LMFDB - Embedded newform 216.2.l.b.35.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(35,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("216.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.l (of order $6$, degree $2$, not 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 7x^14 - 12x^13 + 16x^12 - 12x^11 - 8x^10 + 36x^9 - 68x^8 + 72x^7 - 32x^6 - 96x^5 + 256x^4 - 384x^3 + 448x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.3
Root			$-1.37702 - 0.322193i$ of defining polynomial
Character	$\chi$	$=$	216.35
Dual form			216.2.l.b.179.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.409484 - 1.35363i) q^{2} +(-1.66465 + 1.10858i) q^{4} +(0.565188 + 0.978934i) q^{5} +(3.71499 + 2.14485i) q^{7} +(2.18226 + 1.79937i) q^{8} +O(q^{10})$	\(q+(-0.409484 - 1.35363i) q^{2} +(-1.66465 + 1.10858i) q^{4} +(0.565188 + 0.978934i) q^{5} +(3.71499 + 2.14485i) q^{7} +(2.18226 + 1.79937i) q^{8} +(1.09368 - 1.16591i) q^{10} +(-1.00953 - 0.582853i) q^{11} +(2.64466 - 1.52689i) q^{13} +(1.38211 - 5.90701i) q^{14} +(1.54209 - 3.69079i) q^{16} -1.49654i q^{17} -3.42378 q^{19} +(-2.02607 - 1.00302i) q^{20} +(-0.375582 + 1.60520i) q^{22} +(3.85938 + 6.68464i) q^{23} +(1.86113 - 3.22356i) q^{25} +(-3.14980 - 2.95466i) q^{26} +(-8.56188 + 0.547960i) q^{28} +(0.709580 - 1.22903i) q^{29} +(-4.66408 + 2.69281i) q^{31} +(-5.62744 - 0.576097i) q^{32} +(-2.02576 + 0.612808i) q^{34} +4.84897i q^{35} -2.97201i q^{37} +(1.40198 + 4.63454i) q^{38} +(-0.528079 + 3.15327i) q^{40} +(4.23339 - 2.44415i) q^{41} +(-1.74292 + 3.01882i) q^{43} +(2.32665 - 0.148906i) q^{44} +(7.46820 - 7.96144i) q^{46} +(1.77991 - 3.08289i) q^{47} +(5.70075 + 9.87399i) q^{49} +(-5.12562 - 1.19928i) q^{50} +(-2.70973 + 5.47356i) q^{52} -11.2786 q^{53} -1.31769i q^{55} +(4.24769 + 11.3653i) q^{56} +(-1.95422 - 0.457243i) q^{58} +(-7.50935 + 4.33553i) q^{59} +(-3.16057 - 1.82476i) q^{61} +(5.55494 + 5.21079i) q^{62} +(1.52453 + 7.85340i) q^{64} +(2.98946 + 1.72596i) q^{65} +(-5.58255 - 9.66925i) q^{67} +(1.65904 + 2.49120i) q^{68} +(6.56373 - 1.98558i) q^{70} -2.54954 q^{71} -7.06491 q^{73} +(-4.02301 + 1.21699i) q^{74} +(5.69937 - 3.79554i) q^{76} +(-2.50026 - 4.33059i) q^{77} +(-2.24998 - 1.29902i) q^{79} +(4.48461 - 0.576391i) q^{80} +(-5.04198 - 4.72961i) q^{82} +(3.98482 + 2.30064i) q^{83} +(1.46501 - 0.845824i) q^{85} +(4.80008 + 1.12311i) q^{86} +(-1.15429 - 3.08846i) q^{88} -8.63803i q^{89} +13.0998 q^{91} +(-13.8350 - 6.84911i) q^{92} +(-4.90195 - 1.14695i) q^{94} +(-1.93508 - 3.35165i) q^{95} +(3.35869 - 5.81742i) q^{97} +(11.0314 - 11.7600i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 5 q^{4}+O(q^{10}) $ 16 * q + 3 * q^2 - 5 * q^4	$ 16 q + 3 q^{2} - 5 q^{4} - 12 q^{11} + 18 q^{14} + 7 q^{16} - 4 q^{19} - 18 q^{20} - q^{22} - 14 q^{25} - 12 q^{28} - 27 q^{32} - 13 q^{34} + 15 q^{38} - 12 q^{40} + 36 q^{41} + 8 q^{43} + 12 q^{46} + 10 q^{49} - 51 q^{50} - 18 q^{52} + 66 q^{56} + 12 q^{58} - 12 q^{59} + 34 q^{64} + 6 q^{65} - 16 q^{67} + 9 q^{68} + 18 q^{70} - 4 q^{73} + 60 q^{74} - 7 q^{76} - 22 q^{82} - 54 q^{83} + 51 q^{86} - 13 q^{88} - 36 q^{91} - 84 q^{92} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 16 * q + 3 * q^2 - 5 * q^4 - 12 * q^11 + 18 * q^14 + 7 * q^16 - 4 * q^19 - 18 * q^20 - q^22 - 14 * q^25 - 12 * q^28 - 27 * q^32 - 13 * q^34 + 15 * q^38 - 12 * q^40 + 36 * q^41 + 8 * q^43 + 12 * q^46 + 10 * q^49 - 51 * q^50 - 18 * q^52 + 66 * q^56 + 12 * q^58 - 12 * q^59 + 34 * q^64 + 6 * q^65 - 16 * q^67 + 9 * q^68 + 18 * q^70 - 4 * q^73 + 60 * q^74 - 7 * q^76 - 22 * q^82 - 54 * q^83 + 51 * q^86 - 13 * q^88 - 36 * q^91 - 84 * q^92 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.409484	−	1.35363i	−0.289549	−	0.957163i
$2$	−0.409484	−	1.35363i	−0.289549	−	0.957163i
$3$		0			0
$3$		0			0
$4$	−1.66465	+	1.10858i	−0.832323	+	0.554292i
$5$	0.565188	+	0.978934i	0.252760	+	0.437793i	0.964285	−	0.264868i	$-0.0853285\pi$
$5$	0.565188	+	0.978934i	0.252760	+	0.437793i	−0.711525	+	0.702661i	$0.751995\pi$
$6$		0			0
$7$	3.71499	+	2.14485i	1.40413	+	0.810677i	0.994814	−	0.101714i	$-0.0324328\pi$
$7$	3.71499	+	2.14485i	1.40413	+	0.810677i	0.409320	+	0.912391i	$0.365766\pi$
$8$	2.18226	+	1.79937i	0.771546	+	0.636174i
$9$		0			0
$10$	1.09368	−	1.16591i	0.345853	−	0.368695i
$11$	−1.00953	−	0.582853i	−0.304385	−	0.175737i	0.340026	−	0.940416i	$-0.389564\pi$
$11$	−1.00953	−	0.582853i	−0.304385	−	0.175737i	−0.644411	+	0.764679i	$0.722897\pi$
$12$		0			0
$13$	2.64466	−	1.52689i	0.733496	−	0.423484i	−0.0862038	−	0.996278i	$-0.527474\pi$
$13$	2.64466	−	1.52689i	0.733496	−	0.423484i	0.819700	+	0.572793i	$0.194140\pi$
$14$	1.38211	−	5.90701i	0.369384	−	1.57872i
$15$		0			0
$16$	1.54209	−	3.69079i	0.385522	−	0.922699i
$17$		−	1.49654i		−	0.362963i	−0.983394	−	0.181482i	$-0.941911\pi$
$17$		−	1.49654i		−	0.362963i	0.983394	−	0.181482i	$-0.0580893\pi$
$18$		0			0
$19$	−3.42378			−0.785468			−0.392734	−	0.919652i	$-0.628471\pi$
$19$	−3.42378			−0.785468			−0.392734	+	0.919652i	$0.628471\pi$
$20$	−2.02607	−	1.00302i	−0.453042	−	0.224282i
$21$		0			0
$22$	−0.375582	+	1.60520i	−0.0800744	+	0.342231i
$23$	3.85938	+	6.68464i	0.804736	+	1.39384i	0.916469	+	0.400106i	$0.131027\pi$
$23$	3.85938	+	6.68464i	0.804736	+	1.39384i	−0.111733	+	0.993738i	$0.535640\pi$
$24$		0			0
$25$	1.86113	−	3.22356i	0.372225	−	0.644713i
$26$	−3.14980	−	2.95466i	−0.617726	−	0.579456i
$27$		0			0
$28$	−8.56188	+	0.547960i	−1.61804	+	0.103555i
$29$	0.709580	−	1.22903i	0.131766	−	0.228225i	−0.792592	−	0.609753i	$-0.791269\pi$
$29$	0.709580	−	1.22903i	0.131766	−	0.228225i	0.924357	+	0.381528i	$0.124602\pi$
$30$		0			0
$31$	−4.66408	+	2.69281i	−0.837694	+	0.483643i	−0.856480	−	0.516181i	$-0.827353\pi$
$31$	−4.66408	+	2.69281i	−0.837694	+	0.483643i	0.0187859	+	0.999824i	$0.494020\pi$
$32$	−5.62744	−	0.576097i	−0.994801	−	0.101841i
$33$		0			0
$34$	−2.02576	+	0.612808i	−0.347415	+	0.105096i
$35$			4.84897i			0.819625i
$36$		0			0
$37$		−	2.97201i		−	0.488596i	−0.969700	−	0.244298i	$-0.921443\pi$
$37$		−	2.97201i		−	0.488596i	0.969700	−	0.244298i	$-0.0785575\pi$
$38$	1.40198	+	4.63454i	0.227432	+	0.751821i
$39$		0			0
$40$	−0.528079	+	3.15327i	−0.0834965	+	0.498576i
$41$	4.23339	−	2.44415i	0.661144	−	0.381712i	−0.131569	−	0.991307i	$-0.542001\pi$
$41$	4.23339	−	2.44415i	0.661144	−	0.381712i	0.792713	+	0.609595i	$0.208668\pi$
$42$		0			0
$43$	−1.74292	+	3.01882i	−0.265793	+	0.460366i	−0.967771	−	0.251832i	$-0.918967\pi$
$43$	−1.74292	+	3.01882i	−0.265793	+	0.460366i	0.701978	+	0.712198i	$0.252300\pi$
$44$	2.32665	−	0.148906i	0.350756	−	0.0224484i
$45$		0			0
$46$	7.46820	−	7.96144i	1.10113	−	1.17385i
$47$	1.77991	−	3.08289i	0.259627	−	0.449686i	−0.706515	−	0.707698i	$-0.749734\pi$
$47$	1.77991	−	3.08289i	0.259627	−	0.449686i	0.966142	+	0.258011i	$0.0830672\pi$
$48$		0			0
$49$	5.70075	+	9.87399i	0.814393	+	1.41057i
$50$	−5.12562	−	1.19928i	−0.724873	−	0.169604i
$51$		0			0
$52$	−2.70973	+	5.47356i	−0.375772	+	0.759046i
$53$	−11.2786			−1.54923			−0.774616	−	0.632432i	$-0.782057\pi$
$53$	−11.2786			−1.54923			−0.774616	+	0.632432i	$0.782057\pi$
$54$		0			0
$55$		−	1.31769i		−	0.177677i
$56$	4.24769	+	11.3653i	0.567622	+	1.51875i
$57$		0			0
$58$	−1.95422	−	0.457243i	−0.256601	−	0.0600390i
$59$	−7.50935	+	4.33553i	−0.977634	+	0.564437i	−0.901555	−	0.432664i	$-0.857573\pi$
$59$	−7.50935	+	4.33553i	−0.977634	+	0.564437i	−0.0760791	+	0.997102i	$0.524240\pi$
$60$		0			0
$61$	−3.16057	−	1.82476i	−0.404670	−	0.233636i	0.283827	−	0.958875i	$-0.408396\pi$
$61$	−3.16057	−	1.82476i	−0.404670	−	0.233636i	−0.688497	+	0.725239i	$0.741729\pi$
$62$	5.55494	+	5.21079i	0.705478	+	0.661771i
$63$		0			0
$64$	1.52453	+	7.85340i	0.190566	+	0.981674i
$65$	2.98946	+	1.72596i	0.370796	+	0.214079i
$66$		0			0
$67$	−5.58255	−	9.66925i	−0.682017	−	1.18129i	−0.974364	−	0.224975i	$-0.927770\pi$
$67$	−5.58255	−	9.66925i	−0.682017	−	1.18129i	0.292348	−	0.956312i	$-0.405563\pi$
$68$	1.65904	+	2.49120i	0.201188	+	0.302103i
$69$		0			0
$70$	6.56373	−	1.98558i	0.784515	−	0.237322i
$71$	−2.54954			−0.302574			−0.151287	−	0.988490i	$-0.548342\pi$
$71$	−2.54954			−0.302574			−0.151287	+	0.988490i	$0.548342\pi$
$72$		0			0
$73$	−7.06491			−0.826885			−0.413442	−	0.910530i	$-0.635674\pi$
$73$	−7.06491			−0.826885			−0.413442	+	0.910530i	$0.635674\pi$
$74$	−4.02301	+	1.21699i	−0.467666	+	0.141472i
$75$		0			0
$76$	5.69937	−	3.79554i	0.653763	−	0.435378i
$77$	−2.50026	−	4.33059i	−0.284932	−	0.493516i
$78$		0			0
$79$	−2.24998	−	1.29902i	−0.253142	−	0.146152i	0.368060	−	0.929802i	$-0.380022\pi$
$79$	−2.24998	−	1.29902i	−0.253142	−	0.146152i	−0.621202	+	0.783650i	$0.713355\pi$
$80$	4.48461	−	0.576391i	0.501395	−	0.0644424i
$81$		0			0
$82$	−5.04198	−	4.72961i	−0.556794	−	0.522298i
$83$	3.98482	+	2.30064i	0.437391	+	0.252528i	0.702490	−	0.711693i	$-0.252071\pi$
$83$	3.98482	+	2.30064i	0.437391	+	0.252528i	−0.265099	+	0.964221i	$0.585405\pi$
$84$		0			0
$85$	1.46501	−	0.845824i	0.158903	−	0.0917425i
$86$	4.80008	+	1.12311i	0.517606	+	0.121108i
$87$		0			0
$88$	−1.15429	−	3.08846i	−0.123048	−	0.329231i
$89$		−	8.63803i		−	0.915630i	−0.889048	−	0.457815i	$-0.848632\pi$
$89$		−	8.63803i		−	0.915630i	0.889048	−	0.457815i	$-0.151368\pi$
$90$		0			0
$91$	13.0998			1.37323
$92$	−13.8350	−	6.84911i	−1.44240	−	0.714069i
$93$		0			0
$94$	−4.90195	−	1.14695i	−0.505598	−	0.118299i
$95$	−1.93508	−	3.35165i	−0.198535	−	0.343872i
$96$		0			0
$97$	3.35869	−	5.81742i	0.341023	−	0.590670i	−0.643600	−	0.765362i	$-0.722560\pi$
$97$	3.35869	−	5.81742i	0.341023	−	0.590670i	0.984623	+	0.174693i	$0.0558931\pi$
$98$	11.0314	−	11.7600i	1.11434	−	1.18794i
$99$		0			0
$100$	0.475475	+	7.42930i	0.0475475	+	0.742930i
$101$	6.86479	−	11.8902i	0.683072	−	1.18312i	−0.290967	−	0.956733i	$-0.593977\pi$
$101$	6.86479	−	11.8902i	0.683072	−	1.18312i	0.974039	−	0.226382i	$-0.0726897\pi$
$102$		0			0
$103$	−5.48137	+	3.16467i	−0.540095	+	0.311824i	−0.745118	−	0.666933i	$-0.767607\pi$
$103$	−5.48137	+	3.16467i	−0.540095	+	0.311824i	0.205022	+	0.978757i	$0.434273\pi$
$104$	8.51878	+	1.42664i	0.835335	+	0.139894i
$105$		0			0
$106$	4.61840	+	15.2671i	0.448579	+	1.48287i
$107$		−	10.4483i		−	1.01007i	−0.863097	−	0.505037i	$-0.831479\pi$
$107$		−	10.4483i		−	1.01007i	0.863097	−	0.505037i	$-0.168521\pi$
$108$		0			0
$109$			9.67531i			0.926727i	0.886168	+	0.463364i	$0.153358\pi$
$109$			9.67531i			0.926727i	−0.886168	+	0.463364i	$0.846642\pi$
$110$	−1.78366	+	0.539572i	−0.170066	+	0.0514462i
$111$		0			0
$112$	13.6450	−	10.4037i	1.28933	−	0.983058i
$113$	−7.15149	+	4.12891i	−0.672756	+	0.388416i	−0.797120	−	0.603821i	$-0.793644\pi$
$113$	−7.15149	+	4.12891i	−0.672756	+	0.388416i	0.124364	+	0.992237i	$0.460311\pi$
$114$		0			0
$115$	−4.36255	+	7.55615i	−0.406810	+	0.704615i
$116$	0.181281	+	2.83253i	0.0168316	+	0.262993i
$117$		0			0
$118$	8.94367	+	8.38958i	0.823332	+	0.772323i
$119$	3.20984	−	5.55961i	0.294246	−	0.509649i
$120$		0			0
$121$	−4.82056	−	8.34946i	−0.438233	−	0.759042i
$122$	−1.17585	+	5.02547i	−0.106456	+	0.454984i
$123$		0			0
$124$	4.77884	−	9.65309i	0.429152	−	0.866873i
$125$	9.85942			0.881853
$126$		0			0
$127$		−	2.78757i		−	0.247357i	−0.992322	−	0.123678i	$-0.960531\pi$
$127$		−	2.78757i		−	0.247357i	0.992322	−	0.123678i	$-0.0394691\pi$
$128$	10.0063	−	5.27949i	0.884444	−	0.466645i
$129$		0			0
$130$	1.11219	−	4.75338i	0.0975451	−	0.416899i
$131$	13.0529	−	7.53612i	1.14044	−	0.658434i	0.193901	−	0.981021i	$-0.437886\pi$
$131$	13.0529	−	7.53612i	1.14044	−	0.658434i	0.946540	+	0.322587i	$0.104553\pi$
$132$		0			0
$133$	−12.7193	−	7.34348i	−1.10290	−	0.636761i
$134$	−10.8027	+	11.5161i	−0.933207	+	0.994842i
$135$		0			0
$136$	2.69283	−	3.26583i	0.230908	−	0.280043i
$137$	−7.55211	−	4.36021i	−0.645220	−	0.372518i	0.141402	−	0.989952i	$-0.454839\pi$
$137$	−7.55211	−	4.36021i	−0.645220	−	0.372518i	−0.786623	+	0.617434i	$0.788172\pi$
$138$		0			0
$139$	1.18897	+	2.05935i	0.100847	+	0.174672i	0.912034	−	0.410115i	$-0.134511\pi$
$139$	1.18897	+	2.05935i	0.100847	+	0.174672i	−0.811187	+	0.584787i	$0.801178\pi$
$140$	−5.37549	−	8.07181i	−0.454311	−	0.682193i
$141$		0			0
$142$	1.04400	+	3.45114i	0.0876101	+	0.289613i
$143$	−3.55982			−0.297687
$144$		0			0
$145$	1.60418			0.133220
$146$	2.89297	+	9.56329i	0.239424	+	0.791463i
$147$		0			0
$148$	3.29472	+	4.94734i	0.270824	+	0.406669i
$149$	8.94426	+	15.4919i	0.732742	+	1.26915i	0.955707	+	0.294320i	$0.0950931\pi$
$149$	8.94426	+	15.4919i	0.732742	+	1.26915i	−0.222965	+	0.974826i	$0.571574\pi$
$150$		0			0
$151$	2.39162	+	1.38080i	0.194627	+	0.112368i	0.594147	−	0.804357i	$-0.297490\pi$
$151$	2.39162	+	1.38080i	0.194627	+	0.112368i	−0.399520	+	0.916725i	$0.630823\pi$
$152$	−7.47158	−	6.16065i	−0.606025	−	0.499694i
$153$		0			0
$154$	−4.83820	+	5.15775i	−0.389874	+	0.415623i
$155$	−5.27216	−	3.04388i	−0.423470	−	0.244491i
$156$		0			0
$157$	2.21148	−	1.27680i	0.176495	−	0.101900i	−0.409150	−	0.912467i	$-0.634175\pi$
$157$	2.21148	−	1.27680i	0.176495	−	0.101900i	0.585645	+	0.810568i	$0.300841\pi$
$158$	−0.837073	+	3.57757i	−0.0665939	+	0.284616i
$159$		0			0
$160$	−2.61660	−	5.83450i	−0.206860	−	0.461258i
$161$			33.1111i			2.60952i
$162$		0			0
$163$	6.93355			0.543077			0.271539	−	0.962428i	$-0.412468\pi$
$163$	6.93355			0.543077			0.271539	+	0.962428i	$0.412468\pi$
$164$	−4.33755	+	8.76170i	−0.338706	+	0.684174i
$165$		0			0
$166$	1.48250	−	6.33607i	0.115064	−	0.491774i
$167$	−8.36829	−	14.4943i	−0.647558	−	1.12160i	−0.983704	−	0.179794i	$-0.942457\pi$
$167$	−8.36829	−	14.4943i	−0.647558	−	1.12160i	0.336146	−	0.941810i	$-0.390876\pi$
$168$		0			0
$169$	−1.83719	+	3.18211i	−0.141322	+	0.244778i
$170$	−1.74483	−	1.63673i	−0.133823	−	0.125532i
$171$		0			0
$172$	−0.445276	−	6.95744i	−0.0339520	−	0.530500i
$173$	−10.2190	+	17.6999i	−0.776938	+	1.34570i	0.156761	+	0.987637i	$0.449895\pi$
$173$	−10.2190	+	17.6999i	−0.776938	+	1.34570i	−0.933699	+	0.358059i	$0.883438\pi$
$174$		0			0
$175$	13.8281	−	7.98367i	1.04531	−	0.603508i
$176$	−3.70798	+	2.82716i	−0.279499	+	0.213105i
$177$		0			0
$178$	−11.6927	+	3.53714i	−0.876407	+	0.265120i
$179$			4.07982i			0.304940i	0.988308	+	0.152470i	$0.0487227\pi$
$179$			4.07982i			0.304940i	−0.988308	+	0.152470i	$0.951277\pi$
$180$		0			0
$181$			22.3226i			1.65923i	0.558337	+	0.829614i	$0.311440\pi$
$181$			22.3226i			1.65923i	−0.558337	+	0.829614i	$0.688560\pi$
$182$	−5.36417	−	17.7324i	−0.397619	−	1.31441i
$183$		0			0
$184$	−3.60598	+	21.5321i	−0.265836	+	1.58737i
$185$	2.90940	−	1.67974i	0.213904	−	0.123497i
$186$		0			0
$187$	−0.872261	+	1.51080i	−0.0637861	+	0.110481i
$188$	0.454726	+	7.10510i	0.0331643	+	0.518193i
$189$		0			0
$190$	−3.74452	+	3.99183i	−0.271656	+	0.289598i
$191$	−7.27481	+	12.6003i	−0.526387	+	0.911728i	0.473141	+	0.880987i	$0.343120\pi$
$191$	−7.27481	+	12.6003i	−0.526387	+	0.911728i	−0.999527	+	0.0307415i	$0.990213\pi$
$192$		0			0
$193$	2.19526	+	3.80230i	0.158018	+	0.273696i	0.934154	−	0.356870i	$-0.116156\pi$
$193$	2.19526	+	3.80230i	0.158018	+	0.273696i	−0.776136	+	0.630566i	$0.782823\pi$
$194$	−9.24999	−	2.16429i	−0.664110	−	0.155387i
$195$		0			0
$196$	−20.4359	−	10.1169i	−1.45971	−	0.722638i
$197$	7.69721			0.548404			0.274202	−	0.961672i	$-0.411586\pi$
$197$	7.69721			0.548404			0.274202	+	0.961672i	$0.411586\pi$
$198$		0			0
$199$		−	20.9790i		−	1.48716i	−0.668646	−	0.743580i	$-0.733126\pi$
$199$		−	20.9790i		−	1.48716i	0.668646	−	0.743580i	$-0.266874\pi$
$200$	9.86185	−	3.68580i	0.697338	−	0.260626i
$201$		0			0
$202$	−18.9059	−	4.42357i	−1.33022	−	0.311241i
$203$	5.27216	−	3.04388i	0.370033	−	0.213639i
$204$		0			0
$205$	4.78532	+	2.76280i	0.334221	+	0.192963i
$206$	6.52834	+	6.12388i	0.454851	+	0.426671i
$207$		0			0
$208$	−1.55716	−	12.1155i	−0.107970	−	0.840058i
$209$	3.45641	+	1.99556i	0.239085	+	0.138036i
$210$		0			0
$211$	2.38482	+	4.13063i	0.164178	+	0.284364i	0.936363	−	0.351033i	$-0.114170\pi$
$211$	2.38482	+	4.13063i	0.164178	+	0.284364i	−0.772185	+	0.635397i	$0.780836\pi$
$212$	18.7748	−	12.5032i	1.28946	−	0.858726i
$213$		0			0
$214$	−14.1432	+	4.27841i	−0.966806	+	0.292466i
$215$	−3.94031			−0.268727
$216$		0			0
$217$	−23.1027			−1.56831
$218$	13.0968	−	3.96189i	0.887029	−	0.268333i
$219$		0			0
$220$	1.46076	+	2.19348i	0.0984847	+	0.147884i
$221$	−2.28505	−	3.95783i	−0.153709	−	0.266232i
$222$		0			0
$223$	12.5272	+	7.23260i	0.838886	+	0.484331i	0.856885	−	0.515507i	$-0.172396\pi$
$223$	12.5272	+	7.23260i	0.838886	+	0.484331i	−0.0179997	+	0.999838i	$0.505730\pi$
$224$	−19.6702	−	14.2102i	−1.31427	−	0.949459i
$225$		0			0
$226$	8.51746	+	7.98977i	0.566573	+	0.531471i
$227$	−0.561821	−	0.324367i	−0.0372894	−	0.0215290i	0.481239	−	0.876589i	$-0.340187\pi$
$227$	−0.561821	−	0.324367i	−0.0372894	−	0.0215290i	−0.518529	+	0.855060i	$0.673520\pi$
$228$		0			0
$229$	12.0007	−	6.92863i	0.793032	−	0.457857i	−0.0479971	−	0.998847i	$-0.515284\pi$
$229$	12.0007	−	6.92863i	0.793032	−	0.457857i	0.841029	+	0.540990i	$0.181950\pi$
$230$	12.0147	+	2.81116i	0.792223	+	0.185363i
$231$		0			0
$232$	3.75997	−	1.40526i	0.246854	−	0.0922601i
$233$		−	23.1276i		−	1.51514i	−0.652755	−	0.757569i	$-0.726387\pi$
$233$		−	23.1276i		−	1.51514i	0.652755	−	0.757569i	$-0.273613\pi$
$234$		0			0
$235$	4.02393			0.262492
$236$	7.69411	−	15.5418i	0.500844	−	1.01169i
$237$		0			0
$238$	−8.84006	−	2.06838i	−0.573016	−	0.134073i
$239$	7.44075	+	12.8878i	0.481302	+	0.833640i	0.999770	−	0.0214576i	$-0.00683070\pi$
$239$	7.44075	+	12.8878i	0.481302	+	0.833640i	−0.518468	+	0.855097i	$0.673497\pi$
$240$		0			0
$241$	−5.87960	+	10.1838i	−0.378738	+	0.655994i	−0.990879	−	0.134755i	$-0.956975\pi$
$241$	−5.87960	+	10.1838i	−0.378738	+	0.655994i	0.612141	+	0.790749i	$0.290309\pi$
$242$	−9.32816	+	9.94425i	−0.599637	+	0.639241i
$243$		0			0
$244$	7.28413	−	0.466184i	0.466319	−	0.0298444i
$245$	−6.44399	+	11.1613i	−0.411691	+	0.713071i
$246$		0			0
$247$	−9.05472	+	5.22774i	−0.576138	+	0.332633i
$248$	−15.0236	−	2.51600i	−0.954000	−	0.159766i
$249$		0			0
$250$	−4.03728	−	13.3460i	−0.255340	−	0.844077i
$251$		−	5.51619i		−	0.348179i	−0.984730	−	0.174089i	$-0.944302\pi$
$251$		−	5.51619i		−	0.348179i	0.984730	−	0.174089i	$-0.0556981\pi$
$252$		0			0
$253$		−	8.99781i		−	0.565687i
$254$	−3.77334	+	1.14147i	−0.236761	+	0.0716219i
$255$		0			0
$256$	−11.2439	−	11.3831i	−0.702746	−	0.711441i
$257$	−16.9194	+	9.76841i	−1.05540	+	0.609337i	−0.924157	−	0.382013i	$-0.875231\pi$
$257$	−16.9194	+	9.76841i	−1.05540	+	0.609337i	−0.131245	+	0.991350i	$0.541898\pi$
$258$		0			0
$259$	6.37451	−	11.0410i	0.396093	−	0.686053i
$260$	−6.88976	+	0.440944i	−0.427285	+	0.0273462i
$261$		0			0
$262$	−15.5461	−	14.5830i	−0.960442	−	0.900939i
$263$	−5.62576	+	9.74411i	−0.346899	+	0.600847i	−0.985697	−	0.168527i	$-0.946099\pi$
$263$	−5.62576	+	9.74411i	−0.346899	+	0.600847i	0.638798	+	0.769375i	$0.279432\pi$
$264$		0			0
$265$	−6.37451	−	11.0410i	−0.391583	−	0.678242i
$266$	−4.73203	+	20.2243i	−0.290140	+	1.24003i
$267$		0			0
$268$	20.0121	+	9.90716i	1.22244	+	0.605176i
$269$	14.1600			0.863350			0.431675	−	0.902029i	$-0.357923\pi$
$269$	14.1600			0.863350			0.431675	+	0.902029i	$0.357923\pi$
$270$		0			0
$271$			3.91574i			0.237864i	0.992902	+	0.118932i	$0.0379471\pi$
$271$			3.91574i			0.237864i	−0.992902	+	0.118932i	$0.962053\pi$
$272$	−5.52341	−	2.30779i	−0.334906	−	0.139930i
$273$		0			0
$274$	−2.80966	+	12.0082i	−0.169738	+	0.725443i
$275$	−3.75773	+	2.16953i	−0.226600	+	0.130827i
$276$		0			0
$277$	22.9537	+	13.2523i	1.37915	+	0.796253i	0.992057	−	0.125787i	$-0.0401455\pi$
$277$	22.9537	+	13.2523i	1.37915	+	0.796253i	0.387094	+	0.922040i	$0.373479\pi$
$278$	2.30074	−	2.45270i	0.137989	−	0.147103i
$279$		0			0
$280$	−8.72510	+	10.5817i	−0.521424	+	0.632378i
$281$	0.923368	+	0.533106i	0.0550835	+	0.0318025i	0.527289	−	0.849686i	$-0.323209\pi$
$281$	0.923368	+	0.533106i	0.0550835	+	0.0318025i	−0.472205	+	0.881489i	$0.656542\pi$
$282$		0			0
$283$	1.77840	+	3.08028i	0.105715	+	0.183103i	0.914030	−	0.405647i	$-0.132954\pi$
$283$	1.77840	+	3.08028i	0.105715	+	0.183103i	−0.808315	+	0.588750i	$0.799620\pi$
$284$	4.24407	−	2.82637i	0.251839	−	0.167714i
$285$		0			0
$286$	1.45769	+	4.81869i	0.0861951	+	0.284935i
$287$	20.9693			1.23778
$288$		0			0
$289$	14.7604			0.868258
$290$	−0.656888	−	2.17148i	−0.0385738	−	0.127514i
$291$		0			0
$292$	11.7606	−	7.83203i	0.688235	−	0.458335i
$293$	−7.78958	−	13.4919i	−0.455072	−	0.788208i	0.543620	−	0.839331i	$-0.317053\pi$
$293$	−7.78958	−	13.4919i	−0.455072	−	0.788208i	−0.998692	+	0.0511233i	$0.983720\pi$
$294$		0			0
$295$	−8.48839	−	4.90077i	−0.494213	−	0.285334i
$296$	5.34775	−	6.48570i	0.310832	−	0.376974i
$297$		0			0
$298$	17.3078	−	18.4509i	1.00262	−	1.06883i
$299$	20.4135	+	11.7857i	1.18054	+	0.681586i
$300$		0			0
$301$	−12.9498	+	7.47659i	−0.746416	+	0.430944i
$302$	0.889768	−	3.80279i	0.0512004	−	0.218826i
$303$		0			0
$304$	−5.27976	+	12.6365i	−0.302815	+	0.724751i
$305$		−	4.12532i		−	0.236215i
$306$		0			0
$307$	−0.960690			−0.0548295			−0.0274147	−	0.999624i	$-0.508727\pi$
$307$	−0.960690			−0.0548295			−0.0274147	+	0.999624i	$0.508727\pi$
$308$	8.96287	+	4.43714i	0.510707	+	0.252829i
$309$		0			0
$310$	−1.96143	+	8.38300i	−0.111402	+	0.476122i
$311$	−4.49539	−	7.78624i	−0.254910	−	0.441517i	0.709961	−	0.704241i	$-0.248713\pi$
$311$	−4.49539	−	7.78624i	−0.254910	−	0.441517i	−0.964871	+	0.262724i	$0.915379\pi$
$312$		0			0
$313$	8.55885	−	14.8244i	0.483775	−	0.837923i	−0.516051	−	0.856558i	$-0.672599\pi$
$313$	8.55885	−	14.8244i	0.483775	−	0.837923i	0.999826	+	0.0186349i	$0.00593201\pi$
$314$	−2.63388	−	2.47070i	−0.148639	−	0.139430i
$315$		0			0
$316$	5.18549	−	0.331871i	0.291707	−	0.0186692i
$317$	3.96528	−	6.86806i	0.222712	−	0.385749i	−0.732919	−	0.680316i	$-0.761842\pi$
$317$	3.96528	−	6.86806i	0.222712	−	0.385749i	0.955631	+	0.294568i	$0.0951757\pi$
$318$		0			0
$319$	−1.43269	+	0.827162i	−0.0802151	+	0.0463122i
$320$	−6.82631	+	5.93105i	−0.381602	+	0.331556i
$321$		0			0
$322$	44.8203	−	13.5585i	2.49774	−	0.755585i
$323$			5.12381i			0.285096i
$324$		0			0
$325$		−	11.3670i		−	0.630526i
$326$	−2.83918	−	9.38548i	−0.157248	−	0.519814i
$327$		0			0
$328$	13.6363	+	2.28367i	0.752938	+	0.126095i
$329$	13.2247	−	7.63528i	0.729101	−	0.420946i
$330$		0			0
$331$	4.78348	−	8.28523i	0.262924	−	0.455397i	−0.704094	−	0.710107i	$-0.748647\pi$
$331$	4.78348	−	8.28523i	0.262924	−	0.455397i	0.967018	+	0.254710i	$0.0819799\pi$
$332$	−9.18377	+	0.587761i	−0.504025	+	0.0322576i
$333$		0			0
$334$	−16.1933	+	17.2628i	−0.886058	+	0.944578i
$335$	6.31037	−	10.9299i	0.344773	−	0.597164i
$336$		0			0
$337$	17.0727	+	29.5707i	0.930007	+	1.61082i	0.783305	+	0.621638i	$0.213532\pi$
$337$	17.0727	+	29.5707i	0.930007	+	1.61082i	0.146702	+	0.989181i	$0.453134\pi$
$338$	5.05971	+	1.18386i	0.275212	+	0.0643935i
$339$		0			0
$340$	−1.50106	+	3.03208i	−0.0814062	+	0.164438i
$341$	6.27805			0.339975
$342$		0			0
$343$			18.8811i			1.01949i
$344$	−9.23549	+	3.45170i	−0.497944	+	0.186103i
$345$		0			0
$346$	28.1437	+	6.58499i	1.51301	+	0.354011i
$347$	−20.9431	+	12.0915i	−1.12428	+	0.649105i	−0.942491	−	0.334232i	$-0.891523\pi$
$347$	−20.9431	+	12.0915i	−1.12428	+	0.649105i	−0.181792	+	0.983337i	$0.558190\pi$
$348$		0			0
$349$	−9.71845	−	5.61095i	−0.520217	−	0.300347i	0.216807	−	0.976215i	$-0.430436\pi$
$349$	−9.71845	−	5.61095i	−0.520217	−	0.300347i	−0.737023	+	0.675867i	$0.763769\pi$
$350$	−16.4694	−	15.4490i	−0.880324	−	0.825784i
$351$		0			0
$352$	5.34530	+	3.86156i	0.284906	+	0.205822i
$353$	5.85176	+	3.37852i	0.311458	+	0.179820i	0.647579	−	0.761999i	$-0.275782\pi$
$353$	5.85176	+	3.37852i	0.311458	+	0.179820i	−0.336121	+	0.941819i	$0.609115\pi$
$354$		0			0
$355$	−1.44097	−	2.49583i	−0.0764786	−	0.132465i
$356$	9.57598	+	14.3793i	0.507526	+	0.762099i
$357$		0			0
$358$	5.52258	−	1.67062i	0.291877	−	0.0882951i
$359$	20.3395			1.07348			0.536739	−	0.843748i	$-0.319656\pi$
$359$	20.3395			1.07348			0.536739	+	0.843748i	$0.319656\pi$
$360$		0			0
$361$	−7.27775			−0.383039
$362$	30.2167	−	9.14077i	1.58815	−	0.480428i
$363$		0			0
$364$	−21.8066	+	14.5222i	−1.14297	+	0.761172i
$365$	−3.99300	−	6.91608i	−0.209003	−	0.362004i
$366$		0			0
$367$	−11.7198	−	6.76642i	−0.611767	−	0.353204i	0.161889	−	0.986809i	$-0.448241\pi$
$367$	−11.7198	−	6.76642i	−0.611767	−	0.353204i	−0.773657	+	0.633605i	$0.781575\pi$
$368$	30.6231	−	3.93588i	1.59634	−	0.205172i
$369$		0			0
$370$	−3.46511	−	3.25043i	−0.180143	−	0.168982i
$371$	−41.8998	−	24.1908i	−2.17533	−	1.25593i
$372$		0			0
$373$	−23.0364	+	13.3001i	−1.19278	+	0.688651i	−0.958936	−	0.283623i	$-0.908464\pi$
$373$	−23.0364	+	13.3001i	−1.19278	+	0.688651i	−0.233843	+	0.972274i	$0.575130\pi$
$374$	2.40225	+	0.562073i	0.124217	+	0.0290641i
$375$		0			0
$376$	9.43150	−	3.52496i	0.486393	−	0.181786i
$377$		−	4.33381i		−	0.223203i
$378$		0			0
$379$	−28.5030			−1.46410			−0.732050	−	0.681251i	$-0.761436\pi$
$379$	−28.5030			−1.46410			−0.732050	+	0.681251i	$0.761436\pi$
$380$	6.93680	+	3.43412i	0.355850	+	0.176166i
$381$		0			0
$382$	20.0352	+	4.68778i	1.02509	+	0.239848i
$383$	−10.0515	−	17.4097i	−0.513606	−	0.889592i	−0.999875	−	0.0157832i	$-0.994976\pi$
$383$	−10.0515	−	17.4097i	−0.513606	−	0.889592i	0.486269	−	0.873809i	$-0.338357\pi$
$384$		0			0
$385$	2.82624	−	4.89519i	0.144038	−	0.249482i
$386$	4.24800	−	4.52856i	0.216217	−	0.230498i
$387$		0			0
$388$	0.858068	+	13.4073i	0.0435618	+	0.680654i
$389$	−1.08110	+	1.87253i	−0.0548142	+	0.0949409i	−0.892130	−	0.451778i	$-0.850790\pi$
$389$	−1.08110	+	1.87253i	−0.0548142	+	0.0949409i	0.837316	+	0.546719i	$0.184123\pi$
$390$		0			0
$391$	10.0038	−	5.77570i	0.505914	−	0.292090i
$392$	−5.32645	+	31.8054i	−0.269026	+	1.60642i
$393$		0			0
$394$	−3.15189	−	10.4192i	−0.158790	−	0.524912i
$395$		−	2.93677i		−	0.147765i
$396$		0			0
$397$		−	18.8504i		−	0.946076i	−0.881042	−	0.473038i	$-0.843157\pi$
$397$		−	18.8504i		−	0.946076i	0.881042	−	0.473038i	$-0.156843\pi$
$398$	−28.3979	+	8.59057i	−1.42346	+	0.430606i
$399$		0			0
$400$	−9.02750	−	11.8400i	−0.451375	−	0.592002i
$401$	15.0668	−	8.69883i	0.752401	−	0.434399i	−0.0741601	−	0.997246i	$-0.523628\pi$
$401$	15.0668	−	8.69883i	0.752401	−	0.434399i	0.826561	+	0.562848i	$0.190294\pi$
$402$		0			0
$403$	−8.22326	+	14.2431i	−0.409630	+	0.709500i
$404$	1.75380	+	27.4031i	0.0872546	+	1.36335i
$405$		0			0
$406$	−6.27917	−	5.89015i	−0.311630	−	0.292323i
$407$	−1.73225	+	3.00034i	−0.0858643	+	0.148721i
$408$		0			0
$409$	−10.2872	−	17.8179i	−0.508667	−	0.881037i	−0.999950	−	0.0100370i	$-0.996805\pi$
$409$	−10.2872	−	17.8179i	−0.508667	−	0.881037i	0.491282	−	0.871000i	$-0.336528\pi$
$410$	1.78031	−	7.60889i	0.0879233	−	0.375776i
$411$		0			0
$412$	5.61624	−	11.3446i	0.276692	−	0.558909i
$413$	−37.1962			−1.83030
$414$		0			0
$415$			5.20117i			0.255316i
$416$	−15.7623	+	7.06893i	−0.772810	+	0.346583i
$417$		0			0
$418$	1.28591	−	5.49586i	0.0628959	−	0.268811i
$419$	24.1959	−	13.9695i	1.18205	−	0.682455i	0.225560	−	0.974229i	$-0.427579\pi$
$419$	24.1959	−	13.9695i	1.18205	−	0.682455i	0.956487	+	0.291774i	$0.0942454\pi$
$420$		0			0
$421$	−6.27826	−	3.62475i	−0.305983	−	0.176660i	0.339144	−	0.940734i	$-0.389863\pi$
$421$	−6.27826	−	3.62475i	−0.305983	−	0.176660i	−0.645128	+	0.764075i	$0.723196\pi$
$422$	4.61481	−	4.91960i	0.224645	−	0.239482i
$423$		0			0
$424$	−24.6128	−	20.2944i	−1.19530	−	0.985581i
$425$	−4.82418	−	2.78524i	−0.234007	−	0.135104i
$426$		0			0
$427$	−7.82766	−	13.5579i	−0.378807	−	0.656113i
$428$	11.5828	+	17.3927i	0.559876	+	0.840708i
$429$		0			0
$430$	1.61349	+	5.33373i	0.0778096	+	0.257215i
$431$	−37.7004			−1.81596			−0.907982	−	0.419009i	$-0.862377\pi$
$431$	−37.7004			−1.81596			−0.907982	+	0.419009i	$0.862377\pi$
$432$		0			0
$433$	36.1185			1.73575			0.867873	−	0.496787i	$-0.165487\pi$
$433$	36.1185			1.73575			0.867873	+	0.496787i	$0.165487\pi$
$434$	9.46018	+	31.2725i	0.454103	+	1.50113i
$435$		0			0
$436$	−10.7259	−	16.1060i	−0.513677	−	0.771336i
$437$	−13.2137	−	22.8867i	−0.632095	−	1.09482i
$438$		0			0
$439$	9.02239	+	5.20908i	0.430615	+	0.248616i	0.699609	−	0.714526i	$-0.253358\pi$
$439$	9.02239	+	5.20908i	0.430615	+	0.248616i	−0.268993	+	0.963142i	$0.586691\pi$
$440$	2.37101	−	2.87554i	0.113033	−	0.137086i
$441$		0			0
$442$	−4.42175	+	4.71379i	−0.210321	+	0.224212i
$443$	30.7905	+	17.7769i	1.46290	+	0.844606i	0.999144	−	0.0413574i	$-0.0131682\pi$
$443$	30.7905	+	17.7769i	1.46290	+	0.844606i	0.463756	+	0.885963i	$0.346502\pi$
$444$		0			0
$445$	8.45606	−	4.88211i	0.400856	−	0.231434i
$446$	4.66058	−	19.9189i	0.220685	−	0.943188i
$447$		0			0
$448$	−11.1808	+	32.4451i	−0.528241	+	1.53289i
$449$			16.7750i			0.791662i	0.918323	+	0.395831i	$0.129543\pi$
$449$			16.7750i			0.791662i	−0.918323	+	0.395831i	$0.870457\pi$
$450$		0			0
$451$	−5.69832			−0.268323
$452$	7.32745	−	14.8012i	0.344654	−	0.696190i
$453$		0			0
$454$	−0.209018	+	0.893323i	−0.00980968	+	0.0419257i
$455$	7.40386	+	12.8239i	0.347098	+	0.601192i
$456$		0			0
$457$	−0.679436	+	1.17682i	−0.0317827	+	0.0550492i	−0.881479	−	0.472223i	$-0.843452\pi$
$457$	−0.679436	+	1.17682i	−0.0317827	+	0.0550492i	0.849697	+	0.527272i	$0.176785\pi$
$458$	−14.2929	−	13.4074i	−0.667866	−	0.626489i
$459$		0			0
$460$	−1.11453	−	17.4146i	−0.0519653	−	0.811958i
$461$	5.07410	−	8.78860i	0.236324	−	0.409326i	−0.723332	−	0.690500i	$-0.757391\pi$
$461$	5.07410	−	8.78860i	0.236324	−	0.409326i	0.959657	+	0.281174i	$0.0907238\pi$
$462$		0			0
$463$	−23.2656	+	13.4324i	−1.08124	+	0.624256i	−0.931232	−	0.364428i	$-0.881265\pi$
$463$	−23.2656	+	13.4324i	−1.08124	+	0.624256i	−0.150012	+	0.988684i	$0.547931\pi$
$464$	−3.44186	−	4.51419i	−0.159784	−	0.209566i
$465$		0			0
$466$	−31.3062	+	9.47038i	−1.45023	+	0.438707i
$467$			31.4118i			1.45356i	0.686868	+	0.726782i	$0.258985\pi$
$467$			31.4118i			1.45356i	−0.686868	+	0.726782i	$0.741015\pi$
$468$		0			0
$469$		−	47.8949i		−	2.21158i
$470$	−1.64774	−	5.44693i	−0.0760045	−	0.251248i
$471$		0			0
$472$	−24.1886	−	4.05086i	−1.11337	−	0.186456i
$473$	3.51906	−	2.03173i	0.161807	−	0.0934191i
$474$		0			0
$475$	−6.37208	+	11.0368i	−0.292371	+	0.506402i
$476$	0.820042	+	12.8132i	0.0375866	+	0.587290i
$477$		0			0
$478$	14.3984	−	15.3494i	0.658568	−	0.702064i
$479$	−2.42488	+	4.20001i	−0.110796	+	0.191904i	−0.916091	−	0.400970i	$-0.868673\pi$
$479$	−2.42488	+	4.20001i	−0.110796	+	0.191904i	0.805296	+	0.592873i	$0.202007\pi$
$480$		0			0
$481$	−4.53794	−	7.85995i	−0.206912	−	0.358383i
$482$	16.1927	+	3.78873i	0.737556	+	0.172572i
$483$		0			0
$484$	17.2806	+	8.55490i	0.785482	+	0.388859i
$485$	7.59316			0.344788
$486$		0			0
$487$			23.2664i			1.05430i	0.849772	+	0.527150i	$0.176739\pi$
$487$			23.2664i			1.05430i	−0.849772	+	0.527150i	$0.823261\pi$
$488$	−3.61378	−	9.66914i	−0.163588	−	0.437702i
$489$		0			0
$490$	17.7470	+	4.15241i	0.801730	+	0.187587i
$491$	−9.48139	+	5.47408i	−0.427889	+	0.247042i	−0.698447	−	0.715662i	$-0.746125\pi$
$491$	−9.48139	+	5.47408i	−0.427889	+	0.247042i	0.270558	+	0.962704i	$0.412792\pi$
$492$		0			0
$493$	−1.83929	−	1.06191i	−0.0828373	−	0.0478262i
$494$	10.7842	+	10.1161i	0.485205	+	0.455144i
$495$		0			0
$496$	2.74618	+	21.3667i	0.123307	+	0.959394i
$497$	−9.47149	−	5.46837i	−0.424855	−	0.245290i
$498$		0			0
$499$	19.4409	+	33.6726i	0.870293	+	1.50739i	0.861694	+	0.507429i	$0.169404\pi$
$499$	19.4409	+	33.6726i	0.870293	+	1.50739i	0.00859924	+	0.999963i	$0.497263\pi$
$500$	−16.4124	+	10.9300i	−0.733986	+	0.488804i
$501$		0			0
$502$	−7.46689	+	2.25879i	−0.333264	+	0.100815i
$503$	9.97588			0.444803			0.222401	−	0.974955i	$-0.428610\pi$
$503$	9.97588			0.444803			0.222401	+	0.974955i	$0.428610\pi$
$504$		0			0
$505$	15.5196			0.690612
$506$	−12.1797	+	3.68446i	−0.541455	+	0.163794i
$507$		0			0
$508$	3.09025	+	4.64031i	0.137108	+	0.205881i
$509$	7.82922	+	13.5606i	0.347024	+	0.601063i	0.985719	−	0.168396i	$-0.0538589\pi$
$509$	7.82922	+	13.5606i	0.347024	+	0.601063i	−0.638695	+	0.769460i	$0.720526\pi$
$510$		0			0
$511$	−26.2460	−	15.1532i	−1.16106	−	0.670336i
$512$	−10.8043	+	19.8813i	−0.477486	+	0.878640i
$513$		0			0
$514$	20.1511	+	18.9026i	0.888826	+	0.833759i
$515$	−6.19601	−	3.57727i	−0.273029	−	0.157633i
$516$		0			0
$517$	−3.59375	+	2.07485i	−0.158053	+	0.0912519i
$518$	−17.5557	−	4.10764i	−0.771353	−	0.180480i
$519$		0			0
$520$	3.41812	+	9.14564i	0.149895	+	0.401063i
$521$		−	9.78813i		−	0.428826i	−0.976743	−	0.214413i	$-0.931216\pi$
$521$		−	9.78813i		−	0.428826i	0.976743	−	0.214413i	$-0.0687838\pi$
$522$		0			0
$523$	−32.9015			−1.43868			−0.719342	−	0.694656i	$-0.755557\pi$
$523$	−32.9015			−1.43868			−0.719342	+	0.694656i	$0.755557\pi$
$524$	−13.3741	+	27.0152i	−0.584250	+	1.18017i
$525$		0			0
$526$	15.4936	+	3.62516i	0.675553	+	0.158064i
$527$	4.02989	+	6.97997i	0.175545	+	0.304052i
$528$		0			0
$529$	−18.2896	+	31.6786i	−0.795201	+	1.37733i
$530$	−12.3352	+	13.1499i	−0.535806	+	0.571194i
$531$		0			0
$532$	29.3140	−	1.87609i	1.27092	−	0.0813389i
$533$	7.46391	−	12.9279i	0.323298	−	0.559968i
$534$		0			0
$535$	10.2282	−	5.90525i	0.442203	−	0.255306i
$536$	5.21601	−	31.1459i	0.225297	−	1.34530i
$537$		0			0
$538$	−5.79830	−	19.1674i	−0.249982	−	0.826367i
$539$		−	13.2908i		−	0.572476i
$540$		0			0
$541$			26.4228i			1.13601i	0.823027	+	0.568003i	$0.192284\pi$
$541$			26.4228i			1.13601i	−0.823027	+	0.568003i	$0.807716\pi$
$542$	5.30047	−	1.60343i	0.227675	−	0.0688733i
$543$		0			0
$544$	−0.862151	+	8.42167i	−0.0369644	+	0.361076i
$545$	−9.47149	+	5.46837i	−0.405714	+	0.234239i
$546$		0			0
$547$	17.7776	−	30.7917i	0.760116	−	1.31656i	−0.182674	−	0.983174i	$-0.558475\pi$
$547$	17.7776	−	30.7917i	0.760116	−	1.31656i	0.942790	−	0.333387i	$-0.108191\pi$
$548$	17.4052	−	1.11393i	0.743515	−	0.0475849i
$549$		0			0
$550$	4.47547	+	4.19820i	0.190835	+	0.179012i
$551$	−2.42944	+	4.20792i	−0.103498	+	0.179263i
$552$		0			0
$553$	−5.57242	−	9.65172i	−0.236964	−	0.410433i
$554$	8.53959	−	36.4974i	0.362812	−	1.55063i
$555$		0			0
$556$	−4.26217	−	2.11002i	−0.180756	−	0.0894849i
$557$	−18.4413			−0.781384			−0.390692	−	0.920522i	$-0.627764\pi$
$557$	−18.4413			−0.781384			−0.390692	+	0.920522i	$0.627764\pi$
$558$		0			0
$559$			10.6450i			0.450236i
$560$	17.8966	+	7.47753i	0.756267	+	0.315983i
$561$		0			0
$562$	0.343526	−	1.46820i	0.0144908	−	0.0619323i
$563$	−35.4943	+	20.4926i	−1.49591	+	0.863661i	−0.999989	−	0.00470871i	$-0.998501\pi$
$563$	−35.4943	+	20.4926i	−1.49591	+	0.863661i	−0.495917	+	0.868370i	$0.665168\pi$
$564$		0			0
$565$	−8.08387	−	4.66722i	−0.340091	−	0.196352i
$566$	3.44134	−	3.66862i	0.144650	−	0.154204i
$567$		0			0
$568$	−5.56375	−	4.58756i	−0.233450	−	0.192490i
$569$	3.72340	+	2.14971i	0.156093	+	0.0901205i	0.576012	−	0.817441i	$-0.304608\pi$
$569$	3.72340	+	2.14971i	0.156093	+	0.0901205i	−0.419919	+	0.907562i	$0.637941\pi$
$570$		0			0
$571$	−2.17462	−	3.76656i	−0.0910052	−	0.157626i	0.816929	−	0.576738i	$-0.195675\pi$
$571$	−2.17462	−	3.76656i	−0.0910052	−	0.157626i	−0.907934	+	0.419112i	$0.862341\pi$
$572$	5.92584	−	3.94636i	0.247772	−	0.165005i
$573$		0			0
$574$	−8.58660	−	28.3847i	−0.358398	−	1.18476i
$575$	28.7312			1.19817
$576$		0			0
$577$	12.5475			0.522361			0.261180	−	0.965290i	$-0.415888\pi$
$577$	12.5475			0.522361			0.261180	+	0.965290i	$0.415888\pi$
$578$	−6.04414	−	19.9801i	−0.251403	−	0.831064i
$579$		0			0
$580$	−2.67040	+	1.77837i	−0.110882	+	0.0738429i
$581$	9.86905	+	17.0937i	0.409437	+	0.709166i
$582$		0			0
$583$	11.3861	+	6.57376i	0.471563	+	0.272257i
$584$	−15.4175	−	12.7124i	−0.637979	−	0.526042i
$585$		0			0
$586$	−15.0734	+	16.0690i	−0.622678	+	0.663803i
$587$	8.02388	+	4.63259i	0.331181	+	0.191207i	0.656365	−	0.754443i	$-0.272093\pi$
$587$	8.02388	+	4.63259i	0.331181	+	0.191207i	−0.325184	+	0.945651i	$0.605426\pi$
$588$		0			0
$589$	15.9688	−	9.21958i	0.657982	−	0.379886i
$590$	−3.15799	+	13.4969i	−0.130012	+	0.555661i
$591$		0			0
$592$	−10.9691	−	4.58310i	−0.450827	−	0.188364i
$593$		−	11.1342i		−	0.457228i	−0.973517	−	0.228614i	$-0.926581\pi$
$593$		−	11.1342i		−	0.457228i	0.973517	−	0.228614i	$-0.0734193\pi$
$594$		0			0
$595$	7.25666			0.297494
$596$	−32.0631	−	15.8731i	−1.31335	−	0.650186i
$597$		0			0
$598$	7.59455	−	32.4584i	0.310564	−	1.32732i
$599$	22.8693	+	39.6108i	0.934415	+	1.61845i	0.775675	+	0.631133i	$0.217410\pi$
$599$	22.8693	+	39.6108i	0.934415	+	1.61845i	0.158740	+	0.987320i	$0.449257\pi$
$600$		0			0
$601$	−11.2521	+	19.4892i	−0.458982	+	0.794980i	−0.998907	−	0.0467325i	$-0.985119\pi$
$601$	−11.2521	+	19.4892i	−0.458982	+	0.794980i	0.539925	+	0.841713i	$0.318453\pi$
$602$	15.4233	+	14.4678i	0.628608	+	0.589663i
$603$		0			0
$604$	−5.51192	+	0.352763i	−0.224277	+	0.0143537i
$605$	5.44905	−	9.43803i	0.221535	−	0.383710i
$606$		0			0
$607$	24.7306	−	14.2782i	1.00378	−	0.579535i	0.0944185	−	0.995533i	$-0.469901\pi$
$607$	24.7306	−	14.2782i	1.00378	−	0.579535i	0.909366	+	0.415997i	$0.136567\pi$
$608$	19.2671	+	1.97243i	0.781385	+	0.0799926i
$609$		0			0
$610$	−5.58417	+	1.68926i	−0.226097	+	0.0683960i
$611$		−	10.8709i		−	0.439791i
$612$		0			0
$613$			40.4574i			1.63406i	0.576596	+	0.817030i	$0.304381\pi$
$613$			40.4574i			1.63406i	−0.576596	+	0.817030i	$0.695619\pi$
$614$	0.393388	+	1.30042i	0.0158758	+	0.0524808i
$615$		0			0
$616$	2.33610	−	13.9494i	0.0941242	−	0.562036i
$617$	31.6715	−	18.2855i	1.27505	−	0.736148i	0.299112	−	0.954218i	$-0.403309\pi$
$617$	31.6715	−	18.2855i	1.27505	−	0.736148i	0.975933	+	0.218070i	$0.0699761\pi$
$618$		0			0
$619$	20.3697	−	35.2814i	0.818727	−	1.41808i	−0.0878927	−	0.996130i	$-0.528013\pi$
$619$	20.3697	−	35.2814i	0.818727	−	1.41808i	0.906620	−	0.421948i	$-0.138653\pi$
$620$	12.1507	−	0.777643i	0.487983	−	0.0312309i
$621$		0			0
$622$	−8.69892	+	9.27345i	−0.348795	+	0.371831i
$623$	18.5273	−	32.0902i	0.742279	−	1.28567i
$624$		0			0
$625$	−3.73321	−	6.46610i	−0.149328	−	0.258644i
$626$	−23.5715	−	5.51520i	−0.942105	−	0.220432i
$627$		0			0
$628$	−2.26589	+	4.57703i	−0.0904189	+	0.182643i
$629$	−4.44772			−0.177342
$630$		0			0
$631$		−	15.0916i		−	0.600788i	−0.953815	−	0.300394i	$-0.902882\pi$
$631$		−	15.0916i		−	0.600788i	0.953815	−	0.300394i	$-0.0971182\pi$
$632$	−2.57261	−	6.88335i	−0.102333	−	0.273805i
$633$		0			0
$634$	−10.9205	−	2.55517i	−0.433710	−	0.101479i
$635$	2.72884	−	1.57550i	0.108291	−	0.0625218i
$636$		0			0
$637$	30.1531	+	17.4089i	1.19471	+	0.689765i
$638$	1.70634	+	1.60062i	0.0675546	+	0.0633693i
$639$		0			0
$640$	10.8237	+	6.81165i	0.427846	+	0.269254i
$641$	26.9377	+	15.5525i	1.06398	+	0.614287i	0.926529	−	0.376222i	$-0.122777\pi$
$641$	26.9377	+	15.5525i	1.06398	+	0.614287i	0.137447	+	0.990509i	$0.456110\pi$
$642$		0			0
$643$	−1.93125	−	3.34503i	−0.0761612	−	0.131915i	0.825429	−	0.564505i	$-0.190933\pi$
$643$	−1.93125	−	3.34503i	−0.0761612	−	0.131915i	−0.901591	+	0.432590i	$0.857600\pi$
$644$	−36.7065	−	55.1183i	−1.44644	−	2.17197i
$645$		0			0
$646$	6.93576	−	2.09812i	0.272884	−	0.0825494i
$647$	−24.1359			−0.948879			−0.474440	−	0.880288i	$-0.657349\pi$
$647$	−24.1359			−0.948879			−0.474440	+	0.880288i	$0.657349\pi$
$648$		0			0
$649$	10.1079			0.396770
$650$	−15.3867	+	4.65459i	−0.603516	+	0.182568i
$651$		0			0
$652$	−11.5419	+	7.68641i	−0.452016	+	0.301023i
$653$	16.2083	+	28.0736i	0.634279	+	1.09860i	0.986667	+	0.162750i	$0.0520364\pi$
$653$	16.2083	+	28.0736i	0.634279	+	1.09860i	−0.352388	+	0.935854i	$0.614630\pi$
$654$		0			0
$655$	14.7547	+	8.51864i	0.576515	+	0.332851i
$656$	−2.49259	−	19.3937i	−0.0973195	−	0.757195i
$657$		0			0
$658$	−15.7507	−	14.7748i	−0.614025	−	0.575984i
$659$	−19.7202	−	11.3855i	−0.768191	−	0.443515i	0.0640377	−	0.997947i	$-0.479602\pi$
$659$	−19.7202	−	11.3855i	−0.768191	−	0.443515i	−0.832229	+	0.554432i	$0.812936\pi$
$660$		0			0
$661$	25.6004	−	14.7804i	0.995740	−	0.574891i	0.0887549	−	0.996053i	$-0.471711\pi$
$661$	25.6004	−	14.7804i	0.995740	−	0.574891i	0.906985	+	0.421163i	$0.138378\pi$
$662$	−13.1739	−	3.08241i	−0.512019	−	0.119801i
$663$		0			0
$664$	4.55622	+	12.1908i	0.176816	+	0.473094i
$665$		−	16.6018i		−	0.643790i
$666$		0			0
$667$	10.9542			0.424147
$668$	29.9984	+	14.8509i	1.16067	+	0.574600i
$669$		0			0
$670$	−17.3791	−	4.06631i	−0.671411	−	0.157095i
$671$	2.12713	+	3.68430i	0.0821171	+	0.142231i
$672$		0			0
$673$	8.89907	−	15.4136i	0.343034	−	0.594152i	−0.641961	−	0.766738i	$-0.721879\pi$
$673$	8.89907	−	15.4136i	0.343034	−	0.594152i	0.984995	+	0.172585i	$0.0552121\pi$
$674$	33.0369	−	35.2188i	1.27253	−	1.35658i
$675$		0			0
$676$	−0.469360	−	7.33376i	−0.0180523	−	0.282068i
$677$	−22.9383	+	39.7303i	−0.881591	+	1.52696i	−0.0320192	+	0.999487i	$0.510194\pi$
$677$	−22.9383	+	39.7303i	−0.881591	+	1.52696i	−0.849572	+	0.527473i	$0.823140\pi$
$678$		0			0
$679$	24.9550	−	14.4078i	0.957684	−	0.552919i
$680$	4.71899	+	0.790289i	0.180965	+	0.0303062i
$681$		0			0
$682$	−2.57076	−	8.49818i	−0.0984396	−	0.325412i
$683$		−	2.20513i		−	0.0843769i	−0.999110	−	0.0421884i	$-0.986567\pi$
$683$		−	2.20513i		−	0.0843769i	0.999110	−	0.0421884i	$-0.0134330\pi$
$684$		0			0
$685$		−	9.85735i		−	0.376630i
$686$	25.5581	−	7.73153i	0.975814	−	0.295191i
$687$		0			0
$688$	8.45413	+	11.0880i	0.322311	+	0.422728i
$689$	−29.8280	+	17.2212i	−1.13636	+	0.656075i
$690$		0			0
$691$	−10.2512	+	17.7556i	−0.389975	+	0.675457i	−0.992446	−	0.122684i	$-0.960850\pi$
$691$	−10.2512	+	17.7556i	−0.389975	+	0.675457i	0.602471	+	0.798141i	$0.294183\pi$
$692$	−2.61073	−	40.7926i	−0.0992449	−	1.55070i
$693$		0			0
$694$	24.9433	+	23.3980i	0.946835	+	0.888175i
$695$	−1.34398	+	2.32784i	−0.0509801	+	0.0883001i
$696$		0			0
$697$	−3.65776	−	6.33542i	−0.138547	−	0.239971i
$698$	−3.61561	+	15.4528i	−0.136853	+	0.584897i
$699$		0			0
$700$	−14.1683	+	28.6196i	−0.535513	+	1.08172i
$701$	26.6854			1.00789			0.503947	−	0.863734i	$-0.331881\pi$
$701$	26.6854			1.00789			0.503947	+	0.863734i	$0.331881\pi$
$702$		0			0
$703$			10.1755i			0.383776i
$704$	3.03832	−	8.81683i	0.114511	−	0.332297i
$705$		0			0
$706$	2.17707	−	9.30459i	0.0819350	−	0.350183i
$707$	51.0052	−	29.4479i	1.91825	−	1.10750i
$708$		0			0
$709$	37.8684	+	21.8633i	1.42218	+	0.821095i	0.996485	−	0.0837727i	$-0.0266970\pi$
$709$	37.8684	+	21.8633i	1.42218	+	0.821095i	0.425693	+	0.904868i	$0.360030\pi$
$710$	−2.78838	+	2.97254i	−0.104646	+	0.111558i
$711$		0			0
$712$	15.5430	−	18.8504i	0.582500	−	0.706450i
$713$	−36.0009	−	20.7851i	−1.34825	−	0.778410i
$714$		0			0
$715$	−2.01197	−	3.48483i	−0.0752433	−	0.130325i
$716$	−4.52282	−	6.79145i	−0.169026	−	0.253808i
$717$		0			0
$718$	−8.32871	−	27.5322i	−0.310825	−	1.02749i
$719$	−13.9253			−0.519327			−0.259663	−	0.965699i	$-0.583612\pi$
$719$	−13.9253			−0.519327			−0.259663	+	0.965699i	$0.583612\pi$
$720$		0			0
$721$	−27.1510			−1.01115
$722$	2.98012	+	9.85140i	0.110909	+	0.366631i
$723$		0			0
$724$	−24.7465	−	37.1593i	−0.919696	−	1.38101i
$725$	−2.64124	−	4.57475i	−0.0980930	−	0.169902i
$726$		0			0
$727$	−30.9380	−	17.8621i	−1.14743	−	0.662468i	−0.199169	−	0.979965i	$-0.563824\pi$
$727$	−30.9380	−	17.8621i	−1.14743	−	0.662468i	−0.948259	+	0.317497i	$0.897158\pi$
$728$	28.5872	+	23.5714i	1.05951	+	0.873616i
$729$		0			0
$730$	−7.72676	+	8.23708i	−0.285980	+	0.304868i
$731$	4.51778	+	2.60834i	0.167096	+	0.0964730i
$732$		0			0
$733$	−30.2141	+	17.4441i	−1.11598	+	0.644312i	−0.940372	−	0.340148i	$-0.889523\pi$
$733$	−30.2141	+	17.4441i	−1.11598	+	0.644312i	−0.175610	+	0.984460i	$0.556190\pi$
$734$	−4.36018	+	18.6350i	−0.160937	+	0.687831i
$735$		0			0
$736$	−17.8674	−	39.8408i	−0.658602	−	1.46855i
$737$			13.0152i			0.479422i
$738$		0			0
$739$	13.1128			0.482361			0.241181	−	0.970480i	$-0.422465\pi$
$739$	13.1128			0.482361			0.241181	+	0.970480i	$0.422465\pi$
$740$	−2.98099	+	6.02149i	−0.109583	+	0.221354i
$741$		0			0
$742$	−15.5882	+	66.6227i	−0.572262	+	2.44580i
$743$	−11.1665	−	19.3410i	−0.409660	−	0.709551i	0.585192	−	0.810895i	$-0.301019\pi$
$743$	−11.1665	−	19.3410i	−0.409660	−	0.709551i	−0.994851	+	0.101344i	$0.967686\pi$
$744$		0			0
$745$	−10.1104	+	17.5117i	−0.370415	+	0.641578i
$746$	27.4365	+	25.7367i	1.00452	+	0.942286i
$747$		0			0
$748$	−0.222843	−	3.48192i	−0.00814794	−	0.127312i
$749$	22.4100	−	38.8153i	0.818844	−	1.41828i
$750$		0			0
$751$	6.99545	−	4.03882i	0.255267	−	0.147379i	−0.366906	−	0.930258i	$-0.619583\pi$
$751$	6.99545	−	4.03882i	0.255267	−	0.147379i	0.622174	+	0.782879i	$0.286250\pi$
$752$	−8.63356	−	11.3234i	−0.314833	−	0.412921i
$753$		0			0
$754$	−5.86639	+	1.77463i	−0.213641	+	0.0646282i
$755$			3.12165i			0.113608i
$756$		0			0
$757$		−	12.7751i		−	0.464319i	−0.972678	−	0.232160i	$-0.925421\pi$
$757$		−	12.7751i		−	0.464319i	0.972678	−	0.232160i	$-0.0745792\pi$
$758$	11.6715	+	38.5826i	0.423929	+	1.40138i
$759$		0			0
$760$	1.80802	−	10.7961i	0.0655839	−	0.391616i
$761$	−43.2325	+	24.9603i	−1.56718	+	0.904809i	−0.570679	+	0.821173i	$0.693320\pi$
$761$	−43.2325	+	24.9603i	−1.56718	+	0.904809i	−0.996496	+	0.0836361i	$0.973347\pi$
$762$		0			0
$763$	−20.7521	+	35.9437i	−0.751276	+	1.30125i
$764$	−1.85855	−	29.0398i	−0.0672399	−	1.05062i
$765$		0			0
$766$	−19.4504	+	20.7350i	−0.702771	+	0.749186i
$767$	−13.2398	+	22.9320i	−0.478060	+	0.828025i
$768$		0			0
$769$	−14.2517	−	24.6846i	−0.513929	−	0.890150i	−0.999869	−	0.0161588i	$-0.994856\pi$
$769$	−14.2517	−	24.6846i	−0.513929	−	0.890150i	0.485941	−	0.873992i	$-0.338477\pi$
$770$	−7.78359	−	1.82119i	−0.280501	−	0.0656310i
$771$		0			0
$772$	−7.86950	−	3.89586i	−0.283229	−	0.140215i
$773$	−20.8254			−0.749037			−0.374518	−	0.927220i	$-0.622192\pi$
$773$	−20.8254			−0.749037			−0.374518	+	0.927220i	$0.622192\pi$
$774$		0			0
$775$			20.0466i			0.720096i
$776$	17.7972	−	6.65160i	0.638884	−	0.238779i
$777$		0			0
$778$	2.97741	+	0.696648i	0.106745	+	0.0249760i
$779$	−14.4942	+	8.36822i	−0.519308	+	0.299822i
$780$		0			0
$781$	2.57384	+	1.48601i	0.0920991	+	0.0531735i
$782$	−11.9146	−	11.1764i	−0.426065	−	0.399668i
$783$		0			0
$784$	45.2339	−	5.81375i	1.61550	−	0.207634i
$785$	2.49980	+	1.44326i	0.0892218	+	0.0515122i
$786$		0			0
$787$	10.4386	+	18.0802i	0.372096	+	0.644488i	0.989888	−	0.141853i	$-0.0453060\pi$
$787$	10.4386	+	18.0802i	0.372096	+	0.644488i	−0.617792	+	0.786341i	$0.711973\pi$
$788$	−12.8131	+	8.53300i	−0.456449	+	0.303975i
$789$		0			0
$790$	−3.97531	+	1.20256i	−0.141435	+	0.0427852i
$791$	−35.4236			−1.25952
$792$		0			0
$793$	−11.1448			−0.395765
$794$	−25.5166	+	7.71896i	−0.905549	+	0.273936i
$795$		0			0
$796$	23.2570	+	34.9226i	0.824321	+	1.23780i
$797$	14.4238	+	24.9828i	0.510918	+	0.884935i	0.999920	+	0.0126529i	$0.00402764\pi$
$797$	14.4238	+	24.9828i	0.510918	+	0.884935i	−0.489002	+	0.872283i	$0.662639\pi$
$798$		0			0
$799$	−4.61367	−	2.66370i	−0.163220	−	0.0942350i
$800$	−12.3305	+	17.0682i	−0.435948	+	0.603453i
$801$		0			0
$802$	−17.9446	−	16.8329i	−0.633647	−	0.594390i
$803$	7.13225	+	4.11780i	0.251691	+	0.145314i
$804$		0			0
$805$	−32.4136	+	18.7140i	−1.14243	+	0.659582i
$806$	22.6472	+	5.29895i	0.797715	+	0.186648i
$807$		0			0
$808$	36.3756	−	13.5951i	1.27969	−	0.478275i
$809$			43.6746i			1.53552i	0.640739	+	0.767759i	$0.278628\pi$
$809$			43.6746i			1.53552i	−0.640739	+	0.767759i	$0.721372\pi$
$810$		0			0
$811$	42.3445			1.48692			0.743458	−	0.668782i	$-0.233184\pi$
$811$	42.3445			1.48692			0.743458	+	0.668782i	$0.233184\pi$
$812$	−5.40188	+	10.9116i	−0.189569	+	0.382923i
$813$		0			0
$814$	4.77069	+	1.11623i	0.167212	+	0.0391240i
$815$	3.91876	+	6.78749i	0.137268	+	0.237755i
$816$		0			0
$817$	5.96737	−	10.3358i	0.208772	−	0.361603i
$818$	−19.9064	+	21.2212i	−0.696012	+	0.741981i
$819$		0			0
$820$	−11.0287	+	0.705833i	−0.385137	+	0.0246488i
$821$	1.40953	−	2.44138i	0.0491930	−	0.0852047i	−0.840380	−	0.541997i	$-0.817668\pi$
$821$	1.40953	−	2.44138i	0.0491930	−	0.0852047i	0.889573	+	0.456792i	$0.151002\pi$
$822$		0			0
$823$	4.46763	−	2.57939i	0.155732	−	0.0899118i	−0.420109	−	0.907474i	$-0.638008\pi$
$823$	4.46763	−	2.57939i	0.155732	−	0.0899118i	0.575841	+	0.817562i	$0.304675\pi$
$824$	−17.6562	−	2.95688i	−0.615083	−	0.103008i
$825$		0			0
$826$	15.2313	+	50.3500i	0.529963	+	1.75190i
$827$		−	21.8630i		−	0.760251i	−0.924935	−	0.380125i	$-0.875881\pi$
$827$		−	21.8630i		−	0.760251i	0.924935	−	0.380125i	$-0.124119\pi$
$828$		0			0
$829$		−	22.0815i		−	0.766924i	−0.923557	−	0.383462i	$-0.874732\pi$
$829$		−	22.0815i		−	0.766924i	0.923557	−	0.383462i	$-0.125268\pi$
$830$	7.04048	−	2.12980i	0.244379	−	0.0739264i
$831$		0			0
$832$	16.0231	+	18.4418i	0.555503	+	0.639353i
$833$	14.7768	−	8.53139i	0.511986	−	0.295595i
$834$		0			0
$835$	9.45931	−	16.3840i	0.327353	−	0.566992i
$836$	−7.96594	+	0.509820i	−0.275508	+	0.0176325i
$837$		0			0
$838$	−28.8174	−	27.0321i	−0.995482	−	0.933808i
$839$	25.4035	−	44.0002i	0.877026	−	1.51905i	0.0224378	−	0.999748i	$-0.492857\pi$
$839$	25.4035	−	44.0002i	0.877026	−	1.51905i	0.854588	−	0.519306i	$-0.173809\pi$
$840$		0			0
$841$	13.4930	+	23.3705i	0.465276	+	0.805881i
$842$	−2.33574	+	9.98273i	−0.0804948	+	0.344028i
$843$		0			0
$844$	−8.54902	−	4.23226i	−0.294270	−	0.145680i
$845$	−4.15343			−0.142882
$846$		0			0
$847$		−	41.3575i		−	1.42106i
$848$	−17.3926	+	41.6269i	−0.597263	+	1.42947i
$849$		0			0
$850$	−1.79477	+	7.67069i	−0.0615601	+	0.263102i
$851$	19.8668	−	11.4701i	0.681026	−	0.393191i
$852$		0			0
$853$	−45.4891	−	26.2631i	−1.55752	−	0.899233i	−0.997494	−	0.0707558i	$-0.977459\pi$
$853$	−45.4891	−	26.2631i	−1.55752	−	0.899233i	−0.560023	−	0.828477i	$-0.689208\pi$
$854$	−15.1471	+	16.1475i	−0.518324	+	0.552557i
$855$		0			0
$856$	18.8004	−	22.8009i	0.642583	−	0.779319i
$857$	48.4564	+	27.9763i	1.65524	+	0.955653i	0.974867	+	0.222786i	$0.0715151\pi$
$857$	48.4564	+	27.9763i	1.65524	+	0.955653i	0.680372	+	0.732867i	$0.261818\pi$
$858$		0			0
$859$	15.4078	+	26.6871i	0.525708	+	0.910554i	0.999552	+	0.0299443i	$0.00953300\pi$
$859$	15.4078	+	26.6871i	0.525708	+	0.910554i	−0.473843	+	0.880609i	$0.657134\pi$
$860$	6.55921	−	4.36816i	0.223667	−	0.148953i
$861$		0			0
$862$	15.4377	+	51.0325i	0.525811	+	1.73817i
$863$	−25.1750			−0.856966			−0.428483	−	0.903550i	$-0.640952\pi$
$863$	−25.1750			−0.856966			−0.428483	+	0.903550i	$0.640952\pi$
$864$		0			0
$865$	−23.1027			−0.785514
$866$	−14.7900	−	48.8912i	−0.502584	−	1.66139i
$867$		0			0
$868$	38.4577	−	25.6112i	1.30534	−	0.869302i
$869$	1.51428	+	2.62281i	0.0513685	+	0.0889728i
$870$		0			0
$871$	−29.5278	−	17.0479i	−1.00051	−	0.577646i
$872$	−17.4095	+	21.1141i	−0.589560	+	0.715012i
$873$		0			0
$874$	−25.5694	+	27.2582i	−0.864899	+	0.922022i
$875$	36.6276	+	21.1470i	1.23824	+	0.714898i
$876$		0			0
$877$	−31.8486	+	18.3878i	−1.07545	+	0.620913i	−0.929666	−	0.368404i	$-0.879904\pi$
$877$	−31.8486	+	18.3878i	−1.07545	+	0.620913i	−0.145786	+	0.989316i	$0.546571\pi$
$878$	3.35666	−	14.3460i	0.113282	−	0.484156i
$879$		0			0
$880$	−4.86331	−	2.03199i	−0.163942	−	0.0684983i
$881$			8.15439i			0.274728i	0.990521	+	0.137364i	$0.0438631\pi$
$881$			8.15439i			0.274728i	−0.990521	+	0.137364i	$0.956137\pi$
$882$		0			0
$883$	−20.3792			−0.685814			−0.342907	−	0.939369i	$-0.611412\pi$
$883$	−20.3792			−0.685814			−0.342907	+	0.939369i	$0.611412\pi$
$884$	8.19138	+	4.05521i	0.275506	+	0.136391i
$885$		0			0
$886$	11.4552	−	48.9584i	0.384844	−	1.64479i
$887$	−22.3561	−	38.7220i	−0.750646	−	1.30016i	−0.947510	−	0.319726i	$-0.896409\pi$
$887$	−22.3561	−	38.7220i	−0.750646	−	1.30016i	0.196864	−	0.980431i	$-0.436924\pi$
$888$		0			0
$889$	5.97891	−	10.3558i	0.200526	−	0.347322i
$890$	−10.0712	−	9.44726i	−0.337588	−	0.316673i
$891$		0			0
$892$	−28.8713	+	1.84776i	−0.966684	+	0.0618677i
$893$	−6.09402	+	10.5551i	−0.203928	+	0.353214i
$894$		0			0
$895$	−3.99387	+	2.30586i	−0.133500	+	0.0770765i
$896$	48.4972	+	1.84886i	1.62018	+	0.0617662i
$897$		0			0
$898$	22.7072	−	6.86910i	0.757749	−	0.229225i
$899$			7.64305i			0.254910i
$900$		0			0
$901$			16.8788i			0.562315i
$902$	2.33337	+	7.71343i	0.0776928	+	0.256829i
$903$		0			0
$904$	−23.0359	−	3.85782i	−0.766162	−	0.128309i
$905$	−21.8524	+	12.6165i	−0.726398	+	0.419386i
$906$		0			0
$907$	7.99519	−	13.8481i	0.265476	−	0.459818i	−0.702212	−	0.711968i	$-0.747804\pi$
$907$	7.99519	−	13.8481i	0.265476	−	0.459818i	0.967688	+	0.252150i	$0.0811376\pi$
$908$	1.29482	−	0.0828684i	0.0429701	−	0.00275009i
$909$		0			0
$910$	14.3270	−	15.2733i	0.474937	−	0.506304i
$911$	−14.1609	+	24.5275i	−0.469173	+	0.812631i	−0.999379	−	0.0352377i	$-0.988781\pi$
$911$	−14.1609	+	24.5275i	−0.469173	+	0.812631i	0.530206	+	0.847869i	$0.322115\pi$
$912$		0			0
$913$	−2.68187	−	4.64514i	−0.0887570	−	0.153732i
$914$	1.87120	+	0.437819i	0.0618937	+	0.0144818i
$915$		0			0
$916$	−12.2960	+	24.8375i	−0.406272	+	0.820656i
$917$	64.6553			2.13511
$918$		0			0
$919$		−	17.1474i		−	0.565642i	−0.959173	−	0.282821i	$-0.908730\pi$
$919$		−	17.1474i		−	0.565642i	0.959173	−	0.282821i	$-0.0912702\pi$
$920$	−23.1165	+	8.63966i	−0.762130	+	0.284841i
$921$		0			0
$922$	−13.9743	−	3.26968i	−0.460219	−	0.107681i
$923$	−6.74265	+	3.89287i	−0.221937	+	0.128135i
$924$		0			0
$925$	−9.58047	−	5.53129i	−0.315004	−	0.181868i
$926$	27.7094	+	25.9927i	0.910589	+	0.854174i
$927$		0			0
$928$	−4.70116	+	6.50750i	−0.154323	+	0.213619i
$929$	−38.0670	−	21.9780i	−1.24894	−	0.721075i	−0.278040	−	0.960569i	$-0.589685\pi$
$929$	−38.0670	−	21.9780i	−1.24894	−	0.721075i	−0.970898	+	0.239495i	$0.923018\pi$
$930$		0			0
$931$	−19.5181	−	33.8064i	−0.639680	−	1.10796i
$932$	25.6388	+	38.4992i	0.839828	+	1.26108i
$933$		0			0
$934$	42.5201	−	12.8626i	1.39130	−	0.420878i
$935$	−1.97197			−0.0644902
$936$		0			0
$937$	−13.5845			−0.443786			−0.221893	−	0.975071i	$-0.571223\pi$
$937$	−13.5845			−0.443786			−0.221893	+	0.975071i	$0.571223\pi$
$938$	−64.8321	+	19.6122i	−2.11684	+	0.640361i
$939$		0			0
$940$	−6.69842	+	4.46086i	−0.218478	+	0.145497i
$941$	−13.5116	−	23.4028i	−0.440466	−	0.762909i	0.557258	−	0.830339i	$-0.311853\pi$
$941$	−13.5116	−	23.4028i	−0.440466	−	0.762909i	−0.997724	+	0.0674301i	$0.978520\pi$
$942$		0			0
$943$	32.6765	+	18.8658i	1.06409	+	0.614354i
$944$	4.42146	+	34.4012i	0.143906	+	1.11966i
$945$		0			0
$946$	−4.19122	−	3.93156i	−0.136268	−	0.127826i
$947$	−34.5376	−	19.9403i	−1.12232	−	0.647972i	−0.180328	−	0.983607i	$-0.557716\pi$
$947$	−34.5376	−	19.9403i	−1.12232	−	0.647972i	−0.941992	+	0.335634i	$0.891049\pi$
$948$		0			0
$949$	−18.6843	+	10.7874i	−0.606516	+	0.350172i
$950$	17.5490	+	4.10608i	0.569365	+	0.133219i
$951$		0			0
$952$	17.0085	−	6.35683i	0.551250	−	0.206026i
$953$		−	14.0999i		−	0.456741i	−0.973574	−	0.228371i	$-0.926660\pi$
$953$		−	14.0999i		−	0.456741i	0.973574	−	0.228371i	$-0.0733398\pi$
$954$		0			0
$955$	−16.4465			−0.532197
$956$	−26.6734	−	13.2049i	−0.862678	−	0.427075i
$957$		0			0
$958$	6.67823	+	1.56256i	0.215764	+	0.0504839i
$959$	−18.7040	−	32.3963i	−0.603983	−	1.04613i
$960$		0			0
$961$	−0.997565	+	1.72783i	−0.0321795	+	0.0557366i
$962$	−8.78127	+	9.36124i	−0.283120	+	0.301818i
$963$		0			0
$964$	−1.50210	−	23.4704i	−0.0483795	−	0.755930i
$965$	−2.48147	+	4.29803i	−0.0798813	+	0.138358i
$966$		0			0
$967$	−45.4687	+	26.2514i	−1.46217	+	0.844187i	−0.999112	−	0.0421387i	$-0.986583\pi$
$967$	−45.4687	+	26.2514i	−1.46217	+	0.844187i	−0.463063	+	0.886326i	$0.653250\pi$
$968$	4.50405	−	26.8947i	0.144766	−	0.864428i
$969$		0			0
$970$	−3.10928	−	10.2784i	−0.0998330	−	0.330018i
$971$		−	61.3864i		−	1.96998i	−0.172599	−	0.984992i	$-0.555216\pi$
$971$		−	61.3864i		−	1.96998i	0.172599	−	0.984992i	$-0.444784\pi$
$972$		0			0
$973$			10.2006i			0.327017i
$974$	31.4941	−	9.52721i	1.00914	−	0.305272i
$975$		0			0
$976$	−11.6087	+	8.85109i	−0.371585	+	0.283317i
$977$	25.9568	−	14.9862i	0.830431	−	0.479450i	−0.0235691	−	0.999722i	$-0.507503\pi$
$977$	25.9568	−	14.9862i	0.830431	−	0.479450i	0.854000	+	0.520273i	$0.174170\pi$
$978$		0			0
$979$	−5.03471	+	8.72037i	−0.160910	+	0.278704i
$980$	−1.64629	−	25.7233i	−0.0525889	−	0.821702i
$981$		0			0
$982$	11.2924	+	10.5928i	0.360354	+	0.338029i
$983$	21.1703	−	36.6681i	0.675228	−	1.16953i	−0.301174	−	0.953569i	$-0.597378\pi$
$983$	21.1703	−	36.6681i	0.675228	−	1.16953i	0.976402	−	0.215961i	$-0.0692883\pi$
$984$		0			0
$985$	4.35037	+	7.53506i	0.138614	+	0.240087i
$986$	−0.684281	+	2.92456i	−0.0217920	+	0.0931369i
$987$		0			0
$988$	9.27750	−	18.7402i	0.295157	−	0.596207i
$989$	−26.9063			−0.855572
$990$		0			0
$991$		−	12.3787i		−	0.393222i	−0.980482	−	0.196611i	$-0.937006\pi$
$991$		−	12.3787i		−	0.393222i	0.980482	−	0.196611i	$-0.0629937\pi$
$992$	27.7982	−	12.4667i	0.882593	−	0.395817i
$993$		0			0
$994$	−3.52374	+	15.0601i	−0.111766	+	0.477679i
$995$	20.5370	−	11.8571i	0.651068	−	0.375894i
$996$		0			0
$997$	−6.20535	−	3.58266i	−0.196525	−	0.113464i	0.398508	−	0.917165i	$-0.369528\pi$
$997$	−6.20535	−	3.58266i	−0.196525	−	0.113464i	−0.595034	+	0.803701i	$0.702861\pi$
$998$	37.6196	−	40.1042i	1.19083	−	1.26948i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.l.b.35.3		16
3.2	odd	2		72.2.l.b.11.6	✓	16
4.3	odd	2		864.2.p.b.143.5		16
8.3	odd	2	inner	216.2.l.b.35.1		16
8.5	even	2		864.2.p.b.143.4		16
9.2	odd	6		648.2.f.b.323.11		16
9.4	even	3		72.2.l.b.59.8	yes	16
9.5	odd	6	inner	216.2.l.b.179.1		16
9.7	even	3		648.2.f.b.323.6		16
12.11	even	2		288.2.p.b.47.5		16
24.5	odd	2		288.2.p.b.47.6		16
24.11	even	2		72.2.l.b.11.8	yes	16
36.7	odd	6		2592.2.f.b.1295.8		16
36.11	even	6		2592.2.f.b.1295.10		16
36.23	even	6		864.2.p.b.719.4		16
36.31	odd	6		288.2.p.b.239.6		16
72.5	odd	6		864.2.p.b.719.5		16
72.11	even	6		648.2.f.b.323.5		16
72.13	even	6		288.2.p.b.239.5		16
72.29	odd	6		2592.2.f.b.1295.7		16
72.43	odd	6		648.2.f.b.323.12		16
72.59	even	6	inner	216.2.l.b.179.3		16
72.61	even	6		2592.2.f.b.1295.9		16
72.67	odd	6		72.2.l.b.59.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.6	✓	16	3.2	odd	2
72.2.l.b.11.8	yes	16	24.11	even	2
72.2.l.b.59.6	yes	16	72.67	odd	6
72.2.l.b.59.8	yes	16	9.4	even	3
216.2.l.b.35.1		16	8.3	odd	2	inner
216.2.l.b.35.3		16	1.1	even	1	trivial
216.2.l.b.179.1		16	9.5	odd	6	inner
216.2.l.b.179.3		16	72.59	even	6	inner
288.2.p.b.47.5		16	12.11	even	2
288.2.p.b.47.6		16	24.5	odd	2
288.2.p.b.239.5		16	72.13	even	6
288.2.p.b.239.6		16	36.31	odd	6
648.2.f.b.323.5		16	72.11	even	6
648.2.f.b.323.6		16	9.7	even	3
648.2.f.b.323.11		16	9.2	odd	6
648.2.f.b.323.12		16	72.43	odd	6
864.2.p.b.143.4		16	8.5	even	2
864.2.p.b.143.5		16	4.3	odd	2
864.2.p.b.719.4		16	36.23	even	6
864.2.p.b.719.5		16	72.5	odd	6
2592.2.f.b.1295.7		16	72.29	odd	6
2592.2.f.b.1295.8		16	36.7	odd	6
2592.2.f.b.1295.9		16	72.61	even	6
2592.2.f.b.1295.10		16	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.409484 - 1.35363i) q^{2} +(-1.66465 + 1.10858i) q^{4} +(0.565188 + 0.978934i) q^{5} +(3.71499 + 2.14485i) q^{7} +(2.18226 + 1.79937i) q^{8} +O(q^{10})\)	\(q+(-0.409484 - 1.35363i) q^{2} +(-1.66465 + 1.10858i) q^{4} +(0.565188 + 0.978934i) q^{5} +(3.71499 + 2.14485i) q^{7} +(2.18226 + 1.79937i) q^{8} +(1.09368 - 1.16591i) q^{10} +(-1.00953 - 0.582853i) q^{11} +(2.64466 - 1.52689i) q^{13} +(1.38211 - 5.90701i) q^{14} +(1.54209 - 3.69079i) q^{16} -1.49654i q^{17} -3.42378 q^{19} +(-2.02607 - 1.00302i) q^{20} +(-0.375582 + 1.60520i) q^{22} +(3.85938 + 6.68464i) q^{23} +(1.86113 - 3.22356i) q^{25} +(-3.14980 - 2.95466i) q^{26} +(-8.56188 + 0.547960i) q^{28} +(0.709580 - 1.22903i) q^{29} +(-4.66408 + 2.69281i) q^{31} +(-5.62744 - 0.576097i) q^{32} +(-2.02576 + 0.612808i) q^{34} +4.84897i q^{35} -2.97201i q^{37} +(1.40198 + 4.63454i) q^{38} +(-0.528079 + 3.15327i) q^{40} +(4.23339 - 2.44415i) q^{41} +(-1.74292 + 3.01882i) q^{43} +(2.32665 - 0.148906i) q^{44} +(7.46820 - 7.96144i) q^{46} +(1.77991 - 3.08289i) q^{47} +(5.70075 + 9.87399i) q^{49} +(-5.12562 - 1.19928i) q^{50} +(-2.70973 + 5.47356i) q^{52} -11.2786 q^{53} -1.31769i q^{55} +(4.24769 + 11.3653i) q^{56} +(-1.95422 - 0.457243i) q^{58} +(-7.50935 + 4.33553i) q^{59} +(-3.16057 - 1.82476i) q^{61} +(5.55494 + 5.21079i) q^{62} +(1.52453 + 7.85340i) q^{64} +(2.98946 + 1.72596i) q^{65} +(-5.58255 - 9.66925i) q^{67} +(1.65904 + 2.49120i) q^{68} +(6.56373 - 1.98558i) q^{70} -2.54954 q^{71} -7.06491 q^{73} +(-4.02301 + 1.21699i) q^{74} +(5.69937 - 3.79554i) q^{76} +(-2.50026 - 4.33059i) q^{77} +(-2.24998 - 1.29902i) q^{79} +(4.48461 - 0.576391i) q^{80} +(-5.04198 - 4.72961i) q^{82} +(3.98482 + 2.30064i) q^{83} +(1.46501 - 0.845824i) q^{85} +(4.80008 + 1.12311i) q^{86} +(-1.15429 - 3.08846i) q^{88} -8.63803i q^{89} +13.0998 q^{91} +(-13.8350 - 6.84911i) q^{92} +(-4.90195 - 1.14695i) q^{94} +(-1.93508 - 3.35165i) q^{95} +(3.35869 - 5.81742i) q^{97} +(11.0314 - 11.7600i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 5 q^{4}+O(q^{10}) \) 16 * q + 3 * q^2 - 5 * q^4	\( 16 q + 3 q^{2} - 5 q^{4} - 12 q^{11} + 18 q^{14} + 7 q^{16} - 4 q^{19} - 18 q^{20} - q^{22} - 14 q^{25} - 12 q^{28} - 27 q^{32} - 13 q^{34} + 15 q^{38} - 12 q^{40} + 36 q^{41} + 8 q^{43} + 12 q^{46} + 10 q^{49} - 51 q^{50} - 18 q^{52} + 66 q^{56} + 12 q^{58} - 12 q^{59} + 34 q^{64} + 6 q^{65} - 16 q^{67} + 9 q^{68} + 18 q^{70} - 4 q^{73} + 60 q^{74} - 7 q^{76} - 22 q^{82} - 54 q^{83} + 51 q^{86} - 13 q^{88} - 36 q^{91} - 84 q^{92} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 16 * q + 3 * q^2 - 5 * q^4 - 12 * q^11 + 18 * q^14 + 7 * q^16 - 4 * q^19 - 18 * q^20 - q^22 - 14 * q^25 - 12 * q^28 - 27 * q^32 - 13 * q^34 + 15 * q^38 - 12 * q^40 + 36 * q^41 + 8 * q^43 + 12 * q^46 + 10 * q^49 - 51 * q^50 - 18 * q^52 + 66 * q^56 + 12 * q^58 - 12 * q^59 + 34 * q^64 + 6 * q^65 - 16 * q^67 + 9 * q^68 + 18 * q^70 - 4 * q^73 + 60 * q^74 - 7 * q^76 - 22 * q^82 - 54 * q^83 + 51 * q^86 - 13 * q^88 - 36 * q^91 - 84 * q^92 + 24 * q^94 + 8 * q^97

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