LMFDB - Embedded newform 1734.2.f.n.829.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,2,Mod(829,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1734.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1734.f (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.8460597105$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.722204136308736.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{8} + 69x^{4} + 1 $ x^12 + 18x^8 + 69x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.3
Root			$-1.32893 + 1.32893i$ of defining polynomial
Character	$\chi$	$=$	1734.829
Dual form			1734.2.f.n.1483.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.49756 + 2.49756i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.95075 + 1.95075i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.49756 + 2.49756i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.95075 + 1.95075i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-2.49756 + 2.49756i) q^{10} +(2.08141 - 2.08141i) q^{11} +(0.707107 + 0.707107i) q^{12} -5.06418 q^{13} +(-1.95075 - 1.95075i) q^{14} -3.53209i q^{15} +1.00000 q^{16} -1.00000 q^{18} +4.36959i q^{19} +(-2.49756 - 2.49756i) q^{20} +2.75877 q^{21} +(2.08141 + 2.08141i) q^{22} +(-4.24264 + 4.24264i) q^{23} +(-0.707107 + 0.707107i) q^{24} +7.47565i q^{25} -5.06418i q^{26} +(0.707107 - 0.707107i) q^{27} +(1.95075 - 1.95075i) q^{28} +(-3.39458 - 3.39458i) q^{29} +3.53209 q^{30} +(-0.506912 - 0.506912i) q^{31} +1.00000i q^{32} -2.94356 q^{33} -9.74422 q^{35} -1.00000i q^{36} +(-7.22107 - 7.22107i) q^{37} -4.36959 q^{38} +(3.58091 + 3.58091i) q^{39} +(2.49756 - 2.49756i) q^{40} +(8.89662 - 8.89662i) q^{41} +2.75877i q^{42} +10.9067i q^{43} +(-2.08141 + 2.08141i) q^{44} +(-2.49756 + 2.49756i) q^{45} +(-4.24264 - 4.24264i) q^{46} -5.14796 q^{47} +(-0.707107 - 0.707107i) q^{48} -0.610815i q^{49} -7.47565 q^{50} +5.06418 q^{52} -4.57398i q^{53} +(0.707107 + 0.707107i) q^{54} +10.3969 q^{55} +(1.95075 + 1.95075i) q^{56} +(3.08976 - 3.08976i) q^{57} +(3.39458 - 3.39458i) q^{58} +5.53209i q^{59} +3.53209i q^{60} +(-4.41322 + 4.41322i) q^{61} +(0.506912 - 0.506912i) q^{62} +(-1.95075 - 1.95075i) q^{63} -1.00000 q^{64} +(-12.6481 - 12.6481i) q^{65} -2.94356i q^{66} +5.67499 q^{67} +6.00000 q^{69} -9.74422i q^{70} +(6.93201 + 6.93201i) q^{71} +1.00000 q^{72} +(-6.39358 - 6.39358i) q^{73} +(7.22107 - 7.22107i) q^{74} +(5.28608 - 5.28608i) q^{75} -4.36959i q^{76} +8.12061i q^{77} +(-3.58091 + 3.58091i) q^{78} +(4.68003 - 4.68003i) q^{79} +(2.49756 + 2.49756i) q^{80} -1.00000 q^{81} +(8.89662 + 8.89662i) q^{82} +3.32501i q^{83} -2.75877 q^{84} -10.9067 q^{86} +4.80066i q^{87} +(-2.08141 - 2.08141i) q^{88} -13.8425 q^{89} +(-2.49756 - 2.49756i) q^{90} +(9.87892 - 9.87892i) q^{91} +(4.24264 - 4.24264i) q^{92} +0.716881i q^{93} -5.14796i q^{94} +(-10.9133 + 10.9133i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-7.79751 - 7.79751i) q^{97} +0.610815 q^{98} +(2.08141 + 2.08141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4}+O(q^{10}) $ 12 * q - 12 * q^4	$ 12 q - 12 q^{4} - 24 q^{13} + 12 q^{16} - 12 q^{18} - 12 q^{21} + 24 q^{30} + 24 q^{33} - 24 q^{38} - 12 q^{50} + 24 q^{52} + 12 q^{55} - 12 q^{64} + 48 q^{67} + 72 q^{69} + 12 q^{72} - 12 q^{81} + 12 q^{84} - 24 q^{86} - 96 q^{89} + 24 q^{98}+O(q^{100}) $ 12 * q - 12 * q^4 - 24 * q^13 + 12 * q^16 - 12 * q^18 - 12 * q^21 + 24 * q^30 + 24 * q^33 - 24 * q^38 - 12 * q^50 + 24 * q^52 + 12 * q^55 - 12 * q^64 + 48 * q^67 + 72 * q^69 + 12 * q^72 - 12 * q^81 + 12 * q^84 - 24 * q^86 - 96 * q^89 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times$.

$n$	$1157$	$1159$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	2.49756	+	2.49756i	1.11694	+	1.11694i	0.992187	+	0.124757i	$0.0398152\pi$
$5$	2.49756	+	2.49756i	1.11694	+	1.11694i	0.124757	+	0.992187i	$0.460185\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−1.95075	+	1.95075i	−0.737312	+	0.737312i	−0.972057	−	0.234745i	$-0.924575\pi$
$7$	−1.95075	+	1.95075i	−0.737312	+	0.737312i	0.234745	+	0.972057i	$0.424575\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	−2.49756	+	2.49756i	−0.789799	+	0.789799i
$11$	2.08141	−	2.08141i	0.627570	−	0.627570i	−0.319886	−	0.947456i	$-0.603645\pi$
$11$	2.08141	−	2.08141i	0.627570	−	0.627570i	0.947456	+	0.319886i	$0.103645\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−5.06418			−1.40455			−0.702275	−	0.711906i	$-0.747832\pi$
$13$	−5.06418			−1.40455			−0.702275	+	0.711906i	$0.747832\pi$
$14$	−1.95075	−	1.95075i	−0.521359	−	0.521359i
$15$		−	3.53209i		−	0.911981i
$16$	1.00000			0.250000
$17$		0			0
$17$		0			0
$18$	−1.00000			−0.235702
$19$			4.36959i			1.00245i	0.865317	+	0.501226i	$0.167117\pi$
$19$			4.36959i			1.00245i	−0.865317	+	0.501226i	$0.832883\pi$
$20$	−2.49756	−	2.49756i	−0.558472	−	0.558472i
$21$	2.75877			0.602013
$22$	2.08141	+	2.08141i	0.443759	+	0.443759i
$23$	−4.24264	+	4.24264i	−0.884652	+	0.884652i	−0.994003	−	0.109351i	$-0.965123\pi$
$23$	−4.24264	+	4.24264i	−0.884652	+	0.884652i	0.109351	+	0.994003i	$0.465123\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$			7.47565i			1.49513i
$26$		−	5.06418i		−	0.993167i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.95075	−	1.95075i	0.368656	−	0.368656i
$29$	−3.39458	−	3.39458i	−0.630357	−	0.630357i	0.317800	−	0.948158i	$-0.397056\pi$
$29$	−3.39458	−	3.39458i	−0.630357	−	0.630357i	−0.948158	+	0.317800i	$0.897056\pi$
$30$	3.53209			0.644868
$31$	−0.506912	−	0.506912i	−0.0910440	−	0.0910440i	0.660118	−	0.751162i	$-0.270506\pi$
$31$	−0.506912	−	0.506912i	−0.0910440	−	0.0910440i	−0.751162	+	0.660118i	$0.770506\pi$
$32$			1.00000i			0.176777i
$33$	−2.94356			−0.512409
$34$		0			0
$35$	−9.74422			−1.64707
$36$		−	1.00000i		−	0.166667i
$37$	−7.22107	−	7.22107i	−1.18714	−	1.18714i	−0.977856	−	0.209281i	$-0.932888\pi$
$37$	−7.22107	−	7.22107i	−1.18714	−	1.18714i	−0.209281	−	0.977856i	$-0.567112\pi$
$38$	−4.36959			−0.708840
$39$	3.58091	+	3.58091i	0.573405	+	0.573405i
$40$	2.49756	−	2.49756i	0.394900	−	0.394900i
$41$	8.89662	−	8.89662i	1.38942	−	1.38942i	0.562879	−	0.826539i	$-0.309694\pi$
$41$	8.89662	−	8.89662i	1.38942	−	1.38942i	0.826539	−	0.562879i	$-0.190306\pi$
$42$			2.75877i			0.425688i
$43$			10.9067i			1.66326i	0.555330	+	0.831630i	$0.312592\pi$
$43$			10.9067i			1.66326i	−0.555330	+	0.831630i	$0.687408\pi$
$44$	−2.08141	+	2.08141i	−0.313785	+	0.313785i
$45$	−2.49756	+	2.49756i	−0.372315	+	0.372315i
$46$	−4.24264	−	4.24264i	−0.625543	−	0.625543i
$47$	−5.14796			−0.750907			−0.375453	−	0.926841i	$-0.622513\pi$
$47$	−5.14796			−0.750907			−0.375453	+	0.926841i	$0.622513\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	0.610815i		−	0.0872592i
$50$	−7.47565			−1.05722
$51$		0			0
$52$	5.06418			0.702275
$53$		−	4.57398i		−	0.628284i	−0.949376	−	0.314142i	$-0.898283\pi$
$53$		−	4.57398i		−	0.628284i	0.949376	−	0.314142i	$-0.101717\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	10.3969			1.40192
$56$	1.95075	+	1.95075i	0.260679	+	0.260679i
$57$	3.08976	−	3.08976i	0.409249	−	0.409249i
$58$	3.39458	−	3.39458i	0.445730	−	0.445730i
$59$			5.53209i			0.720217i	0.932911	+	0.360108i	$0.117260\pi$
$59$			5.53209i			0.720217i	−0.932911	+	0.360108i	$0.882740\pi$
$60$			3.53209i			0.455991i
$61$	−4.41322	+	4.41322i	−0.565054	+	0.565054i	−0.930739	−	0.365685i	$-0.880835\pi$
$61$	−4.41322	+	4.41322i	−0.565054	+	0.565054i	0.365685	+	0.930739i	$0.380835\pi$
$62$	0.506912	−	0.506912i	0.0643779	−	0.0643779i
$63$	−1.95075	−	1.95075i	−0.245771	−	0.245771i
$64$	−1.00000			−0.125000
$65$	−12.6481	−	12.6481i	−1.56880	−	1.56880i
$66$		−	2.94356i		−	0.362328i
$67$	5.67499			0.693311			0.346655	−	0.937993i	$-0.387317\pi$
$67$	5.67499			0.693311			0.346655	+	0.937993i	$0.387317\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		−	9.74422i		−	1.16466i
$71$	6.93201	+	6.93201i	0.822679	+	0.822679i	0.986491	−	0.163813i	$-0.0523793\pi$
$71$	6.93201	+	6.93201i	0.822679	+	0.822679i	−0.163813	+	0.986491i	$0.552379\pi$
$72$	1.00000			0.117851
$73$	−6.39358	−	6.39358i	−0.748312	−	0.748312i	0.225850	−	0.974162i	$-0.427484\pi$
$73$	−6.39358	−	6.39358i	−0.748312	−	0.748312i	−0.974162	+	0.225850i	$0.927484\pi$
$74$	7.22107	−	7.22107i	0.839432	−	0.839432i
$75$	5.28608	−	5.28608i	0.610384	−	0.610384i
$76$		−	4.36959i		−	0.501226i
$77$			8.12061i			0.925430i
$78$	−3.58091	+	3.58091i	−0.405459	+	0.405459i
$79$	4.68003	−	4.68003i	0.526544	−	0.526544i	−0.392996	−	0.919540i	$-0.628561\pi$
$79$	4.68003	−	4.68003i	0.526544	−	0.526544i	0.919540	+	0.392996i	$0.128561\pi$
$80$	2.49756	+	2.49756i	0.279236	+	0.279236i
$81$	−1.00000			−0.111111
$82$	8.89662	+	8.89662i	0.982467	+	0.982467i
$83$			3.32501i			0.364967i	0.983209	+	0.182484i	$0.0584136\pi$
$83$			3.32501i			0.364967i	−0.983209	+	0.182484i	$0.941586\pi$
$84$	−2.75877			−0.301007
$85$		0			0
$86$	−10.9067			−1.17610
$87$			4.80066i			0.514685i
$88$	−2.08141	−	2.08141i	−0.221879	−	0.221879i
$89$	−13.8425			−1.46731			−0.733654	−	0.679524i	$-0.762186\pi$
$89$	−13.8425			−1.46731			−0.733654	+	0.679524i	$0.762186\pi$
$90$	−2.49756	−	2.49756i	−0.263266	−	0.263266i
$91$	9.87892	−	9.87892i	1.03559	−	1.03559i
$92$	4.24264	−	4.24264i	0.442326	−	0.442326i
$93$			0.716881i			0.0743371i
$94$		−	5.14796i		−	0.530971i
$95$	−10.9133	+	10.9133i	−1.11968	+	1.11968i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−7.79751	−	7.79751i	−0.791717	−	0.791717i	0.190056	−	0.981773i	$-0.439133\pi$
$97$	−7.79751	−	7.79751i	−0.791717	−	0.791717i	−0.981773	+	0.190056i	$0.939133\pi$
$98$	0.610815			0.0617016
$99$	2.08141	+	2.08141i	0.209190	+	0.209190i
$100$		−	7.47565i		−	0.747565i
$101$	0.921274			0.0916702			0.0458351	−	0.998949i	$-0.485405\pi$
$101$	0.921274			0.0916702			0.0458351	+	0.998949i	$0.485405\pi$
$102$		0			0
$103$	−16.9736			−1.67246			−0.836229	−	0.548381i	$-0.815245\pi$
$103$	−16.9736			−1.67246			−0.836229	+	0.548381i	$0.815245\pi$
$104$			5.06418i			0.496583i
$105$	6.89021	+	6.89021i	0.672415	+	0.672415i
$106$	4.57398			0.444264
$107$	−2.18246	−	2.18246i	−0.210987	−	0.210987i	0.593700	−	0.804686i	$-0.297667\pi$
$107$	−2.18246	−	2.18246i	−0.210987	−	0.210987i	−0.804686	+	0.593700i	$0.797667\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	−1.58479	+	1.58479i	−0.151795	+	0.151795i	−0.778919	−	0.627124i	$-0.784232\pi$
$109$	−1.58479	+	1.58479i	−0.151795	+	0.151795i	0.627124	+	0.778919i	$0.284232\pi$
$110$			10.3969i			0.991308i
$111$			10.2121i			0.969293i
$112$	−1.95075	+	1.95075i	−0.184328	+	0.184328i
$113$	−8.08489	+	8.08489i	−0.760563	+	0.760563i	−0.976424	−	0.215861i	$-0.930744\pi$
$113$	−8.08489	+	8.08489i	−0.760563	+	0.760563i	0.215861	+	0.976424i	$0.430744\pi$
$114$	3.08976	+	3.08976i	0.289383	+	0.289383i
$115$	−21.1925			−1.97621
$116$	3.39458	+	3.39458i	0.315179	+	0.315179i
$117$		−	5.06418i		−	0.468183i
$118$	−5.53209			−0.509270
$119$		0			0
$120$	−3.53209			−0.322434
$121$			2.33544i			0.212312i
$122$	−4.41322	−	4.41322i	−0.399554	−	0.399554i
$123$	−12.5817			−1.13446
$124$	0.506912	+	0.506912i	0.0455220	+	0.0455220i
$125$	−6.18310	+	6.18310i	−0.553033	+	0.553033i
$126$	1.95075	−	1.95075i	0.173786	−	0.173786i
$127$		−	8.75877i		−	0.777215i	−0.921403	−	0.388608i	$-0.872956\pi$
$127$		−	8.75877i		−	0.777215i	0.921403	−	0.388608i	$-0.127044\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	7.71222	−	7.71222i	0.679023	−	0.679023i
$130$	12.6481	−	12.6481i	1.10931	−	1.10931i
$131$	0.909203	+	0.909203i	0.0794374	+	0.0794374i	0.745709	−	0.666272i	$-0.232111\pi$
$131$	0.909203	+	0.909203i	0.0794374	+	0.0794374i	−0.666272	+	0.745709i	$0.732111\pi$
$132$	2.94356			0.256204
$133$	−8.52395	−	8.52395i	−0.739120	−	0.739120i
$134$			5.67499i			0.490245i
$135$	3.53209			0.303994
$136$		0			0
$137$	2.36959			0.202447			0.101224	−	0.994864i	$-0.467724\pi$
$137$	2.36959			0.202447			0.101224	+	0.994864i	$0.467724\pi$
$138$			6.00000i			0.510754i
$139$	−3.99225	−	3.99225i	−0.338618	−	0.338618i	0.517229	−	0.855847i	$-0.326964\pi$
$139$	−3.99225	−	3.99225i	−0.338618	−	0.338618i	−0.855847	+	0.517229i	$0.826964\pi$
$140$	9.74422			0.823537
$141$	3.64015	+	3.64015i	0.306556	+	0.306556i
$142$	−6.93201	+	6.93201i	−0.581722	+	0.581722i
$143$	−10.5406	+	10.5406i	−0.881453	+	0.881453i
$144$			1.00000i			0.0833333i
$145$		−	16.9564i		−	1.40815i
$146$	6.39358	−	6.39358i	0.529137	−	0.529137i
$147$	−0.431911	+	0.431911i	−0.0356234	+	0.0356234i
$148$	7.22107	+	7.22107i	0.593568	+	0.593568i
$149$	−11.4260			−0.936056			−0.468028	−	0.883714i	$-0.655035\pi$
$149$	−11.4260			−0.936056			−0.468028	+	0.883714i	$0.655035\pi$
$150$	5.28608	+	5.28608i	0.431607	+	0.431607i
$151$		−	11.7510i		−	0.956285i	−0.878282	−	0.478143i	$-0.841310\pi$
$151$		−	11.7510i		−	0.956285i	0.878282	−	0.478143i	$-0.158690\pi$
$152$	4.36959			0.354420
$153$		0			0
$154$	−8.12061			−0.654378
$155$		−	2.53209i		−	0.203382i
$156$	−3.58091	−	3.58091i	−0.286703	−	0.286703i
$157$	3.51754			0.280730			0.140365	−	0.990100i	$-0.455172\pi$
$157$	3.51754			0.280730			0.140365	+	0.990100i	$0.455172\pi$
$158$	4.68003	+	4.68003i	0.372323	+	0.372323i
$159$	−3.23429	+	3.23429i	−0.256496	+	0.256496i
$160$	−2.49756	+	2.49756i	−0.197450	+	0.197450i
$161$		−	16.5526i		−	1.30453i
$162$		−	1.00000i		−	0.0785674i
$163$	−4.47246	+	4.47246i	−0.350310	+	0.350310i	−0.860225	−	0.509915i	$-0.829677\pi$
$163$	−4.47246	+	4.47246i	−0.350310	+	0.350310i	0.509915	+	0.860225i	$0.329677\pi$
$164$	−8.89662	+	8.89662i	−0.694709	+	0.694709i
$165$	−7.35174	−	7.35174i	−0.572332	−	0.572332i
$166$	−3.32501			−0.258071
$167$	10.1403	+	10.1403i	0.784677	+	0.784677i	0.980616	−	0.195939i	$-0.0627756\pi$
$167$	10.1403	+	10.1403i	0.784677	+	0.784677i	−0.195939	+	0.980616i	$0.562776\pi$
$168$		−	2.75877i		−	0.212844i
$169$	12.6459			0.972761
$170$		0			0
$171$	−4.36959			−0.334151
$172$		−	10.9067i		−	0.831630i
$173$	0.576439	+	0.576439i	0.0438258	+	0.0438258i	0.728680	−	0.684854i	$-0.240134\pi$
$173$	0.576439	+	0.576439i	0.0438258	+	0.0438258i	−0.684854	+	0.728680i	$0.740134\pi$
$174$	−4.80066			−0.363937
$175$	−14.5831	−	14.5831i	−1.10238	−	1.10238i
$176$	2.08141	−	2.08141i	0.156892	−	0.156892i
$177$	3.91178	−	3.91178i	0.294027	−	0.294027i
$178$		−	13.8425i		−	1.03754i
$179$			14.0642i			1.05121i	0.850730	+	0.525603i	$0.176160\pi$
$179$			14.0642i			1.05121i	−0.850730	+	0.525603i	$0.823840\pi$
$180$	2.49756	−	2.49756i	0.186157	−	0.186157i
$181$	14.3829	−	14.3829i	1.06907	−	1.06907i	0.0716420	−	0.997430i	$-0.477176\pi$
$181$	14.3829	−	14.3829i	1.06907	−	1.06907i	0.997430	−	0.0716420i	$-0.0228239\pi$
$182$	9.87892	+	9.87892i	0.732274	+	0.732274i
$183$	6.24123			0.461365
$184$	4.24264	+	4.24264i	0.312772	+	0.312772i
$185$		−	36.0702i		−	2.65193i
$186$	−0.716881			−0.0525643
$187$		0			0
$188$	5.14796			0.375453
$189$			2.75877i			0.200671i
$190$	−10.9133	−	10.9133i	−0.791735	−	0.791735i
$191$	−15.6459			−1.13210			−0.566049	−	0.824372i	$-0.691529\pi$
$191$	−15.6459			−1.13210			−0.566049	+	0.824372i	$0.691529\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−7.26288	+	7.26288i	−0.522793	+	0.522793i	−0.918414	−	0.395621i	$-0.870529\pi$
$193$	−7.26288	+	7.26288i	−0.522793	+	0.522793i	0.395621	+	0.918414i	$0.370529\pi$
$194$	7.79751	−	7.79751i	0.559828	−	0.559828i
$195$			17.8871i			1.28092i
$196$			0.610815i			0.0436296i
$197$	−6.17281	+	6.17281i	−0.439795	+	0.439795i	−0.891943	−	0.452148i	$-0.850658\pi$
$197$	−6.17281	+	6.17281i	−0.439795	+	0.439795i	0.452148	+	0.891943i	$0.350658\pi$
$198$	−2.08141	+	2.08141i	−0.147920	+	0.147920i
$199$	11.9446	+	11.9446i	0.846728	+	0.846728i	0.989723	−	0.142995i	$-0.0456733\pi$
$199$	11.9446	+	11.9446i	0.846728	+	0.846728i	−0.142995	+	0.989723i	$0.545673\pi$
$200$	7.47565			0.528608
$201$	−4.01283	−	4.01283i	−0.283043	−	0.283043i
$202$			0.921274i			0.0648206i
$203$	13.2439			0.929541
$204$		0			0
$205$	44.4397			3.10381
$206$		−	16.9736i		−	1.18261i
$207$	−4.24264	−	4.24264i	−0.294884	−	0.294884i
$208$	−5.06418			−0.351138
$209$	9.09491	+	9.09491i	0.629108	+	0.629108i
$210$	−6.89021	+	6.89021i	−0.475469	+	0.475469i
$211$	−9.96968	+	9.96968i	−0.686341	+	0.686341i	−0.961421	−	0.275080i	$-0.911296\pi$
$211$	−9.96968	+	9.96968i	−0.686341	+	0.686341i	0.275080	+	0.961421i	$0.411296\pi$
$212$			4.57398i			0.314142i
$213$		−	9.80335i		−	0.671714i
$214$	2.18246	−	2.18246i	0.149190	−	0.149190i
$215$	−27.2402	+	27.2402i	−1.85777	+	1.85777i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	1.97771			0.134256
$218$	−1.58479	−	1.58479i	−0.107335	−	0.107335i
$219$			9.04189i			0.610994i
$220$	−10.3969			−0.700961
$221$		0			0
$222$	−10.2121			−0.685394
$223$			26.3037i			1.76142i	0.473653	+	0.880711i	$0.342935\pi$
$223$			26.3037i			1.76142i	−0.473653	+	0.880711i	$0.657065\pi$
$224$	−1.95075	−	1.95075i	−0.130340	−	0.130340i
$225$	−7.47565			−0.498377
$226$	−8.08489	−	8.08489i	−0.537799	−	0.537799i
$227$	4.28802	−	4.28802i	0.284606	−	0.284606i	−0.550337	−	0.834943i	$-0.685501\pi$
$227$	4.28802	−	4.28802i	0.284606	−	0.284606i	0.834943	+	0.550337i	$0.185501\pi$
$228$	−3.08976	+	3.08976i	−0.204625	+	0.204625i
$229$			8.56624i			0.566073i	0.959109	+	0.283036i	$0.0913417\pi$
$229$			8.56624i			0.566073i	−0.959109	+	0.283036i	$0.908658\pi$
$230$		−	21.1925i		−	1.39739i
$231$	5.74214	−	5.74214i	0.377805	−	0.377805i
$232$	−3.39458	+	3.39458i	−0.222865	+	0.222865i
$233$	8.63528	+	8.63528i	0.565716	+	0.565716i	0.930925	−	0.365209i	$-0.119003\pi$
$233$	8.63528	+	8.63528i	0.565716	+	0.565716i	−0.365209	+	0.930925i	$0.619003\pi$
$234$	5.06418			0.331056
$235$	−12.8573	−	12.8573i	−0.838721	−	0.838721i
$236$		−	5.53209i		−	0.360108i
$237$	−6.61856			−0.429921
$238$		0			0
$239$	11.8716			0.767913			0.383956	−	0.923351i	$-0.374561\pi$
$239$	11.8716			0.767913			0.383956	+	0.923351i	$0.374561\pi$
$240$		−	3.53209i		−	0.227995i
$241$	16.9120	+	16.9120i	1.08940	+	1.08940i	0.995590	+	0.0938061i	$0.0299034\pi$
$241$	16.9120	+	16.9120i	1.08940	+	1.08940i	0.0938061	+	0.995590i	$0.470097\pi$
$242$	−2.33544			−0.150128
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	4.41322	−	4.41322i	0.282527	−	0.282527i
$245$	1.52555	−	1.52555i	0.0974637	−	0.0974637i
$246$		−	12.5817i		−	0.802181i
$247$		−	22.1284i		−	1.40799i
$248$	−0.506912	+	0.506912i	−0.0321889	+	0.0321889i
$249$	2.35114	−	2.35114i	0.148997	−	0.148997i
$250$	−6.18310	−	6.18310i	−0.391054	−	0.391054i
$251$	18.6040			1.17427			0.587137	−	0.809487i	$-0.300255\pi$
$251$	18.6040			1.17427			0.587137	+	0.809487i	$0.300255\pi$
$252$	1.95075	+	1.95075i	0.122885	+	0.122885i
$253$			17.6614i			1.11036i
$254$	8.75877			0.549574
$255$		0			0
$256$	1.00000			0.0625000
$257$			4.16756i			0.259965i	0.991516	+	0.129983i	$0.0414921\pi$
$257$			4.16756i			0.259965i	−0.991516	+	0.129983i	$0.958508\pi$
$258$	7.71222	+	7.71222i	0.480142	+	0.480142i
$259$	28.1729			1.75058
$260$	12.6481	+	12.6481i	0.784402	+	0.784402i
$261$	3.39458	−	3.39458i	0.210119	−	0.210119i
$262$	−0.909203	+	0.909203i	−0.0561707	+	0.0561707i
$263$			7.97090i			0.491507i	0.969332	+	0.245754i	$0.0790354\pi$
$263$			7.97090i			0.491507i	−0.969332	+	0.245754i	$0.920965\pi$
$264$			2.94356i			0.181164i
$265$	11.4238	−	11.4238i	0.701759	−	0.701759i
$266$	8.52395	−	8.52395i	0.522637	−	0.522637i
$267$	9.78816	+	9.78816i	0.599026	+	0.599026i
$268$	−5.67499			−0.346655
$269$	4.21659	+	4.21659i	0.257090	+	0.257090i	0.823870	−	0.566779i	$-0.191811\pi$
$269$	4.21659	+	4.21659i	0.257090	+	0.257090i	−0.566779	+	0.823870i	$0.691811\pi$
$270$			3.53209i			0.214956i
$271$	−3.07098			−0.186549			−0.0932745	−	0.995640i	$-0.529733\pi$
$271$	−3.07098			−0.186549			−0.0932745	+	0.995640i	$0.529733\pi$
$272$		0			0
$273$	−13.9709			−0.845558
$274$			2.36959i			0.143152i
$275$	15.5599	+	15.5599i	0.938299	+	0.938299i
$276$	−6.00000			−0.361158
$277$	−16.4383	−	16.4383i	−0.987680	−	0.987680i	0.0122455	−	0.999925i	$-0.496102\pi$
$277$	−16.4383	−	16.4383i	−0.987680	−	0.987680i	−0.999925	+	0.0122455i	$0.996102\pi$
$278$	3.99225	−	3.99225i	0.239439	−	0.239439i
$279$	0.506912	−	0.506912i	0.0303480	−	0.0303480i
$280$			9.74422i			0.582329i
$281$			21.7297i			1.29628i	0.761520	+	0.648142i	$0.224454\pi$
$281$			21.7297i			1.29628i	−0.761520	+	0.648142i	$0.775546\pi$
$282$	−3.64015	+	3.64015i	−0.216768	+	0.216768i
$283$	12.1570	−	12.1570i	0.722656	−	0.722656i	−0.246489	−	0.969145i	$-0.579277\pi$
$283$	12.1570	−	12.1570i	0.722656	−	0.722656i	0.969145	+	0.246489i	$0.0792771\pi$
$284$	−6.93201	−	6.93201i	−0.411339	−	0.411339i
$285$	15.4338			0.914217
$286$	−10.5406	−	10.5406i	−0.623282	−	0.623282i
$287$			34.7101i			2.04887i
$288$	−1.00000			−0.0589256
$289$		0			0
$290$	16.9564			0.995712
$291$			11.0273i			0.646434i
$292$	6.39358	+	6.39358i	0.374156	+	0.374156i
$293$	9.20708			0.537883			0.268942	−	0.963156i	$-0.413326\pi$
$293$	9.20708			0.537883			0.268942	+	0.963156i	$0.413326\pi$
$294$	−0.431911	−	0.431911i	−0.0251896	−	0.0251896i
$295$	−13.8167	+	13.8167i	−0.804442	+	0.804442i
$296$	−7.22107	+	7.22107i	−0.419716	+	0.419716i
$297$		−	2.94356i		−	0.170803i
$298$		−	11.4260i		−	0.661892i
$299$	21.4855	−	21.4855i	1.24254	−	1.24254i
$300$	−5.28608	+	5.28608i	−0.305192	+	0.305192i
$301$	−21.2762	−	21.2762i	−1.22634	−	1.22634i
$302$	11.7510			0.676196
$303$	−0.651439	−	0.651439i	−0.0374242	−	0.0374242i
$304$			4.36959i			0.250613i
$305$	−22.0446			−1.26227
$306$		0			0
$307$	2.90673			0.165896			0.0829478	−	0.996554i	$-0.473567\pi$
$307$	2.90673			0.165896			0.0829478	+	0.996554i	$0.473567\pi$
$308$		−	8.12061i		−	0.462715i
$309$	12.0021	+	12.0021i	0.682778	+	0.682778i
$310$	2.53209			0.143813
$311$	−9.21719	−	9.21719i	−0.522659	−	0.522659i	0.395714	−	0.918374i	$-0.370497\pi$
$311$	−9.21719	−	9.21719i	−0.522659	−	0.522659i	−0.918374	+	0.395714i	$0.870497\pi$
$312$	3.58091	−	3.58091i	0.202729	−	0.202729i
$313$	2.27804	−	2.27804i	0.128762	−	0.128762i	−0.639789	−	0.768551i	$-0.720978\pi$
$313$	2.27804	−	2.27804i	0.128762	−	0.128762i	0.768551	+	0.639789i	$0.220978\pi$
$314$			3.51754i			0.198506i
$315$		−	9.74422i		−	0.549025i
$316$	−4.68003	+	4.68003i	−0.263272	+	0.263272i
$317$	13.4943	−	13.4943i	0.757914	−	0.757914i	−0.218029	−	0.975942i	$-0.569963\pi$
$317$	13.4943	−	13.4943i	0.757914	−	0.757914i	0.975942	+	0.218029i	$0.0699626\pi$
$318$	−3.23429	−	3.23429i	−0.181370	−	0.181370i
$319$	−14.1310			−0.791187
$320$	−2.49756	−	2.49756i	−0.139618	−	0.139618i
$321$			3.08647i			0.172270i
$322$	16.5526			0.922442
$323$		0			0
$324$	1.00000			0.0555556
$325$		−	37.8580i		−	2.09999i
$326$	−4.47246	−	4.47246i	−0.247706	−	0.247706i
$327$	2.24123			0.123940
$328$	−8.89662	−	8.89662i	−0.491234	−	0.491234i
$329$	10.0424	−	10.0424i	0.553653	−	0.553653i
$330$	7.35174	−	7.35174i	0.404700	−	0.404700i
$331$			3.43376i			0.188737i	0.995537	+	0.0943683i	$0.0300831\pi$
$331$			3.43376i			0.188737i	−0.995537	+	0.0943683i	$0.969917\pi$
$332$		−	3.32501i		−	0.182484i
$333$	7.22107	−	7.22107i	0.395712	−	0.395712i
$334$	−10.1403	+	10.1403i	−0.554850	+	0.554850i
$335$	14.1737	+	14.1737i	0.774390	+	0.774390i
$336$	2.75877			0.150503
$337$	25.2580	+	25.2580i	1.37589	+	1.37589i	0.851443	+	0.524446i	$0.175728\pi$
$337$	25.2580	+	25.2580i	1.37589	+	1.37589i	0.524446	+	0.851443i	$0.324272\pi$
$338$			12.6459i			0.687846i
$339$	11.4338			0.620997
$340$		0			0
$341$	−2.11019			−0.114273
$342$		−	4.36959i		−	0.236280i
$343$	−12.4637	−	12.4637i	−0.672975	−	0.672975i
$344$	10.9067			0.588051
$345$	14.9854	+	14.9854i	0.806786	+	0.806786i
$346$	−0.576439	+	0.576439i	−0.0309895	+	0.0309895i
$347$	−0.783348	+	0.783348i	−0.0420523	+	0.0420523i	−0.727820	−	0.685768i	$-0.759466\pi$
$347$	−0.783348	+	0.783348i	−0.0420523	+	0.0420523i	0.685768	+	0.727820i	$0.259466\pi$
$348$		−	4.80066i		−	0.257342i
$349$			11.2371i			0.601509i	0.953702	+	0.300754i	$0.0972384\pi$
$349$			11.2371i			0.601509i	−0.953702	+	0.300754i	$0.902762\pi$
$350$	14.5831	−	14.5831i	0.779499	−	0.779499i
$351$	−3.58091	+	3.58091i	−0.191135	+	0.191135i
$352$	2.08141	+	2.08141i	0.110940	+	0.110940i
$353$	11.2608			0.599353			0.299677	−	0.954041i	$-0.403121\pi$
$353$	11.2608			0.599353			0.299677	+	0.954041i	$0.403121\pi$
$354$	3.91178	+	3.91178i	0.207909	+	0.207909i
$355$			34.6263i			1.83777i
$356$	13.8425			0.733654
$357$		0			0
$358$	−14.0642			−0.743315
$359$		−	2.04458i		−	0.107909i	−0.998543	−	0.0539543i	$-0.982817\pi$
$359$		−	2.04458i		−	0.107909i	0.998543	−	0.0539543i	$-0.0171825\pi$
$360$	2.49756	+	2.49756i	0.131633	+	0.131633i
$361$	−0.0932736			−0.00490914
$362$	14.3829	+	14.3829i	0.755948	+	0.755948i
$363$	1.65140	−	1.65140i	0.0866762	−	0.0866762i
$364$	−9.87892	+	9.87892i	−0.517796	+	0.517796i
$365$		−	31.9368i		−	1.67165i
$366$			6.24123i			0.326234i
$367$	17.2603	−	17.2603i	0.900979	−	0.900979i	−0.0945417	−	0.995521i	$-0.530139\pi$
$367$	17.2603	−	17.2603i	0.900979	−	0.900979i	0.995521	+	0.0945417i	$0.0301386\pi$
$368$	−4.24264	+	4.24264i	−0.221163	+	0.221163i
$369$	8.89662	+	8.89662i	0.463139	+	0.463139i
$370$	36.0702			1.87520
$371$	8.92267	+	8.92267i	0.463242	+	0.463242i
$372$		−	0.716881i		−	0.0371686i
$373$	27.3756			1.41745			0.708727	−	0.705483i	$-0.249270\pi$
$373$	27.3756			1.41745			0.708727	+	0.705483i	$0.249270\pi$
$374$		0			0
$375$	8.74422			0.451550
$376$			5.14796i			0.265486i
$377$	17.1908	+	17.1908i	0.885369	+	0.885369i
$378$	−2.75877			−0.141896
$379$	15.9084	+	15.9084i	0.817162	+	0.817162i	0.985696	−	0.168534i	$-0.0539033\pi$
$379$	15.9084	+	15.9084i	0.817162	+	0.817162i	−0.168534	+	0.985696i	$0.553903\pi$
$380$	10.9133	−	10.9133i	0.559841	−	0.559841i
$381$	−6.19339	+	6.19339i	−0.317297	+	0.317297i
$382$		−	15.6459i		−	0.800514i
$383$			16.5972i			0.848077i	0.905644	+	0.424039i	$0.139388\pi$
$383$			16.5972i			0.848077i	−0.905644	+	0.424039i	$0.860612\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−20.2818	+	20.2818i	−1.03365	+	1.03365i
$386$	−7.26288	−	7.26288i	−0.369671	−	0.369671i
$387$	−10.9067			−0.554420
$388$	7.79751	+	7.79751i	0.395858	+	0.395858i
$389$			17.2249i			0.873338i	0.899622	+	0.436669i	$0.143842\pi$
$389$			17.2249i			0.873338i	−0.899622	+	0.436669i	$0.856158\pi$
$390$	−17.8871			−0.905750
$391$		0			0
$392$	−0.610815			−0.0308508
$393$		−	1.28581i		−	0.0648604i
$394$	−6.17281	−	6.17281i	−0.310982	−	0.310982i
$395$	23.3773			1.17624
$396$	−2.08141	−	2.08141i	−0.104595	−	0.104595i
$397$	−3.18052	+	3.18052i	−0.159626	+	0.159626i	−0.782401	−	0.622775i	$-0.786005\pi$
$397$	−3.18052	+	3.18052i	−0.159626	+	0.159626i	0.622775	+	0.782401i	$0.286005\pi$
$398$	−11.9446	+	11.9446i	−0.598727	+	0.598727i
$399$			12.0547i			0.603489i
$400$			7.47565i			0.373783i
$401$	1.44573	−	1.44573i	0.0721965	−	0.0721965i	−0.670086	−	0.742283i	$-0.733743\pi$
$401$	1.44573	−	1.44573i	0.0721965	−	0.0721965i	0.742283	+	0.670086i	$0.233743\pi$
$402$	4.01283	−	4.01283i	0.200142	−	0.200142i
$403$	2.56709	+	2.56709i	0.127876	+	0.127876i
$404$	−0.921274			−0.0458351
$405$	−2.49756	−	2.49756i	−0.124105	−	0.124105i
$406$			13.2439i			0.657285i
$407$	−30.0601			−1.49002
$408$		0			0
$409$	23.2841			1.15132			0.575661	−	0.817688i	$-0.304745\pi$
$409$	23.2841			1.15132			0.575661	+	0.817688i	$0.304745\pi$
$410$			44.4397i			2.19472i
$411$	−1.67555	−	1.67555i	−0.0826488	−	0.0826488i
$412$	16.9736			0.836229
$413$	−10.7917	−	10.7917i	−0.531025	−	0.531025i
$414$	4.24264	−	4.24264i	0.208514	−	0.208514i
$415$	−8.30442	+	8.30442i	−0.407648	+	0.407648i
$416$		−	5.06418i		−	0.248292i
$417$			5.64590i			0.276481i
$418$	−9.09491	+	9.09491i	−0.444847	+	0.444847i
$419$	−1.06278	+	1.06278i	−0.0519200	+	0.0519200i	−0.732590	−	0.680670i	$-0.761689\pi$
$419$	−1.06278	+	1.06278i	−0.0519200	+	0.0519200i	0.680670	+	0.732590i	$0.261689\pi$
$420$	−6.89021	−	6.89021i	−0.336208	−	0.336208i
$421$	−18.1438			−0.884277			−0.442138	−	0.896947i	$-0.645780\pi$
$421$	−18.1438			−0.884277			−0.442138	+	0.896947i	$0.645780\pi$
$422$	−9.96968	−	9.96968i	−0.485317	−	0.485317i
$423$		−	5.14796i		−	0.250302i
$424$	−4.57398			−0.222132
$425$		0			0
$426$	9.80335			0.474974
$427$		−	17.2181i		−	0.833243i
$428$	2.18246	+	2.18246i	0.105493	+	0.105493i
$429$	14.9067			0.719704
$430$	−27.2402	−	27.2402i	−1.31364	−	1.31364i
$431$	−18.5457	+	18.5457i	−0.893316	+	0.893316i	−0.994834	−	0.101518i	$-0.967630\pi$
$431$	−18.5457	+	18.5457i	−0.893316	+	0.893316i	0.101518	+	0.994834i	$0.467630\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$		−	27.6604i		−	1.32928i	−0.747165	−	0.664638i	$-0.768586\pi$
$433$		−	27.6604i		−	1.32928i	0.747165	−	0.664638i	$-0.231414\pi$
$434$			1.97771i			0.0949332i
$435$	−11.9900	+	11.9900i	−0.574874	+	0.574874i
$436$	1.58479	−	1.58479i	0.0758976	−	0.0758976i
$437$	−18.5386	−	18.5386i	−0.886821	−	0.886821i
$438$	−9.04189			−0.432038
$439$	−20.9628	−	20.9628i	−1.00050	−	1.00050i	−1.00000		0.000500672i	$-0.999841\pi$
$439$	−20.9628	−	20.9628i	−1.00050	−	1.00050i	−0.000500672	−	1.00000i	$-0.500159\pi$
$440$		−	10.3969i		−	0.495654i
$441$	0.610815			0.0290864
$442$		0			0
$443$	−34.3209			−1.63063			−0.815317	−	0.579014i	$-0.803437\pi$
$443$	−34.3209			−1.63063			−0.815317	+	0.579014i	$0.803437\pi$
$444$		−	10.2121i		−	0.484646i
$445$	−34.5727	−	34.5727i	−1.63890	−	1.63890i
$446$	−26.3037			−1.24551
$447$	8.07942	+	8.07942i	0.382143	+	0.382143i
$448$	1.95075	−	1.95075i	0.0921641	−	0.0921641i
$449$	−16.8425	+	16.8425i	−0.794845	+	0.794845i	−0.982277	−	0.187433i	$-0.939983\pi$
$449$	−16.8425	+	16.8425i	−0.794845	+	0.794845i	0.187433	+	0.982277i	$0.439983\pi$
$450$		−	7.47565i		−	0.352406i
$451$		−	37.0351i		−	1.74391i
$452$	8.08489	−	8.08489i	0.380281	−	0.380281i
$453$	−8.30923	+	8.30923i	−0.390402	+	0.390402i
$454$	4.28802	+	4.28802i	0.201247	+	0.201247i
$455$	49.3465			2.31340
$456$	−3.08976	−	3.08976i	−0.144691	−	0.144691i
$457$			21.4662i			1.00414i	0.864826	+	0.502072i	$0.167429\pi$
$457$			21.4662i			1.00414i	−0.864826	+	0.502072i	$0.832571\pi$
$458$	−8.56624			−0.400274
$459$		0			0
$460$	21.1925			0.988107
$461$			16.8898i			0.786637i	0.919402	+	0.393319i	$0.128673\pi$
$461$			16.8898i			0.786637i	−0.919402	+	0.393319i	$0.871327\pi$
$462$	5.74214	+	5.74214i	0.267149	+	0.267149i
$463$	3.75784			0.174641			0.0873207	−	0.996180i	$-0.472169\pi$
$463$	3.75784			0.174641			0.0873207	+	0.996180i	$0.472169\pi$
$464$	−3.39458	−	3.39458i	−0.157589	−	0.157589i
$465$	−1.79046	+	1.79046i	−0.0830305	+	0.0830305i
$466$	−8.63528	+	8.63528i	−0.400022	+	0.400022i
$467$			12.4311i			0.575242i	0.957744	+	0.287621i	$0.0928643\pi$
$467$			12.4311i			0.575242i	−0.957744	+	0.287621i	$0.907136\pi$
$468$			5.06418i			0.234092i
$469$	−11.0705	+	11.0705i	−0.511187	+	0.511187i
$470$	12.8573	−	12.8573i	0.593065	−	0.593065i
$471$	−2.48728	−	2.48728i	−0.114608	−	0.114608i
$472$	5.53209			0.254635
$473$	22.7014	+	22.7014i	1.04381	+	1.04381i
$474$		−	6.61856i		−	0.304000i
$475$	−32.6655			−1.49880
$476$		0			0
$477$	4.57398			0.209428
$478$			11.8716i			0.542996i
$479$	−8.26641	−	8.26641i	−0.377702	−	0.377702i	0.492570	−	0.870273i	$-0.336057\pi$
$479$	−8.26641	−	8.26641i	−0.377702	−	0.377702i	−0.870273	+	0.492570i	$0.836057\pi$
$480$	3.53209			0.161217
$481$	36.5688	+	36.5688i	1.66739	+	1.66739i
$482$	−16.9120	+	16.9120i	−0.770320	+	0.770320i
$483$	−11.7045	+	11.7045i	−0.532572	+	0.532572i
$484$		−	2.33544i		−	0.106156i
$485$		−	38.9495i		−	1.76861i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	5.18694	−	5.18694i	0.235043	−	0.235043i	−0.579751	−	0.814794i	$-0.696850\pi$
$487$	5.18694	−	5.18694i	0.235043	−	0.235043i	0.814794	+	0.579751i	$0.196850\pi$
$488$	4.41322	+	4.41322i	0.199777	+	0.199777i
$489$	6.32501			0.286027
$490$	1.52555	+	1.52555i	0.0689173	+	0.0689173i
$491$		−	2.27126i		−	0.102500i	−0.998686	−	0.0512502i	$-0.983679\pi$
$491$		−	2.27126i		−	0.102500i	0.998686	−	0.0512502i	$-0.0163206\pi$
$492$	12.5817			0.567228
$493$		0			0
$494$	22.1284			0.995602
$495$			10.3969i			0.467307i
$496$	−0.506912	−	0.506912i	−0.0227610	−	0.0227610i
$497$	−27.0452			−1.21314
$498$	2.35114	+	2.35114i	0.105357	+	0.105357i
$499$	6.87277	−	6.87277i	0.307668	−	0.307668i	−0.536337	−	0.844004i	$-0.680192\pi$
$499$	6.87277	−	6.87277i	0.307668	−	0.307668i	0.844004	+	0.536337i	$0.180192\pi$
$500$	6.18310	−	6.18310i	0.276517	−	0.276517i
$501$		−	14.3405i		−	0.640686i
$502$			18.6040i			0.830337i
$503$	−12.5573	+	12.5573i	−0.559904	+	0.559904i	−0.929280	−	0.369376i	$-0.879572\pi$
$503$	−12.5573	+	12.5573i	−0.559904	+	0.559904i	0.369376	+	0.929280i	$0.379572\pi$
$504$	−1.95075	+	1.95075i	−0.0868931	+	0.0868931i
$505$	2.30094	+	2.30094i	0.102391	+	0.102391i
$506$	−17.6614			−0.785144
$507$	−8.94200	−	8.94200i	−0.397128	−	0.397128i
$508$			8.75877i			0.388608i
$509$	−7.39786			−0.327904			−0.163952	−	0.986468i	$-0.552424\pi$
$509$	−7.39786			−0.327904			−0.163952	+	0.986468i	$0.552424\pi$
$510$		0			0
$511$	24.9445			1.10348
$512$			1.00000i			0.0441942i
$513$	3.08976	+	3.08976i	0.136416	+	0.136416i
$514$	−4.16756			−0.183823
$515$	−42.3926	−	42.3926i	−1.86804	−	1.86804i
$516$	−7.71222	+	7.71222i	−0.339512	+	0.339512i
$517$	−10.7150	+	10.7150i	−0.471246	+	0.471246i
$518$			28.1729i			1.23785i
$519$		−	0.815207i		−	0.0357836i
$520$	−12.6481	+	12.6481i	−0.554656	+	0.554656i
$521$	2.91539	−	2.91539i	0.127725	−	0.127725i	−0.640354	−	0.768080i	$-0.721212\pi$
$521$	2.91539	−	2.91539i	0.127725	−	0.127725i	0.768080	+	0.640354i	$0.221212\pi$
$522$	3.39458	+	3.39458i	0.148577	+	0.148577i
$523$	36.5134			1.59662			0.798310	−	0.602246i	$-0.205728\pi$
$523$	36.5134			1.59662			0.798310	+	0.602246i	$0.205728\pi$
$524$	−0.909203	−	0.909203i	−0.0397187	−	0.0397187i
$525$			20.6236i			0.900088i
$526$	−7.97090			−0.347548
$527$		0			0
$528$	−2.94356			−0.128102
$529$		−	13.0000i		−	0.565217i
$530$	11.4238	+	11.4238i	0.496218	+	0.496218i
$531$	−5.53209			−0.240072
$532$	8.52395	+	8.52395i	0.369560	+	0.369560i
$533$	−45.0541	+	45.0541i	−1.95151	+	1.95151i
$534$	−9.78816	+	9.78816i	−0.423575	+	0.423575i
$535$		−	10.9017i		−	0.471320i
$536$		−	5.67499i		−	0.245122i
$537$	9.94488	−	9.94488i	0.429153	−	0.429153i
$538$	−4.21659	+	4.21659i	−0.181790	+	0.181790i
$539$	−1.27136	−	1.27136i	−0.0547612	−	0.0547612i
$540$	−3.53209			−0.151997
$541$	31.6740	+	31.6740i	1.36177	+	1.36177i	0.871657	+	0.490116i	$0.163046\pi$
$541$	31.6740	+	31.6740i	1.36177	+	1.36177i	0.490116	+	0.871657i	$0.336954\pi$
$542$		−	3.07098i		−	0.131910i
$543$	−20.3405			−0.872894
$544$		0			0
$545$	−7.91622			−0.339094
$546$		−	13.9709i		−	0.597900i
$547$	15.6265	+	15.6265i	0.668142	+	0.668142i	0.957286	−	0.289143i	$-0.0933704\pi$
$547$	15.6265	+	15.6265i	0.668142	+	0.668142i	−0.289143	+	0.957286i	$0.593370\pi$
$548$	−2.36959			−0.101224
$549$	−4.41322	−	4.41322i	−0.188351	−	0.188351i
$550$	−15.5599	+	15.5599i	−0.663477	+	0.663477i
$551$	14.8329	−	14.8329i	0.631903	−	0.631903i
$552$		−	6.00000i		−	0.255377i
$553$			18.2591i			0.776455i
$554$	16.4383	−	16.4383i	0.698395	−	0.698395i
$555$	−25.5055	+	25.5055i	−1.08265	+	1.08265i
$556$	3.99225	+	3.99225i	0.169309	+	0.169309i
$557$	−21.9905			−0.931768			−0.465884	−	0.884846i	$-0.654264\pi$
$557$	−21.9905			−0.931768			−0.465884	+	0.884846i	$0.654264\pi$
$558$	0.506912	+	0.506912i	0.0214593	+	0.0214593i
$559$		−	55.2336i		−	2.33613i
$560$	−9.74422			−0.411769
$561$		0			0
$562$	−21.7297			−0.916611
$563$			31.9486i			1.34647i	0.739427	+	0.673237i	$0.235097\pi$
$563$			31.9486i			1.34647i	−0.739427	+	0.673237i	$0.764903\pi$
$564$	−3.64015	−	3.64015i	−0.153278	−	0.153278i
$565$	−40.3851			−1.69901
$566$	12.1570	+	12.1570i	0.510995	+	0.510995i
$567$	1.95075	−	1.95075i	0.0819236	−	0.0819236i
$568$	6.93201	−	6.93201i	0.290861	−	0.290861i
$569$		−	30.9614i		−	1.29797i	−0.760801	−	0.648985i	$-0.775194\pi$
$569$		−	30.9614i		−	1.29797i	0.760801	−	0.648985i	$-0.224806\pi$
$570$			15.4338i			0.646449i
$571$	−11.6730	+	11.6730i	−0.488498	+	0.488498i	−0.907832	−	0.419334i	$-0.862264\pi$
$571$	−11.6730	+	11.6730i	−0.488498	+	0.488498i	0.419334	+	0.907832i	$0.362264\pi$
$572$	10.5406	−	10.5406i	0.440727	−	0.440727i
$573$	11.0633	+	11.0633i	0.462177	+	0.462177i
$574$	−34.7101			−1.44877
$575$	−31.7165	−	31.7165i	−1.32267	−	1.32267i
$576$		−	1.00000i		−	0.0416667i
$577$	−18.9026			−0.786926			−0.393463	−	0.919340i	$-0.628723\pi$
$577$	−18.9026			−0.786926			−0.393463	+	0.919340i	$0.628723\pi$
$578$		0			0
$579$	10.2713			0.426859
$580$			16.9564i			0.704074i
$581$	−6.48624	−	6.48624i	−0.269095	−	0.269095i
$582$	−11.0273			−0.457098
$583$	−9.52034	−	9.52034i	−0.394292	−	0.394292i
$584$	−6.39358	+	6.39358i	−0.264568	+	0.264568i
$585$	12.6481	−	12.6481i	0.522935	−	0.522935i
$586$			9.20708i			0.380341i
$587$			7.17799i			0.296267i	0.988967	+	0.148134i	$0.0473266\pi$
$587$			7.17799i			0.296267i	−0.988967	+	0.148134i	$0.952673\pi$
$588$	0.431911	−	0.431911i	0.0178117	−	0.0178117i
$589$	2.21499	−	2.21499i	0.0912672	−	0.0912672i
$590$	−13.8167	−	13.8167i	−0.568826	−	0.568826i
$591$	8.72967			0.359091
$592$	−7.22107	−	7.22107i	−0.296784	−	0.296784i
$593$		−	26.2823i		−	1.07928i	−0.841894	−	0.539642i	$-0.818559\pi$
$593$		−	26.2823i		−	1.07928i	0.841894	−	0.539642i	$-0.181441\pi$
$594$	2.94356			0.120776
$595$		0			0
$596$	11.4260			0.468028
$597$		−	16.8922i		−	0.691351i
$598$	21.4855	+	21.4855i	0.878607	+	0.878607i
$599$	28.3114			1.15677			0.578386	−	0.815763i	$-0.303683\pi$
$599$	28.3114			1.15677			0.578386	+	0.815763i	$0.303683\pi$
$600$	−5.28608	−	5.28608i	−0.215803	−	0.215803i
$601$	8.08970	−	8.08970i	0.329986	−	0.329986i	−0.522595	−	0.852581i	$-0.675036\pi$
$601$	8.08970	−	8.08970i	0.329986	−	0.329986i	0.852581	+	0.522595i	$0.175036\pi$
$602$	21.2762	−	21.2762i	0.867155	−	0.867155i
$603$			5.67499i			0.231104i
$604$			11.7510i			0.478143i
$605$	−5.83290	+	5.83290i	−0.237141	+	0.237141i
$606$	0.651439	−	0.651439i	0.0264629	−	0.0264629i
$607$	22.9747	+	22.9747i	0.932514	+	0.932514i	0.997863	−	0.0653482i	$-0.0208158\pi$
$607$	22.9747	+	22.9747i	0.932514	+	0.932514i	−0.0653482	+	0.997863i	$0.520816\pi$
$608$	−4.36959			−0.177210
$609$	−9.36486	−	9.36486i	−0.379483	−	0.379483i
$610$		−	22.0446i		−	0.892559i
$611$	26.0702			1.05469
$612$		0			0
$613$	−14.2959			−0.577406			−0.288703	−	0.957419i	$-0.593224\pi$
$613$	−14.2959			−0.577406			−0.288703	+	0.957419i	$0.593224\pi$
$614$			2.90673i			0.117306i
$615$	−31.4236	−	31.4236i	−1.26712	−	1.26712i
$616$	8.12061			0.327189
$617$	29.2994	+	29.2994i	1.17955	+	1.17955i	0.979859	+	0.199691i	$0.0639939\pi$
$617$	29.2994	+	29.2994i	1.17955	+	1.17955i	0.199691	+	0.979859i	$0.436006\pi$
$618$	−12.0021	+	12.0021i	−0.482797	+	0.482797i
$619$	−5.69552	+	5.69552i	−0.228922	+	0.228922i	−0.812242	−	0.583320i	$-0.801753\pi$
$619$	−5.69552	+	5.69552i	−0.228922	+	0.228922i	0.583320	+	0.812242i	$0.301753\pi$
$620$			2.53209i			0.101691i
$621$			6.00000i			0.240772i
$622$	9.21719	−	9.21719i	0.369576	−	0.369576i
$623$	27.0033	−	27.0033i	1.08186	−	1.08186i
$624$	3.58091	+	3.58091i	0.143351	+	0.143351i
$625$	6.49289			0.259716
$626$	2.27804	+	2.27804i	0.0910486	+	0.0910486i
$627$		−	12.8621i		−	0.513665i
$628$	−3.51754			−0.140365
$629$		0			0
$630$	9.74422			0.388219
$631$		−	10.5885i		−	0.421523i	−0.977538	−	0.210761i	$-0.932406\pi$
$631$		−	10.5885i		−	0.421523i	0.977538	−	0.210761i	$-0.0675943\pi$
$632$	−4.68003	−	4.68003i	−0.186161	−	0.186161i
$633$	14.0993			0.560395
$634$	13.4943	+	13.4943i	0.535926	+	0.535926i
$635$	21.8756	−	21.8756i	0.868106	−	0.868106i
$636$	3.23429	−	3.23429i	0.128248	−	0.128248i
$637$			3.09327i			0.122560i
$638$		−	14.1310i		−	0.559453i
$639$	−6.93201	+	6.93201i	−0.274226	+	0.274226i
$640$	2.49756	−	2.49756i	0.0987249	−	0.0987249i
$641$	−23.0182	−	23.0182i	−0.909163	−	0.909163i	0.0870412	−	0.996205i	$-0.472259\pi$
$641$	−23.0182	−	23.0182i	−0.909163	−	0.909163i	−0.996205	+	0.0870412i	$0.972259\pi$
$642$	−3.08647			−0.121813
$643$	−7.48241	−	7.48241i	−0.295077	−	0.295077i	0.544005	−	0.839082i	$-0.316907\pi$
$643$	−7.48241	−	7.48241i	−0.295077	−	0.295077i	−0.839082	+	0.544005i	$0.816907\pi$
$644$			16.5526i			0.652265i
$645$	38.5235			1.51686
$646$		0			0
$647$	−25.4884			−1.00205			−0.501027	−	0.865432i	$-0.667044\pi$
$647$	−25.4884			−1.00205			−0.501027	+	0.865432i	$0.667044\pi$
$648$			1.00000i			0.0392837i
$649$	11.5146	+	11.5146i	0.451986	+	0.451986i
$650$	37.8580			1.48491
$651$	−1.39845	−	1.39845i	−0.0548097	−	0.0548097i
$652$	4.47246	−	4.47246i	0.175155	−	0.175155i
$653$	−14.5740	+	14.5740i	−0.570327	+	0.570327i	−0.932220	−	0.361893i	$-0.882131\pi$
$653$	−14.5740	+	14.5740i	−0.570327	+	0.570327i	0.361893	+	0.932220i	$0.382131\pi$
$654$			2.24123i			0.0876390i
$655$			4.54158i			0.177454i
$656$	8.89662	−	8.89662i	0.347355	−	0.347355i
$657$	6.39358	−	6.39358i	0.249437	−	0.249437i
$658$	10.0424	+	10.0424i	0.391492	+	0.391492i
$659$	41.5117			1.61706			0.808532	−	0.588452i	$-0.200262\pi$
$659$	41.5117			1.61706			0.808532	+	0.588452i	$0.200262\pi$
$660$	7.35174	+	7.35174i	0.286166	+	0.286166i
$661$			17.0060i			0.661456i	0.943726	+	0.330728i	$0.107294\pi$
$661$			17.0060i			0.661456i	−0.943726	+	0.330728i	$0.892706\pi$
$662$	−3.43376			−0.133457
$663$		0			0
$664$	3.32501			0.129035
$665$		−	42.5782i		−	1.65111i
$666$	7.22107	+	7.22107i	0.279811	+	0.279811i
$667$	28.8040			1.11529
$668$	−10.1403	−	10.1403i	−0.392338	−	0.392338i
$669$	18.5995	−	18.5995i	0.719098	−	0.719098i
$670$	−14.1737	+	14.1737i	−0.547576	+	0.547576i
$671$			18.3715i			0.709222i
$672$			2.75877i			0.106422i
$673$	14.1699	−	14.1699i	0.546208	−	0.546208i	−0.379134	−	0.925342i	$-0.623778\pi$
$673$	14.1699	−	14.1699i	0.546208	−	0.546208i	0.925342	+	0.379134i	$0.123778\pi$
$674$	−25.2580	+	25.2580i	−0.972901	+	0.972901i
$675$	5.28608	+	5.28608i	0.203461	+	0.203461i
$676$	−12.6459			−0.486381
$677$	33.9286	+	33.9286i	1.30398	+	1.30398i	0.925684	+	0.378297i	$0.123490\pi$
$677$	33.9286	+	33.9286i	1.30398	+	1.30398i	0.378297	+	0.925684i	$0.376510\pi$
$678$			11.4338i			0.439111i
$679$	30.4219			1.16749
$680$		0			0
$681$	−6.06418			−0.232380
$682$		−	2.11019i		−	0.0808032i
$683$	−23.6696	−	23.6696i	−0.905693	−	0.905693i	0.0902283	−	0.995921i	$-0.471240\pi$
$683$	−23.6696	−	23.6696i	−0.905693	−	0.905693i	−0.995921	+	0.0902283i	$0.971240\pi$
$684$	4.36959			0.167075
$685$	5.91819	+	5.91819i	0.226122	+	0.226122i
$686$	12.4637	−	12.4637i	0.475865	−	0.475865i
$687$	6.05724	−	6.05724i	0.231098	−	0.231098i
$688$			10.9067i			0.415815i
$689$			23.1634i			0.882457i
$690$	−14.9854	+	14.9854i	−0.570484	+	0.570484i
$691$	−14.4942	+	14.4942i	−0.551387	+	0.551387i	−0.926841	−	0.375454i	$-0.877487\pi$
$691$	−14.4942	+	14.4942i	−0.551387	+	0.551387i	0.375454	+	0.926841i	$0.377487\pi$
$692$	−0.576439	−	0.576439i	−0.0219129	−	0.0219129i
$693$	−8.12061			−0.308477
$694$	−0.783348	−	0.783348i	−0.0297355	−	0.0297355i
$695$		−	19.9418i		−	0.756436i
$696$	4.80066			0.181969
$697$		0			0
$698$	−11.2371			−0.425331
$699$		−	12.2121i		−	0.461905i
$700$	14.5831	+	14.5831i	0.551189	+	0.551189i
$701$	−51.4415			−1.94292			−0.971459	−	0.237206i	$-0.923768\pi$
$701$	−51.4415			−1.94292			−0.971459	+	0.237206i	$0.923768\pi$
$702$	−3.58091	−	3.58091i	−0.135153	−	0.135153i
$703$	31.5531	−	31.5531i	1.19005	−	1.19005i
$704$	−2.08141	+	2.08141i	−0.0784462	+	0.0784462i
$705$			18.1830i			0.684813i
$706$			11.2608i			0.423807i
$707$	−1.79717	+	1.79717i	−0.0675896	+	0.0675896i
$708$	−3.91178	+	3.91178i	−0.147014	+	0.147014i
$709$	−7.17278	−	7.17278i	−0.269379	−	0.269379i	0.559471	−	0.828850i	$-0.311004\pi$
$709$	−7.17278	−	7.17278i	−0.269379	−	0.269379i	−0.828850	+	0.559471i	$0.811004\pi$
$710$	−34.6263			−1.29950
$711$	4.68003	+	4.68003i	0.175515	+	0.175515i
$712$			13.8425i			0.518771i
$713$	4.30129			0.161085
$714$		0			0
$715$	−52.6519			−1.96907
$716$		−	14.0642i		−	0.525603i
$717$	−8.39452	−	8.39452i	−0.313499	−	0.313499i
$718$	2.04458			0.0763030
$719$	−10.8927	−	10.8927i	−0.406231	−	0.406231i	0.474191	−	0.880422i	$-0.342741\pi$
$719$	−10.8927	−	10.8927i	−0.406231	−	0.406231i	−0.880422	+	0.474191i	$0.842741\pi$
$720$	−2.49756	+	2.49756i	−0.0930787	+	0.0930787i
$721$	33.1112	−	33.1112i	1.23312	−	1.23312i
$722$		−	0.0932736i		−	0.00347128i
$723$		−	23.9172i		−	0.889489i
$724$	−14.3829	+	14.3829i	−0.534536	+	0.534536i
$725$	25.3767	−	25.3767i	0.942467	−	0.942467i
$726$	1.65140	+	1.65140i	0.0612893	+	0.0612893i
$727$	23.1097			0.857091			0.428545	−	0.903520i	$-0.359026\pi$
$727$	23.1097			0.857091			0.428545	+	0.903520i	$0.359026\pi$
$728$	−9.87892	−	9.87892i	−0.366137	−	0.366137i
$729$		−	1.00000i		−	0.0370370i
$730$	31.9368			1.18203
$731$		0			0
$732$	−6.24123			−0.230682
$733$			4.20676i			0.155380i	0.996978	+	0.0776901i	$0.0247545\pi$
$733$			4.20676i			0.155380i	−0.996978	+	0.0776901i	$0.975246\pi$
$734$	17.2603	+	17.2603i	0.637088	+	0.637088i
$735$	−2.15745			−0.0795788
$736$	−4.24264	−	4.24264i	−0.156386	−	0.156386i
$737$	11.8120	−	11.8120i	0.435101	−	0.435101i
$738$	−8.89662	+	8.89662i	−0.327489	+	0.327489i
$739$			7.79797i			0.286853i	0.989661	+	0.143427i	$0.0458121\pi$
$739$			7.79797i			0.286853i	−0.989661	+	0.143427i	$0.954188\pi$
$740$			36.0702i			1.32597i
$741$	−15.6471	+	15.6471i	−0.574811	+	0.574811i
$742$	−8.92267	+	8.92267i	−0.327561	+	0.327561i
$743$	−8.17185	−	8.17185i	−0.299796	−	0.299796i	0.541138	−	0.840934i	$-0.317994\pi$
$743$	−8.17185	−	8.17185i	−0.299796	−	0.299796i	−0.840934	+	0.541138i	$0.817994\pi$
$744$	0.716881			0.0262821
$745$	−28.5372	−	28.5372i	−1.04552	−	1.04552i
$746$			27.3756i			1.00229i
$747$	−3.32501			−0.121656
$748$		0			0
$749$	8.51485			0.311126
$750$			8.74422i			0.319294i
$751$	9.84092	+	9.84092i	0.359100	+	0.359100i	0.863481	−	0.504381i	$-0.168279\pi$
$751$	9.84092	+	9.84092i	0.359100	+	0.359100i	−0.504381	+	0.863481i	$0.668279\pi$
$752$	−5.14796			−0.187727
$753$	−13.1550	−	13.1550i	−0.479396	−	0.479396i
$754$	−17.1908	+	17.1908i	−0.626050	+	0.626050i
$755$	29.3489	−	29.3489i	1.06812	−	1.06812i
$756$		−	2.75877i		−	0.100336i
$757$		−	18.0702i		−	0.656771i	−0.944544	−	0.328386i	$-0.893495\pi$
$757$		−	18.0702i		−	0.656771i	0.944544	−	0.328386i	$-0.106505\pi$
$758$	−15.9084	+	15.9084i	−0.577821	+	0.577821i
$759$	12.4885	−	12.4885i	0.453303	−	0.453303i
$760$	10.9133	+	10.9133i	0.395868	+	0.395868i
$761$	0.241230			0.00874456			0.00437228	−	0.999990i	$-0.498608\pi$
$761$	0.241230			0.00874456			0.00437228	+	0.999990i	$0.498608\pi$
$762$	−6.19339	−	6.19339i	−0.224363	−	0.224363i
$763$		−	6.18304i		−	0.223841i
$764$	15.6459			0.566049
$765$		0			0
$766$	−16.5972			−0.599681
$767$		−	28.0155i		−	1.01158i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−12.5963			−0.454233			−0.227116	−	0.973868i	$-0.572930\pi$
$769$	−12.5963			−0.454233			−0.227116	+	0.973868i	$0.572930\pi$
$770$	−20.2818	−	20.2818i	−0.730904	−	0.730904i
$771$	2.94691	−	2.94691i	0.106130	−	0.106130i
$772$	7.26288	−	7.26288i	0.261397	−	0.261397i
$773$			33.4807i			1.20422i	0.798414	+	0.602109i	$0.205673\pi$
$773$			33.4807i			1.20422i	−0.798414	+	0.602109i	$0.794327\pi$
$774$		−	10.9067i		−	0.392034i
$775$	3.78950	−	3.78950i	0.136123	−	0.136123i
$776$	−7.79751	+	7.79751i	−0.279914	+	0.279914i
$777$	−19.9213	−	19.9213i	−0.714672	−	0.714672i
$778$	−17.2249			−0.617544
$779$	38.8745	+	38.8745i	1.39282	+	1.39282i
$780$		−	17.8871i		−	0.640462i
$781$	28.8568			1.03258
$782$		0			0
$783$	−4.80066			−0.171562
$784$		−	0.610815i		−	0.0218148i
$785$	8.78528	+	8.78528i	0.313560	+	0.313560i
$786$	1.28581			0.0458632
$787$	18.3269	+	18.3269i	0.653282	+	0.653282i	0.953782	−	0.300500i	$-0.0971535\pi$
$787$	18.3269	+	18.3269i	0.653282	+	0.653282i	−0.300500	+	0.953782i	$0.597154\pi$
$788$	6.17281	−	6.17281i	0.219897	−	0.219897i
$789$	5.63628	−	5.63628i	0.200657	−	0.200657i
$790$			23.3773i			0.831728i
$791$		−	31.5431i		−	1.12154i
$792$	2.08141	−	2.08141i	0.0739598	−	0.0739598i
$793$	22.3493	−	22.3493i	0.793647	−	0.793647i
$794$	−3.18052	−	3.18052i	−0.112873	−	0.112873i
$795$	−16.1557			−0.572984
$796$	−11.9446	−	11.9446i	−0.423364	−	0.423364i
$797$		−	55.5580i		−	1.96797i	−0.178264	−	0.983983i	$-0.557048\pi$
$797$		−	55.5580i		−	1.96797i	0.178264	−	0.983983i	$-0.442952\pi$
$798$	−12.0547			−0.426731
$799$		0			0
$800$	−7.47565			−0.264304
$801$		−	13.8425i		−	0.489102i
$802$	1.44573	+	1.44573i	0.0510507	+	0.0510507i
$803$	−26.6154			−0.939236
$804$	4.01283	+	4.01283i	0.141521	+	0.141521i
$805$	41.3412	−	41.3412i	1.45709	−	1.45709i
$806$	−2.56709	+	2.56709i	−0.0904219	+	0.0904219i
$807$		−	5.96316i		−	0.209913i
$808$		−	0.921274i		−	0.0324103i
$809$	−12.6796	+	12.6796i	−0.445792	+	0.445792i	−0.893953	−	0.448161i	$-0.852079\pi$
$809$	−12.6796	+	12.6796i	−0.445792	+	0.445792i	0.448161	+	0.893953i	$0.352079\pi$
$810$	2.49756	−	2.49756i	0.0877555	−	0.0877555i
$811$	−17.8525	−	17.8525i	−0.626885	−	0.626885i	0.320398	−	0.947283i	$-0.396183\pi$
$811$	−17.8525	−	17.8525i	−0.626885	−	0.626885i	−0.947283	+	0.320398i	$0.896183\pi$
$812$	−13.2439			−0.464770
$813$	2.17151	+	2.17151i	0.0761583	+	0.0761583i
$814$		−	30.0601i		−	1.05360i
$815$	−22.3405			−0.782553
$816$		0			0
$817$	−47.6579			−1.66734
$818$			23.2841i			0.814108i
$819$	9.87892	+	9.87892i	0.345197	+	0.345197i
$820$	−44.4397			−1.55190
$821$	1.89574	+	1.89574i	0.0661617	+	0.0661617i	0.739413	−	0.673252i	$-0.235103\pi$
$821$	1.89574	+	1.89574i	0.0661617	+	0.0661617i	−0.673252	+	0.739413i	$0.735103\pi$
$822$	1.67555	−	1.67555i	0.0584415	−	0.0584415i
$823$	17.7987	−	17.7987i	0.620424	−	0.620424i	−0.325216	−	0.945640i	$-0.605437\pi$
$823$	17.7987	−	17.7987i	0.620424	−	0.620424i	0.945640	+	0.325216i	$0.105437\pi$
$824$			16.9736i			0.591303i
$825$		−	22.0051i		−	0.766118i
$826$	10.7917	−	10.7917i	0.375491	−	0.375491i
$827$	8.10613	−	8.10613i	0.281878	−	0.281878i	−0.551980	−	0.833857i	$-0.686127\pi$
$827$	8.10613	−	8.10613i	0.281878	−	0.281878i	0.833857	+	0.551980i	$0.186127\pi$
$828$	4.24264	+	4.24264i	0.147442	+	0.147442i
$829$	−49.4593			−1.71779			−0.858897	−	0.512148i	$-0.828850\pi$
$829$	−49.4593			−1.71779			−0.858897	+	0.512148i	$0.828850\pi$
$830$	−8.30442	−	8.30442i	−0.288251	−	0.288251i
$831$			23.2472i			0.806437i
$832$	5.06418			0.175569
$833$		0			0
$834$	−5.64590			−0.195501
$835$			50.6519i			1.75288i
$836$	−9.09491	−	9.09491i	−0.314554	−	0.314554i
$837$	−0.716881			−0.0247790
$838$	−1.06278	−	1.06278i	−0.0367130	−	0.0367130i
$839$	23.7984	−	23.7984i	0.821612	−	0.821612i	−0.164728	−	0.986339i	$-0.552674\pi$
$839$	23.7984	−	23.7984i	0.821612	−	0.821612i	0.986339	+	0.164728i	$0.0526745\pi$
$840$	6.89021	−	6.89021i	0.237735	−	0.237735i
$841$		−	5.95367i		−	0.205299i
$842$		−	18.1438i		−	0.625278i
$843$	15.3652	−	15.3652i	0.529206	−	0.529206i
$844$	9.96968	−	9.96968i	0.343171	−	0.343171i
$845$	31.5839	+	31.5839i	1.08652	+	1.08652i
$846$	5.14796			0.176990
$847$	−4.55584	−	4.55584i	−0.156541	−	0.156541i
$848$		−	4.57398i		−	0.157071i
$849$	−17.1925			−0.590046
$850$		0			0
$851$	61.2728			2.10040
$852$			9.80335i			0.335857i
$853$	1.71422	+	1.71422i	0.0586936	+	0.0586936i	0.735844	−	0.677151i	$-0.236785\pi$
$853$	1.71422	+	1.71422i	0.0586936	+	0.0586936i	−0.677151	+	0.735844i	$0.736785\pi$
$854$	17.2181			0.589192
$855$	−10.9133	−	10.9133i	−0.373228	−	0.373228i
$856$	−2.18246	+	2.18246i	−0.0745950	+	0.0745950i
$857$	2.27423	−	2.27423i	0.0776864	−	0.0776864i	−0.667196	−	0.744882i	$-0.732506\pi$
$857$	2.27423	−	2.27423i	0.0776864	−	0.0776864i	0.744882	+	0.667196i	$0.232506\pi$
$858$			14.9067i			0.508907i
$859$			23.4831i			0.801232i	0.916246	+	0.400616i	$0.131204\pi$
$859$			23.4831i			0.801232i	−0.916246	+	0.400616i	$0.868796\pi$
$860$	27.2402	−	27.2402i	0.928885	−	0.928885i
$861$	24.5437	−	24.5437i	0.836448	−	0.836448i
$862$	−18.5457	−	18.5457i	−0.631670	−	0.631670i
$863$	−44.4344			−1.51256			−0.756282	−	0.654246i	$-0.772986\pi$
$863$	−44.4344			−1.51256			−0.756282	+	0.654246i	$0.772986\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$			2.87939i			0.0979020i
$866$	27.6604			0.939940
$867$		0			0
$868$	−1.97771			−0.0671279
$869$		−	19.4821i		−	0.660886i
$870$	−11.9900	−	11.9900i	−0.406498	−	0.406498i
$871$	−28.7392			−0.973790
$872$	1.58479	+	1.58479i	0.0536677	+	0.0536677i
$873$	7.79751	−	7.79751i	0.263906	−	0.263906i
$874$	18.5386	−	18.5386i	0.627077	−	0.627077i
$875$		−	24.1233i		−	0.815516i
$876$		−	9.04189i		−	0.305497i
$877$	6.42029	−	6.42029i	0.216798	−	0.216798i	−0.590350	−	0.807148i	$-0.701010\pi$
$877$	6.42029	−	6.42029i	0.216798	−	0.216798i	0.807148	+	0.590350i	$0.201010\pi$
$878$	20.9628	−	20.9628i	0.707461	−	0.707461i
$879$	−6.51039	−	6.51039i	−0.219590	−	0.219590i
$880$	10.3969			0.350480
$881$	−18.0957	−	18.0957i	−0.609660	−	0.609660i	0.333197	−	0.942857i	$-0.391873\pi$
$881$	−18.0957	−	18.0957i	−0.609660	−	0.609660i	−0.942857	+	0.333197i	$0.891873\pi$
$882$			0.610815i			0.0205672i
$883$	−22.3506			−0.752157			−0.376079	−	0.926588i	$-0.622728\pi$
$883$	−22.3506			−0.752157			−0.376079	+	0.926588i	$0.622728\pi$
$884$		0			0
$885$	19.5398			0.656824
$886$		−	34.3209i		−	1.15303i
$887$	−18.7163	−	18.7163i	−0.628432	−	0.628432i	0.319242	−	0.947673i	$-0.396572\pi$
$887$	−18.7163	−	18.7163i	−0.628432	−	0.628432i	−0.947673	+	0.319242i	$0.896572\pi$
$888$	10.2121			0.342697
$889$	17.0861	+	17.0861i	0.573050	+	0.573050i
$890$	34.5727	−	34.5727i	1.15888	−	1.15888i
$891$	−2.08141	+	2.08141i	−0.0697300	+	0.0697300i
$892$		−	26.3037i		−	0.880711i
$893$		−	22.4944i		−	0.752747i
$894$	−8.07942	+	8.07942i	−0.270216	+	0.270216i
$895$	−35.1262	+	35.1262i	−1.17414	+	1.17414i
$896$	1.95075	+	1.95075i	0.0651698	+	0.0651698i
$897$	−30.3851			−1.01453
$898$	−16.8425	−	16.8425i	−0.562040	−	0.562040i
$899$			3.44150i			0.114781i
$900$	7.47565			0.249188
$901$		0			0
$902$	37.0351			1.23313
$903$			30.0892i			1.00130i
$904$	8.08489	+	8.08489i	0.268899	+	0.268899i
$905$	71.8444			2.38819
$906$	−8.30923	−	8.30923i	−0.276056	−	0.276056i
$907$	−39.2955	+	39.2955i	−1.30479	+	1.30479i	−0.379659	+	0.925126i	$0.623959\pi$
$907$	−39.2955	+	39.2955i	−1.30479	+	1.30479i	−0.925126	+	0.379659i	$0.876041\pi$
$908$	−4.28802	+	4.28802i	−0.142303	+	0.142303i
$909$			0.921274i			0.0305567i
$910$			49.3465i			1.63582i
$911$	−34.6840	+	34.6840i	−1.14913	+	1.14913i	−0.162408	+	0.986724i	$0.551926\pi$
$911$	−34.6840	+	34.6840i	−1.14913	+	1.14913i	−0.986724	+	0.162408i	$0.948074\pi$
$912$	3.08976	−	3.08976i	0.102312	−	0.102312i
$913$	6.92072	+	6.92072i	0.229042	+	0.229042i
$914$	−21.4662			−0.710037
$915$	15.5879	+	15.5879i	0.515319	+	0.515319i
$916$		−	8.56624i		−	0.283036i
$917$	−3.54725			−0.117140
$918$		0			0
$919$	−15.2020			−0.501469			−0.250734	−	0.968056i	$-0.580672\pi$
$919$	−15.2020			−0.501469			−0.250734	+	0.968056i	$0.580672\pi$
$920$			21.1925i			0.698697i
$921$	−2.05537	−	2.05537i	−0.0677266	−	0.0677266i
$922$	−16.8898			−0.556236
$923$	−35.1050	−	35.1050i	−1.15549	−	1.15549i
$924$	−5.74214	+	5.74214i	−0.188903	+	0.188903i
$925$	53.9822	−	53.9822i	1.77492	−	1.77492i
$926$			3.75784i			0.123490i
$927$		−	16.9736i		−	0.557486i
$928$	3.39458	−	3.39458i	0.111433	−	0.111433i
$929$	−16.1904	+	16.1904i	−0.531188	+	0.531188i	−0.920926	−	0.389738i	$-0.872566\pi$
$929$	−16.1904	+	16.1904i	−0.531188	+	0.531188i	0.389738	+	0.920926i	$0.372566\pi$
$930$	−1.79046	−	1.79046i	−0.0587114	−	0.0587114i
$931$	2.66901			0.0874731
$932$	−8.63528	−	8.63528i	−0.282858	−	0.282858i
$933$			13.0351i			0.426749i
$934$	−12.4311			−0.406757
$935$		0			0
$936$	−5.06418			−0.165528
$937$		−	3.34554i		−	0.109294i	−0.998506	−	0.0546470i	$-0.982597\pi$
$937$		−	3.34554i		−	0.109294i	0.998506	−	0.0546470i	$-0.0174034\pi$
$938$	−11.0705	−	11.0705i	−0.361463	−	0.361463i
$939$	−3.22163			−0.105134
$940$	12.8573	+	12.8573i	0.419360	+	0.419360i
$941$	−8.19374	+	8.19374i	−0.267108	+	0.267108i	−0.827934	−	0.560826i	$-0.810484\pi$
$941$	−8.19374	+	8.19374i	−0.267108	+	0.267108i	0.560826	+	0.827934i	$0.310484\pi$
$942$	2.48728	−	2.48728i	0.0810399	−	0.0810399i
$943$			75.4903i			2.45830i
$944$			5.53209i			0.180054i
$945$	−6.89021	+	6.89021i	−0.224138	+	0.224138i
$946$	−22.7014	+	22.7014i	−0.738086	+	0.738086i
$947$	23.8148	+	23.8148i	0.773877	+	0.773877i	0.978782	−	0.204905i	$-0.0656884\pi$
$947$	23.8148	+	23.8148i	0.773877	+	0.773877i	−0.204905	+	0.978782i	$0.565688\pi$
$948$	6.61856			0.214961
$949$	32.3782	+	32.3782i	1.05104	+	1.05104i
$950$		−	32.6655i		−	1.05981i
$951$	−19.0838			−0.618834
$952$		0			0
$953$	−13.9655			−0.452388			−0.226194	−	0.974082i	$-0.572628\pi$
$953$	−13.9655			−0.452388			−0.226194	+	0.974082i	$0.572628\pi$
$954$			4.57398i			0.148088i
$955$	−39.0766	−	39.0766i	−1.26449	−	1.26449i
$956$	−11.8716			−0.383956
$957$	9.99216	+	9.99216i	0.323001	+	0.323001i
$958$	8.26641	−	8.26641i	0.267076	−	0.267076i
$959$	−4.62246	+	4.62246i	−0.149267	+	0.149267i
$960$			3.53209i			0.113998i
$961$		−	30.4861i		−	0.983422i
$962$	−36.5688	+	36.5688i	−1.17902	+	1.17902i
$963$	2.18246	−	2.18246i	0.0703288	−	0.0703288i
$964$	−16.9120	−	16.9120i	−0.544698	−	0.544698i
$965$	−36.2790			−1.16786
$966$	−11.7045	−	11.7045i	−0.376585	−	0.376585i
$967$		−	47.0515i		−	1.51307i	−0.653951	−	0.756537i	$-0.726890\pi$
$967$		−	47.0515i		−	1.51307i	0.653951	−	0.756537i	$-0.273110\pi$
$968$	2.33544			0.0750638
$969$		0			0
$970$	38.9495			1.25059
$971$		−	30.2044i		−	0.969305i	−0.874707	−	0.484653i	$-0.838946\pi$
$971$		−	30.2044i		−	0.969305i	0.874707	−	0.484653i	$-0.161054\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	15.5757			0.499335
$974$	5.18694	+	5.18694i	0.166200	+	0.166200i
$975$	−26.7697	+	26.7697i	−0.857316	+	0.857316i
$976$	−4.41322	+	4.41322i	−0.141264	+	0.141264i
$977$			12.4534i			0.398418i	0.979957	+	0.199209i	$0.0638373\pi$
$977$			12.4534i			0.398418i	−0.979957	+	0.199209i	$0.936163\pi$
$978$			6.32501i			0.202251i
$979$	−28.8121	+	28.8121i	−0.920838	+	0.920838i
$980$	−1.52555	+	1.52555i	−0.0487319	+	0.0487319i
$981$	−1.58479	−	1.58479i	−0.0505984	−	0.0505984i
$982$	2.27126			0.0724788
$983$	−30.3893	−	30.3893i	−0.969267	−	0.969267i	0.0302750	−	0.999542i	$-0.490362\pi$
$983$	−30.3893	−	30.3893i	−0.969267	−	0.969267i	−0.999542	+	0.0302750i	$0.990362\pi$
$984$			12.5817i			0.401091i
$985$	−30.8340			−0.982453
$986$		0			0
$987$	−14.2020			−0.452056
$988$			22.1284i			0.703997i
$989$	−46.2733	−	46.2733i	−1.47141	−	1.47141i
$990$	−10.3969			−0.330436
$991$	−6.53454	−	6.53454i	−0.207576	−	0.207576i	0.595660	−	0.803237i	$-0.296891\pi$
$991$	−6.53454	−	6.53454i	−0.207576	−	0.207576i	−0.803237	+	0.595660i	$0.796891\pi$
$992$	0.506912	−	0.506912i	0.0160945	−	0.0160945i
$993$	2.42804	−	2.42804i	0.0770514	−	0.0770514i
$994$		−	27.0452i		−	0.857821i
$995$			59.6647i			1.89150i
$996$	−2.35114	+	2.35114i	−0.0744986	+	0.0744986i
$997$	−19.9805	+	19.9805i	−0.632789	+	0.632789i	−0.948767	−	0.315978i	$-0.897668\pi$
$997$	−19.9805	+	19.9805i	−0.632789	+	0.632789i	0.315978	+	0.948767i	$0.397668\pi$
$998$	6.87277	+	6.87277i	0.217554	+	0.217554i
$999$	−10.2121			−0.323098

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.2.f.n.829.3		12
17.2	even	8		1734.2.a.p.1.1	✓	3
17.4	even	4	inner	1734.2.f.n.1483.3		12
17.8	even	8		1734.2.b.j.577.6		6
17.9	even	8		1734.2.b.j.577.1		6
17.13	even	4	inner	1734.2.f.n.1483.4		12
17.15	even	8		1734.2.a.q.1.3	yes	3
17.16	even	2	inner	1734.2.f.n.829.4		12
51.2	odd	8		5202.2.a.bp.1.3		3
51.32	odd	8		5202.2.a.bm.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1734.2.a.p.1.1	✓	3	17.2	even	8
1734.2.a.q.1.3	yes	3	17.15	even	8
1734.2.b.j.577.1		6	17.9	even	8
1734.2.b.j.577.6		6	17.8	even	8
1734.2.f.n.829.3		12	1.1	even	1	trivial
1734.2.f.n.829.4		12	17.16	even	2	inner
1734.2.f.n.1483.3		12	17.4	even	4	inner
1734.2.f.n.1483.4		12	17.13	even	4	inner
5202.2.a.bm.1.1		3	51.32	odd	8
5202.2.a.bp.1.3		3	51.2	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1734.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.49756 + 2.49756i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.95075 + 1.95075i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.49756 + 2.49756i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.95075 + 1.95075i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-2.49756 + 2.49756i) q^{10} +(2.08141 - 2.08141i) q^{11} +(0.707107 + 0.707107i) q^{12} -5.06418 q^{13} +(-1.95075 - 1.95075i) q^{14} -3.53209i q^{15} +1.00000 q^{16} -1.00000 q^{18} +4.36959i q^{19} +(-2.49756 - 2.49756i) q^{20} +2.75877 q^{21} +(2.08141 + 2.08141i) q^{22} +(-4.24264 + 4.24264i) q^{23} +(-0.707107 + 0.707107i) q^{24} +7.47565i q^{25} -5.06418i q^{26} +(0.707107 - 0.707107i) q^{27} +(1.95075 - 1.95075i) q^{28} +(-3.39458 - 3.39458i) q^{29} +3.53209 q^{30} +(-0.506912 - 0.506912i) q^{31} +1.00000i q^{32} -2.94356 q^{33} -9.74422 q^{35} -1.00000i q^{36} +(-7.22107 - 7.22107i) q^{37} -4.36959 q^{38} +(3.58091 + 3.58091i) q^{39} +(2.49756 - 2.49756i) q^{40} +(8.89662 - 8.89662i) q^{41} +2.75877i q^{42} +10.9067i q^{43} +(-2.08141 + 2.08141i) q^{44} +(-2.49756 + 2.49756i) q^{45} +(-4.24264 - 4.24264i) q^{46} -5.14796 q^{47} +(-0.707107 - 0.707107i) q^{48} -0.610815i q^{49} -7.47565 q^{50} +5.06418 q^{52} -4.57398i q^{53} +(0.707107 + 0.707107i) q^{54} +10.3969 q^{55} +(1.95075 + 1.95075i) q^{56} +(3.08976 - 3.08976i) q^{57} +(3.39458 - 3.39458i) q^{58} +5.53209i q^{59} +3.53209i q^{60} +(-4.41322 + 4.41322i) q^{61} +(0.506912 - 0.506912i) q^{62} +(-1.95075 - 1.95075i) q^{63} -1.00000 q^{64} +(-12.6481 - 12.6481i) q^{65} -2.94356i q^{66} +5.67499 q^{67} +6.00000 q^{69} -9.74422i q^{70} +(6.93201 + 6.93201i) q^{71} +1.00000 q^{72} +(-6.39358 - 6.39358i) q^{73} +(7.22107 - 7.22107i) q^{74} +(5.28608 - 5.28608i) q^{75} -4.36959i q^{76} +8.12061i q^{77} +(-3.58091 + 3.58091i) q^{78} +(4.68003 - 4.68003i) q^{79} +(2.49756 + 2.49756i) q^{80} -1.00000 q^{81} +(8.89662 + 8.89662i) q^{82} +3.32501i q^{83} -2.75877 q^{84} -10.9067 q^{86} +4.80066i q^{87} +(-2.08141 - 2.08141i) q^{88} -13.8425 q^{89} +(-2.49756 - 2.49756i) q^{90} +(9.87892 - 9.87892i) q^{91} +(4.24264 - 4.24264i) q^{92} +0.716881i q^{93} -5.14796i q^{94} +(-10.9133 + 10.9133i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-7.79751 - 7.79751i) q^{97} +0.610815 q^{98} +(2.08141 + 2.08141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4}+O(q^{10}) \) 12 * q - 12 * q^4	\( 12 q - 12 q^{4} - 24 q^{13} + 12 q^{16} - 12 q^{18} - 12 q^{21} + 24 q^{30} + 24 q^{33} - 24 q^{38} - 12 q^{50} + 24 q^{52} + 12 q^{55} - 12 q^{64} + 48 q^{67} + 72 q^{69} + 12 q^{72} - 12 q^{81} + 12 q^{84} - 24 q^{86} - 96 q^{89} + 24 q^{98}+O(q^{100}) \) 12 * q - 12 * q^4 - 24 * q^13 + 12 * q^16 - 12 * q^18 - 12 * q^21 + 24 * q^30 + 24 * q^33 - 24 * q^38 - 12 * q^50 + 24 * q^52 + 12 * q^55 - 12 * q^64 + 48 * q^67 + 72 * q^69 + 12 * q^72 - 12 * q^81 + 12 * q^84 - 24 * q^86 - 96 * q^89 + 24 * q^98

Introduction

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