LMFDB - Embedded newform 189.2.bd.a.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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			47.3
Character	$\chi$	$=$	189.47
Dual form			189.2.bd.a.185.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.26715 - 0.399760i) q^{2} +(0.415691 - 1.68143i) q^{3} +(3.10078 + 1.12859i) q^{4} +(-1.73217 - 0.630457i) q^{5} +(-1.61460 + 3.64587i) q^{6} +(0.678971 - 2.55715i) q^{7} +(-2.59137 - 1.49613i) q^{8} +(-2.65440 - 1.39791i) q^{9} +O(q^{10})$	\(q+(-2.26715 - 0.399760i) q^{2} +(0.415691 - 1.68143i) q^{3} +(3.10078 + 1.12859i) q^{4} +(-1.73217 - 0.630457i) q^{5} +(-1.61460 + 3.64587i) q^{6} +(0.678971 - 2.55715i) q^{7} +(-2.59137 - 1.49613i) q^{8} +(-2.65440 - 1.39791i) q^{9} +(3.67505 + 2.12179i) q^{10} +(-0.0420027 - 0.115401i) q^{11} +(3.18661 - 4.74459i) q^{12} +(-0.0159063 + 0.0437022i) q^{13} +(-2.56157 + 5.52601i) q^{14} +(-1.78012 + 2.65044i) q^{15} +(0.221371 + 0.185752i) q^{16} +(0.0786230 - 0.136179i) q^{17} +(5.45910 + 4.23040i) q^{18} +(-6.57855 + 3.79813i) q^{19} +(-4.65954 - 3.90982i) q^{20} +(-4.01742 - 2.20463i) q^{21} +(0.0490936 + 0.278423i) q^{22} +(-0.957765 + 0.168880i) q^{23} +(-3.59284 + 3.73527i) q^{24} +(-1.22730 - 1.02982i) q^{25} +(0.0535324 - 0.0927208i) q^{26} +(-3.45390 + 3.88209i) q^{27} +(4.99131 - 7.16286i) q^{28} +(-3.33678 - 9.16772i) q^{29} +(5.09533 - 5.29732i) q^{30} +(-1.56144 + 4.29003i) q^{31} +(3.41914 + 4.07477i) q^{32} +(-0.211499 + 0.0226531i) q^{33} +(-0.232689 + 0.277308i) q^{34} +(-2.78826 + 4.00134i) q^{35} +(-6.65304 - 7.33034i) q^{36} +9.37436 q^{37} +(16.4329 - 5.98109i) q^{38} +(0.0668700 + 0.0449120i) q^{39} +(3.54543 + 4.22528i) q^{40} +(5.76925 + 2.09983i) q^{41} +(8.22676 + 6.60422i) q^{42} +(1.67890 - 9.52153i) q^{43} -0.405238i q^{44} +(3.71654 + 4.09490i) q^{45} +2.23891 q^{46} +(3.91757 - 1.42588i) q^{47} +(0.404351 - 0.295003i) q^{48} +(-6.07800 - 3.47246i) q^{49} +(2.37078 + 2.82539i) q^{50} +(-0.196292 - 0.188807i) q^{51} +(-0.0986438 + 0.117559i) q^{52} +(-0.141686 + 0.0818025i) q^{53} +(9.38241 - 7.42054i) q^{54} +0.226376i q^{55} +(-5.58527 + 5.61067i) q^{56} +(3.65163 + 12.6402i) q^{57} +(3.90009 + 22.1185i) q^{58} +(9.06906 - 7.60984i) q^{59} +(-8.51100 + 6.20940i) q^{60} +(1.03823 + 2.85251i) q^{61} +(5.25501 - 9.10194i) q^{62} +(-5.37692 + 5.83855i) q^{63} +(-6.41175 - 11.1055i) q^{64} +(0.0551048 - 0.0656713i) q^{65} +(0.488557 + 0.0331909i) q^{66} +(-1.70755 - 9.68399i) q^{67} +(0.397483 - 0.333527i) q^{68} +(-0.114175 + 1.68062i) q^{69} +(7.92099 - 7.95701i) q^{70} +(-0.863276 + 0.498413i) q^{71} +(4.78707 + 7.59381i) q^{72} -9.18511i q^{73} +(-21.2531 - 3.74749i) q^{74} +(-2.24175 + 1.63552i) q^{75} +(-24.6852 + 4.35266i) q^{76} +(-0.323617 + 0.0290528i) q^{77} +(-0.133650 - 0.128554i) q^{78} +(0.451399 - 2.56001i) q^{79} +(-0.266342 - 0.461318i) q^{80} +(5.09169 + 7.42123i) q^{81} +(-12.2403 - 7.06695i) q^{82} +(-6.02764 + 2.19388i) q^{83} +(-9.96899 - 11.3701i) q^{84} +(-0.222043 + 0.186316i) q^{85} +(-7.61265 + 20.9156i) q^{86} +(-16.8019 + 1.79961i) q^{87} +(-0.0638107 + 0.361889i) q^{88} +(-5.30203 - 9.18338i) q^{89} +(-6.78899 - 10.7695i) q^{90} +(0.100953 + 0.0703473i) q^{91} +(-3.16041 - 0.557266i) q^{92} +(6.56430 + 4.40878i) q^{93} +(-9.45173 + 1.66659i) q^{94} +(13.7897 - 2.43150i) q^{95} +(8.27274 - 4.05519i) q^{96} +(13.2580 + 2.33775i) q^{97} +(12.3916 + 10.3023i) q^{98} +(-0.0498289 + 0.365038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.26715	−	0.399760i	−1.60312	−	0.282673i	−0.700674	−	0.713482i	$-0.747117\pi$
$2$	−2.26715	−	0.399760i	−1.60312	−	0.282673i	−0.902443	+	0.430809i	$0.858228\pi$
$3$	0.415691	−	1.68143i	0.240000	−	0.970773i
$3$	0.415691	−	1.68143i	0.240000	−	0.970773i
$4$	3.10078	+	1.12859i	1.55039	+	0.564295i
$5$	−1.73217	−	0.630457i	−0.774649	−	0.281949i	−0.0757093	−	0.997130i	$-0.524122\pi$
$5$	−1.73217	−	0.630457i	−0.774649	−	0.281949i	−0.698939	+	0.715181i	$0.746344\pi$
$6$	−1.61460	+	3.64587i	−0.659159	+	1.48842i
$7$	0.678971	−	2.55715i	0.256627	−	0.966511i
$7$	0.678971	−	2.55715i	0.256627	−	0.966511i
$8$	−2.59137	−	1.49613i	−0.916186	−	0.528960i
$9$	−2.65440	−	1.39791i	−0.884800	−	0.465970i
$10$	3.67505	+	2.12179i	1.16215	+	0.670970i
$11$	−0.0420027	−	0.115401i	−0.0126643	−	0.0347949i	0.933199	−	0.359359i	$-0.117005\pi$
$11$	−0.0420027	−	0.115401i	−0.0126643	−	0.0347949i	−0.945864	+	0.324564i	$0.894782\pi$
$12$	3.18661	−	4.74459i	0.919895	−	1.36964i
$13$	−0.0159063	+	0.0437022i	−0.00441162	+	0.0121208i	−0.941879	−	0.335953i	$-0.890942\pi$
$13$	−0.0159063	+	0.0437022i	−0.00441162	+	0.0121208i	0.937467	+	0.348073i	$0.113164\pi$
$14$	−2.56157	+	5.52601i	−0.684609	+	1.47689i
$15$	−1.78012	+	2.65044i	−0.459624	+	0.684340i
$16$	0.221371	+	0.185752i	0.0553427	+	0.0464380i
$17$	0.0786230	−	0.136179i	0.0190689	−	0.0330283i	−0.856334	−	0.516423i	$-0.827263\pi$
$17$	0.0786230	−	0.136179i	0.0190689	−	0.0330283i	0.875402	+	0.483395i	$0.160596\pi$
$18$	5.45910	+	4.23040i	1.28672	+	0.997114i
$19$	−6.57855	+	3.79813i	−1.50922	+	0.871350i	−0.509281	+	0.860600i	$0.670089\pi$
$19$	−6.57855	+	3.79813i	−1.50922	+	0.871350i	−0.999942	+	0.0107502i	$0.996578\pi$
$20$	−4.65954	−	3.90982i	−1.04190	−	0.874261i
$21$	−4.01742	−	2.20463i	−0.876672	−	0.481089i
$22$	0.0490936	+	0.278423i	0.0104668	+	0.0593601i
$23$	−0.957765	+	0.168880i	−0.199708	+	0.0352139i	−0.272607	−	0.962125i	$-0.587886\pi$
$23$	−0.957765	+	0.168880i	−0.199708	+	0.0352139i	0.0728993	+	0.997339i	$0.476775\pi$
$24$	−3.59284	+	3.73527i	−0.733385	+	0.762458i
$25$	−1.22730	−	1.02982i	−0.245459	−	0.205965i
$26$	0.0535324	−	0.0927208i	0.0104986	−	0.0181840i
$27$	−3.45390	+	3.88209i	−0.664703	+	0.747108i
$28$	4.99131	−	7.16286i	0.943269	−	1.35365i
$29$	−3.33678	−	9.16772i	−0.619624	−	1.70240i	−0.707906	−	0.706307i	$-0.750360\pi$
$29$	−3.33678	−	9.16772i	−0.619624	−	1.70240i	0.0882816	−	0.996096i	$-0.471862\pi$
$30$	5.09533	−	5.29732i	0.930275	−	0.967155i
$31$	−1.56144	+	4.29003i	−0.280444	+	0.770512i	0.716866	+	0.697211i	$0.245576\pi$
$31$	−1.56144	+	4.29003i	−0.280444	+	0.770512i	−0.997310	+	0.0733016i	$0.976646\pi$
$32$	3.41914	+	4.07477i	0.604424	+	0.720325i
$33$	−0.211499	+	0.0226531i	−0.0368173	+	0.00394340i
$34$	−0.232689	+	0.277308i	−0.0399058	+	0.0475579i
$35$	−2.78826	+	4.00134i	−0.471303	+	0.676350i
$36$	−6.65304	−	7.33034i	−1.10884	−	1.22172i
$37$	9.37436			1.54113			0.770567	−	0.637358i	$-0.219973\pi$
$37$	9.37436			1.54113			0.770567	+	0.637358i	$0.219973\pi$
$38$	16.4329	−	5.98109i	2.66577	−	0.970261i
$39$	0.0668700	+	0.0449120i	0.0107078	+	0.00719167i
$40$	3.54543	+	4.22528i	0.560582	+	0.668076i
$41$	5.76925	+	2.09983i	0.901005	+	0.327939i	0.750656	−	0.660694i	$-0.229738\pi$
$41$	5.76925	+	2.09983i	0.901005	+	0.327939i	0.150350	+	0.988633i	$0.451960\pi$
$42$	8.22676	+	6.60422i	1.26942	+	1.01905i
$43$	1.67890	−	9.52153i	0.256030	−	1.45202i	−0.537384	−	0.843338i	$-0.680587\pi$
$43$	1.67890	−	9.52153i	0.256030	−	1.45202i	0.793414	−	0.608682i	$-0.208301\pi$
$44$		−	0.405238i		−	0.0610919i
$45$	3.71654	+	4.09490i	0.554030	+	0.610432i
$46$	2.23891			0.330109
$47$	3.91757	−	1.42588i	0.571436	−	0.207986i	−0.0401090	−	0.999195i	$-0.512771\pi$
$47$	3.91757	−	1.42588i	0.571436	−	0.207986i	0.611545	+	0.791210i	$0.290548\pi$
$48$	0.404351	−	0.295003i	0.0583630	−	0.0425801i
$49$	−6.07800	−	3.47246i	−0.868285	−	0.496065i
$50$	2.37078	+	2.82539i	0.335279	+	0.399570i
$51$	−0.196292	−	0.188807i	−0.0274864	−	0.0264383i
$52$	−0.0986438	+	0.117559i	−0.0136794	+	0.0163025i
$53$	−0.141686	+	0.0818025i	−0.0194621	+	0.0112364i	−0.509699	−	0.860353i	$-0.670243\pi$
$53$	−0.141686	+	0.0818025i	−0.0194621	+	0.0112364i	0.490237	+	0.871589i	$0.336910\pi$
$54$	9.38241	−	7.42054i	1.27678	−	1.00981i
$55$			0.226376i			0.0305245i
$56$	−5.58527	+	5.61067i	−0.746364	+	0.749758i
$57$	3.65163	+	12.6402i	0.483671	+	1.67424i
$58$	3.90009	+	22.1185i	0.512107	+	2.90430i
$59$	9.06906	−	7.60984i	1.18069	−	0.990717i	0.180717	−	0.983535i	$-0.442158\pi$
$59$	9.06906	−	7.60984i	1.18069	−	0.990717i	0.999974	−	0.00718212i	$-0.00228616\pi$
$60$	−8.51100	+	6.20940i	−1.09877	+	0.801630i
$61$	1.03823	+	2.85251i	0.132932	+	0.365227i	0.988244	−	0.152886i	$-0.0488568\pi$
$61$	1.03823	+	2.85251i	0.132932	+	0.365227i	−0.855312	+	0.518113i	$0.826635\pi$
$62$	5.25501	−	9.10194i	0.667387	−	1.15595i
$63$	−5.37692	+	5.83855i	−0.677429	+	0.735588i
$64$	−6.41175	−	11.1055i	−0.801469	−	1.38818i
$65$	0.0551048	−	0.0656713i	0.00683491	−	0.00814552i
$66$	0.488557	+	0.0331909i	0.0601372	+	0.00408552i
$67$	−1.70755	−	9.68399i	−0.208610	−	1.18309i	−0.891656	−	0.452713i	$-0.850456\pi$
$67$	−1.70755	−	9.68399i	−0.208610	−	1.18309i	0.683046	−	0.730375i	$-0.260655\pi$
$68$	0.397483	−	0.333527i	0.0482018	−	0.0404461i
$69$	−0.114175	+	1.68062i	−0.0137451	+	0.202322i
$70$	7.92099	−	7.95701i	0.946739	−	0.951045i
$71$	−0.863276	+	0.498413i	−0.102452	+	0.0591507i	−0.550351	−	0.834934i	$-0.685506\pi$
$71$	−0.863276	+	0.498413i	−0.102452	+	0.0591507i	0.447899	+	0.894084i	$0.352173\pi$
$72$	4.78707	+	7.59381i	0.564162	+	0.894940i
$73$		−	9.18511i		−	1.07504i	−0.843252	−	0.537518i	$-0.819362\pi$
$73$		−	9.18511i		−	1.07504i	0.843252	−	0.537518i	$-0.180638\pi$
$74$	−21.2531	−	3.74749i	−2.47062	−	0.435637i
$75$	−2.24175	+	1.63552i	−0.258855	+	0.188854i
$76$	−24.6852	+	4.35266i	−2.83158	+	0.499284i
$77$	−0.323617	+	0.0290528i	−0.0368796	+	0.00331087i
$78$	−0.133650	−	0.128554i	−0.0151329	−	0.0145559i
$79$	0.451399	−	2.56001i	0.0507864	−	0.288024i	−0.948828	−	0.315793i	$-0.897729\pi$
$79$	0.451399	−	2.56001i	0.0507864	−	0.288024i	0.999614	+	0.0277696i	$0.00884048\pi$
$80$	−0.266342	−	0.461318i	−0.0297780	−	0.0515769i
$81$	5.09169	+	7.42123i	0.565744	+	0.824581i
$82$	−12.2403	−	7.06695i	−1.35172	−	0.780414i
$83$	−6.02764	+	2.19388i	−0.661619	+	0.240810i	−0.650935	−	0.759133i	$-0.725623\pi$
$83$	−6.02764	+	2.19388i	−0.661619	+	0.240810i	−0.0106840	+	0.999943i	$0.503401\pi$
$84$	−9.96899	−	11.3701i	−1.08771	−	1.24058i
$85$	−0.222043	+	0.186316i	−0.0240840	+	0.0202088i
$86$	−7.61265	+	20.9156i	−0.820893	+	2.25539i
$87$	−16.8019	+	1.79961i	−1.80136	+	0.192938i
$88$	−0.0638107	+	0.361889i	−0.00680225	+	0.0385775i
$89$	−5.30203	−	9.18338i	−0.562014	−	0.973436i	−0.997321	−	0.0731541i	$-0.976694\pi$
$89$	−5.30203	−	9.18338i	−0.562014	−	0.973436i	0.435307	−	0.900282i	$-0.356640\pi$
$90$	−6.78899	−	10.7695i	−0.715622	−	1.13520i
$91$	0.100953	+	0.0703473i	0.0105828	+	0.00737440i
$92$	−3.16041	−	0.557266i	−0.329496	−	0.0580990i
$93$	6.56430	+	4.40878i	0.680686	+	0.457170i
$94$	−9.45173	+	1.66659i	−0.974871	+	0.171896i
$95$	13.7897	−	2.43150i	1.41479	−	0.249466i
$96$	8.27274	−	4.05519i	0.844333	−	0.413881i
$97$	13.2580	+	2.33775i	1.34615	+	0.237363i	0.799836	−	0.600218i	$-0.204920\pi$
$97$	13.2580	+	2.33775i	1.34615	+	0.237363i	0.546313	+	0.837581i	$0.316031\pi$
$98$	12.3916	+	10.3023i	1.25174	+	1.04069i
$99$	−0.0498289	+	0.365038i	−0.00500799	+	0.0366877i
$100$	−2.64332	−	4.57837i	−0.264332	−	0.457837i
$101$	−2.41301	+	13.6848i	−0.240103	+	1.36169i	0.591492	+	0.806311i	$0.298539\pi$
$101$	−2.41301	+	13.6848i	−0.240103	+	1.36169i	−0.831595	+	0.555382i	$0.812572\pi$
$102$	0.369546	+	0.506524i	0.0365906	+	0.0501534i
$103$	−2.66808	+	7.33049i	−0.262894	+	0.722295i	0.736075	+	0.676900i	$0.236677\pi$
$103$	−2.66808	+	7.33049i	−0.262894	+	0.722295i	−0.998969	+	0.0453951i	$0.985545\pi$
$104$	0.106603	−	0.0894506i	0.0104533	−	0.00877135i
$105$	5.56891	+	6.35159i	0.543470	+	0.619852i
$106$	0.353925	−	0.128818i	0.0343762	−	0.0125119i
$107$	−6.46785	−	3.73421i	−0.625271	−	0.361000i	0.153648	−	0.988126i	$-0.450898\pi$
$107$	−6.46785	−	3.73421i	−0.625271	−	0.361000i	−0.778918	+	0.627126i	$0.784231\pi$
$108$	−15.0911	+	8.13945i	−1.45214	+	0.783219i
$109$	4.37239	+	7.57320i	0.418799	+	0.725381i	0.995819	−	0.0913488i	$-0.0291178\pi$
$109$	4.37239	+	7.57320i	0.418799	+	0.725381i	−0.577020	+	0.816730i	$0.695784\pi$
$110$	0.0904958	−	0.513227i	0.00862844	−	0.0489343i
$111$	3.89684	−	15.7623i	0.369872	−	1.49609i
$112$	0.625299	−	0.439957i	0.0590852	−	0.0415720i
$113$	16.2059	−	2.85754i	1.52453	−	0.268815i	0.652317	−	0.757947i	$-0.273797\pi$
$113$	16.2059	−	2.85754i	1.52453	−	0.268815i	0.872210	+	0.489131i	$0.162686\pi$
$114$	−3.22575	−	30.1170i	−0.302119	−	2.82072i
$115$	1.76548	+	0.311302i	0.164632	+	0.0290291i
$116$		−	32.1929i		−	2.98904i
$117$	0.103314	−	0.0937676i	0.00955134	−	0.00866882i
$118$	−23.6030	+	13.6272i	−2.17283	+	1.25449i
$119$	−0.294847	−	0.293512i	−0.0270286	−	0.0269062i
$120$	8.57832	−	4.20498i	0.783090	−	0.383860i
$121$	8.41494	−	7.06097i	0.764994	−	0.641906i
$122$	−1.21350	−	6.88212i	−0.109865	−	0.623078i
$123$	5.92895	−	8.82769i	0.534595	−	0.795966i
$124$	−9.68338	+	11.5402i	−0.869593	+	1.03634i
$125$	6.08496	+	10.5395i	0.544255	+	0.942677i
$126$	14.5243	−	11.0874i	1.29393	−	0.987744i
$127$	−2.14737	+	3.71936i	−0.190549	+	0.330040i	−0.945432	−	0.325819i	$-0.894360\pi$
$127$	−2.14737	+	3.71936i	−0.190549	+	0.330040i	0.754884	+	0.655859i	$0.227693\pi$
$128$	6.45831	+	17.7441i	0.570839	+	1.56837i
$129$	−15.3119	−	6.78097i	−1.34813	−	0.597031i
$130$	−0.151184	+	0.126858i	−0.0132597	+	0.0111262i
$131$	0.751230	+	4.26044i	0.0656353	+	0.372236i	0.999878	+	0.0155992i	$0.00496557\pi$
$131$	0.751230	+	4.26044i	0.0656353	+	0.372236i	−0.934243	+	0.356637i	$0.883923\pi$
$132$	−0.681379	−	0.168454i	−0.0593064	−	0.0146620i
$133$	5.24572	+	19.4011i	0.454862	+	1.68229i
$134$			22.6377i			1.95560i
$135$	8.43022	−	4.54689i	0.725558	−	0.391334i
$136$	−0.407482	+	0.235260i	−0.0349413	+	0.0201733i
$137$	1.12676	−	1.34283i	0.0962660	−	0.114725i	−0.715761	−	0.698346i	$-0.753920\pi$
$137$	1.12676	−	1.34283i	0.0962660	−	0.114725i	0.812027	+	0.583620i	$0.198364\pi$
$138$	0.930695	−	3.76456i	0.0792260	−	0.320461i
$139$	−8.74606	−	10.4232i	−0.741831	−	0.884080i	0.254724	−	0.967014i	$-0.418015\pi$
$139$	−8.74606	−	10.4232i	−0.741831	−	0.884080i	−0.996555	+	0.0829338i	$0.973571\pi$
$140$	−13.1617	+	9.26046i	−1.11236	+	0.782652i
$141$	−0.769013	−	7.17984i	−0.0647625	−	0.604651i
$142$	2.15642	−	0.784874i	0.180963	−	0.0658651i
$143$	0.00571141			0.000477612
$144$	−0.327942	−	0.802517i	−0.0273285	−	0.0668764i
$145$			17.9837i			1.49347i
$146$	−3.67184	+	20.8240i	−0.303884	+	1.72341i
$147$	−8.36526	+	8.77624i	−0.689955	+	0.723852i
$148$	29.0678	+	10.5798i	2.38936	+	0.869655i
$149$	−5.96077	−	7.10377i	−0.488325	−	0.581963i	0.464465	−	0.885591i	$-0.346247\pi$
$149$	−5.96077	−	7.10377i	−0.488325	−	0.581963i	−0.952791	+	0.303628i	$0.901802\pi$
$150$	5.73620	−	2.81181i	0.468359	−	0.229583i
$151$	−9.17350	+	3.33888i	−0.746529	+	0.271714i	−0.687144	−	0.726521i	$-0.741136\pi$
$151$	−9.17350	+	3.33888i	−0.746529	+	0.271714i	−0.0593846	+	0.998235i	$0.518914\pi$
$152$	22.7299			1.84364
$153$	−0.399063	+	0.251566i	−0.0322623	+	0.0203379i
$154$	0.745303	+	0.0635021i	0.0600582	+	0.00511714i
$155$	5.40936	−	6.44663i	0.434490	−	0.517806i
$156$	0.156662	+	0.214731i	0.0125430	+	0.0171922i
$157$	−10.4023	−	12.3970i	−0.830196	−	0.989388i	−0.999992	−	0.00390940i	$-0.998756\pi$
$157$	−10.4023	−	12.3970i	−0.830196	−	0.989388i	0.169797	−	0.985479i	$-0.445689\pi$
$158$	−2.04678	+	5.62348i	−0.162833	+	0.447380i
$159$	0.0786473	+	0.272239i	0.00623714	+	0.0215900i
$160$	−3.35355	−	9.21381i	−0.265122	−	0.728415i
$161$	−0.218444	+	2.56381i	−0.0172158	+	0.202057i
$162$	−8.57692	−	18.8605i	−0.673867	−	1.48182i
$163$	5.65656	−	9.79745i	0.443056	−	0.767396i	−0.554858	−	0.831945i	$-0.687228\pi$
$163$	5.65656	−	9.79745i	0.443056	−	0.767396i	0.997915	+	0.0645491i	$0.0205609\pi$
$164$	15.5193	+	13.0222i	1.21185	+	1.01687i
$165$	0.380634	+	0.0941024i	0.0296323	+	0.00732586i
$166$	14.5426	−	2.56425i	1.12872	−	0.199024i
$167$	−0.331914	−	1.88238i	−0.0256843	−	0.145663i	0.969269	−	0.246004i	$-0.0791176\pi$
$167$	−0.331914	−	1.88238i	−0.0256843	−	0.145663i	−0.994953	+	0.100341i	$0.968007\pi$
$168$	7.11220	+	11.7235i	0.548718	+	0.904491i
$169$	9.95692	+	8.35485i	0.765917	+	0.642681i
$170$	0.577887	−	0.333643i	0.0443219	−	0.0255893i
$171$	22.7716	−	0.885531i	1.74138	−	0.0677183i
$172$	15.9518	−	27.6293i	1.21631	−	2.10672i
$173$	−18.7471	−	15.7306i	−1.42531	−	1.19598i	−0.948420	−	0.317018i	$-0.897319\pi$
$173$	−18.7471	−	15.7306i	−1.42531	−	1.19598i	−0.476893	−	0.878962i	$-0.658237\pi$
$174$	38.8119	+	2.63675i	2.94232	+	0.199892i
$175$	−3.46671	+	2.43915i	−0.262058	+	0.184383i
$176$	0.0121379	−	0.0333486i	0.000914928	−	0.00251374i
$177$	−9.02548	−	18.4123i	−0.678396	−	1.38395i
$178$	8.34934	+	22.9396i	0.625810	+	1.71940i
$179$	−15.9928	−	9.23345i	−1.19536	−	0.690140i	−0.235841	−	0.971792i	$-0.575785\pi$
$179$	−15.9928	−	9.23345i	−1.19536	−	0.690140i	−0.959517	+	0.281651i	$0.909118\pi$
$180$	6.90271	+	16.8918i	0.514497	+	1.25904i
$181$	5.58272	+	3.22319i	0.414960	+	0.239577i	0.692919	−	0.721016i	$-0.256324\pi$
$181$	5.58272	+	3.22319i	0.414960	+	0.239577i	−0.277958	+	0.960593i	$0.589658\pi$
$182$	−0.200754	−	0.199845i	−0.0148809	−	0.0148135i
$183$	5.22788	−	0.559944i	0.386456	−	0.0413922i
$184$	2.73459	+	0.995308i	0.201596	+	0.0733751i
$185$	−16.2380	−	5.91013i	−1.19384	−	0.434522i
$186$	−13.1198	−	12.6195i	−0.961990	−	0.925308i
$187$	−0.0190176	−	0.00335332i	−0.00139071	−	0.000245219i
$188$	13.7567			1.00331
$189$	7.58197	+	11.4679i	0.551507	+	0.834170i
$190$	−32.2354			−2.33860
$191$	9.88047	+	1.74219i	0.714926	+	0.126061i	0.519268	−	0.854612i	$-0.326205\pi$
$191$	9.88047	+	1.74219i	0.714926	+	0.126061i	0.195658	+	0.980672i	$0.437316\pi$
$192$	−21.3384	+	6.16445i	−1.53996	+	0.444881i
$193$	23.1247	+	8.41671i	1.66455	+	0.605848i	0.991069	−	0.133353i	$-0.0425745\pi$
$193$	23.1247	+	8.41671i	1.66455	+	0.605848i	0.673485	+	0.739201i	$0.264797\pi$
$194$	−29.1234	−	10.6001i	−2.09094	−	0.761040i
$195$	−0.0875150	−	0.119954i	−0.00626708	−	0.00859006i
$196$	−14.9275	−	17.6269i	−1.06625	−	1.25906i
$197$	12.0988	+	6.98527i	0.862007	+	0.497680i	0.864684	−	0.502316i	$-0.167519\pi$
$197$	12.0988	+	6.98527i	0.862007	+	0.497680i	−0.00267677	+	0.999996i	$0.500852\pi$
$198$	0.258897	−	0.807676i	0.0183990	−	0.0573990i
$199$	11.1535	+	6.43950i	0.790654	+	0.456484i	0.840193	−	0.542288i	$-0.182442\pi$
$199$	11.1535	+	6.43950i	0.790654	+	0.456484i	−0.0495388	+	0.998772i	$0.515775\pi$
$200$	1.63963	+	4.50484i	0.115939	+	0.318540i
$201$	−16.9928	−	1.15443i	−1.19858	−	0.0814273i
$202$	10.9413	−	30.0610i	0.769827	−	2.11508i
$203$	−25.7088	+	2.30801i	−1.80440	+	0.161991i
$204$	−0.395572	−	0.806983i	−0.0276956	−	0.0565001i
$205$	−8.66945	−	7.27453i	−0.605500	−	0.508075i
$206$	8.97937	−	15.5527i	0.625623	−	1.08361i
$207$	2.77837	+	0.890595i	0.193110	+	0.0619006i
$208$	−0.0116390	+	0.00671976i	−0.000807017	+	0.000465931i
$209$	0.714627	+	0.599643i	0.0494318	+	0.0414782i
$210$	−10.0865	−	16.6262i	−0.696031	−	1.14732i
$211$	−0.918282	−	5.20784i	−0.0632171	−	0.358522i	−0.999964	−	0.00851397i	$-0.997290\pi$
$211$	−0.918282	−	5.20784i	−0.0632171	−	0.358522i	0.936747	−	0.350008i	$-0.113821\pi$
$212$	−0.531658	+	0.0937457i	−0.0365144	+	0.00643848i
$213$	0.479189	+	1.65872i	0.0328335	+	0.113654i
$214$	13.1708	+	11.0516i	0.900337	+	0.755472i
$215$	−8.91106	+	15.4344i	−0.607729	+	1.05262i
$216$	14.7584	−	4.89244i	1.00418	−	0.332888i
$217$	9.91006	+	6.90565i	0.672739	+	0.468786i
$218$	−6.88541	−	18.9175i	−0.466339	−	1.28125i
$219$	−15.4441	−	3.81817i	−1.04362	−	0.258008i
$220$	−0.255485	+	0.701940i	−0.0172248	+	0.0473248i
$221$	0.00470072	+	0.00560210i	0.000316205	+	0.000376838i
$222$	−15.1359	+	34.1777i	−1.01585	+	2.29386i
$223$	5.38046	−	6.41218i	0.360302	−	0.429392i	−0.555192	−	0.831722i	$-0.687355\pi$
$223$	5.38046	−	6.41218i	0.360302	−	0.429392i	0.915495	+	0.402330i	$0.131800\pi$
$224$	12.7413	−	5.97659i	0.851313	−	0.399328i
$225$	1.81813	+	4.44921i	0.121209	+	0.296614i
$226$	−37.8836			−2.51998
$227$	−18.9673	+	6.90355i	−1.25891	+	0.458205i	−0.883402	−	0.468616i	$-0.844753\pi$
$227$	−18.9673	+	6.90355i	−1.25891	+	0.458205i	−0.375505	+	0.926820i	$0.622531\pi$
$228$	−2.94272	+	43.3157i	−0.194887	+	2.86865i
$229$	3.73395	+	4.44995i	0.246746	+	0.294061i	0.875175	−	0.483806i	$-0.160746\pi$
$229$	3.73395	+	4.44995i	0.246746	+	0.294061i	−0.628429	+	0.777867i	$0.716302\pi$
$230$	−3.87817	−	1.41154i	−0.255719	−	0.0930740i
$231$	−0.0856747	+	0.556216i	−0.00563698	+	0.0365963i
$232$	−5.06925	+	28.7491i	−0.332813	+	1.88747i
$233$		−	6.16220i		−	0.403699i	−0.979417	−	0.201850i	$-0.935305\pi$
$233$		−	6.16220i		−	0.403699i	0.979417	−	0.201850i	$-0.0646952\pi$
$234$	−0.271712	+	0.171285i	−0.0177624	+	0.0111972i
$235$	−7.68484			−0.501304
$236$	36.7095	−	13.3612i	2.38959	−	0.869738i
$237$	−4.11683	−	1.82317i	−0.267417	−	0.118428i
$238$	0.551128	+	0.783304i	0.0357243	+	0.0507740i
$239$	11.9974	+	14.2979i	0.776046	+	0.924856i	0.998748	−	0.0500310i	$-0.0159320\pi$
$239$	11.9974	+	14.2979i	0.776046	+	0.924856i	−0.222702	+	0.974887i	$0.571488\pi$
$240$	−0.886390	+	0.256069i	−0.0572162	+	0.0165292i
$241$	−7.83296	+	9.33496i	−0.504565	+	0.601318i	−0.956859	−	0.290551i	$-0.906161\pi$
$241$	−7.83296	+	9.33496i	−0.504565	+	0.601318i	0.452294	+	0.891869i	$0.350606\pi$
$242$	−21.9006	+	12.6443i	−1.40782	+	0.812808i
$243$	14.5948	−	5.47637i	0.936259	−	0.351310i
$244$			10.0167i			0.641256i
$245$	8.33887	+	9.84679i	0.532751	+	0.629089i
$246$	−16.9708	+	17.6436i	−1.08202	+	1.12491i
$247$	−0.0613462	−	0.347912i	−0.00390336	−	0.0221371i
$248$	10.4647	−	8.78092i	0.664509	−	0.557589i
$249$	1.18322	+	11.0470i	0.0749833	+	0.700076i
$250$	−9.58226	−	26.3270i	−0.606035	−	1.66507i
$251$	−1.90241	+	3.29506i	−0.120079	+	0.207983i	−0.919799	−	0.392391i	$-0.871648\pi$
$251$	−1.90241	+	3.29506i	−0.120079	+	0.207983i	0.799720	+	0.600373i	$0.204981\pi$
$252$	−23.2620	+	12.0357i	−1.46537	+	0.758178i
$253$	0.0597177	+	0.103434i	0.00375442	+	0.00650285i
$254$	6.35527	−	7.57392i	0.398765	−	0.475230i
$255$	0.220976	+	0.450800i	0.0138381	+	0.0282302i
$256$	−3.09504	−	17.5528i	−0.193440	−	1.09705i
$257$	16.8941	−	14.1758i	1.05382	−	0.884262i	0.0603326	−	0.998178i	$-0.480784\pi$
$257$	16.8941	−	14.1758i	1.05382	−	0.884262i	0.993490	+	0.113916i	$0.0363394\pi$
$258$	32.0035	+	21.4946i	1.99245	+	1.33819i
$259$	6.36492	−	23.9716i	0.395497	−	1.48952i
$260$	0.244984	−	0.141441i	0.0151932	−	0.00877182i
$261$	−3.95851	+	28.9993i	−0.245025	+	1.79501i
$262$		−	9.95936i		−	0.615291i
$263$	−1.87472	−	0.330563i	−0.115600	−	0.0203834i	0.115549	−	0.993302i	$-0.463137\pi$
$263$	−1.87472	−	0.330563i	−0.115600	−	0.0203834i	−0.231149	+	0.972918i	$0.574248\pi$
$264$	0.581964	+	0.257727i	0.0358174	+	0.0158620i
$265$	0.296997	−	0.0523686i	0.0182444	−	0.00321698i
$266$	−4.13705	−	46.0823i	−0.253659	−	2.82549i
$267$	−17.6452	+	5.09752i	−1.07987	+	0.311963i
$268$	5.63453	−	31.9550i	0.344184	−	1.95196i
$269$	−6.11936	−	10.5990i	−0.373104	−	0.646235i	0.616937	−	0.787012i	$-0.288373\pi$
$269$	−6.11936	−	10.5990i	−0.373104	−	0.646235i	−0.990041	+	0.140777i	$0.955040\pi$
$270$	−20.9302	+	6.93841i	−1.27377	+	0.422258i
$271$	10.1008	+	5.83167i	0.613577	+	0.354249i	0.774364	−	0.632740i	$-0.218070\pi$
$271$	10.1008	+	5.83167i	0.613577	+	0.354249i	−0.160787	+	0.986989i	$0.551403\pi$
$272$	0.0427003	−	0.0155416i	0.00258909	−	0.000942351i
$273$	0.160249	−	0.140503i	0.00969873	−	0.00850360i
$274$	−3.09135	+	2.59395i	−0.186755	+	0.156706i
$275$	−0.0672934	+	0.184887i	−0.00405794	+	0.0111491i
$276$	−2.25076	+	5.08236i	−0.135480	+	0.305922i
$277$	−3.29023	+	18.6598i	−0.197691	+	1.12116i	0.710843	+	0.703351i	$0.248314\pi$
$277$	−3.29023	+	18.6598i	−0.197691	+	1.12116i	−0.908534	+	0.417811i	$0.862798\pi$
$278$	15.6619	+	27.1272i	0.939337	+	1.62698i
$279$	10.1418	−	9.20471i	0.607172	−	0.551071i
$280$	13.2119	−	6.19735i	0.789563	−	0.370362i
$281$	0.401346	+	0.0707682i	0.0239423	+	0.00422168i	0.185607	−	0.982624i	$-0.440575\pi$
$281$	0.401346	+	0.0707682i	0.0239423	+	0.00422168i	−0.161664	+	0.986846i	$0.551686\pi$
$282$	−1.12674	+	16.5852i	−0.0670965	+	0.987634i
$283$	4.58326	−	0.808153i	0.272447	−	0.0480397i	−0.0357555	−	0.999361i	$-0.511384\pi$
$283$	4.58326	−	0.808153i	0.272447	−	0.0480397i	0.308202	+	0.951321i	$0.400273\pi$
$284$	−3.23933	+	0.571182i	−0.192219	+	0.0338934i
$285$	1.64387	−	24.1972i	0.0973747	−	1.43332i
$286$	−0.0129486	−	0.00228319i	−0.000765668	−	0.000135008i
$287$	9.28674	−	13.3271i	0.548179	−	0.786673i
$288$	−3.37960	−	15.5957i	−0.199145	−	0.918987i
$289$	8.48764	+	14.7010i	0.499273	+	0.864766i
$290$	7.18917	−	40.7718i	0.422162	−	2.39420i
$291$	9.44201	−	21.3207i	0.553500	−	1.24984i
$292$	10.3662	−	28.4810i	0.606638	−	1.66672i
$293$	−6.35829	+	5.33524i	−0.371455	+	0.311688i	−0.809337	−	0.587345i	$-0.800173\pi$
$293$	−6.35829	+	5.33524i	−0.371455	+	0.311688i	0.437882	+	0.899033i	$0.355729\pi$
$294$	22.4737	−	16.5530i	1.31069	−	0.965389i
$295$	−20.5068	+	7.46387i	−1.19395	+	0.434563i
$296$	−24.2924	−	14.0252i	−1.41197	−	0.815199i
$297$	0.593072	+	0.235527i	0.0344135	+	0.0136667i
$298$	10.6742	+	18.4882i	0.618338	+	1.07099i
$299$	0.00785408	−	0.0445427i	0.000454213	−	0.00257597i
$300$	−8.79700	+	2.54137i	−0.507895	+	0.146726i
$301$	−23.2080	−	10.7580i	−1.33769	−	0.620083i
$302$	22.1325	−	3.90255i	1.27358	−	0.224567i
$303$	22.0070	+	9.74597i	1.26427	+	0.559891i
$304$	−2.16181	−	0.381185i	−0.123988	−	0.0218625i
$305$		−	5.59559i		−	0.320402i
$306$	1.00530	−	0.410808i	0.0574693	−	0.0234843i
$307$	−5.10853	+	2.94941i	−0.291559	+	0.168332i	−0.638645	−	0.769502i	$-0.720505\pi$
$307$	−5.10853	+	2.94941i	−0.291559	+	0.168332i	0.347086	+	0.937833i	$0.387171\pi$
$308$	−1.03625	−	0.275145i	−0.0590460	−	0.0156778i
$309$	11.2166	+	7.53341i	0.638090	+	0.428561i
$310$	−14.8409	+	12.4530i	−0.842909	+	0.707284i
$311$	2.35699	+	13.3671i	0.133653	+	0.757981i	0.975789	+	0.218716i	$0.0701869\pi$
$311$	2.35699	+	13.3671i	0.133653	+	0.757981i	−0.842136	+	0.539265i	$0.818702\pi$
$312$	−0.106091	−	0.216429i	−0.00600621	−	0.0122529i
$313$	3.67401	−	4.37851i	0.207667	−	0.247488i	−0.652150	−	0.758090i	$-0.726133\pi$
$313$	3.67401	−	4.37851i	0.207667	−	0.247488i	0.859817	+	0.510602i	$0.170577\pi$
$314$	18.6278	+	32.2643i	1.05123	+	1.82078i
$315$	12.9947	−	6.72343i	0.732168	−	0.378822i
$316$	4.28889	−	7.42858i	0.241269	−	0.417890i
$317$	0.823688	+	2.26306i	0.0462629	+	0.127106i	0.960672	−	0.277684i	$-0.0895668\pi$
$317$	0.823688	+	2.26306i	0.0462629	+	0.127106i	−0.914410	+	0.404790i	$0.867345\pi$
$318$	−0.0694749	−	0.648648i	−0.00389596	−	0.0363744i
$319$	−0.917815	+	0.770138i	−0.0513878	+	0.0431194i
$320$	4.10470	+	23.2789i	0.229459	+	1.30133i
$321$	−8.96744	+	9.32294i	−0.500514	+	0.520356i
$322$	1.52015	−	5.72522i	0.0847149	−	0.319054i
$323$			1.19448i			0.0664627i
$324$	7.41267	+	28.7580i	0.411815	+	1.59767i
$325$	0.0645273	−	0.0372549i	0.00357933	−	0.00206653i
$326$	−16.7409	+	19.9510i	−0.927193	+	1.10499i
$327$	14.5514	−	4.20375i	0.804692	−	0.232468i
$328$	−11.8086	−	14.0730i	−0.652022	−	0.777049i
$329$	−0.986264	−	10.9859i	−0.0543745	−	0.605674i
$330$	−0.825337	−	0.365506i	−0.0454333	−	0.0201205i
$331$	−9.95637	+	3.62382i	−0.547251	+	0.199183i	−0.600825	−	0.799381i	$-0.705161\pi$
$331$	−9.95637	+	3.62382i	−0.547251	+	0.199183i	0.0535735	+	0.998564i	$0.482939\pi$
$332$	−21.1664			−1.16165
$333$	−24.8833	−	13.1045i	−1.36360	−	0.718123i
$334$			4.40032i			0.240775i
$335$	−3.14758	+	17.8508i	−0.171971	+	0.975295i
$336$	−0.479824	−	1.23428i	−0.0261766	−	0.0673356i
$337$	−21.6242	−	7.87058i	−1.17795	−	0.428738i	−0.322471	−	0.946579i	$-0.604514\pi$
$337$	−21.6242	−	7.87058i	−1.17795	−	0.428738i	−0.855477	+	0.517841i	$0.826736\pi$
$338$	−19.2339	−	22.9221i	−1.04619	−	1.24680i
$339$	1.93191	−	28.4370i	0.104927	−	1.54448i
$340$	−0.898781	+	0.327130i	−0.0487432	+	0.0177411i
$341$	0.560661			0.0303615
$342$	−51.9805	−	7.09552i	−2.81079	−	0.383682i
$343$	−13.0064	+	13.1846i	−0.702278	+	0.711903i
$344$	−18.5961	+	22.1619i	−1.00263	+	1.19489i
$345$	1.25733	−	2.83912i	0.0676922	−	0.152853i
$346$	36.2139	+	43.1581i	1.94687	+	2.32019i
$347$	1.31719	−	3.61896i	0.0707106	−	0.194276i	−0.899303	−	0.437326i	$-0.855926\pi$
$347$	1.31719	−	3.61896i	0.0707106	−	0.194276i	0.970014	+	0.243050i	$0.0781479\pi$
$348$	−54.1301	−	13.3823i	−2.90168	−	0.717367i
$349$	0.721690	+	1.98283i	0.0386312	+	0.106138i	0.957508	−	0.288405i	$-0.0931250\pi$
$349$	0.721690	+	1.98283i	0.0386312	+	0.106138i	−0.918877	+	0.394543i	$0.870903\pi$
$350$	8.83462	−	4.14408i	0.472230	−	0.221510i
$351$	−0.114717	−	0.212693i	−0.00612314	−	0.0113527i
$352$	0.326622	−	0.565725i	0.0174090	−	0.0301533i
$353$	9.41323	+	7.89864i	0.501016	+	0.420402i	0.857955	−	0.513726i	$-0.171735\pi$
$353$	9.41323	+	7.89864i	0.501016	+	0.420402i	−0.356939	+	0.934128i	$0.616180\pi$
$354$	13.1016	+	45.3515i	0.696343	+	2.41041i
$355$	1.80957	−	0.319075i	0.0960418	−	0.0169348i
$356$	−6.07613	−	34.4594i	−0.322034	−	1.82635i
$357$	−0.616085	+	0.373753i	−0.0326067	+	0.0197811i
$358$	32.5669	+	27.3269i	1.72122	+	1.44427i
$359$	−26.4895	+	15.2937i	−1.39806	+	0.807170i	−0.994189	−	0.107646i	$-0.965669\pi$
$359$	−26.4895	+	15.2937i	−1.39806	+	0.807170i	−0.403871	+	0.914816i	$0.632335\pi$
$360$	−3.50444	−	16.1718i	−0.184700	−	0.852329i
$361$	19.3516	−	33.5179i	1.01850	−	1.76410i
$362$	−11.3684	−	9.53919i	−0.597508	−	0.501369i
$363$	−8.37450	−	17.0843i	−0.439547	−	0.896693i
$364$	0.233640	+	0.332066i	0.0122460	+	0.0174050i
$365$	−5.79082	+	15.9102i	−0.303105	+	0.832775i
$366$	−12.0762	−	0.820419i	−0.631235	−	0.0428840i
$367$	−4.68686	−	12.8771i	−0.244652	−	0.672177i	−0.999861	−	0.0166920i	$-0.994687\pi$
$367$	−4.68686	−	12.8771i	−0.244652	−	0.672177i	0.755208	−	0.655485i	$-0.227536\pi$
$368$	−0.243391	−	0.140522i	−0.0126876	−	0.00732520i
$369$	−12.3785	−	13.6387i	−0.644400	−	0.710002i
$370$	34.4513	+	19.8904i	1.79104	+	1.03405i
$371$	0.112980	+	0.417853i	0.00586564	+	0.0216939i
$372$	15.3787	+	21.0791i	0.797349	+	1.09290i
$373$	10.9812	+	3.99683i	0.568585	+	0.206948i	0.610285	−	0.792182i	$-0.291055\pi$
$373$	10.9812	+	3.99683i	0.568585	+	0.206948i	−0.0416995	+	0.999130i	$0.513277\pi$
$374$	0.0417753	+	0.0152050i	0.00216015	+	0.000786230i
$375$	20.2508	−	5.85026i	1.04575	−	0.302106i
$376$	−12.2851	−	2.16620i	−0.633558	−	0.111713i
$377$	0.453725			0.0233681
$378$	−12.6050	−	29.0305i	−0.648333	−	1.49317i
$379$	−12.7028			−0.652500			−0.326250	−	0.945283i	$-0.605785\pi$
$379$	−12.7028			−0.652500			−0.326250	+	0.945283i	$0.605785\pi$
$380$	45.5030	+	8.02340i	2.33425	+	0.411592i
$381$	5.36119	+	5.15676i	0.274662	+	0.264189i
$382$	−21.7040	−	7.89963i	−1.11048	−	0.404180i
$383$	−7.52651	−	2.73942i	−0.384587	−	0.139978i	0.142489	−	0.989796i	$-0.454489\pi$
$383$	−7.52651	−	2.73942i	−0.384587	−	0.139978i	−0.527076	+	0.849818i	$0.676712\pi$
$384$	32.5200	−	3.48313i	1.65953	−	0.177748i
$385$	0.578876	+	0.153702i	0.0295022	+	0.00783340i
$386$	−49.0625	−	28.3263i	−2.49722	−	1.44177i
$387$	−17.7667	+	22.9270i	−0.903134	+	1.16545i
$388$	38.4719	+	22.2117i	1.95311	+	1.12763i
$389$	−4.38258	−	12.0411i	−0.222206	−	0.610506i	0.777628	−	0.628724i	$-0.216423\pi$
$389$	−4.38258	−	12.0411i	−0.222206	−	0.610506i	−0.999834	+	0.0182189i	$0.994200\pi$
$390$	0.150457	+	0.306938i	0.00761869	+	0.0155424i
$391$	−0.0523045	+	0.143705i	−0.00264515	+	0.00726749i
$392$	10.5551	+	18.0919i	0.533112	+	0.913776i
$393$	7.47590	+	0.507888i	0.377109	+	0.0256195i
$394$	−24.6375	−	20.6733i	−1.24122	−	1.04151i
$395$	−2.39588	+	4.14978i	−0.120550	+	0.208798i
$396$	−0.566487	+	1.07566i	−0.0284670	+	0.0540542i
$397$	8.65774	−	4.99855i	0.434520	−	0.250870i	−0.266750	−	0.963766i	$-0.585950\pi$
$397$	8.65774	−	4.99855i	0.434520	−	0.250870i	0.701270	+	0.712896i	$0.252617\pi$
$398$	−22.7125	−	19.0581i	−1.13848	−	0.955294i
$399$	34.8022	−	0.755422i	1.74229	−	0.0378184i
$400$	−0.0803954	−	0.455945i	−0.00401977	−	0.0227973i
$401$	36.5039	−	6.43662i	1.82292	−	0.321429i	0.845698	−	0.533662i	$-0.179185\pi$
$401$	36.5039	−	6.43662i	1.82292	−	0.321429i	0.977219	+	0.212233i	$0.0680735\pi$
$402$	38.0636	+	9.41029i	1.89844	+	0.469343i
$403$	−0.162647	−	0.136477i	−0.00810203	−	0.00679841i
$404$	−22.9268	+	39.7104i	−1.14065	+	1.97566i
$405$	−4.14089	−	16.0649i	−0.205763	−	0.798272i
$406$	59.2083	+	5.04473i	2.93846	+	0.250366i
$407$	−0.393748	−	1.08181i	−0.0195174	−	0.0536236i
$408$	0.226186	+	0.782947i	0.0111979	+	0.0387616i
$409$	−0.800841	+	2.20029i	−0.0395990	+	0.108797i	−0.957916	−	0.287048i	$-0.907326\pi$
$409$	−0.800841	+	2.20029i	−0.0395990	+	0.108797i	0.918317	+	0.395845i	$0.129548\pi$
$410$	16.7469	+	19.9581i	0.827069	+	0.985663i
$411$	−1.78948	−	2.45277i	−0.0882685	−	0.120986i
$412$	−16.5462	+	19.7190i	−0.815175	+	0.971488i
$413$	−13.3019	−	28.3578i	−0.654542	−	1.39539i
$414$	−5.94296	−	3.12979i	−0.292081	−	0.153821i
$415$	11.8240			0.580419
$416$	−0.232462	+	0.0846094i	−0.0113974	+	0.00414832i
$417$	−21.1614	+	10.3731i	−1.03628	+	0.507971i
$418$	−1.38045	−	1.64516i	−0.0675202	−	0.0804674i
$419$	28.6465	+	10.4265i	1.39947	+	0.509366i	0.928022	−	0.372526i	$-0.121508\pi$
$419$	28.6465	+	10.4265i	1.39947	+	0.509366i	0.471451	+	0.881892i	$0.343730\pi$
$420$	10.0996	+	25.9799i	0.492811	+	1.26769i
$421$	0.369085	−	2.09318i	0.0179881	−	0.102015i	−0.974492	−	0.224423i	$-0.927950\pi$
$421$	0.369085	−	2.09318i	0.0179881	−	0.102015i	0.992480	+	0.122407i	$0.0390614\pi$
$422$			12.1740i			0.592623i
$423$	−12.3921	−	1.69156i	−0.602522	−	0.0822463i
$424$	0.489547			0.0237745
$425$	−0.236734	+	0.0861641i	−0.0114833	+	0.00417957i
$426$	−0.423302	−	3.95213i	−0.0205091	−	0.191482i
$427$	7.99922	−	0.718132i	0.387109	−	0.0347528i
$428$	−15.8410	−	18.8785i	−0.765702	−	0.912528i
$429$	0.00237418	−	0.00960332i	0.000114627	−	0.000463653i
$430$	26.3728	−	31.4298i	1.27181	−	1.51568i
$431$	−1.02928	+	0.594254i	−0.0495786	+	0.0286242i	−0.524584	−	0.851358i	$-0.675779\pi$
$431$	−1.02928	+	0.594254i	−0.0495786	+	0.0286242i	0.475006	+	0.879983i	$0.342446\pi$
$432$	−1.48570	+	0.217811i	−0.0714806	+	0.0104795i
$433$		−	11.1104i		−	0.533930i	−0.963706	−	0.266965i	$-0.913979\pi$
$433$		−	11.1104i		−	0.533930i	0.963706	−	0.266965i	$-0.0860208\pi$
$434$	−19.7070	−	19.6178i	−0.945966	−	0.941684i
$435$	30.2383	+	7.47568i	1.44982	+	0.358431i
$436$	5.01076	+	28.4175i	0.239972	+	1.36095i
$437$	5.65928	−	4.74870i	0.270720	−	0.227161i
$438$	33.4878	+	14.8303i	1.60011	+	0.708619i
$439$	1.90318	+	5.22894i	0.0908337	+	0.249564i	0.976788	−	0.214209i	$-0.0687175\pi$
$439$	1.90318	+	5.22894i	0.0908337	+	0.249564i	−0.885954	+	0.463773i	$0.846495\pi$
$440$	0.338686	−	0.586622i	0.0161462	−	0.0279661i
$441$	11.2793	+	17.7138i	0.537107	+	0.843514i
$442$	−0.00841775	−	0.0145800i	−0.000400391	−	0.000693498i
$443$	17.4915	−	20.8455i	0.831046	−	0.990402i	−0.168943	−	0.985626i	$-0.554035\pi$
$443$	17.4915	−	20.8455i	0.831046	−	0.990402i	0.999989	−	0.00477585i	$-0.00152021\pi$
$444$	29.8724	−	44.4775i	1.41768	−	2.11081i
$445$	3.39427	+	19.2498i	0.160904	+	0.912530i
$446$	−14.7616	+	12.3865i	−0.698984	+	0.586517i
$447$	−14.4223	+	7.06963i	−0.682152	+	0.334382i
$448$	−32.7517	+	8.85549i	−1.54737	+	0.418382i
$449$	−21.3299	+	12.3148i	−1.00662	+	0.581171i	−0.910200	−	0.414170i	$-0.864072\pi$
$449$	−21.3299	+	12.3148i	−1.00662	+	0.581171i	−0.0964182	+	0.995341i	$0.530739\pi$
$450$	−2.34337	−	10.8139i	−0.110467	−	0.509770i
$451$		−	0.753979i		−	0.0355035i
$452$	53.4760	+	9.42926i	2.51530	+	0.443515i
$453$	1.80074	+	16.8125i	0.0846063	+	0.789922i
$454$	45.7616	−	8.06900i	2.14770	−	0.378697i
$455$	−0.130517	−	0.185500i	−0.00611871	−	0.00869637i
$456$	9.44863	−	38.2187i	0.442473	−	1.78976i
$457$	−1.22308	+	6.93645i	−0.0572134	+	0.324473i	−0.999959	−	0.00903894i	$-0.997123\pi$
$457$	−1.22308	+	6.93645i	−0.0572134	+	0.324473i	0.942746	+	0.333512i	$0.108234\pi$
$458$	−6.68651	−	11.5814i	−0.312440	−	0.541162i
$459$	0.257103	+	0.775569i	0.0120005	+	0.0362005i
$460$	5.12303	+	2.95778i	0.238863	+	0.137907i
$461$	−6.82236	+	2.48314i	−0.317749	+	0.115651i	−0.495971	−	0.868339i	$-0.665188\pi$
$461$	−6.82236	+	2.48314i	−0.317749	+	0.115651i	0.178222	+	0.983990i	$0.442966\pi$
$462$	0.416590	−	1.22678i	0.0193815	−	0.0570748i
$463$	6.25076	−	5.24501i	0.290498	−	0.243756i	−0.485878	−	0.874026i	$-0.661500\pi$
$463$	6.25076	−	5.24501i	0.290498	−	0.243756i	0.776376	+	0.630270i	$0.217056\pi$
$464$	0.964258	−	2.64928i	0.0447645	−	0.122990i
$465$	−8.59092	−	11.7753i	−0.398394	−	0.546065i
$466$	−2.46340	+	13.9706i	−0.114115	+	0.647177i
$467$	6.38140	+	11.0529i	0.295296	+	0.511468i	0.975054	−	0.221969i	$-0.0712484\pi$
$467$	6.38140	+	11.0529i	0.295296	+	0.511468i	−0.679758	+	0.733437i	$0.737915\pi$
$468$	0.426177	−	0.174154i	0.0197001	−	0.00805027i
$469$	−25.9228	−	2.20870i	−1.19700	−	0.101988i
$470$	17.4227	+	3.07209i	0.803649	+	0.141705i
$471$	−25.1688	+	12.3374i	−1.15972	+	0.568479i
$472$	−34.8865	+	6.15144i	−1.60578	+	0.283143i
$473$	−1.16932	+	0.206182i	−0.0537653	+	0.00948027i
$474$	8.60465	+	5.77914i	0.395224	+	0.265445i
$475$	11.9852	+	2.11332i	0.549920	+	0.0969657i
$476$	−0.582999	−	1.24288i	−0.0267217	−	0.0569672i
$477$	0.490444	−	0.0190722i	0.0224559	−	0.000873256i
$478$	−21.4841	−	37.2116i	−0.982661	−	1.70202i
$479$	−3.46023	+	19.6239i	−0.158102	+	0.896640i	0.797793	+	0.602931i	$0.206001\pi$
$479$	−3.46023	+	19.6239i	−0.158102	+	0.896640i	−0.955895	+	0.293709i	$0.905110\pi$
$480$	−16.8864	+	1.80866i	−0.770755	+	0.0825535i
$481$	−0.149111	+	0.409680i	−0.00679890	+	0.0186798i
$482$	21.4902	−	18.0325i	0.978854	−	0.821356i
$483$	4.22006	+	1.43305i	0.192019	+	0.0652062i
$484$	34.0618	−	12.3975i	1.54826	−	0.563522i
$485$	−21.4913	−	12.4080i	−0.975869	−	0.563418i
$486$	−35.2779	+	6.58133i	−1.60024	+	0.298535i
$487$	−16.5334	−	28.6367i	−0.749200	−	1.29765i	−0.948207	−	0.317654i	$-0.897105\pi$
$487$	−16.5334	−	28.6367i	−0.749200	−	1.29765i	0.199007	−	0.979998i	$-0.436228\pi$
$488$	1.57728	−	8.94522i	0.0714003	−	0.404931i
$489$	−14.1223	−	13.5838i	−0.638634	−	0.614282i
$490$	−14.9691	−	25.6577i	−0.676236	−	1.15910i
$491$	1.71158	−	0.301798i	0.0772427	−	0.0136200i	−0.134893	−	0.990860i	$-0.543069\pi$
$491$	1.71158	−	0.301798i	0.0772427	−	0.0136200i	0.212136	+	0.977240i	$0.431958\pi$
$492$	28.3472	−	20.6814i	1.27799	−	0.932387i
$493$	−1.51080	−	0.266394i	−0.0680429	−	0.0119978i
$494$			0.813291i			0.0365917i
$495$	0.316453	−	0.600892i	0.0142235	−	0.0270081i
$496$	−1.14254	+	0.659646i	−0.0513015	+	0.0296190i
$497$	0.688375	+	2.54593i	0.0308778	+	0.114201i
$498$	1.73363	−	25.5183i	0.0776856	−	1.14350i
$499$	−26.2943	+	22.0635i	−1.17709	+	0.987699i	−0.177100	+	0.984193i	$0.556671\pi$
$499$	−26.2943	+	22.0635i	−1.17709	+	0.987699i	−0.999994	+	0.00350565i	$0.998884\pi$
$500$	6.97336	+	39.5479i	0.311858	+	1.76864i
$501$	−3.30306	−	0.224399i	−0.147570	−	0.0100254i
$502$	5.63027	−	6.70990i	0.251291	−	0.299478i
$503$	6.14413	+	10.6419i	0.273953	+	0.474501i	0.969870	−	0.243621i	$-0.0783354\pi$
$503$	6.14413	+	10.6419i	0.273953	+	0.474501i	−0.695917	+	0.718122i	$0.745002\pi$
$504$	22.6688	−	7.08527i	1.00975	−	0.315603i
$505$	12.8074	−	22.1831i	0.569924	−	0.987137i
$506$	−0.0940402	−	0.258373i	−0.00418060	−	0.0114861i
$507$	18.1871	−	13.2688i	0.807717	−	0.589288i
$508$	−10.8562	+	9.10940i	−0.481664	+	0.404164i
$509$	4.54581	+	25.7805i	0.201489	+	1.14270i	0.902869	+	0.429915i	$0.141456\pi$
$509$	4.54581	+	25.7805i	0.201489	+	1.14270i	−0.701380	+	0.712787i	$0.747432\pi$
$510$	−0.320774	−	1.11037i	−0.0142041	−	0.0491679i
$511$	−23.4877	−	6.23643i	−1.03903	−	0.275883i
$512$			3.26654i			0.144362i
$513$	7.97698	−	38.6569i	0.352192	−	1.70674i
$514$	−43.9683	+	25.3851i	−1.93936	+	1.11969i
$515$	9.24312	−	11.0155i	0.407301	−	0.485402i
$516$	−39.8257	−	38.3071i	−1.75323	−	1.68638i
$517$	−0.329097	−	0.392203i	−0.0144737	−	0.0172490i
$518$	−24.0131	+	51.8028i	−1.05508	+	2.27608i
$519$	−34.2429	+	24.9827i	−1.50310	+	1.09662i
$520$	−0.241049	+	0.0877347i	−0.0105707	+	0.00384742i
$521$	14.2660			0.625004			0.312502	−	0.949917i	$-0.398833\pi$
$521$	14.2660			0.625004			0.312502	+	0.949917i	$0.398833\pi$
$522$	20.5673	−	64.1634i	0.900206	−	2.80835i
$523$			20.0974i			0.878798i	0.898292	+	0.439399i	$0.144809\pi$
$523$			20.0974i			0.878798i	−0.898292	+	0.439399i	$0.855191\pi$
$524$	−2.47889	+	14.0585i	−0.108291	+	0.614148i
$525$	2.66018	+	6.84295i	0.116100	+	0.298651i
$526$	4.11812	+	1.49887i	0.179559	+	0.0653540i
$527$	0.461447	+	0.549931i	0.0201009	+	0.0239554i
$528$	−0.0510276	−	0.0342717i	−0.00222069	−	0.00149148i
$529$	−20.7241	+	7.54297i	−0.901049	+	0.327955i
$530$	−0.694271			−0.0301572
$531$	−34.7108	+	7.52185i	−1.50632	+	0.326420i
$532$	−5.63012	+	66.0789i	−0.244097	+	2.86488i
$533$	−0.183535	+	0.218728i	−0.00794978	+	0.00947418i
$534$	42.0421	−	4.50301i	1.81934	−	0.194864i
$535$	8.84913	+	10.5460i	0.382581	+	0.455943i
$536$	−10.0636	+	27.6495i	−0.434681	+	1.19428i
$537$	−22.1735	+	23.0525i	−0.956855	+	0.994788i
$538$	9.63644	+	26.4759i	0.415457	+	1.14146i
$539$	−0.145434	+	0.847262i	−0.00626430	+	0.0364942i
$540$	31.2718	−	4.58462i	1.34572	−	0.197291i
$541$	3.47620	−	6.02095i	0.149453	−	0.258861i	−0.781572	−	0.623815i	$-0.785582\pi$
$541$	3.47620	−	6.02095i	0.149453	−	0.258861i	0.931026	+	0.364954i	$0.118915\pi$
$542$	−20.5687	−	17.2592i	−0.883500	−	0.741344i
$543$	7.74024	−	8.04709i	0.332166	−	0.345334i
$544$	0.823721	−	0.145244i	0.0353167	−	0.00622730i
$545$	−2.79913	−	15.8747i	−0.119902	−	0.679996i
$546$	−0.419476	+	0.254479i	−0.0179519	+	0.0108907i
$547$	−10.1175	−	8.48957i	−0.432592	−	0.362988i	0.400337	−	0.916368i	$-0.368893\pi$
$547$	−10.1175	−	8.48957i	−0.432592	−	0.362988i	−0.832929	+	0.553380i	$0.813338\pi$
$548$	5.00934	−	2.89215i	0.213989	−	0.123546i
$549$	1.23168	−	9.02307i	0.0525668	−	0.385095i
$550$	0.226475	−	0.392266i	0.00965691	−	0.0167263i
$551$	56.7713	+	47.6368i	2.41854	+	2.02940i
$552$	2.81028	−	4.18427i	0.119614	−	0.178094i
$553$	−6.23984	−	2.89247i	−0.265345	−	0.123000i
$554$	14.9189	−	40.9894i	0.633844	−	1.74147i
$555$	−16.6874	+	24.8462i	−0.708342	+	1.05466i
$556$	−15.3561	−	42.1906i	−0.651244	−	1.78928i
$557$	36.7504	+	21.2178i	1.55716	+	0.899028i	0.997527	+	0.0702901i	$0.0223925\pi$
$557$	36.7504	+	21.2178i	1.55716	+	0.899028i	0.559636	+	0.828738i	$0.310941\pi$
$558$	−26.6726	+	16.8142i	−1.12914	+	0.711801i
$559$	0.389407	+	0.224824i	0.0164702	+	0.00950905i
$560$	−1.36050	+	0.367854i	−0.0574915	+	0.0155447i
$561$	−0.0135438	+	0.0305828i	−0.000571821	+	0.00129121i
$562$	−0.881622	−	0.320884i	−0.0371890	−	0.0135357i
$563$	−29.1497	−	10.6096i	−1.22852	−	0.447143i	−0.355426	−	0.934704i	$-0.615664\pi$
$563$	−29.1497	−	10.6096i	−1.22852	−	0.447143i	−0.873089	+	0.487561i	$0.837887\pi$
$564$	5.71856	−	23.1310i	0.240795	−	0.973990i
$565$	−29.8730	−	5.26741i	−1.25676	−	0.221602i
$566$	−10.7140			−0.450344
$567$	22.4343	−	7.98140i	0.942151	−	0.335187i
$568$	2.98275			0.125154
$569$	11.2726	+	1.98767i	0.472573	+	0.0833273i	0.404862	−	0.914378i	$-0.367319\pi$
$569$	11.2726	+	1.98767i	0.472573	+	0.0833273i	0.0677106	+	0.997705i	$0.478431\pi$
$570$	−13.4000	+	54.2014i	−0.561263	+	2.27025i
$571$	−14.2946	−	5.20281i	−0.598210	−	0.217731i	0.0251265	−	0.999684i	$-0.492001\pi$
$571$	−14.2946	−	5.20281i	−0.598210	−	0.217731i	−0.623337	+	0.781954i	$0.714223\pi$
$572$	0.0177098	+	0.00644584i	0.000740484	+	0.000269514i
$573$	7.03660	−	15.8891i	0.293958	−	0.663776i
$574$	−26.3821	+	26.5020i	−1.10117	+	1.10617i
$575$	1.34938	+	0.779063i	0.0562729	+	0.0324892i
$576$	1.49490	+	38.4415i	0.0622873	+	1.60173i
$577$	−14.5184	−	8.38222i	−0.604410	−	0.348956i	0.166364	−	0.986064i	$-0.446797\pi$
$577$	−14.5184	−	8.38222i	−0.604410	−	0.348956i	−0.770775	+	0.637108i	$0.780131\pi$
$578$	−13.3659	−	36.7224i	−0.555947	−	1.52745i
$579$	23.7648	−	35.3838i	0.987633	−	1.47050i
$580$	−20.2963	+	55.7635i	−0.842756	+	2.31545i
$581$	1.51748	+	16.9031i	0.0629558	+	0.701260i
$582$	−29.9296	+	44.5626i	−1.24062	+	1.84718i
$583$	0.0153913	+	0.0129149i	0.000637443	+	0.000534879i
$584$	−13.7421	+	23.8020i	−0.568651	+	0.984933i
$585$	−0.238073	+	0.0972865i	−0.00984310	+	0.00402230i
$586$	16.5480	−	9.55400i	0.683592	−	0.394672i
$587$	−1.10643	−	0.928404i	−0.0456672	−	0.0383193i	0.619668	−	0.784864i	$-0.287267\pi$
$587$	−1.10643	−	0.928404i	−0.0456672	−	0.0383193i	−0.665336	+	0.746544i	$0.731712\pi$
$588$	−35.8436	+	17.7722i	−1.47816	+	0.732914i
$589$	−6.02205	−	34.1528i	−0.248134	−	1.40724i
$590$	49.4758	−	8.72391i	2.03689	−	0.359158i
$591$	16.7746	−	17.4396i	0.690016	−	0.717370i
$592$	2.07521	+	1.74131i	0.0852905	+	0.0715672i
$593$	17.6222	−	30.5226i	0.723657	−	1.25341i	−0.235867	−	0.971785i	$-0.575793\pi$
$593$	17.6222	−	30.5226i	0.723657	−	1.25341i	0.959524	−	0.281626i	$-0.0908737\pi$
$594$	−1.25043	−	0.771061i	−0.0513057	−	0.0316370i
$595$	0.325677	+	0.694300i	0.0133515	+	0.0284635i
$596$	−10.4658	−	28.7545i	−0.428695	−	1.17783i
$597$	15.4640	−	16.0770i	0.632899	−	0.657989i
$598$	−0.0356128	+	0.0978453i	−0.00145631	+	0.00400119i
$599$	−27.9181	−	33.2715i	−1.14070	−	1.35944i	−0.923633	−	0.383279i	$-0.874795\pi$
$599$	−27.9181	−	33.2715i	−1.14070	−	1.35944i	−0.217069	−	0.976156i	$-0.569650\pi$
$600$	8.25614	−	0.884292i	0.337055	−	0.0361011i
$601$	12.1502	−	14.4801i	0.495618	−	0.590655i	−0.459019	−	0.888427i	$-0.651799\pi$
$601$	12.1502	−	14.4801i	0.495618	−	0.590655i	0.954637	+	0.297772i	$0.0962434\pi$
$602$	48.3154	+	33.6677i	1.96919	+	1.37219i
$603$	−9.00483	+	28.0922i	−0.366705	+	1.14400i
$604$	−32.2132			−1.31074
$605$	−19.0277	+	6.92552i	−0.773587	+	0.281563i
$606$	−45.9972	−	30.8931i	−1.86851	−	1.25495i
$607$	−1.36629	−	1.62828i	−0.0554560	−	0.0660899i	0.737603	−	0.675234i	$-0.235957\pi$
$607$	−1.36629	−	1.62828i	−0.0554560	−	0.0660899i	−0.793059	+	0.609144i	$0.791513\pi$
$608$	−37.9695	−	13.8198i	−1.53987	−	0.560465i
$609$	−6.80616	+	44.1869i	−0.275800	+	1.79054i
$610$	−2.23689	+	12.6860i	−0.0905691	+	0.513643i
$611$			0.193887i			0.00784383i
$612$	−1.52132	+	0.329671i	−0.0614957	+	0.0133261i
$613$	−18.2547			−0.737301			−0.368650	−	0.929568i	$-0.620180\pi$
$613$	−18.2547			−0.737301			−0.368650	+	0.929568i	$0.620180\pi$
$614$	12.7609	−	4.64457i	0.514987	−	0.187440i
$615$	−15.8354	+	11.5531i	−0.638545	+	0.465866i
$616$	0.882077	+	0.408885i	0.0355399	+	0.0164745i
$617$	−5.58064	−	6.65075i	−0.224668	−	0.267749i	0.641922	−	0.766770i	$-0.278137\pi$
$617$	−5.58064	−	6.65075i	−0.224668	−	0.267749i	−0.866590	+	0.499021i	$0.833693\pi$
$618$	−22.4182	−	21.5633i	−0.901790	−	0.867404i
$619$	−25.2770	+	30.1239i	−1.01597	+	1.21078i	−0.0385946	+	0.999255i	$0.512288\pi$
$619$	−25.2770	+	30.1239i	−1.01597	+	1.21078i	−0.977372	+	0.211527i	$0.932156\pi$
$620$	24.0488	−	13.8846i	0.965824	−	0.557619i
$621$	2.65242	−	4.30142i	0.106438	−	0.172610i
$622$		−	31.2476i		−	1.25291i
$623$	−27.0832	+	7.32281i	−1.08506	+	0.293382i
$624$	0.00646057	+	0.0223634i	0.000258630	+	0.000895254i
$625$	−2.50446	−	14.2035i	−0.100178	−	0.568140i
$626$	−10.0799	+	8.45803i	−0.402873	+	0.338051i
$627$	1.30532	−	0.952327i	0.0521295	−	0.0380323i
$628$	−18.2641	−	50.1803i	−0.728818	−	2.00241i
$629$	0.737040	−	1.27659i	0.0293877	−	0.0509010i
$630$	−32.1487	+	10.0483i	−1.28083	+	0.400333i
$631$	5.26401	+	9.11753i	0.209557	+	0.362963i	0.951575	−	0.307417i	$-0.0994645\pi$
$631$	5.26401	+	9.11753i	0.209557	+	0.362963i	−0.742018	+	0.670380i	$0.766131\pi$
$632$	−4.99984	+	5.95857i	−0.198883	+	0.237019i
$633$	−9.13832	−	0.620827i	−0.363216	−	0.0246757i
$634$	−0.962742	−	5.45998i	−0.0382354	−	0.216844i
$635$	6.06451	−	5.08873i	0.240663	−	0.201940i
$636$	−0.0633791	+	0.932915i	−0.00251315	+	0.0369925i
$637$	0.248433	−	0.210388i	0.00984326	−	0.00833587i
$638$	2.38869	−	1.37911i	0.0945693	−	0.0545996i
$639$	2.98822	−	0.116205i	0.118212	−	0.00459698i
$640$		−	34.8074i		−	1.37588i
$641$	−12.1516	−	2.14265i	−0.479958	−	0.0846295i	−0.0715652	−	0.997436i	$-0.522799\pi$
$641$	−12.1516	−	2.14265i	−0.479958	−	0.0846295i	−0.408392	+	0.912806i	$0.633911\pi$
$642$	24.0575	−	17.5517i	0.949473	−	0.692710i
$643$	−22.7208	+	4.00630i	−0.896023	+	0.157993i	−0.602650	−	0.798005i	$-0.705889\pi$
$643$	−22.7208	+	4.00630i	−0.896023	+	0.157993i	−0.293372	+	0.955998i	$0.594778\pi$
$644$	−3.57084	+	7.70327i	−0.140711	+	0.303551i
$645$	22.2476	+	21.3993i	0.875998	+	0.842595i
$646$	0.477505	−	2.70807i	0.0187872	−	0.106547i
$647$	19.2253	+	33.2993i	0.755826	+	1.30913i	0.944963	+	0.327178i	$0.106098\pi$
$647$	19.2253	+	33.2993i	0.755826	+	1.30913i	−0.189137	+	0.981951i	$0.560569\pi$
$648$	−2.09134	−	26.8489i	−0.0821557	−	1.05473i
$649$	−1.25911	−	0.726949i	−0.0494245	−	0.0285352i
$650$	−0.161186	+	0.0586669i	−0.00632224	+	0.00230111i
$651$	15.7309	−	13.7924i	0.616542	−	0.540568i
$652$	28.5970	−	23.9958i	1.11995	−	0.939747i
$653$	4.84634	−	13.3152i	0.189652	−	0.521064i	−0.808028	−	0.589144i	$-0.799465\pi$
$653$	4.84634	−	13.3152i	0.189652	−	0.521064i	0.997680	+	0.0680800i	$0.0216873\pi$
$654$	−34.6706	+	3.71347i	−1.35573	+	0.145208i
$655$	1.38477	−	7.85341i	0.0541074	−	0.306858i
$656$	0.887094	+	1.53649i	0.0346352	+	0.0599899i
$657$	−12.8400	+	24.3810i	−0.500935	+	0.951192i
$658$	−2.15572	+	25.3010i	−0.0840389	+	0.986336i
$659$	39.3185	+	6.93292i	1.53163	+	0.270068i	0.874993	−	0.484136i	$-0.160866\pi$
$659$	39.3185	+	6.93292i	1.53163	+	0.270068i	0.656640	+	0.754204i	$0.271977\pi$
$660$	1.07406	+	0.721371i	0.0418077	+	0.0280793i
$661$	24.1288	−	4.25455i	0.938500	−	0.165483i	0.316582	−	0.948565i	$-0.397465\pi$
$661$	24.1288	−	4.25455i	0.938500	−	0.165483i	0.621918	+	0.783082i	$0.286354\pi$
$662$	24.0212	−	4.23559i	0.933612	−	0.164621i
$663$	0.0113736	−	0.00557518i	0.000441713	−	0.000216522i
$664$	18.9021	+	3.33296i	0.733545	+	0.129344i
$665$	3.14512	−	36.9132i	0.121962	−	1.43143i
$666$	51.1755	+	39.6572i	1.98301	+	1.53669i
$667$	4.74409	+	8.21701i	0.183692	+	0.318164i
$668$	1.09524	−	6.21143i	0.0423762	−	0.240327i
$669$	−8.54502	−	11.7123i	−0.330369	−	0.452826i
$670$	14.2721	−	39.2122i	0.551379	−	1.51490i
$671$	0.285576	−	0.239627i	0.0110245	−	0.00925068i
$672$	−4.75276	−	23.9080i	−0.183342	−	0.922270i
$673$	−12.2850	+	4.47136i	−0.473551	+	0.172358i	−0.567760	−	0.823194i	$-0.692190\pi$
$673$	−12.2850	+	4.47136i	−0.473551	+	0.172358i	0.0942095	+	0.995552i	$0.469968\pi$
$674$	45.8791	+	26.4883i	1.76720	+	1.02029i
$675$	8.23681	−	1.20756i	0.317035	−	0.0464791i
$676$	21.4450	+	37.1438i	0.824807	+	1.42861i
$677$	4.73038	−	26.8273i	0.181803	−	1.03106i	−0.748191	−	0.663484i	$-0.769077\pi$
$677$	4.73038	−	26.8273i	0.181803	−	1.03106i	0.929994	−	0.367575i	$-0.119812\pi$
$678$	−15.7479	+	63.6986i	−0.604794	+	2.44633i
$679$	14.9798	−	32.3155i	0.574872	−	1.24015i
$680$	0.854147	−	0.150609i	0.0327551	−	0.00577560i
$681$	3.72326	+	34.7620i	0.142676	+	1.33208i
$682$	−1.27110	−	0.224130i	−0.0486730	−	0.00858237i
$683$			46.5851i			1.78253i	0.453482	+	0.891265i	$0.350182\pi$
$683$			46.5851i			1.78253i	−0.453482	+	0.891265i	$0.649818\pi$
$684$	71.6089	+	22.9539i	2.73804	+	0.877666i
$685$	−2.79834	+	1.61562i	−0.106919	+	0.0617297i
$686$	34.7581	−	24.6921i	1.32707	−	0.942749i
$687$	9.03444	−	4.42856i	0.344685	−	0.168960i
$688$	2.14030	−	1.79593i	0.0815983	−	0.0684691i
$689$	−0.00132125	−	0.00749317i	−5.03355e−5	−	0.000285467i
$690$	−3.98552	+	5.93409i	−0.151726	+	0.225907i
$691$	5.79402	−	6.90504i	0.220415	−	0.262680i	−0.644494	−	0.764610i	$-0.722932\pi$
$691$	5.79402	−	6.90504i	0.220415	−	0.262680i	0.864909	+	0.501929i	$0.167376\pi$
$692$	−40.3770	−	69.9350i	−1.53490	−	2.65853i
$693$	0.899623	+	0.375270i	0.0341738	+	0.0142553i
$694$	−4.43299	+	7.67816i	−0.168274	+	0.291459i
$695$	8.57829	+	23.5687i	0.325393	+	0.894010i
$696$	46.2324	+	20.4744i	1.75243	+	0.776078i
$697$	0.739549	−	0.620555i	0.0280124	−	0.0235052i
$698$	−0.843525	−	4.78387i	−0.0319279	−	0.181072i
$699$	−10.3613	−	2.56157i	−0.391900	−	0.0968876i
$700$	−13.5023	+	3.65078i	−0.510339	+	0.137987i
$701$		−	28.1670i		−	1.06385i	−0.846790	−	0.531927i	$-0.821468\pi$
$701$		−	28.1670i		−	1.06385i	0.846790	−	0.531927i	$-0.178532\pi$
$702$	0.175055	+	0.528065i	0.00660701	+	0.0199305i
$703$	−61.6697	+	35.6050i	−2.32592	+	1.34287i
$704$	−1.01228	+	1.20639i	−0.0381517	+	0.0454674i
$705$	−3.19452	+	12.9215i	−0.120313	+	0.486652i
$706$	−18.1837	−	21.6704i	−0.684351	−	0.815578i
$707$	33.3558	+	15.4620i	1.25447	+	0.581509i
$708$	−7.20602	−	67.2786i	−0.270819	−	2.52848i
$709$	33.4746	−	12.1838i	1.25717	−	0.457571i	0.374349	−	0.927288i	$-0.377866\pi$
$709$	33.4746	−	12.1838i	1.25717	−	0.457571i	0.882817	+	0.469717i	$0.155644\pi$
$710$	−4.23011			−0.158753
$711$	−4.77686	+	6.16428i	−0.179146	+	0.231179i
$712$			31.7300i			1.18913i
$713$	0.770997	−	4.37254i	0.0288741	−	0.163753i
$714$	1.54617	−	0.601069i	0.0578639	−	0.0224944i
$715$	−0.00989312	−	0.00360080i	−0.000369982	−	0.000134662i
$716$	−39.1693	−	46.6802i	−1.46383	−	1.74452i
$717$	29.0281	−	14.2292i	1.08408	−	0.531400i
$718$	66.1694	−	24.0837i	2.46942	−	0.898795i
$719$	9.13804			0.340791			0.170396	−	0.985376i	$-0.445495\pi$
$719$	9.13804			0.340791			0.170396	+	0.985376i	$0.445495\pi$
$720$	0.0620975	+	1.59685i	0.00231424	+	0.0595109i
$721$	16.9336	+	11.7999i	0.630640	+	0.439450i
$722$	−57.2720	+	68.2541i	−2.13144	+	2.54016i
$723$	12.4400	+	17.0510i	0.462647	+	0.634134i
$724$	13.6731	+	16.2950i	0.508157	+	0.605598i
$725$	−5.34592	+	14.6878i	−0.198542	+	0.545491i
$726$	12.1566	+	42.0804i	0.451175	+	1.56175i
$727$	3.56316	+	9.78970i	0.132150	+	0.363080i	0.988065	−	0.154037i	$-0.0492275\pi$
$727$	3.56316	+	9.78970i	0.132150	+	0.363080i	−0.855915	+	0.517117i	$0.827005\pi$
$728$	−0.156358	−	0.333334i	−0.00579501	−	0.0123542i
$729$	−3.14118	−	26.8167i	−0.116340	−	0.993209i
$730$	19.4889	−	33.7558i	0.721317	−	1.24936i
$731$	−1.16463	−	0.977242i	−0.0430755	−	0.0361446i
$732$	16.8424	+	4.16387i	0.622514	+	0.153901i
$733$	27.3550	−	4.82343i	1.01038	−	0.178157i	0.356131	−	0.934436i	$-0.384096\pi$
$733$	27.3550	−	4.82343i	1.01038	−	0.178157i	0.654250	+	0.756279i	$0.272985\pi$
$734$	5.47810	+	31.0678i	0.202200	+	1.14673i
$735$	20.0231	−	9.92798i	0.738562	−	0.366199i
$736$	−3.96288	−	3.32525i	−0.146074	−	0.122570i
$737$	−1.04583	+	0.603808i	−0.0385235	+	0.0222415i
$738$	22.6118	+	35.8694i	0.832350	+	1.32037i
$739$	17.8396	−	30.8992i	0.656242	−	1.13664i	−0.325339	−	0.945597i	$-0.605479\pi$
$739$	17.8396	−	30.8992i	0.656242	−	1.13664i	0.981581	−	0.191047i	$-0.0611882\pi$
$740$	−43.6802	−	36.6520i	−1.60571	−	1.34735i
$741$	−0.610489	−	0.0414746i	−0.0224269	−	0.00152361i
$742$	−0.0891020	−	0.992502i	−0.00327104	−	0.0364359i
$743$	2.30236	−	6.32568i	0.0844653	−	0.232067i	−0.890269	−	0.455436i	$-0.849483\pi$
$743$	2.30236	−	6.32568i	0.0844653	−	0.232067i	0.974734	+	0.223369i	$0.0717056\pi$
$744$	−10.4144	−	21.2458i	−0.381811	−	0.778908i
$745$	5.84643	+	16.0629i	0.214197	+	0.588500i
$746$	−23.2983	−	13.4513i	−0.853010	−	0.492486i
$747$	19.0666	+	2.60266i	0.697611	+	0.0952263i
$748$	−0.0551849	−	0.0318610i	−0.00201776	−	0.00116495i
$749$	−13.9404	+	14.0038i	−0.509372	+	0.511688i
$750$	−48.2503	+	5.16796i	−1.76185	+	0.188707i
$751$	44.9691	+	16.3674i	1.64095	+	0.597256i	0.987204	−	0.159462i	$-0.0509759\pi$
$751$	44.9691	+	16.3674i	1.64095	+	0.597256i	0.653742	+	0.756717i	$0.273198\pi$
$752$	1.13209	+	0.412049i	0.0412832	+	0.0150259i
$753$	4.74960	+	4.56849i	0.173085	+	0.166485i
$754$	−1.02866	−	0.181381i	−0.0374617	−	0.00660551i
$755$	17.9951			0.654907
$756$	10.5674	+	44.1165i	0.384331	+	1.60450i
$757$	35.1225			1.27655			0.638274	−	0.769809i	$-0.279649\pi$
$757$	35.1225			1.27655			0.638274	+	0.769809i	$0.279649\pi$
$758$	28.7992	+	5.07808i	1.04603	+	0.184444i
$759$	0.198741	−	0.0574144i	0.00721385	−	0.00208401i
$760$	−39.3720	−	14.3302i	−1.42817	−	0.519812i
$761$	−32.1441	−	11.6995i	−1.16522	−	0.424106i	−0.314262	−	0.949336i	$-0.601757\pi$
$761$	−32.1441	−	11.6995i	−1.16522	−	0.424106i	−0.850960	+	0.525230i	$0.823979\pi$
$762$	−10.0932	−	13.8343i	−0.365637	−	0.501165i
$763$	22.3345	−	6.03886i	0.808564	−	0.218621i
$764$	28.6709	+	16.5532i	1.03728	+	0.598872i
$765$	0.849845	−	0.184162i	0.0307262	−	0.00665839i
$766$	15.9686	+	9.21948i	0.576969	+	0.333113i
$767$	0.188312	+	0.517383i	0.00679955	+	0.0186816i
$768$	−30.8004	−	2.09248i	−1.11141	−	0.0755058i
$769$	3.20130	−	8.79549i	0.115442	−	0.317174i	−0.868493	−	0.495701i	$-0.834911\pi$
$769$	3.20130	−	8.79549i	0.115442	−	0.317174i	0.983935	+	0.178528i	$0.0571334\pi$
$770$	−1.25095	−	0.579878i	−0.0450812	−	0.0208973i
$771$	−16.8129	−	34.2989i	−0.605501	−	1.23525i
$772$	62.2056	+	52.1967i	2.23883	+	1.87860i
$773$	10.0564	−	17.4182i	0.361703	−	0.626488i	−0.626538	−	0.779391i	$-0.715529\pi$
$773$	10.0564	−	17.4182i	0.361703	−	0.626488i	0.988241	+	0.152903i	$0.0488621\pi$
$774$	49.4451	−	44.8765i	1.77727	−	1.61305i
$775$	6.33433	−	3.65712i	0.227536	−	0.131368i
$776$	−30.8589	−	25.8936i	−1.10777	−	0.929528i
$777$	−37.6607	−	20.6669i	−1.35107	−	0.741422i
$778$	5.12245	+	29.0509i	0.183649	+	1.04152i
$779$	−45.9287	+	8.09848i	−1.64557	+	0.290158i
$780$	−0.135986	−	0.470718i	−0.00486908	−	0.0168544i
$781$	0.0937775	+	0.0786887i	0.00335562	+	0.00281570i
$782$	0.176030	−	0.304892i	0.00629481	−	0.0109029i
$783$	47.1148	+	18.7107i	1.68374	+	0.668666i
$784$	−0.700474	−	1.89770i	−0.0250169	−	0.0677750i
$785$	10.2028	+	28.0319i	0.364153	+	1.00050i
$786$	−16.7460	−	4.14002i	−0.597308	−	0.147670i
$787$	16.4562	−	45.2130i	0.586600	−	1.61167i	−0.190075	−	0.981769i	$-0.560873\pi$
$787$	16.4562	−	45.2130i	0.586600	−	1.61167i	0.776675	−	0.629901i	$-0.216905\pi$
$788$	29.6323	+	35.3144i	1.05561	+	1.25802i
$789$	−1.33512	+	3.01479i	−0.0475316	+	0.107329i
$790$	7.09073	−	8.45040i	0.252277	−	0.300652i
$791$	3.69621	−	43.3812i	0.131422	−	1.54246i
$792$	0.675267	−	0.871396i	0.0239946	−	0.0309637i
$793$	−0.141176			−0.00501329
$794$	−21.6266	+	7.87145i	−0.767500	+	0.279347i
$795$	0.0354051	−	0.521148i	0.00125569	−	0.0184832i
$796$	27.3171	+	32.5552i	0.968229	+	1.15389i
$797$	30.7365	+	11.1872i	1.08874	+	0.396270i	0.823155	−	0.567817i	$-0.192212\pi$
$797$	30.7365	+	11.1872i	1.08874	+	0.396270i	0.265588	+	0.964087i	$0.414434\pi$
$798$	−79.2039	−	12.1999i	−2.80379	−	0.431871i
$799$	0.113836	−	0.645597i	0.00402724	−	0.0228396i
$800$		−	8.52206i		−	0.301300i
$801$	1.23616	+	31.7881i	0.0436777	+	1.12318i
$802$	−85.3329			−3.01321
$803$	−1.05998	+	0.385800i	−0.0374057	+	0.0136146i
$804$	−51.3879	−	22.7575i	−1.81231	−	0.802595i
$805$	1.99476	−	4.30323i	0.0703059	−	0.151669i
$806$	0.314187	+	0.374434i	0.0110668	+	0.0131889i
$807$	−20.3653	+	5.88334i	−0.716893	+	0.207103i
$808$	26.7272	−	31.8523i	0.940261	−	1.12056i
$809$	2.72104	−	1.57099i	0.0956666	−	0.0552332i	−0.451403	−	0.892320i	$-0.649076\pi$
$809$	2.72104	−	1.57099i	0.0956666	−	0.0552332i	0.547070	+	0.837087i	$0.315743\pi$
$810$	2.96593	+	38.0769i	0.104212	+	1.33789i
$811$		−	36.4973i		−	1.28159i	−0.767711	−	0.640797i	$-0.778604\pi$
$811$		−	36.4973i		−	1.28159i	0.767711	−	0.640797i	$-0.221396\pi$
$812$	−82.3220	−	21.8581i	−2.88894	−	0.767067i
$813$	14.0043	−	14.5595i	0.491154	−	0.510625i
$814$	0.460221	+	2.61004i	0.0161307	+	0.0914819i
$815$	−15.9750	+	13.4046i	−0.559579	+	0.469543i
$816$	−0.00838201	−	0.0782581i	−0.000293429	−	0.00273958i
$817$	25.1192	+	69.0146i	0.878811	+	2.41451i
$818$	2.69521	−	4.66825i	0.0942360	−	0.163221i
$819$	−0.169631	−	0.327853i	−0.00592738	−	0.0114561i
$820$	−18.6721	−	32.3409i	−0.652056	−	1.12939i
$821$	−29.5789	+	35.2508i	−1.03231	+	1.23026i	−0.0596053	+	0.998222i	$0.518984\pi$
$821$	−29.5789	+	35.2508i	−1.03231	+	1.23026i	−0.972706	+	0.232039i	$0.925460\pi$
$822$	3.07650	+	6.27617i	0.107305	+	0.218907i
$823$	7.37331	+	41.8161i	0.257017	+	1.45762i	0.790841	+	0.612022i	$0.209644\pi$
$823$	7.37331	+	41.8161i	0.257017	+	1.45762i	−0.533823	+	0.845596i	$0.679245\pi$
$824$	17.8813	−	15.0042i	0.622925	−	0.522696i
$825$	0.282901	+	0.190005i	0.00984935	+	0.00661512i
$826$	18.8210	+	69.6089i	0.654867	+	2.42200i
$827$	−9.94149	+	5.73972i	−0.345699	+	0.199590i	−0.662789	−	0.748806i	$-0.730628\pi$
$827$	−9.94149	+	5.73972i	−0.345699	+	0.199590i	0.317090	+	0.948395i	$0.397294\pi$
$828$	7.61000	+	5.89718i	0.264466	+	0.204941i
$829$		−	37.3804i		−	1.29827i	−0.760671	−	0.649137i	$-0.775130\pi$
$829$		−	37.3804i		−	1.29827i	0.760671	−	0.649137i	$-0.224870\pi$
$830$	−26.8068	−	4.72677i	−0.930479	−	0.164069i
$831$	30.0075	+	13.2890i	1.04095	+	0.460991i
$832$	0.587321	−	0.103561i	0.0203617	−	0.00359032i
$833$	−0.950746	+	0.554680i	−0.0329414	+	0.0192185i
$834$	52.1229	−	15.0578i	1.80487	−	0.521409i
$835$	−0.611828	+	3.46985i	−0.0211732	+	0.120079i
$836$	1.53915	+	2.66588i	0.0532325	+	0.0922014i
$837$	−11.2612	−	20.8790i	−0.389244	−	0.721683i
$838$	−60.7778	−	35.0901i	−2.09954	−	1.21217i
$839$	14.8437	−	5.40267i	0.512462	−	0.186521i	−0.0728286	−	0.997344i	$-0.523203\pi$
$839$	14.8437	−	5.40267i	0.512462	−	0.186521i	0.585291	+	0.810824i	$0.300980\pi$
$840$	−4.92832	−	24.7911i	−0.170043	−	0.855373i
$841$	−50.6977	+	42.5404i	−1.74820	+	1.46691i
$842$	−1.67354	+	4.59801i	−0.0576740	+	0.158458i
$843$	0.285828	−	0.645417i	0.00984443	−	0.0222294i
$844$	3.03013	−	17.1847i	0.104301	−	0.591522i
$845$	−11.9797	−	20.7494i	−0.412113	−	0.713801i
$846$	27.4184	+	8.78886i	0.942665	+	0.302167i
$847$	−12.3424	−	26.3124i	−0.424091	−	0.904105i
$848$	−0.0465601	−	0.00820980i	−0.00159888	−	0.000281926i
$849$	0.546372	−	8.04237i	0.0187514	−	0.276013i
$850$	0.571156	−	0.100710i	0.0195905	−	0.00345433i
$851$	−8.97843	+	1.58314i	−0.307777	+	0.0542694i
$852$	−0.386161	+	5.68414i	−0.0132297	+	0.194735i
$853$	−30.8230	−	5.43493i	−1.05536	−	0.186089i	−0.381064	−	0.924549i	$-0.624442\pi$
$853$	−30.8230	−	5.43493i	−1.05536	−	0.186089i	−0.674297	+	0.738460i	$0.735553\pi$
$854$	−18.4225	−	1.56965i	−0.630406	−	0.0537125i
$855$	−40.0024	−	12.8226i	−1.36805	−	0.438524i
$856$	11.1737	+	19.3534i	0.381909	+	0.661486i
$857$	−4.62895	+	26.2521i	−0.158122	+	0.896754i	0.797754	+	0.602983i	$0.206021\pi$
$857$	−4.62895	+	26.2521i	−0.158122	+	0.896754i	−0.955876	+	0.293771i	$0.905090\pi$
$858$	−0.00922165	+	0.0208231i	−0.000314822	+	0.000710888i
$859$	−9.73550	+	26.7481i	−0.332171	+	0.912633i	0.655375	+	0.755304i	$0.272511\pi$
$859$	−9.73550	+	26.7481i	−0.332171	+	0.912633i	−0.987546	+	0.157329i	$0.949712\pi$
$860$	−45.0503	+	37.8017i	−1.53620	+	1.28903i
$861$	−18.5481	−	21.1549i	−0.632118	−	0.720958i
$862$	2.57109	−	0.935799i	0.0875716	−	0.0318734i
$863$	2.69995	+	1.55882i	0.0919074	+	0.0530628i	0.545249	−	0.838274i	$-0.316435\pi$
$863$	2.69995	+	1.55882i	0.0919074	+	0.0530628i	−0.453342	+	0.891337i	$0.649768\pi$
$864$	−27.6280	−	0.800452i	−0.939923	−	0.0272319i
$865$	22.5555	+	39.0673i	0.766911	+	1.32833i
$866$	−4.44148	+	25.1889i	−0.150928	+	0.855953i
$867$	28.2469	−	8.16026i	0.959317	−	0.277137i
$868$	22.9352	+	32.5973i	0.778473	+	1.10642i
$869$	−0.314389	+	0.0554353i	−0.0106649	+	0.00188051i
$870$	−65.5664	−	29.0365i	−2.22291	−	0.984431i
$871$	0.450373	+	0.0794129i	0.0152603	+	0.00269080i
$872$		−	26.1666i		−	0.886112i
$873$	−31.9242	−	24.7389i	−1.08047	−	0.837284i
$874$	−14.7288	+	8.50367i	−0.498208	+	0.287641i
$875$	31.0824	−	8.40414i	1.05078	−	0.284112i
$876$	−43.5796	−	29.2694i	−1.47242	−	0.988920i
$877$	4.99322	−	4.18981i	0.168609	−	0.141480i	−0.554579	−	0.832131i	$-0.687121\pi$
$877$	4.99322	−	4.18981i	0.168609	−	0.141480i	0.723188	+	0.690651i	$0.242676\pi$
$878$	−2.22447	−	12.6156i	−0.0750723	−	0.425756i
$879$	6.32774	+	12.9088i	0.213429	+	0.435404i
$880$	−0.0420497	+	0.0501129i	−0.00141750	+	0.00168931i
$881$	0.192986	+	0.334261i	0.00650186	+	0.0112615i	0.869258	−	0.494359i	$-0.164597\pi$
$881$	0.192986	+	0.334261i	0.00650186	+	0.0112615i	−0.862756	+	0.505620i	$0.831264\pi$
$882$	−18.4905	−	44.6688i	−0.622608	−	1.50408i
$883$	6.61385	−	11.4555i	0.222574	−	0.385509i	−0.733015	−	0.680212i	$-0.761888\pi$
$883$	6.61385	−	11.4555i	0.222574	−	0.385509i	0.955589	+	0.294704i	$0.0952209\pi$
$884$	0.00825341	+	0.0226761i	0.000277592	+	0.000762678i
$885$	4.02545	+	37.5834i	0.135314	+	1.26335i
$886$	−47.9890	+	40.2676i	−1.61222	+	1.35282i
$887$	−4.11247	−	23.3230i	−0.138083	−	0.783109i	−0.972663	−	0.232221i	$-0.925401\pi$
$887$	−4.11247	−	23.3230i	−0.138083	−	0.783109i	0.834580	−	0.550887i	$-0.185711\pi$
$888$	−33.6805	+	35.0157i	−1.13024	+	1.17505i
$889$	8.05295	+	8.01649i	0.270087	+	0.268864i
$890$		−	44.9992i		−	1.50838i
$891$	0.642556	−	0.899301i	0.0215264	−	0.0301277i
$892$	23.9203	−	13.8104i	0.800912	−	0.462407i
$893$	−20.3563	+	24.2596i	−0.681196	+	0.811818i
$894$	35.5237	−	10.2625i	1.18809	−	0.343228i
$895$	21.8809	+	26.0767i	0.731398	+	0.871647i
$896$	49.7592	−	4.46714i	1.66234	−	0.149237i
$897$	−0.0716305	−	0.0317221i	−0.00239167	−	0.00105917i
$898$	53.2809	−	19.3927i	1.77801	−	0.647142i
$899$	44.5400			1.48549
$900$	0.616289	+	15.8479i	0.0205430	+	0.528265i
$901$			0.0257262i			0.000857064i
$902$	−0.301410	+	1.70938i	−0.0100359	+	0.0569162i
$903$	−27.7363	+	34.5506i	−0.923005	+	1.14977i
$904$	−46.2708	−	16.8412i	−1.53894	−	0.560129i
$905$	−7.63812	−	9.10276i	−0.253900	−	0.302586i
$906$	2.63842	−	38.8364i	0.0876555	−	1.29025i
$907$	−11.8281	+	4.30507i	−0.392745	+	0.142948i	−0.530841	−	0.847471i	$-0.678124\pi$
$907$	−11.8281	+	4.30507i	−0.392745	+	0.142948i	0.138096	+	0.990419i	$0.455902\pi$
$908$	−66.6048			−2.21036
$909$	25.5353	−	32.9519i	0.846952	−	1.09295i
$910$	0.221745	+	0.472731i	0.00735079	+	0.0156709i
$911$	12.9220	−	15.3999i	0.428125	−	0.510220i	−0.508255	−	0.861207i	$-0.669709\pi$
$911$	12.9220	−	15.3999i	0.428125	−	0.510220i	0.936380	+	0.350987i	$0.114154\pi$
$912$	−1.53958	+	3.47647i	−0.0509806	+	0.115117i
$913$	0.506354	+	0.603450i	0.0167579	+	0.0199713i
$914$	5.54583	−	15.2370i	0.183440	−	0.503996i
$915$	−9.40858	−	2.32604i	−0.311038	−	0.0768964i
$916$	6.55597	+	18.0124i	0.216615	+	0.595146i
$917$	11.4046	+	0.971709i	0.376614	+	0.0320886i
$918$	−0.272849	−	1.86111i	−0.00900536	−	0.0614258i
$919$	−4.76251	+	8.24891i	−0.157101	+	0.272106i	−0.933822	−	0.357738i	$-0.883548\pi$
$919$	−4.76251	+	8.24891i	−0.157101	+	0.272106i	0.776721	+	0.629845i	$0.216881\pi$
$920$	−4.10926	−	3.44808i	−0.135478	−	0.113680i
$921$	2.83565	+	9.81567i	0.0934379	+	0.323437i
$922$	16.4600	−	2.90234i	0.542081	−	0.0955834i
$923$	−0.00805021	−	0.0456550i	−0.000264976	−	0.00150275i
$924$	−0.893398	+	1.62801i	−0.0293906	+	0.0535576i
$925$	−11.5051	−	9.65393i	−0.378286	−	0.317419i
$926$	−16.2682	+	9.39243i	−0.534605	+	0.308654i
$927$	17.3295	−	15.7283i	0.569176	−	0.516586i
$928$	25.9475	−	44.9423i	0.851767	−	1.47530i
$929$	−37.3866	−	31.3711i	−1.22661	−	1.02925i	−0.998452	−	0.0556286i	$-0.982284\pi$
$929$	−37.3866	−	31.3711i	−1.22661	−	1.02925i	−0.228163	−	0.973623i	$-0.573272\pi$
$930$	14.7696	+	30.1306i	0.484315	+	0.988021i
$931$	53.1733	−	0.241271i	1.74268	−	0.00790735i
$932$	6.95460	−	19.1076i	0.227805	−	0.625890i
$933$	23.4557	+	1.59350i	0.767904	+	0.0521689i
$934$	−10.0491	−	27.6096i	−0.328816	−	0.903415i
$935$	0.0308276	+	0.0177983i	0.00100817	+	0.000582067i
$936$	−0.408011	+	0.0884162i	−0.0133363	+	0.00288997i
$937$	14.6214	+	8.44169i	0.477661	+	0.275778i	0.719441	−	0.694553i	$-0.244398\pi$
$937$	14.6214	+	8.44169i	0.477661	+	0.275778i	−0.241780	+	0.970331i	$0.577731\pi$
$938$	57.8879	+	15.3703i	1.89011	+	0.501859i
$939$	−5.83490	−	7.99770i	−0.190415	−	0.260995i
$940$	−23.8290	−	8.67304i	−0.777215	−	0.282883i
$941$	8.57887	+	3.12245i	0.279663	+	0.101789i	0.478044	−	0.878336i	$-0.341346\pi$
$941$	8.57887	+	3.12245i	0.279663	+	0.101789i	−0.198381	+	0.980125i	$0.563568\pi$
$942$	61.9935	−	17.9093i	2.01986	−	0.583517i
$943$	−5.88021	−	1.03684i	−0.191486	−	0.0337641i
$944$	3.42117			0.111349
$945$	−5.90318	−	24.6445i	−0.192030	−	0.801686i
$946$	2.73344			0.0888718
$947$	−39.6423	−	6.99001i	−1.28820	−	0.227145i	−0.512743	−	0.858542i	$-0.671371\pi$
$947$	−39.6423	−	6.99001i	−1.28820	−	0.227145i	−0.775460	+	0.631397i	$0.782482\pi$
$948$	−10.7078	−	10.2995i	−0.347772	−	0.334511i
$949$	0.401410	+	0.146101i	0.0130303	+	0.00474265i
$950$	−26.3275	−	9.58242i	−0.854177	−	0.310895i
$951$	4.14758	−	0.444236i	0.134494	−	0.0144053i
$952$	0.324925	+	1.20172i	0.0105309	+	0.0389481i
$953$	−15.4047	−	8.89392i	−0.499008	−	0.288102i	0.229296	−	0.973357i	$-0.426358\pi$
$953$	−15.4047	−	8.89392i	−0.499008	−	0.288102i	−0.728304	+	0.685254i	$0.759691\pi$
$954$	−1.11953	−	0.152820i	−0.0362463	−	0.00494774i
$955$	−16.0162	−	9.24698i	−0.518274	−	0.299225i
$956$	21.0647	+	57.8748i	0.681281	+	1.87180i
$957$	0.913404	+	1.86338i	0.0295262	+	0.0602345i
$958$	15.6897	−	43.1071i	0.506911	−	1.39273i
$959$	−2.66876	−	3.79304i	−0.0861788	−	0.122484i
$960$	40.8481	+	2.77508i	1.31837	+	0.0895654i
$961$	7.78112	+	6.52913i	0.251004	+	0.210617i
$962$	0.501832	−	0.869198i	0.0161797	−	0.0280241i
$963$	11.9482	+	18.9536i	0.385024	+	0.610770i
$964$	−34.8236	+	20.1054i	−1.12159	+	0.647552i
$965$	−34.7495	−	29.1583i	−1.11863	−	0.938639i
$966$	−8.99463	−	4.93596i	−0.289397	−	0.158812i
$967$	−2.19010	−	12.4206i	−0.0704287	−	0.399421i	−0.999560	−	0.0296704i	$-0.990554\pi$
$967$	−2.19010	−	12.4206i	−0.0704287	−	0.399421i	0.929131	−	0.369751i	$-0.120557\pi$
$968$	−32.3703	+	5.70775i	−1.04042	+	0.183454i
$969$	2.00843	+	0.496535i	0.0645202	+	0.0159510i
$970$	43.7638	+	36.7221i	1.40517	+	1.17908i
$971$	9.58786	−	16.6067i	0.307689	−	0.532933i	−0.670167	−	0.742210i	$-0.733778\pi$
$971$	9.58786	−	16.6067i	0.307689	−	0.532933i	0.977856	+	0.209277i	$0.0671110\pi$
$972$	51.4359	−	0.509416i	1.64981	−	0.0163395i
$973$	−32.5918	+	15.2879i	−1.04485	+	0.490109i
$974$	26.0359	+	71.5330i	0.834244	+	2.29207i
$975$	−0.0358179	−	0.123985i	−0.00114709	−	0.00397068i
$976$	−0.300026	+	0.824316i	−0.00960361	+	0.0263857i
$977$	15.8858	+	18.9319i	0.508232	+	0.605687i	0.957756	−	0.287581i	$-0.0928511\pi$
$977$	15.8858	+	18.9319i	0.508232	+	0.605687i	−0.449525	+	0.893268i	$0.648407\pi$
$978$	26.5872	+	36.4421i	0.850164	+	1.16529i
$979$	−0.837076	+	0.997588i	−0.0267531	+	0.0318831i
$980$	14.7440	+	39.9439i	0.470979	+	1.27596i
$981$	−1.01942	−	26.2145i	−0.0325476	−	0.836966i
$982$	−4.00106			−0.127679
$983$	15.9748	−	5.81436i	0.509518	−	0.185449i	−0.0744521	−	0.997225i	$-0.523721\pi$
$983$	15.9748	−	5.81436i	0.509518	−	0.185449i	0.583970	+	0.811775i	$0.301499\pi$
$984$	−28.5714	+	14.0053i	−0.910823	+	0.446474i
$985$	−16.5533	−	19.7275i	−0.527432	−	0.628569i
$986$	3.31871	+	1.20791i	0.105689	+	0.0384678i
$987$	−18.8820	−	2.90842i	−0.601022	−	0.0925762i
$988$	0.202429	−	1.14803i	0.00644012	−	0.0365237i
$989$			9.40292i			0.298996i
$990$	−0.957658	+	1.23581i	−0.0304364	+	0.0392765i
$991$	−2.84408			−0.0903450			−0.0451725	−	0.998979i	$-0.514384\pi$
$991$	−2.84408			−0.0903450			−0.0451725	+	0.998979i	$0.514384\pi$
$992$	−22.8197	+	8.30569i	−0.724526	+	0.263706i
$993$	1.95442	+	18.2473i	0.0620216	+	0.579061i
$994$	−0.542888	−	6.04719i	−0.0172194	−	0.191805i
$995$	−15.2600	−	18.1861i	−0.483774	−	0.576539i
$996$	−8.79867	+	35.5897i	−0.278797	+	1.12770i
$997$	22.6186	−	26.9558i	0.716339	−	0.853700i	−0.277930	−	0.960601i	$-0.589648\pi$
$997$	22.6186	−	26.9558i	0.716339	−	0.853700i	0.994270	+	0.106901i	$0.0340929\pi$
$998$	68.4332	−	39.5099i	2.16621	−	1.25066i
$999$	−32.3781	+	36.3921i	−1.02440	+	1.15139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.47.3	yes	132
3.2	odd	2		567.2.bd.a.467.20		132
7.3	odd	6		189.2.ba.a.101.20	✓	132
21.17	even	6		567.2.ba.a.143.3		132
27.4	even	9		567.2.ba.a.341.3		132
27.23	odd	18		189.2.ba.a.131.20	yes	132
189.31	odd	18		567.2.bd.a.17.20		132
189.185	even	18	inner	189.2.bd.a.185.3	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.20	✓	132	7.3	odd	6
189.2.ba.a.131.20	yes	132	27.23	odd	18
189.2.bd.a.47.3	yes	132	1.1	even	1	trivial
189.2.bd.a.185.3	yes	132	189.185	even	18	inner
567.2.ba.a.143.3		132	21.17	even	6
567.2.ba.a.341.3		132	27.4	even	9
567.2.bd.a.17.20		132	189.31	odd	18
567.2.bd.a.467.20		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.26715 - 0.399760i) q^{2} +(0.415691 - 1.68143i) q^{3} +(3.10078 + 1.12859i) q^{4} +(-1.73217 - 0.630457i) q^{5} +(-1.61460 + 3.64587i) q^{6} +(0.678971 - 2.55715i) q^{7} +(-2.59137 - 1.49613i) q^{8} +(-2.65440 - 1.39791i) q^{9} +O(q^{10})\)	\(q+(-2.26715 - 0.399760i) q^{2} +(0.415691 - 1.68143i) q^{3} +(3.10078 + 1.12859i) q^{4} +(-1.73217 - 0.630457i) q^{5} +(-1.61460 + 3.64587i) q^{6} +(0.678971 - 2.55715i) q^{7} +(-2.59137 - 1.49613i) q^{8} +(-2.65440 - 1.39791i) q^{9} +(3.67505 + 2.12179i) q^{10} +(-0.0420027 - 0.115401i) q^{11} +(3.18661 - 4.74459i) q^{12} +(-0.0159063 + 0.0437022i) q^{13} +(-2.56157 + 5.52601i) q^{14} +(-1.78012 + 2.65044i) q^{15} +(0.221371 + 0.185752i) q^{16} +(0.0786230 - 0.136179i) q^{17} +(5.45910 + 4.23040i) q^{18} +(-6.57855 + 3.79813i) q^{19} +(-4.65954 - 3.90982i) q^{20} +(-4.01742 - 2.20463i) q^{21} +(0.0490936 + 0.278423i) q^{22} +(-0.957765 + 0.168880i) q^{23} +(-3.59284 + 3.73527i) q^{24} +(-1.22730 - 1.02982i) q^{25} +(0.0535324 - 0.0927208i) q^{26} +(-3.45390 + 3.88209i) q^{27} +(4.99131 - 7.16286i) q^{28} +(-3.33678 - 9.16772i) q^{29} +(5.09533 - 5.29732i) q^{30} +(-1.56144 + 4.29003i) q^{31} +(3.41914 + 4.07477i) q^{32} +(-0.211499 + 0.0226531i) q^{33} +(-0.232689 + 0.277308i) q^{34} +(-2.78826 + 4.00134i) q^{35} +(-6.65304 - 7.33034i) q^{36} +9.37436 q^{37} +(16.4329 - 5.98109i) q^{38} +(0.0668700 + 0.0449120i) q^{39} +(3.54543 + 4.22528i) q^{40} +(5.76925 + 2.09983i) q^{41} +(8.22676 + 6.60422i) q^{42} +(1.67890 - 9.52153i) q^{43} -0.405238i q^{44} +(3.71654 + 4.09490i) q^{45} +2.23891 q^{46} +(3.91757 - 1.42588i) q^{47} +(0.404351 - 0.295003i) q^{48} +(-6.07800 - 3.47246i) q^{49} +(2.37078 + 2.82539i) q^{50} +(-0.196292 - 0.188807i) q^{51} +(-0.0986438 + 0.117559i) q^{52} +(-0.141686 + 0.0818025i) q^{53} +(9.38241 - 7.42054i) q^{54} +0.226376i q^{55} +(-5.58527 + 5.61067i) q^{56} +(3.65163 + 12.6402i) q^{57} +(3.90009 + 22.1185i) q^{58} +(9.06906 - 7.60984i) q^{59} +(-8.51100 + 6.20940i) q^{60} +(1.03823 + 2.85251i) q^{61} +(5.25501 - 9.10194i) q^{62} +(-5.37692 + 5.83855i) q^{63} +(-6.41175 - 11.1055i) q^{64} +(0.0551048 - 0.0656713i) q^{65} +(0.488557 + 0.0331909i) q^{66} +(-1.70755 - 9.68399i) q^{67} +(0.397483 - 0.333527i) q^{68} +(-0.114175 + 1.68062i) q^{69} +(7.92099 - 7.95701i) q^{70} +(-0.863276 + 0.498413i) q^{71} +(4.78707 + 7.59381i) q^{72} -9.18511i q^{73} +(-21.2531 - 3.74749i) q^{74} +(-2.24175 + 1.63552i) q^{75} +(-24.6852 + 4.35266i) q^{76} +(-0.323617 + 0.0290528i) q^{77} +(-0.133650 - 0.128554i) q^{78} +(0.451399 - 2.56001i) q^{79} +(-0.266342 - 0.461318i) q^{80} +(5.09169 + 7.42123i) q^{81} +(-12.2403 - 7.06695i) q^{82} +(-6.02764 + 2.19388i) q^{83} +(-9.96899 - 11.3701i) q^{84} +(-0.222043 + 0.186316i) q^{85} +(-7.61265 + 20.9156i) q^{86} +(-16.8019 + 1.79961i) q^{87} +(-0.0638107 + 0.361889i) q^{88} +(-5.30203 - 9.18338i) q^{89} +(-6.78899 - 10.7695i) q^{90} +(0.100953 + 0.0703473i) q^{91} +(-3.16041 - 0.557266i) q^{92} +(6.56430 + 4.40878i) q^{93} +(-9.45173 + 1.66659i) q^{94} +(13.7897 - 2.43150i) q^{95} +(8.27274 - 4.05519i) q^{96} +(13.2580 + 2.33775i) q^{97} +(12.3916 + 10.3023i) q^{98} +(-0.0498289 + 0.365038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

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