.672329	−	0.740252i	$-0.734706\pi$
$73$	−3.13921	+	1.81243i	−0.367417	+	0.212128i	0.304912	+	0.952380i	$0.401373\pi$
$74$	6.58144	+	7.84345i	0.765077	+	0.911783i
$75$	3.29291	−	1.02679i	0.380233	−	0.118564i
$76$	0.117742	+	0.0207610i	0.0135059	+	0.00238145i
$77$	−1.52226	−	1.01876i	−0.173478	−	0.116098i
$78$	0.953836	−	0.727115i	0.108001	−	0.0823295i
$79$	9.71572	+	3.53623i	1.09310	+	0.397857i	0.824770	−	0.565469i	$-0.191305\pi$
$79$	9.71572	+	3.53623i	1.09310	+	0.397857i	0.268334	+	0.963326i	$0.413527\pi$
$80$	−10.0207			−1.12035
$81$	−7.73658	−	4.59840i	−0.859620	−	0.510934i
$82$			4.77127i			0.526898i
$83$	−12.8972	−	4.69419i	−1.41565	−	0.515254i	−0.482866	−	0.875694i	$-0.660404\pi$
$83$	−12.8972	−	4.69419i	−1.41565	−	0.515254i	−0.932782	+	0.360440i	$0.882627\pi$
$84$	−0.315910	−	0.332592i	−0.0344686	−	0.0362888i
$85$	−9.81874	−	8.23890i	−1.06499	−	0.893634i
$86$	−14.1784	−	2.50003i	−1.52889	−	0.269585i
$87$	−3.31361	−	10.6267i	−0.355256	−	1.13930i
$88$	−1.53520	+	1.28819i	−0.163653	+	0.137321i
$89$	4.84538	+	8.39244i	0.513609	+	0.889597i	0.999875	+	0.0157861i	$0.00502510\pi$
$89$	4.84538	+	8.39244i	0.513609	+	0.889597i	−0.486266	+	0.873811i	$0.661642\pi$
$90$	−7.78018	+	7.68221i	−0.820103	+	0.809776i
$91$	0.536208	−	1.21620i	0.0562099	−	0.127493i
$92$	−0.728328	+	0.128424i	−0.0759334	+	0.0133891i
$93$	0.652525	−	13.9323i	0.0676637	−	1.44471i
$94$	−1.80397	−	4.95636i	−0.186065	−	0.511209i
$95$	−1.08015	−	2.96769i	−0.110821	−	0.304478i
$96$	−0.870548	+	0.449679i	−0.0888500	+	0.0458952i
$97$	3.19371	−	0.563137i	0.324272	−	0.0571779i	−0.00914255	−	0.999958i	$-0.502910\pi$
$97$	3.19371	−	0.563137i	0.324272	−	0.0571779i	0.333415	+	0.942780i	$0.391799\pi$
$98$	9.19775	+	2.91489i	0.929113	+	0.294448i
$99$	−0.194125	+	2.06787i	−0.0195103	+	0.207828i
$100$	−0.0996710	−	0.172635i	−0.00996710	−	0.0172635i
$101$	−8.65691	+	7.26401i	−0.861394	+	0.722796i	−0.962268	−	0.272104i	$-0.912281\pi$
$101$	−8.65691	+	7.26401i	−0.861394	+	0.722796i	0.100874	+	0.994899i	$0.467836\pi$
$102$	11.2906	+	2.54063i	1.11794	+	0.251560i
$103$	18.1129	+	3.19380i	1.78472	+	0.314694i	0.965815	−	0.259233i	$-0.0834699\pi$
$103$	18.1129	+	3.19380i	1.78472	+	0.314694i	0.818906	+	0.573928i	$0.194581\pi$
$104$	−1.11401	−	0.934763i	−0.109237	−	0.0916610i
$105$	−3.43604	+	11.6196i	−0.335323	+	1.13395i
$106$	−13.3920	−	4.87429i	−1.30075	−	0.473433i
$107$		−	10.3651i		−	1.00203i	−0.865439	−	0.501014i	$-0.832960\pi$
$107$		−	10.3651i		−	1.00203i	0.865439	−	0.501014i	$-0.167040\pi$
$108$	−0.161114	+	0.494548i	−0.0155032	+	0.0475879i
$109$	12.4544			1.19292			0.596459	−	0.802643i	$-0.296574\pi$
$109$	12.4544			1.19292			0.596459	+	0.802643i	$0.296574\pi$
$110$	2.37105	+	0.862993i	0.226071	+	0.0822832i
$111$	−1.63895	−	12.7613i	−0.155562	−	1.21125i
$112$	5.57672	−	8.33291i	0.526951	−	0.787386i
$113$	−2.99092	−	0.527381i	−0.281362	−	0.0496118i	0.0311861	−	0.999514i	$-0.490072\pi$
$113$	−2.99092	−	0.527381i	−0.281362	−	0.0496118i	−0.312548	+	0.949902i	$0.601183\pi$
$114$	2.09624	+	1.93310i	0.196331	+	0.181052i
$115$	12.5573	+	14.9652i	1.17097	+	1.39551i
$116$	−0.557118	+	0.321653i	−0.0517272	+	0.0298647i
$117$	−1.50219	+	0.121839i	−0.138878	+	0.0112641i
$118$	7.77479	+	4.48878i	0.715728	+	0.413226i
$119$	12.3156	−	3.57985i	1.12896	−	0.328164i
$120$	11.1583	+	7.15843i	1.01861	+	0.653473i
$121$	−9.88622	+	3.59829i	−0.898747	+	0.327117i
$122$	−4.75870	+	1.73203i	−0.430833	+	0.156810i
$123$	3.23741	−	5.04636i	0.291907	−	0.455015i
$124$	−0.793815	+	0.139971i	−0.0712867	+	0.0125698i
$125$	3.97751	−	6.88925i	0.355759	−	0.616193i
$126$	−2.05846	−	10.7451i	−0.183382	−	0.957247i
$127$	−1.53317	−	2.65553i	−0.136047	−	0.235640i	0.789950	−	0.613171i	$-0.210107\pi$
$127$	−1.53317	−	2.65553i	−0.136047	−	0.235640i	−0.925997	+	0.377531i	$0.876773\pi$
$128$	−6.67908	−	7.95982i	−0.590353	−	0.703555i
$129$	13.2995	+	12.2645i	1.17096	+	1.07983i
$130$	−0.317942	+	1.80314i	−0.0278854	+	0.158146i
$131$	−3.91000	−	3.28088i	−0.341618	−	0.286652i	0.455796	−	0.890084i	$-0.349355\pi$
$131$	−3.91000	−	3.28088i	−0.341618	−	0.286652i	−0.797414	+	0.603433i	$0.793799\pi$
$132$	0.119054	−	0.0152902i	0.0103623	−	0.00133084i
$133$	3.06897	+	0.753359i	0.266113	+	0.0653245i
$134$			4.75253i			0.410556i
$135$	13.4413	−	2.84612i	1.15684	−	0.244955i
$136$		−	14.0321i		−	1.20325i
$137$	−1.34924	+	3.70701i	−0.115274	+	0.316712i	−0.983890	−	0.178773i	$-0.942787\pi$
$137$	−1.34924	+	3.70701i	−0.115274	+	0.316712i	0.868617	+	0.495484i	$0.165009\pi$
$138$	−16.2747	−	6.80171i	−1.38540	−	0.579000i
$139$	−6.85841	+	8.17354i	−0.581723	+	0.693271i	−0.973993	−	0.226580i	$-0.927246\pi$
$139$	−6.85841	+	8.17354i	−0.581723	+	0.693271i	0.392270	+	0.919850i	$0.371690\pi$
$140$	0.698732	+	0.0463124i	0.0590536	+	0.00391412i
$141$	−1.45502	+	6.46615i	−0.122535	+	0.544548i
$142$	0.349462	−	0.293234i	0.0293262	−	0.0246076i
$143$	0.173902	+	0.301208i	0.0145424	+	0.0251882i
$144$	−11.3196	−	1.06265i	−0.943298	−	0.0885538i
$145$	14.7164	+	8.49651i	1.22213	+	0.705597i
$146$	0.867613	+	4.92048i	0.0718041	+	0.407221i
$147$	−7.75024	−	9.32383i	−0.639229	−	0.769016i
$148$	−0.698721	+	0.254314i	−0.0574345	+	0.0209044i
$149$	−1.04865	−	2.88113i	−0.0859085	−	0.236032i	0.889298	−	0.457328i	$-0.151193\pi$
$149$	−1.04865	−	2.88113i	−0.0859085	−	0.236032i	−0.975207	+	0.221296i	$0.928971\pi$
$150$	0.222430	−	4.74918i	0.0181613	−	0.387769i
$151$	3.79814	+	21.5403i	0.309088	+	1.75293i	0.603609	+	0.797280i	$0.293729\pi$
$151$	3.79814	+	21.5403i	0.309088	+	1.75293i	−0.294521	+	0.955645i	$0.595160\pi$
$152$	1.72872	−	2.99423i	0.140218	−	0.242864i
$153$	−10.2178	−	10.3481i	−0.826056	−	0.836591i
$154$	−2.03718	+	1.49142i	−0.164161	+	0.120182i
$155$	13.6864	+	16.3108i	1.09932	+	1.31012i
$156$	0.0259283	+	0.0831515i	0.00207592	+	0.00665745i
$157$	6.86916	+	1.21122i	0.548218	+	0.0966657i	0.440895	−	0.897558i	$-0.354661\pi$
$157$	6.86916	+	1.21122i	0.548218	+	0.0966657i	0.107323	+	0.994224i	$0.465772\pi$
$158$	9.16056	−	10.9171i	0.728775	−	0.868521i
$159$	10.8568	+	14.2421i	0.861002	+	1.12947i
$160$	0.511594	−	1.40559i	0.0404450	−	0.111122i
$161$	−19.4330	+	2.11383i	−1.53154	+	0.166593i
$162$	−9.60331	+	7.85293i	−0.754507	+	0.616984i
$163$	15.9859			1.25211			0.626057	−	0.779777i	$-0.284668\pi$
$163$	15.9859			1.25211			0.626057	+	0.779777i	$0.284668\pi$
$164$	−0.325600	−	0.118509i	−0.0254251	−	0.00925397i
$165$	−1.92220	−	2.52156i	−0.149643	−	0.196303i
$166$	−12.1602	+	14.4920i	−0.943817	+	1.12480i
$167$	2.43328	−	13.7998i	0.188293	−	1.06786i	−0.733358	−	0.679843i	$-0.762048\pi$
$167$	2.43328	−	13.7998i	0.188293	−	1.06786i	0.921651	−	0.388020i	$-0.126841\pi$
$168$	−12.1626	+	5.29511i	−0.938363	+	0.408527i
$169$	9.76524	−	8.19401i	0.751172	−	0.630309i
$170$	−15.3002	+	8.83359i	−1.17347	+	0.677506i
$171$	−0.905450	−	3.46690i	−0.0692415	−	0.265121i
$172$	0.522769	−	0.905462i	0.0398608	−	0.0690409i
$173$	2.25876	+	12.8101i	0.171731	+	0.973932i	0.941850	+	0.336033i	$0.109085\pi$
$173$	2.25876	+	12.8101i	0.171731	+	0.973932i	−0.770120	+	0.637899i	$0.779804\pi$
$174$	−15.3263	−	0.717814i	−1.16188	−	0.0544173i
$175$	−2.32689	−	4.72722i	−0.175897	−	0.357344i
$176$	0.897372	+	2.46551i	0.0676420	+	0.185845i
$177$	−5.17733	−	10.0230i	−0.389152	−	0.753372i
$178$	13.1545	−	2.31949i	0.985972	−	0.173853i
$179$	−12.8061	−	7.39360i	−0.957172	−	0.552624i	−0.0618708	−	0.998084i	$-0.519707\pi$
$179$	−12.8061	−	7.39360i	−0.957172	−	0.552624i	−0.895302	+	0.445460i	$0.853040\pi$
$180$	−0.331004	−	0.721744i	−0.0246716	−	0.0537956i
$181$	7.71179	−	4.45240i	0.573213	−	0.330944i	−0.185219	−	0.982697i	$-0.559299\pi$
$181$	7.71179	−	4.45240i	0.573213	−	0.330944i	0.758431	+	0.651753i	$0.225966\pi$
$182$	−1.32249	−	1.26787i	−0.0980298	−	0.0939811i
$183$	6.20829	+	1.39699i	0.458930	+	0.103269i
$184$	−3.71382	+	21.0621i	−0.273786	+	1.55272i
$185$	15.0461	+	12.6252i	1.10621	+	0.928224i
$186$	−17.7381	−	7.41328i	−1.30062	−	0.543568i
$187$	−1.14783	+	3.15363i	−0.0839375	+	0.230616i
$188$	0.383037			0.0279359
$189$	−5.11362	+	12.7613i	−0.371961	+	0.928248i
$190$	−4.35309			−0.315807
$191$	−5.14349	+	14.1316i	−0.372170	+	1.02253i	0.602351	+	0.798231i	$0.294231\pi$
$191$	−5.14349	+	14.1316i	−0.372170	+	1.02253i	−0.974521	+	0.224297i	$0.927992\pi$
$192$	1.84437	+	14.3608i	0.133106	+	1.03640i
$193$	−6.14999	−	5.16045i	−0.442686	−	0.371457i	0.394028	−	0.919099i	$-0.371081\pi$
$193$	−6.14999	−	5.16045i	−0.442686	−	0.371457i	−0.836713	+	0.547641i	$0.815526\pi$
$194$	0.776211	−	4.40211i	0.0557287	−	0.316053i
$195$	1.55974	−	1.69137i	0.111695	−	0.121122i
$196$	−0.427371	+	0.555271i	−0.0305265	+	0.0396622i
$197$	0.971081	−	0.560654i	0.0691866	−	0.0399449i	−0.465008	−	0.885307i	$-0.653948\pi$
$197$	0.971081	−	0.560654i	0.0691866	−	0.0399449i	0.534194	+	0.845362i	$0.320615\pi$
$198$	2.58687	+	1.22629i	0.183841	+	0.0871489i
$199$	−19.5563	−	11.2909i	−1.38631	−	0.800388i	−0.393415	−	0.919361i	$-0.628707\pi$
$199$	−19.5563	−	11.2909i	−1.38631	−	0.800388i	−0.992898	+	0.118973i	$0.962040\pi$
$200$	−5.67709	+	1.00102i	−0.401431	+	0.0707831i
$201$	3.22469	−	5.02654i	0.227452	−	0.354545i
$202$	5.32753	+	14.6373i	0.374844	+	1.02987i
$203$	−15.2554	+	7.50922i	−1.07072	+	0.527044i
$204$	−0.453814	+	0.707389i	−0.0317733	+	0.0495272i
$205$	1.58936	+	9.01370i	0.111006	+	0.629544i
$206$	12.6757	−	21.9550i	0.883160	−	1.52968i
$207$	12.5980	+	18.2366i	0.875621	+	1.26753i
$208$	−1.64882	+	0.951947i	−0.114325	+	0.0660057i
$209$	−0.633446	+	0.531524i	−0.0438164	+	0.0367663i
$210$	13.4303	+	9.92831i	0.926778	+	0.685119i
$211$	3.05568	−	17.3296i	0.210362	−	1.19302i	−0.678414	−	0.734679i	$-0.737333\pi$
$211$	3.05568	−	17.3296i	0.210362	−	1.19302i	0.888776	−	0.458341i	$-0.151556\pi$
$212$	0.665260	−	0.792826i	0.0456903	−	0.0544515i
$213$	−0.568577	+	0.0730228i	−0.0389582	+	0.00500344i
$214$	−13.4253	−	4.88640i	−0.917733	−	0.334028i
$215$	−27.6181			−1.88354
$216$	11.8456	+	9.26960i	0.805988	+	0.630716i
$217$	−21.1803	+	2.30389i	−1.43781	+	0.156398i
$218$	5.87140	−	16.1315i	0.397661	−	1.09256i
$219$	2.42101	−	5.79287i	0.163597	−	0.391446i
$220$	−0.117784	+	0.140370i	−0.00794102	+	0.00946374i
$221$	−2.39827	−	0.422880i	−0.161325	−	0.0284460i
$222$	−17.3017	−	3.89323i	−1.16121	−	0.261297i
$223$	−5.47899	−	6.52961i	−0.366901	−	0.437255i	0.550734	−	0.834681i	$-0.314348\pi$
$223$	−5.47899	−	6.52961i	−0.366901	−	0.437255i	−0.917634	+	0.397426i	$0.869904\pi$
$224$	0.884135	+	1.20767i	0.0590738	+	0.0806906i
$225$	−3.45768	+	4.87208i	−0.230512	+	0.324806i
$226$	−2.09310	+	3.62535i	−0.139231	+	0.241155i
$227$	−3.37111	−	19.1185i	−0.223748	−	1.26894i	−0.865063	−	0.501662i	$-0.832722\pi$
$227$	−3.37111	−	19.1185i	−0.223748	−	1.26894i	0.641315	−	0.767278i	$-0.278389\pi$
$228$	−0.183985	+	0.0950368i	−0.0121847	+	0.00629397i
$229$	−8.38379	−	23.0343i	−0.554016	−	1.52215i	−0.828179	−	0.560464i	$-0.810623\pi$
$229$	−8.38379	−	23.0343i	−0.554016	−	1.52215i	0.274163	−	0.961683i	$-0.411599\pi$
$230$	25.3035	−	9.20971i	1.66846	−	0.607270i
$231$	3.16660	−	0.195144i	0.208347	−	0.0128395i
$232$	3.23045	+	18.3208i	0.212089	+	1.20282i
$233$	2.98948	+	1.72598i	0.195847	+	0.113073i	0.594717	−	0.803935i	$-0.297264\pi$
$233$	2.98948	+	1.72598i	0.195847	+	0.113073i	−0.398870	+	0.917008i	$0.630597\pi$
$234$	−0.550368	+	2.00315i	−0.0359787	+	0.130950i
$235$	−5.05900	−	8.76245i	−0.330013	−	0.571599i
$236$	−0.499432	+	0.419074i	−0.0325103	+	0.0272794i
$237$	−17.0962	+	5.33094i	−1.11052	+	0.346282i
$238$	1.16914	−	17.6393i	0.0757843	−	1.14338i
$239$	6.51310	−	7.76201i	0.421297	−	0.502083i	−0.513093	−	0.858333i	$-0.671500\pi$
$239$	6.51310	−	7.76201i	0.421297	−	0.502083i	0.934391	+	0.356250i	$0.115945\pi$
$240$	13.8031	−	10.5222i	0.890988	−	0.679205i
$241$	2.01308	−	5.53089i	0.129674	−	0.356276i	−0.857816	−	0.513956i	$-0.828179\pi$
$241$	2.01308	−	5.53089i	0.129674	−	0.356276i	0.987490	+	0.157680i	$0.0504016\pi$
$242$			14.5014i			0.932185i
$243$	15.4854	−	1.78965i	0.993388	−	0.114806i
$244$		−	0.367762i		−	0.0235436i
$245$	18.3470	+	2.44284i	1.17215	+	0.156067i
$246$	−5.01006	−	6.57224i	−0.319430	−	0.419031i
$247$	−0.459655	−	0.385696i	−0.0292471	−	0.0245412i
$248$	−4.04775	+	22.9559i	−0.257032	+	1.45770i
$249$	22.6945	−	7.07658i	1.43820	−	0.448460i
$250$	−7.04813	−	8.39964i	−0.445763	−	0.531240i
$251$	11.7240	+	20.3066i	0.740014	+	1.28174i	0.952488	+	0.304575i	$0.0985145\pi$
$251$	11.7240	+	20.3066i	0.740014	+	1.28174i	−0.212474	+	0.977167i	$0.568152\pi$
$252$	0.784391	+	0.126413i	0.0494120	+	0.00796325i
$253$	2.55754	−	4.42978i	0.160791	−	0.278498i
$254$	−4.16235	+	0.733934i	−0.261169	+	0.0460511i
$255$	22.1762	+	1.03863i	1.38873	+	0.0650416i
$256$	2.25175	−	0.819569i	0.140734	−	0.0512231i
$257$	11.3427	−	4.12840i	0.707538	−	0.257523i	0.0369120	−	0.999319i	$-0.488248\pi$
$257$	11.3427	−	4.12840i	0.707538	−	0.257523i	0.670626	+	0.741796i	$0.266026\pi$
$258$	22.1553	−	11.4443i	1.37933	−	0.712489i
$259$	−18.8722	+	5.48573i	−1.17266	+	0.340867i
$260$	−0.115152	−	0.0664832i	−0.00714145	−	0.00412312i
$261$	15.7229	+	11.1584i	0.973224	+	0.690689i
$262$	−6.09283	+	3.51770i	−0.376416	+	0.217324i
$263$	−0.100748	−	0.120067i	−0.00621242	−	0.00740367i	0.762929	−	0.646482i	$-0.223760\pi$
$263$	−0.100748	−	0.120067i	−0.00621242	−	0.00740367i	−0.769142	+	0.639078i	$0.779316\pi$
$264$	0.762025	−	3.38647i	0.0468994	−	0.208423i
$265$	−26.9233	−	4.74731i	−1.65389	−	0.291625i
$266$	2.42259	−	3.61990i	0.148538	−	0.221950i
$267$	−15.4868	−	6.47239i	−0.947775	−	0.396104i
$268$	−0.324321	−	0.118043i	−0.0198111	−	0.00721064i
$269$	18.3616			1.11952			0.559762	−	0.828653i	$-0.310893\pi$
$269$	18.3616			1.11952			0.559762	+	0.828653i	$0.310893\pi$
$270$	2.65022	−	18.7515i	0.161287	−	1.14118i
$271$			7.98514i			0.485063i	0.970144	+	0.242531i	$0.0779777\pi$
$271$			7.98514i			0.485063i	−0.970144	+	0.242531i	$0.922022\pi$
$272$	−17.2631	−	6.28325i	−1.04673	−	0.380978i
$273$	0.538465	+	2.23832i	0.0325894	+	0.135469i
$274$	4.16541	+	3.49519i	0.251642	+	0.211152i
$275$	1.35777	+	0.239412i	0.0818767	+	0.0144371i
$276$	0.868392	−	0.941677i	0.0522711	−	0.0566823i
$277$	12.8010	−	10.7413i	0.769135	−	0.645381i	−0.171352	−	0.985210i	$-0.554814\pi$
$277$	12.8010	−	10.7413i	0.769135	−	0.645381i	0.940487	+	0.339829i	$0.110369\pi$
$278$	7.35346	+	12.7366i	0.441031	+	0.763888i
$279$	13.7307	+	19.8764i	0.822038	+	1.18997i
$280$	8.16946	−	18.5296i	0.488219	−	1.10736i
$281$	11.7287	−	2.06809i	0.699676	−	0.123372i	0.187516	−	0.982262i	$-0.439956\pi$
$281$	11.7287	−	2.06809i	0.699676	−	0.123372i	0.512161	+	0.858890i	$0.328845\pi$
$282$	7.68930	+	4.93294i	0.457891	+	0.293752i
$283$	−0.504977	−	1.38741i	−0.0300178	−	0.0824732i	0.923778	−	0.382927i	$-0.125084\pi$
$283$	−0.504977	−	1.38741i	−0.0300178	−	0.0824732i	−0.953796	+	0.300454i	$0.902862\pi$
$284$	0.0113309	+	0.0311313i	0.000672363	+	0.00184730i
$285$	4.60408	+	2.95367i	0.272722	+	0.174960i
$286$	0.472120	−	0.0832475i	0.0279170	−	0.00492253i
$287$	−8.38004	−	3.69465i	−0.494658	−	0.218088i
$288$	0.726963	−	1.53353i	0.0428367	−	0.0903643i
$289$	−3.24916	−	5.62770i	−0.191127	−	0.331041i
$290$	17.9428	−	15.0558i	1.05364	−	0.884106i
$291$	−3.80789	+	4.12925i	−0.223223	+	0.242061i
$292$	−0.357332	−	0.0630072i	−0.0209113	−	0.00368722i
$293$	−1.37473	−	1.15354i	−0.0803126	−	0.0673903i	0.601748	−	0.798686i	$-0.294471\pi$
$293$	−1.37473	−	1.15354i	−0.0803126	−	0.0673903i	−0.682060	+	0.731296i	$0.738916\pi$
$294$	−15.7303	+	5.64292i	−0.917411	+	0.329102i
$295$	16.1831	+	5.89017i	0.942218	+	0.342939i
$296$			21.5027i			1.24982i
$297$	−1.90396	−	3.05225i	−0.110479	−	0.177109i
$298$	−4.22613			−0.244813
$299$	3.48787	+	1.26948i	0.201708	+	0.0734159i
$300$	0.318568	+	0.133139i	0.0183925	+	0.00768679i
$301$	15.3700	−	22.9664i	0.885913	−	1.32376i
$302$	29.6905	+	5.23523i	1.70850	+	0.301254i
$303$	4.29701	−	19.0961i	0.246857	−	1.09704i
$304$	−2.90958	−	3.46750i	−0.166876	−	0.198875i
$305$	−8.41301	+	4.85725i	−0.481728	+	0.278126i
$306$	−18.2202	+	8.35609i	−1.04158	+	0.477686i
$307$	1.04389	+	0.602689i	0.0595778	+	0.0343973i	0.529493	−	0.848314i	$-0.322382\pi$
$307$	1.04389	+	0.602689i	0.0595778	+	0.0343973i	−0.469915	+	0.882712i	$0.655716\pi$
$308$	−0.0511780	−	0.176065i	−0.00291614	−	0.0100322i
$309$	−28.3035	+	14.6201i	−1.61013	+	0.831708i
$310$	27.5786	−	10.0378i	1.56636	−	0.570109i
$311$	−14.9731	+	5.44977i	−0.849048	+	0.309028i	−0.729652	−	0.683819i	$-0.760318\pi$
$311$	−14.9731	+	5.44977i	−0.849048	+	0.309028i	−0.119396	+	0.992847i	$0.538096\pi$
$312$	2.51605	+	0.117840i	0.142443	+	0.00667139i
$313$	−31.6605	+	5.58260i	−1.78956	+	0.315547i	−0.967312	−	0.253588i	$-0.918389\pi$
$313$	−31.6605	+	5.58260i	−1.78956	+	0.315547i	−0.822244	+	0.569135i	$0.807278\pi$
$314$	4.80715	−	8.32623i	0.271283	−	0.469876i
$315$	−7.46807	−	19.6135i	−0.420778	−	1.10510i
$316$	0.517475	+	0.896293i	0.0291102	+	0.0504204i
$317$	−12.6893	−	15.1225i	−0.712701	−	0.849364i	0.281199	−	0.959650i	$-0.409268\pi$
$317$	−12.6893	−	15.1225i	−0.712701	−	0.849364i	−0.993900	+	0.110285i	$0.964824\pi$
$318$	23.5652	−	7.34808i	1.32147	−	0.412060i
$319$	0.772616	−	4.38172i	0.0432582	−	0.245329i
$320$	−16.9320	−	14.2076i	−0.946527	−	0.794231i
$321$	10.8838	+	14.2775i	0.607475	+	0.796891i
$322$	−6.42338	+	26.1670i	−0.357961	+	1.45823i
$323$		−	5.78985i		−	0.322156i
$324$	−0.297371	−	0.850398i	−0.0165206	−	0.0472443i
$325$			1.00045i			0.0554952i
$326$	7.53625	−	20.7057i	0.417394	−	1.14678i
$327$	−17.1555	+	13.0777i	−0.948702	+	0.723201i
$328$	−6.44082	+	7.67587i	−0.355635	+	0.423829i
$329$	10.1020	+	0.669569i	0.556943	+	0.0369145i
$330$	−4.17222	+	1.30098i	−0.229673	+	0.0716165i
$331$	−16.4662	+	13.8168i	−0.905067	+	0.759441i	−0.971174	−	0.238371i	$-0.923386\pi$
$331$	−16.4662	+	13.8168i	−0.905067	+	0.759441i	0.0661072	+	0.997813i	$0.478942\pi$
$332$	−0.686924	−	1.18979i	−0.0376999	−	0.0652981i
$333$	15.6576	+	15.8573i	0.858030	+	0.868973i
$334$	−16.7270	−	9.65734i	−0.915261	−	0.528426i
$335$	1.58312	+	8.97830i	0.0864949	+	0.490537i
$336$	1.06822	+	17.3341i	0.0582764	+	0.945652i
$337$	2.06271	−	0.750766i	0.112363	−	0.0408968i	−0.285227	−	0.958460i	$-0.592069\pi$
$337$	2.06271	−	0.750766i	0.112363	−	0.0408968i	0.397590	+	0.917563i	$0.369847\pi$
$338$	−6.00961	−	16.5113i	−0.326880	−	0.898094i
$339$	4.67366	−	2.41416i	0.253838	−	0.131119i
$340$	−0.222793	−	1.26352i	−0.0120827	−	0.0685242i
$341$	2.78750	−	4.82809i	0.150951	−	0.261456i
$342$	−4.91734	−	0.461624i	−0.265899	−	0.0249618i
$343$	−12.2419	+	13.8973i	−0.661000	+	0.750386i
$344$	−19.4349	−	23.1616i	−1.04786	−	1.24879i
$345$	−33.0114	−	7.42824i	−1.77727	−	0.399923i
$346$	17.6570	+	3.11341i	0.949247	+	0.167378i
$347$	−16.5906	+	19.7719i	−0.890631	+	1.06141i	0.107110	+	0.994247i	$0.465840\pi$
$347$	−16.5906	+	19.7719i	−0.890631	+	1.06141i	−0.997742	+	0.0671660i	$0.978604\pi$
$348$	0.429659	−	1.02806i	0.0230321	−	0.0551101i
$349$	10.6914	−	29.3745i	0.572300	−	1.57238i	−0.228560	−	0.973530i	$-0.573402\pi$
$349$	10.6914	−	29.3745i	0.572300	−	1.57238i	0.800860	−	0.598851i	$-0.204376\pi$
$350$	−7.21986	+	0.785341i	−0.385918	+	0.0419782i
$351$	1.94128	−	1.74520i	0.103618	−	0.0931521i
$352$	−0.391649			−0.0208749
$353$	8.40270	+	3.05833i	0.447231	+	0.162779i	0.555810	−	0.831309i	$-0.312408\pi$
$353$	8.40270	+	3.05833i	0.447231	+	0.162779i	−0.108580	+	0.994088i	$0.534630\pi$
$354$	−15.4229	+	1.98078i	−0.819719	+	0.105277i
$355$	0.562512	−	0.670376i	0.0298551	−	0.0355799i
$356$	−0.168445	+	0.955298i	−0.00892756	+	0.0506307i
$357$	−13.2052	+	17.8630i	−0.698893	+	0.945411i
$358$	−15.6137	+	13.1014i	−0.825209	+	0.692433i
$359$	13.3825	−	7.72637i	0.706300	−	0.407782i	−0.103390	−	0.994641i	$-0.532969\pi$
$359$	13.3825	−	7.72637i	0.706300	−	0.407782i	0.809689	+	0.586859i	$0.199636\pi$
$360$	−22.8869	+	1.85630i	−1.20624	+	0.0978355i
$361$	−8.78671	+	15.2190i	−0.462458	+	0.801001i
$362$	−2.13138	−	12.0876i	−0.112023	−	0.635312i
$363$	9.83951	−	15.3375i	0.516441	−	0.805010i
$364$	0.119370	−	0.0587579i	0.00625669	−	0.00307975i
$365$	3.27812	+	9.00657i	0.171585	+	0.471425i
$366$	4.73622	−	7.38266i	0.247566	−	0.385898i
$367$	16.9007	−	2.98005i	0.882209	−	0.155557i	0.285849	−	0.958275i	$-0.407724\pi$
$367$	16.9007	−	2.98005i	0.882209	−	0.155557i	0.596360	+	0.802717i	$0.296613\pi$
$368$	24.2488	+	14.0000i	1.26406	+	0.729803i
$369$	0.839513	+	10.3506i	0.0437033	+	0.538831i
$370$	23.4459	−	13.5365i	1.21890	−	0.703730i
$371$	18.9311	−	19.7467i	0.982855	−	1.02520i
$372$	0.946474	−	1.02635i	0.0490724	−	0.0532137i
$373$	1.93292	−	10.9621i	0.100083	−	0.567597i	−0.892988	−	0.450080i	$-0.851395\pi$
$373$	1.93292	−	10.9621i	0.100083	−	0.567597i	0.993071	−	0.117517i	$-0.0374935\pi$
$374$	3.54360	+	2.97343i	0.183235	+	0.153752i
$375$	1.75517	+	13.6662i	0.0906365	+	0.705722i
$376$	3.78851	−	10.4088i	0.195377	−	0.536795i
$377$	3.22861			0.166282
$378$	14.1183	+	12.6394i	0.726166	+	0.650103i
$379$	−35.4910			−1.82305			−0.911526	−	0.411242i	$-0.865095\pi$
$379$	−35.4910			−1.82305			−0.911526	+	0.411242i	$0.865095\pi$
$380$	0.108122	−	0.297063i	0.00554654	−	0.0152390i
$381$	4.90032	+	2.04799i	0.251051	+	0.104922i
$382$	15.8791	+	13.3241i	0.812445	+	0.681722i
$383$	3.57786	−	20.2910i	0.182820	−	1.03682i	−0.745904	−	0.666053i	$-0.767982\pi$
$383$	3.57786	−	20.2910i	0.182820	−	1.03682i	0.928724	−	0.370771i	$-0.120906\pi$
$384$	17.5584	+	3.95100i	0.896022	+	0.201623i
$385$	−3.35176	+	3.49615i	−0.170821	+	0.178180i
$386$	−9.58333	+	5.53294i	−0.487779	+	0.281619i
$387$	−31.1979	−	2.92876i	−1.58588	−	0.148877i
$388$	0.281128	+	0.162310i	0.0142721	+	0.00824002i
$389$	−36.5509	+	6.44490i	−1.85320	+	0.326770i	−0.985415	−	0.170166i	$-0.945570\pi$
$389$	−36.5509	+	6.44490i	−1.85320	+	0.326770i	−0.867787	+	0.496936i	$0.834458\pi$
$390$	−1.45543	−	2.81761i	−0.0736985	−	0.142675i
$391$	12.2494	+	33.6550i	0.619479	+	1.70201i
$392$	10.8622	+	17.1056i	0.548623	+	0.863963i
$393$	8.83096	+	0.413602i	0.445463	+	0.0208634i
$394$	−0.268386	−	1.52209i	−0.0135211	−	0.0766820i
$395$	13.6692	−	23.6757i	0.687772	−	1.19126i
$396$	−0.147937	+	0.146074i	−0.00743412	+	0.00734051i
$397$	8.14360	−	4.70171i	0.408715	−	0.235972i	−0.281522	−	0.959555i	$-0.590839\pi$
$397$	8.14360	−	4.70171i	0.408715	−	0.235972i	0.690238	+	0.723583i	$0.257506\pi$
$398$	−23.8439	+	20.0074i	−1.19518	+	1.00288i
$399$	−5.01844	+	2.18484i	−0.251236	+	0.109379i
$400$	−1.31055	+	7.43249i	−0.0655274	+	0.371625i
$401$	3.41094	−	4.06500i	0.170334	−	0.202997i	−0.674123	−	0.738619i	$-0.735478\pi$
$401$	3.41094	−	4.06500i	0.170334	−	0.202997i	0.844458	+	0.535622i	$0.179923\pi$
$402$	−4.99038	−	6.54643i	−0.248898	−	0.326506i
$403$	3.80148	+	1.38362i	0.189365	+	0.0689233i
$404$	−1.13120			−0.0562792
$405$	−15.5263	+	18.0344i	−0.771509	+	0.896138i
$406$	2.53441	+	23.2995i	0.125781	+	1.15634i
$407$	1.75892	−	4.83259i	0.0871864	−	0.239543i
$408$	14.7344	+	19.3287i	0.729461	+	0.956914i
$409$	7.26683	−	8.66028i	0.359322	−	0.428223i	−0.555853	−	0.831281i	$-0.687608\pi$
$409$	7.26683	−	8.66028i	0.359322	−	0.428223i	0.915175	+	0.403058i	$0.132053\pi$
$410$	12.4242	+	2.19072i	0.613588	+	0.108192i
$411$	−2.03401	−	6.52304i	−0.100330	−	0.321758i
$412$	1.18341	+	1.41033i	0.0583024	+	0.0694821i
$413$	−13.9043	+	10.1794i	−0.684187	+	0.500895i
$414$	29.5600	−	7.72016i	1.45279	−	0.379425i
$415$	−18.1452	+	31.4284i	−0.890714	+	1.54276i
$416$	−0.0493502	−	0.279879i	−0.00241959	−	0.0137222i
$417$	0.864601	−	18.4604i	0.0423397	−	0.904009i
$418$	0.389828	+	1.07104i	0.0190671	+	0.0523864i
$419$	2.11015	−	0.768032i	0.103088	−	0.0375208i	−0.289961	−	0.957038i	$-0.593642\pi$
$419$	2.11015	−	0.768032i	0.103088	−	0.0375208i	0.393049	+	0.919518i	$0.371420\pi$
$420$	−1.01111	+	0.669908i	−0.0493370	+	0.0326882i
$421$	−1.36835	−	7.76030i	−0.0666893	−	0.378214i	−0.999825	−	0.0186904i	$-0.994050\pi$
$421$	−1.36835	−	7.76030i	−0.0666893	−	0.378214i	0.933136	−	0.359524i	$-0.117061\pi$
$422$	−21.0055	−	12.1276i	−1.02253	−	0.590360i
$423$	−4.78553	−	10.4347i	−0.232681	−	0.507353i
$424$	−14.9647	−	25.9197i	−0.726752	−	1.25877i
$425$	−7.39505	+	6.20518i	−0.358713	+	0.300996i
$426$	−0.173462	+	0.770870i	−0.00840425	+	0.0373488i
$427$	0.642868	−	9.69917i	0.0311105	−	0.469376i
$428$	0.666914	−	0.794797i	0.0322365	−	0.0384179i
$429$	−0.555826	−	0.232296i	−0.0268355	−	0.0112154i
$430$	−13.0200	+	35.7721i	−0.627879	+	1.72508i
$431$			5.30024i			0.255304i	0.991819	+	0.127652i	$0.0407440\pi$
$431$			5.30024i			0.255304i	−0.991819	+	0.127652i	$0.959256\pi$
$432$	16.7081	−	10.4223i	0.803869	−	0.501445i
$433$		−	19.5707i		−	0.940506i	−0.882532	−	0.470253i	$-0.844163\pi$
$433$		−	19.5707i		−	0.940506i	0.882532	−	0.470253i	$-0.155837\pi$
$434$	−7.00094	+	28.5198i	−0.336056	+	1.36899i
$435$	−29.1930	+	3.74928i	−1.39970	+	0.179764i
$436$	0.955011	+	0.801349i	0.0457367	+	0.0383777i
$437$	−1.53237	+	8.69052i	−0.0733033	+	0.415724i
$438$	−6.36183	−	5.86673i	−0.303980	−	0.280323i
$439$	−0.489008	−	0.582777i	−0.0233391	−	0.0278144i	0.754249	−	0.656589i	$-0.228001\pi$
$439$	−0.489008	−	0.582777i	−0.0233391	−	0.0278144i	−0.777588	+	0.628774i	$0.783557\pi$
$440$	2.64951	+	4.58908i	0.126310	+	0.218776i
$441$	20.4661	+	4.70509i	0.974577	+	0.224052i
$442$	−1.67835	+	2.90699i	−0.0798310	+	0.138271i
$443$	11.3591	−	2.00292i	0.539689	−	0.0951617i	0.102842	−	0.994698i	$-0.467206\pi$
$443$	11.3591	−	2.00292i	0.539689	−	0.0951617i	0.436847	+	0.899536i	$0.356095\pi$
$444$	0.695420	−	1.08400i	0.0330032	−	0.0514442i
$445$	24.0784	−	8.76381i	1.14142	−	0.415444i
$446$	−11.0404	+	4.01837i	−0.522778	+	0.190276i
$447$	4.46980	+	2.86752i	0.211414	+	0.135629i
$448$	21.2376	−	6.17330i	1.00338	−	0.291661i
$449$	25.8403	+	14.9189i	1.21948	+	0.704067i	0.964807	−	0.262960i	$-0.0846986\pi$
$449$	25.8403	+	14.9189i	1.21948	+	0.704067i	0.254674	+	0.967027i	$0.418032\pi$
$450$	4.68048	+	6.77538i	0.220640	+	0.319395i
$451$	2.07542	−	1.19824i	0.0977276	−	0.0564231i
$452$	−0.195412	−	0.232883i	−0.00919141	−	0.0109539i
$453$	−27.8501	−	25.6827i	−1.30851	−	1.20668i
$454$	−26.3524	−	4.64663i	−1.23678	−	0.218077i
$455$	−2.92075	−	1.95469i	−0.136927	−	0.0916371i
$456$	0.762837	+	5.93967i	0.0357231	+	0.278150i
$457$	9.41750	+	3.42769i	0.440532	+	0.160341i	0.552757	−	0.833342i	$-0.313576\pi$
$457$	9.41750	+	3.42769i	0.440532	+	0.160341i	−0.112225	+	0.993683i	$0.535798\pi$
$458$	−33.7873			−1.57878
$459$	24.9405	+	3.52493i	1.16412	+	0.164530i
$460$			1.95550i			0.0911759i
$461$	−13.8192	−	5.02977i	−0.643623	−	0.234260i	−0.000473303	−	1.00000i	$-0.500151\pi$
$461$	−13.8192	−	5.02977i	−0.643623	−	0.234260i	−0.643150	+	0.765740i	$0.722373\pi$
$462$	1.24007	−	4.19351i	0.0576933	−	0.195100i
$463$	21.2160	+	17.8024i	0.985992	+	0.827346i	0.984983	−	0.172654i	$-0.0552342\pi$
$463$	21.2160	+	17.8024i	0.985992	+	0.827346i	0.00100944	+	0.999999i	$0.499679\pi$
$464$	23.9857	+	4.22933i	1.11351	+	0.196342i
$465$	−35.9796	−	8.09616i	−1.66851	−	0.375450i
$466$	3.64489	−	3.05843i	0.168846	−	0.141679i
$467$	−1.24601	−	2.15815i	−0.0576584	−	0.0998673i	0.835755	−	0.549102i	$-0.185030\pi$
$467$	−1.24601	−	2.15815i	−0.0576584	−	0.0998673i	−0.893414	+	0.449235i	$0.851697\pi$
$468$	−0.123028	−	0.0873122i	−0.00568698	−	0.00403601i
$469$	−8.34712	−	3.68014i	−0.385434	−	0.169933i
$470$	−13.7345	+	2.42176i	−0.633523	+	0.111707i
$471$	−10.7338	+	5.54453i	−0.494589	+	0.255479i
$472$	6.44837	+	17.7167i	0.296810	+	0.815479i
$473$	2.47325	+	6.79520i	0.113720	+	0.312444i
$474$	−1.15482	+	24.6570i	−0.0530426	+	1.13253i
$475$	−2.34244	+	0.413036i	−0.107479	+	0.0189514i
$476$	1.17470	+	0.517909i	0.0538421	+	0.0237383i
$477$	−29.9097	−	8.21775i	−1.36947	−	0.376265i
$478$	−6.98322	−	12.0953i	−0.319405	−	0.553226i
$479$	3.12816	−	2.62484i	0.142929	−	0.119932i	−0.568520	−	0.822670i	$-0.692484\pi$
$479$	3.12816	−	2.62484i	0.142929	−	0.119932i	0.711449	+	0.702738i	$0.248039\pi$
$480$	0.771237	+	2.47335i	0.0352020	+	0.112892i
$481$	3.67509	+	0.648017i	0.167570	+	0.0295471i
$482$	−6.21482	−	5.21485i	−0.283077	−	0.237530i
$483$	24.5486	−	23.3173i	1.11700	−	1.06097i
$484$	−0.989601	−	0.360185i	−0.0449819	−	0.0163721i
$485$		−	8.57487i		−	0.389365i
$486$	4.98225	−	20.9010i	0.225999	−	0.948090i
$487$	−27.1662			−1.23102			−0.615508	−	0.788130i	$-0.711049\pi$
$487$	−27.1662			−1.23102			−0.615508	+	0.788130i	$0.711049\pi$
$488$	−9.99375	−	3.63743i	−0.452396	−	0.164659i
$489$	−22.0200	+	16.7860i	−0.995779	+	0.759088i
$490$	11.8134	−	22.6122i	0.533675	−	1.02152i
$491$	−6.79969	−	1.19897i	−0.306865	−	0.0541087i	0.0180950	−	0.999836i	$-0.494240\pi$
$491$	−6.79969	−	1.19897i	−0.306865	−	0.0541087i	−0.324960	+	0.945728i	$0.605351\pi$
$492$	0.572941	−	0.178654i	0.0258302	−	0.00805435i
$493$	20.0250	+	23.8649i	0.901881	+	1.07482i
$494$	−0.716265	+	0.413536i	−0.0322263	+	0.0186059i
$495$	5.29552	+	1.45495i	0.238016	+	0.0653953i
$496$	26.4291	+	15.2589i	1.18670	+	0.685143i
$497$	0.244415	+	0.840846i	0.0109635	+	0.0377171i
$498$	1.53297	−	32.7310i	0.0686940	−	1.46671i
$499$	4.67510	−	1.70160i	0.209286	−	0.0761740i	−0.235250	−	0.971935i	$-0.575591\pi$
$499$	4.67510	−	1.70160i	0.209286	−	0.0761740i	0.444536	+	0.895761i	$0.353369\pi$
$500$	0.748268	−	0.272347i	0.0334635	−	0.0121797i
$501$	11.1387	+	21.5638i	0.497641	+	0.963399i
$502$	31.8291	−	5.61232i	1.42060	−	0.250490i
$503$	−9.79528	+	16.9659i	−0.436750	+	0.756473i	−0.997437	−	0.0715548i	$-0.977204\pi$
$503$	−9.79528	+	16.9659i	−0.436750	+	0.756473i	0.560687	+	0.828028i	$0.310537\pi$
$504$	11.1934	−	20.0651i	0.498592	−	0.893770i
$505$	14.9404	+	25.8775i	0.664839	+	1.15154i
$506$	−4.53195	−	5.40096i	−0.201470	−	0.240102i
$507$	−4.84715	+	21.5409i	−0.215269	+	0.956665i
$508$	0.0532993	−	0.302275i	0.00236477	−	0.0134113i
$509$	30.7820	+	25.8292i	1.36439	+	1.14486i	0.974600	+	0.223954i	$0.0718967\pi$
$509$	30.7820	+	25.8292i	1.36439	+	1.14486i	0.389789	+	0.920904i	$0.372548\pi$
$510$	11.7998	−	28.2339i	0.522504	−	1.25022i
$511$	−9.31394	−	2.28635i	−0.412024	−	0.101142i
$512$		−	24.0845i		−	1.06440i
$513$	4.88764	+	3.82476i	0.215794	+	0.168867i
$514$		−	16.6378i		−	0.733862i
$515$	16.6331	−	45.6990i	0.732941	−	2.01374i
$516$	0.230684	+	1.79617i	0.0101553	+	0.0790721i
$517$	−1.70288	+	2.02942i	−0.0748928	+	0.0892538i
$518$	−1.79159	+	27.0303i	−0.0787177	+	1.18764i
$519$	−16.5625	−	15.2736i	−0.727015	−	0.670436i
$520$	−2.94558	+	2.47164i	−0.129172	+	0.108389i
$521$	−9.63350	−	16.6857i	−0.422051	−	0.731014i	0.574089	−	0.818793i	$-0.305356\pi$
$521$	−9.63350	−	16.6857i	−0.422051	−	0.731014i	−0.996140	+	0.0877789i	$0.972023\pi$
$522$	21.8651	−	15.1046i	0.957011	−	0.661109i
$523$	27.2798	+	15.7500i	1.19286	+	0.688700i	0.958955	−	0.283559i	$-0.0915151\pi$
$523$	27.2798	+	15.7500i	1.19286	+	0.688700i	0.233908	+	0.972259i	$0.424848\pi$
$524$	−0.0887203	−	0.503158i	−0.00387577	−	0.0219806i
$525$	8.16901	+	4.06821i	0.356525	+	0.177551i
$526$	−0.203012	+	0.0738904i	−0.00885175	+	0.00322178i
$527$	13.3508	+	36.6811i	0.581571	+	1.59785i
$528$	−3.82500	−	2.45386i	−0.166462	−	0.106791i
$529$	−5.48505	−	31.1073i	−0.238481	−	1.35249i
$530$	−18.8414	+	32.6343i	−0.818418	+	1.41754i
$531$	17.6562	+	8.36980i	0.766212	+	0.363218i
$532$	0.186856	+	0.255233i	0.00810125	+	0.0110657i
$533$	1.11780	+	1.33214i	0.0484173	+	0.0577015i
$534$	−15.6842	+	17.0079i	−0.678724	+	0.736002i
$535$	−26.9903	−	4.75911i	−1.16689	−	0.205754i
$536$	−6.41552	+	7.64572i	−0.277108	+	0.330245i
$537$	25.4035	−	3.26260i	1.09624	−	0.140792i
$538$	8.65619	−	23.7827i	0.373195	−	1.02534i
$539$	−1.04197	−	4.73290i	−0.0448809	−	0.203860i
$540$	1.21381	+	0.646605i	0.0522341	+	0.0278255i
$541$	35.6863			1.53427			0.767136	−	0.641484i	$-0.221681\pi$
$541$	35.6863			1.53427			0.767136	+	0.641484i	$0.221681\pi$
$542$	10.3427	+	3.76444i	0.444257	+	0.161696i
$543$	−5.94746	+	14.2308i	−0.255230	+	0.610700i
$544$	1.76269	−	2.10069i	0.0755747	−	0.0900664i
$545$	5.71845	−	32.4309i	0.244951	−	1.38919i
$546$	3.15301	+	0.357767i	0.134937	+	0.0153110i
$547$	4.18262	−	3.50963i	0.178836	−	0.150061i	−0.548976	−	0.835838i	$-0.684982\pi$
$547$	4.18262	−	3.50963i	0.178836	−	0.150061i	0.727811	+	0.685777i	$0.240538\pi$
$548$	−0.341979	+	0.197441i	−0.0146086	+	0.00843428i
$549$	−10.0186	+	4.59469i	−0.427583	+	0.196097i
$550$	0.950191	−	1.64578i	0.0405163	−	0.0701763i
$551$	1.33293	+	7.55940i	0.0567846	+	0.322041i
$552$	−17.0006	−	32.9119i	−0.723592	−	1.40083i
$553$	12.0808	+	24.5429i	0.513729	+	1.04367i
$554$	−7.87781	−	21.6441i	−0.334696	−	0.919570i
$555$	−33.9826	−	1.59159i	−1.44248	−	0.0675592i
$556$	−1.05181	+	0.185463i	−0.0446067	+	0.00786537i
$557$	1.02434	+	0.591404i	0.0434027	+	0.0250586i	0.521544	−	0.853224i	$-0.325356\pi$
$557$	1.02434	+	0.591404i	0.0434027	+	0.0250586i	−0.478142	+	0.878283i	$0.658689\pi$
$558$	32.2178	−	8.41432i	1.36389	−	0.356207i
$559$	−4.54432	+	2.62367i	−0.192204	+	0.110969i
$560$	−19.1380	−	18.3476i	−0.808730	−	0.775329i
$561$	−1.73037	−	5.54928i	−0.0730564	−	0.234291i
$562$	2.85059	−	16.1665i	0.120245	−	0.681942i
$563$	0.126009	+	0.105734i	0.00531065	+	0.00445617i	0.645439	−	0.763812i	$-0.276674\pi$
$563$	0.126009	+	0.105734i	0.00531065	+	0.00445617i	−0.640128	+	0.768268i	$0.721119\pi$
$564$	−0.527619	+	0.402207i	−0.0222168	+	0.0169360i
$565$	−2.74656	+	7.54611i	−0.115549	+	0.317467i
$566$	−2.03510			−0.0855416
$567$	−6.35616	−	22.9477i	−0.266934	−	0.963715i
$568$	0.958046			0.0401987
$569$	−0.775698	+	2.13121i	−0.0325189	+	0.0893450i	−0.954890	−	0.296961i	$-0.904027\pi$
$569$	−0.775698	+	2.13121i	−0.0325189	+	0.0893450i	0.922371	+	0.386306i	$0.126249\pi$
$570$	5.99622	−	4.57095i	0.251154	−	0.191456i
$571$	−2.95026	−	2.47556i	−0.123465	−	0.103599i	0.578965	−	0.815353i	$-0.303457\pi$
$571$	−2.95026	−	2.47556i	−0.123465	−	0.103599i	−0.702429	+	0.711754i	$0.747901\pi$
$572$	−0.00604555	+	0.0342860i	−0.000252777	+	0.00143357i
$573$	−7.75391	−	24.8667i	−0.323924	−	1.03882i
$574$	−8.73607	+	9.11241i	−0.364636	+	0.380345i
$575$	12.7422	−	7.35672i	0.531387	−	0.306796i
$576$	−17.6201	−	17.8448i	−0.734170	−	0.743533i
$577$	−21.2066	−	12.2436i	−0.882840	−	0.509708i	−0.0112465	−	0.999937i	$-0.503580\pi$
$577$	−21.2066	−	12.2436i	−0.882840	−	0.509708i	−0.871594	+	0.490229i	$0.836913\pi$
$578$	−8.82099	+	1.55538i	−0.366905	+	0.0646952i
$579$	13.8901	+	0.650549i	0.577252	+	0.0270359i
$580$	0.581771	+	1.59840i	0.0241567	+	0.0663701i
$581$	−16.0368	−	32.5796i	−0.665317	−	1.35163i
$582$	3.55322	+	6.87880i	0.147286	+	0.285135i
$583$	1.24300	+	7.04940i	0.0514798	+	0.291956i
$584$	−5.24645	+	9.08712i	−0.217100	+	0.376027i
$585$	−0.372466	+	3.96760i	−0.0153996	+	0.164040i
$586$	−2.14220	+	1.23680i	−0.0884934	+	0.0510917i
$587$	−22.2020	+	18.6297i	−0.916376	+	0.768931i	−0.973321	−	0.229446i	$-0.926308\pi$
$587$	−22.2020	+	18.6297i	−0.916376	+	0.768931i	0.0569450	+	0.998377i	$0.481864\pi$
$588$	0.00562650	−	1.21362i	0.000232033	−	0.0500490i
$589$	−1.67016	+	9.47193i	−0.0688176	+	0.390284i
$590$	15.2584	−	18.1843i	0.628179	−	0.748634i
$591$	−0.748914	+	1.79196i	−0.0308062	+	0.0737114i
$592$	26.4538	+	9.62839i	1.08724	+	0.395724i
$593$	17.6094			0.723133			0.361566	−	0.932346i	$-0.382242\pi$
$593$	17.6094			0.723133			0.361566	+	0.932346i	$0.382242\pi$
$594$	−4.85099	+	1.02717i	−0.199038	+	0.0421452i
$595$	−3.66713	−	33.7129i	−0.150338	−	1.38210i
$596$	0.104969	−	0.288399i	0.00429968	−	0.0118133i
$597$	38.7941	−	4.98236i	1.58774	−	0.203914i
$598$	3.28857	−	3.91916i	0.134480	−	0.160267i
$599$	−35.3300	−	6.22964i	−1.44355	−	0.254536i	−0.603635	−	0.797261i	$-0.706282\pi$
$599$	−35.3300	−	6.22964i	−1.44355	−	0.254536i	−0.839911	+	0.542725i	$0.817393\pi$
$600$	6.76885	−	7.34008i	0.276337	−	0.299658i
$601$	−12.0878	−	14.4057i	−0.493072	−	0.587621i	0.460924	−	0.887440i	$-0.347518\pi$
$601$	−12.0878	−	14.4057i	−0.493072	−	0.587621i	−0.953996	+	0.299819i	$0.903074\pi$
$602$	−22.5011	−	30.7349i	−0.917077	−	1.25266i
$603$	0.836216	+	10.3100i	0.0340533	+	0.419854i
$604$	−1.09471	+	1.89610i	−0.0445433	+	0.0771512i
$605$	4.83057	+	27.3955i	0.196390	+	1.11379i
$606$	−22.7083	−	14.5681i	−0.922461	−	0.591789i
$607$	7.62058	+	20.9374i	0.309310	+	0.849822i	0.992792	+	0.119854i	$0.0382427\pi$
$607$	7.62058	+	20.9374i	0.309310	+	0.849822i	−0.683482	+	0.729968i	$0.739535\pi$
$608$	0.634928	−	0.231095i	0.0257497	−	0.00937214i
$609$	13.1287	−	26.3626i	0.532002	−	1.06826i
$610$	2.32518	+	13.1868i	0.0941438	+	0.533916i
$611$	−1.66483	−	0.961191i	−0.0673519	−	0.0388856i
$612$	−0.117681	−	1.45093i	−0.00475698	−	0.0586503i
$613$	4.07821	+	7.06368i	0.164718	+	0.285299i	0.936555	−	0.350521i	$-0.113995\pi$
$613$	4.07821	+	7.06368i	0.164718	+	0.285299i	−0.771837	+	0.635820i	$0.780662\pi$
$614$	1.27275	−	1.06796i	0.0513640	−	0.0430995i
$615$	−11.6541	−	10.7471i	−0.469939	−	0.433366i
$616$	−5.29065	−	0.350668i	−0.213166	−	0.0141288i
$617$	−2.71597	+	3.23676i	−0.109341	+	0.130307i	−0.817939	−	0.575305i	$-0.804883\pi$
$617$	−2.71597	+	3.23676i	−0.109341	+	0.130307i	0.708598	+	0.705612i	$0.249328\pi$
$618$	5.59346	+	43.5523i	0.225002	+	1.75193i
$619$	5.39210	−	14.8147i	0.216727	−	0.595452i	−0.782918	−	0.622126i	$-0.786269\pi$
$619$	5.39210	−	14.8147i	0.216727	−	0.595452i	0.999644	+	0.0266739i	$0.00849157\pi$
$620$			2.13133i			0.0855964i
$621$	−36.5026	−	11.8918i	−1.46480	−	0.477201i
$622$			21.9630i			0.880637i
$623$	−6.11238	+	24.9001i	−0.244888	+	0.997600i
$624$	1.27160	−	3.04261i	0.0509047	−	0.121802i
$625$	−23.7408	−	19.9209i	−0.949631	−	0.796835i
$626$	−7.69488	+	43.6398i	−0.307549	+	1.74420i
$627$	0.314422	−	1.39730i	0.0125568	−	0.0558029i
$628$	0.448797	+	0.534855i	0.0179089	+	0.0213430i
$629$	18.0043	+	31.1844i	0.717878	+	1.24340i
$630$	−28.9249	+	0.426574i	−1.15240	+	0.0169951i
$631$	13.4875	−	23.3610i	0.536928	−	0.929986i	−0.462139	−	0.886807i	$-0.652918\pi$
$631$	13.4875	−	23.3610i	0.536928	−	0.929986i	0.999067	−	0.0431791i	$-0.0137486\pi$
$632$	29.4745	−	5.19714i	1.17243	−	0.206731i
$633$	13.9878	+	27.0795i	0.555967	+	1.07631i
$634$	−25.5694	+	9.30651i	−1.01549	+	0.369609i
$635$	−7.61887	+	2.77304i	−0.302346	+	0.110045i
$636$	−0.0838655	+	1.79064i	−0.00332548	+	0.0710036i
$637$	3.25091	−	1.34099i	0.128806	−	0.0531318i
$638$	−5.31116	−	3.06640i	−0.210271	−	0.121400i
$639$	0.706515	−	0.697619i	0.0279493	−	0.0275974i
$640$	−23.7938	+	13.7373i	−0.940532	+	0.543016i
$641$	16.8200	+	20.0453i	0.664351	+	0.791742i	0.988003	−	0.154434i	$-0.0493553\pi$
$641$	16.8200	+	20.0453i	0.664351	+	0.791742i	−0.323653	+	0.946176i	$0.604911\pi$
$642$	23.6238	−	7.36635i	0.932356	−	0.290726i
$643$	−4.19726	−	0.740090i	−0.165524	−	0.0291863i	0.0902720	−	0.995917i	$-0.471226\pi$
$643$	−4.19726	−	0.740090i	−0.165524	−	0.0291863i	−0.255796	+	0.966731i	$0.582337\pi$
$644$	−1.62614	−	1.08828i	−0.0640788	−	0.0428842i
$645$	38.0428	−	29.0003i	1.49794	−	1.14188i
$646$	−7.49926	−	2.72951i	−0.295054	−	0.107391i
$647$	−3.64617			−0.143346			−0.0716728	−	0.997428i	$-0.522834\pi$
$647$	−3.64617			−0.143346			−0.0716728	+	0.997428i	$0.522834\pi$
$648$	−26.0503	−	0.330128i	−1.02335	−	0.0129687i
$649$		−	4.50920i		−	0.177002i
$650$	1.29583	+	0.471644i	0.0508267	+	0.0184994i
$651$	26.7559	−	25.4139i	1.04865	−	0.996048i
$652$	1.22581	+	1.02857i	0.0480063	+	0.0402821i
$653$	13.9617	+	2.46183i	0.546364	+	0.0963388i	0.440016	−	0.897990i	$-0.354973\pi$
$653$	13.9617	+	2.46183i	0.546364	+	0.0963388i	0.106349	+	0.994329i	$0.466084\pi$
$654$	8.85124	+	28.3858i	0.346111	+	1.10997i
$655$	−10.3386	+	8.67509i	−0.403961	+	0.338964i
$656$	6.55923	+	11.3609i	0.256095	+	0.443569i
$657$	2.74793	+	10.5216i	0.107207	+	0.410488i
$658$	5.62965	−	12.7689i	0.219467	−	0.497784i
$659$	−1.27777	+	0.225306i	−0.0497750	+	0.00877668i	−0.198480	−	0.980105i	$-0.563601\pi$
$659$	−1.27777	+	0.225306i	−0.0497750	+	0.00877668i	0.148705	+	0.988882i	$0.452489\pi$
$660$	0.0148484	−	0.317033i	0.000577973	−	0.0123405i
$661$	−8.92686	−	24.5263i	−0.347215	−	0.953964i	−0.983243	−	0.182299i	$-0.941646\pi$
$661$	−8.92686	−	24.5263i	−0.347215	−	0.953964i	0.636029	−	0.771665i	$-0.280576\pi$
$662$	10.1335	+	27.8415i	0.393848	+	1.08209i
$663$	3.74757	−	1.93580i	0.145544	−	0.0751802i
$664$	−39.1260	+	6.89897i	−1.51838	+	0.267732i
$665$	3.37083	−	7.64557i	0.130715	−	0.296483i
$666$	27.9205	−	12.8048i	1.08190	−	0.496176i
$667$	−23.7412	−	41.1209i	−0.919262	−	1.59221i
$668$	1.07450	−	0.901612i	0.0415736	−	0.0348844i
$669$	14.4035	+	3.24109i	0.556872	+	0.125308i
$670$	12.3754	+	2.18212i	0.478104	+	0.0843026i
$671$	1.94849	+	1.63498i	0.0752206	+	0.0631176i
$672$	−2.48597	−	0.735130i	−0.0958983	−	0.0283583i
$673$	3.78929	+	1.37919i	0.146066	+	0.0531638i	0.414019	−	0.910268i	$-0.364125\pi$
$673$	3.78929	+	1.37919i	0.146066	+	0.0531638i	−0.267952	+	0.963432i	$0.586347\pi$
$674$		−	3.02565i		−	0.116544i
$675$	−0.353096	−	10.3418i	−0.0135907	−	0.398057i
$676$	1.27602			0.0490779
$677$	30.6702	+	11.1630i	1.17875	+	0.429031i	0.855761	−	0.517372i	$-0.173089\pi$
$677$	30.6702	+	11.1630i	1.17875	+	0.429031i	0.322991	+	0.946402i	$0.395312\pi$
$678$	−0.923628	−	7.19163i	−0.0354717	−	0.276193i
$679$	7.13060	+	4.77209i	0.273647	+	0.183136i
$680$	−36.5392	−	6.44284i	−1.40121	−	0.247072i
$681$	24.7189	+	22.7952i	0.947231	+	0.873514i
$682$	−4.93944	−	5.88659i	−0.189141	−	0.225409i
$683$	10.2385	−	5.91119i	0.391765	−	0.226185i	−0.291160	−	0.956674i	$-0.594041\pi$
$683$	10.2385	−	5.91119i	0.391765	−	0.226185i	0.682924	+	0.730489i	$0.260708\pi$
$684$	0.153639	−	0.324102i	0.00587453	−	0.0123924i
$685$	9.03343	+	5.21545i	0.345149	+	0.199272i
$686$	12.2292	+	22.4078i	0.466915	+	0.855536i
$687$	35.7354	+	22.9254i	1.36339	+	0.874660i
$688$	−37.1972	+	13.5387i	−1.41813	+	0.516157i
$689$	−4.88100	+	1.77654i	−0.185951	+	0.0676807i
$690$	−25.1839	+	39.2559i	−0.958736	+	1.49445i
$691$	−17.9042	+	3.15699i	−0.681107	+	0.120098i	−0.503489	−	0.864002i	$-0.667950\pi$
$691$	−17.9042	+	3.15699i	−0.681107	+	0.120098i	−0.177619	+	0.984099i	$0.556839\pi$
$692$	−0.651029	+	1.12762i	−0.0247484	+	0.0428655i
$693$	−4.15696	+	3.59388i	−0.157910	+	0.136520i
$694$	17.7881	+	30.8100i	0.675229	+	1.16953i
$695$	18.1346	+	21.6119i	0.687883	+	0.819787i
$696$	−23.6875	−	21.8440i	−0.897872	−	0.827996i
$697$	−2.91378	+	16.5249i	−0.110367	+	0.625924i
$698$	−33.0069	−	27.6960i	−1.24933	−	1.04831i
$699$	−5.93026	+	0.761628i	−0.224303	+	0.0288074i
$700$	0.125734	−	0.512203i	0.00475229	−	0.0193594i
$701$			48.4943i			1.83160i	0.401629	+	0.915802i	$0.368444\pi$
$701$			48.4943i			1.83160i	−0.401629	+	0.915802i	$0.631556\pi$
$702$	−1.34529	−	3.33717i	−0.0507746	−	0.125953i
$703$			8.87231i			0.334625i
$704$	−1.97938	+	5.43830i	−0.0746007	+	0.204964i
$705$	16.1696	+	6.75774i	0.608981	+	0.254511i
$706$	7.92257	−	9.44175i	0.298170	−	0.355345i
$707$	−29.8336	−	1.97739i	−1.12201	−	0.0743675i
$708$	0.247902	−	1.10169i	0.00931673	−	0.0414039i
$709$	10.5955	−	8.89065i	0.397921	−	0.333895i	−0.421768	−	0.906704i	$-0.638590\pi$
$709$	10.5955	−	8.89065i	0.397921	−	0.333895i	0.819689	+	0.572808i	$0.194146\pi$
$710$	−0.603115	−	1.04463i	−0.0226345	−	0.0392041i
$711$	17.9517	−	25.2950i	0.673241	−	0.948638i
$712$	24.2937	+	14.0260i	0.910444	+	0.525645i
$713$	−10.3313	−	58.5915i	−0.386909	−	2.19427i
$714$	16.9116	+	25.5251i	0.632902	+	0.955253i
$715$	0.864181	−	0.314536i	0.0323185	−	0.0117630i
$716$	−0.506253	−	1.39092i	−0.0189196	−	0.0519811i
$717$	−0.821069	+	17.5309i	−0.0306634	+	0.654705i
$718$	−3.69863	−	20.9760i	−0.138032	−	0.782817i
$719$	15.5281	−	26.8955i	0.579102	−	1.00303i	−0.416480	−	0.909145i	$-0.636737\pi$
$719$	15.5281	−	26.8955i	0.579102	−	1.00303i	0.995583	−	0.0938898i	$-0.0299301\pi$
$720$	−7.96447	+	28.9879i	−0.296818	+	1.08031i
$721$	28.7453	+	39.2640i	1.07053	+	1.46227i
$722$	15.5700	+	18.5556i	0.579456	+	0.690569i
$723$	3.03476	+	9.73242i	0.112864	+	0.361952i
$724$	0.877821	+	0.154784i	0.0326240	+	0.00575248i
$725$	8.22665	−	9.80414i	0.305530	−	0.364117i
$726$	−15.2272	−	19.9751i	−0.565133	−	0.741346i
$727$	−5.22873	+	14.3658i	−0.193923	+	0.532799i	−0.998102	−	0.0615888i	$-0.980383\pi$
$727$	−5.22873	+	14.3658i	−0.193923	+	0.532799i	0.804179	+	0.594388i	$0.202605\pi$
$728$	−0.416062	−	3.82498i	−0.0154203	−	0.141763i
$729$	−19.4513	+	18.7256i	−0.720419	+	0.693539i
$730$	13.2111			0.488965
$731$	−47.5788	−	17.3173i	−1.75977	−	0.640503i
$732$	0.386168	+	0.506579i	0.0142732	+	0.0187237i
$733$	2.45103	−	2.92103i	0.0905310	−	0.107891i	−0.718877	−	0.695137i	$-0.755344\pi$
$733$	2.45103	−	2.92103i	0.0905310	−	0.107891i	0.809408	+	0.587246i	$0.199788\pi$
$734$	4.10761	−	23.2954i	0.151615	−	0.859849i
$735$	−27.8374	+	15.9003i	−1.02680	+	0.586492i
$736$	−3.20176	+	2.68660i	−0.118019	+	0.0990293i
$737$	2.06727	−	1.19354i	0.0761488	−	0.0439645i
$738$	13.8023	+	3.79221i	0.508070	+	0.139593i
$739$	7.35130	−	12.7328i	0.270422	−	0.468385i	−0.698548	−	0.715563i	$-0.746170\pi$
$739$	7.35130	−	12.7328i	0.270422	−	0.468385i	0.968970	+	0.247179i	$0.0795034\pi$
$740$	0.341406	+	1.93621i	0.0125503	+	0.0711765i
$741$	1.03816	+	0.0486225i	0.0381376	+	0.00178619i
$742$	−16.6520	−	33.8296i	−0.611316	−	1.24192i
$743$	−1.42412	−	3.91275i	−0.0522460	−	0.143545i	0.910825	−	0.412793i	$-0.135447\pi$
$743$	−1.42412	−	3.91275i	−0.0522460	−	0.143545i	−0.963071	+	0.269249i	$0.913225\pi$
$744$	−18.5292	−	35.8712i	−0.679313	−	1.31510i
$745$	−7.98385	+	1.40777i	−0.292506	+	0.0515767i
$746$	−13.2874	−	7.67147i	−0.486486	−	0.280873i
$747$	−23.8300	+	33.5780i	−0.871896	+	1.22855i
$748$	−0.290928	+	0.167967i	−0.0106374	+	0.00614150i
$749$	18.9782	−	19.7957i	0.693447	−	0.723321i
$750$	18.5286	+	4.16931i	0.676567	+	0.152242i
$751$	7.19549	−	40.8077i	0.262567	−	1.48909i	−0.513307	−	0.858205i	$-0.671580\pi$
$751$	7.19549	−	40.8077i	0.262567	−	1.48909i	0.775874	−	0.630888i	$-0.217309\pi$
$752$	−11.1091	−	9.32165i	−0.405108	−	0.339926i
$753$	−37.4723	−	15.6608i	−1.36557	−	0.570711i
$754$	1.52206	−	4.18184i	0.0554303	−	0.152293i
$755$	57.8341			2.10480
$756$	−1.21321	+	0.649519i	−0.0441239	+	0.0236228i
$757$	4.90770			0.178373			0.0891867	−	0.996015i	$-0.471573\pi$
$757$	4.90770			0.178373			0.0891867	+	0.996015i	$0.471573\pi$
$758$	−16.7315	+	45.9695i	−0.607717	+	1.66969i
$759$	1.12857	+	8.78739i	0.0409646	+	0.318962i
$760$	−7.00312	−	5.87632i	−0.254030	−	0.213156i
$761$	−0.618133	+	3.50561i	−0.0224073	+	0.127078i	−0.993960	−	0.109747i	$-0.964996\pi$
$761$	−0.618133	+	3.50561i	−0.0224073	+	0.127078i	0.971552	+	0.236825i	$0.0761070\pi$
$762$	4.96281	−	5.38162i	0.179783	−	0.194956i
$763$	23.7861	+	22.8038i	0.861116	+	0.825551i
$764$	−1.30367	+	0.752672i	−0.0471650	+	0.0272307i
$765$	−31.6374	+	21.8554i	−1.14385	+	0.790182i
$766$	−24.5951	−	14.2000i	−0.888658	−	0.513067i
$767$	3.22235	−	0.568188i	0.116352	−	0.0205161i
$768$	−2.24111	+	3.49337i	−0.0808691	+	0.126056i
$769$	5.08016	+	13.9576i	0.183195	+	0.503325i	0.996964	−	0.0778641i	$-0.0248100\pi$
$769$	5.08016	+	13.9576i	0.183195	+	0.503325i	−0.813769	+	0.581189i	$0.802588\pi$
$770$	2.94824	+	5.98953i	0.106247	+	0.215848i
$771$	−11.2891	+	17.5971i	−0.406567	+	0.633743i
$772$	−0.139547	−	0.791410i	−0.00502241	−	0.0284835i
$773$	−22.5761	+	39.1030i	−0.812006	+	1.40644i	0.0994515	+	0.995042i	$0.468291\pi$
$773$	−22.5761	+	39.1030i	−0.812006	+	1.40644i	−0.911458	+	0.411394i	$0.865042\pi$
$774$	−18.5011	+	39.0282i	−0.665008	+	1.40284i
$775$	13.8879	−	8.01820i	0.498869	−	0.288022i
$776$	7.19123	−	6.03416i	0.258150	−	0.216614i
$777$	20.2355	−	27.3731i	0.725945	−	0.982005i
$778$	−8.88346	+	50.3806i	−0.318487	+	1.80623i
$779$	−2.65757	+	3.16717i	−0.0952173	+	0.113476i
$780$	0.228429	−	0.0293373i	0.00817905	−	0.00105044i
$781$	−0.215315	−	0.0783681i	−0.00770456	−	0.00280423i
$782$	49.3661			1.76533
$783$	−33.3746	+	1.13949i	−1.19271	+	0.0407221i
$784$	25.9080	−	5.70378i	0.925287	−	0.203707i
$785$	6.30794	−	17.3309i	0.225140	−	0.618567i
$786$	4.69889	−	11.2433i	0.167604	−	0.401033i
$787$	28.1220	−	33.5145i	1.00244	−	1.19466i	0.0216158	−	0.999766i	$-0.493119\pi$
$787$	28.1220	−	33.5145i	1.00244	−	1.19466i	0.980824	−	0.194895i	$-0.0624366\pi$
$788$	0.110537	+	0.0194906i	0.00393770	+	0.000694323i
$789$	0.264854	+	0.0595975i	0.00942904	+	0.00212173i
$790$	−24.2218	−	28.8664i	−0.861772	−	1.02702i
$791$	−4.74660	−	6.48352i	−0.168770	−	0.230527i
$792$	2.50629	+	5.46489i	0.0890571	+	0.194186i
$793$	−0.922860	+	1.59844i	−0.0327717	+	0.0567623i
$794$	−2.25072	−	12.7645i	−0.0798750	−	0.452994i
$795$	42.0708	−	21.7315i	1.49210	−	0.770738i
$796$	−0.773106	−	2.12409i	−0.0274020	−	0.0752864i
$797$	−13.4134	+	4.88208i	−0.475128	+	0.172932i	−0.568474	−	0.822701i	$-0.692466\pi$
$797$	−13.4134	+	4.88208i	−0.475128	+	0.172932i	0.0933461	+	0.995634i	$0.470244\pi$
$798$	0.464047	+	7.53010i	0.0164271	+	0.266563i
$799$	−3.22107	−	18.2676i	−0.113953	−	0.646260i
$800$	−0.975639	−	0.563286i	−0.0344941	−	0.0199152i
$801$	28.1288	−	7.34638i	0.993881	−	0.259572i
$802$	−3.65715	−	6.33437i	−0.129138	−	0.223674i
$803$	1.92243	−	1.61311i	0.0678411	−	0.0569255i
$804$	0.570691	−	0.177952i	0.0201267	−	0.00627590i
$805$	−3.41832	+	51.5734i	−0.120480	+	1.81772i
$806$	3.58426	−	4.27156i	0.126250	−	0.150459i
$807$	−25.2923	+	19.2805i	−0.890333	+	0.678706i
$808$	−11.1883	+	30.7397i	−0.393604	+	1.08142i
$809$		−	0.143221i		−	0.00503539i	−0.999997	−	0.00251770i	$-0.999199\pi$
$809$		−	0.143221i		−	0.00503539i	0.999997	−	0.00251770i	$-0.000801408\pi$
$810$	16.0394	+	28.6123i	0.563567	+	1.00533i
$811$			45.2402i			1.58860i	0.607527	+	0.794299i	$0.292161\pi$
$811$			45.2402i			1.58860i	−0.607527	+	0.794299i	$0.707839\pi$
$812$	−1.65295	−	0.405761i	−0.0580072	−	0.0142394i
$813$	−8.38478	−	10.9992i	−0.294067	−	0.385760i
$814$	−5.43018	−	4.55646i	−0.190328	−	0.159704i
$815$	7.33993	−	41.6268i	0.257106	−	1.45812i
$816$	30.3769	−	9.47212i	1.06341	−	0.331590i
$817$	−8.01911	−	9.55680i	−0.280553	−	0.334350i
$818$	−7.79136	−	13.4950i	−0.272418	−	0.471843i
$819$	−3.09205	−	2.51778i	−0.108045	−	0.0879785i
$820$	−0.458091	+	0.793437i	−0.0159972	+	0.0277080i
$821$	43.5103	−	7.67203i	1.51852	−	0.267756i	0.648668	−	0.761071i	$-0.275326\pi$
$821$	43.5103	−	7.67203i	1.51852	−	0.267756i	0.869850	+	0.493316i	$0.164215\pi$
$822$	−9.40781	−	0.440619i	−0.328135	−	0.0153684i
$823$	−18.7636	+	6.82940i	−0.654059	+	0.238058i	−0.647669	−	0.761922i	$-0.724256\pi$
$823$	−18.7636	+	6.82940i	−0.654059	+	0.238058i	−0.00638963	+	0.999980i	$0.502034\pi$
$824$	50.0298	−	18.2093i	1.74287	−	0.634353i
$825$	−2.12167	+	1.09594i	−0.0738672	+	0.0381559i
$826$	6.62987	+	22.8084i	0.230683	+	0.793604i
$827$	−44.9608	−	25.9581i	−1.56344	−	0.902653i	−0.996905	−	0.0786167i	$-0.974950\pi$
$827$	−44.9608	−	25.9581i	−1.56344	−	0.902653i	−0.566536	−	0.824037i	$-0.691717\pi$
$828$	−0.207372	+	2.20898i	−0.00720667	+	0.0767673i
$829$	−27.6657	+	15.9728i	−0.960871	+	0.554759i	−0.896441	−	0.443163i	$-0.853856\pi$
$829$	−27.6657	+	15.9728i	−0.960871	+	0.554759i	−0.0644299	+	0.997922i	$0.520523\pi$
$830$	32.1533	+	38.3188i	1.11606	+	1.33006i
$831$	−6.35398	+	28.2373i	−0.220417	+	0.979541i
$832$	−4.13572	−	0.729238i	−0.143380	−	0.0252818i
$833$	30.0755	+	15.7125i	1.04205	+	0.544405i
$834$	−23.5031	−	9.82265i	−0.813846	−	0.340131i
$835$	−34.8170	−	12.6724i	−1.20489	−	0.438545i
$836$	−0.0827724			−0.00286274
$837$	−39.7847	−	12.9610i	−1.37516	−	0.447999i
$838$		−	3.09523i		−	0.106923i
$839$	15.3238	+	5.57740i	0.529036	+	0.192553i	0.592708	−	0.805418i	$-0.298059\pi$
$839$	15.3238	+	5.57740i	0.529036	+	0.192553i	−0.0636719	+	0.997971i	$0.520281\pi$
$840$	8.20384	+	34.1022i	0.283059	+	1.17664i
$841$	−9.42408	−	7.90774i	−0.324968	−	0.272681i
$842$	−10.6966	−	1.88609i	−0.368628	−	0.0649990i
$843$	−13.9843	+	15.1644i	−0.481644	+	0.522290i
$844$	1.34934	−	1.13223i	0.0464462	−	0.0389730i
$845$	−16.8532	−	29.1906i	−0.579768	−	1.00419i
$846$	−15.7715	+	1.27919i	−0.542237	+	0.0439795i
$847$	−25.4696	−	11.2292i	−0.875145	−	0.385840i
$848$	−38.5887	+	6.80422i	−1.32514	+	0.233658i
$849$	2.15244	+	1.38086i	0.0738715	+	0.0473910i
$850$	4.55097	+	12.5037i	0.156097	+	0.428873i
$851$	−18.7709	−	51.5726i	−0.643458	−	1.76789i
$852$	−0.0482971	−	0.0309842i	−0.00165463	−	0.00106150i
$853$	35.5687	−	6.27173i	1.21785	−	0.214740i	0.472450	−	0.881357i	$-0.343370\pi$
$853$	35.5687	−	6.27173i	1.21785	−	0.214740i	0.745400	+	0.666618i	$0.232259\pi$
$854$	−12.2597	−	5.40515i	−0.419519	−	0.184960i
$855$	−9.44343	+	0.765934i	−0.322959	+	0.0261944i
$856$	−15.0019	−	25.9841i	−0.512756	−	0.888119i
$857$	9.21540	−	7.73264i	0.314792	−	0.264142i	−0.471677	−	0.881771i	$-0.656351\pi$
$857$	9.21540	−	7.73264i	0.314792	−	0.264142i	0.786469	+	0.617629i	$0.211907\pi$
$858$	−0.562913	+	0.610418i	−0.0192175	+	0.0208393i
$859$	−40.7685	−	7.18859i	−1.39100	−	0.245272i	−0.572563	−	0.819861i	$-0.694051\pi$
$859$	−40.7685	−	7.18859i	−1.39100	−	0.245272i	−0.818442	+	0.574589i	$0.805162\pi$
$860$	−2.11776	−	1.77701i	−0.0722151	−	0.0605957i
$861$	15.4227	−	3.71020i	0.525605	−	0.126443i
$862$	6.86510	+	2.49869i	0.233826	+	0.0851058i
$863$		−	8.37280i		−	0.285014i	−0.989794	−	0.142507i	$-0.954484\pi$
$863$		−	8.37280i		−	0.285014i	0.989794	−	0.142507i	$-0.0455163\pi$
$864$	0.608919	+	2.87573i	0.0207158	+	0.0978342i
$865$	34.3941			1.16943
$866$	−25.3488	−	9.22619i	−0.861386	−	0.313519i
$867$	10.3849	+	4.34018i	0.352691	+	0.147400i
$868$	−1.77235	−	1.18613i	−0.0601576	−	0.0402599i
$869$	−7.04932	−	1.24299i	−0.239132	−	0.0421654i
$870$	−8.90622	+	39.5795i	−0.301949	+	1.34187i
$871$	1.11341	+	1.32691i	0.0377265	+	0.0449607i
$872$	31.2220	−	18.0260i	1.05731	−	0.610437i
$873$	0.909323	−	9.68635i	0.0307759	−	0.327833i
$874$	10.5339	+	6.08176i	0.356315	+	0.205719i
$875$	20.2105	−	5.87473i	0.683239	−	0.198602i
$876$	0.558371	−	0.288425i	0.0188656	−	0.00974498i
$877$	−23.1647	+	8.43126i	−0.782216	+	0.284703i	−0.702096	−	0.712082i	$-0.747752\pi$
$877$	−23.1647	+	8.43126i	−0.782216	+	0.284703i	−0.0801197	+	0.996785i	$0.525530\pi$
$878$	−0.985371	+	0.358646i	−0.0332547	+	0.0121037i
$879$	3.10490	+	0.145420i	0.104726	+	0.00490488i
$880$	6.83213	−	1.20469i	0.230311	−	0.0406100i
$881$	−11.3095	+	19.5887i	−0.381028	+	0.659959i	−0.991209	−	0.132302i	$-0.957763\pi$
$881$	−11.3095	+	19.5887i	−0.381028	+	0.659959i	0.610182	+	0.792261i	$0.291096\pi$
$882$	15.7426	−	24.2905i	0.530080	−	0.817903i
$883$	3.43466	+	5.94900i	0.115585	+	0.200200i	0.918014	−	0.396549i	$-0.129792\pi$
$883$	3.43466	+	5.94900i	0.115585	+	0.200200i	−0.802428	+	0.596749i	$0.796459\pi$
$884$	−0.156691	−	0.186737i	−0.00527009	−	0.00628065i
$885$	−28.4766	+	8.87955i	−0.957230	+	0.298483i
$886$	2.76077	−	15.6571i	0.0927497	−	0.526010i
$887$	23.8414	+	20.0053i	0.800515	+	0.671712i	0.948324	−	0.317304i	$-0.102778\pi$
$887$	23.8414	+	20.0053i	0.800515	+	0.671712i	−0.147809	+	0.989016i	$0.547222\pi$
$888$	−22.5789	−	29.6192i	−0.757697	−	0.993954i
$889$	1.93408	−	7.87888i	0.0648669	−	0.264249i
$890$		−	35.3189i		−	1.18389i
$891$	5.82763	+	2.20511i	0.195233	+	0.0738739i
$892$		−	0.853224i		−	0.0285681i
$893$	1.56319	−	4.29483i	0.0523102	−	0.143721i
$894$	5.82133	−	4.43764i	0.194695	−	0.148417i
$895$	−25.1326	+	29.9518i	−0.840090	+	1.00118i
$896$	1.81817	−	27.4313i	0.0607407	−	0.916416i
$897$	−6.13741	+	1.91376i	−0.204922	+	0.0638987i
$898$	31.5055	−	26.4363i	1.05135	−	0.882190i
$899$	−25.8759	−	44.8183i	−0.863008	−	1.49477i
$900$	−0.578618	+	0.151117i	−0.0192873	+	0.00503725i
$901$	−43.4053	−	25.0601i	−1.44604	−	0.834872i
$902$	−0.573602	−	3.25306i	−0.0190989	−	0.108315i
$903$	2.94414	+	47.7745i	0.0979747	+	1.58984i
$904$	−8.26123	+	3.00684i	−0.274765	+	0.100006i
$905$	−8.05304	−	22.1255i	−0.267692	−	0.735478i
$906$	−46.3948	+	23.9651i	−1.54136	+	0.796186i
$907$	2.17702	+	12.3465i	0.0722867	+	0.409958i	0.999383	+	0.0351341i	$0.0111858\pi$
$907$	2.17702	+	12.3465i	0.0722867	+	0.409958i	−0.927096	+	0.374824i	$0.877703\pi$
$908$	0.971634	−	1.68292i	0.0322448	−	0.0558496i
$909$	14.1328	+	30.8161i	0.468755	+	1.02211i
$910$	−3.90872	+	2.86158i	−0.129573	+	0.0948606i
$911$	13.6756	+	16.2979i	0.453093	+	0.539975i	0.943436	−	0.331554i	$-0.107573\pi$
$911$	13.6756	+	16.2979i	0.453093	+	0.539975i	−0.490343	+	0.871529i	$0.663129\pi$
$912$	7.64888	+	1.72116i	0.253280	+	0.0569932i
$913$	9.35765	+	1.65001i	0.309693	+	0.0546072i
$914$	8.87939	−	10.5820i	0.293704	−	0.350023i
$915$	6.48826	−	15.5247i	0.214495	−	0.513232i
$916$	0.839209	−	2.30571i	0.0277283	−	0.0761827i
$917$	−1.46032	−	13.4251i	−0.0482239	−	0.443336i
$918$	16.3234	−	30.6423i	0.538751	−	1.01135i
$919$	26.7699			0.883059			0.441530	−	0.897247i	$-0.354436\pi$
$919$	26.7699			0.883059			0.441530	+	0.897247i	$0.354436\pi$
$920$	53.1398	+	19.3413i	1.75197	+	0.637664i
$921$	−2.07077	+	0.265951i	−0.0682341	+	0.00876337i
$922$	−13.0296	+	15.5280i	−0.429105	+	0.511388i
$923$	0.0288722	−	0.163742i	0.000950340	−	0.00538965i
$924$	0.255372	+	0.188783i	0.00840112	+	0.00621051i
$925$	11.3321	−	9.50876i	0.372597	−	0.312646i
$926$	33.0602	−	19.0873i	1.08643	−	0.627249i
$927$	23.6352	−	49.8587i	0.776282	−	1.63757i
$928$	−1.81780	+	3.14853i	−0.0596723	+	0.103355i
$929$	−6.04033	−	34.2564i	−0.198177	−	1.12392i	−0.907821	−	0.419357i	$-0.862256\pi$
$929$	−6.04033	−	34.2564i	−0.198177	−	1.12392i	0.709645	−	0.704560i	$-0.248855\pi$
$930$	−27.4484	+	42.7856i	−0.900067	+	1.40299i
$931$	4.48189	+	7.05800i	0.146888	+	0.231317i
$932$	0.118181	+	0.324699i	0.00387114	+	0.0106359i
$933$	14.9024	−	23.2293i	0.487882	−	0.760494i
$934$	−3.38274	+	0.596468i	−0.110687	+	0.0195170i
$935$	7.68492	+	4.43689i	0.251324	+	0.145102i
$936$	−3.58950	+	2.47965i	−0.117326	+	0.0810498i
$937$	19.9911	−	11.5419i	0.653080	−	0.377056i	−0.136555	−	0.990632i	$-0.543603\pi$
$937$	19.9911	−	11.5419i	0.653080	−	0.377056i	0.789635	+	0.613576i	$0.210270\pi$
$938$	−8.70176	+	9.07663i	−0.284122	+	0.296362i
$939$	37.7491	−	40.9348i	1.23190	−	1.33586i
$940$	0.175871	−	0.997416i	0.00573629	−	0.0325321i
$941$	−1.99581	−	1.67468i	−0.0650614	−	0.0545930i	0.609677	−	0.792650i	$-0.291299\pi$
$941$	−1.99581	−	1.67468i	−0.0650614	−	0.0545930i	−0.674738	+	0.738057i	$0.735744\pi$
$942$	2.12127	+	16.5168i	0.0691146	+	0.538146i
$943$	8.74712	−	24.0325i	0.284846	−	0.782607i
$944$	24.6835			0.803380
$945$	30.8821	+	19.1750i	1.00459	+	0.623763i
$946$	9.96740			0.324068
$947$	−4.82731	+	13.2629i	−0.156866	+	0.430987i	−0.993083	−	0.117412i	$-0.962540\pi$
$947$	−4.82731	+	13.2629i	−0.156866	+	0.430987i	0.836217	+	0.548399i	$0.184762\pi$
$948$	−1.65395	−	0.691236i	−0.0537178	−	0.0224503i
$949$	1.39500	+	1.17054i	0.0452835	+	0.0379973i
$950$	−0.569316	+	3.22875i	−0.0184710	+	0.104755i
$951$	33.3583	+	7.50632i	1.08172	+	0.243409i
$952$	25.6925	−	26.7993i	0.832698	−	0.868570i
$953$	−20.2507	+	11.6917i	−0.655984	+	0.378733i	−0.790745	−	0.612145i	$-0.790307\pi$
$953$	−20.2507	+	11.6917i	−0.655984	+	0.378733i	0.134761	+	0.990878i	$0.456973\pi$
$954$	−24.7443	+	34.8663i	−0.801127	+	1.12884i
$955$	34.4366	+	19.8820i	1.11434	+	0.643366i
$956$	0.998853	−	0.176125i	0.0323052	−	0.00569628i
$957$	3.53677	+	6.84694i	0.114327	+	0.221330i
$958$	−1.92509	−	5.28915i	−0.0621970	−	0.170885i
$959$	−9.36430	+	4.60942i	−0.302389	+	0.148846i
$960$	38.2419	+	1.79107i	1.23425	+	0.0578067i
$961$	−5.87711	−	33.3307i	−0.189584	−	1.07518i
$962$	2.57189	−	4.45464i	0.0829210	−	0.143623i
$963$	−29.9841	−	8.23817i	−0.966223	−	0.265471i
$964$	0.510234	−	0.294584i	0.0164335	−	0.00948791i
$965$	−16.2614	+	13.6449i	−0.523473	+	0.439246i
$966$	−18.6286	−	42.7889i	−0.599366	−	1.37671i
$967$	5.97974	−	33.9128i	0.192295	−	1.09056i	−0.723923	−	0.689881i	$-0.757663\pi$
$967$	5.97974	−	33.9128i	0.192295	−	1.09056i	0.916218	−	0.400680i	$-0.131226\pi$
$968$	−19.5757	+	23.3294i	−0.629187	+	0.749835i
$969$	6.07961	+	7.97529i	0.195305	+	0.256203i
$970$	−11.1065	−	4.04245i	−0.356610	−	0.129795i
$971$	−29.1736			−0.936225			−0.468113	−	0.883669i	$-0.655066\pi$
$971$	−29.1736			−0.936225			−0.468113	+	0.883669i	$0.655066\pi$
$972$	1.30257	+	0.859137i	0.0417801	+	0.0275568i
$973$	−28.0641	+	3.05267i	−0.899693	+	0.0978642i
$974$	−12.8069	+	35.1868i	−0.410361	+	1.12746i
$975$	−1.05052	−	1.37809i	−0.0336437	−	0.0441341i
$976$	−8.94992	+	10.6661i	−0.286480	+	0.341413i
$977$	30.5820	+	5.39243i	0.978405	+	0.172519i	0.639911	−	0.768449i	$-0.278971\pi$
$977$	30.5820	+	5.39243i	0.978405	+	0.172519i	0.338494	+	0.940968i	$0.390082\pi$
$978$	11.3610	+	36.4347i	0.363286	+	1.16505i
$979$	−4.31253	−	5.13947i	−0.137829	−	0.164258i
$980$	1.24968	+	1.36781i	0.0399195	+	0.0436931i
$981$	9.89881	−	36.0282i	0.316045	−	1.15029i
$982$	−4.75853	+	8.24202i	−0.151851	+	0.263013i
$983$	9.67981	+	54.8970i	0.308738	+	1.75094i	0.605366	+	0.795948i	$0.293027\pi$
$983$	9.67981	+	54.8970i	0.308738	+	1.75094i	−0.296627	+	0.954993i	$0.595862\pi$
$984$	0.811957	−	17.3364i	0.0258842	−	0.552664i
$985$	−1.01405	−	2.78608i	−0.0323104	−	0.0887720i
$986$	40.3512	−	14.6866i	1.28504	−	0.467718i
$987$	−14.6182	+	9.68529i	−0.465303	+	0.308286i
$988$	−0.0104298	−	0.0591506i	−0.000331818	−	0.00188183i
$989$	66.8322	+	38.5856i	2.12514	+	1.22695i
$990$	4.38098	−	6.17308i	0.139237	−	0.196193i
$991$	12.2215	+	21.1683i	0.388229	+	0.672432i	0.992211	−	0.124565i	$-0.0397537\pi$
$991$	12.2215	+	21.1683i	0.388229	+	0.672432i	−0.603983	+	0.796998i	$0.706420\pi$
$992$	−3.48965	+	2.92816i	−0.110796	+	0.0929693i
$993$	8.17331	−	36.3225i	0.259372	−	1.15266i
$994$	1.20432	+	0.0798235i	0.0381989	+	0.00253185i
$995$	−38.3803	+	45.7398i	−1.21674	+	1.45005i
$996$	2.19554	+	0.917584i	0.0695685	+	0.0290748i
$997$	3.82620	−	10.5124i	0.121177	−	0.332931i	−0.864242	−	0.503076i	$-0.832201\pi$
$997$	3.82620	−	10.5124i	0.121177	−	0.332931i	0.985419	+	0.170145i	$0.0544237\pi$
$998$		−	6.85758i		−	0.217073i
$999$	−38.2186	−	5.40158i	−1.20918	−	0.170898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.104.15	yes	132
3.2	odd	2		567.2.be.a.503.7		132
7.6	odd	2	inner	189.2.be.a.104.16	yes	132
21.20	even	2		567.2.be.a.503.8		132
27.7	even	9		567.2.be.a.62.8		132
27.20	odd	18	inner	189.2.be.a.20.16	yes	132
189.20	even	18	inner	189.2.be.a.20.15	✓	132
189.34	odd	18		567.2.be.a.62.7		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.15	✓	132	189.20	even	18	inner
189.2.be.a.20.16	yes	132	27.20	odd	18	inner
189.2.be.a.104.15	yes	132	1.1	even	1	trivial
189.2.be.a.104.16	yes	132	7.6	odd	2	inner
567.2.be.a.62.7		132	189.34	odd	18
567.2.be.a.62.8		132	27.7	even	9
567.2.be.a.503.7		132	3.2	odd	2
567.2.be.a.503.8		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+(0.471430 - 1.29524i) q^{2} +(-1.37746 + 1.05005i) q^{3} +(0.0766803 + 0.0643424i) q^{4} +(0.459149 - 2.60396i) q^{5} +(0.710690 + 2.27917i) q^{6} +(1.90985 + 1.83097i) q^{7} +(2.50689 - 1.44736i) q^{8} +(0.794802 - 2.89280i) q^{9} +(-3.15631 - 1.82230i) q^{10} +(-0.681802 + 0.120220i) q^{11} +(-0.173187 - 0.00811128i) q^{12} +(-0.171823 - 0.472079i) q^{13} +(3.27192 - 1.61055i) q^{14} +(2.10182 + 4.06899i) q^{15} +(-0.658089 - 3.73221i) q^{16} +(2.42375 - 4.19806i) q^{17} +(-3.37219 - 2.39321i) q^{18} +(1.03438 - 0.597199i) q^{19} +(0.202753 - 0.170130i) q^{20} +(-4.55336 - 0.516662i) q^{21} +(-0.165708 + 0.939774i) q^{22} +(-4.74912 + 5.65978i) q^{23} +(-1.93336 + 4.62603i) q^{24} +(-1.87135 - 0.681115i) q^{25} -0.692459 q^{26} +(1.94277 + 4.81930i) q^{27} +(0.0286387 + 0.263284i) q^{28} +(-2.19806 + 6.03911i) q^{29} +(6.26119 - 0.804131i) q^{30} +(-5.17613 + 6.16868i) q^{31} +(0.557110 + 0.0982336i) q^{32} +(0.812919 - 0.881523i) q^{33} +(-4.29488 - 5.11844i) q^{34} +(5.64470 - 4.13250i) q^{35} +(0.247075 - 0.170681i) q^{36} +(-3.71414 + 6.43307i) q^{37} +(-0.285881 - 1.62131i) q^{38} +(0.732384 + 0.469849i) q^{39} +(-2.61782 - 7.19241i) q^{40} +(-3.25278 + 1.18391i) q^{41} +(-2.81579 + 5.65413i) q^{42} +(-1.81376 - 10.2863i) q^{43} +(-0.0600160 - 0.0346503i) q^{44} +(-7.16781 - 3.39786i) q^{45} +(5.09191 + 8.81945i) q^{46} +(2.93133 - 2.45968i) q^{47} +(4.82549 + 4.44995i) q^{48} +(0.295069 + 6.99378i) q^{49} +(-1.76442 + 2.10275i) q^{50} +(1.06954 + 8.32773i) q^{51} +(0.0171993 - 0.0472546i) q^{52} -10.3394i q^{53} +(7.15804 - 0.244393i) q^{54} +1.83059i q^{55} +(7.43787 + 1.82582i) q^{56} +(-0.797730 + 1.90876i) q^{57} +(6.78588 + 5.69403i) q^{58} +(-1.13100 + 6.41423i) q^{59} +(-0.100640 + 0.447248i) q^{60} +(-2.36159 - 2.81444i) q^{61} +(5.54975 + 9.61245i) q^{62} +(6.81459 - 4.06956i) q^{63} +(4.17966 - 7.23938i) q^{64} +(-1.30817 + 0.230665i) q^{65} +(-0.758552 - 1.46850i) q^{66} +(-3.24000 + 1.17926i) q^{67} +(0.455968 - 0.165959i) q^{68} +(0.598694 - 12.7829i) q^{69} +(-2.69151 - 9.25944i) q^{70} +(0.286623 + 0.165482i) q^{71} +(-2.19443 - 8.40230i) q^{72} +(-3.13921 + 1.81243i) q^{73} +(6.58144 + 7.84345i) q^{74} +(3.29291 - 1.02679i) q^{75} +(0.117742 + 0.0207610i) q^{76} +(-1.52226 - 1.01876i) q^{77} +(0.953836 - 0.727115i) q^{78} +(9.71572 + 3.53623i) q^{79} -10.0207 q^{80} +(-7.73658 - 4.59840i) q^{81} +4.77127i q^{82} +(-12.8972 - 4.69419i) q^{83} +(-0.315910 - 0.332592i) q^{84} +(-9.81874 - 8.23890i) q^{85} +(-14.1784 - 2.50003i) q^{86} +(-3.31361 - 10.6267i) q^{87} +(-1.53520 + 1.28819i) q^{88} +(4.84538 + 8.39244i) q^{89} +(-7.78018 + 7.68221i) q^{90} +(0.536208 - 1.21620i) q^{91} +(-0.728328 + 0.128424i) q^{92} +(0.652525 - 13.9323i) q^{93} +(-1.80397 - 4.95636i) q^{94} +(-1.08015 - 2.96769i) q^{95} +(-0.870548 + 0.449679i) q^{96} +(3.19371 - 0.563137i) q^{97} +(9.19775 + 2.91489i) q^{98} +(-0.194125 + 2.06787i) 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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