LMFDB - Embedded newform 1734.2.f.n.829.4

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			829.4
Root			$1.32893 - 1.32893i$ of defining polynomial
Character	$\chi$	$=$	1734.829
Dual form			1734.2.f.n.1483.4

$q$-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	$-0.960185\pi$
$5$	−2.49756	−	2.49756i	−1.11694	−	1.11694i	−0.124757	−	0.992187i	$-0.539815\pi$
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	1.95075	−	1.95075i	0.737312	−	0.737312i	−0.234745	−	0.972057i	$-0.575425\pi$
$7$	1.95075	−	1.95075i	0.737312	−	0.737312i	0.972057	+	0.234745i	$0.0754254\pi$
$8$		−	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	−0.947456	−	0.319886i	$-0.896355\pi$
$11$	−2.08141	+	2.08141i	−0.627570	+	0.627570i	0.319886	+	0.947456i	$0.396355\pi$
$12$	−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	−0.109351	−	0.994003i	$-0.534877\pi$
$23$	4.24264	−	4.24264i	0.884652	−	0.884652i	0.994003	+	0.109351i	$0.0348774\pi$
$24$	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	0.948158	−	0.317800i	$-0.102944\pi$
$29$	3.39458	+	3.39458i	0.630357	+	0.630357i	−0.317800	+	0.948158i	$0.602944\pi$
$30$	3.53209			0.644868
$31$	0.506912	+	0.506912i	0.0910440	+	0.0910440i	0.751162	−	0.660118i	$-0.229494\pi$
$31$	0.506912	+	0.506912i	0.0910440	+	0.0910440i	−0.660118	+	0.751162i	$0.729494\pi$
$32$			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	$0.0671123\pi$
$37$	7.22107	+	7.22107i	1.18714	+	1.18714i	0.209281	+	0.977856i	$0.432888\pi$
$38$	−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	$0.690306\pi$
$41$	−8.89662	+	8.89662i	−1.38942	+	1.38942i	−0.826539	+	0.562879i	$0.809694\pi$
$42$			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	−0.365685	−	0.930739i	$-0.619165\pi$
$61$	4.41322	−	4.41322i	0.565054	−	0.565054i	0.930739	+	0.365685i	$0.119165\pi$
$62$	−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	0.163813	−	0.986491i	$-0.447621\pi$
$71$	−6.93201	−	6.93201i	−0.822679	−	0.822679i	−0.986491	+	0.163813i	$0.947621\pi$
$72$	1.00000			0.117851
$73$	6.39358	+	6.39358i	0.748312	+	0.748312i	0.974162	−	0.225850i	$-0.0725159\pi$
$73$	6.39358	+	6.39358i	0.748312	+	0.748312i	−0.225850	+	0.974162i	$0.572516\pi$
$74$	−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	−0.919540	−	0.392996i	$-0.871439\pi$
$79$	−4.68003	+	4.68003i	−0.526544	+	0.526544i	0.392996	+	0.919540i	$0.371439\pi$
$80$	−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	0.981773	−	0.190056i	$-0.0608670\pi$
$97$	7.79751	+	7.79751i	0.791717	+	0.791717i	−0.190056	+	0.981773i	$0.560867\pi$
$98$	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	0.804686	−	0.593700i	$-0.202333\pi$
$107$	2.18246	+	2.18246i	0.210987	+	0.210987i	−0.593700	+	0.804686i	$0.702333\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	1.58479	−	1.58479i	0.151795	−	0.151795i	−0.627124	−	0.778919i	$-0.715768\pi$
$109$	1.58479	−	1.58479i	0.151795	−	0.151795i	0.778919	+	0.627124i	$0.215768\pi$
$110$			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	−0.215861	−	0.976424i	$-0.569256\pi$
$113$	8.08489	−	8.08489i	0.760563	−	0.760563i	0.976424	+	0.215861i	$0.0692559\pi$
$114$	−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	0.666272	−	0.745709i	$-0.267889\pi$
$131$	−0.909203	−	0.909203i	−0.0794374	−	0.0794374i	−0.745709	+	0.666272i	$0.767889\pi$
$132$	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	0.855847	−	0.517229i	$-0.173036\pi$
$139$	3.99225	+	3.99225i	0.338618	+	0.338618i	−0.517229	+	0.855847i	$0.673036\pi$
$140$	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	−0.509915	−	0.860225i	$-0.670323\pi$
$163$	4.47246	−	4.47246i	0.350310	−	0.350310i	0.860225	+	0.509915i	$0.170323\pi$
$164$	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	0.195939	−	0.980616i	$-0.437224\pi$
$167$	−10.1403	−	10.1403i	−0.784677	−	0.784677i	−0.980616	+	0.195939i	$0.937224\pi$
$168$		−	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	0.684854	−	0.728680i	$-0.259866\pi$
$173$	−0.576439	−	0.576439i	−0.0438258	−	0.0438258i	−0.728680	+	0.684854i	$0.759866\pi$
$174$	−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	$0.522824\pi$
$181$	−14.3829	+	14.3829i	−1.06907	+	1.06907i	−0.997430	+	0.0716420i	$0.977176\pi$
$182$	−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	−0.395621	−	0.918414i	$-0.629471\pi$
$193$	7.26288	−	7.26288i	0.522793	−	0.522793i	0.918414	+	0.395621i	$0.129471\pi$
$194$	−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	−0.452148	−	0.891943i	$-0.649342\pi$
$197$	6.17281	−	6.17281i	0.439795	−	0.439795i	0.891943	+	0.452148i	$0.149342\pi$
$198$	2.08141	−	2.08141i	0.147920	−	0.147920i
$199$	−11.9446	−	11.9446i	−0.846728	−	0.846728i	0.142995	−	0.989723i	$-0.454327\pi$
$199$	−11.9446	−	11.9446i	−0.846728	−	0.846728i	−0.989723	+	0.142995i	$0.954327\pi$
$200$	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	−0.275080	−	0.961421i	$-0.588704\pi$
$211$	9.96968	−	9.96968i	0.686341	−	0.686341i	0.961421	+	0.275080i	$0.0887044\pi$
$212$			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	−0.834943	−	0.550337i	$-0.814499\pi$
$227$	−4.28802	+	4.28802i	−0.284606	+	0.284606i	0.550337	+	0.834943i	$0.314499\pi$
$228$	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	0.365209	−	0.930925i	$-0.380997\pi$
$233$	−8.63528	−	8.63528i	−0.565716	−	0.565716i	−0.930925	+	0.365209i	$0.880997\pi$
$234$	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	$-0.970097\pi$
$241$	−16.9120	−	16.9120i	−1.08940	−	1.08940i	−0.0938061	−	0.995590i	$-0.529903\pi$
$242$	−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	0.566779	−	0.823870i	$-0.308189\pi$
$269$	−4.21659	−	4.21659i	−0.257090	−	0.257090i	−0.823870	+	0.566779i	$0.808189\pi$
$270$			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	0.999925	−	0.0122455i	$-0.00389795\pi$
$277$	16.4383	+	16.4383i	0.987680	+	0.987680i	−0.0122455	+	0.999925i	$0.503898\pi$
$278$	−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	−0.969145	−	0.246489i	$-0.920723\pi$
$283$	−12.1570	+	12.1570i	−0.722656	+	0.722656i	0.246489	+	0.969145i	$0.420723\pi$
$284$	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	0.918374	−	0.395714i	$-0.129503\pi$
$311$	9.21719	+	9.21719i	0.522659	+	0.522659i	−0.395714	+	0.918374i	$0.629503\pi$
$312$	−3.58091	+	3.58091i	−0.202729	+	0.202729i
$313$	−2.27804	+	2.27804i	−0.128762	+	0.128762i	−0.768551	−	0.639789i	$-0.779022\pi$
$313$	−2.27804	+	2.27804i	−0.128762	+	0.128762i	0.639789	+	0.768551i	$0.279022\pi$
$314$			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	−0.975942	−	0.218029i	$-0.930037\pi$
$317$	−13.4943	+	13.4943i	−0.757914	+	0.757914i	0.218029	+	0.975942i	$0.430037\pi$
$318$	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	$-0.824272\pi$
$337$	−25.2580	−	25.2580i	−1.37589	−	1.37589i	−0.524446	−	0.851443i	$-0.675728\pi$
$338$			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	−0.685768	−	0.727820i	$-0.740534\pi$
$347$	0.783348	−	0.783348i	0.0420523	−	0.0420523i	0.727820	+	0.685768i	$0.240534\pi$
$348$		−	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	−0.995521	−	0.0945417i	$-0.969861\pi$
$367$	−17.2603	+	17.2603i	−0.900979	+	0.900979i	0.0945417	+	0.995521i	$0.469861\pi$
$368$	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	0.168534	−	0.985696i	$-0.446097\pi$
$379$	−15.9084	−	15.9084i	−0.817162	−	0.817162i	−0.985696	+	0.168534i	$0.946097\pi$
$380$	−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	−0.622775	−	0.782401i	$-0.713995\pi$
$397$	3.18052	−	3.18052i	0.159626	−	0.159626i	0.782401	+	0.622775i	$0.213995\pi$
$398$	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	−0.742283	−	0.670086i	$-0.766257\pi$
$401$	−1.44573	+	1.44573i	−0.0721965	+	0.0721965i	0.670086	+	0.742283i	$0.266257\pi$
$402$	−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	−0.680670	−	0.732590i	$-0.738311\pi$
$419$	1.06278	−	1.06278i	0.0519200	−	0.0519200i	0.732590	+	0.680670i	$0.238311\pi$
$420$	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	−0.101518	−	0.994834i	$-0.532370\pi$
$431$	18.5457	−	18.5457i	0.893316	−	0.893316i	0.994834	+	0.101518i	$0.0323698\pi$
$432$	−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	$0.000159369\pi$
$439$	20.9628	+	20.9628i	1.00050	+	1.00050i	0.000500672		1.00000i	$0.499841\pi$
$440$		−	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	−0.187433	−	0.982277i	$-0.560017\pi$
$449$	16.8425	−	16.8425i	0.794845	−	0.794845i	0.982277	+	0.187433i	$0.0600167\pi$
$450$		−	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	0.870273	−	0.492570i	$-0.163943\pi$
$479$	8.26641	+	8.26641i	0.377702	+	0.377702i	−0.492570	+	0.870273i	$0.663943\pi$
$480$	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	−0.814794	−	0.579751i	$-0.803150\pi$
$487$	−5.18694	+	5.18694i	−0.235043	+	0.235043i	0.579751	+	0.814794i	$0.303150\pi$
$488$	−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	−0.844004	−	0.536337i	$-0.819808\pi$
$499$	−6.87277	+	6.87277i	−0.307668	+	0.307668i	0.536337	+	0.844004i	$0.319808\pi$
$500$	−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	−0.369376	−	0.929280i	$-0.620428\pi$
$503$	12.5573	−	12.5573i	0.559904	−	0.559904i	0.929280	+	0.369376i	$0.120428\pi$
$504$	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	−0.768080	−	0.640354i	$-0.778788\pi$
$521$	−2.91539	+	2.91539i	−0.127725	+	0.127725i	0.640354	+	0.768080i	$0.278788\pi$
$522$	−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	$-0.836954\pi$
$541$	−31.6740	−	31.6740i	−1.36177	−	1.36177i	−0.490116	−	0.871657i	$-0.663046\pi$
$542$		−	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	0.289143	−	0.957286i	$-0.406630\pi$
$547$	−15.6265	−	15.6265i	−0.668142	−	0.668142i	−0.957286	+	0.289143i	$0.906630\pi$
$548$	−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	−0.419334	−	0.907832i	$-0.637736\pi$
$571$	11.6730	−	11.6730i	0.488498	−	0.488498i	0.907832	+	0.419334i	$0.137736\pi$
$572$	−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	−0.852581	−	0.522595i	$-0.824964\pi$
$601$	−8.08970	+	8.08970i	−0.329986	+	0.329986i	0.522595	+	0.852581i	$0.324964\pi$
$602$	−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	0.0653482	−	0.997863i	$-0.479184\pi$
$607$	−22.9747	−	22.9747i	−0.932514	−	0.932514i	−0.997863	+	0.0653482i	$0.979184\pi$
$608$	−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	$-0.936006\pi$
$617$	−29.2994	−	29.2994i	−1.17955	−	1.17955i	−0.199691	−	0.979859i	$-0.563994\pi$
$618$	12.0021	−	12.0021i	0.482797	−	0.482797i
$619$	5.69552	−	5.69552i	0.228922	−	0.228922i	−0.583320	−	0.812242i	$-0.698247\pi$
$619$	5.69552	−	5.69552i	0.228922	−	0.228922i	0.812242	+	0.583320i	$0.198247\pi$
$620$			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	0.996205	−	0.0870412i	$-0.0277412\pi$
$641$	23.0182	+	23.0182i	0.909163	+	0.909163i	−0.0870412	+	0.996205i	$0.527741\pi$
$642$	−3.08647			−0.121813
$643$	7.48241	+	7.48241i	0.295077	+	0.295077i	0.839082	−	0.544005i	$-0.183093\pi$
$643$	7.48241	+	7.48241i	0.295077	+	0.295077i	−0.544005	+	0.839082i	$0.683093\pi$
$644$			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	−0.361893	−	0.932220i	$-0.617869\pi$
$653$	14.5740	−	14.5740i	0.570327	−	0.570327i	0.932220	+	0.361893i	$0.117869\pi$
$654$			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	−0.925342	−	0.379134i	$-0.876222\pi$
$673$	−14.1699	+	14.1699i	−0.546208	+	0.546208i	0.379134	+	0.925342i	$0.376222\pi$
$674$	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	$-0.876510\pi$
$677$	−33.9286	−	33.9286i	−1.30398	−	1.30398i	−0.378297	−	0.925684i	$-0.623490\pi$
$678$			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	0.995921	−	0.0902283i	$-0.0287597\pi$
$683$	23.6696	+	23.6696i	0.905693	+	0.905693i	−0.0902283	+	0.995921i	$0.528760\pi$
$684$	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	−0.375454	−	0.926841i	$-0.622513\pi$
$691$	14.4942	−	14.4942i	0.551387	−	0.551387i	0.926841	+	0.375454i	$0.122513\pi$
$692$	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	0.828850	−	0.559471i	$-0.188996\pi$
$709$	7.17278	+	7.17278i	0.269379	+	0.269379i	−0.559471	+	0.828850i	$0.688996\pi$
$710$	−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	0.880422	−	0.474191i	$-0.157259\pi$
$719$	10.8927	+	10.8927i	0.406231	+	0.406231i	−0.474191	+	0.880422i	$0.657259\pi$
$720$	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	0.840934	−	0.541138i	$-0.182006\pi$
$743$	8.17185	+	8.17185i	0.299796	+	0.299796i	−0.541138	+	0.840934i	$0.682006\pi$
$744$	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	0.504381	−	0.863481i	$-0.331721\pi$
$751$	−9.84092	−	9.84092i	−0.359100	−	0.359100i	−0.863481	+	0.504381i	$0.831721\pi$
$752$	−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	0.300500	−	0.953782i	$-0.402846\pi$
$787$	−18.3269	−	18.3269i	−0.653282	−	0.653282i	−0.953782	+	0.300500i	$0.902846\pi$
$788$	−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	−0.448161	−	0.893953i	$-0.647921\pi$
$809$	12.6796	−	12.6796i	0.445792	−	0.445792i	0.893953	+	0.448161i	$0.147921\pi$
$810$	−2.49756	+	2.49756i	−0.0877555	+	0.0877555i
$811$	17.8525	+	17.8525i	0.626885	+	0.626885i	0.947283	−	0.320398i	$-0.103817\pi$
$811$	17.8525	+	17.8525i	0.626885	+	0.626885i	−0.320398	+	0.947283i	$0.603817\pi$
$812$	−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	0.673252	−	0.739413i	$-0.264897\pi$
$821$	−1.89574	−	1.89574i	−0.0661617	−	0.0661617i	−0.739413	+	0.673252i	$0.764897\pi$
$822$	−1.67555	+	1.67555i	−0.0584415	+	0.0584415i
$823$	−17.7987	+	17.7987i	−0.620424	+	0.620424i	−0.945640	−	0.325216i	$-0.894563\pi$
$823$	−17.7987	+	17.7987i	−0.620424	+	0.620424i	0.325216	+	0.945640i	$0.394563\pi$
$824$			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	−0.833857	−	0.551980i	$-0.813873\pi$
$827$	−8.10613	+	8.10613i	−0.281878	+	0.281878i	0.551980	+	0.833857i	$0.313873\pi$
$828$	−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	−0.986339	−	0.164728i	$-0.947326\pi$
$839$	−23.7984	+	23.7984i	−0.821612	+	0.821612i	0.164728	+	0.986339i	$0.447326\pi$
$840$	−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	0.677151	−	0.735844i	$-0.263215\pi$
$853$	−1.71422	−	1.71422i	−0.0586936	−	0.0586936i	−0.735844	+	0.677151i	$0.763215\pi$
$854$	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	−0.744882	−	0.667196i	$-0.767494\pi$
$857$	−2.27423	+	2.27423i	−0.0776864	+	0.0776864i	0.667196	+	0.744882i	$0.267494\pi$
$858$			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	−0.807148	−	0.590350i	$-0.798990\pi$
$877$	−6.42029	+	6.42029i	−0.216798	+	0.216798i	0.590350	+	0.807148i	$0.298990\pi$
$878$	−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	0.942857	−	0.333197i	$-0.108127\pi$
$881$	18.0957	+	18.0957i	0.609660	+	0.609660i	−0.333197	+	0.942857i	$0.608127\pi$
$882$			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	0.947673	−	0.319242i	$-0.103428\pi$
$887$	18.7163	+	18.7163i	0.628432	+	0.628432i	−0.319242	+	0.947673i	$0.603428\pi$
$888$	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	$-0.376041\pi$
$907$	39.2955	−	39.2955i	1.30479	−	1.30479i	0.925126	−	0.379659i	$-0.123959\pi$
$908$	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	$-0.448074\pi$
$911$	34.6840	−	34.6840i	1.14913	−	1.14913i	0.986724	−	0.162408i	$-0.0519261\pi$
$912$	−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	−0.389738	−	0.920926i	$-0.627434\pi$
$929$	16.1904	−	16.1904i	0.531188	−	0.531188i	0.920926	+	0.389738i	$0.127434\pi$
$930$	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	−0.560826	−	0.827934i	$-0.689516\pi$
$941$	8.19374	−	8.19374i	0.267108	−	0.267108i	0.827934	+	0.560826i	$0.189516\pi$
$942$	−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	0.204905	−	0.978782i	$-0.434312\pi$
$947$	−23.8148	−	23.8148i	−0.773877	−	0.773877i	−0.978782	+	0.204905i	$0.934312\pi$
$948$	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	0.999542	−	0.0302750i	$-0.00963832\pi$
$983$	30.3893	+	30.3893i	0.969267	+	0.969267i	−0.0302750	+	0.999542i	$0.509638\pi$
$984$			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	0.803237	−	0.595660i	$-0.203109\pi$
$991$	6.53454	+	6.53454i	0.207576	+	0.207576i	−0.595660	+	0.803237i	$0.703109\pi$
$992$	−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	−0.315978	−	0.948767i	$-0.602332\pi$
$997$	19.9805	−	19.9805i	0.632789	−	0.632789i	0.948767	+	0.315978i	$0.102332\pi$
$998$	−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.829.4		12
17.2	even	8		1734.2.a.q.1.3	yes	3
17.4	even	4	inner	1734.2.f.n.1483.4		12
17.8	even	8		1734.2.b.j.577.1		6
17.9	even	8		1734.2.b.j.577.6		6
17.13	even	4	inner	1734.2.f.n.1483.3		12
17.15	even	8		1734.2.a.p.1.1	✓	3
17.16	even	2	inner	1734.2.f.n.829.3		12
51.2	odd	8		5202.2.a.bm.1.1		3
51.32	odd	8		5202.2.a.bp.1.3		3

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