LMFDB - Embedded newform 189.2.be.a.104.10

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			104.10
Character	$\chi$	$=$	189.104
Dual form			189.2.be.a.20.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.234777 + 0.645045i) q^{2} +(0.440723 - 1.67504i) q^{3} +(1.17113 + 0.982692i) q^{4} +(0.231854 - 1.31491i) q^{5} +(0.977005 + 0.677547i) q^{6} +(1.38106 - 2.25670i) q^{7} +(-2.09779 + 1.21116i) q^{8} +(-2.61153 - 1.47646i) q^{9} +(0.793741 + 0.458267i) q^{10} +(0.216508 - 0.0381762i) q^{11} +(2.16219 - 1.52859i) q^{12} +(0.673991 + 1.85178i) q^{13} +(1.13143 + 1.42066i) q^{14} +(-2.10034 - 0.967875i) q^{15} +(0.242207 + 1.37362i) q^{16} +(-0.469803 + 0.813723i) q^{17} +(1.56551 - 1.33791i) q^{18} +(3.04150 - 1.75601i) q^{19} +(1.56368 - 1.31208i) q^{20} +(-3.17140 - 3.30790i) q^{21} +(-0.0262057 + 0.148620i) q^{22} +(1.17579 - 1.40126i) q^{23} +(1.10420 + 4.04766i) q^{24} +(3.02323 + 1.10037i) q^{25} -1.35272 q^{26} +(-3.62409 + 3.72371i) q^{27} +(3.83503 - 1.28572i) q^{28} +(-1.33239 + 3.66070i) q^{29} +(1.11744 - 1.12758i) q^{30} +(-5.95195 + 7.09326i) q^{31} +(-5.71394 - 1.00752i) q^{32} +(0.0314733 - 0.379485i) q^{33} +(-0.414589 - 0.494088i) q^{34} +(-2.64715 - 2.33919i) q^{35} +(-1.60753 - 4.29544i) q^{36} +(-1.56504 + 2.71072i) q^{37} +(0.418631 + 2.37418i) q^{38} +(3.39885 - 0.312844i) q^{39} +(1.10618 + 3.03921i) q^{40} +(-10.8664 + 3.95506i) q^{41} +(2.87832 - 1.26907i) q^{42} +(-0.261843 - 1.48498i) q^{43} +(0.291074 + 0.168051i) q^{44} +(-2.54690 + 3.09160i) q^{45} +(0.627824 + 1.08742i) q^{46} +(5.18484 - 4.35059i) q^{47} +(2.40762 + 0.199681i) q^{48} +(-3.18536 - 6.23325i) q^{49} +(-1.41957 + 1.69178i) q^{50} +(1.15597 + 1.14557i) q^{51} +(-1.03040 + 2.83099i) q^{52} -3.77077i q^{53} +(-1.55111 - 3.21194i) q^{54} -0.293540i q^{55} +(-0.163947 + 6.40675i) q^{56} +(-1.60093 - 5.86856i) q^{57} +(-2.04850 - 1.71890i) q^{58} +(-1.72130 + 9.76195i) q^{59} +(-1.50865 - 3.19750i) q^{60} +(-6.04827 - 7.20805i) q^{61} +(-3.17809 - 5.50461i) q^{62} +(-6.93858 + 3.85435i) q^{63} +(0.596586 - 1.03332i) q^{64} +(2.59119 - 0.456896i) q^{65} +(0.237395 + 0.109396i) q^{66} +(-6.36714 + 2.31745i) q^{67} +(-1.34984 + 0.491301i) q^{68} +(-1.82897 - 2.58707i) q^{69} +(2.13037 - 1.15834i) q^{70} +(11.8706 + 6.85351i) q^{71} +(7.26665 - 0.0656782i) q^{72} +(7.68223 - 4.43534i) q^{73} +(-1.38110 - 1.64593i) q^{74} +(3.17557 - 4.57908i) q^{75} +(5.28760 + 0.932347i) q^{76} +(0.212858 - 0.541316i) q^{77} +(-0.596173 + 2.26586i) q^{78} +(-7.91776 - 2.88183i) q^{79} +1.86235 q^{80} +(4.64015 + 7.71162i) q^{81} -7.93789i q^{82} +(16.1714 + 5.88589i) q^{83} +(-0.463457 - 6.99048i) q^{84} +(0.961047 + 0.806414i) q^{85} +(1.01936 + 0.179740i) q^{86} +(5.54462 + 3.84516i) q^{87} +(-0.407950 + 0.342311i) q^{88} +(-3.46240 - 5.99705i) q^{89} +(-1.39627 - 2.36870i) q^{90} +(5.10972 + 1.03641i) q^{91} +(2.75401 - 0.485606i) q^{92} +(9.25834 + 13.0959i) q^{93} +(1.58905 + 4.36587i) q^{94} +(-1.60381 - 4.40644i) q^{95} +(-4.20591 + 9.12705i) q^{96} +(-4.42872 + 0.780904i) q^{97} +(4.76858 - 0.591277i) q^{98} +(-0.621782 - 0.219967i) 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 $

$2$	−0.234777	+	0.645045i	−0.166012	+	0.456116i	−0.994605	−	0.103737i	$-0.966920\pi$
$2$	−0.234777	+	0.645045i	−0.166012	+	0.456116i	0.828592	+	0.559852i	$0.189142\pi$
$3$	0.440723	−	1.67504i	0.254451	−	0.967086i
$3$	0.440723	−	1.67504i	0.254451	−	0.967086i
$4$	1.17113	+	0.982692i	0.585563	+	0.491346i
$5$	0.231854	−	1.31491i	0.103688	−	0.588045i	−0.888048	−	0.459751i	$-0.847939\pi$
$5$	0.231854	−	1.31491i	0.103688	−	0.588045i	0.991736	−	0.128294i	$-0.0409502\pi$
$6$	0.977005	+	0.677547i	0.398861	+	0.276607i
$7$	1.38106	−	2.25670i	0.521990	−	0.852951i
$7$	1.38106	−	2.25670i	0.521990	−	0.852951i
$8$	−2.09779	+	1.21116i	−0.741680	+	0.428209i
$9$	−2.61153	−	1.47646i	−0.870509	−	0.492152i
$10$	0.793741	+	0.458267i	0.251003	+	0.144917i
$11$	0.216508	−	0.0381762i	0.0652796	−	0.0115106i	−0.140913	−	0.990022i	$-0.545004\pi$
$11$	0.216508	−	0.0381762i	0.0652796	−	0.0115106i	0.206193	+	0.978511i	$0.433893\pi$
$12$	2.16219	−	1.52859i	0.624171	−	0.441266i
$13$	0.673991	+	1.85178i	0.186932	+	0.513590i	0.997390	−	0.0722062i	$-0.0230040\pi$
$13$	0.673991	+	1.85178i	0.186932	+	0.513590i	−0.810458	+	0.585797i	$0.800782\pi$
$14$	1.13143	+	1.42066i	0.302387	+	0.379689i
$15$	−2.10034	−	0.967875i	−0.542307	−	0.249904i
$16$	0.242207	+	1.37362i	0.0605517	+	0.343406i
$17$	−0.469803	+	0.813723i	−0.113944	+	0.197357i	−0.917357	−	0.398065i	$-0.869682\pi$
$17$	−0.469803	+	0.813723i	−0.113944	+	0.197357i	0.803413	+	0.595422i	$0.203015\pi$
$18$	1.56551	−	1.33791i	0.368994	−	0.315349i
$19$	3.04150	−	1.75601i	0.697768	−	0.402857i	−0.108747	−	0.994069i	$-0.534684\pi$
$19$	3.04150	−	1.75601i	0.697768	−	0.402857i	0.806516	+	0.591213i	$0.201351\pi$
$20$	1.56368	−	1.31208i	0.349650	−	0.293391i
$21$	−3.17140	−	3.30790i	−0.692056	−	0.721844i
$22$	−0.0262057	+	0.148620i	−0.00558708	+	0.0316859i
$23$	1.17579	−	1.40126i	0.245170	−	0.292182i	−0.629400	−	0.777082i	$-0.716699\pi$
$23$	1.17579	−	1.40126i	0.245170	−	0.292182i	0.874570	+	0.484899i	$0.161144\pi$
$24$	1.10420	+	4.04766i	0.225393	+	0.826226i
$25$	3.02323	+	1.10037i	0.604647	+	0.220073i
$26$	−1.35272			−0.265289
$27$	−3.62409	+	3.72371i	−0.697456	+	0.716628i
$28$	3.83503	−	1.28572i	0.724753	−	0.242979i
$29$	−1.33239	+	3.66070i	−0.247418	+	0.679776i	0.752361	+	0.658751i	$0.228915\pi$
$29$	−1.33239	+	3.66070i	−0.247418	+	0.679776i	−0.999779	+	0.0210245i	$0.993307\pi$
$30$	1.11744	−	1.12758i	0.204015	−	0.205867i
$31$	−5.95195	+	7.09326i	−1.06900	+	1.27399i	−0.108985	+	0.994043i	$0.534760\pi$
$31$	−5.95195	+	7.09326i	−1.06900	+	1.27399i	−0.960017	+	0.279943i	$0.909684\pi$
$32$	−5.71394	−	1.00752i	−1.01009	−	0.178106i
$33$	0.0314733	−	0.379485i	0.00547879	−	0.0660598i
$34$	−0.414589	−	0.494088i	−0.0711014	−	0.0847353i
$35$	−2.64715	−	2.33919i	−0.447450	−	0.395395i
$36$	−1.60753	−	4.29544i	−0.267921	−	0.715907i
$37$	−1.56504	+	2.71072i	−0.257290	+	0.445640i	−0.965515	−	0.260347i	$-0.916163\pi$
$37$	−1.56504	+	2.71072i	−0.257290	+	0.445640i	0.708225	+	0.705987i	$0.249496\pi$
$38$	0.418631	+	2.37418i	0.0679110	+	0.385142i
$39$	3.39885	−	0.312844i	0.544251	−	0.0500951i
$40$	1.10618	+	3.03921i	0.174903	+	0.480542i
$41$	−10.8664	+	3.95506i	−1.69705	+	0.617676i	−0.995484	−	0.0949267i	$-0.969738\pi$
$41$	−10.8664	+	3.95506i	−1.69705	+	0.617676i	−0.701567	+	0.712603i	$0.747516\pi$
$42$	2.87832	−	1.26907i	0.444134	−	0.195822i
$43$	−0.261843	−	1.48498i	−0.0399307	−	0.226458i	0.958311	−	0.285726i	$-0.0922346\pi$
$43$	−0.261843	−	1.48498i	−0.0399307	−	0.226458i	−0.998242	+	0.0592676i	$0.981123\pi$
$44$	0.291074	+	0.168051i	0.0438810	+	0.0253347i
$45$	−2.54690	+	3.09160i	−0.379670	+	0.460868i
$46$	0.627824	+	1.08742i	0.0925676	+	0.160332i
$47$	5.18484	−	4.35059i	0.756286	−	0.634599i	−0.180871	−	0.983507i	$-0.557892\pi$
$47$	5.18484	−	4.35059i	0.756286	−	0.634599i	0.937157	+	0.348907i	$0.113447\pi$
$48$	2.40762	+	0.199681i	0.347510	+	0.0288214i
$49$	−3.18536	−	6.23325i	−0.455052	−	0.890465i
$50$	−1.41957	+	1.69178i	−0.200758	+	0.239254i
$51$	1.15597	+	1.14557i	0.161868	+	0.160411i
$52$	−1.03040	+	2.83099i	−0.142890	+	0.392588i
$53$		−	3.77077i		−	0.517954i	−0.965883	−	0.258977i	$-0.916615\pi$
$53$		−	3.77077i		−	0.517954i	0.965883	−	0.258977i	$-0.0833855\pi$
$54$	−1.55111	−	3.21194i	−0.211079	−	0.437090i
$55$		−	0.293540i		−	0.0395809i
$56$	−0.163947	+	6.40675i	−0.0219083	+	0.856138i
$57$	−1.60093	−	5.86856i	−0.212049	−	0.777309i
$58$	−2.04850	−	1.71890i	−0.268982	−	0.225703i
$59$	−1.72130	+	9.76195i	−0.224094	+	1.27090i	0.640317	+	0.768111i	$0.278803\pi$
$59$	−1.72130	+	9.76195i	−0.224094	+	1.27090i	−0.864410	+	0.502787i	$0.832308\pi$
$60$	−1.50865	−	3.19750i	−0.194765	−	0.412795i
$61$	−6.04827	−	7.20805i	−0.774402	−	0.922896i	0.224264	−	0.974528i	$-0.428002\pi$
$61$	−6.04827	−	7.20805i	−0.774402	−	0.922896i	−0.998666	+	0.0516319i	$0.983558\pi$
$62$	−3.17809	−	5.50461i	−0.403617	−	0.699086i
$63$	−6.93858	+	3.85435i	−0.874179	+	0.485603i
$64$	0.596586	−	1.03332i	0.0745733	−	0.129165i
$65$	2.59119	−	0.456896i	0.321397	−	0.0566710i
$66$	0.237395	+	0.109396i	0.0292214	+	0.0134657i
$67$	−6.36714	+	2.31745i	−0.777871	+	0.283122i	−0.700284	−	0.713864i	$-0.746943\pi$
$67$	−6.36714	+	2.31745i	−0.777871	+	0.283122i	−0.0775861	+	0.996986i	$0.524721\pi$
$68$	−1.34984	+	0.491301i	−0.163692	+	0.0595790i
$69$	−1.82897	−	2.58707i	−0.220182	−	0.311447i
$70$	2.13037	−	1.15834i	0.254628	−	0.138448i
$71$	11.8706	+	6.85351i	1.40879	+	0.813362i	0.995271	−	0.0971354i	$-0.0309680\pi$
$71$	11.8706	+	6.85351i	1.40879	+	0.813362i	0.413514	+	0.910498i	$0.364301\pi$
$72$	7.26665	−	0.0656782i	0.856383	−	0.00774025i
$73$	7.68223	−	4.43534i	0.899137	−	0.519117i	0.0222170	−	0.999753i	$-0.492928\pi$
$73$	7.68223	−	4.43534i	0.899137	−	0.519117i	0.876920	+	0.480636i	$0.159594\pi$
$74$	−1.38110	−	1.64593i	−0.160550	−	0.191336i
$75$	3.17557	−	4.57908i	0.366683	−	0.528747i
$76$	5.28760	+	0.932347i	0.606529	+	0.106948i
$77$	0.212858	−	0.541316i	0.0242574	−	0.0616887i
$78$	−0.596173	+	2.26586i	−0.0675033	+	0.256558i
$79$	−7.91776	−	2.88183i	−0.890818	−	0.324231i	−0.144251	−	0.989541i	$-0.546077\pi$
$79$	−7.91776	−	2.88183i	−0.890818	−	0.324231i	−0.746567	+	0.665310i	$0.768299\pi$
$80$	1.86235			0.208217
$81$	4.64015	+	7.71162i	0.515572	+	0.856846i
$82$		−	7.93789i		−	0.876594i
$83$	16.1714	+	5.88589i	1.77504	+	0.646061i	0.999898	+	0.0142697i	$0.00454236\pi$
$83$	16.1714	+	5.88589i	1.77504	+	0.646061i	0.775139	+	0.631791i	$0.217680\pi$
$84$	−0.463457	−	6.99048i	−0.0505673	−	0.762724i
$85$	0.961047	+	0.806414i	0.104240	+	0.0874679i
$86$	1.01936	+	0.179740i	0.109920	+	0.0193819i
$87$	5.54462	+	3.84516i	0.594445	+	0.412244i
$88$	−0.407950	+	0.342311i	−0.0434876	+	0.0364904i
$89$	−3.46240	−	5.99705i	−0.367014	−	0.635686i	0.622084	−	0.782951i	$-0.286286\pi$
$89$	−3.46240	−	5.99705i	−0.367014	−	0.635686i	−0.989097	+	0.147265i	$0.952953\pi$
$90$	−1.39627	−	2.36870i	−0.147179	−	0.249683i
$91$	5.10972	+	1.03641i	0.535644	+	0.108646i
$92$	2.75401	−	0.485606i	0.287125	−	0.0506279i
$93$	9.25834	+	13.0959i	0.960045	+	1.35798i
$94$	1.58905	+	4.36587i	0.163898	+	0.450305i
$95$	−1.60381	−	4.40644i	−0.164548	−	0.452091i
$96$	−4.20591	+	9.12705i	−0.429264	+	0.931526i
$97$	−4.42872	+	0.780904i	−0.449669	+	0.0792887i	−0.393897	−	0.919155i	$-0.628873\pi$
$97$	−4.42872	+	0.780904i	−0.449669	+	0.0792887i	−0.0557722	+	0.998444i	$0.517762\pi$
$98$	4.76858	−	0.591277i	0.481699	−	0.0597280i
$99$	−0.621782	−	0.219967i	−0.0624914	−	0.0221075i
$100$	2.45927	+	4.25957i	0.245927	+	0.425957i
$101$	0.750944	−	0.630116i	0.0747217	−	0.0626989i	−0.604662	−	0.796482i	$-0.706692\pi$
$101$	0.750944	−	0.630116i	0.0747217	−	0.0626989i	0.679384	+	0.733783i	$0.262247\pi$
$102$	−1.01034	+	0.476698i	−0.100038	+	0.0472001i
$103$	13.1659	+	2.32150i	1.29727	+	0.228744i	0.779299	−	0.626652i	$-0.215575\pi$
$103$	13.1659	+	2.32150i	1.29727	+	0.228744i	0.517974	+	0.855396i	$0.326686\pi$
$104$	−3.65668	−	3.06832i	−0.358567	−	0.300874i
$105$	−5.08490	+	3.40315i	−0.496235	+	0.332113i
$106$	2.43231	+	0.885289i	0.236247	+	0.0859869i
$107$		−	18.7220i		−	1.80992i	−0.425496	−	0.904960i	$-0.639900\pi$
$107$		−	18.7220i		−	1.80992i	0.425496	−	0.904960i	$-0.360100\pi$
$108$	−7.90352	+	0.799572i	−0.760517	+	0.0769389i
$109$	−5.24050			−0.501949			−0.250975	−	0.967994i	$-0.580751\pi$
$109$	−5.24050			−0.501949			−0.250975	+	0.967994i	$0.580751\pi$
$110$	0.189346	+	0.0689164i	0.0180534	+	0.00657092i
$111$	3.85083	+	3.81618i	0.365504	+	0.362216i
$112$	3.43435	+	1.35046i	0.324516	+	0.127607i
$113$	8.07557	+	1.42394i	0.759686	+	0.133953i	0.540055	−	0.841630i	$-0.318404\pi$
$113$	8.07557	+	1.42394i	0.759686	+	0.133953i	0.219631	+	0.975583i	$0.429515\pi$
$114$	4.16134	+	0.345129i	0.389746	+	0.0323243i
$115$	−1.56991	−	1.87095i	−0.146395	−	0.174467i
$116$	−5.15774	+	2.97782i	−0.478884	+	0.276484i
$117$	0.973922	−	5.83108i	0.0900391	−	0.539084i
$118$	−5.89278	−	3.40220i	−0.542474	−	0.313198i
$119$	1.18750	+	2.18400i	0.108858	+	0.200207i
$120$	5.57832	−	0.513452i	0.509229	−	0.0468715i
$121$	−10.2912	+	3.74569i	−0.935564	+	0.340517i
$122$	6.06951	−	2.20912i	0.549508	−	0.200004i
$123$	1.83580	+	19.9448i	0.165529	+	1.79836i
$124$	−13.9410	+	2.45817i	−1.25194	+	0.220750i
$125$	5.48582	−	9.50171i	0.490666	−	0.849859i
$126$	−0.857210	−	5.38061i	−0.0763663	−	0.479343i
$127$	−0.479905	−	0.831220i	−0.0425847	−	0.0737588i	0.843947	−	0.536426i	$-0.180226\pi$
$127$	−0.479905	−	0.831220i	−0.0425847	−	0.0737588i	−0.886532	+	0.462667i	$0.846893\pi$
$128$	−6.93255	−	8.26189i	−0.612757	−	0.730255i
$129$	−2.60281	−	0.215869i	−0.229165	−	0.0190062i
$130$	−0.313633	+	1.77870i	−0.0275074	+	0.156002i
$131$	3.74843	+	3.14531i	0.327502	+	0.274807i	0.791681	−	0.610935i	$-0.209206\pi$
$131$	3.74843	+	3.14531i	0.327502	+	0.274807i	−0.464179	+	0.885741i	$0.653651\pi$
$132$	0.409776	−	0.413496i	0.0356664	−	0.0359902i
$133$	0.237700	−	9.28890i	0.0206112	−	0.805450i
$134$		−	4.65118i		−	0.401801i
$135$	4.05608	+	5.62870i	0.349092	+	0.484442i
$136$		−	2.27602i		−	0.195167i
$137$	3.97977	−	10.9343i	0.340015	−	0.934183i	−0.645375	−	0.763866i	$-0.723299\pi$
$137$	3.97977	−	10.9343i	0.340015	−	0.934183i	0.985389	−	0.170317i	$-0.0544791\pi$
$138$	2.09818	−	0.572379i	0.178609	−	0.0487242i
$139$	5.90509	−	7.03742i	0.500864	−	0.596906i	−0.455082	−	0.890449i	$-0.650390\pi$
$139$	5.90509	−	7.03742i	0.500864	−	0.596906i	0.955946	+	0.293544i	$0.0948346\pi$
$140$	−0.801444	−	5.34082i	−0.0677344	−	0.451381i
$141$	−5.00235	−	10.6022i	−0.421274	−	0.892868i
$142$	−7.20778	+	6.04804i	−0.604863	+	0.507540i
$143$	0.216618	+	0.375194i	0.0181145	+	0.0313753i
$144$	1.39557	−	3.94486i	0.116297	−	0.328739i
$145$	4.50458	+	2.60072i	0.374085	+	0.215978i
$146$	1.05738	+	5.99670i	0.0875094	+	0.496290i
$147$	−11.8448	+	2.58848i	−0.976944	+	0.213494i
$148$	−4.49666	+	1.63665i	−0.369623	+	0.134532i
$149$	−5.20678	−	14.3055i	−0.426556	−	1.17195i	−0.947889	−	0.318600i	$-0.896787\pi$
$149$	−5.20678	−	14.3055i	−0.426556	−	1.17195i	0.521333	−	0.853353i	$-0.325435\pi$
$150$	2.20816	+	3.12345i	0.180296	+	0.255028i
$151$	−1.95736	−	11.1008i	−0.159288	−	0.903366i	−0.954760	−	0.297376i	$-0.903888\pi$
$151$	−1.95736	−	11.1008i	−0.159288	−	0.903366i	0.795472	−	0.605990i	$-0.207223\pi$
$152$	−4.25361	+	7.36748i	−0.345014	+	0.597581i
$153$	2.42833	−	1.43142i	0.196319	−	0.115723i
$154$	0.299199	+	0.264391i	0.0241101	+	0.0213053i
$155$	7.94701	+	9.47087i	0.638319	+	0.760719i
$156$	4.28791	+	2.97364i	0.343307	+	0.238082i
$157$	−12.3894	−	2.18459i	−0.988784	−	0.174349i	−0.344211	−	0.938892i	$-0.611854\pi$
$157$	−12.3894	−	2.18459i	−0.988784	−	0.174349i	−0.644573	+	0.764543i	$0.722965\pi$
$158$	3.71782	−	4.43072i	0.295774	−	0.352489i
$159$	−6.31619	−	1.66186i	−0.500906	−	0.131794i
$160$	−2.64960	+	7.27972i	−0.209469	+	0.575512i
$161$	−1.53837	−	4.58863i	−0.121241	−	0.361635i
$162$	−6.06374	+	1.18259i	−0.476412	+	0.0929131i
$163$	−15.4955			−1.21370			−0.606850	−	0.794816i	$-0.707567\pi$
$163$	−15.4955			−1.21370			−0.606850	+	0.794816i	$0.707567\pi$
$164$	−16.6126	−	6.04648i	−1.29722	−	0.472151i
$165$	−0.491691	−	0.129370i	−0.0382781	−	0.0100714i
$166$	−7.59333	+	9.04938i	−0.589357	+	0.702368i
$167$	−3.86013	+	21.8919i	−0.298706	+	1.69405i	0.353040	+	0.935608i	$0.385148\pi$
$167$	−3.86013	+	21.8919i	−0.298706	+	1.69405i	−0.651746	+	0.758437i	$0.725963\pi$
$168$	10.6593	+	3.09822i	0.822384	+	0.239033i
$169$	6.98377	−	5.86008i	0.537213	−	0.450775i
$170$	−0.745805	+	0.430591i	−0.0572006	+	0.0330248i
$171$	−10.5356	+	0.0952243i	−0.805681	+	0.00728199i
$172$	1.15263	−	1.99642i	0.0878873	−	0.152225i
$173$	0.814058	+	4.61675i	0.0618917	+	0.351005i	0.999989	+	0.00463414i	$0.00147510\pi$
$173$	0.814058	+	4.61675i	0.0618917	+	0.351005i	−0.938098	+	0.346371i	$0.887414\pi$
$174$	−3.78205	+	2.67377i	−0.286716	+	0.202698i
$175$	6.65845	−	5.30285i	0.503332	−	0.400858i
$176$	0.104879	+	0.288154i	0.00790558	+	0.0217204i
$177$	15.5931	+	7.18556i	1.17205	+	0.540099i
$178$	4.68126	−	0.825432i	0.350875	−	0.0618688i
$179$	13.7669	+	7.94833i	1.02899	+	0.594086i	0.916694	−	0.399589i	$-0.130847\pi$
$179$	13.7669	+	7.94833i	1.02899	+	0.594086i	0.112293	+	0.993675i	$0.464180\pi$
$180$	−6.02083	+	1.11783i	−0.448766	+	0.0833185i
$181$	−4.81888	+	2.78218i	−0.358185	+	0.206798i	−0.668284	−	0.743906i	$-0.732971\pi$
$181$	−4.81888	+	2.78218i	−0.358185	+	0.206798i	0.310100	+	0.950704i	$0.399638\pi$
$182$	−1.86818	+	3.05267i	−0.138479	+	0.226279i
$183$	−14.7394	+	6.95436i	−1.08957	+	0.514081i
$184$	−0.769423	+	4.36361i	−0.0567226	+	0.321690i
$185$	3.20150	+	2.68637i	0.235379	+	0.197506i
$186$	−10.6211	+	2.89742i	−0.778777	+	0.212449i
$187$	−0.0706513	+	0.194113i	−0.00516653	+	0.0141949i
$188$	10.3474			0.754661
$189$	3.39821	+	13.3211i	0.247183	+	0.968969i
$190$	3.21889			0.233523
$191$	0.626662	−	1.72174i	0.0453437	−	0.124581i	−0.914954	−	0.403558i	$-0.867773\pi$
$191$	0.626662	−	1.72174i	0.0453437	−	0.124581i	0.960298	+	0.278978i	$0.0899955\pi$
$192$	−1.46792	−	1.45471i	−0.105938	−	0.104985i
$193$	0.0889424	+	0.0746315i	0.00640221	+	0.00537209i	0.645983	−	0.763352i	$-0.276448\pi$
$193$	0.0889424	+	0.0746315i	0.00640221	+	0.00537209i	−0.639581	+	0.768724i	$0.720892\pi$
$194$	0.536045	−	3.04006i	0.0384858	−	0.218264i
$195$	0.376675	−	4.54171i	0.0269742	−	0.325238i
$196$	2.39490	−	10.4302i	0.171065	−	0.745011i
$197$	−13.5481	+	7.82201i	−0.965264	+	0.557295i	−0.897789	−	0.440425i	$-0.854828\pi$
$197$	−13.5481	+	7.82201i	−0.965264	+	0.557295i	−0.0674749	+	0.997721i	$0.521494\pi$
$198$	0.287868	−	0.349434i	0.0204579	−	0.0248332i
$199$	8.33355	+	4.81138i	0.590750	+	0.341069i	0.765394	−	0.643562i	$-0.222544\pi$
$199$	8.33355	+	4.81138i	0.590750	+	0.341069i	−0.174644	+	0.984632i	$0.555878\pi$
$200$	−7.67481	+	1.35328i	−0.542691	+	0.0956911i
$201$	1.07568	+	11.6866i	0.0758727	+	0.824308i
$202$	0.230149	+	0.632329i	0.0161932	+	0.0444905i
$203$	6.42100	+	8.06244i	0.450666	+	0.565872i
$204$	0.228045	+	2.47756i	0.0159663	+	0.173464i
$205$	2.68112	+	15.2054i	0.187257	+	1.06199i
$206$	−4.58852	+	7.94755i	−0.319697	+	0.553732i
$207$	−5.13952	+	1.92341i	−0.357221	+	0.133686i
$208$	−2.38040	+	1.37432i	−0.165051	+	0.0952922i
$209$	0.591471	−	0.496303i	0.0409129	−	0.0343300i
$210$	−1.00137	−	4.07897i	−0.0691009	−	0.281476i
$211$	2.41262	−	13.6827i	0.166092	−	0.941954i	−0.781840	−	0.623479i	$-0.785719\pi$
$211$	2.41262	−	13.6827i	0.166092	−	0.941954i	0.947932	−	0.318474i	$-0.103170\pi$
$212$	3.70550	−	4.41604i	0.254495	−	0.303295i
$213$	16.7116	−	16.8633i	1.14506	−	1.15545i
$214$	12.0765	+	4.39549i	0.825533	+	0.300469i
$215$	−2.01333			−0.137308
$216$	3.09256	−	12.2009i	0.210422	−	0.830165i
$217$	7.78735	+	23.2279i	0.528640	+	1.57682i
$218$	1.23035	−	3.38036i	0.0833298	−	0.228947i
$219$	−4.04364	−	14.8228i	−0.273244	−	1.00163i
$220$	0.288459	−	0.343772i	0.0194479	−	0.0231771i
$221$	−1.82348	−	0.321528i	−0.122660	−	0.0216283i
$222$	−3.36569	+	1.58800i	−0.225890	+	0.106580i
$223$	11.6645	+	13.9012i	0.781115	+	0.930896i	0.998983	−	0.0450820i	$-0.0143549\pi$
$223$	11.6645	+	13.9012i	0.781115	+	0.930896i	−0.217869	+	0.975978i	$0.569910\pi$
$224$	−10.1650	+	11.5032i	−0.679175	+	0.768590i
$225$	−6.27061	−	7.33731i	−0.418041	−	0.489154i
$226$	−2.81446	+	4.87479i	−0.187215	+	0.324267i
$227$	−4.49086	−	25.4689i	−0.298069	−	1.69043i	−0.654462	−	0.756095i	$-0.727105\pi$
$227$	−4.49086	−	25.4689i	−0.298069	−	1.69043i	0.356393	−	0.934336i	$-0.384006\pi$
$228$	3.89209	−	8.44604i	0.257760	−	0.559353i
$229$	−3.70816	−	10.1881i	−0.245042	−	0.673247i	−0.999850	−	0.0173016i	$-0.994492\pi$
$229$	−3.70816	−	10.1881i	−0.245042	−	0.673247i	0.754809	−	0.655945i	$-0.227730\pi$
$230$	1.57543	−	0.573409i	0.103881	−	0.0378094i
$231$	−0.812916	−	0.595116i	−0.0534859	−	0.0391557i
$232$	−1.63863	−	9.29311i	−0.107581	−	0.610122i
$233$	2.36196	+	1.36368i	0.154737	+	0.0893375i	0.575369	−	0.817894i	$-0.304858\pi$
$233$	2.36196	+	1.36368i	0.154737	+	0.0893375i	−0.420632	+	0.907231i	$0.638192\pi$
$234$	3.53266	+	1.99723i	0.230937	+	0.130563i
$235$	−4.51851	−	7.82629i	−0.294755	−	0.510531i
$236$	−11.6088	+	9.74098i	−0.755672	+	0.634084i
$237$	−8.31672	+	11.9925i	−0.540229	+	0.778996i
$238$	−1.68758	+	0.253238i	−0.109389	+	0.0164150i
$239$	−19.4562	+	23.1870i	−1.25852	+	1.49984i	−0.472919	+	0.881106i	$0.656800\pi$
$239$	−19.4562	+	23.1870i	−1.25852	+	1.49984i	−0.785599	+	0.618736i	$0.787645\pi$
$240$	0.820779	−	3.11951i	0.0529810	−	0.201363i
$241$	8.39131	−	23.0549i	0.540531	−	1.48510i	−0.305619	−	0.952154i	$-0.598863\pi$
$241$	8.39131	−	23.0549i	0.540531	−	1.48510i	0.846150	−	0.532944i	$-0.178914\pi$
$242$		−	7.51769i		−	0.483255i
$243$	14.9623	−	4.37375i	0.959832	−	0.280576i
$244$		−	14.3851i		−	0.920914i
$245$	−8.93470	+	2.74326i	−0.570817	+	0.175260i
$246$	−13.2963	−	3.49841i	−0.847741	−	0.223050i
$247$	5.30169	+	4.44864i	0.337338	+	0.283060i
$248$	3.89487	−	22.0889i	0.247324	−	1.40265i
$249$	16.9862	−	24.4936i	1.07646	−	1.55222i
$250$	4.84109	+	5.76938i	0.306177	+	0.364888i
$251$	−12.0630	−	20.8937i	−0.761409	−	1.31880i	−0.942124	−	0.335264i	$-0.891174\pi$
$251$	−12.0630	−	20.8937i	−0.761409	−	1.31880i	0.180715	−	0.983536i	$-0.442159\pi$
$252$	−11.9136	−	2.30455i	−0.750486	−	0.145173i
$253$	0.201074	−	0.348271i	0.0126414	−	0.0218956i
$254$	0.648845	−	0.114409i	0.0407121	−	0.00717865i
$255$	1.77433	−	1.25439i	0.111113	−	0.0785528i
$256$	9.19933	−	3.34828i	0.574958	−	0.209268i
$257$	11.0337	−	4.01595i	0.688265	−	0.250508i	0.0258727	−	0.999665i	$-0.491764\pi$
$257$	11.0337	−	4.01595i	0.688265	−	0.250508i	0.662392	+	0.749157i	$0.269541\pi$
$258$	0.750325	−	1.62825i	0.0467132	−	0.101370i
$259$	3.95588	+	7.27548i	0.245806	+	0.452076i
$260$	3.48359	+	2.01125i	0.216043	+	0.124733i
$261$	8.88444	−	7.59282i	0.549933	−	0.469983i
$262$	−2.90891	+	1.67946i	−0.179713	+	0.103757i
$263$	12.7126	+	15.1503i	0.783891	+	0.934205i	0.999102	−	0.0423623i	$-0.0134884\pi$
$263$	12.7126	+	15.1503i	0.783891	+	0.934205i	−0.215211	+	0.976568i	$0.569044\pi$
$264$	0.393592	+	0.834197i	0.0242239	+	0.0513413i
$265$	−4.95821	−	0.874267i	−0.304581	−	0.0537058i
$266$	5.93595	+	2.33415i	0.363956	+	0.143116i
$267$	−11.5713	+	3.15663i	−0.708150	+	0.193182i
$268$	−9.73407	−	3.54291i	−0.594603	−	0.216418i
$269$	17.1269			1.04424			0.522122	−	0.852871i	$-0.325141\pi$
$269$	17.1269			1.04424			0.522122	+	0.852871i	$0.325141\pi$
$270$	−4.58304	+	1.29486i	−0.278915	+	0.0788028i
$271$			16.5484i			1.00525i	0.864506	+	0.502623i	$0.167632\pi$
$271$			16.5484i			1.00525i	−0.864506	+	0.502623i	$0.832368\pi$
$272$	−1.23154	−	0.448244i	−0.0746730	−	0.0271788i
$273$	3.98800	−	8.10222i	0.241365	−	0.490369i
$274$	6.11877	+	5.13426i	0.369649	+	0.310172i
$275$	0.696561	+	0.122823i	0.0420042	+	0.00740648i
$276$	0.400344	−	4.82710i	0.0240979	−	0.290557i
$277$	−13.1995	+	11.0757i	−0.793078	+	0.665472i	−0.946505	−	0.322688i	$-0.895413\pi$
$277$	−13.1995	+	11.0757i	−0.793078	+	0.665472i	0.153427	+	0.988160i	$0.450969\pi$
$278$	3.15307	+	5.46127i	0.189108	+	0.327545i
$279$	26.0166	−	9.73643i	1.55757	−	0.582905i
$280$	8.38628	+	1.70100i	0.501176	+	0.101654i
$281$	−14.1177	+	2.48933i	−0.842190	+	0.148501i	−0.578068	−	0.815988i	$-0.696193\pi$
$281$	−14.1177	+	2.48933i	−0.842190	+	0.148501i	−0.264122	+	0.964489i	$0.585082\pi$
$282$	8.01335	−	0.737581i	0.477188	−	0.0439223i
$283$	−4.76130	−	13.0816i	−0.283030	−	0.777618i	−0.996997	−	0.0774390i	$-0.975326\pi$
$283$	−4.76130	−	13.0816i	−0.283030	−	0.777618i	0.713967	−	0.700179i	$-0.246897\pi$
$284$	7.16712	+	19.6915i	0.425290	+	1.16848i
$285$	−8.08780	+	0.744435i	−0.479080	+	0.0440965i
$286$	−0.292874	+	0.0516415i	−0.0173180	+	0.00305363i
$287$	−6.08179	+	29.9844i	−0.358997	+	1.76992i
$288$	13.4346	+	11.0676i	0.791639	+	0.652163i
$289$	8.05857	+	13.9579i	0.474034	+	0.821050i
$290$	−2.73515	+	2.29506i	−0.160614	+	0.134771i
$291$	−0.643794	+	7.76246i	−0.0377398	+	0.455043i
$292$	13.3554	+	2.35492i	0.781568	+	0.137811i
$293$	−9.24858	−	7.76048i	−0.540308	−	0.453372i	0.331335	−	0.943513i	$-0.392501\pi$
$293$	−9.24858	−	7.76048i	−0.540308	−	0.453372i	−0.871643	+	0.490141i	$0.836945\pi$
$294$	1.11121	−	8.24816i	0.0648069	−	0.481042i
$295$	12.4370	+	4.52670i	0.724110	+	0.263554i
$296$		−	7.58203i		−	0.440696i
$297$	−0.642486	+	0.944566i	−0.0372808	+	0.0548093i
$298$	10.4501			0.605359
$299$	3.38729	+	1.23287i	0.195892	+	0.0712989i
$300$	8.21882	−	2.24208i	0.474514	−	0.129447i
$301$	−3.71278	−	1.45995i	−0.214001	−	0.0841500i
$302$	7.62002	+	1.34362i	0.438483	+	0.0773164i
$303$	−0.724513	−	1.53557i	−0.0416222	−	0.0882161i
$304$	3.14877	+	3.75256i	0.180594	+	0.215224i
$305$	−10.8803	+	6.28172i	−0.623001	+	0.359690i
$306$	0.353210	+	1.90245i	0.0201917	+	0.108756i
$307$	−19.5181	−	11.2688i	−1.11396	−	0.643144i	−0.174107	−	0.984727i	$-0.555704\pi$
$307$	−19.5181	−	11.2688i	−1.11396	−	0.643144i	−0.939852	+	0.341583i	$0.889037\pi$
$308$	0.781230	−	0.424776i	0.0445147	−	0.0242039i
$309$	9.69111	−	21.0303i	0.551308	−	1.19637i
$310$	−7.97491	+	2.90263i	−0.452945	+	0.164858i
$311$	2.46202	−	0.896103i	0.139608	−	0.0508133i	−0.271271	−	0.962503i	$-0.587444\pi$
$311$	2.46202	−	0.896103i	0.139608	−	0.0508133i	0.410879	+	0.911690i	$0.365222\pi$
$312$	−6.75115	+	4.77282i	−0.382209	+	0.270208i
$313$	5.70705	−	1.00631i	0.322582	−	0.0568798i	−0.0100126	−	0.999950i	$-0.503187\pi$
$313$	5.70705	−	1.00631i	0.322582	−	0.0568798i	0.332594	+	0.943070i	$0.392076\pi$
$314$	4.31791	−	7.47885i	0.243674	−	0.422056i
$315$	3.45939	+	10.0173i	0.194914	+	0.564409i
$316$	−6.44075	−	11.1557i	−0.362320	−	0.627557i
$317$	−9.51195	−	11.3359i	−0.534244	−	0.636687i	0.429643	−	0.902999i	$-0.358639\pi$
$317$	−9.51195	−	11.3359i	−0.534244	−	0.636687i	−0.963887	+	0.266312i	$0.914195\pi$
$318$	2.55487	−	3.68406i	0.143270	−	0.206592i
$319$	−0.148721	+	0.843437i	−0.00832676	+	0.0472234i
$320$	−1.22040	−	1.02404i	−0.0682223	−	0.0572453i
$321$	−31.3601	−	8.25119i	−1.75035	−	0.460537i
$322$	3.32105	+	0.0849845i	0.185075	+	0.00473600i
$323$			3.29992i			0.183612i
$324$	−2.14394	+	13.5911i	−0.119108	+	0.755062i
$325$			6.33999i			0.351679i
$326$	3.63798	−	9.99528i	0.201489	−	0.553587i
$327$	−2.30961	+	8.77806i	−0.127722	+	0.485428i
$328$	18.0053	−	21.4578i	0.994174	−	1.18481i
$329$	−2.65742	−	17.7090i	−0.146508	−	0.976330i
$330$	0.198887	−	0.286790i	0.0109484	−	0.0157872i
$331$	7.87879	−	6.61109i	0.433057	−	0.363378i	−0.400047	−	0.916495i	$-0.631006\pi$
$331$	7.87879	−	6.61109i	0.433057	−	0.363378i	0.833104	+	0.553117i	$0.186562\pi$
$332$	13.1547	+	22.7846i	0.721957	+	1.25047i
$333$	8.08940	−	4.76842i	0.443297	−	0.261308i
$334$	−13.2150	−	7.62967i	−0.723092	−	0.417477i
$335$	1.57099	+	8.90953i	0.0858324	+	0.486780i
$336$	3.77568	−	5.15750i	0.205980	−	0.281365i
$337$	25.9383	−	9.44078i	1.41295	−	0.514272i	0.480957	−	0.876744i	$-0.340289\pi$
$337$	25.9383	−	9.44078i	1.41295	−	0.514272i	0.931995	+	0.362472i	$0.118067\pi$
$338$	2.14038	+	5.88065i	0.116421	+	0.319865i
$339$	5.94425	−	12.8993i	0.322847	−	0.700596i
$340$	0.333051	+	1.88883i	0.0180622	+	0.102436i
$341$	−1.01785	+	1.76297i	−0.0551197	+	0.0954701i
$342$	2.41210	−	6.81832i	0.130432	−	0.368692i
$343$	−18.4657	−	1.42008i	−0.997056	−	0.0766769i
$344$	2.34784	+	2.79805i	0.126587	+	0.150861i
$345$	−3.82582	+	1.80510i	−0.205975	+	0.0971834i
$346$	−3.16913	−	0.558804i	−0.170374	−	0.0300415i
$347$	4.96950	−	5.92242i	0.266777	−	0.317932i	−0.615981	−	0.787761i	$-0.711240\pi$
$347$	4.96950	−	5.92242i	0.266777	−	0.317932i	0.882757	+	0.469829i	$0.155684\pi$
$348$	2.71484	+	9.95182i	0.145531	+	0.533473i
$349$	−10.3198	+	28.3535i	−0.552407	+	1.51773i	0.278007	+	0.960579i	$0.410326\pi$
$349$	−10.3198	+	28.3535i	−0.552407	+	1.51773i	−0.830414	+	0.557147i	$0.811896\pi$
$350$	1.85732	+	5.53999i	0.0992782	+	0.296125i
$351$	−9.33808	−	4.20125i	−0.498430	−	0.224246i
$352$	−1.27558			−0.0679885
$353$	−13.2988	−	4.84037i	−0.707824	−	0.257627i	−0.0370764	−	0.999312i	$-0.511804\pi$
$353$	−13.2988	−	4.84037i	−0.707824	−	0.257627i	−0.670748	+	0.741685i	$0.734027\pi$
$354$	−8.29590	+	8.37122i	−0.440922	+	0.444925i
$355$	11.7640	−	14.0198i	0.624369	−	0.744093i
$356$	1.83835	−	10.4258i	0.0974321	−	0.552565i
$357$	4.18165	−	1.02658i	0.221317	−	0.0543321i
$358$	−8.35919	+	7.01419i	−0.441797	+	0.370711i
$359$	−22.1647	+	12.7968i	−1.16981	+	0.675389i	−0.953635	−	0.300966i	$-0.902691\pi$
$359$	−22.1647	+	12.7968i	−1.16981	+	0.675389i	−0.216174	+	0.976355i	$0.569358\pi$
$360$	1.59844	−	9.57021i	0.0842452	−	0.504395i
$361$	−3.33285	+	5.77266i	−0.175413	+	0.303824i
$362$	−0.663269	−	3.76159i	−0.0348607	−	0.197705i
$363$	1.73862	+	18.8890i	0.0912539	+	0.991415i
$364$	4.96565	+	6.23505i	0.260271	+	0.326805i
$365$	−4.05091	−	11.1298i	−0.212034	−	0.582560i
$366$	−1.02540	−	11.1403i	−0.0535984	−	0.582313i
$367$	17.3863	−	3.06568i	0.907559	−	0.160027i	0.299664	−	0.954045i	$-0.403125\pi$
$367$	17.3863	−	3.06568i	0.907559	−	0.160027i	0.607895	+	0.794017i	$0.292014\pi$
$368$	2.20959	+	1.27571i	0.115183	+	0.0665007i
$369$	34.2175	+	5.71509i	1.78129	+	0.297515i
$370$	−2.48447	+	1.43441i	−0.129161	+	0.0745714i
$371$	−8.50947	−	5.20764i	−0.441790	−	0.270367i
$372$	−2.02657	+	24.4351i	−0.105073	+	1.26690i
$373$	−1.01057	+	5.73121i	−0.0523252	+	0.296751i	−0.999729	−	0.0232906i	$-0.992586\pi$
$373$	−1.01057	+	5.73121i	−0.0523252	+	0.296751i	0.947404	+	0.320041i	$0.103697\pi$
$374$	−0.108624	−	0.0911465i	−0.00561682	−	0.00471307i
$375$	−13.4980	−	13.3766i	−0.697036	−	0.690764i
$376$	−5.60743	+	15.4063i	−0.289181	+	0.794518i
$377$	−7.67682			−0.395377
$378$	−9.39054	−	0.935496i	−0.482997	−	0.0481167i
$379$	28.0324			1.43993			0.719964	−	0.694011i	$-0.244158\pi$
$379$	28.0324			1.43993			0.719964	+	0.694011i	$0.244158\pi$
$380$	2.45190	−	6.73655i	0.125780	−	0.345578i
$381$	−1.60383	+	0.437523i	−0.0821668	+	0.0224150i
$382$	0.963473	+	0.808450i	0.0492956	+	0.0413639i
$383$	0.202834	−	1.15033i	0.0103643	−	0.0587790i	−0.979187	−	0.202960i	$-0.934944\pi$
$383$	0.202834	−	1.15033i	0.0103643	−	0.0587790i	0.989551	+	0.144181i	$0.0460549\pi$
$384$	−16.8943	+	7.97111i	−0.862136	+	0.406774i
$385$	−0.662430	−	0.405395i	−0.0337606	−	0.0206608i
$386$	−0.0690223	+	0.0398500i	−0.00351314	+	0.00202831i
$387$	−1.50871	+	4.26468i	−0.0766919	+	0.216786i
$388$	−5.95398	−	3.43753i	−0.302268	−	0.174514i
$389$	−22.4622	+	3.96069i	−1.13888	+	0.200815i	−0.711115	−	0.703076i	$-0.751809\pi$
$389$	−22.4622	+	3.96069i	−1.13888	+	0.200815i	−0.427763	+	0.903891i	$0.640698\pi$
$390$	2.84117	+	1.30926i	0.143868	+	0.0662970i
$391$	0.587844	+	1.61509i	0.0297285	+	0.0816785i
$392$	14.2317	+	9.21806i	0.718808	+	0.465582i
$393$	6.92054	−	4.89257i	0.349095	−	0.246797i
$394$	−1.86476	−	10.5756i	−0.0939452	−	0.532790i
$395$	−5.62511	+	9.74298i	−0.283030	+	0.490222i
$396$	−0.512026	−	0.868628i	−0.0257303	−	0.0436502i
$397$	−13.0866	+	7.55554i	−0.656797	+	0.379202i	−0.791055	−	0.611745i	$-0.790468\pi$
$397$	−13.0866	+	7.55554i	−0.656797	+	0.379202i	0.134259	+	0.990946i	$0.457135\pi$
$398$	−5.06008	+	4.24591i	−0.253639	+	0.212828i
$399$	−15.4545	−	4.49199i	−0.773694	−	0.224881i
$400$	−0.779242	+	4.41930i	−0.0389621	+	0.220965i
$401$	−2.49029	+	2.96781i	−0.124359	+	0.148205i	−0.824631	−	0.565670i	$-0.808617\pi$
$401$	−2.49029	+	2.96781i	−0.124359	+	0.148205i	0.700272	+	0.713876i	$0.253062\pi$
$402$	−7.79091	−	2.04988i	−0.388576	−	0.102239i
$403$	−17.1467	−	6.24088i	−0.854137	−	0.310881i
$404$	1.49866			0.0745611
$405$	11.2159	−	4.31340i	0.557323	−	0.214335i
$406$	−6.70814	+	2.24896i	−0.332919	+	0.111614i
$407$	−0.235358	+	0.646640i	−0.0116663	+	0.0320528i
$408$	−3.81243	−	1.00310i	−0.188744	−	0.0496606i
$409$	−15.1865	+	18.0986i	−0.750926	+	0.894919i	−0.997238	−	0.0742715i	$-0.976337\pi$
$409$	−15.1865	+	18.0986i	−0.750926	+	0.894919i	0.246312	+	0.969191i	$0.420781\pi$
$410$	−10.4376	−	1.84043i	−0.515477	−	0.0908925i
$411$	−16.5615	−	11.4853i	−0.816918	−	0.566528i
$412$	13.1376	+	15.6568i	0.647243	+	0.771354i
$413$	19.6526	+	17.3663i	0.967040	+	0.854538i
$414$	−0.0340454	−	3.76679i	−0.00167324	−	0.185128i
$415$	11.4888	−	19.8992i	0.563963	−	0.976813i
$416$	−1.98544	−	11.2600i	−0.0973443	−	0.552067i
$417$	−9.18546	−	12.9928i	−0.449814	−	0.636261i
$418$	0.181274	+	0.498046i	0.00886640	+	0.0243602i
$419$	−19.8064	+	7.20893i	−0.967605	+	0.352179i	−0.777009	−	0.629489i	$-0.783264\pi$
$419$	−19.8064	+	7.20893i	−0.967605	+	0.352179i	−0.190596	+	0.981669i	$0.561042\pi$
$420$	−9.29930	−	1.01137i	−0.453760	−	0.0493497i
$421$	2.68706	+	15.2391i	0.130959	+	0.742708i	0.977589	+	0.210524i	$0.0675172\pi$
$421$	2.68706	+	15.2391i	0.130959	+	0.742708i	−0.846629	+	0.532183i	$0.821372\pi$
$422$	8.25950	+	4.76863i	0.402066	+	0.232133i
$423$	−19.9638	+	3.70650i	−0.970674	+	0.180216i
$424$	4.56699	+	7.91026i	0.221793	+	0.384156i
$425$	−2.31572	+	1.94312i	−0.112329	+	0.0942551i
$426$	6.95409	+	14.7388i	0.336927	+	0.714099i
$427$	−24.6194	+	3.69439i	−1.19142	+	0.178784i
$428$	18.3979	−	21.9258i	0.889297	−	1.05982i
$429$	0.723934	−	0.197488i	0.0349518	−	0.00953481i
$430$	0.472684	−	1.29869i	0.0227948	−	0.0626283i
$431$		−	22.9807i		−	1.10694i	−0.832868	−	0.553472i	$-0.813303\pi$
$431$		−	22.9807i		−	1.10694i	0.832868	−	0.553472i	$-0.186697\pi$
$432$	−5.99275	−	4.07622i	−0.288326	−	0.196117i
$433$		−	24.6163i		−	1.18299i	−0.806310	−	0.591493i	$-0.798539\pi$
$433$		−	24.6163i		−	1.18299i	0.806310	−	0.591493i	$-0.201461\pi$
$434$	−16.8114	−	0.430197i	−0.806971	−	0.0206501i
$435$	6.34158	−	6.39915i	0.304055	−	0.306816i
$436$	−6.13729	−	5.14980i	−0.293923	−	0.246631i
$437$	1.11556	−	6.32664i	0.0533643	−	0.302644i
$438$	10.5107	+	0.871726i	0.502222	+	0.0416527i
$439$	12.4166	+	14.7975i	0.592613	+	0.706248i	0.976106	−	0.217296i	$-0.0697235\pi$
$439$	12.4166	+	14.7975i	0.592613	+	0.706248i	−0.383493	+	0.923544i	$0.625279\pi$
$440$	0.355523	+	0.615783i	0.0169489	+	0.0293563i
$441$	−0.884471	+	20.9814i	−0.0421176	+	0.999113i
$442$	0.635511	−	1.10074i	0.0302282	−	0.0523567i
$443$	19.7211	−	3.47737i	0.936980	−	0.165215i	0.315749	−	0.948843i	$-0.397744\pi$
$443$	19.7211	−	3.47737i	0.936980	−	0.165215i	0.621231	+	0.783628i	$0.286633\pi$
$444$	0.759677	+	8.25340i	0.0360527	+	0.391689i
$445$	−8.68835	+	3.16230i	−0.411867	+	0.149907i
$446$	−11.7055	+	4.26045i	−0.554271	+	0.201738i
$447$	−26.2571	+	2.41681i	−1.24192	+	0.114311i
$448$	−1.50797	−	2.77338i	−0.0712447	−	0.131030i
$449$	−10.4575	−	6.03767i	−0.493522	−	0.284935i	0.232512	−	0.972593i	$-0.425305\pi$
$449$	−10.4575	−	6.03767i	−0.493522	−	0.284935i	−0.726034	+	0.687658i	$0.758639\pi$
$450$	6.20509	−	2.32219i	0.292511	−	0.109469i
$451$	−2.20168	+	1.27114i	−0.103673	+	0.0598557i
$452$	8.05822	+	9.60341i	0.379027	+	0.451706i
$453$	−19.4569	−	1.61369i	−0.914163	−	0.0758178i
$454$	17.4829	+	3.08271i	0.820515	+	0.144679i
$455$	2.54750	−	6.47852i	0.119429	−	0.303718i
$456$	10.4662	+	10.3720i	0.490123	+	0.485713i
$457$	16.7442	+	6.09438i	0.783259	+	0.285083i	0.702531	−	0.711653i	$-0.252053\pi$
$457$	16.7442	+	6.09438i	0.783259	+	0.285083i	0.0807282	+	0.996736i	$0.474275\pi$
$458$	7.44235			0.347758
$459$	−1.32746	−	4.69841i	−0.0619605	−	0.219303i
$460$		−	3.73386i		−	0.174092i
$461$	11.0937	+	4.03778i	0.516685	+	0.188058i	0.587183	−	0.809454i	$-0.300237\pi$
$461$	11.0937	+	4.03778i	0.516685	+	0.188058i	−0.0704983	+	0.997512i	$0.522459\pi$
$462$	0.574730	−	0.384648i	0.0267389	−	0.0178954i
$463$	−5.77577	−	4.84645i	−0.268423	−	0.225234i	0.498634	−	0.866813i	$-0.333835\pi$
$463$	−5.77577	−	4.84645i	−0.268423	−	0.225234i	−0.767057	+	0.641579i	$0.778280\pi$
$464$	−5.35114	−	0.943551i	−0.248421	−	0.0438033i
$465$	19.3665	−	9.13754i	0.898101	−	0.423743i
$466$	−1.43417	+	1.20341i	−0.0664365	+	0.0557468i
$467$	−5.54773	−	9.60896i	−0.256719	−	0.444650i	0.708642	−	0.705568i	$-0.249308\pi$
$467$	−5.54773	−	9.60896i	−0.256719	−	0.444650i	−0.965361	+	0.260918i	$0.915975\pi$
$468$	6.87074	−	5.87187i	0.317600	−	0.271427i
$469$	−3.56360	+	17.5692i	−0.164552	+	0.811273i
$470$	6.10915	−	1.07721i	0.281794	−	0.0496879i
$471$	−9.11958	+	19.7900i	−0.420208	+	0.911876i
$472$	−8.21235	−	22.5633i	−0.378004	−	1.03856i
$473$	−0.113382	−	0.311515i	−0.00521331	−	0.0143235i
$474$	−5.78312	−	8.18022i	−0.265627	−	0.375730i
$475$	11.1274	−	1.96206i	0.510561	−	0.0900257i
$476$	−0.755486	+	3.72469i	−0.0346276	+	0.170721i
$477$	−5.56737	+	9.84745i	−0.254913	+	0.450884i
$478$	−10.3888	−	17.9939i	−0.475172	−	0.823022i
$479$	0.344634	−	0.289182i	0.0157467	−	0.0132131i	−0.634880	−	0.772611i	$-0.718951\pi$
$479$	0.344634	−	0.289182i	0.0157467	−	0.0132131i	0.650627	+	0.759397i	$0.274506\pi$
$480$	11.0261	+	7.64653i	0.503270	+	0.349015i
$481$	−6.07448	−	1.07109i	−0.276972	−	0.0488377i
$482$	12.9014	+	10.8255i	0.587641	+	0.493090i
$483$	−8.36414	+	0.554528i	−0.380582	+	0.0252319i
$484$	−15.7332	−	5.72640i	−0.715143	−	0.260291i
$485$			6.00443i			0.272647i
$486$	−0.691538	+	10.6782i	−0.0313688	+	0.484373i
$487$	−24.3678			−1.10421			−0.552105	−	0.833774i	$-0.686175\pi$
$487$	−24.3678			−1.10421			−0.552105	+	0.833774i	$0.686175\pi$
$488$	21.4181	+	7.79554i	0.969551	+	0.352888i
$489$	−6.82921	+	25.9556i	−0.308828	+	1.17375i
$490$	0.328138	−	6.40734i	0.0148238	−	0.289454i
$491$	12.6614	+	2.23255i	0.571402	+	0.100754i	0.451881	−	0.892078i	$-0.350753\pi$
$491$	12.6614	+	2.23255i	0.571402	+	0.100754i	0.119521	+	0.992832i	$0.461864\pi$
$492$	−17.4496	+	25.1619i	−0.786691	+	1.13439i
$493$	−2.35284	−	2.80401i	−0.105967	−	0.126286i
$494$	−4.11429	+	2.37539i	−0.185111	+	0.106874i
$495$	−0.433399	+	0.766586i	−0.0194798	+	0.0344555i
$496$	−11.1851	−	6.45770i	−0.502224	−	0.289959i
$497$	31.8603	−	17.3233i	1.42913	−	0.777058i
$498$	11.8115	+	16.7074i	0.529287	+	0.748677i
$499$	27.7006	−	10.0822i	1.24005	−	0.451341i	0.363022	−	0.931781i	$-0.381745\pi$
$499$	27.7006	−	10.0822i	1.24005	−	0.451341i	0.877028	+	0.480439i	$0.159523\pi$
$500$	15.7618	−	5.73684i	0.704891	−	0.256559i
$501$	34.9686	+	16.1141i	1.56228	+	0.719926i
$502$	16.3095	−	2.87580i	0.727929	−	0.128353i
$503$	6.61558	−	11.4585i	0.294974	−	0.510910i	−0.680005	−	0.733208i	$-0.738022\pi$
$503$	6.61558	−	11.4585i	0.294974	−	0.510910i	0.974979	+	0.222298i	$0.0713557\pi$
$504$	9.88744	−	16.4893i	0.440422	−	0.734493i
$505$	−0.654437	−	1.13352i	−0.0291221	−	0.0504409i
$506$	0.177443	+	0.211468i	0.00788829	+	0.00940089i
$507$	−6.73797	−	14.2808i	−0.299244	−	0.634231i
$508$	0.254803	−	1.44506i	0.0113051	−	0.0641143i
$509$	−10.7916	−	9.05526i	−0.478331	−	0.401367i	0.371491	−	0.928436i	$-0.378847\pi$
$509$	−10.7916	−	9.05526i	−0.478331	−	0.401367i	−0.849823	+	0.527069i	$0.823291\pi$
$510$	0.392564	+	1.43902i	0.0173830	+	0.0637211i
$511$	0.600383	−	23.4619i	0.0265594	−	1.03789i
$512$		−	14.8502i		−	0.656292i
$513$	−4.48379	+	17.6896i	−0.197964	+	0.781015i
$514$			8.06010i			0.355516i
$515$	6.10512	−	16.7737i	0.269024	−	0.739137i
$516$	−2.83609	−	2.81057i	−0.124852	−	0.123728i
$517$	0.956469	−	1.13988i	0.0420655	−	0.0501317i
$518$	−5.62176	+	0.843602i	−0.247006	+	0.0370658i
$519$	8.09203	+	0.671127i	0.355201	+	0.0294592i
$520$	−4.88238	+	4.09680i	−0.214107	+	0.179657i
$521$	4.03394	+	6.98699i	0.176730	+	0.306105i	0.940759	−	0.339077i	$-0.110115\pi$
$521$	4.03394	+	6.98699i	0.176730	+	0.306105i	−0.764029	+	0.645182i	$0.776781\pi$
$522$	2.81184	+	7.51348i	0.123071	+	0.328856i
$523$	−10.5643	−	6.09931i	−0.461945	−	0.266704i	0.250917	−	0.968009i	$-0.419268\pi$
$523$	−10.5643	−	6.09931i	−0.461945	−	0.266704i	−0.712862	+	0.701305i	$0.752601\pi$
$524$	1.29902	+	7.36711i	0.0567479	+	0.321833i
$525$	−5.94797	−	13.4903i	−0.259590	−	0.588763i
$526$	−12.7572	+	4.64325i	−0.556241	+	0.202455i
$527$	−2.97570	−	8.17568i	−0.129624	−	0.356138i
$528$	0.528892	−	0.0486814i	0.0230171	−	0.00211859i
$529$	3.41288	+	19.3554i	0.148386	+	0.841539i
$530$	1.72802	−	2.99301i	0.0750602	−	0.130008i
$531$	18.9083	−	22.9522i	0.820551	−	0.996040i
$532$	9.40650	−	10.6449i	0.407824	−	0.461515i
$533$	−14.6478	−	17.4565i	−0.634465	−	0.756126i
$534$	0.680504	−	8.20509i	0.0294483	−	0.355069i
$535$	−24.6177	−	4.34076i	−1.06432	−	0.187668i
$536$	10.5501	−	12.5731i	0.455695	−	0.543077i
$537$	19.3812	−	19.5571i	0.836360	−	0.843953i
$538$	−4.02100	+	11.0476i	−0.173357	+	0.476296i
$539$	−0.927618	−	1.22794i	−0.0399553	−	0.0528913i
$540$	−0.781098	+	10.5778i	−0.0336131	+	0.455196i
$541$	−17.3576			−0.746264			−0.373132	−	0.927778i	$-0.621716\pi$
$541$	−17.3576			−0.746264			−0.373132	+	0.927778i	$0.621716\pi$
$542$	−10.6745	−	3.88519i	−0.458508	−	0.166883i
$543$	2.53648	+	9.29800i	0.108851	+	0.399015i
$544$	3.50427	−	4.17623i	0.150245	−	0.179054i
$545$	−1.21503	+	6.89079i	−0.0520462	+	0.295169i
$546$	4.29000	+	4.47466i	0.183595	+	0.191498i
$547$	5.51648	−	4.62888i	0.235868	−	0.197916i	−0.517191	−	0.855870i	$-0.673022\pi$
$547$	5.51648	−	4.62888i	0.235868	−	0.197916i	0.753058	+	0.657954i	$0.228578\pi$
$548$	15.4059	−	8.89460i	0.658107	−	0.379958i
$549$	5.15285	+	27.7540i	0.219918	+	1.18451i
$550$	−0.242763	+	0.420477i	−0.0103514	+	0.0179292i
$551$	2.37578	+	13.4737i	0.101212	+	0.574000i
$552$	6.97013	+	3.21196i	0.296668	+	0.136710i
$553$	−17.4383	+	13.8880i	−0.741552	+	0.590579i
$554$	−4.04537	−	11.1145i	−0.171871	−	0.472212i
$555$	5.91076	−	4.17869i	0.250898	−	0.177376i
$556$	13.8312	−	2.43882i	0.586575	−	0.103429i
$557$	−15.7336	−	9.08382i	−0.666655	−	0.384894i	0.128153	−	0.991754i	$-0.459095\pi$
$557$	−15.7336	−	9.08382i	−0.666655	−	0.384894i	−0.794808	+	0.606861i	$0.792429\pi$
$558$	0.172340	+	19.0677i	0.00729574	+	0.807202i
$559$	2.57338	−	1.48574i	0.108842	−	0.0628402i
$560$	2.57201	−	4.20275i	0.108687	−	0.177599i
$561$	0.294009	+	0.203894i	0.0124131	+	0.00860840i
$562$	1.70878	−	9.69097i	0.0720805	−	0.408789i
$563$	6.45074	+	5.41282i	0.271866	+	0.228123i	0.768520	−	0.639826i	$-0.220994\pi$
$563$	6.45074	+	5.41282i	0.271866	+	0.228123i	−0.496653	+	0.867949i	$0.665438\pi$
$564$	4.56033	−	17.3323i	0.192025	−	0.729822i
$565$	3.74471	−	10.2885i	0.157541	−	0.432840i
$566$	9.55604			0.401670
$567$	23.8111	+	0.178776i	0.999972	+	0.00750789i
$568$	−33.2027			−1.39316
$569$	−13.8694	+	38.1057i	−0.581434	+	1.59748i	0.204298	+	0.978909i	$0.434509\pi$
$569$	−13.8694	+	38.1057i	−0.581434	+	1.59748i	−0.785732	+	0.618567i	$0.787714\pi$
$570$	1.41864	−	5.39177i	0.0594202	−	0.225836i
$571$	−15.0780	−	12.6519i	−0.630994	−	0.529467i	0.270244	−	0.962792i	$-0.412896\pi$
$571$	−15.0780	−	12.6519i	−0.630994	−	0.529467i	−0.901238	+	0.433325i	$0.857340\pi$
$572$	−0.115012	+	0.652268i	−0.00480891	+	0.0272727i
$573$	−2.60780	−	1.80849i	−0.108942	−	0.0755509i
$574$	−17.9134	−	10.9627i	−0.747692	−	0.457573i
$575$	5.09660	−	2.94252i	0.212543	−	0.122712i
$576$	−3.08365	+	1.81770i	−0.128485	+	0.0757376i
$577$	33.4084	+	19.2884i	1.39081	+	0.802985i	0.993405	−	0.114658i	$-0.0365774\pi$
$577$	33.4084	+	19.2884i	1.39081	+	0.802985i	0.397405	+	0.917643i	$0.369911\pi$
$578$	−10.8954	+	1.92115i	−0.453189	+	0.0799095i
$579$	0.164210	−	0.116090i	0.00682433	−	0.00482455i
$580$	2.71972	+	7.47238i	0.112930	+	0.310274i
$581$	35.6162	−	28.3651i	1.47761	−	1.17678i
$582$	−4.85598	−	2.23772i	−0.201287	−	0.0927566i
$583$	−0.143953	−	0.816400i	−0.00596194	−	0.0338118i
$584$	−10.7438	+	18.6088i	−0.444581	+	0.770037i
$585$	−7.44154	−	2.63258i	−0.307670	−	0.108844i
$586$	7.17721	−	4.14376i	0.296488	−	0.171177i
$587$	26.1514	−	21.9436i	1.07938	−	0.905710i	0.0835134	−	0.996507i	$-0.473386\pi$
$587$	26.1514	−	21.9436i	1.07938	−	0.905710i	0.995869	+	0.0907969i	$0.0289414\pi$
$588$	−16.4155	−	8.60837i	−0.676962	−	0.355003i
$589$	−5.64702	+	32.0258i	−0.232681	+	1.31960i
$590$	−5.83984	+	6.95965i	−0.240423	+	0.286524i
$591$	7.13123	+	26.1410i	0.293340	+	1.07530i
$592$	−4.10258	−	1.49322i	−0.168615	−	0.0613708i
$593$	6.67349			0.274048			0.137024	−	0.990568i	$-0.456246\pi$
$593$	6.67349			0.274048			0.137024	+	0.990568i	$0.456246\pi$
$594$	−0.458446	−	0.636195i	−0.0188103	−	0.0261034i
$595$	3.14709	−	1.05509i	0.129018	−	0.0432544i
$596$	7.96011	−	21.8702i	0.326059	−	0.895839i
$597$	11.7320	−	11.8386i	0.480160	−	0.484520i
$598$	−1.59052	+	1.89550i	−0.0650411	+	0.0775129i
$599$	25.4041	+	4.47942i	1.03798	+	0.183024i	0.666569	−	0.745443i	$-0.267762\pi$
$599$	25.4041	+	4.47942i	1.03798	+	0.183024i	0.371413	+	0.928468i	$0.378873\pi$
$600$	−1.11567	+	13.4521i	−0.0455471	+	0.549178i
$601$	−12.8387	−	15.3005i	−0.523699	−	0.624121i	0.437752	−	0.899096i	$-0.355775\pi$
$601$	−12.8387	−	15.3005i	−0.523699	−	0.624121i	−0.961451	+	0.274975i	$0.911330\pi$
$602$	1.81341	−	2.05215i	0.0739090	−	0.0836393i
$603$	20.0496	+	3.34873i	0.816482	+	0.136371i
$604$	8.61630	−	14.9239i	0.350592	−	0.607243i
$605$	2.53919	+	14.4005i	0.103233	+	0.585462i
$606$	1.16061	−	0.106827i	0.0471465	−	0.00433956i
$607$	−11.2649	−	30.9501i	−0.457228	−	1.25622i	−0.927540	−	0.373724i	$-0.878081\pi$
$607$	−11.2649	−	30.9501i	−0.457228	−	1.25622i	0.470312	−	0.882500i	$-0.344141\pi$
$608$	−19.1482	+	6.96937i	−0.776562	+	0.282645i
$609$	16.3348	−	7.20214i	0.661919	−	0.291845i
$610$	−1.49755	−	8.49305i	−0.0606342	−	0.343874i
$611$	11.5509	+	6.66889i	0.467298	+	0.269795i
$612$	4.25052	+	0.709933i	0.171817	+	0.0286973i
$613$	15.5747	+	26.9761i	0.629055	+	1.08956i	0.987742	+	0.156097i	$0.0498913\pi$
$613$	15.5747	+	26.9761i	0.629055	+	1.08956i	−0.358687	+	0.933458i	$0.616775\pi$
$614$	11.8513	−	9.94441i	0.478279	−	0.401324i
$615$	26.6513	+	2.21037i	1.07468	+	0.0891307i
$616$	0.209089	+	1.39337i	0.00842445	+	0.0561405i
$617$	−21.5216	+	25.6485i	−0.866428	+	1.03257i	0.132714	+	0.991154i	$0.457631\pi$
$617$	−21.5216	+	25.6485i	−0.866428	+	1.03257i	−0.999142	+	0.0414139i	$0.986814\pi$
$618$	11.2902	+	11.1886i	0.454159	+	0.450072i
$619$	1.15081	−	3.16183i	0.0462550	−	0.127085i	−0.914414	−	0.404780i	$-0.867348\pi$
$619$	1.15081	−	3.16183i	0.0462550	−	0.127085i	0.960669	+	0.277695i	$0.0895705\pi$
$620$			18.9011i			0.759084i
$621$	0.956691	+	9.45660i	0.0383907	+	0.379480i
$622$			1.79850i			0.0721132i
$623$	−18.3153	−	0.468682i	−0.733787	−	0.0187774i
$624$	1.25295	+	4.59296i	0.0501583	+	0.183866i
$625$	1.10083	+	0.923703i	0.0440330	+	0.0369481i
$626$	−0.690772	+	3.91756i	−0.0276088	+	0.156577i
$627$	−0.570654	−	1.20947i	−0.0227897	−	0.0483016i
$628$	−12.3628	−	14.7334i	−0.493330	−	0.587928i
$629$	−1.47052	−	2.54701i	−0.0586334	−	0.101556i
$630$	−7.27376	−	0.120363i	−0.289794	−	0.00479537i
$631$	−9.48269	+	16.4245i	−0.377500	+	0.653849i	−0.990698	−	0.136080i	$-0.956549\pi$
$631$	−9.48269	+	16.4245i	−0.377500	+	0.653849i	0.613198	+	0.789929i	$0.289883\pi$
$632$	20.1001	−	3.54419i	0.799540	−	0.140980i
$633$	−21.8557	−	10.0715i	−0.868687	−	0.400306i
$634$	9.54535	−	3.47422i	0.379094	−	0.137979i
$635$	−1.20425	+	0.438310i	−0.0477891	+	0.0173938i
$636$	−5.76396	−	8.15312i	−0.228556	−	0.323292i
$637$	9.39568	−	10.0997i	0.372271	−	0.400166i
$638$	−0.509138	−	0.293951i	−0.0201570	−	0.0116376i
$639$	−20.8816	−	35.4246i	−0.826062	−	1.40138i
$640$	−12.4710	+	7.20013i	−0.492959	+	0.284610i
$641$	12.8204	+	15.2788i	0.506376	+	0.603475i	0.957303	−	0.289085i	$-0.0933511\pi$
$641$	12.8204	+	15.2788i	0.506376	+	0.603475i	−0.450927	+	0.892561i	$0.648907\pi$
$642$	12.6850	−	18.2915i	0.500638	−	0.721906i
$643$	32.5518	+	5.73976i	1.28372	+	0.226354i	0.773558	−	0.633726i	$-0.218475\pi$
$643$	32.5518	+	5.73976i	1.28372	+	0.226354i	0.510160	+	0.860080i	$0.329586\pi$
$644$	2.70758	−	6.88561i	0.106693	−	0.271331i
$645$	−0.887320	+	3.37241i	−0.0349382	+	0.132789i
$646$	−2.12860	−	0.774746i	−0.0837485	−	0.0304820i
$647$	−22.6934			−0.892168			−0.446084	−	0.894991i	$-0.647182\pi$
$647$	−22.6934			−0.892168			−0.446084	+	0.894991i	$0.647182\pi$
$648$	−19.0740	−	10.5574i	−0.749298	−	0.414733i
$649$			2.17925i			0.0855431i
$650$	−4.08958	−	1.48848i	−0.160406	−	0.0583831i
$651$	42.3398	−	2.80706i	1.65943	−	0.110017i
$652$	−18.1472	−	15.2273i	−0.710698	−	0.596346i
$653$	17.5842	+	3.10057i	0.688122	+	0.121335i	0.506767	−	0.862083i	$-0.330840\pi$
$653$	17.5842	+	3.10057i	0.688122	+	0.121335i	0.181355	+	0.983418i	$0.441952\pi$
$654$	−5.12000	−	3.55069i	−0.200208	−	0.138843i
$655$	5.00488	−	4.19960i	0.195557	−	0.164092i
$656$	−8.06469	−	13.9684i	−0.314873	−	0.545376i
$657$	−26.6109	+	0.240518i	−1.03819	+	0.00938349i
$658$	12.0470	+	2.44352i	0.469642	+	0.0952583i
$659$	−15.8260	+	2.79056i	−0.616495	+	0.108705i	−0.473170	−	0.880971i	$-0.656891\pi$
$659$	−15.8260	+	2.79056i	−0.616495	+	0.108705i	−0.143325	+	0.989676i	$0.545779\pi$
$660$	−0.448702	−	0.634689i	−0.0174657	−	0.0247052i
$661$	14.4940	+	39.8218i	0.563750	+	1.54889i	0.814094	+	0.580733i	$0.197234\pi$
$661$	14.4940	+	39.8218i	0.563750	+	1.54889i	−0.250344	+	0.968157i	$0.580544\pi$
$662$	2.41469	+	6.63430i	0.0938495	+	0.257849i
$663$	−1.34222	+	2.91269i	−0.0521275	+	0.113120i
$664$	−41.0528	+	7.23872i	−1.59316	+	0.280917i
$665$	−12.1590	−	2.46622i	−0.471504	−	0.0956360i
$666$	1.17664	+	6.33754i	0.0455937	+	0.245575i
$667$	3.56298	+	6.17126i	0.137959	+	0.238952i
$668$	−26.0337	+	21.8449i	−1.00727	+	0.845203i
$669$	28.4260	−	13.4120i	1.09901	−	0.518537i
$670$	−6.11588	−	1.07839i	−0.236277	−	0.0416620i
$671$	−1.58467	−	1.32970i	−0.0611757	−	0.0513325i
$672$	14.7884	+	22.0964i	0.570475	+	0.852389i
$673$	−10.5299	−	3.83256i	−0.405897	−	0.147734i	0.131000	−	0.991382i	$-0.458181\pi$
$673$	−10.5299	−	3.83256i	−0.405897	−	0.147734i	−0.536897	+	0.843648i	$0.680403\pi$
$674$			18.9479i			0.729845i
$675$	−15.0539	+	7.26981i	−0.579425	+	0.279815i
$676$	13.9375			0.536059
$677$	−4.46954	−	1.62678i	−0.171778	−	0.0625222i	0.254699	−	0.967020i	$-0.418024\pi$
$677$	−4.46954	−	1.62678i	−0.171778	−	0.0625222i	−0.426478	+	0.904498i	$0.640246\pi$
$678$	6.92508	+	6.86278i	0.265956	+	0.263563i
$679$	−4.35406	+	11.0728i	−0.167093	+	0.424934i
$680$	−2.99277	−	0.527705i	−0.114767	−	0.0202366i
$681$	−44.6407	−	3.70236i	−1.71064	−	0.141875i
$682$	−0.898226	−	1.07046i	−0.0343948	−	0.0409902i
$683$	22.2708	−	12.8581i	0.852170	−	0.492001i	−0.00921244	−	0.999958i	$-0.502932\pi$
$683$	22.2708	−	12.8581i	0.852170	−	0.492001i	0.861382	+	0.507957i	$0.169599\pi$
$684$	−12.4321	−	10.2418i	−0.475355	−	0.391604i
$685$	−13.4549	−	7.76821i	−0.514086	−	0.296808i
$686$	5.25134	−	11.5778i	0.200497	−	0.442043i
$687$	−18.6997	+	1.72120i	−0.713439	+	0.0656678i
$688$	1.97639	−	0.719347i	0.0753492	−	0.0274248i
$689$	6.98261	−	2.54146i	0.266016	−	0.0968220i
$690$	−0.266157	−	2.89162i	−0.0101324	−	0.110082i
$691$	−6.87549	+	1.21234i	−0.261556	+	0.0461194i	−0.302888	−	0.953026i	$-0.597951\pi$
$691$	−6.87549	+	1.21234i	−0.261556	+	0.0461194i	0.0413322	+	0.999145i	$0.486840\pi$
$692$	−3.58348	+	6.20677i	−0.136223	+	0.235946i
$693$	−1.35511	+	1.09939i	−0.0514765	+	0.0417622i
$694$	2.65350	+	4.59600i	0.100726	+	0.174462i
$695$	−7.88445	−	9.39632i	−0.299074	−	0.356423i
$696$	−16.2885	−	1.35092i	−0.617415	−	0.0512064i
$697$	1.88676	−	10.7004i	0.0714663	−	0.405305i
$698$	−15.8664	−	13.3135i	−0.600552	−	0.503923i
$699$	3.32518	−	3.35537i	0.125770	−	0.126912i
$700$	13.0090	+	0.332895i	0.491692	+	0.0125822i
$701$			4.24261i			0.160241i	0.996785	+	0.0801206i	$0.0255305\pi$
$701$			4.24261i			0.160241i	−0.996785	+	0.0801206i	$0.974469\pi$
$702$	4.90236	−	5.03712i	0.185028	−	0.190114i
$703$			10.9929i			0.414605i
$704$	0.0897175	−	0.246497i	0.00338135	−	0.00929020i
$705$	−15.1008	+	4.11947i	−0.568728	+	0.155148i
$706$	6.24451	−	7.44192i	0.235015	−	0.280080i
$707$	−0.384886	−	2.56488i	−0.0144751	−	0.0964622i
$708$	11.2003	+	23.7384i	0.420932	+	0.892142i
$709$	20.5679	−	17.2586i	0.772445	−	0.648159i	−0.168889	−	0.985635i	$-0.554018\pi$
$709$	20.5679	−	17.2586i	0.772445	−	0.648159i	0.941334	+	0.337477i	$0.109573\pi$
$710$	6.28148	+	10.8798i	0.235740	+	0.408313i
$711$	16.4226	+	19.2162i	0.615894	+	0.720664i
$712$	14.5268	+	8.38702i	0.544413	+	0.314317i
$713$	2.94121	+	16.6804i	0.110149	+	0.624687i
$714$	−0.319569	+	2.93837i	−0.0119596	+	0.109966i
$715$	0.543570	−	0.197843i	0.0203283	−	0.00739891i
$716$	8.31204	+	22.8371i	0.310635	+	0.853464i
$717$	30.2644	+	42.8090i	1.13024	+	1.59873i
$718$	−3.05074	−	17.3016i	−0.113853	−	0.645691i
$719$	18.0874	−	31.3282i	0.674545	−	1.16835i	−0.302056	−	0.953290i	$-0.597673\pi$
$719$	18.0874	−	31.3282i	0.674545	−	1.16835i	0.976602	−	0.215057i	$-0.0689936\pi$
$720$	−4.86357	−	2.74968i	−0.181255	−	0.102474i
$721$	23.4218	−	26.5053i	0.872272	−	0.987108i
$722$	−2.94115	−	3.50512i	−0.109458	−	0.130447i
$723$	−34.9197	−	24.2166i	−1.29868	−	0.900625i
$724$	−8.37755	−	1.47719i	−0.311349	−	0.0548992i
$725$	−8.05623	+	9.60105i	−0.299201	+	0.356574i
$726$	−12.5924	−	3.31322i	−0.467349	−	0.122965i
$727$	−6.90637	+	18.9751i	−0.256143	+	0.703748i	0.743253	+	0.669010i	$0.233282\pi$
$727$	−6.90637	+	18.9751i	−0.256143	+	0.703748i	−0.999396	+	0.0347375i	$0.988940\pi$
$728$	−11.9744	+	4.01450i	−0.443799	+	0.148787i
$729$	−0.731993	−	26.9901i	−0.0271109	−	0.999632i
$730$	8.13027			0.300915
$731$	1.33138	+	0.484583i	0.0492429	+	0.0179230i
$732$	−24.0957	−	6.33985i	−0.890602	−	0.234328i
$733$	−0.867738	+	1.03413i	−0.0320506	+	0.0381965i	−0.781832	−	0.623490i	$-0.785714\pi$
$733$	−0.867738	+	1.03413i	−0.0320506	+	0.0381965i	0.749781	+	0.661686i	$0.230159\pi$
$734$	−2.10441	+	11.9347i	−0.0776753	+	0.440518i
$735$	0.657347	+	16.1750i	0.0242466	+	0.596624i
$736$	−8.13022	+	6.82207i	−0.299684	+	0.251465i
$737$	−1.29007	+	0.744820i	−0.0475202	+	0.0274358i
$738$	−11.7200	+	20.7300i	−0.431418	+	0.763083i
$739$	8.05469	−	13.9511i	0.296297	−	0.513201i	−0.678989	−	0.734148i	$-0.737582\pi$
$739$	8.05469	−	13.9511i	0.296297	−	0.513201i	0.975286	+	0.220948i	$0.0709150\pi$
$740$	1.10948	+	6.29217i	0.0407853	+	0.231305i
$741$	9.78824	−	6.91993i	0.359580	−	0.254210i
$742$	5.35699	−	4.26636i	0.196661	−	0.156623i
$743$	−10.0891	−	27.7195i	−0.370132	−	1.01693i	−0.975310	−	0.220840i	$-0.929120\pi$
$743$	−10.0891	−	27.7195i	−0.370132	−	1.01693i	0.605178	−	0.796090i	$-0.293102\pi$
$744$	−35.2832	−	16.2591i	−1.29355	−	0.596089i
$745$	−20.0177	+	3.52965i	−0.733390	+	0.129316i
$746$	−3.45963	−	1.99742i	−0.126666	−	0.0731307i
$747$	−33.5417	−	39.2475i	−1.22723	−	1.43599i
$748$	−0.273495	+	0.157902i	−0.00999995	+	0.00577348i
$749$	−42.2498	−	25.8561i	−1.54377	−	0.944761i
$750$	11.7975	−	5.56632i	0.430785	−	0.203253i
$751$	−1.81313	+	10.2828i	−0.0661622	+	0.375224i	0.933691	+	0.358080i	$0.116569\pi$
$751$	−1.81313	+	10.2828i	−0.0661622	+	0.375224i	−0.999853	+	0.0171442i	$0.994543\pi$
$752$	7.23188	+	6.06827i	0.263720	+	0.221287i
$753$	−40.3143	+	10.9977i	−1.46913	+	0.400778i
$754$	1.80234	−	4.95189i	0.0656374	−	0.180337i
$755$	−15.0503			−0.547737
$756$	−9.11082	+	18.9401i	−0.331357	+	0.688845i
$757$	28.0501			1.01950			0.509749	−	0.860323i	$-0.329738\pi$
$757$	28.0501			1.01950			0.509749	+	0.860323i	$0.329738\pi$
$758$	−6.58137	+	18.0822i	−0.239046	+	0.656774i
$759$	−0.494750	−	0.490298i	−0.0179583	−	0.0177967i
$760$	8.70135	+	7.30130i	0.315631	+	0.264846i
$761$	−4.79778	+	27.2096i	−0.173919	+	0.986346i	0.765464	+	0.643478i	$0.222509\pi$
$761$	−4.79778	+	27.2096i	−0.173919	+	0.986346i	−0.939384	+	0.342867i	$0.888602\pi$
$762$	0.0943211	−	1.13726i	0.00341689	−	0.0411987i
$763$	−7.23743	+	11.8262i	−0.262013	+	0.428138i
$764$	2.42584	−	1.40056i	0.0877638	−	0.0506704i
$765$	−1.31916	−	3.52492i	−0.0476945	−	0.127444i
$766$	0.694392	+	0.400908i	0.0250894	+	0.0144854i
$767$	−19.2371	+	3.39202i	−0.694611	+	0.122479i
$768$	−1.55416	−	16.8849i	−0.0560808	−	0.609282i
$769$	13.9253	+	38.2594i	0.502159	+	1.37967i	0.889162	+	0.457592i	$0.151288\pi$
$769$	13.9253	+	38.2594i	0.502159	+	1.37967i	−0.387004	+	0.922078i	$0.626490\pi$
$770$	0.417021	−	0.332120i	0.0150284	−	0.0119688i
$771$	−1.86406	−	20.2519i	−0.0671326	−	0.729353i
$772$	0.0308230	+	0.174806i	0.00110934	+	0.00629140i
$773$	10.5422	−	18.2596i	0.379176	−	0.656752i	−0.611767	−	0.791038i	$-0.709541\pi$
$773$	10.5422	−	18.2596i	0.379176	−	0.656752i	0.990943	+	0.134286i	$0.0428742\pi$
$774$	−2.39670	−	1.97443i	−0.0861475	−	0.0709695i
$775$	−25.7993	+	14.8952i	−0.926739	+	0.535053i
$776$	8.34472	−	7.00205i	0.299558	−	0.251359i
$777$	13.9302	−	3.41979i	0.499742	−	0.122684i
$778$	2.71878	−	15.4190i	0.0974732	−	0.552798i
$779$	−26.1051	+	31.1109i	−0.935314	+	1.11466i
$780$	4.90423	−	4.94876i	0.175600	−	0.177194i
$781$	2.83173	+	1.03066i	0.101327	+	0.0368801i
$782$	−1.17982			−0.0421901
$783$	−8.80270	−	18.2281i	−0.314583	−	0.651420i
$784$	7.79063	−	5.88523i	0.278237	−	0.210187i
$785$	−5.74508	+	15.7845i	−0.205051	+	0.563372i
$786$	1.53114	+	5.61272i	0.0546140	+	0.200199i
$787$	−9.72249	+	11.5868i	−0.346569	+	0.413025i	−0.910968	−	0.412477i	$-0.864664\pi$
$787$	−9.72249	+	11.5868i	−0.346569	+	0.413025i	0.564399	+	0.825502i	$0.309108\pi$
$788$	−23.5532	−	4.15306i	−0.839048	−	0.147947i
$789$	30.9800	−	14.6170i	1.10292	−	0.520380i
$790$	−4.96401	−	5.91588i	−0.176612	−	0.210477i
$791$	14.3662	−	16.2576i	0.510804	−	0.578053i
$792$	1.57078	−	0.291633i	0.0558152	−	0.0103627i
$793$	9.27121	−	16.0582i	0.329230	−	0.570244i
$794$	−1.80123	−	10.2153i	−0.0639234	−	0.362527i
$795$	−3.64963	+	7.91991i	−0.129439	+	0.280890i
$796$	5.03154	+	13.8240i	0.178338	+	0.489980i
$797$	−21.7035	+	7.89942i	−0.768776	+	0.279812i	−0.696484	−	0.717572i	$-0.745254\pi$
$797$	−21.7035	+	7.89942i	−0.768776	+	0.279812i	−0.0722918	+	0.997384i	$0.523031\pi$
$798$	6.52590	−	8.91425i	0.231014	−	0.315561i
$799$	1.10433	+	6.26295i	0.0390683	+	0.221567i
$800$	−16.1659	−	9.33341i	−0.571552	−	0.329986i
$801$	0.187758	+	20.7735i	0.00663409	+	0.733997i
$802$	−1.32971	−	2.30312i	−0.0469536	−	0.0813260i
$803$	1.49394	−	1.25356i	0.0527200	−	0.0442373i
$804$	−10.2246	+	14.7435i	−0.360592	+	0.519964i
$805$	−6.39031	+	0.958931i	−0.225229	+	0.0337979i
$806$	8.05130	−	9.59516i	0.283595	−	0.337975i
$807$	7.54820	−	28.6882i	0.265709	−	1.00987i
$808$	−0.812149	+	2.23136i	−0.0285713	+	0.0784990i
$809$			28.4204i			0.999209i	0.866254	+	0.499604i	$0.166521\pi$
$809$			28.4204i			0.999209i	−0.866254	+	0.499604i	$0.833479\pi$
$810$	0.149098	+	8.24746i	0.00523878	+	0.289786i
$811$		−	19.4101i		−	0.681580i	−0.940139	−	0.340790i	$-0.889305\pi$
$811$		−	19.4101i		−	0.681580i	0.940139	−	0.340790i	$-0.110695\pi$
$812$	−0.403088	+	15.7520i	−0.0141456	+	0.552787i
$813$	27.7193	+	7.29327i	0.972159	+	0.255786i
$814$	−0.361855	−	0.303633i	−0.0126830	−	0.0106423i
$815$	−3.59269	+	20.3752i	−0.125846	+	0.713711i
$816$	−1.29359	+	1.86533i	−0.0452848	+	0.0652995i
$817$	−3.40405	−	4.05678i	−0.119092	−	0.141929i
$818$	−8.10897	−	14.0451i	−0.283523	−	0.491077i
$819$	−11.8139	−	10.2509i	−0.412813	−	0.358196i
$820$	−11.8023	+	20.4421i	−0.412153	+	0.713870i
$821$	20.0727	−	3.53937i	0.700544	−	0.123525i	0.187979	−	0.982173i	$-0.439806\pi$
$821$	20.0727	−	3.53937i	0.700544	−	0.123525i	0.512565	+	0.858648i	$0.328695\pi$
$822$	11.2968	−	7.98641i	0.394021	−	0.278558i
$823$	16.5465	−	6.02243i	0.576774	−	0.209929i	−0.0371281	−	0.999311i	$-0.511821\pi$
$823$	16.5465	−	6.02243i	0.576774	−	0.209929i	0.613903	+	0.789382i	$0.289599\pi$
$824$	−30.4309	+	11.0759i	−1.06011	+	0.385849i
$825$	0.512723	−	1.11264i	0.0178507	−	0.0387371i
$826$	−15.8160	+	8.59959i	−0.550309	+	0.299218i
$827$	−15.2517	−	8.80555i	−0.530352	−	0.306199i	0.210808	−	0.977528i	$-0.432391\pi$
$827$	−15.2517	−	8.80555i	−0.530352	−	0.306199i	−0.741160	+	0.671329i	$0.765724\pi$
$828$	−7.90915	−	2.79800i	−0.274862	−	0.0972373i
$829$	35.2758	−	20.3665i	1.22518	−	0.707357i	0.259161	−	0.965834i	$-0.416554\pi$
$829$	35.2758	−	20.3665i	1.22518	−	0.707357i	0.966017	+	0.258477i	$0.0832206\pi$
$830$	10.1386	+	12.0827i	0.351915	+	0.419396i
$831$	12.7349	+	26.9909i	0.441768	+	0.936305i
$832$	2.31557	+	0.408297i	0.0802778	+	0.0141551i
$833$	6.56864	+	0.336399i	0.227590	+	0.0116555i
$834$	10.5375	−	2.87461i	0.364883	−	0.0995397i
$835$	27.8909	+	10.1514i	0.965203	+	0.351305i
$836$	1.18040			0.0408250
$837$	−4.84283	−	47.8699i	−0.167393	−	1.65463i
$838$		−	14.4685i		−	0.499806i
$839$	48.4147	+	17.6215i	1.67146	+	0.608362i	0.992101	−	0.125442i	$-0.0400348\pi$
$839$	48.4147	+	17.6215i	1.67146	+	0.608362i	0.679361	+	0.733804i	$0.262257\pi$
$840$	6.54528	−	13.2977i	0.225834	−	0.458814i
$841$	10.5898	+	8.88589i	0.365165	+	0.306410i
$842$	−10.4608	−	1.84451i	−0.360501	−	0.0635661i
$843$	−2.05225	+	24.7448i	−0.0706834	+	0.852256i
$844$	16.2713	−	13.6533i	0.560082	−	0.469965i
$845$	−6.08626	−	10.5417i	−0.209374	−	0.362646i
$846$	2.29618	−	13.7478i	0.0789444	−	0.472657i
$847$	−5.75984	+	28.3971i	−0.197911	+	0.975737i
$848$	5.17961	−	0.913305i	0.177869	−	0.0313630i
$849$	−24.0106	+	2.21003i	−0.824041	+	0.0758481i
$850$	−0.709721	−	1.94994i	−0.0243432	−	0.0668825i
$851$	1.95826	+	5.38028i	0.0671283	+	0.184433i
$852$	36.1428	−	3.32673i	1.23823	−	0.113972i
$853$	−34.7100	+	6.12032i	−1.18845	+	0.209556i	−0.732700	−	0.680552i	$-0.761740\pi$
$853$	−34.7100	+	6.12032i	−1.18845	+	0.209556i	−0.455750	+	0.890108i	$0.650629\pi$
$854$	3.39702	−	16.7480i	0.116244	−	0.573104i
$855$	−2.31752	+	13.8755i	−0.0792575	+	0.474532i
$856$	22.6753	+	39.2747i	0.775024	+	1.34238i
$857$	11.0923	−	9.30753i	0.378905	−	0.317939i	−0.433367	−	0.901217i	$-0.642675\pi$
$857$	11.0923	−	9.30753i	0.378905	−	0.317939i	0.812272	+	0.583278i	$0.198230\pi$
$858$	−0.0425744	+	0.513335i	−0.00145347	+	0.0175250i
$859$	25.8833	+	4.56392i	0.883125	+	0.155719i	0.596777	−	0.802407i	$-0.296448\pi$
$859$	25.8833	+	4.56392i	0.883125	+	0.155719i	0.286348	+	0.958126i	$0.407559\pi$
$860$	−2.35786	−	1.97848i	−0.0804025	−	0.0674657i
$861$	47.5447	+	23.4021i	1.62032	+	0.797540i
$862$	14.8236	+	5.39535i	0.504894	+	0.183766i
$863$			30.3370i			1.03269i	0.856382	+	0.516343i	$0.172707\pi$
$863$			30.3370i			1.03269i	−0.856382	+	0.516343i	$0.827293\pi$
$864$	24.4595	−	17.6257i	0.832131	−	0.599639i
$865$	6.25936			0.212824
$866$	15.8786	+	5.77935i	0.539578	+	0.196390i
$867$	26.9316	−	7.34690i	0.914644	−	0.249514i
$868$	−13.7059	+	34.8554i	−0.465210	+	1.18307i
$869$	−1.82428	−	0.321669i	−0.0618843	−	0.0109119i
$870$	2.63888	+	5.59298i	0.0894665	+	0.189620i
$871$	−8.58280	−	10.2286i	−0.290817	−	0.346582i
$872$	10.9935	−	6.34707i	0.372285	−	0.214939i
$873$	12.7187	+	4.49947i	0.430463	+	0.152284i
$874$	3.81906	+	2.20493i	0.129182	+	0.0745830i
$875$	−13.8663	−	25.5022i	−0.468765	−	0.862133i
$876$	9.83064	−	21.3330i	0.332146	−	0.720776i
$877$	9.84932	−	3.58486i	0.332588	−	0.121052i	−0.170328	−	0.985387i	$-0.554483\pi$
$877$	9.84932	−	3.58486i	0.332588	−	0.121052i	0.502916	+	0.864335i	$0.332261\pi$
$878$	−12.4602	+	4.53515i	−0.420512	+	0.153054i
$879$	−17.0752	+	12.0715i	−0.575931	+	0.407163i
$880$	0.403213	−	0.0710973i	0.0135923	−	0.00239669i
$881$	11.9814	−	20.7524i	0.403664	−	0.699166i	−0.590501	−	0.807037i	$-0.701070\pi$
$881$	11.9814	−	20.7524i	0.403664	−	0.699166i	0.994165	+	0.107871i	$0.0344033\pi$
$882$	−13.3263	−	5.49647i	−0.448719	−	0.185076i
$883$	−4.74787	−	8.22356i	−0.159779	−	0.276745i	0.775010	−	0.631949i	$-0.217745\pi$
$883$	−4.74787	−	8.22356i	−0.159779	−	0.276745i	−0.934789	+	0.355204i	$0.884411\pi$
$884$	−1.81956	−	2.16847i	−0.0611984	−	0.0729334i
$885$	13.0637	−	18.8375i	0.439130	−	0.633214i
$886$	−2.38701	+	13.5374i	−0.0801933	+	0.454799i
$887$	7.75777	+	6.50955i	0.260481	+	0.218569i	0.763670	−	0.645607i	$-0.223396\pi$
$887$	7.75777	+	6.50955i	0.260481	+	0.218569i	−0.503189	+	0.864176i	$0.667840\pi$
$888$	−12.7002	−	3.34157i	−0.426191	−	0.112136i
$889$	−2.53859	−	0.0649616i	−0.0851415	−	0.00217874i
$890$		−	6.34681i		−	0.212746i
$891$	1.29903	+	1.49248i	0.0435191	+	0.0500001i
$892$			27.7427i			0.928896i
$893$	8.12999	−	22.3370i	0.272060	−	0.747478i
$894$	4.60561	−	17.5044i	0.154035	−	0.585434i
$895$	13.6433	−	16.2594i	0.456044	−	0.543492i
$896$	−28.2188	+	4.23453i	−0.942725	+	0.141466i
$897$	3.55797	−	5.13050i	0.118797	−	0.171302i
$898$	6.34976	−	5.32808i	0.211894	−	0.177800i
$899$	−18.0360	−	31.2393i	−0.601535	−	1.04189i
$900$	−0.133360	−	14.7550i	−0.00444534	−	0.491833i
$901$	3.06836	+	1.77152i	0.102222	+	0.0590178i
$902$	−0.303038	−	1.71862i	−0.0100901	−	0.0572237i
$903$	−4.08178	+	5.57563i	−0.135833	+	0.185545i
$904$	−18.6654	+	6.79366i	−0.620803	+	0.225954i
$905$	2.54104	+	6.98145i	0.0844671	+	0.232071i
$906$	5.60893	−	12.1717i	0.186344	−	0.404377i
$907$	1.43669	+	8.14786i	0.0477044	+	0.270545i	0.999325	−	0.0367297i	$-0.0116940\pi$
$907$	1.43669	+	8.14786i	0.0477044	+	0.270545i	−0.951621	+	0.307275i	$0.900583\pi$
$908$	19.7687	−	34.2405i	0.656048	−	1.13631i
$909$	−2.89145	+	0.536830i	−0.0959033	+	0.0178055i
$910$	3.58084	+	3.16426i	0.118704	+	0.104894i
$911$	29.3546	+	34.9835i	0.972562	+	1.15905i	0.987252	+	0.159163i	$0.0508794\pi$
$911$	29.3546	+	34.9835i	0.972562	+	1.15905i	−0.0146900	+	0.999892i	$0.504676\pi$
$912$	7.67343	−	3.62048i	0.254093	−	0.119886i
$913$	3.72593	+	0.656981i	0.123310	+	0.0217429i
$914$	−7.86230	+	9.36992i	−0.260062	+	0.309929i
$915$	5.72696	+	20.9934i	0.189327	+	0.694019i
$916$	5.66902	−	15.5755i	0.187310	−	0.514629i
$917$	12.2748	−	4.11523i	0.405350	−	0.135897i
$918$	3.34234	+	0.246809i	0.110314	+	0.00814592i
$919$	30.8173			1.01657			0.508285	−	0.861189i	$-0.330280\pi$
$919$	30.8173			1.01657			0.508285	+	0.861189i	$0.330280\pi$
$920$	5.55936	+	2.02344i	0.183287	+	0.0667109i
$921$	−27.4778	+	27.7273i	−0.905424	+	0.913644i
$922$	−5.20909	+	6.20796i	−0.171552	+	0.204448i
$923$	−4.69047	+	26.6010i	−0.154389	+	0.875582i
$924$	−0.367212	−	1.49580i	−0.0120804	−	0.0492082i
$925$	−7.71426	+	6.47303i	−0.253643	+	0.212832i
$926$	4.48220	−	2.58780i	0.147294	−	0.0850403i
$927$	−30.9555	−	25.5015i	−1.01671	−	0.837580i
$928$	11.3014	−	19.5746i	0.370988	−	0.642569i
$929$	2.61616	+	14.8370i	0.0858334	+	0.486786i	0.997174	+	0.0751316i	$0.0239377\pi$
$929$	2.61616	+	14.8370i	0.0858334	+	0.486786i	−0.911340	+	0.411654i	$0.864951\pi$
$930$	1.34730	+	14.6376i	0.0441798	+	0.479985i
$931$	−20.6340	−	13.3649i	−0.676251	−	0.438017i
$932$	1.42608	+	3.91812i	0.0467127	+	0.128342i
$933$	−0.415940	−	4.51892i	−0.0136173	−	0.147943i
$934$	7.50069	−	1.32257i	0.245430	−	0.0432759i
$935$	0.238860	+	0.137906i	0.00781156	+	0.00451000i
$936$	5.01928	+	13.4119i	0.164060	+	0.438383i
$937$	3.52097	−	2.03283i	0.115025	−	0.0664097i	−0.441384	−	0.897318i	$-0.645512\pi$
$937$	3.52097	−	2.03283i	0.115025	−	0.0664097i	0.556409	+	0.830909i	$0.312179\pi$
$938$	−10.4963	−	6.42354i	−0.342716	−	0.209736i
$939$	0.829621	−	10.0030i	0.0270737	−	0.326437i
$940$	2.39908	−	13.6059i	0.0782495	−	0.443775i
$941$	7.66760	+	6.43388i	0.249957	+	0.209738i	0.759154	−	0.650912i	$-0.225613\pi$
$941$	7.66760	+	6.43388i	0.249957	+	0.209738i	−0.509197	+	0.860650i	$0.670058\pi$
$942$	−10.6244	−	10.5288i	−0.346161	−	0.343046i
$943$	−7.23464	+	19.8770i	−0.235592	+	0.647285i
$944$	−13.8262			−0.450003
$945$	18.3040	−	1.37978i	0.595428	−	0.0448844i
$946$	0.227560			0.00739863
$947$	−17.9748	+	49.3853i	−0.584102	+	1.60481i	0.197001	+	0.980403i	$0.436880\pi$
$947$	−17.9748	+	49.3853i	−0.584102	+	1.60481i	−0.781102	+	0.624403i	$0.785342\pi$
$948$	−21.5249	+	5.87195i	−0.699095	+	0.190712i
$949$	13.3910	+	11.2364i	0.434691	+	0.364749i
$950$	−1.34684	+	7.63833i	−0.0436974	+	0.247820i
$951$	−23.1802	+	10.9369i	−0.751670	+	0.354654i
$952$	−5.13630	−	3.14332i	−0.166468	−	0.101876i
$953$	40.6849	−	23.4895i	1.31791	−	0.760898i	0.334521	−	0.942388i	$-0.391425\pi$
$953$	40.6849	−	23.4895i	1.31791	−	0.760898i	0.983393	+	0.181490i	$0.0580920\pi$
$954$	−5.04496	−	5.90316i	−0.163337	−	0.191122i
$955$	−2.11864	−	1.22320i	−0.0685575	−	0.0395817i
$956$	−45.5714	+	8.03546i	−1.47388	+	0.259885i
$957$	1.34725	+	0.620835i	0.0435503	+	0.0200687i
$958$	0.105623	+	0.290197i	0.00341253	+	0.00937585i
$959$	−19.1792	−	24.0821i	−0.619328	−	0.777651i
$960$	−2.25316	+	1.59290i	−0.0727204	+	0.0514107i
$961$	−9.50550	−	53.9084i	−0.306629	−	1.73898i
$962$	2.11705	−	3.66684i	0.0682565	−	0.118224i
$963$	−27.6422	+	48.8929i	−0.890757	+	1.57555i
$964$	32.4832	−	18.7542i	1.04621	−	0.604031i
$965$	0.118755	−	0.0996476i	0.00382287	−	0.00320777i
$966$	1.60601	−	5.52544i	0.0516726	−	0.177778i
$967$	1.24818	−	7.07876i	0.0401386	−	0.227638i	−0.958139	−	0.286303i	$-0.907574\pi$
$967$	1.24818	−	7.07876i	0.0401386	−	0.227638i	0.998278	+	0.0586658i	$0.0186846\pi$
$968$	17.0521	−	20.3219i	0.548076	−	0.653172i
$969$	5.52750	+	1.45435i	0.177569	+	0.0467204i
$970$	−3.87312	−	1.40970i	−0.124359	−	0.0452628i
$971$	−13.7938			−0.442663			−0.221331	−	0.975199i	$-0.571040\pi$
$971$	−13.7938			−0.442663			−0.221331	+	0.975199i	$0.571040\pi$
$972$	21.8208	+	9.58111i	0.699902	+	0.307314i
$973$	−7.72605	−	23.0451i	−0.247686	−	0.738791i
$974$	5.72100	−	15.7183i	0.183313	−	0.503648i
$975$	10.6197	+	2.79418i	0.340104	+	0.0894853i
$976$	8.43622	−	10.0539i	0.270037	−	0.321817i
$977$	−12.3023	−	2.16922i	−0.393584	−	0.0693996i	−0.0266464	−	0.999645i	$-0.508483\pi$
$977$	−12.3023	−	2.16922i	−0.393584	−	0.0693996i	−0.366938	+	0.930245i	$0.619594\pi$
$978$	−15.1392	−	10.4989i	−0.484097	−	0.335718i
$979$	−0.978581	−	1.16623i	−0.0312756	−	0.0372728i
$980$	−13.1594	−	5.56736i	−0.420363	−	0.177843i
$981$	13.6857	+	7.73738i	0.436951	+	0.247035i
$982$	−4.41271	+	7.64304i	−0.140815	+	0.243899i
$983$	5.29506	+	30.0298i	0.168886	+	0.957801i	0.944967	+	0.327167i	$0.106094\pi$
$983$	5.29506	+	30.0298i	0.168886	+	0.957801i	−0.776081	+	0.630634i	$0.782795\pi$
$984$	−28.0074	−	39.6165i	−0.892844	−	1.26293i
$985$	7.14405	+	19.6281i	0.227628	+	0.625404i
$986$	2.36110	−	0.859371i	0.0751928	−	0.0273679i
$987$	−30.8345	−	3.35348i	−0.981474	−	0.106742i
$988$	1.83730	+	10.4198i	0.0584523	+	0.331500i
$989$	−2.38872	−	1.37913i	−0.0759569	−	0.0438537i
$990$	−0.392731	−	0.459538i	−0.0124818	−	0.0146051i
$991$	−26.4504	−	45.8134i	−0.840224	−	1.45531i	−0.889705	−	0.456536i	$-0.849090\pi$
$991$	−26.4504	−	45.8134i	−0.840224	−	1.45531i	0.0494806	−	0.998775i	$-0.484243\pi$
$992$	41.1557	−	34.5337i	1.30670	−	1.09645i
$993$	−7.60148	−	16.1110i	−0.241226	−	0.511266i
$994$	3.69425	+	24.6185i	0.117175	+	0.780850i
$995$	8.25869	−	9.84233i	0.261818	−	0.312023i
$996$	43.9627	−	11.9930i	1.39301	−	0.380011i
$997$	12.3634	−	33.9682i	0.391553	−	1.07578i	−0.574740	−	0.818336i	$-0.694897\pi$
$997$	12.3634	−	33.9682i	0.391553	−	1.07578i	0.966293	−	0.257446i	$-0.0828811\pi$
$998$			20.2352i			0.640534i
$999$	−4.42211	−	15.6516i	−0.139909	−	0.495196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.104.10	yes	132
3.2	odd	2		567.2.be.a.503.13		132
7.6	odd	2	inner	189.2.be.a.104.9	yes	132
21.20	even	2		567.2.be.a.503.14		132
27.7	even	9		567.2.be.a.62.14		132
27.20	odd	18	inner	189.2.be.a.20.9	✓	132
189.20	even	18	inner	189.2.be.a.20.10	yes	132
189.34	odd	18		567.2.be.a.62.13		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.9	✓	132	27.20	odd	18	inner
189.2.be.a.20.10	yes	132	189.20	even	18	inner
189.2.be.a.104.9	yes	132	7.6	odd	2	inner
189.2.be.a.104.10	yes	132	1.1	even	1	trivial
567.2.be.a.62.13		132	189.34	odd	18
567.2.be.a.62.14		132	27.7	even	9
567.2.be.a.503.13		132	3.2	odd	2
567.2.be.a.503.14		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+(-0.234777 + 0.645045i) q^{2} +(0.440723 - 1.67504i) q^{3} +(1.17113 + 0.982692i) q^{4} +(0.231854 - 1.31491i) q^{5} +(0.977005 + 0.677547i) q^{6} +(1.38106 - 2.25670i) q^{7} +(-2.09779 + 1.21116i) q^{8} +(-2.61153 - 1.47646i) q^{9} +(0.793741 + 0.458267i) q^{10} +(0.216508 - 0.0381762i) q^{11} +(2.16219 - 1.52859i) q^{12} +(0.673991 + 1.85178i) q^{13} +(1.13143 + 1.42066i) q^{14} +(-2.10034 - 0.967875i) q^{15} +(0.242207 + 1.37362i) q^{16} +(-0.469803 + 0.813723i) q^{17} +(1.56551 - 1.33791i) q^{18} +(3.04150 - 1.75601i) q^{19} +(1.56368 - 1.31208i) q^{20} +(-3.17140 - 3.30790i) q^{21} +(-0.0262057 + 0.148620i) q^{22} +(1.17579 - 1.40126i) q^{23} +(1.10420 + 4.04766i) q^{24} +(3.02323 + 1.10037i) q^{25} -1.35272 q^{26} +(-3.62409 + 3.72371i) q^{27} +(3.83503 - 1.28572i) q^{28} +(-1.33239 + 3.66070i) q^{29} +(1.11744 - 1.12758i) q^{30} +(-5.95195 + 7.09326i) q^{31} +(-5.71394 - 1.00752i) q^{32} +(0.0314733 - 0.379485i) q^{33} +(-0.414589 - 0.494088i) q^{34} +(-2.64715 - 2.33919i) q^{35} +(-1.60753 - 4.29544i) q^{36} +(-1.56504 + 2.71072i) q^{37} +(0.418631 + 2.37418i) q^{38} +(3.39885 - 0.312844i) q^{39} +(1.10618 + 3.03921i) q^{40} +(-10.8664 + 3.95506i) q^{41} +(2.87832 - 1.26907i) q^{42} +(-0.261843 - 1.48498i) q^{43} +(0.291074 + 0.168051i) q^{44} +(-2.54690 + 3.09160i) q^{45} +(0.627824 + 1.08742i) q^{46} +(5.18484 - 4.35059i) q^{47} +(2.40762 + 0.199681i) q^{48} +(-3.18536 - 6.23325i) q^{49} +(-1.41957 + 1.69178i) q^{50} +(1.15597 + 1.14557i) q^{51} +(-1.03040 + 2.83099i) q^{52} -3.77077i q^{53} +(-1.55111 - 3.21194i) q^{54} -0.293540i q^{55} +(-0.163947 + 6.40675i) q^{56} +(-1.60093 - 5.86856i) q^{57} +(-2.04850 - 1.71890i) q^{58} +(-1.72130 + 9.76195i) q^{59} +(-1.50865 - 3.19750i) q^{60} +(-6.04827 - 7.20805i) q^{61} +(-3.17809 - 5.50461i) q^{62} +(-6.93858 + 3.85435i) q^{63} +(0.596586 - 1.03332i) q^{64} +(2.59119 - 0.456896i) q^{65} +(0.237395 + 0.109396i) q^{66} +(-6.36714 + 2.31745i) q^{67} +(-1.34984 + 0.491301i) q^{68} +(-1.82897 - 2.58707i) q^{69} +(2.13037 - 1.15834i) q^{70} +(11.8706 + 6.85351i) q^{71} +(7.26665 - 0.0656782i) q^{72} +(7.68223 - 4.43534i) q^{73} +(-1.38110 - 1.64593i) q^{74} +(3.17557 - 4.57908i) q^{75} +(5.28760 + 0.932347i) q^{76} +(0.212858 - 0.541316i) q^{77} +(-0.596173 + 2.26586i) q^{78} +(-7.91776 - 2.88183i) q^{79} +1.86235 q^{80} +(4.64015 + 7.71162i) q^{81} -7.93789i q^{82} +(16.1714 + 5.88589i) q^{83} +(-0.463457 - 6.99048i) q^{84} +(0.961047 + 0.806414i) q^{85} +(1.01936 + 0.179740i) q^{86} +(5.54462 + 3.84516i) q^{87} +(-0.407950 + 0.342311i) q^{88} +(-3.46240 - 5.99705i) q^{89} +(-1.39627 - 2.36870i) q^{90} +(5.10972 + 1.03641i) q^{91} +(2.75401 - 0.485606i) q^{92} +(9.25834 + 13.0959i) q^{93} +(1.58905 + 4.36587i) q^{94} +(-1.60381 - 4.40644i) q^{95} +(-4.20591 + 9.12705i) q^{96} +(-4.42872 + 0.780904i) q^{97} +(4.76858 - 0.591277i) q^{98} +(-0.621782 - 0.219967i) 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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