LMFDB - Embedded newform 189.2.be.a.104.9

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			104.9
Character	$\chi$	$=$	189.104
Dual form			189.2.be.a.20.9

$q$-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} +(2.46223 - 0.968204i) 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} +(0.0464596 + 1.81556i) 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} +(0.536621 + 4.55105i) 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} +(0.702223 + 3.46209i) 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} +(-3.06162 - 0.722337i) 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} +(5.12516 - 4.76788i) 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} +(-3.99259 + 5.01324i) 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} +(-7.85969 - 1.10689i) 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} +(-2.39807 - 0.359855i) 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} +(0.496130 - 0.303622i) 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} +(-3.84383 + 5.85719i) 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} +(-3.45242 - 3.90694i) 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} +(1.87223 + 4.42535i) 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	$0.152061\pi$
$5$	−0.231854	+	1.31491i	−0.103688	+	0.588045i	−0.991736	+	0.128294i	$0.959050\pi$
$6$	−0.977005	−	0.677547i	−0.398861	−	0.276607i
$7$	2.46223	−	0.968204i	0.930636	−	0.365947i
$7$	2.46223	−	0.968204i	0.930636	−	0.365947i
$8$	−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	0.810458	−	0.585797i	$-0.199218\pi$
$13$	−0.673991	−	1.85178i	−0.186932	−	0.513590i	−0.997390	+	0.0722062i	$0.976996\pi$
$14$	0.0464596	+	1.81556i	0.0124169	+	0.485229i
$15$	−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	−0.803413	−	0.595422i	$-0.796985\pi$
$17$	0.469803	−	0.813723i	0.113944	−	0.197357i	0.917357	+	0.398065i	$0.130318\pi$
$18$	1.56551	−	1.33791i	0.368994	−	0.315349i
$19$	−3.04150	+	1.75601i	−0.697768	+	0.402857i	−0.806516	−	0.591213i	$-0.798649\pi$
$19$	−3.04150	+	1.75601i	−0.697768	+	0.402857i	0.108747	+	0.994069i	$0.465316\pi$
$20$	−1.56368	+	1.31208i	−0.349650	+	0.293391i
$21$	0.536621	+	4.55105i	0.117100	+	0.993120i
$22$	−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	$-0.465240\pi$
$31$	5.95195	−	7.09326i	1.06900	−	1.27399i	0.960017	−	0.279943i	$-0.0903156\pi$
$32$	−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
$35$	0.702223	+	3.46209i	0.118697	+	0.585200i
$36$	−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	0.701567	−	0.712603i	$-0.252484\pi$
$41$	10.8664	−	3.95506i	1.69705	−	0.617676i	0.995484	+	0.0949267i	$0.0302617\pi$
$42$	−3.06162	−	0.722337i	−0.472418	−	0.111459i
$43$	−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	−0.937157	−	0.348907i	$-0.886553\pi$
$47$	−5.18484	+	4.35059i	−0.756286	+	0.634599i	0.180871	+	0.983507i	$0.442108\pi$
$48$	−2.40762	−	0.199681i	−0.347510	−	0.0288214i
$49$	5.12516	−	4.76788i	0.732166	−	0.681126i
$50$	−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
$56$	−3.99259	+	5.01324i	−0.533532	+	0.669922i
$57$	−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	$-0.721197\pi$
$59$	1.72130	−	9.76195i	0.224094	−	1.27090i	0.864410	−	0.502787i	$-0.167692\pi$
$60$	−1.50865	−	3.19750i	−0.194765	−	0.412795i
$61$	6.04827	+	7.20805i	0.774402	+	0.922896i	0.998666	−	0.0516319i	$-0.0164423\pi$
$61$	6.04827	+	7.20805i	0.774402	+	0.922896i	−0.224264	+	0.974528i	$0.571998\pi$
$62$	3.17809	+	5.50461i	0.403617	+	0.699086i
$63$	−7.85969	−	1.10689i	−0.990228	−	0.139455i
$64$	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
$70$	−2.39807	−	0.359855i	−0.286624	−	0.0430109i
$71$	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	−0.876920	−	0.480636i	$-0.840406\pi$
$73$	−7.68223	+	4.43534i	−0.899137	+	0.519117i	−0.0222170	+	0.999753i	$0.507072\pi$
$74$	−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
$77$	0.496130	−	0.303622i	0.0565393	−	0.0346010i
$78$	−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	$-0.995458\pi$
$83$	−16.1714	−	5.88589i	−1.77504	−	0.646061i	−0.775139	−	0.631791i	$-0.782320\pi$
$84$	−3.84383	+	5.85719i	−0.419396	+	0.639071i
$85$	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	0.989097	−	0.147265i	$-0.0470469\pi$
$89$	3.46240	+	5.99705i	0.367014	+	0.635686i	−0.622084	+	0.782951i	$0.713714\pi$
$90$	1.39627	+	2.36870i	0.147179	+	0.249683i
$91$	−3.45242	−	3.90694i	−0.361912	−	0.409559i
$92$	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	0.0557722	−	0.998444i	$-0.482238\pi$
$97$	4.42872	−	0.780904i	0.449669	−	0.0792887i	0.393897	+	0.919155i	$0.371127\pi$
$98$	1.87223	+	4.42535i	0.189124	+	0.447028i
$99$	−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	−0.679384	−	0.733783i	$-0.737753\pi$
$101$	−0.750944	+	0.630116i	−0.0747217	+	0.0626989i	0.604662	+	0.796482i	$0.293308\pi$
$102$	−1.01034	+	0.476698i	−0.100038	+	0.0472001i
$103$	−13.1659	−	2.32150i	−1.29727	−	0.228744i	−0.517974	−	0.855396i	$-0.673314\pi$
$103$	−13.1659	−	2.32150i	−1.29727	−	0.228744i	−0.779299	+	0.626652i	$0.784425\pi$
$104$	3.65668	+	3.06832i	0.358567	+	0.300874i
$105$	−6.10863	−	0.349571i	−0.596142	−	0.0341146i
$106$	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
$112$	1.92632	+	3.14767i	0.182020	+	0.297427i
$113$	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
$119$	0.368914	−	2.45844i	0.0338183	−	0.225365i
$120$	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
$126$	2.55927	−	4.80998i	0.227998	−	0.428507i
$127$	−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	0.464179	−	0.885741i	$-0.346349\pi$
$131$	−3.74843	−	3.14531i	−0.327502	−	0.274807i	−0.791681	+	0.610935i	$0.790794\pi$
$132$	−0.409776	+	0.413496i	−0.0356664	+	0.0359902i
$133$	−5.78870	+	7.26850i	−0.501944	+	0.630259i
$134$		−	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	−0.955946	−	0.293544i	$-0.905165\pi$
$139$	−5.90509	+	7.03742i	−0.500864	+	0.596906i	0.455082	+	0.890449i	$0.349610\pi$
$140$	−2.57978	+	4.74462i	−0.218031	+	0.400993i
$141$	−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
$147$	5.72763	+	10.6862i	0.472407	+	0.881381i
$148$	−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
$154$	0.0793701	+	0.391310i	0.00639582	+	0.0315326i
$155$	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	0.644573	−	0.764543i	$-0.277035\pi$
$157$	12.3894	+	2.18459i	0.988784	+	0.174349i	0.344211	+	0.938892i	$0.388146\pi$
$158$	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	$-0.614852\pi$
$167$	3.86013	−	21.8919i	0.298706	−	1.69405i	0.651746	−	0.758437i	$-0.274037\pi$
$168$	−6.63775	−	8.89720i	−0.512114	−	0.686434i
$169$	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	$-0.998525\pi$
$173$	−0.814058	−	4.61675i	−0.0618917	−	0.351005i	0.938098	−	0.346371i	$-0.112586\pi$
$174$	3.78205	−	2.67377i	0.286716	−	0.202698i
$175$	8.50928	−	0.217750i	0.643241	−	0.0164603i
$176$	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	−0.310100	−	0.950704i	$-0.600362\pi$
$181$	4.81888	−	2.78218i	0.358185	−	0.206798i	0.668284	+	0.743906i	$0.267029\pi$
$182$	3.33070	−	1.30971i	0.246888	−	0.0970818i
$183$	−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
$189$	5.31803	−	12.6775i	0.386830	−	0.922151i
$190$	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
$196$	10.6876	−	0.547341i	0.763398	−	0.0390958i
$197$	−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	0.174644	−	0.984632i	$-0.444122\pi$
$199$	−8.33355	−	4.81138i	−0.590750	−	0.341069i	−0.765394	+	0.643562i	$0.777456\pi$
$200$	−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
$203$	0.263664	+	10.3035i	0.0185056	+	0.723166i
$204$	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
$210$	1.65966	−	3.85827i	0.114527	−	0.266246i
$211$	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	0.217869	−	0.975978i	$-0.430090\pi$
$223$	−11.6645	−	13.9012i	−0.781115	−	0.930896i	−0.998983	+	0.0450820i	$0.985645\pi$
$224$	−15.0445	+	3.05151i	−1.00521	+	0.203888i
$225$	−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	$0.272895\pi$
$227$	4.49086	+	25.4689i	0.298069	+	1.69043i	−0.356393	+	0.934336i	$0.615994\pi$
$228$	3.89209	−	8.44604i	0.257760	−	0.559353i
$229$	3.70816	+	10.1881i	0.245042	+	0.673247i	0.999850	+	0.0173016i	$0.00550755\pi$
$229$	3.70816	+	10.1881i	0.245042	+	0.673247i	−0.754809	+	0.655945i	$0.772270\pi$
$230$	−1.57543	+	0.573409i	−0.103881	+	0.0378094i
$231$	0.289924	+	0.964852i	0.0190756	+	0.0634826i
$232$	−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
$238$	1.49919	+	0.815151i	0.0971781	+	0.0528384i
$239$	−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	$0.401137\pi$
$241$	−8.39131	+	23.0549i	−0.540531	+	1.48510i	−0.846150	+	0.532944i	$0.821086\pi$
$242$		−	7.51769i		−	0.483255i
$243$	−14.9623	+	4.37375i	−0.959832	+	0.280576i
$244$			14.3851i			0.920914i
$245$	5.08105	+	7.84458i	0.324616	+	0.501172i
$246$	−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	$0.108826\pi$
$251$	12.0630	+	20.8937i	0.761409	+	1.31880i	−0.180715	+	0.983536i	$0.557841\pi$
$252$	−8.11697	−	9.01996i	−0.511321	−	0.568204i
$253$	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	−0.662392	−	0.749157i	$-0.730459\pi$
$257$	−11.0337	+	4.01595i	−0.688265	+	0.250508i	−0.0258727	+	0.999665i	$0.508236\pi$
$258$	−0.750325	+	1.62825i	−0.0467132	+	0.101370i
$259$	−1.22895	+	8.18970i	−0.0763631	+	0.508883i
$260$	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
$266$	−3.32945	−	5.44045i	−0.204142	−	0.333575i
$267$	−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	$-0.674859\pi$
$269$	−17.1269			−1.04424			−0.522122	+	0.852871i	$0.674859\pi$
$270$	−4.58304	+	1.29486i	−0.278915	+	0.0788028i
$271$		−	16.5484i		−	1.00525i	−0.864506	−	0.502623i	$-0.832368\pi$
$271$		−	16.5484i		−	1.00525i	0.864506	−	0.502623i	$-0.167632\pi$
$272$	1.23154	+	0.448244i	0.0746730	+	0.0271788i
$273$	8.06584	−	4.06107i	0.488167	−	0.245787i
$274$	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
$280$	−5.66625	−	6.41223i	−0.338623	−	0.383204i
$281$	−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	$0.0246743\pi$
$283$	4.76130	+	13.0816i	0.283030	+	0.777618i	−0.713967	+	0.700179i	$0.753103\pi$
$284$	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
$287$	22.9264	−	20.2592i	1.35330	−	1.19586i
$288$	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	0.871643	−	0.490141i	$-0.163055\pi$
$293$	9.24858	+	7.76048i	0.540308	+	0.453372i	−0.331335	+	0.943513i	$0.607499\pi$
$294$	−8.23778	+	1.18571i	−0.480437	+	0.0691519i
$295$	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
$301$	−2.08249	−	3.40286i	−0.120032	−	0.196137i
$302$	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	0.939852	−	0.341583i	$-0.110963\pi$
$307$	19.5181	+	11.2688i	1.11396	+	0.643144i	0.174107	+	0.984727i	$0.444296\pi$
$308$	0.879398	+	0.131963i	0.0501084	+	0.00751927i
$309$	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	−0.410879	−	0.911690i	$-0.634778\pi$
$311$	−2.46202	+	0.896103i	−0.139608	+	0.0508133i	0.271271	+	0.962503i	$0.412556\pi$
$312$	−6.75115	+	4.77282i	−0.382209	+	0.270208i
$313$	−5.70705	+	1.00631i	−0.322582	+	0.0568798i	−0.332594	−	0.943070i	$-0.607924\pi$
$313$	−5.70705	+	1.00631i	−0.322582	+	0.0568798i	0.0100126	+	0.999950i	$0.496813\pi$
$314$	−4.31791	+	7.47885i	−0.243674	+	0.422056i
$315$	3.27776	−	10.0782i	0.184681	−	0.567839i
$316$	−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
$322$	2.59870	+	2.06963i	0.144820	+	0.115336i
$323$			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
$329$	−8.55400	+	15.7321i	−0.471597	+	0.867341i
$330$	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
$336$	−6.12145	+	1.83941i	−0.333953	+	0.100348i
$337$	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
$343$	8.00305	−	16.7018i	0.432124	−	0.901814i
$344$	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	$-0.589674\pi$
$349$	10.3198	−	28.3535i	0.552407	−	1.51773i	0.830414	−	0.557147i	$-0.188104\pi$
$350$	−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	0.670748	−	0.741685i	$-0.265973\pi$
$353$	13.2988	+	4.84037i	0.707824	+	0.257627i	0.0370764	+	0.999312i	$0.488196\pi$
$354$	−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
$357$	3.95540	+	1.70144i	0.209342	+	0.0900496i
$358$	−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
$364$	−0.203903	−	7.96818i	−0.0106874	−	0.417646i
$365$	−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	−0.607895	−	0.794017i	$-0.707986\pi$
$367$	−17.3863	+	3.06568i	−0.907559	+	0.160027i	−0.299664	+	0.954045i	$0.596875\pi$
$368$	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
$371$	−3.65087	−	9.28449i	−0.189544	−	0.482027i
$372$	−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
$378$	6.92899	+	6.40675i	0.356389	+	0.329528i
$379$	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	−0.989551	−	0.144181i	$-0.953945\pi$
$383$	−0.202834	+	1.15033i	−0.0103643	+	0.0587790i	0.979187	+	0.202960i	$0.0650563\pi$
$384$	16.8943	−	7.97111i	0.862136	−	0.406774i
$385$	0.284206	+	0.722762i	0.0144845	+	0.0368354i
$386$	−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
$392$	−4.97684	+	16.2094i	−0.251368	+	0.818698i
$393$	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	−0.134259	−	0.990946i	$-0.542865\pi$
$397$	13.0866	−	7.55554i	0.656797	−	0.379202i	0.791055	+	0.611745i	$0.209532\pi$
$398$	5.06008	−	4.24591i	0.253639	−	0.212828i
$399$	−9.62383	−	12.8997i	−0.481794	−	0.645793i
$400$	−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	−0.246312	−	0.969191i	$-0.579219\pi$
$409$	15.1865	−	18.0986i	0.750926	−	0.894919i	0.997238	+	0.0742715i	$0.0236631\pi$
$410$	−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
$413$	−5.21334	−	25.7027i	−0.256532	−	1.26475i
$414$	−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	0.190596	−	0.981669i	$-0.438958\pi$
$419$	19.8064	−	7.20893i	0.967605	−	0.352179i	0.777009	+	0.629489i	$0.216736\pi$
$420$	−6.81046	−	6.41230i	−0.332317	−	0.312888i
$421$	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
$427$	21.8711	+	11.8919i	1.05842	+	0.575491i
$428$	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	$0.201461\pi$
$433$			24.6163i			1.18299i	−0.806310	+	0.591493i	$0.798539\pi$
$434$	13.1548	+	10.4766i	0.631449	+	0.502892i
$435$	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	0.383493	−	0.923544i	$-0.374721\pi$
$439$	−12.4166	−	14.7975i	−0.592613	−	0.706248i	−0.976106	+	0.217296i	$0.930276\pi$
$440$	−0.355523	−	0.615783i	−0.0169489	−	0.0293563i
$441$	−20.4241	+	4.88438i	−0.972575	+	0.232589i
$442$	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
$448$	0.468471	−	3.12188i	0.0221332	−	0.147495i
$449$	−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
$455$	5.93773	−	3.63378i	0.278365	−	0.170354i
$456$	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	0.0704983	−	0.997512i	$-0.477541\pi$
$461$	−11.0937	−	4.03778i	−0.516685	−	0.188058i	−0.587183	+	0.809454i	$0.699763\pi$
$462$	−0.690440	−	0.0395109i	−0.0321222	−	0.00183821i
$463$	−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	0.965361	−	0.260918i	$-0.0840253\pi$
$467$	5.54773	+	9.60896i	0.256719	+	0.444650i	−0.708642	+	0.705568i	$0.750692\pi$
$468$	−6.87074	+	5.87187i	−0.317600	+	0.271427i
$469$	−13.4336	+	11.8708i	−0.620307	+	0.548142i
$470$	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
$476$	2.84793	−	2.51662i	0.130535	−	0.115349i
$477$	−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	−0.650627	−	0.759397i	$-0.725494\pi$
$479$	−0.344634	+	0.289182i	−0.0157467	+	0.0132131i	0.634880	+	0.772611i	$0.281049\pi$
$480$	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
$483$	7.00815	+	4.59915i	0.318882	+	0.209269i
$484$	−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
$490$	−6.25302	+	1.43578i	−0.282482	+	0.0648617i
$491$	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
$497$	35.8638	+	5.38174i	1.60871	+	0.241404i
$498$	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	−0.974979	−	0.222298i	$-0.928644\pi$
$503$	−6.61558	+	11.4585i	−0.294974	+	0.510910i	0.680005	+	0.733208i	$0.261978\pi$
$504$	17.8286	−	7.19732i	0.794148	−	0.320594i
$505$	−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	0.849823	−	0.527069i	$-0.176709\pi$
$509$	10.7916	+	9.05526i	0.478331	+	0.401367i	−0.371491	+	0.928436i	$0.621153\pi$
$510$	−0.392564	−	1.43902i	−0.0173830	−	0.0637211i
$511$	−14.6211	+	18.3588i	−0.646800	+	0.812145i
$512$		−	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
$518$	−4.99420	−	2.71548i	−0.219432	−	0.119311i
$519$	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	0.764029	−	0.645182i	$-0.223219\pi$
$521$	−4.03394	−	6.98699i	−0.176730	−	0.306105i	−0.940759	+	0.339077i	$0.889885\pi$
$522$	2.81184	+	7.51348i	0.123071	+	0.328856i
$523$	10.5643	+	6.09931i	0.461945	+	0.266704i	0.712862	−	0.701305i	$-0.247399\pi$
$523$	10.5643	+	6.09931i	0.461945	+	0.266704i	−0.250917	+	0.968009i	$0.580732\pi$
$524$	−1.29902	−	7.36711i	−0.0567479	−	0.321833i
$525$	−3.38549	+	14.3494i	−0.147755	+	0.626257i
$526$	−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
$532$	−13.9220	+	2.82382i	−0.603595	+	0.122428i
$533$	−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
$546$	0.725896	+	6.15628i	0.0310655	+	0.263464i
$547$	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
$553$	−22.2856	+	0.570280i	−0.947678	+	0.0242508i
$554$	−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
$560$	−4.58553	+	1.80313i	−0.193774	+	0.0761963i
$561$	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	0.496653	−	0.867949i	$-0.334562\pi$
$563$	−6.45074	−	5.41282i	−0.271866	−	0.228123i	−0.768520	+	0.639826i	$0.779006\pi$
$564$	4.56033	−	17.3323i	0.192025	−	0.729822i
$565$	−3.74471	+	10.2885i	−0.157541	+	0.432840i
$566$	−9.55604			−0.401670
$567$	18.8915	+	14.4952i	0.793370	+	0.608740i
$568$	−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
$574$	7.68550	+	19.5449i	0.320787	+	0.815789i
$575$	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	−0.397405	−	0.917643i	$-0.630089\pi$
$577$	−33.4084	−	19.2884i	−1.39081	−	0.802985i	−0.993405	+	0.114658i	$0.963423\pi$
$578$	−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
$581$	−45.5164	+	1.16475i	−1.88834	+	0.0483219i
$582$	−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	−0.995869	−	0.0907969i	$-0.971059\pi$
$587$	−26.1514	+	21.9436i	−1.07938	+	0.905710i	−0.0835134	+	0.996507i	$0.526614\pi$
$588$	−3.79344	+	18.1434i	−0.156439	+	0.748219i
$589$	−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	$-0.543754\pi$
$593$	−6.67349			−0.274048			−0.137024	+	0.990568i	$0.543754\pi$
$594$	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	0.961451	−	0.274975i	$-0.0886696\pi$
$601$	12.8387	+	15.3005i	0.523699	+	0.624121i	−0.437752	+	0.899096i	$0.644225\pi$
$602$	2.68392	−	0.544384i	0.109388	−	0.0221874i
$603$	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	$0.121919\pi$
$607$	11.2649	+	30.9501i	0.457228	+	1.25622i	−0.470312	+	0.882500i	$0.655859\pi$
$608$	19.1482	−	6.96937i	0.776562	−	0.282645i
$609$	−17.3750	−	4.09935i	−0.704072	−	0.166114i
$610$	−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
$616$	−0.673040	+	1.23783i	−0.0271176	+	0.0498735i
$617$	−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	−0.960669	−	0.277695i	$-0.910430\pi$
$619$	−1.15081	+	3.16183i	−0.0462550	+	0.127085i	0.914414	+	0.404780i	$0.132652\pi$
$620$			18.9011i			0.759084i
$621$	−0.956691	−	9.45660i	−0.0383907	−	0.379480i
$622$		−	1.79850i		−	0.0721132i
$623$	14.3316	+	11.4138i	0.574183	+	0.457285i
$624$	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
$630$	5.73132	+	4.48042i	0.228341	+	0.178504i
$631$	−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
$637$	−12.2834	−	6.27714i	−0.486685	−	0.248709i
$638$	−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	−0.510160	−	0.860080i	$-0.670414\pi$
$643$	−32.5518	−	5.73976i	−1.28372	−	0.226354i	−0.773558	+	0.633726i	$0.781525\pi$
$644$	6.31084	−	3.86212i	0.248682	−	0.152189i
$645$	−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	$-0.352818\pi$
$647$	22.6934			0.892168			0.446084	+	0.894991i	$0.352818\pi$
$648$	−19.0740	−	10.5574i	−0.749298	−	0.414733i
$649$		−	2.17925i		−	0.0855431i
$650$	4.08958	+	1.48848i	0.160406	+	0.0583831i
$651$	35.4757	+	23.2812i	1.39040	+	0.912463i
$652$	−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
$658$	−8.13966	−	9.21126i	−0.317317	−	0.359092i
$659$	−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	$-0.802766\pi$
$661$	−14.4940	−	39.8218i	−0.563750	−	1.54889i	0.250344	−	0.968157i	$-0.419456\pi$
$662$	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
$665$	−8.21529	−	9.29685i	−0.318575	−	0.360516i
$666$	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
$672$	1.51906	−	26.5451i	0.0585991	−	1.02400i
$673$	−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	0.426478	−	0.904498i	$-0.359754\pi$
$677$	4.46954	+	1.62678i	0.171778	+	0.0625222i	−0.254699	+	0.967020i	$0.581976\pi$
$678$	−6.92508	−	6.86278i	−0.265956	−	0.263563i
$679$	10.1485	−	6.21067i	0.389462	−	0.238344i
$680$	−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
$686$	8.89450	+	9.08353i	0.339594	+	0.346811i
$687$	−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	−0.0413322	−	0.999145i	$-0.513160\pi$
$691$	6.87549	−	1.21234i	0.261556	−	0.0461194i	0.302888	+	0.953026i	$0.402049\pi$
$692$	3.58348	−	6.20677i	0.136223	−	0.235946i
$693$	−1.74394	+	0.0604032i	−0.0662469	+	0.00229453i
$694$	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
$700$	10.1794	+	8.10698i	0.384746	+	0.306415i
$701$			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
$707$	−1.23892	+	2.27856i	−0.0465942	+	0.0856940i
$708$	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
$714$	−2.02614	+	2.15195i	−0.0758264	+	0.0805348i
$715$	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	$0.402327\pi$
$719$	−18.0874	+	31.3282i	−0.674545	+	1.16835i	−0.976602	+	0.215057i	$0.931006\pi$
$720$	4.86357	+	2.74968i	0.181255	+	0.102474i
$721$	−34.6651	+	7.03119i	−1.29100	+	0.261855i
$722$	−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	$-0.766718\pi$
$727$	6.90637	−	18.9751i	0.256143	−	0.703748i	0.999396	−	0.0347375i	$-0.0110595\pi$
$728$	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	−0.749781	−	0.661686i	$-0.769841\pi$
$733$	0.867738	−	1.03413i	0.0320506	−	0.0381965i	0.781832	+	0.623490i	$0.214286\pi$
$734$	2.10441	−	11.9347i	0.0776753	−	0.440518i
$735$	−15.3793	+	5.05368i	−0.567275	+	0.186408i
$736$	−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
$742$	6.84606	−	0.175188i	0.251327	−	0.00643136i
$743$	−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
$749$	−18.1267	−	46.0978i	−0.662335	−	1.68438i
$750$	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
$756$	18.6861	−	9.62095i	0.679608	−	0.349911i
$757$	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	$-0.777491\pi$
$761$	4.79778	−	27.2096i	0.173919	−	0.986346i	0.939384	−	0.342867i	$-0.111398\pi$
$762$	−0.0943211	+	1.13726i	−0.00341689	+	0.0411987i
$763$	−12.9033	+	5.07388i	−0.467132	+	0.183687i
$764$	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	$-0.848712\pi$
$769$	−13.9253	−	38.2594i	−0.502159	−	1.37967i	0.387004	−	0.922078i	$-0.373510\pi$
$770$	−0.532939	+	0.0136377i	−0.0192058	+	0.000491470i
$771$	−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	−0.990943	−	0.134286i	$-0.957126\pi$
$773$	−10.5422	+	18.2596i	−0.379176	+	0.656752i	0.611767	+	0.791038i	$0.290459\pi$
$774$	−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
$777$	−13.1765	−	5.66793i	−0.472703	−	0.203336i
$778$	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	−0.564399	−	0.825502i	$-0.690892\pi$
$787$	9.72249	−	11.5868i	0.346569	−	0.413025i	0.910968	+	0.412477i	$0.135336\pi$
$788$	−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
$791$	21.2626	−	4.31273i	0.756010	−	0.153343i
$792$	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	0.0722918	−	0.997384i	$-0.476969\pi$
$797$	21.7035	−	7.89942i	0.768776	−	0.279812i	0.696484	+	0.717572i	$0.254746\pi$
$798$	10.5803	−	3.17924i	0.374540	−	0.112544i
$799$	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
$805$	5.67695	+	3.08672i	0.200086	+	0.108792i
$806$	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	$0.110695\pi$
$811$			19.4101i			0.681580i	−0.940139	+	0.340790i	$0.889305\pi$
$812$	−9.81640	+	12.3258i	−0.344488	+	0.432552i
$813$	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
$819$	3.24766	+	15.3004i	0.113482	+	0.534640i
$820$	−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
$826$	17.8034	+	2.67158i	0.619459	+	0.0929562i
$827$	−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	−0.966017	−	0.258477i	$-0.916779\pi$
$829$	−35.2758	+	20.3665i	−1.22518	+	0.707357i	−0.259161	+	0.965834i	$0.583446\pi$
$830$	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
$833$	−1.47192	−	6.41043i	−0.0509990	−	0.222108i
$834$	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	−0.679361	−	0.733804i	$-0.737743\pi$
$839$	−48.4147	−	17.6215i	−1.67146	−	0.608362i	−0.992101	+	0.125442i	$0.959965\pi$
$840$	13.2380	−	6.66519i	0.456754	−	0.229971i
$841$	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
$847$	−21.7127	+	19.1867i	−0.746058	+	0.659264i
$848$	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	0.455750	−	0.890108i	$-0.349371\pi$
$853$	34.7100	−	6.12032i	1.18845	−	0.209556i	0.732700	+	0.680552i	$0.238260\pi$
$854$	−12.8057	+	11.3159i	−0.438201	+	0.387222i
$855$	−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	−0.812272	−	0.583278i	$-0.801770\pi$
$857$	−11.0923	+	9.30753i	−0.378905	+	0.317939i	0.433367	+	0.901217i	$0.357325\pi$
$858$	−0.0425744	+	0.513335i	−0.00145347	+	0.0175250i
$859$	−25.8833	−	4.56392i	−0.883125	−	0.155719i	−0.286348	−	0.958126i	$-0.592441\pi$
$859$	−25.8833	−	4.56392i	−0.883125	−	0.155719i	−0.596777	+	0.802407i	$0.703552\pi$
$860$	2.35786	+	1.97848i	0.0804025	+	0.0674657i
$861$	23.8308	+	47.3313i	0.812152	+	1.61305i
$862$	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
$868$	31.9459	−	19.5503i	1.08431	−	0.663580i
$869$	−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
$875$	−4.30775	+	28.7068i	−0.145628	+	0.970467i
$876$	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	−0.994165	−	0.107871i	$-0.965597\pi$
$881$	−11.9814	+	20.7524i	−0.403664	+	0.699166i	0.590501	+	0.807037i	$0.298930\pi$
$882$	1.64446	−	14.3212i	0.0553720	−	0.482219i
$883$	−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	0.503189	−	0.864176i	$-0.332160\pi$
$887$	−7.75777	−	6.50955i	−0.260481	−	0.218569i	−0.763670	+	0.645607i	$0.776604\pi$
$888$	12.7002	+	3.34157i	0.426191	+	0.112136i
$889$	−1.98643	−	1.58201i	−0.0666226	−	0.0530589i
$890$		−	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
$896$	−25.0687	−	13.6306i	−0.837488	−	0.455365i
$897$	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
$903$	6.61773	−	1.98853i	0.220224	−	0.0661742i
$904$	−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
$910$	0.949908	+	4.68323i	0.0314891	+	0.155248i
$911$	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
$924$	−0.608614	+	1.41487i	−0.0200219	+	0.0465458i
$925$	−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	$-0.976062\pi$
$929$	−2.61616	−	14.8370i	−0.0858334	−	0.486786i	0.911340	−	0.411654i	$-0.135049\pi$
$930$	−1.34730	−	14.6376i	−0.0441798	−	0.479985i
$931$	−7.21573	+	23.5014i	−0.236486	+	0.770226i
$932$	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	−0.556409	−	0.830909i	$-0.687821\pi$
$937$	−3.52097	+	2.03283i	−0.115025	+	0.0664097i	0.441384	+	0.897318i	$0.354488\pi$
$938$	−4.50329	−	11.4523i	−0.147038	−	0.373930i
$939$	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	0.509197	−	0.860650i	$-0.329942\pi$
$941$	−7.66760	−	6.43388i	−0.249957	−	0.209738i	−0.759154	+	0.650912i	$0.774387\pi$
$942$	−10.6244	−	10.5288i	−0.346161	−	0.343046i
$943$	7.23464	−	19.8770i	0.235592	−	0.647285i
$944$	13.8262			0.450003
$945$	15.4367	+	9.93205i	0.502157	+	0.323090i
$946$	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
$952$	2.20366	+	5.60410i	0.0714209	+	0.181630i
$953$	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
$959$	−0.787550	−	30.7761i	−0.0254313	−	0.993811i
$960$	−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
$966$	−4.61201	+	3.44079i	−0.148389	+	0.110706i
$967$	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	$-0.428960\pi$
$971$	13.7938			0.442663			0.221331	+	0.975199i	$0.428960\pi$
$972$	−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
$980$	−1.75825	+	14.1801i	−0.0561653	+	0.452966i
$981$	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	$-0.893906\pi$
$983$	−5.29506	−	30.0298i	−0.168886	−	0.957801i	0.776081	−	0.630634i	$-0.217205\pi$
$984$	−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
$987$	−22.5821	−	21.2618i	−0.718795	−	0.676771i
$988$	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
$994$	−11.8915	+	21.8703i	−0.377175	+	0.693683i
$995$	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	$0.305103\pi$
$997$	−12.3634	+	33.9682i	−0.391553	+	1.07578i	−0.966293	+	0.257446i	$0.917119\pi$
$998$			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.104.9	yes	132
3.2	odd	2		567.2.be.a.503.14		132
7.6	odd	2	inner	189.2.be.a.104.10	yes	132
21.20	even	2		567.2.be.a.503.13		132
27.7	even	9		567.2.be.a.62.13		132
27.20	odd	18	inner	189.2.be.a.20.10	yes	132
189.20	even	18	inner	189.2.be.a.20.9	✓	132
189.34	odd	18		567.2.be.a.62.14		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.9	✓	132	189.20	even	18	inner
189.2.be.a.20.10	yes	132	27.20	odd	18	inner
189.2.be.a.104.9	yes	132	1.1	even	1	trivial
189.2.be.a.104.10	yes	132	7.6	odd	2	inner
567.2.be.a.62.13		132	27.7	even	9
567.2.be.a.62.14		132	189.34	odd	18
567.2.be.a.503.13		132	21.20	even	2
567.2.be.a.503.14		132	3.2	odd	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} +(2.46223 - 0.968204i) 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} +(0.0464596 + 1.81556i) 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} +(0.536621 + 4.55105i) 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} +(0.702223 + 3.46209i) 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} +(-3.06162 - 0.722337i) 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} +(5.12516 - 4.76788i) 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} +(-3.99259 + 5.01324i) 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} +(-7.85969 - 1.10689i) 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} +(-2.39807 - 0.359855i) 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} +(0.496130 - 0.303622i) 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} +(-3.84383 + 5.85719i) 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} +(-3.45242 - 3.90694i) 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} +(1.87223 + 4.42535i) 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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