LMFDB - Embedded newform 162.2.g.a.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			7.3
Character	$\chi$	$=$	162.7
Dual form			162.2.g.a.139.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.597159 - 0.802123i) q^{2} +(0.967452 + 1.43668i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(1.46985 - 0.966735i) q^{5} +(0.574669 - 1.63394i) q^{6} +(-0.262959 + 0.278720i) q^{7} +(0.939693 - 0.342020i) q^{8} +(-1.12808 + 2.77983i) q^{9} +O(q^{10})$	\(q+(-0.597159 - 0.802123i) q^{2} +(0.967452 + 1.43668i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(1.46985 - 0.966735i) q^{5} +(0.574669 - 1.63394i) q^{6} +(-0.262959 + 0.278720i) q^{7} +(0.939693 - 0.342020i) q^{8} +(-1.12808 + 2.77983i) q^{9} +(-1.65317 - 0.601706i) q^{10} +(1.99838 - 1.00362i) q^{11} +(-1.65379 + 0.514765i) q^{12} +(2.14573 + 4.97437i) q^{13} +(0.380596 + 0.0444853i) q^{14} +(2.81089 + 1.17643i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(3.74519 - 3.14258i) q^{17} +(2.90340 - 0.755143i) q^{18} +(-5.05464 - 4.24135i) q^{19} +(0.504565 + 1.68536i) q^{20} +(-0.654830 - 0.108138i) q^{21} +(-1.99838 - 1.00362i) q^{22} +(-3.62452 - 3.84176i) q^{23} +(1.40048 + 1.01915i) q^{24} +(-0.754519 + 1.74917i) q^{25} +(2.70871 - 4.69163i) q^{26} +(-5.08507 + 1.06867i) q^{27} +(-0.191593 - 0.331850i) q^{28} +(-0.748788 + 0.0875208i) q^{29} +(-0.734909 - 2.95720i) q^{30} +(-0.512900 + 0.121559i) q^{31} +(0.0581448 + 0.998308i) q^{32} +(3.37522 + 1.90007i) q^{33} +(-4.75721 - 1.12748i) q^{34} +(-0.117061 + 0.663888i) q^{35} +(-2.33951 - 1.87795i) q^{36} +(-1.32861 - 7.53491i) q^{37} +(-0.383661 + 6.58720i) q^{38} +(-5.07066 + 7.89519i) q^{39} +(1.05056 - 1.41115i) q^{40} +(-2.79931 + 3.76013i) q^{41} +(0.304297 + 0.589830i) q^{42} +(-0.0801025 + 1.37531i) q^{43} +(0.388319 + 2.20227i) q^{44} +(1.02926 + 5.17648i) q^{45} +(-0.917156 + 5.20145i) q^{46} +(-8.99944 - 2.13291i) q^{47} +(-0.0188277 - 1.73195i) q^{48} +(0.398476 + 6.84157i) q^{49} +(1.85362 - 0.439316i) q^{50} +(8.13816 + 2.34032i) q^{51} +(-5.38080 + 0.628925i) q^{52} +(-5.09624 - 8.82695i) q^{53} +(3.89380 + 3.44069i) q^{54} +(1.96708 - 3.40708i) q^{55} +(-0.151773 + 0.351848i) q^{56} +(1.20332 - 11.3652i) q^{57} +(0.517348 + 0.548357i) q^{58} +(-4.46980 - 2.24482i) q^{59} +(-1.93318 + 2.35540i) q^{60} +(-1.74715 - 5.83587i) q^{61} +(0.403788 + 0.338819i) q^{62} +(-0.478157 - 1.04540i) q^{63} +(0.766044 - 0.642788i) q^{64} +(7.96280 + 5.23722i) q^{65} +(-0.491453 - 3.84198i) q^{66} +(10.4454 + 1.22090i) q^{67} +(1.93643 + 4.48915i) q^{68} +(2.01282 - 8.92398i) q^{69} +(0.602424 - 0.302549i) q^{70} +(2.04789 + 0.745370i) q^{71} +(-0.109287 + 2.99801i) q^{72} +(5.68140 - 2.06786i) q^{73} +(-5.25054 + 5.56525i) q^{74} +(-3.24295 + 0.608239i) q^{75} +(5.51285 - 3.62586i) q^{76} +(-0.245761 + 0.820900i) q^{77} +(9.36090 - 0.647381i) q^{78} +(1.59862 + 2.14732i) q^{79} -1.75927 q^{80} +(-6.45489 - 6.27171i) q^{81} +4.68772 q^{82} +(6.43738 + 8.64690i) q^{83} +(0.291403 - 0.596306i) q^{84} +(2.46681 - 8.23973i) q^{85} +(1.15100 - 0.757024i) q^{86} +(-0.850155 - 0.991094i) q^{87} +(1.53460 - 1.62658i) q^{88} +(9.43534 - 3.43418i) q^{89} +(3.53754 - 3.91677i) q^{90} +(-1.95070 - 0.709995i) q^{91} +(4.71989 - 2.37042i) q^{92} +(-0.670847 - 0.619268i) q^{93} +(3.66324 + 8.49235i) q^{94} +(-11.5298 - 1.34764i) q^{95} +(-1.37799 + 1.04935i) q^{96} +(13.7429 + 9.03883i) q^{97} +(5.24983 - 4.40513i) q^{98} +(0.535580 + 6.68732i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

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 $

$2$	−0.597159	−	0.802123i	−0.422255	−	0.567187i
$2$	−0.597159	−	0.802123i	−0.422255	−	0.567187i
$3$	0.967452	+	1.43668i	0.558558	+	0.829465i
$3$	0.967452	+	1.43668i	0.558558	+	0.829465i
$4$	−0.286803	+	0.957990i	−0.143402	+	0.478995i
$5$	1.46985	−	0.966735i	0.657337	−	0.432337i	−0.176536	−	0.984294i	$-0.556489\pi$
$5$	1.46985	−	0.966735i	0.657337	−	0.432337i	0.833872	+	0.551957i	$0.186119\pi$
$6$	0.574669	−	1.63394i	0.234608	−	0.667053i
$7$	−0.262959	+	0.278720i	−0.0993891	+	0.105346i	−0.775158	−	0.631767i	$-0.782330\pi$
$7$	−0.262959	+	0.278720i	−0.0993891	+	0.105346i	0.675769	+	0.737113i	$0.263812\pi$
$8$	0.939693	−	0.342020i	0.332232	−	0.120922i
$9$	−1.12808	+	2.77983i	−0.376025	+	0.926610i
$10$	−1.65317	−	0.601706i	−0.522779	−	0.190276i
$11$	1.99838	−	1.00362i	0.602534	−	0.302604i	−0.121259	−	0.992621i	$-0.538693\pi$
$11$	1.99838	−	1.00362i	0.602534	−	0.302604i	0.723793	+	0.690017i	$0.242397\pi$
$12$	−1.65379	+	0.514765i	−0.477408	+	0.148600i
$13$	2.14573	+	4.97437i	0.595120	+	1.37964i	0.903586	+	0.428407i	$0.140925\pi$
$13$	2.14573	+	4.97437i	0.595120	+	1.37964i	−0.308466	+	0.951235i	$0.599816\pi$
$14$	0.380596	+	0.0444853i	0.101719	+	0.0118892i
$15$	2.81089	+	1.17643i	0.725769	+	0.303752i
$16$	−0.835488	−	0.549509i	−0.208872	−	0.137377i
$17$	3.74519	−	3.14258i	0.908341	−	0.762189i	−0.0634615	−	0.997984i	$-0.520214\pi$
$17$	3.74519	−	3.14258i	0.908341	−	0.762189i	0.971803	+	0.235795i	$0.0757696\pi$
$18$	2.90340	−	0.755143i	0.684339	−	0.177989i
$19$	−5.05464	−	4.24135i	−1.15961	−	0.973032i	−0.159714	−	0.987163i	$-0.551057\pi$
$19$	−5.05464	−	4.24135i	−1.15961	−	0.973032i	−0.999900	+	0.0141317i	$0.995502\pi$
$20$	0.504565	+	1.68536i	0.112824	+	0.376859i
$21$	−0.654830	−	0.108138i	−0.142896	−	0.0235977i
$22$	−1.99838	−	1.00362i	−0.426056	−	0.213973i
$23$	−3.62452	−	3.84176i	−0.755764	−	0.801063i	0.229281	−	0.973360i	$-0.426363\pi$
$23$	−3.62452	−	3.84176i	−0.755764	−	0.801063i	−0.985045	+	0.172297i	$0.944881\pi$
$24$	1.40048	+	1.01915i	0.285872	+	0.208032i
$25$	−0.754519	+	1.74917i	−0.150904	+	0.349834i
$26$	2.70871	−	4.69163i	0.531223	−	0.920105i
$27$	−5.08507	+	1.06867i	−0.978622	+	0.205666i
$28$	−0.191593	−	0.331850i	−0.0362078	−	0.0627137i
$29$	−0.748788	+	0.0875208i	−0.139046	+	0.0162522i	−0.185331	−	0.982676i	$-0.559336\pi$
$29$	−0.748788	+	0.0875208i	−0.139046	+	0.0162522i	0.0462849	+	0.998928i	$0.485262\pi$
$30$	−0.734909	−	2.95720i	−0.134175	−	0.539908i
$31$	−0.512900	+	0.121559i	−0.0921195	+	0.0218327i	−0.276417	−	0.961038i	$-0.589147\pi$
$31$	−0.512900	+	0.121559i	−0.0921195	+	0.0218327i	0.184298	+	0.982870i	$0.440999\pi$
$32$	0.0581448	+	0.998308i	0.0102787	+	0.176478i
$33$	3.37522	+	1.90007i	0.587550	+	0.330759i
$34$	−4.75721	−	1.12748i	−0.815855	−	0.193361i
$35$	−0.117061	+	0.663888i	−0.0197870	+	0.112218i
$36$	−2.33951	−	1.87795i	−0.389918	−	0.312991i
$37$	−1.32861	−	7.53491i	−0.218422	−	1.23873i	−0.874869	−	0.484360i	$-0.839053\pi$
$37$	−1.32861	−	7.53491i	−0.218422	−	1.23873i	0.656447	−	0.754372i	$-0.272059\pi$
$38$	−0.383661	+	6.58720i	−0.0622380	+	1.06859i
$39$	−5.07066	+	7.89519i	−0.811956	+	1.26424i
$40$	1.05056	−	1.41115i	0.166109	−	0.223123i
$41$	−2.79931	+	3.76013i	−0.437179	+	0.587234i	−0.965042	−	0.262096i	$-0.915586\pi$
$41$	−2.79931	+	3.76013i	−0.437179	+	0.587234i	0.527862	+	0.849330i	$0.322994\pi$
$42$	0.304297	+	0.589830i	0.0469541	+	0.0910128i
$43$	−0.0801025	+	1.37531i	−0.0122155	+	0.209732i	0.986677	+	0.162689i	$0.0520168\pi$
$43$	−0.0801025	+	1.37531i	−0.0122155	+	0.209732i	−0.998893	+	0.0470430i	$0.985020\pi$
$44$	0.388319	+	2.20227i	0.0585414	+	0.332005i
$45$	1.02926	+	5.17648i	0.153433	+	0.771664i
$46$	−0.917156	+	5.20145i	−0.135227	+	0.766912i
$47$	−8.99944	−	2.13291i	−1.31270	−	0.311117i	−0.486101	−	0.873902i	$-0.661581\pi$
$47$	−8.99944	−	2.13291i	−1.31270	−	0.311117i	−0.826603	+	0.562786i	$0.809730\pi$
$48$	−0.0188277	−	1.73195i	−0.00271754	−	0.249985i
$49$	0.398476	+	6.84157i	0.0569252	+	0.977368i
$50$	1.85362	−	0.439316i	0.262141	−	0.0621286i
$51$	8.13816	+	2.34032i	1.13957	+	0.327710i
$52$	−5.38080	+	0.628925i	−0.746182	+	0.0872162i
$53$	−5.09624	−	8.82695i	−0.700023	−	1.21247i	−0.968458	−	0.249177i	$-0.919840\pi$
$53$	−5.09624	−	8.82695i	−0.700023	−	1.21247i	0.268435	−	0.963298i	$-0.413493\pi$
$54$	3.89380	+	3.44069i	0.529879	+	0.468218i
$55$	1.96708	−	3.40708i	0.265241	−	0.459410i
$56$	−0.151773	+	0.351848i	−0.0202815	+	0.0470177i
$57$	1.20332	−	11.3652i	0.159384	−	1.50535i
$58$	0.517348	+	0.548357i	0.0679311	+	0.0720027i
$59$	−4.46980	−	2.24482i	−0.581918	−	0.292250i	0.133385	−	0.991064i	$-0.457415\pi$
$59$	−4.46980	−	2.24482i	−0.581918	−	0.292250i	−0.715304	+	0.698814i	$0.753712\pi$
$60$	−1.93318	+	2.35540i	−0.249572	+	0.304081i
$61$	−1.74715	−	5.83587i	−0.223699	−	0.747207i	−0.993986	−	0.109509i	$-0.965072\pi$
$61$	−1.74715	−	5.83587i	−0.223699	−	0.747207i	0.770287	−	0.637698i	$-0.220113\pi$
$62$	0.403788	+	0.338819i	0.0512812	+	0.0430300i
$63$	−0.478157	−	1.04540i	−0.0602421	−	0.131708i
$64$	0.766044	−	0.642788i	0.0957556	−	0.0803485i
$65$	7.96280	+	5.23722i	0.987664	+	0.649597i
$66$	−0.491453	−	3.84198i	−0.0604937	−	0.472915i
$67$	10.4454	+	1.22090i	1.27611	+	0.149156i	0.727026	−	0.686610i	$-0.240902\pi$
$67$	10.4454	+	1.22090i	1.27611	+	0.149156i	0.549086	+	0.835766i	$0.314976\pi$
$68$	1.93643	+	4.48915i	0.234827	+	0.544390i
$69$	2.01282	−	8.92398i	0.242316	−	1.07432i
$70$	0.602424	−	0.302549i	0.0720034	−	0.0361615i
$71$	2.04789	+	0.745370i	0.243039	+	0.0884591i	0.460668	−	0.887573i	$-0.347610\pi$
$71$	2.04789	+	0.745370i	0.243039	+	0.0884591i	−0.217628	+	0.976032i	$0.569832\pi$
$72$	−0.109287	+	2.99801i	−0.0128795	+	0.353319i
$73$	5.68140	−	2.06786i	0.664958	−	0.242025i	0.0125823	−	0.999921i	$-0.495995\pi$
$73$	5.68140	−	2.06786i	0.664958	−	0.242025i	0.652375	+	0.757896i	$0.273773\pi$
$74$	−5.25054	+	5.56525i	−0.610363	+	0.646947i
$75$	−3.24295	+	0.608239i	−0.374464	+	0.0702334i
$76$	5.51285	−	3.62586i	0.632368	−	0.415915i
$77$	−0.245761	+	0.820900i	−0.0280071	+	0.0935502i
$78$	9.36090	−	0.647381i	1.05991	−	0.0733015i
$79$	1.59862	+	2.14732i	0.179859	+	0.241592i	0.882905	−	0.469552i	$-0.155585\pi$
$79$	1.59862	+	2.14732i	0.179859	+	0.241592i	−0.703046	+	0.711144i	$0.748177\pi$
$80$	−1.75927			−0.196692
$81$	−6.45489	−	6.27171i	−0.717210	−	0.696857i
$82$	4.68772			0.517672
$83$	6.43738	+	8.64690i	0.706594	+	0.949121i	0.999976	−	0.00687428i	$-0.00218817\pi$
$83$	6.43738	+	8.64690i	0.706594	+	0.949121i	−0.293382	+	0.955995i	$0.594781\pi$
$84$	0.291403	−	0.596306i	0.0317947	−	0.0650623i
$85$	2.46681	−	8.23973i	0.267563	−	0.893724i
$86$	1.15100	−	0.757024i	0.124115	−	0.0816320i
$87$	−0.850155	−	0.991094i	−0.0911462	−	0.106256i
$88$	1.53460	−	1.62658i	0.163589	−	0.173394i
$89$	9.43534	−	3.43418i	1.00014	−	0.364023i	0.210504	−	0.977593i	$-0.432490\pi$
$89$	9.43534	−	3.43418i	1.00014	−	0.364023i	0.789640	+	0.613571i	$0.210267\pi$
$90$	3.53754	−	3.91677i	0.372890	−	0.412864i
$91$	−1.95070	−	0.709995i	−0.204489	−	0.0744277i
$92$	4.71989	−	2.37042i	0.492083	−	0.247133i
$93$	−0.670847	−	0.619268i	−0.0695636	−	0.0642151i
$94$	3.66324	+	8.49235i	0.377834	+	0.875919i
$95$	−11.5298	−	1.34764i	−1.18293	−	0.138265i
$96$	−1.37799	+	1.04935i	−0.140641	+	0.107099i
$97$	13.7429	+	9.03883i	1.39538	+	0.917754i	1.00000		0.000764107i	$-0.000243223\pi$
$97$	13.7429	+	9.03883i	1.39538	+	0.917754i	0.395378	+	0.918518i	$0.370614\pi$
$98$	5.24983	−	4.40513i	0.530313	−	0.444985i
$99$	0.535580	+	6.68732i	0.0538278	+	0.672100i
$100$	−1.45929	−	1.22449i	−0.145929	−	0.122449i
$101$	1.88485	+	6.29584i	0.187550	+	0.626460i	0.999110	+	0.0421905i	$0.0134337\pi$
$101$	1.88485	+	6.29584i	0.187550	+	0.626460i	−0.811560	+	0.584269i	$0.801381\pi$
$102$	−2.98255	−	7.92535i	−0.295316	−	0.784727i
$103$	−10.7162	−	5.38188i	−1.05590	−	0.530293i	−0.165847	−	0.986151i	$-0.553036\pi$
$103$	−10.7162	−	5.38188i	−1.05590	−	0.530293i	−0.890052	+	0.455859i	$0.849332\pi$
$104$	3.71767	+	3.94050i	0.364547	+	0.386397i
$105$	−1.06704	+	0.474100i	−0.104133	+	0.0462674i
$106$	−4.03704	+	9.35890i	−0.392112	+	0.909017i
$107$	−4.87659	+	8.44650i	−0.471438	+	0.816554i	−0.999466	−	0.0326729i	$-0.989598\pi$
$107$	−4.87659	+	8.44650i	−0.471438	+	0.816554i	0.528029	+	0.849227i	$0.322931\pi$
$108$	0.434639	−	5.17794i	0.0418232	−	0.498248i
$109$	7.36714	+	12.7603i	0.705644	+	1.22221i	0.966459	+	0.256822i	$0.0826753\pi$
$109$	7.36714	+	12.7603i	0.705644	+	1.22221i	−0.260815	+	0.965389i	$0.583991\pi$
$110$	−3.90755	+	0.456728i	−0.372571	+	0.0435473i
$111$	9.53986	−	9.19844i	0.905484	−	0.873077i
$112$	0.372858	−	0.0883690i	0.0352318	−	0.00835008i
$113$	−0.638982	−	10.9709i	−0.0601103	−	1.03205i	−0.884652	−	0.466253i	$-0.845604\pi$
$113$	−0.638982	−	10.9709i	−0.0601103	−	1.03205i	0.824541	−	0.565802i	$-0.191433\pi$
$114$	−9.83485	+	5.82160i	−0.921118	+	0.545243i
$115$	−9.04146	−	2.14287i	−0.843121	−	0.199823i
$116$	0.130911	−	0.742432i	0.0121548	−	0.0689331i
$117$	−16.2484	+	0.353309i	−1.50217	+	0.0326634i
$118$	0.868559	+	4.92584i	0.0799573	+	0.453460i
$119$	−0.108928	+	1.87023i	−0.00998545	+	0.171444i
$120$	3.04374	+	0.144098i	0.277854	+	0.0131543i
$121$	−3.58248	+	4.81211i	−0.325680	+	0.437465i
$122$	−3.63777	+	4.88637i	−0.329348	+	0.442391i
$123$	−8.11029	−	0.383962i	−0.731280	−	0.0346207i
$124$	0.0306486	−	0.526216i	0.00275233	−	0.0472556i
$125$	2.10943	+	11.9632i	0.188673	+	1.07002i
$126$	−0.553002	+	1.00781i	−0.0492654	+	0.0897827i
$127$	3.15358	−	17.8848i	0.279835	−	1.58702i	−0.443336	−	0.896355i	$-0.646205\pi$
$127$	3.15358	−	17.8848i	0.279835	−	1.58702i	0.723172	−	0.690668i	$-0.242684\pi$
$128$	−0.973045	−	0.230616i	−0.0860058	−	0.0203838i
$129$	−2.05337	+	1.21546i	−0.180789	+	0.107015i
$130$	−0.554162	−	9.51460i	−0.0486032	−	0.834486i
$131$	−19.1504	+	4.53872i	−1.67318	+	0.396550i	−0.954362	−	0.298653i	$-0.903463\pi$
$131$	−19.1504	+	4.53872i	−1.67318	+	0.396550i	−0.718814	+	0.695203i	$0.755315\pi$
$132$	−2.78827	+	2.68848i	−0.242687	+	0.234002i
$133$	2.51131	−	0.293530i	0.217758	−	0.0254523i
$134$	−5.25827	−	9.10759i	−0.454245	−	0.786776i
$135$	−6.44117	+	6.48670i	−0.554367	+	0.558286i
$136$	2.44450	−	4.23399i	0.209614	−	0.363062i
$137$	5.46870	−	12.6779i	0.467222	−	1.08314i	−0.507888	−	0.861423i	$-0.669574\pi$
$137$	5.46870	−	12.6779i	0.467222	−	1.08314i	0.975110	−	0.221720i	$-0.0711671\pi$
$138$	−8.36010	+	3.71450i	−0.711659	+	0.316199i
$139$	13.8687	+	14.6999i	1.17633	+	1.24683i	0.962896	+	0.269875i	$0.0869822\pi$
$139$	13.8687	+	14.6999i	1.17633	+	1.24683i	0.213431	+	0.976958i	$0.431536\pi$
$140$	−0.602424	−	0.302549i	−0.0509141	−	0.0255700i
$141$	−5.64223	−	14.9928i	−0.475161	−	1.26262i
$142$	−0.625035	−	2.08776i	−0.0524518	−	0.175201i
$143$	9.28039	+	7.78717i	0.776065	+	0.651196i
$144$	2.47003	−	1.70263i	0.205836	−	0.141885i
$145$	−1.01600	+	0.852522i	−0.0843739	+	0.0707981i
$146$	−5.05138	−	3.32234i	−0.418055	−	0.274959i
$147$	−9.44362	+	7.19137i	−0.778896	+	0.593134i
$148$	7.59942	+	0.888244i	0.624668	+	0.0730132i
$149$	2.38640	+	5.53231i	0.195502	+	0.453224i	0.987564	−	0.157216i	$-0.0502518\pi$
$149$	2.38640	+	5.53231i	0.195502	+	0.453224i	−0.792062	+	0.610440i	$0.790993\pi$
$150$	2.42444	+	2.23803i	0.197955	+	0.182735i
$151$	4.26653	−	2.14273i	0.347205	−	0.174373i	−0.266646	−	0.963794i	$-0.585916\pi$
$151$	4.26653	−	2.14273i	0.347205	−	0.174373i	0.613852	+	0.789421i	$0.289619\pi$
$152$	−6.20043	−	2.25677i	−0.502922	−	0.183048i
$153$	4.51100	+	13.9560i	0.364692	+	1.12828i
$154$	0.805222	−	0.293077i	0.0648866	−	0.0236168i
$155$	−0.636370	+	0.674512i	−0.0511144	+	0.0541781i
$156$	−6.10922	−	7.12201i	−0.489129	−	0.570217i
$157$	−9.71998	+	6.39293i	−0.775739	+	0.510212i	−0.874574	−	0.484892i	$-0.838859\pi$
$157$	−9.71998	+	6.39293i	−0.775739	+	0.510212i	0.0988348	+	0.995104i	$0.468488\pi$
$158$	0.767785	−	2.56458i	0.0610817	−	0.204027i
$159$	7.75110	−	15.8613i	0.614702	−	1.25788i
$160$	1.05056	+	1.41115i	0.0830543	+	0.111561i
$161$	2.02388			0.159504
$162$	−1.17609	+	8.92283i	−0.0924023	+	0.701043i
$163$	0.104711			0.00820156			0.00410078	−	0.999992i	$-0.498695\pi$
$163$	0.104711			0.00820156			0.00410078	+	0.999992i	$0.498695\pi$
$164$	−2.79931	−	3.76013i	−0.218590	−	0.293617i
$165$	6.79792	−	0.470130i	0.529217	−	0.0365996i
$166$	3.09174	−	10.3271i	0.239966	−	0.801542i
$167$	12.9606	−	8.52434i	1.00292	−	0.659634i	0.0619385	−	0.998080i	$-0.480272\pi$
$167$	12.9606	−	8.52434i	1.00292	−	0.659634i	0.940986	+	0.338446i	$0.109901\pi$
$168$	−0.652325	+	0.122348i	−0.0503279	+	0.00943937i
$169$	−11.2190	+	11.8915i	−0.863004	+	0.914730i
$170$	−8.08236	+	2.94174i	−0.619888	+	0.225621i
$171$	17.4922	−	9.26647i	1.33766	−	0.708625i
$172$	−1.29456	−	0.471180i	−0.0987090	−	0.0359271i
$173$	15.5456	−	7.80731i	1.18191	−	0.593578i	0.254301	−	0.967125i	$-0.418155\pi$
$173$	15.5456	−	7.80731i	1.18191	−	0.593578i	0.927611	+	0.373547i	$0.121858\pi$
$174$	−0.287302	+	1.27377i	−0.0217803	+	0.0965642i
$175$	−0.289122	−	0.670259i	−0.0218555	−	0.0506669i
$176$	−2.22112	−	0.259612i	−0.167423	−	0.0195690i
$177$	−1.09924	−	8.59340i	−0.0826239	−	0.645920i
$178$	−8.38903	−	5.51755i	−0.628784	−	0.413558i
$179$	−15.3191	+	12.8543i	−1.14501	+	0.960775i	−0.999591	−	0.0285959i	$-0.990896\pi$
$179$	−15.3191	+	12.8543i	−1.14501	+	0.960775i	−0.145416	+	0.989371i	$0.546452\pi$
$180$	−5.25421	−	0.498613i	−0.391625	−	0.0371644i
$181$	−10.3680	−	8.69979i	−0.770648	−	0.646651i	0.170227	−	0.985405i	$-0.445550\pi$
$181$	−10.3680	−	8.69979i	−0.770648	−	0.646651i	−0.940875	+	0.338754i	$0.889994\pi$
$182$	0.595371	+	1.98868i	0.0441319	+	0.147411i
$183$	6.69398	−	8.15601i	0.494833	−	0.602909i
$184$	−4.71989	−	2.37042i	−0.347955	−	0.174750i
$185$	−9.23712	−	9.79077i	−0.679126	−	0.719832i
$186$	−0.0961269	+	0.907903i	−0.00704837	+	0.0665707i
$187$	4.33033	−	10.0388i	0.316665	−	0.734112i
$188$	4.62437	−	8.00965i	0.337267	−	0.584164i
$189$	1.03930	−	1.69833i	0.0755982	−	0.123535i
$190$	5.80415	+	10.0531i	0.421078	+	0.729328i
$191$	0.446253	−	0.0521595i	0.0322897	−	0.00377413i	−0.0999327	−	0.994994i	$-0.531863\pi$
$191$	0.446253	−	0.0521595i	0.0322897	−	0.00377413i	0.132222	+	0.991220i	$0.457789\pi$
$192$	1.66459	+	0.478692i	0.120131	+	0.0345466i
$193$	−12.0719	+	2.86109i	−0.868952	+	0.205945i	−0.640826	−	0.767686i	$-0.721408\pi$
$193$	−12.0719	+	2.86109i	−0.868952	+	0.205945i	−0.228126	+	0.973632i	$0.573260\pi$
$194$	−0.956420	−	16.4211i	−0.0686670	−	1.17897i
$195$	0.179441	+	16.5067i	0.0128501	+	1.18207i
$196$	−6.66844	−	1.58045i	−0.476317	−	0.112889i
$197$	−2.25910	+	12.8120i	−0.160954	+	0.912818i	0.792184	+	0.610283i	$0.208944\pi$
$197$	−2.25910	+	12.8120i	−0.160954	+	0.912818i	−0.953138	+	0.302535i	$0.902167\pi$
$198$	5.04422	−	4.42299i	0.358477	−	0.314328i
$199$	2.99008	+	16.9576i	0.211961	+	1.20209i	0.886102	+	0.463490i	$0.153403\pi$
$199$	2.99008	+	16.9576i	0.211961	+	1.20209i	−0.674141	+	0.738603i	$0.735486\pi$
$200$	−0.110764	+	1.90174i	−0.00783220	+	0.134474i
$201$	8.35141	+	16.1878i	0.589063	+	1.14180i
$202$	3.92449	−	5.27150i	0.276126	−	0.370902i
$203$	0.172507	−	0.231717i	0.0121076	−	0.0162633i
$204$	−4.57605	+	7.12506i	−0.320388	+	0.498854i
$205$	−0.479519	+	8.23302i	−0.0334911	+	0.575019i
$206$	2.08234	+	11.8096i	0.145084	+	0.822811i
$207$	14.7682	−	5.74174i	1.02646	−	0.399078i
$208$	0.940727	−	5.33513i	0.0652277	−	0.369924i
$209$	−14.3578	−	3.40286i	−0.993150	−	0.235381i
$210$	1.01748	+	0.572787i	0.0702128	+	0.0395260i
$211$	0.0172113	+	0.295507i	0.00118487	+	0.0203435i	0.998849	−	0.0479701i	$-0.0152752\pi$
$211$	0.0172113	+	0.295507i	0.00118487	+	0.0203435i	−0.997664	+	0.0683136i	$0.978238\pi$
$212$	9.91774	−	2.35055i	0.681153	−	0.161436i
$213$	0.910376	+	3.66326i	0.0623780	+	0.251002i
$214$	9.68723	−	1.13227i	0.662205	−	0.0774007i
$215$	1.21182	+	2.09893i	0.0826454	+	0.143146i
$216$	−4.41290	+	2.74342i	−0.300260	+	0.186666i
$217$	0.100990	−	0.174921i	0.00685568	−	0.0118744i
$218$	5.83595	−	13.5292i	0.395260	−	0.916316i
$219$	8.46733	+	6.16178i	0.572169	+	0.416374i
$220$	2.69978	+	2.86160i	0.182019	+	0.192929i
$221$	23.6686	+	11.8868i	1.59212	+	0.799592i
$222$	−13.0751	−	2.15922i	−0.877543	−	0.144917i
$223$	−4.98547	−	16.6526i	−0.333852	−	1.11514i	−0.945937	−	0.324350i	$-0.894854\pi$
$223$	−4.98547	−	16.6526i	−0.333852	−	1.11514i	0.612086	−	0.790792i	$-0.290331\pi$
$224$	−0.293538	−	0.246308i	−0.0196128	−	0.0164571i
$225$	−4.01124	−	4.07063i	−0.267416	−	0.271375i
$226$	−8.41843	+	7.06390i	−0.559986	+	0.469884i
$227$	4.52710	+	2.97752i	0.300474	+	0.197625i	0.690789	−	0.723056i	$-0.257263\pi$
$227$	4.52710	+	2.97752i	0.300474	+	0.197625i	−0.390315	+	0.920682i	$0.627634\pi$
$228$	10.5426	+	4.41234i	0.698201	+	0.292214i
$229$	−26.9977	−	3.15558i	−1.78406	−	0.208527i	−0.840974	−	0.541076i	$-0.818017\pi$
$229$	−26.9977	−	3.15558i	−1.78406	−	0.208527i	−0.943086	+	0.332550i	$0.892091\pi$
$230$	3.68034	+	8.53200i	0.242675	+	0.562583i
$231$	−1.41713	+	0.441102i	−0.0932403	+	0.0290224i
$232$	−0.673697	+	0.338343i	−0.0442304	+	0.0222133i
$233$	−16.6048	−	6.04367i	−1.08782	−	0.395934i	−0.265007	−	0.964246i	$-0.585374\pi$
$233$	−16.6048	−	6.04367i	−1.08782	−	0.395934i	−0.822813	+	0.568312i	$0.807596\pi$
$234$	9.98630	+	12.8223i	0.652825	+	0.838218i
$235$	−15.2898	+	5.56503i	−0.997395	+	0.363022i
$236$	3.43246	−	3.63820i	0.223434	−	0.236827i
$237$	−1.53842	+	4.37413i	−0.0999308	+	0.284130i
$238$	1.56520	−	1.02945i	0.101457	−	0.0667293i
$239$	−2.16040	+	7.21623i	−0.139744	+	0.466779i	−0.998997	−	0.0447722i	$-0.985744\pi$
$239$	−2.16040	+	7.21623i	−0.139744	+	0.466779i	0.859253	+	0.511551i	$0.170929\pi$
$240$	−1.70201	−	2.52750i	−0.109864	−	0.163150i
$241$	8.34725	+	11.2123i	0.537694	+	0.722248i	0.985081	−	0.172093i	$-0.0550528\pi$
$241$	8.34725	+	11.2123i	0.537694	+	0.722248i	−0.447387	+	0.894340i	$0.647645\pi$
$242$	5.99922			0.385644
$243$	2.76562	−	15.3412i	0.177415	−	0.984136i
$244$	6.09179			0.389987
$245$	7.19969	+	9.67086i	0.459971	+	0.617849i
$246$	4.53514	+	6.73474i	0.289150	+	0.429391i
$247$	10.2521	−	34.2445i	0.652327	−	2.17892i
$248$	−0.440392	+	0.289651i	−0.0279649	+	0.0183928i
$249$	−6.19494	+	17.6139i	−0.392589	+	1.11624i
$250$	8.33626	−	8.83592i	0.527231	−	0.558833i
$251$	26.8547	−	9.77431i	1.69505	−	0.616949i	0.699807	−	0.714332i	$-0.253269\pi$
$251$	26.8547	−	9.77431i	1.69505	−	0.616949i	0.995247	+	0.0973825i	$0.0310470\pi$
$252$	1.13862	−	0.158246i	0.0717261	−	0.00996854i
$253$	−11.0988	−	4.03965i	−0.697779	−	0.253971i
$254$	−16.2290	+	8.15053i	−1.01830	+	0.511410i
$255$	14.2243	−	4.42753i	0.890763	−	0.277263i
$256$	0.396080	+	0.918216i	0.0247550	+	0.0573885i
$257$	23.3432	+	2.72843i	1.45611	+	0.170195i	0.807024	−	0.590519i	$-0.201077\pi$
$257$	23.3432	+	2.72843i	1.45611	+	0.170195i	0.649088	+	0.760714i	$0.275151\pi$
$258$	2.20114	+	0.921229i	0.137037	+	0.0573532i
$259$	2.44950	+	1.61106i	0.152205	+	0.100106i
$260$	−7.30096	+	6.12623i	−0.452786	+	0.379933i
$261$	0.601397	−	2.18023i	0.0372255	−	0.134953i
$262$	15.0764	+	12.6506i	0.931424	+	0.781558i
$263$	−5.89525	−	19.6915i	−0.363517	−	1.21423i	−0.922808	−	0.385259i	$-0.874112\pi$
$263$	−5.89525	−	19.6915i	−0.363517	−	1.21423i	0.559292	−	0.828971i	$-0.311073\pi$
$264$	3.82153	+	0.631086i	0.235199	+	0.0388406i
$265$	−16.0240	−	8.04757i	−0.984348	−	0.494358i
$266$	−1.73510	−	1.83910i	−0.106386	−	0.112762i
$267$	14.0620	+	10.2331i	0.860583	+	0.626257i
$268$	−4.16539	+	9.65645i	−0.254441	+	0.589862i
$269$	3.15858	−	5.47082i	0.192582	−	0.333562i	−0.753523	−	0.657421i	$-0.771647\pi$
$269$	3.15858	−	5.47082i	0.192582	−	0.333562i	0.946105	+	0.323859i	$0.104980\pi$
$270$	9.04953	+	1.29302i	0.550737	+	0.0786906i
$271$	4.92724	+	8.53423i	0.299309	+	0.518418i	0.975978	−	0.217869i	$-0.0699107\pi$
$271$	4.92724	+	8.53423i	0.299309	+	0.518418i	−0.676669	+	0.736287i	$0.736577\pi$
$272$	−4.85594	+	0.567578i	−0.294434	+	0.0344144i
$273$	−0.867171	−	3.48940i	−0.0524836	−	0.211188i
$274$	−13.4349	+	3.18413i	−0.811631	+	0.192360i
$275$	0.247695	+	4.25276i	0.0149366	+	0.256451i
$276$	7.97179	+	4.48769i	0.479845	+	0.270127i
$277$	−5.17796	−	1.22720i	−0.311113	−	0.0737352i	0.0720931	−	0.997398i	$-0.477032\pi$
$277$	−5.17796	−	1.22720i	−0.311113	−	0.0737352i	−0.383207	+	0.923663i	$0.625180\pi$
$278$	3.50936	−	19.9026i	0.210478	−	1.19368i
$279$	0.240675	−	1.56290i	0.0144088	−	0.0935685i
$280$	0.117061	+	0.663888i	0.00699575	+	0.0396749i
$281$	0.353128	−	6.06297i	0.0210658	−	0.361686i	−0.971259	−	0.238026i	$-0.923500\pi$
$281$	0.353128	−	6.06297i	0.0210658	−	0.361686i	0.992325	−	0.123660i	$-0.0394633\pi$
$282$	−8.65674	+	13.4788i	−0.515502	+	0.802652i
$283$	1.60669	−	2.15816i	0.0955080	−	0.128289i	−0.751800	−	0.659391i	$-0.770814\pi$
$283$	1.60669	−	2.15816i	0.0955080	−	0.128289i	0.847308	+	0.531101i	$0.178222\pi$
$284$	−1.30140	+	1.74808i	−0.0772237	+	0.103729i
$285$	−9.21841	−	17.8684i	−0.546052	−	1.05843i
$286$	0.704406	−	12.0942i	0.0416524	−	0.715144i
$287$	−0.311920	−	1.76898i	−0.0184120	−	0.104420i
$288$	−2.84072	−	0.964534i	−0.167391	−	0.0568357i
$289$	1.19857	−	6.79740i	0.0705039	−	0.399847i
$290$	1.29054	+	0.305863i	0.0757830	+	0.0179609i
$291$	0.309695	+	28.4887i	0.0181546	+	1.67004i
$292$	0.351545	+	6.03579i	0.0205726	+	0.353218i
$293$	2.98763	−	0.708081i	0.174539	−	0.0413666i	−0.142417	−	0.989807i	$-0.545487\pi$
$293$	2.98763	−	0.708081i	0.174539	−	0.0413666i	0.316956	+	0.948440i	$0.397339\pi$
$294$	11.4077	+	3.28055i	0.665311	+	0.191326i
$295$	−8.74007	+	1.02157i	−0.508867	+	0.0594780i
$296$	−3.82558	−	6.62609i	−0.222357	−	0.385134i
$297$	−9.08936	+	7.23911i	−0.527418	+	0.420056i
$298$	3.01253	−	5.21786i	0.174511	−	0.302262i
$299$	11.3331	−	26.2731i	0.655411	−	1.51941i
$300$	0.347402	−	3.28116i	0.0200573	−	0.189438i
$301$	−0.362262	−	0.383975i	−0.0208804	−	0.0221320i
$302$	−4.26653	−	2.14273i	−0.245511	−	0.123300i
$303$	−7.22158	+	8.79885i	−0.414869	+	0.505480i
$304$	1.89243	+	6.32116i	0.108538	+	0.362544i
$305$	−8.20979	−	6.88883i	−0.470091	−	0.394453i
$306$	8.50069	−	11.9523i	0.485952	−	0.683270i
$307$	−2.51815	+	2.11298i	−0.143718	+	0.120594i	−0.711812	−	0.702370i	$-0.752125\pi$
$307$	−2.51815	+	2.11298i	−0.143718	+	0.120594i	0.568094	+	0.822964i	$0.307681\pi$
$308$	−0.715929	−	0.470874i	−0.0407938	−	0.0268305i
$309$	−2.63539	−	20.6024i	−0.149922	−	1.17203i
$310$	0.921055	+	0.107656i	0.0523124	+	0.00611445i
$311$	−2.38107	−	5.51994i	−0.135018	−	0.313007i	0.837271	−	0.546788i	$-0.184150\pi$
$311$	−2.38107	−	5.51994i	−0.135018	−	0.313007i	−0.972289	+	0.233781i	$0.924890\pi$
$312$	−2.06455	+	9.15332i	−0.116882	+	0.518205i
$313$	18.5765	−	9.32948i	1.05001	−	0.527334i	0.161823	−	0.986820i	$-0.448263\pi$
$313$	18.5765	−	9.32948i	1.05001	−	0.527334i	0.888185	+	0.459486i	$0.151966\pi$
$314$	10.9323	+	3.97903i	0.616945	+	0.224550i
$315$	−1.71344	−	1.07433i	−0.0965414	−	0.0605314i
$316$	−2.51560	+	0.915604i	−0.141514	+	0.0515067i
$317$	−15.9253	+	16.8798i	−0.894452	+	0.948064i	−0.998920	−	0.0464647i	$-0.985204\pi$
$317$	−15.9253	+	16.8798i	−0.894452	+	0.948064i	0.104468	+	0.994528i	$0.466686\pi$
$318$	−17.3513	+	3.25437i	−0.973015	+	0.182496i
$319$	−1.40853	+	0.926401i	−0.0788623	+	0.0518685i
$320$	0.504565	−	1.68536i	0.0282060	−	0.0942146i
$321$	−16.8527	+	1.16550i	−0.940628	+	0.0650519i
$322$	−1.20857	−	1.62340i	−0.0673512	−	0.0904684i
$323$	−32.2594			−1.79496
$324$	7.85952	−	4.38497i	0.436640	−	0.243610i
$325$	−10.3200			−0.572452
$326$	−0.0625288	−	0.0839907i	−0.00346315	−	0.00465182i
$327$	−11.2050	+	22.9291i	−0.619638	+	1.26798i
$328$	−1.34445	+	4.49079i	−0.0742351	+	0.247962i
$329$	2.96097	−	1.94746i	0.163243	−	0.107367i
$330$	−4.43654	−	5.17203i	−0.244223	−	0.284711i
$331$	8.34285	−	8.84290i	0.458564	−	0.486050i	−0.456292	−	0.889830i	$-0.650823\pi$
$331$	8.34285	−	8.84290i	0.458564	−	0.486050i	0.914856	+	0.403781i	$0.132304\pi$
$332$	−10.1299	+	3.68698i	−0.555951	+	0.202350i
$333$	22.4445	+	4.80664i	1.22995	+	0.263402i
$334$	−14.5771	−	5.30564i	−0.797625	−	0.290312i
$335$	16.5335	−	8.30343i	0.903321	−	0.453665i
$336$	0.487680	+	0.450183i	0.0266051	+	0.0245595i
$337$	8.12784	+	18.8424i	0.442752	+	1.02641i	0.982782	+	0.184768i	$0.0591534\pi$
$337$	8.12784	+	18.8424i	0.442752	+	1.02641i	−0.540031	+	0.841645i	$0.681587\pi$
$338$	16.2380	+	1.89795i	0.883230	+	0.103235i
$339$	15.1434	−	11.5318i	0.822478	−	0.626322i
$340$	7.18608	+	4.72636i	0.389720	+	0.256323i
$341$	−0.902968	+	0.757680i	−0.0488985	+	0.0410307i
$342$	−17.8785	−	8.49737i	−0.966758	−	0.459485i
$343$	−4.06643	−	3.41214i	−0.219567	−	0.184238i
$344$	0.395111	+	1.31976i	0.0213030	+	0.0711568i
$345$	−5.66857	−	15.0628i	−0.305186	−	0.810952i
$346$	−15.5456	−	7.80731i	−0.835738	−	0.419723i
$347$	12.7406	+	13.5042i	0.683951	+	0.724946i	0.972599	−	0.232490i	$-0.0746872\pi$
$347$	12.7406	+	13.5042i	0.683951	+	0.724946i	−0.288648	+	0.957435i	$0.593206\pi$
$348$	1.19328	−	0.530191i	0.0639668	−	0.0284212i
$349$	−2.40316	+	5.57115i	−0.128638	+	0.298217i	−0.970347	−	0.241714i	$-0.922290\pi$
$349$	−2.40316	+	5.57115i	−0.128638	+	0.298217i	0.841709	+	0.539931i	$0.181550\pi$
$350$	−0.364979	+	0.632162i	−0.0195090	+	0.0337905i
$351$	−16.2272	−	23.0019i	−0.866142	−	1.22775i
$352$	1.11812	+	1.93664i	0.0595961	+	0.103223i
$353$	−19.2939	+	2.25514i	−1.02691	+	0.120029i	−0.612834	−	0.790212i	$-0.709970\pi$
$353$	−19.2939	+	2.25514i	−1.02691	+	0.120029i	−0.414079	+	0.910241i	$0.635896\pi$
$354$	−6.23655	+	6.01335i	−0.331469	+	0.319606i
$355$	3.73066	−	0.884183i	0.198003	−	0.0469275i
$356$	0.583825	+	10.0239i	0.0309427	+	0.531265i
$357$	−2.79230	+	1.65286i	−0.147784	+	0.0874787i
$358$	19.4587	+	4.61179i	1.02842	+	0.243741i
$359$	−2.76371	+	15.6738i	−0.145863	+	0.827229i	0.820807	+	0.571205i	$0.193524\pi$
$359$	−2.76371	+	15.6738i	−0.145863	+	0.827229i	−0.966670	+	0.256024i	$0.917587\pi$
$360$	2.73765	+	4.51227i	0.144287	+	0.237818i
$361$	4.26105	+	24.1656i	0.224266	+	1.27187i
$362$	−0.786960	+	13.5116i	−0.0413617	+	0.710153i
$363$	−10.3793	−	0.491384i	−0.544773	−	0.0257910i
$364$	1.23963	−	1.66512i	0.0649745	−	0.0872759i
$365$	6.35173	−	8.53185i	0.332465	−	0.446578i
$366$	−10.5395	−	0.498967i	−0.550908	−	0.0260814i
$367$	1.22179	−	20.9773i	0.0637769	−	1.09501i	−0.802893	−	0.596124i	$-0.796707\pi$
$367$	1.22179	−	20.9773i	0.0637769	−	1.09501i	0.866669	−	0.498883i	$-0.166256\pi$
$368$	0.917156	+	5.20145i	0.0478101	+	0.271144i
$369$	−7.29468	−	12.0233i	−0.379746	−	0.625909i
$370$	−2.33738	+	13.2560i	−0.121515	+	0.689144i
$371$	3.80035	+	0.900699i	0.197304	+	0.0467620i
$372$	0.785653	−	0.465057i	0.0407342	−	0.0241121i
$373$	1.50294	+	25.8044i	0.0778191	+	1.33610i	0.780750	+	0.624844i	$0.214837\pi$
$373$	1.50294	+	25.8044i	0.0778191	+	1.33610i	−0.702931	+	0.711258i	$0.748126\pi$
$374$	−10.6383	+	2.52132i	−0.550092	+	0.130374i
$375$	−15.1464	+	14.6043i	−0.782157	+	0.754165i
$376$	−9.18621	+	1.07371i	−0.473743	+	0.0553726i
$377$	−2.04206	−	3.53695i	−0.105171	−	0.182162i
$378$	−1.98290	+	0.180521i	−0.101989	+	0.00928500i
$379$	−16.6386	+	28.8189i	−0.854667	+	1.48033i	0.0222873	+	0.999752i	$0.492905\pi$
$379$	−16.6386	+	28.8189i	−0.854667	+	1.48033i	−0.876954	+	0.480574i	$0.840428\pi$
$380$	4.59782	−	10.6589i	0.235863	−	0.546792i
$381$	28.7457	−	12.7721i	1.47269	−	0.654332i
$382$	−0.308322	−	0.326802i	−0.0157751	−	0.0167207i
$383$	−11.9767	−	6.01492i	−0.611981	−	0.307348i	0.115679	−	0.993287i	$-0.463096\pi$
$383$	−11.9767	−	6.01492i	−0.611981	−	0.307348i	−0.727660	+	0.685938i	$0.759392\pi$
$384$	−0.610053	−	1.62106i	−0.0311317	−	0.0827244i
$385$	0.432361	+	1.44419i	0.0220351	+	0.0736025i
$386$	9.50376	+	7.97461i	0.483729	+	0.405897i
$387$	−3.73276	−	1.77412i	−0.189747	−	0.0901836i
$388$	−12.6006	+	10.5732i	−0.639699	+	0.536771i
$389$	−24.7962	−	16.3087i	−1.25722	−	0.826886i	−0.266636	−	0.963797i	$-0.585912\pi$
$389$	−24.7962	−	16.3087i	−1.25722	−	0.826886i	−0.990583	+	0.136911i	$0.956283\pi$
$390$	13.1333	−	10.0011i	0.665029	−	0.506424i
$391$	−25.6476	−	2.99777i	−1.29705	−	0.151604i
$392$	2.71440	+	6.29269i	0.137098	+	0.317829i
$393$	−25.0477	−	23.1219i	−1.26349	−	1.16634i
$394$	11.6259	−	5.83872i	0.585702	−	0.294151i
$395$	4.42562	+	1.61079i	0.222677	+	0.0810479i
$396$	−6.55998	−	1.40486i	−0.329652	−	0.0705970i
$397$	27.5785	−	10.0377i	1.38412	−	0.503780i	0.460699	−	0.887557i	$-0.347599\pi$
$397$	27.5785	−	10.0377i	1.38412	−	0.503780i	0.923426	+	0.383776i	$0.125377\pi$
$398$	11.8165	−	12.5248i	0.592309	−	0.627811i
$399$	2.85128	+	3.32396i	0.142742	+	0.166406i
$400$	1.59158	−	1.04680i	0.0795788	−	0.0523398i
$401$	0.0406575	−	0.135806i	0.00203034	−	0.00678181i	−0.956968	−	0.290192i	$-0.906281\pi$
$401$	0.0406575	−	0.135806i	0.00203034	−	0.00678181i	0.958999	+	0.283411i	$0.0914659\pi$
$402$	7.99753	−	16.3656i	0.398881	−	0.816241i
$403$	−1.70523	−	2.29052i	−0.0849435	−	0.114099i
$404$	−6.57193			−0.326966
$405$	−15.5508	−	2.97830i	−0.772726	−	0.147993i
$406$	−0.288879			−0.0143368
$407$	−10.2173	−	13.7242i	−0.506452	−	0.680283i
$408$	8.44781	−	0.584233i	0.418229	−	0.0289239i
$409$	7.15874	−	23.9119i	0.353977	−	1.18236i	−0.576833	−	0.816862i	$-0.695712\pi$
$409$	7.15874	−	23.9119i	0.353977	−	1.18236i	0.930810	−	0.365503i	$-0.119103\pi$
$410$	6.89025	−	4.53179i	0.340285	−	0.223809i
$411$	23.5047	−	4.40848i	1.15940	−	0.217454i
$412$	8.22923	−	8.72247i	0.405425	−	0.429725i
$413$	1.80105	−	0.655528i	0.0886238	−	0.0322564i
$414$	−13.4245	−	8.41717i	−0.659779	−	0.413681i
$415$	17.8212	+	6.48640i	0.874811	+	0.318405i
$416$	−4.84119	+	2.43134i	−0.237359	+	0.119206i
$417$	−7.70178	+	34.1463i	−0.377158	+	1.67215i
$418$	5.84437	+	13.5488i	0.285858	+	0.662692i
$419$	12.1685	+	1.42230i	0.594472	+	0.0694838i	0.408008	−	0.912978i	$-0.366223\pi$
$419$	12.1685	+	1.42230i	0.594472	+	0.0694838i	0.186463	+	0.982462i	$0.440297\pi$
$420$	−0.148152	−	1.15819i	−0.00722906	−	0.0565139i
$421$	12.3445	+	8.11913i	0.601636	+	0.395702i	0.813473	−	0.581603i	$-0.197574\pi$
$421$	12.3445	+	8.11913i	0.601636	+	0.395702i	−0.211837	+	0.977305i	$0.567945\pi$
$422$	0.226755	−	0.190270i	0.0110383	−	0.00926219i
$423$	16.0812	−	22.6108i	0.781893	−	1.09938i
$424$	−7.80789	−	6.55160i	−0.379185	−	0.318174i
$425$	2.67111	+	8.92211i	0.129568	+	0.432786i
$426$	2.39475	−	2.91778i	0.116026	−	0.141367i
$427$	2.08600	+	1.04763i	0.100949	+	0.0506984i
$428$	−6.69304	−	7.09420i	−0.323520	−	0.342911i
$429$	−2.20931	+	20.8666i	−0.106667	+	1.00745i
$430$	0.959954	−	2.22542i	0.0462931	−	0.107319i
$431$	−5.12514	+	8.87701i	−0.246869	+	0.427590i	−0.962656	−	0.270729i	$-0.912735\pi$
$431$	−5.12514	+	8.87701i	−0.246869	+	0.427590i	0.715786	+	0.698320i	$0.246069\pi$
$432$	4.83576	+	1.90143i	0.232661	+	0.0914826i
$433$	−10.7494	−	18.6185i	−0.516584	−	0.894750i	−0.999815	−	0.0192568i	$-0.993870\pi$
$433$	−10.7494	−	18.6185i	−0.516584	−	0.894750i	0.483230	−	0.875493i	$-0.339463\pi$
$434$	−0.200615	+	0.0234485i	−0.00962984	+	0.00112557i
$435$	−2.20773	−	0.634884i	−0.105852	−	0.0304403i
$436$	−14.3371	+	3.39796i	−0.686623	+	0.162733i
$437$	2.02638	+	34.7916i	0.0969348	+	1.66431i
$438$	−0.113832	−	10.4714i	−0.00543912	−	0.500343i
$439$	20.4041	+	4.83586i	0.973835	+	0.230803i	0.686583	−	0.727052i	$-0.259110\pi$
$439$	20.4041	+	4.83586i	0.973835	+	0.230803i	0.287253	+	0.957855i	$0.407258\pi$
$440$	0.683159	−	3.87439i	0.0325683	−	0.184704i
$441$	−19.4679	−	6.61011i	−0.927043	−	0.314767i
$442$	−4.59921	−	26.0834i	−0.218762	−	1.24066i
$443$	−1.66506	+	28.5880i	−0.0791093	+	1.35825i	0.692159	+	0.721745i	$0.256660\pi$
$443$	−1.66506	+	28.5880i	−0.0791093	+	1.35825i	−0.771268	+	0.636510i	$0.780377\pi$
$444$	6.07595	+	11.7772i	0.288352	+	0.558923i
$445$	10.5486	−	14.1692i	0.500051	−	0.671684i
$446$	−10.3803	+	13.9432i	−0.491523	+	0.660230i
$447$	−5.63940	+	8.78073i	−0.266735	+	0.415314i
$448$	−0.0222803	+	0.382539i	−0.00105265	+	0.0180732i
$449$	−5.48471	−	31.1054i	−0.258840	−	1.46795i	−0.786021	−	0.618200i	$-0.787862\pi$
$449$	−5.48471	−	31.1054i	−0.258840	−	1.46795i	0.527181	−	0.849753i	$-0.323249\pi$
$450$	−0.869799	+	5.64832i	−0.0410027	+	0.266264i
$451$	−1.82033	+	10.3236i	−0.0857162	+	0.486121i
$452$	10.6933	+	2.53435i	0.502969	+	0.119206i
$453$	7.20607	+	4.05663i	0.338571	+	0.190597i
$454$	−0.315059	−	5.40935i	−0.0147864	−	0.253873i
$455$	−3.55361	+	0.842220i	−0.166596	+	0.0394839i
$456$	−2.75637	−	11.0913i	−0.129079	−	0.519399i
$457$	22.0765	−	2.58037i	1.03270	−	0.120705i	0.417175	−	0.908826i	$-0.363020\pi$
$457$	22.0765	−	2.58037i	1.03270	−	0.120705i	0.615520	+	0.788121i	$0.288946\pi$
$458$	13.5908	+	23.5399i	0.635054	+	1.09995i
$459$	−15.6861	+	19.9826i	−0.732167	+	0.932710i
$460$	4.64596	−	8.04704i	0.216619	−	0.375195i
$461$	−10.7214	+	24.8549i	−0.499344	+	1.15761i	0.463144	+	0.886283i	$0.346721\pi$
$461$	−10.7214	+	24.8549i	−0.499344	+	1.15761i	−0.962487	+	0.271326i	$0.912538\pi$
$462$	1.20007	+	0.873305i	0.0558323	+	0.0406298i
$463$	25.3988	+	26.9211i	1.18038	+	1.25113i	0.961325	+	0.275418i	$0.0888162\pi$
$463$	25.3988	+	26.9211i	1.18038	+	1.25113i	0.219056	+	0.975712i	$0.429702\pi$
$464$	0.673697	+	0.338343i	0.0312756	+	0.0157072i
$465$	−1.58471	−	0.261699i	−0.0734893	−	0.0121360i
$466$	5.06796	+	16.9282i	0.234769	+	0.784182i
$467$	3.36943	+	2.82728i	0.155918	+	0.130831i	0.717410	−	0.696652i	$-0.245328\pi$
$467$	3.36943	+	2.82728i	0.155918	+	0.130831i	−0.561491	+	0.827483i	$0.689772\pi$
$468$	4.32164	−	15.6672i	0.199768	−	0.724215i
$469$	−3.08700	+	2.59030i	−0.142545	+	0.119609i
$470$	13.5943	+	8.94109i	0.627057	+	0.412422i
$471$	−18.5882	−	7.77961i	−0.856498	−	0.358466i
$472$	−4.96801	−	0.580677i	−0.228671	−	0.0267278i
$473$	1.22022	+	2.82878i	0.0561056	+	0.130067i
$474$	4.42727	−	1.37805i	0.203351	−	0.0632959i
$475$	11.2327	−	5.64126i	0.515390	−	0.258839i
$476$	−1.76042	−	0.640740i	−0.0806887	−	0.0293683i
$477$	30.2863	−	4.20922i	1.38672	−	0.192727i
$478$	7.07841	−	2.57633i	0.323759	−	0.117839i
$479$	17.2677	−	18.3027i	0.788981	−	0.836271i	−0.200686	−	0.979656i	$-0.564317\pi$
$479$	17.2677	−	18.3027i	0.788981	−	0.836271i	0.989667	+	0.143385i	$0.0457987\pi$
$480$	−1.01100	+	2.87454i	−0.0461456	+	0.131204i
$481$	34.6306	−	22.7769i	1.57902	−	1.03854i
$482$	4.00902	−	13.3910i	0.182606	−	0.609945i
$483$	1.95800	+	2.90765i	0.0890921	+	0.132303i
$484$	−3.58248	−	4.81211i	−0.162840	−	0.218732i
$485$	28.9381			1.31401
$486$	−13.9570	+	6.94274i	−0.633103	+	0.314929i
$487$	19.4537			0.881532			0.440766	−	0.897622i	$-0.354707\pi$
$487$	19.4537			0.881532			0.440766	+	0.897622i	$0.354707\pi$
$488$	−3.63777	−	4.88637i	−0.164674	−	0.221196i
$489$	0.101302	+	0.150435i	0.00458105	+	0.00680291i
$490$	3.45787	−	11.5501i	0.156210	−	0.521779i
$491$	−6.60836	+	4.34639i	−0.298231	+	0.196150i	−0.689802	−	0.723998i	$-0.742302\pi$
$491$	−6.60836	+	4.34639i	−0.298231	+	0.196150i	0.391570	+	0.920148i	$0.371932\pi$
$492$	2.69389	−	7.65945i	0.121450	−	0.345315i
$493$	−2.52931	+	2.68091i	−0.113914	+	0.120742i
$494$	−33.5904	+	12.2259i	−1.51130	+	0.550070i
$495$	7.25208	+	9.31158i	0.325957	+	0.418524i
$496$	0.495320	+	0.180282i	0.0222405	+	0.00809488i
$497$	−0.746259	+	0.374786i	−0.0334743	+	0.0168114i
$498$	17.8279	−	5.54918i	0.798886	−	0.248665i
$499$	−0.404514	−	0.937769i	−0.0181085	−	0.0419803i	0.908922	−	0.416966i	$-0.136907\pi$
$499$	−0.404514	−	0.937769i	−0.0181085	−	0.0419803i	−0.927030	+	0.374986i	$0.877647\pi$
$500$	−12.0656	−	1.41026i	−0.539589	−	0.0630689i
$501$	24.7855	+	10.3733i	1.10733	+	0.463447i
$502$	−23.8767	−	15.7040i	−1.06567	−	0.700902i
$503$	−20.4536	+	17.1626i	−0.911979	+	0.765241i	−0.972494	−	0.232926i	$-0.925170\pi$
$503$	−20.4536	+	17.1626i	−0.911979	+	0.765241i	0.0605155	+	0.998167i	$0.480726\pi$
$504$	−0.806867	−	0.818813i	−0.0359407	−	0.0364728i
$505$	8.85686	+	7.43179i	0.394125	+	0.330710i
$506$	3.38747	+	11.3150i	0.150592	+	0.503011i
$507$	−27.9381	−	4.61369i	−1.24077	−	0.204901i
$508$	16.2290	+	8.15053i	0.720047	+	0.361621i
$509$	−13.7296	−	14.5525i	−0.608553	−	0.645028i	0.347688	−	0.937610i	$-0.386967\pi$
$509$	−13.7296	−	14.5525i	−0.608553	−	0.645028i	−0.956240	+	0.292582i	$0.905485\pi$
$510$	−12.0456	−	8.76574i	−0.533389	−	0.388153i
$511$	−0.917620	+	2.12728i	−0.0405931	+	0.0941054i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$	30.2358	+	16.1658i	1.33494	+	0.713737i
$514$	−11.7511	−	20.3535i	−0.518318	−	0.897753i
$515$	−20.9541	+	2.44918i	−0.923346	+	0.107924i
$516$	−0.575488	−	2.31570i	−0.0253344	−	0.101943i
$517$	−20.1249	+	4.76970i	−0.885094	+	0.209771i
$518$	−0.170470	−	2.92686i	−0.00749003	−	0.128599i
$519$	26.2562	+	14.7808i	1.15252	+	0.648807i
$520$	9.27382	+	2.19794i	0.406684	+	0.0963859i
$521$	3.28803	−	18.6473i	0.144051	−	0.816955i	−0.824073	−	0.566484i	$-0.808303\pi$
$521$	3.28803	−	18.6473i	0.144051	−	0.816955i	0.968124	−	0.250471i	$-0.0805854\pi$
$522$	−2.10794	+	0.819551i	−0.0922622	+	0.0358708i
$523$	−2.52162	−	14.3008i	−0.110263	−	0.625331i	−0.988987	−	0.148002i	$-0.952716\pi$
$523$	−2.52162	−	14.3008i	−0.110263	−	0.625331i	0.878724	−	0.477330i	$-0.158395\pi$
$524$	1.14434	−	19.6476i	0.0499908	−	0.858308i
$525$	0.683234	−	1.06382i	0.0298188	−	0.0464288i
$526$	−12.2746	+	16.4877i	−0.535199	+	0.718897i
$527$	−1.53889	+	2.06709i	−0.0670353	+	0.0900440i
$528$	−1.77585	−	3.44219i	−0.0772839	−	0.149802i
$529$	−0.284693	+	4.88799i	−0.0123780	+	0.212521i
$530$	3.11374	+	17.6589i	0.135252	+	0.767054i
$531$	11.2825	−	9.89295i	0.489618	−	0.429318i
$532$	−0.439053	+	2.48999i	−0.0190354	+	0.107955i
$533$	−24.7109	−	5.85658i	−1.07035	−	0.253677i
$534$	−0.189046	−	17.3903i	−0.00818083	−	0.752551i
$535$	0.997677	+	17.1294i	0.0431333	+	0.740571i
$536$	10.2331	−	2.42528i	0.442001	−	0.104756i
$537$	−33.2880	−	9.57275i	−1.43648	−	0.413094i
$538$	−6.27445	+	0.733378i	−0.270511	+	0.0316182i
$539$	7.66267	+	13.2721i	0.330055	+	0.571672i
$540$	−4.36684	−	8.03098i	−0.187919	−	0.345598i
$541$	14.8696	−	25.7548i	0.639293	−	1.10729i	−0.346296	−	0.938125i	$-0.612561\pi$
$541$	14.8696	−	25.7548i	0.639293	−	1.10729i	0.985588	−	0.169162i	$-0.0541061\pi$
$542$	3.90316	−	9.04854i	0.167655	−	0.388668i
$543$	2.46824	−	23.3121i	0.105922	−	1.00042i
$544$	3.35503	+	3.55613i	0.143846	+	0.152468i
$545$	23.1644	+	11.6336i	0.992252	+	0.498328i
$546$	−2.28109	+	2.77931i	−0.0976218	+	0.118943i
$547$	1.69833	+	5.67282i	0.0726154	+	0.242552i	0.986590	−	0.163220i	$-0.0521879\pi$
$547$	1.69833	+	5.67282i	0.0726154	+	0.242552i	−0.913974	+	0.405772i	$0.867003\pi$
$548$	10.5768	+	8.87501i	0.451819	+	0.379122i
$549$	18.1936	+	1.72654i	0.776486	+	0.0736869i
$550$	3.26332	−	2.73825i	0.139149	−	0.116760i
$551$	4.15606	+	2.73348i	0.177054	+	0.116450i
$552$	−1.16074	−	9.07422i	−0.0494045	−	0.386225i
$553$	−1.01887	−	0.119089i	−0.0433269	−	0.00506419i
$554$	2.10770	+	4.88619i	0.0895475	+	0.207595i
$555$	5.12970	−	22.7428i	0.217744	−	0.965380i
$556$	−18.0600	+	9.07006i	−0.765913	+	0.384656i
$557$	9.35869	+	3.40628i	0.396540	+	0.144329i	0.532590	−	0.846373i	$-0.321219\pi$
$557$	9.35869	+	3.40628i	0.396540	+	0.144329i	−0.136050	+	0.990702i	$0.543441\pi$
$558$	−1.39736	+	0.740249i	−0.0591550	+	0.0313372i
$559$	−7.01317	+	2.55258i	−0.296625	+	0.107963i
$560$	0.462616	−	0.490344i	0.0195491	−	0.0207208i
$561$	18.6119	−	3.49080i	0.785797	−	0.147382i
$562$	−5.07412	+	3.33730i	−0.214039	+	0.140776i
$563$	2.14070	−	7.15042i	0.0902195	−	0.301354i	−0.900956	−	0.433911i	$-0.857133\pi$
$563$	2.14070	−	7.15042i	0.0902195	−	0.301354i	0.991175	+	0.132556i	$0.0423186\pi$
$564$	15.9811	−	1.10522i	0.672927	−	0.0465382i
$565$	−11.5451	−	15.5078i	−0.485708	−	0.652419i
$566$	−2.69056			−0.113093
$567$	3.44542	−	0.149907i	0.144694	−	0.00629548i
$568$	2.17932			0.0914421
$569$	5.25751	+	7.06207i	0.220406	+	0.296057i	0.898549	−	0.438873i	$-0.144622\pi$
$569$	5.25751	+	7.06207i	0.220406	+	0.296057i	−0.678143	+	0.734930i	$0.737215\pi$
$570$	−8.82779	+	18.0646i	−0.369756	+	0.756641i
$571$	7.11022	−	23.7498i	0.297553	−	0.993897i	−0.670239	−	0.742146i	$-0.733808\pi$
$571$	7.11022	−	23.7498i	0.297553	−	0.993897i	0.967792	−	0.251751i	$-0.0810065\pi$
$572$	−10.1217	+	6.65713i	−0.423208	+	0.278349i
$573$	0.506664	+	0.590659i	0.0211662	+	0.0246751i
$574$	−1.23268	+	1.30656i	−0.0514510	+	0.0545349i
$575$	9.45467	−	3.44122i	0.394287	−	0.143509i
$576$	0.922684	+	2.85458i	0.0384452	+	0.118941i
$577$	27.5124	+	10.0137i	1.14536	+	0.416876i	0.843846	−	0.536586i	$-0.180286\pi$
$577$	27.5124	+	10.0137i	1.14536	+	0.416876i	0.301512	+	0.953462i	$0.402509\pi$
$578$	−6.16809	+	3.09773i	−0.256559	+	0.128849i
$579$	−15.7894	−	14.5754i	−0.656185	−	0.605733i
$580$	−0.525316	−	1.21782i	−0.0218126	−	0.0505672i
$581$	−4.10283	−	0.479552i	−0.170214	−	0.0198952i
$582$	22.6665	−	17.2607i	0.939557	−	0.715478i
$583$	−19.0432	−	12.5249i	−0.788687	−	0.518728i
$584$	4.63152	−	3.88631i	0.191654	−	0.160817i
$585$	−23.5412	+	16.2273i	−0.973309	+	0.670914i
$586$	−2.35206	−	1.97361i	−0.0971626	−	0.0815291i
$587$	3.76126	+	12.5635i	0.155244	+	0.518550i	0.999858	−	0.0168245i	$-0.00535567\pi$
$587$	3.76126	+	12.5635i	0.155244	+	0.518550i	−0.844615	+	0.535374i	$0.820170\pi$
$588$	−4.18080	−	11.1094i	−0.172413	−	0.458144i
$589$	3.10810	+	1.56095i	0.128067	+	0.0643177i
$590$	6.03863	+	6.40058i	0.248607	+	0.263508i
$591$	−20.5923	+	9.14940i	−0.847053	+	0.376356i
$592$	−3.03047	+	7.02541i	−0.124551	+	0.288743i
$593$	−9.61201	+	16.6485i	−0.394718	+	0.683672i	−0.993065	−	0.117565i	$-0.962491\pi$
$593$	−9.61201	+	16.6485i	−0.394718	+	0.683672i	0.598347	+	0.801237i	$0.295824\pi$
$594$	11.2344	+	2.96789i	0.460955	+	0.121774i
$595$	1.64791	+	2.85426i	0.0675576	+	0.117013i
$596$	−5.98432	+	0.699467i	−0.245127	+	0.0286513i
$597$	−21.4698	+	20.7014i	−0.878701	+	0.847254i
$598$	−27.8419	+	6.59866i	−1.13854	+	0.269839i
$599$	−0.181027	−	3.10811i	−0.00739655	−	0.126994i	−0.999985	−	0.00546986i	$-0.998259\pi$
$599$	−0.181027	−	3.10811i	−0.00739655	−	0.126994i	0.992588	−	0.121524i	$-0.0387782\pi$
$600$	−2.83935	+	1.68071i	−0.115916	+	0.0686148i
$601$	−25.7693	−	6.10745i	−1.05115	−	0.249128i	−0.331496	−	0.943457i	$-0.607553\pi$
$601$	−25.7693	−	6.10745i	−1.05115	−	0.249128i	−0.719658	+	0.694329i	$0.755701\pi$
$602$	−0.0916676	+	0.519873i	−0.00373609	+	0.0211884i
$603$	−15.1771	+	27.6592i	−0.618059	+	1.12637i
$604$	0.829060	+	4.70183i	0.0337340	+	0.191315i
$605$	−0.613675	+	10.5364i	−0.0249494	+	0.428365i
$606$	11.3702	+	0.538294i	0.461882	+	0.0218667i
$607$	6.42079	−	8.62462i	0.260612	−	0.350063i	−0.652488	−	0.757799i	$-0.726275\pi$
$607$	6.42079	−	8.62462i	0.260612	−	0.350063i	0.913099	+	0.407737i	$0.133682\pi$
$608$	3.94027	−	5.29270i	0.159799	−	0.214647i
$609$	0.499794	+	0.0236615i	0.0202527	+	0.000958813i
$610$	−0.623145	+	10.6990i	−0.0252304	+	0.433189i
$611$	−8.70054	−	49.3432i	−0.351986	−	1.99621i
$612$	−14.6635	+	0.318846i	−0.592738	+	0.0128886i
$613$	−2.43335	+	13.8002i	−0.0982822	+	0.557386i	0.895410	+	0.445243i	$0.146883\pi$
$613$	−2.43335	+	13.8002i	−0.0982822	+	0.557386i	−0.993692	+	0.112143i	$0.964228\pi$
$614$	3.19860	+	0.758082i	0.129085	+	0.0305937i
$615$	−12.2921	+	7.27614i	−0.495665	+	0.293402i
$616$	0.0498242	+	0.855449i	0.00200748	+	0.0344670i
$617$	−16.4465	+	3.89790i	−0.662113	+	0.156924i	−0.547915	−	0.836534i	$-0.684578\pi$
$617$	−16.4465	+	3.89790i	−0.662113	+	0.156924i	−0.114198	+	0.993458i	$0.536430\pi$
$618$	−14.9519	+	14.4168i	−0.601455	+	0.579930i
$619$	−40.3326	+	4.71421i	−1.62111	+	0.189480i	−0.877649	−	0.479304i	$-0.840889\pi$
$619$	−40.3326	+	4.71421i	−1.62111	+	0.189480i	−0.743457	+	0.668784i	$0.766815\pi$
$620$	−0.463663	−	0.803088i	−0.0186211	−	0.0322528i
$621$	22.5365	+	15.6622i	0.904359	+	0.628503i
$622$	−3.00580	+	5.20619i	−0.120521	+	0.208749i
$623$	−1.52393	+	3.53287i	−0.0610549	+	0.141541i
$624$	8.57495	−	3.80996i	0.343273	−	0.152520i
$625$	8.12940	+	8.61666i	0.325176	+	0.344666i
$626$	−18.5765	−	9.32948i	−0.742468	−	0.372881i
$627$	−9.00167	−	23.9196i	−0.359492	−	0.955257i
$628$	−3.33664	−	11.1452i	−0.133146	−	0.444740i
$629$	−28.6550	−	24.0444i	−1.14255	−	0.958713i
$630$	0.161454	+	2.01593i	0.00643248	+	0.0803167i
$631$	1.34586	−	1.12931i	0.0535779	−	0.0449572i	−0.615606	−	0.788054i	$-0.711089\pi$
$631$	1.34586	−	1.12931i	0.0535779	−	0.0449572i	0.669183	+	0.743097i	$0.266644\pi$
$632$	2.23664	+	1.47106i	0.0889687	+	0.0585157i
$633$	−0.407896	+	0.310615i	−0.0162124	+	0.0123459i
$634$	23.0496	+	2.69411i	0.915416	+	0.106997i
$635$	−12.6546	−	29.3367i	−0.502183	−	1.16419i
$636$	12.9719	+	11.9745i	0.514370	+	0.474821i
$637$	−33.1775	+	16.6624i	−1.31454	+	0.660187i
$638$	1.58420	+	0.576602i	0.0627191	+	0.0228279i
$639$	−4.38217	+	4.85194i	−0.173356	+	0.191940i
$640$	−1.65317	+	0.601706i	−0.0653474	+	0.0237845i
$641$	−5.16941	+	5.47925i	−0.204179	+	0.216417i	−0.821369	−	0.570397i	$-0.806789\pi$
$641$	−5.16941	+	5.47925i	−0.204179	+	0.216417i	0.617190	+	0.786814i	$0.288271\pi$
$642$	10.9986	+	12.8220i	0.434081	+	0.506043i
$643$	8.58186	−	5.64438i	0.338436	−	0.222593i	−0.368902	−	0.929468i	$-0.620266\pi$
$643$	8.58186	−	5.64438i	0.338436	−	0.222593i	0.707338	+	0.706876i	$0.249896\pi$
$644$	−0.580454	+	1.93885i	−0.0228731	+	0.0764014i
$645$	−1.84311	+	3.77161i	−0.0725723	+	0.148507i
$646$	19.2640	+	25.8760i	0.757930	+	1.01808i
$647$	13.1563			0.517226			0.258613	−	0.965981i	$-0.416735\pi$
$647$	13.1563			0.517226			0.258613	+	0.965981i	$0.416735\pi$
$648$	−8.21067	−	3.68578i	−0.322545	−	0.144791i
$649$	−11.1853			−0.439062
$650$	6.16269	+	8.27793i	0.241721	+	0.324687i
$651$	0.349008	−	0.0241366i	0.0136787	−	0.000945990i
$652$	−0.0300313	+	0.100312i	−0.00117612	+	0.00392850i
$653$	−18.7286	+	12.3180i	−0.732908	+	0.482041i	−0.860285	−	0.509813i	$-0.829714\pi$
$653$	−18.7286	+	12.3180i	−0.732908	+	0.482041i	0.127377	+	0.991854i	$0.459344\pi$
$654$	25.0831	−	4.70452i	0.980828	−	0.183961i
$655$	−23.7604	+	25.1846i	−0.928396	+	0.984042i
$656$	4.40502	−	1.60330i	0.171987	−	0.0625982i
$657$	−0.660748	+	18.1260i	−0.0257783	+	0.707163i
$658$	−3.33027	−	1.21212i	−0.129827	−	0.0472533i
$659$	−7.92174	+	3.97845i	−0.308587	+	0.154978i	−0.596353	−	0.802723i	$-0.703384\pi$
$659$	−7.92174	+	3.97845i	−0.308587	+	0.154978i	0.287765	+	0.957701i	$0.407088\pi$
$660$	−1.49929	+	6.64717i	−0.0583596	+	0.258741i
$661$	−15.3980	−	35.6966i	−0.598913	−	1.38844i	−0.900441	−	0.434979i	$-0.856756\pi$
$661$	−15.3980	−	35.6966i	−0.598913	−	1.38844i	0.301528	−	0.953457i	$-0.402503\pi$
$662$	−12.0751	−	1.41138i	−0.469312	−	0.0548547i
$663$	5.82071	+	45.5039i	0.226058	+	1.76723i
$664$	9.00658	+	5.92372i	0.349523	+	0.229885i
$665$	3.40748	−	2.85922i	0.132136	−	0.110876i
$666$	−9.54743	−	20.8736i	−0.369955	−	0.808836i
$667$	3.05023	+	2.55945i	0.118105	+	0.0991022i
$668$	4.44908	+	14.8610i	0.172140	+	0.574988i
$669$	19.1012	−	23.2731i	0.738496	−	0.899790i
$670$	−16.5335	−	8.30343i	−0.638744	−	0.320789i
$671$	−9.34848	−	9.90881i	−0.360894	−	0.382526i
$672$	0.0698805	−	0.660010i	0.00269570	−	0.0254604i
$673$	−1.87337	+	4.34296i	−0.0722132	+	0.167409i	−0.950499	−	0.310726i	$-0.899428\pi$
$673$	−1.87337	+	4.34296i	−0.0722132	+	0.167409i	0.878286	+	0.478135i	$0.158687\pi$
$674$	10.2604	−	17.7715i	0.395214	−	0.684531i
$675$	1.96749	−	9.70099i	0.0757288	−	0.373391i
$676$	−8.17427	−	14.1582i	−0.314395	−	0.544548i
$677$	22.7389	−	2.65780i	0.873927	−	0.102147i	0.332709	−	0.943030i	$-0.392037\pi$
$677$	22.7389	−	2.65780i	0.873927	−	0.102147i	0.541218	+	0.840882i	$0.317963\pi$
$678$	−18.2930	−	5.26057i	−0.702537	−	0.202031i
$679$	−6.13311	+	1.45357i	−0.235367	+	0.0557831i
$680$	−0.500107	−	8.58651i	−0.0191782	−	0.329278i
$681$	0.102018	+	9.38459i	0.00390934	+	0.359618i
$682$	1.14697	+	0.271836i	0.0439197	+	0.0104092i
$683$	4.07429	−	23.1064i	0.155898	−	0.884143i	−0.802062	−	0.597241i	$-0.796263\pi$
$683$	4.07429	−	23.1064i	0.155898	−	0.884143i	0.957960	−	0.286902i	$-0.0926254\pi$
$684$	3.86036	+	19.4150i	0.147604	+	0.742352i
$685$	−4.21798	−	23.9213i	−0.161161	−	0.913987i
$686$	−0.308653	+	5.29937i	−0.0117844	+	0.202331i
$687$	−21.5854	−	41.8398i	−0.823536	−	1.59629i
$688$	0.822668	−	1.10504i	0.0313639	−	0.0421291i
$689$	32.9733	−	44.2909i	1.25618	−	1.68735i
$690$	−8.69716	+	13.5418i	−0.331095	+	0.515526i
$691$	−0.765437	+	13.1420i	−0.0291186	+	0.499947i	0.951946	+	0.306266i	$0.0990797\pi$
$691$	−0.765437	+	13.1420i	−0.0291186	+	0.499947i	−0.981065	+	0.193681i	$0.937957\pi$
$692$	3.02078	+	17.1317i	0.114833	+	0.651250i
$693$	−2.00472	−	1.60921i	−0.0761532	−	0.0611289i
$694$	3.22391	−	18.2837i	0.122378	−	0.694040i
$695$	34.5958	+	8.19936i	1.31229	+	0.311019i
$696$	−1.13786	−	0.640553i	−0.0431304	−	0.0242801i
$697$	1.33258	+	22.8795i	0.0504750	+	0.866622i
$698$	5.90381	−	1.39923i	0.223463	−	0.0529616i
$699$	−7.38159	−	29.7027i	−0.279197	−	1.12346i
$700$	0.725023	−	0.0847430i	0.0274033	−	0.00320298i
$701$	−3.37930	−	5.85313i	−0.127635	−	0.221070i	0.795125	−	0.606445i	$-0.207405\pi$
$701$	−3.37930	−	5.85313i	−0.127635	−	0.221070i	−0.922760	+	0.385376i	$0.874072\pi$
$702$	−8.76019	+	26.7520i	−0.330632	+	1.00969i
$703$	−25.2425	+	43.7214i	−0.952040	+	1.64898i
$704$	0.885730	−	2.05335i	0.0333822	−	0.0773887i
$705$	−22.7873	−	16.5826i	−0.858218	−	0.624536i
$706$	13.3304	+	14.1294i	0.501698	+	0.531769i
$707$	−2.25042	−	1.13020i	−0.0846356	−	0.0425056i
$708$	8.54766	+	1.41156i	0.321241	+	0.0530496i
$709$	−0.857216	−	2.86330i	−0.0321934	−	0.107534i	0.940383	−	0.340118i	$-0.110467\pi$
$709$	−0.857216	−	2.86330i	−0.0321934	−	0.107534i	−0.972576	+	0.232584i	$0.925282\pi$
$710$	−2.93702	−	2.46445i	−0.110224	−	0.0924892i
$711$	−7.77255	+	2.02155i	−0.291493	+	0.0758142i
$712$	7.69176	−	6.45415i	0.288261	−	0.241880i
$713$	2.32602	+	1.52985i	0.0871100	+	0.0572932i
$714$	2.99324	+	1.25275i	0.112019	+	0.0468828i
$715$	21.1689	+	2.47429i	0.791672	+	0.0925332i
$716$	−7.92069	−	18.3622i	−0.296010	−	0.686229i
$717$	−12.4575	+	3.87756i	−0.465233	+	0.144810i
$718$	14.2227	−	7.14289i	0.530785	−	0.266570i
$719$	26.2448	+	9.55231i	0.978764	+	0.356241i	0.781360	−	0.624081i	$-0.214526\pi$
$719$	26.2448	+	9.55231i	0.978764	+	0.356241i	0.197405	+	0.980322i	$0.436749\pi$
$720$	1.98459	−	4.89047i	0.0739613	−	0.182257i
$721$	4.31796	−	1.57161i	0.160809	−	0.0585298i
$722$	16.8393	−	17.8486i	0.626693	−	0.664256i
$723$	−8.03288	+	22.8397i	−0.298746	+	0.849416i
$724$	11.3079	−	7.43732i	0.420254	−	0.276406i
$725$	0.411886	−	1.37579i	0.0152971	−	0.0510957i
$726$	5.80395	+	8.61893i	0.215405	+	0.319879i
$727$	−22.3844	−	30.0675i	−0.830192	−	1.11514i	−0.991738	−	0.128276i	$-0.959056\pi$
$727$	−22.3844	−	30.0675i	−0.830192	−	1.11514i	0.161546	−	0.986865i	$-0.448352\pi$
$728$	−2.07589			−0.0769375
$729$	24.7159	−	10.8685i	0.915403	−	0.402538i
$730$	−10.6366			−0.393678
$731$	4.02202	+	5.40251i	0.148760	+	0.199819i
$732$	5.89352	+	8.75193i	0.217831	+	0.323481i
$733$	7.42724	−	24.8087i	0.274331	−	0.916330i	−0.704160	−	0.710041i	$-0.748676\pi$
$733$	7.42724	−	24.8087i	0.274331	−	0.916330i	0.978491	−	0.206289i	$-0.0661386\pi$
$734$	−17.5560	+	11.5468i	−0.648003	+	0.426198i
$735$	−6.92854	+	19.6997i	−0.255563	+	0.726635i
$736$	3.62452	−	3.84176i	0.133601	−	0.141609i
$737$	22.0992	−	8.04347i	0.814036	−	0.296285i
$738$	−5.28810	+	13.0311i	−0.194658	+	0.479680i
$739$	25.7324	+	9.36582i	0.946581	+	0.344527i	0.768761	−	0.639536i	$-0.220873\pi$
$739$	25.7324	+	9.36582i	0.946581	+	0.344527i	0.177820	+	0.984063i	$0.443096\pi$
$740$	12.0287	−	6.04104i	0.442184	−	0.222073i
$741$	59.1166	−	18.4009i	2.17170	−	0.675973i
$742$	−1.54694	−	3.58621i	−0.0567899	−	0.131654i
$743$	−32.5489	−	3.80443i	−1.19410	−	0.139571i	−0.504275	−	0.863543i	$-0.668240\pi$
$743$	−32.5489	−	3.80443i	−1.19410	−	0.139571i	−0.689829	+	0.723972i	$0.742314\pi$
$744$	−0.842192	−	0.352478i	−0.0308763	−	0.0129225i
$745$	8.85593	+	5.82464i	0.324456	+	0.213398i
$746$	19.8008	−	16.6149i	0.724960	−	0.608314i
$747$	−31.2988	+	8.14046i	−1.14516	+	0.297844i
$748$	8.37515	+	7.02758i	0.306226	+	0.256954i
$749$	−1.07187	−	3.58028i	−0.0391651	−	0.130821i
$750$	20.7593	+	3.42818i	0.758022	+	0.125179i
$751$	−8.25021	−	4.14341i	−0.301054	−	0.151195i	0.291859	−	0.956461i	$-0.405726\pi$
$751$	−8.25021	−	4.14341i	−0.301054	−	0.151195i	−0.592914	+	0.805266i	$0.702022\pi$
$752$	6.34687	+	6.72729i	0.231447	+	0.245319i
$753$	40.0232	+	29.1253i	1.45852	+	1.06139i
$754$	−1.61764	+	3.75011i	−0.0589109	+	0.136571i
$755$	4.19970	−	7.27410i	0.152843	−	0.264731i
$756$	1.32890	+	1.48273i	0.0483318	+	0.0539263i
$757$	−16.0190	−	27.7457i	−0.582220	−	1.00843i	−0.995216	−	0.0977011i	$-0.968851\pi$
$757$	−16.0190	−	27.7457i	−0.582220	−	1.00843i	0.412996	−	0.910733i	$-0.364482\pi$
$758$	33.0522	−	3.86324i	1.20051	−	0.140319i
$759$	−4.93393	−	19.8536i	−0.179090	−	0.720640i
$760$	−11.2954	+	2.67706i	−0.409727	+	0.0971072i
$761$	−0.939963	−	16.1385i	−0.0340736	−	0.585022i	−0.971530	−	0.236918i	$-0.923863\pi$
$761$	−0.939963	−	16.1385i	−0.0340736	−	0.585022i	0.937456	−	0.348104i	$-0.113174\pi$
$762$	−27.4105	−	15.4306i	−0.992977	−	0.558993i
$763$	−5.49379	−	1.30205i	−0.198889	−	0.0471375i
$764$	−0.0780186	+	0.442465i	−0.00282261	+	0.0160078i
$765$	20.1223	+	16.1524i	0.727523	+	0.583989i
$766$	2.32728	+	13.1986i	0.0840880	+	0.476887i
$767$	1.57555	−	27.0512i

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.597159 - 0.802123i) q^{2} +(0.967452 + 1.43668i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(1.46985 - 0.966735i) q^{5} +(0.574669 - 1.63394i) q^{6} +(-0.262959 + 0.278720i) q^{7} +(0.939693 - 0.342020i) q^{8} +(-1.12808 + 2.77983i) q^{9} +O(q^{10})\)	\(q+(-0.597159 - 0.802123i) q^{2} +(0.967452 + 1.43668i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(1.46985 - 0.966735i) q^{5} +(0.574669 - 1.63394i) q^{6} +(-0.262959 + 0.278720i) q^{7} +(0.939693 - 0.342020i) q^{8} +(-1.12808 + 2.77983i) q^{9} +(-1.65317 - 0.601706i) q^{10} +(1.99838 - 1.00362i) q^{11} +(-1.65379 + 0.514765i) q^{12} +(2.14573 + 4.97437i) q^{13} +(0.380596 + 0.0444853i) q^{14} +(2.81089 + 1.17643i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(3.74519 - 3.14258i) q^{17} +(2.90340 - 0.755143i) q^{18} +(-5.05464 - 4.24135i) q^{19} +(0.504565 + 1.68536i) q^{20} +(-0.654830 - 0.108138i) q^{21} +(-1.99838 - 1.00362i) q^{22} +(-3.62452 - 3.84176i) q^{23} +(1.40048 + 1.01915i) q^{24} +(-0.754519 + 1.74917i) q^{25} +(2.70871 - 4.69163i) q^{26} +(-5.08507 + 1.06867i) q^{27} +(-0.191593 - 0.331850i) q^{28} +(-0.748788 + 0.0875208i) q^{29} +(-0.734909 - 2.95720i) q^{30} +(-0.512900 + 0.121559i) q^{31} +(0.0581448 + 0.998308i) q^{32} +(3.37522 + 1.90007i) q^{33} +(-4.75721 - 1.12748i) q^{34} +(-0.117061 + 0.663888i) q^{35} +(-2.33951 - 1.87795i) q^{36} +(-1.32861 - 7.53491i) q^{37} +(-0.383661 + 6.58720i) q^{38} +(-5.07066 + 7.89519i) q^{39} +(1.05056 - 1.41115i) q^{40} +(-2.79931 + 3.76013i) q^{41} +(0.304297 + 0.589830i) q^{42} +(-0.0801025 + 1.37531i) q^{43} +(0.388319 + 2.20227i) q^{44} +(1.02926 + 5.17648i) q^{45} +(-0.917156 + 5.20145i) q^{46} +(-8.99944 - 2.13291i) q^{47} +(-0.0188277 - 1.73195i) q^{48} +(0.398476 + 6.84157i) q^{49} +(1.85362 - 0.439316i) q^{50} +(8.13816 + 2.34032i) q^{51} +(-5.38080 + 0.628925i) q^{52} +(-5.09624 - 8.82695i) q^{53} +(3.89380 + 3.44069i) q^{54} +(1.96708 - 3.40708i) q^{55} +(-0.151773 + 0.351848i) q^{56} +(1.20332 - 11.3652i) q^{57} +(0.517348 + 0.548357i) q^{58} +(-4.46980 - 2.24482i) q^{59} +(-1.93318 + 2.35540i) q^{60} +(-1.74715 - 5.83587i) q^{61} +(0.403788 + 0.338819i) q^{62} +(-0.478157 - 1.04540i) q^{63} +(0.766044 - 0.642788i) q^{64} +(7.96280 + 5.23722i) q^{65} +(-0.491453 - 3.84198i) q^{66} +(10.4454 + 1.22090i) q^{67} +(1.93643 + 4.48915i) q^{68} +(2.01282 - 8.92398i) q^{69} +(0.602424 - 0.302549i) q^{70} +(2.04789 + 0.745370i) q^{71} +(-0.109287 + 2.99801i) q^{72} +(5.68140 - 2.06786i) q^{73} +(-5.25054 + 5.56525i) q^{74} +(-3.24295 + 0.608239i) q^{75} +(5.51285 - 3.62586i) q^{76} +(-0.245761 + 0.820900i) q^{77} +(9.36090 - 0.647381i) q^{78} +(1.59862 + 2.14732i) q^{79} -1.75927 q^{80} +(-6.45489 - 6.27171i) q^{81} +4.68772 q^{82} +(6.43738 + 8.64690i) q^{83} +(0.291403 - 0.596306i) q^{84} +(2.46681 - 8.23973i) q^{85} +(1.15100 - 0.757024i) q^{86} +(-0.850155 - 0.991094i) q^{87} +(1.53460 - 1.62658i) q^{88} +(9.43534 - 3.43418i) q^{89} +(3.53754 - 3.91677i) q^{90} +(-1.95070 - 0.709995i) q^{91} +(4.71989 - 2.37042i) q^{92} +(-0.670847 - 0.619268i) q^{93} +(3.66324 + 8.49235i) q^{94} +(-11.5298 - 1.34764i) q^{95} +(-1.37799 + 1.04935i) q^{96} +(13.7429 + 9.03883i) q^{97} +(5.24983 - 4.40513i) q^{98} +(0.535580 + 6.68732i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

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