LMFDB - Embedded newform 585.2.dp.a.253.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(28,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.28"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.dp (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,6,0,6,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			253.3
Root			$0.131303i$ of defining polynomial
Character	$\chi$	$=$	585.253
Dual form			585.2.dp.a.37.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.113711 + 0.0656513i) q^{2} +(-0.991380 - 1.71712i) q^{4} +(-2.08297 + 0.813169i) q^{5} +(1.39069 + 2.40874i) q^{7} -0.522947i q^{8} +(-0.290243 - 0.0442830i) q^{10} +(3.91706 - 1.04957i) q^{11} +(0.756068 - 3.52539i) q^{13} +0.365201i q^{14} +(-1.94843 + 3.37478i) q^{16} +(0.627499 - 2.34186i) q^{17} +(0.491577 - 1.83459i) q^{19} +(3.46132 + 2.77055i) q^{20} +(0.514321 + 0.137812i) q^{22} +(-2.06467 - 7.70544i) q^{23} +(3.67751 - 3.38761i) q^{25} +(0.317420 - 0.351240i) q^{26} +(2.75740 - 4.77595i) q^{28} +(3.96565 + 2.28957i) q^{29} +(3.87352 - 3.87352i) q^{31} +(-1.34889 + 0.778780i) q^{32} +(0.225100 - 0.225100i) q^{34} +(-4.85547 - 3.88646i) q^{35} +(3.50510 - 6.07101i) q^{37} +(0.176341 - 0.176341i) q^{38} +(0.425244 + 1.08928i) q^{40} +(1.66178 + 6.20184i) q^{41} +(-6.24368 - 1.67299i) q^{43} +(-5.68554 - 5.68554i) q^{44} +(0.271096 - 1.01174i) q^{46} +0.512375 q^{47} +(-0.368015 + 0.637420i) q^{49} +(0.640576 - 0.143776i) q^{50} +(-6.80307 + 2.19674i) q^{52} +(1.32662 + 1.32662i) q^{53} +(-7.30564 + 5.37147i) q^{55} +(1.25964 - 0.727255i) q^{56} +(0.300626 + 0.520700i) q^{58} +(-2.53667 - 0.679700i) q^{59} +(0.641767 + 1.11157i) q^{61} +(0.694764 - 0.186162i) q^{62} +7.58920 q^{64} +(1.29187 + 7.95808i) q^{65} +(3.13180 + 1.80814i) q^{67} +(-4.64334 + 1.24418i) q^{68} +(-0.296970 - 0.760703i) q^{70} +(6.20800 + 1.66343i) q^{71} +9.93250i q^{73} +(0.797139 - 0.460228i) q^{74} +(-3.63755 + 0.974678i) q^{76} +(7.97556 + 7.97556i) q^{77} +8.37577i q^{79} +(1.31425 - 8.61395i) q^{80} +(-0.218196 + 0.814318i) q^{82} -3.17194 q^{83} +(0.597266 + 5.38828i) q^{85} +(-0.600143 - 0.600143i) q^{86} +(-0.548871 - 2.04842i) q^{88} +(-1.61226 - 6.01705i) q^{89} +(9.54319 - 3.08154i) q^{91} +(-11.1843 + 11.1843i) q^{92} +(0.0582629 + 0.0336381i) q^{94} +(0.467892 + 4.22112i) q^{95} +(10.1931 - 5.88500i) q^{97} +(-0.0836950 + 0.0483213i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} + 6 q^{4} - 2 q^{7} - 2 q^{10} + 16 q^{11} - 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 16 q^{22} + 10 q^{23} + 18 q^{25} + 24 q^{26} + 18 q^{28} - 48 q^{32} + 2 q^{34} - 40 q^{35} - 4 q^{37}+ \cdots + 30 q^{98}+O(q^{100}) $ 20 * q + 6 * q^2 + 6 * q^4 - 2 * q^7 - 2 * q^10 + 16 * q^11 - 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 16 * q^22 + 10 * q^23 + 18 * q^25 + 24 * q^26 + 18 * q^28 - 48 * q^32 + 2 * q^34 - 40 * q^35 - 4 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 + 10 * q^43 + 36 * q^44 + 4 * q^46 + 40 * q^47 + 18 * q^49 - 36 * q^50 - 30 * q^52 + 10 * q^53 - 10 * q^55 + 16 * q^59 - 16 * q^61 + 44 * q^62 + 20 * q^64 + 14 * q^65 + 18 * q^67 - 22 * q^68 - 12 * q^70 + 16 * q^71 - 18 * q^74 - 64 * q^76 + 28 * q^77 + 2 * q^80 + 56 * q^82 - 48 * q^83 - 26 * q^85 - 60 * q^86 + 82 * q^88 + 6 * q^89 + 8 * q^91 + 8 * q^92 - 48 * q^94 + 26 * q^95 + 66 * q^97 + 30 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$	0.113711	+	0.0656513i	0.0804061	+	0.0464225i	0.539664	−	0.841881i	$-0.318551\pi$
$2$	0.113711	+	0.0656513i	0.0804061	+	0.0464225i	−0.459258	+	0.888303i	$0.651885\pi$
$3$		0			0
$3$		0			0
$4$	−0.991380	−	1.71712i	−0.495690	−	0.858560i
$5$	−2.08297	+	0.813169i	−0.931532	+	0.363660i
$5$	−2.08297	+	0.813169i	−0.931532	+	0.363660i
$6$		0			0
$7$	1.39069	+	2.40874i	0.525630	+	0.910418i	0.999554	+	0.0298522i	$0.00950365\pi$
$7$	1.39069	+	2.40874i	0.525630	+	0.910418i	−0.473924	+	0.880566i	$0.657163\pi$
$8$		−	0.522947i		−	0.184890i
$9$		0			0
$10$	−0.290243	−	0.0442830i	−0.0917828	−	0.0140035i
$11$	3.91706	−	1.04957i	1.18104	−	0.316459i	0.385701	−	0.922624i	$-0.373960\pi$
$11$	3.91706	−	1.04957i	1.18104	−	0.316459i	0.795339	+	0.606165i	$0.207293\pi$
$12$		0			0
$13$	0.756068	−	3.52539i	0.209695	−	0.977767i
$13$	0.756068	−	3.52539i	0.209695	−	0.977767i
$14$			0.365201i			0.0976042i
$15$		0			0
$16$	−1.94843	+	3.37478i	−0.487107	+	0.843694i
$17$	0.627499	−	2.34186i	0.152191	−	0.567984i	−0.847139	−	0.531372i	$-0.821677\pi$
$17$	0.627499	−	2.34186i	0.152191	−	0.567984i	0.999330	−	0.0366120i	$-0.0116566\pi$
$18$		0			0
$19$	0.491577	−	1.83459i	0.112775	−	0.420883i	−0.886335	−	0.463044i	$-0.846757\pi$
$19$	0.491577	−	1.83459i	0.112775	−	0.420883i	0.999111	+	0.0421602i	$0.0134240\pi$
$20$	3.46132	+	2.77055i	0.773975	+	0.619513i
$21$		0			0
$22$	0.514321	+	0.137812i	0.109654	+	0.0293816i
$23$	−2.06467	−	7.70544i	−0.430513	−	1.60670i	−0.751582	−	0.659640i	$-0.770709\pi$
$23$	−2.06467	−	7.70544i	−0.430513	−	1.60670i	0.321069	−	0.947056i	$-0.395958\pi$
$24$		0			0
$25$	3.67751	−	3.38761i	0.735502	−	0.677522i
$26$	0.317420	−	0.351240i	0.0622511	−	0.0688838i
$27$		0			0
$28$	2.75740	−	4.77595i	0.521099	−	0.902570i
$29$	3.96565	+	2.28957i	0.736403	+	0.425162i	0.820760	−	0.571273i	$-0.193550\pi$
$29$	3.96565	+	2.28957i	0.736403	+	0.425162i	−0.0843571	+	0.996436i	$0.526884\pi$
$30$		0			0
$31$	3.87352	−	3.87352i	0.695704	−	0.695704i	−0.267777	−	0.963481i	$-0.586289\pi$
$31$	3.87352	−	3.87352i	0.695704	−	0.695704i	0.963481	+	0.267777i	$0.0862890\pi$
$32$	−1.34889	+	0.778780i	−0.238452	+	0.137670i
$33$		0			0
$34$	0.225100	−	0.225100i	0.0386043	−	0.0386043i
$35$	−4.85547	−	3.88646i	−0.820724	−	0.656932i
$36$		0			0
$37$	3.50510	−	6.07101i	0.576234	−	0.998067i	−0.419672	−	0.907676i	$-0.637855\pi$
$37$	3.50510	−	6.07101i	0.576234	−	0.998067i	0.995906	−	0.0903914i	$-0.0288118\pi$
$38$	0.176341	−	0.176341i	0.0286063	−	0.0286063i
$39$		0			0
$40$	0.425244	+	1.08928i	0.0672370	+	0.172230i
$41$	1.66178	+	6.20184i	0.259526	+	0.968565i	0.965516	+	0.260343i	$0.0838357\pi$
$41$	1.66178	+	6.20184i	0.259526	+	0.968565i	−0.705990	+	0.708222i	$0.749498\pi$
$42$		0			0
$43$	−6.24368	−	1.67299i	−0.952152	−	0.255128i	−0.250877	−	0.968019i	$-0.580719\pi$
$43$	−6.24368	−	1.67299i	−0.952152	−	0.255128i	−0.701275	+	0.712891i	$0.747386\pi$
$44$	−5.68554	−	5.68554i	−0.857128	−	0.857128i
$45$		0			0
$46$	0.271096	−	1.01174i	0.0399709	−	0.149174i
$47$	0.512375			0.0747376			0.0373688	−	0.999302i	$-0.488102\pi$
$47$	0.512375			0.0747376			0.0373688	+	0.999302i	$0.488102\pi$
$48$		0			0
$49$	−0.368015	+	0.637420i	−0.0525736	+	0.0910601i
$50$	0.640576	−	0.143776i	0.0905911	−	0.0203331i
$51$		0			0
$52$	−6.80307	+	2.19674i	−0.943415	+	0.304633i
$53$	1.32662	+	1.32662i	0.182225	+	0.182225i	0.792325	−	0.610100i	$-0.208871\pi$
$53$	1.32662	+	1.32662i	0.182225	+	0.182225i	−0.610100	+	0.792325i	$0.708871\pi$
$54$		0			0
$55$	−7.30564	+	5.37147i	−0.985092	+	0.724288i
$56$	1.25964	−	0.727255i	0.168327	−	0.0971835i
$57$		0			0
$58$	0.300626	+	0.520700i	0.0394742	+	0.0683713i
$59$	−2.53667	−	0.679700i	−0.330247	−	0.0884894i	0.0898858	−	0.995952i	$-0.471350\pi$
$59$	−2.53667	−	0.679700i	−0.330247	−	0.0884894i	−0.420133	+	0.907463i	$0.638016\pi$
$60$		0			0
$61$	0.641767	+	1.11157i	0.0821698	+	0.142322i	0.904182	−	0.427148i	$-0.140482\pi$
$61$	0.641767	+	1.11157i	0.0821698	+	0.142322i	−0.822012	+	0.569470i	$0.807148\pi$
$62$	0.694764	−	0.186162i	0.0882352	−	0.0236425i
$63$		0			0
$64$	7.58920			0.948650
$65$	1.29187	+	7.95808i	0.160237	+	0.987079i
$66$		0			0
$67$	3.13180	+	1.80814i	0.382610	+	0.220900i	0.678953	−	0.734181i	$-0.262434\pi$
$67$	3.13180	+	1.80814i	0.382610	+	0.220900i	−0.296343	+	0.955082i	$0.595767\pi$
$68$	−4.64334	+	1.24418i	−0.563088	+	0.150879i
$69$		0			0
$70$	−0.296970	−	0.760703i	−0.0354948	−	0.0909214i
$71$	6.20800	+	1.66343i	0.736754	+	0.197413i	0.607635	−	0.794216i	$-0.292118\pi$
$71$	6.20800	+	1.66343i	0.736754	+	0.197413i	0.129119	+	0.991629i	$0.458785\pi$
$72$		0			0
$73$			9.93250i			1.16251i	0.813721	+	0.581256i	$0.197438\pi$
$73$			9.93250i			1.16251i	−0.813721	+	0.581256i	$0.802562\pi$
$74$	0.797139	−	0.460228i	0.0926655	−	0.0535005i
$75$		0			0
$76$	−3.63755	+	0.974678i	−0.417255	+	0.111803i
$77$	7.97556	+	7.97556i	0.908899	+	0.908899i
$78$		0			0
$79$			8.37577i			0.942347i	0.882040	+	0.471174i	$0.156169\pi$
$79$			8.37577i			0.942347i	−0.882040	+	0.471174i	$0.843831\pi$
$80$	1.31425	−	8.61395i	0.146938	−	0.963069i
$81$		0			0
$82$	−0.218196	+	0.814318i	−0.0240957	+	0.0899264i
$83$	−3.17194			−0.348166			−0.174083	−	0.984731i	$-0.555696\pi$
$83$	−3.17194			−0.348166			−0.174083	+	0.984731i	$0.555696\pi$
$84$		0			0
$85$	0.597266	+	5.38828i	0.0647826	+	0.584441i
$86$	−0.600143	−	0.600143i	−0.0647151	−	0.0647151i
$87$		0			0
$88$	−0.548871	−	2.04842i	−0.0585099	−	0.218362i
$89$	−1.61226	−	6.01705i	−0.170900	−	0.637806i	−0.997214	−	0.0745967i	$-0.976233\pi$
$89$	−1.61226	−	6.01705i	−0.170900	−	0.637806i	0.826314	−	0.563210i	$-0.190434\pi$
$90$		0			0
$91$	9.54319	−	3.08154i	1.00040	−	0.323033i
$92$	−11.1843	+	11.1843i	−1.16604	+	1.16604i
$93$		0			0
$94$	0.0582629	+	0.0336381i	0.00600936	+	0.00346951i
$95$	0.467892	+	4.22112i	0.0480048	+	0.433078i
$96$		0			0
$97$	10.1931	−	5.88500i	1.03495	−	0.597531i	0.116554	−	0.993184i	$-0.462815\pi$
$97$	10.1931	−	5.88500i	1.03495	−	0.597531i	0.918400	+	0.395654i	$0.129482\pi$
$98$	−0.0836950	+	0.0483213i	−0.00845447	+	0.00488119i
$99$		0			0
$100$	−9.46275	−	2.95632i	−0.946275	−	0.295632i
$101$	−0.873807	−	0.504493i	−0.0869471	−	0.0501989i	0.455896	−	0.890033i	$-0.349319\pi$
$101$	−0.873807	−	0.504493i	−0.0869471	−	0.0501989i	−0.542843	+	0.839834i	$0.682652\pi$
$102$		0			0
$103$	−6.00002	+	6.00002i	−0.591200	+	0.591200i	−0.937955	−	0.346756i	$-0.887283\pi$
$103$	−6.00002	+	6.00002i	−0.591200	+	0.591200i	0.346756	+	0.937955i	$0.387283\pi$
$104$	−1.84359	−	0.395383i	−0.180779	−	0.0387705i
$105$		0			0
$106$	0.0637574	+	0.237946i	0.00619267	+	0.0231113i
$107$	−1.28261	−	4.78678i	−0.123995	−	0.462755i	0.875807	−	0.482662i	$-0.160330\pi$
$107$	−1.28261	−	4.78678i	−0.123995	−	0.462755i	−0.999802	+	0.0199063i	$0.993663\pi$
$108$		0			0
$109$	−6.51002	−	6.51002i	−0.623546	−	0.623546i	0.322890	−	0.946436i	$-0.395346\pi$
$109$	−6.51002	−	6.51002i	−0.623546	−	0.623546i	−0.946436	+	0.322890i	$0.895346\pi$
$110$	−1.18338	+	0.131172i	−0.112831	+	0.0125068i
$111$		0			0
$112$	−10.8386			−1.02415
$113$	−1.94191	+	7.24731i	−0.182680	+	0.681769i	0.812436	+	0.583051i	$0.198141\pi$
$113$	−1.94191	+	7.24731i	−0.182680	+	0.681769i	−0.995115	+	0.0987188i	$0.968526\pi$
$114$		0			0
$115$	10.5665	+	14.3713i	0.985327	+	1.34013i
$116$		−	9.07933i		−	0.842995i
$117$		0			0
$118$	−0.243826	−	0.243826i	−0.0224460	−	0.0224460i
$119$	6.51358	−	1.74531i	0.597099	−	0.159992i
$120$		0			0
$121$	4.71551	−	2.72250i	0.428683	−	0.247500i
$122$			0.168531i			0.0152581i
$123$		0			0
$124$	−10.4914	−	2.81117i	−0.942157	−	0.252450i
$125$	−4.90544	+	10.0467i	−0.438756	+	0.898606i
$126$		0			0
$127$	−15.9847	+	4.28310i	−1.41842	+	0.380064i	−0.884922	−	0.465739i	$-0.845788\pi$
$127$	−15.9847	+	4.28310i	−1.41842	+	0.380064i	−0.533495	+	0.845803i	$0.679122\pi$
$128$	3.56075	+	2.05580i	0.314729	+	0.181709i
$129$		0			0
$130$	−0.375558	+	0.989737i	−0.0329386	+	0.0868057i
$131$	12.6880			1.10856			0.554278	−	0.832332i	$-0.312994\pi$
$131$	12.6880			1.10856			0.554278	+	0.832332i	$0.312994\pi$
$132$		0			0
$133$	5.10267	−	1.36726i	0.442458	−	0.118556i
$134$	0.237414	+	0.411213i	0.0205095	+	0.0355234i
$135$		0			0
$136$	−1.22467	−	0.328148i	−0.105014	−	0.0281385i
$137$	−7.47254	−	12.9428i	−0.638422	−	1.10578i	−0.985779	−	0.168046i	$-0.946254\pi$
$137$	−7.47254	−	12.9428i	−0.638422	−	1.10578i	0.347357	−	0.937733i	$-0.387079\pi$
$138$		0			0
$139$	7.42380	−	4.28613i	0.629679	−	0.363545i	−0.150949	−	0.988542i	$-0.548233\pi$
$139$	7.42380	−	4.28613i	0.629679	−	0.363545i	0.780628	+	0.624996i	$0.214900\pi$
$140$	−1.85991	+	12.1904i	−0.157191	+	1.03028i
$141$		0			0
$142$	0.596714	+	0.596714i	0.0500751	+	0.0500751i
$143$	−0.738590	−	14.6027i	−0.0617640	−	1.22114i
$144$		0			0
$145$	−10.1221	−	1.54436i	−0.840597	−	0.128252i
$146$	−0.652082	+	1.12944i	−0.0539666	+	0.0934730i
$147$		0			0
$148$	−13.8995			−1.14253
$149$	3.14239	−	11.7276i	0.257435	−	0.960759i	−0.709285	−	0.704922i	$-0.750982\pi$
$149$	3.14239	−	11.7276i	0.257435	−	0.960759i	0.966720	−	0.255837i	$-0.0823511\pi$
$150$		0			0
$151$	1.86999	+	1.86999i	0.152177	+	0.152177i	0.779090	−	0.626912i	$-0.215682\pi$
$151$	1.86999	+	1.86999i	0.152177	+	0.152177i	−0.626912	+	0.779090i	$0.715682\pi$
$152$	−0.959392	−	0.257068i	−0.0778170	−	0.0208510i
$153$		0			0
$154$	0.383306	+	1.43052i	0.0308877	+	0.115274i
$155$	−4.91859	+	11.2182i	−0.395071	+	0.901071i
$156$		0			0
$157$	−10.3194	+	10.3194i	−0.823581	+	0.823581i	−0.986620	−	0.163039i	$-0.947870\pi$
$157$	−10.3194	+	10.3194i	−0.823581	+	0.823581i	0.163039	+	0.986620i	$0.447870\pi$
$158$	−0.549880	+	0.952420i	−0.0437461	+	0.0757705i
$159$		0			0
$160$	2.17641	−	2.71905i	0.172060	−	0.214960i
$161$	15.6891	−	15.6891i	1.23647	−	1.23647i
$162$		0			0
$163$	16.1907	−	9.34772i	1.26815	−	0.732170i	0.293516	−	0.955954i	$-0.405174\pi$
$163$	16.1907	−	9.34772i	1.26815	−	0.732170i	0.974639	+	0.223784i	$0.0718412\pi$
$164$	9.00186	−	9.00186i	0.702927	−	0.702927i
$165$		0			0
$166$	−0.360686	−	0.208242i	−0.0279947	−	0.0161627i
$167$	−10.3389	+	17.9075i	−0.800049	+	1.38572i	0.119535	+	0.992830i	$0.461860\pi$
$167$	−10.3389	+	17.9075i	−0.800049	+	1.38572i	−0.919583	+	0.392895i	$0.871474\pi$
$168$		0			0
$169$	−11.8567	−	5.33087i	−0.912056	−	0.410067i
$170$	−0.285831	+	0.651920i	−0.0219223	+	0.0500000i
$171$		0			0
$172$	3.31713	+	12.3797i	0.252929	+	0.943944i
$173$	−17.5278	−	4.69655i	−1.33261	−	0.357072i	−0.478924	−	0.877856i	$-0.658973\pi$
$173$	−17.5278	−	4.69655i	−1.33261	−	0.357072i	−0.853688	+	0.520784i	$0.825640\pi$
$174$		0			0
$175$	13.2741	+	4.14706i	1.00343	+	0.313489i
$176$	−4.09004	+	15.2642i	−0.308298	+	1.15058i
$177$		0			0
$178$	0.211694	−	0.790055i	0.0158672	−	0.0592171i
$179$	−8.68110	+	15.0361i	−0.648856	+	1.12385i	0.334540	+	0.942382i	$0.391419\pi$
$179$	−8.68110	+	15.0361i	−0.648856	+	1.12385i	−0.983396	+	0.181470i	$0.941914\pi$
$180$		0			0
$181$			24.9284i			1.85291i	0.376406	+	0.926455i	$0.377160\pi$
$181$			24.9284i			1.85291i	−0.376406	+	0.926455i	$0.622840\pi$
$182$	1.28748	+	0.276117i	0.0954341	+	0.0204672i
$183$		0			0
$184$	−4.02953	+	1.07971i	−0.297061	+	0.0795973i
$185$	−2.36425	+	15.4959i	−0.173823	+	1.13928i
$186$		0			0
$187$		−	9.83181i		−	0.718973i
$188$	−0.507958	−	0.879810i	−0.0370467	−	0.0641667i
$189$		0			0
$190$	−0.223918	+	0.510708i	−0.0162447	+	0.0370506i
$191$	3.39354	+	5.87779i	0.245548	+	0.425302i	0.962286	−	0.272041i	$-0.0876987\pi$
$191$	3.39354	+	5.87779i	0.245548	+	0.425302i	−0.716737	+	0.697343i	$0.754365\pi$
$192$		0			0
$193$	−1.03504	−	0.597582i	−0.0745040	−	0.0430149i	0.462285	−	0.886731i	$-0.347030\pi$
$193$	−1.03504	−	0.597582i	−0.0745040	−	0.0430149i	−0.536789	+	0.843716i	$0.680363\pi$
$194$	1.54543			0.110955
$195$		0			0
$196$	1.45937			0.104241
$197$	−17.4253	−	10.0605i	−1.24150	−	0.716780i	−0.272100	−	0.962269i	$-0.587718\pi$
$197$	−17.4253	−	10.0605i	−1.24150	−	0.716780i	−0.969399	+	0.245489i	$0.921051\pi$
$198$		0			0
$199$	−1.08885	−	1.88594i	−0.0771862	−	0.133690i	0.824849	−	0.565354i	$-0.191260\pi$
$199$	−1.08885	−	1.88594i	−0.0771862	−	0.133690i	−0.902035	+	0.431663i	$0.857927\pi$
$200$	−1.77154	−	1.92314i	−0.125267	−	0.135987i
$201$		0			0
$202$	−0.0662412	−	0.114733i	−0.00466071	−	0.00807259i
$203$			12.7363i			0.893912i
$204$		0			0
$205$	−8.50458	−	11.5669i	−0.593986	−	0.807870i
$206$	−1.07618	+	0.288362i	−0.0749810	+	0.0200911i
$207$		0			0
$208$	10.4242	+	9.42052i	0.722792	+	0.653196i
$209$		−	7.70215i		−	0.532769i
$210$		0			0
$211$	9.97642	−	17.2797i	0.686805	−	1.18958i	−0.286061	−	0.958211i	$-0.592346\pi$
$211$	9.97642	−	17.2797i	0.686805	−	1.18958i	0.972866	−	0.231370i	$-0.0743208\pi$
$212$	0.962781	−	3.59315i	0.0661240	−	0.246778i
$213$		0			0
$214$	0.168410	−	0.628516i	0.0115123	−	0.0429645i
$215$	14.3658	−	1.59238i	0.979740	−	0.108600i
$216$		0			0
$217$	14.7171	+	3.94345i	0.999064	+	0.267698i
$218$	−0.312872	−	1.16765i	−0.0211904	−	0.0790835i
$219$		0			0
$220$	16.4661	+	7.21950i	1.11015	+	0.486738i
$221$	−7.78152	−	3.98278i	−0.523442	−	0.267911i
$222$		0			0
$223$	−6.70672	+	11.6164i	−0.449115	+	0.777891i	−0.998329	−	0.0577915i	$-0.981594\pi$
$223$	−6.70672	+	11.6164i	−0.449115	+	0.777891i	0.549213	+	0.835682i	$0.314927\pi$
$224$	−3.75176	−	2.16608i	−0.250675	−	0.144727i
$225$		0			0
$226$	−0.696612	+	0.696612i	−0.0463380	+	0.0463380i
$227$	12.7144	−	7.34064i	0.843882	−	0.487215i	−0.0147000	−	0.999892i	$-0.504679\pi$
$227$	12.7144	−	7.34064i	0.843882	−	0.487215i	0.858582	+	0.512677i	$0.171346\pi$
$228$		0			0
$229$	2.65280	−	2.65280i	0.175302	−	0.175302i	−0.614002	−	0.789304i	$-0.710442\pi$
$229$	2.65280	−	2.65280i	0.175302	−	0.175302i	0.789304	+	0.614002i	$0.210442\pi$
$230$	0.258035	+	2.32788i	0.0170143	+	0.153496i
$231$		0			0
$232$	1.19732	−	2.07382i	0.0786081	−	0.136153i
$233$	13.9459	−	13.9459i	0.913629	−	0.913629i	−0.0829267	−	0.996556i	$-0.526427\pi$
$233$	13.9459	−	13.9459i	0.913629	−	0.913629i	0.996556	+	0.0829267i	$0.0264267\pi$
$234$		0			0
$235$	−1.06726	+	0.416648i	−0.0696205	+	0.0271791i
$236$	1.34768	+	5.02962i	0.0877266	+	0.327400i
$237$		0			0
$238$	0.855249	+	0.229163i	0.0554376	+	0.0148545i
$239$	10.1890	+	10.1890i	0.659074	+	0.659074i	0.955161	−	0.296087i	$-0.0956818\pi$
$239$	10.1890	+	10.1890i	0.659074	+	0.659074i	−0.296087	+	0.955161i	$0.595682\pi$
$240$		0			0
$241$	−2.09750	+	7.82799i	−0.135112	+	0.504245i	0.864885	+	0.501970i	$0.167391\pi$
$241$	−2.09750	+	7.82799i	−0.135112	+	0.504245i	−0.999997	+	0.00227574i	$0.999276\pi$
$242$	0.714943			0.0459582
$243$		0			0
$244$	1.27247	−	2.20398i	0.0814615	−	0.141095i
$245$	0.248233	−	1.62698i	0.0158590	−	0.103944i
$246$		0			0
$247$	−6.09597	−	3.12007i	−0.387877	−	0.198525i
$248$	−2.02564	−	2.02564i	−0.128628	−	0.128628i
$249$		0			0
$250$	−1.21738	+	0.820378i	−0.0769942	+	0.0518853i
$251$	4.04904	−	2.33771i	0.255573	−	0.147555i	−0.366740	−	0.930323i	$-0.619526\pi$
$251$	4.04904	−	2.33771i	0.255573	−	0.147555i	0.622313	+	0.782768i	$0.286193\pi$
$252$		0			0
$253$	−16.1749	−	28.0157i	−1.01690	−	1.76133i
$254$	−2.09884	−	0.562382i	−0.131693	−	0.0352870i
$255$		0			0
$256$	−7.31927	−	12.6773i	−0.457454	−	0.792334i
$257$	16.7639	−	4.49187i	1.04570	−	0.280195i	0.305227	−	0.952280i	$-0.401268\pi$
$257$	16.7639	−	4.49187i	1.04570	−	0.280195i	0.740474	+	0.672085i	$0.234601\pi$
$258$		0			0
$259$	19.4980			1.21154
$260$	12.3842	−	10.1078i	0.768038	−	0.626858i
$261$		0			0
$262$	1.44277	+	0.832984i	0.0891346	+	0.0514619i
$263$	2.33916	−	0.626777i	0.144239	−	0.0386487i	−0.185977	−	0.982554i	$-0.559545\pi$
$263$	2.33916	−	0.626777i	0.144239	−	0.0386487i	0.330216	+	0.943905i	$0.392878\pi$
$264$		0			0
$265$	−3.84207	−	1.68454i	−0.236016	−	0.103480i
$266$	0.669994	+	0.179524i	0.0410800	+	0.0110073i
$267$		0			0
$268$		−	7.17023i		−	0.437992i
$269$	8.42829	−	4.86608i	0.513882	−	0.296690i	−0.220546	−	0.975377i	$-0.570784\pi$
$269$	8.42829	−	4.86608i	0.513882	−	0.296690i	0.734428	+	0.678687i	$0.237451\pi$
$270$		0			0
$271$	−21.1708	+	5.67269i	−1.28603	+	0.344591i	−0.836152	−	0.548498i	$-0.815200\pi$
$271$	−21.1708	+	5.67269i	−1.28603	+	0.344591i	−0.449880	+	0.893089i	$0.648533\pi$
$272$	6.68061	+	6.68061i	0.405071	+	0.405071i
$273$		0			0
$274$		−	1.96233i		−	0.118548i
$275$	10.8495	−	17.1293i	0.654250	−	1.03294i
$276$		0			0
$277$	4.67325	−	17.4408i	0.280788	−	1.04792i	−0.671074	−	0.741390i	$-0.734167\pi$
$277$	4.67325	−	17.4408i	0.280788	−	1.04792i	0.951862	−	0.306526i	$-0.0991666\pi$
$278$	1.12556			0.0675067
$279$		0			0
$280$	−2.03241	+	2.53915i	−0.121460	+	0.151743i
$281$	−11.3739	−	11.3739i	−0.678510	−	0.678510i	0.281153	−	0.959663i	$-0.409283\pi$
$281$	−11.3739	−	11.3739i	−0.678510	−	0.678510i	−0.959663	+	0.281153i	$0.909283\pi$
$282$		0			0
$283$	2.93892	+	10.9682i	0.174700	+	0.651991i	0.996602	+	0.0823620i	$0.0262464\pi$
$283$	2.93892	+	10.9682i	0.174700	+	0.651991i	−0.821902	+	0.569629i	$0.807087\pi$
$284$	−3.29818	−	12.3090i	−0.195711	−	0.730403i
$285$		0			0
$286$	0.874701	−	1.70899i	0.0517222	−	0.101054i
$287$	−12.6276	+	12.6276i	−0.745384	+	0.745384i
$288$		0			0
$289$	9.63189	+	5.56098i	0.566582	+	0.327116i
$290$	−1.04961	−	0.840142i	−0.0616354	−	0.0493348i
$291$		0			0
$292$	17.0553	−	9.84688i	0.998086	−	0.576245i
$293$	−0.605883	+	0.349807i	−0.0353961	+	0.0204359i	−0.517594	−	0.855627i	$-0.673172\pi$
$293$	−0.605883	+	0.349807i	−0.0353961	+	0.0204359i	0.482198	+	0.876063i	$0.339839\pi$
$294$		0			0
$295$	5.83652	−	0.646952i	0.339815	−	0.0376670i
$296$	−3.17481	−	1.83298i	−0.184532	−	0.106540i
$297$		0			0
$298$	1.12725	−	1.12725i	0.0653001	−	0.0653001i
$299$	−28.7257	+	1.45292i	−1.66125	+	0.0840243i
$300$		0			0
$301$	−4.65320	−	17.3660i	−0.268206	−	1.00096i
$302$	0.0898718	+	0.335406i	0.00517154	+	0.0193004i
$303$		0			0
$304$	5.23352	+	5.23352i	0.300163	+	0.300163i
$305$	−2.24068	−	1.79351i	−0.128301	−	0.102696i
$306$		0			0
$307$	−14.2048			−0.810709			−0.405355	−	0.914159i	$-0.632852\pi$
$307$	−14.2048			−0.810709			−0.405355	+	0.914159i	$0.632852\pi$
$308$	5.78818	−	21.6018i	0.329812	−	1.23088i
$309$		0			0
$310$	−1.29579	+	0.952730i	−0.0735960	+	0.0541114i
$311$			21.4961i			1.21893i	0.792812	+	0.609466i	$0.208616\pi$
$311$			21.4961i			1.21893i	−0.792812	+	0.609466i	$0.791384\pi$
$312$		0			0
$313$	−9.36303	−	9.36303i	−0.529230	−	0.529230i	0.391113	−	0.920343i	$-0.372090\pi$
$313$	−9.36303	−	9.36303i	−0.529230	−	0.529230i	−0.920343	+	0.391113i	$0.872090\pi$
$314$	−1.85092	+	0.495953i	−0.104454	+	0.0279882i
$315$		0			0
$316$	14.3822	−	8.30357i	0.809062	−	0.467112i
$317$			17.3024i			0.971798i	0.874015	+	0.485899i	$0.161508\pi$
$317$			17.3024i			0.971798i	−0.874015	+	0.485899i	$0.838492\pi$
$318$		0			0
$319$	17.9368	+	4.80615i	1.00427	+	0.269093i
$320$	−15.8081	+	6.17130i	−0.883697	+	0.344986i
$321$		0			0
$322$	2.81404	−	0.754019i	0.156820	−	0.0420198i
$323$	−3.98788	−	2.30240i	−0.221892	−	0.128109i
$324$		0			0
$325$	−9.16219	−	15.5259i	−0.508227	−	0.861223i
$326$	2.45476			0.135957
$327$		0			0
$328$	3.24323	−	0.869022i	0.179078	−	0.0479837i
$329$	0.712553	+	1.23418i	0.0392843	+	0.0680424i
$330$		0			0
$331$	17.3574	+	4.65090i	0.954049	+	0.255637i	0.702079	−	0.712099i	$-0.252255\pi$
$331$	17.3574	+	4.65090i	0.954049	+	0.255637i	0.251969	+	0.967735i	$0.418922\pi$
$332$	3.14460	+	5.44661i	0.172582	+	0.298921i
$333$		0			0
$334$	−2.35130	+	1.35753i	−0.128658	+	0.0742805i
$335$	−7.99376	−	1.21963i	−0.436746	−	0.0666353i
$336$		0			0
$337$	4.83668	+	4.83668i	0.263471	+	0.263471i	0.826462	−	0.562992i	$-0.190350\pi$
$337$	4.83668	+	4.83668i	0.263471	+	0.263471i	−0.562992	+	0.826462i	$0.690350\pi$
$338$	−0.998266	−	1.38459i	−0.0542985	−	0.0753117i
$339$		0			0
$340$	8.66020	−	6.36741i	0.469665	−	0.345321i
$341$	11.1073	−	19.2384i	0.601493	−	1.04182i
$342$		0			0
$343$	17.4224			0.940723
$344$	−0.874884	+	3.26511i	−0.0471706	+	0.176043i
$345$		0			0
$346$	−1.68477	−	1.68477i	−0.0905740	−	0.0905740i
$347$	17.9682	+	4.81456i	0.964582	+	0.258459i	0.706539	−	0.707674i	$-0.250256\pi$
$347$	17.9682	+	4.81456i	0.964582	+	0.258459i	0.258043	+	0.966133i	$0.416922\pi$
$348$		0			0
$349$	0.651455	+	2.43126i	0.0348716	+	0.130143i	0.981167	−	0.193160i	$-0.0618736\pi$
$349$	0.651455	+	2.43126i	0.0348716	+	0.130143i	−0.946296	+	0.323302i	$0.895207\pi$
$350$	1.23716	+	1.34303i	0.0661290	+	0.0717881i
$351$		0			0
$352$	−4.46629	+	4.46629i	−0.238054	+	0.238054i
$353$	−16.3608	+	28.3377i	−0.870795	+	1.50826i	−0.00962005	+	0.999954i	$0.503062\pi$
$353$	−16.3608	+	28.3377i	−0.870795	+	1.50826i	−0.861175	+	0.508308i	$0.830271\pi$
$354$		0			0
$355$	−14.2837	+	1.58329i	−0.758101	+	0.0840320i
$356$	−8.73364	+	8.73364i	−0.462882	+	0.462882i
$357$		0			0
$358$	−1.97428	+	1.13985i	−0.104344	+	0.0602430i
$359$	0.699684	−	0.699684i	0.0369279	−	0.0369279i	−0.688402	−	0.725330i	$-0.741687\pi$
$359$	0.699684	−	0.699684i	0.0369279	−	0.0369279i	0.725330	+	0.688402i	$0.241687\pi$
$360$		0			0
$361$	13.3304	+	7.69632i	0.701601	+	0.405069i
$362$	−1.63658	+	2.83464i	−0.0860167	+	0.148985i
$363$		0			0
$364$	−14.7523	−	13.3318i	−0.773231	−	0.698778i
$365$	−8.07680	−	20.6891i	−0.422759	−	1.08292i
$366$		0			0
$367$	3.74601	+	13.9803i	0.195540	+	0.729767i	0.992126	+	0.125241i	$0.0399705\pi$
$367$	3.74601	+	13.9803i	0.195540	+	0.729767i	−0.796586	+	0.604525i	$0.793363\pi$
$368$	30.0270	+	8.04571i	1.56526	+	0.419411i
$369$		0			0
$370$	−1.28617	+	1.60685i	−0.0668649	+	0.0835361i
$371$	−1.35057	+	5.04039i	−0.0701180	+	0.261684i
$372$		0			0
$373$	−2.62454	+	9.79493i	−0.135894	+	0.507162i	0.864099	+	0.503322i	$0.167889\pi$
$373$	−2.62454	+	9.79493i	−0.135894	+	0.507162i	−0.999993	+	0.00384023i	$0.998778\pi$
$374$	0.645471	−	1.11799i	0.0333765	−	0.0578098i
$375$		0			0
$376$		−	0.267945i		−	0.0138182i
$377$	11.0699	−	12.2494i	0.570130	−	0.630876i
$378$		0			0
$379$	1.01470	−	0.271887i	0.0521215	−	0.0139659i	−0.232664	−	0.972557i	$-0.574744\pi$
$379$	1.01470	−	0.271887i	0.0521215	−	0.0139659i	0.284786	+	0.958591i	$0.408078\pi$
$380$	6.78432	−	4.98817i	0.348028	−	0.255887i
$381$		0			0
$382$			0.891162i			0.0455958i
$383$	−6.00353	−	10.3984i	−0.306766	−	0.531334i	0.670887	−	0.741560i	$-0.265914\pi$
$383$	−6.00353	−	10.3984i	−0.306766	−	0.531334i	−0.977653	+	0.210225i	$0.932580\pi$
$384$		0			0
$385$	−23.0983	−	10.1274i	−1.17720	−	0.516138i
$386$	−0.0784640	−	0.135904i	−0.00399371	−	0.00691732i
$387$		0			0
$388$	−20.2105	−	11.6685i	−1.02603	−	0.592380i
$389$	−7.37166			−0.373758			−0.186879	−	0.982383i	$-0.559837\pi$
$389$	−7.37166			−0.373758			−0.186879	+	0.982383i	$0.559837\pi$
$390$		0			0
$391$	−19.3406			−0.978097
$392$	0.333337	+	0.192452i	0.0168361	+	0.00972030i
$393$		0			0
$394$	−1.32097	−	2.28798i	−0.0665494	−	0.115267i
$395$	−6.81091	−	17.4465i	−0.342694	−	0.877826i
$396$		0			0
$397$	−3.02739	−	5.24359i	−0.151940	−	0.263168i	0.780001	−	0.625779i	$-0.215219\pi$
$397$	−3.02739	−	5.24359i	−0.151940	−	0.263168i	−0.931941	+	0.362611i	$0.881885\pi$
$398$		−	0.285937i		−	0.0143327i
$399$		0			0
$400$	4.26706	+	19.0113i	0.213353	+	0.950565i
$401$	2.33226	−	0.624928i	0.116468	−	0.0312074i	−0.200114	−	0.979773i	$-0.564131\pi$
$401$	2.33226	−	0.624928i	0.116468	−	0.0312074i	0.316582	+	0.948565i	$0.397465\pi$
$402$		0			0
$403$	−10.7270	−	16.5843i	−0.534350	−	0.826123i
$404$			2.00058i			0.0995324i
$405$		0			0
$406$	−0.836154	+	1.44826i	−0.0414976	+	0.0718760i
$407$	7.35772	−	27.4594i	0.364709	−	1.36111i
$408$		0			0
$409$	5.21187	−	19.4510i	0.257710	−	0.961788i	−0.708852	−	0.705357i	$-0.750787\pi$
$409$	5.21187	−	19.4510i	0.257710	−	0.961788i	0.966563	−	0.256431i	$-0.0825466\pi$
$410$	−0.207683	−	1.87363i	−0.0102567	−	0.0925319i
$411$		0			0
$412$	16.2511	+	4.35446i	0.800632	+	0.214529i
$413$	−1.89050	−	7.05543i	−0.0930253	−	0.347175i
$414$		0			0
$415$	6.60706	−	2.57933i	0.324328	−	0.126614i
$416$	1.72565	+	5.34416i	0.0846071	+	0.262019i
$417$		0			0
$418$	0.505656	−	0.875822i	0.0247324	−	0.0428378i
$419$	26.0503	+	15.0401i	1.27264	+	0.734759i	0.975484	−	0.220070i	$-0.0706287\pi$
$419$	26.0503	+	15.0401i	1.27264	+	0.734759i	0.297156	+	0.954829i	$0.403962\pi$
$420$		0			0
$421$	9.24685	−	9.24685i	0.450664	−	0.450664i	−0.444911	−	0.895575i	$-0.646765\pi$
$421$	9.24685	−	9.24685i	0.450664	−	0.450664i	0.895575	+	0.444911i	$0.146765\pi$
$422$	2.26887	−	1.30993i	0.110447	−	0.0637664i
$423$		0			0
$424$	0.693751	−	0.693751i	0.0336915	−	0.0336915i
$425$	−5.62567	−	10.7379i	−0.272885	−	0.520866i
$426$		0			0
$427$	−1.78499	+	3.09170i	−0.0863818	+	0.149618i
$428$	−6.94792	+	6.94792i	−0.335840	+	0.335840i
$429$		0			0
$430$	1.73810	+	0.762061i	0.0838185	+	0.0367499i
$431$	1.63348	+	6.09624i	0.0786821	+	0.293646i	0.994043	−	0.108989i	$-0.0347613\pi$
$431$	1.63348	+	6.09624i	0.0786821	+	0.293646i	−0.915361	+	0.402634i	$0.868095\pi$
$432$		0			0
$433$	11.8706	+	3.18071i	0.570463	+	0.152855i	0.532509	−	0.846424i	$-0.321249\pi$
$433$	11.8706	+	3.18071i	0.570463	+	0.152855i	0.0379543	+	0.999279i	$0.487916\pi$
$434$	1.41461	+	1.41461i	0.0679036	+	0.0679036i
$435$		0			0
$436$	−4.72458	+	17.6324i	−0.226266	+	0.844438i
$437$	−15.1513			−0.724783
$438$		0			0
$439$	−17.2223	+	29.8300i	−0.821977	+	1.42371i	0.0822306	+	0.996613i	$0.473796\pi$
$439$	−17.2223	+	29.8300i	−0.821977	+	1.42371i	−0.904208	+	0.427093i	$0.859538\pi$
$440$	2.80899	+	3.82046i	0.133913	+	0.182133i
$441$		0			0
$442$	−0.623373	−	0.963754i	−0.0296508	−	0.0458411i
$443$	5.39452	+	5.39452i	0.256301	+	0.256301i	0.823548	−	0.567247i	$-0.191991\pi$
$443$	5.39452	+	5.39452i	0.256301	+	0.256301i	−0.567247	+	0.823548i	$0.691991\pi$
$444$		0			0
$445$	8.25118	+	11.2223i	0.391143	+	0.531987i
$446$	−1.52526	+	0.880610i	−0.0722232	+	0.0416981i
$447$		0			0
$448$	10.5542	+	18.2804i	0.498639	+	0.863668i
$449$	30.0741	+	8.05832i	1.41928	+	0.380296i	0.885229	−	0.465155i	$-0.154002\pi$
$449$	30.0741	+	8.05832i	1.41928	+	0.380296i	0.534053	+	0.845451i	$0.320668\pi$
$450$		0			0
$451$	13.0186	+	22.5489i	0.613021	+	1.06178i
$452$	14.3697	−	3.85034i	0.675892	−	0.181105i
$453$		0			0
$454$	1.92769			0.0904710
$455$	−17.3724	+	14.1790i	−0.814428	+	0.664721i
$456$		0			0
$457$	−2.69118	−	1.55375i	−0.125888	−	0.0726814i	0.435734	−	0.900076i	$-0.356489\pi$
$457$	−2.69118	−	1.55375i	−0.125888	−	0.0726814i	−0.561622	+	0.827394i	$0.689822\pi$
$458$	0.475812	−	0.127494i	0.0222333	−	0.00595738i
$459$		0			0
$460$	14.2018	−	32.3913i	0.662163	−	1.51025i
$461$	16.1274	+	4.32132i	0.751126	+	0.201264i	0.614018	−	0.789292i	$-0.289552\pi$
$461$	16.1274	+	4.32132i	0.751126	+	0.201264i	0.137109	+	0.990556i	$0.456219\pi$
$462$		0			0
$463$			15.6396i			0.726832i	0.931627	+	0.363416i	$0.118390\pi$
$463$			15.6396i			0.726832i	−0.931627	+	0.363416i	$0.881610\pi$
$464$	−15.4536	+	8.92212i	−0.717414	+	0.414199i
$465$		0			0
$466$	2.50138	−	0.670243i	0.115874	−	0.0310484i
$467$	−15.0821	−	15.0821i	−0.697916	−	0.697916i	0.266045	−	0.963961i	$-0.414283\pi$
$467$	−15.0821	−	15.0821i	−0.697916	−	0.697916i	−0.963961	+	0.266045i	$0.914283\pi$
$468$		0			0
$469$			10.0582i			0.464447i
$470$	−0.148713	−	0.0226895i	−0.00685963	−	0.00104659i
$471$		0			0
$472$	−0.355447	+	1.32655i	−0.0163608	+	0.0610592i
$473$	−26.2128			−1.20527
$474$		0			0
$475$	−4.40709	−	8.41199i	−0.202211	−	0.385969i
$476$	−9.45433	−	9.45433i	−0.433339	−	0.433339i
$477$		0			0
$478$	0.489686	+	1.82753i	0.0223977	+	0.0835894i
$479$	11.0386	+	41.1964i	0.504364	+	1.88231i	0.469522	+	0.882921i	$0.344426\pi$
$479$	11.0386	+	41.1964i	0.504364	+	1.88231i	0.0348421	+	0.999393i	$0.488907\pi$
$480$		0			0
$481$	−18.7526	−	16.9469i	−0.855043	−	0.772713i
$482$	−0.752428	+	0.752428i	−0.0342722	+	0.0342722i
$483$		0			0
$484$	−9.34972	−	5.39806i	−0.424987	−	0.245366i
$485$	−16.4464	+	20.5470i	−0.746794	+	0.932990i
$486$		0			0
$487$	13.1780	−	7.60834i	0.597154	−	0.344767i	−0.170767	−	0.985311i	$-0.554625\pi$
$487$	13.1780	−	7.60834i	0.597154	−	0.344767i	0.767921	+	0.640545i	$0.221291\pi$
$488$	0.581293	−	0.335610i	0.0263139	−	0.0151923i
$489$		0			0
$490$	0.135041	−	0.168710i	0.00610051	−	0.00762154i
$491$	−24.2273	−	13.9876i	−1.09336	−	0.631254i	−0.158894	−	0.987296i	$-0.550793\pi$
$491$	−24.2273	−	13.9876i	−1.09336	−	0.631254i	−0.934470	+	0.356042i	$0.884126\pi$
$492$		0			0
$493$	7.85029	−	7.85029i	0.353559	−	0.353559i
$494$	−0.488345	−	0.754996i	−0.0219717	−	0.0339689i
$495$		0			0
$496$	5.52498	+	20.6195i	0.248079	+	0.925844i
$497$	4.62661	+	17.2668i	0.207532	+	0.774520i
$498$		0			0
$499$	−1.67479	−	1.67479i	−0.0749740	−	0.0749740i	0.668625	−	0.743599i	$-0.266883\pi$
$499$	−1.67479	−	1.67479i	−0.0749740	−	0.0749740i	−0.743599	+	0.668625i	$0.766883\pi$
$500$	22.1146	−	1.53689i	0.988994	−	0.0687317i
$501$		0			0
$502$	0.613896			0.0273995
$503$	−5.99415	+	22.3705i	−0.267266	+	0.997451i	0.693583	+	0.720377i	$0.256031\pi$
$503$	−5.99415	+	22.3705i	−0.267266	+	0.997451i	−0.960849	+	0.277073i	$0.910635\pi$
$504$		0			0
$505$	2.23035	+	0.340289i	0.0992493	+	0.0151427i
$506$		−	4.24760i		−	0.188829i
$507$		0			0
$508$	23.2016	+	23.2016i	1.02940	+	1.02940i
$509$	−5.82068	+	1.55965i	−0.257997	+	0.0691301i	−0.385499	−	0.922708i	$-0.625971\pi$
$509$	−5.82068	+	1.55965i	−0.257997	+	0.0691301i	0.127502	+	0.991838i	$0.459304\pi$
$510$		0			0
$511$	−23.9248	+	13.8130i	−1.05837	+	0.611051i
$512$		−	10.1453i		−	0.448362i
$513$		0			0
$514$	2.20114	+	0.589794i	0.0970881	+	0.0260147i
$515$	7.61882	−	17.3769i	0.335725	−	0.765717i
$516$		0			0
$517$	2.00701	−	0.537776i	0.0882681	−	0.0236514i
$518$	2.21714	+	1.28007i	0.0974155	+	0.0562429i
$519$		0			0
$520$	4.16165	−	0.675580i	0.182501	−	0.0296261i
$521$	−27.8183			−1.21874			−0.609371	−	0.792886i	$-0.708578\pi$
$521$	−27.8183			−1.21874			−0.609371	+	0.792886i	$0.708578\pi$
$522$		0			0
$523$	0.529059	−	0.141761i	0.0231341	−	0.00619877i	−0.247233	−	0.968956i	$-0.579521\pi$
$523$	0.529059	−	0.141761i	0.0231341	−	0.00619877i	0.270368	+	0.962757i	$0.412855\pi$
$524$	−12.5786	−	21.7868i	−0.549500	−	0.951762i
$525$		0			0
$526$	0.307138	+	0.0822974i	0.0133919	+	0.00358834i
$527$	−6.64060	−	11.5019i	−0.289269	−	0.501029i
$528$		0			0
$529$	−35.1924	+	20.3183i	−1.53010	+	0.883406i
$530$	−0.326295	−	0.443788i	−0.0141733	−	0.0192769i
$531$		0			0
$532$	−7.40643	−	7.40643i	−0.321110	−	0.321110i
$533$	23.1203	−	1.16940i	1.00145	−	0.0506524i
$534$		0			0
$535$	6.56410	+	8.92772i	0.283791	+	0.385979i
$536$	0.945563	−	1.63776i	0.0408421	−	0.0707406i
$537$		0			0
$538$	1.27786			0.0550923
$539$	−0.772518	+	2.88308i	−0.0332747	+	0.124183i
$540$		0			0
$541$	−29.7507	−	29.7507i	−1.27908	−	1.27908i	−0.941182	−	0.337899i	$-0.890284\pi$
$541$	−29.7507	−	29.7507i	−1.27908	−	1.27908i	−0.337899	−	0.941182i	$-0.609716\pi$
$542$	−2.77978	−	0.744839i	−0.119402	−	0.0319936i
$543$		0			0
$544$	0.977367	+	3.64758i	0.0419043	+	0.156389i
$545$	18.8539	+	8.26641i	0.807612	+	0.354094i
$546$		0			0
$547$	−14.2594	+	14.2594i	−0.609688	+	0.609688i	−0.942864	−	0.333176i	$-0.891880\pi$
$547$	−14.2594	+	14.2594i	−0.609688	+	0.609688i	0.333176	+	0.942864i	$0.391880\pi$
$548$	−14.8162	+	25.6625i	−0.632919	+	1.09625i
$549$		0			0
$550$	2.35827	−	1.23551i	0.100557	−	0.0526825i
$551$	6.14984	−	6.14984i	0.261992	−	0.261992i
$552$		0			0
$553$	−20.1750	+	11.6481i	−0.857930	+	0.495326i
$554$	1.67641	−	1.67641i	0.0712240	−	0.0712240i
$555$		0			0
$556$	−14.7196	−	8.49837i	−0.624251	−	0.360411i
$557$	17.5886	−	30.4644i	0.745254	−	1.29082i	−0.204822	−	0.978799i	$-0.565662\pi$
$557$	17.5886	−	30.4644i	0.745254	−	1.29082i	0.950076	−	0.312018i	$-0.101005\pi$
$558$		0			0
$559$	−10.6186	+	20.7465i	−0.449118	+	0.877483i
$560$	22.5765	−	8.81362i	0.954030	−	0.372443i
$561$		0			0
$562$	−0.546631	−	2.04005i	−0.0230582	−	0.0860545i
$563$	40.5028	+	10.8527i	1.70699	+	0.457387i	0.974684	−	0.223589i	$-0.0717773\pi$
$563$	40.5028	+	10.8527i	1.70699	+	0.457387i	0.732306	+	0.680975i	$0.238444\pi$
$564$		0			0
$565$	−1.84835	−	16.6750i	−0.0777607	−	0.701523i
$566$	−0.385887	+	1.44015i	−0.0162201	+	0.0605341i
$567$		0			0
$568$	0.869884	−	3.24645i	0.0364995	−	0.136218i
$569$	−13.7741	+	23.8575i	−0.577441	+	1.00016i	0.418331	+	0.908295i	$0.362615\pi$
$569$	−13.7741	+	23.8575i	−0.577441	+	1.00016i	−0.995772	+	0.0918621i	$0.970718\pi$
$570$		0			0
$571$		−	4.72029i		−	0.197538i	−0.995110	−	0.0987690i	$-0.968510\pi$
$571$		−	4.72029i		−	0.197538i	0.995110	−	0.0987690i	$-0.0314905\pi$
$572$	−24.3424	+	15.7451i	−1.01781	+	0.658335i
$573$		0			0
$574$	−2.26492	+	0.606884i	−0.0945360	+	0.0253308i
$575$	−33.6959	−	21.3426i	−1.40521	−	0.890046i
$576$		0			0
$577$		−	6.73701i		−	0.280465i	−0.990119	−	0.140233i	$-0.955215\pi$
$577$		−	6.73701i		−	0.280465i	0.990119	−	0.140233i	$-0.0447851\pi$
$578$	0.730170	+	1.26469i	0.0303711	+	0.0526043i
$579$		0			0
$580$	7.38303	+	18.9120i	0.306564	+	0.785276i
$581$	−4.41118	−	7.64038i	−0.183006	−	0.316977i
$582$		0			0
$583$	6.58884	+	3.80407i	0.272882	+	0.157548i
$584$	5.19417			0.214936
$585$		0			0
$586$	−0.0918611			−0.00379475
$587$	4.49847	+	2.59719i	0.185672	+	0.107198i	0.589955	−	0.807436i	$-0.299146\pi$
$587$	4.49847	+	2.59719i	0.185672	+	0.107198i	−0.404283	+	0.914634i	$0.632479\pi$
$588$		0			0
$589$	−5.20218	−	9.01044i	−0.214352	−	0.371269i
$590$	0.706152	+	0.309609i	0.0290718	+	0.0127464i
$591$		0			0
$592$	13.6589	+	23.6578i	0.561375	+	0.972331i
$593$			12.9267i			0.530836i	0.964133	+	0.265418i	$0.0855100\pi$
$593$			12.9267i			0.530836i	−0.964133	+	0.265418i	$0.914490\pi$
$594$		0			0
$595$	−12.1483	+	8.93206i	−0.498033	+	0.366179i
$596$	−23.2529	+	6.23060i	−0.952477	+	0.255215i
$597$		0			0
$598$	−3.36182	−	1.72067i	−0.137475	−	0.0703633i
$599$			16.7523i			0.684481i	0.939612	+	0.342241i	$0.111186\pi$
$599$			16.7523i			0.684481i	−0.939612	+	0.342241i	$0.888814\pi$
$600$		0			0
$601$	−6.28803	+	10.8912i	−0.256494	+	0.444261i	−0.965300	−	0.261142i	$-0.915901\pi$
$601$	−6.28803	+	10.8912i	−0.256494	+	0.444261i	0.708806	+	0.705403i	$0.249234\pi$
$602$	0.610977	−	2.28020i	0.0249016	−	0.0929340i
$603$		0			0
$604$	1.35713	−	5.06486i	0.0552207	−	0.206086i
$605$	−7.60840	+	9.50539i	−0.309325	+	0.386449i
$606$		0			0
$607$	−36.1909	−	9.69731i	−1.46894	−	0.393602i	−0.566374	−	0.824149i	$-0.691654\pi$
$607$	−36.1909	−	9.69731i	−1.46894	−	0.393602i	−0.902568	+	0.430547i	$0.858321\pi$
$608$	0.765660	+	2.85748i	0.0310516	+	0.115886i
$609$		0			0
$610$	−0.137044	−	0.351045i	−0.00554877	−	0.0142134i
$611$	0.387390	−	1.80632i	0.0156721	−	0.0730760i
$612$		0			0
$613$	−8.64732	+	14.9776i	−0.349262	+	0.604940i	−0.986119	−	0.166043i	$-0.946901\pi$
$613$	−8.64732	+	14.9776i	−0.349262	+	0.604940i	0.636856	+	0.770982i	$0.280234\pi$
$614$	−1.61524	−	0.932562i	−0.0651860	−	0.0376351i
$615$		0			0
$616$	4.17079	−	4.17079i	0.168046	−	0.168046i
$617$	10.5136	−	6.07005i	0.423263	−	0.244371i	−0.273210	−	0.961955i	$-0.588085\pi$
$617$	10.5136	−	6.07005i	0.423263	−	0.244371i	0.696472	+	0.717584i	$0.254752\pi$
$618$		0			0
$619$	−2.99993	+	2.99993i	−0.120577	+	0.120577i	−0.764821	−	0.644243i	$-0.777172\pi$
$619$	−2.99993	+	2.99993i	−0.120577	+	0.120577i	0.644243	+	0.764821i	$0.277172\pi$
$620$	24.1393	−	2.67573i	0.969456	−	0.107460i
$621$		0			0
$622$	−1.41125	+	2.44435i	−0.0565858	+	0.0980095i
$623$	12.2514	−	12.2514i	0.490840	−	0.490840i
$624$		0			0
$625$	2.04819	−	24.9160i	0.0819276	−	0.996638i
$626$	−0.449988	−	1.67938i	−0.0179851	−	0.0671215i
$627$		0			0
$628$	27.9502	+	7.48923i	1.11533	+	0.298853i
$629$	−12.0180	−	12.0180i	−0.479188	−	0.479188i
$630$		0			0
$631$	5.60031	−	20.9006i	0.222945	−	0.832041i	−0.760273	−	0.649604i	$-0.774935\pi$
$631$	5.60031	−	20.9006i	0.222945	−	0.832041i	0.983218	−	0.182437i	$-0.0583986\pi$
$632$	4.38008			0.174230
$633$		0			0
$634$	−1.13592	+	1.96748i	−0.0451133	+	0.0781385i
$635$	29.8128	−	21.9199i	1.18309	−	0.869863i
$636$		0			0
$637$	1.96891	+	1.77933i	0.0780111	+	0.0704996i
$638$	1.72409	+	1.72409i	0.0682572	+	0.0682572i
$639$		0			0
$640$	−9.08865	−	1.38667i	−0.359260	−	0.0548131i
$641$	−39.2467	+	22.6591i	−1.55015	+	0.894980i	−0.552022	+	0.833829i	$0.686144\pi$
$641$	−39.2467	+	22.6591i	−1.55015	+	0.894980i	−0.998129	+	0.0611509i	$0.980523\pi$
$642$		0			0
$643$	15.8249	+	27.4095i	0.624072	+	1.08092i	0.988719	+	0.149779i	$0.0478562\pi$
$643$	15.8249	+	27.4095i	0.624072	+	1.08092i	−0.364647	+	0.931146i	$0.618810\pi$
$644$	−42.4939	−	11.3862i	−1.67449	−	0.448679i
$645$		0			0
$646$	−0.302312	−	0.523619i	−0.0118943	−	0.0206015i
$647$	−36.6924	+	9.83169i	−1.44253	+	0.386524i	−0.893418	−	0.449227i	$-0.851699\pi$
$647$	−36.6924	+	9.83169i	−1.44253	+	0.386524i	−0.549109	+	0.835751i	$0.685033\pi$
$648$		0			0
$649$	−10.6497			−0.418038
$650$	−0.0225488	−	2.36698i	−0.000884437	−	0.0928407i
$651$		0			0
$652$	−32.1023	−	18.5343i	−1.25722	−	0.725858i
$653$	2.66385	−	0.713775i	0.104244	−	0.0279322i	−0.206320	−	0.978485i	$-0.566149\pi$
$653$	2.66385	−	0.713775i	0.104244	−	0.0279322i	0.310564	+	0.950552i	$0.399482\pi$
$654$		0			0
$655$	−26.4287	+	10.3175i	−1.03265	+	0.403138i
$656$	−24.1677	−	6.47571i	−0.943590	−	0.252834i
$657$		0			0
$658$			0.187120i			0.00729470i
$659$	−1.80219	+	1.04050i	−0.0702034	+	0.0405320i	−0.534691	−	0.845048i	$-0.679572\pi$
$659$	−1.80219	+	1.04050i	−0.0702034	+	0.0405320i	0.464487	+	0.885580i	$0.346239\pi$
$660$		0			0
$661$	36.3010	−	9.72683i	1.41195	−	0.378330i	0.529326	−	0.848418i	$-0.322445\pi$
$661$	36.3010	−	9.72683i	1.41195	−	0.378330i	0.882619	+	0.470089i	$0.155778\pi$
$662$	1.66840	+	1.66840i	0.0648440	+	0.0648440i
$663$		0			0
$664$			1.65876i			0.0643723i
$665$	−9.51689	+	6.99729i	−0.369049	+	0.271343i
$666$		0			0
$667$	9.45440	−	35.2843i	0.366076	−	1.36621i
$668$	40.9991			1.58630
$669$		0			0
$670$	−0.828912	−	0.663486i	−0.0320237	−	0.0256327i
$671$	3.68052	+	3.68052i	0.142085	+	0.142085i
$672$		0			0
$673$	−4.65984	−	17.3908i	−0.179624	−	0.670364i	−0.995718	−	0.0924454i	$-0.970532\pi$
$673$	−4.65984	−	17.3908i	−0.179624	−	0.670364i	0.816094	−	0.577919i	$-0.196135\pi$
$674$	0.232451	+	0.867519i	0.00895368	+	0.0334156i
$675$		0			0
$676$	2.60078	+	25.6443i	0.100030	+	0.986320i
$677$	−15.4021	+	15.4021i	−0.591952	+	0.591952i	−0.938158	−	0.346206i	$-0.887470\pi$
$677$	−15.4021	+	15.4021i	−0.591952	+	0.591952i	0.346206	+	0.938158i	$0.387470\pi$
$678$		0			0
$679$	28.3508	+	16.3684i	1.08801	+	0.628160i
$680$	2.81778	−	0.312338i	0.108057	−	0.0119776i
$681$		0			0
$682$	2.52605	−	1.45841i	0.0967273	−	0.0558455i
$683$	5.34122	−	3.08376i	0.204376	−	0.117997i	−0.394319	−	0.918974i	$-0.629019\pi$
$683$	5.34122	−	3.08376i	0.204376	−	0.117997i	0.598695	+	0.800977i	$0.295686\pi$
$684$		0			0
$685$	26.0897	+	20.8830i	0.996838	+	0.797900i
$686$	1.98113	+	1.14381i	0.0756398	+	0.0436707i
$687$		0			0
$688$	17.8113	−	17.8113i	0.679050	−	0.679050i
$689$	5.67986	−	3.67383i	0.216385	−	0.139962i
$690$		0			0
$691$	3.39841	+	12.6830i	0.129282	+	0.482486i	0.999956	−	0.00937405i	$-0.00298390\pi$
$691$	3.39841	+	12.6830i	0.129282	+	0.482486i	−0.870674	+	0.491860i	$0.836317\pi$
$692$	9.31214	+	34.7534i	0.353994	+	1.32112i
$693$		0			0
$694$	1.72710	+	1.72710i	0.0655600	+	0.0655600i
$695$	−11.9782	+	14.9647i	−0.454359	+	0.567643i
$696$		0			0
$697$	15.5666			0.589627
$698$	−0.0855377	+	0.319231i	−0.00323765	+	0.0120831i
$699$		0			0
$700$	−6.03870	−	26.9046i	−0.228241	−	1.01690i
$701$			23.2292i			0.877354i	0.898645	+	0.438677i	$0.144553\pi$
$701$			23.2292i			0.877354i	−0.898645	+	0.438677i	$0.855447\pi$
$702$		0			0
$703$	−9.41478	−	9.41478i	−0.355085	−	0.355085i
$704$	29.7274	−	7.96543i	1.12039	−	0.300208i
$705$		0			0
$706$	−3.72081	+	2.14821i	−0.140034	+	0.0808490i
$707$		−	2.80636i		−	0.105544i
$708$		0			0
$709$	2.00482	+	0.537189i	0.0752925	+	0.0201746i	0.296269	−	0.955105i	$-0.404258\pi$
$709$	2.00482	+	0.537189i	0.0752925	+	0.0201746i	−0.220976	+	0.975279i	$0.570924\pi$
$710$	−1.72817	−	0.757707i	−0.0648569	−	0.0284362i
$711$		0			0
$712$	−3.14660	+	0.843128i	−0.117924	+	0.0315976i
$713$	−37.8447	−	21.8496i	−1.41729	−	0.818275i
$714$		0			0
$715$	13.4129	+	29.8164i	0.501616	+	1.11507i
$716$	34.4251			1.28653
$717$		0			0
$718$	0.125497	−	0.0336269i	0.00468351	−	0.00125494i
$719$	−3.36848	−	5.83438i	−0.125623	−	0.217586i	0.796353	−	0.604832i	$-0.206760\pi$
$719$	−3.36848	−	5.83438i	−0.125623	−	0.217586i	−0.921976	+	0.387246i	$0.873426\pi$
$720$		0			0
$721$	−22.7966	−	6.10834i	−0.848991	−	0.227486i
$722$	1.01055	+	1.75032i	0.0376086	+	0.0651401i
$723$		0			0
$724$	42.8050	−	24.7135i	1.59083	−	0.918469i
$725$	22.3399	−	5.01416i	0.829683	−	0.186221i
$726$		0			0
$727$	34.4733	+	34.4733i	1.27854	+	1.27854i	0.941483	+	0.337062i	$0.109433\pi$
$727$	34.4733	+	34.4733i	1.27854	+	1.27854i	0.337062	+	0.941483i	$0.390567\pi$
$728$	−1.61148	−	4.99058i	−0.0597254	−	0.184963i
$729$		0			0
$730$	0.439841	−	2.88284i	0.0162792	−	0.106699i
$731$	−7.83580	+	13.5720i	−0.289817	+	0.501979i
$732$		0			0
$733$	−28.7555			−1.06211			−0.531054	−	0.847338i	$-0.678204\pi$
$733$	−28.7555			−1.06211			−0.531054	+	0.847338i	$0.678204\pi$
$734$	−0.491861	+	1.83565i	−0.0181549	+	0.0677551i
$735$		0			0
$736$	8.78585	+	8.78585i	0.323851	+	0.323851i
$737$	14.1652	+	3.79556i	0.521783	+	0.139811i
$738$		0			0
$739$	7.94129	+	29.6373i	0.292125	+	1.09023i	0.943474	+	0.331447i	$0.107537\pi$
$739$	7.94129	+	29.6373i	0.292125	+	1.09023i	−0.651349	+	0.758778i	$0.725797\pi$
$740$	28.9523	−	11.3027i	1.06431	−	0.415494i
$741$		0			0
$742$	−0.484483	+	0.484483i	−0.0177859	+	0.0177859i
$743$	26.4817	−	45.8676i	0.971519	−	1.68272i	0.280543	−	0.959841i	$-0.409485\pi$
$743$	26.4817	−	45.8676i	0.971519	−	1.68272i	0.690976	−	0.722878i	$-0.257181\pi$
$744$		0			0
$745$	2.99099	+	26.9834i	0.109581	+	0.988596i
$746$	−0.941490	+	0.941490i	−0.0344704	+	0.0344704i
$747$		0			0
$748$	−16.8824	+	9.74706i	−0.617282	+	0.356388i
$749$	9.74639	−	9.74639i	0.356125	−	0.356125i
$750$		0			0
$751$	−40.3780	−	23.3123i	−1.47341	−	0.850676i	−0.473862	−	0.880599i	$-0.657140\pi$
$751$	−40.3780	−	23.3123i	−1.47341	−	0.850676i	−0.999552	+	0.0299230i	$0.990474\pi$
$752$	−0.998326	+	1.72915i	−0.0364052	+	0.0630557i
$753$		0			0
$754$	2.06296	−	0.666140i	0.0751287	−	0.0242594i
$755$	−5.41574	−	2.37451i	−0.197099	−	0.0864172i
$756$		0			0
$757$	−0.323327	−	1.20667i	−0.0117515	−	0.0438572i	0.959801	−	0.280681i	$-0.0905603\pi$
$757$	−0.323327	−	1.20667i	−0.0117515	−	0.0438572i	−0.971553	+	0.236824i	$0.923894\pi$
$758$	0.133232	+	0.0356995i	0.00483922	+	0.00129666i
$759$		0			0
$760$	2.20742	−	0.244683i	0.0800716	−	0.00887558i
$761$	5.28278	−	19.7156i	0.191501	−	0.714690i	−0.801644	−	0.597801i	$-0.796041\pi$
$761$	5.28278	−	19.7156i	0.191501	−	0.714690i	0.993145	−	0.116889i	$-0.0372921\pi$
$762$		0			0
$763$	6.62754	−	24.7343i	0.239933	−	0.895442i
$764$	6.72858	−	11.6542i	0.243432	−	0.421636i
$765$		0			0
$766$		−	1.57656i		−	0.0569633i
$767$	−4.31410	+	8.42886i	−0.155773	+	0.304349i
$768$		0			0
$769$	35.6638	−	9.55609i	1.28607	−	0.344602i	0.449904	−	0.893077i	$-0.351458\pi$
$769$	35.6638	−	9.55609i	1.28607	−	0.344602i	0.836167	+	0.548476i	$0.184792\pi$
$770$	−1.96167	−	2.66803i	−0.0706935	−	0.0961491i
$771$		0			0
$772$			2.36972i			0.0852882i
$773$	10.6918	+	18.5187i	0.384557	+	0.666072i	0.991708	−	0.128515i	$-0.0410209\pi$
$773$	10.6918	+	18.5187i	0.384557	+	0.666072i	−0.607151	+	0.794587i	$0.707688\pi$
$774$		0			0
$775$	1.12294	−	27.3669i	0.0403372	−	0.983047i
$776$	−3.07754	−	5.33045i	−0.110477	−	0.191352i
$777$		0			0
$778$	−0.838242	−	0.483959i	−0.0300524	−	0.0173508i
$779$	12.1947			0.436921
$780$		0			0
$781$	26.0630			0.932608
$782$	−2.19925	−	1.26974i	−0.0786449	−	0.0454057i
$783$		0			0
$784$	−1.43410	−	2.48393i	−0.0512179	−	0.0887120i
$785$	13.1036	−	29.8865i	0.467688	−	1.06670i
$786$		0			0
$787$	−19.6914	−	34.1065i	−0.701923	−	1.21577i	−0.967790	−	0.251757i	$-0.918992\pi$
$787$	−19.6914	−	34.1065i	−0.701923	−	1.21577i	0.265867	−	0.964010i	$-0.414342\pi$
$788$			39.8950i			1.42120i
$789$		0			0
$790$	0.370904	−	2.43101i	0.0131962	−	0.0864913i
$791$	−20.1575	+	5.40118i	−0.716717	+	0.192044i
$792$		0			0
$793$	4.40394	−	1.42205i	0.156389	−	0.0504986i
$794$		−	0.795007i		−	0.0282138i
$795$		0			0
$796$	−2.15892	+	3.73936i	−0.0765209	+	0.132538i
$797$	10.1370	−	37.8319i	0.359072	−	1.34007i	−0.516210	−	0.856462i	$-0.672658\pi$
$797$	10.1370	−	37.8319i	0.359072	−	1.34007i	0.875282	−	0.483612i	$-0.160676\pi$
$798$		0			0
$799$	0.321515	−	1.19991i	0.0113744	−	0.0424498i
$800$	−2.32234	+	7.43348i	−0.0821073	+	0.262813i
$801$		0			0
$802$	0.306232	+	0.0820546i	0.0108134	+	0.00289745i
$803$	10.4249	+	38.9062i	0.367887	+	1.37297i
$804$		0			0
$805$	−19.9220	+	45.4378i	−0.702158	+	1.60147i
$806$	−0.131003	−	2.59006i	−0.00461437	−	0.0912311i
$807$		0			0
$808$	−0.263823	+	0.456954i	−0.00928125	+	0.0160756i
$809$	−23.1644	−	13.3740i	−0.814416	−	0.470203i	0.0340712	−	0.999419i	$-0.489153\pi$
$809$	−23.1644	−	13.3740i	−0.814416	−	0.470203i	−0.848487	+	0.529216i	$0.822486\pi$
$810$		0			0
$811$	−7.93739	+	7.93739i	−0.278720	+	0.278720i	−0.832598	−	0.553878i	$-0.813147\pi$
$811$	−7.93739	+	7.93739i	−0.278720	+	0.278720i	0.553878	+	0.832598i	$0.313147\pi$
$812$	21.8697	−	12.6265i	0.767477	−	0.443103i
$813$		0			0
$814$	2.63940	−	2.63940i	0.0925109	−	0.0925109i
$815$	−26.1235	+	32.6368i	−0.915065	+	1.14322i
$816$		0			0
$817$	−6.13849	+	10.6322i	−0.214759	+	0.371973i
$818$	1.86963	−	1.86963i	0.0653700	−	0.0653700i
$819$		0			0
$820$	−11.4305	+	26.0706i	−0.399172	+	0.910425i
$821$	−6.99144	−	26.0924i	−0.244003	−	0.910632i	−0.973882	−	0.227055i	$-0.927090\pi$
$821$	−6.99144	−	26.0924i	−0.244003	−	0.910632i	0.729879	−	0.683577i	$-0.239576\pi$
$822$		0			0
$823$	−9.05749	−	2.42695i	−0.315724	−	0.0845980i	0.0974771	−	0.995238i	$-0.468923\pi$
$823$	−9.05749	−	2.42695i	−0.315724	−	0.0845980i	−0.413201	+	0.910640i	$0.635589\pi$
$824$	3.13769	+	3.13769i	0.109307	+	0.109307i
$825$		0			0
$826$	0.248227	−	0.926397i	0.00863693	−	0.0322335i
$827$	45.0330			1.56595			0.782976	−	0.622052i	$-0.213701\pi$
$827$	45.0330			1.56595			0.782976	+	0.622052i	$0.213701\pi$
$828$		0			0
$829$	21.0075	−	36.3861i	0.729622	−	1.26374i	−0.227421	−	0.973796i	$-0.573029\pi$
$829$	21.0075	−	36.3861i	0.729622	−	1.26374i	0.957043	−	0.289946i	$-0.0936372\pi$
$830$	0.920634	+	0.140463i	0.0319557	+	0.00487555i
$831$		0			0
$832$	5.73795	−	26.7549i	0.198928	−	0.927558i
$833$	1.26182	+	1.26182i	0.0437194	+	0.0437194i
$834$		0			0
$835$	6.97378	−	45.7081i	0.241338	−	1.58179i
$836$	−13.2255	+	7.63575i	−0.457414	+	0.264088i
$837$		0			0
$838$	1.97481	+	3.42047i	0.0682186	+	0.118158i
$839$	5.24673	+	1.40586i	0.181137	+	0.0485356i	0.348247	−	0.937403i	$-0.386777\pi$
$839$	5.24673	+	1.40586i	0.181137	+	0.0485356i	−0.167110	+	0.985938i	$0.553444\pi$
$840$		0			0
$841$	−4.01574	−	6.95547i	−0.138474	−	0.239844i
$842$	1.65854	−	0.444405i	0.0571571	−	0.0153152i
$843$		0			0
$844$	−39.5617			−1.36177
$845$	29.0321	+	1.46250i	0.998734	+	0.0503116i
$846$		0			0
$847$	13.1156	+	7.57228i	0.450657	+	0.260187i
$848$	−7.06186	+	1.89222i	−0.242505	+	0.0649791i
$849$		0			0
$850$	0.0652568	−	1.59036i	0.00223829	−	0.0545488i
$851$	−54.0166	−	14.4737i	−1.85167	−	0.496152i
$852$		0			0
$853$			23.0805i			0.790260i	0.918625	+	0.395130i	$0.129300\pi$
$853$			23.0805i			0.790260i	−0.918625	+	0.395130i	$0.870700\pi$
$854$	−0.405948	+	0.234374i	−0.0138912	+	0.00802012i
$855$		0			0
$856$	−2.50323	+	0.670738i	−0.0855586	+	0.0229254i
$857$	−37.6679	−	37.6679i	−1.28671	−	1.28671i	−0.936772	−	0.349940i	$-0.886202\pi$
$857$	−37.6679	−	37.6679i	−1.28671	−	1.28671i	−0.349940	−	0.936772i	$-0.613798\pi$
$858$		0			0
$859$		−	5.08674i		−	0.173557i	−0.996228	−	0.0867787i	$-0.972343\pi$
$859$		−	5.08674i		−	0.173557i	0.996228	−	0.0867787i	$-0.0276573\pi$
$860$	−16.9763	−	23.0892i	−0.578886	−	0.787333i
$861$		0			0
$862$	−0.214481	+	0.800452i	−0.00730524	+	0.0272635i
$863$	−45.1879			−1.53821			−0.769107	−	0.639120i	$-0.779299\pi$
$863$	−45.1879			−1.53821			−0.769107	+	0.639120i	$0.779299\pi$
$864$		0			0
$865$	40.3289	−	4.47028i	1.37122	−	0.151994i
$866$	1.14100	+	1.14100i	0.0387728	+	0.0387728i
$867$		0			0
$868$	−7.81890	−	29.1805i	−0.265391	−	0.990452i
$869$	8.79099	+	32.8084i	0.298214	+	1.11295i
$870$		0			0
$871$	8.74226	−	9.67372i	0.296220	−	0.327782i
$872$	−3.40439	+	3.40439i	−0.115287	+	0.115287i
$873$		0			0
$874$	−1.72287	−	0.994699i	−0.0582769	−	0.0336462i
$875$	−31.0219	+	2.15591i	−1.04873	+	0.0728832i
$876$		0			0
$877$	−17.6048	+	10.1641i	−0.594471	+	0.343218i	−0.766863	−	0.641810i	$-0.778184\pi$
$877$	−17.6048	+	10.1641i	−0.594471	+	0.343218i	0.172392	+	0.985028i	$0.444850\pi$
$878$	−3.91675	+	2.26134i	−0.132184	+	0.0763164i
$879$		0			0
$880$	−3.89298	−	35.1208i	−0.131232	−	1.18392i
$881$	28.5961	+	16.5100i	0.963428	+	0.556236i	0.897227	−	0.441571i	$-0.145579\pi$
$881$	28.5961	+	16.5100i	0.963428	+	0.556236i	0.0662019	+	0.997806i	$0.478912\pi$
$882$		0			0
$883$	15.9555	−	15.9555i	0.536944	−	0.536944i	−0.385686	−	0.922630i	$-0.626035\pi$
$883$	15.9555	−	15.9555i	0.536944	−	0.536944i	0.922630	+	0.385686i	$0.126035\pi$
$884$	0.875535	+	17.3103i	0.0294474	+	0.582207i
$885$		0			0
$886$	0.259261	+	0.967576i	0.00871005	+	0.0325063i
$887$	0.163391	+	0.609784i	0.00548614	+	0.0204745i	0.968615	−	0.248567i	$-0.0799597\pi$
$887$	0.163391	+	0.609784i	0.00548614	+	0.0204745i	−0.963129	+	0.269042i	$0.913293\pi$
$888$		0			0
$889$	−32.5466	−	32.5466i	−1.09158	−	1.09158i
$890$	0.201495	+	1.81780i	0.00675413	+	0.0609329i
$891$		0			0
$892$	26.5956			0.890488
$893$	0.251872	−	0.939998i	0.00842856	−	0.0314558i
$894$		0			0
$895$	5.85556	−	38.3790i	0.195730	−	1.28287i
$896$			11.4359i			0.382046i
$897$		0			0
$898$	2.89072	+	2.89072i	0.0964647	+	0.0964647i
$899$	24.2297	−	6.49233i	0.808106	−	0.216531i
$900$		0			0
$901$	3.93920	−	2.27430i	0.131234	−	0.0757679i
$902$			3.41875i			0.113832i
$903$		0			0
$904$	3.78996	+	1.01552i	0.126052	+	0.0337755i
$905$	−20.2710	−	51.9250i	−0.673830	−	1.72604i
$906$		0			0
$907$	37.8383	−	10.1387i	1.25640	−	0.336651i	0.431594	−	0.902068i	$-0.357951\pi$
$907$	37.8383	−	10.1387i	1.25640	−	0.336651i	0.824805	+	0.565417i	$0.191285\pi$
$908$	−25.2095	−	14.5547i	−0.836607	−	0.483015i
$909$		0			0
$910$	−2.90630	+	0.471793i	−0.0963430	+	0.0156398i
$911$	−6.21630			−0.205955			−0.102978	−	0.994684i	$-0.532837\pi$
$911$	−6.21630			−0.205955			−0.102978	+	0.994684i	$0.532837\pi$
$912$		0			0
$913$	−12.4247	+	3.32919i	−0.411198	+	0.110180i
$914$	−0.204012	−	0.353358i	−0.00674810	−	0.0116881i
$915$		0			0
$916$	−7.18510	−	1.92524i	−0.237402	−	0.0636117i
$917$	17.6450	+	30.5621i	0.582690	+	1.00925i
$918$		0			0
$919$	−19.9013	+	11.4900i	−0.656485	+	0.379022i	−0.790936	−	0.611899i	$-0.790406\pi$
$919$	−19.9013	+	11.4900i	−0.656485	+	0.379022i	0.134452	+	0.990920i	$0.457073\pi$
$920$	7.51540	−	5.52569i	0.247776	−	0.182177i
$921$		0			0
$922$	1.55017	+	1.55017i	0.0510520	+	0.0510520i
$923$	10.5579	−	20.6279i	0.347518	−	0.678977i
$924$		0			0
$925$	−7.67617	−	34.2001i	−0.252391	−	1.12449i
$926$	−1.02676	+	1.77840i	−0.0337413	+	0.0584417i
$927$		0			0
$928$	−7.13229			−0.234129
$929$	−0.280692	+	1.04756i	−0.00920921	+	0.0343692i	−0.970378	−	0.241593i	$-0.922330\pi$
$929$	−0.280692	+	1.04756i	−0.00920921	+	0.0343692i	0.961168	+	0.275963i	$0.0889966\pi$
$930$		0			0
$931$	0.988497	+	0.988497i	0.0323967	+	0.0323967i
$932$	−37.7726	−	10.1211i	−1.23728	−	0.331529i
$933$		0			0
$934$	−0.724846	−	2.70516i	−0.0237177	−	0.0885157i
$935$	7.99493	+	20.4794i	0.261462	+	0.669746i
$936$		0			0
$937$	−2.17699	+	2.17699i	−0.0711191	+	0.0711191i	−0.741772	−	0.670653i	$-0.766014\pi$
$937$	−2.17699	+	2.17699i	−0.0711191	+	0.0711191i	0.670653	+	0.741772i	$0.266014\pi$
$938$	−0.660337	+	1.14374i	−0.0215608	+	0.0373443i
$939$		0			0
$940$	1.77350	+	1.41956i	0.0578450	+	0.0463009i
$941$	22.9413	−	22.9413i	0.747866	−	0.747866i	−0.226212	−	0.974078i	$-0.572634\pi$
$941$	22.9413	−	22.9413i	0.747866	−	0.747866i	0.974078	+	0.226212i	$0.0726342\pi$
$942$		0			0
$943$	44.3569	−	25.6095i	1.44446	−	0.833959i
$944$	7.23636	−	7.23636i	0.235523	−	0.235523i
$945$		0			0
$946$	−2.98069	−	1.72090i	−0.0969107	−	0.0559514i
$947$	13.6493	−	23.6413i	0.443543	−	0.768239i	−0.554406	−	0.832246i	$-0.687055\pi$
$947$	13.6493	−	23.6413i	0.443543	−	0.768239i	0.997949	+	0.0640069i	$0.0203880\pi$
$948$		0			0
$949$	35.0159	+	7.50964i	1.13666	+	0.243773i
$950$	0.0511215	−	1.24587i	0.00165860	−	0.0404214i
$951$		0			0
$952$	−0.912703	−	3.40625i	−0.0295809	−	0.110397i
$953$	−6.17827	−	1.65546i	−0.200134	−	0.0536257i	0.157360	−	0.987541i	$-0.449702\pi$
$953$	−6.17827	−	1.65546i	−0.200134	−	0.0536257i	−0.357493	+	0.933916i	$0.616369\pi$
$954$		0			0
$955$	−11.8483	−	9.48372i	−0.383401	−	0.306886i
$956$	7.39460	−	27.5970i	0.239158	−	0.892551i
$957$		0			0
$958$	−1.44939	+	5.40920i	−0.0468277	+	0.174763i
$959$	20.7839	−	35.9988i	0.671147	−	1.16246i
$960$		0			0
$961$			0.991728i			0.0319912i
$962$	−1.01979	−	3.15819i	−0.0328794	−	0.101824i
$963$		0			0
$964$	15.5210	−	4.15885i	0.499899	−	0.133947i
$965$	2.64189	+	0.403080i	0.0850456	+	0.0129756i
$966$		0			0
$967$			28.4424i			0.914647i	0.889300	+	0.457324i	$0.151192\pi$
$967$			28.4424i			0.914647i	−0.889300	+	0.457324i	$0.848808\pi$
$968$	−1.42372	−	2.46596i	−0.0457602	−	0.0792589i
$969$		0			0
$970$	−3.21908	+	1.25670i	−0.103358	+	0.0403501i
$971$	−0.619921	−	1.07374i	−0.0198942	−	0.0344578i	0.855907	−	0.517130i	$-0.173000\pi$
$971$	−0.619921	−	1.07374i	−0.0198942	−	0.0344578i	−0.875801	+	0.482672i	$0.839666\pi$
$972$		0			0
$973$	20.6484	+	11.9213i	0.661956	+	0.382180i
$974$	1.99799			0.0640197
$975$		0			0
$976$	−5.00174			−0.160102
$977$	32.9480	+	19.0226i	1.05410	+	0.608586i	0.923795	−	0.382888i	$-0.125071\pi$
$977$	32.9480	+	19.0226i	1.05410	+	0.608586i	0.130307	+	0.991474i	$0.458404\pi$
$978$		0			0
$979$	−12.6307	−	21.8770i	−0.403678	−	0.699192i
$980$	−3.03982	+	1.18671i	−0.0971035	+	0.0379082i
$981$		0			0
$982$	−1.83661	−	3.18111i	−0.0586087	−	0.101513i
$983$			34.5934i			1.10336i	0.834056	+	0.551679i	$0.186013\pi$
$983$			34.5934i			1.10336i	−0.834056	+	0.551679i	$0.813987\pi$
$984$		0			0
$985$	44.4772	+	6.78598i	1.41716	+	0.216219i
$986$	1.40805	−	0.377285i	0.0448414	−	0.0120152i
$987$		0			0
$988$	0.685885	+	13.5607i	0.0218209	+	0.431423i
$989$			51.5644i			1.63965i
$990$		0			0
$991$	−19.7486	+	34.2056i	−0.627335	+	1.08658i	0.360750	+	0.932663i	$0.382521\pi$
$991$	−19.7486	+	34.2056i	−0.627335	+	1.08658i	−0.988084	+	0.153913i	$0.950813\pi$
$992$	−2.20832	+	8.24156i	−0.0701142	+	0.261670i
$993$		0			0
$994$	−0.607486	+	2.26717i	−0.0192683	+	0.0719103i
$995$	3.80162	+	3.04293i	0.120519	+	0.0964673i
$996$		0			0
$997$	−7.10500	−	1.90378i	−0.225018	−	0.0602933i	0.144549	−	0.989498i	$-0.453827\pi$
$997$	−7.10500	−	1.90378i	−0.225018	−	0.0602933i	−0.369566	+	0.929204i	$0.620494\pi$
$998$	−0.0804906	−	0.300395i	−0.00254789	−	0.00950884i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.dp.a.253.3		20
3.2	odd	2		65.2.t.a.58.3	yes	20
5.2	odd	4		585.2.cf.a.487.3		20
13.11	odd	12		585.2.cf.a.388.3		20
15.2	even	4		65.2.o.a.32.3	✓	20
15.8	even	4		325.2.s.b.32.3		20
15.14	odd	2		325.2.x.b.318.3		20
39.2	even	12		845.2.o.g.258.3		20
39.5	even	4		845.2.o.f.488.3		20
39.8	even	4		845.2.o.e.488.3		20
39.11	even	12		65.2.o.a.63.3	yes	20
39.17	odd	6		845.2.f.d.408.4		20
39.20	even	12		845.2.k.e.268.4		20
39.23	odd	6		845.2.t.e.418.3		20
39.29	odd	6		845.2.t.f.418.3		20
39.32	even	12		845.2.k.d.268.7		20
39.35	odd	6		845.2.f.e.408.7		20
39.38	odd	2		845.2.t.g.188.3		20
65.37	even	12	inner	585.2.dp.a.37.3		20
195.2	odd	12		845.2.t.g.427.3		20
195.17	even	12		845.2.k.d.577.7		20
195.32	odd	12		845.2.f.d.437.7		20
195.47	odd	4		845.2.t.f.657.3		20
195.62	even	12		845.2.o.f.587.3		20
195.77	even	4		845.2.o.g.357.3		20
195.89	even	12		325.2.s.b.193.3		20
195.107	even	12		845.2.o.e.587.3		20
195.122	odd	4		845.2.t.e.657.3		20
195.128	odd	12		325.2.x.b.232.3		20
195.137	odd	12		845.2.f.e.437.4		20
195.152	even	12		845.2.k.e.577.4		20
195.167	odd	12		65.2.t.a.37.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.3	✓	20	15.2	even	4
65.2.o.a.63.3	yes	20	39.11	even	12
65.2.t.a.37.3	yes	20	195.167	odd	12
65.2.t.a.58.3	yes	20	3.2	odd	2
325.2.s.b.32.3		20	15.8	even	4
325.2.s.b.193.3		20	195.89	even	12
325.2.x.b.232.3		20	195.128	odd	12
325.2.x.b.318.3		20	15.14	odd	2
585.2.cf.a.388.3		20	13.11	odd	12
585.2.cf.a.487.3		20	5.2	odd	4
585.2.dp.a.37.3		20	65.37	even	12	inner
585.2.dp.a.253.3		20	1.1	even	1	trivial
845.2.f.d.408.4		20	39.17	odd	6
845.2.f.d.437.7		20	195.32	odd	12
845.2.f.e.408.7		20	39.35	odd	6
845.2.f.e.437.4		20	195.137	odd	12
845.2.k.d.268.7		20	39.32	even	12
845.2.k.d.577.7		20	195.17	even	12
845.2.k.e.268.4		20	39.20	even	12
845.2.k.e.577.4		20	195.152	even	12
845.2.o.e.488.3		20	39.8	even	4
845.2.o.e.587.3		20	195.107	even	12
845.2.o.f.488.3		20	39.5	even	4
845.2.o.f.587.3		20	195.62	even	12
845.2.o.g.258.3		20	39.2	even	12
845.2.o.g.357.3		20	195.77	even	4
845.2.t.e.418.3		20	39.23	odd	6
845.2.t.e.657.3		20	195.122	odd	4
845.2.t.f.418.3		20	39.29	odd	6
845.2.t.f.657.3		20	195.47	odd	4
845.2.t.g.188.3		20	39.38	odd	2
845.2.t.g.427.3		20	195.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.dp (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.113711 + 0.0656513i) q^{2} +(-0.991380 - 1.71712i) q^{4} +(-2.08297 + 0.813169i) q^{5} +(1.39069 + 2.40874i) q^{7} -0.522947i q^{8} +(-0.290243 - 0.0442830i) q^{10} +(3.91706 - 1.04957i) q^{11} +(0.756068 - 3.52539i) q^{13} +0.365201i q^{14} +(-1.94843 + 3.37478i) q^{16} +(0.627499 - 2.34186i) q^{17} +(0.491577 - 1.83459i) q^{19} +(3.46132 + 2.77055i) q^{20} +(0.514321 + 0.137812i) q^{22} +(-2.06467 - 7.70544i) q^{23} +(3.67751 - 3.38761i) q^{25} +(0.317420 - 0.351240i) q^{26} +(2.75740 - 4.77595i) q^{28} +(3.96565 + 2.28957i) q^{29} +(3.87352 - 3.87352i) q^{31} +(-1.34889 + 0.778780i) q^{32} +(0.225100 - 0.225100i) q^{34} +(-4.85547 - 3.88646i) q^{35} +(3.50510 - 6.07101i) q^{37} +(0.176341 - 0.176341i) q^{38} +(0.425244 + 1.08928i) q^{40} +(1.66178 + 6.20184i) q^{41} +(-6.24368 - 1.67299i) q^{43} +(-5.68554 - 5.68554i) q^{44} +(0.271096 - 1.01174i) q^{46} +0.512375 q^{47} +(-0.368015 + 0.637420i) q^{49} +(0.640576 - 0.143776i) q^{50} +(-6.80307 + 2.19674i) q^{52} +(1.32662 + 1.32662i) q^{53} +(-7.30564 + 5.37147i) q^{55} +(1.25964 - 0.727255i) q^{56} +(0.300626 + 0.520700i) q^{58} +(-2.53667 - 0.679700i) q^{59} +(0.641767 + 1.11157i) q^{61} +(0.694764 - 0.186162i) q^{62} +7.58920 q^{64} +(1.29187 + 7.95808i) q^{65} +(3.13180 + 1.80814i) q^{67} +(-4.64334 + 1.24418i) q^{68} +(-0.296970 - 0.760703i) q^{70} +(6.20800 + 1.66343i) q^{71} +9.93250i q^{73} +(0.797139 - 0.460228i) q^{74} +(-3.63755 + 0.974678i) q^{76} +(7.97556 + 7.97556i) q^{77} +8.37577i q^{79} +(1.31425 - 8.61395i) q^{80} +(-0.218196 + 0.814318i) q^{82} -3.17194 q^{83} +(0.597266 + 5.38828i) q^{85} +(-0.600143 - 0.600143i) q^{86} +(-0.548871 - 2.04842i) q^{88} +(-1.61226 - 6.01705i) q^{89} +(9.54319 - 3.08154i) q^{91} +(-11.1843 + 11.1843i) q^{92} +(0.0582629 + 0.0336381i) q^{94} +(0.467892 + 4.22112i) q^{95} +(10.1931 - 5.88500i) q^{97} +(-0.0836950 + 0.0483213i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} + 6 q^{4} - 2 q^{7} - 2 q^{10} + 16 q^{11} - 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 16 q^{22} + 10 q^{23} + 18 q^{25} + 24 q^{26} + 18 q^{28} - 48 q^{32} + 2 q^{34} - 40 q^{35} - 4 q^{37}+ \cdots + 30 q^{98}+O(q^{100}) \) 20 * q + 6 * q^2 + 6 * q^4 - 2 * q^7 - 2 * q^10 + 16 * q^11 - 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 16 * q^22 + 10 * q^23 + 18 * q^25 + 24 * q^26 + 18 * q^28 - 48 * q^32 + 2 * q^34 - 40 * q^35 - 4 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 + 10 * q^43 + 36 * q^44 + 4 * q^46 + 40 * q^47 + 18 * q^49 - 36 * q^50 - 30 * q^52 + 10 * q^53 - 10 * q^55 + 16 * q^59 - 16 * q^61 + 44 * q^62 + 20 * q^64 + 14 * q^65 + 18 * q^67 - 22 * q^68 - 12 * q^70 + 16 * q^71 - 18 * q^74 - 64 * q^76 + 28 * q^77 + 2 * q^80 + 56 * q^82 - 48 * q^83 - 26 * q^85 - 60 * q^86 + 82 * q^88 + 6 * q^89 + 8 * q^91 + 8 * q^92 - 48 * q^94 + 26 * q^95 + 66 * q^97 + 30 * q^98

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