LMFDB - Embedded newform 8022.2.a.q.1.8

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} - 4x^{8} - 11x^{7} + 36x^{6} + 50x^{5} - 70x^{4} - 73x^{3} + 14x^{2} + 22x + 4 $ x^9 - 4x^8 - 11x^7 + 36x^6 + 50x^5 - 70x^4 - 73x^3 + 14x^2 + 22x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.73248$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.78783 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.78783 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.78783 q^{10} +3.87162 q^{11} -1.00000 q^{12} -1.77309 q^{13} -1.00000 q^{14} -2.78783 q^{15} +1.00000 q^{16} -4.92433 q^{17} +1.00000 q^{18} -2.92905 q^{19} +2.78783 q^{20} +1.00000 q^{21} +3.87162 q^{22} -7.45250 q^{23} -1.00000 q^{24} +2.77199 q^{25} -1.77309 q^{26} -1.00000 q^{27} -1.00000 q^{28} +2.32003 q^{29} -2.78783 q^{30} -7.00803 q^{31} +1.00000 q^{32} -3.87162 q^{33} -4.92433 q^{34} -2.78783 q^{35} +1.00000 q^{36} -6.91304 q^{37} -2.92905 q^{38} +1.77309 q^{39} +2.78783 q^{40} +5.49771 q^{41} +1.00000 q^{42} -6.49700 q^{43} +3.87162 q^{44} +2.78783 q^{45} -7.45250 q^{46} -3.08734 q^{47} -1.00000 q^{48} +1.00000 q^{49} +2.77199 q^{50} +4.92433 q^{51} -1.77309 q^{52} -10.1437 q^{53} -1.00000 q^{54} +10.7934 q^{55} -1.00000 q^{56} +2.92905 q^{57} +2.32003 q^{58} -0.307379 q^{59} -2.78783 q^{60} -5.03671 q^{61} -7.00803 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.94308 q^{65} -3.87162 q^{66} -9.27874 q^{67} -4.92433 q^{68} +7.45250 q^{69} -2.78783 q^{70} -9.22153 q^{71} +1.00000 q^{72} +8.55945 q^{73} -6.91304 q^{74} -2.77199 q^{75} -2.92905 q^{76} -3.87162 q^{77} +1.77309 q^{78} -15.1734 q^{79} +2.78783 q^{80} +1.00000 q^{81} +5.49771 q^{82} +9.23135 q^{83} +1.00000 q^{84} -13.7282 q^{85} -6.49700 q^{86} -2.32003 q^{87} +3.87162 q^{88} +0.0377100 q^{89} +2.78783 q^{90} +1.77309 q^{91} -7.45250 q^{92} +7.00803 q^{93} -3.08734 q^{94} -8.16569 q^{95} -1.00000 q^{96} -8.64887 q^{97} +1.00000 q^{98} +3.87162 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 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 + 6 * q^5 - 9 * q^6 - 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} - 9 q^{6} - 9 q^{7} + 9 q^{8} + 9 q^{9} + 6 q^{10} - 7 q^{11} - 9 q^{12} - q^{13} - 9 q^{14} - 6 q^{15} + 9 q^{16} - 10 q^{17} + 9 q^{18} + 6 q^{20} + 9 q^{21} - 7 q^{22} - 19 q^{23} - 9 q^{24} + 5 q^{25} - q^{26} - 9 q^{27} - 9 q^{28} - 21 q^{29} - 6 q^{30} + 6 q^{31} + 9 q^{32} + 7 q^{33} - 10 q^{34} - 6 q^{35} + 9 q^{36} - 14 q^{37} + q^{39} + 6 q^{40} + 12 q^{41} + 9 q^{42} - 17 q^{43} - 7 q^{44} + 6 q^{45} - 19 q^{46} - 11 q^{47} - 9 q^{48} + 9 q^{49} + 5 q^{50} + 10 q^{51} - q^{52} - 12 q^{53} - 9 q^{54} - 21 q^{55} - 9 q^{56} - 21 q^{58} - 8 q^{59} - 6 q^{60} + q^{61} + 6 q^{62} - 9 q^{63} + 9 q^{64} - 8 q^{65} + 7 q^{66} - 31 q^{67} - 10 q^{68} + 19 q^{69} - 6 q^{70} - 41 q^{71} + 9 q^{72} - q^{73} - 14 q^{74} - 5 q^{75} + 7 q^{77} + q^{78} - 17 q^{79} + 6 q^{80} + 9 q^{81} + 12 q^{82} - 36 q^{83} + 9 q^{84} - 30 q^{85} - 17 q^{86} + 21 q^{87} - 7 q^{88} - 17 q^{89} + 6 q^{90} + q^{91} - 19 q^{92} - 6 q^{93} - 11 q^{94} - 50 q^{95} - 9 q^{96} - 14 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 - 9 * q^6 - 9 * q^7 + 9 * q^8 + 9 * q^9 + 6 * q^10 - 7 * q^11 - 9 * q^12 - q^13 - 9 * q^14 - 6 * q^15 + 9 * q^16 - 10 * q^17 + 9 * q^18 + 6 * q^20 + 9 * q^21 - 7 * q^22 - 19 * q^23 - 9 * q^24 + 5 * q^25 - q^26 - 9 * q^27 - 9 * q^28 - 21 * q^29 - 6 * q^30 + 6 * q^31 + 9 * q^32 + 7 * q^33 - 10 * q^34 - 6 * q^35 + 9 * q^36 - 14 * q^37 + q^39 + 6 * q^40 + 12 * q^41 + 9 * q^42 - 17 * q^43 - 7 * q^44 + 6 * q^45 - 19 * q^46 - 11 * q^47 - 9 * q^48 + 9 * q^49 + 5 * q^50 + 10 * q^51 - q^52 - 12 * q^53 - 9 * q^54 - 21 * q^55 - 9 * q^56 - 21 * q^58 - 8 * q^59 - 6 * q^60 + q^61 + 6 * q^62 - 9 * q^63 + 9 * q^64 - 8 * q^65 + 7 * q^66 - 31 * q^67 - 10 * q^68 + 19 * q^69 - 6 * q^70 - 41 * q^71 + 9 * q^72 - q^73 - 14 * q^74 - 5 * q^75 + 7 * q^77 + q^78 - 17 * q^79 + 6 * q^80 + 9 * q^81 + 12 * q^82 - 36 * q^83 + 9 * q^84 - 30 * q^85 - 17 * q^86 + 21 * q^87 - 7 * q^88 - 17 * q^89 + 6 * q^90 + q^91 - 19 * q^92 - 6 * q^93 - 11 * q^94 - 50 * q^95 - 9 * q^96 - 14 * q^97 + 9 * q^98 - 7 * 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
$5$	2.78783	1.24676	0.623378	−	0.781921i	$-0.285760\pi$
$5$	2.78783	1.24676	0.623378	+	0.781921i	$0.285760\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.78783	0.881589
$11$	3.87162	1.16734	0.583669	−	0.811992i	$-0.301617\pi$
$11$	3.87162	1.16734	0.583669	+	0.811992i	$0.301617\pi$
$12$	−1.00000	−0.288675
$13$	−1.77309	−0.491768	−0.245884	−	0.969299i	$-0.579078\pi$
$13$	−1.77309	−0.491768	−0.245884	+	0.969299i	$0.579078\pi$
$14$	−1.00000	−0.267261
$15$	−2.78783	−0.719815
$16$	1.00000	0.250000
$17$	−4.92433	−1.19433	−0.597163	−	0.802120i	$-0.703705\pi$
$17$	−4.92433	−1.19433	−0.597163	+	0.802120i	$0.703705\pi$
$18$	1.00000	0.235702
$19$	−2.92905	−0.671970	−0.335985	−	0.941867i	$-0.609069\pi$
$19$	−2.92905	−0.671970	−0.335985	+	0.941867i	$0.609069\pi$
$20$	2.78783	0.623378
$21$	1.00000	0.218218
$22$	3.87162	0.825433
$23$	−7.45250	−1.55395	−0.776977	−	0.629529i	$-0.783248\pi$
$23$	−7.45250	−1.55395	−0.776977	+	0.629529i	$0.783248\pi$
$24$	−1.00000	−0.204124
$25$	2.77199	0.554399
$26$	−1.77309	−0.347732
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	2.32003	0.430819	0.215409	−	0.976524i	$-0.430891\pi$
$29$	2.32003	0.430819	0.215409	+	0.976524i	$0.430891\pi$
$30$	−2.78783	−0.508986
$31$	−7.00803	−1.25868	−0.629339	−	0.777131i	$-0.716674\pi$
$31$	−7.00803	−1.25868	−0.629339	+	0.777131i	$0.716674\pi$
$32$	1.00000	0.176777
$33$	−3.87162	−0.673963
$34$	−4.92433	−0.844516
$35$	−2.78783	−0.471229
$36$	1.00000	0.166667
$37$	−6.91304	−1.13650	−0.568249	−	0.822857i	$-0.692379\pi$
$37$	−6.91304	−1.13650	−0.568249	+	0.822857i	$0.692379\pi$
$38$	−2.92905	−0.475154
$39$	1.77309	0.283922
$40$	2.78783	0.440795
$41$	5.49771	0.858598	0.429299	−	0.903162i	$-0.358761\pi$
$41$	5.49771	0.858598	0.429299	+	0.903162i	$0.358761\pi$
$42$	1.00000	0.154303
$43$	−6.49700	−0.990784	−0.495392	−	0.868670i	$-0.664976\pi$
$43$	−6.49700	−0.990784	−0.495392	+	0.868670i	$0.664976\pi$
$44$	3.87162	0.583669
$45$	2.78783	0.415585
$46$	−7.45250	−1.09881
$47$	−3.08734	−0.450335	−0.225168	−	0.974320i	$-0.572293\pi$
$47$	−3.08734	−0.450335	−0.225168	+	0.974320i	$0.572293\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	2.77199	0.392019
$51$	4.92433	0.689544
$52$	−1.77309	−0.245884
$53$	−10.1437	−1.39335	−0.696673	−	0.717389i	$-0.745337\pi$
$53$	−10.1437	−1.39335	−0.696673	+	0.717389i	$0.745337\pi$
$54$	−1.00000	−0.136083
$55$	10.7934	1.45539
$56$	−1.00000	−0.133631
$57$	2.92905	0.387962
$58$	2.32003	0.304635
$59$	−0.307379	−0.0400174	−0.0200087	−	0.999800i	$-0.506369\pi$
$59$	−0.307379	−0.0400174	−0.0200087	+	0.999800i	$0.506369\pi$
$60$	−2.78783	−0.359907
$61$	−5.03671	−0.644884	−0.322442	−	0.946589i	$-0.604504\pi$
$61$	−5.03671	−0.644884	−0.322442	+	0.946589i	$0.604504\pi$
$62$	−7.00803	−0.890020
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−4.94308	−0.613114
$66$	−3.87162	−0.476564
$67$	−9.27874	−1.13358	−0.566789	−	0.823863i	$-0.691815\pi$
$67$	−9.27874	−1.13358	−0.566789	+	0.823863i	$0.691815\pi$
$68$	−4.92433	−0.597163
$69$	7.45250	0.897175
$70$	−2.78783	−0.333209
$71$	−9.22153	−1.09439	−0.547197	−	0.837004i	$-0.684305\pi$
$71$	−9.22153	−1.09439	−0.547197	+	0.837004i	$0.684305\pi$
$72$	1.00000	0.117851
$73$	8.55945	1.00181	0.500904	−	0.865503i	$-0.333001\pi$
$73$	8.55945	1.00181	0.500904	+	0.865503i	$0.333001\pi$
$74$	−6.91304	−0.803625
$75$	−2.77199	−0.320082
$76$	−2.92905	−0.335985
$77$	−3.87162	−0.441212
$78$	1.77309	0.200763
$79$	−15.1734	−1.70715	−0.853573	−	0.520974i	$-0.825569\pi$
$79$	−15.1734	−1.70715	−0.853573	+	0.520974i	$0.825569\pi$
$80$	2.78783	0.311689
$81$	1.00000	0.111111
$82$	5.49771	0.607120
$83$	9.23135	1.01327	0.506636	−	0.862160i	$-0.330889\pi$
$83$	9.23135	1.01327	0.506636	+	0.862160i	$0.330889\pi$
$84$	1.00000	0.109109
$85$	−13.7282	−1.48903
$86$	−6.49700	−0.700590
$87$	−2.32003	−0.248733
$88$	3.87162	0.412716
$89$	0.0377100	0.00399726	0.00199863	−	0.999998i	$-0.499364\pi$
$89$	0.0377100	0.00399726	0.00199863	+	0.999998i	$0.499364\pi$
$90$	2.78783	0.293863
$91$	1.77309	0.185871
$92$	−7.45250	−0.776977
$93$	7.00803	0.726698
$94$	−3.08734	−0.318435
$95$	−8.16569	−0.837782
$96$	−1.00000	−0.102062
$97$	−8.64887	−0.878159	−0.439080	−	0.898448i	$-0.644695\pi$
$97$	−8.64887	−0.878159	−0.439080	+	0.898448i	$0.644695\pi$
$98$	1.00000	0.101015
$99$	3.87162	0.389113
$100$	2.77199	0.277199
$101$	16.0777	1.59979	0.799894	−	0.600141i	$-0.204889\pi$
$101$	16.0777	1.59979	0.799894	+	0.600141i	$0.204889\pi$
$102$	4.92433	0.487581
$103$	3.43281	0.338245	0.169123	−	0.985595i	$-0.445907\pi$
$103$	3.43281	0.338245	0.169123	+	0.985595i	$0.445907\pi$
$104$	−1.77309	−0.173866
$105$	2.78783	0.272064
$106$	−10.1437	−0.985244
$107$	5.35495	0.517683	0.258841	−	0.965920i	$-0.416659\pi$
$107$	5.35495	0.517683	0.258841	+	0.965920i	$0.416659\pi$
$108$	−1.00000	−0.0962250
$109$	−13.6218	−1.30473	−0.652365	−	0.757905i	$-0.726223\pi$
$109$	−13.6218	−1.30473	−0.652365	+	0.757905i	$0.726223\pi$
$110$	10.7934	1.02911
$111$	6.91304	0.656157
$112$	−1.00000	−0.0944911
$113$	−5.13925	−0.483460	−0.241730	−	0.970344i	$-0.577715\pi$
$113$	−5.13925	−0.483460	−0.241730	+	0.970344i	$0.577715\pi$
$114$	2.92905	0.274330
$115$	−20.7763	−1.93740
$116$	2.32003	0.215409
$117$	−1.77309	−0.163923
$118$	−0.307379	−0.0282966
$119$	4.92433	0.451413
$120$	−2.78783	−0.254493
$121$	3.98946	0.362678
$122$	−5.03671	−0.456002
$123$	−5.49771	−0.495712
$124$	−7.00803	−0.629339
$125$	−6.21130	−0.555556
$126$	−1.00000	−0.0890871
$127$	11.4828	1.01893	0.509466	−	0.860491i	$-0.329843\pi$
$127$	11.4828	1.01893	0.509466	+	0.860491i	$0.329843\pi$
$128$	1.00000	0.0883883
$129$	6.49700	0.572029
$130$	−4.94308	−0.433537
$131$	−15.3839	−1.34410	−0.672048	−	0.740508i	$-0.734585\pi$
$131$	−15.3839	−1.34410	−0.672048	+	0.740508i	$0.734585\pi$
$132$	−3.87162	−0.336981
$133$	2.92905	0.253981
$134$	−9.27874	−0.801561
$135$	−2.78783	−0.239938
$136$	−4.92433	−0.422258
$137$	1.25320	0.107068	0.0535342	−	0.998566i	$-0.482951\pi$
$137$	1.25320	0.107068	0.0535342	+	0.998566i	$0.482951\pi$
$138$	7.45250	0.634399
$139$	20.6802	1.75407	0.877036	−	0.480424i	$-0.159517\pi$
$139$	20.6802	1.75407	0.877036	+	0.480424i	$0.159517\pi$
$140$	−2.78783	−0.235615
$141$	3.08734	0.260001
$142$	−9.22153	−0.773853
$143$	−6.86475	−0.574059
$144$	1.00000	0.0833333
$145$	6.46785	0.537125
$146$	8.55945	0.708385
$147$	−1.00000	−0.0824786
$148$	−6.91304	−0.568249
$149$	22.8583	1.87263	0.936313	−	0.351167i	$-0.114215\pi$
$149$	22.8583	1.87263	0.936313	+	0.351167i	$0.114215\pi$
$150$	−2.77199	−0.226332
$151$	5.41118	0.440355	0.220178	−	0.975460i	$-0.429336\pi$
$151$	5.41118	0.440355	0.220178	+	0.975460i	$0.429336\pi$
$152$	−2.92905	−0.237577
$153$	−4.92433	−0.398109
$154$	−3.87162	−0.311984
$155$	−19.5372	−1.56926
$156$	1.77309	0.141961
$157$	18.3916	1.46781	0.733906	−	0.679251i	$-0.237695\pi$
$157$	18.3916	1.46781	0.733906	+	0.679251i	$0.237695\pi$
$158$	−15.1734	−1.20713
$159$	10.1437	0.804448
$160$	2.78783	0.220397
$161$	7.45250	0.587339
$162$	1.00000	0.0785674
$163$	−1.99302	−0.156105	−0.0780527	−	0.996949i	$-0.524870\pi$
$163$	−1.99302	−0.156105	−0.0780527	+	0.996949i	$0.524870\pi$
$164$	5.49771	0.429299
$165$	−10.7934	−0.840267
$166$	9.23135	0.716491
$167$	23.2725	1.80088	0.900441	−	0.434977i	$-0.143244\pi$
$167$	23.2725	1.80088	0.900441	+	0.434977i	$0.143244\pi$
$168$	1.00000	0.0771517
$169$	−9.85614	−0.758165
$170$	−13.7282	−1.05290
$171$	−2.92905	−0.223990
$172$	−6.49700	−0.495392
$173$	22.5193	1.71211	0.856055	−	0.516884i	$-0.172908\pi$
$173$	22.5193	1.71211	0.856055	+	0.516884i	$0.172908\pi$
$174$	−2.32003	−0.175881
$175$	−2.77199	−0.209543
$176$	3.87162	0.291835
$177$	0.307379	0.0231040
$178$	0.0377100	0.00282649
$179$	14.8487	1.10985	0.554923	−	0.831902i	$-0.312748\pi$
$179$	14.8487	1.10985	0.554923	+	0.831902i	$0.312748\pi$
$180$	2.78783	0.207793
$181$	6.93493	0.515470	0.257735	−	0.966216i	$-0.417024\pi$
$181$	6.93493	0.515470	0.257735	+	0.966216i	$0.417024\pi$
$182$	1.77309	0.131430
$183$	5.03671	0.372324
$184$	−7.45250	−0.549405
$185$	−19.2724	−1.41693
$186$	7.00803	0.513853
$187$	−19.0651	−1.39418
$188$	−3.08734	−0.225168
$189$	1.00000	0.0727393
$190$	−8.16569	−0.592401
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−1.00000	−0.0721688
$193$	15.4076	1.10906	0.554532	−	0.832163i	$-0.312897\pi$
$193$	15.4076	1.10906	0.554532	+	0.832163i	$0.312897\pi$
$194$	−8.64887	−0.620952
$195$	4.94308	0.353981
$196$	1.00000	0.0714286
$197$	−11.1559	−0.794826	−0.397413	−	0.917640i	$-0.630092\pi$
$197$	−11.1559	−0.794826	−0.397413	+	0.917640i	$0.630092\pi$
$198$	3.87162	0.275144
$199$	5.86353	0.415655	0.207827	−	0.978166i	$-0.433361\pi$
$199$	5.86353	0.415655	0.207827	+	0.978166i	$0.433361\pi$
$200$	2.77199	0.196010
$201$	9.27874	0.654472
$202$	16.0777	1.13122
$203$	−2.32003	−0.162834
$204$	4.92433	0.344772
$205$	15.3267	1.07046
$206$	3.43281	0.239175
$207$	−7.45250	−0.517984
$208$	−1.77309	−0.122942
$209$	−11.3402	−0.784416
$210$	2.78783	0.192379
$211$	−27.5386	−1.89583	−0.947917	−	0.318518i	$-0.896815\pi$
$211$	−27.5386	−1.89583	−0.947917	+	0.318518i	$0.896815\pi$
$212$	−10.1437	−0.696673
$213$	9.22153	0.631849
$214$	5.35495	0.366057
$215$	−18.1125	−1.23526
$216$	−1.00000	−0.0680414
$217$	7.00803	0.475736
$218$	−13.6218	−0.922583
$219$	−8.55945	−0.578394
$220$	10.7934	0.727693
$221$	8.73130	0.587331
$222$	6.91304	0.463973
$223$	−18.5167	−1.23997	−0.619984	−	0.784614i	$-0.712861\pi$
$223$	−18.5167	−1.23997	−0.619984	+	0.784614i	$0.712861\pi$
$224$	−1.00000	−0.0668153
$225$	2.77199	0.184800
$226$	−5.13925	−0.341858
$227$	−1.43455	−0.0952146	−0.0476073	−	0.998866i	$-0.515160\pi$
$227$	−1.43455	−0.0952146	−0.0476073	+	0.998866i	$0.515160\pi$
$228$	2.92905	0.193981
$229$	−24.5752	−1.62398	−0.811989	−	0.583673i	$-0.801615\pi$
$229$	−24.5752	−1.62398	−0.811989	+	0.583673i	$0.801615\pi$
$230$	−20.7763	−1.36995
$231$	3.87162	0.254734
$232$	2.32003	0.152317
$233$	−4.06656	−0.266409	−0.133205	−	0.991089i	$-0.542527\pi$
$233$	−4.06656	−0.266409	−0.133205	+	0.991089i	$0.542527\pi$
$234$	−1.77309	−0.115911
$235$	−8.60699	−0.561458
$236$	−0.307379	−0.0200087
$237$	15.1734	0.985621
$238$	4.92433	0.319197
$239$	5.87574	0.380070	0.190035	−	0.981777i	$-0.439140\pi$
$239$	5.87574	0.380070	0.190035	+	0.981777i	$0.439140\pi$
$240$	−2.78783	−0.179954
$241$	3.46514	0.223209	0.111605	−	0.993753i	$-0.464401\pi$
$241$	3.46514	0.223209	0.111605	+	0.993753i	$0.464401\pi$
$242$	3.98946	0.256452
$243$	−1.00000	−0.0641500
$244$	−5.03671	−0.322442
$245$	2.78783	0.178108
$246$	−5.49771	−0.350521
$247$	5.19347	0.330453
$248$	−7.00803	−0.445010
$249$	−9.23135	−0.585013
$250$	−6.21130	−0.392837
$251$	25.7524	1.62548	0.812738	−	0.582629i	$-0.197976\pi$
$251$	25.7524	1.62548	0.812738	+	0.582629i	$0.197976\pi$
$252$	−1.00000	−0.0629941
$253$	−28.8533	−1.81399
$254$	11.4828	0.720494
$255$	13.7282	0.859693
$256$	1.00000	0.0625000
$257$	−19.8977	−1.24119	−0.620593	−	0.784133i	$-0.713108\pi$
$257$	−19.8977	−1.24119	−0.620593	+	0.784133i	$0.713108\pi$
$258$	6.49700	0.404486
$259$	6.91304	0.429556
$260$	−4.94308	−0.306557
$261$	2.32003	0.143606
$262$	−15.3839	−0.950419
$263$	−29.2868	−1.80590	−0.902952	−	0.429742i	$-0.858605\pi$
$263$	−29.2868	−1.80590	−0.902952	+	0.429742i	$0.858605\pi$
$264$	−3.87162	−0.238282
$265$	−28.2789	−1.73716
$266$	2.92905	0.179591
$267$	−0.0377100	−0.00230782
$268$	−9.27874	−0.566789
$269$	15.2375	0.929044	0.464522	−	0.885562i	$-0.346226\pi$
$269$	15.2375	0.929044	0.464522	+	0.885562i	$0.346226\pi$
$270$	−2.78783	−0.169662
$271$	1.55854	0.0946743	0.0473371	−	0.998879i	$-0.484926\pi$
$271$	1.55854	0.0946743	0.0473371	+	0.998879i	$0.484926\pi$
$272$	−4.92433	−0.298581
$273$	−1.77309	−0.107312
$274$	1.25320	0.0757088
$275$	10.7321	0.647171
$276$	7.45250	0.448588
$277$	11.4321	0.686888	0.343444	−	0.939173i	$-0.388406\pi$
$277$	11.4321	0.686888	0.343444	+	0.939173i	$0.388406\pi$
$278$	20.6802	1.24032
$279$	−7.00803	−0.419560
$280$	−2.78783	−0.166605
$281$	9.53076	0.568558	0.284279	−	0.958742i	$-0.408246\pi$
$281$	9.53076	0.568558	0.284279	+	0.958742i	$0.408246\pi$
$282$	3.08734	0.183849
$283$	−6.90599	−0.410518	−0.205259	−	0.978708i	$-0.565804\pi$
$283$	−6.90599	−0.410518	−0.205259	+	0.978708i	$0.565804\pi$
$284$	−9.22153	−0.547197
$285$	8.16569	0.483693
$286$	−6.86475	−0.405921
$287$	−5.49771	−0.324519
$288$	1.00000	0.0589256
$289$	7.24903	0.426413
$290$	6.46785	0.379805
$291$	8.64887	0.507006
$292$	8.55945	0.500904
$293$	−1.40839	−0.0822789	−0.0411394	−	0.999153i	$-0.513099\pi$
$293$	−1.40839	−0.0822789	−0.0411394	+	0.999153i	$0.513099\pi$
$294$	−1.00000	−0.0583212
$295$	−0.856921	−0.0498919
$296$	−6.91304	−0.401813
$297$	−3.87162	−0.224654
$298$	22.8583	1.32415
$299$	13.2140	0.764184
$300$	−2.77199	−0.160041
$301$	6.49700	0.374481
$302$	5.41118	0.311378
$303$	−16.0777	−0.923638
$304$	−2.92905	−0.167992
$305$	−14.0415	−0.804013
$306$	−4.92433	−0.281505
$307$	−33.5833	−1.91670	−0.958349	−	0.285600i	$-0.907807\pi$
$307$	−33.5833	−1.91670	−0.958349	+	0.285600i	$0.907807\pi$
$308$	−3.87162	−0.220606
$309$	−3.43281	−0.195286
$310$	−19.5372	−1.10964
$311$	11.9862	0.679673	0.339837	−	0.940485i	$-0.389628\pi$
$311$	11.9862	0.679673	0.339837	+	0.940485i	$0.389628\pi$
$312$	1.77309	0.100382
$313$	19.7449	1.11605	0.558023	−	0.829825i	$-0.311560\pi$
$313$	19.7449	1.11605	0.558023	+	0.829825i	$0.311560\pi$
$314$	18.3916	1.03790
$315$	−2.78783	−0.157076
$316$	−15.1734	−0.853573
$317$	30.9056	1.73583	0.867916	−	0.496712i	$-0.165459\pi$
$317$	30.9056	1.73583	0.867916	+	0.496712i	$0.165459\pi$
$318$	10.1437	0.568831
$319$	8.98228	0.502911
$320$	2.78783	0.155844
$321$	−5.35495	−0.298884
$322$	7.45250	0.415311
$323$	14.4236	0.802550
$324$	1.00000	0.0555556
$325$	−4.91500	−0.272635
$326$	−1.99302	−0.110383
$327$	13.6218	0.753286
$328$	5.49771	0.303560
$329$	3.08734	0.170211
$330$	−10.7934	−0.594158
$331$	4.79568	0.263594	0.131797	−	0.991277i	$-0.457925\pi$
$331$	4.79568	0.263594	0.131797	+	0.991277i	$0.457925\pi$
$332$	9.23135	0.506636
$333$	−6.91304	−0.378833
$334$	23.2725	1.27342
$335$	−25.8675	−1.41329
$336$	1.00000	0.0545545
$337$	−24.7618	−1.34886	−0.674431	−	0.738338i	$-0.735611\pi$
$337$	−24.7618	−1.34886	−0.674431	+	0.738338i	$0.735611\pi$
$338$	−9.85614	−0.536103
$339$	5.13925	0.279126
$340$	−13.7282	−0.744516
$341$	−27.1324	−1.46930
$342$	−2.92905	−0.158385
$343$	−1.00000	−0.0539949
$344$	−6.49700	−0.350295
$345$	20.7763	1.11856
$346$	22.5193	1.21065
$347$	7.60240	0.408118	0.204059	−	0.978959i	$-0.434587\pi$
$347$	7.60240	0.408118	0.204059	+	0.978959i	$0.434587\pi$
$348$	−2.32003	−0.124367
$349$	6.48199	0.346973	0.173486	−	0.984836i	$-0.444497\pi$
$349$	6.48199	0.346973	0.173486	+	0.984836i	$0.444497\pi$
$350$	−2.77199	−0.148169
$351$	1.77309	0.0946407
$352$	3.87162	0.206358
$353$	27.0847	1.44158	0.720788	−	0.693156i	$-0.243780\pi$
$353$	27.0847	1.44158	0.720788	+	0.693156i	$0.243780\pi$
$354$	0.307379	0.0163370
$355$	−25.7081	−1.36444
$356$	0.0377100	0.00199863
$357$	−4.92433	−0.260623
$358$	14.8487	0.784780
$359$	29.4111	1.55226	0.776128	−	0.630575i	$-0.217181\pi$
$359$	29.4111	1.55226	0.776128	+	0.630575i	$0.217181\pi$
$360$	2.78783	0.146932
$361$	−10.4207	−0.548457
$362$	6.93493	0.364492
$363$	−3.98946	−0.209392
$364$	1.77309	0.0929353
$365$	23.8623	1.24901
$366$	5.03671	0.263273
$367$	0.776610	0.0405387	0.0202694	−	0.999795i	$-0.493548\pi$
$367$	0.776610	0.0405387	0.0202694	+	0.999795i	$0.493548\pi$
$368$	−7.45250	−0.388488
$369$	5.49771	0.286199
$370$	−19.2724	−1.00192
$371$	10.1437	0.526635
$372$	7.00803	0.363349
$373$	−30.1083	−1.55895	−0.779474	−	0.626435i	$-0.784513\pi$
$373$	−30.1083	−1.55895	−0.779474	+	0.626435i	$0.784513\pi$
$374$	−19.0651	−0.985835
$375$	6.21130	0.320750
$376$	−3.08734	−0.159218
$377$	−4.11363	−0.211863
$378$	1.00000	0.0514344
$379$	−35.6850	−1.83302	−0.916509	−	0.400015i	$-0.869005\pi$
$379$	−35.6850	−1.83302	−0.916509	+	0.400015i	$0.869005\pi$
$380$	−8.16569	−0.418891
$381$	−11.4828	−0.588281
$382$	1.00000	0.0511645
$383$	−10.4311	−0.533004	−0.266502	−	0.963834i	$-0.585868\pi$
$383$	−10.4311	−0.533004	−0.266502	+	0.963834i	$0.585868\pi$
$384$	−1.00000	−0.0510310
$385$	−10.7934	−0.550084
$386$	15.4076	0.784226
$387$	−6.49700	−0.330261
$388$	−8.64887	−0.439080
$389$	12.2465	0.620921	0.310460	−	0.950586i	$-0.399517\pi$
$389$	12.2465	0.620921	0.310460	+	0.950586i	$0.399517\pi$
$390$	4.94308	0.250303
$391$	36.6986	1.85593
$392$	1.00000	0.0505076
$393$	15.3839	0.776014
$394$	−11.1559	−0.562027
$395$	−42.3010	−2.12839
$396$	3.87162	0.194556
$397$	−7.11612	−0.357148	−0.178574	−	0.983927i	$-0.557148\pi$
$397$	−7.11612	−0.357148	−0.178574	+	0.983927i	$0.557148\pi$
$398$	5.86353	0.293912
$399$	−2.92905	−0.146636
$400$	2.77199	0.138600
$401$	−6.85352	−0.342248	−0.171124	−	0.985249i	$-0.554740\pi$
$401$	−6.85352	−0.342248	−0.171124	+	0.985249i	$0.554740\pi$
$402$	9.27874	0.462781
$403$	12.4259	0.618977
$404$	16.0777	0.799894
$405$	2.78783	0.138528
$406$	−2.32003	−0.115141
$407$	−26.7647	−1.32668
$408$	4.92433	0.243791
$409$	−33.2511	−1.64416	−0.822080	−	0.569371i	$-0.807187\pi$
$409$	−33.2511	−1.64416	−0.822080	+	0.569371i	$0.807187\pi$
$410$	15.3267	0.756931
$411$	−1.25320	−0.0618159
$412$	3.43281	0.169123
$413$	0.307379	0.0151252
$414$	−7.45250	−0.366270
$415$	25.7354	1.26330
$416$	−1.77309	−0.0869330
$417$	−20.6802	−1.01271
$418$	−11.3402	−0.554666
$419$	−29.7758	−1.45464	−0.727320	−	0.686298i	$-0.759235\pi$
$419$	−29.7758	−1.45464	−0.727320	+	0.686298i	$0.759235\pi$
$420$	2.78783	0.136032
$421$	3.86948	0.188587	0.0942936	−	0.995544i	$-0.469941\pi$
$421$	3.86948	0.188587	0.0942936	+	0.995544i	$0.469941\pi$
$422$	−27.5386	−1.34056
$423$	−3.08734	−0.150112
$424$	−10.1437	−0.492622
$425$	−13.6502	−0.662133
$426$	9.22153	0.446785
$427$	5.03671	0.243743
$428$	5.35495	0.258841
$429$	6.86475	0.331433
$430$	−18.1125	−0.873464
$431$	3.10033	0.149338	0.0746689	−	0.997208i	$-0.476210\pi$
$431$	3.10033	0.149338	0.0746689	+	0.997208i	$0.476210\pi$
$432$	−1.00000	−0.0481125
$433$	−30.8597	−1.48302	−0.741512	−	0.670939i	$-0.765891\pi$
$433$	−30.8597	−1.48302	−0.741512	+	0.670939i	$0.765891\pi$
$434$	7.00803	0.336396
$435$	−6.46785	−0.310110
$436$	−13.6218	−0.652365
$437$	21.8287	1.04421
$438$	−8.55945	−0.408986
$439$	32.8178	1.56631	0.783154	−	0.621828i	$-0.213610\pi$
$439$	32.8178	1.56631	0.783154	+	0.621828i	$0.213610\pi$
$440$	10.7934	0.514556
$441$	1.00000	0.0476190
$442$	8.73130	0.415305
$443$	−18.5230	−0.880053	−0.440026	−	0.897985i	$-0.645031\pi$
$443$	−18.5230	−0.880053	−0.440026	+	0.897985i	$0.645031\pi$
$444$	6.91304	0.328079
$445$	0.105129	0.00498360
$446$	−18.5167	−0.876790
$447$	−22.8583	−1.08116
$448$	−1.00000	−0.0472456
$449$	38.3628	1.81045	0.905226	−	0.424930i	$-0.139701\pi$
$449$	38.3628	1.81045	0.905226	+	0.424930i	$0.139701\pi$
$450$	2.77199	0.130673
$451$	21.2851	1.00227
$452$	−5.13925	−0.241730
$453$	−5.41118	−0.254239
$454$	−1.43455	−0.0673269
$455$	4.94308	0.231735
$456$	2.92905	0.137165
$457$	18.7196	0.875665	0.437833	−	0.899057i	$-0.355746\pi$
$457$	18.7196	0.875665	0.437833	+	0.899057i	$0.355746\pi$
$458$	−24.5752	−1.14833
$459$	4.92433	0.229848
$460$	−20.7763	−0.968700
$461$	4.46377	0.207898	0.103949	−	0.994583i	$-0.466852\pi$
$461$	4.46377	0.207898	0.103949	+	0.994583i	$0.466852\pi$
$462$	3.87162	0.180124
$463$	−22.7087	−1.05536	−0.527682	−	0.849442i	$-0.676939\pi$
$463$	−22.7087	−1.05536	−0.527682	+	0.849442i	$0.676939\pi$
$464$	2.32003	0.107705
$465$	19.5372	0.906015
$466$	−4.06656	−0.188380
$467$	−35.4033	−1.63827	−0.819135	−	0.573601i	$-0.805546\pi$
$467$	−35.4033	−1.63827	−0.819135	+	0.573601i	$0.805546\pi$
$468$	−1.77309	−0.0819613
$469$	9.27874	0.428452
$470$	−8.60699	−0.397011
$471$	−18.3916	−0.847442
$472$	−0.307379	−0.0141483
$473$	−25.1539	−1.15658
$474$	15.1734	0.696939
$475$	−8.11930	−0.372539
$476$	4.92433	0.225706
$477$	−10.1437	−0.464448
$478$	5.87574	0.268750
$479$	23.9289	1.09334	0.546670	−	0.837348i	$-0.315895\pi$
$479$	23.9289	1.09334	0.546670	+	0.837348i	$0.315895\pi$
$480$	−2.78783	−0.127246
$481$	12.2575	0.558893
$482$	3.46514	0.157833
$483$	−7.45250	−0.339100
$484$	3.98946	0.181339
$485$	−24.1116	−1.09485
$486$	−1.00000	−0.0453609
$487$	28.4828	1.29068	0.645339	−	0.763896i	$-0.276716\pi$
$487$	28.4828	1.29068	0.645339	+	0.763896i	$0.276716\pi$
$488$	−5.03671	−0.228001
$489$	1.99302	0.0901275
$490$	2.78783	0.125941
$491$	−31.0556	−1.40152	−0.700759	−	0.713398i	$-0.747155\pi$
$491$	−31.0556	−1.40152	−0.700759	+	0.713398i	$0.747155\pi$
$492$	−5.49771	−0.247856
$493$	−11.4246	−0.514538
$494$	5.19347	0.233665
$495$	10.7934	0.485128
$496$	−7.00803	−0.314670
$497$	9.22153	0.413642
$498$	−9.23135	−0.413667
$499$	−15.7916	−0.706930	−0.353465	−	0.935448i	$-0.614997\pi$
$499$	−15.7916	−0.706930	−0.353465	+	0.935448i	$0.614997\pi$
$500$	−6.21130	−0.277778
$501$	−23.2725	−1.03974
$502$	25.7524	1.14939
$503$	−40.0938	−1.78769	−0.893846	−	0.448374i	$-0.852003\pi$
$503$	−40.0938	−1.78769	−0.893846	+	0.448374i	$0.852003\pi$
$504$	−1.00000	−0.0445435
$505$	44.8218	1.99454
$506$	−28.8533	−1.28268
$507$	9.85614	0.437727
$508$	11.4828	0.509466
$509$	−25.3125	−1.12196	−0.560978	−	0.827831i	$-0.689575\pi$
$509$	−25.3125	−1.12196	−0.560978	+	0.827831i	$0.689575\pi$
$510$	13.7282	0.607895
$511$	−8.55945	−0.378648
$512$	1.00000	0.0441942
$513$	2.92905	0.129321
$514$	−19.8977	−0.877651
$515$	9.57010	0.421709
$516$	6.49700	0.286015
$517$	−11.9530	−0.525693
$518$	6.91304	0.303742
$519$	−22.5193	−0.988488
$520$	−4.94308	−0.216768
$521$	36.0957	1.58138	0.790690	−	0.612216i	$-0.209722\pi$
$521$	36.0957	1.58138	0.790690	+	0.612216i	$0.209722\pi$
$522$	2.32003	0.101545
$523$	−17.0978	−0.747635	−0.373818	−	0.927502i	$-0.621951\pi$
$523$	−17.0978	−0.747635	−0.373818	+	0.927502i	$0.621951\pi$
$524$	−15.3839	−0.672048
$525$	2.77199	0.120980
$526$	−29.2868	−1.27697
$527$	34.5098	1.50327
$528$	−3.87162	−0.168491
$529$	32.5397	1.41477
$530$	−28.2789	−1.22836
$531$	−0.307379	−0.0133391
$532$	2.92905	0.126990
$533$	−9.74795	−0.422231
$534$	−0.0377100	−0.00163187
$535$	14.9287	0.645424
$536$	−9.27874	−0.400780
$537$	−14.8487	−0.640770
$538$	15.2375	0.656933
$539$	3.87162	0.166763
$540$	−2.78783	−0.119969
$541$	−1.23999	−0.0533114	−0.0266557	−	0.999645i	$-0.508486\pi$
$541$	−1.23999	−0.0533114	−0.0266557	+	0.999645i	$0.508486\pi$
$542$	1.55854	0.0669448
$543$	−6.93493	−0.297606
$544$	−4.92433	−0.211129
$545$	−37.9752	−1.62668
$546$	−1.77309	−0.0758814
$547$	39.0296	1.66879	0.834394	−	0.551169i	$-0.185818\pi$
$547$	39.0296	1.66879	0.834394	+	0.551169i	$0.185818\pi$
$548$	1.25320	0.0535342
$549$	−5.03671	−0.214961
$550$	10.7321	0.457619
$551$	−6.79548	−0.289497
$552$	7.45250	0.317199
$553$	15.1734	0.645240
$554$	11.4321	0.485703
$555$	19.2724	0.818067
$556$	20.6802	0.877036
$557$	−40.9829	−1.73650	−0.868250	−	0.496127i	$-0.834755\pi$
$557$	−40.9829	−1.73650	−0.868250	+	0.496127i	$0.834755\pi$
$558$	−7.00803	−0.296673
$559$	11.5198	0.487235
$560$	−2.78783	−0.117807
$561$	19.0651	0.804931
$562$	9.53076	0.402031
$563$	−28.6298	−1.20660	−0.603301	−	0.797514i	$-0.706148\pi$
$563$	−28.6298	−1.20660	−0.603301	+	0.797514i	$0.706148\pi$
$564$	3.08734	0.130001
$565$	−14.3274	−0.602756
$566$	−6.90599	−0.290280
$567$	−1.00000	−0.0419961
$568$	−9.22153	−0.386927
$569$	−25.6660	−1.07598	−0.537988	−	0.842953i	$-0.680815\pi$
$569$	−25.6660	−1.07598	−0.537988	+	0.842953i	$0.680815\pi$
$570$	8.16569	0.342023
$571$	12.0126	0.502713	0.251357	−	0.967895i	$-0.419123\pi$
$571$	12.0126	0.502713	0.251357	+	0.967895i	$0.419123\pi$
$572$	−6.86475	−0.287030
$573$	−1.00000	−0.0417756
$574$	−5.49771	−0.229470
$575$	−20.6583	−0.861510
$576$	1.00000	0.0416667
$577$	19.2600	0.801802	0.400901	−	0.916121i	$-0.368697\pi$
$577$	19.2600	0.801802	0.400901	+	0.916121i	$0.368697\pi$
$578$	7.24903	0.301520
$579$	−15.4076	−0.640318
$580$	6.46785	0.268563
$581$	−9.23135	−0.382981
$582$	8.64887	0.358507
$583$	−39.2726	−1.62651
$584$	8.55945	0.354192
$585$	−4.94308	−0.204371
$586$	−1.40839	−0.0581800
$587$	−35.8508	−1.47972	−0.739861	−	0.672759i	$-0.765109\pi$
$587$	−35.8508	−1.47972	−0.739861	+	0.672759i	$0.765109\pi$
$588$	−1.00000	−0.0412393
$589$	20.5268	0.845794
$590$	−0.856921	−0.0352789
$591$	11.1559	0.458893
$592$	−6.91304	−0.284124
$593$	−36.5392	−1.50048	−0.750242	−	0.661163i	$-0.770063\pi$
$593$	−36.5392	−1.50048	−0.750242	+	0.661163i	$0.770063\pi$
$594$	−3.87162	−0.158855
$595$	13.7282	0.562801
$596$	22.8583	0.936313
$597$	−5.86353	−0.239978
$598$	13.2140	0.540360
$599$	−15.3868	−0.628687	−0.314343	−	0.949309i	$-0.601784\pi$
$599$	−15.3868	−0.628687	−0.314343	+	0.949309i	$0.601784\pi$
$600$	−2.77199	−0.113166
$601$	15.2877	0.623598	0.311799	−	0.950148i	$-0.399069\pi$
$601$	15.2877	0.623598	0.311799	+	0.950148i	$0.399069\pi$
$602$	6.49700	0.264798
$603$	−9.27874	−0.377859
$604$	5.41118	0.220178
$605$	11.1219	0.452171
$606$	−16.0777	−0.653111
$607$	33.8375	1.37342	0.686712	−	0.726930i	$-0.259054\pi$
$607$	33.8375	1.37342	0.686712	+	0.726930i	$0.259054\pi$
$608$	−2.92905	−0.118789
$609$	2.32003	0.0940123
$610$	−14.0415	−0.568523
$611$	5.47415	0.221460
$612$	−4.92433	−0.199054
$613$	45.8449	1.85166	0.925830	−	0.377940i	$-0.123368\pi$
$613$	45.8449	1.85166	0.925830	+	0.377940i	$0.123368\pi$
$614$	−33.5833	−1.35531
$615$	−15.3267	−0.618031
$616$	−3.87162	−0.155992
$617$	−13.1397	−0.528983	−0.264491	−	0.964388i	$-0.585204\pi$
$617$	−13.1397	−0.528983	−0.264491	+	0.964388i	$0.585204\pi$
$618$	−3.43281	−0.138088
$619$	−32.4023	−1.30236	−0.651180	−	0.758923i	$-0.725726\pi$
$619$	−32.4023	−1.30236	−0.651180	+	0.758923i	$0.725726\pi$
$620$	−19.5372	−0.784632
$621$	7.45250	0.299058
$622$	11.9862	0.480601
$623$	−0.0377100	−0.00151082
$624$	1.77309	0.0709805
$625$	−31.1760	−1.24704
$626$	19.7449	0.789164
$627$	11.3402	0.452883
$628$	18.3916	0.733906
$629$	34.0421	1.35735
$630$	−2.78783	−0.111070
$631$	26.2438	1.04475	0.522375	−	0.852716i	$-0.325046\pi$
$631$	26.2438	1.04475	0.522375	+	0.852716i	$0.325046\pi$
$632$	−15.1734	−0.603567
$633$	27.5386	1.09456
$634$	30.9056	1.22742
$635$	32.0121	1.27036
$636$	10.1437	0.402224
$637$	−1.77309	−0.0702525
$638$	8.98228	0.355612
$639$	−9.22153	−0.364798
$640$	2.78783	0.110199
$641$	34.1002	1.34688	0.673439	−	0.739243i	$-0.264816\pi$
$641$	34.1002	1.34688	0.673439	+	0.739243i	$0.264816\pi$
$642$	−5.35495	−0.211343
$643$	−8.71617	−0.343732	−0.171866	−	0.985120i	$-0.554980\pi$
$643$	−8.71617	−0.343732	−0.171866	+	0.985120i	$0.554980\pi$
$644$	7.45250	0.293670
$645$	18.1125	0.713181
$646$	14.4236	0.567489
$647$	48.7339	1.91593	0.957964	−	0.286888i	$-0.0926207\pi$
$647$	48.7339	1.91593	0.957964	+	0.286888i	$0.0926207\pi$
$648$	1.00000	0.0392837
$649$	−1.19006	−0.0467138
$650$	−4.91500	−0.192782
$651$	−7.00803	−0.274666
$652$	−1.99302	−0.0780527
$653$	−26.1447	−1.02312	−0.511561	−	0.859247i	$-0.670933\pi$
$653$	−26.1447	−1.02312	−0.511561	+	0.859247i	$0.670933\pi$
$654$	13.6218	0.532654
$655$	−42.8876	−1.67576
$656$	5.49771	0.214649
$657$	8.55945	0.333936
$658$	3.08734	0.120357
$659$	−3.15701	−0.122980	−0.0614899	−	0.998108i	$-0.519585\pi$
$659$	−3.15701	−0.122980	−0.0614899	+	0.998108i	$0.519585\pi$
$660$	−10.7934	−0.420133
$661$	−15.1860	−0.590669	−0.295334	−	0.955394i	$-0.595431\pi$
$661$	−15.1860	−0.590669	−0.295334	+	0.955394i	$0.595431\pi$
$662$	4.79568	0.186389
$663$	−8.73130	−0.339095
$664$	9.23135	0.358246
$665$	8.16569	0.316652
$666$	−6.91304	−0.267875
$667$	−17.2900	−0.669472
$668$	23.2725	0.900441
$669$	18.5167	0.715896
$670$	−25.8675	−0.999350
$671$	−19.5002	−0.752798
$672$	1.00000	0.0385758
$673$	−35.0107	−1.34956	−0.674782	−	0.738017i	$-0.735763\pi$
$673$	−35.0107	−1.34956	−0.674782	+	0.738017i	$0.735763\pi$
$674$	−24.7618	−0.953789
$675$	−2.77199	−0.106694
$676$	−9.85614	−0.379082
$677$	−6.54488	−0.251540	−0.125770	−	0.992059i	$-0.540140\pi$
$677$	−6.54488	−0.251540	−0.125770	+	0.992059i	$0.540140\pi$
$678$	5.13925	0.197372
$679$	8.64887	0.331913
$680$	−13.7282	−0.526452
$681$	1.43455	0.0549722
$682$	−27.1324	−1.03895
$683$	4.29005	0.164154	0.0820771	−	0.996626i	$-0.473845\pi$
$683$	4.29005	0.164154	0.0820771	+	0.996626i	$0.473845\pi$
$684$	−2.92905	−0.111995
$685$	3.49372	0.133488
$686$	−1.00000	−0.0381802
$687$	24.5752	0.937604
$688$	−6.49700	−0.247696
$689$	17.9857	0.685202
$690$	20.7763	0.790940
$691$	41.2096	1.56769	0.783843	−	0.620959i	$-0.213257\pi$
$691$	41.2096	1.56769	0.783843	+	0.620959i	$0.213257\pi$
$692$	22.5193	0.856055
$693$	−3.87162	−0.147071
$694$	7.60240	0.288583
$695$	57.6529	2.18690
$696$	−2.32003	−0.0879405
$697$	−27.0725	−1.02545
$698$	6.48199	0.245347
$699$	4.06656	0.153812
$700$	−2.77199	−0.104772
$701$	−6.62290	−0.250143	−0.125072	−	0.992148i	$-0.539916\pi$
$701$	−6.62290	−0.250143	−0.125072	+	0.992148i	$0.539916\pi$
$702$	1.77309	0.0669211
$703$	20.2486	0.763692
$704$	3.87162	0.145917
$705$	8.60699	0.324158
$706$	27.0847	1.01935
$707$	−16.0777	−0.604663
$708$	0.307379	0.0115520
$709$	21.1125	0.792895	0.396447	−	0.918057i	$-0.370243\pi$
$709$	21.1125	0.792895	0.396447	+	0.918057i	$0.370243\pi$
$710$	−25.7081	−0.964806
$711$	−15.1734	−0.569048
$712$	0.0377100	0.00141324
$713$	52.2273	1.95593
$714$	−4.92433	−0.184288
$715$	−19.1377	−0.715711
$716$	14.8487	0.554923
$717$	−5.87574	−0.219434
$718$	29.4111	1.09761
$719$	−3.20232	−0.119426	−0.0597132	−	0.998216i	$-0.519019\pi$
$719$	−3.20232	−0.119426	−0.0597132	+	0.998216i	$0.519019\pi$
$720$	2.78783	0.103896
$721$	−3.43281	−0.127845
$722$	−10.4207	−0.387818
$723$	−3.46514	−0.128870
$724$	6.93493	0.257735
$725$	6.43111	0.238845
$726$	−3.98946	−0.148063
$727$	11.4125	0.423267	0.211633	−	0.977349i	$-0.432122\pi$
$727$	11.4125	0.423267	0.211633	+	0.977349i	$0.432122\pi$
$728$	1.77309	0.0657152
$729$	1.00000	0.0370370
$730$	23.8623	0.883182
$731$	31.9934	1.18332
$732$	5.03671	0.186162
$733$	27.2532	1.00662	0.503309	−	0.864106i	$-0.332116\pi$
$733$	27.2532	1.00662	0.503309	+	0.864106i	$0.332116\pi$
$734$	0.776610	0.0286652
$735$	−2.78783	−0.102831
$736$	−7.45250	−0.274703
$737$	−35.9238	−1.32327
$738$	5.49771	0.202373
$739$	−20.3398	−0.748211	−0.374106	−	0.927386i	$-0.622050\pi$
$739$	−20.3398	−0.748211	−0.374106	+	0.927386i	$0.622050\pi$
$740$	−19.2724	−0.708467
$741$	−5.19347	−0.190787
$742$	10.1437	0.372387
$743$	−20.7156	−0.759981	−0.379991	−	0.924990i	$-0.624073\pi$
$743$	−20.7156	−0.759981	−0.379991	+	0.924990i	$0.624073\pi$
$744$	7.00803	0.256927
$745$	63.7251	2.33471
$746$	−30.1083	−1.10234
$747$	9.23135	0.337757
$748$	−19.0651	−0.697091
$749$	−5.35495	−0.195666
$750$	6.21130	0.226805
$751$	−46.3317	−1.69067	−0.845334	−	0.534239i	$-0.820598\pi$
$751$	−46.3317	−1.69067	−0.845334	+	0.534239i	$0.820598\pi$
$752$	−3.08734	−0.112584
$753$	−25.7524	−0.938469
$754$	−4.11363	−0.149810
$755$	15.0854	0.549015
$756$	1.00000	0.0363696
$757$	−25.3444	−0.921159	−0.460579	−	0.887619i	$-0.652358\pi$
$757$	−25.3444	−0.921159	−0.460579	+	0.887619i	$0.652358\pi$
$758$	−35.6850	−1.29614
$759$	28.8533	1.04731
$760$	−8.16569	−0.296201
$761$	−23.7054	−0.859319	−0.429660	−	0.902991i	$-0.641366\pi$
$761$	−23.7054	−0.859319	−0.429660	+	0.902991i	$0.641366\pi$
$762$	−11.4828	−0.415978
$763$	13.6218	0.493142
$764$	1.00000	0.0361787
$765$	−13.7282	−0.496344
$766$	−10.4311	−0.376891
$767$	0.545012	0.0196793
$768$	−1.00000	−0.0360844
$769$	50.1741	1.80932	0.904662	−	0.426131i	$-0.140124\pi$
$769$	50.1741	1.80932	0.904662	+	0.426131i	$0.140124\pi$
$770$	−10.7934	−0.388968
$771$	19.8977	0.716599
$772$	15.4076	0.554532
$773$	−32.7065	−1.17637	−0.588185	−	0.808727i	$-0.700157\pi$
$773$	−32.7065	−1.17637	−0.588185	+	0.808727i	$0.700157\pi$
$774$	−6.49700	−0.233530
$775$	−19.4262	−0.697810
$776$	−8.64887	−0.310476
$777$	−6.91304	−0.248004
$778$	12.2465	0.439057
$779$	−16.1031	−0.576952
$780$	4.94308	0.176991
$781$	−35.7023	−1.27753
$782$	36.6986	1.31234
$783$	−2.32003	−0.0829111
$784$	1.00000	0.0357143
$785$	51.2727	1.83000
$786$	15.3839	0.548725
$787$	−4.04373	−0.144143	−0.0720717	−	0.997399i	$-0.522961\pi$
$787$	−4.04373	−0.144143	−0.0720717	+	0.997399i	$0.522961\pi$
$788$	−11.1559	−0.397413
$789$	29.2868	1.04264
$790$	−42.3010	−1.50500
$791$	5.13925	0.182731
$792$	3.87162	0.137572
$793$	8.93055	0.317133
$794$	−7.11612	−0.252542
$795$	28.2789	1.00295
$796$	5.86353	0.207827
$797$	28.9156	1.02424	0.512121	−	0.858913i	$-0.328860\pi$
$797$	28.9156	1.02424	0.512121	+	0.858913i	$0.328860\pi$
$798$	−2.92905	−0.103687
$799$	15.2031	0.537847
$800$	2.77199	0.0980048
$801$	0.0377100	0.00133242
$802$	−6.85352	−0.242006
$803$	33.1389	1.16945
$804$	9.27874	0.327236
$805$	20.7763	0.732268
$806$	12.4259	0.437683
$807$	−15.2375	−0.536384
$808$	16.0777	0.565611
$809$	13.9761	0.491374	0.245687	−	0.969349i	$-0.420986\pi$
$809$	13.9761	0.491374	0.245687	+	0.969349i	$0.420986\pi$
$810$	2.78783	0.0979543
$811$	−7.30306	−0.256445	−0.128223	−	0.991745i	$-0.540927\pi$
$811$	−7.30306	−0.256445	−0.128223	+	0.991745i	$0.540927\pi$
$812$	−2.32003	−0.0814171
$813$	−1.55854	−0.0546602
$814$	−26.7647	−0.938102
$815$	−5.55620	−0.194625
$816$	4.92433	0.172386
$817$	19.0300	0.665777
$818$	−33.2511	−1.16260
$819$	1.77309	0.0619569
$820$	15.3267	0.535231
$821$	47.7746	1.66735	0.833673	−	0.552259i	$-0.186234\pi$
$821$	47.7746	1.66735	0.833673	+	0.552259i	$0.186234\pi$
$822$	−1.25320	−0.0437105
$823$	1.32487	0.0461822	0.0230911	−	0.999733i	$-0.492649\pi$
$823$	1.32487	0.0461822	0.0230911	+	0.999733i	$0.492649\pi$
$824$	3.43281	0.119588
$825$	−10.7321	−0.373644
$826$	0.307379	0.0106951
$827$	−35.3121	−1.22792	−0.613961	−	0.789337i	$-0.710425\pi$
$827$	−35.3121	−1.22792	−0.613961	+	0.789337i	$0.710425\pi$
$828$	−7.45250	−0.258992
$829$	48.0918	1.67030	0.835148	−	0.550025i	$-0.185382\pi$
$829$	48.0918	1.67030	0.835148	+	0.550025i	$0.185382\pi$
$830$	25.7354	0.893289
$831$	−11.4321	−0.396575
$832$	−1.77309	−0.0614709
$833$	−4.92433	−0.170618
$834$	−20.6802	−0.716097
$835$	64.8799	2.24526
$836$	−11.3402	−0.392208
$837$	7.00803	0.242233
$838$	−29.7758	−1.02859
$839$	12.6600	0.437071	0.218535	−	0.975829i	$-0.429872\pi$
$839$	12.6600	0.437071	0.218535	+	0.975829i	$0.429872\pi$
$840$	2.78783	0.0961893
$841$	−23.6175	−0.814395
$842$	3.86948	0.133351
$843$	−9.53076	−0.328257
$844$	−27.5386	−0.947917
$845$	−27.4772	−0.945246
$846$	−3.08734	−0.106145
$847$	−3.98946	−0.137080
$848$	−10.1437	−0.348336
$849$	6.90599	0.237013
$850$	−13.6502	−0.468198
$851$	51.5195	1.76606
$852$	9.22153	0.315924
$853$	−13.4540	−0.460656	−0.230328	−	0.973113i	$-0.573980\pi$
$853$	−13.4540	−0.460656	−0.230328	+	0.973113i	$0.573980\pi$
$854$	5.03671	0.172353
$855$	−8.16569	−0.279261
$856$	5.35495	0.183029
$857$	−18.1353	−0.619492	−0.309746	−	0.950819i	$-0.600244\pi$
$857$	−18.1353	−0.619492	−0.309746	+	0.950819i	$0.600244\pi$
$858$	6.86475	0.234359
$859$	−18.0011	−0.614188	−0.307094	−	0.951679i	$-0.599357\pi$
$859$	−18.0011	−0.614188	−0.307094	+	0.951679i	$0.599357\pi$
$860$	−18.1125	−0.617632
$861$	5.49771	0.187361
$862$	3.10033	0.105598
$863$	12.2975	0.418611	0.209305	−	0.977850i	$-0.432880\pi$
$863$	12.2975	0.418611	0.209305	+	0.977850i	$0.432880\pi$
$864$	−1.00000	−0.0340207
$865$	62.7800	2.13458
$866$	−30.8597	−1.04866
$867$	−7.24903	−0.246190
$868$	7.00803	0.237868
$869$	−58.7458	−1.99282
$870$	−6.46785	−0.219281
$871$	16.4521	0.557457
$872$	−13.6218	−0.461292
$873$	−8.64887	−0.292720
$874$	21.8287	0.738368
$875$	6.21130	0.209980
$876$	−8.55945	−0.289197
$877$	4.17732	0.141058	0.0705290	−	0.997510i	$-0.477531\pi$
$877$	4.17732	0.141058	0.0705290	+	0.997510i	$0.477531\pi$
$878$	32.8178	1.10755
$879$	1.40839	0.0475037
$880$	10.7934	0.363846
$881$	−0.465733	−0.0156910	−0.00784548	−	0.999969i	$-0.502497\pi$
$881$	−0.465733	−0.0156910	−0.00784548	+	0.999969i	$0.502497\pi$
$882$	1.00000	0.0336718
$883$	−2.79594	−0.0940908	−0.0470454	−	0.998893i	$-0.514981\pi$
$883$	−2.79594	−0.0940908	−0.0470454	+	0.998893i	$0.514981\pi$
$884$	8.73130	0.293665
$885$	0.856921	0.0288051
$886$	−18.5230	−0.622291
$887$	−34.9594	−1.17382	−0.586910	−	0.809652i	$-0.699656\pi$
$887$	−34.9594	−1.17382	−0.586910	+	0.809652i	$0.699656\pi$
$888$	6.91304	0.231987
$889$	−11.4828	−0.385120
$890$	0.105129	0.00352394
$891$	3.87162	0.129704
$892$	−18.5167	−0.619984
$893$	9.04297	0.302612
$894$	−22.8583	−0.764496
$895$	41.3957	1.38371
$896$	−1.00000	−0.0334077
$897$	−13.2140	−0.441202
$898$	38.3628	1.28018
$899$	−16.2588	−0.542262
$900$	2.77199	0.0923998
$901$	49.9510	1.66411
$902$	21.2851	0.708715
$903$	−6.49700	−0.216207
$904$	−5.13925	−0.170929
$905$	19.3334	0.642664
$906$	−5.41118	−0.179774
$907$	−46.4330	−1.54178	−0.770892	−	0.636966i	$-0.780189\pi$
$907$	−46.4330	−1.54178	−0.770892	+	0.636966i	$0.780189\pi$
$908$	−1.43455	−0.0476073
$909$	16.0777	0.533263
$910$	4.94308	0.163862
$911$	−42.2531	−1.39991	−0.699954	−	0.714188i	$-0.746796\pi$
$911$	−42.2531	−1.39991	−0.699954	+	0.714188i	$0.746796\pi$
$912$	2.92905	0.0969905
$913$	35.7403	1.18283
$914$	18.7196	0.619189
$915$	14.0415	0.464197
$916$	−24.5752	−0.811989
$917$	15.3839	0.508020
$918$	4.92433	0.162527
$919$	26.2337	0.865371	0.432685	−	0.901545i	$-0.357566\pi$
$919$	26.2337	0.865371	0.432685	+	0.901545i	$0.357566\pi$
$920$	−20.7763	−0.684974
$921$	33.5833	1.10661
$922$	4.46377	0.147006
$923$	16.3506	0.538187
$924$	3.87162	0.127367
$925$	−19.1629	−0.630073
$926$	−22.7087	−0.746256
$927$	3.43281	0.112748
$928$	2.32003	0.0761587
$929$	−10.6388	−0.349049	−0.174525	−	0.984653i	$-0.555839\pi$
$929$	−10.6388	−0.349049	−0.174525	+	0.984653i	$0.555839\pi$
$930$	19.5372	0.640649
$931$	−2.92905	−0.0959957
$932$	−4.06656	−0.133205
$933$	−11.9862	−0.392409
$934$	−35.4033	−1.15843
$935$	−53.1504	−1.73820
$936$	−1.77309	−0.0579554
$937$	4.97332	0.162471	0.0812356	−	0.996695i	$-0.474113\pi$
$937$	4.97332	0.162471	0.0812356	+	0.996695i	$0.474113\pi$
$938$	9.27874	0.302961
$939$	−19.7449	−0.644349
$940$	−8.60699	−0.280729
$941$	−5.39648	−0.175920	−0.0879601	−	0.996124i	$-0.528035\pi$
$941$	−5.39648	−0.175920	−0.0879601	+	0.996124i	$0.528035\pi$
$942$	−18.3916	−0.599232
$943$	−40.9717	−1.33422
$944$	−0.307379	−0.0100043
$945$	2.78783	0.0906881
$946$	−25.1539	−0.817825
$947$	54.0893	1.75767	0.878833	−	0.477129i	$-0.158322\pi$
$947$	54.0893	1.75767	0.878833	+	0.477129i	$0.158322\pi$
$948$	15.1734	0.492810
$949$	−15.1767	−0.492656
$950$	−8.11930	−0.263425
$951$	−30.9056	−1.00218
$952$	4.92433	0.159598
$953$	48.0044	1.55502	0.777508	−	0.628873i	$-0.216484\pi$
$953$	48.0044	1.55502	0.777508	+	0.628873i	$0.216484\pi$
$954$	−10.1437	−0.328415
$955$	2.78783	0.0902120
$956$	5.87574	0.190035
$957$	−8.98228	−0.290356
$958$	23.9289	0.773107
$959$	−1.25320	−0.0404680
$960$	−2.78783	−0.0899768
$961$	18.1124	0.584272
$962$	12.2575	0.395197
$963$	5.35495	0.172561
$964$	3.46514	0.111605
$965$	42.9538	1.38273
$966$	−7.45250	−0.239780
$967$	26.9909	0.867968	0.433984	−	0.900921i	$-0.357107\pi$
$967$	26.9909	0.867968	0.433984	+	0.900921i	$0.357107\pi$
$968$	3.98946	0.128226
$969$	−14.4236	−0.463353
$970$	−24.1116	−0.774176
$971$	−28.2464	−0.906471	−0.453235	−	0.891391i	$-0.649730\pi$
$971$	−28.2464	−0.906471	−0.453235	+	0.891391i	$0.649730\pi$
$972$	−1.00000	−0.0320750
$973$	−20.6802	−0.662977
$974$	28.4828	0.912647
$975$	4.91500	0.157406
$976$	−5.03671	−0.161221
$977$	15.3471	0.490998	0.245499	−	0.969397i	$-0.421048\pi$
$977$	15.3471	0.490998	0.245499	+	0.969397i	$0.421048\pi$
$978$	1.99302	0.0637297
$979$	0.145999	0.00466615
$980$	2.78783	0.0890540
$981$	−13.6218	−0.434910
$982$	−31.0556	−0.991023
$983$	12.8463	0.409733	0.204867	−	0.978790i	$-0.434324\pi$
$983$	12.8463	0.409733	0.204867	+	0.978790i	$0.434324\pi$
$984$	−5.49771	−0.175261
$985$	−31.1008	−0.990954
$986$	−11.4246	−0.363833
$987$	−3.08734	−0.0982712
$988$	5.19347	0.165226
$989$	48.4189	1.53963
$990$	10.7934	0.343038
$991$	−40.7440	−1.29428	−0.647138	−	0.762373i	$-0.724034\pi$
$991$	−40.7440	−1.29428	−0.647138	+	0.762373i	$0.724034\pi$
$992$	−7.00803	−0.222505
$993$	−4.79568	−0.152186
$994$	9.22153	0.292489
$995$	16.3465	0.518220
$996$	−9.23135	−0.292506
$997$	−20.5508	−0.650850	−0.325425	−	0.945568i	$-0.605507\pi$
$997$	−20.5508	−0.650850	−0.325425	+	0.945568i	$0.605507\pi$
$998$	−15.7916	−0.499875
$999$	6.91304	0.218719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.q.1.8	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.q.1.8	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.78783 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.78783 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.78783 q^{10} +3.87162 q^{11} -1.00000 q^{12} -1.77309 q^{13} -1.00000 q^{14} -2.78783 q^{15} +1.00000 q^{16} -4.92433 q^{17} +1.00000 q^{18} -2.92905 q^{19} +2.78783 q^{20} +1.00000 q^{21} +3.87162 q^{22} -7.45250 q^{23} -1.00000 q^{24} +2.77199 q^{25} -1.77309 q^{26} -1.00000 q^{27} -1.00000 q^{28} +2.32003 q^{29} -2.78783 q^{30} -7.00803 q^{31} +1.00000 q^{32} -3.87162 q^{33} -4.92433 q^{34} -2.78783 q^{35} +1.00000 q^{36} -6.91304 q^{37} -2.92905 q^{38} +1.77309 q^{39} +2.78783 q^{40} +5.49771 q^{41} +1.00000 q^{42} -6.49700 q^{43} +3.87162 q^{44} +2.78783 q^{45} -7.45250 q^{46} -3.08734 q^{47} -1.00000 q^{48} +1.00000 q^{49} +2.77199 q^{50} +4.92433 q^{51} -1.77309 q^{52} -10.1437 q^{53} -1.00000 q^{54} +10.7934 q^{55} -1.00000 q^{56} +2.92905 q^{57} +2.32003 q^{58} -0.307379 q^{59} -2.78783 q^{60} -5.03671 q^{61} -7.00803 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.94308 q^{65} -3.87162 q^{66} -9.27874 q^{67} -4.92433 q^{68} +7.45250 q^{69} -2.78783 q^{70} -9.22153 q^{71} +1.00000 q^{72} +8.55945 q^{73} -6.91304 q^{74} -2.77199 q^{75} -2.92905 q^{76} -3.87162 q^{77} +1.77309 q^{78} -15.1734 q^{79} +2.78783 q^{80} +1.00000 q^{81} +5.49771 q^{82} +9.23135 q^{83} +1.00000 q^{84} -13.7282 q^{85} -6.49700 q^{86} -2.32003 q^{87} +3.87162 q^{88} +0.0377100 q^{89} +2.78783 q^{90} +1.77309 q^{91} -7.45250 q^{92} +7.00803 q^{93} -3.08734 q^{94} -8.16569 q^{95} -1.00000 q^{96} -8.64887 q^{97} +1.00000 q^{98} +3.87162 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} - 9 q^{6} - 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 - 9 * q^6 - 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} - 9 q^{6} - 9 q^{7} + 9 q^{8} + 9 q^{9} + 6 q^{10} - 7 q^{11} - 9 q^{12} - q^{13} - 9 q^{14} - 6 q^{15} + 9 q^{16} - 10 q^{17} + 9 q^{18} + 6 q^{20} + 9 q^{21} - 7 q^{22} - 19 q^{23} - 9 q^{24} + 5 q^{25} - q^{26} - 9 q^{27} - 9 q^{28} - 21 q^{29} - 6 q^{30} + 6 q^{31} + 9 q^{32} + 7 q^{33} - 10 q^{34} - 6 q^{35} + 9 q^{36} - 14 q^{37} + q^{39} + 6 q^{40} + 12 q^{41} + 9 q^{42} - 17 q^{43} - 7 q^{44} + 6 q^{45} - 19 q^{46} - 11 q^{47} - 9 q^{48} + 9 q^{49} + 5 q^{50} + 10 q^{51} - q^{52} - 12 q^{53} - 9 q^{54} - 21 q^{55} - 9 q^{56} - 21 q^{58} - 8 q^{59} - 6 q^{60} + q^{61} + 6 q^{62} - 9 q^{63} + 9 q^{64} - 8 q^{65} + 7 q^{66} - 31 q^{67} - 10 q^{68} + 19 q^{69} - 6 q^{70} - 41 q^{71} + 9 q^{72} - q^{73} - 14 q^{74} - 5 q^{75} + 7 q^{77} + q^{78} - 17 q^{79} + 6 q^{80} + 9 q^{81} + 12 q^{82} - 36 q^{83} + 9 q^{84} - 30 q^{85} - 17 q^{86} + 21 q^{87} - 7 q^{88} - 17 q^{89} + 6 q^{90} + q^{91} - 19 q^{92} - 6 q^{93} - 11 q^{94} - 50 q^{95} - 9 q^{96} - 14 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 - 9 * q^6 - 9 * q^7 + 9 * q^8 + 9 * q^9 + 6 * q^10 - 7 * q^11 - 9 * q^12 - q^13 - 9 * q^14 - 6 * q^15 + 9 * q^16 - 10 * q^17 + 9 * q^18 + 6 * q^20 + 9 * q^21 - 7 * q^22 - 19 * q^23 - 9 * q^24 + 5 * q^25 - q^26 - 9 * q^27 - 9 * q^28 - 21 * q^29 - 6 * q^30 + 6 * q^31 + 9 * q^32 + 7 * q^33 - 10 * q^34 - 6 * q^35 + 9 * q^36 - 14 * q^37 + q^39 + 6 * q^40 + 12 * q^41 + 9 * q^42 - 17 * q^43 - 7 * q^44 + 6 * q^45 - 19 * q^46 - 11 * q^47 - 9 * q^48 + 9 * q^49 + 5 * q^50 + 10 * q^51 - q^52 - 12 * q^53 - 9 * q^54 - 21 * q^55 - 9 * q^56 - 21 * q^58 - 8 * q^59 - 6 * q^60 + q^61 + 6 * q^62 - 9 * q^63 + 9 * q^64 - 8 * q^65 + 7 * q^66 - 31 * q^67 - 10 * q^68 + 19 * q^69 - 6 * q^70 - 41 * q^71 + 9 * q^72 - q^73 - 14 * q^74 - 5 * q^75 + 7 * q^77 + q^78 - 17 * q^79 + 6 * q^80 + 9 * q^81 + 12 * q^82 - 36 * q^83 + 9 * q^84 - 30 * q^85 - 17 * q^86 + 21 * q^87 - 7 * q^88 - 17 * q^89 + 6 * q^90 + q^91 - 19 * q^92 - 6 * q^93 - 11 * q^94 - 50 * q^95 - 9 * q^96 - 14 * q^97 + 9 * q^98 - 7 * q^99

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