LMFDB - Embedded newform 405.2.k.a.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(46,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.46"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.k (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			361.1
Character	$\chi$	$=$	405.361
Dual form			405.2.k.a.46.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.62376 + 1.36249i) q^{2} +(0.432902 - 2.45511i) q^{4} +(-0.939693 + 0.342020i) q^{5} +(-0.0109747 - 0.0622407i) q^{7} +(0.522478 + 0.904959i) q^{8} +(1.05983 - 1.83568i) q^{10} +(1.08697 + 0.395623i) q^{11} +(-4.71203 - 3.95386i) q^{13} +(0.102623 + 0.0861109i) q^{14} +(2.60389 + 0.947740i) q^{16} +(1.03593 - 1.79428i) q^{17} +(0.296045 + 0.512766i) q^{19} +(0.432902 + 2.45511i) q^{20} +(-2.30400 + 0.838589i) q^{22} +(1.29518 - 7.34532i) q^{23} +(0.766044 - 0.642788i) q^{25} +13.0383 q^{26} -0.157559 q^{28} +(1.76698 - 1.48267i) q^{29} +(1.49057 - 8.45346i) q^{31} +(-7.48326 + 2.72368i) q^{32} +(0.762600 + 4.32492i) q^{34} +(0.0316004 + 0.0547336i) q^{35} +(-2.17037 + 3.75919i) q^{37} +(-1.17935 - 0.429247i) q^{38} +(-0.800483 - 0.671685i) q^{40} +(5.08956 + 4.27065i) q^{41} +(10.3772 + 3.77698i) q^{43} +(1.44185 - 2.49735i) q^{44} +(7.90491 + 13.6917i) q^{46} +(-1.02536 - 5.81510i) q^{47} +(6.57409 - 2.39277i) q^{49} +(-0.368076 + 2.08746i) q^{50} +(-11.7470 + 9.85691i) q^{52} -0.617222 q^{53} -1.15673 q^{55} +(0.0505913 - 0.0424511i) q^{56} +(-0.849014 + 4.81500i) q^{58} +(-10.3506 + 3.76730i) q^{59} +(-2.06979 - 11.7384i) q^{61} +(9.09747 + 15.7573i) q^{62} +(5.66899 - 9.81898i) q^{64} +(5.78016 + 2.10381i) q^{65} +(-3.61207 - 3.03089i) q^{67} +(-3.95669 - 3.32006i) q^{68} +(-0.125886 - 0.0458186i) q^{70} +(1.42779 - 2.47301i) q^{71} +(1.45719 + 2.52392i) q^{73} +(-1.59772 - 9.06114i) q^{74} +(1.38705 - 0.504846i) q^{76} +(0.0126947 - 0.0719954i) q^{77} +(-3.93760 + 3.30404i) q^{79} -2.77101 q^{80} -14.0830 q^{82} +(2.57261 - 2.15868i) q^{83} +(-0.359774 + 2.04038i) q^{85} +(-21.9962 + 8.00594i) q^{86} +(0.209893 + 1.19036i) q^{88} +(-5.76784 - 9.99019i) q^{89} +(-0.194378 + 0.336673i) q^{91} +(-17.4729 - 6.35961i) q^{92} +(9.58798 + 8.04527i) q^{94} +(-0.453568 - 0.380589i) q^{95} +(-12.0991 - 4.40371i) q^{97} +(-7.41460 + 12.8425i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 9 q^{8} + 3 q^{10} + 6 q^{11} + 3 q^{13} + 9 q^{14} + 12 q^{16} + 12 q^{17} + 24 q^{19} - 51 q^{22} - 18 q^{23} + 18 q^{26} - 60 q^{28} - 18 q^{29} + 12 q^{31} - 36 q^{32} - 69 q^{34} + 12 q^{35}+ \cdots + 15 q^{98}+O(q^{100}) $ 30 * q + 9 * q^8 + 3 * q^10 + 6 * q^11 + 3 * q^13 + 9 * q^14 + 12 * q^16 + 12 * q^17 + 24 * q^19 - 51 * q^22 - 18 * q^23 + 18 * q^26 - 60 * q^28 - 18 * q^29 + 12 * q^31 - 36 * q^32 - 69 * q^34 + 12 * q^35 + 24 * q^37 + 24 * q^38 + 9 * q^40 + 75 * q^41 + 6 * q^43 - 12 * q^44 + 30 * q^46 - 45 * q^47 - 36 * q^49 + 30 * q^52 - 36 * q^53 - 30 * q^56 + 27 * q^58 + 27 * q^59 - 12 * q^61 - 36 * q^62 + 27 * q^64 - 6 * q^65 - 30 * q^67 - 69 * q^68 + 27 * q^70 - 12 * q^71 + 21 * q^73 - 30 * q^76 + 36 * q^77 + 54 * q^79 - 6 * q^80 - 48 * q^82 + 87 * q^83 + 27 * q^85 - 18 * q^86 - 18 * q^88 - 9 * q^89 + 51 * q^91 - 24 * q^92 + 15 * q^94 - 21 * q^95 - 75 * q^97 + 15 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−1.62376	+	1.36249i	−1.14817	+	0.963429i	−0.999675	−	0.0254839i	$-0.991887\pi$
$2$	−1.62376	+	1.36249i	−1.14817	+	0.963429i	−0.148495	+	0.988913i	$0.547443\pi$
$3$		0			0
$3$		0			0
$4$	0.432902	−	2.45511i	0.216451	−	1.22755i
$5$	−0.939693	+	0.342020i	−0.420243	+	0.152956i
$5$	−0.939693	+	0.342020i	−0.420243	+	0.152956i
$6$		0			0
$7$	−0.0109747	−	0.0622407i	−0.00414805	−	0.0235248i	0.982663	−	0.185398i	$-0.0593575\pi$
$7$	−0.0109747	−	0.0622407i	−0.00414805	−	0.0235248i	−0.986812	+	0.161873i	$0.948246\pi$
$8$	0.522478	+	0.904959i	0.184724	+	0.319951i
$9$		0			0
$10$	1.05983	−	1.83568i	0.335149	−	0.580494i
$11$	1.08697	+	0.395623i	0.327733	+	0.119285i	0.500646	−	0.865652i	$-0.333096\pi$
$11$	1.08697	+	0.395623i	0.327733	+	0.119285i	−0.172913	+	0.984937i	$0.555318\pi$
$12$		0			0
$13$	−4.71203	−	3.95386i	−1.30688	−	1.09660i	−0.988912	−	0.148504i	$-0.952554\pi$
$13$	−4.71203	−	3.95386i	−1.30688	−	1.09660i	−0.317970	−	0.948101i	$-0.603001\pi$
$14$	0.102623	+	0.0861109i	0.0274271	+	0.0230141i
$15$		0			0
$16$	2.60389	+	0.947740i	0.650973	+	0.236935i
$17$	1.03593	−	1.79428i	0.251249	−	0.435176i	−0.712621	−	0.701549i	$-0.752492\pi$
$17$	1.03593	−	1.79428i	0.251249	−	0.435176i	0.963870	+	0.266373i	$0.0858253\pi$
$18$		0			0
$19$	0.296045	+	0.512766i	0.0679175	+	0.117636i	0.897984	−	0.440027i	$-0.145031\pi$
$19$	0.296045	+	0.512766i	0.0679175	+	0.117636i	−0.830067	+	0.557664i	$0.811698\pi$
$20$	0.432902	+	2.45511i	0.0967998	+	0.548979i
$21$		0			0
$22$	−2.30400	+	0.838589i	−0.491216	+	0.178788i
$23$	1.29518	−	7.34532i	0.270063	−	1.53161i	−0.484155	−	0.874982i	$-0.660873\pi$
$23$	1.29518	−	7.34532i	0.270063	−	1.53161i	0.754218	−	0.656624i	$-0.228016\pi$
$24$		0			0
$25$	0.766044	−	0.642788i	0.153209	−	0.128558i
$26$	13.0383			2.55702
$27$		0			0
$28$	−0.157559			−0.0297758
$29$	1.76698	−	1.48267i	0.328120	−	0.275325i	−0.463814	−	0.885933i	$-0.653519\pi$
$29$	1.76698	−	1.48267i	0.328120	−	0.275325i	0.791933	+	0.610608i	$0.209075\pi$
$30$		0			0
$31$	1.49057	−	8.45346i	0.267715	−	1.51829i	−0.493476	−	0.869759i	$-0.664274\pi$
$31$	1.49057	−	8.45346i	0.267715	−	1.51829i	0.761191	−	0.648528i	$-0.224615\pi$
$32$	−7.48326	+	2.72368i	−1.32287	+	0.481484i
$33$		0			0
$34$	0.762600	+	4.32492i	0.130785	+	0.741717i
$35$	0.0316004	+	0.0547336i	0.00534145	+	0.00925166i
$36$		0			0
$37$	−2.17037	+	3.75919i	−0.356807	+	0.618007i	−0.987425	−	0.158085i	$-0.949468\pi$
$37$	−2.17037	+	3.75919i	−0.356807	+	0.618007i	0.630619	+	0.776093i	$0.282801\pi$
$38$	−1.17935	−	0.429247i	−0.191315	−	0.0696331i
$39$		0			0
$40$	−0.800483	−	0.671685i	−0.126568	−	0.106203i
$41$	5.08956	+	4.27065i	0.794856	+	0.666963i	0.946942	−	0.321404i	$-0.104155\pi$
$41$	5.08956	+	4.27065i	0.794856	+	0.666963i	−0.152086	+	0.988367i	$0.548599\pi$
$42$		0			0
$43$	10.3772	+	3.77698i	1.58251	+	0.575985i	0.975747	−	0.218902i	$-0.0702474\pi$
$43$	10.3772	+	3.77698i	1.58251	+	0.575985i	0.606758	+	0.794886i	$0.292470\pi$
$44$	1.44185	−	2.49735i	0.217367	−	0.376490i
$45$		0			0
$46$	7.90491	+	13.6917i	1.16552	+	2.01873i
$47$	−1.02536	−	5.81510i	−0.149564	−	0.848219i	−0.963589	−	0.267389i	$-0.913839\pi$
$47$	−1.02536	−	5.81510i	−0.149564	−	0.848219i	0.814025	−	0.580830i	$-0.197272\pi$
$48$		0			0
$49$	6.57409	−	2.39277i	0.939156	−	0.341825i
$50$	−0.368076	+	2.08746i	−0.0520538	+	0.295212i
$51$		0			0
$52$	−11.7470	+	9.85691i	−1.62902	+	1.36691i
$53$	−0.617222			−0.0847820			−0.0423910	−	0.999101i	$-0.513498\pi$
$53$	−0.617222			−0.0847820			−0.0423910	+	0.999101i	$0.513498\pi$
$54$		0			0
$55$	−1.15673			−0.155973
$56$	0.0505913	−	0.0424511i	0.00676054	−	0.00567277i
$57$		0			0
$58$	−0.849014	+	4.81500i	−0.111481	+	0.632240i
$59$	−10.3506	+	3.76730i	−1.34753	+	0.490460i	−0.912175	−	0.409800i	$-0.865599\pi$
$59$	−10.3506	+	3.76730i	−1.34753	+	0.490460i	−0.435353	+	0.900260i	$0.643376\pi$
$60$		0			0
$61$	−2.06979	−	11.7384i	−0.265010	−	1.50295i	−0.769007	−	0.639241i	$-0.779249\pi$
$61$	−2.06979	−	11.7384i	−0.265010	−	1.50295i	0.503997	−	0.863705i	$-0.331862\pi$
$62$	9.09747	+	15.7573i	1.15538	+	2.00118i
$63$		0			0
$64$	5.66899	−	9.81898i	0.708624	−	1.22737i
$65$	5.78016	+	2.10381i	0.716941	+	0.260945i
$66$		0			0
$67$	−3.61207	−	3.03089i	−0.441285	−	0.370282i	0.394905	−	0.918722i	$-0.370777\pi$
$67$	−3.61207	−	3.03089i	−0.441285	−	0.370282i	−0.836190	+	0.548440i	$0.815222\pi$
$68$	−3.95669	−	3.32006i	−0.479819	−	0.402616i
$69$		0			0
$70$	−0.125886	−	0.0458186i	−0.0150462	−	0.00547637i
$71$	1.42779	−	2.47301i	0.169448	−	0.293493i	−0.768778	−	0.639516i	$-0.779135\pi$
$71$	1.42779	−	2.47301i	0.169448	−	0.293493i	0.938226	+	0.346023i	$0.112468\pi$
$72$		0			0
$73$	1.45719	+	2.52392i	0.170551	+	0.295403i	0.938613	−	0.344973i	$-0.112112\pi$
$73$	1.45719	+	2.52392i	0.170551	+	0.295403i	−0.768062	+	0.640376i	$0.778779\pi$
$74$	−1.59772	−	9.06114i	−0.185732	−	1.05334i
$75$		0			0
$76$	1.38705	−	0.504846i	0.159106	−	0.0579098i
$77$	0.0126947	−	0.0719954i	0.00144670	−	0.00820464i
$78$		0			0
$79$	−3.93760	+	3.30404i	−0.443014	+	0.371733i	−0.836836	−	0.547454i	$-0.815597\pi$
$79$	−3.93760	+	3.30404i	−0.443014	+	0.371733i	0.393822	+	0.919187i	$0.371153\pi$
$80$	−2.77101			−0.309808
$81$		0			0
$82$	−14.0830			−1.55520
$83$	2.57261	−	2.15868i	0.282381	−	0.236946i	−0.490585	−	0.871393i	$-0.663217\pi$
$83$	2.57261	−	2.15868i	0.282381	−	0.236946i	0.772966	+	0.634448i	$0.218772\pi$
$84$		0			0
$85$	−0.359774	+	2.04038i	−0.0390229	+	0.221310i
$86$	−21.9962	+	8.00594i	−2.37191	+	0.863303i
$87$		0			0
$88$	0.209893	+	1.19036i	0.0223747	+	0.126893i
$89$	−5.76784	−	9.99019i	−0.611390	−	1.05896i	−0.991006	−	0.133814i	$-0.957277\pi$
$89$	−5.76784	−	9.99019i	−0.611390	−	1.05896i	0.379617	−	0.925144i	$-0.376056\pi$
$90$		0			0
$91$	−0.194378	+	0.336673i	−0.0203764	+	0.0352929i
$92$	−17.4729	−	6.35961i	−1.82167	−	0.663035i
$93$		0			0
$94$	9.58798	+	8.04527i	0.988924	+	0.829806i
$95$	−0.453568	−	0.380589i	−0.0465351	−	0.0390476i
$96$		0			0
$97$	−12.0991	−	4.40371i	−1.22848	−	0.447129i	−0.355401	−	0.934714i	$-0.615656\pi$
$97$	−12.0991	−	4.40371i	−1.22848	−	0.447129i	−0.873075	+	0.487585i	$0.837878\pi$
$98$	−7.41460	+	12.8425i	−0.748987	+	1.29728i
$99$		0			0
$100$	−1.24649	−	2.15899i	−0.124649	−	0.215899i
$101$	−1.57002	−	8.90402i	−0.156223	−	0.885983i	−0.957659	−	0.287903i	$-0.907042\pi$
$101$	−1.57002	−	8.90402i	−0.156223	−	0.885983i	0.801437	−	0.598080i	$-0.204069\pi$
$102$		0			0
$103$	−13.3270	+	4.85061i	−1.31314	+	0.477945i	−0.901255	−	0.433289i	$-0.857353\pi$
$103$	−13.3270	+	4.85061i	−1.31314	+	0.477945i	−0.411888	+	0.911234i	$0.635131\pi$
$104$	1.11615	−	6.33000i	0.109448	−	0.620708i
$105$		0			0
$106$	1.00222	−	0.840962i	0.0973442	−	0.0816814i
$107$	−20.5665			−1.98824			−0.994118	−	0.108303i	$-0.965458\pi$
$107$	−20.5665			−1.98824			−0.994118	+	0.108303i	$0.965458\pi$
$108$		0			0
$109$	2.72255			0.260773			0.130386	−	0.991463i	$-0.458378\pi$
$109$	2.72255			0.260773			0.130386	+	0.991463i	$0.458378\pi$
$110$	1.87824	−	1.57603i	0.179083	−	0.150269i
$111$		0			0
$112$	0.0304110	−	0.172469i	0.00287357	−	0.0162968i
$113$	14.3503	−	5.22307i	1.34996	−	0.491345i	0.437024	−	0.899450i	$-0.356032\pi$
$113$	14.3503	−	5.22307i	1.34996	−	0.491345i	0.912935	+	0.408105i	$0.133810\pi$
$114$		0			0
$115$	1.29518	+	7.34532i	0.120776	+	0.684955i
$116$	−2.87519	−	4.97997i	−0.266955	−	0.462379i
$117$		0			0
$118$	11.6739	−	20.2198i	1.07467	−	1.86138i
$119$	−0.123046	−	0.0447851i	−0.0112796	−	0.00410545i
$120$		0			0
$121$	−7.40151	−	6.21061i	−0.672865	−	0.564600i
$122$	19.3543	+	16.2402i	1.75226	+	1.47032i
$123$		0			0
$124$	−20.1089	−	7.31904i	−1.80583	−	0.657269i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$		0			0
$127$	2.99285	+	5.18376i	0.265572	+	0.459984i	0.967713	−	0.252053i	$-0.0811058\pi$
$127$	2.99285	+	5.18376i	0.265572	+	0.459984i	−0.702141	+	0.712038i	$0.747773\pi$
$128$	1.40754	+	7.98255i	0.124410	+	0.705565i
$129$		0			0
$130$	−12.2520	+	4.45937i	−1.07457	+	0.391112i
$131$	−0.810965	+	4.59921i	−0.0708543	+	0.401835i	0.928668	+	0.370913i	$0.120955\pi$
$131$	−0.810965	+	4.59921i	−0.0708543	+	0.401835i	−0.999522	+	0.0309215i	$0.990156\pi$
$132$		0			0
$133$	0.0286659	−	0.0240535i	0.00248565	−	0.00208571i
$134$	9.99470			0.863410
$135$		0			0
$136$	2.16500			0.185647
$137$	−2.83974	+	2.38282i	−0.242615	+	0.203578i	−0.755985	−	0.654589i	$-0.772842\pi$
$137$	−2.83974	+	2.38282i	−0.242615	+	0.203578i	0.513369	+	0.858168i	$0.328397\pi$
$138$		0			0
$139$	−1.10921	+	6.29062i	−0.0940816	+	0.533563i	0.900943	+	0.433937i	$0.142876\pi$
$139$	−1.10921	+	6.29062i	−0.0940816	+	0.533563i	−0.995025	+	0.0996265i	$0.968235\pi$
$140$	0.148057	−	0.0538882i	0.0125131	−	0.00455439i
$141$		0			0
$142$	1.05107	+	5.96094i	0.0882042	+	0.500231i
$143$	−3.55758	−	6.16191i	−0.297500	−	0.515284i
$144$		0			0
$145$	−1.15331	+	1.99760i	−0.0957775	+	0.165891i
$146$	−5.80495	−	2.11283i	−0.480421	−	0.174859i
$147$		0			0
$148$	8.28967	+	6.95586i	0.681406	+	0.571768i
$149$	11.2316	+	9.42447i	0.920132	+	0.772083i	0.974019	−	0.226464i	$-0.0727167\pi$
$149$	11.2316	+	9.42447i	0.920132	+	0.772083i	−0.0538872	+	0.998547i	$0.517161\pi$
$150$		0			0
$151$	−11.1537	−	4.05962i	−0.907676	−	0.330367i	−0.154352	−	0.988016i	$-0.549329\pi$
$151$	−11.1537	−	4.05962i	−0.907676	−	0.330367i	−0.753325	+	0.657649i	$0.771551\pi$
$152$	−0.309355	+	0.535818i	−0.0250920	+	0.0434606i
$153$		0			0
$154$	0.0774802	+	0.134200i	0.00624353	+	0.0108141i
$155$	1.49057	+	8.45346i	0.119726	+	0.678998i
$156$		0			0
$157$	21.4638	−	7.81218i	1.71300	−	0.623480i	0.715801	−	0.698304i	$-0.246062\pi$
$157$	21.4638	−	7.81218i	1.71300	−	0.623480i	0.997197	+	0.0748243i	$0.0238396\pi$
$158$	1.89197	−	10.7299i	0.150517	−	0.853626i
$159$		0			0
$160$	6.10041	−	5.11885i	0.482280	−	0.404681i
$161$	−0.471392			−0.0371509
$162$		0			0
$163$	−4.08982			−0.320340			−0.160170	−	0.987089i	$-0.551204\pi$
$163$	−4.08982			−0.320340			−0.160170	+	0.987089i	$0.551204\pi$
$164$	12.6882	−	10.6466i	0.990781	−	0.831364i
$165$		0			0
$166$	−1.23611	+	7.01034i	−0.0959408	+	0.544108i
$167$	6.87588	−	2.50261i	0.532071	−	0.193658i	−0.0619917	−	0.998077i	$-0.519745\pi$
$167$	6.87588	−	2.50261i	0.532071	−	0.193658i	0.594063	+	0.804419i	$0.297523\pi$
$168$		0			0
$169$	4.31277	+	24.4590i	0.331752	+	1.88146i
$170$	−2.19582	−	3.80327i	−0.168412	−	0.291697i
$171$		0			0
$172$	13.7652	−	23.8420i	1.04959	−	1.81794i
$173$	17.6451	+	6.42229i	1.34153	+	0.488277i	0.910294	−	0.413961i	$-0.135855\pi$
$173$	17.6451	+	6.42229i	1.34153	+	0.488277i	0.431237	+	0.902239i	$0.358077\pi$
$174$		0			0
$175$	−0.0484147	−	0.0406247i	−0.00365981	−	0.00307094i
$176$	2.45540	+	2.06032i	0.185082	+	0.155303i
$177$		0			0
$178$	22.9772	+	8.36300i	1.72221	+	0.626833i
$179$	−5.41651	+	9.38167i	−0.404849	+	0.701219i	−0.994304	−	0.106582i	$-0.966009\pi$
$179$	−5.41651	+	9.38167i	−0.404849	+	0.701219i	0.589455	+	0.807801i	$0.299343\pi$
$180$		0			0
$181$	8.00831	+	13.8708i	0.595253	+	1.03101i	0.993511	+	0.113735i	$0.0362815\pi$
$181$	8.00831	+	13.8708i	0.595253	+	1.03101i	−0.398258	+	0.917273i	$0.630385\pi$
$182$	−0.143092	−	0.811514i	−0.0106067	−	0.0601534i
$183$		0			0
$184$	7.32392	−	2.66569i	0.539927	−	0.196517i
$185$	0.753762	−	4.27480i	0.0554177	−	0.314289i
$186$		0			0
$187$	1.83588	−	1.54048i	0.134253	−	0.112651i
$188$	−14.7206			−1.07361
$189$		0			0
$190$	1.25503			0.0910498
$191$	−0.840063	+	0.704896i	−0.0607848	+	0.0510045i	−0.672674	−	0.739939i	$-0.734854\pi$
$191$	−0.840063	+	0.704896i	−0.0607848	+	0.0510045i	0.611889	+	0.790944i	$0.290410\pi$
$192$		0			0
$193$	0.0958856	−	0.543795i	0.00690200	−	0.0391432i	−0.981162	−	0.193185i	$-0.938118\pi$
$193$	0.0958856	−	0.543795i	0.00690200	−	0.0391432i	0.988064	+	0.154042i	$0.0492292\pi$
$194$	25.6460	−	9.33439i	1.84128	−	0.670170i
$195$		0			0
$196$	−3.02858	−	17.1759i	−0.216327	−	1.22685i
$197$	7.41735	+	12.8472i	0.528464	+	0.915327i	0.999449	+	0.0331858i	$0.0105653\pi$
$197$	7.41735	+	12.8472i	0.528464	+	0.915327i	−0.470985	+	0.882141i	$0.656101\pi$
$198$		0			0
$199$	2.77326	−	4.80343i	0.196591	−	0.340506i	−0.750830	−	0.660496i	$-0.770346\pi$
$199$	2.77326	−	4.80343i	0.196591	−	0.340506i	0.947421	+	0.319990i	$0.103679\pi$
$200$	0.981938	+	0.357396i	0.0694335	+	0.0252717i
$201$		0			0
$202$	14.6810	+	12.3188i	1.03295	+	0.866750i
$203$	−0.111675	−	0.0937061i	−0.00783802	−	0.00657688i
$204$		0			0
$205$	−6.24327	−	2.27236i	−0.436049	−	0.158709i
$206$	15.0308	−	26.0341i	1.04725	−	1.81388i
$207$		0			0
$208$	−8.52239	−	14.7612i	−0.590922	−	1.02351i
$209$	0.118929	+	0.674481i	0.00822651	+	0.0466549i
$210$		0			0
$211$	−2.70774	+	0.985537i	−0.186409	+	0.0678471i	−0.433538	−	0.901135i	$-0.642735\pi$
$211$	−2.70774	+	0.985537i	−0.186409	+	0.0678471i	0.247129	+	0.968982i	$0.420513\pi$
$212$	−0.267197	+	1.51535i	−0.0183511	+	0.104074i
$213$		0			0
$214$	33.3950	−	28.0217i	2.28283	−	1.91552i
$215$	−11.0432			−0.753138
$216$		0			0
$217$	−0.542508			−0.0368279
$218$	−4.42076	+	3.70946i	−0.299412	+	0.251236i
$219$		0			0
$220$	−0.500748	+	2.83989i	−0.0337605	+	0.191465i
$221$	−11.9757	+	4.35878i	−0.805569	+	0.293203i
$222$		0			0
$223$	−1.99412	−	11.3092i	−0.133536	−	0.757321i	−0.975868	−	0.218361i	$-0.929929\pi$
$223$	−1.99412	−	11.3092i	−0.133536	−	0.757321i	0.842332	−	0.538959i	$-0.181182\pi$
$224$	0.251651	+	0.435872i	0.0168141	+	0.0291229i
$225$		0			0
$226$	−16.1850	+	28.0332i	−1.07661	+	1.86474i
$227$	19.5140	+	7.10252i	1.29519	+	0.471411i	0.895427	−	0.445208i	$-0.146870\pi$
$227$	19.5140	+	7.10252i	1.29519	+	0.471411i	0.399763	+	0.916618i	$0.369092\pi$
$228$		0			0
$229$	−9.01009	−	7.56037i	−0.595404	−	0.499603i	0.294561	−	0.955633i	$-0.404827\pi$
$229$	−9.01009	−	7.56037i	−0.595404	−	0.499603i	−0.889965	+	0.456030i	$0.849271\pi$
$230$	−12.1110	−	10.1624i	−0.798577	−	0.670086i
$231$		0			0
$232$	2.26496	+	0.824380i	0.148702	+	0.0541232i
$233$	−4.00167	+	6.93110i	−0.262158	+	0.454072i	−0.966815	−	0.255477i	$-0.917768\pi$
$233$	−4.00167	+	6.93110i	−0.262158	+	0.454072i	0.704657	+	0.709548i	$0.251101\pi$
$234$		0			0
$235$	2.95240	+	5.11371i	0.192594	+	0.333582i
$236$	4.76834	+	27.0426i	0.310393	+	1.76032i
$237$		0			0
$238$	0.260817	−	0.0949295i	0.0169062	−	0.00615337i
$239$	0.910140	−	5.16166i	0.0588720	−	0.333880i	−0.941119	−	0.338075i	$-0.890224\pi$
$239$	0.910140	−	5.16166i	0.0588720	−	0.333880i	0.999991	+	0.00419508i	$0.00133534\pi$
$240$		0			0
$241$	0.901265	−	0.756251i	0.0580556	−	0.0487144i	−0.613298	−	0.789851i	$-0.710158\pi$
$241$	0.901265	−	0.756251i	0.0580556	−	0.0487144i	0.671354	+	0.741137i	$0.265713\pi$
$242$	20.4802			1.31652
$243$		0			0
$244$	−29.7150			−1.90231
$245$	−5.35925	+	4.49695i	−0.342390	+	0.287299i
$246$		0			0
$247$	0.632430	−	3.58669i	0.0402406	−	0.228216i
$248$	8.42883	−	3.06784i	0.535231	−	0.194808i
$249$		0			0
$250$	−0.368076	−	2.08746i	−0.0232792	−	0.132023i
$251$	−7.69016	−	13.3198i	−0.485399	−	0.840735i	0.514460	−	0.857514i	$-0.327992\pi$
$251$	−7.69016	−	13.3198i	−0.485399	−	0.840735i	−0.999859	+	0.0167787i	$0.994659\pi$
$252$		0			0
$253$	4.31380	−	7.47172i	0.271206	−	0.469743i
$254$	−11.9225	−	4.33944i	−0.748084	−	0.272280i
$255$		0			0
$256$	4.20911	+	3.53186i	0.263069	+	0.220741i
$257$	−7.27559	−	6.10495i	−0.453839	−	0.380816i	0.387019	−	0.922072i	$-0.373505\pi$
$257$	−7.27559	−	6.10495i	−0.453839	−	0.380816i	−0.840858	+	0.541255i	$0.817949\pi$
$258$		0			0
$259$	0.257794	+	0.0938294i	0.0160185	+	0.00583027i
$260$	7.66732	−	13.2802i	0.475507	−	0.823602i
$261$		0			0
$262$	−4.94959	−	8.57294i	−0.305787	−	0.529638i
$263$	0.431805	+	2.44889i	0.0266262	+	0.151005i	0.995222	−	0.0976346i	$-0.0311277\pi$
$263$	0.431805	+	2.44889i	0.0266262	+	0.151005i	−0.968596	+	0.248640i	$0.920017\pi$
$264$		0			0
$265$	0.579999	−	0.211102i	0.0356291	−	0.0129679i
$266$	−0.0137736	+	0.0781142i	−0.000844516	+	0.00478949i
$267$		0			0
$268$	−9.00483	+	7.55595i	−0.550057	+	0.461553i
$269$	19.1404			1.16701			0.583506	−	0.812109i	$-0.301680\pi$
$269$	19.1404			1.16701			0.583506	+	0.812109i	$0.301680\pi$
$270$		0			0
$271$	−14.2245			−0.864077			−0.432039	−	0.901855i	$-0.642206\pi$
$271$	−14.2245			−0.864077			−0.432039	+	0.901855i	$0.642206\pi$
$272$	4.39795	−	3.69032i	0.266665	−	0.223758i
$273$		0			0
$274$	1.36446	−	7.73826i	0.0824303	−	0.467485i
$275$	1.08697	−	0.395623i	0.0655465	−	0.0238570i
$276$		0			0
$277$	−2.34467	−	13.2973i	−0.140877	−	0.798956i	−0.970585	−	0.240758i	$-0.922604\pi$
$277$	−2.34467	−	13.2973i	−0.140877	−	0.798956i	0.829708	−	0.558198i	$-0.188507\pi$
$278$	−6.76985	−	11.7257i	−0.406029	−	0.703263i
$279$		0			0
$280$	−0.0330211	+	0.0571942i	−0.00197339	+	0.00341801i
$281$	4.14803	+	1.50976i	0.247451	+	0.0900648i	0.462768	−	0.886479i	$-0.346856\pi$
$281$	4.14803	+	1.50976i	0.247451	+	0.0900648i	−0.215317	+	0.976544i	$0.569079\pi$
$282$		0			0
$283$	−0.974304	−	0.817538i	−0.0579163	−	0.0485976i	0.613370	−	0.789796i	$-0.289813\pi$
$283$	−0.974304	−	0.817538i	−0.0579163	−	0.0485976i	−0.671286	+	0.741198i	$0.734258\pi$
$284$	−5.45342	−	4.57596i	−0.323601	−	0.271533i
$285$		0			0
$286$	14.1722	+	5.15826i	0.838020	+	0.305014i
$287$	0.209952	−	0.363647i	0.0123931	−	0.0214654i
$288$		0			0
$289$	6.35371	+	11.0049i	0.373748	+	0.647350i
$290$	−0.849014	−	4.81500i	−0.0498558	−	0.282746i
$291$		0			0
$292$	6.82732	−	2.48494i	0.399538	−	0.145420i
$293$	−5.09348	+	28.8865i	−0.297564	+	1.68757i	0.359031	+	0.933326i	$0.383107\pi$
$293$	−5.09348	+	28.8865i	−0.297564	+	1.68757i	−0.656595	+	0.754244i	$0.728004\pi$
$294$		0			0
$295$	8.43785	−	7.08020i	0.491271	−	0.412225i
$296$	−4.53589			−0.263643
$297$		0			0
$298$	−31.0783			−1.80032
$299$	−35.1453	+	29.4904i	−2.03251	+	1.70548i
$300$		0			0
$301$	0.121196	−	0.687335i	0.00698560	−	0.0396173i
$302$	23.6421	−	8.60503i	1.36045	−	0.495164i
$303$		0			0
$304$	0.284902	+	1.61576i	0.0163403	+	0.0926702i
$305$	5.95973	+	10.3226i	0.341253	+	0.591068i
$306$		0			0
$307$	−8.95982	+	15.5189i	−0.511364	+	0.885708i	0.488550	+	0.872536i	$0.337526\pi$
$307$	−8.95982	+	15.5189i	−0.511364	+	0.885708i	−0.999913	+	0.0131717i	$0.995807\pi$
$308$	−0.171261	−	0.0623339i	−0.00975850	−	0.00355180i
$309$		0			0
$310$	−13.9381	−	11.6955i	−0.791633	−	0.664259i
$311$	−14.4414	−	12.1178i	−0.818895	−	0.687135i	0.133818	−	0.991006i	$-0.457276\pi$
$311$	−14.4414	−	12.1178i	−0.818895	−	0.687135i	−0.952713	+	0.303871i	$0.901721\pi$
$312$		0			0
$313$	5.39093	+	1.96214i	0.304713	+	0.110907i	0.489851	−	0.871806i	$-0.337051\pi$
$313$	5.39093	+	1.96214i	0.304713	+	0.110907i	−0.185138	+	0.982713i	$0.559273\pi$
$314$	−24.2080	+	41.9294i	−1.36613	+	2.36621i
$315$		0			0
$316$	6.40717	+	11.0975i	0.360432	+	0.624286i
$317$	0.181646	+	1.03017i	0.0102023	+	0.0578599i	0.989484	−	0.144643i	$-0.0462035\pi$
$317$	0.181646	+	1.03017i	0.0102023	+	0.0578599i	−0.979282	+	0.202503i	$0.935092\pi$
$318$		0			0
$319$	2.50723	−	0.912555i	0.140378	−	0.0510933i
$320$	−1.96882	+	11.1657i	−0.110060	+	0.624183i
$321$		0			0
$322$	0.765427	−	0.642270i	0.0426556	−	0.0357923i
$323$	1.22673			0.0682568
$324$		0			0
$325$	−6.15112			−0.341203
$326$	6.64089	−	5.57236i	0.367805	−	0.308625i
$327$		0			0
$328$	−1.20558	+	6.83717i	−0.0665668	+	0.377519i
$329$	−0.350683	+	0.127638i	−0.0193338	+	0.00703692i
$330$		0			0
$331$	−0.0366642	−	0.207933i	−0.00201525	−	0.0114290i	0.983784	−	0.179360i	$-0.0574026\pi$
$331$	−0.0366642	−	0.207933i	−0.00201525	−	0.0114290i	−0.985799	+	0.167931i	$0.946292\pi$
$332$	−4.18610	−	7.25053i	−0.229742	−	0.397925i
$333$		0			0
$334$	−7.75496	+	13.4320i	−0.424333	+	0.734966i
$335$	4.43086	+	1.61270i	0.242084	+	0.0881113i
$336$		0			0
$337$	16.7769	+	14.0775i	0.913898	+	0.766851i	0.972857	−	0.231409i	$-0.0743336\pi$
$337$	16.7769	+	14.0775i	0.913898	+	0.766851i	−0.0589586	+	0.998260i	$0.518778\pi$
$338$	−40.3281	−	33.8393i	−2.19356	−	1.84061i
$339$		0			0
$340$	4.85360	+	1.76657i	0.263223	+	0.0958055i
$341$	4.96459	−	8.59892i	0.268848	−	0.465658i
$342$		0			0
$343$	−0.442280	−	0.766051i	−0.0238809	−	0.0413629i
$344$	2.00384	+	11.3643i	0.108040	+	0.612723i
$345$		0			0
$346$	−37.4017	+	13.6131i	−2.01073	+	0.731845i
$347$	5.00368	−	28.3773i	0.268611	−	1.52337i	−0.489939	−	0.871757i	$-0.662981\pi$
$347$	5.00368	−	28.3773i	0.268611	−	1.52337i	0.758550	−	0.651615i	$-0.225908\pi$
$348$		0			0
$349$	13.1242	−	11.0125i	0.702521	−	0.589485i	−0.219969	−	0.975507i	$-0.570596\pi$
$349$	13.1242	−	11.0125i	0.702521	−	0.589485i	0.922490	+	0.386022i	$0.126151\pi$
$350$	0.133965			0.00716072
$351$		0			0
$352$	−9.21160			−0.490980
$353$	−1.85957	+	1.56036i	−0.0989747	+	0.0830497i	−0.690932	−	0.722919i	$-0.742800\pi$
$353$	−1.85957	+	1.56036i	−0.0989747	+	0.0830497i	0.591958	+	0.805969i	$0.298355\pi$
$354$		0			0
$355$	−0.495868	+	2.81221i	−0.0263179	+	0.149256i
$356$	−27.0239	+	9.83590i	−1.43226	+	0.521301i
$357$		0			0
$358$	−3.98738	−	22.6135i	−0.210739	−	1.19516i
$359$	4.55147	+	7.88338i	0.240217	+	0.416069i	0.960776	−	0.277325i	$-0.0894479\pi$
$359$	4.55147	+	7.88338i	0.240217	+	0.416069i	−0.720559	+	0.693394i	$0.756115\pi$
$360$		0			0
$361$	9.32471	−	16.1509i	0.490774	−	0.850046i
$362$	−31.9024	−	11.6115i	−1.67676	−	0.610289i
$363$		0			0
$364$	0.742421	+	0.622965i	0.0389134	+	0.0326523i
$365$	−2.23254	−	1.87332i	−0.116856	−	0.0980542i
$366$		0			0
$367$	14.0175	+	5.10194i	0.731706	+	0.266319i	0.680887	−	0.732389i	$-0.261595\pi$
$367$	14.0175	+	5.10194i	0.731706	+	0.266319i	0.0508190	+	0.998708i	$0.483817\pi$
$368$	10.3340	−	17.8989i	0.538695	−	0.933047i
$369$		0			0
$370$	4.60046	+	7.96823i	0.239167	+	0.414249i
$371$	0.00677384	+	0.0384164i	0.000351680	+	0.00199448i
$372$		0			0
$373$	18.4154	−	6.70266i	0.953513	−	0.347050i	0.182025	−	0.983294i	$-0.441735\pi$
$373$	18.4154	−	6.70266i	0.953513	−	0.347050i	0.771488	+	0.636243i	$0.219513\pi$
$374$	−0.882119	+	5.00274i	−0.0456133	+	0.258686i
$375$		0			0
$376$	4.72670	−	3.96617i	0.243761	−	0.204540i
$377$	−14.1883			−0.730737
$378$		0			0
$379$	7.13880			0.366696			0.183348	−	0.983048i	$-0.441307\pi$
$379$	7.13880			0.366696			0.183348	+	0.983048i	$0.441307\pi$
$380$	−1.13074	+	0.948800i	−0.0580055	+	0.0486724i
$381$		0			0
$382$	0.403641	−	2.28916i	0.0206521	−	0.117124i
$383$	32.4131	−	11.7974i	1.65623	−	0.602820i	0.666470	−	0.745532i	$-0.267805\pi$
$383$	32.4131	−	11.7974i	1.65623	−	0.602820i	0.989764	+	0.142712i	$0.0455823\pi$
$384$		0			0
$385$	0.0126947	+	0.0719954i	0.000646984	+	0.00366923i
$386$	0.585222	+	1.01363i	0.0297870	+	0.0515926i
$387$		0			0
$388$	−16.0493	+	27.7982i	−0.814780	+	1.41124i
$389$	−9.11176	−	3.31641i	−0.461985	−	0.168149i	0.100533	−	0.994934i	$-0.467945\pi$
$389$	−9.11176	−	3.31641i	−0.461985	−	0.168149i	−0.562518	+	0.826785i	$0.690167\pi$
$390$		0			0
$391$	−11.8378	−	9.93313i	−0.598666	−	0.502340i
$392$	5.60019	+	4.69911i	0.282852	+	0.237341i
$393$		0			0
$394$	−29.5483	−	10.7547i	−1.48862	−	0.541813i
$395$	2.57008	−	4.45151i	0.129315	−	0.223980i
$396$		0			0
$397$	−10.0679	−	17.4381i	−0.505293	−	0.875193i	−0.999981	−	0.00612241i	$-0.998051\pi$
$397$	−10.0679	−	17.4381i	−0.505293	−	0.875193i	0.494688	−	0.869070i	$-0.335282\pi$
$398$	2.04154	+	11.5782i	0.102333	+	0.580361i
$399$		0			0
$400$	2.60389	−	0.947740i	0.130195	−	0.0473870i
$401$	2.00191	−	11.3534i	0.0999706	−	0.566962i	−0.893140	−	0.449779i	$-0.851503\pi$
$401$	2.00191	−	11.3534i	0.0999706	−	0.566962i	0.993110	−	0.117182i	$-0.0373862\pi$
$402$		0			0
$403$	−40.4475	+	33.9395i	−2.01483	+	1.69064i
$404$	−22.5400			−1.12141
$405$		0			0
$406$	0.309007			0.0153357
$407$	−3.84634	+	3.22747i	−0.190656	+	0.159980i
$408$		0			0
$409$	0.783389	−	4.44282i	0.0387361	−	0.219683i	−0.959295	−	0.282406i	$-0.908867\pi$
$409$	0.783389	−	4.44282i	0.0387361	−	0.219683i	0.998031	+	0.0627230i	$0.0199785\pi$
$410$	13.2336	−	4.81665i	0.653563	−	0.237878i
$411$		0			0
$412$	6.13952	+	34.8189i	0.302472	+	1.71541i
$413$	0.348074	+	0.602881i	0.0171276	+	0.0296658i
$414$		0			0
$415$	−1.67915	+	2.90838i	−0.0824263	+	0.142767i
$416$	46.0304	+	16.7537i	2.25683	+	0.821418i
$417$		0			0
$418$	−1.11209	−	0.933154i	−0.0543941	−	0.0456421i
$419$	−16.6030	−	13.9316i	−0.811111	−	0.680603i	0.139762	−	0.990185i	$-0.455366\pi$
$419$	−16.6030	−	13.9316i	−0.811111	−	0.680603i	−0.950873	+	0.309582i	$0.899811\pi$
$420$		0			0
$421$	19.0158	+	6.92118i	0.926773	+	0.337318i	0.760930	−	0.648834i	$-0.224743\pi$
$421$	19.0158	+	6.92118i	0.926773	+	0.337318i	0.165843	+	0.986152i	$0.446965\pi$
$422$	3.05393	−	5.28955i	0.148663	−	0.257491i
$423$		0			0
$424$	−0.322485	−	0.558561i	−0.0156613	−	0.0271261i
$425$	−0.359774	−	2.04038i	−0.0174516	−	0.0989729i
$426$		0			0
$427$	−0.707890	+	0.257651i	−0.0342572	+	0.0124686i
$428$	−8.90326	+	50.4929i	−0.430355	+	2.44067i
$429$		0			0
$430$	17.9314	−	15.0463i	0.864730	−	0.725595i
$431$	−12.2741			−0.591224			−0.295612	−	0.955308i	$-0.595524\pi$
$431$	−12.2741			−0.591224			−0.295612	+	0.955308i	$0.595524\pi$
$432$		0			0
$433$	34.5905			1.66231			0.831156	−	0.556039i	$-0.187679\pi$
$433$	34.5905			1.66231			0.831156	+	0.556039i	$0.187679\pi$
$434$	0.880902	−	0.739165i	0.0422847	−	0.0354810i
$435$		0			0
$436$	1.17860	−	6.68415i	0.0564445	−	0.320113i
$437$	4.14986	−	1.51043i	0.198515	−	0.0722535i
$438$		0			0
$439$	5.53151	+	31.3708i	0.264005	+	1.49724i	0.771854	+	0.635799i	$0.219329\pi$
$439$	5.53151	+	31.3708i	0.264005	+	1.49724i	−0.507850	+	0.861446i	$0.669559\pi$
$440$	−0.604364	−	1.04679i	−0.0288119	−	0.0499037i
$441$		0			0
$442$	13.5067	−	23.3944i	0.642450	−	1.11276i
$443$	−1.75440	−	0.638551i	−0.0833543	−	0.0303385i	0.300006	−	0.953937i	$-0.403011\pi$
$443$	−1.75440	−	0.638551i	−0.0833543	−	0.0303385i	−0.383361	+	0.923599i	$0.625233\pi$
$444$		0			0
$445$	8.83684	+	7.41499i	0.418906	+	0.351504i
$446$	18.6467	+	15.6464i	0.882947	+	0.740880i
$447$		0			0
$448$	−0.673356	−	0.245082i	−0.0318131	−	0.0115790i
$449$	11.2063	−	19.4098i	0.528856	−	0.916006i	−0.470577	−	0.882359i	$-0.655954\pi$
$449$	11.2063	−	19.4098i	0.528856	−	0.916006i	0.999434	−	0.0336474i	$-0.0107123\pi$
$450$		0			0
$451$	3.84261	+	6.65560i	0.180942	+	0.313400i
$452$	−6.61094	−	37.4925i	−0.310953	−	1.76350i
$453$		0			0
$454$	−41.3632	+	15.0550i	−1.94127	+	0.706565i
$455$	0.0675068	−	0.382850i	0.00316477	−	0.0179483i
$456$		0			0
$457$	−12.2376	+	10.2686i	−0.572453	+	0.480345i	−0.882459	−	0.470390i	$-0.844113\pi$
$457$	−12.2376	+	10.2686i	−0.572453	+	0.480345i	0.310006	+	0.950735i	$0.399669\pi$
$458$	24.9312			1.16496
$459$		0			0
$460$	18.5942			0.866961
$461$	−19.0270	+	15.9655i	−0.886174	+	0.743588i	−0.967439	−	0.253104i	$-0.918548\pi$
$461$	−19.0270	+	15.9655i	−0.886174	+	0.743588i	0.0812651	+	0.996693i	$0.474104\pi$
$462$		0			0
$463$	−6.23114	+	35.3386i	−0.289586	+	1.64232i	0.398844	+	0.917019i	$0.369412\pi$
$463$	−6.23114	+	35.3386i	−0.289586	+	1.64232i	−0.688429	+	0.725303i	$0.741699\pi$
$464$	6.00621	−	2.18608i	0.278831	−	0.101486i
$465$		0			0
$466$	−2.94584	−	16.7067i	−0.136463	−	0.773923i
$467$	−5.20775	−	9.02009i	−0.240986	−	0.417400i	0.720009	−	0.693964i	$-0.244137\pi$
$467$	−5.20775	−	9.02009i	−0.240986	−	0.417400i	−0.960995	+	0.276564i	$0.910804\pi$
$468$		0			0
$469$	−0.149003	+	0.258081i	−0.00688033	+	0.0119171i
$470$	−11.7614	−	4.28080i	−0.542513	−	0.197458i
$471$		0			0
$472$	−8.81719	−	7.39850i	−0.405844	−	0.340544i
$473$	9.78538	+	8.21091i	0.449932	+	0.377538i
$474$		0			0
$475$	0.556383	+	0.202507i	0.0255286	+	0.00929166i
$476$	−0.163219	+	0.282704i	−0.00748114	+	0.0129577i
$477$		0			0
$478$	5.55489	+	9.62135i	0.254075	+	0.440070i
$479$	1.11318	+	6.31318i	0.0508627	+	0.288457i	0.999620	−	0.0275476i	$-0.00876978\pi$
$479$	1.11318	+	6.31318i	0.0508627	+	0.288457i	−0.948758	+	0.316004i	$0.897659\pi$
$480$		0			0
$481$	25.0902	−	9.13208i	1.14401	−	0.416387i
$482$	−0.433048	+	2.45594i	−0.0197248	+	0.111865i
$483$		0			0
$484$	−18.4518	+	15.4829i	−0.838720	+	0.703769i
$485$	12.8756			0.584650
$486$		0			0
$487$	15.0810			0.683385			0.341692	−	0.939812i	$-0.389000\pi$
$487$	15.0810			0.683385			0.341692	+	0.939812i	$0.389000\pi$
$488$	9.54133	−	8.00613i	0.431916	−	0.362420i
$489$		0			0
$490$	2.57506	−	14.6039i	0.116329	−	0.659737i
$491$	21.6911	−	7.89490i	0.978904	−	0.356292i	0.197490	−	0.980305i	$-0.436721\pi$
$491$	21.6911	−	7.89490i	0.978904	−	0.356292i	0.781414	+	0.624013i	$0.214499\pi$
$492$		0			0
$493$	−0.829863	−	4.70639i	−0.0373752	−	0.211965i
$494$	3.85993	+	6.68560i	0.173667	+	0.300799i
$495$		0			0
$496$	11.8930	−	20.5992i	0.534010	−	0.924933i
$497$	−0.169592	−	0.0617263i	−0.00760723	−	0.00276880i
$498$		0			0
$499$	−2.92703	−	2.45607i	−0.131032	−	0.109949i	0.574917	−	0.818212i	$-0.305035\pi$
$499$	−2.92703	−	2.45607i	−0.131032	−	0.109949i	−0.705948	+	0.708263i	$0.749479\pi$
$500$	1.90973	+	1.60246i	0.0854059	+	0.0716641i
$501$		0			0
$502$	30.6351	+	11.1503i	1.36731	+	0.497660i
$503$	−4.25813	+	7.37530i	−0.189861	+	0.328848i	−0.945204	−	0.326481i	$-0.894137\pi$
$503$	−4.25813	+	7.37530i	−0.189861	+	0.328848i	0.755343	+	0.655330i	$0.227470\pi$
$504$		0			0
$505$	4.52069	+	7.83006i	0.201168	+	0.348433i
$506$	3.17561	+	18.0098i	0.141173	+	0.800633i
$507$		0			0
$508$	14.0223	−	5.10370i	0.622139	−	0.226440i
$509$	−2.56080	+	14.5230i	−0.113506	+	0.643722i	0.873974	+	0.485973i	$0.161535\pi$
$509$	−2.56080	+	14.5230i	−0.113506	+	0.643722i	−0.987479	+	0.157749i	$0.949576\pi$
$510$		0			0
$511$	0.141098	−	0.118396i	0.00624183	−	0.00523752i
$512$	−27.8581			−1.23117
$513$		0			0
$514$	20.1318			0.887974
$515$	10.8642	−	9.11617i	0.478735	−	0.401706i
$516$		0			0
$517$	1.18606	−	6.72647i	0.0521628	−	0.295830i
$518$	−0.546437	+	0.198887i	−0.0240091	+	0.00873859i
$519$		0			0
$520$	1.11615	+	6.33000i	0.0489464	+	0.277589i
$521$	0.0788938	+	0.136648i	0.00345640	+	0.00598666i	0.867748	−	0.497004i	$-0.165566\pi$
$521$	0.0788938	+	0.136648i	0.00345640	+	0.00598666i	−0.864292	+	0.502990i	$0.832233\pi$
$522$		0			0
$523$	0.656230	−	1.13662i	0.0286949	−	0.0497011i	−0.851321	−	0.524645i	$-0.824198\pi$
$523$	0.656230	−	1.13662i	0.0286949	−	0.0497011i	0.880016	+	0.474944i	$0.157532\pi$
$524$	10.9405	+	3.98201i	0.477937	+	0.173955i
$525$		0			0
$526$	−4.03774	−	3.38807i	−0.176054	−	0.147727i
$527$	−13.6237	−	11.4317i	−0.593459	−	0.497972i
$528$		0			0
$529$	−30.6634	−	11.1606i	−1.33319	−	0.485242i
$530$	−0.654152	+	1.13303i	−0.0284146	+	0.0492155i
$531$		0			0
$532$	−0.0466445	−	0.0807907i	−0.00202230	−	0.00350272i
$533$	−7.09661	−	40.2469i	−0.307388	−	1.74328i
$534$		0			0
$535$	19.3262	−	7.03415i	0.835543	−	0.304113i
$536$	0.855600	−	4.85235i	0.0369563	−	0.209590i
$537$		0			0
$538$	−31.0794	+	26.0787i	−1.33993	+	1.12433i
$539$	8.09246			0.348567
$540$		0			0
$541$	19.1191			0.821995			0.410998	−	0.911636i	$-0.365180\pi$
$541$	19.1191			0.821995			0.410998	+	0.911636i	$0.365180\pi$
$542$	23.0972	−	19.3808i	0.992108	−	0.832477i
$543$		0			0
$544$	−2.86506	+	16.2486i	−0.122839	+	0.696652i
$545$	−2.55836	+	0.931166i	−0.109588	+	0.0398868i
$546$		0			0
$547$	−5.42945	−	30.7920i	−0.232147	−	1.31657i	−0.848540	−	0.529131i	$-0.822518\pi$
$547$	−5.42945	−	30.7920i	−0.232147	−	1.31657i	0.616394	−	0.787438i	$-0.288593\pi$
$548$	4.62076	+	8.00340i	0.197389	+	0.341888i
$549$		0			0
$550$	−1.22594	+	2.12338i	−0.0522741	+	0.0905413i
$551$	1.28337	+	0.467108i	0.0546733	+	0.0198995i
$552$		0			0
$553$	0.248860	+	0.208818i	0.0105826	+	0.00887984i
$554$	21.9246	+	18.3970i	0.931489	+	0.781612i
$555$		0			0
$556$	14.9640	+	5.44644i	0.634614	+	0.230981i
$557$	−18.4658	+	31.9837i	−0.782422	+	1.35519i	0.148105	+	0.988972i	$0.452682\pi$
$557$	−18.4658	+	31.9837i	−0.782422	+	1.35519i	−0.930527	+	0.366223i	$0.880651\pi$
$558$		0			0
$559$	−33.9639	−	58.8272i	−1.43652	−	2.48813i
$560$	0.0304110	+	0.172469i	0.00128510	+	0.00728816i
$561$		0			0
$562$	−8.79244	+	3.20019i	−0.370887	+	0.134992i
$563$	−5.80924	+	32.9458i	−0.244830	+	1.38850i	0.576056	+	0.817410i	$0.304591\pi$
$563$	−5.80924	+	32.9458i	−0.244830	+	1.38850i	−0.820887	+	0.571091i	$0.806520\pi$
$564$		0			0
$565$	−11.6984	+	9.81616i	−0.492157	+	0.412969i
$566$	2.69592			0.113318
$567$		0			0
$568$	2.98397			0.125204
$569$	18.5935	−	15.6018i	0.779481	−	0.654062i	−0.163637	−	0.986521i	$-0.552323\pi$
$569$	18.5935	−	15.6018i	0.779481	−	0.654062i	0.943118	+	0.332459i	$0.107878\pi$
$570$		0			0
$571$	−5.71582	+	32.4160i	−0.239200	+	1.35657i	0.594387	+	0.804179i	$0.297395\pi$
$571$	−5.71582	+	32.4160i	−0.239200	+	1.35657i	−0.833586	+	0.552389i	$0.813716\pi$
$572$	−16.6682	+	6.06674i	−0.696934	+	0.253663i
$573$		0			0
$574$	0.154556	+	0.876533i	0.00645106	+	0.0365858i
$575$	−3.72932	−	6.45937i	−0.155523	−	0.269374i
$576$		0			0
$577$	−8.73471	+	15.1290i	−0.363631	+	0.629827i	−0.988555	−	0.150858i	$-0.951796\pi$
$577$	−8.73471	+	15.1290i	−0.363631	+	0.629827i	0.624925	+	0.780685i	$0.285130\pi$
$578$	−25.3111	−	9.21248i	−1.05280	−	0.383189i
$579$		0			0
$580$	4.40505	+	3.69627i	0.182910	+	0.153479i
$581$	−0.162591	−	0.136430i	−0.00674542	−	0.00566008i
$582$		0			0
$583$	−0.670900	−	0.244188i	−0.0277858	−	0.0101132i
$584$	−1.52270	+	2.63739i	−0.0630096	+	0.109136i
$585$		0			0
$586$	−31.0872	−	53.8446i	−1.28420	−	2.22430i
$587$	−1.98349	−	11.2489i	−0.0818675	−	0.464294i	−0.997989	−	0.0633922i	$-0.979808\pi$
$587$	−1.98349	−	11.2489i	−0.0818675	−	0.464294i	0.916121	−	0.400901i	$-0.131303\pi$
$588$		0			0
$589$	4.77592	−	1.73829i	0.196788	−	0.0716251i
$590$	−4.05430	+	22.9931i	−0.166913	+	0.946609i
$591$		0			0
$592$	−9.21415	+	7.73159i	−0.378699	+	0.317766i
$593$	21.5568			0.885230			0.442615	−	0.896712i	$-0.354051\pi$
$593$	21.5568			0.885230			0.442615	+	0.896712i	$0.354051\pi$
$594$		0			0
$595$	0.130943			0.00536814
$596$	28.0003	−	23.4950i	1.14694	−	0.962394i
$597$		0			0
$598$	16.8870	−	95.7707i	0.690559	−	3.91635i
$599$	−9.12886	+	3.32263i	−0.372995	+	0.135759i	−0.521714	−	0.853120i	$-0.674707\pi$
$599$	−9.12886	+	3.32263i	−0.372995	+	0.135759i	0.148719	+	0.988880i	$0.452485\pi$
$600$		0			0
$601$	−4.26938	−	24.2129i	−0.174152	−	0.987663i	−0.939118	−	0.343594i	$-0.888356\pi$
$601$	−4.26938	−	24.2129i	−0.174152	−	0.987663i	0.764967	−	0.644070i	$-0.222755\pi$
$602$	0.739697	+	1.28119i	0.0301478	+	0.0522175i
$603$		0			0
$604$	−14.7953	+	25.6261i	−0.602011	+	1.04271i
$605$	9.07930	+	3.30459i	0.369126	+	0.134351i
$606$		0			0
$607$	−0.351918	−	0.295294i	−0.0142839	−	0.0119856i	0.635618	−	0.772004i	$-0.280745\pi$
$607$	−0.351918	−	0.295294i	−0.0142839	−	0.0119856i	−0.649902	+	0.760018i	$0.725190\pi$
$608$	−3.61199	−	3.03082i	−0.146486	−	0.122916i
$609$		0			0
$610$	−23.7416	−	8.64124i	−0.961269	−	0.349873i
$611$	−18.1606	+	31.4551i	−0.734699	+	1.27254i
$612$		0			0
$613$	14.2020	+	24.5986i	0.573613	+	0.993527i	0.996191	+	0.0872001i	$0.0277920\pi$
$613$	14.2020	+	24.5986i	0.573613	+	0.993527i	−0.422578	+	0.906327i	$0.638875\pi$
$614$	−6.59579	−	37.4066i	−0.266184	−	1.50961i
$615$		0			0
$616$	0.0717856	−	0.0261278i	0.00289233	−	0.00105272i
$617$	2.19222	−	12.4327i	0.0882553	−	0.500520i	−0.908351	−	0.418208i	$-0.862658\pi$
$617$	2.19222	−	12.4327i	0.0882553	−	0.500520i	0.996607	−	0.0823125i	$-0.0262306\pi$
$618$		0			0
$619$	−6.34778	+	5.32642i	−0.255139	+	0.214087i	−0.761381	−	0.648304i	$-0.775479\pi$
$619$	−6.34778	+	5.32642i	−0.255139	+	0.214087i	0.506243	+	0.862391i	$0.331034\pi$
$620$	21.3994			0.859422
$621$		0			0
$622$	39.9597			1.60224
$623$	−0.558496	+	0.468634i	−0.0223757	+	0.0187754i
$624$		0			0
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$	−11.4270	+	4.15908i	−0.456714	+	0.166230i
$627$		0			0
$628$	−9.88804	−	56.0778i	−0.394576	−	2.23775i
$629$	4.49669	+	7.78850i	0.179295	+	0.310548i
$630$		0			0
$631$	14.5655	−	25.2281i	0.579842	−	1.00432i	−0.415655	−	0.909522i	$-0.636448\pi$
$631$	14.5655	−	25.2281i	0.579842	−	1.00432i	0.995497	−	0.0947935i	$-0.0302191\pi$
$632$	−5.04733	−	1.83708i	−0.200772	−	0.0730750i
$633$		0			0
$634$	−1.69854	−	1.42525i	−0.0674578	−	0.0566038i
$635$	−4.58531	−	3.84753i	−0.181962	−	0.152684i
$636$		0			0
$637$	−40.4380	−	14.7182i	−1.60221	−	0.583158i
$638$	−2.82778	+	4.89785i	−0.111953	+	0.193908i
$639$		0			0
$640$	−4.05285	−	7.01974i	−0.160203	−	0.277480i
$641$	1.01054	+	5.73104i	0.0399138	+	0.226362i	0.998239	−	0.0593164i	$-0.0188921\pi$
$641$	1.01054	+	5.73104i	0.0399138	+	0.226362i	−0.958325	+	0.285679i	$0.907781\pi$
$642$		0			0
$643$	−13.0877	+	4.76353i	−0.516128	+	0.187855i	−0.586934	−	0.809635i	$-0.699665\pi$
$643$	−13.0877	+	4.76353i	−0.516128	+	0.187855i	0.0708056	+	0.997490i	$0.477443\pi$
$644$	−0.204067	+	1.15732i	−0.00804135	+	0.0456048i
$645$		0			0
$646$	−1.99191	+	1.67141i	−0.0783705	+	0.0657606i
$647$	12.0852			0.475119			0.237559	−	0.971373i	$-0.423653\pi$
$647$	12.0852			0.475119			0.237559	+	0.971373i	$0.423653\pi$
$648$		0			0
$649$	−12.7411			−0.500133
$650$	9.98793	−	8.38087i	0.391759	−	0.328725i
$651$		0			0
$652$	−1.77049	+	10.0410i	−0.0693378	+	0.393234i
$653$	−22.4836	+	8.18336i	−0.879851	+	0.320240i	−0.742150	−	0.670234i	$-0.766194\pi$
$653$	−22.4836	+	8.18336i	−0.879851	+	0.320240i	−0.137701	+	0.990474i	$0.543971\pi$
$654$		0			0
$655$	−0.810965	−	4.59921i	−0.0316870	−	0.179706i
$656$	9.20521	+	15.9439i	0.359403	+	0.622504i
$657$		0			0
$658$	0.395518	−	0.685057i	0.0154189	−	0.0267063i
$659$	−12.1165	−	4.41004i	−0.471991	−	0.171791i	0.0950632	−	0.995471i	$-0.469695\pi$
$659$	−12.1165	−	4.41004i	−0.471991	−	0.171791i	−0.567054	+	0.823681i	$0.691917\pi$
$660$		0			0
$661$	−14.3143	−	12.0111i	−0.556761	−	0.467178i	0.320462	−	0.947261i	$-0.396162\pi$
$661$	−14.3143	−	12.0111i	−0.556761	−	0.467178i	−0.877223	+	0.480083i	$0.840606\pi$
$662$	0.342842	+	0.287678i	0.0133249	+	0.0111809i
$663$		0			0
$664$	3.29765	+	1.20025i	0.127974	+	0.0465786i
$665$	−0.0187103	+	0.0324072i	−0.000725555	+	0.00125670i
$666$		0			0
$667$	−8.60215	−	14.8994i	−0.333076	−	0.576905i
$668$	−3.16761	−	17.9644i	−0.122558	−	0.695064i
$669$		0			0
$670$	−9.39194	+	3.41839i	−0.362842	+	0.132064i
$671$	2.39418	−	13.5781i	0.0924264	−	0.524176i
$672$		0			0
$673$	21.8080	−	18.2991i	0.840637	−	0.705378i	−0.117070	−	0.993124i	$-0.537350\pi$
$673$	21.8080	−	18.2991i	0.840637	−	0.705378i	0.957707	+	0.287746i	$0.0929058\pi$
$674$	−46.4222			−1.78812
$675$		0			0
$676$	61.9164			2.38140
$677$	−14.4949	+	12.1627i	−0.557085	+	0.467450i	−0.877332	−	0.479884i	$-0.840679\pi$
$677$	−14.4949	+	12.1627i	−0.557085	+	0.467450i	0.320247	+	0.947334i	$0.396234\pi$
$678$		0			0
$679$	−0.141306	+	0.801385i	−0.00542282	+	0.0307544i
$680$	−2.03443	+	0.740473i	−0.0780169	+	0.0283958i
$681$		0			0
$682$	3.65469	+	20.7268i	0.139945	+	0.793670i
$683$	21.5693	+	37.3592i	0.825328	+	1.42951i	0.901668	+	0.432428i	$0.142343\pi$
$683$	21.5693	+	37.3592i	0.825328	+	1.42951i	−0.0763404	+	0.997082i	$0.524324\pi$
$684$		0			0
$685$	1.85351	−	3.21037i	0.0708189	−	0.122662i
$686$	1.76190	+	0.641278i	0.0672695	+	0.0244841i
$687$		0			0
$688$	23.4415	+	19.6697i	0.893698	+	0.749901i
$689$	2.90837	+	2.44041i	0.110800	+	0.0929723i
$690$		0			0
$691$	35.1209	+	12.7830i	1.33606	+	0.486287i	0.908570	−	0.417732i	$-0.137175\pi$
$691$	35.1209	+	12.7830i	1.33606	+	0.486287i	0.427492	+	0.904019i	$0.359397\pi$
$692$	23.4060	−	40.5404i	0.889762	−	1.54111i
$693$		0			0
$694$	30.5391	+	52.8953i	1.15925	+	2.00788i
$695$	−1.10921	−	6.29062i	−0.0420746	−	0.238617i
$696$		0			0
$697$	12.9351	−	4.70801i	0.489953	−	0.178328i
$698$	−6.30602	+	35.7632i	−0.238687	+	1.35366i
$699$		0			0
$700$	−0.120697	+	0.101277i	−0.00456192	+	0.00382790i
$701$	15.4800			0.584670			0.292335	−	0.956316i	$-0.405568\pi$
$701$	15.4800			0.584670			0.292335	+	0.956316i	$0.405568\pi$
$702$		0			0
$703$	−2.57011			−0.0969336
$704$	10.0466	−	8.43012i	0.378646	−	0.317722i
$705$		0			0
$706$	0.893502	−	5.06730i	0.0336274	−	0.190710i
$707$	−0.536962	+	0.195438i	−0.0201945	+	0.00735021i
$708$		0			0
$709$	7.54820	+	42.8080i	0.283479	+	1.60769i	0.710669	+	0.703526i	$0.248392\pi$
$709$	7.54820	+	42.8080i	0.283479	+	1.60769i	−0.427191	+	0.904162i	$0.640497\pi$
$710$	−3.02645	−	5.24196i	−0.113581	−	0.196727i
$711$		0			0
$712$	6.02714	−	10.4393i	0.225877	−	0.391230i
$713$	−60.1629	−	21.8975i	−2.25312	−	0.820068i
$714$		0			0
$715$	5.45053	+	4.57353i	0.203838	+	0.171040i
$716$	20.6882	+	17.3595i	0.773154	+	0.648753i
$717$		0			0
$718$	−18.1315	−	6.59934i	−0.676663	−	0.246285i
$719$	17.5213	−	30.3477i	0.653433	−	1.13178i	−0.328851	−	0.944382i	$-0.606661\pi$
$719$	17.5213	−	30.3477i	0.653433	−	1.13178i	0.982284	−	0.187397i	$-0.0600052\pi$
$720$		0			0
$721$	0.448165	+	0.776245i	0.0166905	+	0.0289089i
$722$	6.86441	+	38.9300i	0.255467	+	1.44882i
$723$		0			0
$724$	37.5211	−	13.6566i	1.39446	−	0.507542i
$725$	0.400542	−	2.27158i	0.0148757	−	0.0843645i
$726$		0			0
$727$	2.88728	−	2.42271i	0.107083	−	0.0898534i	−0.587674	−	0.809098i	$-0.699956\pi$
$727$	2.88728	−	2.42271i	0.107083	−	0.0898534i	0.694757	+	0.719244i	$0.255512\pi$
$728$	−0.406233			−0.0150560
$729$		0			0
$730$	6.17750			0.228639
$731$	17.5270	−	14.7069i	0.648258	−	0.543953i
$732$		0			0
$733$	0.290284	−	1.64628i	0.0107219	−	0.0608068i	−0.978977	−	0.203969i	$-0.934616\pi$
$733$	0.290284	−	1.64628i	0.0107219	−	0.0608068i	0.989699	+	0.143162i	$0.0457270\pi$
$734$	−29.7123	+	10.8144i	−1.09670	+	0.399167i
$735$		0			0
$736$	10.3142	+	58.4946i	0.380186	+	2.15614i
$737$	−2.72711	−	4.72349i	−0.100454	−	0.173992i
$738$		0			0
$739$	22.4813	−	38.9388i	0.826989	−	1.43239i	−0.0734007	−	0.997303i	$-0.523385\pi$
$739$	22.4813	−	38.9388i	0.826989	−	1.43239i	0.900390	−	0.435084i	$-0.143281\pi$
$740$	−10.1688	−	3.70113i	−0.373812	−	0.136056i
$741$		0			0
$742$	−0.0633412	−	0.0531495i	−0.00232533	−	0.00195118i
$743$	−0.0794857	−	0.0666964i	−0.00291605	−	0.00244685i	0.641328	−	0.767266i	$-0.278384\pi$
$743$	−0.0794857	−	0.0666964i	−0.00291605	−	0.00244685i	−0.644244	+	0.764820i	$0.722828\pi$
$744$		0			0
$745$	−13.7777	−	5.01466i	−0.504774	−	0.183723i
$746$	−20.7698	+	35.9744i	−0.760437	+	1.31712i
$747$		0			0
$748$	−2.98730	−	5.17415i	−0.109226	−	0.189186i
$749$	0.225711	+	1.28007i	0.00824731	+	0.0467728i
$750$		0			0
$751$	−21.8427	+	7.95008i	−0.797050	+	0.290102i	−0.708263	−	0.705948i	$-0.750521\pi$
$751$	−21.8427	+	7.95008i	−0.797050	+	0.290102i	−0.0887866	+	0.996051i	$0.528299\pi$
$752$	2.84127	−	16.1137i	0.103611	−	0.587605i
$753$		0			0
$754$	23.0384	−	19.3315i	0.839010	−	0.704013i
$755$	11.8695			0.431976
$756$		0			0
$757$	−10.9327			−0.397356			−0.198678	−	0.980065i	$-0.563665\pi$
$757$	−10.9327			−0.397356			−0.198678	+	0.980065i	$0.563665\pi$
$758$	−11.5917	+	9.72658i	−0.421029	+	0.353285i
$759$		0			0
$760$	0.107438	−	0.609310i	0.00389718	−	0.0221020i
$761$	−25.8243	+	9.39926i	−0.936129	+	0.340723i	−0.764636	−	0.644462i	$-0.777081\pi$
$761$	−25.8243	+	9.39926i	−0.936129	+	0.340723i	−0.171493	+	0.985185i	$0.554859\pi$
$762$		0			0
$763$	−0.0298792	−	0.169453i	−0.00108170	−	0.00613462i
$764$	1.36693	+	2.36760i	0.0494539	+	0.0856566i
$765$		0			0
$766$	−36.5572	+	63.3189i	−1.32086	+	2.28780i
$767$	63.6675	+	23.1731i	2.29890	+	0.836732i
$768$		0			0
$769$	14.3237	+	12.0190i	0.516525	+	0.433416i	0.863418	−	0.504489i	$-0.168319\pi$
$769$	14.3237	+	12.0190i	0.516525	+	0.433416i	−0.346893	+	0.937905i	$0.612763\pi$
$770$	−0.118707	−	0.0996066i	−0.00427789	−	0.00358957i
$771$		0			0
$772$	−1.29357	−	0.470819i	−0.0465564	−	0.0169452i
$773$	15.4294	−	26.7246i	0.554959	−	0.961216i	−0.442948	−	0.896547i	$-0.646067\pi$
$773$	15.4294	−	26.7246i	0.554959	−	0.961216i	0.997907	−	0.0646692i	$-0.0205992\pi$
$774$		0			0
$775$	−4.29194	−	7.43385i	−0.154171	−	0.267032i
$776$	−2.33634	−	13.2500i	−0.0838696	−	0.475648i
$777$		0			0
$778$	19.3139	−	7.02968i	0.692436	−	0.252026i
$779$	−0.683101	+	3.87406i	−0.0244746	+	0.138802i
$780$		0			0
$781$	2.53035	−	2.12321i	0.0905429	−	0.0759745i
$782$	32.7556			1.17134
$783$		0			0
$784$	19.3860			0.692356
$785$	−17.4974	+	14.6821i	−0.624511	+	0.524027i
$786$		0			0
$787$	−6.66381	+	37.7923i	−0.237539	+	1.34715i	0.599661	+	0.800254i	$0.295302\pi$
$787$	−6.66381	+	37.7923i	−0.237539	+	1.34715i	−0.837200	+	0.546897i	$0.815809\pi$
$788$	34.7523	−	12.6488i	1.23800	−	0.450595i
$789$		0			0
$790$	1.89197	+	10.7299i	0.0673133	+	0.381753i
$791$	−0.482578	−	0.835849i	−0.0171585	−	0.0297194i
$792$		0			0
$793$	−36.6590	+	63.4953i	−1.30180	+	2.25478i
$794$	40.1071	+	14.5978i	1.42335	+	0.518056i
$795$		0			0
$796$	−10.5924	−	8.88807i	−0.375437	−	0.315029i
$797$	28.3650	+	23.8010i	1.00474	+	0.843076i	0.987634	−	0.156778i	$-0.0501107\pi$
$797$	28.3650	+	23.8010i	1.00474	+	0.843076i	0.0171048	+	0.999854i	$0.494555\pi$
$798$		0			0
$799$	−11.4961	−	4.18424i	−0.406703	−	0.148028i
$800$	−3.98176	+	6.89661i	−0.140776	+	0.243832i
$801$		0			0
$802$	12.2183	+	21.1628i	0.431444	+	0.747283i
$803$	0.585390	+	3.31991i	0.0206580	+	0.117157i
$804$		0			0
$805$	0.442964	−	0.161226i	0.0156124	−	0.00568246i
$806$	19.4346	−	110.219i	0.684554	−	3.88230i
$807$		0			0
$808$	7.23747	−	6.07296i	0.254613	−	0.213646i
$809$	34.2586			1.20447			0.602234	−	0.798320i	$-0.294278\pi$
$809$	34.2586			1.20447			0.602234	+	0.798320i	$0.294278\pi$
$810$		0			0
$811$	−28.6218			−1.00505			−0.502524	−	0.864563i	$-0.667595\pi$
$811$	−28.6218			−1.00505			−0.502524	+	0.864563i	$0.667595\pi$
$812$	−0.278403	+	0.233608i	−0.00977002	+	0.00819802i
$813$		0			0
$814$	1.84813	−	10.4812i	0.0647768	−	0.367368i
$815$	3.84318	−	1.39880i	0.134621	−	0.0489979i
$816$		0			0
$817$	1.13541	+	6.43922i	0.0397229	+	0.225280i
$818$	4.78129	+	8.28143i	0.167174	+	0.289553i
$819$		0			0
$820$	−8.28162	+	14.3442i	−0.289207	+	0.500921i
$821$	−19.3893	−	7.05712i	−0.676690	−	0.246295i	−0.0192644	−	0.999814i	$-0.506132\pi$
$821$	−19.3893	−	7.05712i	−0.676690	−	0.246295i	−0.657426	+	0.753519i	$0.728355\pi$
$822$		0			0
$823$	−40.4390	−	33.9324i	−1.40962	−	1.18281i	−0.956636	−	0.291287i	$-0.905916\pi$
$823$	−40.4390	−	33.9324i	−1.40962	−	1.18281i	−0.452980	−	0.891521i	$-0.649639\pi$
$824$	−11.3526	−	9.52600i	−0.395488	−	0.331854i
$825$		0			0
$826$	−1.38661	−	0.504685i	−0.0482463	−	0.0175602i
$827$	−11.5236	+	19.9595i	−0.400715	+	0.694058i	−0.993812	−	0.111072i	$-0.964572\pi$
$827$	−11.5236	+	19.9595i	−0.400715	+	0.694058i	0.593098	+	0.805131i	$0.297905\pi$
$828$		0			0
$829$	−22.7628	−	39.4264i	−0.790586	−	1.36934i	−0.925605	−	0.378492i	$-0.876443\pi$
$829$	−22.7628	−	39.4264i	−0.790586	−	1.36934i	0.135018	−	0.990843i	$-0.456891\pi$
$830$	−1.23611	−	7.01034i	−0.0429061	−	0.243332i
$831$		0			0
$832$	−65.5354	+	23.8529i	−2.27203	+	0.826951i
$833$	2.51698	−	14.2745i	0.0872081	−	0.494582i
$834$		0			0
$835$	−5.60527	+	4.70338i	−0.193978	+	0.162767i
$836$	1.70741			0.0590520
$837$		0			0
$838$	45.9410			1.58701
$839$	11.6668	−	9.78962i	0.402783	−	0.337975i	−0.418785	−	0.908085i	$-0.637544\pi$
$839$	11.6668	−	9.78962i	0.402783	−	0.337975i	0.821568	+	0.570110i	$0.193099\pi$
$840$		0			0
$841$	−4.11190	+	23.3197i	−0.141790	+	0.804129i
$842$	−40.3071	+	14.6706i	−1.38908	+	0.505582i
$843$		0			0
$844$	1.24741	+	7.07443i	0.0429377	+	0.243512i
$845$	−12.4181	−	21.5088i	−0.427197	−	0.739927i
$846$		0			0
$847$	−0.305323	+	0.528835i	−0.0104910	+	0.0181710i
$848$	−1.60718	−	0.584966i	−0.0551908	−	0.0200878i
$849$		0			0
$850$	3.36419	+	2.82289i	0.115391	+	0.0968243i
$851$	24.8015	+	20.8109i	0.850183	+	0.713389i
$852$		0			0
$853$	−5.05116	−	1.83847i	−0.172948	−	0.0629481i	0.254095	−	0.967179i	$-0.418223\pi$
$853$	−5.05116	−	1.83847i	−0.172948	−	0.0629481i	−0.427043	+	0.904231i	$0.640445\pi$
$854$	0.798394	−	1.38286i	0.0273205	−	0.0473205i
$855$		0			0
$856$	−10.7455	−	18.6118i	−0.367275	−	0.636139i
$857$	3.23480	+	18.3455i	0.110499	+	0.626670i	0.988881	+	0.148710i	$0.0475122\pi$
$857$	3.23480	+	18.3455i	0.110499	+	0.626670i	−0.878382	+	0.477959i	$0.841377\pi$
$858$		0			0
$859$	−17.0674	+	6.21203i	−0.582333	+	0.211952i	−0.616354	−	0.787469i	$-0.711391\pi$
$859$	−17.0674	+	6.21203i	−0.582333	+	0.211952i	0.0340211	+	0.999421i	$0.489169\pi$
$860$	−4.78061	+	27.1122i	−0.163017	+	0.924517i
$861$		0			0
$862$	19.9302	−	16.7234i	0.678825	−	0.569602i
$863$	−5.04898			−0.171869			−0.0859346	−	0.996301i	$-0.527388\pi$
$863$	−5.04898			−0.171869			−0.0859346	+	0.996301i	$0.527388\pi$
$864$		0			0
$865$	−18.7775			−0.638455
$866$	−56.1666	+	47.1294i	−1.90862	+	1.60152i
$867$		0			0
$868$	−0.234853	+	1.33192i	−0.00797142	+	0.0452082i
$869$	−5.58719	+	2.03357i	−0.189532	+	0.0689841i
$870$		0			0
$871$	5.03648	+	28.5633i	0.170654	+	0.967830i
$872$	1.42247	+	2.46379i	0.0481710	+	0.0834346i
$873$		0			0
$874$	−4.68042	+	8.10673i	−0.158318	+	0.274214i
$875$	0.0593894	+	0.0216160i	0.00200773	+	0.000730753i
$876$		0			0
$877$	−34.4946	−	28.9444i	−1.16480	−	0.977382i	−0.164839	−	0.986321i	$-0.552710\pi$
$877$	−34.4946	−	28.9444i	−1.16480	−	0.977382i	−0.999960	+	0.00893847i	$0.997155\pi$
$878$	−51.7243	−	43.4019i	−1.74561	−	1.46474i
$879$		0			0
$880$	−3.01199	−	1.09627i	−0.101534	−	0.0369554i
$881$	2.77972	−	4.81462i	0.0936512	−	0.162209i	−0.815394	−	0.578907i	$-0.803479\pi$
$881$	2.77972	−	4.81462i	0.0936512	−	0.162209i	0.909045	+	0.416698i	$0.136813\pi$
$882$		0			0
$883$	10.1759	+	17.6251i	0.342445	+	0.593132i	0.984886	−	0.173203i	$-0.0554117\pi$
$883$	10.1759	+	17.6251i	0.342445	+	0.593132i	−0.642441	+	0.766335i	$0.722078\pi$
$884$	5.51700	+	31.2884i	0.185557	+	1.05234i
$885$		0			0
$886$	3.71875	−	1.35351i	0.124934	−	0.0454722i
$887$	5.11824	−	29.0270i	0.171854	−	0.974630i	−0.769860	−	0.638213i	$-0.779674\pi$
$887$	5.11824	−	29.0270i	0.171854	−	0.974630i	0.941713	−	0.336417i	$-0.109215\pi$
$888$		0			0
$889$	0.289795	−	0.243167i	0.00971942	−	0.00815556i
$890$	−24.4518			−0.819625
$891$		0			0
$892$	−28.6286			−0.958556
$893$	2.67823	−	2.24730i	0.0896236	−	0.0752031i
$894$		0			0
$895$	1.88113	−	10.6684i	0.0628794	−	0.356607i
$896$	0.481392	−	0.175213i	0.0160822	−	0.00585344i
$897$		0			0
$898$	8.24952	+	46.7853i	0.275290	+	1.56125i
$899$	−9.89989	−	17.1471i	−0.330180	−	0.571888i
$900$		0			0
$901$	−0.639397	+	1.10747i	−0.0213014	+	0.0368951i
$902$	−15.3077	−	5.57154i	−0.509690	−	0.185512i
$903$		0			0
$904$	12.2244	+	10.2575i	0.406576	+	0.341158i
$905$	−12.2694	−	10.2953i	−0.407850	−	0.342227i
$906$		0			0
$907$	49.9658	+	18.1861i	1.65909	+	0.603859i	0.990219	−	0.139521i	$-0.0445563\pi$
$907$	49.9658	+	18.1861i	1.65909	+	0.603859i	0.668870	+	0.743380i	$0.266778\pi$
$908$	25.8851	−	44.8343i	0.859027	−	1.48788i
$909$		0			0
$910$	0.412017	+	0.713634i	0.0136582	+	0.0236567i
$911$	−1.42089	−	8.05828i	−0.0470763	−	0.266983i	0.952180	−	0.305537i	$-0.0988359\pi$
$911$	−1.42089	−	8.05828i	−0.0470763	−	0.266983i	−0.999257	+	0.0385540i	$0.987725\pi$
$912$		0			0
$913$	3.65036	−	1.32862i	0.120809	−	0.0439710i
$914$	5.88005	−	33.3474i	0.194495	−	1.10303i
$915$		0			0
$916$	−22.4620	+	18.8479i	−0.742165	+	0.622751i
$917$	0.295158			0.00974698
$918$		0			0
$919$	5.96363			0.196722			0.0983609	−	0.995151i	$-0.468640\pi$
$919$	5.96363			0.196722			0.0983609	+	0.995151i	$0.468640\pi$
$920$	−5.97052	+	5.00986i	−0.196842	+	0.165170i
$921$		0			0
$922$	9.14225	−	51.8483i	0.301084	−	1.70753i
$923$	−16.5058	+	6.00761i	−0.543294	+	0.197743i
$924$		0			0
$925$	0.753762	+	4.27480i	0.0247835	+	0.140554i
$926$	−38.0307	−	65.8712i	−1.24977	−	2.16466i
$927$		0			0
$928$	−9.18443	+	15.9079i	−0.301494	+	0.522202i
$929$	5.31666	+	1.93510i	0.174434	+	0.0634887i	0.427761	−	0.903892i	$-0.359303\pi$
$929$	5.31666	+	1.93510i	0.174434	+	0.0634887i	−0.253327	+	0.967381i	$0.581525\pi$
$930$		0			0
$931$	3.17316	+	2.66260i	0.103996	+	0.0872632i
$932$	15.2843	+	12.8250i	0.500653	+	0.420098i
$933$		0			0
$934$	20.7460	+	7.55091i	0.678829	+	0.247073i
$935$	−1.19828	+	2.07549i	−0.0391880	+	0.0678757i
$936$		0			0
$937$	−2.84697	−	4.93110i	−0.0930065	−	0.161092i	0.815768	−	0.578379i	$-0.196314\pi$
$937$	−2.84697	−	4.93110i	−0.0930065	−	0.161092i	−0.908775	+	0.417287i	$0.862981\pi$
$938$	−0.109689	−	0.622077i	−0.00358147	−	0.0203115i
$939$		0			0
$940$	13.8328	−	5.03473i	0.451177	−	0.164215i
$941$	0.178790	−	1.01397i	0.00582839	−	0.0330545i	−0.981755	−	0.190151i	$-0.939102\pi$
$941$	0.178790	−	1.01397i	0.00582839	−	0.0330545i	0.987583	+	0.157096i	$0.0502134\pi$
$942$		0			0
$943$	37.9612	−	31.8532i	1.23619	−	1.03728i
$944$	−30.5222			−0.993412
$945$		0			0
$946$	−27.0764			−0.880330
$947$	−7.84590	+	6.58349i	−0.254958	+	0.213935i	−0.761304	−	0.648396i	$-0.775440\pi$
$947$	−7.84590	+	6.58349i	−0.254958	+	0.213935i	0.506346	+	0.862330i	$0.330996\pi$
$948$		0			0
$949$	3.11293	−	17.6543i	0.101050	−	0.573083i
$950$	−1.17935	+	0.429247i	−0.0382631	+	0.0139266i
$951$		0			0
$952$	−0.0237602	−	0.134751i	−0.000770074	−	0.00436731i
$953$	8.46948	+	14.6696i	0.274353	+	0.475194i	0.969972	−	0.243217i	$-0.0782029\pi$
$953$	8.46948	+	14.6696i	0.274353	+	0.475194i	−0.695618	+	0.718411i	$0.744870\pi$
$954$		0			0
$955$	0.548312	−	0.949704i	0.0177430	−	0.0307317i
$956$	−12.2784	−	4.46898i	−0.397113	−	0.144537i
$957$		0			0
$958$	−10.4092	−	8.73437i	−0.336306	−	0.282195i
$959$	0.179474	+	0.150597i	0.00579552	+	0.00486302i
$960$		0			0
$961$	−40.1088	−	14.5984i	−1.29383	−	0.470916i
$962$	−28.2980	+	49.0135i	−0.912363	+	1.58026i
$963$		0			0
$964$	−1.46652	−	2.54009i	−0.0472334	−	0.0818107i
$965$	0.0958856	+	0.543795i	0.00308667	+	0.0175054i
$966$		0			0
$967$	27.9101	−	10.1584i	0.897528	−	0.326673i	0.148266	−	0.988947i	$-0.452631\pi$
$967$	27.9101	−	10.1584i	0.897528	−	0.326673i	0.749262	+	0.662274i	$0.230409\pi$
$968$	1.75321	−	9.94297i	0.0563504	−	0.319579i
$969$		0			0
$970$	−20.9068	+	17.5429i	−0.671278	+	0.563269i
$971$	−54.1443			−1.73757			−0.868787	−	0.495187i	$-0.835100\pi$
$971$	−54.1443			−1.73757			−0.868787	+	0.495187i	$0.835100\pi$
$972$		0			0
$973$	0.403706			0.0129422
$974$	−24.4879	+	20.5478i	−0.784642	+	0.658393i
$975$		0			0
$976$	5.73541	−	32.5271i	0.183586	−	1.04117i
$977$	−36.6787	+	13.3499i	−1.17345	+	0.427103i	−0.853886	−	0.520460i	$-0.825760\pi$
$977$	−36.6787	+	13.3499i	−1.17345	+	0.427103i	−0.319569	+	0.947563i	$0.603538\pi$
$978$		0			0
$979$	−2.31709	−	13.1409i	−0.0740546	−	0.419985i
$980$	8.72046	+	15.1043i	0.278565	+	0.482488i
$981$		0			0
$982$	−24.4643	+	42.3734i	−0.780686	+	1.35219i
$983$	−4.33786	−	1.57885i	−0.138356	−	0.0503575i	0.271914	−	0.962322i	$-0.412343\pi$
$983$	−4.33786	−	1.57885i	−0.138356	−	0.0503575i	−0.410270	+	0.911964i	$0.634566\pi$
$984$		0			0
$985$	−11.3640	−	9.53556i	−0.362088	−	0.303828i
$986$	7.75993	+	6.51135i	0.247126	+	0.207364i
$987$		0			0
$988$	−8.53193	−	3.10537i	−0.271437	−	0.0987950i
$989$	41.1835	−	71.3319i	1.30956	−	2.26822i
$990$		0			0
$991$	−3.70329	−	6.41429i	−0.117639	−	0.203757i	0.801193	−	0.598407i	$-0.204199\pi$
$991$	−3.70329	−	6.41429i	−0.117639	−	0.203757i	−0.918832	+	0.394650i	$0.870866\pi$
$992$	11.8702	+	67.3193i	0.376879	+	2.13739i
$993$		0			0
$994$	0.359478	−	0.130839i	0.0114019	−	0.00414997i
$995$	−0.963144	+	5.46226i	−0.0305337	+	0.173165i
$996$		0			0
$997$	33.5151	−	28.1225i	1.06143	−	0.890648i	0.0671838	−	0.997741i	$-0.478599\pi$
$997$	33.5151	−	28.1225i	1.06143	−	0.890648i	0.994249	+	0.107093i	$0.0341542\pi$
$998$	8.09917			0.256375
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.k.a.361.1		30
3.2	odd	2		135.2.k.a.76.5	yes	30
15.2	even	4		675.2.u.c.49.9		60
15.8	even	4		675.2.u.c.49.2		60
15.14	odd	2		675.2.l.d.76.1		30
27.4	even	9		3645.2.a.g.1.3		15
27.11	odd	18		135.2.k.a.16.5	✓	30
27.16	even	9	inner	405.2.k.a.46.1		30
27.23	odd	18		3645.2.a.h.1.13		15
135.38	even	36		675.2.u.c.124.9		60
135.92	even	36		675.2.u.c.124.2		60
135.119	odd	18		675.2.l.d.151.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.a.16.5	✓	30	27.11	odd	18
135.2.k.a.76.5	yes	30	3.2	odd	2
405.2.k.a.46.1		30	27.16	even	9	inner
405.2.k.a.361.1		30	1.1	even	1	trivial
675.2.l.d.76.1		30	15.14	odd	2
675.2.l.d.151.1		30	135.119	odd	18
675.2.u.c.49.2		60	15.8	even	4
675.2.u.c.49.9		60	15.2	even	4
675.2.u.c.124.2		60	135.92	even	36
675.2.u.c.124.9		60	135.38	even	36
3645.2.a.g.1.3		15	27.4	even	9
3645.2.a.h.1.13		15	27.23	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.k (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.62376 + 1.36249i) q^{2} +(0.432902 - 2.45511i) q^{4} +(-0.939693 + 0.342020i) q^{5} +(-0.0109747 - 0.0622407i) q^{7} +(0.522478 + 0.904959i) q^{8} +(1.05983 - 1.83568i) q^{10} +(1.08697 + 0.395623i) q^{11} +(-4.71203 - 3.95386i) q^{13} +(0.102623 + 0.0861109i) q^{14} +(2.60389 + 0.947740i) q^{16} +(1.03593 - 1.79428i) q^{17} +(0.296045 + 0.512766i) q^{19} +(0.432902 + 2.45511i) q^{20} +(-2.30400 + 0.838589i) q^{22} +(1.29518 - 7.34532i) q^{23} +(0.766044 - 0.642788i) q^{25} +13.0383 q^{26} -0.157559 q^{28} +(1.76698 - 1.48267i) q^{29} +(1.49057 - 8.45346i) q^{31} +(-7.48326 + 2.72368i) q^{32} +(0.762600 + 4.32492i) q^{34} +(0.0316004 + 0.0547336i) q^{35} +(-2.17037 + 3.75919i) q^{37} +(-1.17935 - 0.429247i) q^{38} +(-0.800483 - 0.671685i) q^{40} +(5.08956 + 4.27065i) q^{41} +(10.3772 + 3.77698i) q^{43} +(1.44185 - 2.49735i) q^{44} +(7.90491 + 13.6917i) q^{46} +(-1.02536 - 5.81510i) q^{47} +(6.57409 - 2.39277i) q^{49} +(-0.368076 + 2.08746i) q^{50} +(-11.7470 + 9.85691i) q^{52} -0.617222 q^{53} -1.15673 q^{55} +(0.0505913 - 0.0424511i) q^{56} +(-0.849014 + 4.81500i) q^{58} +(-10.3506 + 3.76730i) q^{59} +(-2.06979 - 11.7384i) q^{61} +(9.09747 + 15.7573i) q^{62} +(5.66899 - 9.81898i) q^{64} +(5.78016 + 2.10381i) q^{65} +(-3.61207 - 3.03089i) q^{67} +(-3.95669 - 3.32006i) q^{68} +(-0.125886 - 0.0458186i) q^{70} +(1.42779 - 2.47301i) q^{71} +(1.45719 + 2.52392i) q^{73} +(-1.59772 - 9.06114i) q^{74} +(1.38705 - 0.504846i) q^{76} +(0.0126947 - 0.0719954i) q^{77} +(-3.93760 + 3.30404i) q^{79} -2.77101 q^{80} -14.0830 q^{82} +(2.57261 - 2.15868i) q^{83} +(-0.359774 + 2.04038i) q^{85} +(-21.9962 + 8.00594i) q^{86} +(0.209893 + 1.19036i) q^{88} +(-5.76784 - 9.99019i) q^{89} +(-0.194378 + 0.336673i) q^{91} +(-17.4729 - 6.35961i) q^{92} +(9.58798 + 8.04527i) q^{94} +(-0.453568 - 0.380589i) q^{95} +(-12.0991 - 4.40371i) q^{97} +(-7.41460 + 12.8425i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{8} + 3 q^{10} + 6 q^{11} + 3 q^{13} + 9 q^{14} + 12 q^{16} + 12 q^{17} + 24 q^{19} - 51 q^{22} - 18 q^{23} + 18 q^{26} - 60 q^{28} - 18 q^{29} + 12 q^{31} - 36 q^{32} - 69 q^{34} + 12 q^{35}+ \cdots + 15 q^{98}+O(q^{100}) \) 30 * q + 9 * q^8 + 3 * q^10 + 6 * q^11 + 3 * q^13 + 9 * q^14 + 12 * q^16 + 12 * q^17 + 24 * q^19 - 51 * q^22 - 18 * q^23 + 18 * q^26 - 60 * q^28 - 18 * q^29 + 12 * q^31 - 36 * q^32 - 69 * q^34 + 12 * q^35 + 24 * q^37 + 24 * q^38 + 9 * q^40 + 75 * q^41 + 6 * q^43 - 12 * q^44 + 30 * q^46 - 45 * q^47 - 36 * q^49 + 30 * q^52 - 36 * q^53 - 30 * q^56 + 27 * q^58 + 27 * q^59 - 12 * q^61 - 36 * q^62 + 27 * q^64 - 6 * q^65 - 30 * q^67 - 69 * q^68 + 27 * q^70 - 12 * q^71 + 21 * q^73 - 30 * q^76 + 36 * q^77 + 54 * q^79 - 6 * q^80 - 48 * q^82 + 87 * q^83 + 27 * q^85 - 18 * q^86 - 18 * q^88 - 9 * q^89 + 51 * q^91 - 24 * q^92 + 15 * q^94 - 21 * q^95 - 75 * q^97 + 15 * q^98

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