LMFDB - Embedded newform 6042.2.a.bb.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
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} - 16x^{7} + 76x^{6} + 30x^{5} - 366x^{4} + 300x^{3} + 101x^{2} - 106x + 16 $ x^9 - 4x^8 - 16x^7 + 76x^6 + 30x^5 - 366x^4 + 300x^3 + 101x^2 - 106x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.42636$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.03181 q^{5} -1.00000 q^{6} +2.42636 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.03181 q^{5} -1.00000 q^{6} +2.42636 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.03181 q^{10} -0.928729 q^{11} -1.00000 q^{12} +1.56758 q^{13} +2.42636 q^{14} +2.03181 q^{15} +1.00000 q^{16} +0.177461 q^{17} +1.00000 q^{18} -1.00000 q^{19} -2.03181 q^{20} -2.42636 q^{21} -0.928729 q^{22} -5.67451 q^{23} -1.00000 q^{24} -0.871760 q^{25} +1.56758 q^{26} -1.00000 q^{27} +2.42636 q^{28} -7.54062 q^{29} +2.03181 q^{30} -2.56546 q^{31} +1.00000 q^{32} +0.928729 q^{33} +0.177461 q^{34} -4.92990 q^{35} +1.00000 q^{36} +1.57141 q^{37} -1.00000 q^{38} -1.56758 q^{39} -2.03181 q^{40} +6.20941 q^{41} -2.42636 q^{42} +11.1802 q^{43} -0.928729 q^{44} -2.03181 q^{45} -5.67451 q^{46} -4.47540 q^{47} -1.00000 q^{48} -1.11276 q^{49} -0.871760 q^{50} -0.177461 q^{51} +1.56758 q^{52} +1.00000 q^{53} -1.00000 q^{54} +1.88700 q^{55} +2.42636 q^{56} +1.00000 q^{57} -7.54062 q^{58} -4.45954 q^{59} +2.03181 q^{60} -12.0404 q^{61} -2.56546 q^{62} +2.42636 q^{63} +1.00000 q^{64} -3.18502 q^{65} +0.928729 q^{66} +14.5225 q^{67} +0.177461 q^{68} +5.67451 q^{69} -4.92990 q^{70} -8.14558 q^{71} +1.00000 q^{72} -2.41532 q^{73} +1.57141 q^{74} +0.871760 q^{75} -1.00000 q^{76} -2.25343 q^{77} -1.56758 q^{78} -9.39537 q^{79} -2.03181 q^{80} +1.00000 q^{81} +6.20941 q^{82} -7.01329 q^{83} -2.42636 q^{84} -0.360566 q^{85} +11.1802 q^{86} +7.54062 q^{87} -0.928729 q^{88} +1.16289 q^{89} -2.03181 q^{90} +3.80352 q^{91} -5.67451 q^{92} +2.56546 q^{93} -4.47540 q^{94} +2.03181 q^{95} -1.00000 q^{96} +3.18543 q^{97} -1.11276 q^{98} -0.928729 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 5 q^{5} - 9 q^{6} - 5 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 5 * q^5 - 9 * q^6 - 5 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 5 q^{5} - 9 q^{6} - 5 q^{7} + 9 q^{8} + 9 q^{9} - 5 q^{10} + 3 q^{11} - 9 q^{12} - 4 q^{13} - 5 q^{14} + 5 q^{15} + 9 q^{16} - 16 q^{17} + 9 q^{18} - 9 q^{19} - 5 q^{20} + 5 q^{21} + 3 q^{22} - 9 q^{24} + 8 q^{25} - 4 q^{26} - 9 q^{27} - 5 q^{28} - 2 q^{29} + 5 q^{30} - 10 q^{31} + 9 q^{32} - 3 q^{33} - 16 q^{34} - q^{35} + 9 q^{36} - 14 q^{37} - 9 q^{38} + 4 q^{39} - 5 q^{40} - 21 q^{41} + 5 q^{42} - 4 q^{43} + 3 q^{44} - 5 q^{45} - 8 q^{47} - 9 q^{48} - 14 q^{49} + 8 q^{50} + 16 q^{51} - 4 q^{52} + 9 q^{53} - 9 q^{54} - 14 q^{55} - 5 q^{56} + 9 q^{57} - 2 q^{58} - 12 q^{59} + 5 q^{60} - 13 q^{61} - 10 q^{62} - 5 q^{63} + 9 q^{64} - 13 q^{65} - 3 q^{66} + 22 q^{67} - 16 q^{68} - q^{70} - 13 q^{71} + 9 q^{72} - 17 q^{73} - 14 q^{74} - 8 q^{75} - 9 q^{76} - 25 q^{77} + 4 q^{78} - 5 q^{80} + 9 q^{81} - 21 q^{82} - 24 q^{83} + 5 q^{84} - 16 q^{85} - 4 q^{86} + 2 q^{87} + 3 q^{88} - 23 q^{89} - 5 q^{90} - 11 q^{91} + 10 q^{93} - 8 q^{94} + 5 q^{95} - 9 q^{96} - 29 q^{97} - 14 q^{98} + 3 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 5 * q^5 - 9 * q^6 - 5 * q^7 + 9 * q^8 + 9 * q^9 - 5 * q^10 + 3 * q^11 - 9 * q^12 - 4 * q^13 - 5 * q^14 + 5 * q^15 + 9 * q^16 - 16 * q^17 + 9 * q^18 - 9 * q^19 - 5 * q^20 + 5 * q^21 + 3 * q^22 - 9 * q^24 + 8 * q^25 - 4 * q^26 - 9 * q^27 - 5 * q^28 - 2 * q^29 + 5 * q^30 - 10 * q^31 + 9 * q^32 - 3 * q^33 - 16 * q^34 - q^35 + 9 * q^36 - 14 * q^37 - 9 * q^38 + 4 * q^39 - 5 * q^40 - 21 * q^41 + 5 * q^42 - 4 * q^43 + 3 * q^44 - 5 * q^45 - 8 * q^47 - 9 * q^48 - 14 * q^49 + 8 * q^50 + 16 * q^51 - 4 * q^52 + 9 * q^53 - 9 * q^54 - 14 * q^55 - 5 * q^56 + 9 * q^57 - 2 * q^58 - 12 * q^59 + 5 * q^60 - 13 * q^61 - 10 * q^62 - 5 * q^63 + 9 * q^64 - 13 * q^65 - 3 * q^66 + 22 * q^67 - 16 * q^68 - q^70 - 13 * q^71 + 9 * q^72 - 17 * q^73 - 14 * q^74 - 8 * q^75 - 9 * q^76 - 25 * q^77 + 4 * q^78 - 5 * q^80 + 9 * q^81 - 21 * q^82 - 24 * q^83 + 5 * q^84 - 16 * q^85 - 4 * q^86 + 2 * q^87 + 3 * q^88 - 23 * q^89 - 5 * q^90 - 11 * q^91 + 10 * q^93 - 8 * q^94 + 5 * q^95 - 9 * q^96 - 29 * q^97 - 14 * 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
$5$	−2.03181	−0.908652	−0.454326	−	0.890836i	$-0.650120\pi$
$5$	−2.03181	−0.908652	−0.454326	+	0.890836i	$0.650120\pi$
$6$	−1.00000	−0.408248
$7$	2.42636	0.917079	0.458540	−	0.888674i	$-0.348373\pi$
$7$	2.42636	0.917079	0.458540	+	0.888674i	$0.348373\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.03181	−0.642514
$11$	−0.928729	−0.280022	−0.140011	−	0.990150i	$-0.544714\pi$
$11$	−0.928729	−0.280022	−0.140011	+	0.990150i	$0.544714\pi$
$12$	−1.00000	−0.288675
$13$	1.56758	0.434769	0.217384	−	0.976086i	$-0.430248\pi$
$13$	1.56758	0.434769	0.217384	+	0.976086i	$0.430248\pi$
$14$	2.42636	0.648473
$15$	2.03181	0.524610
$16$	1.00000	0.250000
$17$	0.177461	0.0430406	0.0215203	−	0.999768i	$-0.493149\pi$
$17$	0.177461	0.0430406	0.0215203	+	0.999768i	$0.493149\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.03181	−0.454326
$21$	−2.42636	−0.529476
$22$	−0.928729	−0.198006
$23$	−5.67451	−1.18322	−0.591609	−	0.806225i	$-0.701507\pi$
$23$	−5.67451	−1.18322	−0.591609	+	0.806225i	$0.701507\pi$
$24$	−1.00000	−0.204124
$25$	−0.871760	−0.174352
$26$	1.56758	0.307428
$27$	−1.00000	−0.192450
$28$	2.42636	0.458540
$29$	−7.54062	−1.40026	−0.700129	−	0.714017i	$-0.746874\pi$
$29$	−7.54062	−1.40026	−0.700129	+	0.714017i	$0.746874\pi$
$30$	2.03181	0.370956
$31$	−2.56546	−0.460771	−0.230385	−	0.973099i	$-0.573999\pi$
$31$	−2.56546	−0.460771	−0.230385	+	0.973099i	$0.573999\pi$
$32$	1.00000	0.176777
$33$	0.928729	0.161671
$34$	0.177461	0.0304343
$35$	−4.92990	−0.833306
$36$	1.00000	0.166667
$37$	1.57141	0.258338	0.129169	−	0.991623i	$-0.458769\pi$
$37$	1.57141	0.258338	0.129169	+	0.991623i	$0.458769\pi$
$38$	−1.00000	−0.162221
$39$	−1.56758	−0.251014
$40$	−2.03181	−0.321257
$41$	6.20941	0.969747	0.484873	−	0.874584i	$-0.338866\pi$
$41$	6.20941	0.969747	0.484873	+	0.874584i	$0.338866\pi$
$42$	−2.42636	−0.374396
$43$	11.1802	1.70497	0.852486	−	0.522750i	$-0.175094\pi$
$43$	11.1802	1.70497	0.852486	+	0.522750i	$0.175094\pi$
$44$	−0.928729	−0.140011
$45$	−2.03181	−0.302884
$46$	−5.67451	−0.836661
$47$	−4.47540	−0.652804	−0.326402	−	0.945231i	$-0.605836\pi$
$47$	−4.47540	−0.652804	−0.326402	+	0.945231i	$0.605836\pi$
$48$	−1.00000	−0.144338
$49$	−1.11276	−0.158966
$50$	−0.871760	−0.123285
$51$	−0.177461	−0.0248495
$52$	1.56758	0.217384
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−1.00000	−0.136083
$55$	1.88700	0.254443
$56$	2.42636	0.324236
$57$	1.00000	0.132453
$58$	−7.54062	−0.990131
$59$	−4.45954	−0.580582	−0.290291	−	0.956938i	$-0.593752\pi$
$59$	−4.45954	−0.580582	−0.290291	+	0.956938i	$0.593752\pi$
$60$	2.03181	0.262305
$61$	−12.0404	−1.54162	−0.770809	−	0.637066i	$-0.780148\pi$
$61$	−12.0404	−1.54162	−0.770809	+	0.637066i	$0.780148\pi$
$62$	−2.56546	−0.325814
$63$	2.42636	0.305693
$64$	1.00000	0.125000
$65$	−3.18502	−0.395053
$66$	0.928729	0.114319
$67$	14.5225	1.77420	0.887100	−	0.461577i	$-0.152716\pi$
$67$	14.5225	1.77420	0.887100	+	0.461577i	$0.152716\pi$
$68$	0.177461	0.0215203
$69$	5.67451	0.683131
$70$	−4.92990	−0.589236
$71$	−8.14558	−0.966703	−0.483351	−	0.875426i	$-0.660581\pi$
$71$	−8.14558	−0.966703	−0.483351	+	0.875426i	$0.660581\pi$
$72$	1.00000	0.117851
$73$	−2.41532	−0.282692	−0.141346	−	0.989960i	$-0.545143\pi$
$73$	−2.41532	−0.282692	−0.141346	+	0.989960i	$0.545143\pi$
$74$	1.57141	0.182672
$75$	0.871760	0.100662
$76$	−1.00000	−0.114708
$77$	−2.25343	−0.256803
$78$	−1.56758	−0.177493
$79$	−9.39537	−1.05706	−0.528531	−	0.848914i	$-0.677257\pi$
$79$	−9.39537	−1.05706	−0.528531	+	0.848914i	$0.677257\pi$
$80$	−2.03181	−0.227163
$81$	1.00000	0.111111
$82$	6.20941	0.685715
$83$	−7.01329	−0.769809	−0.384904	−	0.922956i	$-0.625766\pi$
$83$	−7.01329	−0.769809	−0.384904	+	0.922956i	$0.625766\pi$
$84$	−2.42636	−0.264738
$85$	−0.360566	−0.0391089
$86$	11.1802	1.20560
$87$	7.54062	0.808439
$88$	−0.928729	−0.0990028
$89$	1.16289	0.123267	0.0616333	−	0.998099i	$-0.480369\pi$
$89$	1.16289	0.123267	0.0616333	+	0.998099i	$0.480369\pi$
$90$	−2.03181	−0.214171
$91$	3.80352	0.398717
$92$	−5.67451	−0.591609
$93$	2.56546	0.266026
$94$	−4.47540	−0.461602
$95$	2.03181	0.208459
$96$	−1.00000	−0.102062
$97$	3.18543	0.323432	0.161716	−	0.986837i	$-0.448297\pi$
$97$	3.18543	0.323432	0.161716	+	0.986837i	$0.448297\pi$
$98$	−1.11276	−0.112406
$99$	−0.928729	−0.0933408
$100$	−0.871760	−0.0871760
$101$	4.97683	0.495213	0.247607	−	0.968861i	$-0.420356\pi$
$101$	4.97683	0.495213	0.247607	+	0.968861i	$0.420356\pi$
$102$	−0.177461	−0.0175712
$103$	−0.0114160	−0.00112485	−0.000562424	−	1.00000i	$-0.500179\pi$
$103$	−0.0114160	−0.00112485	−0.000562424		1.00000i	$0.500179\pi$
$104$	1.56758	0.153714
$105$	4.92990	0.481109
$106$	1.00000	0.0971286
$107$	−9.35321	−0.904209	−0.452104	−	0.891965i	$-0.649327\pi$
$107$	−9.35321	−0.904209	−0.452104	+	0.891965i	$0.649327\pi$
$108$	−1.00000	−0.0962250
$109$	−0.437341	−0.0418897	−0.0209448	−	0.999781i	$-0.506667\pi$
$109$	−0.437341	−0.0418897	−0.0209448	+	0.999781i	$0.506667\pi$
$110$	1.88700	0.179918
$111$	−1.57141	−0.149151
$112$	2.42636	0.229270
$113$	−9.91182	−0.932425	−0.466213	−	0.884673i	$-0.654382\pi$
$113$	−9.91182	−0.932425	−0.466213	+	0.884673i	$0.654382\pi$
$114$	1.00000	0.0936586
$115$	11.5295	1.07513
$116$	−7.54062	−0.700129
$117$	1.56758	0.144923
$118$	−4.45954	−0.410534
$119$	0.430585	0.0394716
$120$	2.03181	0.185478
$121$	−10.1375	−0.921588
$122$	−12.0404	−1.09009
$123$	−6.20941	−0.559884
$124$	−2.56546	−0.230385
$125$	11.9303	1.06708
$126$	2.42636	0.216158
$127$	3.33700	0.296111	0.148056	−	0.988979i	$-0.452699\pi$
$127$	3.33700	0.296111	0.148056	+	0.988979i	$0.452699\pi$
$128$	1.00000	0.0883883
$129$	−11.1802	−0.984366
$130$	−3.18502	−0.279345
$131$	5.35875	0.468196	0.234098	−	0.972213i	$-0.424786\pi$
$131$	5.35875	0.468196	0.234098	+	0.972213i	$0.424786\pi$
$132$	0.928729	0.0808355
$133$	−2.42636	−0.210392
$134$	14.5225	1.25455
$135$	2.03181	0.174870
$136$	0.177461	0.0152171
$137$	18.6789	1.59585	0.797924	−	0.602758i	$-0.205932\pi$
$137$	18.6789	1.59585	0.797924	+	0.602758i	$0.205932\pi$
$138$	5.67451	0.483046
$139$	0.349336	0.0296303	0.0148152	−	0.999890i	$-0.495284\pi$
$139$	0.349336	0.0296303	0.0148152	+	0.999890i	$0.495284\pi$
$140$	−4.92990	−0.416653
$141$	4.47540	0.376897
$142$	−8.14558	−0.683562
$143$	−1.45586	−0.121745
$144$	1.00000	0.0833333
$145$	15.3211	1.27235
$146$	−2.41532	−0.199893
$147$	1.11276	0.0917788
$148$	1.57141	0.129169
$149$	−14.0262	−1.14907	−0.574536	−	0.818479i	$-0.694817\pi$
$149$	−14.0262	−1.14907	−0.574536	+	0.818479i	$0.694817\pi$
$150$	0.871760	0.0711789
$151$	−4.58818	−0.373380	−0.186690	−	0.982419i	$-0.559776\pi$
$151$	−4.58818	−0.373380	−0.186690	+	0.982419i	$0.559776\pi$
$152$	−1.00000	−0.0811107
$153$	0.177461	0.0143469
$154$	−2.25343	−0.181587
$155$	5.21253	0.418680
$156$	−1.56758	−0.125507
$157$	13.7741	1.09929	0.549645	−	0.835399i	$-0.314763\pi$
$157$	13.7741	1.09929	0.549645	+	0.835399i	$0.314763\pi$
$158$	−9.39537	−0.747456
$159$	−1.00000	−0.0793052
$160$	−2.03181	−0.160628
$161$	−13.7684	−1.08510
$162$	1.00000	0.0785674
$163$	0.133285	0.0104397	0.00521985	−	0.999986i	$-0.498338\pi$
$163$	0.133285	0.0104397	0.00521985	+	0.999986i	$0.498338\pi$
$164$	6.20941	0.484873
$165$	−1.88700	−0.146903
$166$	−7.01329	−0.544337
$167$	−20.0437	−1.55103	−0.775513	−	0.631332i	$-0.782509\pi$
$167$	−20.0437	−1.55103	−0.775513	+	0.631332i	$0.782509\pi$
$168$	−2.42636	−0.187198
$169$	−10.5427	−0.810976
$170$	−0.360566	−0.0276542
$171$	−1.00000	−0.0764719
$172$	11.1802	0.852486
$173$	−8.85237	−0.673033	−0.336517	−	0.941678i	$-0.609249\pi$
$173$	−8.85237	−0.673033	−0.336517	+	0.941678i	$0.609249\pi$
$174$	7.54062	0.571653
$175$	−2.11521	−0.159895
$176$	−0.928729	−0.0700056
$177$	4.45954	0.335199
$178$	1.16289	0.0871626
$179$	6.90591	0.516172	0.258086	−	0.966122i	$-0.416908\pi$
$179$	6.90591	0.516172	0.258086	+	0.966122i	$0.416908\pi$
$180$	−2.03181	−0.151442
$181$	−16.5846	−1.23272	−0.616360	−	0.787464i	$-0.711394\pi$
$181$	−16.5846	−1.23272	−0.616360	+	0.787464i	$0.711394\pi$
$182$	3.80352	0.281936
$183$	12.0404	0.890054
$184$	−5.67451	−0.418330
$185$	−3.19280	−0.234739
$186$	2.56546	0.188109
$187$	−0.164813	−0.0120523
$188$	−4.47540	−0.326402
$189$	−2.42636	−0.176492
$190$	2.03181	0.147403
$191$	16.4338	1.18911	0.594555	−	0.804055i	$-0.297328\pi$
$191$	16.4338	1.18911	0.594555	+	0.804055i	$0.297328\pi$
$192$	−1.00000	−0.0721688
$193$	0.304285	0.0219029	0.0109515	−	0.999940i	$-0.496514\pi$
$193$	0.304285	0.0219029	0.0109515	+	0.999940i	$0.496514\pi$
$194$	3.18543	0.228701
$195$	3.18502	0.228084
$196$	−1.11276	−0.0794828
$197$	−19.0267	−1.35560	−0.677799	−	0.735248i	$-0.737066\pi$
$197$	−19.0267	−1.35560	−0.677799	+	0.735248i	$0.737066\pi$
$198$	−0.928729	−0.0660019
$199$	−7.63927	−0.541534	−0.270767	−	0.962645i	$-0.587277\pi$
$199$	−7.63927	−0.541534	−0.270767	+	0.962645i	$0.587277\pi$
$200$	−0.871760	−0.0616427
$201$	−14.5225	−1.02434
$202$	4.97683	0.350169
$203$	−18.2963	−1.28415
$204$	−0.177461	−0.0124247
$205$	−12.6163	−0.881162
$206$	−0.0114160	−0.000795388 0
$207$	−5.67451	−0.394406
$208$	1.56758	0.108692
$209$	0.928729	0.0642415
$210$	4.92990	0.340196
$211$	−8.09719	−0.557433	−0.278717	−	0.960373i	$-0.589909\pi$
$211$	−8.09719	−0.557433	−0.278717	+	0.960373i	$0.589909\pi$
$212$	1.00000	0.0686803
$213$	8.14558	0.558126
$214$	−9.35321	−0.639372
$215$	−22.7161	−1.54923
$216$	−1.00000	−0.0680414
$217$	−6.22475	−0.422563
$218$	−0.437341	−0.0296205
$219$	2.41532	0.163212
$220$	1.88700	0.127221
$221$	0.278184	0.0187127
$222$	−1.57141	−0.105466
$223$	−8.82476	−0.590949	−0.295475	−	0.955351i	$-0.595478\pi$
$223$	−8.82476	−0.590949	−0.295475	+	0.955351i	$0.595478\pi$
$224$	2.42636	0.162118
$225$	−0.871760	−0.0581173
$226$	−9.91182	−0.659324
$227$	−28.7764	−1.90996	−0.954979	−	0.296674i	$-0.904123\pi$
$227$	−28.7764	−1.90996	−0.954979	+	0.296674i	$0.904123\pi$
$228$	1.00000	0.0662266
$229$	−3.75069	−0.247852	−0.123926	−	0.992291i	$-0.539549\pi$
$229$	−3.75069	−0.247852	−0.123926	+	0.992291i	$0.539549\pi$
$230$	11.5295	0.760233
$231$	2.25343	0.148265
$232$	−7.54062	−0.495066
$233$	−0.225631	−0.0147816	−0.00739080	−	0.999973i	$-0.502353\pi$
$233$	−0.225631	−0.0147816	−0.00739080	+	0.999973i	$0.502353\pi$
$234$	1.56758	0.102476
$235$	9.09315	0.593172
$236$	−4.45954	−0.290291
$237$	9.39537	0.610295
$238$	0.430585	0.0279107
$239$	−24.8282	−1.60600	−0.803002	−	0.595977i	$-0.796765\pi$
$239$	−24.8282	−1.60600	−0.803002	+	0.595977i	$0.796765\pi$
$240$	2.03181	0.131153
$241$	16.9573	1.09232	0.546158	−	0.837682i	$-0.316090\pi$
$241$	16.9573	1.09232	0.546158	+	0.837682i	$0.316090\pi$
$242$	−10.1375	−0.651661
$243$	−1.00000	−0.0641500
$244$	−12.0404	−0.770809
$245$	2.26091	0.144444
$246$	−6.20941	−0.395897
$247$	−1.56758	−0.0997427
$248$	−2.56546	−0.162907
$249$	7.01329	0.444449
$250$	11.9303	0.754537
$251$	−0.527668	−0.0333061	−0.0166531	−	0.999861i	$-0.505301\pi$
$251$	−0.527668	−0.0333061	−0.0166531	+	0.999861i	$0.505301\pi$
$252$	2.42636	0.152847
$253$	5.27008	0.331327
$254$	3.33700	0.209382
$255$	0.360566	0.0225795
$256$	1.00000	0.0625000
$257$	−14.9666	−0.933589	−0.466795	−	0.884366i	$-0.654591\pi$
$257$	−14.9666	−0.933589	−0.466795	+	0.884366i	$0.654591\pi$
$258$	−11.1802	−0.696052
$259$	3.81281	0.236916
$260$	−3.18502	−0.197527
$261$	−7.54062	−0.466752
$262$	5.35875	0.331064
$263$	28.1746	1.73732	0.868661	−	0.495407i	$-0.164981\pi$
$263$	28.1746	1.73732	0.868661	+	0.495407i	$0.164981\pi$
$264$	0.928729	0.0571593
$265$	−2.03181	−0.124813
$266$	−2.42636	−0.148770
$267$	−1.16289	−0.0711680
$268$	14.5225	0.887100
$269$	−21.6035	−1.31719	−0.658595	−	0.752498i	$-0.728849\pi$
$269$	−21.6035	−1.31719	−0.658595	+	0.752498i	$0.728849\pi$
$270$	2.03181	0.123652
$271$	−28.8205	−1.75072	−0.875362	−	0.483468i	$-0.839377\pi$
$271$	−28.8205	−1.75072	−0.875362	+	0.483468i	$0.839377\pi$
$272$	0.177461	0.0107601
$273$	−3.80352	−0.230199
$274$	18.6789	1.12844
$275$	0.809628	0.0488224
$276$	5.67451	0.341565
$277$	−27.2992	−1.64025	−0.820125	−	0.572185i	$-0.806096\pi$
$277$	−27.2992	−1.64025	−0.820125	+	0.572185i	$0.806096\pi$
$278$	0.349336	0.0209518
$279$	−2.56546	−0.153590
$280$	−4.92990	−0.294618
$281$	−25.3937	−1.51486	−0.757430	−	0.652916i	$-0.773545\pi$
$281$	−25.3937	−1.51486	−0.757430	+	0.652916i	$0.773545\pi$
$282$	4.47540	0.266506
$283$	8.71833	0.518251	0.259125	−	0.965844i	$-0.416566\pi$
$283$	8.71833	0.518251	0.259125	+	0.965844i	$0.416566\pi$
$284$	−8.14558	−0.483351
$285$	−2.03181	−0.120354
$286$	−1.45586	−0.0860866
$287$	15.0663	0.889335
$288$	1.00000	0.0589256
$289$	−16.9685	−0.998148
$290$	15.3211	0.899685
$291$	−3.18543	−0.186733
$292$	−2.41532	−0.141346
$293$	9.21846	0.538548	0.269274	−	0.963064i	$-0.413216\pi$
$293$	9.21846	0.538548	0.269274	+	0.963064i	$0.413216\pi$
$294$	1.11276	0.0648974
$295$	9.06092	0.527547
$296$	1.57141	0.0913362
$297$	0.928729	0.0538903
$298$	−14.0262	−0.812517
$299$	−8.89525	−0.514426
$300$	0.871760	0.0503311
$301$	27.1273	1.56359
$302$	−4.58818	−0.264020
$303$	−4.97683	−0.285912
$304$	−1.00000	−0.0573539
$305$	24.4638	1.40079
$306$	0.177461	0.0101448
$307$	4.22150	0.240934	0.120467	−	0.992717i	$-0.461561\pi$
$307$	4.22150	0.240934	0.120467	+	0.992717i	$0.461561\pi$
$308$	−2.25343	−0.128401
$309$	0.0114160	0.000649432 0
$310$	5.21253	0.296052
$311$	−26.4017	−1.49711	−0.748553	−	0.663075i	$-0.769251\pi$
$311$	−26.4017	−1.49711	−0.748553	+	0.663075i	$0.769251\pi$
$312$	−1.56758	−0.0887467
$313$	25.3841	1.43479	0.717396	−	0.696666i	$-0.245334\pi$
$313$	25.3841	1.43479	0.717396	+	0.696666i	$0.245334\pi$
$314$	13.7741	0.777315
$315$	−4.92990	−0.277769
$316$	−9.39537	−0.528531
$317$	−24.9217	−1.39974	−0.699870	−	0.714270i	$-0.746759\pi$
$317$	−24.9217	−1.39974	−0.699870	+	0.714270i	$0.746759\pi$
$318$	−1.00000	−0.0560772
$319$	7.00319	0.392103
$320$	−2.03181	−0.113581
$321$	9.35321	0.522045
$322$	−13.7684	−0.767284
$323$	−0.177461	−0.00987419
$324$	1.00000	0.0555556
$325$	−1.36655	−0.0758027
$326$	0.133285	0.00738198
$327$	0.437341	0.0241850
$328$	6.20941	0.342857
$329$	−10.8590	−0.598673
$330$	−1.88700	−0.103876
$331$	19.9605	1.09713	0.548564	−	0.836109i	$-0.315175\pi$
$331$	19.9605	1.09713	0.548564	+	0.836109i	$0.315175\pi$
$332$	−7.01329	−0.384904
$333$	1.57141	0.0861126
$334$	−20.0437	−1.09674
$335$	−29.5068	−1.61213
$336$	−2.42636	−0.132369
$337$	4.37244	0.238182	0.119091	−	0.992883i	$-0.462002\pi$
$337$	4.37244	0.238182	0.119091	+	0.992883i	$0.462002\pi$
$338$	−10.5427	−0.573447
$339$	9.91182	0.538336
$340$	−0.360566	−0.0195545
$341$	2.38262	0.129026
$342$	−1.00000	−0.0540738
$343$	−19.6845	−1.06286
$344$	11.1802	0.602799
$345$	−11.5295	−0.620728
$346$	−8.85237	−0.475906
$347$	13.3078	0.714399	0.357200	−	0.934028i	$-0.383732\pi$
$347$	13.3078	0.714399	0.357200	+	0.934028i	$0.383732\pi$
$348$	7.54062	0.404219
$349$	−13.4810	−0.721619	−0.360810	−	0.932640i	$-0.617500\pi$
$349$	−13.4810	−0.721619	−0.360810	+	0.932640i	$0.617500\pi$
$350$	−2.11521	−0.113063
$351$	−1.56758	−0.0836712
$352$	−0.928729	−0.0495014
$353$	−13.5184	−0.719514	−0.359757	−	0.933046i	$-0.617140\pi$
$353$	−13.5184	−0.719514	−0.359757	+	0.933046i	$0.617140\pi$
$354$	4.45954	0.237022
$355$	16.5503	0.878396
$356$	1.16289	0.0616333
$357$	−0.430585	−0.0227890
$358$	6.90591	0.364989
$359$	8.40654	0.443680	0.221840	−	0.975083i	$-0.428794\pi$
$359$	8.40654	0.443680	0.221840	+	0.975083i	$0.428794\pi$
$360$	−2.03181	−0.107086
$361$	1.00000	0.0526316
$362$	−16.5846	−0.871665
$363$	10.1375	0.532079
$364$	3.80352	0.199359
$365$	4.90746	0.256868
$366$	12.0404	0.629363
$367$	−5.60050	−0.292344	−0.146172	−	0.989259i	$-0.546695\pi$
$367$	−5.60050	−0.292344	−0.146172	+	0.989259i	$0.546695\pi$
$368$	−5.67451	−0.295804
$369$	6.20941	0.323249
$370$	−3.19280	−0.165986
$371$	2.42636	0.125971
$372$	2.56546	0.133013
$373$	11.1399	0.576800	0.288400	−	0.957510i	$-0.406877\pi$
$373$	11.1399	0.576800	0.288400	+	0.957510i	$0.406877\pi$
$374$	−0.164813	−0.00852228
$375$	−11.9303	−0.616077
$376$	−4.47540	−0.230801
$377$	−11.8205	−0.608788
$378$	−2.42636	−0.124799
$379$	25.0432	1.28638	0.643190	−	0.765706i	$-0.277610\pi$
$379$	25.0432	1.28638	0.643190	+	0.765706i	$0.277610\pi$
$380$	2.03181	0.104230
$381$	−3.33700	−0.170960
$382$	16.4338	0.840828
$383$	25.6171	1.30897	0.654485	−	0.756075i	$-0.272885\pi$
$383$	25.6171	1.30897	0.654485	+	0.756075i	$0.272885\pi$
$384$	−1.00000	−0.0510310
$385$	4.57854	0.233344
$386$	0.304285	0.0154877
$387$	11.1802	0.568324
$388$	3.18543	0.161716
$389$	30.9100	1.56720	0.783601	−	0.621265i	$-0.213381\pi$
$389$	30.9100	1.56720	0.783601	+	0.621265i	$0.213381\pi$
$390$	3.18502	0.161280
$391$	−1.00700	−0.0509264
$392$	−1.11276	−0.0562028
$393$	−5.35875	−0.270313
$394$	−19.0267	−0.958552
$395$	19.0896	0.960501
$396$	−0.928729	−0.0466704
$397$	37.3032	1.87220	0.936098	−	0.351739i	$-0.114410\pi$
$397$	37.3032	1.87220	0.936098	+	0.351739i	$0.114410\pi$
$398$	−7.63927	−0.382922
$399$	2.42636	0.121470
$400$	−0.871760	−0.0435880
$401$	36.7159	1.83350	0.916752	−	0.399458i	$-0.130802\pi$
$401$	36.7159	1.83350	0.916752	+	0.399458i	$0.130802\pi$
$402$	−14.5225	−0.724314
$403$	−4.02157	−0.200329
$404$	4.97683	0.247607
$405$	−2.03181	−0.100961
$406$	−18.2963	−0.908029
$407$	−1.45941	−0.0723404
$408$	−0.177461	−0.00878562
$409$	13.3792	0.661560	0.330780	−	0.943708i	$-0.392688\pi$
$409$	13.3792	0.661560	0.330780	+	0.943708i	$0.392688\pi$
$410$	−12.6163	−0.623076
$411$	−18.6789	−0.921363
$412$	−0.0114160	−0.000562424 0
$413$	−10.8205	−0.532440
$414$	−5.67451	−0.278887
$415$	14.2497	0.699488
$416$	1.56758	0.0768569
$417$	−0.349336	−0.0171071
$418$	0.928729	0.0454256
$419$	−30.8495	−1.50710	−0.753548	−	0.657393i	$-0.771659\pi$
$419$	−30.8495	−1.50710	−0.753548	+	0.657393i	$0.771659\pi$
$420$	4.92990	0.240555
$421$	27.6772	1.34890	0.674452	−	0.738319i	$-0.264380\pi$
$421$	27.6772	1.34890	0.674452	+	0.738319i	$0.264380\pi$
$422$	−8.09719	−0.394165
$423$	−4.47540	−0.217601
$424$	1.00000	0.0485643
$425$	−0.154703	−0.00750421
$426$	8.14558	0.394655
$427$	−29.2144	−1.41379
$428$	−9.35321	−0.452104
$429$	1.45586	0.0702894
$430$	−22.7161	−1.09547
$431$	−0.445330	−0.0214508	−0.0107254	−	0.999942i	$-0.503414\pi$
$431$	−0.445330	−0.0214508	−0.0107254	+	0.999942i	$0.503414\pi$
$432$	−1.00000	−0.0481125
$433$	−4.01493	−0.192945	−0.0964725	−	0.995336i	$-0.530756\pi$
$433$	−4.01493	−0.192945	−0.0964725	+	0.995336i	$0.530756\pi$
$434$	−6.22475	−0.298797
$435$	−15.3211	−0.734589
$436$	−0.437341	−0.0209448
$437$	5.67451	0.271449
$438$	2.41532	0.115408
$439$	−40.4060	−1.92847	−0.964236	−	0.265044i	$-0.914614\pi$
$439$	−40.4060	−1.92847	−0.964236	+	0.265044i	$0.914614\pi$
$440$	1.88700	0.0899591
$441$	−1.11276	−0.0529885
$442$	0.278184	0.0132319
$443$	30.0359	1.42705	0.713525	−	0.700630i	$-0.247097\pi$
$443$	30.0359	1.42705	0.713525	+	0.700630i	$0.247097\pi$
$444$	−1.57141	−0.0745757
$445$	−2.36278	−0.112006
$446$	−8.82476	−0.417864
$447$	14.0262	0.663417
$448$	2.42636	0.114635
$449$	−5.71740	−0.269821	−0.134910	−	0.990858i	$-0.543075\pi$
$449$	−5.71740	−0.269821	−0.134910	+	0.990858i	$0.543075\pi$
$450$	−0.871760	−0.0410951
$451$	−5.76686	−0.271551
$452$	−9.91182	−0.466213
$453$	4.58818	0.215571
$454$	−28.7764	−1.35054
$455$	−7.72802	−0.362295
$456$	1.00000	0.0468293
$457$	−1.59023	−0.0743877	−0.0371939	−	0.999308i	$-0.511842\pi$
$457$	−1.59023	−0.0743877	−0.0371939	+	0.999308i	$0.511842\pi$
$458$	−3.75069	−0.175258
$459$	−0.177461	−0.00828316
$460$	11.5295	0.537566
$461$	−30.9359	−1.44083	−0.720414	−	0.693544i	$-0.756048\pi$
$461$	−30.9359	−1.44083	−0.720414	+	0.693544i	$0.756048\pi$
$462$	2.25343	0.104839
$463$	−28.5039	−1.32469	−0.662344	−	0.749200i	$-0.730438\pi$
$463$	−28.5039	−1.32469	−0.662344	+	0.749200i	$0.730438\pi$
$464$	−7.54062	−0.350064
$465$	−5.21253	−0.241725
$466$	−0.225631	−0.0104522
$467$	39.0769	1.80826	0.904131	−	0.427255i	$-0.140519\pi$
$467$	39.0769	1.80826	0.904131	+	0.427255i	$0.140519\pi$
$468$	1.56758	0.0724614
$469$	35.2368	1.62708
$470$	9.09315	0.419436
$471$	−13.7741	−0.634675
$472$	−4.45954	−0.205267
$473$	−10.3834	−0.477430
$474$	9.39537	0.431544
$475$	0.871760	0.0399991
$476$	0.430585	0.0197358
$477$	1.00000	0.0457869
$478$	−24.8282	−1.13562
$479$	−1.55623	−0.0711059	−0.0355529	−	0.999368i	$-0.511319\pi$
$479$	−1.55623	−0.0711059	−0.0355529	+	0.999368i	$0.511319\pi$
$480$	2.03181	0.0927389
$481$	2.46331	0.112317
$482$	16.9573	0.772384
$483$	13.7684	0.626485
$484$	−10.1375	−0.460794
$485$	−6.47218	−0.293887
$486$	−1.00000	−0.0453609
$487$	41.8167	1.89490	0.947449	−	0.319908i	$-0.103652\pi$
$487$	41.8167	1.89490	0.947449	+	0.319908i	$0.103652\pi$
$488$	−12.0404	−0.545044
$489$	−0.133285	−0.00602736
$490$	2.26091	0.102138
$491$	11.0174	0.497210	0.248605	−	0.968605i	$-0.420028\pi$
$491$	11.0174	0.497210	0.248605	+	0.968605i	$0.420028\pi$
$492$	−6.20941	−0.279942
$493$	−1.33816	−0.0602679
$494$	−1.56758	−0.0705288
$495$	1.88700	0.0848142
$496$	−2.56546	−0.115193
$497$	−19.7641	−0.886543
$498$	7.01329	0.314273
$499$	−5.70132	−0.255226	−0.127613	−	0.991824i	$-0.540732\pi$
$499$	−5.70132	−0.255226	−0.127613	+	0.991824i	$0.540732\pi$
$500$	11.9303	0.533538
$501$	20.0437	0.895485
$502$	−0.527668	−0.0235510
$503$	−33.3569	−1.48731	−0.743656	−	0.668562i	$-0.766910\pi$
$503$	−33.3569	−1.48731	−0.743656	+	0.668562i	$0.766910\pi$
$504$	2.42636	0.108079
$505$	−10.1120	−0.449977
$506$	5.27008	0.234284
$507$	10.5427	0.468217
$508$	3.33700	0.148056
$509$	14.2238	0.630458	0.315229	−	0.949016i	$-0.397919\pi$
$509$	14.2238	0.630458	0.315229	+	0.949016i	$0.397919\pi$
$510$	0.360566	0.0159661
$511$	−5.86045	−0.259251
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−14.9666	−0.660147
$515$	0.0231950	0.00102210
$516$	−11.1802	−0.492183
$517$	4.15643	0.182800
$518$	3.81281	0.167525
$519$	8.85237	0.388576
$520$	−3.18502	−0.139672
$521$	25.0818	1.09885	0.549426	−	0.835542i	$-0.314846\pi$
$521$	25.0818	1.09885	0.549426	+	0.835542i	$0.314846\pi$
$522$	−7.54062	−0.330044
$523$	−36.8866	−1.61294	−0.806470	−	0.591275i	$-0.798625\pi$
$523$	−36.8866	−1.61294	−0.806470	+	0.591275i	$0.798625\pi$
$524$	5.35875	0.234098
$525$	2.11521	0.0923151
$526$	28.1746	1.22847
$527$	−0.455269	−0.0198318
$528$	0.928729	0.0404177
$529$	9.20007	0.400003
$530$	−2.03181	−0.0882561
$531$	−4.45954	−0.193527
$532$	−2.42636	−0.105196
$533$	9.73375	0.421615
$534$	−1.16289	−0.0503233
$535$	19.0039	0.821611
$536$	14.5225	0.627275
$537$	−6.90591	−0.298012
$538$	−21.6035	−0.931394
$539$	1.03345	0.0445139
$540$	2.03181	0.0874351
$541$	17.7566	0.763415	0.381708	−	0.924283i	$-0.375336\pi$
$541$	17.7566	0.763415	0.381708	+	0.924283i	$0.375336\pi$
$542$	−28.8205	−1.23795
$543$	16.5846	0.711712
$544$	0.177461	0.00760857
$545$	0.888593	0.0380631
$546$	−3.80352	−0.162776
$547$	22.1608	0.947529	0.473765	−	0.880651i	$-0.342895\pi$
$547$	22.1608	0.947529	0.473765	+	0.880651i	$0.342895\pi$
$548$	18.6789	0.797924
$549$	−12.0404	−0.513873
$550$	0.809628	0.0345227
$551$	7.54062	0.321241
$552$	5.67451	0.241523
$553$	−22.7966	−0.969410
$554$	−27.2992	−1.15983
$555$	3.19280	0.135527
$556$	0.349336	0.0148152
$557$	−24.2763	−1.02862	−0.514310	−	0.857604i	$-0.671952\pi$
$557$	−24.2763	−1.02862	−0.514310	+	0.857604i	$0.671952\pi$
$558$	−2.56546	−0.108605
$559$	17.5259	0.741268
$560$	−4.92990	−0.208326
$561$	0.164813	0.00695841
$562$	−25.3937	−1.07117
$563$	30.9434	1.30411	0.652055	−	0.758172i	$-0.273907\pi$
$563$	30.9434	1.30411	0.652055	+	0.758172i	$0.273907\pi$
$564$	4.47540	0.188448
$565$	20.1389	0.847250
$566$	8.71833	0.366459
$567$	2.42636	0.101898
$568$	−8.14558	−0.341781
$569$	−38.3524	−1.60782	−0.803909	−	0.594752i	$-0.797250\pi$
$569$	−38.3524	−1.60782	−0.803909	+	0.594752i	$0.797250\pi$
$570$	−2.03181	−0.0851030
$571$	23.9116	1.00067	0.500334	−	0.865832i	$-0.333210\pi$
$571$	23.9116	1.00067	0.500334	+	0.865832i	$0.333210\pi$
$572$	−1.45586	−0.0608724
$573$	−16.4338	−0.686533
$574$	15.0663	0.628855
$575$	4.94681	0.206296
$576$	1.00000	0.0416667
$577$	−7.99743	−0.332937	−0.166469	−	0.986047i	$-0.553236\pi$
$577$	−7.99743	−0.332937	−0.166469	+	0.986047i	$0.553236\pi$
$578$	−16.9685	−0.705797
$579$	−0.304285	−0.0126457
$580$	15.3211	0.636173
$581$	−17.0168	−0.705976
$582$	−3.18543	−0.132040
$583$	−0.928729	−0.0384640
$584$	−2.41532	−0.0999467
$585$	−3.18502	−0.131684
$586$	9.21846	0.380811
$587$	−34.6690	−1.43094	−0.715472	−	0.698641i	$-0.753788\pi$
$587$	−34.6690	−1.43094	−0.715472	+	0.698641i	$0.753788\pi$
$588$	1.11276	0.0458894
$589$	2.56546	0.105708
$590$	9.06092	0.373032
$591$	19.0267	0.782654
$592$	1.57141	0.0645845
$593$	−1.12472	−0.0461866	−0.0230933	−	0.999733i	$-0.507351\pi$
$593$	−1.12472	−0.0461866	−0.0230933	+	0.999733i	$0.507351\pi$
$594$	0.928729	0.0381062
$595$	−0.874865	−0.0358660
$596$	−14.0262	−0.574536
$597$	7.63927	0.312655
$598$	−8.89525	−0.363754
$599$	−0.776698	−0.0317350	−0.0158675	−	0.999874i	$-0.505051\pi$
$599$	−0.776698	−0.0317350	−0.0158675	+	0.999874i	$0.505051\pi$
$600$	0.871760	0.0355894
$601$	−26.2457	−1.07059	−0.535293	−	0.844666i	$-0.679799\pi$
$601$	−26.2457	−1.07059	−0.535293	+	0.844666i	$0.679799\pi$
$602$	27.1273	1.10563
$603$	14.5225	0.591400
$604$	−4.58818	−0.186690
$605$	20.5974	0.837402
$606$	−4.97683	−0.202170
$607$	−43.8589	−1.78018	−0.890089	−	0.455786i	$-0.849358\pi$
$607$	−43.8589	−1.78018	−0.890089	+	0.455786i	$0.849358\pi$
$608$	−1.00000	−0.0405554
$609$	18.2963	0.741403
$610$	24.4638	0.990511
$611$	−7.01555	−0.283819
$612$	0.177461	0.00717343
$613$	−2.89754	−0.117031	−0.0585154	−	0.998287i	$-0.518637\pi$
$613$	−2.89754	−0.117031	−0.0585154	+	0.998287i	$0.518637\pi$
$614$	4.22150	0.170366
$615$	12.6163	0.508739
$616$	−2.25343	−0.0907934
$617$	27.0026	1.08708	0.543542	−	0.839382i	$-0.317083\pi$
$617$	27.0026	1.08708	0.543542	+	0.839382i	$0.317083\pi$
$618$	0.0114160	0.000459218 0
$619$	−43.9758	−1.76754	−0.883769	−	0.467923i	$-0.845002\pi$
$619$	−43.9758	−1.76754	−0.883769	+	0.467923i	$0.845002\pi$
$620$	5.21253	0.209340
$621$	5.67451	0.227710
$622$	−26.4017	−1.05861
$623$	2.82160	0.113045
$624$	−1.56758	−0.0627534
$625$	−19.8812	−0.795249
$626$	25.3841	1.01455
$627$	−0.928729	−0.0370899
$628$	13.7741	0.549645
$629$	0.278863	0.0111190
$630$	−4.92990	−0.196412
$631$	0.510546	0.0203245	0.0101623	−	0.999948i	$-0.496765\pi$
$631$	0.510546	0.0203245	0.0101623	+	0.999948i	$0.496765\pi$
$632$	−9.39537	−0.373728
$633$	8.09719	0.321834
$634$	−24.9217	−0.989766
$635$	−6.78014	−0.269062
$636$	−1.00000	−0.0396526
$637$	−1.74434	−0.0691132
$638$	7.00319	0.277259
$639$	−8.14558	−0.322234
$640$	−2.03181	−0.0803142
$641$	−32.3420	−1.27743	−0.638716	−	0.769442i	$-0.720534\pi$
$641$	−32.3420	−1.27743	−0.638716	+	0.769442i	$0.720534\pi$
$642$	9.35321	0.369142
$643$	22.0703	0.870366	0.435183	−	0.900342i	$-0.356684\pi$
$643$	22.0703	0.870366	0.435183	+	0.900342i	$0.356684\pi$
$644$	−13.7684	−0.542552
$645$	22.7161	0.894446
$646$	−0.177461	−0.00698210
$647$	29.8676	1.17422	0.587108	−	0.809509i	$-0.300267\pi$
$647$	29.8676	1.17422	0.587108	+	0.809509i	$0.300267\pi$
$648$	1.00000	0.0392837
$649$	4.14170	0.162576
$650$	−1.36655	−0.0536006
$651$	6.22475	0.243967
$652$	0.133285	0.00521985
$653$	−44.4525	−1.73956	−0.869780	−	0.493439i	$-0.835740\pi$
$653$	−44.4525	−1.73956	−0.869780	+	0.493439i	$0.835740\pi$
$654$	0.437341	0.0171014
$655$	−10.8879	−0.425427
$656$	6.20941	0.242437
$657$	−2.41532	−0.0942306
$658$	−10.8590	−0.423326
$659$	40.1460	1.56387	0.781934	−	0.623362i	$-0.214234\pi$
$659$	40.1460	1.56387	0.781934	+	0.623362i	$0.214234\pi$
$660$	−1.88700	−0.0734513
$661$	17.5289	0.681797	0.340899	−	0.940100i	$-0.389269\pi$
$661$	17.5289	0.681797	0.340899	+	0.940100i	$0.389269\pi$
$662$	19.9605	0.775786
$663$	−0.278184	−0.0108038
$664$	−7.01329	−0.272168
$665$	4.92990	0.191173
$666$	1.57141	0.0608908
$667$	42.7893	1.65681
$668$	−20.0437	−0.775513
$669$	8.82476	0.341185
$670$	−29.5068	−1.13995
$671$	11.1823	0.431687
$672$	−2.42636	−0.0935990
$673$	−25.1198	−0.968297	−0.484148	−	0.874986i	$-0.660871\pi$
$673$	−25.1198	−0.968297	−0.484148	+	0.874986i	$0.660871\pi$
$674$	4.37244	0.168420
$675$	0.871760	0.0335540
$676$	−10.5427	−0.405488
$677$	28.5574	1.09755	0.548775	−	0.835970i	$-0.315094\pi$
$677$	28.5574	1.09755	0.548775	+	0.835970i	$0.315094\pi$
$678$	9.91182	0.380661
$679$	7.72901	0.296612
$680$	−0.360566	−0.0138271
$681$	28.7764	1.10271
$682$	2.38262	0.0912352
$683$	13.2203	0.505861	0.252931	−	0.967484i	$-0.418606\pi$
$683$	13.2203	0.505861	0.252931	+	0.967484i	$0.418606\pi$
$684$	−1.00000	−0.0382360
$685$	−37.9520	−1.45007
$686$	−19.6845	−0.751558
$687$	3.75069	0.143098
$688$	11.1802	0.426243
$689$	1.56758	0.0597200
$690$	−11.5295	−0.438921
$691$	−10.6429	−0.404876	−0.202438	−	0.979295i	$-0.564886\pi$
$691$	−10.6429	−0.404876	−0.202438	+	0.979295i	$0.564886\pi$
$692$	−8.85237	−0.336517
$693$	−2.25343	−0.0856009
$694$	13.3078	0.505156
$695$	−0.709784	−0.0269236
$696$	7.54062	0.285826
$697$	1.10193	0.0417385
$698$	−13.4810	−0.510262
$699$	0.225631	0.00853417
$700$	−2.11521	−0.0799473
$701$	8.40314	0.317382	0.158691	−	0.987328i	$-0.449273\pi$
$701$	8.40314	0.317382	0.158691	+	0.987328i	$0.449273\pi$
$702$	−1.56758	−0.0591645
$703$	−1.57141	−0.0592668
$704$	−0.928729	−0.0350028
$705$	−9.09315	−0.342468
$706$	−13.5184	−0.508773
$707$	12.0756	0.454150
$708$	4.45954	0.167600
$709$	37.5436	1.40998	0.704991	−	0.709217i	$-0.250951\pi$
$709$	37.5436	1.40998	0.704991	+	0.709217i	$0.250951\pi$
$710$	16.5503	0.621120
$711$	−9.39537	−0.352354
$712$	1.16289	0.0435813
$713$	14.5577	0.545192
$714$	−0.430585	−0.0161142
$715$	2.95802	0.110624
$716$	6.90591	0.258086
$717$	24.8282	0.927226
$718$	8.40654	0.313729
$719$	32.1854	1.20031	0.600156	−	0.799883i	$-0.295105\pi$
$719$	32.1854	1.20031	0.600156	+	0.799883i	$0.295105\pi$
$720$	−2.03181	−0.0757210
$721$	−0.0276993	−0.00103158
$722$	1.00000	0.0372161
$723$	−16.9573	−0.630649
$724$	−16.5846	−0.616360
$725$	6.57360	0.244138
$726$	10.1375	0.376237
$727$	7.28831	0.270309	0.135154	−	0.990825i	$-0.456847\pi$
$727$	7.28831	0.270309	0.135154	+	0.990825i	$0.456847\pi$
$728$	3.80352	0.140968
$729$	1.00000	0.0370370
$730$	4.90746	0.181633
$731$	1.98406	0.0733830
$732$	12.0404	0.445027
$733$	4.07192	0.150400	0.0752000	−	0.997168i	$-0.476040\pi$
$733$	4.07192	0.150400	0.0752000	+	0.997168i	$0.476040\pi$
$734$	−5.60050	−0.206718
$735$	−2.26091	−0.0833950
$736$	−5.67451	−0.209165
$737$	−13.4874	−0.496816
$738$	6.20941	0.228572
$739$	−17.7101	−0.651478	−0.325739	−	0.945460i	$-0.605613\pi$
$739$	−17.7101	−0.651478	−0.325739	+	0.945460i	$0.605613\pi$
$740$	−3.19280	−0.117370
$741$	1.56758	0.0575865
$742$	2.42636	0.0890746
$743$	−11.6329	−0.426770	−0.213385	−	0.976968i	$-0.568449\pi$
$743$	−11.6329	−0.426770	−0.213385	+	0.976968i	$0.568449\pi$
$744$	2.56546	0.0940544
$745$	28.4986	1.04411
$746$	11.1399	0.407859
$747$	−7.01329	−0.256603
$748$	−0.164813	−0.00602616
$749$	−22.6943	−0.829231
$750$	−11.9303	−0.435632
$751$	43.4907	1.58700	0.793499	−	0.608571i	$-0.208257\pi$
$751$	43.4907	1.58700	0.793499	+	0.608571i	$0.208257\pi$
$752$	−4.47540	−0.163201
$753$	0.527668	0.0192293
$754$	−11.8205	−0.430478
$755$	9.32229	0.339273
$756$	−2.42636	−0.0882460
$757$	−16.5283	−0.600730	−0.300365	−	0.953824i	$-0.597109\pi$
$757$	−16.5283	−0.600730	−0.300365	+	0.953824i	$0.597109\pi$
$758$	25.0432	0.909608
$759$	−5.27008	−0.191292
$760$	2.03181	0.0737014
$761$	−8.40562	−0.304704	−0.152352	−	0.988326i	$-0.548685\pi$
$761$	−8.40562	−0.304704	−0.152352	+	0.988326i	$0.548685\pi$
$762$	−3.33700	−0.120887
$763$	−1.06115	−0.0384161
$764$	16.4338	0.594555
$765$	−0.360566	−0.0130363
$766$	25.6171	0.925582
$767$	−6.99068	−0.252419
$768$	−1.00000	−0.0360844
$769$	9.63056	0.347287	0.173643	−	0.984809i	$-0.444446\pi$
$769$	9.63056	0.347287	0.173643	+	0.984809i	$0.444446\pi$
$770$	4.57854	0.164999
$771$	14.9666	0.539008
$772$	0.304285	0.0109515
$773$	−14.5077	−0.521806	−0.260903	−	0.965365i	$-0.584020\pi$
$773$	−14.5077	−0.521806	−0.260903	+	0.965365i	$0.584020\pi$
$774$	11.1802	0.401866
$775$	2.23647	0.0803362
$776$	3.18543	0.114350
$777$	−3.81281	−0.136784
$778$	30.9100	1.10818
$779$	−6.20941	−0.222475
$780$	3.18502	0.114042
$781$	7.56504	0.270698
$782$	−1.00700	−0.0360104
$783$	7.54062	0.269480
$784$	−1.11276	−0.0397414
$785$	−27.9862	−0.998871
$786$	−5.35875	−0.191140
$787$	−15.8156	−0.563765	−0.281883	−	0.959449i	$-0.590959\pi$
$787$	−15.8156	−0.563765	−0.281883	+	0.959449i	$0.590959\pi$
$788$	−19.0267	−0.677799
$789$	−28.1746	−1.00304
$790$	19.0896	0.679177
$791$	−24.0497	−0.855108
$792$	−0.928729	−0.0330009
$793$	−18.8743	−0.670247
$794$	37.3032	1.32384
$795$	2.03181	0.0720608
$796$	−7.63927	−0.270767
$797$	21.0829	0.746796	0.373398	−	0.927671i	$-0.378193\pi$
$797$	21.0829	0.746796	0.373398	+	0.927671i	$0.378193\pi$
$798$	2.42636	0.0858923
$799$	−0.794209	−0.0280971
$800$	−0.871760	−0.0308214
$801$	1.16289	0.0410888
$802$	36.7159	1.29648
$803$	2.24318	0.0791600
$804$	−14.5225	−0.512168
$805$	27.9748	0.985982
$806$	−4.02157	−0.141654
$807$	21.6035	0.760480
$808$	4.97683	0.175084
$809$	43.9902	1.54661	0.773306	−	0.634033i	$-0.218602\pi$
$809$	43.9902	1.54661	0.773306	+	0.634033i	$0.218602\pi$
$810$	−2.03181	−0.0713904
$811$	44.9819	1.57953	0.789763	−	0.613412i	$-0.210203\pi$
$811$	44.9819	1.57953	0.789763	+	0.613412i	$0.210203\pi$
$812$	−18.2963	−0.642073
$813$	28.8205	1.01078
$814$	−1.45941	−0.0511524
$815$	−0.270810	−0.00948605
$816$	−0.177461	−0.00621237
$817$	−11.1802	−0.391147
$818$	13.3792	0.467794
$819$	3.80352	0.132906
$820$	−12.6163	−0.440581
$821$	28.5714	0.997148	0.498574	−	0.866847i	$-0.333857\pi$
$821$	28.5714	0.997148	0.498574	+	0.866847i	$0.333857\pi$
$822$	−18.6789	−0.651502
$823$	46.9540	1.63672	0.818358	−	0.574709i	$-0.194885\pi$
$823$	46.9540	1.63672	0.818358	+	0.574709i	$0.194885\pi$
$824$	−0.0114160	−0.000397694 0
$825$	−0.809628	−0.0281876
$826$	−10.8205	−0.376492
$827$	−22.9289	−0.797317	−0.398659	−	0.917099i	$-0.630524\pi$
$827$	−22.9289	−0.797317	−0.398659	+	0.917099i	$0.630524\pi$
$828$	−5.67451	−0.197203
$829$	−0.655028	−0.0227500	−0.0113750	−	0.999935i	$-0.503621\pi$
$829$	−0.655028	−0.0227500	−0.0113750	+	0.999935i	$0.503621\pi$
$830$	14.2497	0.494613
$831$	27.2992	0.946999
$832$	1.56758	0.0543461
$833$	−0.197471	−0.00684197
$834$	−0.349336	−0.0120965
$835$	40.7249	1.40934
$836$	0.928729	0.0321208
$837$	2.56546	0.0886754
$838$	−30.8495	−1.06568
$839$	21.4799	0.741570	0.370785	−	0.928719i	$-0.379089\pi$
$839$	21.4799	0.741570	0.370785	+	0.928719i	$0.379089\pi$
$840$	4.92990	0.170098
$841$	27.8609	0.960720
$842$	27.6772	0.953819
$843$	25.3937	0.874605
$844$	−8.09719	−0.278717
$845$	21.4207	0.736895
$846$	−4.47540	−0.153867
$847$	−24.5972	−0.845169
$848$	1.00000	0.0343401
$849$	−8.71833	−0.299212
$850$	−0.154703	−0.00530628
$851$	−8.91697	−0.305670
$852$	8.14558	0.279063
$853$	15.2127	0.520875	0.260437	−	0.965491i	$-0.416133\pi$
$853$	15.2127	0.520875	0.260437	+	0.965491i	$0.416133\pi$
$854$	−29.2144	−0.999698
$855$	2.03181	0.0694863
$856$	−9.35321	−0.319686
$857$	−26.3490	−0.900064	−0.450032	−	0.893012i	$-0.648587\pi$
$857$	−26.3490	−0.900064	−0.450032	+	0.893012i	$0.648587\pi$
$858$	1.45586	0.0497021
$859$	19.5343	0.666501	0.333251	−	0.942838i	$-0.391854\pi$
$859$	19.5343	0.666501	0.333251	+	0.942838i	$0.391854\pi$
$860$	−22.7161	−0.774613
$861$	−15.0663	−0.513458
$862$	−0.445330	−0.0151680
$863$	22.5358	0.767129	0.383564	−	0.923514i	$-0.374696\pi$
$863$	22.5358	0.767129	0.383564	+	0.923514i	$0.374696\pi$
$864$	−1.00000	−0.0340207
$865$	17.9863	0.611553
$866$	−4.01493	−0.136433
$867$	16.9685	0.576281
$868$	−6.22475	−0.211282
$869$	8.72575	0.296001
$870$	−15.3211	−0.519433
$871$	22.7651	0.771367
$872$	−0.437341	−0.0148102
$873$	3.18543	0.107811
$874$	5.67451	0.191943
$875$	28.9472	0.978594
$876$	2.41532	0.0816061
$877$	25.6318	0.865523	0.432762	−	0.901508i	$-0.357539\pi$
$877$	25.6318	0.865523	0.432762	+	0.901508i	$0.357539\pi$
$878$	−40.4060	−1.36364
$879$	−9.21846	−0.310931
$880$	1.88700	0.0636107
$881$	21.2733	0.716715	0.358357	−	0.933584i	$-0.383337\pi$
$881$	21.2733	0.716715	0.358357	+	0.933584i	$0.383337\pi$
$882$	−1.11276	−0.0374685
$883$	−29.1391	−0.980608	−0.490304	−	0.871552i	$-0.663114\pi$
$883$	−29.1391	−0.980608	−0.490304	+	0.871552i	$0.663114\pi$
$884$	0.278184	0.00935635
$885$	−9.06092	−0.304579
$886$	30.0359	1.00908
$887$	39.1767	1.31543	0.657713	−	0.753268i	$-0.271524\pi$
$887$	39.1767	1.31543	0.657713	+	0.753268i	$0.271524\pi$
$888$	−1.57141	−0.0527330
$889$	8.09678	0.271557
$890$	−2.36278	−0.0792004
$891$	−0.928729	−0.0311136
$892$	−8.82476	−0.295475
$893$	4.47540	0.149764
$894$	14.0262	0.469107
$895$	−14.0315	−0.469021
$896$	2.42636	0.0810591
$897$	8.89525	0.297004
$898$	−5.71740	−0.190792
$899$	19.3452	0.645197
$900$	−0.871760	−0.0290587
$901$	0.177461	0.00591208
$902$	−5.76686	−0.192015
$903$	−27.1273	−0.902742
$904$	−9.91182	−0.329662
$905$	33.6966	1.12011
$906$	4.58818	0.152432
$907$	53.3650	1.77196	0.885978	−	0.463727i	$-0.153488\pi$
$907$	53.3650	1.77196	0.885978	+	0.463727i	$0.153488\pi$
$908$	−28.7764	−0.954979
$909$	4.97683	0.165071
$910$	−7.72802	−0.256181
$911$	−16.0923	−0.533160	−0.266580	−	0.963813i	$-0.585894\pi$
$911$	−16.0923	−0.533160	−0.266580	+	0.963813i	$0.585894\pi$
$912$	1.00000	0.0331133
$913$	6.51345	0.215564
$914$	−1.59023	−0.0526001
$915$	−24.4638	−0.808749
$916$	−3.75069	−0.123926
$917$	13.0023	0.429373
$918$	−0.177461	−0.00585708
$919$	15.9010	0.524527	0.262264	−	0.964996i	$-0.415531\pi$
$919$	15.9010	0.524527	0.262264	+	0.964996i	$0.415531\pi$
$920$	11.5295	0.380117
$921$	−4.22150	−0.139103
$922$	−30.9359	−1.01882
$923$	−12.7689	−0.420292
$924$	2.25343	0.0741325
$925$	−1.36989	−0.0450417
$926$	−28.5039	−0.936696
$927$	−0.0114160	−0.000374950 0
$928$	−7.54062	−0.247533
$929$	−8.50047	−0.278891	−0.139446	−	0.990230i	$-0.544532\pi$
$929$	−8.50047	−0.278891	−0.139446	+	0.990230i	$0.544532\pi$
$930$	−5.21253	−0.170925
$931$	1.11276	0.0364692
$932$	−0.225631	−0.00739080
$933$	26.4017	0.864354
$934$	39.0769	1.27863
$935$	0.334868	0.0109514
$936$	1.56758	0.0512380
$937$	−53.2478	−1.73953	−0.869765	−	0.493466i	$-0.835730\pi$
$937$	−53.2478	−1.73953	−0.869765	+	0.493466i	$0.835730\pi$
$938$	35.2368	1.15052
$939$	−25.3841	−0.828377
$940$	9.09315	0.296586
$941$	2.22441	0.0725137	0.0362569	−	0.999343i	$-0.488457\pi$
$941$	2.22441	0.0725137	0.0362569	+	0.999343i	$0.488457\pi$
$942$	−13.7741	−0.448783
$943$	−35.2354	−1.14742
$944$	−4.45954	−0.145146
$945$	4.92990	0.160370
$946$	−10.3834	−0.337594
$947$	49.9405	1.62285	0.811424	−	0.584458i	$-0.198693\pi$
$947$	49.9405	1.62285	0.811424	+	0.584458i	$0.198693\pi$
$948$	9.39537	0.305148
$949$	−3.78621	−0.122906
$950$	0.871760	0.0282836
$951$	24.9217	0.808140
$952$	0.430585	0.0139553
$953$	−3.88004	−0.125687	−0.0628433	−	0.998023i	$-0.520017\pi$
$953$	−3.88004	−0.125687	−0.0628433	+	0.998023i	$0.520017\pi$
$954$	1.00000	0.0323762
$955$	−33.3904	−1.08049
$956$	−24.8282	−0.803002
$957$	−7.00319	−0.226381
$958$	−1.55623	−0.0502795
$959$	45.3219	1.46352
$960$	2.03181	0.0655763
$961$	−24.4184	−0.787690
$962$	2.46331	0.0794202
$963$	−9.35321	−0.301403
$964$	16.9573	0.546158
$965$	−0.618249	−0.0199021
$966$	13.7684	0.442992
$967$	1.35800	0.0436705	0.0218352	−	0.999762i	$-0.493049\pi$
$967$	1.35800	0.0436705	0.0218352	+	0.999762i	$0.493049\pi$
$968$	−10.1375	−0.325830
$969$	0.177461	0.00570086
$970$	−6.47218	−0.207809
$971$	57.9712	1.86038	0.930192	−	0.367073i	$-0.119640\pi$
$971$	57.9712	1.86038	0.930192	+	0.367073i	$0.119640\pi$
$972$	−1.00000	−0.0320750
$973$	0.847617	0.0271734
$974$	41.8167	1.33989
$975$	1.36655	0.0437647
$976$	−12.0404	−0.385405
$977$	−13.7208	−0.438968	−0.219484	−	0.975616i	$-0.570437\pi$
$977$	−13.7208	−0.438968	−0.219484	+	0.975616i	$0.570437\pi$
$978$	−0.133285	−0.00426199
$979$	−1.08001	−0.0345174
$980$	2.26091	0.0722222
$981$	−0.437341	−0.0139632
$982$	11.0174	0.351581
$983$	−28.3255	−0.903443	−0.451722	−	0.892159i	$-0.649190\pi$
$983$	−28.3255	−0.903443	−0.451722	+	0.892159i	$0.649190\pi$
$984$	−6.20941	−0.197949
$985$	38.6586	1.23177
$986$	−1.33816	−0.0426158
$987$	10.8590	0.345644
$988$	−1.56758	−0.0498714
$989$	−63.4424	−2.01735
$990$	1.88700	0.0599727
$991$	22.1355	0.703157	0.351579	−	0.936158i	$-0.385645\pi$
$991$	22.1355	0.703157	0.351579	+	0.936158i	$0.385645\pi$
$992$	−2.56546	−0.0814535
$993$	−19.9605	−0.633427
$994$	−19.7641	−0.626881
$995$	15.5215	0.492066
$996$	7.01329	0.222225
$997$	17.4473	0.552560	0.276280	−	0.961077i	$-0.410898\pi$
$997$	17.4473	0.552560	0.276280	+	0.961077i	$0.410898\pi$
$998$	−5.70132	−0.180472
$999$	−1.57141	−0.0497171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bb.1.4	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bb.1.4	✓	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.03181 q^{5} -1.00000 q^{6} +2.42636 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.03181 q^{5} -1.00000 q^{6} +2.42636 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.03181 q^{10} -0.928729 q^{11} -1.00000 q^{12} +1.56758 q^{13} +2.42636 q^{14} +2.03181 q^{15} +1.00000 q^{16} +0.177461 q^{17} +1.00000 q^{18} -1.00000 q^{19} -2.03181 q^{20} -2.42636 q^{21} -0.928729 q^{22} -5.67451 q^{23} -1.00000 q^{24} -0.871760 q^{25} +1.56758 q^{26} -1.00000 q^{27} +2.42636 q^{28} -7.54062 q^{29} +2.03181 q^{30} -2.56546 q^{31} +1.00000 q^{32} +0.928729 q^{33} +0.177461 q^{34} -4.92990 q^{35} +1.00000 q^{36} +1.57141 q^{37} -1.00000 q^{38} -1.56758 q^{39} -2.03181 q^{40} +6.20941 q^{41} -2.42636 q^{42} +11.1802 q^{43} -0.928729 q^{44} -2.03181 q^{45} -5.67451 q^{46} -4.47540 q^{47} -1.00000 q^{48} -1.11276 q^{49} -0.871760 q^{50} -0.177461 q^{51} +1.56758 q^{52} +1.00000 q^{53} -1.00000 q^{54} +1.88700 q^{55} +2.42636 q^{56} +1.00000 q^{57} -7.54062 q^{58} -4.45954 q^{59} +2.03181 q^{60} -12.0404 q^{61} -2.56546 q^{62} +2.42636 q^{63} +1.00000 q^{64} -3.18502 q^{65} +0.928729 q^{66} +14.5225 q^{67} +0.177461 q^{68} +5.67451 q^{69} -4.92990 q^{70} -8.14558 q^{71} +1.00000 q^{72} -2.41532 q^{73} +1.57141 q^{74} +0.871760 q^{75} -1.00000 q^{76} -2.25343 q^{77} -1.56758 q^{78} -9.39537 q^{79} -2.03181 q^{80} +1.00000 q^{81} +6.20941 q^{82} -7.01329 q^{83} -2.42636 q^{84} -0.360566 q^{85} +11.1802 q^{86} +7.54062 q^{87} -0.928729 q^{88} +1.16289 q^{89} -2.03181 q^{90} +3.80352 q^{91} -5.67451 q^{92} +2.56546 q^{93} -4.47540 q^{94} +2.03181 q^{95} -1.00000 q^{96} +3.18543 q^{97} -1.11276 q^{98} -0.928729 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 5 q^{5} - 9 q^{6} - 5 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 5 * q^5 - 9 * q^6 - 5 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 5 q^{5} - 9 q^{6} - 5 q^{7} + 9 q^{8} + 9 q^{9} - 5 q^{10} + 3 q^{11} - 9 q^{12} - 4 q^{13} - 5 q^{14} + 5 q^{15} + 9 q^{16} - 16 q^{17} + 9 q^{18} - 9 q^{19} - 5 q^{20} + 5 q^{21} + 3 q^{22} - 9 q^{24} + 8 q^{25} - 4 q^{26} - 9 q^{27} - 5 q^{28} - 2 q^{29} + 5 q^{30} - 10 q^{31} + 9 q^{32} - 3 q^{33} - 16 q^{34} - q^{35} + 9 q^{36} - 14 q^{37} - 9 q^{38} + 4 q^{39} - 5 q^{40} - 21 q^{41} + 5 q^{42} - 4 q^{43} + 3 q^{44} - 5 q^{45} - 8 q^{47} - 9 q^{48} - 14 q^{49} + 8 q^{50} + 16 q^{51} - 4 q^{52} + 9 q^{53} - 9 q^{54} - 14 q^{55} - 5 q^{56} + 9 q^{57} - 2 q^{58} - 12 q^{59} + 5 q^{60} - 13 q^{61} - 10 q^{62} - 5 q^{63} + 9 q^{64} - 13 q^{65} - 3 q^{66} + 22 q^{67} - 16 q^{68} - q^{70} - 13 q^{71} + 9 q^{72} - 17 q^{73} - 14 q^{74} - 8 q^{75} - 9 q^{76} - 25 q^{77} + 4 q^{78} - 5 q^{80} + 9 q^{81} - 21 q^{82} - 24 q^{83} + 5 q^{84} - 16 q^{85} - 4 q^{86} + 2 q^{87} + 3 q^{88} - 23 q^{89} - 5 q^{90} - 11 q^{91} + 10 q^{93} - 8 q^{94} + 5 q^{95} - 9 q^{96} - 29 q^{97} - 14 q^{98} + 3 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 5 * q^5 - 9 * q^6 - 5 * q^7 + 9 * q^8 + 9 * q^9 - 5 * q^10 + 3 * q^11 - 9 * q^12 - 4 * q^13 - 5 * q^14 + 5 * q^15 + 9 * q^16 - 16 * q^17 + 9 * q^18 - 9 * q^19 - 5 * q^20 + 5 * q^21 + 3 * q^22 - 9 * q^24 + 8 * q^25 - 4 * q^26 - 9 * q^27 - 5 * q^28 - 2 * q^29 + 5 * q^30 - 10 * q^31 + 9 * q^32 - 3 * q^33 - 16 * q^34 - q^35 + 9 * q^36 - 14 * q^37 - 9 * q^38 + 4 * q^39 - 5 * q^40 - 21 * q^41 + 5 * q^42 - 4 * q^43 + 3 * q^44 - 5 * q^45 - 8 * q^47 - 9 * q^48 - 14 * q^49 + 8 * q^50 + 16 * q^51 - 4 * q^52 + 9 * q^53 - 9 * q^54 - 14 * q^55 - 5 * q^56 + 9 * q^57 - 2 * q^58 - 12 * q^59 + 5 * q^60 - 13 * q^61 - 10 * q^62 - 5 * q^63 + 9 * q^64 - 13 * q^65 - 3 * q^66 + 22 * q^67 - 16 * q^68 - q^70 - 13 * q^71 + 9 * q^72 - 17 * q^73 - 14 * q^74 - 8 * q^75 - 9 * q^76 - 25 * q^77 + 4 * q^78 - 5 * q^80 + 9 * q^81 - 21 * q^82 - 24 * q^83 + 5 * q^84 - 16 * q^85 - 4 * q^86 + 2 * q^87 + 3 * q^88 - 23 * q^89 - 5 * q^90 - 11 * q^91 + 10 * q^93 - 8 * q^94 + 5 * q^95 - 9 * q^96 - 29 * q^97 - 14 * q^98 + 3 * q^99

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