LMFDB - Embedded newform 241.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [241,2,Mod(1,241)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(241, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("241.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	241.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:	$1.92439468871$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 $ x^12 - 3x^11 - 14x^10 + 44x^9 + 65x^8 - 219x^7 - 123x^6 + 444x^5 + 105x^4 - 328x^3 - 45x^2 + 18*x - 1
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			1.11
Root			$2.49073$ of defining polynomial
Character	$\chi$	$=$	241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.49073 q^{2} +1.22208 q^{3} +4.20371 q^{4} -3.14843 q^{5} +3.04385 q^{6} +0.136122 q^{7} +5.48885 q^{8} -1.50653 q^{9} +O(q^{10})$	\(q+2.49073 q^{2} +1.22208 q^{3} +4.20371 q^{4} -3.14843 q^{5} +3.04385 q^{6} +0.136122 q^{7} +5.48885 q^{8} -1.50653 q^{9} -7.84189 q^{10} -0.905365 q^{11} +5.13726 q^{12} -0.123706 q^{13} +0.339044 q^{14} -3.84762 q^{15} +5.26378 q^{16} +1.26034 q^{17} -3.75236 q^{18} -2.13460 q^{19} -13.2351 q^{20} +0.166352 q^{21} -2.25502 q^{22} +6.64978 q^{23} +6.70778 q^{24} +4.91264 q^{25} -0.308118 q^{26} -5.50732 q^{27} +0.572220 q^{28} +5.36862 q^{29} -9.58338 q^{30} -9.78467 q^{31} +2.13295 q^{32} -1.10642 q^{33} +3.13917 q^{34} -0.428573 q^{35} -6.33303 q^{36} +5.76688 q^{37} -5.31669 q^{38} -0.151178 q^{39} -17.2813 q^{40} +6.43642 q^{41} +0.414337 q^{42} -3.18712 q^{43} -3.80590 q^{44} +4.74322 q^{45} +16.5628 q^{46} +12.9849 q^{47} +6.43274 q^{48} -6.98147 q^{49} +12.2360 q^{50} +1.54023 q^{51} -0.520025 q^{52} +3.90862 q^{53} -13.7172 q^{54} +2.85048 q^{55} +0.747155 q^{56} -2.60864 q^{57} +13.3718 q^{58} +8.15085 q^{59} -16.1743 q^{60} -14.3712 q^{61} -24.3709 q^{62} -0.205073 q^{63} -5.21498 q^{64} +0.389481 q^{65} -2.75580 q^{66} -4.89534 q^{67} +5.29812 q^{68} +8.12653 q^{69} -1.06746 q^{70} +4.32869 q^{71} -8.26912 q^{72} +5.64935 q^{73} +14.3637 q^{74} +6.00362 q^{75} -8.97323 q^{76} -0.123241 q^{77} -0.376543 q^{78} +1.43490 q^{79} -16.5727 q^{80} -2.21077 q^{81} +16.0314 q^{82} -11.7625 q^{83} +0.699296 q^{84} -3.96811 q^{85} -7.93825 q^{86} +6.56086 q^{87} -4.96941 q^{88} -13.7381 q^{89} +11.8141 q^{90} -0.0168392 q^{91} +27.9538 q^{92} -11.9576 q^{93} +32.3419 q^{94} +6.72063 q^{95} +2.60662 q^{96} +13.6204 q^{97} -17.3889 q^{98} +1.36396 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9} - 7 q^{10} + 22 q^{11} - 7 q^{12} - 5 q^{13} + 6 q^{14} + 13 q^{15} + 15 q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + 10 q^{20} - 14 q^{21} - 12 q^{22} + 32 q^{23} - 15 q^{24} + 4 q^{25} + 8 q^{26} - 5 q^{27} - 11 q^{28} + 6 q^{29} - 19 q^{30} + 8 q^{31} + q^{32} - 24 q^{33} - 19 q^{34} + 15 q^{35} - 8 q^{36} - 8 q^{37} - 10 q^{38} + 31 q^{39} - 52 q^{40} - q^{41} - 49 q^{42} - 2 q^{43} + 42 q^{44} - 15 q^{45} - 25 q^{46} + 34 q^{47} - 49 q^{48} - 9 q^{49} - 27 q^{50} - 3 q^{51} - 41 q^{52} + 5 q^{53} - 40 q^{54} - 3 q^{55} + q^{56} - 22 q^{57} - 33 q^{58} + 26 q^{59} - 57 q^{60} - 26 q^{61} - 17 q^{62} - 4 q^{63} + 13 q^{64} - 25 q^{65} - 2 q^{66} + 6 q^{67} - 35 q^{68} - 2 q^{69} - 4 q^{70} + 94 q^{71} + 17 q^{72} - 22 q^{73} + 26 q^{74} - 20 q^{76} - 7 q^{77} + 54 q^{78} + 9 q^{79} + 19 q^{80} + 4 q^{81} + 15 q^{82} - 8 q^{83} + 2 q^{84} + 4 q^{85} + 9 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + 11 q^{90} - 20 q^{91} + 36 q^{92} + 12 q^{93} + 48 q^{94} + 33 q^{95} - 23 q^{96} - 29 q^{97} + 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9 - 7 * q^10 + 22 * q^11 - 7 * q^12 - 5 * q^13 + 6 * q^14 + 13 * q^15 + 15 * q^16 - 4 * q^17 - q^18 - 6 * q^19 + 10 * q^20 - 14 * q^21 - 12 * q^22 + 32 * q^23 - 15 * q^24 + 4 * q^25 + 8 * q^26 - 5 * q^27 - 11 * q^28 + 6 * q^29 - 19 * q^30 + 8 * q^31 + q^32 - 24 * q^33 - 19 * q^34 + 15 * q^35 - 8 * q^36 - 8 * q^37 - 10 * q^38 + 31 * q^39 - 52 * q^40 - q^41 - 49 * q^42 - 2 * q^43 + 42 * q^44 - 15 * q^45 - 25 * q^46 + 34 * q^47 - 49 * q^48 - 9 * q^49 - 27 * q^50 - 3 * q^51 - 41 * q^52 + 5 * q^53 - 40 * q^54 - 3 * q^55 + q^56 - 22 * q^57 - 33 * q^58 + 26 * q^59 - 57 * q^60 - 26 * q^61 - 17 * q^62 - 4 * q^63 + 13 * q^64 - 25 * q^65 - 2 * q^66 + 6 * q^67 - 35 * q^68 - 2 * q^69 - 4 * q^70 + 94 * q^71 + 17 * q^72 - 22 * q^73 + 26 * q^74 - 20 * q^76 - 7 * q^77 + 54 * q^78 + 9 * q^79 + 19 * q^80 + 4 * q^81 + 15 * q^82 - 8 * q^83 + 2 * q^84 + 4 * q^85 + 9 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + 11 * q^90 - 20 * q^91 + 36 * q^92 + 12 * q^93 + 48 * q^94 + 33 * q^95 - 23 * q^96 - 29 * q^97 + 28 * q^98 + 36 * 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 $

$2$	2.49073	1.76121	0.880604	−	0.473852i	$-0.157137\pi$
$2$	2.49073	1.76121	0.880604	+	0.473852i	$0.157137\pi$
$3$	1.22208	0.705566	0.352783	−	0.935705i	$-0.385235\pi$
$3$	1.22208	0.705566	0.352783	+	0.935705i	$0.385235\pi$
$4$	4.20371	2.10186
$5$	−3.14843	−1.40802	−0.704011	−	0.710189i	$-0.748610\pi$
$5$	−3.14843	−1.40802	−0.704011	+	0.710189i	$0.748610\pi$
$6$	3.04385	1.24265
$7$	0.136122	0.0514495	0.0257247	−	0.999669i	$-0.491811\pi$
$7$	0.136122	0.0514495	0.0257247	+	0.999669i	$0.491811\pi$
$8$	5.48885	1.94060
$9$	−1.50653	−0.502177
$10$	−7.84189	−2.47982
$11$	−0.905365	−0.272978	−0.136489	−	0.990642i	$-0.543582\pi$
$11$	−0.905365	−0.272978	−0.136489	+	0.990642i	$0.543582\pi$
$12$	5.13726	1.48300
$13$	−0.123706	−0.0343099	−0.0171549	−	0.999853i	$-0.505461\pi$
$13$	−0.123706	−0.0343099	−0.0171549	+	0.999853i	$0.505461\pi$
$14$	0.339044	0.0906133
$15$	−3.84762	−0.993452
$16$	5.26378	1.31595
$17$	1.26034	0.305678	0.152839	−	0.988251i	$-0.451158\pi$
$17$	1.26034	0.305678	0.152839	+	0.988251i	$0.451158\pi$
$18$	−3.75236	−0.884439
$19$	−2.13460	−0.489710	−0.244855	−	0.969560i	$-0.578740\pi$
$19$	−2.13460	−0.489710	−0.244855	+	0.969560i	$0.578740\pi$
$20$	−13.2351	−2.95946
$21$	0.166352	0.0363010
$22$	−2.25502	−0.480771
$23$	6.64978	1.38657	0.693287	−	0.720661i	$-0.256162\pi$
$23$	6.64978	1.38657	0.693287	+	0.720661i	$0.256162\pi$
$24$	6.70778	1.36922
$25$	4.91264	0.982528
$26$	−0.308118	−0.0604269
$27$	−5.50732	−1.05988
$28$	0.572220	0.108139
$29$	5.36862	0.996928	0.498464	−	0.866911i	$-0.333898\pi$
$29$	5.36862	0.996928	0.498464	+	0.866911i	$0.333898\pi$
$30$	−9.58338	−1.74968
$31$	−9.78467	−1.75738	−0.878689	−	0.477395i	$-0.841581\pi$
$31$	−9.78467	−1.75738	−0.878689	+	0.477395i	$0.841581\pi$
$32$	2.13295	0.377055
$33$	−1.10642	−0.192604
$34$	3.13917	0.538363
$35$	−0.428573	−0.0724420
$36$	−6.33303	−1.05550
$37$	5.76688	0.948070	0.474035	−	0.880506i	$-0.342797\pi$
$37$	5.76688	0.948070	0.474035	+	0.880506i	$0.342797\pi$
$38$	−5.31669	−0.862481
$39$	−0.151178	−0.0242079
$40$	−17.2813	−2.73241
$41$	6.43642	1.00520	0.502600	−	0.864519i	$-0.332377\pi$
$41$	6.43642	1.00520	0.502600	+	0.864519i	$0.332377\pi$
$42$	0.414337	0.0639336
$43$	−3.18712	−0.486032	−0.243016	−	0.970022i	$-0.578137\pi$
$43$	−3.18712	−0.486032	−0.243016	+	0.970022i	$0.578137\pi$
$44$	−3.80590	−0.573761
$45$	4.74322	0.707077
$46$	16.5628	2.44205
$47$	12.9849	1.89404	0.947022	−	0.321168i	$-0.104075\pi$
$47$	12.9849	1.89404	0.947022	+	0.321168i	$0.104075\pi$
$48$	6.43274	0.928486
$49$	−6.98147	−0.997353
$50$	12.2360	1.73044
$51$	1.54023	0.215676
$52$	−0.520025	−0.0721145
$53$	3.90862	0.536890	0.268445	−	0.963295i	$-0.413490\pi$
$53$	3.90862	0.536890	0.268445	+	0.963295i	$0.413490\pi$
$54$	−13.7172	−1.86668
$55$	2.85048	0.384359
$56$	0.747155	0.0998429
$57$	−2.60864	−0.345522
$58$	13.3718	1.75580
$59$	8.15085	1.06115	0.530575	−	0.847638i	$-0.321976\pi$
$59$	8.15085	1.06115	0.530575	+	0.847638i	$0.321976\pi$
$60$	−16.1743	−2.08809
$61$	−14.3712	−1.84004	−0.920021	−	0.391870i	$-0.871828\pi$
$61$	−14.3712	−1.84004	−0.920021	+	0.391870i	$0.871828\pi$
$62$	−24.3709	−3.09511
$63$	−0.205073	−0.0258368
$64$	−5.21498	−0.651873
$65$	0.389481	0.0483091
$66$	−2.75580	−0.339216
$67$	−4.89534	−0.598062	−0.299031	−	0.954243i	$-0.596663\pi$
$67$	−4.89534	−0.598062	−0.299031	+	0.954243i	$0.596663\pi$
$68$	5.29812	0.642491
$69$	8.12653	0.978319
$70$	−1.06746	−0.127586
$71$	4.32869	0.513720	0.256860	−	0.966449i	$-0.417312\pi$
$71$	4.32869	0.513720	0.256860	+	0.966449i	$0.417312\pi$
$72$	−8.26912	−0.974525
$73$	5.64935	0.661206	0.330603	−	0.943770i	$-0.392748\pi$
$73$	5.64935	0.661206	0.330603	+	0.943770i	$0.392748\pi$
$74$	14.3637	1.66975
$75$	6.00362	0.693238
$76$	−8.97323	−1.02930
$77$	−0.123241	−0.0140446
$78$	−0.376543	−0.0426351
$79$	1.43490	0.161439	0.0807195	−	0.996737i	$-0.474278\pi$
$79$	1.43490	0.161439	0.0807195	+	0.996737i	$0.474278\pi$
$80$	−16.5727	−1.85288
$81$	−2.21077	−0.245641
$82$	16.0314	1.77037
$83$	−11.7625	−1.29110	−0.645549	−	0.763718i	$-0.723372\pi$
$83$	−11.7625	−1.29110	−0.645549	+	0.763718i	$0.723372\pi$
$84$	0.699296	0.0762994
$85$	−3.96811	−0.430402
$86$	−7.93825	−0.856004
$87$	6.56086	0.703398
$88$	−4.96941	−0.529741
$89$	−13.7381	−1.45624	−0.728118	−	0.685452i	$-0.759605\pi$
$89$	−13.7381	−1.45624	−0.728118	+	0.685452i	$0.759605\pi$
$90$	11.8141	1.24531
$91$	−0.0168392	−0.00176523
$92$	27.9538	2.91438
$93$	−11.9576	−1.23995
$94$	32.3419	3.33581
$95$	6.72063	0.689522
$96$	2.60662	0.266037
$97$	13.6204	1.38294	0.691472	−	0.722404i	$-0.256963\pi$
$97$	13.6204	1.38294	0.691472	+	0.722404i	$0.256963\pi$
$98$	−17.3889	−1.75655
$99$	1.36396	0.137083
$100$	20.6513	2.06513
$101$	−0.0787660	−0.00783751	−0.00391876	−	0.999992i	$-0.501247\pi$
$101$	−0.0787660	−0.00783751	−0.00391876	+	0.999992i	$0.501247\pi$
$102$	3.83630	0.379850
$103$	−6.36701	−0.627360	−0.313680	−	0.949529i	$-0.601562\pi$
$103$	−6.36701	−0.627360	−0.313680	+	0.949529i	$0.601562\pi$
$104$	−0.679004	−0.0665818
$105$	−0.523748	−0.0511126
$106$	9.73529	0.945575
$107$	−1.99570	−0.192932	−0.0964660	−	0.995336i	$-0.530754\pi$
$107$	−1.99570	−0.192932	−0.0964660	+	0.995336i	$0.530754\pi$
$108$	−23.1512	−2.22773
$109$	14.8223	1.41972	0.709861	−	0.704341i	$-0.248758\pi$
$109$	14.8223	1.41972	0.709861	+	0.704341i	$0.248758\pi$
$110$	7.09977	0.676937
$111$	7.04756	0.668925
$112$	0.716519	0.0677047
$113$	−12.3669	−1.16338	−0.581690	−	0.813410i	$-0.697608\pi$
$113$	−12.3669	−1.16338	−0.581690	+	0.813410i	$0.697608\pi$
$114$	−6.49740	−0.608537
$115$	−20.9364	−1.95233
$116$	22.5681	2.09540
$117$	0.186367	0.0172296
$118$	20.3015	1.86891
$119$	0.171561	0.0157270
$120$	−21.1190	−1.92789
$121$	−10.1803	−0.925483
$122$	−35.7947	−3.24070
$123$	7.86579	0.709234
$124$	−41.1319	−3.69376
$125$	0.275046	0.0246009
$126$	−0.510780	−0.0455039
$127$	15.9678	1.41691	0.708456	−	0.705754i	$-0.249392\pi$
$127$	15.9678	1.41691	0.708456	+	0.705754i	$0.249392\pi$
$128$	−17.2550	−1.52514
$129$	−3.89491	−0.342927
$130$	0.970089	0.0850824
$131$	−12.1390	−1.06059	−0.530293	−	0.847814i	$-0.677918\pi$
$131$	−12.1390	−1.06059	−0.530293	+	0.847814i	$0.677918\pi$
$132$	−4.65109	−0.404826
$133$	−0.290566	−0.0251953
$134$	−12.1930	−1.05331
$135$	17.3394	1.49234
$136$	6.91783	0.593199
$137$	0.846052	0.0722831	0.0361416	−	0.999347i	$-0.488493\pi$
$137$	0.846052	0.0722831	0.0361416	+	0.999347i	$0.488493\pi$
$138$	20.2410	1.72302
$139$	15.6472	1.32717	0.663587	−	0.748099i	$-0.269033\pi$
$139$	15.6472	1.32717	0.663587	+	0.748099i	$0.269033\pi$
$140$	−1.80160	−0.152263
$141$	15.8685	1.33637
$142$	10.7816	0.904769
$143$	0.111999	0.00936584
$144$	−7.93006	−0.660838
$145$	−16.9027	−1.40370
$146$	14.0710	1.16452
$147$	−8.53188	−0.703698
$148$	24.2423	1.99271
$149$	−0.542212	−0.0444198	−0.0222099	−	0.999753i	$-0.507070\pi$
$149$	−0.542212	−0.0444198	−0.0222099	+	0.999753i	$0.507070\pi$
$150$	14.9534	1.22094
$151$	8.53046	0.694199	0.347100	−	0.937828i	$-0.387167\pi$
$151$	8.53046	0.694199	0.347100	+	0.937828i	$0.387167\pi$
$152$	−11.7165	−0.950331
$153$	−1.89875	−0.153505
$154$	−0.306958	−0.0247354
$155$	30.8064	2.47443
$156$	−0.635510	−0.0508815
$157$	−16.2204	−1.29453	−0.647263	−	0.762267i	$-0.724086\pi$
$157$	−16.2204	−1.29453	−0.647263	+	0.762267i	$0.724086\pi$
$158$	3.57394	0.284328
$159$	4.77662	0.378811
$160$	−6.71544	−0.530902
$161$	0.905184	0.0713385
$162$	−5.50641	−0.432625
$163$	1.36363	0.106808	0.0534039	−	0.998573i	$-0.482993\pi$
$163$	1.36363	0.106808	0.0534039	+	0.998573i	$0.482993\pi$
$164$	27.0569	2.11279
$165$	3.48351	0.271191
$166$	−29.2971	−2.27389
$167$	13.4045	1.03727	0.518636	−	0.854995i	$-0.326440\pi$
$167$	13.4045	1.03727	0.518636	+	0.854995i	$0.326440\pi$
$168$	0.913080	0.0704457
$169$	−12.9847	−0.998823
$170$	−9.88346	−0.758027
$171$	3.21584	0.245921
$172$	−13.3978	−1.02157
$173$	−13.6007	−1.03404	−0.517022	−	0.855972i	$-0.672959\pi$
$173$	−13.6007	−1.03404	−0.517022	+	0.855972i	$0.672959\pi$
$174$	16.3413	1.23883
$175$	0.668721	0.0505505
$176$	−4.76565	−0.359224
$177$	9.96096	0.748711
$178$	−34.2179	−2.56474
$179$	23.9070	1.78689	0.893445	−	0.449172i	$-0.148281\pi$
$179$	23.9070	1.78689	0.893445	+	0.449172i	$0.148281\pi$
$180$	19.9391	1.48617
$181$	−11.6044	−0.862545	−0.431273	−	0.902222i	$-0.641935\pi$
$181$	−11.6044	−0.862545	−0.431273	+	0.902222i	$0.641935\pi$
$182$	−0.0419418	−0.00310893
$183$	−17.5627	−1.29827
$184$	36.4996	2.69079
$185$	−18.1567	−1.33490
$186$	−29.7831	−2.18380
$187$	−1.14107	−0.0834433
$188$	54.5849	3.98101
$189$	−0.749670	−0.0545305
$190$	16.7393	1.21439
$191$	−4.85929	−0.351606	−0.175803	−	0.984425i	$-0.556252\pi$
$191$	−4.85929	−0.351606	−0.175803	+	0.984425i	$0.556252\pi$
$192$	−6.37310	−0.459939
$193$	25.6451	1.84597	0.922987	−	0.384831i	$-0.125740\pi$
$193$	25.6451	1.84597	0.922987	+	0.384831i	$0.125740\pi$
$194$	33.9247	2.43565
$195$	0.475975	0.0340852
$196$	−29.3481	−2.09629
$197$	1.46990	0.104726	0.0523629	−	0.998628i	$-0.483325\pi$
$197$	1.46990	0.104726	0.0523629	+	0.998628i	$0.483325\pi$
$198$	3.39725	0.241432
$199$	7.46714	0.529332	0.264666	−	0.964340i	$-0.414738\pi$
$199$	7.46714	0.529332	0.264666	+	0.964340i	$0.414738\pi$
$200$	26.9647	1.90669
$201$	−5.98248	−0.421972
$202$	−0.196185	−0.0138035
$203$	0.730790	0.0512914
$204$	6.47470	0.453320
$205$	−20.2646	−1.41534
$206$	−15.8585	−1.10491
$207$	−10.0181	−0.696306
$208$	−0.651162	−0.0451500
$209$	1.93259	0.133680
$210$	−1.30451	−0.0900200
$211$	−20.1549	−1.38752	−0.693759	−	0.720208i	$-0.744047\pi$
$211$	−20.1549	−1.38752	−0.693759	+	0.720208i	$0.744047\pi$
$212$	16.4307	1.12847
$213$	5.28998	0.362463
$214$	−4.97075	−0.339793
$215$	10.0345	0.684344
$216$	−30.2288	−2.05681
$217$	−1.33191	−0.0904162
$218$	36.9184	2.50043
$219$	6.90393	0.466524
$220$	11.9826	0.807868
$221$	−0.155912	−0.0104878
$222$	17.5535	1.17812
$223$	−8.91317	−0.596870	−0.298435	−	0.954430i	$-0.596465\pi$
$223$	−8.91317	−0.596870	−0.298435	+	0.954430i	$0.596465\pi$
$224$	0.290342	0.0193993
$225$	−7.40105	−0.493403
$226$	−30.8026	−2.04896
$227$	−17.2725	−1.14642	−0.573209	−	0.819409i	$-0.694302\pi$
$227$	−17.2725	−1.14642	−0.573209	+	0.819409i	$0.694302\pi$
$228$	−10.9660	−0.726239
$229$	−12.9392	−0.855044	−0.427522	−	0.904005i	$-0.640613\pi$
$229$	−12.9392	−0.855044	−0.427522	+	0.904005i	$0.640613\pi$
$230$	−52.1468	−3.43846
$231$	−0.150609	−0.00990936
$232$	29.4675	1.93464
$233$	−24.8301	−1.62668	−0.813338	−	0.581791i	$-0.802352\pi$
$233$	−24.8301	−1.62668	−0.813338	+	0.581791i	$0.802352\pi$
$234$	0.464189	0.0303450
$235$	−40.8822	−2.66686
$236$	34.2639	2.23039
$237$	1.75356	0.113906
$238$	0.427311	0.0276985
$239$	7.52122	0.486507	0.243254	−	0.969963i	$-0.421785\pi$
$239$	7.52122	0.486507	0.243254	+	0.969963i	$0.421785\pi$
$240$	−20.2531	−1.30733
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−25.3564	−1.62997
$243$	13.8202	0.886569
$244$	−60.4123	−3.86750
$245$	21.9807	1.40430
$246$	19.5915	1.24911
$247$	0.264062	0.0168019
$248$	−53.7065	−3.41037
$249$	−14.3746	−0.910955
$250$	0.685064	0.0433272
$251$	−30.0279	−1.89534	−0.947671	−	0.319250i	$-0.896569\pi$
$251$	−30.0279	−1.89534	−0.947671	+	0.319250i	$0.896569\pi$
$252$	−0.862068	−0.0543052
$253$	−6.02048	−0.378504
$254$	39.7714	2.49548
$255$	−4.84932	−0.303677
$256$	−32.5475	−2.03422
$257$	−9.93458	−0.619702	−0.309851	−	0.950785i	$-0.600279\pi$
$257$	−9.93458	−0.619702	−0.309851	+	0.950785i	$0.600279\pi$
$258$	−9.70114	−0.603967
$259$	0.785002	0.0487777
$260$	1.63726	0.101539
$261$	−8.08800	−0.500634
$262$	−30.2348	−1.86791
$263$	18.4575	1.13814	0.569069	−	0.822290i	$-0.307304\pi$
$263$	18.4575	1.13814	0.569069	+	0.822290i	$0.307304\pi$
$264$	−6.07300	−0.373767
$265$	−12.3060	−0.755953
$266$	−0.723721	−0.0443742
$267$	−16.7890	−1.02747
$268$	−20.5786	−1.25704
$269$	−1.14902	−0.0700569	−0.0350285	−	0.999386i	$-0.511152\pi$
$269$	−1.14902	−0.0700569	−0.0350285	+	0.999386i	$0.511152\pi$
$270$	43.1878	2.62833
$271$	12.2034	0.741303	0.370651	−	0.928772i	$-0.379134\pi$
$271$	12.2034	0.741303	0.370651	+	0.928772i	$0.379134\pi$
$272$	6.63417	0.402256
$273$	−0.0205787	−0.00124548
$274$	2.10728	0.127306
$275$	−4.44773	−0.268208
$276$	34.1616	2.05629
$277$	−4.31327	−0.259159	−0.129580	−	0.991569i	$-0.541363\pi$
$277$	−4.31327	−0.259159	−0.129580	+	0.991569i	$0.541363\pi$
$278$	38.9728	2.33743
$279$	14.7409	0.882515
$280$	−2.35237	−0.140581
$281$	−17.1399	−1.02248	−0.511240	−	0.859438i	$-0.670814\pi$
$281$	−17.1399	−1.02248	−0.511240	+	0.859438i	$0.670814\pi$
$282$	39.5242	2.35363
$283$	13.8905	0.825704	0.412852	−	0.910798i	$-0.364533\pi$
$283$	13.8905	0.825704	0.412852	+	0.910798i	$0.364533\pi$
$284$	18.1966	1.07977
$285$	8.21312	0.486503
$286$	0.278959	0.0164952
$287$	0.876142	0.0517170
$288$	−3.21335	−0.189349
$289$	−15.4115	−0.906561
$290$	−42.1001	−2.47220
$291$	16.6452	0.975757
$292$	23.7482	1.38976
$293$	−0.325090	−0.0189920	−0.00949598	−	0.999955i	$-0.503023\pi$
$293$	−0.325090	−0.0189920	−0.00949598	+	0.999955i	$0.503023\pi$
$294$	−21.2506	−1.23936
$295$	−25.6624	−1.49412
$296$	31.6535	1.83982
$297$	4.98614	0.289325
$298$	−1.35050	−0.0782325
$299$	−0.822618	−0.0475732
$300$	25.2375	1.45709
$301$	−0.433839	−0.0250061
$302$	21.2470	1.22263
$303$	−0.0962580	−0.00552988
$304$	−11.2360	−0.644432
$305$	45.2467	2.59082
$306$	−4.72926	−0.270354
$307$	−14.3600	−0.819566	−0.409783	−	0.912183i	$-0.634396\pi$
$307$	−14.3600	−0.819566	−0.409783	+	0.912183i	$0.634396\pi$
$308$	−0.518068	−0.0295197
$309$	−7.78096	−0.442644
$310$	76.7302	4.35798
$311$	−11.2072	−0.635502	−0.317751	−	0.948174i	$-0.602928\pi$
$311$	−11.2072	−0.635502	−0.317751	+	0.948174i	$0.602928\pi$
$312$	−0.829794	−0.0469778
$313$	19.3860	1.09576	0.547879	−	0.836557i	$-0.315435\pi$
$313$	19.3860	1.09576	0.547879	+	0.836557i	$0.315435\pi$
$314$	−40.4005	−2.27993
$315$	0.645658	0.0363787
$316$	6.03191	0.339322
$317$	5.19578	0.291824	0.145912	−	0.989298i	$-0.453388\pi$
$317$	5.19578	0.291824	0.145912	+	0.989298i	$0.453388\pi$
$318$	11.8973	0.667165
$319$	−4.86056	−0.272139
$320$	16.4190	0.917852
$321$	−2.43890	−0.136126
$322$	2.25457	0.125642
$323$	−2.69032	−0.149693
$324$	−9.29343	−0.516302
$325$	−0.607724	−0.0337104
$326$	3.39643	0.188111
$327$	18.1140	1.00171
$328$	35.3285	1.95069
$329$	1.76754	0.0974476
$330$	8.67646	0.477623
$331$	0.0173250	0.000952268 0	0.000476134	−	1.00000i	$-0.499848\pi$
$331$	0.0173250	0.000952268 0	0.000476134		1.00000i	$0.499848\pi$
$332$	−49.4461	−2.71371
$333$	−8.68799	−0.476099
$334$	33.3869	1.82685
$335$	15.4127	0.842084
$336$	0.875641	0.0477701
$337$	0.347899	0.0189513	0.00947563	−	0.999955i	$-0.496984\pi$
$337$	0.347899	0.0189513	0.00947563	+	0.999955i	$0.496984\pi$
$338$	−32.3413	−1.75914
$339$	−15.1133	−0.820841
$340$	−16.6808	−0.904642
$341$	8.85870	0.479725
$342$	8.00976	0.433118
$343$	−1.90319	−0.102763
$344$	−17.4936	−0.943194
$345$	−25.5858	−1.37750
$346$	−33.8756	−1.82117
$347$	6.37601	0.342282	0.171141	−	0.985247i	$-0.445255\pi$
$347$	6.37601	0.342282	0.171141	+	0.985247i	$0.445255\pi$
$348$	27.5800	1.47844
$349$	−0.970720	−0.0519614	−0.0259807	−	0.999662i	$-0.508271\pi$
$349$	−0.970720	−0.0519614	−0.0259807	+	0.999662i	$0.508271\pi$
$350$	1.66560	0.0890301
$351$	0.681289	0.0363645
$352$	−1.93110	−0.102928
$353$	30.5488	1.62595	0.812975	−	0.582299i	$-0.197847\pi$
$353$	30.5488	1.62595	0.812975	+	0.582299i	$0.197847\pi$
$354$	24.8100	1.31864
$355$	−13.6286	−0.723330
$356$	−57.7511	−3.06080
$357$	0.209660	0.0110964
$358$	59.5457	3.14709
$359$	8.22124	0.433901	0.216950	−	0.976183i	$-0.430389\pi$
$359$	8.22124	0.433901	0.216950	+	0.976183i	$0.430389\pi$
$360$	26.0348	1.37215
$361$	−14.4435	−0.760184
$362$	−28.9033	−1.51912
$363$	−12.4411	−0.652989
$364$	−0.0707871	−0.00371025
$365$	−17.7866	−0.930994
$366$	−43.7438	−2.28652
$367$	25.1108	1.31077	0.655387	−	0.755294i	$-0.272506\pi$
$367$	25.1108	1.31077	0.655387	+	0.755294i	$0.272506\pi$
$368$	35.0030	1.82466
$369$	−9.69667	−0.504789
$370$	−45.2232	−2.35104
$371$	0.532051	0.0276227
$372$	−50.2663	−2.60619
$373$	−27.0231	−1.39920	−0.699601	−	0.714534i	$-0.746639\pi$
$373$	−27.0231	−1.39920	−0.699601	+	0.714534i	$0.746639\pi$
$374$	−2.84209	−0.146961
$375$	0.336127	0.0173575
$376$	71.2722	3.67558
$377$	−0.664131	−0.0342045
$378$	−1.86722	−0.0960396
$379$	22.9961	1.18123	0.590616	−	0.806953i	$-0.298885\pi$
$379$	22.9961	1.18123	0.590616	+	0.806953i	$0.298885\pi$
$380$	28.2516	1.44928
$381$	19.5139	0.999725
$382$	−12.1032	−0.619252
$383$	3.72670	0.190425	0.0952126	−	0.995457i	$-0.469647\pi$
$383$	3.72670	0.190425	0.0952126	+	0.995457i	$0.469647\pi$
$384$	−21.0869	−1.07609
$385$	0.388015	0.0197751
$386$	63.8749	3.25115
$387$	4.80151	0.244074
$388$	57.2563	2.90675
$389$	4.72525	0.239580	0.119790	−	0.992799i	$-0.461778\pi$
$389$	4.72525	0.239580	0.119790	+	0.992799i	$0.461778\pi$
$390$	1.18552	0.0600312
$391$	8.38100	0.423845
$392$	−38.3202	−1.93546
$393$	−14.8347	−0.748313
$394$	3.66111	0.184444
$395$	−4.51769	−0.227310
$396$	5.73370	0.288129
$397$	32.2227	1.61721	0.808606	−	0.588350i	$-0.200222\pi$
$397$	32.2227	1.61721	0.808606	+	0.588350i	$0.200222\pi$
$398$	18.5986	0.932264
$399$	−0.355094	−0.0177769
$400$	25.8591	1.29295
$401$	−6.02370	−0.300809	−0.150405	−	0.988625i	$-0.548058\pi$
$401$	−6.02370	−0.300809	−0.150405	+	0.988625i	$0.548058\pi$
$402$	−14.9007	−0.743180
$403$	1.21042	0.0602955
$404$	−0.331110	−0.0164733
$405$	6.96045	0.345868
$406$	1.82020	0.0903349
$407$	−5.22113	−0.258802
$408$	8.45411	0.418541
$409$	18.5405	0.916767	0.458384	−	0.888754i	$-0.348429\pi$
$409$	18.5405	0.916767	0.458384	+	0.888754i	$0.348429\pi$
$410$	−50.4737	−2.49272
$411$	1.03394	0.0510005
$412$	−26.7651	−1.31862
$413$	1.10951	0.0545956
$414$	−24.9523	−1.22634
$415$	37.0334	1.81790
$416$	−0.263858	−0.0129367
$417$	19.1220	0.936409
$418$	4.81355	0.235438
$419$	29.7394	1.45286	0.726432	−	0.687238i	$-0.241177\pi$
$419$	29.7394	1.45286	0.726432	+	0.687238i	$0.241177\pi$
$420$	−2.20169	−0.107431
$421$	2.65516	0.129405	0.0647023	−	0.997905i	$-0.479390\pi$
$421$	2.65516	0.129405	0.0647023	+	0.997905i	$0.479390\pi$
$422$	−50.2002	−2.44371
$423$	−19.5622	−0.951146
$424$	21.4538	1.04189
$425$	6.19161	0.300337
$426$	13.1759	0.638374
$427$	−1.95624	−0.0946691
$428$	−8.38937	−0.405515
$429$	0.136871	0.00660822
$430$	24.9931	1.20527
$431$	27.9512	1.34636	0.673181	−	0.739478i	$-0.264927\pi$
$431$	27.9512	1.34636	0.673181	+	0.739478i	$0.264927\pi$
$432$	−28.9893	−1.39475
$433$	13.5815	0.652687	0.326344	−	0.945251i	$-0.394183\pi$
$433$	13.5815	0.652687	0.326344	+	0.945251i	$0.394183\pi$
$434$	−3.31743	−0.159242
$435$	−20.6564	−0.990400
$436$	62.3089	2.98405
$437$	−14.1946	−0.679019
$438$	17.1958	0.821647
$439$	27.3113	1.30350	0.651748	−	0.758435i	$-0.274036\pi$
$439$	27.3113	1.30350	0.651748	+	0.758435i	$0.274036\pi$
$440$	15.6459	0.745887
$441$	10.5178	0.500848
$442$	−0.388334	−0.0184712
$443$	4.06001	0.192897	0.0964484	−	0.995338i	$-0.469252\pi$
$443$	4.06001	0.192897	0.0964484	+	0.995338i	$0.469252\pi$
$444$	29.6259	1.40599
$445$	43.2535	2.05041
$446$	−22.2003	−1.05121
$447$	−0.662624	−0.0313410
$448$	−0.709876	−0.0335385
$449$	−1.53571	−0.0724746	−0.0362373	−	0.999343i	$-0.511537\pi$
$449$	−1.53571	−0.0724746	−0.0362373	+	0.999343i	$0.511537\pi$
$450$	−18.4340	−0.868986
$451$	−5.82731	−0.274397
$452$	−51.9869	−2.44526
$453$	10.4249	0.489803
$454$	−43.0211	−2.01908
$455$	0.0530171	0.00248548
$456$	−14.3184	−0.670521
$457$	−4.50705	−0.210831	−0.105415	−	0.994428i	$-0.533617\pi$
$457$	−4.50705	−0.210831	−0.105415	+	0.994428i	$0.533617\pi$
$458$	−32.2279	−1.50591
$459$	−6.94111	−0.323983
$460$	−88.0106	−4.10352
$461$	17.5820	0.818875	0.409438	−	0.912338i	$-0.365725\pi$
$461$	17.5820	0.818875	0.409438	+	0.912338i	$0.365725\pi$
$462$	−0.375126	−0.0174525
$463$	−42.1082	−1.95693	−0.978466	−	0.206407i	$-0.933823\pi$
$463$	−42.1082	−1.95693	−0.978466	+	0.206407i	$0.933823\pi$
$464$	28.2592	1.31190
$465$	37.6477	1.74587
$466$	−61.8451	−2.86492
$467$	10.6368	0.492210	0.246105	−	0.969243i	$-0.420849\pi$
$467$	10.6368	0.492210	0.246105	+	0.969243i	$0.420849\pi$
$468$	0.783434	0.0362143
$469$	−0.666367	−0.0307699
$470$	−101.826	−4.69689
$471$	−19.8225	−0.913373
$472$	44.7388	2.05927
$473$	2.88551	0.132676
$474$	4.36763	0.200612
$475$	−10.4865	−0.481154
$476$	0.721193	0.0330558
$477$	−5.88845	−0.269614
$478$	18.7333	0.856841
$479$	24.3303	1.11168	0.555839	−	0.831290i	$-0.312397\pi$
$479$	24.3303	1.11168	0.555839	+	0.831290i	$0.312397\pi$
$480$	−8.20678	−0.374586
$481$	−0.713398	−0.0325282
$482$	2.49073	0.113449
$483$	1.10620	0.0503340
$484$	−42.7951	−1.94523
$485$	−42.8830	−1.94722
$486$	34.4224	1.56143
$487$	15.1777	0.687768	0.343884	−	0.939012i	$-0.388257\pi$
$487$	15.1777	0.687768	0.343884	+	0.939012i	$0.388257\pi$
$488$	−78.8812	−3.57079
$489$	1.66646	0.0753598
$490$	54.7479	2.47326
$491$	10.0194	0.452169	0.226084	−	0.974108i	$-0.427408\pi$
$491$	10.0194	0.452169	0.226084	+	0.974108i	$0.427408\pi$
$492$	33.0655	1.49071
$493$	6.76630	0.304739
$494$	0.657707	0.0295916
$495$	−4.29434	−0.193016
$496$	−51.5044	−2.31261
$497$	0.589231	0.0264306
$498$	−35.8032	−1.60438
$499$	−7.82989	−0.350514	−0.175257	−	0.984523i	$-0.556076\pi$
$499$	−7.82989	−0.350514	−0.175257	+	0.984523i	$0.556076\pi$
$500$	1.15621	0.0517075
$501$	16.3813	0.731863
$502$	−74.7911	−3.33809
$503$	−7.39455	−0.329707	−0.164853	−	0.986318i	$-0.552715\pi$
$503$	−7.39455	−0.329707	−0.164853	+	0.986318i	$0.552715\pi$
$504$	−1.12561	−0.0501388
$505$	0.247990	0.0110354
$506$	−14.9954	−0.666625
$507$	−15.8683	−0.704735
$508$	67.1241	2.97815
$509$	13.7526	0.609572	0.304786	−	0.952421i	$-0.401415\pi$
$509$	13.7526	0.609572	0.304786	+	0.952421i	$0.401415\pi$
$510$	−12.0783	−0.534838
$511$	0.769003	0.0340187
$512$	−46.5568	−2.05754
$513$	11.7559	0.519036
$514$	−24.7443	−1.09143
$515$	20.0461	0.883337
$516$	−16.3731	−0.720784
$517$	−11.7561	−0.517032
$518$	1.95523	0.0859077
$519$	−16.6211	−0.729585
$520$	2.13780	0.0937487
$521$	−14.2825	−0.625730	−0.312865	−	0.949798i	$-0.601289\pi$
$521$	−14.2825	−0.625730	−0.312865	+	0.949798i	$0.601289\pi$
$522$	−20.1450	−0.881722
$523$	−29.4674	−1.28852	−0.644260	−	0.764806i	$-0.722835\pi$
$523$	−29.4674	−1.28852	−0.644260	+	0.764806i	$0.722835\pi$
$524$	−51.0287	−2.22920
$525$	0.817227	0.0356667
$526$	45.9726	2.00450
$527$	−12.3320	−0.537192
$528$	−5.82398	−0.253456
$529$	21.2195	0.922589
$530$	−30.6509	−1.33139
$531$	−12.2795	−0.532886
$532$	−1.22146	−0.0529569
$533$	−0.796224	−0.0344883
$534$	−41.8168	−1.80959
$535$	6.28334	0.271653
$536$	−26.8698	−1.16060
$537$	29.2161	1.26077
$538$	−2.86189	−0.123385
$539$	6.32078	0.272255
$540$	72.8901	3.13669
$541$	31.6583	1.36110	0.680549	−	0.732703i	$-0.261741\pi$
$541$	31.6583	1.36110	0.680549	+	0.732703i	$0.261741\pi$
$542$	30.3953	1.30559
$543$	−14.1814	−0.608582
$544$	2.68824	0.115257
$545$	−46.6672	−1.99900
$546$	−0.0512560	−0.00219355
$547$	−31.5186	−1.34764	−0.673820	−	0.738896i	$-0.735348\pi$
$547$	−31.5186	−1.34764	−0.673820	+	0.738896i	$0.735348\pi$
$548$	3.55656	0.151929
$549$	21.6506	0.924027
$550$	−11.0781	−0.472371
$551$	−11.4598	−0.488205
$552$	44.6053	1.89853
$553$	0.195322	0.00830595
$554$	−10.7432	−0.456434
$555$	−22.1888	−0.941862
$556$	65.7762	2.78953
$557$	−32.3589	−1.37109	−0.685545	−	0.728030i	$-0.740436\pi$
$557$	−32.3589	−1.37109	−0.685545	+	0.728030i	$0.740436\pi$
$558$	36.7156	1.55429
$559$	0.394267	0.0166757
$560$	−2.25591	−0.0953298
$561$	−1.39447	−0.0588747
$562$	−42.6907	−1.80080
$563$	20.8428	0.878419	0.439209	−	0.898385i	$-0.355259\pi$
$563$	20.8428	0.878419	0.439209	+	0.898385i	$0.355259\pi$
$564$	66.7068	2.80886
$565$	38.9364	1.63807
$566$	34.5974	1.45424
$567$	−0.300935	−0.0126381
$568$	23.7595	0.996926
$569$	26.6787	1.11843	0.559215	−	0.829022i	$-0.311103\pi$
$569$	26.6787	1.11843	0.559215	+	0.829022i	$0.311103\pi$
$570$	20.4566	0.856834
$571$	0.500659	0.0209519	0.0104760	−	0.999945i	$-0.496665\pi$
$571$	0.500659	0.0209519	0.0104760	+	0.999945i	$0.496665\pi$
$572$	0.470813	0.0196857
$573$	−5.93842	−0.248081
$574$	2.18223	0.0910844
$575$	32.6680	1.36235
$576$	7.85654	0.327356
$577$	−9.59281	−0.399354	−0.199677	−	0.979862i	$-0.563989\pi$
$577$	−9.59281	−0.399354	−0.199677	+	0.979862i	$0.563989\pi$
$578$	−38.3859	−1.59664
$579$	31.3402	1.30246
$580$	−71.0543	−2.95037
$581$	−1.60114	−0.0664263
$582$	41.4586	1.71851
$583$	−3.53873	−0.146559
$584$	31.0084	1.28314
$585$	−0.586765	−0.0242597
$586$	−0.809710	−0.0334488
$587$	19.6676	0.811770	0.405885	−	0.913924i	$-0.366963\pi$
$587$	19.6676	0.811770	0.405885	+	0.913924i	$0.366963\pi$
$588$	−35.8656	−1.47907
$589$	20.8863	0.860605
$590$	−63.9181	−2.63146
$591$	1.79632	0.0738909
$592$	30.3556	1.24761
$593$	35.9622	1.47679	0.738394	−	0.674369i	$-0.235584\pi$
$593$	35.9622	1.47679	0.738394	+	0.674369i	$0.235584\pi$
$594$	12.4191	0.509562
$595$	−0.540148	−0.0221439
$596$	−2.27931	−0.0933640
$597$	9.12541	0.373478
$598$	−2.04892	−0.0837864
$599$	−8.60123	−0.351437	−0.175718	−	0.984440i	$-0.556225\pi$
$599$	−8.60123	−0.351437	−0.175718	+	0.984440i	$0.556225\pi$
$600$	32.9529	1.34530
$601$	36.8567	1.50342	0.751708	−	0.659496i	$-0.229230\pi$
$601$	36.8567	1.50342	0.751708	+	0.659496i	$0.229230\pi$
$602$	−1.08057	−0.0440409
$603$	7.37499	0.300333
$604$	35.8596	1.45911
$605$	32.0521	1.30310
$606$	−0.239752	−0.00973927
$607$	−38.6665	−1.56942	−0.784712	−	0.619861i	$-0.787189\pi$
$607$	−38.6665	−1.56942	−0.784712	+	0.619861i	$0.787189\pi$
$608$	−4.55298	−0.184648
$609$	0.893080	0.0361894
$610$	112.697	4.56298
$611$	−1.60631	−0.0649845
$612$	−7.98179	−0.322645
$613$	−38.3341	−1.54830	−0.774150	−	0.633002i	$-0.781822\pi$
$613$	−38.3341	−1.54830	−0.774150	+	0.633002i	$0.781822\pi$
$614$	−35.7667	−1.44343
$615$	−24.7649	−0.998618
$616$	−0.676449	−0.0272549
$617$	−44.3829	−1.78679	−0.893395	−	0.449272i	$-0.851683\pi$
$617$	−44.3829	−1.78679	−0.893395	+	0.449272i	$0.851683\pi$
$618$	−19.3802	−0.779588
$619$	−15.6150	−0.627619	−0.313810	−	0.949486i	$-0.601605\pi$
$619$	−15.6150	−0.627619	−0.313810	+	0.949486i	$0.601605\pi$
$620$	129.501	5.20089
$621$	−36.6225	−1.46961
$622$	−27.9141	−1.11925
$623$	−1.87007	−0.0749226
$624$	−0.795769	−0.0318563
$625$	−25.4292	−1.01717
$626$	48.2851	1.92986
$627$	2.36177	0.0943200
$628$	−68.1858	−2.72091
$629$	7.26825	0.289804
$630$	1.60816	0.0640705
$631$	−7.52472	−0.299555	−0.149777	−	0.988720i	$-0.547856\pi$
$631$	−7.52472	−0.299555	−0.149777	+	0.988720i	$0.547856\pi$
$632$	7.87595	0.313288
$633$	−24.6307	−0.978984
$634$	12.9413	0.513963
$635$	−50.2736	−1.99505
$636$	20.0796	0.796206
$637$	0.863650	0.0342191
$638$	−12.1063	−0.479294
$639$	−6.52130	−0.257979
$640$	54.3262	2.14743
$641$	2.42509	0.0957851	0.0478926	−	0.998852i	$-0.484749\pi$
$641$	2.42509	0.0957851	0.0478926	+	0.998852i	$0.484749\pi$
$642$	−6.07463	−0.239747
$643$	12.1224	0.478061	0.239030	−	0.971012i	$-0.423170\pi$
$643$	12.1224	0.478061	0.239030	+	0.971012i	$0.423170\pi$
$644$	3.80514	0.149943
$645$	12.2629	0.482850
$646$	−6.70085	−0.263642
$647$	12.4628	0.489964	0.244982	−	0.969528i	$-0.421218\pi$
$647$	12.4628	0.489964	0.244982	+	0.969528i	$0.421218\pi$
$648$	−12.1346	−0.476691
$649$	−7.37950	−0.289671
$650$	−1.51367	−0.0593711
$651$	−1.62770	−0.0637945
$652$	5.73231	0.224495
$653$	−49.4695	−1.93589	−0.967945	−	0.251163i	$-0.919187\pi$
$653$	−49.4695	−1.93589	−0.967945	+	0.251163i	$0.919187\pi$
$654$	45.1171	1.76422
$655$	38.2187	1.49333
$656$	33.8799	1.32279
$657$	−8.51092	−0.332043
$658$	4.40245	0.171626
$659$	19.5067	0.759874	0.379937	−	0.925012i	$-0.375946\pi$
$659$	19.5067	0.759874	0.379937	+	0.925012i	$0.375946\pi$
$660$	14.6437	0.570004
$661$	33.2398	1.29288	0.646439	−	0.762966i	$-0.276258\pi$
$661$	33.2398	1.29288	0.646439	+	0.762966i	$0.276258\pi$
$662$	0.0431518	0.00167714
$663$	−0.190536	−0.00739982
$664$	−64.5624	−2.50551
$665$	0.914829	0.0354756
$666$	−21.6394	−0.838510
$667$	35.7001	1.38231
$668$	56.3487	2.18020
$669$	−10.8926	−0.421131
$670$	38.3887	1.48309
$671$	13.0112	0.502291
$672$	0.354820	0.0136875
$673$	28.8764	1.11310	0.556552	−	0.830813i	$-0.312124\pi$
$673$	28.8764	1.11310	0.556552	+	0.830813i	$0.312124\pi$
$674$	0.866521	0.0333771
$675$	−27.0555	−1.04137
$676$	−54.5840	−2.09938
$677$	29.4480	1.13178	0.565889	−	0.824482i	$-0.308533\pi$
$677$	29.4480	1.13178	0.565889	+	0.824482i	$0.308533\pi$
$678$	−37.6431	−1.44567
$679$	1.85404	0.0711517
$680$	−21.7803	−0.835237
$681$	−21.1083	−0.808873
$682$	22.0646	0.844897
$683$	19.6959	0.753643	0.376821	−	0.926286i	$-0.377017\pi$
$683$	19.6959	0.753643	0.376821	+	0.926286i	$0.377017\pi$
$684$	13.5185	0.516891
$685$	−2.66374	−0.101776
$686$	−4.74033	−0.180987
$687$	−15.8126	−0.603289
$688$	−16.7763	−0.639592
$689$	−0.483520	−0.0184206
$690$	−63.7273	−2.42606
$691$	15.6587	0.595683	0.297842	−	0.954615i	$-0.403733\pi$
$691$	15.6587	0.595683	0.297842	+	0.954615i	$0.403733\pi$
$692$	−57.1735	−2.17341
$693$	0.185666	0.00705286
$694$	15.8809	0.602830
$695$	−49.2641	−1.86869
$696$	36.0115	1.36501
$697$	8.11209	0.307267
$698$	−2.41780	−0.0915149
$699$	−30.3443	−1.14773
$700$	2.81111	0.106250
$701$	32.6726	1.23403	0.617014	−	0.786952i	$-0.288342\pi$
$701$	32.6726	1.23403	0.617014	+	0.786952i	$0.288342\pi$
$702$	1.69690	0.0640455
$703$	−12.3100	−0.464279
$704$	4.72146	0.177947
$705$	−49.9611	−1.88164
$706$	76.0887	2.86364
$707$	−0.0107218	−0.000403236 0
$708$	41.8730	1.57368
$709$	−5.63690	−0.211698	−0.105849	−	0.994382i	$-0.533756\pi$
$709$	−5.63690	−0.211698	−0.105849	+	0.994382i	$0.533756\pi$
$710$	−33.9451	−1.27394
$711$	−2.16172	−0.0810710
$712$	−75.4064	−2.82597
$713$	−65.0659	−2.43674
$714$	0.522207	0.0195431
$715$	−0.352622	−0.0131873
$716$	100.498	3.75579
$717$	9.19150	0.343263
$718$	20.4769	0.764190
$719$	13.2196	0.493006	0.246503	−	0.969142i	$-0.420718\pi$
$719$	13.2196	0.493006	0.246503	+	0.969142i	$0.420718\pi$
$720$	24.9673	0.930475
$721$	−0.866693	−0.0322773
$722$	−35.9748	−1.33884
$723$	1.22208	0.0454495
$724$	−48.7814	−1.81295
$725$	26.3741	0.979509
$726$	−30.9874	−1.15005
$727$	21.6517	0.803018	0.401509	−	0.915855i	$-0.368486\pi$
$727$	21.6517	0.803018	0.401509	+	0.915855i	$0.368486\pi$
$728$	−0.0924277	−0.00342560
$729$	23.5217	0.871173
$730$	−44.3016	−1.63967
$731$	−4.01687	−0.148569
$732$	−73.8284	−2.72878
$733$	−37.5385	−1.38651	−0.693257	−	0.720690i	$-0.743825\pi$
$733$	−37.5385	−1.38651	−0.693257	+	0.720690i	$0.743825\pi$
$734$	62.5441	2.30855
$735$	26.8621	0.990823
$736$	14.1836	0.522815
$737$	4.43208	0.163258
$738$	−24.1517	−0.889038
$739$	−28.8751	−1.06219	−0.531093	−	0.847313i	$-0.678219\pi$
$739$	−28.8751	−1.06219	−0.531093	+	0.847313i	$0.678219\pi$
$740$	−76.3254	−2.80578
$741$	0.322704	0.0118548
$742$	1.32519	0.0486493
$743$	−24.5272	−0.899817	−0.449909	−	0.893075i	$-0.648543\pi$
$743$	−24.5272	−0.899817	−0.449909	+	0.893075i	$0.648543\pi$
$744$	−65.6334	−2.40624
$745$	1.70712	0.0625440
$746$	−67.3070	−2.46429
$747$	17.7205	0.648361
$748$	−4.79673	−0.175386
$749$	−0.271660	−0.00992624
$750$	0.837200	0.0305702
$751$	38.3355	1.39888	0.699442	−	0.714689i	$-0.253432\pi$
$751$	38.3355	1.39888	0.699442	+	0.714689i	$0.253432\pi$
$752$	68.3498	2.49246
$753$	−36.6963	−1.33729
$754$	−1.65417	−0.0602412
$755$	−26.8576	−0.977448
$756$	−3.15140	−0.114615
$757$	31.6239	1.14939	0.574694	−	0.818368i	$-0.305121\pi$
$757$	31.6239	1.14939	0.574694	+	0.818368i	$0.305121\pi$
$758$	57.2771	2.08040
$759$	−7.35748	−0.267060
$760$	36.8885	1.33809
$761$	−28.4924	−1.03285	−0.516424	−	0.856333i	$-0.672737\pi$
$761$	−28.4924	−1.03285	−0.516424	+	0.856333i	$0.672737\pi$
$762$	48.6037	1.76072
$763$	2.01765	0.0730440
$764$	−20.4271	−0.739026
$765$	5.97808	0.216138
$766$	9.28218	0.335379
$767$	−1.00831	−0.0364080
$768$	−39.7755	−1.43527
$769$	−8.72245	−0.314539	−0.157270	−	0.987556i	$-0.550269\pi$
$769$	−8.72245	−0.314539	−0.157270	+	0.987556i	$0.550269\pi$
$770$	0.966439	0.0348280
$771$	−12.1408	−0.437241
$772$	107.805	3.87997
$773$	−42.2655	−1.52019	−0.760093	−	0.649814i	$-0.774847\pi$
$773$	−42.2655	−1.52019	−0.760093	+	0.649814i	$0.774847\pi$
$774$	11.9592	0.429866
$775$	−48.0685	−1.72667
$776$	74.7604	2.68374
$777$	0.959332	0.0344158
$778$	11.7693	0.421950
$779$	−13.7392	−0.492256
$780$	2.00086	0.0716423
$781$	−3.91904	−0.140234
$782$	20.8748	0.746480
$783$	−29.5667	−1.05663
$784$	−36.7490	−1.31246
$785$	51.0687	1.82272
$786$	−36.9492	−1.31794
$787$	17.5127	0.624261	0.312130	−	0.950039i	$-0.398957\pi$
$787$	17.5127	0.624261	0.312130	+	0.950039i	$0.398957\pi$
$788$	6.17903	0.220119
$789$	22.5565	0.803031
$790$	−11.2523	−0.400340
$791$	−1.68341	−0.0598553
$792$	7.48658	0.266024
$793$	1.77780	0.0631316
$794$	80.2580	2.84825
$795$	−15.0389	−0.533374
$796$	31.3897	1.11258
$797$	−44.6851	−1.58283	−0.791413	−	0.611281i	$-0.790654\pi$
$797$	−44.6851	−1.58283	−0.791413	+	0.611281i	$0.790654\pi$
$798$	−0.884442	−0.0313089
$799$	16.3654	0.578968
$800$	10.4784	0.370467
$801$	20.6969	0.731289
$802$	−15.0034	−0.529788
$803$	−5.11472	−0.180495
$804$	−25.1486	−0.886924
$805$	−2.84991	−0.100446
$806$	3.01483	0.106193
$807$	−1.40419	−0.0494297
$808$	−0.432335	−0.0152095
$809$	37.7898	1.32862	0.664309	−	0.747458i	$-0.268726\pi$
$809$	37.7898	1.32862	0.664309	+	0.747458i	$0.268726\pi$
$810$	17.3366	0.609145
$811$	17.5453	0.616097	0.308049	−	0.951371i	$-0.400324\pi$
$811$	17.5453	0.616097	0.308049	+	0.951371i	$0.400324\pi$
$812$	3.07203	0.107807
$813$	14.9135	0.523038
$814$	−13.0044	−0.455804
$815$	−4.29330	−0.150388
$816$	8.10746	0.283818
$817$	6.80322	0.238015
$818$	46.1792	1.61462
$819$	0.0253688	0.000886456 0
$820$	−85.1868	−2.97485
$821$	−21.1741	−0.738980	−0.369490	−	0.929235i	$-0.620468\pi$
$821$	−21.1741	−0.738980	−0.369490	+	0.929235i	$0.620468\pi$
$822$	2.57526	0.0898225
$823$	−47.1268	−1.64274	−0.821369	−	0.570397i	$-0.806789\pi$
$823$	−47.1268	−1.64274	−0.821369	+	0.570397i	$0.806789\pi$
$824$	−34.9475	−1.21746
$825$	−5.43547	−0.189239
$826$	2.76350	0.0961543
$827$	−13.3177	−0.463103	−0.231552	−	0.972823i	$-0.574380\pi$
$827$	−13.3177	−0.463103	−0.231552	+	0.972823i	$0.574380\pi$
$828$	−42.1132	−1.46354
$829$	−41.6063	−1.44505	−0.722523	−	0.691347i	$-0.757017\pi$
$829$	−41.6063	−1.44505	−0.722523	+	0.691347i	$0.757017\pi$
$830$	92.2400	3.20170
$831$	−5.27114	−0.182854
$832$	0.645125	0.0223657
$833$	−8.79904	−0.304869
$834$	47.6277	1.64921
$835$	−42.2032	−1.46050
$836$	8.12405	0.280976
$837$	53.8873	1.86262
$838$	74.0726	2.55880
$839$	20.2863	0.700359	0.350180	−	0.936683i	$-0.386121\pi$
$839$	20.2863	0.700359	0.350180	+	0.936683i	$0.386121\pi$
$840$	−2.87477	−0.0991891
$841$	−0.177928	−0.00613546
$842$	6.61327	0.227908
$843$	−20.9462	−0.721426
$844$	−84.7252	−2.91636
$845$	40.8815	1.40637
$846$	−48.7240	−1.67517
$847$	−1.38577	−0.0476156
$848$	20.5741	0.706518
$849$	16.9752	0.582588
$850$	15.4216	0.528957
$851$	38.3485	1.31457
$852$	22.2376	0.761846
$853$	−26.7153	−0.914715	−0.457358	−	0.889283i	$-0.651204\pi$
$853$	−26.7153	−0.914715	−0.457358	+	0.889283i	$0.651204\pi$
$854$	−4.87246	−0.166732
$855$	−10.1248	−0.346263
$856$	−10.9541	−0.374404
$857$	−1.26642	−0.0432602	−0.0216301	−	0.999766i	$-0.506886\pi$
$857$	−1.26642	−0.0432602	−0.0216301	+	0.999766i	$0.506886\pi$
$858$	0.340909	0.0116385
$859$	−45.0089	−1.53569	−0.767843	−	0.640638i	$-0.778670\pi$
$859$	−45.0089	−1.53569	−0.767843	+	0.640638i	$0.778670\pi$
$860$	42.1820	1.43839
$861$	1.07071	0.0364897
$862$	69.6188	2.37122
$863$	26.1118	0.888855	0.444428	−	0.895815i	$-0.353407\pi$
$863$	26.1118	0.888855	0.444428	+	0.895815i	$0.353407\pi$
$864$	−11.7468	−0.399635
$865$	42.8210	1.45596
$866$	33.8279	1.14952
$867$	−18.8341	−0.639638
$868$	−5.59898	−0.190042
$869$	−1.29911	−0.0440693
$870$	−51.4495	−1.74430
$871$	0.605584	0.0205194
$872$	81.3576	2.75511
$873$	−20.5196	−0.694483
$874$	−35.3548	−1.19589
$875$	0.0374399	0.00126570
$876$	29.0222	0.980568
$877$	18.2107	0.614931	0.307466	−	0.951559i	$-0.400519\pi$
$877$	18.2107	0.614931	0.307466	+	0.951559i	$0.400519\pi$
$878$	68.0249	2.29573
$879$	−0.397285	−0.0134001
$880$	15.0043	0.505796
$881$	7.40050	0.249329	0.124665	−	0.992199i	$-0.460214\pi$
$881$	7.40050	0.249329	0.124665	+	0.992199i	$0.460214\pi$
$882$	26.1970	0.882098
$883$	−1.57266	−0.0529243	−0.0264621	−	0.999650i	$-0.508424\pi$
$883$	−1.57266	−0.0529243	−0.0264621	+	0.999650i	$0.508424\pi$
$884$	−0.655410	−0.0220438
$885$	−31.3614	−1.05420
$886$	10.1124	0.339732
$887$	−1.08367	−0.0363861	−0.0181930	−	0.999834i	$-0.505791\pi$
$887$	−1.08367	−0.0363861	−0.0181930	+	0.999834i	$0.505791\pi$
$888$	38.6830	1.29812
$889$	2.17358	0.0728994
$890$	107.733	3.61121
$891$	2.00155	0.0670545
$892$	−37.4684	−1.25453
$893$	−27.7175	−0.927532
$894$	−1.65042	−0.0551981
$895$	−75.2695	−2.51598
$896$	−2.34879	−0.0784676
$897$	−1.00530	−0.0335660
$898$	−3.82503	−0.127643
$899$	−52.5301	−1.75198
$900$	−31.1119	−1.03706
$901$	4.92620	0.164115
$902$	−14.5142	−0.483271
$903$	−0.530184	−0.0176434
$904$	−67.8801	−2.25766
$905$	36.5356	1.21448
$906$	25.9655	0.862646
$907$	39.1868	1.30118	0.650588	−	0.759431i	$-0.274522\pi$
$907$	39.1868	1.30118	0.650588	+	0.759431i	$0.274522\pi$
$908$	−72.6088	−2.40961
$909$	0.118664	0.00393582
$910$	0.132051	0.00437745
$911$	11.8818	0.393662	0.196831	−	0.980437i	$-0.436935\pi$
$911$	11.8818	0.393662	0.196831	+	0.980437i	$0.436935\pi$
$912$	−13.7313	−0.454689
$913$	10.6493	0.352441
$914$	−11.2258	−0.371317
$915$	55.2949	1.82799
$916$	−54.3925	−1.79718
$917$	−1.65239	−0.0545666
$918$	−17.2884	−0.570602
$919$	−28.1347	−0.928077	−0.464039	−	0.885815i	$-0.653600\pi$
$919$	−28.1347	−0.928077	−0.464039	+	0.885815i	$0.653600\pi$
$920$	−114.917	−3.78869
$921$	−17.5490	−0.578258
$922$	43.7919	1.44221
$923$	−0.535485	−0.0176257
$924$	−0.633118	−0.0208281
$925$	28.3306	0.931505
$926$	−104.880	−3.44657
$927$	9.59210	0.315046
$928$	11.4510	0.375897
$929$	59.5689	1.95439	0.977197	−	0.212335i	$-0.0681068\pi$
$929$	59.5689	1.95439	0.977197	+	0.212335i	$0.0681068\pi$
$930$	93.7701	3.07484
$931$	14.9026	0.488413
$932$	−104.379	−3.41904
$933$	−13.6961	−0.448389
$934$	26.4932	0.866885
$935$	3.59259	0.117490
$936$	1.02294	0.0334359
$937$	25.8722	0.845209	0.422605	−	0.906314i	$-0.361116\pi$
$937$	25.8722	0.845209	0.422605	+	0.906314i	$0.361116\pi$
$938$	−1.65974	−0.0541923
$939$	23.6911	0.773130
$940$	−171.857	−5.60535
$941$	−43.2143	−1.40875	−0.704373	−	0.709830i	$-0.748772\pi$
$941$	−43.2143	−1.40875	−0.704373	+	0.709830i	$0.748772\pi$
$942$	−49.3724	−1.60864
$943$	42.8008	1.39378
$944$	42.9043	1.39642
$945$	2.36029	0.0767802
$946$	7.18702	0.233670
$947$	−53.0980	−1.72545	−0.862726	−	0.505672i	$-0.831245\pi$
$947$	−53.0980	−1.72545	−0.862726	+	0.505672i	$0.831245\pi$
$948$	7.37145	0.239414
$949$	−0.698859	−0.0226859
$950$	−26.1190	−0.847412
$951$	6.34963	0.205901
$952$	0.941672	0.0305198
$953$	−28.8397	−0.934210	−0.467105	−	0.884202i	$-0.654703\pi$
$953$	−28.8397	−0.934210	−0.467105	+	0.884202i	$0.654703\pi$
$954$	−14.6665	−0.474846
$955$	15.2992	0.495069
$956$	31.6171	1.02257
$957$	−5.93997	−0.192012
$958$	60.6000	1.95790
$959$	0.115167	0.00371893
$960$	20.0653	0.647605
$961$	64.7397	2.08838
$962$	−1.77688	−0.0572889
$963$	3.00659	0.0968860
$964$	4.20371	0.135393
$965$	−80.7419	−2.59917
$966$	2.75525	0.0886487
$967$	6.08196	0.195583	0.0977914	−	0.995207i	$-0.468822\pi$
$967$	6.08196	0.195583	0.0977914	+	0.995207i	$0.468822\pi$
$968$	−55.8782	−1.79599
$969$	−3.28778	−0.105619
$970$	−106.810	−3.42945
$971$	2.57155	0.0825251	0.0412626	−	0.999148i	$-0.486862\pi$
$971$	2.57155	0.0825251	0.0412626	+	0.999148i	$0.486862\pi$
$972$	58.0963	1.86344
$973$	2.12993	0.0682824
$974$	37.8035	1.21130
$975$	−0.742684	−0.0237849
$976$	−75.6468	−2.42139
$977$	52.2605	1.67196	0.835980	−	0.548760i	$-0.184900\pi$
$977$	52.2605	1.67196	0.835980	+	0.548760i	$0.184900\pi$
$978$	4.15069	0.132724
$979$	12.4380	0.397520
$980$	92.4006	2.95163
$981$	−22.3303	−0.712953
$982$	24.9555	0.796363
$983$	5.96528	0.190263	0.0951314	−	0.995465i	$-0.469673\pi$
$983$	5.96528	0.190263	0.0951314	+	0.995465i	$0.469673\pi$
$984$	43.1741	1.37634
$985$	−4.62787	−0.147456
$986$	16.8530	0.536709
$987$	2.16007	0.0687557
$988$	1.11004	0.0353152
$989$	−21.1937	−0.673920
$990$	−10.6960	−0.339942
$991$	1.36771	0.0434466	0.0217233	−	0.999764i	$-0.493085\pi$
$991$	1.36771	0.0434466	0.0217233	+	0.999764i	$0.493085\pi$
$992$	−20.8702	−0.662629
$993$	0.0211725	0.000671888 0
$994$	1.46761	0.0465499
$995$	−23.5098	−0.745311
$996$	−60.4268	−1.91470
$997$	−17.2016	−0.544780	−0.272390	−	0.962187i	$-0.587814\pi$
$997$	−17.2016	−0.544780	−0.272390	+	0.962187i	$0.587814\pi$
$998$	−19.5021	−0.617329
$999$	−31.7601	−1.00484

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.a.b.1.11	✓	12
3.2	odd	2		2169.2.a.h.1.2		12
4.3	odd	2		3856.2.a.n.1.5		12
5.4	even	2		6025.2.a.h.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.11	✓	12	1.1	even	1	trivial
2169.2.a.h.1.2		12	3.2	odd	2
3856.2.a.n.1.5		12	4.3	odd	2
6025.2.a.h.1.2		12	5.4	even	2

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:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	241.a (trivial)

\(f(q)\)	\(=\)	\(q+2.49073 q^{2} +1.22208 q^{3} +4.20371 q^{4} -3.14843 q^{5} +3.04385 q^{6} +0.136122 q^{7} +5.48885 q^{8} -1.50653 q^{9} +O(q^{10})\)	\(q+2.49073 q^{2} +1.22208 q^{3} +4.20371 q^{4} -3.14843 q^{5} +3.04385 q^{6} +0.136122 q^{7} +5.48885 q^{8} -1.50653 q^{9} -7.84189 q^{10} -0.905365 q^{11} +5.13726 q^{12} -0.123706 q^{13} +0.339044 q^{14} -3.84762 q^{15} +5.26378 q^{16} +1.26034 q^{17} -3.75236 q^{18} -2.13460 q^{19} -13.2351 q^{20} +0.166352 q^{21} -2.25502 q^{22} +6.64978 q^{23} +6.70778 q^{24} +4.91264 q^{25} -0.308118 q^{26} -5.50732 q^{27} +0.572220 q^{28} +5.36862 q^{29} -9.58338 q^{30} -9.78467 q^{31} +2.13295 q^{32} -1.10642 q^{33} +3.13917 q^{34} -0.428573 q^{35} -6.33303 q^{36} +5.76688 q^{37} -5.31669 q^{38} -0.151178 q^{39} -17.2813 q^{40} +6.43642 q^{41} +0.414337 q^{42} -3.18712 q^{43} -3.80590 q^{44} +4.74322 q^{45} +16.5628 q^{46} +12.9849 q^{47} +6.43274 q^{48} -6.98147 q^{49} +12.2360 q^{50} +1.54023 q^{51} -0.520025 q^{52} +3.90862 q^{53} -13.7172 q^{54} +2.85048 q^{55} +0.747155 q^{56} -2.60864 q^{57} +13.3718 q^{58} +8.15085 q^{59} -16.1743 q^{60} -14.3712 q^{61} -24.3709 q^{62} -0.205073 q^{63} -5.21498 q^{64} +0.389481 q^{65} -2.75580 q^{66} -4.89534 q^{67} +5.29812 q^{68} +8.12653 q^{69} -1.06746 q^{70} +4.32869 q^{71} -8.26912 q^{72} +5.64935 q^{73} +14.3637 q^{74} +6.00362 q^{75} -8.97323 q^{76} -0.123241 q^{77} -0.376543 q^{78} +1.43490 q^{79} -16.5727 q^{80} -2.21077 q^{81} +16.0314 q^{82} -11.7625 q^{83} +0.699296 q^{84} -3.96811 q^{85} -7.93825 q^{86} +6.56086 q^{87} -4.96941 q^{88} -13.7381 q^{89} +11.8141 q^{90} -0.0168392 q^{91} +27.9538 q^{92} -11.9576 q^{93} +32.3419 q^{94} +6.72063 q^{95} +2.60662 q^{96} +13.6204 q^{97} -17.3889 q^{98} +1.36396 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9} - 7 q^{10} + 22 q^{11} - 7 q^{12} - 5 q^{13} + 6 q^{14} + 13 q^{15} + 15 q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + 10 q^{20} - 14 q^{21} - 12 q^{22} + 32 q^{23} - 15 q^{24} + 4 q^{25} + 8 q^{26} - 5 q^{27} - 11 q^{28} + 6 q^{29} - 19 q^{30} + 8 q^{31} + q^{32} - 24 q^{33} - 19 q^{34} + 15 q^{35} - 8 q^{36} - 8 q^{37} - 10 q^{38} + 31 q^{39} - 52 q^{40} - q^{41} - 49 q^{42} - 2 q^{43} + 42 q^{44} - 15 q^{45} - 25 q^{46} + 34 q^{47} - 49 q^{48} - 9 q^{49} - 27 q^{50} - 3 q^{51} - 41 q^{52} + 5 q^{53} - 40 q^{54} - 3 q^{55} + q^{56} - 22 q^{57} - 33 q^{58} + 26 q^{59} - 57 q^{60} - 26 q^{61} - 17 q^{62} - 4 q^{63} + 13 q^{64} - 25 q^{65} - 2 q^{66} + 6 q^{67} - 35 q^{68} - 2 q^{69} - 4 q^{70} + 94 q^{71} + 17 q^{72} - 22 q^{73} + 26 q^{74} - 20 q^{76} - 7 q^{77} + 54 q^{78} + 9 q^{79} + 19 q^{80} + 4 q^{81} + 15 q^{82} - 8 q^{83} + 2 q^{84} + 4 q^{85} + 9 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + 11 q^{90} - 20 q^{91} + 36 q^{92} + 12 q^{93} + 48 q^{94} + 33 q^{95} - 23 q^{96} - 29 q^{97} + 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9 - 7 * q^10 + 22 * q^11 - 7 * q^12 - 5 * q^13 + 6 * q^14 + 13 * q^15 + 15 * q^16 - 4 * q^17 - q^18 - 6 * q^19 + 10 * q^20 - 14 * q^21 - 12 * q^22 + 32 * q^23 - 15 * q^24 + 4 * q^25 + 8 * q^26 - 5 * q^27 - 11 * q^28 + 6 * q^29 - 19 * q^30 + 8 * q^31 + q^32 - 24 * q^33 - 19 * q^34 + 15 * q^35 - 8 * q^36 - 8 * q^37 - 10 * q^38 + 31 * q^39 - 52 * q^40 - q^41 - 49 * q^42 - 2 * q^43 + 42 * q^44 - 15 * q^45 - 25 * q^46 + 34 * q^47 - 49 * q^48 - 9 * q^49 - 27 * q^50 - 3 * q^51 - 41 * q^52 + 5 * q^53 - 40 * q^54 - 3 * q^55 + q^56 - 22 * q^57 - 33 * q^58 + 26 * q^59 - 57 * q^60 - 26 * q^61 - 17 * q^62 - 4 * q^63 + 13 * q^64 - 25 * q^65 - 2 * q^66 + 6 * q^67 - 35 * q^68 - 2 * q^69 - 4 * q^70 + 94 * q^71 + 17 * q^72 - 22 * q^73 + 26 * q^74 - 20 * q^76 - 7 * q^77 + 54 * q^78 + 9 * q^79 + 19 * q^80 + 4 * q^81 + 15 * q^82 - 8 * q^83 + 2 * q^84 + 4 * q^85 + 9 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + 11 * q^90 - 20 * q^91 + 36 * q^92 + 12 * q^93 + 48 * q^94 + 33 * q^95 - 23 * q^96 - 29 * q^97 + 28 * q^98 + 36 * q^99

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