LMFDB - Embedded newform 1342.2.a.n.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1342,2,Mod(1,1342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1342, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1342.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1342 = 2 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1342.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:	$10.7159239513$
Analytic rank:	$0$
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} - 15x^{7} + 55x^{6} + 84x^{5} - 239x^{4} - 184x^{3} + 334x^{2} + 54x - 102 $ x^9 - 4x^8 - 15x^7 + 55x^6 + 84x^5 - 239x^4 - 184x^3 + 334x^2 + 54x - 102
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			1.3
Root			$2.34314$ of defining polynomial
Character	$\chi$	$=$	1342.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.34314 q^{3} +1.00000 q^{4} -3.04006 q^{5} +1.34314 q^{6} -0.109279 q^{7} -1.00000 q^{8} -1.19597 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.34314 q^{3} +1.00000 q^{4} -3.04006 q^{5} +1.34314 q^{6} -0.109279 q^{7} -1.00000 q^{8} -1.19597 q^{9} +3.04006 q^{10} +1.00000 q^{11} -1.34314 q^{12} -3.86186 q^{13} +0.109279 q^{14} +4.08324 q^{15} +1.00000 q^{16} -5.00895 q^{17} +1.19597 q^{18} -5.59039 q^{19} -3.04006 q^{20} +0.146778 q^{21} -1.00000 q^{22} +9.16452 q^{23} +1.34314 q^{24} +4.24198 q^{25} +3.86186 q^{26} +5.63578 q^{27} -0.109279 q^{28} -6.97131 q^{29} -4.08324 q^{30} -8.25814 q^{31} -1.00000 q^{32} -1.34314 q^{33} +5.00895 q^{34} +0.332216 q^{35} -1.19597 q^{36} -3.04767 q^{37} +5.59039 q^{38} +5.18703 q^{39} +3.04006 q^{40} +10.5444 q^{41} -0.146778 q^{42} -7.20121 q^{43} +1.00000 q^{44} +3.63581 q^{45} -9.16452 q^{46} +2.87412 q^{47} -1.34314 q^{48} -6.98806 q^{49} -4.24198 q^{50} +6.72773 q^{51} -3.86186 q^{52} -2.07593 q^{53} -5.63578 q^{54} -3.04006 q^{55} +0.109279 q^{56} +7.50869 q^{57} +6.97131 q^{58} +8.69511 q^{59} +4.08324 q^{60} -1.00000 q^{61} +8.25814 q^{62} +0.130694 q^{63} +1.00000 q^{64} +11.7403 q^{65} +1.34314 q^{66} +6.24566 q^{67} -5.00895 q^{68} -12.3093 q^{69} -0.332216 q^{70} +10.8422 q^{71} +1.19597 q^{72} +16.0845 q^{73} +3.04767 q^{74} -5.69759 q^{75} -5.59039 q^{76} -0.109279 q^{77} -5.18703 q^{78} -0.244892 q^{79} -3.04006 q^{80} -3.98177 q^{81} -10.5444 q^{82} -1.75407 q^{83} +0.146778 q^{84} +15.2275 q^{85} +7.20121 q^{86} +9.36346 q^{87} -1.00000 q^{88} -8.60441 q^{89} -3.63581 q^{90} +0.422022 q^{91} +9.16452 q^{92} +11.0919 q^{93} -2.87412 q^{94} +16.9951 q^{95} +1.34314 q^{96} +0.113606 q^{97} +6.98806 q^{98} -1.19597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} + 5 q^{3} + 9 q^{4} + 6 q^{5} - 5 q^{6} - 2 q^{7} - 9 q^{8} + 20 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 + 5 * q^3 + 9 * q^4 + 6 * q^5 - 5 * q^6 - 2 * q^7 - 9 * q^8 + 20 * q^9	\( 9 q - 9 q^{2} + 5 q^{3} + 9 q^{4} + 6 q^{5} - 5 q^{6} - 2 q^{7} - 9 q^{8} + 20 q^{9} - 6 q^{10} + 9 q^{11} + 5 q^{12} - q^{13} + 2 q^{14} + 6 q^{15} + 9 q^{16} + 11 q^{17} - 20 q^{18} - 6 q^{19} + 6 q^{20} - 2 q^{21} - 9 q^{22} + 21 q^{23} - 5 q^{24} + 19 q^{25} + q^{26} + 26 q^{27} - 2 q^{28} - 5 q^{29} - 6 q^{30} - 7 q^{31} - 9 q^{32} + 5 q^{33} - 11 q^{34} + 6 q^{35} + 20 q^{36} + 16 q^{37} + 6 q^{38} - 18 q^{39} - 6 q^{40} + 13 q^{41} + 2 q^{42} + 9 q^{44} + 42 q^{45} - 21 q^{46} + 9 q^{47} + 5 q^{48} + 27 q^{49} - 19 q^{50} - 4 q^{51} - q^{52} + 18 q^{53} - 26 q^{54} + 6 q^{55} + 2 q^{56} - 12 q^{57} + 5 q^{58} + q^{59} + 6 q^{60} - 9 q^{61} + 7 q^{62} + 37 q^{63} + 9 q^{64} + 20 q^{65} - 5 q^{66} + 17 q^{67} + 11 q^{68} + 3 q^{69} - 6 q^{70} + 5 q^{71} - 20 q^{72} - 5 q^{73} - 16 q^{74} + q^{75} - 6 q^{76} - 2 q^{77} + 18 q^{78} - 39 q^{79} + 6 q^{80} + 61 q^{81} - 13 q^{82} + 43 q^{83} - 2 q^{84} + 10 q^{85} + 8 q^{87} - 9 q^{88} + 32 q^{89} - 42 q^{90} - 62 q^{91} + 21 q^{92} + 41 q^{93} - 9 q^{94} + 36 q^{95} - 5 q^{96} + 22 q^{97} - 27 q^{98} + 20 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 + 5 * q^3 + 9 * q^4 + 6 * q^5 - 5 * q^6 - 2 * q^7 - 9 * q^8 + 20 * q^9 - 6 * q^10 + 9 * q^11 + 5 * q^12 - q^13 + 2 * q^14 + 6 * q^15 + 9 * q^16 + 11 * q^17 - 20 * q^18 - 6 * q^19 + 6 * q^20 - 2 * q^21 - 9 * q^22 + 21 * q^23 - 5 * q^24 + 19 * q^25 + q^26 + 26 * q^27 - 2 * q^28 - 5 * q^29 - 6 * q^30 - 7 * q^31 - 9 * q^32 + 5 * q^33 - 11 * q^34 + 6 * q^35 + 20 * q^36 + 16 * q^37 + 6 * q^38 - 18 * q^39 - 6 * q^40 + 13 * q^41 + 2 * q^42 + 9 * q^44 + 42 * q^45 - 21 * q^46 + 9 * q^47 + 5 * q^48 + 27 * q^49 - 19 * q^50 - 4 * q^51 - q^52 + 18 * q^53 - 26 * q^54 + 6 * q^55 + 2 * q^56 - 12 * q^57 + 5 * q^58 + q^59 + 6 * q^60 - 9 * q^61 + 7 * q^62 + 37 * q^63 + 9 * q^64 + 20 * q^65 - 5 * q^66 + 17 * q^67 + 11 * q^68 + 3 * q^69 - 6 * q^70 + 5 * q^71 - 20 * q^72 - 5 * q^73 - 16 * q^74 + q^75 - 6 * q^76 - 2 * q^77 + 18 * q^78 - 39 * q^79 + 6 * q^80 + 61 * q^81 - 13 * q^82 + 43 * q^83 - 2 * q^84 + 10 * q^85 + 8 * q^87 - 9 * q^88 + 32 * q^89 - 42 * q^90 - 62 * q^91 + 21 * q^92 + 41 * q^93 - 9 * q^94 + 36 * q^95 - 5 * q^96 + 22 * q^97 - 27 * q^98 + 20 * 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
$3$	−1.34314	−0.775464	−0.387732	−	0.921772i	$-0.626741\pi$
$3$	−1.34314	−0.775464	−0.387732	+	0.921772i	$0.626741\pi$
$4$	1.00000	0.500000
$5$	−3.04006	−1.35956	−0.679779	−	0.733417i	$-0.737924\pi$
$5$	−3.04006	−1.35956	−0.679779	+	0.733417i	$0.737924\pi$
$6$	1.34314	0.548336
$7$	−0.109279	−0.0413038	−0.0206519	−	0.999787i	$-0.506574\pi$
$7$	−0.109279	−0.0413038	−0.0206519	+	0.999787i	$0.506574\pi$
$8$	−1.00000	−0.353553
$9$	−1.19597	−0.398655
$10$	3.04006	0.961352
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.34314	−0.387732
$13$	−3.86186	−1.07109	−0.535543	−	0.844508i	$-0.679893\pi$
$13$	−3.86186	−1.07109	−0.535543	+	0.844508i	$0.679893\pi$
$14$	0.109279	0.0292062
$15$	4.08324	1.05429
$16$	1.00000	0.250000
$17$	−5.00895	−1.21485	−0.607424	−	0.794378i	$-0.707797\pi$
$17$	−5.00895	−1.21485	−0.607424	+	0.794378i	$0.707797\pi$
$18$	1.19597	0.281892
$19$	−5.59039	−1.28252	−0.641261	−	0.767323i	$-0.721589\pi$
$19$	−5.59039	−1.28252	−0.641261	+	0.767323i	$0.721589\pi$
$20$	−3.04006	−0.679779
$21$	0.146778	0.0320296
$22$	−1.00000	−0.213201
$23$	9.16452	1.91094	0.955468	−	0.295096i	$-0.0953515\pi$
$23$	9.16452	1.91094	0.955468	+	0.295096i	$0.0953515\pi$
$24$	1.34314	0.274168
$25$	4.24198	0.848396
$26$	3.86186	0.757373
$27$	5.63578	1.08461
$28$	−0.109279	−0.0206519
$29$	−6.97131	−1.29454	−0.647270	−	0.762261i	$-0.724089\pi$
$29$	−6.97131	−1.29454	−0.647270	+	0.762261i	$0.724089\pi$
$30$	−4.08324	−0.745494
$31$	−8.25814	−1.48321	−0.741603	−	0.670839i	$-0.765934\pi$
$31$	−8.25814	−1.48321	−0.741603	+	0.670839i	$0.765934\pi$
$32$	−1.00000	−0.176777
$33$	−1.34314	−0.233811
$34$	5.00895	0.859027
$35$	0.332216	0.0561548
$36$	−1.19597	−0.199328
$37$	−3.04767	−0.501033	−0.250517	−	0.968112i	$-0.580600\pi$
$37$	−3.04767	−0.501033	−0.250517	+	0.968112i	$0.580600\pi$
$38$	5.59039	0.906880
$39$	5.18703	0.830589
$40$	3.04006	0.480676
$41$	10.5444	1.64675	0.823376	−	0.567496i	$-0.192088\pi$
$41$	10.5444	1.64675	0.823376	+	0.567496i	$0.192088\pi$
$42$	−0.146778	−0.0226483
$43$	−7.20121	−1.09817	−0.549087	−	0.835765i	$-0.685025\pi$
$43$	−7.20121	−1.09817	−0.549087	+	0.835765i	$0.685025\pi$
$44$	1.00000	0.150756
$45$	3.63581	0.541995
$46$	−9.16452	−1.35124
$47$	2.87412	0.419233	0.209616	−	0.977784i	$-0.432778\pi$
$47$	2.87412	0.419233	0.209616	+	0.977784i	$0.432778\pi$
$48$	−1.34314	−0.193866
$49$	−6.98806	−0.998294
$50$	−4.24198	−0.599907
$51$	6.72773	0.942071
$52$	−3.86186	−0.535543
$53$	−2.07593	−0.285151	−0.142575	−	0.989784i	$-0.545538\pi$
$53$	−2.07593	−0.285151	−0.142575	+	0.989784i	$0.545538\pi$
$54$	−5.63578	−0.766933
$55$	−3.04006	−0.409922
$56$	0.109279	0.0146031
$57$	7.50869	0.994551
$58$	6.97131	0.915377
$59$	8.69511	1.13201	0.566003	−	0.824403i	$-0.308489\pi$
$59$	8.69511	1.13201	0.566003	+	0.824403i	$0.308489\pi$
$60$	4.08324	0.527144
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	8.25814	1.04879
$63$	0.130694	0.0164660
$64$	1.00000	0.125000
$65$	11.7403	1.45620
$66$	1.34314	0.165330
$67$	6.24566	0.763029	0.381515	−	0.924363i	$-0.375403\pi$
$67$	6.24566	0.763029	0.381515	+	0.924363i	$0.375403\pi$
$68$	−5.00895	−0.607424
$69$	−12.3093	−1.48186
$70$	−0.332216	−0.0397074
$71$	10.8422	1.28673	0.643366	−	0.765559i	$-0.277537\pi$
$71$	10.8422	1.28673	0.643366	+	0.765559i	$0.277537\pi$
$72$	1.19597	0.140946
$73$	16.0845	1.88255	0.941274	−	0.337645i	$-0.109630\pi$
$73$	16.0845	1.88255	0.941274	+	0.337645i	$0.109630\pi$
$74$	3.04767	0.354284
$75$	−5.69759	−0.657901
$76$	−5.59039	−0.641261
$77$	−0.109279	−0.0124535
$78$	−5.18703	−0.587315
$79$	−0.244892	−0.0275525	−0.0137762	−	0.999905i	$-0.504385\pi$
$79$	−0.244892	−0.0275525	−0.0137762	+	0.999905i	$0.504385\pi$
$80$	−3.04006	−0.339889
$81$	−3.98177	−0.442419
$82$	−10.5444	−1.16443
$83$	−1.75407	−0.192534	−0.0962670	−	0.995356i	$-0.530690\pi$
$83$	−1.75407	−0.192534	−0.0962670	+	0.995356i	$0.530690\pi$
$84$	0.146778	0.0160148
$85$	15.2275	1.65166
$86$	7.20121	0.776527
$87$	9.36346	1.00387
$88$	−1.00000	−0.106600
$89$	−8.60441	−0.912066	−0.456033	−	0.889963i	$-0.650730\pi$
$89$	−8.60441	−0.912066	−0.456033	+	0.889963i	$0.650730\pi$
$90$	−3.63581	−0.383248
$91$	0.422022	0.0442399
$92$	9.16452	0.955468
$93$	11.0919	1.15017
$94$	−2.87412	−0.296442
$95$	16.9951	1.74366
$96$	1.34314	0.137084
$97$	0.113606	0.0115349	0.00576746	−	0.999983i	$-0.498164\pi$
$97$	0.113606	0.0115349	0.00576746	+	0.999983i	$0.498164\pi$
$98$	6.98806	0.705900
$99$	−1.19597	−0.120199
$100$	4.24198	0.424198
$101$	1.93525	0.192565	0.0962824	−	0.995354i	$-0.469305\pi$
$101$	1.93525	0.192565	0.0962824	+	0.995354i	$0.469305\pi$
$102$	−6.72773	−0.666145
$103$	−10.5488	−1.03940	−0.519701	−	0.854348i	$-0.673957\pi$
$103$	−10.5488	−1.03940	−0.519701	+	0.854348i	$0.673957\pi$
$104$	3.86186	0.378686
$105$	−0.446214	−0.0435461
$106$	2.07593	0.201632
$107$	14.2971	1.38215	0.691076	−	0.722782i	$-0.257137\pi$
$107$	14.2971	1.38215	0.691076	+	0.722782i	$0.257137\pi$
$108$	5.63578	0.542304
$109$	1.12224	0.107491	0.0537457	−	0.998555i	$-0.482884\pi$
$109$	1.12224	0.107491	0.0537457	+	0.998555i	$0.482884\pi$
$110$	3.04006	0.289859
$111$	4.09345	0.388533
$112$	−0.109279	−0.0103259
$113$	10.0860	0.948813	0.474406	−	0.880306i	$-0.342663\pi$
$113$	10.0860	0.948813	0.474406	+	0.880306i	$0.342663\pi$
$114$	−7.50869	−0.703253
$115$	−27.8607	−2.59803
$116$	−6.97131	−0.647270
$117$	4.61865	0.426994
$118$	−8.69511	−0.800450
$119$	0.547375	0.0501778
$120$	−4.08324	−0.372747
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−14.1626	−1.27700
$124$	−8.25814	−0.741603
$125$	2.30443	0.206114
$126$	−0.130694	−0.0116432
$127$	0.942032	0.0835918	0.0417959	−	0.999126i	$-0.486692\pi$
$127$	0.942032	0.0835918	0.0417959	+	0.999126i	$0.486692\pi$
$128$	−1.00000	−0.0883883
$129$	9.67226	0.851595
$130$	−11.7403	−1.02969
$131$	−14.5666	−1.27269	−0.636343	−	0.771406i	$-0.719554\pi$
$131$	−14.5666	−1.27269	−0.636343	+	0.771406i	$0.719554\pi$
$132$	−1.34314	−0.116906
$133$	0.610914	0.0529730
$134$	−6.24566	−0.539543
$135$	−17.1331	−1.47459
$136$	5.00895	0.429514
$137$	5.99028	0.511784	0.255892	−	0.966705i	$-0.417631\pi$
$137$	5.99028	0.511784	0.255892	+	0.966705i	$0.417631\pi$
$138$	12.3093	1.04783
$139$	−1.44198	−0.122307	−0.0611537	−	0.998128i	$-0.519478\pi$
$139$	−1.44198	−0.122307	−0.0611537	+	0.998128i	$0.519478\pi$
$140$	0.332216	0.0280774
$141$	−3.86035	−0.325100
$142$	−10.8422	−0.909857
$143$	−3.86186	−0.322945
$144$	−1.19597	−0.0996638
$145$	21.1932	1.76000
$146$	−16.0845	−1.33116
$147$	9.38596	0.774141
$148$	−3.04767	−0.250517
$149$	−3.76244	−0.308231	−0.154115	−	0.988053i	$-0.549253\pi$
$149$	−3.76244	−0.308231	−0.154115	+	0.988053i	$0.549253\pi$
$150$	5.69759	0.465206
$151$	13.2738	1.08020	0.540102	−	0.841600i	$-0.318386\pi$
$151$	13.2738	1.08020	0.540102	+	0.841600i	$0.318386\pi$
$152$	5.59039	0.453440
$153$	5.99053	0.484305
$154$	0.109279	0.00880599
$155$	25.1053	2.01650
$156$	5.18703	0.415295
$157$	13.4573	1.07401	0.537005	−	0.843579i	$-0.319555\pi$
$157$	13.4573	1.07401	0.537005	+	0.843579i	$0.319555\pi$
$158$	0.244892	0.0194826
$159$	2.78827	0.221124
$160$	3.04006	0.240338
$161$	−1.00149	−0.0789288
$162$	3.98177	0.312837
$163$	15.9096	1.24614	0.623070	−	0.782166i	$-0.285885\pi$
$163$	15.9096	1.24614	0.623070	+	0.782166i	$0.285885\pi$
$164$	10.5444	0.823376
$165$	4.08324	0.317880
$166$	1.75407	0.136142
$167$	−10.7269	−0.830071	−0.415035	−	0.909805i	$-0.636231\pi$
$167$	−10.7269	−0.830071	−0.415035	+	0.909805i	$0.636231\pi$
$168$	−0.146778	−0.0113242
$169$	1.91394	0.147226
$170$	−15.2275	−1.16790
$171$	6.68591	0.511284
$172$	−7.20121	−0.549087
$173$	20.1922	1.53518	0.767590	−	0.640941i	$-0.221456\pi$
$173$	20.1922	1.53518	0.767590	+	0.640941i	$0.221456\pi$
$174$	−9.36346	−0.709842
$175$	−0.463561	−0.0350419
$176$	1.00000	0.0753778
$177$	−11.6788	−0.877831
$178$	8.60441	0.644928
$179$	−11.7950	−0.881598	−0.440799	−	0.897606i	$-0.645305\pi$
$179$	−11.7950	−0.881598	−0.440799	+	0.897606i	$0.645305\pi$
$180$	3.63581	0.270997
$181$	14.9029	1.10772	0.553861	−	0.832609i	$-0.313154\pi$
$181$	14.9029	1.10772	0.553861	+	0.832609i	$0.313154\pi$
$182$	−0.422022	−0.0312823
$183$	1.34314	0.0992880
$184$	−9.16452	−0.675618
$185$	9.26510	0.681183
$186$	−11.0919	−0.813295
$187$	−5.00895	−0.366290
$188$	2.87412	0.209616
$189$	−0.615875	−0.0447983
$190$	−16.9951	−1.23296
$191$	0.632662	0.0457779	0.0228889	−	0.999738i	$-0.492714\pi$
$191$	0.632662	0.0457779	0.0228889	+	0.999738i	$0.492714\pi$
$192$	−1.34314	−0.0969330
$193$	11.7508	0.845841	0.422921	−	0.906167i	$-0.361005\pi$
$193$	11.7508	0.845841	0.422921	+	0.906167i	$0.361005\pi$
$194$	−0.113606	−0.00815641
$195$	−15.7689	−1.12923
$196$	−6.98806	−0.499147
$197$	−18.1871	−1.29578	−0.647890	−	0.761734i	$-0.724348\pi$
$197$	−18.1871	−1.29578	−0.647890	+	0.761734i	$0.724348\pi$
$198$	1.19597	0.0849936
$199$	5.08484	0.360455	0.180227	−	0.983625i	$-0.442317\pi$
$199$	5.08484	0.360455	0.180227	+	0.983625i	$0.442317\pi$
$200$	−4.24198	−0.299953
$201$	−8.38882	−0.591702
$202$	−1.93525	−0.136164
$203$	0.761820	0.0534693
$204$	6.72773	0.471036
$205$	−32.0555	−2.23885
$206$	10.5488	0.734969
$207$	−10.9605	−0.761804
$208$	−3.86186	−0.267772
$209$	−5.59039	−0.386695
$210$	0.446214	0.0307917
$211$	−26.0373	−1.79248	−0.896242	−	0.443566i	$-0.853713\pi$
$211$	−26.0373	−1.79248	−0.896242	+	0.443566i	$0.853713\pi$
$212$	−2.07593	−0.142575
$213$	−14.5626	−0.997815
$214$	−14.2971	−0.977329
$215$	21.8921	1.49303
$216$	−5.63578	−0.383467
$217$	0.902445	0.0612620
$218$	−1.12224	−0.0760078
$219$	−21.6038	−1.45985
$220$	−3.04006	−0.204961
$221$	19.3438	1.30121
$222$	−4.09345	−0.274735
$223$	−14.0923	−0.943689	−0.471845	−	0.881682i	$-0.656412\pi$
$223$	−14.0923	−0.943689	−0.471845	+	0.881682i	$0.656412\pi$
$224$	0.109279	0.00730154
$225$	−5.07326	−0.338217
$226$	−10.0860	−0.670912
$227$	−2.08414	−0.138329	−0.0691645	−	0.997605i	$-0.522033\pi$
$227$	−2.08414	−0.138329	−0.0691645	+	0.997605i	$0.522033\pi$
$228$	7.50869	0.497275
$229$	−1.04606	−0.0691256	−0.0345628	−	0.999403i	$-0.511004\pi$
$229$	−1.04606	−0.0691256	−0.0345628	+	0.999403i	$0.511004\pi$
$230$	27.8607	1.83708
$231$	0.146778	0.00965728
$232$	6.97131	0.457689
$233$	7.39890	0.484718	0.242359	−	0.970187i	$-0.422079\pi$
$233$	7.39890	0.484718	0.242359	+	0.970187i	$0.422079\pi$
$234$	−4.61865	−0.301930
$235$	−8.73749	−0.569971
$236$	8.69511	0.566003
$237$	0.328925	0.0213660
$238$	−0.547375	−0.0354810
$239$	−7.12156	−0.460656	−0.230328	−	0.973113i	$-0.573980\pi$
$239$	−7.12156	−0.460656	−0.230328	+	0.973113i	$0.573980\pi$
$240$	4.08324	0.263572
$241$	−23.1056	−1.48837	−0.744183	−	0.667976i	$-0.767161\pi$
$241$	−23.1056	−1.48837	−0.744183	+	0.667976i	$0.767161\pi$
$242$	−1.00000	−0.0642824
$243$	−11.5593	−0.741527
$244$	−1.00000	−0.0640184
$245$	21.2441	1.35724
$246$	14.1626	0.902973
$247$	21.5893	1.37369
$248$	8.25814	0.524393
$249$	2.35597	0.149303
$250$	−2.30443	−0.145745
$251$	−20.9878	−1.32474	−0.662369	−	0.749177i	$-0.730449\pi$
$251$	−20.9878	−1.32474	−0.662369	+	0.749177i	$0.730449\pi$
$252$	0.130694	0.00823298
$253$	9.16452	0.576169
$254$	−0.942032	−0.0591083
$255$	−20.4527	−1.28080
$256$	1.00000	0.0625000
$257$	−6.08230	−0.379403	−0.189702	−	0.981842i	$-0.560752\pi$
$257$	−6.08230	−0.379403	−0.189702	+	0.981842i	$0.560752\pi$
$258$	−9.67226	−0.602169
$259$	0.333047	0.0206946
$260$	11.7403	0.728102
$261$	8.33744	0.516075
$262$	14.5666	0.899925
$263$	26.5257	1.63564	0.817822	−	0.575471i	$-0.195181\pi$
$263$	26.5257	1.63564	0.817822	+	0.575471i	$0.195181\pi$
$264$	1.34314	0.0826648
$265$	6.31095	0.387679
$266$	−0.610914	−0.0374576
$267$	11.5570	0.707274
$268$	6.24566	0.381515
$269$	−18.1085	−1.10409	−0.552047	−	0.833813i	$-0.686153\pi$
$269$	−18.1085	−1.10409	−0.552047	+	0.833813i	$0.686153\pi$
$270$	17.1331	1.04269
$271$	−20.6507	−1.25444	−0.627221	−	0.778841i	$-0.715808\pi$
$271$	−20.6507	−1.25444	−0.627221	+	0.778841i	$0.715808\pi$
$272$	−5.00895	−0.303712
$273$	−0.566836	−0.0343065
$274$	−5.99028	−0.361886
$275$	4.24198	0.255801
$276$	−12.3093	−0.740931
$277$	21.2251	1.27529	0.637645	−	0.770330i	$-0.279909\pi$
$277$	21.2251	1.27529	0.637645	+	0.770330i	$0.279909\pi$
$278$	1.44198	0.0864844
$279$	9.87645	0.591288
$280$	−0.332216	−0.0198537
$281$	−4.27359	−0.254941	−0.127471	−	0.991842i	$-0.540686\pi$
$281$	−4.27359	−0.254941	−0.127471	+	0.991842i	$0.540686\pi$
$282$	3.86035	0.229880
$283$	−10.8245	−0.643449	−0.321724	−	0.946833i	$-0.604262\pi$
$283$	−10.8245	−0.643449	−0.321724	+	0.946833i	$0.604262\pi$
$284$	10.8422	0.643366
$285$	−22.8269	−1.35215
$286$	3.86186	0.228356
$287$	−1.15228	−0.0680170
$288$	1.19597	0.0704729
$289$	8.08954	0.475855
$290$	−21.1932	−1.24451
$291$	−0.152589	−0.00894491
$292$	16.0845	0.941274
$293$	−4.22149	−0.246622	−0.123311	−	0.992368i	$-0.539351\pi$
$293$	−4.22149	−0.246622	−0.123311	+	0.992368i	$0.539351\pi$
$294$	−9.38596	−0.547401
$295$	−26.4337	−1.53903
$296$	3.04767	0.177142
$297$	5.63578	0.327021
$298$	3.76244	0.217952
$299$	−35.3921	−2.04678
$300$	−5.69759	−0.328950
$301$	0.786944	0.0453587
$302$	−13.2738	−0.763820
$303$	−2.59932	−0.149327
$304$	−5.59039	−0.320631
$305$	3.04006	0.174073
$306$	−5.99053	−0.342456
$307$	−19.3928	−1.10680	−0.553402	−	0.832915i	$-0.686670\pi$
$307$	−19.3928	−1.10680	−0.553402	+	0.832915i	$0.686670\pi$
$308$	−0.109279	−0.00622677
$309$	14.1685	0.806019
$310$	−25.1053	−1.42588
$311$	22.7938	1.29252	0.646258	−	0.763119i	$-0.276333\pi$
$311$	22.7938	1.29252	0.646258	+	0.763119i	$0.276333\pi$
$312$	−5.18703	−0.293658
$313$	5.81686	0.328788	0.164394	−	0.986395i	$-0.447433\pi$
$313$	5.81686	0.328788	0.164394	+	0.986395i	$0.447433\pi$
$314$	−13.4573	−0.759440
$315$	−0.397319	−0.0223864
$316$	−0.244892	−0.0137762
$317$	−28.6198	−1.60745	−0.803723	−	0.595004i	$-0.797151\pi$
$317$	−28.6198	−1.60745	−0.803723	+	0.595004i	$0.797151\pi$
$318$	−2.78827	−0.156358
$319$	−6.97131	−0.390318
$320$	−3.04006	−0.169945
$321$	−19.2030	−1.07181
$322$	1.00149	0.0558111
$323$	28.0019	1.55807
$324$	−3.98177	−0.221209
$325$	−16.3819	−0.908705
$326$	−15.9096	−0.881154
$327$	−1.50733	−0.0833557
$328$	−10.5444	−0.582215
$329$	−0.314082	−0.0173159
$330$	−4.08324	−0.224775
$331$	33.5929	1.84643	0.923216	−	0.384282i	$-0.125551\pi$
$331$	33.5929	1.84643	0.923216	+	0.384282i	$0.125551\pi$
$332$	−1.75407	−0.0962670
$333$	3.64490	0.199740
$334$	10.7269	0.586949
$335$	−18.9872	−1.03738
$336$	0.146778	0.00800740
$337$	−20.5379	−1.11877	−0.559385	−	0.828908i	$-0.688963\pi$
$337$	−20.5379	−1.11877	−0.559385	+	0.828908i	$0.688963\pi$
$338$	−1.91394	−0.104105
$339$	−13.5470	−0.735770
$340$	15.2275	0.825828
$341$	−8.25814	−0.447204
$342$	−6.68591	−0.361533
$343$	1.52861	0.0825370
$344$	7.20121	0.388263
$345$	37.4210	2.01468
$346$	−20.1922	−1.08554
$347$	5.27517	0.283186	0.141593	−	0.989925i	$-0.454778\pi$
$347$	5.27517	0.283186	0.141593	+	0.989925i	$0.454778\pi$
$348$	9.36346	0.501934
$349$	−24.2923	−1.30034	−0.650169	−	0.759790i	$-0.725302\pi$
$349$	−24.2923	−1.30034	−0.650169	+	0.759790i	$0.725302\pi$
$350$	0.463561	0.0247784
$351$	−21.7646	−1.16171
$352$	−1.00000	−0.0533002
$353$	4.90339	0.260981	0.130490	−	0.991450i	$-0.458345\pi$
$353$	4.90339	0.260981	0.130490	+	0.991450i	$0.458345\pi$
$354$	11.6788	0.620720
$355$	−32.9610	−1.74939
$356$	−8.60441	−0.456033
$357$	−0.735203	−0.0389111
$358$	11.7950	0.623384
$359$	−22.4894	−1.18695	−0.593474	−	0.804853i	$-0.702244\pi$
$359$	−22.4894	−1.18695	−0.593474	+	0.804853i	$0.702244\pi$
$360$	−3.63581	−0.191624
$361$	12.2524	0.644864
$362$	−14.9029	−0.783278
$363$	−1.34314	−0.0704968
$364$	0.422022	0.0221199
$365$	−48.8979	−2.55943
$366$	−1.34314	−0.0702072
$367$	10.9056	0.569269	0.284635	−	0.958636i	$-0.408128\pi$
$367$	10.9056	0.569269	0.284635	+	0.958636i	$0.408128\pi$
$368$	9.16452	0.477734
$369$	−12.6107	−0.656486
$370$	−9.26510	−0.481669
$371$	0.226856	0.0117778
$372$	11.0919	0.575087
$373$	7.25605	0.375704	0.187852	−	0.982197i	$-0.439847\pi$
$373$	7.25605	0.375704	0.187852	+	0.982197i	$0.439847\pi$
$374$	5.00895	0.259006
$375$	−3.09518	−0.159834
$376$	−2.87412	−0.148221
$377$	26.9222	1.38656
$378$	0.615875	0.0316772
$379$	31.3233	1.60897	0.804485	−	0.593973i	$-0.202441\pi$
$379$	31.3233	1.60897	0.804485	+	0.593973i	$0.202441\pi$
$380$	16.9951	0.871832
$381$	−1.26528	−0.0648225
$382$	−0.632662	−0.0323698
$383$	−24.8605	−1.27031	−0.635155	−	0.772384i	$-0.719064\pi$
$383$	−24.8605	−1.27031	−0.635155	+	0.772384i	$0.719064\pi$
$384$	1.34314	0.0685420
$385$	0.332216	0.0169313
$386$	−11.7508	−0.598100
$387$	8.61240	0.437793
$388$	0.113606	0.00576746
$389$	31.1775	1.58076	0.790382	−	0.612615i	$-0.209882\pi$
$389$	31.1775	1.58076	0.790382	+	0.612615i	$0.209882\pi$
$390$	15.7689	0.798489
$391$	−45.9046	−2.32150
$392$	6.98806	0.352950
$393$	19.5650	0.986923
$394$	18.1871	0.916254
$395$	0.744487	0.0374592
$396$	−1.19597	−0.0600995
$397$	5.61996	0.282058	0.141029	−	0.990005i	$-0.454959\pi$
$397$	5.61996	0.282058	0.141029	+	0.990005i	$0.454959\pi$
$398$	−5.08484	−0.254880
$399$	−0.820546	−0.0410787
$400$	4.24198	0.212099
$401$	1.62146	0.0809718	0.0404859	−	0.999180i	$-0.487109\pi$
$401$	1.62146	0.0809718	0.0404859	+	0.999180i	$0.487109\pi$
$402$	8.38882	0.418396
$403$	31.8918	1.58864
$404$	1.93525	0.0962824
$405$	12.1048	0.601494
$406$	−0.761820	−0.0378085
$407$	−3.04767	−0.151067
$408$	−6.72773	−0.333072
$409$	29.5043	1.45889	0.729447	−	0.684038i	$-0.239778\pi$
$409$	29.5043	1.45889	0.729447	+	0.684038i	$0.239778\pi$
$410$	32.0555	1.58311
$411$	−8.04581	−0.396871
$412$	−10.5488	−0.519701
$413$	−0.950197	−0.0467561
$414$	10.9605	0.538677
$415$	5.33248	0.261761
$416$	3.86186	0.189343
$417$	1.93679	0.0948450
$418$	5.59039	0.273435
$419$	−5.17126	−0.252633	−0.126316	−	0.991990i	$-0.540315\pi$
$419$	−5.17126	−0.252633	−0.126316	+	0.991990i	$0.540315\pi$
$420$	−0.446214	−0.0217730
$421$	−29.4960	−1.43754	−0.718772	−	0.695245i	$-0.755296\pi$
$421$	−29.4960	−1.43754	−0.718772	+	0.695245i	$0.755296\pi$
$422$	26.0373	1.26748
$423$	−3.43734	−0.167129
$424$	2.07593	0.100816
$425$	−21.2478	−1.03067
$426$	14.5626	0.705562
$427$	0.109279	0.00528840
$428$	14.2971	0.691076
$429$	5.18703	0.250432
$430$	−21.8921	−1.05573
$431$	−24.3540	−1.17309	−0.586546	−	0.809916i	$-0.699513\pi$
$431$	−24.3540	−1.17309	−0.586546	+	0.809916i	$0.699513\pi$
$432$	5.63578	0.271152
$433$	28.0796	1.34942	0.674710	−	0.738083i	$-0.264269\pi$
$433$	28.0796	1.34942	0.674710	+	0.738083i	$0.264269\pi$
$434$	−0.902445	−0.0433188
$435$	−28.4655	−1.36482
$436$	1.12224	0.0537457
$437$	−51.2332	−2.45082
$438$	21.6038	1.03227
$439$	−18.1096	−0.864324	−0.432162	−	0.901796i	$-0.642249\pi$
$439$	−18.1096	−0.864324	−0.432162	+	0.901796i	$0.642249\pi$
$440$	3.04006	0.144929
$441$	8.35748	0.397975
$442$	−19.3438	−0.920092
$443$	−8.34002	−0.396246	−0.198123	−	0.980177i	$-0.563485\pi$
$443$	−8.34002	−0.396246	−0.198123	+	0.980177i	$0.563485\pi$
$444$	4.09345	0.194267
$445$	26.1579	1.24001
$446$	14.0923	0.667289
$447$	5.05349	0.239022
$448$	−0.109279	−0.00516297
$449$	33.2168	1.56760	0.783800	−	0.621014i	$-0.213279\pi$
$449$	33.2168	1.56760	0.783800	+	0.621014i	$0.213279\pi$
$450$	5.07326	0.239156
$451$	10.5444	0.496514
$452$	10.0860	0.474406
$453$	−17.8286	−0.837660
$454$	2.08414	0.0978134
$455$	−1.28297	−0.0601467
$456$	−7.50869	−0.351627
$457$	−0.181292	−0.00848048	−0.00424024	−	0.999991i	$-0.501350\pi$
$457$	−0.181292	−0.00848048	−0.00424024	+	0.999991i	$0.501350\pi$
$458$	1.04606	0.0488792
$459$	−28.2293	−1.31763
$460$	−27.8607	−1.29901
$461$	17.7070	0.824697	0.412348	−	0.911026i	$-0.364709\pi$
$461$	17.7070	0.824697	0.412348	+	0.911026i	$0.364709\pi$
$462$	−0.146778	−0.00682873
$463$	−9.28790	−0.431645	−0.215823	−	0.976433i	$-0.569243\pi$
$463$	−9.28790	−0.431645	−0.215823	+	0.976433i	$0.569243\pi$
$464$	−6.97131	−0.323635
$465$	−33.7200	−1.56373
$466$	−7.39890	−0.342747
$467$	−0.662209	−0.0306434	−0.0153217	−	0.999883i	$-0.504877\pi$
$467$	−0.662209	−0.0306434	−0.0153217	+	0.999883i	$0.504877\pi$
$468$	4.61865	0.213497
$469$	−0.682523	−0.0315160
$470$	8.73749	0.403030
$471$	−18.0751	−0.832857
$472$	−8.69511	−0.400225
$473$	−7.20121	−0.331112
$474$	−0.328925	−0.0151080
$475$	−23.7143	−1.08809
$476$	0.547375	0.0250889
$477$	2.48274	0.113677
$478$	7.12156	0.325733
$479$	25.1703	1.15006	0.575029	−	0.818133i	$-0.304991\pi$
$479$	25.1703	1.15006	0.575029	+	0.818133i	$0.304991\pi$
$480$	−4.08324	−0.186374
$481$	11.7697	0.536650
$482$	23.1056	1.05243
$483$	1.34515	0.0612065
$484$	1.00000	0.0454545
$485$	−0.345368	−0.0156824
$486$	11.5593	0.524339
$487$	34.7695	1.57556	0.787779	−	0.615958i	$-0.211231\pi$
$487$	34.7695	1.57556	0.787779	+	0.615958i	$0.211231\pi$
$488$	1.00000	0.0452679
$489$	−21.3689	−0.966337
$490$	−21.2441	−0.959712
$491$	32.2483	1.45534	0.727672	−	0.685925i	$-0.240602\pi$
$491$	32.2483	1.45534	0.727672	+	0.685925i	$0.240602\pi$
$492$	−14.1626	−0.638499
$493$	34.9189	1.57267
$494$	−21.5893	−0.971347
$495$	3.63581	0.163417
$496$	−8.25814	−0.370802
$497$	−1.18483	−0.0531469
$498$	−2.35597	−0.105573
$499$	−23.9478	−1.07205	−0.536026	−	0.844201i	$-0.680075\pi$
$499$	−23.9478	−1.07205	−0.536026	+	0.844201i	$0.680075\pi$
$500$	2.30443	0.103057
$501$	14.4077	0.643690
$502$	20.9878	0.936732
$503$	−3.32867	−0.148418	−0.0742091	−	0.997243i	$-0.523643\pi$
$503$	−3.32867	−0.148418	−0.0742091	+	0.997243i	$0.523643\pi$
$504$	−0.130694	−0.00582159
$505$	−5.88329	−0.261803
$506$	−9.16452	−0.407413
$507$	−2.57070	−0.114169
$508$	0.942032	0.0417959
$509$	−42.7841	−1.89637	−0.948186	−	0.317717i	$-0.897084\pi$
$509$	−42.7841	−1.89637	−0.948186	+	0.317717i	$0.897084\pi$
$510$	20.4527	0.905662
$511$	−1.75770	−0.0777563
$512$	−1.00000	−0.0441942
$513$	−31.5062	−1.39103
$514$	6.08230	0.268279
$515$	32.0690	1.41313
$516$	9.67226	0.425798
$517$	2.87412	0.126403
$518$	−0.333047	−0.0146333
$519$	−27.1210	−1.19048
$520$	−11.7403	−0.514846
$521$	16.0293	0.702256	0.351128	−	0.936328i	$-0.385798\pi$
$521$	16.0293	0.702256	0.351128	+	0.936328i	$0.385798\pi$
$522$	−8.33744	−0.364920
$523$	42.5457	1.86039	0.930197	−	0.367060i	$-0.119635\pi$
$523$	42.5457	1.86039	0.930197	+	0.367060i	$0.119635\pi$
$524$	−14.5666	−0.636343
$525$	0.622629	0.0271738
$526$	−26.5257	−1.15658
$527$	41.3646	1.80187
$528$	−1.34314	−0.0584528
$529$	60.9885	2.65167
$530$	−6.31095	−0.274130
$531$	−10.3990	−0.451280
$532$	0.610914	0.0264865
$533$	−40.7208	−1.76381
$534$	−11.5570	−0.500118
$535$	−43.4640	−1.87911
$536$	−6.24566	−0.269772
$537$	15.8424	0.683648
$538$	18.1085	0.780713
$539$	−6.98806	−0.300997
$540$	−17.1331	−0.737293
$541$	−15.4899	−0.665962	−0.332981	−	0.942934i	$-0.608054\pi$
$541$	−15.4899	−0.665962	−0.332981	+	0.942934i	$0.608054\pi$
$542$	20.6507	0.887025
$543$	−20.0167	−0.858999
$544$	5.00895	0.214757
$545$	−3.41169	−0.146141
$546$	0.566836	0.0242583
$547$	21.6350	0.925046	0.462523	−	0.886607i	$-0.346944\pi$
$547$	21.6350	0.925046	0.462523	+	0.886607i	$0.346944\pi$
$548$	5.99028	0.255892
$549$	1.19597	0.0510426
$550$	−4.24198	−0.180879
$551$	38.9723	1.66028
$552$	12.3093	0.523917
$553$	0.0267617	0.00113802
$554$	−21.2251	−0.901766
$555$	−12.4444	−0.528233
$556$	−1.44198	−0.0611537
$557$	22.8008	0.966101	0.483051	−	0.875592i	$-0.339529\pi$
$557$	22.8008	0.966101	0.483051	+	0.875592i	$0.339529\pi$
$558$	−9.87645	−0.418104
$559$	27.8101	1.17624
$560$	0.332216	0.0140387
$561$	6.72773	0.284045
$562$	4.27359	0.180271
$563$	14.9948	0.631954	0.315977	−	0.948767i	$-0.397668\pi$
$563$	14.9948	0.631954	0.315977	+	0.948767i	$0.397668\pi$
$564$	−3.86035	−0.162550
$565$	−30.6621	−1.28997
$566$	10.8245	0.454987
$567$	0.435126	0.0182736
$568$	−10.8422	−0.454929
$569$	15.4019	0.645683	0.322841	−	0.946453i	$-0.395362\pi$
$569$	15.4019	0.645683	0.322841	+	0.946453i	$0.395362\pi$
$570$	22.8269	0.956113
$571$	31.9627	1.33760	0.668799	−	0.743443i	$-0.266809\pi$
$571$	31.9627	1.33760	0.668799	+	0.743443i	$0.266809\pi$
$572$	−3.86186	−0.161472
$573$	−0.849757	−0.0354991
$574$	1.15228	0.0480953
$575$	38.8757	1.62123
$576$	−1.19597	−0.0498319
$577$	10.3723	0.431805	0.215903	−	0.976415i	$-0.430731\pi$
$577$	10.3723	0.431805	0.215903	+	0.976415i	$0.430731\pi$
$578$	−8.08954	−0.336481
$579$	−15.7830	−0.655920
$580$	21.1932	0.880000
$581$	0.191684	0.00795238
$582$	0.152589	0.00632501
$583$	−2.07593	−0.0859762
$584$	−16.0845	−0.665581
$585$	−14.0410	−0.580523
$586$	4.22149	0.174388
$587$	−9.14418	−0.377421	−0.188710	−	0.982033i	$-0.560431\pi$
$587$	−9.14418	−0.377421	−0.188710	+	0.982033i	$0.560431\pi$
$588$	9.38596	0.387071
$589$	46.1662	1.90225
$590$	26.4337	1.08826
$591$	24.4279	1.00483
$592$	−3.04767	−0.125258
$593$	−24.1240	−0.990653	−0.495327	−	0.868707i	$-0.664952\pi$
$593$	−24.1240	−0.990653	−0.495327	+	0.868707i	$0.664952\pi$
$594$	−5.63578	−0.231239
$595$	−1.66405	−0.0682196
$596$	−3.76244	−0.154115
$597$	−6.82967	−0.279520
$598$	35.3921	1.44729
$599$	3.51691	0.143697	0.0718486	−	0.997416i	$-0.477110\pi$
$599$	3.51691	0.143697	0.0718486	+	0.997416i	$0.477110\pi$
$600$	5.69759	0.232603
$601$	29.3167	1.19585	0.597926	−	0.801551i	$-0.295991\pi$
$601$	29.3167	1.19585	0.597926	+	0.801551i	$0.295991\pi$
$602$	−0.786944	−0.0320735
$603$	−7.46960	−0.304186
$604$	13.2738	0.540102
$605$	−3.04006	−0.123596
$606$	2.59932	0.105590
$607$	−16.3588	−0.663984	−0.331992	−	0.943282i	$-0.607721\pi$
$607$	−16.3588	−0.663984	−0.331992	+	0.943282i	$0.607721\pi$
$608$	5.59039	0.226720
$609$	−1.02323	−0.0414635
$610$	−3.04006	−0.123089
$611$	−11.0994	−0.449035
$612$	5.99053	0.242153
$613$	−21.9988	−0.888524	−0.444262	−	0.895897i	$-0.646534\pi$
$613$	−21.9988	−0.888524	−0.444262	+	0.895897i	$0.646534\pi$
$614$	19.3928	0.782628
$615$	43.0551	1.73615
$616$	0.109279	0.00440299
$617$	46.9144	1.88870	0.944350	−	0.328941i	$-0.106692\pi$
$617$	46.9144	1.88870	0.944350	+	0.328941i	$0.106692\pi$
$618$	−14.1685	−0.569942
$619$	−28.0899	−1.12903	−0.564514	−	0.825423i	$-0.690937\pi$
$619$	−28.0899	−1.12903	−0.564514	+	0.825423i	$0.690937\pi$
$620$	25.1053	1.00825
$621$	51.6493	2.07261
$622$	−22.7938	−0.913947
$623$	0.940285	0.0376717
$624$	5.18703	0.207647
$625$	−28.2155	−1.12862
$626$	−5.81686	−0.232489
$627$	7.50869	0.299868
$628$	13.4573	0.537005
$629$	15.2656	0.608679
$630$	0.397319	0.0158296
$631$	−42.5227	−1.69280	−0.846402	−	0.532545i	$-0.821236\pi$
$631$	−42.5227	−1.69280	−0.846402	+	0.532545i	$0.821236\pi$
$632$	0.244892	0.00974128
$633$	34.9719	1.39001
$634$	28.6198	1.13664
$635$	−2.86384	−0.113648
$636$	2.78827	0.110562
$637$	26.9869	1.06926
$638$	6.97131	0.275997
$639$	−12.9669	−0.512962
$640$	3.04006	0.120169
$641$	42.7049	1.68674	0.843372	−	0.537330i	$-0.180567\pi$
$641$	42.7049	1.68674	0.843372	+	0.537330i	$0.180567\pi$
$642$	19.2030	0.757884
$643$	15.7242	0.620101	0.310051	−	0.950720i	$-0.399654\pi$
$643$	15.7242	0.620101	0.310051	+	0.950720i	$0.399654\pi$
$644$	−1.00149	−0.0394644
$645$	−29.4043	−1.15779
$646$	−28.0019	−1.10172
$647$	−19.4738	−0.765596	−0.382798	−	0.923832i	$-0.625039\pi$
$647$	−19.4738	−0.765596	−0.382798	+	0.923832i	$0.625039\pi$
$648$	3.98177	0.156419
$649$	8.69511	0.341313
$650$	16.3819	0.642552
$651$	−1.21211	−0.0475065
$652$	15.9096	0.623070
$653$	19.3879	0.758706	0.379353	−	0.925252i	$-0.376147\pi$
$653$	19.3879	0.758706	0.379353	+	0.925252i	$0.376147\pi$
$654$	1.50733	0.0589414
$655$	44.2832	1.73029
$656$	10.5444	0.411688
$657$	−19.2365	−0.750487
$658$	0.314082	0.0122442
$659$	−6.12813	−0.238718	−0.119359	−	0.992851i	$-0.538084\pi$
$659$	−6.12813	−0.238718	−0.119359	+	0.992851i	$0.538084\pi$
$660$	4.08324	0.158940
$661$	−36.2501	−1.40997	−0.704983	−	0.709224i	$-0.749045\pi$
$661$	−36.2501	−1.40997	−0.704983	+	0.709224i	$0.749045\pi$
$662$	−33.5929	−1.30562
$663$	−25.9815	−1.00904
$664$	1.75407	0.0680710
$665$	−1.85722	−0.0720198
$666$	−3.64490	−0.141237
$667$	−63.8887	−2.47378
$668$	−10.7269	−0.415035
$669$	18.9280	0.731797
$670$	18.9872	0.733540
$671$	−1.00000	−0.0386046
$672$	−0.146778	−0.00566208
$673$	−8.57981	−0.330727	−0.165364	−	0.986233i	$-0.552880\pi$
$673$	−8.57981	−0.330727	−0.165364	+	0.986233i	$0.552880\pi$
$674$	20.5379	0.791090
$675$	23.9069	0.920176
$676$	1.91394	0.0736131
$677$	26.3377	1.01224	0.506120	−	0.862463i	$-0.331079\pi$
$677$	26.3377	1.01224	0.506120	+	0.862463i	$0.331079\pi$
$678$	13.5470	0.520268
$679$	−0.0124148	−0.000476435 0
$680$	−15.2275	−0.583948
$681$	2.79929	0.107269
$682$	8.25814	0.316221
$683$	−37.7355	−1.44391	−0.721954	−	0.691941i	$-0.756756\pi$
$683$	−37.7355	−1.44391	−0.721954	+	0.691941i	$0.756756\pi$
$684$	6.68591	0.255642
$685$	−18.2108	−0.695800
$686$	−1.52861	−0.0583625
$687$	1.40501	0.0536044
$688$	−7.20121	−0.274544
$689$	8.01694	0.305421
$690$	−37.4210	−1.42459
$691$	38.5015	1.46467	0.732334	−	0.680946i	$-0.238431\pi$
$691$	38.5015	1.46467	0.732334	+	0.680946i	$0.238431\pi$
$692$	20.1922	0.767590
$693$	0.130694	0.00496467
$694$	−5.27517	−0.200243
$695$	4.38372	0.166284
$696$	−9.36346	−0.354921
$697$	−52.8161	−2.00055
$698$	24.2923	0.919478
$699$	−9.93778	−0.375881
$700$	−0.463561	−0.0175210
$701$	33.2387	1.25541	0.627705	−	0.778451i	$-0.283994\pi$
$701$	33.2387	1.25541	0.627705	+	0.778451i	$0.283994\pi$
$702$	21.7646	0.821452
$703$	17.0376	0.642587
$704$	1.00000	0.0376889
$705$	11.7357	0.441992
$706$	−4.90339	−0.184541
$707$	−0.211483	−0.00795365
$708$	−11.6788	−0.438915
$709$	25.7781	0.968118	0.484059	−	0.875035i	$-0.339162\pi$
$709$	25.7781	0.968118	0.484059	+	0.875035i	$0.339162\pi$
$710$	32.9610	1.23700
$711$	0.292882	0.0109839
$712$	8.60441	0.322464
$713$	−75.6820	−2.83431
$714$	0.735203	0.0275143
$715$	11.7403	0.439062
$716$	−11.7950	−0.440799
$717$	9.56528	0.357222
$718$	22.4894	0.839299
$719$	−6.73690	−0.251244	−0.125622	−	0.992078i	$-0.540093\pi$
$719$	−6.73690	−0.251244	−0.125622	+	0.992078i	$0.540093\pi$
$720$	3.63581	0.135499
$721$	1.15277	0.0429312
$722$	−12.2524	−0.455988
$723$	31.0342	1.15417
$724$	14.9029	0.553861
$725$	−29.5721	−1.09828
$726$	1.34314	0.0498487
$727$	30.2199	1.12079	0.560397	−	0.828224i	$-0.310648\pi$
$727$	30.2199	1.12079	0.560397	+	0.828224i	$0.310648\pi$
$728$	−0.422022	−0.0156412
$729$	27.4711	1.01745
$730$	48.8979	1.80979
$731$	36.0705	1.33411
$732$	1.34314	0.0496440
$733$	−15.9557	−0.589337	−0.294668	−	0.955600i	$-0.595209\pi$
$733$	−15.9557	−0.589337	−0.294668	+	0.955600i	$0.595209\pi$
$734$	−10.9056	−0.402534
$735$	−28.5339	−1.05249
$736$	−9.16452	−0.337809
$737$	6.24566	0.230062
$738$	12.6107	0.464206
$739$	−31.0338	−1.14160	−0.570798	−	0.821091i	$-0.693366\pi$
$739$	−31.0338	−1.14160	−0.570798	+	0.821091i	$0.693366\pi$
$740$	9.26510	0.340592
$741$	−28.9975	−1.06525
$742$	−0.226856	−0.00832816
$743$	16.0663	0.589416	0.294708	−	0.955587i	$-0.404778\pi$
$743$	16.0663	0.589416	0.294708	+	0.955587i	$0.404778\pi$
$744$	−11.0919	−0.406648
$745$	11.4380	0.419058
$746$	−7.25605	−0.265663
$747$	2.09780	0.0767547
$748$	−5.00895	−0.183145
$749$	−1.56238	−0.0570880
$750$	3.09518	0.113020
$751$	30.0264	1.09568	0.547840	−	0.836583i	$-0.315450\pi$
$751$	30.0264	1.09568	0.547840	+	0.836583i	$0.315450\pi$
$752$	2.87412	0.104808
$753$	28.1896	1.02729
$754$	−26.9222	−0.980448
$755$	−40.3531	−1.46860
$756$	−0.615875	−0.0223992
$757$	−48.5704	−1.76532	−0.882661	−	0.470010i	$-0.844250\pi$
$757$	−48.5704	−1.76532	−0.882661	+	0.470010i	$0.844250\pi$
$758$	−31.3233	−1.13771
$759$	−12.3093	−0.446798
$760$	−16.9951	−0.616478
$761$	29.0480	1.05299	0.526495	−	0.850178i	$-0.323506\pi$
$761$	29.0480	1.05299	0.526495	+	0.850178i	$0.323506\pi$
$762$	1.26528	0.0458364
$763$	−0.122638	−0.00443980
$764$	0.632662	0.0228889
$765$	−18.2116	−0.658441
$766$	24.8605	0.898245
$767$	−33.5793	−1.21248
$768$	−1.34314	−0.0484665
$769$	−33.4573	−1.20650	−0.603250	−	0.797552i	$-0.706128\pi$
$769$	−33.4573	−1.20650	−0.603250	+	0.797552i	$0.706128\pi$
$770$	−0.332216	−0.0119722
$771$	8.16940	0.294214
$772$	11.7508	0.422921
$773$	32.1780	1.15736	0.578682	−	0.815553i	$-0.303567\pi$
$773$	32.1780	1.15736	0.578682	+	0.815553i	$0.303567\pi$
$774$	−8.61240	−0.309566
$775$	−35.0309	−1.25835
$776$	−0.113606	−0.00407821
$777$	−0.447330	−0.0160479
$778$	−31.1775	−1.11777
$779$	−58.9470	−2.11200
$780$	−15.7689	−0.564617
$781$	10.8422	0.387964
$782$	45.9046	1.64155
$783$	−39.2888	−1.40407
$784$	−6.98806	−0.249574
$785$	−40.9111	−1.46018
$786$	−19.5650	−0.697860
$787$	−14.8208	−0.528303	−0.264151	−	0.964481i	$-0.585092\pi$
$787$	−14.8208	−0.528303	−0.264151	+	0.964481i	$0.585092\pi$
$788$	−18.1871	−0.647890
$789$	−35.6278	−1.26838
$790$	−0.744487	−0.0264876
$791$	−1.10219	−0.0391895
$792$	1.19597	0.0424968
$793$	3.86186	0.137139
$794$	−5.61996	−0.199445
$795$	−8.47651	−0.300631
$796$	5.08484	0.180227
$797$	−32.2664	−1.14294	−0.571468	−	0.820624i	$-0.693626\pi$
$797$	−32.2664	−1.14294	−0.571468	+	0.820624i	$0.693626\pi$
$798$	0.820546	0.0290470
$799$	−14.3963	−0.509304
$800$	−4.24198	−0.149977
$801$	10.2906	0.363600
$802$	−1.62146	−0.0572557
$803$	16.0845	0.567609
$804$	−8.38882	−0.295851
$805$	3.04460	0.107308
$806$	−31.8918	−1.12334
$807$	24.3223	0.856186
$808$	−1.93525	−0.0680820
$809$	7.39108	0.259856	0.129928	−	0.991523i	$-0.458525\pi$
$809$	7.39108	0.259856	0.129928	+	0.991523i	$0.458525\pi$
$810$	−12.1048	−0.425320
$811$	−12.7177	−0.446579	−0.223290	−	0.974752i	$-0.571680\pi$
$811$	−12.7177	−0.446579	−0.223290	+	0.974752i	$0.571680\pi$
$812$	0.761820	0.0267347
$813$	27.7369	0.972776
$814$	3.04767	0.106821
$815$	−48.3663	−1.69420
$816$	6.72773	0.235518
$817$	40.2576	1.40843
$818$	−29.5043	−1.03159
$819$	−0.504723	−0.0176365
$820$	−32.0555	−1.11943
$821$	27.8800	0.973018	0.486509	−	0.873676i	$-0.338270\pi$
$821$	27.8800	0.973018	0.486509	+	0.873676i	$0.338270\pi$
$822$	8.04581	0.280630
$823$	39.8983	1.39077	0.695384	−	0.718638i	$-0.255234\pi$
$823$	39.8983	1.39077	0.695384	+	0.718638i	$0.255234\pi$
$824$	10.5488	0.367484
$825$	−5.69759	−0.198365
$826$	0.950197	0.0330616
$827$	49.2576	1.71285	0.856427	−	0.516269i	$-0.172679\pi$
$827$	49.2576	1.71285	0.856427	+	0.516269i	$0.172679\pi$
$828$	−10.9605	−0.380902
$829$	40.6080	1.41038	0.705188	−	0.709020i	$-0.250863\pi$
$829$	40.6080	1.41038	0.705188	+	0.709020i	$0.250863\pi$
$830$	−5.33248	−0.185093
$831$	−28.5083	−0.988942
$832$	−3.86186	−0.133886
$833$	35.0028	1.21278
$834$	−1.93679	−0.0670655
$835$	32.6104	1.12853
$836$	−5.59039	−0.193348
$837$	−46.5411	−1.60870
$838$	5.17126	0.178638
$839$	−42.0859	−1.45297	−0.726484	−	0.687184i	$-0.758847\pi$
$839$	−42.0859	−1.45297	−0.726484	+	0.687184i	$0.758847\pi$
$840$	0.446214	0.0153959
$841$	19.5991	0.675831
$842$	29.4960	1.01650
$843$	5.74005	0.197698
$844$	−26.0373	−0.896242
$845$	−5.81850	−0.200163
$846$	3.43734	0.118178
$847$	−0.109279	−0.00375489
$848$	−2.07593	−0.0712877
$849$	14.5388	0.498972
$850$	21.2478	0.728795
$851$	−27.9304	−0.957442
$852$	−14.5626	−0.498907
$853$	−6.15281	−0.210668	−0.105334	−	0.994437i	$-0.533591\pi$
$853$	−6.15281	−0.210668	−0.105334	+	0.994437i	$0.533591\pi$
$854$	−0.109279	−0.00373947
$855$	−20.3256	−0.695120
$856$	−14.2971	−0.488664
$857$	−20.0460	−0.684758	−0.342379	−	0.939562i	$-0.611233\pi$
$857$	−20.0460	−0.684758	−0.342379	+	0.939562i	$0.611233\pi$
$858$	−5.18703	−0.177082
$859$	31.2448	1.06606	0.533029	−	0.846097i	$-0.321054\pi$
$859$	31.2448	1.06606	0.533029	+	0.846097i	$0.321054\pi$
$860$	21.8921	0.746516
$861$	1.54768	0.0527448
$862$	24.3540	0.829501
$863$	25.8320	0.879330	0.439665	−	0.898162i	$-0.355097\pi$
$863$	25.8320	0.879330	0.439665	+	0.898162i	$0.355097\pi$
$864$	−5.63578	−0.191733
$865$	−61.3854	−2.08717
$866$	−28.0796	−0.954184
$867$	−10.8654	−0.369009
$868$	0.902445	0.0306310
$869$	−0.244892	−0.00830739
$870$	28.4655	0.965071
$871$	−24.1199	−0.817270
$872$	−1.12224	−0.0380039
$873$	−0.135869	−0.00459845
$874$	51.2332	1.73299
$875$	−0.251827	−0.00851330
$876$	−21.6038	−0.729924
$877$	−31.0726	−1.04925	−0.524623	−	0.851335i	$-0.675794\pi$
$877$	−31.0726	−1.04925	−0.524623	+	0.851335i	$0.675794\pi$
$878$	18.1096	0.611169
$879$	5.67007	0.191247
$880$	−3.04006	−0.102480
$881$	39.0136	1.31440	0.657200	−	0.753716i	$-0.271741\pi$
$881$	39.0136	1.31440	0.657200	+	0.753716i	$0.271741\pi$
$882$	−8.35748	−0.281411
$883$	−13.4433	−0.452403	−0.226202	−	0.974081i	$-0.572631\pi$
$883$	−13.4433	−0.452403	−0.226202	+	0.974081i	$0.572631\pi$
$884$	19.3438	0.650604
$885$	35.5042	1.19346
$886$	8.34002	0.280188
$887$	6.21196	0.208577	0.104289	−	0.994547i	$-0.466743\pi$
$887$	6.21196	0.208577	0.104289	+	0.994547i	$0.466743\pi$
$888$	−4.09345	−0.137367
$889$	−0.102945	−0.00345266
$890$	−26.1579	−0.876816
$891$	−3.98177	−0.133394
$892$	−14.0923	−0.471845
$893$	−16.0674	−0.537676
$894$	−5.05349	−0.169014
$895$	35.8575	1.19858
$896$	0.109279	0.00365077
$897$	47.5366	1.58720
$898$	−33.2168	−1.10846
$899$	57.5700	1.92007
$900$	−5.07326	−0.169109
$901$	10.3982	0.346415
$902$	−10.5444	−0.351089
$903$	−1.05698	−0.0351741
$904$	−10.0860	−0.335456
$905$	−45.3057	−1.50601
$906$	17.8286	0.592315
$907$	−5.90026	−0.195915	−0.0979575	−	0.995191i	$-0.531231\pi$
$907$	−5.90026	−0.195915	−0.0979575	+	0.995191i	$0.531231\pi$
$908$	−2.08414	−0.0691645
$909$	−2.31450	−0.0767670
$910$	1.28297	0.0425301
$911$	34.3622	1.13847	0.569236	−	0.822174i	$-0.307239\pi$
$911$	34.3622	1.13847	0.569236	+	0.822174i	$0.307239\pi$
$912$	7.50869	0.248638
$913$	−1.75407	−0.0580512
$914$	0.181292	0.00599660
$915$	−4.08324	−0.134988
$916$	−1.04606	−0.0345628
$917$	1.59183	0.0525667
$918$	28.2293	0.931707
$919$	−3.10829	−0.102533	−0.0512666	−	0.998685i	$-0.516326\pi$
$919$	−3.10829	−0.102533	−0.0512666	+	0.998685i	$0.516326\pi$
$920$	27.8607	0.918541
$921$	26.0473	0.858286
$922$	−17.7070	−0.583149
$923$	−41.8710	−1.37820
$924$	0.146778	0.00482864
$925$	−12.9281	−0.425075
$926$	9.28790	0.305219
$927$	12.6160	0.414363
$928$	6.97131	0.228844
$929$	23.5661	0.773180	0.386590	−	0.922252i	$-0.373653\pi$
$929$	23.5661	0.773180	0.386590	+	0.922252i	$0.373653\pi$
$930$	33.7200	1.10572
$931$	39.0659	1.28033
$932$	7.39890	0.242359
$933$	−30.6153	−1.00230
$934$	0.662209	0.0216681
$935$	15.2275	0.497993
$936$	−4.61865	−0.150965
$937$	59.6942	1.95013	0.975063	−	0.221928i	$-0.0712350\pi$
$937$	59.6942	1.95013	0.975063	+	0.221928i	$0.0712350\pi$
$938$	0.682523	0.0222852
$939$	−7.81288	−0.254964
$940$	−8.73749	−0.284986
$941$	40.0188	1.30458	0.652289	−	0.757971i	$-0.273809\pi$
$941$	40.0188	1.30458	0.652289	+	0.757971i	$0.273809\pi$
$942$	18.0751	0.588919
$943$	96.6340	3.14684
$944$	8.69511	0.283002
$945$	1.87230	0.0609059
$946$	7.20121	0.234132
$947$	17.4903	0.568358	0.284179	−	0.958771i	$-0.408279\pi$
$947$	17.4903	0.568358	0.284179	+	0.958771i	$0.408279\pi$
$948$	0.328925	0.0106830
$949$	−62.1160	−2.01637
$950$	23.7143	0.769394
$951$	38.4404	1.24652
$952$	−0.547375	−0.0177405
$953$	8.38245	0.271534	0.135767	−	0.990741i	$-0.456650\pi$
$953$	8.38245	0.271534	0.135767	+	0.990741i	$0.456650\pi$
$954$	−2.48274	−0.0803816
$955$	−1.92333	−0.0622376
$956$	−7.12156	−0.230328
$957$	9.36346	0.302678
$958$	−25.1703	−0.813214
$959$	−0.654615	−0.0211386
$960$	4.08324	0.131786
$961$	37.1969	1.19990
$962$	−11.7697	−0.379469
$963$	−17.0988	−0.551002
$964$	−23.1056	−0.744183
$965$	−35.7232	−1.14997
$966$	−1.34515	−0.0432795
$967$	−40.8586	−1.31393	−0.656963	−	0.753923i	$-0.728159\pi$
$967$	−40.8586	−1.31393	−0.656963	+	0.753923i	$0.728159\pi$
$968$	−1.00000	−0.0321412
$969$	−37.6106	−1.20823
$970$	0.345368	0.0110891
$971$	0.111325	0.00357258	0.00178629	−	0.999998i	$-0.499431\pi$
$971$	0.111325	0.00357258	0.00178629	+	0.999998i	$0.499431\pi$
$972$	−11.5593	−0.370764
$973$	0.157579	0.00505175
$974$	−34.7695	−1.11409
$975$	22.0033	0.704669
$976$	−1.00000	−0.0320092
$977$	−4.42766	−0.141653	−0.0708266	−	0.997489i	$-0.522564\pi$
$977$	−4.42766	−0.141653	−0.0708266	+	0.997489i	$0.522564\pi$
$978$	21.3689	0.683303
$979$	−8.60441	−0.274998
$980$	21.2441	0.678619
$981$	−1.34216	−0.0428520
$982$	−32.2483	−1.02908
$983$	30.1236	0.960792	0.480396	−	0.877052i	$-0.340493\pi$
$983$	30.1236	0.960792	0.480396	+	0.877052i	$0.340493\pi$
$984$	14.1626	0.451487
$985$	55.2900	1.76169
$986$	−34.9189	−1.11204
$987$	0.421857	0.0134279
$988$	21.5893	0.686846
$989$	−65.9957	−2.09854
$990$	−3.63581	−0.115554
$991$	−27.6696	−0.878955	−0.439477	−	0.898254i	$-0.644836\pi$
$991$	−27.6696	−0.878955	−0.439477	+	0.898254i	$0.644836\pi$
$992$	8.25814	0.262196
$993$	−45.1201	−1.43184
$994$	1.18483	0.0375805
$995$	−15.4582	−0.490059
$996$	2.35597	0.0746516
$997$	−34.3340	−1.08737	−0.543684	−	0.839290i	$-0.682971\pi$
$997$	−34.3340	−1.08737	−0.543684	+	0.839290i	$0.682971\pi$
$998$	23.9478	0.758056
$999$	−17.1760	−0.543424

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1342.2.a.n.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1342.2.a.n.1.3	✓	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:	\( N \)	\(=\)	\( 1342 = 2 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1342.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.34314 q^{3} +1.00000 q^{4} -3.04006 q^{5} +1.34314 q^{6} -0.109279 q^{7} -1.00000 q^{8} -1.19597 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.34314 q^{3} +1.00000 q^{4} -3.04006 q^{5} +1.34314 q^{6} -0.109279 q^{7} -1.00000 q^{8} -1.19597 q^{9} +3.04006 q^{10} +1.00000 q^{11} -1.34314 q^{12} -3.86186 q^{13} +0.109279 q^{14} +4.08324 q^{15} +1.00000 q^{16} -5.00895 q^{17} +1.19597 q^{18} -5.59039 q^{19} -3.04006 q^{20} +0.146778 q^{21} -1.00000 q^{22} +9.16452 q^{23} +1.34314 q^{24} +4.24198 q^{25} +3.86186 q^{26} +5.63578 q^{27} -0.109279 q^{28} -6.97131 q^{29} -4.08324 q^{30} -8.25814 q^{31} -1.00000 q^{32} -1.34314 q^{33} +5.00895 q^{34} +0.332216 q^{35} -1.19597 q^{36} -3.04767 q^{37} +5.59039 q^{38} +5.18703 q^{39} +3.04006 q^{40} +10.5444 q^{41} -0.146778 q^{42} -7.20121 q^{43} +1.00000 q^{44} +3.63581 q^{45} -9.16452 q^{46} +2.87412 q^{47} -1.34314 q^{48} -6.98806 q^{49} -4.24198 q^{50} +6.72773 q^{51} -3.86186 q^{52} -2.07593 q^{53} -5.63578 q^{54} -3.04006 q^{55} +0.109279 q^{56} +7.50869 q^{57} +6.97131 q^{58} +8.69511 q^{59} +4.08324 q^{60} -1.00000 q^{61} +8.25814 q^{62} +0.130694 q^{63} +1.00000 q^{64} +11.7403 q^{65} +1.34314 q^{66} +6.24566 q^{67} -5.00895 q^{68} -12.3093 q^{69} -0.332216 q^{70} +10.8422 q^{71} +1.19597 q^{72} +16.0845 q^{73} +3.04767 q^{74} -5.69759 q^{75} -5.59039 q^{76} -0.109279 q^{77} -5.18703 q^{78} -0.244892 q^{79} -3.04006 q^{80} -3.98177 q^{81} -10.5444 q^{82} -1.75407 q^{83} +0.146778 q^{84} +15.2275 q^{85} +7.20121 q^{86} +9.36346 q^{87} -1.00000 q^{88} -8.60441 q^{89} -3.63581 q^{90} +0.422022 q^{91} +9.16452 q^{92} +11.0919 q^{93} -2.87412 q^{94} +16.9951 q^{95} +1.34314 q^{96} +0.113606 q^{97} +6.98806 q^{98} -1.19597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} + 5 q^{3} + 9 q^{4} + 6 q^{5} - 5 q^{6} - 2 q^{7} - 9 q^{8} + 20 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 + 5 * q^3 + 9 * q^4 + 6 * q^5 - 5 * q^6 - 2 * q^7 - 9 * q^8 + 20 * q^9	\( 9 q - 9 q^{2} + 5 q^{3} + 9 q^{4} + 6 q^{5} - 5 q^{6} - 2 q^{7} - 9 q^{8} + 20 q^{9} - 6 q^{10} + 9 q^{11} + 5 q^{12} - q^{13} + 2 q^{14} + 6 q^{15} + 9 q^{16} + 11 q^{17} - 20 q^{18} - 6 q^{19} + 6 q^{20} - 2 q^{21} - 9 q^{22} + 21 q^{23} - 5 q^{24} + 19 q^{25} + q^{26} + 26 q^{27} - 2 q^{28} - 5 q^{29} - 6 q^{30} - 7 q^{31} - 9 q^{32} + 5 q^{33} - 11 q^{34} + 6 q^{35} + 20 q^{36} + 16 q^{37} + 6 q^{38} - 18 q^{39} - 6 q^{40} + 13 q^{41} + 2 q^{42} + 9 q^{44} + 42 q^{45} - 21 q^{46} + 9 q^{47} + 5 q^{48} + 27 q^{49} - 19 q^{50} - 4 q^{51} - q^{52} + 18 q^{53} - 26 q^{54} + 6 q^{55} + 2 q^{56} - 12 q^{57} + 5 q^{58} + q^{59} + 6 q^{60} - 9 q^{61} + 7 q^{62} + 37 q^{63} + 9 q^{64} + 20 q^{65} - 5 q^{66} + 17 q^{67} + 11 q^{68} + 3 q^{69} - 6 q^{70} + 5 q^{71} - 20 q^{72} - 5 q^{73} - 16 q^{74} + q^{75} - 6 q^{76} - 2 q^{77} + 18 q^{78} - 39 q^{79} + 6 q^{80} + 61 q^{81} - 13 q^{82} + 43 q^{83} - 2 q^{84} + 10 q^{85} + 8 q^{87} - 9 q^{88} + 32 q^{89} - 42 q^{90} - 62 q^{91} + 21 q^{92} + 41 q^{93} - 9 q^{94} + 36 q^{95} - 5 q^{96} + 22 q^{97} - 27 q^{98} + 20 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 + 5 * q^3 + 9 * q^4 + 6 * q^5 - 5 * q^6 - 2 * q^7 - 9 * q^8 + 20 * q^9 - 6 * q^10 + 9 * q^11 + 5 * q^12 - q^13 + 2 * q^14 + 6 * q^15 + 9 * q^16 + 11 * q^17 - 20 * q^18 - 6 * q^19 + 6 * q^20 - 2 * q^21 - 9 * q^22 + 21 * q^23 - 5 * q^24 + 19 * q^25 + q^26 + 26 * q^27 - 2 * q^28 - 5 * q^29 - 6 * q^30 - 7 * q^31 - 9 * q^32 + 5 * q^33 - 11 * q^34 + 6 * q^35 + 20 * q^36 + 16 * q^37 + 6 * q^38 - 18 * q^39 - 6 * q^40 + 13 * q^41 + 2 * q^42 + 9 * q^44 + 42 * q^45 - 21 * q^46 + 9 * q^47 + 5 * q^48 + 27 * q^49 - 19 * q^50 - 4 * q^51 - q^52 + 18 * q^53 - 26 * q^54 + 6 * q^55 + 2 * q^56 - 12 * q^57 + 5 * q^58 + q^59 + 6 * q^60 - 9 * q^61 + 7 * q^62 + 37 * q^63 + 9 * q^64 + 20 * q^65 - 5 * q^66 + 17 * q^67 + 11 * q^68 + 3 * q^69 - 6 * q^70 + 5 * q^71 - 20 * q^72 - 5 * q^73 - 16 * q^74 + q^75 - 6 * q^76 - 2 * q^77 + 18 * q^78 - 39 * q^79 + 6 * q^80 + 61 * q^81 - 13 * q^82 + 43 * q^83 - 2 * q^84 + 10 * q^85 + 8 * q^87 - 9 * q^88 + 32 * q^89 - 42 * q^90 - 62 * q^91 + 21 * q^92 + 41 * q^93 - 9 * q^94 + 36 * q^95 - 5 * q^96 + 22 * q^97 - 27 * q^98 + 20 * q^99

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