LMFDB - Embedded newform 8022.2.a.p.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.a (trivial)

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:	yes
Analytic conductor:	$64.0559925015$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 17x^{7} - 12x^{6} + 72x^{5} + 81x^{4} - 67x^{3} - 105x^{2} - 17x + 6 $ x^9 - 17x^7 - 12x^6 + 72x^5 + 81x^4 - 67x^3 - 105x^2 - 17*x + 6
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.166868$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.787345 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.787345 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.787345 q^{10} +3.10786 q^{11} -1.00000 q^{12} -3.17609 q^{13} +1.00000 q^{14} -0.787345 q^{15} +1.00000 q^{16} -6.03246 q^{17} +1.00000 q^{18} -6.57371 q^{19} +0.787345 q^{20} -1.00000 q^{21} +3.10786 q^{22} +7.72908 q^{23} -1.00000 q^{24} -4.38009 q^{25} -3.17609 q^{26} -1.00000 q^{27} +1.00000 q^{28} -2.30852 q^{29} -0.787345 q^{30} +7.45011 q^{31} +1.00000 q^{32} -3.10786 q^{33} -6.03246 q^{34} +0.787345 q^{35} +1.00000 q^{36} -2.94964 q^{37} -6.57371 q^{38} +3.17609 q^{39} +0.787345 q^{40} +0.573298 q^{41} -1.00000 q^{42} -11.6859 q^{43} +3.10786 q^{44} +0.787345 q^{45} +7.72908 q^{46} -12.3604 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.38009 q^{50} +6.03246 q^{51} -3.17609 q^{52} -4.55300 q^{53} -1.00000 q^{54} +2.44696 q^{55} +1.00000 q^{56} +6.57371 q^{57} -2.30852 q^{58} +2.31491 q^{59} -0.787345 q^{60} -2.16410 q^{61} +7.45011 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.50068 q^{65} -3.10786 q^{66} +1.26056 q^{67} -6.03246 q^{68} -7.72908 q^{69} +0.787345 q^{70} +10.7445 q^{71} +1.00000 q^{72} -12.3749 q^{73} -2.94964 q^{74} +4.38009 q^{75} -6.57371 q^{76} +3.10786 q^{77} +3.17609 q^{78} -4.55084 q^{79} +0.787345 q^{80} +1.00000 q^{81} +0.573298 q^{82} -15.8764 q^{83} -1.00000 q^{84} -4.74963 q^{85} -11.6859 q^{86} +2.30852 q^{87} +3.10786 q^{88} -6.99840 q^{89} +0.787345 q^{90} -3.17609 q^{91} +7.72908 q^{92} -7.45011 q^{93} -12.3604 q^{94} -5.17578 q^{95} -1.00000 q^{96} +10.3262 q^{97} +1.00000 q^{98} +3.10786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} - 4 q^{10} - 3 q^{11} - 9 q^{12} - 9 q^{13} + 9 q^{14} + 4 q^{15} + 9 q^{16} - 12 q^{17} + 9 q^{18} - 18 q^{19} - 4 q^{20} - 9 q^{21} - 3 q^{22} + q^{23} - 9 q^{24} + 9 q^{25} - 9 q^{26} - 9 q^{27} + 9 q^{28} - 11 q^{29} + 4 q^{30} - 22 q^{31} + 9 q^{32} + 3 q^{33} - 12 q^{34} - 4 q^{35} + 9 q^{36} + 8 q^{37} - 18 q^{38} + 9 q^{39} - 4 q^{40} - 22 q^{41} - 9 q^{42} - 3 q^{43} - 3 q^{44} - 4 q^{45} + q^{46} - 49 q^{47} - 9 q^{48} + 9 q^{49} + 9 q^{50} + 12 q^{51} - 9 q^{52} + 8 q^{53} - 9 q^{54} - 19 q^{55} + 9 q^{56} + 18 q^{57} - 11 q^{58} - 18 q^{59} + 4 q^{60} + 3 q^{61} - 22 q^{62} + 9 q^{63} + 9 q^{64} - 32 q^{65} + 3 q^{66} - 11 q^{67} - 12 q^{68} - q^{69} - 4 q^{70} - 7 q^{71} + 9 q^{72} - 23 q^{73} + 8 q^{74} - 9 q^{75} - 18 q^{76} - 3 q^{77} + 9 q^{78} - 17 q^{79} - 4 q^{80} + 9 q^{81} - 22 q^{82} - 30 q^{83} - 9 q^{84} + 18 q^{85} - 3 q^{86} + 11 q^{87} - 3 q^{88} + 23 q^{89} - 4 q^{90} - 9 q^{91} + q^{92} + 22 q^{93} - 49 q^{94} - 30 q^{95} - 9 q^{96} - 46 q^{97} + 9 q^{98} - 3 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 - 4 * q^10 - 3 * q^11 - 9 * q^12 - 9 * q^13 + 9 * q^14 + 4 * q^15 + 9 * q^16 - 12 * q^17 + 9 * q^18 - 18 * q^19 - 4 * q^20 - 9 * q^21 - 3 * q^22 + q^23 - 9 * q^24 + 9 * q^25 - 9 * q^26 - 9 * q^27 + 9 * q^28 - 11 * q^29 + 4 * q^30 - 22 * q^31 + 9 * q^32 + 3 * q^33 - 12 * q^34 - 4 * q^35 + 9 * q^36 + 8 * q^37 - 18 * q^38 + 9 * q^39 - 4 * q^40 - 22 * q^41 - 9 * q^42 - 3 * q^43 - 3 * q^44 - 4 * q^45 + q^46 - 49 * q^47 - 9 * q^48 + 9 * q^49 + 9 * q^50 + 12 * q^51 - 9 * q^52 + 8 * q^53 - 9 * q^54 - 19 * q^55 + 9 * q^56 + 18 * q^57 - 11 * q^58 - 18 * q^59 + 4 * q^60 + 3 * q^61 - 22 * q^62 + 9 * q^63 + 9 * q^64 - 32 * q^65 + 3 * q^66 - 11 * q^67 - 12 * q^68 - q^69 - 4 * q^70 - 7 * q^71 + 9 * q^72 - 23 * q^73 + 8 * q^74 - 9 * q^75 - 18 * q^76 - 3 * q^77 + 9 * q^78 - 17 * q^79 - 4 * q^80 + 9 * q^81 - 22 * q^82 - 30 * q^83 - 9 * q^84 + 18 * q^85 - 3 * q^86 + 11 * q^87 - 3 * q^88 + 23 * q^89 - 4 * q^90 - 9 * q^91 + q^92 + 22 * q^93 - 49 * q^94 - 30 * q^95 - 9 * q^96 - 46 * q^97 + 9 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0.787345	0.352112	0.176056	−	0.984380i	$-0.443666\pi$
$5$	0.787345	0.352112	0.176056	+	0.984380i	$0.443666\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.787345	0.248980
$11$	3.10786	0.937054	0.468527	−	0.883449i	$-0.344785\pi$
$11$	3.10786	0.937054	0.468527	+	0.883449i	$0.344785\pi$
$12$	−1.00000	−0.288675
$13$	−3.17609	−0.880888	−0.440444	−	0.897780i	$-0.645179\pi$
$13$	−3.17609	−0.880888	−0.440444	+	0.897780i	$0.645179\pi$
$14$	1.00000	0.267261
$15$	−0.787345	−0.203292
$16$	1.00000	0.250000
$17$	−6.03246	−1.46309	−0.731543	−	0.681795i	$-0.761200\pi$
$17$	−6.03246	−1.46309	−0.731543	+	0.681795i	$0.761200\pi$
$18$	1.00000	0.235702
$19$	−6.57371	−1.50811	−0.754056	−	0.656810i	$-0.771905\pi$
$19$	−6.57371	−1.50811	−0.754056	+	0.656810i	$0.771905\pi$
$20$	0.787345	0.176056
$21$	−1.00000	−0.218218
$22$	3.10786	0.662597
$23$	7.72908	1.61163	0.805813	−	0.592170i	$-0.201729\pi$
$23$	7.72908	1.61163	0.805813	+	0.592170i	$0.201729\pi$
$24$	−1.00000	−0.204124
$25$	−4.38009	−0.876017
$26$	−3.17609	−0.622882
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−2.30852	−0.428681	−0.214341	−	0.976759i	$-0.568760\pi$
$29$	−2.30852	−0.428681	−0.214341	+	0.976759i	$0.568760\pi$
$30$	−0.787345	−0.143749
$31$	7.45011	1.33808	0.669039	−	0.743227i	$-0.266706\pi$
$31$	7.45011	1.33808	0.669039	+	0.743227i	$0.266706\pi$
$32$	1.00000	0.176777
$33$	−3.10786	−0.541008
$34$	−6.03246	−1.03456
$35$	0.787345	0.133086
$36$	1.00000	0.166667
$37$	−2.94964	−0.484917	−0.242459	−	0.970162i	$-0.577954\pi$
$37$	−2.94964	−0.484917	−0.242459	+	0.970162i	$0.577954\pi$
$38$	−6.57371	−1.06640
$39$	3.17609	0.508581
$40$	0.787345	0.124490
$41$	0.573298	0.0895341	0.0447671	−	0.998997i	$-0.485745\pi$
$41$	0.573298	0.0895341	0.0447671	+	0.998997i	$0.485745\pi$
$42$	−1.00000	−0.154303
$43$	−11.6859	−1.78208	−0.891041	−	0.453923i	$-0.850024\pi$
$43$	−11.6859	−1.78208	−0.891041	+	0.453923i	$0.850024\pi$
$44$	3.10786	0.468527
$45$	0.787345	0.117371
$46$	7.72908	1.13959
$47$	−12.3604	−1.80295	−0.901475	−	0.432832i	$-0.857514\pi$
$47$	−12.3604	−1.80295	−0.901475	+	0.432832i	$0.857514\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.38009	−0.619438
$51$	6.03246	0.844714
$52$	−3.17609	−0.440444
$53$	−4.55300	−0.625402	−0.312701	−	0.949852i	$-0.601234\pi$
$53$	−4.55300	−0.625402	−0.312701	+	0.949852i	$0.601234\pi$
$54$	−1.00000	−0.136083
$55$	2.44696	0.329948
$56$	1.00000	0.133631
$57$	6.57371	0.870709
$58$	−2.30852	−0.303123
$59$	2.31491	0.301375	0.150688	−	0.988581i	$-0.451851\pi$
$59$	2.31491	0.301375	0.150688	+	0.988581i	$0.451851\pi$
$60$	−0.787345	−0.101646
$61$	−2.16410	−0.277084	−0.138542	−	0.990357i	$-0.544242\pi$
$61$	−2.16410	−0.277084	−0.138542	+	0.990357i	$0.544242\pi$
$62$	7.45011	0.946164
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−2.50068	−0.310171
$66$	−3.10786	−0.382551
$67$	1.26056	0.154002	0.0770008	−	0.997031i	$-0.475466\pi$
$67$	1.26056	0.154002	0.0770008	+	0.997031i	$0.475466\pi$
$68$	−6.03246	−0.731543
$69$	−7.72908	−0.930472
$70$	0.787345	0.0941058
$71$	10.7445	1.27514	0.637571	−	0.770391i	$-0.279939\pi$
$71$	10.7445	1.27514	0.637571	+	0.770391i	$0.279939\pi$
$72$	1.00000	0.117851
$73$	−12.3749	−1.44837	−0.724184	−	0.689607i	$-0.757783\pi$
$73$	−12.3749	−1.44837	−0.724184	+	0.689607i	$0.757783\pi$
$74$	−2.94964	−0.342888
$75$	4.38009	0.505769
$76$	−6.57371	−0.754056
$77$	3.10786	0.354173
$78$	3.17609	0.359621
$79$	−4.55084	−0.512009	−0.256004	−	0.966676i	$-0.582406\pi$
$79$	−4.55084	−0.512009	−0.256004	+	0.966676i	$0.582406\pi$
$80$	0.787345	0.0880279
$81$	1.00000	0.111111
$82$	0.573298	0.0633102
$83$	−15.8764	−1.74266	−0.871331	−	0.490696i	$-0.836743\pi$
$83$	−15.8764	−1.74266	−0.871331	+	0.490696i	$0.836743\pi$
$84$	−1.00000	−0.109109
$85$	−4.74963	−0.515170
$86$	−11.6859	−1.26012
$87$	2.30852	0.247499
$88$	3.10786	0.331299
$89$	−6.99840	−0.741829	−0.370915	−	0.928667i	$-0.620956\pi$
$89$	−6.99840	−0.741829	−0.370915	+	0.928667i	$0.620956\pi$
$90$	0.787345	0.0829935
$91$	−3.17609	−0.332944
$92$	7.72908	0.805813
$93$	−7.45011	−0.772540
$94$	−12.3604	−1.27488
$95$	−5.17578	−0.531024
$96$	−1.00000	−0.102062
$97$	10.3262	1.04847	0.524234	−	0.851574i	$-0.324352\pi$
$97$	10.3262	1.04847	0.524234	+	0.851574i	$0.324352\pi$
$98$	1.00000	0.101015
$99$	3.10786	0.312351
$100$	−4.38009	−0.438009
$101$	9.13693	0.909159	0.454579	−	0.890706i	$-0.349790\pi$
$101$	9.13693	0.909159	0.454579	+	0.890706i	$0.349790\pi$
$102$	6.03246	0.597303
$103$	−18.4793	−1.82082	−0.910409	−	0.413709i	$-0.864233\pi$
$103$	−18.4793	−1.82082	−0.910409	+	0.413709i	$0.864233\pi$
$104$	−3.17609	−0.311441
$105$	−0.787345	−0.0768370
$106$	−4.55300	−0.442226
$107$	19.8339	1.91742	0.958710	−	0.284386i	$-0.0917898\pi$
$107$	19.8339	1.91742	0.958710	+	0.284386i	$0.0917898\pi$
$108$	−1.00000	−0.0962250
$109$	−10.8371	−1.03800	−0.519002	−	0.854773i	$-0.673696\pi$
$109$	−10.8371	−1.03800	−0.519002	+	0.854773i	$0.673696\pi$
$110$	2.44696	0.233308
$111$	2.94964	0.279967
$112$	1.00000	0.0944911
$113$	−6.68394	−0.628773	−0.314386	−	0.949295i	$-0.601799\pi$
$113$	−6.68394	−0.628773	−0.314386	+	0.949295i	$0.601799\pi$
$114$	6.57371	0.615684
$115$	6.08546	0.567472
$116$	−2.30852	−0.214341
$117$	−3.17609	−0.293629
$118$	2.31491	0.213105
$119$	−6.03246	−0.552995
$120$	−0.787345	−0.0718745
$121$	−1.34123	−0.121930
$122$	−2.16410	−0.195928
$123$	−0.573298	−0.0516926
$124$	7.45011	0.669039
$125$	−7.38537	−0.660567
$126$	1.00000	0.0890871
$127$	12.3489	1.09578	0.547892	−	0.836549i	$-0.315430\pi$
$127$	12.3489	1.09578	0.547892	+	0.836549i	$0.315430\pi$
$128$	1.00000	0.0883883
$129$	11.6859	1.02889
$130$	−2.50068	−0.219324
$131$	−3.25247	−0.284170	−0.142085	−	0.989854i	$-0.545381\pi$
$131$	−3.25247	−0.284170	−0.142085	+	0.989854i	$0.545381\pi$
$132$	−3.10786	−0.270504
$133$	−6.57371	−0.570013
$134$	1.26056	0.108896
$135$	−0.787345	−0.0677639
$136$	−6.03246	−0.517279
$137$	0.660427	0.0564241	0.0282121	−	0.999602i	$-0.491019\pi$
$137$	0.660427	0.0564241	0.0282121	+	0.999602i	$0.491019\pi$
$138$	−7.72908	−0.657943
$139$	17.1408	1.45386	0.726932	−	0.686709i	$-0.240945\pi$
$139$	17.1408	1.45386	0.726932	+	0.686709i	$0.240945\pi$
$140$	0.787345	0.0665428
$141$	12.3604	1.04093
$142$	10.7445	0.901662
$143$	−9.87082	−0.825439
$144$	1.00000	0.0833333
$145$	−1.81760	−0.150944
$146$	−12.3749	−1.02415
$147$	−1.00000	−0.0824786
$148$	−2.94964	−0.242459
$149$	13.4481	1.10171	0.550854	−	0.834601i	$-0.314302\pi$
$149$	13.4481	1.10171	0.550854	+	0.834601i	$0.314302\pi$
$150$	4.38009	0.357633
$151$	−5.02461	−0.408897	−0.204448	−	0.978877i	$-0.565540\pi$
$151$	−5.02461	−0.408897	−0.204448	+	0.978877i	$0.565540\pi$
$152$	−6.57371	−0.533198
$153$	−6.03246	−0.487696
$154$	3.10786	0.250438
$155$	5.86581	0.471153
$156$	3.17609	0.254290
$157$	−14.1881	−1.13233	−0.566166	−	0.824291i	$-0.691574\pi$
$157$	−14.1881	−1.13233	−0.566166	+	0.824291i	$0.691574\pi$
$158$	−4.55084	−0.362045
$159$	4.55300	0.361076
$160$	0.787345	0.0622451
$161$	7.72908	0.609137
$162$	1.00000	0.0785674
$163$	−0.339013	−0.0265535	−0.0132768	−	0.999912i	$-0.504226\pi$
$163$	−0.339013	−0.0265535	−0.0132768	+	0.999912i	$0.504226\pi$
$164$	0.573298	0.0447671
$165$	−2.44696	−0.190495
$166$	−15.8764	−1.23225
$167$	−7.76873	−0.601162	−0.300581	−	0.953756i	$-0.597181\pi$
$167$	−7.76873	−0.601162	−0.300581	+	0.953756i	$0.597181\pi$
$168$	−1.00000	−0.0771517
$169$	−2.91248	−0.224037
$170$	−4.74963	−0.364280
$171$	−6.57371	−0.502704
$172$	−11.6859	−0.891041
$173$	11.6793	0.887959	0.443979	−	0.896037i	$-0.353566\pi$
$173$	11.6793	0.887959	0.443979	+	0.896037i	$0.353566\pi$
$174$	2.30852	0.175008
$175$	−4.38009	−0.331103
$176$	3.10786	0.234264
$177$	−2.31491	−0.173999
$178$	−6.99840	−0.524553
$179$	25.9592	1.94028	0.970142	−	0.242537i	$-0.0779796\pi$
$179$	25.9592	1.94028	0.970142	+	0.242537i	$0.0779796\pi$
$180$	0.787345	0.0586853
$181$	10.5309	0.782757	0.391379	−	0.920230i	$-0.371998\pi$
$181$	10.5309	0.782757	0.391379	+	0.920230i	$0.371998\pi$
$182$	−3.17609	−0.235427
$183$	2.16410	0.159975
$184$	7.72908	0.569796
$185$	−2.32238	−0.170745
$186$	−7.45011	−0.546268
$187$	−18.7480	−1.37099
$188$	−12.3604	−0.901475
$189$	−1.00000	−0.0727393
$190$	−5.17578	−0.375490
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−1.00000	−0.0721688
$193$	−13.3011	−0.957436	−0.478718	−	0.877969i	$-0.658898\pi$
$193$	−13.3011	−0.957436	−0.478718	+	0.877969i	$0.658898\pi$
$194$	10.3262	0.741379
$195$	2.50068	0.179077
$196$	1.00000	0.0714286
$197$	−3.71297	−0.264538	−0.132269	−	0.991214i	$-0.542226\pi$
$197$	−3.71297	−0.264538	−0.132269	+	0.991214i	$0.542226\pi$
$198$	3.10786	0.220866
$199$	0.795350	0.0563808	0.0281904	−	0.999603i	$-0.491026\pi$
$199$	0.795350	0.0563808	0.0281904	+	0.999603i	$0.491026\pi$
$200$	−4.38009	−0.309719
$201$	−1.26056	−0.0889129
$202$	9.13693	0.642872
$203$	−2.30852	−0.162026
$204$	6.03246	0.422357
$205$	0.451384	0.0315260
$206$	−18.4793	−1.28751
$207$	7.72908	0.537209
$208$	−3.17609	−0.220222
$209$	−20.4301	−1.41318
$210$	−0.787345	−0.0543320
$211$	9.64774	0.664178	0.332089	−	0.943248i	$-0.392247\pi$
$211$	9.64774	0.664178	0.332089	+	0.943248i	$0.392247\pi$
$212$	−4.55300	−0.312701
$213$	−10.7445	−0.736204
$214$	19.8339	1.35582
$215$	−9.20083	−0.627492
$216$	−1.00000	−0.0680414
$217$	7.45011	0.505746
$218$	−10.8371	−0.733980
$219$	12.3749	0.836216
$220$	2.44696	0.164974
$221$	19.1596	1.28882
$222$	2.94964	0.197967
$223$	3.52177	0.235835	0.117918	−	0.993023i	$-0.462378\pi$
$223$	3.52177	0.235835	0.117918	+	0.993023i	$0.462378\pi$
$224$	1.00000	0.0668153
$225$	−4.38009	−0.292006
$226$	−6.68394	−0.444609
$227$	−4.06783	−0.269992	−0.134996	−	0.990846i	$-0.543102\pi$
$227$	−4.06783	−0.269992	−0.134996	+	0.990846i	$0.543102\pi$
$228$	6.57371	0.435354
$229$	14.6188	0.966037	0.483018	−	0.875610i	$-0.339540\pi$
$229$	14.6188	0.966037	0.483018	+	0.875610i	$0.339540\pi$
$230$	6.08546	0.401263
$231$	−3.10786	−0.204482
$232$	−2.30852	−0.151562
$233$	−22.5258	−1.47572	−0.737858	−	0.674956i	$-0.764163\pi$
$233$	−22.5258	−1.47572	−0.737858	+	0.674956i	$0.764163\pi$
$234$	−3.17609	−0.207627
$235$	−9.73190	−0.634839
$236$	2.31491	0.150688
$237$	4.55084	0.295609
$238$	−6.03246	−0.391026
$239$	−29.4502	−1.90498	−0.952489	−	0.304574i	$-0.901486\pi$
$239$	−29.4502	−1.90498	−0.952489	+	0.304574i	$0.901486\pi$
$240$	−0.787345	−0.0508229
$241$	−20.2144	−1.30213	−0.651063	−	0.759023i	$-0.725677\pi$
$241$	−20.2144	−1.30213	−0.651063	+	0.759023i	$0.725677\pi$
$242$	−1.34123	−0.0862173
$243$	−1.00000	−0.0641500
$244$	−2.16410	−0.138542
$245$	0.787345	0.0503017
$246$	−0.573298	−0.0365522
$247$	20.8787	1.32848
$248$	7.45011	0.473082
$249$	15.8764	1.00613
$250$	−7.38537	−0.467092
$251$	−3.52489	−0.222489	−0.111244	−	0.993793i	$-0.535484\pi$
$251$	−3.52489	−0.222489	−0.111244	+	0.993793i	$0.535484\pi$
$252$	1.00000	0.0629941
$253$	24.0209	1.51018
$254$	12.3489	0.774837
$255$	4.74963	0.297433
$256$	1.00000	0.0625000
$257$	23.1174	1.44203	0.721013	−	0.692921i	$-0.243677\pi$
$257$	23.1174	1.44203	0.721013	+	0.692921i	$0.243677\pi$
$258$	11.6859	0.727532
$259$	−2.94964	−0.183282
$260$	−2.50068	−0.155085
$261$	−2.30852	−0.142894
$262$	−3.25247	−0.200938
$263$	1.49805	0.0923735	0.0461868	−	0.998933i	$-0.485293\pi$
$263$	1.49805	0.0923735	0.0461868	+	0.998933i	$0.485293\pi$
$264$	−3.10786	−0.191275
$265$	−3.58478	−0.220211
$266$	−6.57371	−0.403060
$267$	6.99840	0.428295
$268$	1.26056	0.0770008
$269$	17.3321	1.05676	0.528379	−	0.849009i	$-0.322800\pi$
$269$	17.3321	1.05676	0.528379	+	0.849009i	$0.322800\pi$
$270$	−0.787345	−0.0479163
$271$	7.64931	0.464662	0.232331	−	0.972637i	$-0.425365\pi$
$271$	7.64931	0.464662	0.232331	+	0.972637i	$0.425365\pi$
$272$	−6.03246	−0.365772
$273$	3.17609	0.192225
$274$	0.660427	0.0398979
$275$	−13.6127	−0.820876
$276$	−7.72908	−0.465236
$277$	−19.7297	−1.18544	−0.592722	−	0.805407i	$-0.701947\pi$
$277$	−19.7297	−1.18544	−0.592722	+	0.805407i	$0.701947\pi$
$278$	17.1408	1.02804
$279$	7.45011	0.446026
$280$	0.787345	0.0470529
$281$	1.62172	0.0967435	0.0483718	−	0.998829i	$-0.484597\pi$
$281$	1.62172	0.0967435	0.0483718	+	0.998829i	$0.484597\pi$
$282$	12.3604	0.736051
$283$	23.0942	1.37281	0.686405	−	0.727219i	$-0.259188\pi$
$283$	23.0942	1.37281	0.686405	+	0.727219i	$0.259188\pi$
$284$	10.7445	0.637571
$285$	5.17578	0.306587
$286$	−9.87082	−0.583674
$287$	0.573298	0.0338407
$288$	1.00000	0.0589256
$289$	19.3906	1.14062
$290$	−1.81760	−0.106733
$291$	−10.3262	−0.605333
$292$	−12.3749	−0.724184
$293$	−18.9162	−1.10510	−0.552549	−	0.833481i	$-0.686345\pi$
$293$	−18.9162	−1.10510	−0.552549	+	0.833481i	$0.686345\pi$
$294$	−1.00000	−0.0583212
$295$	1.82263	0.106118
$296$	−2.94964	−0.171444
$297$	−3.10786	−0.180336
$298$	13.4481	0.779026
$299$	−24.5482	−1.41966
$300$	4.38009	0.252884
$301$	−11.6859	−0.673564
$302$	−5.02461	−0.289134
$303$	−9.13693	−0.524903
$304$	−6.57371	−0.377028
$305$	−1.70389	−0.0975646
$306$	−6.03246	−0.344853
$307$	33.3994	1.90621	0.953103	−	0.302645i	$-0.0978695\pi$
$307$	33.3994	1.90621	0.953103	+	0.302645i	$0.0978695\pi$
$308$	3.10786	0.177087
$309$	18.4793	1.05125
$310$	5.86581	0.333155
$311$	−26.5715	−1.50673	−0.753365	−	0.657603i	$-0.771571\pi$
$311$	−26.5715	−1.50673	−0.753365	+	0.657603i	$0.771571\pi$
$312$	3.17609	0.179810
$313$	6.53029	0.369114	0.184557	−	0.982822i	$-0.440915\pi$
$313$	6.53029	0.369114	0.184557	+	0.982822i	$0.440915\pi$
$314$	−14.1881	−0.800679
$315$	0.787345	0.0443619
$316$	−4.55084	−0.256004
$317$	−20.9817	−1.17845	−0.589226	−	0.807968i	$-0.700567\pi$
$317$	−20.9817	−1.17845	−0.589226	+	0.807968i	$0.700567\pi$
$318$	4.55300	0.255319
$319$	−7.17455	−0.401697
$320$	0.787345	0.0440139
$321$	−19.8339	−1.10702
$322$	7.72908	0.430725
$323$	39.6556	2.20650
$324$	1.00000	0.0555556
$325$	13.9115	0.771673
$326$	−0.339013	−0.0187762
$327$	10.8371	0.599292
$328$	0.573298	0.0316551
$329$	−12.3604	−0.681451
$330$	−2.44696	−0.134701
$331$	−7.12861	−0.391824	−0.195912	−	0.980622i	$-0.562767\pi$
$331$	−7.12861	−0.391824	−0.195912	+	0.980622i	$0.562767\pi$
$332$	−15.8764	−0.871331
$333$	−2.94964	−0.161639
$334$	−7.76873	−0.425086
$335$	0.992494	0.0542257
$336$	−1.00000	−0.0545545
$337$	−33.6815	−1.83475	−0.917373	−	0.398028i	$-0.869695\pi$
$337$	−33.6815	−1.83475	−0.917373	+	0.398028i	$0.869695\pi$
$338$	−2.91248	−0.158418
$339$	6.68394	0.363022
$340$	−4.74963	−0.257585
$341$	23.1539	1.25385
$342$	−6.57371	−0.355465
$343$	1.00000	0.0539949
$344$	−11.6859	−0.630061
$345$	−6.08546	−0.327630
$346$	11.6793	0.627882
$347$	10.1472	0.544732	0.272366	−	0.962194i	$-0.412194\pi$
$347$	10.1472	0.544732	0.272366	+	0.962194i	$0.412194\pi$
$348$	2.30852	0.123750
$349$	−5.72472	−0.306437	−0.153219	−	0.988192i	$-0.548964\pi$
$349$	−5.72472	−0.306437	−0.153219	+	0.988192i	$0.548964\pi$
$350$	−4.38009	−0.234126
$351$	3.17609	0.169527
$352$	3.10786	0.165649
$353$	−7.20843	−0.383666	−0.191833	−	0.981428i	$-0.561443\pi$
$353$	−7.20843	−0.383666	−0.191833	+	0.981428i	$0.561443\pi$
$354$	−2.31491	−0.123036
$355$	8.45967	0.448993
$356$	−6.99840	−0.370915
$357$	6.03246	0.319272
$358$	25.9592	1.37199
$359$	−26.2771	−1.38685	−0.693427	−	0.720527i	$-0.743900\pi$
$359$	−26.2771	−1.38685	−0.693427	+	0.720527i	$0.743900\pi$
$360$	0.787345	0.0414967
$361$	24.2136	1.27440
$362$	10.5309	0.553493
$363$	1.34123	0.0703962
$364$	−3.17609	−0.166472
$365$	−9.74329	−0.509987
$366$	2.16410	0.113119
$367$	−31.9647	−1.66854	−0.834272	−	0.551353i	$-0.814112\pi$
$367$	−31.9647	−1.66854	−0.834272	+	0.551353i	$0.814112\pi$
$368$	7.72908	0.402906
$369$	0.573298	0.0298447
$370$	−2.32238	−0.120735
$371$	−4.55300	−0.236380
$372$	−7.45011	−0.386270
$373$	−10.7555	−0.556901	−0.278450	−	0.960451i	$-0.589821\pi$
$373$	−10.7555	−0.556901	−0.278450	+	0.960451i	$0.589821\pi$
$374$	−18.7480	−0.969437
$375$	7.38537	0.381379
$376$	−12.3604	−0.637439
$377$	7.33205	0.377620
$378$	−1.00000	−0.0514344
$379$	7.96093	0.408925	0.204463	−	0.978874i	$-0.434455\pi$
$379$	7.96093	0.408925	0.204463	+	0.978874i	$0.434455\pi$
$380$	−5.17578	−0.265512
$381$	−12.3489	−0.632652
$382$	−1.00000	−0.0511645
$383$	−8.06773	−0.412242	−0.206121	−	0.978527i	$-0.566084\pi$
$383$	−8.06773	−0.412242	−0.206121	+	0.978527i	$0.566084\pi$
$384$	−1.00000	−0.0510310
$385$	2.44696	0.124708
$386$	−13.3011	−0.677009
$387$	−11.6859	−0.594027
$388$	10.3262	0.524234
$389$	0.624901	0.0316838	0.0158419	−	0.999875i	$-0.494957\pi$
$389$	0.624901	0.0316838	0.0158419	+	0.999875i	$0.494957\pi$
$390$	2.50068	0.126627
$391$	−46.6254	−2.35795
$392$	1.00000	0.0505076
$393$	3.25247	0.164065
$394$	−3.71297	−0.187057
$395$	−3.58308	−0.180284
$396$	3.10786	0.156176
$397$	1.33912	0.0672083	0.0336042	−	0.999435i	$-0.489301\pi$
$397$	1.33912	0.0672083	0.0336042	+	0.999435i	$0.489301\pi$
$398$	0.795350	0.0398673
$399$	6.57371	0.329097
$400$	−4.38009	−0.219004
$401$	4.53664	0.226549	0.113274	−	0.993564i	$-0.463866\pi$
$401$	4.53664	0.226549	0.113274	+	0.993564i	$0.463866\pi$
$402$	−1.26056	−0.0628709
$403$	−23.6622	−1.17870
$404$	9.13693	0.454579
$405$	0.787345	0.0391235
$406$	−2.30852	−0.114570
$407$	−9.16705	−0.454394
$408$	6.03246	0.298651
$409$	37.3683	1.84774	0.923871	−	0.382704i	$-0.125007\pi$
$409$	37.3683	1.84774	0.923871	+	0.382704i	$0.125007\pi$
$410$	0.451384	0.0222923
$411$	−0.660427	−0.0325765
$412$	−18.4793	−0.910409
$413$	2.31491	0.113909
$414$	7.72908	0.379864
$415$	−12.5002	−0.613611
$416$	−3.17609	−0.155720
$417$	−17.1408	−0.839389
$418$	−20.4301	−0.999271
$419$	−17.5722	−0.858459	−0.429229	−	0.903196i	$-0.641215\pi$
$419$	−17.5722	−0.858459	−0.429229	+	0.903196i	$0.641215\pi$
$420$	−0.787345	−0.0384185
$421$	−20.1464	−0.981874	−0.490937	−	0.871195i	$-0.663345\pi$
$421$	−20.1464	−0.981874	−0.490937	+	0.871195i	$0.663345\pi$
$422$	9.64774	0.469645
$423$	−12.3604	−0.600983
$424$	−4.55300	−0.221113
$425$	26.4227	1.28169
$426$	−10.7445	−0.520575
$427$	−2.16410	−0.104728
$428$	19.8339	0.958710
$429$	9.87082	0.476568
$430$	−9.20083	−0.443704
$431$	3.49811	0.168498	0.0842489	−	0.996445i	$-0.473151\pi$
$431$	3.49811	0.168498	0.0842489	+	0.996445i	$0.473151\pi$
$432$	−1.00000	−0.0481125
$433$	−31.9108	−1.53353	−0.766767	−	0.641925i	$-0.778136\pi$
$433$	−31.9108	−1.53353	−0.766767	+	0.641925i	$0.778136\pi$
$434$	7.45011	0.357617
$435$	1.81760	0.0871473
$436$	−10.8371	−0.519002
$437$	−50.8087	−2.43051
$438$	12.3749	0.591294
$439$	−29.9329	−1.42862	−0.714310	−	0.699829i	$-0.753259\pi$
$439$	−29.9329	−1.42862	−0.714310	+	0.699829i	$0.753259\pi$
$440$	2.44696	0.116654
$441$	1.00000	0.0476190
$442$	19.1596	0.911330
$443$	−13.4259	−0.637884	−0.318942	−	0.947774i	$-0.603328\pi$
$443$	−13.4259	−0.637884	−0.318942	+	0.947774i	$0.603328\pi$
$444$	2.94964	0.139984
$445$	−5.51016	−0.261207
$446$	3.52177	0.166761
$447$	−13.4481	−0.636072
$448$	1.00000	0.0472456
$449$	21.6324	1.02090	0.510448	−	0.859908i	$-0.329479\pi$
$449$	21.6324	1.02090	0.510448	+	0.859908i	$0.329479\pi$
$450$	−4.38009	−0.206479
$451$	1.78173	0.0838983
$452$	−6.68394	−0.314386
$453$	5.02461	0.236077
$454$	−4.06783	−0.190913
$455$	−2.50068	−0.117234
$456$	6.57371	0.307842
$457$	6.57289	0.307467	0.153733	−	0.988112i	$-0.450870\pi$
$457$	6.57289	0.307467	0.153733	+	0.988112i	$0.450870\pi$
$458$	14.6188	0.683091
$459$	6.03246	0.281571
$460$	6.08546	0.283736
$461$	23.0106	1.07171	0.535854	−	0.844310i	$-0.319990\pi$
$461$	23.0106	1.07171	0.535854	+	0.844310i	$0.319990\pi$
$462$	−3.10786	−0.144591
$463$	31.5609	1.46676	0.733380	−	0.679819i	$-0.237942\pi$
$463$	31.5609	1.46676	0.733380	+	0.679819i	$0.237942\pi$
$464$	−2.30852	−0.107170
$465$	−5.86581	−0.272020
$466$	−22.5258	−1.04349
$467$	8.81747	0.408024	0.204012	−	0.978968i	$-0.434602\pi$
$467$	8.81747	0.408024	0.204012	+	0.978968i	$0.434602\pi$
$468$	−3.17609	−0.146815
$469$	1.26056	0.0582071
$470$	−9.73190	−0.448899
$471$	14.1881	0.653752
$472$	2.31491	0.106552
$473$	−36.3181	−1.66991
$474$	4.55084	0.209027
$475$	28.7934	1.32113
$476$	−6.03246	−0.276497
$477$	−4.55300	−0.208467
$478$	−29.4502	−1.34702
$479$	−2.42342	−0.110729	−0.0553646	−	0.998466i	$-0.517632\pi$
$479$	−2.42342	−0.110729	−0.0553646	+	0.998466i	$0.517632\pi$
$480$	−0.787345	−0.0359372
$481$	9.36830	0.427158
$482$	−20.2144	−0.920743
$483$	−7.72908	−0.351686
$484$	−1.34123	−0.0609649
$485$	8.13030	0.369178
$486$	−1.00000	−0.0453609
$487$	−13.6494	−0.618512	−0.309256	−	0.950979i	$-0.600080\pi$
$487$	−13.6494	−0.618512	−0.309256	+	0.950979i	$0.600080\pi$
$488$	−2.16410	−0.0979641
$489$	0.339013	0.0153307
$490$	0.787345	0.0355686
$491$	−8.36703	−0.377599	−0.188799	−	0.982016i	$-0.560460\pi$
$491$	−8.36703	−0.377599	−0.188799	+	0.982016i	$0.560460\pi$
$492$	−0.573298	−0.0258463
$493$	13.9261	0.627198
$494$	20.8787	0.939375
$495$	2.44696	0.109983
$496$	7.45011	0.334520
$497$	10.7445	0.481959
$498$	15.8764	0.711439
$499$	−6.77635	−0.303351	−0.151676	−	0.988430i	$-0.548467\pi$
$499$	−6.77635	−0.303351	−0.151676	+	0.988430i	$0.548467\pi$
$500$	−7.38537	−0.330284
$501$	7.76873	0.347081
$502$	−3.52489	−0.157323
$503$	−39.5394	−1.76297	−0.881487	−	0.472209i	$-0.843457\pi$
$503$	−39.5394	−1.76297	−0.881487	+	0.472209i	$0.843457\pi$
$504$	1.00000	0.0445435
$505$	7.19392	0.320125
$506$	24.0209	1.06786
$507$	2.91248	0.129348
$508$	12.3489	0.547892
$509$	−17.6877	−0.783995	−0.391998	−	0.919966i	$-0.628216\pi$
$509$	−17.6877	−0.783995	−0.391998	+	0.919966i	$0.628216\pi$
$510$	4.74963	0.210317
$511$	−12.3749	−0.547432
$512$	1.00000	0.0441942
$513$	6.57371	0.290236
$514$	23.1174	1.01967
$515$	−14.5496	−0.641131
$516$	11.6859	0.514443
$517$	−38.4143	−1.68946
$518$	−2.94964	−0.129600
$519$	−11.6793	−0.512663
$520$	−2.50068	−0.109662
$521$	−33.2313	−1.45589	−0.727944	−	0.685637i	$-0.759524\pi$
$521$	−33.2313	−1.45589	−0.727944	+	0.685637i	$0.759524\pi$
$522$	−2.30852	−0.101041
$523$	8.29716	0.362809	0.181405	−	0.983409i	$-0.441936\pi$
$523$	8.29716	0.362809	0.181405	+	0.983409i	$0.441936\pi$
$524$	−3.25247	−0.142085
$525$	4.38009	0.191163
$526$	1.49805	0.0653180
$527$	−44.9425	−1.95773
$528$	−3.10786	−0.135252
$529$	36.7387	1.59734
$530$	−3.58478	−0.155713
$531$	2.31491	0.100458
$532$	−6.57371	−0.285006
$533$	−1.82084	−0.0788695
$534$	6.99840	0.302851
$535$	15.6162	0.675146
$536$	1.26056	0.0544478
$537$	−25.9592	−1.12022
$538$	17.3321	0.747240
$539$	3.10786	0.133865
$540$	−0.787345	−0.0338820
$541$	18.9639	0.815320	0.407660	−	0.913134i	$-0.366345\pi$
$541$	18.9639	0.815320	0.407660	+	0.913134i	$0.366345\pi$
$542$	7.64931	0.328566
$543$	−10.5309	−0.451925
$544$	−6.03246	−0.258640
$545$	−8.53253	−0.365493
$546$	3.17609	0.135924
$547$	−26.1908	−1.11984	−0.559919	−	0.828547i	$-0.689168\pi$
$547$	−26.1908	−1.11984	−0.559919	+	0.828547i	$0.689168\pi$
$548$	0.660427	0.0282121
$549$	−2.16410	−0.0923614
$550$	−13.6127	−0.580447
$551$	15.1755	0.646499
$552$	−7.72908	−0.328972
$553$	−4.55084	−0.193521
$554$	−19.7297	−0.838236
$555$	2.32238	0.0985797
$556$	17.1408	0.726932
$557$	23.5653	0.998495	0.499248	−	0.866459i	$-0.333610\pi$
$557$	23.5653	0.998495	0.499248	+	0.866459i	$0.333610\pi$
$558$	7.45011	0.315388
$559$	37.1154	1.56981
$560$	0.787345	0.0332714
$561$	18.7480	0.791542
$562$	1.62172	0.0684080
$563$	−40.8196	−1.72034	−0.860170	−	0.510007i	$-0.829643\pi$
$563$	−40.8196	−1.72034	−0.860170	+	0.510007i	$0.829643\pi$
$564$	12.3604	0.520467
$565$	−5.26257	−0.221398
$566$	23.0942	0.970723
$567$	1.00000	0.0419961
$568$	10.7445	0.450831
$569$	−4.16797	−0.174730	−0.0873652	−	0.996176i	$-0.527845\pi$
$569$	−4.16797	−0.174730	−0.0873652	+	0.996176i	$0.527845\pi$
$570$	5.17578	0.216789
$571$	−13.4206	−0.561633	−0.280817	−	0.959761i	$-0.590605\pi$
$571$	−13.4206	−0.561633	−0.280817	+	0.959761i	$0.590605\pi$
$572$	−9.87082	−0.412720
$573$	1.00000	0.0417756
$574$	0.573298	0.0239290
$575$	−33.8541	−1.41181
$576$	1.00000	0.0416667
$577$	13.0445	0.543049	0.271525	−	0.962431i	$-0.412472\pi$
$577$	13.0445	0.543049	0.271525	+	0.962431i	$0.412472\pi$
$578$	19.3906	0.806543
$579$	13.3011	0.552776
$580$	−1.81760	−0.0754718
$581$	−15.8764	−0.658664
$582$	−10.3262	−0.428035
$583$	−14.1501	−0.586036
$584$	−12.3749	−0.512075
$585$	−2.50068	−0.103390
$586$	−18.9162	−0.781422
$587$	−6.13758	−0.253325	−0.126662	−	0.991946i	$-0.540427\pi$
$587$	−6.13758	−0.253325	−0.126662	+	0.991946i	$0.540427\pi$
$588$	−1.00000	−0.0412393
$589$	−48.9748	−2.01797
$590$	1.82263	0.0750366
$591$	3.71297	0.152731
$592$	−2.94964	−0.121229
$593$	15.4665	0.635133	0.317567	−	0.948236i	$-0.397134\pi$
$593$	15.4665	0.635133	0.317567	+	0.948236i	$0.397134\pi$
$594$	−3.10786	−0.127517
$595$	−4.74963	−0.194716
$596$	13.4481	0.550854
$597$	−0.795350	−0.0325515
$598$	−24.5482	−1.00385
$599$	−3.38749	−0.138409	−0.0692045	−	0.997602i	$-0.522046\pi$
$599$	−3.38749	−0.138409	−0.0692045	+	0.997602i	$0.522046\pi$
$600$	4.38009	0.178816
$601$	46.0725	1.87934	0.939668	−	0.342087i	$-0.111134\pi$
$601$	46.0725	1.87934	0.939668	+	0.342087i	$0.111134\pi$
$602$	−11.6859	−0.476281
$603$	1.26056	0.0513339
$604$	−5.02461	−0.204448
$605$	−1.05601	−0.0429329
$606$	−9.13693	−0.371162
$607$	−2.15066	−0.0872928	−0.0436464	−	0.999047i	$-0.513897\pi$
$607$	−2.15066	−0.0872928	−0.0436464	+	0.999047i	$0.513897\pi$
$608$	−6.57371	−0.266599
$609$	2.30852	0.0935459
$610$	−1.70389	−0.0689886
$611$	39.2577	1.58820
$612$	−6.03246	−0.243848
$613$	10.3845	0.419424	0.209712	−	0.977763i	$-0.432747\pi$
$613$	10.3845	0.419424	0.209712	+	0.977763i	$0.432747\pi$
$614$	33.3994	1.34789
$615$	−0.451384	−0.0182015
$616$	3.10786	0.125219
$617$	33.0758	1.33158	0.665790	−	0.746139i	$-0.268094\pi$
$617$	33.0758	1.33158	0.665790	+	0.746139i	$0.268094\pi$
$618$	18.4793	0.743346
$619$	0.219252	0.00881248	0.00440624	−	0.999990i	$-0.498597\pi$
$619$	0.219252	0.00881248	0.00440624	+	0.999990i	$0.498597\pi$
$620$	5.86581	0.235576
$621$	−7.72908	−0.310157
$622$	−26.5715	−1.06542
$623$	−6.99840	−0.280385
$624$	3.17609	0.127145
$625$	16.0856	0.643424
$626$	6.53029	0.261003
$627$	20.4301	0.815901
$628$	−14.1881	−0.566166
$629$	17.7936	0.709476
$630$	0.787345	0.0313686
$631$	10.3762	0.413070	0.206535	−	0.978439i	$-0.433781\pi$
$631$	10.3762	0.413070	0.206535	+	0.978439i	$0.433781\pi$
$632$	−4.55084	−0.181023
$633$	−9.64774	−0.383463
$634$	−20.9817	−0.833292
$635$	9.72282	0.385838
$636$	4.55300	0.180538
$637$	−3.17609	−0.125841
$638$	−7.17455	−0.284043
$639$	10.7445	0.425048
$640$	0.787345	0.0311226
$641$	−41.5838	−1.64246	−0.821231	−	0.570595i	$-0.806713\pi$
$641$	−41.5838	−1.64246	−0.821231	+	0.570595i	$0.806713\pi$
$642$	−19.8339	−0.782783
$643$	34.6305	1.36569	0.682846	−	0.730562i	$-0.260742\pi$
$643$	34.6305	1.36569	0.682846	+	0.730562i	$0.260742\pi$
$644$	7.72908	0.304569
$645$	9.20083	0.362283
$646$	39.6556	1.56023
$647$	−30.0432	−1.18112	−0.590561	−	0.806993i	$-0.701093\pi$
$647$	−30.0432	−1.18112	−0.590561	+	0.806993i	$0.701093\pi$
$648$	1.00000	0.0392837
$649$	7.19441	0.282405
$650$	13.9115	0.545655
$651$	−7.45011	−0.291993
$652$	−0.339013	−0.0132768
$653$	−2.73514	−0.107034	−0.0535172	−	0.998567i	$-0.517043\pi$
$653$	−2.73514	−0.107034	−0.0535172	+	0.998567i	$0.517043\pi$
$654$	10.8371	0.423764
$655$	−2.56082	−0.100059
$656$	0.573298	0.0223835
$657$	−12.3749	−0.482789
$658$	−12.3604	−0.481859
$659$	−8.78312	−0.342142	−0.171071	−	0.985259i	$-0.554723\pi$
$659$	−8.78312	−0.342142	−0.171071	+	0.985259i	$0.554723\pi$
$660$	−2.44696	−0.0952477
$661$	−28.3497	−1.10268	−0.551338	−	0.834282i	$-0.685883\pi$
$661$	−28.3497	−1.10268	−0.551338	+	0.834282i	$0.685883\pi$
$662$	−7.12861	−0.277061
$663$	−19.1596	−0.744098
$664$	−15.8764	−0.616124
$665$	−5.17578	−0.200708
$666$	−2.94964	−0.114296
$667$	−17.8427	−0.690874
$668$	−7.76873	−0.300581
$669$	−3.52177	−0.136159
$670$	0.992494	0.0383434
$671$	−6.72570	−0.259643
$672$	−1.00000	−0.0385758
$673$	36.5498	1.40889	0.704445	−	0.709759i	$-0.251196\pi$
$673$	36.5498	1.40889	0.704445	+	0.709759i	$0.251196\pi$
$674$	−33.6815	−1.29736
$675$	4.38009	0.168590
$676$	−2.91248	−0.112018
$677$	35.6680	1.37083	0.685417	−	0.728151i	$-0.259620\pi$
$677$	35.6680	1.37083	0.685417	+	0.728151i	$0.259620\pi$
$678$	6.68394	0.256695
$679$	10.3262	0.396284
$680$	−4.74963	−0.182140
$681$	4.06783	0.155880
$682$	23.1539	0.886607
$683$	−4.60274	−0.176119	−0.0880594	−	0.996115i	$-0.528067\pi$
$683$	−4.60274	−0.176119	−0.0880594	+	0.996115i	$0.528067\pi$
$684$	−6.57371	−0.251352
$685$	0.519984	0.0198676
$686$	1.00000	0.0381802
$687$	−14.6188	−0.557742
$688$	−11.6859	−0.445521
$689$	14.4607	0.550909
$690$	−6.08546	−0.231669
$691$	−31.8827	−1.21287	−0.606437	−	0.795131i	$-0.707402\pi$
$691$	−31.8827	−1.21287	−0.606437	+	0.795131i	$0.707402\pi$
$692$	11.6793	0.443979
$693$	3.10786	0.118058
$694$	10.1472	0.385183
$695$	13.4957	0.511923
$696$	2.30852	0.0875042
$697$	−3.45840	−0.130996
$698$	−5.72472	−0.216684
$699$	22.5258	0.852005
$700$	−4.38009	−0.165552
$701$	38.0069	1.43550	0.717750	−	0.696301i	$-0.245172\pi$
$701$	38.0069	1.43550	0.717750	+	0.696301i	$0.245172\pi$
$702$	3.17609	0.119874
$703$	19.3900	0.731309
$704$	3.10786	0.117132
$705$	9.73190	0.366525
$706$	−7.20843	−0.271293
$707$	9.13693	0.343630
$708$	−2.31491	−0.0869996
$709$	−19.3979	−0.728504	−0.364252	−	0.931300i	$-0.618675\pi$
$709$	−19.3979	−0.728504	−0.364252	+	0.931300i	$0.618675\pi$
$710$	8.45967	0.317486
$711$	−4.55084	−0.170670
$712$	−6.99840	−0.262276
$713$	57.5825	2.15648
$714$	6.03246	0.225759
$715$	−7.77174	−0.290647
$716$	25.9592	0.970142
$717$	29.4502	1.09984
$718$	−26.2771	−0.980654
$719$	−33.5200	−1.25009	−0.625043	−	0.780590i	$-0.714919\pi$
$719$	−33.5200	−1.25009	−0.625043	+	0.780590i	$0.714919\pi$
$720$	0.787345	0.0293426
$721$	−18.4793	−0.688205
$722$	24.2136	0.901137
$723$	20.2144	0.751783
$724$	10.5309	0.391379
$725$	10.1115	0.375532
$726$	1.34123	0.0497776
$727$	−4.11719	−0.152698	−0.0763491	−	0.997081i	$-0.524326\pi$
$727$	−4.11719	−0.152698	−0.0763491	+	0.997081i	$0.524326\pi$
$728$	−3.17609	−0.117714
$729$	1.00000	0.0370370
$730$	−9.74329	−0.360615
$731$	70.4947	2.60734
$732$	2.16410	0.0799873
$733$	40.6643	1.50197	0.750984	−	0.660320i	$-0.229579\pi$
$733$	40.6643	1.50197	0.750984	+	0.660320i	$0.229579\pi$
$734$	−31.9647	−1.17984
$735$	−0.787345	−0.0290417
$736$	7.72908	0.284898
$737$	3.91763	0.144308
$738$	0.573298	0.0211034
$739$	11.2177	0.412650	0.206325	−	0.978483i	$-0.433850\pi$
$739$	11.2177	0.412650	0.206325	+	0.978483i	$0.433850\pi$
$740$	−2.32238	−0.0853725
$741$	−20.8787	−0.766997
$742$	−4.55300	−0.167146
$743$	−19.3706	−0.710638	−0.355319	−	0.934745i	$-0.615628\pi$
$743$	−19.3706	−0.710638	−0.355319	+	0.934745i	$0.615628\pi$
$744$	−7.45011	−0.273134
$745$	10.5883	0.387924
$746$	−10.7555	−0.393788
$747$	−15.8764	−0.580887
$748$	−18.7480	−0.685496
$749$	19.8339	0.724716
$750$	7.38537	0.269676
$751$	−22.9462	−0.837320	−0.418660	−	0.908143i	$-0.637500\pi$
$751$	−22.9462	−0.837320	−0.418660	+	0.908143i	$0.637500\pi$
$752$	−12.3604	−0.450737
$753$	3.52489	0.128454
$754$	7.33205	0.267018
$755$	−3.95610	−0.143977
$756$	−1.00000	−0.0363696
$757$	27.5933	1.00290	0.501449	−	0.865187i	$-0.332801\pi$
$757$	27.5933	1.00290	0.501449	+	0.865187i	$0.332801\pi$
$758$	7.96093	0.289154
$759$	−24.0209	−0.871903
$760$	−5.17578	−0.187745
$761$	53.0225	1.92206	0.961032	−	0.276438i	$-0.0891541\pi$
$761$	53.0225	1.92206	0.961032	+	0.276438i	$0.0891541\pi$
$762$	−12.3489	−0.447352
$763$	−10.8371	−0.392329
$764$	−1.00000	−0.0361787
$765$	−4.74963	−0.171723
$766$	−8.06773	−0.291499
$767$	−7.35235	−0.265478
$768$	−1.00000	−0.0360844
$769$	27.8732	1.00513	0.502566	−	0.864539i	$-0.332389\pi$
$769$	27.8732	1.00513	0.502566	+	0.864539i	$0.332389\pi$
$770$	2.44696	0.0881822
$771$	−23.1174	−0.832554
$772$	−13.3011	−0.478718
$773$	7.36357	0.264849	0.132425	−	0.991193i	$-0.457724\pi$
$773$	7.36357	0.264849	0.132425	+	0.991193i	$0.457724\pi$
$774$	−11.6859	−0.420041
$775$	−32.6321	−1.17218
$776$	10.3262	0.370689
$777$	2.94964	0.105818
$778$	0.624901	0.0224038
$779$	−3.76869	−0.135027
$780$	2.50068	0.0895386
$781$	33.3925	1.19488
$782$	−46.6254	−1.66732
$783$	2.30852	0.0824997
$784$	1.00000	0.0357143
$785$	−11.1709	−0.398707
$786$	3.25247	0.116012
$787$	24.0899	0.858711	0.429356	−	0.903135i	$-0.358741\pi$
$787$	24.0899	0.858711	0.429356	+	0.903135i	$0.358741\pi$
$788$	−3.71297	−0.132269
$789$	−1.49805	−0.0533319
$790$	−3.58308	−0.127480
$791$	−6.68394	−0.237654
$792$	3.10786	0.110433
$793$	6.87336	0.244080
$794$	1.33912	0.0475235
$795$	3.58478	0.127139
$796$	0.795350	0.0281904
$797$	16.5023	0.584542	0.292271	−	0.956336i	$-0.405589\pi$
$797$	16.5023	0.584542	0.292271	+	0.956336i	$0.405589\pi$
$798$	6.57371	0.232707
$799$	74.5636	2.63787
$800$	−4.38009	−0.154859
$801$	−6.99840	−0.247276
$802$	4.53664	0.160194
$803$	−38.4593	−1.35720
$804$	−1.26056	−0.0444564
$805$	6.08546	0.214484
$806$	−23.6622	−0.833465
$807$	−17.3321	−0.610119
$808$	9.13693	0.321436
$809$	−20.7379	−0.729107	−0.364553	−	0.931182i	$-0.618778\pi$
$809$	−20.7379	−0.729107	−0.364553	+	0.931182i	$0.618778\pi$
$810$	0.787345	0.0276645
$811$	32.8723	1.15430	0.577151	−	0.816637i	$-0.304164\pi$
$811$	32.8723	1.15430	0.577151	+	0.816637i	$0.304164\pi$
$812$	−2.30852	−0.0810131
$813$	−7.64931	−0.268273
$814$	−9.16705	−0.321305
$815$	−0.266920	−0.00934981
$816$	6.03246	0.211178
$817$	76.8196	2.68758
$818$	37.3683	1.30655
$819$	−3.17609	−0.110981
$820$	0.451384	0.0157630
$821$	−38.9292	−1.35864	−0.679319	−	0.733843i	$-0.737725\pi$
$821$	−38.9292	−1.35864	−0.679319	+	0.733843i	$0.737725\pi$
$822$	−0.660427	−0.0230350
$823$	41.4787	1.44586	0.722928	−	0.690924i	$-0.242796\pi$
$823$	41.4787	1.44586	0.722928	+	0.690924i	$0.242796\pi$
$824$	−18.4793	−0.643757
$825$	13.6127	0.473933
$826$	2.31491	0.0805460
$827$	31.9800	1.11205	0.556027	−	0.831164i	$-0.312325\pi$
$827$	31.9800	1.11205	0.556027	+	0.831164i	$0.312325\pi$
$828$	7.72908	0.268604
$829$	8.77347	0.304715	0.152358	−	0.988325i	$-0.451313\pi$
$829$	8.77347	0.304715	0.152358	+	0.988325i	$0.451313\pi$
$830$	−12.5002	−0.433889
$831$	19.7297	0.684416
$832$	−3.17609	−0.110111
$833$	−6.03246	−0.209012
$834$	−17.1408	−0.593538
$835$	−6.11667	−0.211676
$836$	−20.4301	−0.706591
$837$	−7.45011	−0.257513
$838$	−17.5722	−0.607022
$839$	−0.421934	−0.0145668	−0.00728340	−	0.999973i	$-0.502318\pi$
$839$	−0.421934	−0.0145668	−0.00728340	+	0.999973i	$0.502318\pi$
$840$	−0.787345	−0.0271660
$841$	−23.6707	−0.816232
$842$	−20.1464	−0.694290
$843$	−1.62172	−0.0558549
$844$	9.64774	0.332089
$845$	−2.29313	−0.0788860
$846$	−12.3604	−0.424959
$847$	−1.34123	−0.0460851
$848$	−4.55300	−0.156351
$849$	−23.0942	−0.792592
$850$	26.4227	0.906291
$851$	−22.7980	−0.781505
$852$	−10.7445	−0.368102
$853$	−14.7406	−0.504708	−0.252354	−	0.967635i	$-0.581205\pi$
$853$	−14.7406	−0.504708	−0.252354	+	0.967635i	$0.581205\pi$
$854$	−2.16410	−0.0740539
$855$	−5.17578	−0.177008
$856$	19.8339	0.677910
$857$	12.4809	0.426338	0.213169	−	0.977015i	$-0.431621\pi$
$857$	12.4809	0.426338	0.213169	+	0.977015i	$0.431621\pi$
$858$	9.87082	0.336984
$859$	19.2658	0.657339	0.328670	−	0.944445i	$-0.393400\pi$
$859$	19.2658	0.657339	0.328670	+	0.944445i	$0.393400\pi$
$860$	−9.20083	−0.313746
$861$	−0.573298	−0.0195380
$862$	3.49811	0.119146
$863$	21.2641	0.723838	0.361919	−	0.932210i	$-0.382122\pi$
$863$	21.2641	0.723838	0.361919	+	0.932210i	$0.382122\pi$
$864$	−1.00000	−0.0340207
$865$	9.19562	0.312661
$866$	−31.9108	−1.08437
$867$	−19.3906	−0.658539
$868$	7.45011	0.252873
$869$	−14.1433	−0.479780
$870$	1.81760	0.0616225
$871$	−4.00364	−0.135658
$872$	−10.8371	−0.366990
$873$	10.3262	0.349489
$874$	−50.8087	−1.71863
$875$	−7.38537	−0.249671
$876$	12.3749	0.418108
$877$	37.7141	1.27352	0.636758	−	0.771064i	$-0.280275\pi$
$877$	37.7141	1.27352	0.636758	+	0.771064i	$0.280275\pi$
$878$	−29.9329	−1.01019
$879$	18.9162	0.638028
$880$	2.44696	0.0824869
$881$	8.81234	0.296895	0.148448	−	0.988920i	$-0.452572\pi$
$881$	8.81234	0.296895	0.148448	+	0.988920i	$0.452572\pi$
$882$	1.00000	0.0336718
$883$	−30.8629	−1.03862	−0.519309	−	0.854586i	$-0.673811\pi$
$883$	−30.8629	−1.03862	−0.519309	+	0.854586i	$0.673811\pi$
$884$	19.1596	0.644408
$885$	−1.82263	−0.0612671
$886$	−13.4259	−0.451052
$887$	49.5227	1.66281	0.831405	−	0.555667i	$-0.187537\pi$
$887$	49.5227	1.66281	0.831405	+	0.555667i	$0.187537\pi$
$888$	2.94964	0.0989833
$889$	12.3489	0.414168
$890$	−5.51016	−0.184701
$891$	3.10786	0.104117
$892$	3.52177	0.117918
$893$	81.2536	2.71905
$894$	−13.4481	−0.449771
$895$	20.4389	0.683197
$896$	1.00000	0.0334077
$897$	24.5482	0.819642
$898$	21.6324	0.721883
$899$	−17.1987	−0.573609
$900$	−4.38009	−0.146003
$901$	27.4658	0.915018
$902$	1.78173	0.0593251
$903$	11.6859	0.388882
$904$	−6.68394	−0.222305
$905$	8.29147	0.275618
$906$	5.02461	0.166931
$907$	5.74690	0.190823	0.0954113	−	0.995438i	$-0.469583\pi$
$907$	5.74690	0.190823	0.0954113	+	0.995438i	$0.469583\pi$
$908$	−4.06783	−0.134996
$909$	9.13693	0.303053
$910$	−2.50068	−0.0828966
$911$	−4.05088	−0.134212	−0.0671059	−	0.997746i	$-0.521377\pi$
$911$	−4.05088	−0.134212	−0.0671059	+	0.997746i	$0.521377\pi$
$912$	6.57371	0.217677
$913$	−49.3416	−1.63297
$914$	6.57289	0.217412
$915$	1.70389	0.0563289
$916$	14.6188	0.483018
$917$	−3.25247	−0.107406
$918$	6.03246	0.199101
$919$	−15.5746	−0.513758	−0.256879	−	0.966444i	$-0.582694\pi$
$919$	−15.5746	−0.513758	−0.256879	+	0.966444i	$0.582694\pi$
$920$	6.08546	0.200632
$921$	−33.3994	−1.10055
$922$	23.0106	0.757813
$923$	−34.1256	−1.12326
$924$	−3.10786	−0.102241
$925$	12.9197	0.424796
$926$	31.5609	1.03716
$927$	−18.4793	−0.606939
$928$	−2.30852	−0.0757808
$929$	51.2961	1.68297	0.841485	−	0.540281i	$-0.181682\pi$
$929$	51.2961	1.68297	0.841485	+	0.540281i	$0.181682\pi$
$930$	−5.86581	−0.192347
$931$	−6.57371	−0.215445
$932$	−22.5258	−0.737858
$933$	26.5715	0.869911
$934$	8.81747	0.288516
$935$	−14.7612	−0.482742
$936$	−3.17609	−0.103814
$937$	5.99308	0.195786	0.0978928	−	0.995197i	$-0.468790\pi$
$937$	5.99308	0.195786	0.0978928	+	0.995197i	$0.468790\pi$
$938$	1.26056	0.0411587
$939$	−6.53029	−0.213108
$940$	−9.73190	−0.317420
$941$	−14.1375	−0.460869	−0.230434	−	0.973088i	$-0.574015\pi$
$941$	−14.1375	−0.460869	−0.230434	+	0.973088i	$0.574015\pi$
$942$	14.1881	0.462272
$943$	4.43107	0.144295
$944$	2.31491	0.0753439
$945$	−0.787345	−0.0256123
$946$	−36.3181	−1.18080
$947$	34.3338	1.11570	0.557849	−	0.829942i	$-0.311627\pi$
$947$	34.3338	1.11570	0.557849	+	0.829942i	$0.311627\pi$
$948$	4.55084	0.147804
$949$	39.3036	1.27585
$950$	28.7934	0.934181
$951$	20.9817	0.680380
$952$	−6.03246	−0.195513
$953$	7.53330	0.244028	0.122014	−	0.992528i	$-0.461065\pi$
$953$	7.53330	0.244028	0.122014	+	0.992528i	$0.461065\pi$
$954$	−4.55300	−0.147409
$955$	−0.787345	−0.0254779
$956$	−29.4502	−0.952489
$957$	7.17455	0.231920
$958$	−2.42342	−0.0782973
$959$	0.660427	0.0213263
$960$	−0.787345	−0.0254115
$961$	24.5041	0.790454
$962$	9.36830	0.302046
$963$	19.8339	0.639140
$964$	−20.2144	−0.651063
$965$	−10.4726	−0.337124
$966$	−7.72908	−0.248679
$967$	−1.97482	−0.0635058	−0.0317529	−	0.999496i	$-0.510109\pi$
$967$	−1.97482	−0.0635058	−0.0317529	+	0.999496i	$0.510109\pi$
$968$	−1.34123	−0.0431087
$969$	−39.6556	−1.27392
$970$	8.13030	0.261048
$971$	−41.4281	−1.32949	−0.664745	−	0.747070i	$-0.731460\pi$
$971$	−41.4281	−1.32949	−0.664745	+	0.747070i	$0.731460\pi$
$972$	−1.00000	−0.0320750
$973$	17.1408	0.549509
$974$	−13.6494	−0.437354
$975$	−13.9115	−0.445526
$976$	−2.16410	−0.0692711
$977$	39.5705	1.26597	0.632986	−	0.774163i	$-0.281829\pi$
$977$	39.5705	1.26597	0.632986	+	0.774163i	$0.281829\pi$
$978$	0.339013	0.0108404
$979$	−21.7500	−0.695134
$980$	0.787345	0.0251508
$981$	−10.8371	−0.346002
$982$	−8.36703	−0.267003
$983$	−13.0392	−0.415885	−0.207943	−	0.978141i	$-0.566677\pi$
$983$	−13.0392	−0.415885	−0.207943	+	0.978141i	$0.566677\pi$
$984$	−0.573298	−0.0182761
$985$	−2.92339	−0.0931470
$986$	13.9261	0.443496
$987$	12.3604	0.393436
$988$	20.8787	0.664239
$989$	−90.3213	−2.87205
$990$	2.44696	0.0777694
$991$	−12.1218	−0.385063	−0.192531	−	0.981291i	$-0.561670\pi$
$991$	−12.1218	−0.385063	−0.192531	+	0.981291i	$0.561670\pi$
$992$	7.45011	0.236541
$993$	7.12861	0.226220
$994$	10.7445	0.340796
$995$	0.626215	0.0198523
$996$	15.8764	0.503063
$997$	−36.2094	−1.14676	−0.573381	−	0.819289i	$-0.694368\pi$
$997$	−36.2094	−1.14676	−0.573381	+	0.819289i	$0.694368\pi$
$998$	−6.77635	−0.214502
$999$	2.94964	0.0933224

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.p.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.p.1.7	✓	9	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.787345 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.787345 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.787345 q^{10} +3.10786 q^{11} -1.00000 q^{12} -3.17609 q^{13} +1.00000 q^{14} -0.787345 q^{15} +1.00000 q^{16} -6.03246 q^{17} +1.00000 q^{18} -6.57371 q^{19} +0.787345 q^{20} -1.00000 q^{21} +3.10786 q^{22} +7.72908 q^{23} -1.00000 q^{24} -4.38009 q^{25} -3.17609 q^{26} -1.00000 q^{27} +1.00000 q^{28} -2.30852 q^{29} -0.787345 q^{30} +7.45011 q^{31} +1.00000 q^{32} -3.10786 q^{33} -6.03246 q^{34} +0.787345 q^{35} +1.00000 q^{36} -2.94964 q^{37} -6.57371 q^{38} +3.17609 q^{39} +0.787345 q^{40} +0.573298 q^{41} -1.00000 q^{42} -11.6859 q^{43} +3.10786 q^{44} +0.787345 q^{45} +7.72908 q^{46} -12.3604 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.38009 q^{50} +6.03246 q^{51} -3.17609 q^{52} -4.55300 q^{53} -1.00000 q^{54} +2.44696 q^{55} +1.00000 q^{56} +6.57371 q^{57} -2.30852 q^{58} +2.31491 q^{59} -0.787345 q^{60} -2.16410 q^{61} +7.45011 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.50068 q^{65} -3.10786 q^{66} +1.26056 q^{67} -6.03246 q^{68} -7.72908 q^{69} +0.787345 q^{70} +10.7445 q^{71} +1.00000 q^{72} -12.3749 q^{73} -2.94964 q^{74} +4.38009 q^{75} -6.57371 q^{76} +3.10786 q^{77} +3.17609 q^{78} -4.55084 q^{79} +0.787345 q^{80} +1.00000 q^{81} +0.573298 q^{82} -15.8764 q^{83} -1.00000 q^{84} -4.74963 q^{85} -11.6859 q^{86} +2.30852 q^{87} +3.10786 q^{88} -6.99840 q^{89} +0.787345 q^{90} -3.17609 q^{91} +7.72908 q^{92} -7.45011 q^{93} -12.3604 q^{94} -5.17578 q^{95} -1.00000 q^{96} +10.3262 q^{97} +1.00000 q^{98} +3.10786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} - 4 q^{10} - 3 q^{11} - 9 q^{12} - 9 q^{13} + 9 q^{14} + 4 q^{15} + 9 q^{16} - 12 q^{17} + 9 q^{18} - 18 q^{19} - 4 q^{20} - 9 q^{21} - 3 q^{22} + q^{23} - 9 q^{24} + 9 q^{25} - 9 q^{26} - 9 q^{27} + 9 q^{28} - 11 q^{29} + 4 q^{30} - 22 q^{31} + 9 q^{32} + 3 q^{33} - 12 q^{34} - 4 q^{35} + 9 q^{36} + 8 q^{37} - 18 q^{38} + 9 q^{39} - 4 q^{40} - 22 q^{41} - 9 q^{42} - 3 q^{43} - 3 q^{44} - 4 q^{45} + q^{46} - 49 q^{47} - 9 q^{48} + 9 q^{49} + 9 q^{50} + 12 q^{51} - 9 q^{52} + 8 q^{53} - 9 q^{54} - 19 q^{55} + 9 q^{56} + 18 q^{57} - 11 q^{58} - 18 q^{59} + 4 q^{60} + 3 q^{61} - 22 q^{62} + 9 q^{63} + 9 q^{64} - 32 q^{65} + 3 q^{66} - 11 q^{67} - 12 q^{68} - q^{69} - 4 q^{70} - 7 q^{71} + 9 q^{72} - 23 q^{73} + 8 q^{74} - 9 q^{75} - 18 q^{76} - 3 q^{77} + 9 q^{78} - 17 q^{79} - 4 q^{80} + 9 q^{81} - 22 q^{82} - 30 q^{83} - 9 q^{84} + 18 q^{85} - 3 q^{86} + 11 q^{87} - 3 q^{88} + 23 q^{89} - 4 q^{90} - 9 q^{91} + q^{92} + 22 q^{93} - 49 q^{94} - 30 q^{95} - 9 q^{96} - 46 q^{97} + 9 q^{98} - 3 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 - 4 * q^10 - 3 * q^11 - 9 * q^12 - 9 * q^13 + 9 * q^14 + 4 * q^15 + 9 * q^16 - 12 * q^17 + 9 * q^18 - 18 * q^19 - 4 * q^20 - 9 * q^21 - 3 * q^22 + q^23 - 9 * q^24 + 9 * q^25 - 9 * q^26 - 9 * q^27 + 9 * q^28 - 11 * q^29 + 4 * q^30 - 22 * q^31 + 9 * q^32 + 3 * q^33 - 12 * q^34 - 4 * q^35 + 9 * q^36 + 8 * q^37 - 18 * q^38 + 9 * q^39 - 4 * q^40 - 22 * q^41 - 9 * q^42 - 3 * q^43 - 3 * q^44 - 4 * q^45 + q^46 - 49 * q^47 - 9 * q^48 + 9 * q^49 + 9 * q^50 + 12 * q^51 - 9 * q^52 + 8 * q^53 - 9 * q^54 - 19 * q^55 + 9 * q^56 + 18 * q^57 - 11 * q^58 - 18 * q^59 + 4 * q^60 + 3 * q^61 - 22 * q^62 + 9 * q^63 + 9 * q^64 - 32 * q^65 + 3 * q^66 - 11 * q^67 - 12 * q^68 - q^69 - 4 * q^70 - 7 * q^71 + 9 * q^72 - 23 * q^73 + 8 * q^74 - 9 * q^75 - 18 * q^76 - 3 * q^77 + 9 * q^78 - 17 * q^79 - 4 * q^80 + 9 * q^81 - 22 * q^82 - 30 * q^83 - 9 * q^84 + 18 * q^85 - 3 * q^86 + 11 * q^87 - 3 * q^88 + 23 * q^89 - 4 * q^90 - 9 * q^91 + q^92 + 22 * q^93 - 49 * q^94 - 30 * q^95 - 9 * q^96 - 46 * q^97 + 9 * q^98 - 3 * q^99

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