LMFDB - Embedded newform 189.2.ba.a.38.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (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			38.10
Character	$\chi$	$=$	189.38
Dual form			189.2.ba.a.5.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.408566 - 0.0720413i) q^{2} +(1.12900 + 1.31353i) q^{3} +(-1.71765 - 0.625173i) q^{4} +(0.0312679 + 0.177329i) q^{5} +(-0.366645 - 0.617997i) q^{6} +(1.82229 + 1.91814i) q^{7} +(1.37531 + 0.794036i) q^{8} +(-0.450699 + 2.96595i) q^{9} -0.0747032i q^{10} +(1.56303 + 0.275605i) q^{11} +(-1.11805 - 2.96200i) q^{12} +(3.21910 + 3.83638i) q^{13} +(-0.606342 - 0.914967i) q^{14} +(-0.197625 + 0.241276i) q^{15} +(2.29578 + 1.92639i) q^{16} -7.76129 q^{17} +(0.397812 - 1.17932i) q^{18} -4.34679i q^{19} +(0.0571540 - 0.324137i) q^{20} +(-0.462149 + 4.55921i) q^{21} +(-0.618747 - 0.225206i) q^{22} +(-1.56305 - 1.86277i) q^{23} +(0.509745 + 2.70297i) q^{24} +(4.66800 - 1.69901i) q^{25} +(-1.03884 - 1.79932i) q^{26} +(-4.40469 + 2.75657i) q^{27} +(-1.93089 - 4.43393i) q^{28} +(2.81590 - 3.35586i) q^{29} +(0.0981246 - 0.0843403i) q^{30} +(0.459948 - 1.26370i) q^{31} +(-2.84078 - 3.38551i) q^{32} +(1.40266 + 2.36424i) q^{33} +(3.17100 + 0.559134i) q^{34} +(-0.283162 + 0.383121i) q^{35} +(2.62838 - 4.81270i) q^{36} +(2.09041 - 3.62070i) q^{37} +(-0.313148 + 1.77595i) q^{38} +(-1.40480 + 8.55966i) q^{39} +(-0.0978025 + 0.268710i) q^{40} +(8.48927 - 7.12335i) q^{41} +(0.517270 - 1.82945i) q^{42} +(-0.714703 + 0.260131i) q^{43} +(-2.51244 - 1.45056i) q^{44} +(-0.540041 + 0.0128170i) q^{45} +(0.504413 + 0.873669i) q^{46} +(-8.67893 + 3.15887i) q^{47} +(0.0615850 + 5.19046i) q^{48} +(-0.358507 + 6.99081i) q^{49} +(-2.02959 + 0.357871i) q^{50} +(-8.76253 - 10.1947i) q^{51} +(-3.13089 - 8.60205i) q^{52} +(-8.42703 - 4.86535i) q^{53} +(1.99820 - 0.808921i) q^{54} +0.285788i q^{55} +(0.983146 + 4.08500i) q^{56} +(5.70962 - 4.90754i) q^{57} +(-1.39224 + 1.16823i) q^{58} +(1.51017 - 1.26718i) q^{59} +(0.490289 - 0.290878i) q^{60} +(-0.916897 - 2.51916i) q^{61} +(-0.278957 + 0.483169i) q^{62} +(-6.51041 + 4.54033i) q^{63} +(-2.08017 - 3.60297i) q^{64} +(-0.579646 + 0.690796i) q^{65} +(-0.402755 - 1.06700i) q^{66} +(-0.722307 - 4.09641i) q^{67} +(13.3312 + 4.85215i) q^{68} +(0.682106 - 4.15618i) q^{69} +(0.143291 - 0.136131i) q^{70} +(5.04844 - 2.91472i) q^{71} +(-2.97492 + 3.72123i) q^{72} +(-7.42228 + 4.28526i) q^{73} +(-1.11491 + 1.32870i) q^{74} +(7.50188 + 4.21334i) q^{75} +(-2.71749 + 7.46625i) q^{76} +(2.31965 + 3.50034i) q^{77} +(1.19060 - 3.39599i) q^{78} +(-0.884454 + 5.01599i) q^{79} +(-0.269820 + 0.467342i) q^{80} +(-8.59374 - 2.67350i) q^{81} +(-3.98161 + 2.29878i) q^{82} +(10.1615 + 8.52653i) q^{83} +(3.64411 - 7.54220i) q^{84} +(-0.242679 - 1.37630i) q^{85} +(0.310744 - 0.0547926i) q^{86} +(7.58716 - 0.0900220i) q^{87} +(1.93081 + 1.62014i) q^{88} +8.19131 q^{89} +(0.221566 + 0.0336687i) q^{90} +(-1.49256 + 13.1657i) q^{91} +(1.52022 + 4.17676i) q^{92} +(2.17918 - 0.822565i) q^{93} +(3.77349 - 0.665368i) q^{94} +(0.770811 - 0.135915i) q^{95} +(1.23970 - 7.55370i) q^{96} +(1.63818 + 4.50085i) q^{97} +(0.650101 - 2.83038i) q^{98} +(-1.52189 + 4.51166i) 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} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 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 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.408566	−	0.0720413i	−0.288900	−	0.0509409i	0.0273200	−	0.999627i	$-0.491303\pi$
$2$	−0.408566	−	0.0720413i	−0.288900	−	0.0509409i	−0.316220	+	0.948686i	$0.602414\pi$
$3$	1.12900	+	1.31353i	0.651831	+	0.758364i
$3$	1.12900	+	1.31353i	0.651831	+	0.758364i
$4$	−1.71765	−	0.625173i	−0.858824	−	0.312586i
$5$	0.0312679	+	0.177329i	0.0139834	+	0.0793039i	0.991001	−	0.133855i	$-0.0427358\pi$
$5$	0.0312679	+	0.177329i	0.0139834	+	0.0793039i	−0.977017	+	0.213159i	$0.931625\pi$
$6$	−0.366645	−	0.617997i	−0.149682	−	0.252296i
$7$	1.82229	+	1.91814i	0.688761	+	0.724988i
$7$	1.82229	+	1.91814i	0.688761	+	0.724988i
$8$	1.37531	+	0.794036i	0.486246	+	0.280734i
$9$	−0.450699	+	2.96595i	−0.150233	+	0.988651i
$10$		−	0.0747032i		−	0.0236232i
$11$	1.56303	+	0.275605i	0.471272	+	0.0830979i	0.404240	−	0.914653i	$-0.367536\pi$
$11$	1.56303	+	0.275605i	0.471272	+	0.0830979i	0.0670317	+	0.997751i	$0.478647\pi$
$12$	−1.11805	−	2.96200i	−0.322754	−	0.855055i
$13$	3.21910	+	3.83638i	0.892819	+	1.06402i	0.997580	+	0.0695228i	$0.0221477\pi$
$13$	3.21910	+	3.83638i	0.892819	+	1.06402i	−0.104761	+	0.994497i	$0.533408\pi$
$14$	−0.606342	−	0.914967i	−0.162052	−	0.244535i
$15$	−0.197625	+	0.241276i	−0.0510264	+	0.0622973i
$16$	2.29578	+	1.92639i	0.573944	+	0.481597i
$17$	−7.76129			−1.88239			−0.941195	−	0.337864i	$-0.890296\pi$
$17$	−7.76129			−1.88239			−0.941195	+	0.337864i	$0.890296\pi$
$18$	0.397812	−	1.17932i	0.0937651	−	0.277968i
$19$		−	4.34679i		−	0.997221i	−0.866826	−	0.498611i	$-0.833844\pi$
$19$		−	4.34679i		−	0.997221i	0.866826	−	0.498611i	$-0.166156\pi$
$20$	0.0571540	−	0.324137i	0.0127800	−	0.0724791i
$21$	−0.462149	+	4.55921i	−0.100849	+	0.994902i
$22$	−0.618747	−	0.225206i	−0.131917	−	0.0480140i
$23$	−1.56305	−	1.86277i	−0.325918	−	0.388414i	0.578059	−	0.815995i	$-0.303810\pi$
$23$	−1.56305	−	1.86277i	−0.325918	−	0.388414i	−0.903977	+	0.427581i	$0.859366\pi$
$24$	0.509745	+	2.70297i	0.104051	+	0.551742i
$25$	4.66800	−	1.69901i	0.933599	−	0.339802i
$26$	−1.03884	−	1.79932i	−0.203733	−	0.352877i
$27$	−4.40469	+	2.75657i	−0.847684	+	0.530502i
$28$	−1.93089	−	4.43393i	−0.364904	−	0.837935i
$29$	2.81590	−	3.35586i	0.522899	−	0.623167i	−0.438365	−	0.898797i	$-0.644442\pi$
$29$	2.81590	−	3.35586i	0.522899	−	0.623167i	0.961264	+	0.275630i	$0.0888866\pi$
$30$	0.0981246	−	0.0843403i	0.0179150	−	0.0153984i
$31$	0.459948	−	1.26370i	0.0826090	−	0.226966i	−0.891510	−	0.453000i	$-0.850354\pi$
$31$	0.459948	−	1.26370i	0.0826090	−	0.226966i	0.974119	+	0.226034i	$0.0725759\pi$
$32$	−2.84078	−	3.38551i	−0.502184	−	0.598480i
$33$	1.40266	+	2.36424i	0.244171	+	0.411562i
$34$	3.17100	+	0.559134i	0.543823	+	0.0958906i
$35$	−0.283162	+	0.383121i	−0.0478631	+	0.0647593i
$36$	2.62838	−	4.81270i	0.438063	−	0.802116i
$37$	2.09041	−	3.62070i	0.343662	−	0.595240i	−0.641448	−	0.767167i	$-0.721666\pi$
$37$	2.09041	−	3.62070i	0.343662	−	0.595240i	0.985110	+	0.171927i	$0.0549992\pi$
$38$	−0.313148	+	1.77595i	−0.0507993	+	0.288097i
$39$	−1.40480	+	8.55966i	−0.224948	+	1.37064i
$40$	−0.0978025	+	0.268710i	−0.0154639	+	0.0424868i
$41$	8.48927	−	7.12335i	1.32580	−	1.11248i	0.340763	−	0.940149i	$-0.389315\pi$
$41$	8.48927	−	7.12335i	1.32580	−	1.11248i	0.985039	−	0.172331i	$-0.0551297\pi$
$42$	0.517270	−	1.82945i	0.0798165	−	0.282290i
$43$	−0.714703	+	0.260131i	−0.108991	+	0.0396696i	−0.395940	−	0.918276i	$-0.629581\pi$
$43$	−0.714703	+	0.260131i	−0.108991	+	0.0396696i	0.286949	+	0.957946i	$0.407359\pi$
$44$	−2.51244	−	1.45056i	−0.378764	−	0.218680i
$45$	−0.540041	+	0.0128170i	−0.0805046	+	0.00191065i
$46$	0.504413	+	0.873669i	0.0743716	+	0.128815i
$47$	−8.67893	+	3.15887i	−1.26595	+	0.460769i	−0.885762	−	0.464139i	$-0.846364\pi$
$47$	−8.67893	+	3.15887i	−1.26595	+	0.460769i	−0.380190	+	0.924908i	$0.624141\pi$
$48$	0.0615850	+	5.19046i	0.00888903	+	0.749179i
$49$	−0.358507	+	6.99081i	−0.0512153	+	0.998688i
$50$	−2.02959	+	0.357871i	−0.287027	+	0.0506106i
$51$	−8.76253	−	10.1947i	−1.22700	−	1.42754i
$52$	−3.13089	−	8.60205i	−0.434176	−	1.19289i
$53$	−8.42703	−	4.86535i	−1.15754	−	0.668307i	−0.206828	−	0.978377i	$-0.566314\pi$
$53$	−8.42703	−	4.86535i	−1.15754	−	0.668307i	−0.950714	+	0.310071i	$0.899647\pi$
$54$	1.99820	−	0.808921i	0.271920	−	0.110080i
$55$			0.285788i			0.0385357i
$56$	0.983146	+	4.08500i	0.131378	+	0.545881i
$57$	5.70962	−	4.90754i	0.756257	−	0.650020i
$58$	−1.39224	+	1.16823i	−0.182810	+	0.153396i
$59$	1.51017	−	1.26718i	0.196608	−	0.164973i	−0.539169	−	0.842197i	$-0.681262\pi$
$59$	1.51017	−	1.26718i	0.196608	−	0.164973i	0.735777	+	0.677224i	$0.236817\pi$
$60$	0.490289	−	0.290878i	0.0632960	−	0.0375522i
$61$	−0.916897	−	2.51916i	−0.117397	−	0.322545i	0.867052	−	0.498218i	$-0.166012\pi$
$61$	−0.916897	−	2.51916i	−0.117397	−	0.322545i	−0.984449	+	0.175673i	$0.943790\pi$
$62$	−0.278957	+	0.483169i	−0.0354276	+	0.0613625i
$63$	−6.51041	+	4.54033i	−0.820235	+	0.572027i
$64$	−2.08017	−	3.60297i	−0.260022	−	0.450371i
$65$	−0.579646	+	0.690796i	−0.0718963	+	0.0856827i
$66$	−0.402755	−	1.06700i	−0.0495757	−	0.131338i
$67$	−0.722307	−	4.09641i	−0.0882438	−	0.500456i	−0.996609	−	0.0822786i	$-0.973780\pi$
$67$	−0.722307	−	4.09641i	−0.0882438	−	0.500456i	0.908366	−	0.418177i	$-0.137331\pi$
$68$	13.3312	+	4.85215i	1.61664	+	0.588410i
$69$	0.682106	−	4.15618i	0.0821159	−	0.500345i
$70$	0.143291	−	0.136131i	0.0171266	−	0.0162708i
$71$	5.04844	−	2.91472i	0.599139	−	0.345913i	−0.169564	−	0.985519i	$-0.554236\pi$
$71$	5.04844	−	2.91472i	0.599139	−	0.345913i	0.768703	+	0.639606i	$0.220903\pi$
$72$	−2.97492	+	3.72123i	−0.350598	+	0.438551i
$73$	−7.42228	+	4.28526i	−0.868712	+	0.501551i	−0.866920	−	0.498447i	$-0.833904\pi$
$73$	−7.42228	+	4.28526i	−0.868712	+	0.501551i	−0.00179209	+	0.999998i	$0.500570\pi$
$74$	−1.11491	+	1.32870i	−0.129606	+	0.154458i
$75$	7.50188	+	4.21334i	0.866243	+	0.486515i
$76$	−2.71749	+	7.46625i	−0.311718	+	0.856438i
$77$	2.31965	+	3.50034i	0.264349	+	0.398901i
$78$	1.19060	−	3.39599i	0.134809	−	0.384520i
$79$	−0.884454	+	5.01599i	−0.0995088	+	0.564343i	0.893763	+	0.448539i	$0.148055\pi$
$79$	−0.884454	+	5.01599i	−0.0995088	+	0.564343i	−0.993272	+	0.115804i	$0.963056\pi$
$80$	−0.269820	+	0.467342i	−0.0301668	+	0.0522504i
$81$	−8.59374	−	2.67350i	−0.954860	−	0.297056i
$82$	−3.98161	+	2.29878i	−0.439695	+	0.253858i
$83$	10.1615	+	8.52653i	1.11537	+	0.935909i	0.998361	−	0.0572219i	$-0.0182242\pi$
$83$	10.1615	+	8.52653i	1.11537	+	0.935909i	0.117011	+	0.993131i	$0.462669\pi$
$84$	3.64411	−	7.54220i	0.397605	−	0.822922i
$85$	−0.242679	−	1.37630i	−0.0263222	−	0.149281i
$86$	0.310744	−	0.0547926i	0.0335084	−	0.00590843i
$87$	7.58716	−	0.0900220i	0.813429	−	0.00965137i
$88$	1.93081	+	1.62014i	0.205825	+	0.172708i
$89$	8.19131			0.868278			0.434139	−	0.900846i	$-0.357053\pi$
$89$	8.19131			0.868278			0.434139	+	0.900846i	$0.357053\pi$
$90$	0.221566	+	0.0336687i	0.0233551	+	0.00354899i
$91$	−1.49256	+	13.1657i	−0.156463	+	1.38014i
$92$	1.52022	+	4.17676i	0.158493	+	0.435457i
$93$	2.17918	−	0.822565i	0.225970	−	0.0852960i
$94$	3.77349	−	0.665368i	0.389206	−	0.0686275i
$95$	0.770811	−	0.135915i	0.0790835	−	0.0139446i
$96$	1.23970	−	7.55370i	0.126527	−	0.770946i
$97$	1.63818	+	4.50085i	0.166332	+	0.456993i	0.994655	−	0.103258i	$-0.0329269\pi$
$97$	1.63818	+	4.50085i	0.166332	+	0.456993i	−0.828323	+	0.560251i	$0.810705\pi$
$98$	0.650101	−	2.83038i	0.0656701	−	0.285912i
$99$	−1.52189	+	4.51166i	−0.152955	+	0.453439i
$100$	−9.08015			−0.908015
$101$	9.59097	+	8.04778i	0.954337	+	0.800784i	0.980023	−	0.198886i	$-0.0637324\pi$
$101$	9.59097	+	8.04778i	0.954337	+	0.800784i	−0.0256856	+	0.999670i	$0.508177\pi$
$102$	2.84564	+	4.79646i	0.281760	+	0.474920i
$103$	2.76125	−	0.486882i	0.272074	−	0.0479739i	−0.0359467	−	0.999354i	$-0.511445\pi$
$103$	2.76125	−	0.486882i	0.272074	−	0.0479739i	0.308020	+	0.951380i	$0.400334\pi$
$104$	1.38104	+	7.83229i	0.135423	+	0.768020i
$105$	−0.822931	+	0.0606045i	−0.0803098	+	0.00591440i
$106$	3.09250	+	2.59491i	0.300370	+	0.252040i
$107$	−6.82463	+	3.94020i	−0.659762	+	0.380913i	−0.792186	−	0.610280i	$-0.791057\pi$
$107$	−6.82463	+	3.94020i	−0.659762	+	0.380913i	0.132425	+	0.991193i	$0.457724\pi$
$108$	9.28905	−	1.98112i	0.893839	−	0.190633i
$109$	8.69846	−	15.0662i	0.833161	−	1.44308i	−0.0623578	−	0.998054i	$-0.519862\pi$
$109$	8.69846	−	15.0662i	0.833161	−	1.44308i	0.895519	−	0.445024i	$-0.146805\pi$
$110$	0.0205886	−	0.116764i	0.00196304	−	0.0111330i
$111$	7.11597	−	1.34198i	0.675418	−	0.127375i
$112$	0.488502	+	7.91406i	0.0461591	+	0.747808i
$113$	1.02719	−	2.82219i	0.0966304	−	0.265490i	−0.881954	−	0.471335i	$-0.843772\pi$
$113$	1.02719	−	2.82219i	0.0966304	−	0.265490i	0.978585	+	0.205845i	$0.0659944\pi$
$114$	−2.68630	+	1.59373i	−0.251595	+	0.149266i
$115$	0.281450	−	0.335419i	0.0262453	−	0.0312779i
$116$	−6.93471	+	4.00376i	−0.643872	+	0.371740i
$117$	−12.8294	+	7.81866i	−1.18608	+	0.722835i
$118$	−0.708295	+	0.408934i	−0.0652038	+	0.0376455i
$119$	−14.1433	−	14.8872i	−1.29652	−	1.36471i
$120$	−0.463377	+	0.174909i	−0.0423003	+	0.0159669i
$121$	−7.96951	−	2.90066i	−0.724501	−	0.263697i
$122$	0.193130	+	1.09530i	0.0174852	+	0.0991635i
$123$	18.9411	+	3.10859i	1.70786	+	0.280292i
$124$	−1.58006	+	1.88304i	−0.141893	+	0.169102i
$125$	0.897403	+	1.55435i	0.0802662	+	0.139025i
$126$	2.98703	−	1.38601i	0.266105	−	0.123475i
$127$	5.25357	−	9.09945i	0.466179	−	0.807446i	−0.533075	−	0.846068i	$-0.678964\pi$
$127$	5.25357	−	9.09945i	0.466179	−	0.807446i	0.999254	+	0.0386222i	$0.0122969\pi$
$128$	3.61343	+	9.92780i	0.319385	+	0.877502i
$129$	−1.14859	−	0.645092i	−0.101128	−	0.0567972i
$130$	0.286590	−	0.240477i	0.0251356	−	0.0210913i
$131$	−11.1700	+	9.37272i	−0.975925	+	0.818898i	−0.983470	−	0.181073i	$-0.942043\pi$
$131$	−11.1700	+	9.37272i	−0.975925	+	0.818898i	0.00754465	+	0.999972i	$0.497598\pi$
$132$	−0.931210	−	4.93784i	−0.0810514	−	0.429784i
$133$	8.33774	−	7.92111i	0.722973	−	0.686848i
$134$			1.72569i			0.149077i
$135$	−0.626545	−	0.694888i	−0.0539244	−	0.0598064i
$136$	−10.6742	−	6.16274i	−0.915304	−	0.528451i
$137$	−2.17300	−	5.97027i	−0.185652	−	0.510075i	0.811595	−	0.584220i	$-0.198599\pi$
$137$	−2.17300	−	5.97027i	−0.185652	−	0.510075i	−0.997247	+	0.0741452i	$0.976377\pi$
$138$	−0.578102	+	1.64894i	−0.0492113	+	0.140367i
$139$	−15.1483	+	2.67106i	−1.28487	+	0.226556i	−0.774045	−	0.633131i	$-0.781769\pi$
$139$	−15.1483	+	2.67106i	−1.28487	+	0.226556i	−0.510821	+	0.859687i	$0.670658\pi$
$140$	0.725890	−	0.481042i	0.0613489	−	0.0406555i
$141$	−13.9478	−	7.83362i	−1.17462	−	0.659710i
$142$	−2.27260	+	0.827159i	−0.190713	+	0.0694137i
$143$	3.97424	+	6.88358i	0.332343	+	0.575634i
$144$	−6.74827	+	5.94095i	−0.562356	+	0.495079i
$145$	0.683138	+	0.394410i	0.0567315	+	0.0327539i
$146$	3.34121	−	1.21610i	0.276521	−	0.100645i
$147$	−9.58737	+	7.42175i	−0.790753	+	0.612136i
$148$	−5.85416	+	4.91223i	−0.481209	+	0.403783i
$149$	5.96220	−	16.3810i	0.488442	−	1.34198i	−0.413648	−	0.910437i	$-0.635746\pi$
$149$	5.96220	−	16.3810i	0.488442	−	1.34198i	0.902090	−	0.431547i	$-0.142032\pi$
$150$	−2.76148	−	2.26187i	−0.225474	−	0.184681i
$151$	0.399188	−	2.26391i	0.0324854	−	0.184234i	−0.964247	−	0.265004i	$-0.914627\pi$
$151$	0.399188	−	2.26391i	0.0324854	−	0.184234i	0.996733	+	0.0807699i	$0.0257379\pi$
$152$	3.45150	−	5.97818i	0.279954	−	0.484894i
$153$	3.49801	−	23.0196i	0.282797	−	1.86103i
$154$	−0.695563	−	1.59723i	−0.0560500	−	0.128709i
$155$	0.238471	+	0.0420489i	0.0191545	+	0.00337745i
$156$	7.76422	−	13.8243i	0.621635	−	1.10683i
$157$	−3.60935	−	4.30145i	−0.288057	−	0.343293i	0.602538	−	0.798090i	$-0.294156\pi$
$157$	−3.60935	−	4.30145i	−0.288057	−	0.343293i	−0.890595	+	0.454797i	$0.849712\pi$
$158$	0.722716	−	1.98565i	0.0574962	−	0.157970i
$159$	−3.12339	−	16.5621i	−0.247701	−	1.31346i
$160$	0.511524	−	0.609611i	0.0404395	−	0.0481940i
$161$	0.724718	−	6.39265i	0.0571157	−	0.503811i
$162$	3.31851	+	1.71141i	0.260727	+	0.134461i
$163$	9.58450	+	16.6008i	0.750716	+	1.30028i	0.947476	+	0.319827i	$0.103625\pi$
$163$	9.58450	+	16.6008i	0.750716	+	1.30028i	−0.196760	+	0.980452i	$0.563042\pi$
$164$	−19.0349	+	6.92814i	−1.48638	+	0.540997i
$165$	−0.375390	+	0.322656i	−0.0292241	+	0.0251188i
$166$	−3.53740	−	4.21571i	−0.274555	−	0.327202i
$167$	−8.84469	−	3.21920i	−0.684422	−	0.249109i	−0.0236772	−	0.999720i	$-0.507537\pi$
$167$	−8.84469	−	3.21920i	−0.684422	−	0.249109i	−0.660745	+	0.750610i	$0.729760\pi$
$168$	−4.25577	+	5.90337i	−0.328340	+	0.455455i
$169$	−2.09775	+	11.8969i	−0.161365	+	0.915147i
$170$			0.579794i			0.0444681i
$171$	12.8924	+	1.95909i	0.985903	+	0.149816i
$172$	1.39024			0.106005
$173$	4.11126	+	3.44976i	0.312573	+	0.262280i	0.785555	−	0.618792i	$-0.212378\pi$
$173$	4.11126	+	3.44976i	0.312573	+	0.262280i	−0.472981	+	0.881072i	$0.656822\pi$
$174$	−3.10635	−	0.509809i	−0.235492	−	0.0386485i
$175$	11.7654	+	5.85777i	0.889380	+	0.442805i
$176$	3.05745	+	3.64373i	0.230464	+	0.274656i
$177$	3.36947	+	0.552992i	0.253265	+	0.0415655i
$178$	−3.34670	−	0.590113i	−0.250846	−	0.0442308i
$179$			14.8693i			1.11138i	0.831389	+	0.555691i	$0.187546\pi$
$179$			14.8693i			1.11138i	−0.831389	+	0.555691i	$0.812454\pi$
$180$	0.935614	+	0.315604i	0.0697366	+	0.0235237i
$181$	−5.48950	−	3.16937i	−0.408031	−	0.235577i	0.281912	−	0.959440i	$-0.409031\pi$
$181$	−5.48950	−	3.16937i	−0.408031	−	0.235577i	−0.689944	+	0.723863i	$0.742365\pi$
$182$	1.55828	−	5.27153i	0.115508	−	0.390752i
$183$	2.27379	−	4.04851i	0.168084	−	0.299274i
$184$	−0.670572	−	3.80300i	−0.0494352	−	0.280361i
$185$	0.707418	+	0.257479i	0.0520104	+	0.0189302i
$186$	−0.949598	+	0.179082i	−0.0696279	+	0.0131309i
$187$	−12.1311	−	2.13905i	−0.887117	−	0.156423i
$188$	16.8822			1.23126
$189$	−13.3141	−	3.42554i	−0.968459	−	0.249172i
$190$	−0.324719			−0.0235576
$191$	16.6883	+	2.94260i	1.20752	+	0.212919i	0.740947	−	0.671563i	$-0.234377\pi$
$191$	16.6883	+	2.94260i	1.20752	+	0.212919i	0.466575	+	0.884482i	$0.345488\pi$
$192$	2.38406	−	6.80012i	0.172055	−	0.490757i
$193$	11.5156	+	4.19135i	0.828915	+	0.301700i	0.721413	−	0.692505i	$-0.243493\pi$
$193$	11.5156	+	4.19135i	0.828915	+	0.301700i	0.107501	+	0.994205i	$0.465715\pi$
$194$	−0.345057	−	1.95691i	−0.0247736	−	0.140498i
$195$	−1.56180	+	0.0185308i	−0.111843	+	0.00132702i
$196$	4.98626	−	11.7836i	0.356161	−	0.841688i
$197$	−11.7644	−	6.79216i	−0.838176	−	0.483921i	0.0184676	−	0.999829i	$-0.494121\pi$
$197$	−11.7644	−	6.79216i	−0.838176	−	0.483921i	−0.856644	+	0.515908i	$0.827455\pi$
$198$	0.946818	−	1.73368i	0.0672874	−	0.123207i
$199$		−	7.03966i		−	0.499028i	−0.968371	−	0.249514i	$-0.919729\pi$
$199$		−	7.03966i		−	0.499028i	0.968371	−	0.249514i	$-0.0802709\pi$
$200$	7.76902	+	1.36989i	0.549352	+	0.0968657i
$201$	4.56525	−	5.57363i	0.322008	−	0.393133i
$202$	−3.33878	−	3.97900i	−0.234915	−	0.279961i
$203$	11.5684	−	0.714068i	0.811941	−	0.0501177i
$204$	8.67753	+	22.9889i	0.607548	+	1.60955i
$205$	1.52862	+	1.28266i	0.106763	+	0.0895850i
$206$	−1.16323			−0.0810459
$207$	6.22935	−	3.79638i	0.432970	−	0.263867i
$208$			15.0087i			1.04067i
$209$	1.19799	−	6.79417i	0.0828670	−	0.469962i
$210$	0.340588	+	0.0345240i	0.0235028	+	0.00238238i
$211$	−12.4387	−	4.52733i	−0.856318	−	0.311674i	−0.123704	−	0.992319i	$-0.539477\pi$
$211$	−12.4387	−	4.52733i	−0.856318	−	0.311674i	−0.732613	+	0.680645i	$0.761700\pi$
$212$	11.4330	+	13.6253i	0.785221	+	0.935790i
$213$	9.52826	+	3.34052i	0.652866	+	0.228889i
$214$	3.07217	−	1.11818i	0.210009	−	0.0764371i
$215$	−0.0684760	−	0.118604i	−0.00467002	−	0.00808871i
$216$	−8.24663	+	0.293650i	−0.561112	+	0.0199804i
$217$	3.26210	−	1.42058i	0.221446	−	0.0964352i
$218$	−4.63928	+	5.52888i	−0.314212	+	0.374463i
$219$	−14.0086	−	4.91128i	−0.946612	−	0.331874i
$220$	0.178667	−	0.490884i	0.0120457	−	0.0330954i
$221$	−24.9844	−	29.7753i	−1.68063	−	2.00290i
$222$	−3.00403	+	0.0356429i	−0.201617	+	0.00239219i
$223$	−12.9495	−	2.28334i	−0.867162	−	0.152904i	−0.277668	−	0.960677i	$-0.589562\pi$
$223$	−12.9495	−	2.28334i	−0.867162	−	0.152904i	−0.589494	+	0.807773i	$0.700673\pi$
$224$	1.31715	−	11.6184i	0.0880056	−	0.776288i
$225$	2.93532	+	14.6108i	0.195688	+	0.974053i
$226$	−0.622992	+	1.07905i	−0.0414408	+	0.0717776i
$227$	−1.26546	+	7.17680i	−0.0839918	+	0.476341i	0.913578	+	0.406664i	$0.133308\pi$
$227$	−1.26546	+	7.17680i	−0.0839918	+	0.476341i	−0.997570	+	0.0696770i	$0.977803\pi$
$228$	−12.8752	+	4.85993i	−0.852679	+	0.321857i
$229$	1.41178	−	3.87883i	0.0932930	−	0.256321i	−0.884265	−	0.466985i	$-0.845340\pi$
$229$	1.41178	−	3.87883i	0.0932930	−	0.256321i	0.977559	+	0.210664i	$0.0675626\pi$
$230$	−0.139155	+	0.116765i	−0.00917560	+	0.00769924i
$231$	−1.97889	+	6.99882i	−0.130202	+	0.460489i
$232$	6.53740	−	2.37942i	0.429202	−	0.156217i
$233$	−12.6906	−	7.32691i	−0.831388	−	0.480002i	0.0229398	−	0.999737i	$-0.492697\pi$
$233$	−12.6906	−	7.32691i	−0.831388	−	0.480002i	−0.854328	+	0.519735i	$0.826031\pi$
$234$	5.80491	−	2.27020i	0.379479	−	0.148407i
$235$	−0.831531	−	1.44025i	−0.0542431	−	0.0939518i
$236$	−3.38615	+	1.23246i	−0.220420	+	0.0802262i
$237$	−7.58718	+	4.50132i	−0.492840	+	0.292392i
$238$	4.70600	+	7.10133i	0.305045	+	0.460311i
$239$	−22.4643	+	3.96107i	−1.45310	+	0.256220i	−0.843773	−	0.536701i	$-0.819670\pi$
$239$	−22.4643	+	3.96107i	−1.45310	+	0.256220i	−0.609324	+	0.792921i	$0.708559\pi$
$240$	−0.918493	+	0.173215i	−0.0592885	+	0.0111810i
$241$	0.269437	+	0.740271i	0.0173559	+	0.0476851i	0.948068	−	0.318068i	$-0.103034\pi$
$241$	0.269437	+	0.740271i	0.0173559	+	0.0476851i	−0.930712	+	0.365753i	$0.880812\pi$
$242$	3.04711	+	1.75925i	0.195875	+	0.113089i
$243$	−6.19065	−	14.3065i	−0.397131	−	0.917762i
$244$			4.90024i			0.313706i
$245$	−1.25088	+	0.155014i	−0.0799160	+	0.00990349i
$246$	−7.51476	−	2.63461i	−0.479124	−	0.167977i
$247$	16.6759	−	13.9928i	1.06106	−	0.890338i
$248$	1.63599	−	1.37276i	0.103885	−	0.0871703i
$249$	0.272586	+	22.9739i	0.0172745	+	1.45591i
$250$	−0.254672	−	0.699705i	−0.0161069	−	0.0442532i
$251$	−5.78209	+	10.0149i	−0.364962	+	0.632133i	−0.988770	−	0.149444i	$-0.952251\pi$
$251$	−5.78209	+	10.0149i	−0.364962	+	0.632133i	0.623808	+	0.781578i	$0.285585\pi$
$252$	14.0211	−	3.72855i	0.883245	−	0.234877i
$253$	−1.92971	−	3.34235i	−0.121320	−	0.210132i
$254$	−2.80197	+	3.33926i	−0.175811	+	0.209524i
$255$	1.53382	−	1.87262i	0.0960516	−	0.117268i
$256$	0.683760	+	3.87780i	0.0427350	+	0.242362i
$257$	9.55906	+	3.47921i	0.596278	+	0.217027i	0.622488	−	0.782629i	$-0.286122\pi$
$257$	9.55906	+	3.47921i	0.596278	+	0.217027i	−0.0262107	+	0.999656i	$0.508344\pi$
$258$	0.422803	+	0.346309i	0.0263225	+	0.0215603i
$259$	10.7544	−	2.58827i	0.668243	−	0.160828i
$260$	1.42750	−	0.824165i	0.0885295	−	0.0511125i
$261$	8.68419	+	9.86430i	0.537538	+	0.610585i
$262$	5.23890	−	3.02468i	0.323660	−	0.186865i
$263$	11.0604	−	13.1813i	0.682014	−	0.812793i	−0.308351	−	0.951273i	$-0.599777\pi$
$263$	11.0604	−	13.1813i	0.682014	−	0.812793i	0.990365	+	0.138480i	$0.0442216\pi$
$264$	0.0517947	+	4.36532i	0.00318774	+	0.268667i
$265$	0.599271	−	1.64648i	0.0368129	−	0.101143i
$266$	−3.97717	+	2.63564i	−0.243856	+	0.161601i
$267$	9.24803	+	10.7595i	0.565970	+	0.658471i
$268$	−1.32029	+	7.48775i	−0.0806497	+	0.457387i
$269$	−5.09560	+	8.82584i	−0.310684	+	0.538121i	−0.978511	−	0.206196i	$-0.933891\pi$
$269$	−5.09560	+	8.82584i	−0.310684	+	0.538121i	0.667826	+	0.744317i	$0.267225\pi$
$270$	0.205924	+	0.329045i	0.0125322	+	0.0200250i
$271$	−6.85061	+	3.95520i	−0.416145	+	0.240261i	−0.693426	−	0.720527i	$-0.743900\pi$
$271$	−6.85061	+	3.95520i	−0.416145	+	0.240261i	0.277282	+	0.960789i	$0.410566\pi$
$272$	−17.8182	−	14.9512i	−1.08039	−	0.906552i
$273$	−18.9786	+	12.9036i	−1.14864	+	0.780962i
$274$	0.457709	+	2.59580i	0.0276512	+	0.156818i
$275$	7.76448	−	1.36909i	0.468216	−	0.0825591i
$276$	−3.76995	+	6.71242i	−0.226924	+	0.404040i
$277$	10.5255	+	8.83194i	0.632416	+	0.530660i	0.901679	−	0.432407i	$-0.142336\pi$
$277$	10.5255	+	8.83194i	0.632416	+	0.530660i	−0.269263	+	0.963067i	$0.586780\pi$
$278$	6.38153			0.382739
$279$	3.54076	+	1.93373i	0.211980	+	0.115769i
$280$	−0.693648	+	0.302069i	−0.0414534	+	0.0180521i
$281$	0.953112	+	2.61865i	0.0568579	+	0.156216i	0.964870	−	0.262729i	$-0.0846224\pi$
$281$	0.953112	+	2.61865i	0.0568579	+	0.156216i	−0.908012	+	0.418944i	$0.862400\pi$
$282$	5.13426	+	4.20537i	0.305741	+	0.250426i
$283$	−16.1660	+	2.85051i	−0.960972	+	0.169445i	−0.632063	−	0.774917i	$-0.717792\pi$
$283$	−16.1660	+	2.85051i	−0.960972	+	0.169445i	−0.328908	+	0.944362i	$0.606681\pi$
$284$	−10.4936	+	1.85031i	−0.622683	+	0.109796i
$285$	1.04878	+	0.859032i	0.0621241	+	0.0508846i
$286$	−1.12784	−	3.09871i	−0.0666905	−	0.183231i
$287$	29.1335	+	3.30279i	1.71970	+	0.194957i
$288$	11.3216	−	6.89978i	0.667132	−	0.406573i
$289$	43.2377			2.54339
$290$	−0.250693	−	0.210357i	−0.0147212	−	0.0123526i
$291$	−4.06248	+	7.23327i	−0.238147	+	0.424022i
$292$	15.4279	−	2.72035i	0.902849	−	0.159197i
$293$	−0.270460	−	1.53385i	−0.0158004	−	0.0896087i	0.975888	−	0.218273i	$-0.0700422\pi$
$293$	−0.270460	−	1.53385i	−0.0158004	−	0.0896087i	−0.991688	+	0.128664i	$0.958931\pi$
$294$	4.45175	−	2.34159i	0.259631	−	0.136564i
$295$	0.271928	+	0.228175i	0.0158323	+	0.0132849i
$296$	5.74994	−	3.31973i	0.334208	−	0.192955i
$297$	−7.64440	+	3.09465i	−0.443573	+	0.179570i
$298$	−3.61606	+	6.26320i	−0.209473	+	0.362818i
$299$	2.11467	−	11.9929i	0.122295	−	0.693567i
$300$	−10.2515	−	11.9270i	−0.591872	−	0.688606i
$301$	−1.80136	−	0.896866i	−0.103829	−	0.0516945i
$302$	−0.326189	+	0.896198i	−0.0187701	+	0.0515704i
$303$	0.257281	+	21.6840i	0.0147804	+	1.24571i
$304$	8.37359	−	9.97926i	0.480258	−	0.572350i
$305$	0.418050	−	0.241361i	0.0239375	−	0.0138203i
$306$	−3.08753	+	9.15304i	−0.176502	+	0.523245i
$307$	1.41615	−	0.817613i	0.0808238	−	0.0466637i	−0.459043	−	0.888414i	$-0.651808\pi$
$307$	1.41615	−	0.817613i	0.0808238	−	0.0466637i	0.539867	+	0.841750i	$0.318474\pi$
$308$	−1.79603	−	7.46254i	−0.102338	−	0.425218i
$309$	3.75699	+	3.07727i	0.213728	+	0.175060i
$310$	−0.0944022	−	0.0343596i	−0.00536168	−	0.00195149i
$311$	2.06271	+	11.6982i	0.116965	+	0.663344i	0.985758	+	0.168168i	$0.0537852\pi$
$311$	2.06271	+	11.6982i	0.116965	+	0.663344i	−0.868793	+	0.495176i	$0.835104\pi$
$312$	−8.72871	+	10.6567i	−0.494166	+	0.603319i
$313$	−1.19230	+	1.42093i	−0.0673929	+	0.0803157i	−0.798688	−	0.601746i	$-0.794472\pi$
$313$	−1.19230	+	1.42093i	−0.0673929	+	0.0803157i	0.731295	+	0.682062i	$0.238916\pi$
$314$	1.16478	+	2.01745i	0.0657321	+	0.113851i
$315$	−1.00870	−	1.01252i	−0.0568337	−	0.0570489i
$316$	4.65504	−	8.06276i	0.261866	−	0.453566i
$317$	−7.22432	−	19.8487i	−0.405758	−	1.11481i	−0.959398	−	0.282055i	$-0.908984\pi$
$317$	−7.22432	−	19.8487i	−0.405758	−	1.11481i	0.553640	−	0.832756i	$-0.313238\pi$
$318$	0.0829572	+	6.99174i	0.00465201	+	0.392077i
$319$	5.32623	−	4.46924i	0.298212	−	0.250229i
$320$	0.573867	−	0.481532i	0.0320802	−	0.0269184i
$321$	−12.8806	−	4.51582i	−0.718924	−	0.252048i
$322$	−0.756630	+	2.55961i	−0.0421653	+	0.142642i
$323$			33.7367i			1.87716i
$324$	13.0896	+	9.96471i	0.727201	+	0.553595i
$325$	21.5448	+	12.4389i	1.19509	+	0.689986i
$326$	−2.71996	−	7.47303i	−0.150645	−	0.413893i
$327$	29.6104	−	5.58412i	1.63746	−	0.308803i
$328$	17.3316	−	3.05602i	0.956976	−	0.168741i
$329$	−21.8747	−	10.8910i	−1.20599	−	0.600440i
$330$	0.176616	−	0.104783i	0.00972242	−	0.00576811i
$331$	−23.4181	+	8.52351i	−1.28718	+	0.468494i	−0.892800	−	0.450454i	$-0.851262\pi$
$331$	−23.4181	+	8.52351i	−1.28718	+	0.468494i	−0.394378	+	0.918948i	$0.629040\pi$
$332$	−12.1234	−	20.9983i	−0.665357	−	1.15243i
$333$	9.79669	+	7.83192i	0.536855	+	0.429186i
$334$	3.38173	+	1.95244i	0.185040	+	0.106833i
$335$	0.703826	−	0.256172i	0.0384541	−	0.0139962i
$336$	−9.84380	+	9.57666i	−0.537023	+	0.522450i
$337$	4.61488	−	3.87234i	0.251388	−	0.210940i	−0.508382	−	0.861132i	$-0.669756\pi$
$337$	4.61488	−	3.87234i	0.251388	−	0.210940i	0.759770	+	0.650192i	$0.225312\pi$
$338$	1.71414	−	4.70955i	0.0932368	−	0.256166i
$339$	4.86673	−	1.83702i	0.264325	−	0.0997734i
$340$	−0.443589	+	2.51572i	−0.0240570	+	0.136434i
$341$	1.06719	−	1.84843i	0.0577918	−	0.100098i
$342$	−5.12625	−	1.72920i	−0.277196	−	0.0935045i
$343$	−14.0627	+	12.0516i	−0.759312	+	0.650727i
$344$	−1.18949	−	0.209740i	−0.0641331	−	0.0113084i
$345$	0.758339	−	0.00899772i	0.0408276	−	0.000484421i
$346$	−1.43120	−	1.70563i	−0.0769416	−	0.0916955i
$347$	−11.1036	+	30.5068i	−0.596071	+	1.63769i	0.162958	+	0.986633i	$0.447897\pi$
$347$	−11.1036	+	30.5068i	−0.596071	+	1.63769i	−0.759028	+	0.651057i	$0.774326\pi$
$348$	−13.0884	−	4.58866i	−0.701610	−	0.245978i
$349$	−6.71581	+	8.00359i	−0.359489	+	0.428422i	−0.915229	−	0.402934i	$-0.867990\pi$
$349$	−6.71581	+	8.00359i	−0.359489	+	0.428422i	0.555740	+	0.831356i	$0.312435\pi$
$350$	−4.38494	−	3.24088i	−0.234385	−	0.173232i
$351$	−24.7544	−	8.02440i	−1.32129	−	0.428311i
$352$	−3.50717	−	6.07460i	−0.186933	−	0.323777i
$353$	4.68991	−	1.70699i	0.249618	−	0.0908537i	−0.214181	−	0.976794i	$-0.568708\pi$
$353$	4.68991	−	1.70699i	0.249618	−	0.0908537i	0.463799	+	0.885940i	$0.346486\pi$
$354$	−1.33681	−	0.468675i	−0.0710508	−	0.0249098i
$355$	0.674717	+	0.804097i	0.0358103	+	0.0426770i
$356$	−14.0698	−	5.12099i	−0.745698	−	0.271412i
$357$	3.58687	−	35.3854i	0.189837	−	1.87279i
$358$	1.07120	−	6.07508i	0.0566148	−	0.321078i
$359$		−	16.1906i		−	0.854506i	−0.904132	−	0.427253i	$-0.859481\pi$
$359$		−	16.1906i		−	0.854506i	0.904132	−	0.427253i	$-0.140519\pi$
$360$	−0.752902	−	0.411185i	−0.0396814	−	0.0216713i
$361$	0.105445			0.00554976
$362$	2.01450	+	1.69037i	0.105880	+	0.0888437i
$363$	−5.18751	−	13.7430i	−0.272274	−	0.721321i
$364$	10.7945	−	21.6809i	0.565787	−	1.13639i
$365$	−0.991979	−	1.18219i	−0.0519225	−	0.0618789i
$366$	−1.22066	+	1.49028i	−0.0638047	+	0.0778980i
$367$	−11.3391	−	1.99938i	−0.591895	−	0.104367i	−0.130326	−	0.991471i	$-0.541602\pi$
$367$	−11.3391	−	1.99938i	−0.591895	−	0.104367i	−0.461569	+	0.887104i	$0.652713\pi$
$368$		−	7.28754i		−	0.379889i
$369$	17.3014	+	28.3893i	0.900675	+	1.47789i
$370$	−0.270478	−	0.156161i	−0.0140615	−	0.00811841i
$371$	−6.02409	−	25.0303i	−0.312755	−	1.29951i
$372$	−4.25731	+	0.0505132i	−0.220731	+	0.00261898i
$373$	−5.79313	−	32.8545i	−0.299957	−	1.70114i	−0.646343	−	0.763047i	$-0.723702\pi$
$373$	−5.79313	−	32.8545i	−0.299957	−	1.70114i	0.346386	−	0.938092i	$-0.387409\pi$
$374$	4.80228	+	1.74789i	0.248320	+	0.0903811i
$375$	−1.02850	+	2.93363i	−0.0531117	+	0.151492i
$376$	−14.4445	−	2.54695i	−0.744917	−	0.131349i
$377$	21.9390			1.12992
$378$	5.19292	+	2.35873i	0.267095	+	0.121320i
$379$	−12.4601			−0.640032			−0.320016	−	0.947412i	$-0.603688\pi$
$379$	−12.4601			−0.640032			−0.320016	+	0.947412i	$0.603688\pi$
$380$	−1.40895	−	0.248436i	−0.0722777	−	0.0127445i
$381$	17.8837	−	3.37262i	0.916208	−	0.172785i
$382$	−6.60629	−	2.40449i	−0.338007	−	0.123024i
$383$	5.05101	+	28.6457i	0.258094	+	1.46373i	0.788003	+	0.615672i	$0.211115\pi$
$383$	5.05101	+	28.6457i	0.258094	+	1.46373i	−0.529908	+	0.848055i	$0.677774\pi$
$384$	−8.96085	+	15.9549i	−0.457282	+	0.814193i
$385$	−0.548181	+	0.520790i	−0.0279379	+	0.0265419i
$386$	−4.40296	−	2.54205i	−0.224105	−	0.129387i
$387$	−0.449419	−	2.23702i	−0.0228453	−	0.113714i
$388$		−	8.75503i		−	0.444469i
$389$	10.6003	+	1.86913i	0.537459	+	0.0947685i	0.435788	−	0.900050i	$-0.356470\pi$
$389$	10.6003	+	1.86913i	0.537459	+	0.0947685i	0.101671	+	0.994818i	$0.467581\pi$
$390$	0.639435	+	0.104943i	0.0323790	+	0.00531400i
$391$	12.1313	+	14.4575i	0.613505	+	0.731147i
$392$	−6.04401	+	9.32987i	−0.305269	+	0.471230i
$393$	−24.9223	−	4.09020i	−1.25716	−	0.206324i
$394$	4.31721	+	3.62257i	0.217498	+	0.182502i
$395$	−0.917134			−0.0461460
$396$	5.43464	−	6.79801i	0.273101	−	0.341613i
$397$			39.1821i			1.96650i	0.182275	+	0.983248i	$0.441654\pi$
$397$			39.1821i			1.96650i	−0.182275	+	0.983248i	$0.558346\pi$
$398$	−0.507146	+	2.87617i	−0.0254209	+	0.144169i
$399$	19.8179	+	2.00886i	0.992137	+	0.100569i
$400$	13.9896	+	5.09181i	0.699482	+	0.254590i
$401$	6.65975	+	7.93679i	0.332572	+	0.396344i	0.906254	−	0.422734i	$-0.138930\pi$
$401$	6.65975	+	7.93679i	0.332572	+	0.396344i	−0.573681	+	0.819079i	$0.694485\pi$
$402$	−2.26674	+	1.94831i	−0.113055	+	0.0971729i
$403$	6.32864	−	2.30344i	0.315252	−	0.114742i
$404$	−11.4427	−	19.8193i	−0.569294	−	0.986045i
$405$	0.205381	−	1.60751i	0.0102055	−	0.0798780i
$406$	−4.77790	−	0.541657i	−0.237123	−	0.0268820i
$407$	4.26527	−	5.08315i	0.211421	−	0.251962i
$408$	−3.95628	−	20.9786i	−0.195865	−	1.03859i
$409$	8.09126	−	22.2306i	0.400087	−	1.09923i	−0.562154	−	0.827033i	$-0.690027\pi$
$409$	8.09126	−	22.2306i	0.400087	−	1.09923i	0.962241	−	0.272198i	$-0.0877506\pi$
$410$	−0.532137	−	0.634176i	−0.0262804	−	0.0313197i
$411$	5.38878	−	9.59475i	0.265809	−	0.473274i
$412$	−5.04723	−	0.889964i	−0.248659	−	0.0438454i
$413$	5.18261	+	0.587538i	0.255019	+	0.0289109i
$414$	−2.81860	+	1.10230i	−0.138527	+	0.0541752i
$415$	−1.19427	+	2.06854i	−0.0586245	+	0.101541i
$416$	3.84334	−	21.7966i	0.188435	−	1.06867i
$417$	−20.6110	−	16.8821i	−1.00933	−	0.826720i
$418$	−0.978921	+	2.68956i	−0.0478806	+	0.131551i
$419$	0.297747	−	0.249839i	0.0145459	−	0.0122054i	−0.635486	−	0.772113i	$-0.719200\pi$
$419$	0.297747	−	0.249839i	0.0145459	−	0.0122054i	0.650032	+	0.759907i	$0.274756\pi$
$420$	1.45139	+	0.410377i	0.0708208	+	0.0200243i
$421$	−29.2829	+	10.6581i	−1.42716	+	0.519444i	−0.936116	−	0.351691i	$-0.885607\pi$
$421$	−29.2829	+	10.6581i	−1.42716	+	0.519444i	−0.491044	+	0.871135i	$0.663385\pi$
$422$	4.75590	+	2.74582i	0.231513	+	0.133664i
$423$	−5.45748	−	27.1650i	−0.265352	−	1.32081i
$424$	−7.72652	−	13.3827i	−0.375233	−	0.649922i
$425$	−36.2297	+	13.1865i	−1.75740	+	0.639640i
$426$	−3.65227	−	2.05125i	−0.176953	−	0.0993836i
$427$	3.16123	−	6.34937i	0.152983	−	0.307268i
$428$	14.1856	−	2.50131i	0.685688	−	0.120905i
$429$	−4.55483	+	12.9919i	−0.219909	+	0.627253i
$430$	0.0194326	+	0.0533907i	0.000937124	+	0.00257473i
$431$	20.9763	+	12.1107i	1.01039	+	0.583352i	0.911307	−	0.411727i	$-0.135074\pi$
$431$	20.9763	+	12.1107i	1.01039	+	0.583352i	0.0990874	+	0.995079i	$0.468408\pi$
$432$	−15.4224	−	2.15668i	−0.742011	−	0.103763i
$433$			10.0296i			0.481991i	0.970526	+	0.240995i	$0.0774739\pi$
$433$			10.0296i			0.481991i	−0.970526	+	0.240995i	$0.922526\pi$
$434$	−1.43513	+	0.345395i	−0.0688882	+	0.0165795i
$435$	0.253198	+	1.34261i	0.0121399	+	0.0643732i
$436$	−24.3599	+	20.4403i	−1.16663	+	0.978915i
$437$	−8.09706	+	6.79424i	−0.387335	+	0.325013i
$438$	5.36962	+	3.01578i	0.256570	+	0.144100i
$439$	−14.0388	−	38.5712i	−0.670034	−	1.84090i	−0.524200	−	0.851595i	$-0.675636\pi$
$439$	−14.0388	−	38.5712i	−0.670034	−	1.84090i	−0.145834	−	0.989309i	$-0.546587\pi$
$440$	−0.226926	+	0.393048i	−0.0108183	+	0.0187378i
$441$	−20.5728	−	4.21407i	−0.979659	−	0.200670i
$442$	8.06274	+	13.9651i	0.383506	+	0.664251i
$443$	−22.4132	+	26.7110i	−1.06488	+	1.26908i	−0.103273	+	0.994653i	$0.532932\pi$
$443$	−22.4132	+	26.7110i	−1.06488	+	1.26908i	−0.961609	+	0.274424i	$0.911513\pi$
$444$	−13.0617	−	2.14367i	−0.619881	−	0.101734i
$445$	0.256125	+	1.45256i	0.0121415	+	0.0688578i
$446$	5.12623	+	1.86580i	0.242734	+	0.0883480i
$447$	28.2482	−	10.6627i	1.33609	−	0.504329i
$448$	3.12030	−	10.5557i	0.147420	−	0.498711i
$449$	0.655683	−	0.378559i	0.0309436	−	0.0178653i	−0.484448	−	0.874820i	$-0.660980\pi$
$449$	0.655683	−	0.378559i	0.0309436	−	0.0178653i	0.515392	+	0.856955i	$0.327646\pi$
$450$	−0.146695	−	6.18094i	−0.00691527	−	0.291373i
$451$	15.2322	−	8.79433i	0.717258	−	0.414109i
$452$	−3.52872	+	4.20536i	−0.165977	+	0.197804i
$453$	3.42438	−	2.03162i	0.160891	−	0.0954536i
$454$	1.03405	−	2.84103i	0.0485305	−	0.133336i
$455$	−2.38133	+	0.146989i	−0.111638	+	0.00689096i
$456$	11.7493	−	2.21575i	0.550209	−	0.103762i
$457$	−5.45161	+	30.9176i	−0.255015	+	1.44626i	0.541018	+	0.841011i	$0.318039\pi$
$457$	−5.45161	+	30.9176i	−0.255015	+	1.44626i	−0.796033	+	0.605253i	$0.793072\pi$
$458$	−0.856242	+	1.48305i	−0.0400096	+	0.0692986i
$459$	34.1861	−	21.3945i	1.59567	−	0.998611i
$460$	−0.693126	+	0.400177i	−0.0323172	+	0.0186583i
$461$	−8.35408	−	7.00990i	−0.389088	−	0.326484i	0.427170	−	0.904171i	$-0.359511\pi$
$461$	−8.35408	−	7.00990i	−0.389088	−	0.326484i	−0.816258	+	0.577688i	$0.803955\pi$
$462$	1.31271	−	2.71692i	0.0610730	−	0.126403i
$463$	1.23596	+	7.00945i	0.0574397	+	0.325757i	0.999965	−	0.00837823i	$-0.00266690\pi$
$463$	1.23596	+	7.00945i	0.0574397	+	0.325757i	−0.942525	+	0.334135i	$0.891556\pi$
$464$	12.9294	−	2.27979i	0.600230	−	0.105837i
$465$	0.214003	+	0.360712i	0.00992414	+	0.0167276i
$466$	4.65711	+	3.90778i	0.215736	+	0.181024i
$467$	13.2274			0.612090			0.306045	−	0.952017i	$-0.400994\pi$
$467$	13.2274			0.612090			0.306045	+	0.952017i	$0.400994\pi$
$468$	26.9244	−	5.40913i	1.24458	−	0.250037i
$469$	6.54122	−	8.85033i	0.302045	−	0.408670i
$470$	0.235978	+	0.648344i	0.0108849	+	0.0299059i
$471$	1.57510	−	9.59733i	0.0725768	−	0.442222i
$472$	3.08314	−	0.543641i	0.141913	−	0.0250231i
$473$	−1.18880	+	0.209617i	−0.0546610	+	0.00963820i
$474$	3.42415	−	1.29250i	0.157276	−	0.0593664i
$475$	−7.38524	−	20.2908i	−0.338858	−	0.931005i
$476$	14.9862	+	34.4131i	0.686891	+	1.57732i
$477$	18.2284	−	22.8014i	0.834623	−	1.04400i
$478$	9.46353			0.432852
$479$	1.52575	+	1.28025i	0.0697132	+	0.0584963i	0.676978	−	0.736003i	$-0.263289\pi$
$479$	1.52575	+	1.28025i	0.0697132	+	0.0584963i	−0.607265	+	0.794499i	$0.707733\pi$
$480$	1.37825	−	0.0163530i	0.0629083	−	0.000746410i
$481$	20.6197	−	3.63580i	0.940175	−	0.165778i
$482$	−0.0567527	−	0.321861i	−0.00258501	−	0.0146603i
$483$	9.21512	−	6.26539i	0.419302	−	0.285085i
$484$	11.8754	+	9.96464i	0.539791	+	0.452938i
$485$	−0.746909	+	0.431228i	−0.0339154	+	0.0195811i
$486$	1.49864	+	6.29114i	0.0679795	+	0.285372i
$487$	−7.16028	+	12.4020i	−0.324463	+	0.561987i	−0.981404	−	0.191956i	$-0.938517\pi$
$487$	−7.16028	+	12.4020i	−0.324463	+	0.561987i	0.656940	+	0.753943i	$0.271850\pi$
$488$	0.739281	−	4.19267i	0.0334657	−	0.189793i
$489$	−10.9847	+	31.3319i	−0.496745	+	1.41688i
$490$	0.522236	+	0.0267816i	0.0235922	+	0.00120987i
$491$	9.11592	−	25.0458i	0.411396	−	1.13030i	−0.545053	−	0.838401i	$-0.683491\pi$
$491$	9.11592	−	25.0458i	0.411396	−	1.13030i	0.956449	−	0.291899i	$-0.0942871\pi$
$492$	−30.5908	−	17.1809i	−1.37914	−	0.774577i
$493$	−21.8550	+	26.0458i	−0.984300	+	1.17304i
$494$	−7.82128	+	4.51562i	−0.351896	+	0.203167i
$495$	−0.847634	−	0.128805i	−0.0380983	−	0.00578933i
$496$	3.49030	−	2.01513i	0.156719	−	0.0904819i
$497$	14.7906	+	4.37214i	0.663447	+	0.196117i
$498$	1.54370	−	9.40601i	0.0691749	−	0.421493i
$499$	−20.0327	−	7.29129i	−0.896785	−	0.326403i	−0.147821	−	0.989014i	$-0.547226\pi$
$499$	−20.0327	−	7.29129i	−0.896785	−	0.326403i	−0.748964	+	0.662611i	$0.769448\pi$
$500$	−0.569687	−	3.23086i	−0.0254772	−	0.144488i
$501$	−5.75718	−	15.2522i	−0.257212	−	0.681419i
$502$	3.08385	−	3.67519i	0.137639	−	0.164032i
$503$	−6.74300	−	11.6792i	−0.300655	−	0.520751i	0.675629	−	0.737242i	$-0.263872\pi$
$503$	−6.74300	−	11.6792i	−0.300655	−	0.520751i	−0.976285	+	0.216491i	$0.930539\pi$
$504$	−12.5590	+	1.07486i	−0.559423	+	0.0478780i
$505$	−1.12721	+	1.95239i	−0.0501604	+	0.0868803i
$506$	0.547626	+	1.50459i	0.0243450	+	0.0668872i
$507$	−17.9953	+	10.6762i	−0.799198	+	0.474147i
$508$	−14.7125	+	12.3453i	−0.652763	+	0.547733i
$509$	−6.79910	+	5.70512i	−0.301365	+	0.252875i	−0.780912	−	0.624641i	$-0.785245\pi$
$509$	−6.79910	+	5.70512i	−0.301365	+	0.252875i	0.479547	+	0.877516i	$0.340801\pi$
$510$	−0.761574	+	0.654589i	−0.0337231	+	0.0289857i
$511$	−21.7453	−	6.42797i	−0.961954	−	0.284357i
$512$		−	22.7635i		−	1.00601i
$513$	11.9822	+	19.1463i	0.529028	+	0.845328i
$514$	−3.65486	−	2.11014i	−0.161209	−	0.0930741i
$515$	0.172677	+	0.474425i	0.00760904	+	0.0209057i
$516$	1.56958	+	1.82611i	0.0690970	+	0.0803900i
$517$	−14.4360	+	2.54546i	−0.634897	+	0.111949i
$518$	−4.58033	+	0.282725i	−0.201248	+	0.0124222i
$519$	0.110286	+	9.29503i	0.00484101	+	0.408007i
$520$	−1.34571	+	0.489798i	−0.0590133	+	0.0214791i
$521$	21.3144	+	36.9177i	0.933802	+	1.61739i	0.776756	+	0.629802i	$0.216864\pi$
$521$	21.3144	+	36.9177i	0.933802	+	1.61739i	0.157046	+	0.987591i	$0.449803\pi$
$522$	−2.83743	−	4.65584i	−0.124191	−	0.203781i
$523$	−19.7089	−	11.3789i	−0.861809	−	0.497565i	0.00280898	−	0.999996i	$-0.499106\pi$
$523$	−19.7089	−	11.3789i	−0.861809	−	0.497565i	−0.864617	+	0.502431i	$0.832439\pi$
$524$	25.0457	−	9.11587i	1.09412	−	0.398229i
$525$	5.58885	+	22.0676i	0.243917	+	0.963108i
$526$	−5.46851	+	4.58862i	−0.238438	+	0.200074i
$527$	−3.56979	+	9.80791i	−0.155502	+	0.427239i
$528$	−1.33426	+	8.12983i	−0.0580660	+	0.353805i
$529$	2.96712	−	16.8274i	0.129005	−	0.731625i
$530$	−0.363457	+	0.629526i	−0.0157876	+	0.0273449i
$531$	3.07777	+	5.05021i	0.133564	+	0.219161i
$532$	−19.2734	+	8.39316i	−0.835606	+	0.363890i
$533$	54.6557	+	9.63728i	2.36740	+	0.417437i
$534$	−3.00331	−	5.06221i	−0.129966	−	0.219063i
$535$	−0.912103	−	1.08700i	−0.0394336	−	0.0469952i
$536$	2.25930	−	6.20737i	0.0975867	−	0.268117i
$537$	−19.5312	+	16.7875i	−0.842832	+	0.724433i
$538$	2.71772	−	3.23885i	0.117169	−	0.139637i
$539$	−2.48706	+	10.8281i	−0.107125	+	0.466397i
$540$	0.641758	+	1.58527i	0.0276169	+	0.0682192i
$541$	−1.69482	−	2.93552i	−0.0728660	−	0.126208i	0.827290	−	0.561775i	$-0.189881\pi$
$541$	−1.69482	−	2.93552i	−0.0728660	−	0.126208i	−0.900156	+	0.435567i	$0.856548\pi$
$542$	3.08387	−	1.12244i	0.132463	−	0.0482127i
$543$	−2.03463	−	10.7888i	−0.0873142	−	0.462993i
$544$	22.0482	+	26.2760i	0.945307	+	1.12657i
$545$	2.94365	+	1.07140i	0.126092	+	0.0458938i
$546$	8.68360	−	3.90474i	0.371624	−	0.167107i
$547$	−0.794100	+	4.50356i	−0.0339532	+	0.192558i	−0.997067	−	0.0765371i	$-0.975614\pi$
$547$	−0.794100	+	4.50356i	−0.0339532	+	0.192558i	0.963113	+	0.269096i	$0.0867247\pi$
$548$			11.6133i			0.496097i
$549$	7.88494	−	1.58409i	0.336521	−	0.0676074i
$550$	−3.27094			−0.139473
$551$	−14.5872	−	12.2401i	−0.621435	−	0.521446i
$552$	4.23826	−	5.17442i	0.180392	−	0.220238i
$553$	−11.2331	+	7.44408i	−0.477679	+	0.316555i
$554$	−3.66410	−	4.36671i	−0.155673	−	0.185524i
$555$	0.460473	+	1.21991i	0.0195460	+	0.0517822i
$556$	27.6894	+	4.88239i	1.17429	+	0.207059i
$557$			28.3433i			1.20094i	0.799646	+	0.600472i	$0.205021\pi$
$557$			28.3433i			1.20094i	−0.799646	+	0.600472i	$0.794979\pi$
$558$	−1.30733	−	1.04514i	−0.0553436	−	0.0442442i
$559$	−3.29867	−	1.90449i	−0.139519	−	0.0805511i
$560$	−1.38812	+	0.334081i	−0.0586586	+	0.0141175i
$561$	−10.8864	−	18.3496i	−0.459625	−	0.774719i
$562$	−0.200758	−	1.13856i	−0.00846848	−	0.0480271i
$563$	4.56240	+	1.66058i	0.192282	+	0.0699851i	0.436367	−	0.899769i	$-0.356265\pi$
$563$	4.56240	+	1.66058i	0.192282	+	0.0699851i	−0.244084	+	0.969754i	$0.578487\pi$
$564$	19.0601	+	22.1752i	0.802574	+	0.933744i
$565$	0.532575	+	0.0939073i	0.0224056	+	0.00395071i
$566$	6.81026			0.286257
$567$	−10.5322	−	21.3559i	−0.442309	−	0.896863i
$568$	9.25755			0.388438
$569$	24.0084	+	4.23332i	1.00648	+	0.177470i	0.652506	−	0.757784i	$-0.273718\pi$
$569$	24.0084	+	4.23332i	1.00648	+	0.177470i	0.353978	+	0.935254i	$0.384829\pi$
$570$	−0.366609	−	0.426527i	−0.0153556	−	0.0178652i
$571$	6.78414	+	2.46923i	0.283908	+	0.103334i	0.480049	−	0.877242i	$-0.340619\pi$
$571$	6.78414	+	2.46923i	0.283908	+	0.103334i	−0.196141	+	0.980576i	$0.562841\pi$
$572$	−2.52292	−	14.3082i	−0.105488	−	0.598254i
$573$	14.9760	+	25.2427i	0.625630	+	1.05453i
$574$	−11.6650	−	3.44822i	−0.486889	−	0.143926i
$575$	−10.4612	−	6.03976i	−0.436261	−	0.251875i
$576$	11.6238	−	4.54584i	0.484323	−	0.189410i
$577$			26.1510i			1.08868i	0.838864	+	0.544340i	$0.183220\pi$
$577$			26.1510i			1.08868i	−0.838864	+	0.544340i	$0.816780\pi$
$578$	−17.6655	−	3.11490i	−0.734786	−	0.129563i
$579$	7.49577	+	19.8582i	0.311513	+	0.825277i
$580$	−0.926816	−	1.10454i	−0.0384839	−	0.0458634i
$581$	2.16220	+	35.0290i	0.0897030	+	1.45325i
$582$	2.18089	−	2.66261i	0.0904007	−	0.110369i
$583$	−11.8308	−	9.92722i	−0.489982	−	0.411143i
$584$	−13.6106			−0.563210
$585$	−1.78762	−	2.03054i	−0.0739090	−	0.0839527i
$586$			0.646165i			0.0266928i
$587$	−3.34943	+	18.9956i	−0.138246	+	0.784031i	0.834298	+	0.551313i	$0.185873\pi$
$587$	−3.34943	+	18.9956i	−0.138246	+	0.784031i	−0.972544	+	0.232718i	$0.925238\pi$
$588$	21.1076	−	6.75419i	0.870463	−	0.278538i
$589$	−5.49302	−	1.99929i	−0.226336	−	0.0823795i
$590$	−0.0946628	−	0.112815i	−0.00389720	−	0.00464451i
$591$	−4.36034	−	23.1212i	−0.179361	−	0.951078i
$592$	11.7740	−	4.28539i	0.483908	−	0.176128i
$593$	−19.5311	−	33.8289i	−0.802047	−	1.38919i	−0.918266	−	0.395963i	$-0.870411\pi$
$593$	−19.5311	−	33.8289i	−0.802047	−	1.38919i	0.116219	−	0.993224i	$-0.462922\pi$
$594$	3.34619	−	0.713657i	0.137296	−	0.0292817i
$595$	2.19770	−	2.97351i	0.0900971	−	0.121902i
$596$	−20.4819	+	24.4094i	−0.838972	+	0.999848i
$597$	9.24677	−	7.94781i	0.378445	−	0.325282i
$598$	−1.72797	+	4.74755i	−0.0706618	+	0.194142i
$599$	5.53430	+	6.59552i	0.226125	+	0.269486i	0.867164	−	0.498023i	$-0.165941\pi$
$599$	5.53430	+	6.59552i	0.226125	+	0.269486i	−0.641038	+	0.767509i	$0.721496\pi$
$600$	6.97187	+	11.7514i	0.284625	+	0.479749i
$601$	41.3305	+	7.28768i	1.68591	+	0.297271i	0.932737	−	0.360557i	$-0.117413\pi$
$601$	41.3305	+	7.28768i	1.68591	+	0.297271i	0.753168	+	0.657828i	$0.228525\pi$
$602$	0.671366	+	0.496202i	0.0273628	+	0.0202237i
$603$	12.4753	−	0.296081i	0.508033	−	0.0120574i
$604$	−2.10100	+	3.63903i	−0.0854883	+	0.148070i
$605$	0.265182	−	1.50392i	0.0107812	−	0.0611431i
$606$	1.45702	−	8.87787i	0.0591875	−	0.360639i
$607$	15.1581	−	41.6466i	0.615249	−	1.69038i	−0.103073	−	0.994674i	$-0.532868\pi$
$607$	15.1581	−	41.6466i	0.615249	−	1.69038i	0.718323	−	0.695710i	$-0.244910\pi$
$608$	−14.7161	+	12.3483i	−0.596817	+	0.500789i
$609$	13.9987	+	14.3892i	0.567256	+	0.583079i
$610$	−0.188189	+	0.0684952i	−0.00761955	+	0.00277329i
$611$	−40.0570	−	23.1269i	−1.62053	−	0.935615i
$612$	−20.3996	+	37.3528i	−0.824605	+	1.50990i
$613$	−22.3176	−	38.6553i	−0.901401	−	1.56127i	−0.825677	−	0.564143i	$-0.809207\pi$
$613$	−22.3176	−	38.6553i	−0.901401	−	1.56127i	−0.0757236	−	0.997129i	$-0.524127\pi$
$614$	−0.637493	+	0.232028i	−0.0257271	+	0.00936390i
$615$	0.0410057	+	3.45601i	0.00165351	+	0.139360i
$616$	0.410843	+	6.65594i	0.0165534	+	0.268176i
$617$	26.5556	−	4.68248i	1.06909	−	0.188509i	0.388703	−	0.921363i	$-0.372923\pi$
$617$	26.5556	−	4.68248i	1.06909	−	0.188509i	0.680386	+	0.732854i	$0.261812\pi$
$618$	−1.31329	−	1.52793i	−0.0528282	−	0.0614623i
$619$	13.2165	+	36.3120i	0.531215	+	1.45950i	0.857626	+	0.514274i	$0.171939\pi$
$619$	13.2165	+	36.3120i	0.531215	+	1.45950i	−0.326411	+	0.945228i	$0.605839\pi$
$620$	−0.383322	−	0.221311i	−0.0153946	−	0.00888807i
$621$	12.0196	+	3.89628i	0.482330	+	0.156352i
$622$		−	4.92809i		−	0.197599i
$623$	14.9270	+	15.7121i	0.598036	+	0.629491i
$624$	−19.7143	+	16.9449i	−0.789205	+	0.678339i
$625$	18.7794	−	15.7577i	0.751174	−	0.630310i
$626$	0.589500	−	0.494650i	0.0235612	−	0.0197702i
$627$	10.2769	−	6.09705i	0.410418	−	0.243493i
$628$	3.51044	+	9.64485i	0.140082	+	0.384871i
$629$	−16.2243	+	28.1013i	−0.646906	+	1.12047i
$630$	0.339177	+	0.486349i	0.0135131	+	0.0193766i
$631$	−5.01811	−	8.69163i	−0.199768	−	0.346008i	0.748685	−	0.662926i	$-0.230686\pi$
$631$	−5.01811	−	8.69163i	−0.199768	−	0.346008i	−0.948453	+	0.316917i	$0.897352\pi$
$632$	−5.19927	+	6.19625i	−0.206816	+	0.246474i
$633$	−8.09662	−	21.4500i	−0.321812	−	0.852560i
$634$	1.52169	+	8.62995i	0.0604341	+	0.342739i
$635$	1.77786	+	0.647090i	0.0705524	+	0.0256790i
$636$	−4.98930	+	30.4006i	−0.197838	+	1.20546i
$637$	−27.9735	+	21.1288i	−1.10835	+	0.837153i
$638$	−2.49809	+	1.44227i	−0.0989002	+	0.0571001i
$639$	6.36958	+	16.2871i	0.251977	+	0.644307i
$640$	−1.64750	+	0.951186i	−0.0651233	+	0.0375989i
$641$	20.4966	−	24.4269i	0.809567	−	0.964804i	−0.190290	−	0.981728i	$-0.560943\pi$
$641$	20.4966	−	24.4269i	0.809567	−	0.964804i	0.999857	+	0.0169239i	$0.00538730\pi$
$642$	4.93725	+	2.77295i	0.194858	+	0.109439i
$643$	−4.12226	+	11.3258i	−0.162566	+	0.446646i	−0.994053	−	0.108898i	$-0.965268\pi$
$643$	−4.12226	+	11.3258i	−0.162566	+	0.446646i	0.831487	+	0.555544i	$0.187490\pi$
$644$	−5.24132	+	10.5273i	−0.206537	+	0.414832i
$645$	0.0784795	−	0.223849i	0.00309013	−	0.00881405i
$646$	2.43043	−	13.7837i	0.0956242	−	0.542312i
$647$	21.3692	−	37.0126i	0.840111	−	1.45512i	−0.0496886	−	0.998765i	$-0.515823\pi$
$647$	21.3692	−	37.0126i	0.840111	−	1.45512i	0.889800	−	0.456351i	$-0.150844\pi$
$648$	−9.69620	−	10.5006i	−0.380903	−	0.412504i
$649$	2.70969	−	1.56444i	0.106365	−	0.0614096i
$650$	−7.90637	−	6.63424i	−0.310114	−	0.260216i
$651$	5.54889	+	2.68101i	0.217478	+	0.105077i
$652$	−6.08441	−	34.5064i	−0.238284	−	1.35137i
$653$	14.0027	−	2.46906i	0.547970	−	0.0966218i	0.107192	−	0.994238i	$-0.465814\pi$
$653$	14.0027	−	2.46906i	0.547970	−	0.0966218i	0.440777	+	0.897616i	$0.354703\pi$
$654$	−12.5001	+	0.148314i	−0.488793	+	0.00579954i
$655$	−2.01132	−	1.68769i	−0.0785886	−	0.0659437i
$656$	33.2118			1.29670
$657$	−9.36465	−	23.9455i	−0.365350	−	0.934202i
$658$	8.15267	+	6.02558i	0.317824	+	0.234902i
$659$	0.747205	+	2.05293i	0.0291070	+	0.0799707i	0.953395	−	0.301725i	$-0.0975624\pi$
$659$	0.747205	+	2.05293i	0.0291070	+	0.0799707i	−0.924288	+	0.381696i	$0.875340\pi$
$660$	0.846505	−	0.319526i	0.0329501	−	0.0124375i
$661$	−19.1020	+	3.36819i	−0.742980	+	0.131007i	−0.532310	−	0.846550i	$-0.678676\pi$
$661$	−19.1020	+	3.36819i	−0.742980	+	0.131007i	−0.210670	+	0.977557i	$0.567565\pi$
$662$	10.1819	−	1.79535i	0.395731	−	0.0697781i
$663$	10.9031	−	66.4341i	0.423440	−	2.58008i
$664$	7.20488	+	19.7952i	0.279604	+	0.768204i
$665$	1.66535	+	1.23085i	0.0645793	+	0.0477301i
$666$	−3.43838	−	3.90562i	−0.133234	−	0.151340i
$667$	−10.6526			−0.412469
$668$	13.1795	+	11.0589i	0.509930	+	0.427882i
$669$	−11.6208	−	19.5874i	−0.449286	−	0.757292i
$670$	−0.306015	+	0.0539587i	−0.0118224	+	0.00208460i
$671$	−0.738849	−	4.19022i	−0.0285229	−	0.161762i
$672$	16.7481	−	11.3871i	0.646074	−	0.439268i
$673$	−8.85877	−	7.43339i	−0.341480	−	0.286536i	0.455878	−	0.890042i	$-0.349325\pi$
$673$	−8.85877	−	7.43339i	−0.341480	−	0.286536i	−0.797358	+	0.603506i	$0.793770\pi$
$674$	−2.16445	+	1.24965i	−0.0833716	+	0.0481346i
$675$	−15.8777	+	20.3513i	−0.611131	+	0.783321i
$676$	11.0408	−	19.1233i	0.424647	−	0.735510i
$677$	−2.04862	+	11.6183i	−0.0787348	+	0.446527i	0.919799	+	0.392390i	$0.128352\pi$
$677$	−2.04862	+	11.6183i	−0.0787348	+	0.446527i	−0.998534	+	0.0541367i	$0.982759\pi$
$678$	−2.12073	+	0.399940i	−0.0814460	+	0.0153596i
$679$	−5.64802	+	11.3441i	−0.216751	+	0.435347i
$680$	0.759073	−	2.08554i	0.0291091	−	0.0799767i
$681$	−10.8556	+	6.44042i	−0.415988	+	0.246797i
$682$	−0.569183	+	0.678326i	−0.0217951	+	0.0259744i
$683$	20.5498	−	11.8644i	0.786317	−	0.453980i	−0.0523472	−	0.998629i	$-0.516670\pi$
$683$	20.5498	−	11.8644i	0.786317	−	0.453980i	0.838664	+	0.544648i	$0.183337\pi$
$684$	−20.9198	−	11.4250i	−0.799888	−	0.436845i
$685$	0.990756	−	0.572013i	0.0378549	−	0.0218555i
$686$	6.61374	−	3.91080i	0.252514	−	0.149315i
$687$	6.68885	−	2.52481i	0.255196	−	0.0963275i
$688$	−2.14191	−	0.779592i	−0.0816596	−	0.0297217i
$689$	−8.46217	−	47.9913i	−0.322383	−	1.82832i
$690$	−0.310480	−	0.0509555i	−0.0118198	−	0.00193984i
$691$	−4.08371	+	4.86678i	−0.155352	+	0.185141i	−0.838107	−	0.545507i	$-0.816337\pi$
$691$	−4.08371	+	4.86678i	−0.155352	+	0.185141i	0.682755	+	0.730648i	$0.260782\pi$
$692$	−4.90500	−	8.49571i	−0.186460	−	0.322959i
$693$	−11.4273	+	5.30237i	−0.434088	+	0.201421i
$694$	6.73429	−	11.6641i	0.255630	−	0.442765i
$695$	−0.947313	−	2.60272i	−0.0359336	−	0.0987268i
$696$	10.5062	+	5.90067i	0.398236	+	0.223664i
$697$	−65.8877	+	55.2864i	−2.49568	+	2.09412i
$698$	3.32044	−	2.78618i	0.125681	−	0.105459i
$699$	−4.70364	−	24.9415i	−0.177908	−	0.943375i
$700$	−16.5467	−	17.4170i	−0.625406	−	0.658300i
$701$			30.6664i			1.15825i	0.815238	+	0.579126i	$0.196606\pi$
$701$			30.6664i			1.15825i	−0.815238	+	0.579126i	$0.803394\pi$
$702$	9.53573	+	5.06184i	0.359903	+	0.191047i
$703$	−15.7384	−	9.08659i	−0.593586	−	0.342707i
$704$	−2.25838	−	6.20485i	−0.0851160	−	0.233854i
$705$	0.953009	−	2.71829i	0.0358924	−	0.102377i
$706$	−2.03911	+	0.359550i	−0.0767430	+	0.0135319i
$707$	2.04079	+	33.0622i	0.0767518	+	1.24343i
$708$	−5.44185	−	3.05635i	−0.204517	−	0.114865i
$709$	13.9023	−	5.06001i	0.522111	−	0.190033i	−0.0675015	−	0.997719i	$-0.521503\pi$
$709$	13.9023	−	5.06001i	0.522111	−	0.190033i	0.589612	+	0.807686i	$0.299281\pi$
$710$	−0.217739	−	0.377134i	−0.00817159	−	0.0141536i
$711$	−14.4786	−	4.88395i	−0.542988	−	0.183162i
$712$	11.2656	+	6.50420i	0.422196	+	0.243755i
$713$	−3.07289	+	1.11844i	−0.115081	+	0.0418860i
$714$	−4.01468	+	14.1989i	−0.150246	+	0.531380i
$715$	−1.09639	+	0.919982i	−0.0410027	+	0.0344054i
$716$	9.29587	−	25.5402i	0.347403	−	0.954481i
$717$	−30.5653	−	25.0354i	−1.14148	−	0.934965i
$718$	−1.16639	+	6.61492i	−0.0435293	+	0.246867i
$719$	−4.89820	+	8.48393i	−0.182672	+	0.316397i	−0.942790	−	0.333388i	$-0.891808\pi$
$719$	−4.89820	+	8.48393i	−0.182672	+	0.316397i	0.760118	+	0.649786i	$0.225141\pi$
$720$	−1.26451	−	1.01090i	−0.0471253	−	0.0376741i
$721$	5.96570	+	4.40921i	0.222174	+	0.164208i
$722$	−0.0430815	−	0.00759643i	−0.00160333	−	0.000282710i
$723$	−0.668170	+	1.18968i	−0.0248495	+	0.0442447i
$724$	7.44763	+	8.87574i	0.276789	+	0.329864i
$725$	7.44296	−	20.4494i	0.276425	−	0.759470i
$726$	1.12938	+	5.98865i	0.0419152	+	0.222260i
$727$	29.0898	−	34.6679i	1.07888	−	1.28576i	0.122873	−	0.992422i	$-0.460789\pi$
$727$	29.0898	−	34.6679i	1.07888	−	1.28576i	0.956009	−	0.293339i	$-0.0947663\pi$
$728$	−12.5068	+	16.9218i	−0.463531	+	0.627162i
$729$	11.8027	−	24.2837i	0.437136	−	0.899395i
$730$	0.320122	+	0.554468i	0.0118483	+	0.0205218i
$731$	5.54702	−	2.01895i	0.205164	−	0.0746736i
$732$	−6.43659	+	5.53239i	−0.237903	+	0.204483i
$733$	−15.4136	−	18.3692i	−0.569315	−	0.678483i	0.402175	−	0.915563i	$-0.368254\pi$
$733$	−15.4136	−	18.3692i	−0.569315	−	0.678483i	−0.971490	+	0.237079i	$0.923810\pi$
$734$	4.48873	+	1.63376i	0.165682	+	0.0603033i
$735$	−1.61587	−	1.46806i	−0.0596022	−	0.0541500i
$736$	−1.86615	+	10.5834i	−0.0687871	+	0.390111i
$737$		−	6.60188i		−	0.243184i
$738$	−5.02357	−	12.8453i	−0.184920	−	0.472843i
$739$	−22.3128			−0.820790			−0.410395	−	0.911908i	$-0.634609\pi$
$739$	−22.3128			−0.820790			−0.410395	+	0.911908i	$0.634609\pi$
$740$	−1.05413	−	0.884518i	−0.0387505	−	0.0325155i
$741$	37.2070	+	6.10637i	1.36683	+	0.224323i
$742$	0.658029	+	10.6605i	0.0241570	+	0.391360i
$743$	−28.1973	−	33.6043i	−1.03446	−	1.23282i	−0.972051	−	0.234770i	$-0.924566\pi$
$743$	−28.1973	−	33.6043i	−1.03446	−	1.23282i	−0.0624085	−	0.998051i	$-0.519878\pi$
$744$	3.65019	+	0.599065i	0.133823	+	0.0219628i
$745$	3.09125	+	0.545071i	0.113255	+	0.0199699i
$746$			13.8406i			0.506739i
$747$	−29.8691	+	26.2957i	−1.09285	+	0.962109i
$748$	19.4998	+	11.2582i	0.712982	+	0.411641i
$749$	−19.9943	−	5.91038i	−0.730576	−	0.215961i
$750$	0.631555	−	1.12449i	0.0230611	−	0.0410605i
$751$	−3.23209	−	18.3301i	−0.117941	−	0.668875i	−0.985252	−	0.171109i	$-0.945265\pi$
$751$	−3.23209	−	18.3301i	−0.117941	−	0.668875i	0.867311	−	0.497766i	$-0.165846\pi$
$752$	−26.0101	−	9.46690i	−0.948491	−	0.345222i
$753$	−19.6828	+	3.71191i	−0.717281	+	0.135270i
$754$	−8.96354	−	1.58051i	−0.326433	−	0.0575589i
$755$	0.413938			0.0150647
$756$	20.7274	+	14.2075i	0.753849	+	0.516722i
$757$	26.2705			0.954819			0.477410	−	0.878681i	$-0.341576\pi$
$757$	26.2705			0.954819			0.477410	+	0.878681i	$0.341576\pi$
$758$	5.09078	+	0.897641i	0.184905	+	0.0326038i
$759$	2.21162	−	6.30825i	0.0802766	−	0.228975i
$760$	1.16803	+	0.425126i	0.0423687	+	0.0154210i
$761$	2.11972	+	12.0216i	0.0768399	+	0.435781i	0.998821	+	0.0485459i	$0.0154587\pi$
$761$	2.11972	+	12.0216i	0.0768399	+	0.435781i	−0.921981	+	0.387235i	$0.873430\pi$
$762$	−7.54964	+	0.0895767i	−0.273494	+	0.00324502i
$763$	44.7501	−	10.7701i	1.62006	−	0.389904i
$764$	−26.8250	−	15.4874i	−0.970494	−	0.560315i
$765$	4.19142	−	0.0994767i	0.151541	−	0.00359659i
$766$		−	12.0676i		−	0.436018i
$767$	9.72280	+	1.71439i	0.351070	+	0.0619031i
$768$	−4.32162	+	5.27619i	−0.155943	+	0.190388i
$769$	5.10850	+	6.08807i	0.184217	+	0.219541i	0.850247	−	0.526383i	$-0.176452\pi$
$769$	5.10850	+	6.08807i	0.184217	+	0.219541i	−0.666030	+	0.745925i	$0.732008\pi$
$770$	0.261487	−	0.173285i	0.00942333	−	0.00624478i
$771$	6.22218	+	16.4841i	0.224086	+	0.593661i
$772$	−17.1595	−	14.3985i	−0.617585	−	0.518215i
$773$	7.78940			0.280165			0.140083	−	0.990140i	$-0.455263\pi$
$773$	7.78940			0.280165			0.140083	+	0.990140i	$0.455263\pi$
$774$	0.0224600	+	0.946347i	0.000807310	+	0.0340157i
$775$		−	6.68038i		−	0.239966i
$776$	−1.32084	+	7.49084i	−0.0474153	+	0.268906i
$777$	15.5415	+	11.2039i	0.557547	+	0.401939i
$778$	−4.19629	−	1.52733i	−0.150444	−	0.0547573i
$779$	−30.9637	−	36.9011i	−1.10939	−	1.32212i
$780$	2.69421	+	0.944566i	0.0964682	+	0.0338209i
$781$	8.69418	−	3.16442i	0.311102	−	0.113232i
$782$	−3.91490	−	6.78080i	−0.139996	−	0.242481i
$783$	−3.15253	+	22.5437i	−0.112662	+	0.805647i
$784$	−14.2901	+	15.3587i	−0.510359	+	0.548526i
$785$	0.649915	−	0.774539i	0.0231965	−	0.0276445i
$786$	9.88773	+	3.46655i	0.352684	+	0.123648i
$787$	−8.13240	+	22.3436i	−0.289889	+	0.796463i	0.706193	+	0.708020i	$0.250411\pi$
$787$	−8.13240	+	22.3436i	−0.289889	+	0.796463i	−0.996081	+	0.0884429i	$0.971811\pi$
$788$	15.9608	+	19.0213i	0.568579	+	0.677606i
$789$	29.8012	−	0.353592i	1.06095	−	0.0125882i
$790$	0.374710	+	0.0660715i	0.0133316	+	0.00235072i
$791$	7.28521	−	3.17256i	0.259032	−	0.112803i
$792$	−5.67549	+	4.99650i	−0.201670	+	0.177543i
$793$	6.71285	−	11.6270i	0.238380	−	0.412887i
$794$	2.82273	−	16.0085i	0.100175	−	0.568121i
$795$	2.83928	−	1.07173i	0.100699	−	0.0380103i
$796$	−4.40101	+	12.0917i	−0.155989	+	0.428578i
$797$	−10.6111	+	8.90378i	−0.375865	+	0.315388i	−0.811077	−	0.584940i	$-0.801118\pi$
$797$	−10.6111	+	8.90378i	−0.375865	+	0.315388i	0.435212	+	0.900328i	$0.356674\pi$
$798$	−7.95222	−	2.24846i	−0.281505	−	0.0795947i
$799$	67.3597	−	24.5169i	2.38302	−	0.867347i
$800$	−19.0128	−	10.9770i	−0.672204	−	0.388097i
$801$	−3.69182	+	24.2950i	−0.130444	+	0.858423i
$802$	−2.14918	−	3.72248i	−0.0758900	−	0.131445i
$803$	−12.7823	+	4.65238i	−0.451077	+	0.164179i
$804$	−11.3260	+	6.71947i	−0.399436	+	0.236977i
$805$	1.15626	−	0.0713712i	0.0407529	−	0.00251551i
$806$	−2.75161	+	0.485183i	−0.0969214	+	0.0170899i
$807$	−17.3459	+	3.27121i	−0.610605	+	0.115152i
$808$	6.80033	+	18.6838i	0.239235	+	0.657292i
$809$	−28.3326	−	16.3578i	−0.996122	−	0.575111i	−0.0890233	−	0.996030i	$-0.528375\pi$
$809$	−28.3326	−	16.3578i	−0.996122	−	0.575111i	−0.907099	+	0.420918i	$0.861708\pi$
$810$	−0.199719	+	0.641980i	−0.00701742	+	0.0225569i
$811$		−	47.6172i		−	1.67207i	−0.548679	−	0.836033i	$-0.684869\pi$
$811$		−	47.6172i		−	1.67207i	0.548679	−	0.836033i	$-0.315131\pi$
$812$	−20.3168	−	6.00572i	−0.712981	−	0.210760i
$813$	−12.9296	−	4.53301i	−0.453462	−	0.158980i
$814$	−2.10884	+	1.76953i	−0.0739149	+	0.0620219i
$815$	−2.64412	+	2.21868i	−0.0926196	+	0.0777171i
$816$	−0.477979	−	40.2847i	−0.0167326	−	1.41025i
$817$	1.13073	+	3.10666i	0.0395593	+	0.108688i
$818$	−4.90734	+	8.49976i	−0.171581	+	0.297187i
$819$	−38.3761	−	10.3606i	−1.34097	−	0.362029i
$820$	−1.82374	−	3.15881i	−0.0636878	−	0.110311i
$821$	−31.4248	+	37.4506i	−1.09673	+	1.30703i	−0.148691	+	0.988884i	$0.547506\pi$
$821$	−31.4248	+	37.4506i	−1.09673	+	1.30703i	−0.948040	+	0.318150i	$0.896938\pi$
$822$	−2.89289	+	3.53188i	−0.100901	+	0.123188i
$823$	3.43354	+	19.4726i	0.119686	+	0.678771i	0.984323	+	0.176375i	$0.0564371\pi$
$823$	3.43354	+	19.4726i	0.119686	+	0.678771i	−0.864637	+	0.502396i	$0.832452\pi$
$824$	4.18417	+	1.52291i	0.145762	+	0.0530532i
$825$	10.5645	+	8.65314i	0.367807	+	0.301264i
$826$	−2.07511	−	0.613410i	−0.0722024	−	0.0213433i
$827$	33.5168	−	19.3510i	1.16549	−	0.672899i	0.212880	−	0.977078i	$-0.431716\pi$
$827$	33.5168	−	19.3510i	1.16549	−	0.672899i	0.952615	+	0.304180i	$0.0983823\pi$
$828$	−13.0732	+	2.62643i	−0.454326	+	0.0912746i
$829$	11.1500	−	6.43746i	0.387256	−	0.223582i	−0.293715	−	0.955893i	$-0.594892\pi$
$829$	11.1500	−	6.43746i	0.387256	−	0.223582i	0.680970	+	0.732311i	$0.261558\pi$
$830$	0.636960	−	0.759099i	0.0221092	−	0.0263487i
$831$	0.282350	+	23.7968i	0.00979461	+	0.825502i
$832$	7.12605	−	19.5787i	0.247051	−	0.678768i
$833$	2.78248	−	54.2577i	0.0964072	−	1.87992i
$834$	7.20477	+	8.38230i	0.249481	+	0.290255i
$835$	0.294303	−	1.66908i	0.0101848	−	0.0577608i
$836$	−6.30526	+	10.9210i	−0.218072	+	0.377712i
$837$	1.45753	+	6.83407i	0.0503797	+	0.236220i
$838$	−0.139648	+	0.0806258i	−0.00482406	+	0.00278517i
$839$	10.7228	+	8.99751i	0.370193	+	0.310628i	0.808838	−	0.588032i	$-0.200097\pi$
$839$	10.7228	+	8.99751i	0.370193	+	0.310628i	−0.438645	+	0.898660i	$0.644541\pi$
$840$	−1.17991	−	0.570086i	−0.0407107	−	0.0196698i
$841$	1.70331	+	9.65992i	0.0587347	+	0.333101i
$842$	12.7318	−	2.24496i	0.438768	−	0.0773666i
$843$	−2.36360	+	4.20841i	−0.0814067	+	0.144945i
$844$	18.5350	+	15.5527i	0.638001	+	0.535347i
$845$	−2.17526			−0.0748312
$846$	0.272741	+	11.4919i	0.00937704	+	0.395099i
$847$	−8.95889	−	20.5725i	−0.307831	−	0.706879i
$848$	−9.97405	−	27.4035i	−0.342510	−	0.941039i
$849$	−21.9958	−	18.0163i	−0.754892	−	0.618317i
$850$	15.7522	−	2.77754i	0.540296	−	0.0952688i
$851$	−10.0120	+	1.76538i	−0.343205	+	0.0605164i
$852$	−14.2778	−	11.6947i	−0.489149	−	0.400652i
$853$	1.21924	+	3.34982i	0.0417458	+	0.114696i	0.958814	−	0.284035i	$-0.0916731\pi$
$853$	1.21924	+	3.34982i	0.0417458	+	0.114696i	−0.917068	+	0.398730i	$0.869451\pi$
$854$	−1.74899	+	2.36640i	−0.0598492	+	0.0809766i
$855$	0.0557129	+	2.34744i	0.00190534	+	0.0802809i
$856$	−12.5146			−0.427741
$857$	−22.6428	−	18.9996i	−0.773464	−	0.649013i	0.168130	−	0.985765i	$-0.446227\pi$
$857$	−22.6428	−	18.9996i	−0.773464	−	0.649013i	−0.941593	+	0.336752i	$0.890672\pi$
$858$	2.79690	−	4.97990i	0.0954846	−	0.170011i
$859$	26.8449	−	4.73347i	0.915935	−	0.161504i	0.304238	−	0.952596i	$-0.401598\pi$
$859$	26.8449	−	4.73347i	0.915935	−	0.161504i	0.611697	+	0.791092i	$0.290487\pi$
$860$	0.0434697	+	0.246529i	0.00148231	+	0.00840657i
$861$	28.5535	+	41.9965i	0.973102	+	1.43124i
$862$	−7.69776	−	6.45919i	−0.262187	−	0.220001i
$863$	−23.1530	+	13.3674i	−0.788136	+	0.455031i	−0.839306	−	0.543659i	$-0.817038\pi$
$863$	−23.1530	+	13.3674i	−0.788136	+	0.455031i	0.0511699	+	0.998690i	$0.483705\pi$
$864$	21.8452	+	7.08134i	0.743188	+	0.240912i
$865$	−0.483191	+	0.836911i	−0.0164290	+	0.0284558i
$866$	0.722544	−	4.09775i	0.0245530	−	0.139247i
$867$	48.8155	+	56.7938i	1.65786	+	1.92882i
$868$	−6.49125	+	0.400678i	−0.220327	+	0.0135999i
$869$	−2.76486	+	7.59639i	−0.0937914	+	0.257690i
$870$	−0.00672493	−	0.566786i	−0.000227997	−	0.0192158i
$871$	13.3902	−	15.9578i	0.453709	−	0.540710i
$872$	23.9262	−	13.8138i	0.810242	−	0.467793i
$873$	−14.0876	+	2.83022i	−0.476794	+	0.0957886i
$874$	3.79765	−	2.19258i	0.128458	−	0.0741650i
$875$	−1.34612	+	4.55382i	−0.0455073	+	0.153947i
$876$	20.9914	+	17.1936i	0.709234	+	0.580919i
$877$	39.7412	+	14.4646i	1.34196	+	0.488435i	0.910430	−	0.413662i	$-0.135751\pi$
$877$	39.7412	+	14.4646i	1.34196	+	0.488435i	0.431533	+	0.902097i	$0.357973\pi$
$878$	2.95705	+	16.7703i	0.0997957	+	0.565970i
$879$	1.70941	−	2.08698i	0.0576568	−	0.0703922i
$880$	−0.550539	+	0.656106i	−0.0185587	+	0.0221173i
$881$	−24.9251	−	43.1715i	−0.839747	−	1.45448i	−0.890106	−	0.455753i	$-0.849370\pi$
$881$	−24.9251	−	43.1715i	−0.839747	−	1.45448i	0.0503592	−	0.998731i	$-0.483963\pi$
$882$	8.10178	+	3.20382i	0.272801	+	0.107878i
$883$	−19.7615	+	34.2280i	−0.665028	+	1.15186i	0.314249	+	0.949340i	$0.398247\pi$
$883$	−19.7615	+	34.2280i	−0.665028	+	1.15186i	−0.979278	+	0.202522i	$0.935086\pi$
$884$	24.2997	+	66.7630i	0.817289	+	2.24548i
$885$	0.00729457	+	0.614795i	0.000245204	+	0.0206661i
$886$	11.0816	−	9.29854i	0.372293	−	0.312391i
$887$	28.4361	−	23.8607i	0.954791	−	0.801165i	−0.0253071	−	0.999680i	$-0.508056\pi$
$887$	28.4361	−	23.8607i	0.954791	−	0.801165i	0.980098	+	0.198515i	$0.0636119\pi$
$888$	10.8522	+	3.80470i	0.364178	+	0.127677i
$889$	27.0275	−	6.50478i	0.906475	−	0.218163i
$890$		−	0.611918i		−	0.0205115i
$891$	−12.6955	−	6.54725i	−0.425314	−	0.219341i
$892$	20.8152	+	12.0176i	0.696944	+	0.402381i
$893$	13.7309	+	37.7255i	0.459489	+	1.26243i
$894$	−12.3094	+	2.32139i	−0.411689	+	0.0776390i
$895$	−2.63675	+	0.464930i	−0.0881369	+	0.0155409i
$896$	−12.4582	+	25.0224i	−0.416199	+	0.835940i
$897$	18.1404	−	10.7624i	0.605692	−	0.359345i
$898$	−0.295162	+	0.107430i	−0.00984968	+	0.00358499i
$899$	−2.94562	−	5.10196i	−0.0982418	−	0.170160i
$900$	4.09242	−	26.9313i	0.136414	−	0.897710i
$901$	65.4046	+	37.7614i	2.17894	+	1.25801i
$902$	−6.85694	+	2.49572i	−0.228311	+	0.0830984i
$903$	−0.855692	−	3.37870i	−0.0284757	−	0.112436i
$904$	3.65363	−	3.06576i	0.121518	−	0.101966i
$905$	0.390375	−	1.07255i	0.0129765	−	0.0356527i
$906$	−1.54545	+	0.583353i	−0.0513441	+	0.0193806i
$907$	−5.56403	+	31.5552i	−0.184751	+	1.04777i	0.741525	+	0.670926i	$0.234103\pi$
$907$	−5.56403	+	31.5552i	−0.184751	+	1.04777i	−0.926275	+	0.376847i	$0.877008\pi$
$908$	6.66036	−	11.5361i	0.221032	−	0.382838i
$909$	−28.1920	+	24.8192i	−0.935068	+	0.823202i
$910$	0.983519	+	0.111499i	0.0326034	+	0.00369615i
$911$	−17.5085	−	3.08722i	−0.580082	−	0.102284i	−0.124095	−	0.992270i	$-0.539603\pi$
$911$	−17.5085	−	3.08722i	−0.580082	−	0.102284i	−0.455988	+	0.889986i	$0.650714\pi$
$912$	22.5618	−	0.267697i	0.747097	−	0.00886433i
$913$	13.5328	+	16.1278i	0.447872	+	0.533753i
$914$	4.45469	−	12.2392i	0.147348	−	0.404835i
$915$	0.789014	+	0.276621i	0.0260840	+	0.00914482i
$916$	−4.84988	+	5.77987i	−0.160245	+	0.190972i
$917$	−38.3331	−	4.34572i	−1.26587	−	0.143508i
$918$	−15.5086	+	6.27827i	−0.511860	+	0.207214i
$919$	10.1037	+	17.5002i	0.333292	+	0.577279i	0.983155	−	0.182773i	$-0.0585072\pi$
$919$	10.1037	+	17.5002i	0.333292	+	0.577279i	−0.649863	+	0.760051i	$0.725174\pi$
$920$	0.653415	−	0.237823i	0.0215424	−	0.00784081i
$921$	2.67279	+	0.937058i	0.0880715	+	0.0308771i
$922$	2.90819	+	3.46585i	0.0957762	+	0.114142i
$923$	27.4334	+	9.98494i	0.902981	+	0.328658i
$924$	7.77452	−	10.7844i	0.255763	−	0.354780i
$925$	3.60643	−	20.4531i	0.118579	−	0.672493i
$926$		−	2.95287i		−	0.0970373i
$927$	0.199578	+	8.40916i	0.00655500	+	0.276193i
$928$	−19.3607			−0.635545
$929$	−5.15862	−	4.32860i	−0.169249	−	0.142017i	0.554229	−	0.832364i	$-0.313013\pi$
$929$	−5.15862	−	4.32860i	−0.169249	−	0.142017i	−0.723478	+	0.690348i	$0.757458\pi$
$930$	−0.0614483	−	0.162792i	−0.00201497	−	0.00533815i
$931$	30.3876	+	1.55835i	0.995913	+	0.0510730i
$932$	17.2174	+	20.5189i	0.563974	+	0.672118i
$933$	−13.0371	+	15.9167i	−0.426815	+	0.521091i
$934$	−5.40427	−	0.952918i	−0.176833	−	0.0311804i
$935$		−	2.21809i		−	0.0725392i
$936$	−23.8526	+	0.566105i	−0.779648	+	0.0185037i
$937$	−37.6538	−	21.7394i	−1.23009	−	0.710196i	−0.263045	−	0.964784i	$-0.584727\pi$
$937$	−37.6538	−	21.7394i	−1.23009	−	0.710196i	−0.967050	+	0.254588i	$0.918060\pi$
$938$	−3.31011	+	3.14471i	−0.108079	+	0.102678i
$939$	−3.21254	+	0.0381169i	−0.104837	+	0.00124390i
$940$	0.527870	+	2.99370i	0.0172172	+	0.0976438i
$941$	11.5099	+	4.18926i	0.375212	+	0.136566i	0.522741	−	0.852492i	$-0.324910\pi$
$941$	11.5099	+	4.18926i	0.375212	+	0.136566i	−0.147529	+	0.989058i	$0.547132\pi$
$942$	−1.33494	+	3.80767i	−0.0434946	+	0.124061i
$943$	−26.5383	−	4.67942i	−0.864206	−	0.152383i
$944$	5.90810			0.192292
$945$	0.191144	−	2.46809i	0.00621791	−	0.0802869i
$946$	0.500804			0.0162825
$947$	−13.5396	−	2.38739i	−0.439977	−	0.0775798i	−0.0507283	−	0.998712i	$-0.516154\pi$
$947$	−13.5396	−	2.38739i	−0.439977	−	0.0775798i	−0.389249	+	0.921133i	$0.627265\pi$
$948$	15.8462	−	2.98838i	0.514661	−	0.0970581i
$949$	−40.3330	−	14.6800i	−1.30926	−	0.476533i
$950$	1.55559	+	8.82217i	0.0504699	+	0.286229i
$951$	17.9154	−	31.8985i	0.580948	−	1.03438i
$952$	−7.63048	−	31.7049i	−0.247305	−	1.02756i
$953$	−41.3778	−	23.8895i	−1.34036	−	0.773857i	−0.353499	−	0.935435i	$-0.615008\pi$
$953$	−41.3778	−	23.8895i	−1.34036	−	0.773857i	−0.986860	+	0.161578i	$0.948342\pi$
$954$	−9.09017	+	8.00267i	−0.294305	+	0.259096i
$955$			3.05132i			0.0987385i
$956$	41.0622	+	7.24037i	1.32805	+	0.234170i
$957$	11.8838	+	1.95035i	0.384148	+	0.0630459i
$958$	−0.531138	−	0.632986i	−0.0171603	−	0.0204508i
$959$	7.49196	−	15.0477i	0.241928	−	0.485915i
$960$	1.28040	+	0.210138i	0.0413248	+	0.00678217i
$961$	22.3620	+	18.7639i	0.721355	+	0.605289i
$962$	−8.68643			−0.280062
$963$	−8.61059	−	22.0174i	−0.277472	−	0.709499i
$964$		−	1.43997i		−	0.0463783i
$965$	−0.383178	+	2.17311i	−0.0123349	+	0.0699550i
$966$	−4.21636	+	1.89596i	−0.135659	+	0.0610015i
$967$	42.4888	+	15.4647i	1.36635	+	0.497310i	0.918011	−	0.396555i	$-0.129795\pi$
$967$	42.4888	+	15.4647i	1.36635	+	0.497310i	0.448336	+	0.893865i	$0.352017\pi$
$968$	−8.65731	−	10.3174i	−0.278257	−	0.331613i
$969$	−44.3140	+	38.0889i	−1.42357	+	1.22359i
$970$	0.336228	−	0.122377i	0.0107956	−	0.00392929i
$971$	−7.07273	−	12.2503i	−0.226975	−	0.393132i	0.729935	−	0.683516i	$-0.239550\pi$
$971$	−7.07273	−	12.2503i	−0.226975	−	0.393132i	−0.956910	+	0.290384i	$0.906217\pi$
$972$	1.68933	+	28.4438i	0.0541854	+	0.912334i
$973$	−32.7282	−	24.1892i	−1.04922	−	0.775469i
$974$	3.81890	−	4.55119i	0.122366	−	0.145830i
$975$	7.98537	+	42.3432i	0.255736	+	1.35607i
$976$	2.74787	−	7.54972i	0.0879573	−	0.241661i
$977$	23.6226	+	28.1523i	0.755753	+	0.900672i	0.997572	−	0.0696497i	$-0.0221882\pi$
$977$	23.6226	+	28.1523i	0.755753	+	0.900672i	−0.241818	+	0.970322i	$0.577744\pi$
$978$	6.74517	−	12.0098i	0.215687	−	0.384032i
$979$	12.8033	+	2.25756i	0.409195	+	0.0721521i
$980$	2.24549	+	0.515758i	0.0717295	+	0.0164753i
$981$	40.7651	+	32.5895i	1.30153	+	1.04050i
$982$	−5.52879	+	9.57614i	−0.176431	+	0.305587i
$983$	1.70439	−	9.66609i	0.0543617	−	0.308300i	−0.945488	−	0.325658i	$-0.894414\pi$
$983$	1.70439	−	9.66609i	0.0543617	−	0.308300i	0.999849	+	0.0173575i	$0.00552533\pi$
$984$	23.5816	+	19.3152i	0.751754	+	0.615746i
$985$	0.836600	−	2.29854i	0.0266563	−	0.0732375i
$986$	10.8056	−	9.06697i	0.344120	−	0.288751i
$987$	−10.3910	−	41.0290i	−0.330750	−	1.30597i
$988$	−37.3913	+	13.6093i	−1.18957	+	0.432970i
$989$	1.60168	+	0.924730i	0.0509305	+	0.0294047i
$990$	0.337036	+	0.113690i	0.0107117	+	0.00361330i
$991$	15.3744	+	26.6292i	0.488384	+	0.845905i	0.999911	−	0.0133618i	$-0.00425333\pi$
$991$	15.3744	+	26.6292i	0.488384	+	0.845905i	−0.511527	+	0.859267i	$0.670920\pi$
$992$	−5.58487	+	2.03273i	−0.177320	+	0.0645392i
$993$	−37.6350	−	21.1373i	−1.19431	−	0.670770i
$994$	−5.72795	−	2.85184i	−0.181680	−	0.0904548i
$995$	1.24834	−	0.220115i	0.0395749	−	0.00697812i
$996$	13.8945	−	39.6315i	0.440263	−	1.25577i
$997$	−14.3109	−	39.3189i	−0.453231	−	1.24524i	−0.930437	−	0.366451i	$-0.880573\pi$
$997$	−14.3109	−	39.3189i	−0.453231	−	1.24524i	0.477206	−	0.878791i	$-0.341650\pi$
$998$	7.65940	+	4.42216i	0.242454	+	0.139981i
$999$	0.773077	+	21.7105i	0.0244591	+	0.686889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.38.10	yes	132
3.2	odd	2		567.2.ba.a.521.13		132
7.5	odd	6		189.2.bd.a.173.13	yes	132
21.5	even	6		567.2.bd.a.278.10		132
27.5	odd	18		189.2.bd.a.59.13	yes	132
27.22	even	9		567.2.bd.a.206.10		132
189.5	even	18	inner	189.2.ba.a.5.10	✓	132
189.103	odd	18		567.2.ba.a.530.13		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.10	✓	132	189.5	even	18	inner
189.2.ba.a.38.10	yes	132	1.1	even	1	trivial
189.2.bd.a.59.13	yes	132	27.5	odd	18
189.2.bd.a.173.13	yes	132	7.5	odd	6
567.2.ba.a.521.13		132	3.2	odd	2
567.2.ba.a.530.13		132	189.103	odd	18
567.2.bd.a.206.10		132	27.22	even	9
567.2.bd.a.278.10		132	21.5	even	6

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.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.408566 - 0.0720413i) q^{2} +(1.12900 + 1.31353i) q^{3} +(-1.71765 - 0.625173i) q^{4} +(0.0312679 + 0.177329i) q^{5} +(-0.366645 - 0.617997i) q^{6} +(1.82229 + 1.91814i) q^{7} +(1.37531 + 0.794036i) q^{8} +(-0.450699 + 2.96595i) q^{9} -0.0747032i q^{10} +(1.56303 + 0.275605i) q^{11} +(-1.11805 - 2.96200i) q^{12} +(3.21910 + 3.83638i) q^{13} +(-0.606342 - 0.914967i) q^{14} +(-0.197625 + 0.241276i) q^{15} +(2.29578 + 1.92639i) q^{16} -7.76129 q^{17} +(0.397812 - 1.17932i) q^{18} -4.34679i q^{19} +(0.0571540 - 0.324137i) q^{20} +(-0.462149 + 4.55921i) q^{21} +(-0.618747 - 0.225206i) q^{22} +(-1.56305 - 1.86277i) q^{23} +(0.509745 + 2.70297i) q^{24} +(4.66800 - 1.69901i) q^{25} +(-1.03884 - 1.79932i) q^{26} +(-4.40469 + 2.75657i) q^{27} +(-1.93089 - 4.43393i) q^{28} +(2.81590 - 3.35586i) q^{29} +(0.0981246 - 0.0843403i) q^{30} +(0.459948 - 1.26370i) q^{31} +(-2.84078 - 3.38551i) q^{32} +(1.40266 + 2.36424i) q^{33} +(3.17100 + 0.559134i) q^{34} +(-0.283162 + 0.383121i) q^{35} +(2.62838 - 4.81270i) q^{36} +(2.09041 - 3.62070i) q^{37} +(-0.313148 + 1.77595i) q^{38} +(-1.40480 + 8.55966i) q^{39} +(-0.0978025 + 0.268710i) q^{40} +(8.48927 - 7.12335i) q^{41} +(0.517270 - 1.82945i) q^{42} +(-0.714703 + 0.260131i) q^{43} +(-2.51244 - 1.45056i) q^{44} +(-0.540041 + 0.0128170i) q^{45} +(0.504413 + 0.873669i) q^{46} +(-8.67893 + 3.15887i) q^{47} +(0.0615850 + 5.19046i) q^{48} +(-0.358507 + 6.99081i) q^{49} +(-2.02959 + 0.357871i) q^{50} +(-8.76253 - 10.1947i) q^{51} +(-3.13089 - 8.60205i) q^{52} +(-8.42703 - 4.86535i) q^{53} +(1.99820 - 0.808921i) q^{54} +0.285788i q^{55} +(0.983146 + 4.08500i) q^{56} +(5.70962 - 4.90754i) q^{57} +(-1.39224 + 1.16823i) q^{58} +(1.51017 - 1.26718i) q^{59} +(0.490289 - 0.290878i) q^{60} +(-0.916897 - 2.51916i) q^{61} +(-0.278957 + 0.483169i) q^{62} +(-6.51041 + 4.54033i) q^{63} +(-2.08017 - 3.60297i) q^{64} +(-0.579646 + 0.690796i) q^{65} +(-0.402755 - 1.06700i) q^{66} +(-0.722307 - 4.09641i) q^{67} +(13.3312 + 4.85215i) q^{68} +(0.682106 - 4.15618i) q^{69} +(0.143291 - 0.136131i) q^{70} +(5.04844 - 2.91472i) q^{71} +(-2.97492 + 3.72123i) q^{72} +(-7.42228 + 4.28526i) q^{73} +(-1.11491 + 1.32870i) q^{74} +(7.50188 + 4.21334i) q^{75} +(-2.71749 + 7.46625i) q^{76} +(2.31965 + 3.50034i) q^{77} +(1.19060 - 3.39599i) q^{78} +(-0.884454 + 5.01599i) q^{79} +(-0.269820 + 0.467342i) q^{80} +(-8.59374 - 2.67350i) q^{81} +(-3.98161 + 2.29878i) q^{82} +(10.1615 + 8.52653i) q^{83} +(3.64411 - 7.54220i) q^{84} +(-0.242679 - 1.37630i) q^{85} +(0.310744 - 0.0547926i) q^{86} +(7.58716 - 0.0900220i) q^{87} +(1.93081 + 1.62014i) q^{88} +8.19131 q^{89} +(0.221566 + 0.0336687i) q^{90} +(-1.49256 + 13.1657i) q^{91} +(1.52022 + 4.17676i) q^{92} +(2.17918 - 0.822565i) q^{93} +(3.77349 - 0.665368i) q^{94} +(0.770811 - 0.135915i) q^{95} +(1.23970 - 7.55370i) q^{96} +(1.63818 + 4.50085i) q^{97} +(0.650101 - 2.83038i) q^{98} +(-1.52189 + 4.51166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

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