LMFDB - Embedded newform 162.2.g.b.13.1

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:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	162.13
Dual form			162.2.g.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.893633 + 0.448799i) q^{2} +(-1.57770 - 0.714739i) q^{3} +(0.597159 + 0.802123i) q^{4} +(0.891212 + 2.97686i) q^{5} +(-1.08911 - 1.34679i) q^{6} +(0.275210 + 0.638009i) q^{7} +(0.173648 + 0.984808i) q^{8} +(1.97830 + 2.25529i) q^{9} +(-0.539594 + 3.06019i) q^{10} +(5.37847 - 1.27472i) q^{11} +(-0.368831 - 1.69232i) q^{12} +(-2.73022 - 1.79570i) q^{13} +(-0.0404011 + 0.693660i) q^{14} +(0.721605 - 5.33358i) q^{15} +(-0.286803 + 0.957990i) q^{16} +(-4.35745 + 1.58598i) q^{17} +(0.755699 + 2.90326i) q^{18} +(-2.23534 - 0.813599i) q^{19} +(-1.85561 + 2.49252i) q^{20} +(0.0218094 - 1.20329i) q^{21} +(5.37847 + 1.27472i) q^{22} +(2.79341 - 6.47585i) q^{23} +(0.429915 - 1.67785i) q^{24} +(-3.88998 + 2.55848i) q^{25} +(-1.63391 - 2.83001i) q^{26} +(-1.50922 - 4.97215i) q^{27} +(-0.347418 + 0.601745i) q^{28} +(0.0802101 + 1.37715i) q^{29} +(3.03856 - 4.44241i) q^{30} +(-3.53161 + 0.412786i) q^{31} +(-0.686242 + 0.727374i) q^{32} +(-9.39673 - 1.83307i) q^{33} +(-4.60574 - 0.538334i) q^{34} +(-1.65399 + 1.38786i) q^{35} +(-0.627664 + 2.93360i) q^{36} +(-0.935772 - 0.785206i) q^{37} +(-1.63243 - 1.73028i) q^{38} +(3.02403 + 4.78447i) q^{39} +(-2.77687 + 1.39460i) q^{40} +(10.1420 - 5.09352i) q^{41} +(0.559527 - 1.06551i) q^{42} +(-6.37841 - 6.76072i) q^{43} +(4.23428 + 3.55299i) q^{44} +(-4.95059 + 7.89905i) q^{45} +(5.40264 - 4.53335i) q^{46} +(10.4074 + 1.21645i) q^{47} +(1.13720 - 1.30643i) q^{48} +(4.47238 - 4.74044i) q^{49} +(-4.62445 + 0.540521i) q^{50} +(8.00832 + 0.612227i) q^{51} +(-0.190007 - 3.26229i) q^{52} +(-2.11764 + 3.66786i) q^{53} +(0.882803 - 5.12061i) q^{54} +(8.58802 + 14.8749i) q^{55} +(-0.580527 + 0.381818i) q^{56} +(2.94520 + 2.88130i) q^{57} +(-0.546388 + 1.26667i) q^{58} +(-5.60397 - 1.32817i) q^{59} +(4.70910 - 2.60618i) q^{60} +(1.03387 - 1.38873i) q^{61} +(-3.34122 - 1.21611i) q^{62} +(-0.894449 + 1.88285i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(2.91232 - 9.72783i) q^{65} +(-7.57454 - 5.85533i) q^{66} +(-0.0594932 + 1.02146i) q^{67} +(-3.87424 - 2.54813i) q^{68} +(-9.03571 + 8.22041i) q^{69} +(-2.10093 + 0.497930i) q^{70} +(-2.04677 + 11.6078i) q^{71} +(-1.87750 + 2.33987i) q^{72} +(1.49312 + 8.46788i) q^{73} +(-0.483836 - 1.12166i) q^{74} +(7.96587 - 1.25620i) q^{75} +(-0.682248 - 2.27887i) q^{76} +(2.29349 + 3.08070i) q^{77} +(0.555105 + 5.63274i) q^{78} +(-7.86088 - 3.94788i) q^{79} -3.10740 q^{80} +(-1.17268 + 8.92327i) q^{81} +11.3492 q^{82} +(-8.11371 - 4.07486i) q^{83} +(0.978213 - 0.701063i) q^{84} +(-8.60465 - 11.5580i) q^{85} +(-2.66575 - 8.90423i) q^{86} +(0.857758 - 2.23007i) q^{87} +(2.18932 + 5.07541i) q^{88} +(-0.642803 - 3.64552i) q^{89} +(-7.96910 + 4.83703i) q^{90} +(0.394285 - 2.23610i) q^{91} +(6.86253 - 1.62645i) q^{92} +(5.86687 + 1.87293i) q^{93} +(8.75447 + 5.75790i) q^{94} +(0.429800 - 7.37939i) q^{95} +(1.60257 - 0.657097i) q^{96} +(0.260981 - 0.871736i) q^{97} +(6.12417 - 2.22901i) q^{98} +(13.5151 + 9.60824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38}+ \cdots - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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 $

$2$	0.893633	+	0.448799i	0.631894	+	0.317349i
$2$	0.893633	+	0.448799i	0.631894	+	0.317349i
$3$	−1.57770	−	0.714739i	−0.910888	−	0.412654i
$3$	−1.57770	−	0.714739i	−0.910888	−	0.412654i
$4$	0.597159	+	0.802123i	0.298579	+	0.401062i
$5$	0.891212	+	2.97686i	0.398562	+	1.33129i	0.888237	+	0.459385i	$0.151930\pi$
$5$	0.891212	+	2.97686i	0.398562	+	1.33129i	−0.489675	+	0.871905i	$0.662884\pi$
$6$	−1.08911	−	1.34679i	−0.444629	−	0.549823i
$7$	0.275210	+	0.638009i	0.104020	+	0.241145i	0.962275	−	0.272078i	$-0.0877108\pi$
$7$	0.275210	+	0.638009i	0.104020	+	0.241145i	−0.858256	+	0.513223i	$0.828452\pi$
$8$	0.173648	+	0.984808i	0.0613939	+	0.348182i
$9$	1.97830	+	2.25529i	0.659433	+	0.751764i
$10$	−0.539594	+	3.06019i	−0.170635	+	0.967717i
$11$	5.37847	−	1.27472i	1.62167	−	0.384343i	0.683345	−	0.730096i	$-0.260525\pi$
$11$	5.37847	−	1.27472i	1.62167	−	0.384343i	0.938325	+	0.345753i	$0.112377\pi$
$12$	−0.368831	−	1.69232i	−0.106472	−	0.488532i
$13$	−2.73022	−	1.79570i	−0.757227	−	0.498036i	0.111233	−	0.993794i	$-0.464520\pi$
$13$	−2.73022	−	1.79570i	−0.757227	−	0.498036i	−0.868461	+	0.495758i	$0.834890\pi$
$14$	−0.0404011	+	0.693660i	−0.0107976	+	0.185388i
$15$	0.721605	−	5.33358i	0.186318	−	1.37712i
$16$	−0.286803	+	0.957990i	−0.0717008	+	0.239497i
$17$	−4.35745	+	1.58598i	−1.05684	+	0.384657i	−0.811239	−	0.584715i	$-0.801206\pi$
$17$	−4.35745	+	1.58598i	−1.05684	+	0.384657i	−0.245597	+	0.969372i	$0.578984\pi$
$18$	0.755699	+	2.90326i	0.178120	+	0.684305i
$19$	−2.23534	−	0.813599i	−0.512823	−	0.186652i	0.0726295	−	0.997359i	$-0.476861\pi$
$19$	−2.23534	−	0.813599i	−0.512823	−	0.186652i	−0.585453	+	0.810707i	$0.699083\pi$
$20$	−1.85561	+	2.49252i	−0.414927	+	0.557344i
$21$	0.0218094	−	1.20329i	0.00475921	−	0.262580i
$22$	5.37847	+	1.27472i	1.14669	+	0.271771i
$23$	2.79341	−	6.47585i	0.582466	−	1.35031i	−0.331092	−	0.943598i	$-0.607417\pi$
$23$	2.79341	−	6.47585i	0.582466	−	1.35031i	0.913558	−	0.406709i	$-0.133324\pi$
$24$	0.429915	−	1.67785i	0.0877560	−	0.342489i
$25$	−3.88998	+	2.55848i	−0.777995	+	0.511695i
$26$	−1.63391	−	2.83001i	−0.320436	−	0.555011i
$27$	−1.50922	−	4.97215i	−0.290450	−	0.956890i
$28$	−0.347418	+	0.601745i	−0.0656558	+	0.113719i
$29$	0.0802101	+	1.37715i	0.0148946	+	0.255731i	0.997533	+	0.0701997i	$0.0223637\pi$
$29$	0.0802101	+	1.37715i	0.0148946	+	0.255731i	−0.982638	+	0.185532i	$0.940599\pi$
$30$	3.03856	−	4.44241i	0.554762	−	0.811069i
$31$	−3.53161	+	0.412786i	−0.634296	+	0.0741386i	−0.427164	−	0.904174i	$-0.640487\pi$
$31$	−3.53161	+	0.412786i	−0.634296	+	0.0741386i	−0.207133	+	0.978313i	$0.566413\pi$
$32$	−0.686242	+	0.727374i	−0.121312	+	0.128583i
$33$	−9.39673	−	1.83307i	−1.63576	−	0.319096i
$34$	−4.60574	−	0.538334i	−0.789879	−	0.0923236i
$35$	−1.65399	+	1.38786i	−0.279576	+	0.234592i
$36$	−0.627664	+	2.93360i	−0.104611	+	0.488934i
$37$	−0.935772	−	0.785206i	−0.153840	−	0.129087i	0.562619	−	0.826716i	$-0.309794\pi$
$37$	−0.935772	−	0.785206i	−0.153840	−	0.129087i	−0.716459	+	0.697629i	$0.754238\pi$
$38$	−1.63243	−	1.73028i	−0.264816	−	0.280688i
$39$	3.02403	+	4.78447i	0.484232	+	0.766128i
$40$	−2.77687	+	1.39460i	−0.439062	+	0.220505i
$41$	10.1420	−	5.09352i	1.58392	−	0.795474i	0.584052	−	0.811716i	$-0.301466\pi$
$41$	10.1420	−	5.09352i	1.58392	−	0.795474i	0.999868	+	0.0162419i	$0.00517017\pi$
$42$	0.559527	−	1.06551i	0.0863368	−	0.164412i
$43$	−6.37841	−	6.76072i	−0.972699	−	1.03100i	−0.999508	−	0.0313600i	$-0.990016\pi$
$43$	−6.37841	−	6.76072i	−0.972699	−	1.03100i	0.0268093	−	0.999641i	$-0.491465\pi$
$44$	4.23428	+	3.55299i	0.638342	+	0.535633i
$45$	−4.95059	+	7.89905i	−0.737991	+	1.17752i
$46$	5.40264	−	4.53335i	0.796575	−	0.668406i
$47$	10.4074	+	1.21645i	1.51808	+	0.177438i	0.833916	−	0.551892i	$-0.186094\pi$
$47$	10.4074	+	1.21645i	1.51808	+	0.177438i	0.684162	+	0.729330i	$0.260168\pi$
$48$	1.13720	−	1.30643i	0.164141	−	0.188568i
$49$	4.47238	−	4.74044i	0.638911	−	0.677206i
$50$	−4.62445	+	0.540521i	−0.653996	+	0.0764412i
$51$	8.00832	+	0.612227i	1.12139	+	0.0857289i
$52$	−0.190007	−	3.26229i	−0.0263492	−	0.452398i
$53$	−2.11764	+	3.66786i	−0.290880	+	0.503819i	−0.974018	−	0.226470i	$-0.927281\pi$
$53$	−2.11764	+	3.66786i	−0.290880	+	0.503819i	0.683138	+	0.730289i	$0.260615\pi$
$54$	0.882803	−	5.12061i	0.120134	−	0.696827i
$55$	8.58802	+	14.8749i	1.15801	+	2.00573i
$56$	−0.580527	+	0.381818i	−0.0775762	+	0.0510226i
$57$	2.94520	+	2.88130i	0.390101	+	0.381638i
$58$	−0.546388	+	1.26667i	−0.0717442	+	0.166322i
$59$	−5.60397	−	1.32817i	−0.729575	−	0.172913i	−0.150991	−	0.988535i	$-0.548246\pi$
$59$	−5.60397	−	1.32817i	−0.729575	−	0.172913i	−0.578584	+	0.815623i	$0.696395\pi$
$60$	4.70910	−	2.60618i	0.607942	−	0.336456i
$61$	1.03387	−	1.38873i	0.132374	−	0.177809i	−0.730994	−	0.682384i	$-0.760943\pi$
$61$	1.03387	−	1.38873i	0.132374	−	0.177809i	0.863368	+	0.504575i	$0.168351\pi$
$62$	−3.34122	−	1.21611i	−0.424336	−	0.154446i
$63$	−0.894449	+	1.88285i	−0.112690	+	0.237217i
$64$	−0.939693	+	0.342020i	−0.117462	+	0.0427525i
$65$	2.91232	−	9.72783i	0.361229	−	1.20659i
$66$	−7.57454	−	5.85533i	−0.932362	−	0.720742i
$67$	−0.0594932	+	1.02146i	−0.00726825	+	0.124791i	0.992722	+	0.120427i	$0.0384263\pi$
$67$	−0.0594932	+	1.02146i	−0.00726825	+	0.124791i	−0.999990	+	0.00436439i	$0.998611\pi$
$68$	−3.87424	−	2.54813i	−0.469821	−	0.309006i
$69$	−9.03571	+	8.22041i	−1.08777	+	0.989621i
$70$	−2.10093	+	0.497930i	−0.251109	+	0.0595140i
$71$	−2.04677	+	11.6078i	−0.242907	+	1.37759i	0.582397	+	0.812904i	$0.302115\pi$
$71$	−2.04677	+	11.6078i	−0.242907	+	1.37759i	−0.825304	+	0.564688i	$0.808996\pi$
$72$	−1.87750	+	2.33987i	−0.221266	+	0.275756i
$73$	1.49312	+	8.46788i	0.174756	+	0.991090i	0.938425	+	0.345482i	$0.112285\pi$
$73$	1.49312	+	8.46788i	0.174756	+	0.991090i	−0.763669	+	0.645608i	$0.776604\pi$
$74$	−0.483836	−	1.12166i	−0.0562448	−	0.130390i
$75$	7.96587	−	1.25620i	0.919819	−	0.145054i
$76$	−0.682248	−	2.27887i	−0.0782593	−	0.261404i
$77$	2.29349	+	3.08070i	0.261368	+	0.351078i
$78$	0.555105	+	5.63274i	0.0628532	+	0.637782i
$79$	−7.86088	−	3.94788i	−0.884418	−	0.444171i	−0.0522107	−	0.998636i	$-0.516627\pi$
$79$	−7.86088	−	3.94788i	−0.884418	−	0.444171i	−0.832207	+	0.554465i	$0.812923\pi$
$80$	−3.10740			−0.347418
$81$	−1.17268	+	8.92327i	−0.130297	+	0.991475i
$82$	11.3492			1.25331
$83$	−8.11371	−	4.07486i	−0.890596	−	0.447274i	−0.0561870	−	0.998420i	$-0.517894\pi$
$83$	−8.11371	−	4.07486i	−0.890596	−	0.447274i	−0.834409	+	0.551146i	$0.814191\pi$
$84$	0.978213	−	0.701063i	0.106732	−	0.0764922i
$85$	−8.60465	−	11.5580i	−0.933305	−	1.25365i
$86$	−2.66575	−	8.90423i	−0.287455	−	0.960168i
$87$	0.857758	−	2.23007i	0.0919613	−	0.239089i
$88$	2.18932	+	5.07541i	0.233382	+	0.541040i
$89$	−0.642803	−	3.64552i	−0.0681370	−	0.386424i	−0.999737	−	0.0229387i	$-0.992698\pi$
$89$	−0.642803	−	3.64552i	−0.0681370	−	0.386424i	0.931600	−	0.363485i	$-0.118413\pi$
$90$	−7.96910	+	4.83703i	−0.840017	+	0.509867i
$91$	0.394285	−	2.23610i	0.0413323	−	0.234407i
$92$	6.86253	−	1.62645i	0.715469	−	0.169569i
$93$	5.86687	+	1.87293i	0.608366	+	0.194213i
$94$	8.75447	+	5.75790i	0.902954	+	0.593882i
$95$	0.429800	−	7.37939i	0.0440966	−	0.757109i
$96$	1.60257	−	0.657097i	0.163561	−	0.0670647i
$97$	0.260981	−	0.871736i	0.0264986	−	0.0885113i	−0.943717	−	0.330753i	$-0.892697\pi$
$97$	0.260981	−	0.871736i	0.0264986	−	0.0885113i	0.970216	+	0.242241i	$0.0778826\pi$
$98$	6.12417	−	2.22901i	0.618634	−	0.225165i
$99$	13.5151	+	9.60824i	1.35832	+	0.965664i
$100$	−4.37515	−	1.59242i	−0.437515	−	0.159242i
$101$	−11.7954	+	15.8440i	−1.17368	+	1.57653i	−0.438391	+	0.898785i	$0.644451\pi$
$101$	−11.7954	+	15.8440i	−1.17368	+	1.57653i	−0.735294	+	0.677748i	$0.762956\pi$
$102$	6.88173	+	4.14123i	0.681393	+	0.410043i
$103$	5.78007	+	1.36990i	0.569527	+	0.134980i	0.505283	−	0.862954i	$-0.331388\pi$
$103$	5.78007	+	1.36990i	0.569527	+	0.134980i	0.0642442	+	0.997934i	$0.479536\pi$
$104$	1.29432	−	3.00056i	0.126918	−	0.294229i
$105$	3.60147	−	1.00747i	0.351467	−	0.0983186i
$106$	−3.53852	+	2.32732i	−0.343692	+	0.226050i
$107$	−1.62313	−	2.81135i	−0.156914	−	0.271783i	0.776840	−	0.629698i	$-0.216821\pi$
$107$	−1.62313	−	2.81135i	−0.156914	−	0.271783i	−0.933754	+	0.357914i	$0.883488\pi$
$108$	3.08703	−	4.17974i	0.297049	−	0.402196i
$109$	4.22282	−	7.31415i	0.404473	−	0.700568i	−0.589787	−	0.807559i	$-0.700788\pi$
$109$	4.22282	−	7.31415i	0.404473	−	0.700568i	0.994260	+	0.106991i	$0.0341215\pi$
$110$	0.998698	+	17.1470i	0.0952221	+	1.63490i
$111$	0.915154	+	1.90765i	0.0868625	+	0.181067i
$112$	−0.690137	+	0.0806655i	−0.0652119	+	0.00762217i
$113$	−7.98089	+	8.45925i	−0.750779	+	0.795779i	−0.984287	−	0.176576i	$-0.943498\pi$
$113$	−7.98089	+	8.45925i	−0.750779	+	0.795779i	0.233508	+	0.972355i	$0.424980\pi$
$114$	1.33880	+	3.89663i	0.125390	+	0.364953i
$115$	21.7672	+	2.54422i	2.02980	+	0.237250i
$116$	−1.05675	+	0.886718i	−0.0981168	+	0.0823297i
$117$	−1.35138	−	9.70987i	−0.124935	−	0.897677i
$118$	−4.41181	−	3.70195i	−0.406140	−	0.340792i
$119$	−2.21109	−	2.34361i	−0.202690	−	0.214839i
$120$	5.37786	−	0.215524i	0.490929	−	0.0196746i
$121$	17.4731	−	8.77531i	1.58846	−	0.797755i
$122$	1.54717	−	0.777016i	0.140074	−	0.0703478i
$123$	−19.6417	+	0.787165i	−1.77103	+	0.0709762i
$124$	−2.44004	−	2.58629i	−0.219122	−	0.232256i
$125$	0.819020	+	0.687239i	0.0732553	+	0.0614685i
$126$	−1.64433	+	1.28115i	−0.146489	+	0.114134i
$127$	−7.51805	+	6.30840i	−0.667119	+	0.559780i	−0.912211	−	0.409720i	$-0.865626\pi$
$127$	−7.51805	+	6.30840i	−0.667119	+	0.559780i	0.245092	+	0.969500i	$0.421182\pi$
$128$	−0.993238	−	0.116093i	−0.0877907	−	0.0102613i
$129$	5.23110	+	15.2253i	0.460572	+	1.34051i
$130$	6.96838	−	7.38606i	0.611168	−	0.647800i
$131$	−18.3590	+	2.14586i	−1.60403	+	0.187484i	−0.870499	−	0.492169i	$-0.836204\pi$
$131$	−18.3590	+	2.14586i	−1.60403	+	0.187484i	−0.733533	+	0.679654i	$0.762130\pi$
$132$	−4.14099	−	8.63196i	−0.360427	−	0.751316i
$133$	−0.0961063	−	1.65008i	−0.00833347	−	0.143080i
$134$	−0.511595	+	0.886109i	−0.0441951	+	0.0765481i
$135$	13.4563	−	8.92398i	1.15814	−	0.768054i
$136$	−2.31855	−	4.01585i	−0.198814	−	0.344356i
$137$	12.2593	−	8.06304i	1.04738	−	0.688872i	0.0955257	−	0.995427i	$-0.469547\pi$
$137$	12.2593	−	8.06304i	1.04738	−	0.688872i	0.951853	+	0.306555i	$0.0991764\pi$
$138$	−11.7639	+	3.29081i	−1.00141	+	0.280132i
$139$	5.07402	−	11.7629i	0.430373	−	0.997716i	−0.555697	−	0.831385i	$-0.687549\pi$
$139$	5.07402	−	11.7629i	0.430373	−	0.997716i	0.986070	−	0.166331i	$-0.0531921\pi$
$140$	−2.10093	−	0.497930i	−0.177561	−	0.0420828i
$141$	−15.5504	−	9.35779i	−1.30958	−	0.788068i
$142$	−7.03863	+	9.45452i	−0.590669	+	0.793406i
$143$	−16.9734	−	6.17782i	−1.41939	−	0.516616i
$144$	−2.72793	+	1.24836i	−0.227327	+	0.104030i
$145$	−4.02811	+	1.46611i	−0.334516	+	0.121754i
$146$	−2.46608	+	8.23728i	−0.204094	+	0.681722i
$147$	−10.4443	+	4.28243i	−0.861428	+	0.353209i
$148$	0.0710276	−	1.21950i	0.00583843	−	0.100242i
$149$	14.8005	+	9.73443i	1.21250	+	0.797476i	0.984363	−	0.176153i	$-0.0563652\pi$
$149$	14.8005	+	9.73443i	1.21250	+	0.797476i	0.228140	+	0.973628i	$0.426736\pi$
$150$	7.68234	+	2.45249i	0.627261	+	0.200245i
$151$	15.3504	−	3.63812i	1.24920	−	0.296066i	0.447768	−	0.894150i	$-0.352219\pi$
$151$	15.3504	−	3.63812i	1.24920	−	0.296066i	0.801434	+	0.598084i	$0.204071\pi$
$152$	0.413075	−	2.34266i	0.0335048	−	0.190015i
$153$	−12.1972	−	6.68977i	−0.986083	−	0.540836i
$154$	0.666927	+	3.78233i	0.0537425	+	0.304789i
$155$	−4.37622	−	10.1452i	−0.351507	−	0.814884i
$156$	−2.03191	+	5.28273i	−0.162683	+	0.422957i
$157$	0.902664	+	3.01511i	0.0720404	+	0.240632i	0.986424	−	0.164216i	$-0.0525096\pi$
$157$	0.902664	+	3.01511i	0.0720404	+	0.240632i	−0.914384	+	0.404848i	$0.867324\pi$
$158$	−5.25293	−	7.05591i	−0.417901	−	0.561338i
$159$	5.96257	−	4.27324i	0.472863	−	0.338890i
$160$	−2.77687	−	1.39460i	−0.219531	−	0.110253i
$161$	4.90043			0.386208
$162$	−5.05270	+	7.44783i	−0.396978	+	0.585157i
$163$	−10.6732			−0.835986			−0.417993	−	0.908450i	$-0.637266\pi$
$163$	−10.6732			−0.835986			−0.417993	+	0.908450i	$0.637266\pi$
$164$	10.1420	+	5.09352i	0.791960	+	0.397737i
$165$	−2.91770	−	29.6064i	−0.227142	−	2.30485i
$166$	−5.42188	−	7.28285i	−0.420820	−	0.565259i
$167$	−0.546468	−	1.82533i	−0.0422870	−	0.141248i	0.934239	−	0.356647i	$-0.116080\pi$
$167$	−0.546468	−	1.82533i	−0.0422870	−	0.141248i	−0.976526	+	0.215399i	$0.930895\pi$
$168$	1.18880	−	0.187472i	0.0917179	−	0.0144637i
$169$	−0.919445	−	2.13151i	−0.0707265	−	0.163963i
$170$	−2.50215	−	14.1904i	−0.191906	−	1.08835i
$171$	−2.58727	−	6.65089i	−0.197854	−	0.508606i
$172$	1.61401	−	9.15350i	0.123067	−	0.697948i
$173$	1.41829	−	0.336142i	0.107831	−	0.0255564i	−0.176346	−	0.984328i	$-0.556428\pi$
$173$	1.41829	−	0.336142i	0.107831	−	0.0255564i	0.284177	+	0.958772i	$0.408280\pi$
$174$	1.76737	−	1.60790i	0.133984	−	0.121895i
$175$	−2.70289	−	1.77772i	−0.204320	−	0.134383i
$176$	−0.321393	+	5.51811i	−0.0242259	+	0.415943i
$177$	7.89212	+	6.10083i	0.593208	+	0.458566i
$178$	1.06168	−	3.54624i	0.0795759	−	0.265802i
$179$	3.40456	−	1.23916i	0.254469	−	0.0926191i	−0.211636	−	0.977349i	$-0.567879\pi$
$179$	3.40456	−	1.23916i	0.254469	−	0.0926191i	0.466105	+	0.884729i	$0.345657\pi$
$180$	−9.29230	+	0.746000i	−0.692607	+	0.0556035i
$181$	−20.8444	−	7.58675i	−1.54935	−	0.563919i	−0.581088	−	0.813841i	$-0.697373\pi$
$181$	−20.8444	−	7.58675i	−1.54935	−	0.563919i	−0.968266	+	0.249922i	$0.919595\pi$
$182$	1.35591	−	1.82130i	0.100506	−	0.135004i
$183$	−2.62373	+	1.45206i	−0.193952	+	0.107339i
$184$	6.86253	+	1.62645i	0.505913	+	0.119904i
$185$	1.50347	−	3.48544i	0.110538	−	0.256255i
$186$	4.40226	+	4.30675i	0.322790	+	0.315787i
$187$	−21.4147	+	14.0847i	−1.56600	+	1.02997i
$188$	5.23914	+	9.07445i	0.382103	+	0.661822i
$189$	2.75692	−	2.33129i	0.200537	−	0.169576i
$190$	3.69595	−	6.40157i	0.268132	−	0.464418i
$191$	0.340269	+	5.84219i	0.0246210	+	0.422726i	0.987987	+	0.154536i	$0.0493883\pi$
$191$	0.340269	+	5.84219i	0.0246210	+	0.422726i	−0.963366	+	0.268190i	$0.913575\pi$
$192$	1.72701	+	0.132028i	0.124636	+	0.00952830i
$193$	−14.3530	+	1.67762i	−1.03315	+	0.120758i	−0.615731	−	0.787957i	$-0.711139\pi$
$193$	−14.3530	+	1.67762i	−1.03315	+	0.120758i	−0.417418	+	0.908714i	$0.637065\pi$
$194$	0.624455	−	0.661884i	0.0448333	−	0.0475205i
$195$	−11.5476	+	13.2661i	−0.826943	+	0.950004i
$196$	6.47314	+	0.756601i	0.462367	+	0.0540429i
$197$	−3.66493	+	3.07525i	−0.261116	+	0.219102i	−0.763941	−	0.645286i	$-0.776738\pi$
$197$	−3.66493	+	3.07525i	−0.261116	+	0.219102i	0.502825	+	0.864388i	$0.332294\pi$
$198$	7.76535	+	14.6518i	0.551859	+	1.04126i
$199$	11.9225	+	10.0042i	0.845166	+	0.709178i	0.958719	−	0.284354i	$-0.0917790\pi$
$199$	11.9225	+	10.0042i	0.845166	+	0.709178i	−0.113554	+	0.993532i	$0.536223\pi$
$200$	−3.19509	−	3.38660i	−0.225927	−	0.239469i
$201$	0.823939	−	1.56904i	0.0581162	−	0.110671i
$202$	−17.6515	+	8.86492i	−1.24196	+	0.623733i
$203$	−0.856563	+	0.430182i	−0.0601189	+	0.0301929i
$204$	4.29116	+	6.78926i	0.300441	+	0.475343i
$205$	24.2014	+	25.6520i	1.69030	+	1.79161i
$206$	4.55045	+	3.81828i	0.317045	+	0.266032i
$207$	20.1311	−	6.51121i	1.39921	−	0.452560i
$208$	2.50329	−	2.10051i	0.173572	−	0.145644i
$209$	−13.0598	−	1.52648i	−0.903368	−	0.105589i
$210$	3.67054	+	0.716031i	0.253291	+	0.0494108i
$211$	−10.1033	+	10.7089i	−0.695542	+	0.737231i	−0.974824	−	0.222978i	$-0.928422\pi$
$211$	−10.1033	+	10.7089i	−0.695542	+	0.737231i	0.279282	+	0.960209i	$0.409904\pi$
$212$	−4.20664	+	0.491686i	−0.288913	+	0.0337691i
$213$	11.5257	−	16.8508i	0.789731	−	1.15460i
$214$	−0.188754	−	3.24077i	−0.0129029	−	0.221535i
$215$	14.4412	−	25.0129i	0.984880	−	1.70586i
$216$	4.63453	−	2.34970i	0.315340	−	0.159877i
$217$	−1.23530	−	2.13960i	−0.0838575	−	0.145245i
$218$	7.05624	−	4.64096i	0.477909	−	0.314325i
$219$	3.69662	−	14.4270i	0.249795	−	0.974886i
$220$	−6.80308	+	15.7713i	−0.458664	+	1.06330i
$221$	14.7447	+	3.49457i	0.991838	+	0.235070i
$222$	−0.0383423	+	2.11546i	−0.00257337	+	0.141981i
$223$	6.19591	−	8.32255i	0.414909	−	0.557319i	−0.544710	−	0.838625i	$-0.683360\pi$
$223$	6.19591	−	8.32255i	0.414909	−	0.557319i	0.959618	+	0.281306i	$0.0907675\pi$
$224$	−0.652932	−	0.237648i	−0.0436259	−	0.0158785i
$225$	−13.4656	−	3.71160i	−0.897709	−	0.247440i
$226$	−10.9285	+	3.97765i	−0.726952	+	0.264589i
$227$	2.85714	−	9.54350i	0.189635	−	0.633424i	−0.809305	−	0.587389i	$-0.800156\pi$
$227$	2.85714	−	9.54350i	0.189635	−	0.633424i	0.998940	−	0.0460357i	$-0.0146588\pi$
$228$	−0.552409	+	4.08301i	−0.0365842	+	0.270404i
$229$	−1.21402	+	20.8439i	−0.0802247	+	1.37740i	0.682597	+	0.730795i	$0.260851\pi$
$229$	−1.21402	+	20.8439i	−0.0802247	+	1.37740i	−0.762821	+	0.646609i	$0.776186\pi$
$230$	18.3100	+	12.0427i	1.20733	+	0.794072i
$231$	−1.41656	−	6.49968i	−0.0932029	−	0.427647i
$232$	−1.34230	+	0.318132i	−0.0881266	+	0.0208864i
$233$	−2.00393	+	11.3648i	−0.131282	+	0.744535i	0.846095	+	0.533031i	$0.178947\pi$
$233$	−2.00393	+	11.3648i	−0.131282	+	0.744535i	−0.977377	+	0.211504i	$0.932164\pi$
$234$	3.15015	−	9.28355i	0.205931	−	0.606885i
$235$	5.65402	+	32.0655i	0.368827	+	2.09172i
$236$	−2.28111	−	5.28820i	−0.148488	−	0.344233i
$237$	9.58043	+	11.8471i	0.622316	+	0.769549i
$238$	−0.924086	−	3.08666i	−0.0598996	−	0.200079i
$239$	1.72538	+	2.31759i	0.111606	+	0.149913i	0.854416	−	0.519589i	$-0.173915\pi$
$239$	1.72538	+	2.31759i	0.111606	+	0.149913i	−0.742810	+	0.669502i	$0.766508\pi$
$240$	4.90256	+	2.22098i	0.316459	+	0.143364i
$241$	0.0473887	+	0.0237995i	0.00305257	+	0.00153306i	0.450325	−	0.892865i	$-0.351308\pi$
$241$	0.0473887	+	0.0237995i	0.00305257	+	0.00153306i	−0.447272	+	0.894398i	$0.647604\pi$
$242$	19.5529			1.25691
$243$	8.22794	−	13.2401i	0.527823	−	0.849355i
$244$	1.73132			0.110837
$245$	18.0975	+	9.08888i	1.15620	+	0.580667i
$246$	−17.9057	−	8.11173i	−1.14163	−	0.517185i
$247$	4.64201	+	6.23530i	0.295364	+	0.396743i
$248$	−1.01977	−	3.40628i	−0.0647557	−	0.216299i
$249$	9.88857	+	12.2281i	0.626663	+	0.774925i
$250$	0.423470	+	0.981715i	0.0267826	+	0.0620891i
$251$	1.45888	+	8.27374i	0.0920839	+	0.522234i	0.995602	+	0.0936838i	$0.0298643\pi$
$251$	1.45888	+	8.27374i	0.0920839	+	0.522234i	−0.903518	+	0.428550i	$0.859025\pi$
$252$	−2.04441	+	0.406903i	−0.128786	+	0.0256325i
$253$	6.76936	−	38.3910i	0.425586	−	2.41362i
$254$	−9.54958	+	2.26329i	−0.599194	+	0.142012i
$255$	5.31460	+	24.3852i	0.332813	+	1.52706i
$256$	−0.835488	−	0.549509i	−0.0522180	−	0.0343443i
$257$	0.825207	−	14.1683i	0.0514750	−	0.883792i	−0.869442	−	0.494034i	$-0.835522\pi$
$257$	0.825207	−	14.1683i	0.0514750	−	0.883792i	0.920917	−	0.389758i	$-0.127441\pi$
$258$	−2.15843	+	15.9535i	−0.134378	+	0.993225i
$259$	0.243434	−	0.813128i	0.0151263	−	0.0505253i
$260$	9.54203	−	3.47302i	0.591772	−	0.215387i
$261$	−2.94721	+	2.90532i	−0.182427	+	0.179835i
$262$	−17.3693	−	6.32189i	−1.07308	−	0.390568i
$263$	−14.3710	+	19.3035i	−0.886151	+	1.19031i	0.0946919	+	0.995507i	$0.469813\pi$
$263$	−14.3710	+	19.3035i	−0.886151	+	1.19031i	−0.980843	+	0.194801i	$0.937594\pi$
$264$	0.173496	−	9.57228i	0.0106779	−	0.589133i
$265$	−12.8060	−	3.03507i	−0.786664	−	0.186443i
$266$	0.654671	−	1.51770i	0.0401405	−	0.0930561i
$267$	−1.59144	+	6.21098i	−0.0973945	+	0.380106i
$268$	−0.854863	+	0.562252i	−0.0522191	+	0.0343450i
$269$	4.00049	+	6.92906i	0.243914	+	0.422472i	0.961826	−	0.273662i	$-0.0882351\pi$
$269$	4.00049	+	6.92906i	0.243914	+	0.422472i	−0.717911	+	0.696134i	$0.754902\pi$
$270$	16.0301	−	1.93557i	0.975560	−	0.117795i
$271$	1.88940	−	3.27253i	0.114773	−	0.198792i	−0.802916	−	0.596092i	$-0.796719\pi$
$271$	1.88940	−	3.27253i	0.114773	−	0.198792i	0.917689	+	0.397300i	$0.130053\pi$
$272$	−0.269623	−	4.62925i	−0.0163483	−	0.280690i
$273$	−2.22029	+	3.24609i	−0.134378	+	0.196463i
$274$	14.5740	−	1.70345i	0.880445	−	0.102909i
$275$	−17.6608	+	18.7193i	−1.06498	+	1.12882i
$276$	−11.9895	−	2.33886i	−0.721685	−	0.140783i
$277$	−9.30469	−	1.08756i	−0.559064	−	0.0653453i	−0.168132	−	0.985765i	$-0.553773\pi$
$277$	−9.30469	−	1.08756i	−0.559064	−	0.0653453i	−0.390933	+	0.920419i	$0.627847\pi$
$278$	9.81349	−	8.23449i	0.588574	−	0.493872i
$279$	−7.91754	−	7.14820i	−0.474010	−	0.427952i
$280$	−1.65399	−	1.38786i	−0.0988449	−	0.0829407i
$281$	−5.32890	−	5.64830i	−0.317895	−	0.336949i	0.548646	−	0.836055i	$-0.315144\pi$
$281$	−5.32890	−	5.64830i	−0.317895	−	0.336949i	−0.866541	+	0.499105i	$0.833662\pi$
$282$	−9.69656	−	15.3414i	−0.577422	−	0.913568i
$283$	−17.1311	+	8.60354i	−1.01834	+	0.511427i	−0.877992	−	0.478676i	$-0.841117\pi$
$283$	−17.1311	+	8.60354i	−1.01834	+	0.511427i	−0.140344	+	0.990103i	$0.544821\pi$
$284$	−10.5331	+	5.28994i	−0.625026	+	0.313900i
$285$	−5.95243	+	11.3353i	−0.352591	+	0.671445i
$286$	−12.3954	−	13.1384i	−0.732956	−	0.776888i
$287$	6.04091	+	5.06892i	0.356584	+	0.299209i
$288$	−2.99803	−	0.108713i	−0.176661	−	0.00640598i
$289$	3.44925	−	2.89427i	0.202897	−	0.170251i
$290$	−4.25764	−	0.497647i	−0.250017	−	0.0292228i
$291$	−1.03481	+	1.18881i	−0.0606618	+	0.0696891i
$292$	−5.90065	+	6.25433i	−0.345310	+	0.366007i
$293$	17.5250	−	2.04838i	1.02382	−	0.119668i	0.412425	−	0.910991i	$-0.364682\pi$
$293$	17.5250	−	2.04838i	1.02382	−	0.119668i	0.611398	+	0.791324i	$0.290608\pi$
$294$	−11.2553	−	0.860454i	−0.656422	−	0.0501827i
$295$	−1.04057	−	17.8659i	−0.0605844	−	1.04019i
$296$	0.610782	−	1.05790i	0.0355010	−	0.0614895i
$297$	−14.4554	−	24.8187i	−0.838788	−	1.44013i
$298$	8.85739	+	15.3415i	0.513095	+	0.888706i
$299$	−19.2553	+	12.6644i	−1.11356	+	0.732401i
$300$	5.76452	+	5.63946i	0.332815	+	0.325594i
$301$	2.55800	−	5.93011i	0.147441	−	0.341806i
$302$	15.3504	+	3.63812i	0.883319	+	0.209350i
$303$	29.9339	−	16.5664i	1.71966	−	0.951718i
$304$	1.42052	−	1.90809i	0.0814726	−	0.109437i
$305$	5.05546	+	1.84004i	0.289475	+	0.105360i
$306$	−7.89743	−	11.4523i	−0.451466	−	0.654683i
$307$	−12.9189	+	4.70209i	−0.737320	+	0.268363i	−0.683260	−	0.730175i	$-0.739438\pi$
$307$	−12.9189	+	4.70209i	−0.737320	+	0.268363i	−0.0540601	+	0.998538i	$0.517216\pi$
$308$	−1.10152	+	3.67933i	−0.0627649	+	0.209649i
$309$	−8.14011	−	6.29254i	−0.463075	−	0.357970i
$310$	0.642433	−	11.0301i	0.0364877	−	0.626470i
$311$	14.9898	+	9.85896i	0.849995	+	0.559050i	0.898100	−	0.439792i	$-0.144948\pi$
$311$	14.9898	+	9.85896i	0.849995	+	0.559050i	−0.0481050	+	0.998842i	$0.515318\pi$
$312$	−4.18667	+	3.80890i	−0.237023	+	0.215637i
$313$	4.64166	−	1.10009i	0.262362	−	0.0621810i	−0.0973294	−	0.995252i	$-0.531030\pi$
$313$	4.64166	−	1.10009i	0.262362	−	0.0621810i	0.359692	+	0.933071i	$0.382882\pi$
$314$	−0.546528	+	3.09951i	−0.0308423	+	0.174916i
$315$	−6.40212	−	0.984625i	−0.360719	−	0.0554773i
$316$	−1.52750	−	8.66290i	−0.0859288	−	0.487326i
$317$	−1.95397	−	4.52981i	−0.109746	−	0.254420i	0.854489	−	0.519470i	$-0.173871\pi$
$317$	−1.95397	−	4.52981i	−0.109746	−	0.254420i	−0.964235	+	0.265050i	$0.914611\pi$
$318$	7.24617	−	1.14271i	0.406345	−	0.0640799i
$319$	2.18690	+	7.30474i	0.122443	+	0.408987i
$320$	−1.85561	−	2.49252i	−0.103732	−	0.139336i
$321$	0.551444	+	5.59559i	0.0307786	+	0.312315i
$322$	4.37918	+	2.19931i	0.244042	+	0.122563i
$323$	11.0307			0.613767
$324$	−7.85784	+	4.38798i	−0.436547	+	0.243777i
$325$	15.2147			0.843962
$326$	−9.53788	−	4.79010i	−0.528254	−	0.265299i
$327$	−11.8901	+	8.52134i	−0.657522	+	0.471231i
$328$	6.77729	+	9.10348i	0.374213	+	0.502655i
$329$	2.08812	+	6.97481i	0.115122	+	0.384534i
$330$	10.6800	−	27.7667i	0.587912	−	1.52850i
$331$	8.20945	+	19.0316i	0.451232	+	1.04607i	0.980304	+	0.197497i	$0.0632812\pi$
$331$	8.20945	+	19.0316i	0.451232	+	1.04607i	−0.529071	+	0.848577i	$0.677460\pi$
$332$	−1.57663	−	8.94153i	−0.0865290	−	0.490730i
$333$	−0.0803676	−	3.66381i	−0.00440412	−	0.200775i
$334$	0.330865	−	1.87643i	0.0181041	−	0.102674i
$335$	−3.09376	+	0.733234i	−0.169030	+	0.0400609i
$336$	1.14649	+	0.366002i	0.0625460	+	0.0199670i
$337$	23.4132	+	15.3991i	1.27540	+	0.838843i	0.992729	−	0.120374i	$-0.0384095\pi$
$337$	23.4132	+	15.3991i	1.27540	+	0.838843i	0.282670	+	0.959217i	$0.408780\pi$
$338$	0.134975	−	2.31744i	0.00734169	−	0.126052i
$339$	18.6376	−	7.64194i	1.01226	−	0.415053i
$340$	4.13264	−	13.8040i	0.224124	−	0.748626i
$341$	−18.4685	+	6.72198i	−1.00012	+	0.364016i
$342$	0.672842	−	7.10462i	0.0363831	−	0.384174i
$343$	8.82581	+	3.21233i	0.476549	+	0.173450i
$344$	5.55041	−	7.45550i	0.299258	−	0.401973i
$345$	−32.5237	−	19.5719i	−1.75102	−	1.05371i
$346$	1.41829	+	0.336142i	0.0762480	+	0.0180711i
$347$	4.31805	−	10.0104i	0.231805	−	0.537384i	−0.762121	−	0.647435i	$-0.775842\pi$
$347$	4.31805	−	10.0104i	0.231805	−	0.537384i	0.993926	+	0.110050i	$0.0351011\pi$
$348$	2.30101	−	0.643679i	0.123347	−	0.0345048i
$349$	13.5397	−	8.90522i	0.724765	−	0.476685i	−0.132747	−	0.991150i	$-0.542380\pi$
$349$	13.5397	−	8.90522i	0.724765	−	0.476685i	0.857512	+	0.514465i	$0.172009\pi$
$350$	−1.61755	−	2.80169i	−0.0864619	−	0.149756i
$351$	−4.80794	+	16.2852i	−0.256629	+	0.869238i
$352$	−2.76373	+	4.78692i	−0.147307	+	0.255144i
$353$	−1.59059	−	27.3094i	−0.0846586	−	1.45353i	−0.726749	−	0.686903i	$-0.758970\pi$
$353$	−1.59059	−	27.3094i	−0.0846586	−	1.45353i	0.642090	−	0.766629i	$-0.278067\pi$
$354$	4.31461	+	8.99388i	0.229319	+	0.478019i
$355$	−36.3789	+	4.25208i	−1.93079	+	0.225677i
$356$	2.54030	−	2.69256i	0.134636	−	0.142705i
$357$	1.81337	+	5.27788i	0.0959735	+	0.279335i
$358$	3.59856	+	0.420611i	0.190190	+	0.0222300i
$359$	−4.66035	+	3.91050i	−0.245964	+	0.206388i	−0.757432	−	0.652914i	$-0.773546\pi$
$359$	−4.66035	+	3.91050i	−0.245964	+	0.206388i	0.511468	+	0.859302i	$0.329102\pi$
$360$	−8.63871	−	3.50373i	−0.455300	−	0.184663i
$361$	−10.2200	−	8.57562i	−0.537896	−	0.451348i
$362$	−15.2223	−	16.1347i	−0.800068	−	0.848023i
$363$	−33.8394	+	1.35616i	−1.77611	+	0.0711798i
$364$	2.02908	−	1.01904i	0.106353	−	0.0534123i
$365$	−23.8770	+	11.9915i	−1.24978	+	0.627662i
$366$	−2.99633	+	0.120082i	−0.156621	+	0.00627678i
$367$	−12.3462	−	13.0862i	−0.644468	−	0.683096i	0.319963	−	0.947430i	$-0.396329\pi$
$367$	−12.3462	−	13.0862i	−0.644468	−	0.683096i	−0.964431	+	0.264334i	$0.914848\pi$
$368$	5.40264	+	4.53335i	0.281632	+	0.236317i
$369$	31.5513	+	12.7967i	1.64250	+	0.666172i
$370$	2.90782	−	2.43995i	0.151170	−	0.126847i
$371$	−2.92293	−	0.341641i	−0.151751	−	0.0177371i
$372$	2.00114	+	5.82439i	0.103754	+	0.301980i
$373$	16.3827	−	17.3646i	0.848262	−	0.899106i	−0.147686	−	0.989034i	$-0.547182\pi$
$373$	16.3827	−	17.3646i	0.848262	−	0.899106i	0.995948	+	0.0899288i	$0.0286639\pi$
$374$	−25.4581	+	2.97562i	−1.31641	+	0.153866i
$375$	−0.800974	−	1.66964i	−0.0413621	−	0.0862201i
$376$	0.609257	+	10.4605i	0.0314200	+	0.539461i
$377$	2.25396	−	3.90397i	0.116085	−	0.201065i
$378$	3.50995	−	0.846008i	0.180533	−	0.0435140i
$379$	−11.8242	−	20.4801i	−0.607367	−	1.05199i	−0.991673	−	0.128785i	$-0.958892\pi$
$379$	−11.8242	−	20.4801i	−0.607367	−	1.05199i	0.384305	−	0.923206i	$-0.374441\pi$
$380$	6.17584	−	4.06191i	0.316814	−	0.208372i
$381$	16.3701	−	4.57934i	0.838666	−	0.234607i
$382$	−2.31789	+	5.37348i	−0.118594	+	0.274931i
$383$	−13.8773	−	3.28898i	−0.709097	−	0.168059i	−0.139787	−	0.990182i	$-0.544642\pi$
$383$	−13.8773	−	3.28898i	−0.709097	−	0.168059i	−0.569311	+	0.822123i	$0.692790\pi$
$384$	1.48406	+	0.893066i	0.0757331	+	0.0455741i
$385$	−7.12681	+	9.57296i	−0.363216	+	0.487883i
$386$	−13.5792	−	4.94242i	−0.691163	−	0.251563i
$387$	2.62900	−	27.7599i	0.133639	−	1.41112i
$388$	0.855086	−	0.311226i	0.0434104	−	0.0158001i
$389$	10.2329	−	34.1803i	0.518829	−	1.73301i	−0.149135	−	0.988817i	$-0.547649\pi$
$389$	10.2329	−	34.1803i	0.518829	−	1.73301i	0.667964	−	0.744193i	$-0.267166\pi$
$390$	−16.2731	+	6.67243i	−0.824023	+	0.337872i
$391$	−1.90156	+	32.6485i	−0.0961658	+	1.65110i
$392$	5.44504	+	3.58126i	0.275016	+	0.180881i
$393$	30.4988	+	9.73635i	1.53846	+	0.491134i
$394$	−4.65527	+	1.10332i	−0.234529	+	0.0555845i
$395$	4.74656	−	26.9191i	0.238826	−	1.35445i
$396$	0.363656	+	16.5784i	0.0182744	+	0.833096i
$397$	4.23676	+	24.0278i	0.212637	+	1.20592i	0.884961	+	0.465666i	$0.154185\pi$
$397$	4.23676	+	24.0278i	0.212637	+	1.20592i	−0.672324	+	0.740257i	$0.734704\pi$
$398$	6.16449	+	14.2909i	0.308998	+	0.716338i
$399$	−1.02775	+	2.67203i	−0.0514518	+	0.133769i
$400$	−1.33534	−	4.46033i	−0.0667668	−	0.223017i
$401$	23.3072	+	31.3070i	1.16391	+	1.56340i	0.761812	+	0.647798i	$0.224310\pi$
$401$	23.3072	+	31.3070i	1.16391	+	1.56340i	0.402093	+	0.915599i	$0.368283\pi$
$402$	1.44048	−	1.03236i	0.0718447	−	0.0514894i
$403$	10.3833	+	5.21470i	0.517230	+	0.259763i
$404$	−19.7525			−0.982725
$405$	−27.6084	+	4.46164i	−1.37187	+	0.221701i
$406$	−0.958518			−0.0475705
$407$	−6.03394	−	3.03036i	−0.299091	−	0.150209i
$408$	0.787705	+	7.99297i	0.0389972	+	0.395711i
$409$	−10.6428	−	14.2958i	−0.526254	−	0.706882i	0.456929	−	0.889503i	$-0.348949\pi$
$409$	−10.6428	−	14.2958i	−0.526254	−	0.706882i	−0.983183	+	0.182621i	$0.941542\pi$
$410$	10.1146	+	33.7850i	0.499523	+	1.66852i
$411$	−25.1044	+	3.95892i	−1.23831	+	0.195279i
$412$	2.35279	+	5.45437i	0.115914	+	0.268718i
$413$	−0.694889	−	3.94091i	−0.0341933	−	0.193920i
$414$	20.9120	+	3.21620i	1.02777	+	0.158068i
$415$	4.89923	−	27.7849i	0.240494	−	1.36391i
$416$	3.17973	−	0.753611i	0.155899	−	0.0369488i
$417$	−16.4127	+	14.9318i	−0.803733	+	0.731212i
$418$	−10.9856	−	7.22536i	−0.537324	−	0.353404i
$419$	−0.463457	+	7.95725i	−0.0226414	+	0.388737i	0.967883	+	0.251401i	$0.0808912\pi$
$419$	−0.463457	+	7.95725i	−0.0226414	+	0.388737i	−0.990524	+	0.137336i	$0.956146\pi$
$420$	2.95876	+	2.28720i	0.144373	+	0.111604i
$421$	8.16468	−	27.2719i	0.397922	−	1.32915i	−0.491026	−	0.871145i	$-0.663378\pi$
$421$	8.16468	−	27.2719i	0.397922	−	1.32915i	0.888948	−	0.458008i	$-0.151437\pi$
$422$	−13.8348	+	5.03546i	−0.673468	+	0.245122i
$423$	17.8455	+	25.8783i	0.867679	+	1.25824i
$424$	−3.97986	−	1.44855i	−0.193279	−	0.0703479i
$425$	12.8927	−	17.3179i	0.625386	−	0.840039i
$426$	17.8624	−	9.88565i	0.865435	−	0.478962i
$427$	1.17056	+	0.277427i	0.0566473	+	0.0134257i
$428$	1.28578	−	2.98077i	0.0621505	−	0.144081i
$429$	22.3635	+	21.8783i	1.07972	+	1.05630i
$430$	24.1309	−	15.8711i	1.16369	−	0.765373i
$431$	−13.7252	−	23.7728i	−0.661122	−	1.14510i	−0.980321	−	0.197409i	$-0.936747\pi$
$431$	−13.7252	−	23.7728i	−0.661122	−	1.14510i	0.319200	−	0.947688i	$-0.396586\pi$
$432$	5.19611	−	0.0197932i	0.249998	−	0.000952301i
$433$	1.90681	−	3.30270i	0.0916356	−	0.158717i	−0.816564	−	0.577255i	$-0.804124\pi$
$433$	1.90681	−	3.30270i	0.0916356	−	0.158717i	0.908199	+	0.418538i	$0.137457\pi$
$434$	−0.143652	−	2.46642i	−0.00689553	−	0.118392i
$435$	7.40305	+	0.565955i	0.354949	+	0.0271354i
$436$	8.38854	−	0.980480i	0.401738	−	0.0469565i
$437$	−11.5130	+	12.2030i	−0.550740	+	0.583750i
$438$	9.77825	−	11.2334i	0.467223	−	0.536752i
$439$	−5.47284	−	0.639683i	−0.261204	−	0.0305304i	−0.0155172	−	0.999880i	$-0.504939\pi$
$439$	−5.47284	−	0.639683i	−0.261204	−	0.0305304i	−0.245687	+	0.969349i	$0.579014\pi$
$440$	−13.1576	+	11.0405i	−0.627265	+	0.526337i
$441$	19.5388	+	0.708505i	0.930418	+	0.0337383i
$442$	11.6080	+	9.74029i	0.552137	+	0.463298i
$443$	17.7115	+	18.7731i	0.841499	+	0.891937i	0.995366	−	0.0961548i	$-0.0306544\pi$
$443$	17.7115	+	18.7731i	0.841499	+	0.891937i	−0.153868	+	0.988091i	$0.549173\pi$
$444$	−0.983682	+	1.87324i	−0.0466835	+	0.0888999i
$445$	10.2793	−	5.16246i	0.487286	−	0.244724i
$446$	9.27202	−	4.65658i	0.439043	−	0.220496i
$447$	−16.3932	−	25.9365i	−0.775372	−	1.22676i
$448$	−0.476825	−	0.505405i	−0.0225279	−	0.0238781i
$449$	−7.95557	−	6.67552i	−0.375447	−	0.315037i	0.435465	−	0.900206i	$-0.356584\pi$
$449$	−7.95557	−	6.67552i	−0.375447	−	0.315037i	−0.810912	+	0.585168i	$0.801028\pi$
$450$	−10.3676	−	9.36017i	−0.488732	−	0.441243i
$451$	48.0558	−	40.3236i	2.26286	−	1.89877i
$452$	−11.5512	−	1.35014i	−0.543324	−	0.0635054i
$453$	−26.8188	−	5.23167i	−1.26005	−	0.245805i
$454$	6.83635	−	7.24610i	0.320846	−	0.340076i
$455$	7.00794	−	0.819111i	0.328537	−	0.0384005i
$456$	−2.32610	+	3.40079i	−0.108930	+	0.159257i
$457$	2.03404	+	34.9231i	0.0951485	+	1.63364i	0.621532	+	0.783389i	$0.286511\pi$
$457$	2.03404	+	34.9231i	0.0951485	+	1.63364i	−0.526384	+	0.850247i	$0.676452\pi$
$458$	−10.4396	+	18.0819i	−0.487811	+	0.844914i
$459$	14.4621	+	19.2723i	0.675033	+	0.899552i
$460$	10.9577	+	18.9793i	0.510905	+	0.884913i
$461$	−13.1697	+	8.66185i	−0.613374	+	0.403423i	−0.817836	−	0.575452i	$-0.804826\pi$
$461$	−13.1697	+	8.66185i	−0.613374	+	0.403423i	0.204461	+	0.978875i	$0.434456\pi$
$462$	1.65116	−	6.44408i	0.0768191	−	0.299806i
$463$	1.50290	−	3.48411i	0.0698456	−	0.161920i	−0.879717	−	0.475497i	$-0.842268\pi$
$463$	1.50290	−	3.48411i	0.0698456	−	0.161920i	0.949563	+	0.313577i	$0.101527\pi$
$464$	−1.34230	−	0.318132i	−0.0623149	−	0.0147689i
$465$	−0.346800	+	19.1340i	−0.0160825	+	0.887319i
$466$	−6.89131	+	9.25663i	−0.319234	+	0.428805i
$467$	37.6811	+	13.7148i	1.74367	+	0.634645i	0.999446	−	0.0332831i	$-0.0105963\pi$
$467$	37.6811	+	13.7148i	1.74367	+	0.634645i	0.744226	+	0.667928i	$0.232819\pi$
$468$	6.98152	−	6.88230i	0.322721	−	0.318134i
$469$	−0.668073	+	0.243159i	−0.0308488	+	0.0112280i
$470$	−9.33836	+	31.1923i	−0.430747	+	1.43879i
$471$	0.730877	−	5.40211i	0.0336770	−	0.248916i
$472$	0.334869	−	5.74947i	0.0154136	−	0.264641i
$473$	−42.9241	−	28.2317i	−1.97365	−	1.29809i
$474$	3.24444	+	14.8866i	0.149022	+	0.683765i
$475$	10.7770	−	2.55420i	0.494483	−	0.117195i
$476$	0.559498	−	3.17307i	0.0256446	−	0.145438i
$477$	−12.4614	+	2.48022i	−0.570569	+	0.113562i
$478$	0.501726	+	2.84543i	0.0229484	+	0.130147i
$479$	8.98549	+	20.8307i	0.410558	+	0.951780i	0.990549	+	0.137157i	$0.0437966\pi$
$479$	8.98549	+	20.8307i	0.410558	+	0.951780i	−0.579992	+	0.814622i	$0.696944\pi$
$480$	3.38431	+	4.18500i	0.154472	+	0.191018i
$481$	1.14487	+	3.82415i	0.0522018	+	0.174366i
$482$	0.0316669	+	0.0425360i	0.00144239	+	0.00193746i
$483$	−7.73142	−	3.50252i	−0.351792	−	0.159370i
$484$	17.4731	+	8.77531i	0.794231	+	0.398878i
$485$	2.82762			0.128396
$486$	13.2949	−	8.13911i	0.603070	−	0.369198i
$487$	−27.0825			−1.22723			−0.613613	−	0.789607i	$-0.710285\pi$
$487$	−27.0825			−1.22723			−0.613613	+	0.789607i	$0.710285\pi$
$488$	1.54717	+	0.777016i	0.0700369	+	0.0351739i
$489$	16.8391	+	7.62852i	0.761490	+	0.344973i
$490$	12.0934	+	16.2442i	0.546324	+	0.733840i
$491$	−2.03944	−	6.81222i	−0.0920388	−	0.307431i	0.899557	−	0.436803i	$-0.143889\pi$
$491$	−2.03944	−	6.81222i	−0.0920388	−	0.307431i	−0.991596	+	0.129372i	$0.958704\pi$
$492$	−12.3606	−	15.2850i	−0.557258	−	0.689100i
$493$	−2.53365	−	5.87367i	−0.114110	−	0.264537i
$494$	1.34985	+	7.65540i	0.0607328	+	0.344433i
$495$	−16.5575	+	48.7954i	−0.744206	+	2.19319i
$496$	0.617433	−	3.50164i	0.0277236	−	0.157228i
$497$	−7.96918	+	1.88873i	−0.357466	+	0.0847211i
$498$	3.34879	+	15.3654i	0.150063	+	0.688541i
$499$	−24.8765	−	16.3615i	−1.11362	−	0.732442i	−0.147127	−	0.989118i	$-0.547002\pi$
$499$	−24.8765	−	16.3615i	−1.11362	−	0.732442i	−0.966498	+	0.256676i	$0.917373\pi$
$500$	−0.0621658	+	1.06735i	−0.00278014	+	0.0477331i
$501$	−0.442469	+	3.27041i	−0.0197681	+	0.146111i
$502$	−2.40954	+	8.04843i	−0.107543	+	0.359219i
$503$	0.405417	−	0.147560i	0.0180767	−	0.00657936i	−0.332966	−	0.942939i	$-0.608049\pi$
$503$	0.405417	−	0.147560i	0.0180767	−	0.00657936i	0.351043	+	0.936359i	$0.385827\pi$
$504$	−2.00957	−	0.553906i	−0.0895132	−	0.0246729i
$505$	−57.6774	−	20.9928i	−2.56661	−	0.934169i
$506$	23.2792	−	31.2693i	1.03488	−	1.39009i
$507$	−0.0728627	+	4.02006i	−0.00323595	+	0.178537i
$508$	−9.54958	−	2.26329i	−0.423694	−	0.100417i
$509$	8.75229	−	20.2901i	0.387939	−	0.899343i	−0.606603	−	0.795005i	$-0.707468\pi$
$509$	8.75229	−	20.2901i	0.387939	−	0.899343i	0.994542	−	0.104338i	$-0.0332724\pi$
$510$	−6.19478	+	24.1766i	−0.274309	+	1.07056i
$511$	−4.99166	+	3.28307i	−0.220818	+	0.145234i
$512$	−0.500000	−	0.866025i	−0.0220971	−	0.0382733i
$513$	−0.671697	+	12.3424i	−0.0296561	+	0.544928i
$514$	7.09614	−	12.2909i	0.312997	−	0.542127i
$515$	1.07327	+	18.4273i	0.0472939	+	0.812004i
$516$	−9.08878	+	13.2879i	−0.400111	+	0.584968i
$517$	57.5266	−	6.72390i	2.53002	−	0.295717i
$518$	0.582472	−	0.617384i	0.0255924	−	0.0271263i
$519$	−2.47790	−	0.483377i	−0.108768	−	0.0212179i
$520$	10.0858	+	1.17886i	0.442290	+	0.0516963i
$521$	0.934191	−	0.783879i	0.0409276	−	0.0343424i	−0.622094	−	0.782942i	$-0.713718\pi$
$521$	0.934191	−	0.783879i	0.0409276	−	0.0343424i	0.663022	+	0.748600i	$0.269274\pi$
$522$	−3.93762	+	1.27359i	−0.172345	+	0.0557433i
$523$	7.65711	+	6.42508i	0.334822	+	0.280949i	0.794661	−	0.607053i	$-0.207648\pi$
$523$	7.65711	+	6.42508i	0.334822	+	0.280949i	−0.459839	+	0.888002i	$0.652093\pi$
$524$	−12.6845	−	13.4448i	−0.554124	−	0.587337i
$525$	2.99376	+	4.73658i	0.130658	+	0.206721i
$526$	−21.5058	+	10.8006i	−0.937696	+	0.470929i
$527$	14.7341	−	7.39977i	0.641829	−	0.322339i
$528$	4.45107	−	8.47623i	0.193708	−	0.368881i
$529$	−18.3499	−	19.4498i	−0.797822	−	0.845642i
$530$	−10.0817	−	8.45954i	−0.437921	−	0.367459i
$531$	−8.09093	−	15.2661i	−0.351116	−	0.662492i
$532$	1.26618	−	1.06245i	0.0548958	−	0.0460630i
$533$	−36.8364	−	4.30556i	−1.59556	−	0.186495i
$534$	−4.20965	+	4.83610i	−0.182169	+	0.209279i
$535$	6.92243	−	7.33734i	0.299283	−	0.317221i
$536$	−1.01627	+	0.118785i	−0.0438962	+	0.00513074i
$537$	−6.25706	−	0.478345i	−0.270012	−	0.0206421i
$538$	0.465216	+	7.98745i	0.0200569	+	0.344363i
$539$	18.0118	−	31.1974i	0.775823	−	1.34377i
$540$	15.1937	+	5.46460i	0.653832	+	0.235159i
$541$	−1.46755	−	2.54188i	−0.0630951	−	0.109284i	0.832752	−	0.553646i	$-0.186764\pi$
$541$	−1.46755	−	2.54188i	−0.0630951	−	0.109284i	−0.895847	+	0.444362i	$0.853430\pi$
$542$	3.15714	−	2.07648i	0.135611	−	0.0891925i
$543$	27.4638	+	26.8680i	1.17858	+	1.15301i
$544$	1.83666	−	4.25786i	0.0787462	−	0.182554i
$545$	25.5366	+	6.05228i	1.09387	+	0.259251i
$546$	−3.44097	+	1.90435i	−0.147260	+	0.0814987i
$547$	9.40820	−	12.6374i	0.402266	−	0.540336i	−0.554123	−	0.832435i	$-0.686946\pi$
$547$	9.40820	−	12.6374i	0.402266	−	0.540336i	0.956388	+	0.292099i	$0.0943535\pi$
$548$	13.7883	+	5.01852i	0.589006	+	0.214380i
$549$	5.17731	−	0.415642i	0.220962	−	0.0177392i
$550$	−24.1835	+	8.80206i	−1.03119	+	0.375321i
$551$	0.941154	−	3.14367i	0.0400945	−	0.133925i
$552$	−9.66456	−	7.47097i	−0.411351	−	0.317986i
$553$	0.355390	−	6.10181i	0.0151127	−	0.259475i
$554$	−7.82687	−	5.14782i	−0.332532	−	0.218710i
$555$	−4.86322	+	4.42441i	−0.206432	+	0.187806i
$556$	12.4653	−	2.95433i	0.528646	−	0.125291i
$557$	−2.45674	+	13.9329i	−0.104095	+	0.590354i	0.887482	+	0.460841i	$0.152452\pi$
$557$	−2.45674	+	13.9329i	−0.104095	+	0.590354i	−0.991578	+	0.129512i	$0.958659\pi$
$558$	−3.86726	−	9.94125i	−0.163714	−	0.420847i
$559$	5.27429	+	29.9120i	0.223079	+	1.26514i
$560$	−0.855189	−	1.98255i	−0.0361383	−	0.0837780i
$561$	43.8529	−	6.91553i	1.85147	−	0.291974i
$562$	−2.22712	−	7.43911i	−0.0939455	−	0.313800i
$563$	−14.2152	−	19.0944i	−0.599101	−	0.804732i	0.394354	−	0.918959i	$-0.370968\pi$
$563$	−14.2152	−	19.0944i	−0.599101	−	0.804732i	−0.993455	+	0.114226i	$0.963561\pi$
$564$	−1.77995	−	18.0614i	−0.0749492	−	0.760522i
$565$	−32.2946	−	16.2190i	−1.35865	−	0.682338i
$566$	−19.1701			−0.805781
$567$	−6.01587	+	1.70760i	−0.252643	+	0.0717124i
$568$	−11.7869			−0.494566
$569$	−1.76778	−	0.887811i	−0.0741091	−	0.0372190i	0.411359	−	0.911474i	$-0.365054\pi$
$569$	−1.76778	−	0.887811i	−0.0741091	−	0.0372190i	−0.485468	+	0.874255i	$0.661351\pi$
$570$	−10.4066	+	7.45814i	−0.435883	+	0.312387i
$571$	5.08064	+	6.82448i	0.212618	+	0.285596i	0.895619	−	0.444822i	$-0.146733\pi$
$571$	5.08064	+	6.82448i	0.212618	+	0.285596i	−0.683001	+	0.730417i	$0.739326\pi$
$572$	−5.18046	−	17.3039i	−0.216606	−	0.723513i
$573$	3.63879	−	9.46044i	0.152013	−	0.395216i
$574$	3.12342	+	7.24091i	0.130369	+	0.302230i
$575$	5.70202	+	32.3378i	0.237791	+	1.34858i
$576$	−2.63035	−	1.44266i	−0.109598	−	0.0601109i
$577$	−6.90467	+	39.1583i	−0.287445	+	1.63018i	0.408973	+	0.912546i	$0.365887\pi$
$577$	−6.90467	+	39.1583i	−0.287445	+	1.63018i	−0.696418	+	0.717636i	$0.745224\pi$
$578$	4.38131	−	1.03839i	0.182239	−	0.0431913i
$579$	23.8438	+	7.61183i	0.990914	+	0.316337i
$580$	−3.58142	−	2.35554i	−0.148710	−	0.0978084i
$581$	0.366821	−	6.29807i	0.0152183	−	0.261288i
$582$	−1.45828	+	0.597934i	−0.0604476	+	0.0247852i
$583$	−6.71417	+	22.4269i	−0.278072	+	0.928826i
$584$	−8.07995	+	2.94086i	−0.334351	+	0.121694i
$585$	27.7005	−	12.6764i	1.14528	−	0.524105i
$586$	16.5802	+	6.03472i	0.684924	+	0.249292i
$587$	6.53316	−	8.77555i	0.269652	−	0.362206i	−0.646585	−	0.762842i	$-0.723803\pi$
$587$	6.53316	−	8.77555i	0.269652	−	0.362206i	0.916237	+	0.400636i	$0.131211\pi$
$588$	−9.67192	−	5.82029i	−0.398863	−	0.240025i
$589$	8.23021	+	1.95060i	0.339120	+	0.0803729i
$590$	7.08832	−	16.4326i	0.291821	−	0.676518i
$591$	7.98018	−	2.23236i	0.328261	−	0.0918268i
$592$	1.02060	−	0.671260i	0.0419465	−	0.0275886i
$593$	−6.95035	−	12.0384i	−0.285417	−	0.494356i	0.687293	−	0.726380i	$-0.258799\pi$
$593$	−6.95035	−	12.0384i	−0.285417	−	0.494356i	−0.972710	+	0.232024i	$0.925465\pi$
$594$	−1.77922	−	28.6664i	−0.0730022	−	1.17620i
$595$	5.00605	−	8.67074i	0.205228	−	0.355466i
$596$	1.03002	+	17.6848i	0.0421914	+	0.724398i
$597$	−11.6598	−	24.3051i	−0.477205	−	0.994743i
$598$	−22.8909	+	2.67556i	−0.936079	+	0.109412i
$599$	8.55657	−	9.06943i	0.349612	−	0.370567i	−0.528573	−	0.848888i	$-0.677273\pi$
$599$	8.55657	−	9.06943i	0.349612	−	0.370567i	0.878185	+	0.478321i	$0.158754\pi$
$600$	2.62038	+	7.62671i	0.106976	+	0.311359i
$601$	−33.8011	−	3.95078i	−1.37877	−	0.161156i	−0.605813	−	0.795607i	$-0.707152\pi$
$601$	−33.8011	−	3.95078i	−1.37877	−	0.161156i	−0.772962	+	0.634452i	$0.781226\pi$
$602$	4.94734	−	4.15131i	0.201638	−	0.169195i
$603$	−2.42138	+	1.88658i	−0.0986063	+	0.0768273i
$604$	12.0849	+	10.1404i	0.491726	+	0.412607i
$605$	41.6951	+	44.1942i	1.69515	+	1.79675i
$606$	34.1849	−	1.37000i	1.38867	−	0.0556526i
$607$	−0.126803	+	0.0636828i	−0.00514677	+	0.00258481i	−0.451371	−	0.892337i	$-0.649065\pi$
$607$	−0.126803	+	0.0636828i	−0.00514677	+	0.00258481i	0.446224	+	0.894921i	$0.352768\pi$
$608$	2.12578	−	1.06760i	0.0862116	−	0.0432971i
$609$	1.65887	−	0.0664813i	0.0672208	−	0.00269396i
$610$	3.69192	+	3.91321i	0.149481	+	0.158441i
$611$	−26.2302	−	22.0097i	−1.06116	−	0.890419i
$612$	−1.91763	−	13.7785i	−0.0775156	−	0.556963i
$613$	5.46537	−	4.58599i	0.220744	−	0.185226i	−0.525709	−	0.850665i	$-0.676200\pi$
$613$	5.46537	−	4.58599i	0.220744	−	0.185226i	0.746453	+	0.665438i	$0.231755\pi$
$614$	−13.6550	−	1.59605i	−0.551073	−	0.0644111i
$615$	−19.8482	−	57.7689i	−0.800355	−	2.32947i
$616$	−2.63563	+	2.79361i	−0.106193	+	0.112558i
$617$	−12.3620	+	1.44491i	−0.497674	+	0.0581698i	−0.361228	−	0.932478i	$-0.617642\pi$
$617$	−12.3620	+	1.44491i	−0.497674	+	0.0581698i	−0.136447	+	0.990647i	$0.543568\pi$
$618$	−4.45019	−	9.27649i	−0.179013	−	0.373155i
$619$	−0.942223	−	16.1773i	−0.0378711	−	0.650222i	−0.962822	−	0.270136i	$-0.912931\pi$
$619$	−0.942223	−	16.1773i	−0.0378711	−	0.650222i	0.924951	−	0.380086i	$-0.124106\pi$
$620$	5.52442	−	9.56858i	0.221866	−	0.384283i
$621$	−36.4147	−	4.11573i	−1.46127	−	0.165158i
$622$	8.97070	+	15.5377i	0.359692	+	0.623005i
$623$	2.14897	−	1.41340i	0.0860966	−	0.0566266i
$624$	−5.45077	+	1.52479i	−0.218206	+	0.0610403i
$625$	−10.5365	+	24.4263i	−0.421460	+	0.977054i
$626$	4.64166	+	1.10009i	0.185518	+	0.0439686i
$627$	19.5135	+	11.7427i	0.779295	+	0.468958i
$628$	−1.87945	+	2.52454i	−0.0749984	+	0.100740i
$629$	5.32290	+	1.93738i	0.212238	+	0.0772482i
$630$	−5.27925	−	3.75316i	−0.210330	−	0.149529i
$631$	30.2871	−	11.0236i	1.20571	−	0.438843i	0.340497	−	0.940246i	$-0.389405\pi$
$631$	30.2871	−	11.0236i	1.20571	−	0.438843i	0.865214	+	0.501402i	$0.167182\pi$
$632$	2.52288	−	8.42700i	0.100355	−	0.335208i
$633$	23.5941	−	9.67424i	0.937782	−	0.384517i
$634$	0.286844	−	4.92493i	0.0113920	−	0.195594i
$635$	−25.4794	−	16.7580i	−1.01112	−	0.665023i
$636$	6.98826	+	2.23091i	0.277103	+	0.0884615i
$637$	−20.7230	+	4.91143i	−0.821074	+	0.194598i
$638$	−1.32408	+	7.50923i	−0.0524208	+	0.297293i
$639$	−30.2281	+	18.3476i	−1.19580	+	0.725821i
$640$	−0.539594	−	3.06019i	−0.0213293	−	0.120965i
$641$	2.93257	+	6.79846i	0.115829	+	0.268523i	0.966262	−	0.257561i	$-0.0829189\pi$
$641$	2.93257	+	6.79846i	0.115829	+	0.268523i	−0.850432	+	0.526084i	$0.823660\pi$
$642$	−2.01851	+	5.24789i	−0.0796642	+	0.207118i
$643$	−2.09220	−	6.98845i	−0.0825085	−	0.275597i	0.906773	−	0.421619i	$-0.138538\pi$
$643$	−2.09220	−	6.98845i	−0.0825085	−	0.275597i	−0.989281	+	0.146022i	$0.953353\pi$
$644$	2.92633	+	3.93074i	0.115314	+	0.154893i
$645$	−40.6616	+	29.1412i	−1.60105	+	1.14743i
$646$	9.85743	+	4.95059i	0.387835	+	0.194778i
$647$	25.8659			1.01689			0.508446	−	0.861094i	$-0.330220\pi$
$647$	25.8659			1.01689			0.508446	+	0.861094i	$0.330220\pi$
$648$	−8.99134	+	0.394650i	−0.353213	+	0.0155033i
$649$	−31.8339			−1.24959
$650$	13.5964	+	6.82836i	0.533294	+	0.267830i
$651$	0.419680	+	4.25857i	0.0164486	+	0.166906i
$652$	−6.37357	−	8.56119i	−0.249608	−	0.335282i
$653$	0.658203	+	2.19855i	0.0257575	+	0.0860360i	0.969902	−	0.243496i	$-0.0782943\pi$
$653$	0.658203	+	2.19855i	0.0257575	+	0.0860360i	−0.944144	+	0.329532i	$0.893109\pi$
$654$	−14.4497	+	2.27870i	−0.565029	+	0.0891040i
$655$	−22.7497	−	52.7397i	−0.888903	−	2.06071i
$656$	1.97077	+	11.1768i	0.0769457	+	0.436381i
$657$	−16.1437	+	20.1194i	−0.629826	+	0.784932i
$658$	−1.26428	+	7.17007i	−0.0492866	+	0.279518i
$659$	−32.6804	+	7.74540i	−1.27305	+	0.301718i	−0.810952	−	0.585113i	$-0.801050\pi$
$659$	−32.6804	+	7.74540i	−1.27305	+	0.301718i	−0.462095	+	0.886830i	$0.652902\pi$
$660$	22.0056	−	20.0200i	0.856567	−	0.779279i
$661$	15.0448	+	9.89512i	0.585175	+	0.384875i	0.807299	−	0.590143i	$-0.200929\pi$
$661$	15.0448	+	9.89512i	0.585175	+	0.384875i	−0.222124	+	0.975018i	$0.571299\pi$
$662$	−1.20515	+	20.6917i	−0.0468396	+	0.804206i
$663$	−20.7651	−	16.0520i	−0.806451	−	0.623409i
$664$	2.60402	−	8.69804i	0.101056	−	0.337549i
$665$	4.82640	−	1.75667i	0.187160	−	0.0681206i
$666$	1.57250	−	3.31017i	0.0609329	−	0.128266i
$667$	9.14230	+	3.32753i	0.353991	+	0.128842i
$668$	1.13781	−	1.52835i	0.0440232	−	0.0591335i
$669$	−15.7238	+	8.70206i	−0.607915	+	0.336441i
$670$	−3.09376	−	0.733234i	−0.119522	−	0.0283273i
$671$	3.79041	−	8.78717i	0.146327	−	0.339225i
$672$	0.860277	+	0.841613i	0.0331859	+	0.0324659i
$673$	7.51146	−	4.94036i	0.289545	−	0.190437i	−0.396424	−	0.918068i	$-0.629749\pi$
$673$	7.51146	−	4.94036i	0.289545	−	0.190437i	0.685969	+	0.727631i	$0.259378\pi$
$674$	14.0117	+	24.2690i	0.539710	+	0.934806i
$675$	18.5920	+	15.4802i	0.715605	+	0.595834i
$676$	1.16068	−	2.01036i	0.0446416	−	0.0773215i
$677$	−1.07919	−	18.5289i	−0.0414765	−	0.712124i	−0.953390	−	0.301741i	$-0.902432\pi$
$677$	−1.07919	−	18.5289i	−0.0414765	−	0.712124i	0.911913	−	0.410383i	$-0.134605\pi$
$678$	20.0849	+	1.53547i	0.771356	+	0.0589693i
$679$	0.628000	−	0.0734027i	0.0241004	−	0.00281694i
$680$	9.88827	−	10.4810i	0.379198	−	0.401926i
$681$	−11.3288	+	13.0147i	−0.434121	+	0.498725i
$682$	−19.5209	−	2.28166i	−0.747493	−	0.0873694i
$683$	6.63544	−	5.56779i	0.253898	−	0.213046i	−0.506951	−	0.861975i	$-0.669227\pi$
$683$	6.63544	−	5.56779i	0.253898	−	0.213046i	0.760849	+	0.648929i	$0.224783\pi$
$684$	3.78982	−	6.04695i	0.144907	−	0.231211i
$685$	34.9281	+	29.3082i	1.33453	+	1.11981i
$686$	6.44534	+	6.83166i	0.246084	+	0.260834i
$687$	16.8133	−	32.0178i	0.641468	−	1.22156i
$688$	8.30605	−	4.17146i	0.316665	−	0.159035i
$689$	12.3680	−	6.21144i	0.471183	−	0.236637i
$690$	−20.2804	−	32.0867i	−0.772062	−	1.22152i
$691$	25.2925	+	26.8085i	0.962172	+	1.01984i	0.999789	+	0.0205505i	$0.00654189\pi$
$691$	25.2925	+	26.8085i	0.962172	+	1.01984i	−0.0376168	+	0.999292i	$0.511977\pi$
$692$	1.11657	+	0.936917i	0.0424458	+	0.0356162i
$693$	−2.41066	+	11.2670i	−0.0915732	+	0.427999i
$694$	8.35139	−	7.00765i	0.317015	−	0.266007i
$695$	39.5385	+	4.62139i	1.49978	+	0.175299i
$696$	2.34514	+	0.457479i	0.0888923	+	0.0173407i
$697$	−36.1152	+	38.2798i	−1.36796	+	1.44995i
$698$	16.0962	−	1.88138i	0.609250	−	0.0712111i
$699$	11.2845	−	16.4981i	0.426819	−	0.624014i
$700$	−0.188105	−	3.22964i	−0.00710969	−	0.122069i
$701$	−18.8835	+	32.7071i	−0.713218	+	1.23533i	0.250425	+	0.968136i	$0.419430\pi$
$701$	−18.8835	+	32.7071i	−0.713218	+	1.23533i	−0.963643	+	0.267194i	$0.913904\pi$
$702$	−11.6053	+	12.3952i	−0.438014	+	0.467825i
$703$	1.45293	+	2.51655i	0.0547983	+	0.0949134i
$704$	−4.61813	+	3.03739i	−0.174052	+	0.114476i
$705$	13.9981	−	54.6310i	0.527199	−	2.05752i
$706$	10.8350	−	25.1184i	0.407782	−	0.945344i
$707$	−13.3548	−	3.16515i	−0.502259	−	0.119038i
$708$	−0.180770	+	9.97361i	−0.00679374	+	0.374831i
$709$	−9.95354	+	13.3699i	−0.373813	+	0.502118i	−0.948727	−	0.316096i	$-0.897628\pi$
$709$	−9.95354	+	13.3699i	−0.373813	+	0.502118i	0.574914	+	0.818214i	$0.305035\pi$
$710$	−34.4177	−	12.5270i	−1.29167	−	0.470130i
$711$	−6.64754	−	25.5387i	−0.249302	−	0.957774i
$712$	3.47851	−	1.26608i	0.130363	−	0.0474482i
$713$	−7.19209	+	24.0233i	−0.269346	+	0.899678i
$714$	−0.748223	+	5.53032i	−0.0280015	+	0.206967i
$715$	3.26356	−	56.0332i	0.122050	−	2.09552i
$716$	3.02702	+	1.99090i	0.113125	+	0.0744035i
$717$	−1.06567	−	4.88967i	−0.0397983	−	0.182608i
$718$	−5.91967	+	1.40299i	−0.220920	+	0.0523590i
$719$	−0.219237	+	1.24336i	−0.00817617	+	0.0463694i	−0.988623	−	0.150415i	$-0.951939\pi$
$719$	−0.219237	+	1.24336i	−0.00817617	+	0.0463694i	0.980447	+	0.196785i	$0.0630500\pi$
$720$	−6.14736	−	7.00809i	−0.229099	−	0.261176i
$721$	0.716725	+	4.06475i	0.0266922	+	0.151379i
$722$	−5.28422	−	12.2502i	−0.196658	−	0.455905i
$723$	−0.0577549	−	0.0714191i	−0.00214793	−	0.00265610i
$724$	−6.36192	−	21.2503i	−0.236439	−	0.789761i
$725$	−3.83543	−	5.15188i	−0.142444	−	0.191336i
$726$	−30.8486	−	13.9752i	−1.14490	−	0.518668i
$727$	5.85101	+	2.93849i	0.217002	+	0.108982i	0.553980	−	0.832530i	$-0.313108\pi$
$727$	5.85101	+	2.93849i	0.217002	+	0.108982i	−0.336978	+	0.941513i	$0.609405\pi$
$728$	2.27060			0.0841539
$729$	−22.4445	+	15.0082i	−0.831277	+	0.555858i
$730$	−26.7190			−0.988915
$731$	38.5160	+	19.3434i	1.42456	+	0.715443i
$732$	−2.73151	−	1.23744i	−0.100960	−	0.0457372i
$733$	4.97694	+	6.68519i	0.183827	+	0.246923i	0.884478	−	0.466581i	$-0.154514\pi$
$733$	4.97694	+	6.68519i	0.183827	+	0.246923i	−0.700651	+	0.713504i	$0.747107\pi$
$734$	−5.15990	−	17.2353i	−0.190455	−	0.636166i
$735$	−22.0562	−	27.2745i	−0.813557	−	1.00604i
$736$	2.79341	+	6.47585i	0.102966	+	0.238703i
$737$	0.982093	+	5.56972i	0.0361759	+	0.205163i
$738$	22.4521	+	25.5958i	0.826475	+	0.942194i
$739$	2.08267	−	11.8114i	0.0766121	−	0.434489i	−0.922241	−	0.386615i	$-0.873644\pi$
$739$	2.08267	−	11.8114i	0.0766121	−	0.434489i	0.998853	−	0.0478740i	$-0.0152446\pi$
$740$	3.69357	−	0.875391i	0.135778	−	0.0321800i
$741$	−2.86711	−	13.1553i	−0.105326	−	0.483271i
$742$	−2.45869	−	1.61711i	−0.0902615	−	0.0593659i
$743$	−1.67970	+	28.8393i	−0.0616222	+	1.05801i	0.815813	+	0.578316i	$0.196290\pi$
$743$	−1.67970	+	28.8393i	−0.0616222	+	1.05801i	−0.877435	+	0.479696i	$0.840747\pi$
$744$	−0.825699	+	6.10297i	−0.0302716	+	0.223746i
$745$	−15.7876	+	52.7344i	−0.578414	+	1.93204i
$746$	22.4333	−	8.16506i	0.821342	−	0.298944i
$747$	−6.86134	−	26.3601i	−0.251043	−	0.964464i
$748$	−24.0856	−	8.76645i	−0.880658	−	0.320533i
$749$	1.34696	−	1.80929i	0.0492170	−	0.0661099i
$750$	0.0335585	−	1.85153i	0.00122538	−	0.0676081i
$751$	−6.59190	−	1.56231i	−0.240542	−	0.0570094i	0.108577	−	0.994088i	$-0.465371\pi$
$751$	−6.59190	−	1.56231i	−0.240542	−	0.0570094i	−0.349118	+	0.937079i	$0.613519\pi$
$752$	−4.15023	+	9.62132i	−0.151343	+	0.350853i
$753$	3.61187	−	14.0962i	0.131624	−	0.513695i
$754$	3.76631	−	2.47714i	0.137161	−	0.0902122i
$755$	24.5107	+	42.4537i	0.892034	+	1.54505i
$756$	3.51630	+	0.819244i	0.127887	+	0.0297956i
$757$	−10.9210	+	18.9158i	−0.396932	+	0.687506i	−0.993346	−	0.115171i	$-0.963258\pi$
$757$	−10.9210	+	18.9158i	−0.396932	+	0.687506i	0.596414	+	0.802677i	$0.296592\pi$
$758$	−1.37503	−	23.6084i	−0.0499433	−	0.857494i
$759$	−38.1196	+	55.7313i	−1.38365	+	2.02292i
$760$	7.34191	−	0.858146i	0.266319	−	0.0311282i
$761$	16.0381	−	16.9994i	0.581381	−	0.616228i	−0.368201	−	0.929746i	$-0.620026\pi$
$761$	16.0381	−	16.9994i	0.581381	−	0.616228i	0.949582	+	0.313518i	$0.101508\pi$
$762$	16.6841	+	3.25465i	0.604400	+	0.117903i
$763$	5.82866	+	0.681273i	0.211012	+	0.0246637i
$764$	−4.48296	+	3.76165i	−0.162188	+	0.136092i
$765$	9.04421	−	42.2712i	0.326994	−	1.52832i
$766$	−10.9251	−	9.16727i	−0.394741	−	0.331227i
$767$	12.9151	+	13.6892i	0.466338	+	0.494289i
$768$	0.925397	+	1.46412i	0.0333924	+	0.0528318i
$769$	34.6714	−	17.4126i	1.25028

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+(0.893633 + 0.448799i) q^{2} +(-1.57770 - 0.714739i) q^{3} +(0.597159 + 0.802123i) q^{4} +(0.891212 + 2.97686i) q^{5} +(-1.08911 - 1.34679i) q^{6} +(0.275210 + 0.638009i) q^{7} +(0.173648 + 0.984808i) q^{8} +(1.97830 + 2.25529i) q^{9} +(-0.539594 + 3.06019i) q^{10} +(5.37847 - 1.27472i) q^{11} +(-0.368831 - 1.69232i) q^{12} +(-2.73022 - 1.79570i) q^{13} +(-0.0404011 + 0.693660i) q^{14} +(0.721605 - 5.33358i) q^{15} +(-0.286803 + 0.957990i) q^{16} +(-4.35745 + 1.58598i) q^{17} +(0.755699 + 2.90326i) q^{18} +(-2.23534 - 0.813599i) q^{19} +(-1.85561 + 2.49252i) q^{20} +(0.0218094 - 1.20329i) q^{21} +(5.37847 + 1.27472i) q^{22} +(2.79341 - 6.47585i) q^{23} +(0.429915 - 1.67785i) q^{24} +(-3.88998 + 2.55848i) q^{25} +(-1.63391 - 2.83001i) q^{26} +(-1.50922 - 4.97215i) q^{27} +(-0.347418 + 0.601745i) q^{28} +(0.0802101 + 1.37715i) q^{29} +(3.03856 - 4.44241i) q^{30} +(-3.53161 + 0.412786i) q^{31} +(-0.686242 + 0.727374i) q^{32} +(-9.39673 - 1.83307i) q^{33} +(-4.60574 - 0.538334i) q^{34} +(-1.65399 + 1.38786i) q^{35} +(-0.627664 + 2.93360i) q^{36} +(-0.935772 - 0.785206i) q^{37} +(-1.63243 - 1.73028i) q^{38} +(3.02403 + 4.78447i) q^{39} +(-2.77687 + 1.39460i) q^{40} +(10.1420 - 5.09352i) q^{41} +(0.559527 - 1.06551i) q^{42} +(-6.37841 - 6.76072i) q^{43} +(4.23428 + 3.55299i) q^{44} +(-4.95059 + 7.89905i) q^{45} +(5.40264 - 4.53335i) q^{46} +(10.4074 + 1.21645i) q^{47} +(1.13720 - 1.30643i) q^{48} +(4.47238 - 4.74044i) q^{49} +(-4.62445 + 0.540521i) q^{50} +(8.00832 + 0.612227i) q^{51} +(-0.190007 - 3.26229i) q^{52} +(-2.11764 + 3.66786i) q^{53} +(0.882803 - 5.12061i) q^{54} +(8.58802 + 14.8749i) q^{55} +(-0.580527 + 0.381818i) q^{56} +(2.94520 + 2.88130i) q^{57} +(-0.546388 + 1.26667i) q^{58} +(-5.60397 - 1.32817i) q^{59} +(4.70910 - 2.60618i) q^{60} +(1.03387 - 1.38873i) q^{61} +(-3.34122 - 1.21611i) q^{62} +(-0.894449 + 1.88285i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(2.91232 - 9.72783i) q^{65} +(-7.57454 - 5.85533i) q^{66} +(-0.0594932 + 1.02146i) q^{67} +(-3.87424 - 2.54813i) q^{68} +(-9.03571 + 8.22041i) q^{69} +(-2.10093 + 0.497930i) q^{70} +(-2.04677 + 11.6078i) q^{71} +(-1.87750 + 2.33987i) q^{72} +(1.49312 + 8.46788i) q^{73} +(-0.483836 - 1.12166i) q^{74} +(7.96587 - 1.25620i) q^{75} +(-0.682248 - 2.27887i) q^{76} +(2.29349 + 3.08070i) q^{77} +(0.555105 + 5.63274i) q^{78} +(-7.86088 - 3.94788i) q^{79} -3.10740 q^{80} +(-1.17268 + 8.92327i) q^{81} +11.3492 q^{82} +(-8.11371 - 4.07486i) q^{83} +(0.978213 - 0.701063i) q^{84} +(-8.60465 - 11.5580i) q^{85} +(-2.66575 - 8.90423i) q^{86} +(0.857758 - 2.23007i) q^{87} +(2.18932 + 5.07541i) q^{88} +(-0.642803 - 3.64552i) q^{89} +(-7.96910 + 4.83703i) q^{90} +(0.394285 - 2.23610i) q^{91} +(6.86253 - 1.62645i) q^{92} +(5.86687 + 1.87293i) q^{93} +(8.75447 + 5.75790i) q^{94} +(0.429800 - 7.37939i) q^{95} +(1.60257 - 0.657097i) q^{96} +(0.260981 - 0.871736i) q^{97} +(6.12417 - 2.22901i) q^{98} +(13.5151 + 9.60824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38}+ \cdots - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

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