LMFDB - Embedded newform 588.2.e.d.491.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(491,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.491"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,2,0,0,0,0,2,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.312013725601644544.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} - 2x^{8} + 8x^{6} - 8x^{4} - 16x^{2} + 64 $ x^12 - x^10 - 2x^8 + 8x^6 - 8x^4 - 16x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.7
Root			$0.225298 - 1.39615i$ of defining polynomial
Character	$\chi$	$=$	588.491
Dual form			588.2.e.d.491.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.225298 - 1.39615i) q^{2} +(-0.687941 - 1.58957i) q^{3} +(-1.89848 - 0.629100i) q^{4} -2.07605i q^{5} +(-2.37428 + 0.602344i) q^{6} +(-1.30604 + 2.50883i) q^{8} +(-2.05347 + 2.18706i) q^{9} +(-2.89848 - 0.467730i) q^{10} -3.98797 q^{11} +(0.306044 + 3.45056i) q^{12} +1.30998 q^{13} +(-3.30003 + 1.42820i) q^{15} +(3.20847 + 2.38867i) q^{16} -2.94162i q^{17} +(2.59083 + 3.35970i) q^{18} +1.09683i q^{19} +(-1.30604 + 3.94134i) q^{20} +(-0.898482 + 5.56781i) q^{22} -7.50125 q^{23} +(4.88645 + 0.350119i) q^{24} +0.690016 q^{25} +(0.295137 - 1.82894i) q^{26} +(4.88916 + 1.75957i) q^{27} +0.865568i q^{29} +(1.25050 + 4.92911i) q^{30} -3.68051i q^{31} +(4.05781 - 3.94134i) q^{32} +(2.74349 + 6.33916i) q^{33} +(-4.10695 - 0.662741i) q^{34} +(5.27436 - 2.86026i) q^{36} +4.17700 q^{37} +(1.53134 + 0.247114i) q^{38} +(-0.901192 - 2.08231i) q^{39} +(5.20847 + 2.71141i) q^{40} -7.01712i q^{41} +4.27597i q^{43} +(7.57109 + 2.50883i) q^{44} +(4.54045 + 4.26311i) q^{45} +(-1.69002 + 10.4729i) q^{46} -7.50125 q^{47} +(1.58973 - 6.74335i) q^{48} +(0.155459 - 0.963368i) q^{50} +(-4.67591 + 2.02366i) q^{51} +(-2.48698 - 0.824111i) q^{52} +4.94107i q^{53} +(3.55815 - 6.42959i) q^{54} +8.27923i q^{55} +(1.74349 - 0.754555i) q^{57} +(1.20847 + 0.195011i) q^{58} -4.88916 q^{59} +(7.16353 - 0.635363i) q^{60} -4.10695 q^{61} +(-5.13856 - 0.829212i) q^{62} +(-4.58850 - 6.55330i) q^{64} -2.71959i q^{65} +(9.46854 - 2.40213i) q^{66} -2.42231i q^{67} +(-1.85057 + 5.58461i) q^{68} +(5.16042 + 11.9238i) q^{69} -0.901192 q^{71} +(-2.80505 - 8.00823i) q^{72} -13.0109 q^{73} +(0.941069 - 5.83172i) q^{74} +(-0.474691 - 1.09683i) q^{75} +(0.690016 - 2.08231i) q^{76} +(-3.11026 + 0.789060i) q^{78} -10.3615i q^{79} +(4.95900 - 6.66093i) q^{80} +(-0.566494 - 8.98215i) q^{81} +(-9.79696 - 1.58094i) q^{82} +12.4386 q^{83} -6.10695 q^{85} +(5.96991 + 0.963368i) q^{86} +(1.37588 - 0.595460i) q^{87} +(5.20847 - 10.0052i) q^{88} -8.52623i q^{89} +(6.97491 - 5.37869i) q^{90} +(14.2410 + 4.71904i) q^{92} +(-5.85044 + 2.53198i) q^{93} +(-1.69002 + 10.4729i) q^{94} +2.27707 q^{95} +(-9.05658 - 3.73876i) q^{96} -15.3909 q^{97} +(8.18919 - 8.72195i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{4} + 2 q^{9} - 10 q^{10} - 12 q^{12} + 12 q^{13} + 10 q^{16} + 10 q^{18} + 14 q^{22} - 14 q^{24} + 12 q^{25} + 14 q^{30} + 10 q^{33} + 4 q^{34} + 22 q^{36} + 8 q^{37} + 34 q^{40} - 18 q^{45}+ \cdots - 36 q^{97}+O(q^{100}) $ 12 * q + 2 * q^4 + 2 * q^9 - 10 * q^10 - 12 * q^12 + 12 * q^13 + 10 * q^16 + 10 * q^18 + 14 * q^22 - 14 * q^24 + 12 * q^25 + 14 * q^30 + 10 * q^33 + 4 * q^34 + 22 * q^36 + 8 * q^37 + 34 * q^40 - 18 * q^45 - 24 * q^46 - 4 * q^48 + 16 * q^52 + 38 * q^54 - 2 * q^57 - 14 * q^58 - 14 * q^60 + 4 * q^61 - 34 * q^64 + 30 * q^66 - 18 * q^69 - 20 * q^72 + 12 * q^76 - 52 * q^78 - 26 * q^81 - 68 * q^82 - 20 * q^85 + 34 * q^88 + 20 * q^90 + 6 * q^93 - 24 * q^94 - 62 * q^96 - 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	0.225298	−	1.39615i	0.159310	−	0.987229i
$2$	0.225298	−	1.39615i	0.159310	−	0.987229i
$3$	−0.687941	−	1.58957i	−0.397183	−	0.917739i
$3$	−0.687941	−	1.58957i	−0.397183	−	0.917739i
$4$	−1.89848	−	0.629100i	−0.949241	−	0.314550i
$5$		−	2.07605i		−	0.928438i	−0.885721	−	0.464219i	$-0.846335\pi$
$5$		−	2.07605i		−	0.928438i	0.885721	−	0.464219i	$-0.153665\pi$
$6$	−2.37428	+	0.602344i	−0.969294	+	0.245906i
$7$		0			0
$7$		0			0
$8$	−1.30604	+	2.50883i	−0.461756	+	0.887007i
$9$	−2.05347	+	2.18706i	−0.684491	+	0.729021i
$10$	−2.89848	−	0.467730i	−0.916580	−	0.147909i
$11$	−3.98797			−1.20242			−0.601209	−	0.799092i	$-0.705314\pi$
$11$	−3.98797			−1.20242			−0.601209	+	0.799092i	$0.705314\pi$
$12$	0.306044	+	3.45056i	0.0883473	+	0.996090i
$13$	1.30998			0.363324			0.181662	−	0.983361i	$-0.441852\pi$
$13$	1.30998			0.363324			0.181662	+	0.983361i	$0.441852\pi$
$14$		0			0
$15$	−3.30003	+	1.42820i	−0.852064	+	0.368760i
$16$	3.20847	+	2.38867i	0.802116	+	0.597168i
$17$		−	2.94162i		−	0.713447i	−0.934210	−	0.356724i	$-0.883894\pi$
$17$		−	2.94162i		−	0.713447i	0.934210	−	0.356724i	$-0.116106\pi$
$18$	2.59083	+	3.35970i	0.610665	+	0.791889i
$19$			1.09683i			0.251630i	0.992054	+	0.125815i	$0.0401546\pi$
$19$			1.09683i			0.251630i	−0.992054	+	0.125815i	$0.959845\pi$
$20$	−1.30604	+	3.94134i	−0.292040	+	0.881311i
$21$		0			0
$22$	−0.898482	+	5.56781i	−0.191557	+	1.18706i
$23$	−7.50125			−1.56412			−0.782059	−	0.623204i	$-0.785831\pi$
$23$	−7.50125			−1.56412			−0.782059	+	0.623204i	$0.785831\pi$
$24$	4.88645	+	0.350119i	0.997443	+	0.0714678i
$25$	0.690016			0.138003
$26$	0.295137	−	1.82894i	0.0578811	−	0.358684i
$27$	4.88916	+	1.75957i	0.940920	+	0.338630i
$28$		0			0
$29$			0.865568i			0.160732i	0.996765	+	0.0803660i	$0.0256089\pi$
$29$			0.865568i			0.160732i	−0.996765	+	0.0803660i	$0.974391\pi$
$30$	1.25050	+	4.92911i	0.228308	+	0.899929i
$31$		−	3.68051i		−	0.661040i	−0.943799	−	0.330520i	$-0.892776\pi$
$31$		−	3.68051i		−	0.661040i	0.943799	−	0.330520i	$-0.107224\pi$
$32$	4.05781	−	3.94134i	0.717326	−	0.696738i
$33$	2.74349	+	6.33916i	0.477580	+	1.10351i
$34$	−4.10695	−	0.662741i	−0.704336	−	0.113659i
$35$		0			0
$36$	5.27436	−	2.86026i	0.879061	−	0.476710i
$37$	4.17700			0.686694			0.343347	−	0.939209i	$-0.388439\pi$
$37$	4.17700			0.686694			0.343347	+	0.939209i	$0.388439\pi$
$38$	1.53134	+	0.247114i	0.248416	+	0.0400871i
$39$	−0.901192	−	2.08231i	−0.144306	−	0.333437i
$40$	5.20847	+	2.71141i	0.823531	+	0.428712i
$41$		−	7.01712i		−	1.09589i	−0.836514	−	0.547945i	$-0.815410\pi$
$41$		−	7.01712i		−	1.09589i	0.836514	−	0.547945i	$-0.184590\pi$
$42$		0			0
$43$			4.27597i			0.652080i	0.945356	+	0.326040i	$0.105714\pi$
$43$			4.27597i			0.652080i	−0.945356	+	0.326040i	$0.894286\pi$
$44$	7.57109	+	2.50883i	1.14138	+	0.378221i
$45$	4.54045	+	4.26311i	0.676851	+	0.635507i
$46$	−1.69002	+	10.4729i	−0.249179	+	1.54414i
$47$	−7.50125			−1.09417			−0.547085	−	0.837077i	$-0.684263\pi$
$47$	−7.50125			−1.09417			−0.547085	+	0.837077i	$0.684263\pi$
$48$	1.58973	−	6.74335i	0.229457	−	0.973319i
$49$		0			0
$50$	0.155459	−	0.963368i	0.0219853	−	0.136241i
$51$	−4.67591	+	2.02366i	−0.654759	+	0.283369i
$52$	−2.48698	−	0.824111i	−0.344882	−	0.114284i
$53$			4.94107i			0.678708i	0.940659	+	0.339354i	$0.110208\pi$
$53$			4.94107i			0.678708i	−0.940659	+	0.339354i	$0.889792\pi$
$54$	3.55815	−	6.42959i	0.484202	−	0.874956i
$55$			8.27923i			1.11637i
$56$		0			0
$57$	1.74349	−	0.754555i	0.230931	−	0.0999432i
$58$	1.20847	+	0.195011i	0.158679	+	0.0256062i
$59$	−4.88916			−0.636515			−0.318257	−	0.948004i	$-0.603098\pi$
$59$	−4.88916			−0.636515			−0.318257	+	0.948004i	$0.603098\pi$
$60$	7.16353	−	0.635363i	0.924807	−	0.0820250i
$61$	−4.10695			−0.525841			−0.262920	−	0.964818i	$-0.584686\pi$
$61$	−4.10695			−0.525841			−0.262920	+	0.964818i	$0.584686\pi$
$62$	−5.13856	−	0.829212i	−0.652597	−	0.105310i
$63$		0			0
$64$	−4.58850	−	6.55330i	−0.573562	−	0.819162i
$65$		−	2.71959i		−	0.337324i
$66$	9.46854	−	2.40213i	1.16550	−	0.295682i
$67$		−	2.42231i		−	0.295932i	−0.988992	−	0.147966i	$-0.952727\pi$
$67$		−	2.42231i		−	0.295932i	0.988992	−	0.147966i	$-0.0472727\pi$
$68$	−1.85057	+	5.58461i	−0.224415	+	0.677233i
$69$	5.16042	+	11.9238i	0.621242	+	1.43545i
$70$		0			0
$71$	−0.901192			−0.106952			−0.0534759	−	0.998569i	$-0.517030\pi$
$71$	−0.901192			−0.106952			−0.0534759	+	0.998569i	$0.517030\pi$
$72$	−2.80505	−	8.00823i	−0.330579	−	0.943778i
$73$	−13.0109			−1.52281			−0.761403	−	0.648279i	$-0.775489\pi$
$73$	−13.0109			−1.52281			−0.761403	+	0.648279i	$0.775489\pi$
$74$	0.941069	−	5.83172i	0.109397	−	0.677924i
$75$	−0.474691	−	1.09683i	−0.0548126	−	0.126651i
$76$	0.690016	−	2.08231i	0.0791503	−	0.238858i
$77$		0			0
$78$	−3.11026	+	0.789060i	−0.352168	+	0.0893435i
$79$		−	10.3615i		−	1.16576i	−0.812557	−	0.582882i	$-0.801925\pi$
$79$		−	10.3615i		−	1.16576i	0.812557	−	0.582882i	$-0.198075\pi$
$80$	4.95900	−	6.66093i	0.554433	−	0.744715i
$81$	−0.566494	−	8.98215i	−0.0629437	−	0.998017i
$82$	−9.79696	−	1.58094i	−1.08189	−	0.174586i
$83$	12.4386			1.36531			0.682657	−	0.730739i	$-0.260824\pi$
$83$	12.4386			1.36531			0.682657	+	0.730739i	$0.260824\pi$
$84$		0			0
$85$	−6.10695			−0.662391
$86$	5.96991	+	0.963368i	0.643752	+	0.103883i
$87$	1.37588	−	0.595460i	0.147510	−	0.0638400i
$88$	5.20847	−	10.0052i	0.555224	−	1.06655i
$89$		−	8.52623i		−	0.903778i	−0.892074	−	0.451889i	$-0.850750\pi$
$89$		−	8.52623i		−	0.903778i	0.892074	−	0.451889i	$-0.149250\pi$
$90$	6.97491	−	5.37869i	0.735220	−	0.566964i
$91$		0			0
$92$	14.2410	+	4.71904i	1.48473	+	0.491994i
$93$	−5.85044	+	2.53198i	−0.606662	+	0.262554i
$94$	−1.69002	+	10.4729i	−0.174312	+	1.08020i
$95$	2.27707			0.233623
$96$	−9.05658	−	3.73876i	−0.924333	−	0.381586i
$97$	−15.3909			−1.56271			−0.781354	−	0.624088i	$-0.785471\pi$
$97$	−15.3909			−1.56271			−0.781354	+	0.624088i	$0.785471\pi$
$98$		0			0
$99$	8.18919	−	8.72195i	0.823045	−	0.876588i
$100$	−1.30998	−	0.434090i	−0.130998	−	0.0434090i
$101$			6.10526i			0.607496i	0.952752	+	0.303748i	$0.0982382\pi$
$101$			6.10526i			0.607496i	−0.952752	+	0.303748i	$0.901762\pi$
$102$	1.77187	+	6.98421i	0.175441	+	0.691540i
$103$		−	7.13237i		−	0.702774i	−0.936230	−	0.351387i	$-0.885710\pi$
$103$		−	7.13237i		−	0.702774i	0.936230	−	0.351387i	$-0.114290\pi$
$104$	−1.71090	+	3.28653i	−0.167767	+	0.322271i
$105$		0			0
$106$	6.89848	+	1.11321i	0.670040	+	0.108125i
$107$	−2.41675			−0.233636			−0.116818	−	0.993153i	$-0.537269\pi$
$107$	−2.41675			−0.233636			−0.116818	+	0.993153i	$0.537269\pi$
$108$	−8.17504	−	6.41629i	−0.786643	−	0.617408i
$109$	−6.79696			−0.651031			−0.325516	−	0.945537i	$-0.605538\pi$
$109$	−6.79696			−0.651031			−0.325516	+	0.945537i	$0.605538\pi$
$110$	11.5591	+	1.86529i	1.10211	+	0.177849i
$111$	−2.87353	−	6.63963i	−0.272743	−	0.630206i
$112$		0			0
$113$		−	3.16365i		−	0.297611i	−0.988867	−	0.148805i	$-0.952457\pi$
$113$		−	3.16365i		−	0.297611i	0.988867	−	0.148805i	$-0.0475428\pi$
$114$	−0.660669	−	2.60418i	−0.0618773	−	0.243904i
$115$			15.5730i			1.45219i
$116$	0.544529	−	1.64327i	0.0505583	−	0.152573i
$117$	−2.69002	+	2.86502i	−0.248692	+	0.264871i
$118$	−1.10152	+	6.82601i	−0.101403	+	0.628386i
$119$		0			0
$120$	0.726865	−	10.1445i	0.0663534	−	0.926064i
$121$	4.90391			0.445810
$122$	−0.925287	+	5.73392i	−0.0837715	+	0.519125i
$123$	−11.1542	+	4.82736i	−1.00574	+	0.435269i
$124$	−2.31541	+	6.98739i	−0.207930	+	0.627486i
$125$		−	11.8128i		−	1.05657i
$126$		0			0
$127$		−	15.0889i		−	1.33892i	−0.742848	−	0.669460i	$-0.766526\pi$
$127$		−	15.0889i		−	1.33892i	0.742848	−	0.669460i	$-0.233474\pi$
$128$	−10.1832	+	4.92980i	−0.900074	+	0.435737i
$129$	6.79696	−	2.94162i	0.598439	−	0.258995i
$130$	−3.79696	−	0.612718i	−0.333016	−	0.0537390i
$131$	7.40976			0.647394			0.323697	−	0.946161i	$-0.395074\pi$
$131$	7.40976			0.647394			0.323697	+	0.946161i	$0.395074\pi$
$132$	−1.22049	−	13.7607i	−0.106230	−	1.19772i
$133$		0			0
$134$	−3.38192	−	0.545742i	−0.292153	−	0.0471449i
$135$	3.65296	−	10.1501i	0.314396	−	0.873585i
$136$	7.38003	+	3.84188i	0.632833	+	0.329439i
$137$			15.0993i			1.29002i	0.764174	+	0.645010i	$0.223147\pi$
$137$			15.0993i			1.29002i	−0.764174	+	0.645010i	$0.776853\pi$
$138$	17.8100	−	4.51833i	1.51609	−	0.384626i
$139$		−	14.4761i		−	1.22785i	−0.789364	−	0.613925i	$-0.789590\pi$
$139$		−	14.4761i		−	1.22785i	0.789364	−	0.613925i	$-0.210410\pi$
$140$		0			0
$141$	5.16042	+	11.9238i	0.434586	+	1.00416i
$142$	−0.203037	+	1.25820i	−0.0170385	+	0.105586i
$143$	−5.22418			−0.436868
$144$	−11.8127	+	2.11204i	−0.984390	+	0.176004i
$145$	1.79696			0.149230
$146$	−2.93132	+	18.1651i	−0.242598	+	1.50336i
$147$		0			0
$148$	−7.92995	−	2.62775i	−0.651838	−	0.216000i
$149$		−	11.3912i		−	0.933207i	−0.884467	−	0.466604i	$-0.845477\pi$
$149$		−	11.3912i		−	0.933207i	0.884467	−	0.466604i	$-0.154523\pi$
$150$	−1.63829	+	0.415627i	−0.133766	+	0.0339358i
$151$		−	0.918202i		−	0.0747222i	−0.999302	−	0.0373611i	$-0.988105\pi$
$151$		−	0.918202i		−	0.0747222i	0.999302	−	0.0373611i	$-0.0118952\pi$
$152$	−2.75177	−	1.43251i	−0.223198	−	0.116192i
$153$	6.43351	+	6.04054i	0.520118	+	0.488348i
$154$		0			0
$155$	−7.64093			−0.613734
$156$	0.400913	+	4.52017i	0.0320987	+	0.361903i
$157$	8.72691			0.696484			0.348242	−	0.937405i	$-0.386779\pi$
$157$	8.72691			0.696484			0.348242	+	0.937405i	$0.386779\pi$
$158$	−14.4663	−	2.33443i	−1.15088	−	0.185718i
$159$	7.85418	−	3.39916i	0.622877	−	0.269571i
$160$	−8.18242	−	8.42422i	−0.646877	−	0.665993i
$161$		0			0
$162$	−12.6681	−	1.23275i	−0.995299	−	0.0968540i
$163$			8.99199i			0.704307i	0.935942	+	0.352153i	$0.114550\pi$
$163$			8.99199i			0.704307i	−0.935942	+	0.352153i	$0.885450\pi$
$164$	−4.41447	+	13.3219i	−0.344712	+	1.04026i
$165$	13.1604	−	5.69562i	1.02454	−	0.443404i
$166$	2.80239	−	17.3662i	0.217508	−	1.34788i
$167$	−16.1830			−1.25228			−0.626141	−	0.779710i	$-0.715367\pi$
$167$	−16.1830			−1.25228			−0.626141	+	0.779710i	$0.715367\pi$
$168$		0			0
$169$	−11.2839			−0.867996
$170$	−1.37588	+	8.52623i	−0.105525	+	0.653932i
$171$	−2.39884	−	2.25231i	−0.183444	−	0.172239i
$172$	2.69002	−	8.11786i	0.205112	−	0.618981i
$173$			4.22870i			0.321502i	0.986995	+	0.160751i	$0.0513916\pi$
$173$			4.22870i			0.321502i	−0.986995	+	0.160751i	$0.948608\pi$
$174$	−0.521370	−	2.05510i	−0.0395249	−	0.155797i
$175$		0			0
$176$	−12.7953	−	9.52595i	−0.964479	−	0.718046i
$177$	3.36346	+	7.77167i	0.252813	+	0.584155i
$178$	−11.9039	−	1.92094i	−0.892236	−	0.143981i
$179$	6.55187			0.489710			0.244855	−	0.969560i	$-0.421260\pi$
$179$	6.55187			0.489710			0.244855	+	0.969560i	$0.421260\pi$
$180$	−5.93804	−	10.9498i	−0.442595	−	0.816153i
$181$	12.2839			0.913058			0.456529	−	0.889708i	$-0.349092\pi$
$181$	12.2839			0.913058			0.456529	+	0.889708i	$0.349092\pi$
$182$		0			0
$183$	2.82534	+	6.52828i	0.208855	+	0.482585i
$184$	9.79696	−	18.8194i	0.722242	−	1.38738i
$185$		−	8.67165i		−	0.637553i
$186$	2.21693	+	8.73855i	0.162553	+	0.640742i
$187$			11.7311i			0.857862i
$188$	14.2410	+	4.71904i	1.03863	+	0.344171i
$189$		0			0
$190$	0.513020	−	3.17914i	0.0372184	−	0.230639i
$191$	23.7325			1.71722			0.858611	−	0.512627i	$-0.171328\pi$
$191$	23.7325			1.71722			0.858611	+	0.512627i	$0.171328\pi$
$192$	−7.26031	+	11.8020i	−0.523968	+	0.851738i
$193$	−3.97396			−0.286052			−0.143026	−	0.989719i	$-0.545683\pi$
$193$	−3.97396			−0.286052			−0.143026	+	0.989719i	$0.545683\pi$
$194$	−3.46754	+	21.4880i	−0.248955	+	1.54275i
$195$	−4.32298	+	1.87092i	−0.309575	+	0.133979i
$196$		0			0
$197$		−	19.7720i		−	1.40870i	−0.709853	−	0.704350i	$-0.751239\pi$
$197$		−	19.7720i		−	1.40870i	0.709853	−	0.704350i	$-0.248761\pi$
$198$	−10.3322	−	13.3984i	−0.734274	−	0.952182i
$199$		−	7.66651i		−	0.543464i	−0.962373	−	0.271732i	$-0.912404\pi$
$199$		−	7.66651i		−	0.543464i	0.962373	−	0.271732i	$-0.0875965\pi$
$200$	−0.901192	+	1.73114i	−0.0637239	+	0.122410i
$201$	−3.85044	+	1.66641i	−0.271589	+	0.117539i
$202$	8.52388	+	1.37550i	0.599738	+	0.0967801i
$203$		0			0
$204$	10.1502	−	0.900265i	0.710657	−	0.0630311i
$205$	−14.5679			−1.01747
$206$	−9.95788	−	1.60691i	−0.693798	−	0.111959i
$207$	15.4036	−	16.4057i	1.07063	−	1.14028i
$208$	4.20304	+	3.12912i	0.291428	+	0.216965i
$209$		−	4.37413i		−	0.302565i
$210$		0			0
$211$			11.7483i			0.808789i	0.914585	+	0.404395i	$0.132518\pi$
$211$			11.7483i			0.808789i	−0.914585	+	0.404395i	$0.867482\pi$
$212$	3.10843	−	9.38053i	0.213488	−	0.644257i
$213$	0.619967	+	1.43251i	0.0424794	+	0.0981539i
$214$	−0.544489	+	3.37415i	−0.0372205	+	0.230652i
$215$	8.87713			0.605415
$216$	−10.7999	+	9.96802i	−0.734842	+	0.678238i
$217$		0			0
$218$	−1.53134	+	9.48959i	−0.103716	+	0.642716i
$219$	8.95071	+	20.6817i	0.604833	+	1.39754i
$220$	5.20847	−	15.7180i	0.351155	−	1.05970i
$221$		−	3.85347i		−	0.259213i
$222$	−9.91734	+	2.51599i	−0.665608	+	0.168862i
$223$			14.5202i			0.972345i	0.873863	+	0.486173i	$0.161607\pi$
$223$			14.5202i			0.972345i	−0.873863	+	0.486173i	$0.838393\pi$
$224$		0			0
$225$	−1.41693	+	1.50911i	−0.0944620	+	0.100607i
$226$	−4.41693	−	0.712763i	−0.293810	−	0.0474123i
$227$	21.4629			1.42454			0.712271	−	0.701905i	$-0.247667\pi$
$227$	21.4629			1.42454			0.712271	+	0.701905i	$0.247667\pi$
$228$	−3.78467	+	0.335678i	−0.250646	+	0.0222308i
$229$	19.6308			1.29724			0.648621	−	0.761112i	$-0.275346\pi$
$229$	19.6308			1.29724			0.648621	+	0.761112i	$0.275346\pi$
$230$	21.7422	+	3.50856i	1.43364	+	0.231348i
$231$		0			0
$232$	−2.17157	−	1.13047i	−0.142570	−	0.0742190i
$233$			14.2640i			0.934468i	0.884134	+	0.467234i	$0.154749\pi$
$233$			14.2640i			0.934468i	−0.884134	+	0.467234i	$0.845251\pi$
$234$	3.39394	+	4.40115i	0.221869	+	0.287712i
$235$			15.5730i			1.01587i
$236$	9.28199	+	3.07577i	0.604206	+	0.200216i
$237$	−16.4704	+	7.12813i	−1.06987	+	0.463022i
$238$		0			0
$239$	15.2819			0.988501			0.494251	−	0.869320i	$-0.335443\pi$
$239$	15.2819			0.988501			0.494251	+	0.869320i	$0.335443\pi$
$240$	−13.9995	−	3.30035i	−0.903666	−	0.213037i
$241$	5.90391			0.380304			0.190152	−	0.981755i	$-0.439102\pi$
$241$	5.90391			0.380304			0.190152	+	0.981755i	$0.439102\pi$
$242$	1.10484	−	6.84660i	0.0710219	−	0.440116i
$243$	−13.8881	+	7.07968i	−0.890919	+	0.454161i
$244$	7.79696	+	2.58368i	0.499149	+	0.165403i
$245$		0			0
$246$	4.22672	+	16.6606i	0.269486	+	1.06224i
$247$			1.43683i			0.0914233i
$248$	9.23380	+	4.80691i	0.586347	+	0.305239i
$249$	−8.55703	−	19.7720i	−0.542280	−	1.25300i
$250$	−16.4924	−	2.66139i	−1.04307	−	0.168321i
$251$	−23.7400			−1.49845			−0.749226	−	0.662314i	$-0.769575\pi$
$251$	−23.7400			−1.49845			−0.749226	+	0.662314i	$0.769575\pi$
$252$		0			0
$253$	29.9148			1.88073
$254$	−21.0663	−	3.39949i	−1.32182	−	0.213303i
$255$	4.20122	+	9.70743i	0.263091	+	0.607903i
$256$	4.58850	+	15.3279i	0.286781	+	0.957996i
$257$		−	14.8007i		−	0.923240i	−0.887078	−	0.461620i	$-0.847268\pi$
$257$		−	14.8007i		−	0.923240i	0.887078	−	0.461620i	$-0.152732\pi$
$258$	−2.57560	−	10.1523i	−0.160350	−	0.632057i
$259$		0			0
$260$	−1.71090	+	5.16309i	−0.106105	+	0.320202i
$261$	−1.89305	−	1.77742i	−0.117177	−	0.110020i
$262$	1.66940	−	10.3452i	0.103136	−	0.639126i
$263$	13.9060			0.857479			0.428740	−	0.903428i	$-0.358958\pi$
$263$	13.9060			0.857479			0.428740	+	0.903428i	$0.358958\pi$
$264$	−19.4870	−	1.39627i	−1.19934	−	0.0859342i
$265$	10.2579			0.630138
$266$		0			0
$267$	−13.5530	+	5.86554i	−0.829433	+	0.358965i
$268$	−1.52388	+	4.59871i	−0.0930856	+	0.280911i
$269$		−	8.25792i		−	0.503494i	−0.967793	−	0.251747i	$-0.918995\pi$
$269$		−	8.25792i		−	0.503494i	0.967793	−	0.251747i	$-0.0810051\pi$
$270$	−13.3481	−	7.38689i	−0.812342	−	0.449552i
$271$		−	5.30552i		−	0.322288i	−0.986931	−	0.161144i	$-0.948482\pi$
$271$		−	5.30552i		−	0.322288i	0.986931	−	0.161144i	$-0.0515183\pi$
$272$	7.02656	−	9.43808i	0.426048	−	0.572268i
$273$		0			0
$274$	21.0809	+	3.40184i	1.27354	+	0.205513i
$275$	−2.75177			−0.165938
$276$	−2.29571	−	25.8835i	−0.138186	−	1.55800i
$277$	12.6048			0.757348			0.378674	−	0.925530i	$-0.376380\pi$
$277$	12.6048			0.757348			0.378674	+	0.925530i	$0.376380\pi$
$278$	−20.2109	−	3.26144i	−1.21217	−	0.195608i
$279$	8.04951	+	7.55783i	0.481912	+	0.452476i
$280$		0			0
$281$			2.02977i			0.121086i	0.998166	+	0.0605428i	$0.0192832\pi$
$281$			2.02977i			0.121086i	−0.998166	+	0.0605428i	$0.980717\pi$
$282$	17.8100	−	4.51833i	1.06057	−	0.269063i
$283$		−	7.67781i		−	0.456399i	−0.973614	−	0.228199i	$-0.926716\pi$
$283$		−	7.67781i		−	0.456399i	0.973614	−	0.228199i	$-0.0732838\pi$
$284$	1.71090	+	0.566940i	0.101523	+	0.0336417i
$285$	−1.56649	−	3.61957i	−0.0927911	−	0.214405i
$286$	−1.17700	+	7.29374i	−0.0695972	+	0.431288i
$287$		0			0
$288$	0.287363	+	16.9681i	0.0169331	+	0.999857i
$289$	8.34688			0.490993
$290$	0.404852	−	2.50883i	0.0237737	−	0.147324i
$291$	10.5880	+	24.4649i	0.620681	+	1.43416i
$292$	24.7009	+	8.18514i	1.44551	+	0.478999i
$293$		−	1.55539i		−	0.0908671i	−0.998967	−	0.0454336i	$-0.985533\pi$
$293$		−	1.55539i		−	0.0908671i	0.998967	−	0.0454336i	$-0.0144669\pi$
$294$		0			0
$295$			10.1501i			0.590964i
$296$	−5.45534	+	10.4794i	−0.317085	+	0.609102i
$297$	−19.4978	−	7.01712i	−1.13138	−	0.407174i
$298$	−15.9039	−	2.56642i	−0.921289	−	0.148669i
$299$	−9.82651			−0.568282
$300$	0.211175	+	2.38094i	0.0121922	+	0.137464i
$301$		0			0
$302$	−1.28195	−	0.206869i	−0.0737679	−	0.0119040i
$303$	9.70475	−	4.20006i	0.557523	−	0.241287i
$304$	−2.61997	+	3.51914i	−0.150265	+	0.201837i
$305$			8.52623i			0.488210i
$306$	9.88296	−	7.62123i	0.564971	−	0.435677i
$307$		−	31.5800i		−	1.80237i	−0.433437	−	0.901184i	$-0.642699\pi$
$307$		−	31.5800i		−	1.80237i	0.433437	−	0.901184i	$-0.357301\pi$
$308$		0			0
$309$	−11.3374	+	4.90665i	−0.644963	+	0.279130i
$310$	−1.72149	+	10.6679i	−0.0977738	+	0.605896i
$311$	18.2771			1.03640			0.518201	−	0.855259i	$-0.326602\pi$
$311$	18.2771			1.03640			0.518201	+	0.855259i	$0.326602\pi$
$312$	6.40117	+	0.458650i	0.362395	+	0.0259660i
$313$	−29.7818			−1.68337			−0.841683	−	0.539972i	$-0.818435\pi$
$313$	−29.7818			−1.68337			−0.841683	+	0.539972i	$0.818435\pi$
$314$	1.96616	−	12.1841i	0.110957	−	0.687589i
$315$		0			0
$316$	−6.51845	+	19.6712i	−0.366691	+	1.10659i
$317$		−	17.6960i		−	0.993906i	−0.867777	−	0.496953i	$-0.834452\pi$
$317$		−	17.6960i		−	0.993906i	0.867777	−	0.496953i	$-0.165548\pi$
$318$	−2.97622	−	11.7315i	−0.166898	−	0.657867i
$319$		−	3.45186i		−	0.193267i
$320$	−13.6050	+	9.52595i	−0.760541	+	0.532517i
$321$	1.66258	+	3.84160i	0.0927964	+	0.214417i
$322$		0			0
$323$	3.22646			0.179525
$324$	−4.57520	+	17.4088i	−0.254178	+	0.967158i
$325$	0.903910			0.0501399
$326$	12.5542	+	2.02588i	0.695312	+	0.112203i
$327$	4.67591	+	10.8043i	0.258579	+	0.597477i
$328$	17.6048	+	9.16466i	0.972062	+	0.506034i
$329$		0			0
$330$	−4.98694	−	19.6572i	−0.274522	−	1.08209i
$331$			35.0819i			1.92828i	0.265401	+	0.964138i	$0.414496\pi$
$331$			35.0819i			1.92828i	−0.265401	+	0.964138i	$0.585504\pi$
$332$	−23.6145	−	7.82513i	−1.29601	−	0.429460i
$333$	−8.57735	+	9.13536i	−0.470036	+	0.500614i
$334$	−3.64601	+	22.5940i	−0.199501	+	1.23629i
$335$	−5.02884			−0.274755
$336$		0			0
$337$	−0.132987			−0.00724428			−0.00362214	−	0.999993i	$-0.501153\pi$
$337$	−0.132987			−0.00724428			−0.00362214	+	0.999993i	$0.501153\pi$
$338$	−2.54225	+	15.7541i	−0.138280	+	0.856910i
$339$	−5.02884	+	2.17640i	−0.273129	+	0.118206i
$340$	11.5939	+	3.84188i	0.628769	+	0.208355i
$341$			14.6778i			0.794846i
$342$	−3.68502	+	2.84170i	−0.199263	+	0.153662i
$343$		0			0
$344$	−10.7277	−	5.58461i	−0.578399	−	0.301102i
$345$	24.7543	−	10.7133i	1.33273	−	0.576784i
$346$	5.90391	+	0.952718i	0.317396	+	0.0512184i
$347$	0.195336			0.0104862			0.00524310	−	0.999986i	$-0.498331\pi$
$347$	0.195336			0.0104862			0.00524310	+	0.999986i	$0.498331\pi$
$348$	−2.98669	+	0.264902i	−0.160104	+	0.0142002i
$349$	−5.80782			−0.310885			−0.155443	−	0.987845i	$-0.549680\pi$
$349$	−5.80782			−0.310885			−0.155443	+	0.987845i	$0.549680\pi$
$350$		0			0
$351$	6.40472	+	2.30501i	0.341859	+	0.123032i
$352$	−16.1824	+	15.7180i	−0.862526	+	0.837770i
$353$			19.9941i			1.06418i	0.846689	+	0.532089i	$0.178593\pi$
$353$			19.9941i			1.06418i	−0.846689	+	0.532089i	$0.821407\pi$
$354$	11.6082	−	2.94496i	0.616970	−	0.156523i
$355$			1.87092i			0.0992981i
$356$	−5.36385	+	16.1869i	−0.284284	+	0.857903i
$357$		0			0
$358$	1.47612	−	9.14741i	0.0780155	−	0.483455i
$359$	13.9060			0.733929			0.366965	−	0.930235i	$-0.380397\pi$
$359$	13.9060			0.733929			0.366965	+	0.930235i	$0.380397\pi$
$360$	−16.6255	+	5.82343i	−0.876240	+	0.306922i
$361$	17.7970			0.936682
$362$	2.76755	−	17.1503i	0.145459	−	0.901397i
$363$	−3.37360	−	7.79511i	−0.177068	−	0.409137i
$364$		0			0
$365$			27.0112i			1.41383i
$366$	9.75102	−	2.47379i	0.509694	−	0.129307i
$367$		−	18.8134i		−	0.982054i	−0.871144	−	0.491027i	$-0.836622\pi$
$367$		−	18.8134i		−	0.982054i	0.871144	−	0.491027i	$-0.163378\pi$
$368$	−24.0675	−	17.9180i	−1.25461	−	0.934041i
$369$	15.3469	+	14.4095i	0.798927	+	0.750127i
$370$	−12.1069	−	1.95371i	−0.629410	−	0.101568i
$371$		0			0
$372$	12.6998	−	1.12640i	0.658455	−	0.0584011i
$373$	5.82300			0.301504			0.150752	−	0.988572i	$-0.451831\pi$
$373$	5.82300			0.301504			0.150752	+	0.988572i	$0.451831\pi$
$374$	16.3784	+	2.64299i	0.846906	+	0.136666i
$375$	−18.7772	+	8.12648i	−0.969652	+	0.419650i
$376$	9.79696	−	18.8194i	0.505240	−	0.970536i
$377$			1.13388i			0.0583978i
$378$		0			0
$379$			12.0598i			0.619469i	0.950823	+	0.309735i	$0.100240\pi$
$379$			12.0598i			0.619469i	−0.950823	+	0.309735i	$0.899760\pi$
$380$	−4.32298	−	1.43251i	−0.221764	−	0.0734861i
$381$	−23.9848	+	10.3802i	−1.22878	+	0.531796i
$382$	5.34688	−	33.1342i	0.273570	−	1.69529i
$383$	12.1518			0.620927			0.310463	−	0.950585i	$-0.399516\pi$
$383$	12.1518			0.620927			0.310463	+	0.950585i	$0.399516\pi$
$384$	14.8417	+	12.7955i	0.757387	+	0.652966i
$385$		0			0
$386$	−0.895325	+	5.54825i	−0.0455708	+	0.282399i
$387$	−9.35182	−	8.78060i	−0.475380	−	0.446343i
$388$	29.2193	+	9.68242i	1.48339	+	0.491550i
$389$			1.21048i			0.0613739i	0.999529	+	0.0306869i	$0.00976949\pi$
$389$			1.21048i			0.0613739i	−0.999529	+	0.0306869i	$0.990231\pi$
$390$	1.63813	+	6.45706i	0.0829499	+	0.326966i
$391$			22.0658i			1.11592i
$392$		0			0
$393$	−5.09748	−	11.7783i	−0.257134	−	0.594139i
$394$	−27.6048	−	4.45460i	−1.39071	−	0.224420i
$395$	−21.5111			−1.08234
$396$	−21.0340	+	11.4066i	−1.05700	+	0.573205i
$397$	9.55703			0.479654			0.239827	−	0.970816i	$-0.422909\pi$
$397$	9.55703			0.479654			0.239827	+	0.970816i	$0.422909\pi$
$398$	−10.7036	−	1.72725i	−0.536524	−	0.0865792i
$399$		0			0
$400$	2.21389	+	1.64822i	0.110695	+	0.0824111i
$401$		−	11.2458i		−	0.561589i	−0.959768	−	0.280795i	$-0.909402\pi$
$401$		−	11.2458i		−	0.561589i	0.959768	−	0.280795i	$-0.0905980\pi$
$402$	1.45906	+	5.75123i	0.0727715	+	0.286845i
$403$		−	4.82141i		−	0.240172i
$404$	3.84082	−	11.5907i	0.191088	−	0.576660i
$405$	−18.6474	+	1.17607i	−0.926597	+	0.0584393i
$406$		0			0
$407$	−16.6577			−0.825693
$408$	1.02992	−	14.3741i	0.0509885	−	0.711623i
$409$	15.5679			0.769782			0.384891	−	0.922962i	$-0.374239\pi$
$409$	15.5679			0.769782			0.384891	+	0.922962i	$0.374239\pi$
$410$	−3.28212	+	20.3390i	−0.162092	+	1.00447i
$411$	24.0014	−	10.3874i	1.18390	−	0.512374i
$412$	−4.48698	+	13.5407i	−0.221058	+	0.667101i
$413$		0			0
$414$	−19.4345	−	25.2020i	−0.955152	−	1.23861i
$415$		−	25.8232i		−	1.26761i
$416$	5.31566	−	5.16309i	0.260622	−	0.253142i
$417$	−23.0109	+	9.95874i	−1.12685	+	0.487681i
$418$	−6.10695	−	0.985482i	−0.298701	−	0.0482015i
$419$	18.0336			0.881000			0.440500	−	0.897753i	$-0.354801\pi$
$419$	18.0336			0.881000			0.440500	+	0.897753i	$0.354801\pi$
$420$		0			0
$421$	−12.4978			−0.609107			−0.304554	−	0.952495i	$-0.598507\pi$
$421$	−12.4978			−0.609107			−0.304554	+	0.952495i	$0.598507\pi$
$422$	16.4025	+	2.64688i	0.798460	+	0.128848i
$423$	15.4036	−	16.4057i	0.748950	−	0.797673i
$424$	−12.3963	−	6.45325i	−0.602018	−	0.313398i
$425$		−	2.02977i		−	0.0984581i
$426$	2.13968	−	0.542827i	0.103668	−	0.0263001i
$427$		0			0
$428$	4.58816	+	1.52038i	0.221777	+	0.0734903i
$429$	3.59393	+	8.30420i	0.173516	+	0.400931i
$430$	2.00000	−	12.3938i	0.0964486	−	0.597683i
$431$	−12.4461			−0.599506			−0.299753	−	0.954017i	$-0.596904\pi$
$431$	−12.4461			−0.599506			−0.299753	+	0.954017i	$0.596904\pi$
$432$	11.4837	+	17.3241i	0.552508	+	0.833507i
$433$	0.497837			0.0239245			0.0119623	−	0.999928i	$-0.496192\pi$
$433$	0.497837			0.0239245			0.0119623	+	0.999928i	$0.496192\pi$
$434$		0			0
$435$	−1.23621	−	2.85640i	−0.0592715	−	0.136954i
$436$	12.9039	+	4.27597i	0.617985	+	0.204782i
$437$		−	8.22760i		−	0.393579i
$438$	30.8914	−	7.83701i	1.47605	−	0.374467i
$439$			4.66004i			0.222412i	0.993797	+	0.111206i	$0.0354713\pi$
$439$			4.66004i			0.222412i	−0.993797	+	0.111206i	$0.964529\pi$
$440$	−20.7712	−	10.8130i	−0.990228	−	0.515491i
$441$		0			0
$442$	−5.38003	−	0.868179i	−0.255902	−	0.0412951i
$443$	−22.0698			−1.04857			−0.524283	−	0.851544i	$-0.675667\pi$
$443$	−22.0698			−1.04857			−0.524283	+	0.851544i	$0.675667\pi$
$444$	1.27834	+	14.4130i	0.0606676	+	0.684009i
$445$	−17.7009			−0.839102
$446$	20.2724	+	3.27137i	0.959927	+	0.154904i
$447$	−18.1072	+	7.83651i	−0.856441	+	0.370654i
$448$		0			0
$449$		−	6.02866i		−	0.284510i	−0.989830	−	0.142255i	$-0.954565\pi$
$449$		−	6.02866i		−	0.284510i	0.989830	−	0.142255i	$-0.0454353\pi$
$450$	1.78772	+	2.31825i	0.0842737	+	0.109283i
$451$			27.9841i			1.31772i
$452$	−1.99025	+	6.00612i	−0.0936135	+	0.282504i
$453$	−1.45955	+	0.631669i	−0.0685755	+	0.0296784i
$454$	4.83554	−	29.9654i	0.226943	−	1.40635i
$455$		0			0
$456$	−0.384021	+	5.35961i	−0.0179834	+	0.250987i
$457$	−38.2616			−1.78980			−0.894902	−	0.446262i	$-0.852755\pi$
$457$	−38.2616			−1.78980			−0.894902	+	0.446262i	$0.852755\pi$
$458$	4.42278	−	27.4076i	0.206663	−	1.28067i
$459$	5.17599	−	14.3821i	0.241594	−	0.671297i
$460$	9.79696	−	29.5650i	0.456786	−	1.37848i
$461$			12.4563i			0.580148i	0.957004	+	0.290074i	$0.0936799\pi$
$461$			12.4563i			0.580148i	−0.957004	+	0.290074i	$0.906320\pi$
$462$		0			0
$463$		−	28.0609i		−	1.30410i	−0.758176	−	0.652050i	$-0.773909\pi$
$463$		−	28.0609i		−	1.30410i	0.758176	−	0.652050i	$-0.226091\pi$
$464$	−2.06756	+	2.77715i	−0.0959840	+	0.128926i
$465$	5.25651	+	12.1458i	0.243765	+	0.563248i
$466$	19.9148	+	3.21366i	0.922534	+	0.148870i
$467$	−17.0966			−0.791136			−0.395568	−	0.918437i	$-0.629452\pi$
$467$	−17.0966			−0.791136			−0.395568	+	0.918437i	$0.629452\pi$
$468$	6.90933	−	3.74689i	0.319384	−	0.173200i
$469$		0			0
$470$	21.7422	+	3.50856i	1.00289	+	0.161838i
$471$	−6.00360	−	13.8721i	−0.276632	−	0.639190i
$472$	6.38546	−	12.2661i	0.293915	−	0.564593i
$473$		−	17.0525i		−	0.784073i
$474$	6.24121	+	24.6011i	0.286668	+	1.12997i
$475$			0.756831i			0.0347258i
$476$		0			0
$477$	−10.8064	−	10.1464i	−0.494792	−	0.464569i
$478$	3.44297	−	21.3358i	0.157478	−	0.975877i
$479$	−16.4266			−0.750549			−0.375275	−	0.926914i	$-0.622452\pi$
$479$	−16.4266			−0.750549			−0.375275	+	0.926914i	$0.622452\pi$
$480$	−7.76186	+	18.8019i	−0.354279	+	0.858186i
$481$	5.47180			0.249492
$482$	1.33014	−	8.24276i	0.0605862	−	0.375447i
$483$		0			0
$484$	−9.30998	−	3.08505i	−0.423181	−	0.140230i
$485$			31.9523i			1.45088i
$486$	6.75535	+	20.9849i	0.306429	+	0.951893i
$487$		−	31.9873i		−	1.44948i	−0.689021	−	0.724742i	$-0.741959\pi$
$487$		−	31.9873i		−	1.44948i	0.689021	−	0.724742i	$-0.258041\pi$
$488$	5.36385	−	10.3036i	0.242810	−	0.466424i
$489$	14.2934	−	6.18596i	0.646370	−	0.279739i
$490$		0			0
$491$	−2.03844			−0.0919935			−0.0459968	−	0.998942i	$-0.514646\pi$
$491$	−2.03844			−0.0919935			−0.0459968	+	0.998942i	$0.514646\pi$
$492$	24.2130	−	2.14755i	1.09160	−	0.0968189i
$493$	2.54617			0.114674
$494$	2.00603	+	0.323715i	0.0902557	+	0.0145646i
$495$	−18.1072	−	17.0012i	−0.813858	−	0.764146i
$496$	8.79153	−	11.8088i	0.394752	−	0.530231i
$497$		0			0
$498$	−29.5327	+	7.49231i	−1.32339	+	0.335739i
$499$		−	4.29323i		−	0.192191i	−0.995372	−	0.0960957i	$-0.969365\pi$
$499$		−	4.29323i		−	0.192191i	0.995372	−	0.0960957i	$-0.0306355\pi$
$500$	−7.43141	+	22.4263i	−0.332343	+	1.00293i
$501$	11.1330	+	25.7241i	0.497385	+	1.14927i
$502$	−5.34856	+	33.1446i	−0.238718	+	1.47932i
$503$	26.3039			1.17283			0.586415	−	0.810010i	$-0.300539\pi$
$503$	26.3039			1.17283			0.586415	+	0.810010i	$0.300539\pi$
$504$		0			0
$505$	12.6748			0.564023
$506$	6.73974	−	41.7656i	0.299618	−	1.85671i
$507$	7.76269	+	17.9366i	0.344753	+	0.796594i
$508$	−9.49241	+	28.6459i	−0.421158	+	1.27096i
$509$		−	40.7771i		−	1.80741i	−0.428152	−	0.903707i	$-0.640835\pi$
$509$		−	40.7771i		−	1.80741i	0.428152	−	0.903707i	$-0.359165\pi$
$510$	14.4996	−	3.67848i	0.642052	−	0.162886i
$511$		0			0
$512$	22.4339	−	2.95289i	0.991448	−	0.130500i
$513$	−1.92995	+	5.36258i	−0.0852094	+	0.236764i
$514$	−20.6640	−	3.33456i	−0.911449	−	0.147081i
$515$	−14.8072			−0.652482
$516$	−14.7545	+	1.30864i	−0.649530	+	0.0576095i
$517$	29.9148			1.31565
$518$		0			0
$519$	6.72182	−	2.90910i	0.295055	−	0.127695i
$520$	6.82300	+	3.55191i	0.299209	+	0.155761i
$521$		−	6.94829i		−	0.304410i	−0.988349	−	0.152205i	$-0.951363\pi$
$521$		−	6.94829i		−	0.304410i	0.988349	−	0.152205i	$-0.0486374\pi$
$522$	−2.90805	+	2.24254i	−0.127282	+	0.0981533i
$523$			7.55516i			0.330364i	0.986263	+	0.165182i	$0.0528212\pi$
$523$			7.55516i			0.330364i	−0.986263	+	0.165182i	$0.947179\pi$
$524$	−14.0673	−	4.66149i	−0.614533	−	0.203638i
$525$		0			0
$526$	3.13299	−	19.4149i	0.136605	−	0.846528i
$527$	−10.8267			−0.471617
$528$	−6.33979	+	26.8923i	−0.275904	+	1.17034i
$529$	33.2688			1.44647
$530$	2.31108	−	14.3216i	0.100387	−	0.622090i
$531$	10.0398	−	10.6929i	0.435689	−	0.464033i
$532$		0			0
$533$		−	9.19231i		−	0.398163i
$534$	5.13572	+	20.2436i	0.222244	+	0.876027i
$535$			5.01730i			0.216917i
$536$	6.07718	+	3.16365i	0.262494	+	0.136649i
$537$	−4.50730	−	10.4147i	−0.194504	−	0.449426i
$538$	−11.5293	−	1.86049i	−0.497064	−	0.0802115i
$539$		0			0
$540$	−13.3205	+	16.9718i	−0.573224	+	0.730349i
$541$	11.1510			0.479417			0.239709	−	0.970845i	$-0.422948\pi$
$541$	11.1510			0.479417			0.239709	+	0.970845i	$0.422948\pi$
$542$	−7.40732	−	1.19532i	−0.318172	−	0.0513435i
$543$	−8.45063	−	19.5262i	−0.362651	−	0.837950i
$544$	−11.5939	−	11.9365i	−0.497086	−	0.511774i
$545$			14.1108i			0.604442i
$546$		0			0
$547$		−	39.2870i		−	1.67979i	−0.542748	−	0.839896i	$-0.682616\pi$
$547$		−	39.2870i		−	1.67979i	0.542748	−	0.839896i	$-0.317384\pi$
$548$	9.49897	−	28.6657i	0.405776	−	1.22454i
$549$	8.43351	−	8.98215i	0.359933	−	0.383349i
$550$	−0.619967	+	3.84188i	−0.0264355	+	0.163818i
$551$	−0.949382			−0.0404450
$552$	−36.6545	−	2.62633i	−1.56012	−	0.111784i
$553$		0			0
$554$	2.83983	−	17.5982i	0.120653	−	0.747676i
$555$	−13.7842	+	5.96559i	−0.585107	+	0.253225i
$556$	−9.10695	+	27.4827i	−0.386221	+	1.16553i
$557$		−	29.4625i		−	1.24836i	−0.781279	−	0.624182i	$-0.785432\pi$
$557$		−	29.4625i		−	1.24836i	0.781279	−	0.624182i	$-0.214568\pi$
$558$	12.3654	−	9.53558i	0.523470	−	0.403673i
$559$			5.60145i			0.236916i
$560$		0			0
$561$	18.6474	−	8.07030i	0.787294	−	0.340728i
$562$	2.83386	+	0.457302i	0.119539	+	0.0192901i
$563$	−40.6771			−1.71433			−0.857167	−	0.515039i	$-0.827777\pi$
$563$	−40.6771			−1.71433			−0.857167	+	0.515039i	$0.827777\pi$
$564$	−2.29571	−	25.8835i	−0.0966669	−	1.08989i
$565$	−6.56789			−0.276313
$566$	−10.7194	−	1.72980i	−0.450570	−	0.0727087i
$567$		0			0
$568$	1.17700	−	2.26094i	0.0493857	−	0.0948670i
$569$		−	4.97138i		−	0.208411i	−0.994556	−	0.104206i	$-0.966770\pi$
$569$		−	4.97138i		−	0.208411i	0.994556	−	0.104206i	$-0.0332300\pi$
$570$	−5.40640	+	1.37158i	−0.226449	+	0.0574492i
$571$			34.9819i			1.46395i	0.681334	+	0.731973i	$0.261400\pi$
$571$			34.9819i			1.46395i	−0.681334	+	0.731973i	$0.738600\pi$
$572$	9.91800	+	3.28653i	0.414693	+	0.137417i
$573$	−16.3266	−	37.7245i	−0.682052	−	1.57596i
$574$		0			0
$575$	−5.17599			−0.215854
$576$	23.7548	+	3.42168i	0.989785	+	0.142570i
$577$	14.6677			0.610625			0.305313	−	0.952252i	$-0.401239\pi$
$577$	14.6677			0.610625			0.305313	+	0.952252i	$0.401239\pi$
$578$	1.88054	−	11.6535i	0.0782200	−	0.484722i
$579$	2.73385	+	6.31689i	0.113615	+	0.262521i
$580$	−3.41150	−	1.13047i	−0.141655	−	0.0469402i
$581$		0			0
$582$	36.5422	−	9.27060i	1.51472	−	0.384279i
$583$		−	19.7048i		−	0.816091i
$584$	16.9928	−	32.6421i	0.703165	−	1.35074i
$585$	5.94792	+	5.58461i	0.245916	+	0.230895i
$586$	−2.17157	−	0.350427i	−0.0897066	−	0.0144760i
$587$	18.7469			0.773769			0.386885	−	0.922128i	$-0.373551\pi$
$587$	18.7469			0.773769			0.386885	+	0.922128i	$0.373551\pi$
$588$		0			0
$589$	4.03690			0.166337
$590$	14.1711	+	2.28681i	0.583417	+	0.0941464i
$591$	−31.4291	+	13.6020i	−1.29282	+	0.559512i
$592$	13.4017	+	9.97747i	0.550808	+	0.410072i
$593$			44.8989i			1.84378i	0.387456	+	0.921888i	$0.373354\pi$
$593$			44.8989i			1.84378i	−0.387456	+	0.921888i	$0.626646\pi$
$594$	−14.1898	+	25.6410i	−0.582214	+	1.05206i
$595$		0			0
$596$	−7.16624	+	21.6261i	−0.293541	+	0.885838i
$597$	−12.1865	+	5.27411i	−0.498759	+	0.215855i
$598$	−2.21389	+	13.7193i	−0.0905328	+	0.561024i
$599$	1.19291			0.0487409			0.0243704	−	0.999703i	$-0.492242\pi$
$599$	1.19291			0.0487409			0.0243704	+	0.999703i	$0.492242\pi$
$600$	3.37173	+	0.241588i	0.137650	+	0.00986279i
$601$	−37.4089			−1.52594			−0.762970	−	0.646434i	$-0.776259\pi$
$601$	−37.4089			−1.52594			−0.762970	+	0.646434i	$0.776259\pi$
$602$		0			0
$603$	5.29775	+	4.97415i	0.215741	+	0.202563i
$604$	−0.577641	+	1.74319i	−0.0235039	+	0.0709293i
$605$		−	10.1808i		−	0.413907i
$606$	−3.67747	−	14.4956i	−0.149387	−	0.588843i
$607$		−	21.4299i		−	0.869812i	−0.900476	−	0.434906i	$-0.856782\pi$
$607$		−	21.4299i		−	0.869812i	0.900476	−	0.434906i	$-0.143218\pi$
$608$	4.32298	+	4.45073i	0.175320	+	0.180501i
$609$		0			0
$610$	11.9039	+	1.92094i	0.481975	+	0.0777766i
$611$	−9.82651			−0.397538
$612$	−8.41379	−	15.5152i	−0.340107	−	0.627163i
$613$	−40.5347			−1.63718			−0.818591	−	0.574377i	$-0.805245\pi$
$613$	−40.5347			−1.63718			−0.818591	+	0.574377i	$0.805245\pi$
$614$	−44.0905	−	7.11492i	−1.77935	−	0.287135i
$615$	10.0219	+	23.1567i	0.404120	+	0.933768i
$616$		0			0
$617$			46.2548i			1.86215i	0.364830	+	0.931074i	$0.381127\pi$
$617$			46.2548i			1.86215i	−0.364830	+	0.931074i	$0.618873\pi$
$618$	4.29614	+	16.9342i	0.172816	+	0.681194i
$619$		−	25.7964i		−	1.03684i	−0.855125	−	0.518421i	$-0.826520\pi$
$619$		−	25.7964i		−	1.03684i	0.855125	−	0.518421i	$-0.173480\pi$
$620$	14.5062	+	4.80691i	0.582581	+	0.193050i
$621$	−36.6748	−	13.1990i	−1.47171	−	0.529657i
$622$	4.11780	−	25.5177i	0.165109	−	1.02317i
$623$		0			0
$624$	2.08252	−	8.83368i	0.0833674	−	0.353630i
$625$	−21.0738			−0.842952
$626$	−6.70977	+	41.5799i	−0.268177	+	1.66187i
$627$	−6.95299	+	3.00914i	−0.277676	+	0.120174i
$628$	−16.5679	−	5.49011i	−0.661131	−	0.219079i
$629$		−	12.2871i		−	0.489920i
$630$		0			0
$631$			26.5913i			1.05858i	0.848440	+	0.529291i	$0.177542\pi$
$631$			26.5913i			1.05858i	−0.848440	+	0.529291i	$0.822458\pi$
$632$	25.9954	+	13.5326i	1.03404	+	0.538299i
$633$	18.6748	−	8.08217i	0.742258	−	0.321238i
$634$	−24.7063	−	3.98687i	−0.981213	−	0.158339i
$635$	−31.3252			−1.24310
$636$	−17.0494	+	1.51218i	−0.676054	+	0.0599620i
$637$		0			0
$638$	−4.81932	−	0.777697i	−0.190799	−	0.0307893i
$639$	1.85057	−	1.97096i	0.0732076	−	0.0779701i
$640$	10.2345	+	21.1408i	0.404554	+	0.835663i
$641$		−	6.05241i		−	0.239056i	−0.992831	−	0.119528i	$-0.961862\pi$
$641$		−	6.05241i		−	0.239056i	0.992831	−	0.119528i	$-0.0381381\pi$
$642$	5.73803	−	1.45572i	0.226462	−	0.0574525i
$643$		−	9.95426i		−	0.392558i	−0.980548	−	0.196279i	$-0.937114\pi$
$643$		−	9.95426i		−	0.392558i	0.980548	−	0.196279i	$-0.0628858\pi$
$644$		0			0
$645$	−6.10695	−	14.1108i	−0.240461	−	0.555614i
$646$	0.726914	−	4.50462i	0.0286000	−	0.177232i
$647$	30.9902			1.21835			0.609175	−	0.793035i	$-0.291501\pi$
$647$	30.9902			1.21835			0.609175	+	0.793035i	$0.291501\pi$
$648$	23.2746	+	10.3098i	0.914313	+	0.405009i
$649$	19.4978			0.765357
$650$	0.203649	−	1.26200i	0.00798778	−	0.0494996i
$651$		0			0
$652$	5.65686	−	17.0711i	0.221540	−	0.668557i
$653$			8.10471i			0.317162i	0.987346	+	0.158581i	$0.0506919\pi$
$653$			8.10471i			0.317162i	−0.987346	+	0.158581i	$0.949308\pi$
$654$	16.1379	−	4.09411i	0.631040	−	0.160092i
$655$		−	15.3830i		−	0.601065i
$656$	16.7616	−	22.5142i	0.654430	−	0.879031i
$657$	26.7174	−	28.4556i	1.04235	−	1.11016i
$658$		0			0
$659$	38.3085			1.49229			0.746143	−	0.665785i	$-0.231903\pi$
$659$	38.3085			1.49229			0.746143	+	0.665785i	$0.231903\pi$
$660$	−28.5679	+	2.53381i	−1.11201	+	0.0986283i
$661$	−6.65686			−0.258922			−0.129461	−	0.991585i	$-0.541325\pi$
$661$	−6.65686			−0.258922			−0.129461	+	0.991585i	$0.541325\pi$
$662$	48.9797	+	7.90388i	1.90365	+	0.307193i
$663$	−6.12537	+	2.65096i	−0.237890	+	0.102955i
$664$	−16.2454	+	31.2064i	−0.630442	+	1.21104i
$665$		0			0
$666$	10.8219	+	14.0335i	0.419340	+	0.543786i
$667$		−	6.49285i		−	0.251404i
$668$	30.7232	+	10.1808i	1.18872	+	0.393906i
$669$	23.0809	−	9.98905i	0.892359	−	0.386199i
$670$	−1.13299	+	7.02103i	−0.0437711	+	0.271246i
$671$	16.3784			0.632280
$672$		0			0
$673$	−22.0809			−0.851156			−0.425578	−	0.904922i	$-0.639929\pi$
$673$	−22.0809			−0.851156			−0.425578	+	0.904922i	$0.639929\pi$
$674$	−0.0299618	+	0.185671i	−0.00115408	+	0.00715176i
$675$	3.37360	+	1.21413i	0.129850	+	0.0467320i
$676$	21.4224	+	7.09873i	0.823937	+	0.273028i
$677$			45.0746i			1.73236i	0.499733	+	0.866180i	$0.333431\pi$
$677$			45.0746i			1.73236i	−0.499733	+	0.866180i	$0.666569\pi$
$678$	1.90560	+	7.51136i	0.0731842	+	0.288472i
$679$		0			0
$680$	7.97594	−	15.3213i	0.305863	−	0.587546i
$681$	−14.7652	−	34.1168i	−0.565804	−	1.30736i
$682$	20.4924	+	3.30687i	0.784695	+	0.126627i
$683$	−15.6169			−0.597563			−0.298781	−	0.954322i	$-0.596580\pi$
$683$	−15.6169			−0.597563			−0.298781	+	0.954322i	$0.596580\pi$
$684$	3.13722	+	5.78508i	0.119955	+	0.221198i
$685$	31.3469			1.19770
$686$		0			0
$687$	−13.5049	−	31.2046i	−0.515242	−	1.19053i
$688$	−10.2139	+	13.7193i	−0.389401	+	0.523044i
$689$			6.47272i			0.246591i
$690$	−9.38028	−	36.9745i	−0.357101	−	1.40760i
$691$		−	38.3128i		−	1.45749i	−0.684786	−	0.728744i	$-0.740104\pi$
$691$		−	38.3128i		−	1.45749i	0.684786	−	0.728744i	$-0.259896\pi$
$692$	2.66028	−	8.02811i	0.101129	−	0.305183i
$693$		0			0
$694$	0.0440088	−	0.272719i	0.00167055	−	0.0103523i
$695$	−30.0532			−1.13998
$696$	−0.303052	+	4.22956i	−0.0114872	+	0.160321i
$697$	−20.6417			−0.781859
$698$	−1.30849	+	8.10860i	−0.0495271	+	0.306915i
$699$	22.6737	−	9.81282i	0.857598	−	0.371155i
$700$		0			0
$701$		−	36.6488i		−	1.38420i	−0.721799	−	0.692102i	$-0.756685\pi$
$701$		−	36.6488i		−	1.38420i	0.721799	−	0.692102i	$-0.243315\pi$
$702$	4.66111	−	8.42265i	0.175922	−	0.317893i
$703$			4.58146i			0.172793i
$704$	18.2988	+	26.1344i	0.689662	+	0.984975i
$705$	24.7543	−	10.7133i	0.932303	−	0.403486i
$706$	27.9148	+	4.50462i	1.05059	+	0.169534i
$707$		0			0
$708$	−1.49630	−	16.8703i	−0.0562344	−	0.634026i
$709$	36.5347			1.37209			0.686045	−	0.727559i	$-0.259345\pi$
$709$	36.5347			1.37209			0.686045	+	0.727559i	$0.259345\pi$
$710$	2.61209	+	0.421514i	0.0980299	+	0.0158191i
$711$	22.6613	+	21.2771i	0.849867	+	0.797955i
$712$	21.3909	+	11.1356i	0.801657	+	0.417325i
$713$			27.6084i			1.03394i
$714$		0			0
$715$			10.8457i			0.405604i
$716$	−12.4386	−	4.12178i	−0.464852	−	0.154038i
$717$	−10.5130	−	24.2916i	−0.392616	−	0.907186i
$718$	3.13299	−	19.4149i	0.116922	−	0.724556i
$719$	24.5373			0.915087			0.457543	−	0.889187i	$-0.348729\pi$
$719$	24.5373			0.915087			0.457543	+	0.889187i	$0.348729\pi$
$720$	4.38471	+	24.5237i	0.163408	+	0.913944i
$721$		0			0
$722$	4.00962	−	24.8473i	0.149223	−	0.924720i
$723$	−4.06154	−	9.38469i	−0.151050	−	0.349020i
$724$	−23.3208	−	7.72783i	−0.866712	−	0.287203i
$725$			0.597256i			0.0221815i
$726$	−11.6432	+	2.95384i	−0.432121	+	0.109627i
$727$		−	7.89691i		−	0.292880i	−0.989220	−	0.146440i	$-0.953218\pi$
$727$		−	7.89691i		−	0.292880i	0.989220	−	0.146440i	$-0.0467816\pi$
$728$		0			0
$729$	20.8078	+	17.2057i	0.770660	+	0.637247i
$730$	37.7117	+	6.08557i	1.39577	+	0.225237i
$731$	12.5783			0.465224
$732$	−1.25691	−	14.1713i	−0.0464566	−	0.523784i
$733$	−5.84472			−0.215880			−0.107940	−	0.994157i	$-0.534425\pi$
$733$	−5.84472			−0.215880			−0.107940	+	0.994157i	$0.534425\pi$
$734$	−26.2664	−	4.23863i	−0.969511	−	0.156451i
$735$		0			0
$736$	−30.4386	+	29.5650i	−1.12198	+	1.08978i
$737$			9.66011i			0.355835i
$738$	23.5754	−	18.1802i	0.867823	−	0.669221i
$739$			1.41957i			0.0522198i	0.999659	+	0.0261099i	$0.00831198\pi$
$739$			1.41957i			0.0522198i	−0.999659	+	0.0261099i	$0.991688\pi$
$740$	−5.45534	+	16.4630i	−0.200542	+	0.605191i
$741$	2.28394	−	0.988455i	0.0839027	−	0.0363118i
$742$		0			0
$743$	1.70600			0.0625872			0.0312936	−	0.999510i	$-0.490037\pi$
$743$	1.70600			0.0625872			0.0312936	+	0.999510i	$0.490037\pi$
$744$	1.28862	−	17.9846i	0.0472430	−	0.659349i
$745$	−23.6488			−0.866425
$746$	1.31191	−	8.12980i	0.0480325	−	0.297653i
$747$	−25.5423	+	27.2040i	−0.934545	+	0.995343i
$748$	7.38003	−	22.2713i	0.269841	−	0.814318i
$749$		0			0
$750$	7.11534	+	28.0467i	0.259815	+	1.02412i
$751$		−	26.7854i		−	0.977414i	−0.872448	−	0.488707i	$-0.837469\pi$
$751$		−	26.7854i		−	0.977414i	0.872448	−	0.488707i	$-0.162531\pi$
$752$	−24.0675	−	17.9180i	−0.877651	−	0.653403i
$753$	16.3317	+	37.7364i	0.595160	+	1.37519i
$754$	1.58307	+	0.255461i	0.0576520	+	0.00930334i
$755$	−1.90623			−0.0693749
$756$		0			0
$757$	−23.8816			−0.867992			−0.433996	−	0.900915i	$-0.642897\pi$
$757$	−23.8816			−0.867992			−0.433996	+	0.900915i	$0.642897\pi$
$758$	16.8373	+	2.71704i	0.611558	+	0.0986875i
$759$	−20.5796	−	47.5517i	−0.746992	−	1.72602i
$760$	−2.97396	+	5.71280i	−0.107877	+	0.207225i
$761$		−	15.0915i		−	0.547067i	−0.961862	−	0.273533i	$-0.911808\pi$
$761$		−	15.0915i		−	0.547067i	0.961862	−	0.273533i	$-0.0881924\pi$
$762$	9.08868	+	35.8251i	0.329248	+	1.29781i
$763$		0			0
$764$	−45.0557	−	14.9301i	−1.63006	−	0.540153i
$765$	12.5405	−	13.3563i	0.453401	−	0.482897i
$766$	2.73777	−	16.9657i	0.0989197	−	0.612997i
$767$	−6.40472			−0.231261
$768$	21.2082	−	17.8385i	0.765286	−	0.643690i
$769$	−12.6792			−0.457222			−0.228611	−	0.973518i	$-0.573418\pi$
$769$	−12.6792			−0.457222			−0.228611	+	0.973518i	$0.573418\pi$
$770$		0			0
$771$	−23.5267	+	10.1820i	−0.847294	+	0.366695i
$772$	7.54449	+	2.50002i	0.271532	+	0.0899777i
$773$			38.7248i			1.39283i	0.717637	+	0.696417i	$0.245224\pi$
$773$			38.7248i			1.39283i	−0.717637	+	0.696417i	$0.754776\pi$
$774$	−14.3660	+	11.0783i	−0.516375	+	0.398202i
$775$		−	2.53961i		−	0.0912256i
$776$	20.1012	−	38.6132i	0.721590	−	1.38613i
$777$		0			0
$778$	1.69002	+	0.272719i	0.0605900	+	0.00977745i
$779$	7.69659			0.275759
$780$	9.38410	−	0.832315i	0.336005	−	0.0298016i
$781$	3.59393			0.128601
$782$	30.8072	+	4.97138i	1.10166	+	0.177776i
$783$	−1.52303	+	4.23190i	−0.0544286	+	0.151236i
$784$		0			0
$785$		−	18.1175i		−	0.646642i
$786$	−17.5928	+	4.46322i	−0.627515	+	0.159198i
$787$			20.3831i			0.726578i	0.931676	+	0.363289i	$0.118346\pi$
$787$			20.3831i			0.726578i	−0.931676	+	0.363289i	$0.881654\pi$
$788$	−12.4386	+	37.5369i	−0.443107	+	1.33720i
$789$	−9.56649	−	22.1045i	−0.340576	−	0.786942i
$790$	−4.84640	+	30.0327i	−0.172427	+	1.06852i
$791$		0			0
$792$	11.1865	+	31.9366i	0.397494	+	1.13482i
$793$	−5.38003			−0.191051
$794$	2.15318	−	13.3431i	0.0764135	−	0.473528i
$795$	−7.05684	−	16.3057i	−0.250280	−	0.578302i
$796$	−4.82300	+	14.5547i	−0.170947	+	0.515879i
$797$			27.9005i			0.988287i	0.869380	+	0.494143i	$0.164518\pi$
$797$			27.9005i			0.988287i	−0.869380	+	0.494143i	$0.835482\pi$
$798$		0			0
$799$			22.0658i			0.780632i
$800$	2.79996	−	2.71959i	0.0989934	−	0.0961521i
$801$	18.6474	+	17.5084i	0.658873	+	0.618628i
$802$	−15.7009	−	2.53366i	−0.554417	−	0.0894666i
$803$	51.8869			1.83105
$804$	8.35832	−	0.741334i	0.294775	−	0.0261448i
$805$		0			0
$806$	−6.73142	−	1.08625i	−0.237104	−	0.0382617i
$807$	−13.1265	+	5.68096i	−0.462076	+	0.199979i
$808$	−15.3171	−	7.97374i	−0.538854	−	0.280515i
$809$			14.2640i			0.501497i	0.968052	+	0.250748i	$0.0806767\pi$
$809$			14.2640i			0.501497i	−0.968052	+	0.250748i	$0.919323\pi$
$810$	−2.55925	+	26.2996i	−0.0899229	+	0.924073i
$811$			38.4069i			1.34865i	0.738435	+	0.674325i	$0.235565\pi$
$811$			38.4069i			1.34865i	−0.738435	+	0.674325i	$0.764435\pi$
$812$		0			0
$813$	−8.43351	+	3.64989i	−0.295776	+	0.128007i
$814$	−3.75295	+	23.2567i	−0.131541	+	0.815148i
$815$	18.6678			0.653905
$816$	−19.8364	−	4.67637i	−0.694412	−	0.163706i
$817$	−4.69002			−0.164083
$818$	3.50741	−	21.7351i	0.122634	−	0.759951i
$819$		0			0
$820$	27.6569	+	9.16466i	0.965820	+	0.320044i
$821$			52.7894i			1.84236i	0.389135	+	0.921181i	$0.372774\pi$
$821$			52.7894i			1.84236i	−0.389135	+	0.921181i	$0.627226\pi$
$822$	−9.09496	−	35.8499i	−0.317223	−	1.25041i
$823$		−	5.73006i		−	0.199737i	−0.995001	−	0.0998687i	$-0.968158\pi$
$823$		−	5.73006i		−	0.199737i	0.995001	−	0.0998687i	$-0.0318423\pi$
$824$	17.8939	+	9.31519i	0.623365	+	0.324510i
$825$	1.89305	+	4.37413i	0.0659077	+	0.152288i
$826$		0			0
$827$	−44.5253			−1.54830			−0.774149	−	0.633003i	$-0.781822\pi$
$827$	−44.5253			−1.54830			−0.774149	+	0.633003i	$0.781822\pi$
$828$	−39.5643	+	21.4555i	−1.37496	+	0.745631i
$829$	−26.0586			−0.905053			−0.452526	−	0.891751i	$-0.649477\pi$
$829$	−26.0586			−0.905053			−0.452526	+	0.891751i	$0.649477\pi$
$830$	−36.0531	−	5.81791i	−1.25142	−	0.201942i
$831$	−8.67135	−	20.0362i	−0.300806	−	0.695048i
$832$	−6.01086	−	8.58471i	−0.208389	−	0.297621i
$833$		0			0
$834$	8.71961	+	34.3703i	0.301935	+	1.19015i
$835$			33.5968i			1.16267i
$836$	−2.75177	+	8.30420i	−0.0951718	+	0.287207i
$837$	6.47612	−	17.9946i	0.223848	−	0.621985i
$838$	4.06294	−	25.1777i	0.140352	−	0.869748i
$839$	−46.0533			−1.58994			−0.794968	−	0.606652i	$-0.792512\pi$
$839$	−46.0533			−1.58994			−0.794968	+	0.606652i	$0.792512\pi$
$840$		0			0
$841$	28.2508			0.974165
$842$	−2.81574	+	17.4489i	−0.0970367	+	0.601328i
$843$	3.22646	−	1.39636i	0.111125	−	0.0480932i
$844$	7.39089	−	22.3040i	0.254405	−	0.767736i
$845$			23.4260i			0.805880i
$846$	−19.4345	−	25.2020i	−0.668171	−	0.866462i
$847$		0			0
$848$	−11.8026	+	15.8532i	−0.405302	+	0.544403i
$849$	−12.2044	+	5.28188i	−0.418855	+	0.181274i
$850$	−2.83386	−	0.457302i	−0.0972006	−	0.0156853i
$851$	−31.3327			−1.07407
$852$	−0.275804	−	3.10961i	−0.00944890	−	0.106534i
$853$	−46.3274			−1.58622			−0.793109	−	0.609079i	$-0.791539\pi$
$853$	−46.3274			−1.58622			−0.793109	+	0.609079i	$0.791539\pi$
$854$		0			0
$855$	−4.67591	+	4.98011i	−0.159913	+	0.170316i
$856$	3.15638	−	6.06323i	0.107883	−	0.207237i
$857$			41.1458i			1.40551i	0.711431	+	0.702756i	$0.248048\pi$
$857$			41.1458i			1.40551i	−0.711431	+	0.702756i	$0.751952\pi$
$858$	12.4036	−	3.14675i	0.423453	−	0.107428i
$859$			57.4109i			1.95883i	0.201846	+	0.979417i	$0.435306\pi$
$859$			57.4109i			1.95883i	−0.201846	+	0.979417i	$0.564694\pi$
$860$	−16.8531	−	5.58461i	−0.574685	−	0.190434i
$861$		0			0
$862$	−2.80407	+	17.3766i	−0.0955072	+	0.591850i
$863$	25.4867			0.867577			0.433788	−	0.901015i	$-0.357177\pi$
$863$	25.4867			0.867577			0.433788	+	0.901015i	$0.357177\pi$
$864$	26.7744	−	12.1299i	0.910882	−	0.412666i
$865$	8.77899			0.298495
$866$	0.112162	−	0.695056i	0.00381141	−	0.0236190i
$867$	−5.74216	−	13.2680i	−0.195014	−	0.450604i
$868$		0			0
$869$			41.3215i			1.40174i
$870$	−4.26649	+	1.08239i	−0.144647	+	0.0366964i
$871$		−	3.17319i		−	0.107519i
$872$	8.87713	−	17.0525i	0.300618	−	0.577469i
$873$	31.6048	−	33.6609i	1.06966	−	1.13925i
$874$	−11.4870	−	1.85366i	−0.388553	−	0.0627010i
$875$		0			0
$876$	−3.98189	−	44.8947i	−0.134536	−	1.51685i
$877$	41.8627			1.41360			0.706801	−	0.707412i	$-0.250138\pi$
$877$	41.8627			1.41360			0.706801	+	0.707412i	$0.250138\pi$
$878$	6.50613	+	1.04990i	0.219571	+	0.0354323i
$879$	−2.47241	+	1.07002i	−0.0833923	+	0.0360909i
$880$	−19.7764	+	26.5636i	−0.666661	+	0.895459i
$881$			38.5556i			1.29897i	0.760373	+	0.649486i	$0.225016\pi$
$881$			38.5556i			1.29897i	−0.760373	+	0.649486i	$0.774984\pi$
$882$		0			0
$883$		−	4.56420i		−	0.153597i	−0.997047	−	0.0767987i	$-0.975530\pi$
$883$		−	4.56420i		−	0.153597i	0.997047	−	0.0767987i	$-0.0244699\pi$
$884$	−2.42422	+	7.31575i	−0.0815354	+	0.246055i
$885$	16.1344	−	6.98270i	0.542351	−	0.234721i
$886$	−4.97228	+	30.8128i	−0.167047	+	1.03518i
$887$	−40.4892			−1.35949			−0.679747	−	0.733447i	$-0.737910\pi$
$887$	−40.4892			−1.35949			−0.679747	+	0.733447i	$0.737910\pi$
$888$	20.4107	+	1.46245i	0.684938	+	0.0490765i
$889$		0			0
$890$	−3.98797	+	24.7131i	−0.133677	+	0.828385i
$891$	2.25916	+	35.8206i	0.0756847	+	1.20003i
$892$	9.13467	−	27.5664i	0.305851	−	0.922990i
$893$		−	8.22760i		−	0.275326i
$894$	6.86144	+	27.0459i	0.229481	+	0.904552i
$895$		−	13.6020i		−	0.454665i
$896$		0			0
$897$	6.76007	+	15.6199i	0.225712	+	0.521535i
$898$	−8.41693	−	1.35825i	−0.280877	−	0.0453252i
$899$	3.18574			0.106250
$900$	3.63940	−	1.97363i	0.121313	−	0.0657875i
$901$	14.5347			0.484222
$902$	39.0700	+	6.30475i	1.30089	+	0.209925i
$903$		0			0
$904$	7.93706	+	4.13186i	0.263983	+	0.137424i
$905$		−	25.5021i		−	0.847718i
$906$	0.553073	+	2.18006i	0.0183746	+	0.0724277i
$907$		−	2.73314i		−	0.0907526i	−0.998970	−	0.0453763i	$-0.985551\pi$
$907$		−	2.73314i		−	0.0907526i	0.998970	−	0.0453763i	$-0.0144487\pi$
$908$	−40.7469	−	13.5023i	−1.35223	−	0.448090i
$909$	−13.3526	−	12.5370i	−0.442878	−	0.415826i
$910$		0			0
$911$	5.16105			0.170993			0.0854966	−	0.996338i	$-0.472752\pi$
$911$	5.16105			0.170993			0.0854966	+	0.996338i	$0.472752\pi$
$912$	7.39631	+	1.74366i	0.244916	+	0.0577384i
$913$	−49.6048			−1.64168
$914$	−8.62027	+	53.4191i	−0.285133	+	1.76695i
$915$	13.5530	−	5.86554i	0.448050	−	0.193909i
$916$	−37.2688	−	12.3498i	−1.23139	−	0.408048i
$917$		0			0
$918$	−18.9134	−	10.4667i	−0.624235	−	0.345453i
$919$			39.8384i			1.31415i	0.753826	+	0.657074i	$0.228206\pi$
$919$			39.8384i			1.31415i	−0.753826	+	0.657074i	$0.771794\pi$
$920$	−39.0700	−	20.3390i	−1.28810	−	0.670556i
$921$	−50.1987	+	21.7252i	−1.65410	+	0.715870i
$922$	17.3909	+	2.80638i	0.572738	+	0.0924232i
$923$	−1.18055			−0.0388582
$924$		0			0
$925$	2.88220			0.0947660
$926$	−39.1773	−	6.32206i	−1.28745	−	0.207756i
$927$	15.5990	+	14.6461i	0.512337	+	0.481042i
$928$	3.41150	+	3.51231i	0.111988	+	0.115297i
$929$			25.7241i			0.843981i	0.906600	+	0.421990i	$0.138668\pi$
$929$			25.7241i			0.843981i	−0.906600	+	0.421990i	$0.861332\pi$
$930$	18.1417	−	4.60246i	0.594889	−	0.150921i
$931$		0			0
$932$	8.97351	−	27.0800i	0.293937	−	0.887035i
$933$	−12.5736	−	29.0528i	−0.411641	−	0.951147i
$934$	−3.85183	+	23.8695i	−0.126036	+	0.781032i
$935$	24.3543			0.796472
$936$	−3.67457	−	10.4906i	−0.120107	−	0.342897i
$937$	−20.2068			−0.660127			−0.330063	−	0.943959i	$-0.607070\pi$
$937$	−20.2068			−0.660127			−0.330063	+	0.943959i	$0.607070\pi$
$938$		0			0
$939$	20.4881	+	47.3403i	0.668604	+	1.54489i
$940$	9.79696	−	29.5650i	0.319542	−	0.964304i
$941$		−	47.8868i		−	1.56107i	−0.625115	−	0.780533i	$-0.714948\pi$
$941$		−	47.8868i		−	1.56107i	0.625115	−	0.780533i	$-0.285052\pi$
$942$	−20.7201	+	5.25660i	−0.675097	+	0.171269i
$943$			52.6372i			1.71410i
$944$	−15.6867	−	11.6786i	−0.510559	−	0.380106i
$945$		0			0
$946$	−23.8078	−	3.84188i	−0.774059	−	0.124910i
$947$	−6.32070			−0.205395			−0.102698	−	0.994713i	$-0.532747\pi$
$947$	−6.32070			−0.205395			−0.102698	+	0.994713i	$0.532747\pi$
$948$	35.7531	−	3.17109i	1.16121	−	0.102992i
$949$	−17.0440			−0.553272
$950$	1.05665	+	0.170512i	0.0342823	+	0.00553215i
$951$	−28.1290	+	12.1738i	−0.912147	+	0.394763i
$952$		0			0
$953$		−	3.70027i		−	0.119863i	−0.998202	−	0.0599317i	$-0.980912\pi$
$953$		−	3.70027i		−	0.119863i	0.998202	−	0.0599317i	$-0.0190883\pi$
$954$	−16.6005	+	12.8015i	−0.537462	+	0.414463i
$955$		−	49.2698i		−	1.59433i
$956$	−29.0123	−	9.61382i	−0.938326	−	0.310933i
$957$	−5.48698	+	2.37468i	−0.177369	+	0.0767624i
$958$	−3.70087	+	22.9340i	−0.119570	+	0.740964i
$959$		0			0
$960$	24.5016	+	15.0728i	0.790786	+	0.486472i
$961$	17.4538			0.563027
$962$	1.23278	−	7.63946i	0.0397466	−	0.246306i
$963$	4.96274	−	5.28559i	0.159922	−	0.170326i
$964$	−11.2085	−	3.71415i	−0.361000	−	0.119625i
$965$			8.25014i			0.265581i
$966$		0			0
$967$			14.5970i			0.469409i	0.972067	+	0.234705i	$0.0754123\pi$
$967$			14.5970i			0.469409i	−0.972067	+	0.234705i	$0.924588\pi$
$968$	−6.40472	+	12.3031i	−0.205856	+	0.395437i
$969$	−2.21961	−	5.12868i	−0.0713042	−	0.164757i
$970$	44.6102	+	7.19878i	1.43235	+	0.231139i
$971$	8.21458			0.263618			0.131809	−	0.991275i	$-0.457921\pi$
$971$	8.21458			0.263618			0.131809	+	0.991275i	$0.457921\pi$
$972$	30.8201	−	4.70365i	0.988554	−	0.150870i
$973$		0			0
$974$	−44.6592	−	7.20668i	−1.43097	−	0.230917i
$975$	−0.621837	−	1.43683i	−0.0199147	−	0.0460154i
$976$	−13.1770	−	9.81015i	−0.421785	−	0.314015i
$977$		−	35.6140i		−	1.13939i	−0.821855	−	0.569697i	$-0.807061\pi$
$977$		−	35.6140i		−	1.13939i	0.821855	−	0.569697i	$-0.192939\pi$
$978$	−5.41627	−	21.3495i	−0.173193	−	0.682680i
$979$			34.0023i			1.08672i
$980$		0			0
$981$	13.9574	−	14.8654i	0.445625	−	0.474615i
$982$	−0.459257	+	2.84597i	−0.0146555	+	0.0908187i
$983$	−31.1497			−0.993522			−0.496761	−	0.867887i	$-0.665477\pi$
$983$	−31.1497			−0.993522			−0.496761	+	0.867887i	$0.665477\pi$
$984$	2.45683	−	34.2888i	0.0783208	−	1.09309i
$985$	−41.0478			−1.30789
$986$	0.573647	−	3.55484i	0.0182687	−	0.113209i
$987$		0			0
$988$	0.903910	−	2.72779i	0.0287572	−	0.0867827i
$989$		−	32.0751i		−	1.01993i
$990$	−27.8157	+	21.4501i	−0.884042	+	0.681728i
$991$			34.8265i			1.10630i	0.833082	+	0.553149i	$0.186574\pi$
$991$			34.8265i			1.10630i	−0.833082	+	0.553149i	$0.813426\pi$
$992$	−14.5062	−	14.9348i	−0.460571	−	0.474181i
$993$	55.7652	−	24.1343i	1.76966	−	0.765879i
$994$		0			0
$995$	−15.9161			−0.504573
$996$	3.80676	+	42.9201i	0.120622	+	1.35998i
$997$	−8.45719			−0.267842			−0.133921	−	0.990992i	$-0.542757\pi$
$997$	−8.45719			−0.267842			−0.133921	+	0.990992i	$0.542757\pi$
$998$	−5.99400	−	0.967256i	−0.189737	−	0.0306180i
$999$	20.4220	+	7.34972i	0.646124	+	0.232535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.e.d.491.7		12
3.2	odd	2	inner	588.2.e.d.491.6		12
4.3	odd	2	inner	588.2.e.d.491.5		12
7.2	even	3		588.2.n.e.263.1		24
7.3	odd	6		84.2.n.a.23.10	yes	24
7.4	even	3		588.2.n.e.275.10		24
7.5	odd	6		84.2.n.a.11.1	✓	24
7.6	odd	2		588.2.e.e.491.7		12
12.11	even	2	inner	588.2.e.d.491.8		12
21.2	odd	6		588.2.n.e.263.12		24
21.5	even	6		84.2.n.a.11.12	yes	24
21.11	odd	6		588.2.n.e.275.3		24
21.17	even	6		84.2.n.a.23.3	yes	24
21.20	even	2		588.2.e.e.491.6		12
28.3	even	6		84.2.n.a.23.12	yes	24
28.11	odd	6		588.2.n.e.275.12		24
28.19	even	6		84.2.n.a.11.3	yes	24
28.23	odd	6		588.2.n.e.263.3		24
28.27	even	2		588.2.e.e.491.5		12
84.11	even	6		588.2.n.e.275.1		24
84.23	even	6		588.2.n.e.263.10		24
84.47	odd	6		84.2.n.a.11.10	yes	24
84.59	odd	6		84.2.n.a.23.1	yes	24
84.83	odd	2		588.2.e.e.491.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.n.a.11.1	✓	24	7.5	odd	6
84.2.n.a.11.3	yes	24	28.19	even	6
84.2.n.a.11.10	yes	24	84.47	odd	6
84.2.n.a.11.12	yes	24	21.5	even	6
84.2.n.a.23.1	yes	24	84.59	odd	6
84.2.n.a.23.3	yes	24	21.17	even	6
84.2.n.a.23.10	yes	24	7.3	odd	6
84.2.n.a.23.12	yes	24	28.3	even	6
588.2.e.d.491.5		12	4.3	odd	2	inner
588.2.e.d.491.6		12	3.2	odd	2	inner
588.2.e.d.491.7		12	1.1	even	1	trivial
588.2.e.d.491.8		12	12.11	even	2	inner
588.2.e.e.491.5		12	28.27	even	2
588.2.e.e.491.6		12	21.20	even	2
588.2.e.e.491.7		12	7.6	odd	2
588.2.e.e.491.8		12	84.83	odd	2
588.2.n.e.263.1		24	7.2	even	3
588.2.n.e.263.3		24	28.23	odd	6
588.2.n.e.263.10		24	84.23	even	6
588.2.n.e.263.12		24	21.2	odd	6
588.2.n.e.275.1		24	84.11	even	6
588.2.n.e.275.3		24	21.11	odd	6
588.2.n.e.275.10		24	7.4	even	3
588.2.n.e.275.12		24	28.11	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.225298 - 1.39615i) q^{2} +(-0.687941 - 1.58957i) q^{3} +(-1.89848 - 0.629100i) q^{4} -2.07605i q^{5} +(-2.37428 + 0.602344i) q^{6} +(-1.30604 + 2.50883i) q^{8} +(-2.05347 + 2.18706i) q^{9} +(-2.89848 - 0.467730i) q^{10} -3.98797 q^{11} +(0.306044 + 3.45056i) q^{12} +1.30998 q^{13} +(-3.30003 + 1.42820i) q^{15} +(3.20847 + 2.38867i) q^{16} -2.94162i q^{17} +(2.59083 + 3.35970i) q^{18} +1.09683i q^{19} +(-1.30604 + 3.94134i) q^{20} +(-0.898482 + 5.56781i) q^{22} -7.50125 q^{23} +(4.88645 + 0.350119i) q^{24} +0.690016 q^{25} +(0.295137 - 1.82894i) q^{26} +(4.88916 + 1.75957i) q^{27} +0.865568i q^{29} +(1.25050 + 4.92911i) q^{30} -3.68051i q^{31} +(4.05781 - 3.94134i) q^{32} +(2.74349 + 6.33916i) q^{33} +(-4.10695 - 0.662741i) q^{34} +(5.27436 - 2.86026i) q^{36} +4.17700 q^{37} +(1.53134 + 0.247114i) q^{38} +(-0.901192 - 2.08231i) q^{39} +(5.20847 + 2.71141i) q^{40} -7.01712i q^{41} +4.27597i q^{43} +(7.57109 + 2.50883i) q^{44} +(4.54045 + 4.26311i) q^{45} +(-1.69002 + 10.4729i) q^{46} -7.50125 q^{47} +(1.58973 - 6.74335i) q^{48} +(0.155459 - 0.963368i) q^{50} +(-4.67591 + 2.02366i) q^{51} +(-2.48698 - 0.824111i) q^{52} +4.94107i q^{53} +(3.55815 - 6.42959i) q^{54} +8.27923i q^{55} +(1.74349 - 0.754555i) q^{57} +(1.20847 + 0.195011i) q^{58} -4.88916 q^{59} +(7.16353 - 0.635363i) q^{60} -4.10695 q^{61} +(-5.13856 - 0.829212i) q^{62} +(-4.58850 - 6.55330i) q^{64} -2.71959i q^{65} +(9.46854 - 2.40213i) q^{66} -2.42231i q^{67} +(-1.85057 + 5.58461i) q^{68} +(5.16042 + 11.9238i) q^{69} -0.901192 q^{71} +(-2.80505 - 8.00823i) q^{72} -13.0109 q^{73} +(0.941069 - 5.83172i) q^{74} +(-0.474691 - 1.09683i) q^{75} +(0.690016 - 2.08231i) q^{76} +(-3.11026 + 0.789060i) q^{78} -10.3615i q^{79} +(4.95900 - 6.66093i) q^{80} +(-0.566494 - 8.98215i) q^{81} +(-9.79696 - 1.58094i) q^{82} +12.4386 q^{83} -6.10695 q^{85} +(5.96991 + 0.963368i) q^{86} +(1.37588 - 0.595460i) q^{87} +(5.20847 - 10.0052i) q^{88} -8.52623i q^{89} +(6.97491 - 5.37869i) q^{90} +(14.2410 + 4.71904i) q^{92} +(-5.85044 + 2.53198i) q^{93} +(-1.69002 + 10.4729i) q^{94} +2.27707 q^{95} +(-9.05658 - 3.73876i) q^{96} -15.3909 q^{97} +(8.18919 - 8.72195i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{4} + 2 q^{9} - 10 q^{10} - 12 q^{12} + 12 q^{13} + 10 q^{16} + 10 q^{18} + 14 q^{22} - 14 q^{24} + 12 q^{25} + 14 q^{30} + 10 q^{33} + 4 q^{34} + 22 q^{36} + 8 q^{37} + 34 q^{40} - 18 q^{45}+ \cdots - 36 q^{97}+O(q^{100}) \) 12 * q + 2 * q^4 + 2 * q^9 - 10 * q^10 - 12 * q^12 + 12 * q^13 + 10 * q^16 + 10 * q^18 + 14 * q^22 - 14 * q^24 + 12 * q^25 + 14 * q^30 + 10 * q^33 + 4 * q^34 + 22 * q^36 + 8 * q^37 + 34 * q^40 - 18 * q^45 - 24 * q^46 - 4 * q^48 + 16 * q^52 + 38 * q^54 - 2 * q^57 - 14 * q^58 - 14 * q^60 + 4 * q^61 - 34 * q^64 + 30 * q^66 - 18 * q^69 - 20 * q^72 + 12 * q^76 - 52 * q^78 - 26 * q^81 - 68 * q^82 - 20 * q^85 + 34 * q^88 + 20 * q^90 + 6 * q^93 - 24 * q^94 - 62 * q^96 - 36 * q^97

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