LMFDB - Embedded newform 241.2.a.a.1.6

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:	$1$
Dimension:	$7$
Coefficient field:	7.7.31056073.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 $ x^7 - 3x^6 - 3x^5 + 11x^4 + x^3 - 9x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.48734$ 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)

$f(q)$	$=$	$q+0.487343 q^{2} -0.815004 q^{3} -1.76250 q^{4} +0.961999 q^{5} -0.397187 q^{6} -4.61392 q^{7} -1.83363 q^{8} -2.33577 q^{9} +O(q^{10})$	\(q+0.487343 q^{2} -0.815004 q^{3} -1.76250 q^{4} +0.961999 q^{5} -0.397187 q^{6} -4.61392 q^{7} -1.83363 q^{8} -2.33577 q^{9} +0.468824 q^{10} +1.93974 q^{11} +1.43644 q^{12} -3.85571 q^{13} -2.24856 q^{14} -0.784033 q^{15} +2.63139 q^{16} +5.40289 q^{17} -1.13832 q^{18} -4.17145 q^{19} -1.69552 q^{20} +3.76036 q^{21} +0.945321 q^{22} -1.42545 q^{23} +1.49441 q^{24} -4.07456 q^{25} -1.87905 q^{26} +4.34867 q^{27} +8.13202 q^{28} -4.85744 q^{29} -0.382093 q^{30} -7.24699 q^{31} +4.94964 q^{32} -1.58090 q^{33} +2.63306 q^{34} -4.43859 q^{35} +4.11678 q^{36} +7.12597 q^{37} -2.03293 q^{38} +3.14242 q^{39} -1.76395 q^{40} +9.18955 q^{41} +1.83259 q^{42} +2.93624 q^{43} -3.41879 q^{44} -2.24701 q^{45} -0.694685 q^{46} +2.48170 q^{47} -2.14459 q^{48} +14.2883 q^{49} -1.98571 q^{50} -4.40338 q^{51} +6.79568 q^{52} +5.64997 q^{53} +2.11930 q^{54} +1.86603 q^{55} +8.46022 q^{56} +3.39975 q^{57} -2.36724 q^{58} -11.9783 q^{59} +1.38186 q^{60} -13.9214 q^{61} -3.53177 q^{62} +10.7771 q^{63} -2.85060 q^{64} -3.70919 q^{65} -0.770440 q^{66} -7.30682 q^{67} -9.52258 q^{68} +1.16175 q^{69} -2.16312 q^{70} -14.8844 q^{71} +4.28293 q^{72} +0.240264 q^{73} +3.47279 q^{74} +3.32078 q^{75} +7.35217 q^{76} -8.94983 q^{77} +1.53144 q^{78} -3.15128 q^{79} +2.53139 q^{80} +3.46313 q^{81} +4.47847 q^{82} -2.46821 q^{83} -6.62763 q^{84} +5.19758 q^{85} +1.43096 q^{86} +3.95883 q^{87} -3.55677 q^{88} +5.55181 q^{89} -1.09506 q^{90} +17.7900 q^{91} +2.51235 q^{92} +5.90632 q^{93} +1.20944 q^{94} -4.01293 q^{95} -4.03398 q^{96} +5.27964 q^{97} +6.96330 q^{98} -4.53079 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) $ 7 * q - 4 * q^2 - 3 * q^3 + 2 * q^4 - 8 * q^5 - 5 * q^6 - 7 * q^7 - 6 * q^8 - 2 * q^9	\( 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9} + 3 q^{10} - 18 q^{11} + q^{12} - q^{13} - 6 q^{14} - 11 q^{15} + 4 q^{16} - 2 q^{17} + 8 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} + 10 q^{22} - 22 q^{23} - 3 q^{24} + 5 q^{25} + 8 q^{26} + 3 q^{27} + 9 q^{28} - 16 q^{29} + 29 q^{30} - 18 q^{31} - 6 q^{32} + 4 q^{33} + 11 q^{34} + 7 q^{35} - 7 q^{36} + 8 q^{37} + 16 q^{38} - 9 q^{39} + 14 q^{40} - 15 q^{41} + 19 q^{42} + 14 q^{43} - 4 q^{44} + 3 q^{45} + 11 q^{46} - 10 q^{47} + 31 q^{48} + 6 q^{49} - 4 q^{50} + 13 q^{51} + 27 q^{52} + 15 q^{53} + 16 q^{54} + 29 q^{55} + 13 q^{56} + 14 q^{57} + 17 q^{58} - 18 q^{59} + 15 q^{60} + 4 q^{61} + 13 q^{62} - 16 q^{63} + 2 q^{64} - 7 q^{65} + 16 q^{66} + 18 q^{67} - 15 q^{68} + 26 q^{69} + 8 q^{70} - 50 q^{71} + 30 q^{72} + 10 q^{74} + 16 q^{75} - 20 q^{76} + 17 q^{77} - 32 q^{78} - 15 q^{79} - 11 q^{80} - 9 q^{81} + 45 q^{82} - 24 q^{83} + 6 q^{84} - 2 q^{85} - 23 q^{86} + 12 q^{87} + 8 q^{88} - 13 q^{89} - 39 q^{90} - 12 q^{91} - 10 q^{92} + 14 q^{93} - 32 q^{94} - 41 q^{95} - 15 q^{96} + q^{97} + 9 q^{98} - 20 q^{99}+O(q^{100}) \) 7 * q - 4 * q^2 - 3 * q^3 + 2 * q^4 - 8 * q^5 - 5 * q^6 - 7 * q^7 - 6 * q^8 - 2 * q^9 + 3 * q^10 - 18 * q^11 + q^12 - q^13 - 6 * q^14 - 11 * q^15 + 4 * q^16 - 2 * q^17 + 8 * q^18 - 6 * q^19 - 8 * q^20 - 2 * q^21 + 10 * q^22 - 22 * q^23 - 3 * q^24 + 5 * q^25 + 8 * q^26 + 3 * q^27 + 9 * q^28 - 16 * q^29 + 29 * q^30 - 18 * q^31 - 6 * q^32 + 4 * q^33 + 11 * q^34 + 7 * q^35 - 7 * q^36 + 8 * q^37 + 16 * q^38 - 9 * q^39 + 14 * q^40 - 15 * q^41 + 19 * q^42 + 14 * q^43 - 4 * q^44 + 3 * q^45 + 11 * q^46 - 10 * q^47 + 31 * q^48 + 6 * q^49 - 4 * q^50 + 13 * q^51 + 27 * q^52 + 15 * q^53 + 16 * q^54 + 29 * q^55 + 13 * q^56 + 14 * q^57 + 17 * q^58 - 18 * q^59 + 15 * q^60 + 4 * q^61 + 13 * q^62 - 16 * q^63 + 2 * q^64 - 7 * q^65 + 16 * q^66 + 18 * q^67 - 15 * q^68 + 26 * q^69 + 8 * q^70 - 50 * q^71 + 30 * q^72 + 10 * q^74 + 16 * q^75 - 20 * q^76 + 17 * q^77 - 32 * q^78 - 15 * q^79 - 11 * q^80 - 9 * q^81 + 45 * q^82 - 24 * q^83 + 6 * q^84 - 2 * q^85 - 23 * q^86 + 12 * q^87 + 8 * q^88 - 13 * q^89 - 39 * q^90 - 12 * q^91 - 10 * q^92 + 14 * q^93 - 32 * q^94 - 41 * q^95 - 15 * q^96 + q^97 + 9 * 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 $

$2$	0.487343	0.344604	0.172302	−	0.985044i	$-0.444880\pi$
$2$	0.487343	0.344604	0.172302	+	0.985044i	$0.444880\pi$
$3$	−0.815004	−0.470543	−0.235271	−	0.971930i	$-0.575598\pi$
$3$	−0.815004	−0.470543	−0.235271	+	0.971930i	$0.575598\pi$
$4$	−1.76250	−0.881248
$5$	0.961999	0.430219	0.215110	−	0.976590i	$-0.430989\pi$
$5$	0.961999	0.430219	0.215110	+	0.976590i	$0.430989\pi$
$6$	−0.397187	−0.162151
$7$	−4.61392	−1.74390	−0.871950	−	0.489596i	$-0.837144\pi$
$7$	−4.61392	−1.74390	−0.871950	+	0.489596i	$0.837144\pi$
$8$	−1.83363	−0.648285
$9$	−2.33577	−0.778590
$10$	0.468824	0.148255
$11$	1.93974	0.584855	0.292427	−	0.956288i	$-0.405537\pi$
$11$	1.93974	0.584855	0.292427	+	0.956288i	$0.405537\pi$
$12$	1.43644	0.414665
$13$	−3.85571	−1.06938	−0.534691	−	0.845048i	$-0.679572\pi$
$13$	−3.85571	−1.06938	−0.534691	+	0.845048i	$0.679572\pi$
$14$	−2.24856	−0.600954
$15$	−0.784033	−0.202436
$16$	2.63139	0.657847
$17$	5.40289	1.31039	0.655197	−	0.755458i	$-0.272586\pi$
$17$	5.40289	1.31039	0.655197	+	0.755458i	$0.272586\pi$
$18$	−1.13832	−0.268305
$19$	−4.17145	−0.956997	−0.478498	−	0.878088i	$-0.658819\pi$
$19$	−4.17145	−0.956997	−0.478498	+	0.878088i	$0.658819\pi$
$20$	−1.69552	−0.379130
$21$	3.76036	0.820579
$22$	0.945321	0.201543
$23$	−1.42545	−0.297227	−0.148614	−	0.988895i	$-0.547481\pi$
$23$	−1.42545	−0.297227	−0.148614	+	0.988895i	$0.547481\pi$
$24$	1.49441	0.305046
$25$	−4.07456	−0.814911
$26$	−1.87905	−0.368513
$27$	4.34867	0.836902
$28$	8.13202	1.53681
$29$	−4.85744	−0.902003	−0.451002	−	0.892523i	$-0.648933\pi$
$29$	−4.85744	−0.902003	−0.451002	+	0.892523i	$0.648933\pi$
$30$	−0.382093	−0.0697604
$31$	−7.24699	−1.30160	−0.650799	−	0.759250i	$-0.725566\pi$
$31$	−7.24699	−1.30160	−0.650799	+	0.759250i	$0.725566\pi$
$32$	4.94964	0.874982
$33$	−1.58090	−0.275199
$34$	2.63306	0.451567
$35$	−4.43859	−0.750259
$36$	4.11678	0.686131
$37$	7.12597	1.17150	0.585751	−	0.810491i	$-0.300800\pi$
$37$	7.12597	1.17150	0.585751	+	0.810491i	$0.300800\pi$
$38$	−2.03293	−0.329785
$39$	3.14242	0.503190
$40$	−1.76395	−0.278905
$41$	9.18955	1.43517	0.717583	−	0.696473i	$-0.245248\pi$
$41$	9.18955	1.43517	0.717583	+	0.696473i	$0.245248\pi$
$42$	1.83259	0.282775
$43$	2.93624	0.447772	0.223886	−	0.974615i	$-0.428126\pi$
$43$	2.93624	0.447772	0.223886	+	0.974615i	$0.428126\pi$
$44$	−3.41879	−0.515402
$45$	−2.24701	−0.334964
$46$	−0.694685	−0.102426
$47$	2.48170	0.361994	0.180997	−	0.983484i	$-0.442068\pi$
$47$	2.48170	0.361994	0.180997	+	0.983484i	$0.442068\pi$
$48$	−2.14459	−0.309545
$49$	14.2883	2.04118
$50$	−1.98571	−0.280822
$51$	−4.40338	−0.616596
$52$	6.79568	0.942391
$53$	5.64997	0.776083	0.388041	−	0.921642i	$-0.373152\pi$
$53$	5.64997	0.776083	0.388041	+	0.921642i	$0.373152\pi$
$54$	2.11930	0.288400
$55$	1.86603	0.251616
$56$	8.46022	1.13054
$57$	3.39975	0.450308
$58$	−2.36724	−0.310834
$59$	−11.9783	−1.55944	−0.779718	−	0.626131i	$-0.784638\pi$
$59$	−11.9783	−1.55944	−0.779718	+	0.626131i	$0.784638\pi$
$60$	1.38186	0.178397
$61$	−13.9214	−1.78245	−0.891223	−	0.453565i	$-0.850152\pi$
$61$	−13.9214	−1.78245	−0.891223	+	0.453565i	$0.850152\pi$
$62$	−3.53177	−0.448535
$63$	10.7771	1.35778
$64$	−2.85060	−0.356325
$65$	−3.70919	−0.460069
$66$	−0.770440	−0.0948346
$67$	−7.30682	−0.892670	−0.446335	−	0.894866i	$-0.647271\pi$
$67$	−7.30682	−0.892670	−0.446335	+	0.894866i	$0.647271\pi$
$68$	−9.52258	−1.15478
$69$	1.16175	0.139858
$70$	−2.16312	−0.258542
$71$	−14.8844	−1.76645	−0.883226	−	0.468948i	$-0.844633\pi$
$71$	−14.8844	−1.76645	−0.883226	+	0.468948i	$0.844633\pi$
$72$	4.28293	0.504748
$73$	0.240264	0.0281208	0.0140604	−	0.999901i	$-0.495524\pi$
$73$	0.240264	0.0281208	0.0140604	+	0.999901i	$0.495524\pi$
$74$	3.47279	0.403704
$75$	3.32078	0.383450
$76$	7.35217	0.843352
$77$	−8.94983	−1.01993
$78$	1.53144	0.173401
$79$	−3.15128	−0.354546	−0.177273	−	0.984162i	$-0.556728\pi$
$79$	−3.15128	−0.354546	−0.177273	+	0.984162i	$0.556728\pi$
$80$	2.53139	0.283018
$81$	3.46313	0.384792
$82$	4.47847	0.494564
$83$	−2.46821	−0.270922	−0.135461	−	0.990783i	$-0.543251\pi$
$83$	−2.46821	−0.270922	−0.135461	+	0.990783i	$0.543251\pi$
$84$	−6.62763	−0.723134
$85$	5.19758	0.563757
$86$	1.43096	0.154304
$87$	3.95883	0.424431
$88$	−3.55677	−0.379153
$89$	5.55181	0.588491	0.294246	−	0.955730i	$-0.404932\pi$
$89$	5.55181	0.588491	0.294246	+	0.955730i	$0.404932\pi$
$90$	−1.09506	−0.115430
$91$	17.7900	1.86489
$92$	2.51235	0.261931
$93$	5.90632	0.612457
$94$	1.20944	0.124744
$95$	−4.01293	−0.411718
$96$	−4.03398	−0.411716
$97$	5.27964	0.536067	0.268033	−	0.963410i	$-0.413626\pi$
$97$	5.27964	0.536067	0.268033	+	0.963410i	$0.413626\pi$
$98$	6.96330	0.703400
$99$	−4.53079	−0.455362
$100$	7.18139	0.718139
$101$	−12.4239	−1.23623	−0.618113	−	0.786089i	$-0.712103\pi$
$101$	−12.4239	−1.23623	−0.618113	+	0.786089i	$0.712103\pi$
$102$	−2.14596	−0.212481
$103$	−9.80533	−0.966148	−0.483074	−	0.875580i	$-0.660480\pi$
$103$	−9.80533	−0.966148	−0.483074	+	0.875580i	$0.660480\pi$
$104$	7.06994	0.693264
$105$	3.61747	0.353029
$106$	2.75347	0.267441
$107$	−9.15031	−0.884593	−0.442297	−	0.896869i	$-0.645836\pi$
$107$	−9.15031	−0.884593	−0.442297	+	0.896869i	$0.645836\pi$
$108$	−7.66452	−0.737519
$109$	3.24534	0.310847	0.155424	−	0.987848i	$-0.450326\pi$
$109$	3.24534	0.310847	0.155424	+	0.987848i	$0.450326\pi$
$110$	0.909398	0.0867077
$111$	−5.80769	−0.551241
$112$	−12.1410	−1.14722
$113$	−0.842874	−0.0792909	−0.0396455	−	0.999214i	$-0.512623\pi$
$113$	−0.842874	−0.0792909	−0.0396455	+	0.999214i	$0.512623\pi$
$114$	1.65684	0.155178
$115$	−1.37128	−0.127873
$116$	8.56121	0.794889
$117$	9.00605	0.832610
$118$	−5.83752	−0.537387
$119$	−24.9285	−2.28520
$120$	1.43762	0.131237
$121$	−7.23740	−0.657945
$122$	−6.78448	−0.614238
$123$	−7.48952	−0.675307
$124$	12.7728	1.14703
$125$	−8.72972	−0.780810
$126$	5.25213	0.467897
$127$	11.3416	1.00641	0.503203	−	0.864168i	$-0.332155\pi$
$127$	11.3416	1.00641	0.503203	+	0.864168i	$0.332155\pi$
$128$	−11.2885	−0.997773
$129$	−2.39305	−0.210696
$130$	−1.80765	−0.158541
$131$	14.1261	1.23421	0.617103	−	0.786882i	$-0.288306\pi$
$131$	14.1261	1.23421	0.617103	+	0.786882i	$0.288306\pi$
$132$	2.78633	0.242519
$133$	19.2468	1.66891
$134$	−3.56093	−0.307617
$135$	4.18342	0.360051
$136$	−9.90689	−0.849509
$137$	−12.9555	−1.10686	−0.553430	−	0.832896i	$-0.686681\pi$
$137$	−12.9555	−1.10686	−0.553430	+	0.832896i	$0.686681\pi$
$138$	0.566170	0.0481956
$139$	8.23606	0.698574	0.349287	−	0.937016i	$-0.386424\pi$
$139$	8.23606	0.698574	0.349287	+	0.937016i	$0.386424\pi$
$140$	7.82300	0.661164
$141$	−2.02260	−0.170333
$142$	−7.25380	−0.608726
$143$	−7.47909	−0.625433
$144$	−6.14631	−0.512193
$145$	−4.67285	−0.388059
$146$	0.117091	0.00969054
$147$	−11.6450	−0.960464
$148$	−12.5595	−1.03238
$149$	4.48606	0.367513	0.183756	−	0.982972i	$-0.441174\pi$
$149$	4.48606	0.367513	0.183756	+	0.982972i	$0.441174\pi$
$150$	1.61836	0.132138
$151$	0.0933624	0.00759773	0.00379886	−	0.999993i	$-0.498791\pi$
$151$	0.0933624	0.00759773	0.00379886	+	0.999993i	$0.498791\pi$
$152$	7.64889	0.620407
$153$	−12.6199	−1.02026
$154$	−4.36164	−0.351471
$155$	−6.97160	−0.559972
$156$	−5.53850	−0.443435
$157$	−10.1337	−0.808760	−0.404380	−	0.914591i	$-0.632513\pi$
$157$	−10.1337	−0.808760	−0.404380	+	0.914591i	$0.632513\pi$
$158$	−1.53575	−0.122178
$159$	−4.60474	−0.365180
$160$	4.76155	0.376434
$161$	6.57693	0.518334
$162$	1.68773	0.132601
$163$	7.49804	0.587292	0.293646	−	0.955914i	$-0.405131\pi$
$163$	7.49804	0.587292	0.293646	+	0.955914i	$0.405131\pi$
$164$	−16.1965	−1.26474
$165$	−1.52082	−0.118396
$166$	−1.20287	−0.0933606
$167$	17.7922	1.37680	0.688399	−	0.725332i	$-0.258314\pi$
$167$	17.7922	1.37680	0.688399	+	0.725332i	$0.258314\pi$
$168$	−6.89511	−0.531969
$169$	1.86650	0.143577
$170$	2.53301	0.194273
$171$	9.74355	0.745108
$172$	−5.17511	−0.394599
$173$	18.4927	1.40597	0.702987	−	0.711203i	$-0.251849\pi$
$173$	18.4927	1.40597	0.702987	+	0.711203i	$0.251849\pi$
$174$	1.92931	0.146260
$175$	18.7997	1.42112
$176$	5.10421	0.384745
$177$	9.76232	0.733781
$178$	2.70564	0.202796
$179$	−17.3387	−1.29595	−0.647977	−	0.761660i	$-0.724385\pi$
$179$	−17.3387	−1.29595	−0.647977	+	0.761660i	$0.724385\pi$
$180$	3.96034	0.295187
$181$	17.7124	1.31655	0.658275	−	0.752778i	$-0.271287\pi$
$181$	17.7124	1.31655	0.658275	+	0.752778i	$0.271287\pi$
$182$	8.66981	0.642649
$183$	11.3460	0.838717
$184$	2.61375	0.192688
$185$	6.85518	0.504003
$186$	2.87841	0.211055
$187$	10.4802	0.766390
$188$	−4.37400	−0.319006
$189$	−20.0644	−1.45947
$190$	−1.95568	−0.141880
$191$	13.2440	0.958303	0.479151	−	0.877732i	$-0.340944\pi$
$191$	13.2440	0.958303	0.479151	+	0.877732i	$0.340944\pi$
$192$	2.32325	0.167666
$193$	−25.5030	−1.83574	−0.917872	−	0.396877i	$-0.870094\pi$
$193$	−25.5030	−1.83574	−0.917872	+	0.396877i	$0.870094\pi$
$194$	2.57300	0.184731
$195$	3.02300	0.216482
$196$	−25.1831	−1.79879
$197$	−15.0303	−1.07087	−0.535433	−	0.844578i	$-0.679851\pi$
$197$	−15.0303	−1.07087	−0.535433	+	0.844578i	$0.679851\pi$
$198$	−2.20805	−0.156919
$199$	−19.3801	−1.37382	−0.686911	−	0.726742i	$-0.741034\pi$
$199$	−19.3801	−1.37382	−0.686911	+	0.726742i	$0.741034\pi$
$200$	7.47122	0.528295
$201$	5.95508	0.420039
$202$	−6.05472	−0.426008
$203$	22.4118	1.57300
$204$	7.76094	0.543374
$205$	8.84034	0.617436
$206$	−4.77856	−0.332938
$207$	3.32953	0.231418
$208$	−10.1459	−0.703489
$209$	−8.09154	−0.559704
$210$	1.76295	0.121655
$211$	27.9383	1.92335	0.961675	−	0.274192i	$-0.0884105\pi$
$211$	27.9383	1.92335	0.961675	+	0.274192i	$0.0884105\pi$
$212$	−9.95805	−0.683922
$213$	12.1308	0.831191
$214$	−4.45934	−0.304834
$215$	2.82466	0.192640
$216$	−7.97384	−0.542551
$217$	33.4370	2.26985
$218$	1.58160	0.107119
$219$	−0.195816	−0.0132320
$220$	−3.28887	−0.221736
$221$	−20.8320	−1.40131
$222$	−2.83034	−0.189960
$223$	−0.387500	−0.0259489	−0.0129745	−	0.999916i	$-0.504130\pi$
$223$	−0.387500	−0.0259489	−0.0129745	+	0.999916i	$0.504130\pi$
$224$	−22.8373	−1.52588
$225$	9.51722	0.634482
$226$	−0.410769	−0.0273240
$227$	10.2778	0.682161	0.341081	−	0.940034i	$-0.389207\pi$
$227$	10.2778	0.682161	0.341081	+	0.940034i	$0.389207\pi$
$228$	−5.99204	−0.396833
$229$	−10.5346	−0.696147	−0.348074	−	0.937467i	$-0.613164\pi$
$229$	−10.5346	−0.696147	−0.348074	+	0.937467i	$0.613164\pi$
$230$	−0.668286	−0.0440655
$231$	7.29414	0.479919
$232$	8.90673	0.584755
$233$	25.6725	1.68186	0.840932	−	0.541141i	$-0.182007\pi$
$233$	25.6725	1.68186	0.840932	+	0.541141i	$0.182007\pi$
$234$	4.38904	0.286920
$235$	2.38740	0.155737
$236$	21.1116	1.37425
$237$	2.56830	0.166829
$238$	−12.1488	−0.787487
$239$	−25.1312	−1.62560	−0.812801	−	0.582542i	$-0.802058\pi$
$239$	−25.1312	−1.62560	−0.812801	+	0.582542i	$0.802058\pi$
$240$	−2.06309	−0.133172
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−3.52710	−0.226730
$243$	−15.8685	−1.01796
$244$	24.5363	1.57078
$245$	13.7453	0.878157
$246$	−3.64997	−0.232713
$247$	16.0839	1.02339
$248$	13.2883	0.843806
$249$	2.01160	0.127480
$250$	−4.25437	−0.269070
$251$	2.52238	0.159211	0.0796055	−	0.996826i	$-0.474634\pi$
$251$	2.52238	0.159211	0.0796055	+	0.996826i	$0.474634\pi$
$252$	−18.9945	−1.19654
$253$	−2.76501	−0.173835
$254$	5.52726	0.346811
$255$	−4.23605	−0.265272
$256$	0.199817	0.0124886
$257$	3.92348	0.244740	0.122370	−	0.992485i	$-0.460951\pi$
$257$	3.92348	0.244740	0.122370	+	0.992485i	$0.460951\pi$
$258$	−1.16623	−0.0726066
$259$	−32.8787	−2.04298
$260$	6.53744	0.405435
$261$	11.3458	0.702290
$262$	6.88428	0.425312
$263$	6.24984	0.385382	0.192691	−	0.981260i	$-0.438279\pi$
$263$	6.24984	0.385382	0.192691	+	0.981260i	$0.438279\pi$
$264$	2.89878	0.178407
$265$	5.43527	0.333886
$266$	9.37978	0.575111
$267$	−4.52475	−0.276910
$268$	12.8782	0.786664
$269$	20.4943	1.24956	0.624780	−	0.780801i	$-0.285189\pi$
$269$	20.4943	1.24956	0.624780	+	0.780801i	$0.285189\pi$
$270$	2.03876	0.124075
$271$	15.3179	0.930499	0.465249	−	0.885180i	$-0.345965\pi$
$271$	15.3179	0.930499	0.465249	+	0.885180i	$0.345965\pi$
$272$	14.2171	0.862039
$273$	−14.4989	−0.877512
$274$	−6.31376	−0.381428
$275$	−7.90359	−0.476605
$276$	−2.04758	−0.123250
$277$	3.26388	0.196108	0.0980539	−	0.995181i	$-0.468738\pi$
$277$	3.26388	0.196108	0.0980539	+	0.995181i	$0.468738\pi$
$278$	4.01379	0.240731
$279$	16.9273	1.01341
$280$	8.13872	0.486382
$281$	−12.4791	−0.744442	−0.372221	−	0.928144i	$-0.621404\pi$
$281$	−12.4791	−0.744442	−0.372221	+	0.928144i	$0.621404\pi$
$282$	−0.985700	−0.0586976
$283$	−15.8115	−0.939899	−0.469949	−	0.882693i	$-0.655728\pi$
$283$	−15.8115	−0.939899	−0.469949	+	0.882693i	$0.655728\pi$
$284$	26.2337	1.55668
$285$	3.27056	0.193731
$286$	−3.64488	−0.215526
$287$	−42.3999	−2.50279
$288$	−11.5612	−0.681252
$289$	12.1913	0.717133
$290$	−2.27728	−0.133727
$291$	−4.30293	−0.252242
$292$	−0.423465	−0.0247814
$293$	18.7147	1.09333	0.546663	−	0.837353i	$-0.315898\pi$
$293$	18.7147	1.09333	0.546663	+	0.837353i	$0.315898\pi$
$294$	−5.67512	−0.330979
$295$	−11.5231	−0.670899
$296$	−13.0664	−0.759467
$297$	8.43530	0.489466
$298$	2.18625	0.126646
$299$	5.49613	0.317849
$300$	−5.85286	−0.337915
$301$	−13.5476	−0.780870
$302$	0.0454995	0.00261820
$303$	10.1255	0.581697
$304$	−10.9767	−0.629557
$305$	−13.3923	−0.766843
$306$	−6.15023	−0.351585
$307$	5.23477	0.298764	0.149382	−	0.988780i	$-0.452272\pi$
$307$	5.23477	0.298764	0.149382	+	0.988780i	$0.452272\pi$
$308$	15.7740	0.898809
$309$	7.99138	0.454614
$310$	−3.39756	−0.192969
$311$	−26.6878	−1.51332	−0.756662	−	0.653806i	$-0.773171\pi$
$311$	−26.6878	−1.51332	−0.756662	+	0.653806i	$0.773171\pi$
$312$	−5.76202	−0.326210
$313$	6.24141	0.352786	0.176393	−	0.984320i	$-0.443557\pi$
$313$	6.24141	0.352786	0.176393	+	0.984320i	$0.443557\pi$
$314$	−4.93861	−0.278702
$315$	10.3675	0.584144
$316$	5.55412	0.312443
$317$	6.89526	0.387276	0.193638	−	0.981073i	$-0.437971\pi$
$317$	6.89526	0.387276	0.193638	+	0.981073i	$0.437971\pi$
$318$	−2.24409	−0.125842
$319$	−9.42218	−0.527541
$320$	−2.74227	−0.153298
$321$	7.45753	0.416239
$322$	3.20522	0.178620
$323$	−22.5379	−1.25404
$324$	−6.10375	−0.339097
$325$	15.7103	0.871451
$326$	3.65412	0.202383
$327$	−2.64497	−0.146267
$328$	−16.8502	−0.930397
$329$	−11.4504	−0.631281
$330$	−0.741163	−0.0407997
$331$	−13.5697	−0.745860	−0.372930	−	0.927859i	$-0.621647\pi$
$331$	−13.5697	−0.745860	−0.372930	+	0.927859i	$0.621647\pi$
$332$	4.35022	0.238749
$333$	−16.6446	−0.912119
$334$	8.67089	0.474450
$335$	−7.02916	−0.384044
$336$	9.89497	0.539815
$337$	−20.2288	−1.10193	−0.550966	−	0.834528i	$-0.685740\pi$
$337$	−20.2288	−1.10193	−0.550966	+	0.834528i	$0.685740\pi$
$338$	0.909627	0.0494772
$339$	0.686946	0.0373098
$340$	−9.16072	−0.496810
$341$	−14.0573	−0.761245
$342$	4.74845	0.256767
$343$	−33.6276	−1.81572
$344$	−5.38397	−0.290284
$345$	1.11760	0.0601696
$346$	9.01229	0.484504
$347$	1.52458	0.0818437	0.0409219	−	0.999162i	$-0.486971\pi$
$347$	1.52458	0.0818437	0.0409219	+	0.999162i	$0.486971\pi$
$348$	−6.97742	−0.374029
$349$	16.5585	0.886358	0.443179	−	0.896433i	$-0.353851\pi$
$349$	16.5585	0.886358	0.443179	+	0.896433i	$0.353851\pi$
$350$	9.16191	0.489724
$351$	−16.7672	−0.894968
$352$	9.60104	0.511737
$353$	34.6802	1.84584	0.922920	−	0.384992i	$-0.125796\pi$
$353$	34.6802	1.84584	0.922920	+	0.384992i	$0.125796\pi$
$354$	4.75760	0.252864
$355$	−14.3188	−0.759961
$356$	−9.78505	−0.518607
$357$	20.3168	1.07528
$358$	−8.44989	−0.446590
$359$	18.1341	0.957084	0.478542	−	0.878065i	$-0.341165\pi$
$359$	18.1341	0.957084	0.478542	+	0.878065i	$0.341165\pi$
$360$	4.12018	0.217152
$361$	−1.59899	−0.0841573
$362$	8.63200	0.453688
$363$	5.89850	0.309591
$364$	−31.3547	−1.64343
$365$	0.231134	0.0120981
$366$	5.52937	0.289025
$367$	−10.9879	−0.573566	−0.286783	−	0.957996i	$-0.592586\pi$
$367$	−10.9879	−0.573566	−0.286783	+	0.957996i	$0.592586\pi$
$368$	−3.75092	−0.195530
$369$	−21.4647	−1.11741
$370$	3.34082	0.173681
$371$	−26.0685	−1.35341
$372$	−10.4099	−0.539727
$373$	5.23646	0.271134	0.135567	−	0.990768i	$-0.456714\pi$
$373$	5.23646	0.271134	0.135567	+	0.990768i	$0.456714\pi$
$374$	5.10747	0.264101
$375$	7.11475	0.367404
$376$	−4.55052	−0.234675
$377$	18.7289	0.964586
$378$	−9.77827	−0.502940
$379$	8.07101	0.414580	0.207290	−	0.978280i	$-0.433536\pi$
$379$	8.07101	0.414580	0.207290	+	0.978280i	$0.433536\pi$
$380$	7.07278	0.362826
$381$	−9.24346	−0.473557
$382$	6.45438	0.330235
$383$	2.46503	0.125957	0.0629785	−	0.998015i	$-0.479940\pi$
$383$	2.46503	0.125957	0.0629785	+	0.998015i	$0.479940\pi$
$384$	9.20017	0.469494
$385$	−8.60973	−0.438792
$386$	−12.4287	−0.632604
$387$	−6.85838	−0.348631
$388$	−9.30535	−0.472408
$389$	−28.7159	−1.45595	−0.727977	−	0.685601i	$-0.759539\pi$
$389$	−28.7159	−1.45595	−0.727977	+	0.685601i	$0.759539\pi$
$390$	1.47324	0.0746004
$391$	−7.70157	−0.389485
$392$	−26.1994	−1.32327
$393$	−11.5128	−0.580746
$394$	−7.32492	−0.369024
$395$	−3.03153	−0.152533
$396$	7.98550	0.401287
$397$	12.0605	0.605301	0.302651	−	0.953102i	$-0.402129\pi$
$397$	12.0605	0.605301	0.302651	+	0.953102i	$0.402129\pi$
$398$	−9.44478	−0.473424
$399$	−15.6862	−0.785291
$400$	−10.7217	−0.536087
$401$	−31.7082	−1.58343	−0.791716	−	0.610890i	$-0.790812\pi$
$401$	−31.7082	−1.58343	−0.791716	+	0.610890i	$0.790812\pi$
$402$	2.90217	0.144747
$403$	27.9423	1.39190
$404$	21.8971	1.08942
$405$	3.33152	0.165545
$406$	10.9223	0.542063
$407$	13.8225	0.685158
$408$	8.07415	0.399730
$409$	−14.1893	−0.701617	−0.350809	−	0.936447i	$-0.614093\pi$
$409$	−14.1893	−0.701617	−0.350809	+	0.936447i	$0.614093\pi$
$410$	4.30828	0.212771
$411$	10.5587	0.520825
$412$	17.2819	0.851416
$413$	55.2668	2.71950
$414$	1.62262	0.0797476
$415$	−2.37442	−0.116556
$416$	−19.0844	−0.935689
$417$	−6.71242	−0.328709
$418$	−3.94336	−0.192876
$419$	31.1014	1.51941	0.759703	−	0.650271i	$-0.225345\pi$
$419$	31.1014	1.51941	0.759703	+	0.650271i	$0.225345\pi$
$420$	−6.37578	−0.311106
$421$	−27.4415	−1.33742	−0.668709	−	0.743524i	$-0.733153\pi$
$421$	−27.4415	−1.33742	−0.668709	+	0.743524i	$0.733153\pi$
$422$	13.6155	0.662794
$423$	−5.79669	−0.281845
$424$	−10.3599	−0.503123
$425$	−22.0144	−1.06786
$426$	5.91188	0.286431
$427$	64.2321	3.10841
$428$	16.1274	0.779546
$429$	6.09548	0.294293
$430$	1.37658	0.0663846
$431$	−14.1005	−0.679199	−0.339599	−	0.940570i	$-0.610291\pi$
$431$	−14.1005	−0.679199	−0.339599	+	0.940570i	$0.610291\pi$
$432$	11.4430	0.550553
$433$	−17.7403	−0.852546	−0.426273	−	0.904595i	$-0.640174\pi$
$433$	−17.7403	−0.852546	−0.426273	+	0.904595i	$0.640174\pi$
$434$	16.2953	0.782200
$435$	3.80839	0.182598
$436$	−5.71991	−0.273934
$437$	5.94621	0.284446
$438$	−0.0954297	−0.00455981
$439$	−2.52447	−0.120486	−0.0602431	−	0.998184i	$-0.519188\pi$
$439$	−2.52447	−0.120486	−0.0602431	+	0.998184i	$0.519188\pi$
$440$	−3.42161	−0.163119
$441$	−33.3741	−1.58924
$442$	−10.1523	−0.482897
$443$	−16.8382	−0.800008	−0.400004	−	0.916513i	$-0.630991\pi$
$443$	−16.8382	−0.800008	−0.400004	+	0.916513i	$0.630991\pi$
$444$	10.2360	0.485780
$445$	5.34084	0.253180
$446$	−0.188846	−0.00894211
$447$	−3.65616	−0.172930
$448$	13.1524	0.621394
$449$	−30.5688	−1.44263	−0.721314	−	0.692608i	$-0.756462\pi$
$449$	−30.5688	−1.44263	−0.721314	+	0.692608i	$0.756462\pi$
$450$	4.63816	0.218645
$451$	17.8254	0.839364
$452$	1.48556	0.0698750
$453$	−0.0760907	−0.00357505
$454$	5.00882	0.235075
$455$	17.1139	0.802313
$456$	−6.23387	−0.291928
$457$	−32.7043	−1.52984	−0.764922	−	0.644123i	$-0.777223\pi$
$457$	−32.7043	−1.52984	−0.764922	+	0.644123i	$0.777223\pi$
$458$	−5.13398	−0.239895
$459$	23.4954	1.09667
$460$	2.41688	0.112688
$461$	12.3932	0.577210	0.288605	−	0.957448i	$-0.406809\pi$
$461$	12.3932	0.577210	0.288605	+	0.957448i	$0.406809\pi$
$462$	3.55475	0.165382
$463$	12.1379	0.564094	0.282047	−	0.959401i	$-0.408987\pi$
$463$	12.1379	0.564094	0.282047	+	0.959401i	$0.408987\pi$
$464$	−12.7818	−0.593380
$465$	5.68188	0.263491
$466$	12.5113	0.579577
$467$	5.38203	0.249051	0.124525	−	0.992216i	$-0.460259\pi$
$467$	5.38203	0.249051	0.124525	+	0.992216i	$0.460259\pi$
$468$	−15.8731	−0.733736
$469$	33.7131	1.55673
$470$	1.16348	0.0536675
$471$	8.25903	0.380556
$472$	21.9637	1.01096
$473$	5.69555	0.261882
$474$	1.25165	0.0574900
$475$	16.9968	0.779868
$476$	43.9365	2.01382
$477$	−13.1970	−0.604250
$478$	−12.2475	−0.560188
$479$	−25.3752	−1.15942	−0.579711	−	0.814822i	$-0.696834\pi$
$479$	−25.3752	−1.15942	−0.579711	+	0.814822i	$0.696834\pi$
$480$	−3.88068	−0.177128
$481$	−27.4757	−1.25278
$482$	−0.487343	−0.0221979
$483$	−5.36022	−0.243898
$484$	12.7559	0.579813
$485$	5.07901	0.230626
$486$	−7.73339	−0.350794
$487$	−10.4243	−0.472369	−0.236185	−	0.971708i	$-0.575897\pi$
$487$	−10.4243	−0.472369	−0.236185	+	0.971708i	$0.575897\pi$
$488$	25.5266	1.15553
$489$	−6.11093	−0.276346
$490$	6.69869	0.302616
$491$	34.2858	1.54730	0.773649	−	0.633614i	$-0.218429\pi$
$491$	34.2858	1.54730	0.773649	+	0.633614i	$0.218429\pi$
$492$	13.2002	0.595113
$493$	−26.2442	−1.18198
$494$	7.83839	0.352666
$495$	−4.35862	−0.195905
$496$	−19.0696	−0.856252
$497$	68.6754	3.08051
$498$	0.980341	0.0439301
$499$	15.9672	0.714792	0.357396	−	0.933953i	$-0.383665\pi$
$499$	15.9672	0.714792	0.357396	+	0.933953i	$0.383665\pi$
$500$	15.3861	0.688087
$501$	−14.5007	−0.647842
$502$	1.22926	0.0548647
$503$	−4.53174	−0.202060	−0.101030	−	0.994883i	$-0.532214\pi$
$503$	−4.53174	−0.202060	−0.101030	+	0.994883i	$0.532214\pi$
$504$	−19.7611	−0.880230
$505$	−11.9518	−0.531849
$506$	−1.34751	−0.0599041
$507$	−1.52121	−0.0675591
$508$	−19.9896	−0.886893
$509$	−4.08798	−0.181197	−0.0905983	−	0.995888i	$-0.528878\pi$
$509$	−4.08798	−0.181197	−0.0905983	+	0.995888i	$0.528878\pi$
$510$	−2.06441	−0.0914136
$511$	−1.10856	−0.0490398
$512$	22.6744	1.00208
$513$	−18.1403	−0.800913
$514$	1.91208	0.0843384
$515$	−9.43272	−0.415655
$516$	4.21774	0.185675
$517$	4.81387	0.211714
$518$	−16.0232	−0.704019
$519$	−15.0716	−0.661571
$520$	6.80127	0.298256
$521$	34.2884	1.50220	0.751102	−	0.660186i	$-0.229523\pi$
$521$	34.2884	1.50220	0.751102	+	0.660186i	$0.229523\pi$
$522$	5.52932	0.242012
$523$	33.7724	1.47676	0.738382	−	0.674382i	$-0.235590\pi$
$523$	33.7724	1.47676	0.738382	+	0.674382i	$0.235590\pi$
$524$	−24.8973	−1.08764
$525$	−15.3218	−0.668699
$526$	3.04582	0.132804
$527$	−39.1547	−1.70561
$528$	−4.15995	−0.181039
$529$	−20.9681	−0.911656
$530$	2.64884	0.115058
$531$	27.9784	1.21416
$532$	−33.9223	−1.47072
$533$	−35.4322	−1.53474
$534$	−2.20511	−0.0954243
$535$	−8.80259	−0.380569
$536$	13.3980	0.578705
$537$	14.1311	0.609801
$538$	9.98777	0.430603
$539$	27.7156	1.19380
$540$	−7.37326	−0.317295
$541$	−31.0330	−1.33421	−0.667106	−	0.744963i	$-0.732467\pi$
$541$	−31.0330	−1.33421	−0.667106	+	0.744963i	$0.732467\pi$
$542$	7.46510	0.320653
$543$	−14.4356	−0.619492
$544$	26.7424	1.14657
$545$	3.12202	0.133733
$546$	−7.06593	−0.302394
$547$	−33.0104	−1.41142	−0.705712	−	0.708499i	$-0.749373\pi$
$547$	−33.0104	−1.41142	−0.705712	+	0.708499i	$0.749373\pi$
$548$	22.8340	0.975418
$549$	32.5171	1.38779
$550$	−3.85176	−0.164240
$551$	20.2626	0.863214
$552$	−2.13021	−0.0906679
$553$	14.5398	0.618293
$554$	1.59063	0.0675795
$555$	−5.58699	−0.237155
$556$	−14.5160	−0.615617
$557$	15.4826	0.656019	0.328010	−	0.944674i	$-0.393622\pi$
$557$	15.4826	0.656019	0.328010	+	0.944674i	$0.393622\pi$
$558$	8.24940	0.349225
$559$	−11.3213	−0.478840
$560$	−11.6797	−0.493555
$561$	−8.54142	−0.360619
$562$	−6.08161	−0.256537
$563$	6.21072	0.261751	0.130875	−	0.991399i	$-0.458221\pi$
$563$	6.21072	0.261751	0.130875	+	0.991399i	$0.458221\pi$
$564$	3.56482	0.150106
$565$	−0.810845	−0.0341125
$566$	−7.70565	−0.323893
$567$	−15.9786	−0.671038
$568$	27.2924	1.14516
$569$	−20.3014	−0.851078	−0.425539	−	0.904940i	$-0.639916\pi$
$569$	−20.3014	−0.851078	−0.425539	+	0.904940i	$0.639916\pi$
$570$	1.59388	0.0667604
$571$	−38.5209	−1.61205	−0.806024	−	0.591882i	$-0.798385\pi$
$571$	−38.5209	−1.61205	−0.806024	+	0.591882i	$0.798385\pi$
$572$	13.1819	0.551161
$573$	−10.7939	−0.450922
$574$	−20.6633	−0.862469
$575$	5.80809	0.242214
$576$	6.65834	0.277431
$577$	19.3481	0.805472	0.402736	−	0.915316i	$-0.368059\pi$
$577$	19.3481	0.805472	0.402736	+	0.915316i	$0.368059\pi$
$578$	5.94133	0.247127
$579$	20.7850	0.863795
$580$	8.23588	0.341976
$581$	11.3881	0.472460
$582$	−2.09700	−0.0869236
$583$	10.9595	0.453896
$584$	−0.440555	−0.0182303
$585$	8.66381	0.358205
$586$	9.12050	0.376764
$587$	−20.0183	−0.826243	−0.413122	−	0.910676i	$-0.635562\pi$
$587$	−20.0183	−0.826243	−0.413122	+	0.910676i	$0.635562\pi$
$588$	20.5243	0.846407
$589$	30.2305	1.24562
$590$	−5.61569	−0.231194
$591$	12.2498	0.503888
$592$	18.7512	0.770668
$593$	12.5904	0.517027	0.258513	−	0.966008i	$-0.416767\pi$
$593$	12.5904	0.517027	0.258513	+	0.966008i	$0.416767\pi$
$594$	4.11089	0.168672
$595$	−23.9812	−0.983135
$596$	−7.90667	−0.323870
$597$	15.7949	0.646441
$598$	2.67850	0.109532
$599$	24.4282	0.998107	0.499054	−	0.866571i	$-0.333681\pi$
$599$	24.4282	0.998107	0.499054	+	0.866571i	$0.333681\pi$
$600$	−6.08907	−0.248585
$601$	9.02256	0.368038	0.184019	−	0.982923i	$-0.441089\pi$
$601$	9.02256	0.368038	0.184019	+	0.982923i	$0.441089\pi$
$602$	−6.60233	−0.269091
$603$	17.0670	0.695024
$604$	−0.164551	−0.00669548
$605$	−6.96237	−0.283061
$606$	4.93462	0.200455
$607$	−19.0044	−0.771364	−0.385682	−	0.922632i	$-0.626034\pi$
$607$	−19.0044	−0.771364	−0.385682	+	0.922632i	$0.626034\pi$
$608$	−20.6472	−0.837355
$609$	−18.2657	−0.740165
$610$	−6.52666	−0.264257
$611$	−9.56873	−0.387110
$612$	22.2426	0.899102
$613$	3.38617	0.136766	0.0683831	−	0.997659i	$-0.478216\pi$
$613$	3.38617	0.136766	0.0683831	+	0.997659i	$0.478216\pi$
$614$	2.55113	0.102955
$615$	−7.20491	−0.290530
$616$	16.4106	0.661204
$617$	−33.9920	−1.36847	−0.684234	−	0.729263i	$-0.739863\pi$
$617$	−33.9920	−1.36847	−0.684234	+	0.729263i	$0.739863\pi$
$618$	3.89455	0.156662
$619$	29.6477	1.19164	0.595822	−	0.803117i	$-0.296826\pi$
$619$	29.6477	1.19164	0.595822	+	0.803117i	$0.296826\pi$
$620$	12.2874	0.493475
$621$	−6.19882	−0.248750
$622$	−13.0061	−0.521497
$623$	−25.6156	−1.02627
$624$	8.26892	0.331022
$625$	11.9748	0.478992
$626$	3.04171	0.121571
$627$	6.59464	0.263364
$628$	17.8607	0.712718
$629$	38.5008	1.53513
$630$	5.05254	0.201298
$631$	14.6241	0.582176	0.291088	−	0.956696i	$-0.405983\pi$
$631$	14.6241	0.582176	0.291088	+	0.956696i	$0.405983\pi$
$632$	5.77827	0.229847
$633$	−22.7698	−0.905018
$634$	3.36036	0.133457
$635$	10.9106	0.432975
$636$	8.11585	0.321814
$637$	−55.0915	−2.18280
$638$	−4.59184	−0.181793
$639$	34.7665	1.37534
$640$	−10.8595	−0.429261
$641$	4.17547	0.164921	0.0824606	−	0.996594i	$-0.473722\pi$
$641$	4.17547	0.164921	0.0824606	+	0.996594i	$0.473722\pi$
$642$	3.63438	0.143437
$643$	23.1928	0.914635	0.457317	−	0.889304i	$-0.348810\pi$
$643$	23.1928	0.914635	0.457317	+	0.889304i	$0.348810\pi$
$644$	−11.5918	−0.456781
$645$	−2.30211	−0.0906455
$646$	−10.9837	−0.432148
$647$	−31.0975	−1.22257	−0.611284	−	0.791411i	$-0.709347\pi$
$647$	−31.0975	−1.22257	−0.611284	+	0.791411i	$0.709347\pi$
$648$	−6.35008	−0.249455
$649$	−23.2347	−0.912043
$650$	7.65632	0.300305
$651$	−27.2513	−1.06806
$652$	−13.2153	−0.517550
$653$	−31.5439	−1.23441	−0.617204	−	0.786803i	$-0.711735\pi$
$653$	−31.5439	−1.23441	−0.617204	+	0.786803i	$0.711735\pi$
$654$	−1.28901	−0.0504041
$655$	13.5893	0.530979
$656$	24.1813	0.944120
$657$	−0.561202	−0.0218946
$658$	−5.58027	−0.217542
$659$	25.2754	0.984590	0.492295	−	0.870428i	$-0.336158\pi$
$659$	25.2754	0.984590	0.492295	+	0.870428i	$0.336158\pi$
$660$	2.68044	0.104336
$661$	−21.7628	−0.846476	−0.423238	−	0.906018i	$-0.639107\pi$
$661$	−21.7628	−0.846476	−0.423238	+	0.906018i	$0.639107\pi$
$662$	−6.61312	−0.257026
$663$	16.9781	0.659377
$664$	4.52578	0.175634
$665$	18.5154	0.717995
$666$	−8.11164	−0.314320
$667$	6.92404	0.268100
$668$	−31.3586	−1.21330
$669$	0.315814	0.0122101
$670$	−3.42561	−0.132343
$671$	−27.0038	−1.04247
$672$	18.6125	0.717991
$673$	−37.2710	−1.43669	−0.718346	−	0.695686i	$-0.755101\pi$
$673$	−37.2710	−1.43669	−0.718346	+	0.695686i	$0.755101\pi$
$674$	−9.85835	−0.379730
$675$	−17.7189	−0.682001
$676$	−3.28970	−0.126527
$677$	−33.5515	−1.28949	−0.644745	−	0.764398i	$-0.723036\pi$
$677$	−33.5515	−1.28949	−0.644745	+	0.764398i	$0.723036\pi$
$678$	0.334778	0.0128571
$679$	−24.3599	−0.934846
$680$	−9.53043	−0.365475
$681$	−8.37644	−0.320986
$682$	−6.85073	−0.262328
$683$	8.94737	0.342362	0.171181	−	0.985240i	$-0.445242\pi$
$683$	8.94737	0.342362	0.171181	+	0.985240i	$0.445242\pi$
$684$	−17.1730	−0.656625
$685$	−12.4631	−0.476192
$686$	−16.3882	−0.625704
$687$	8.58575	0.327567
$688$	7.72638	0.294566
$689$	−21.7846	−0.829929
$690$	0.544656	0.0207347
$691$	7.04969	0.268183	0.134092	−	0.990969i	$-0.457188\pi$
$691$	7.04969	0.268183	0.134092	+	0.990969i	$0.457188\pi$
$692$	−32.5933	−1.23901
$693$	20.9047	0.794105
$694$	0.742994	0.0282036
$695$	7.92309	0.300540
$696$	−7.25902	−0.275152
$697$	49.6502	1.88063
$698$	8.06969	0.305442
$699$	−20.9232	−0.791389
$700$	−33.1344	−1.25236
$701$	−5.19179	−0.196091	−0.0980456	−	0.995182i	$-0.531259\pi$
$701$	−5.19179	−0.196091	−0.0980456	+	0.995182i	$0.531259\pi$
$702$	−8.17139	−0.308409
$703$	−29.7256	−1.12112
$704$	−5.52943	−0.208398
$705$	−1.94574	−0.0732807
$706$	16.9012	0.636083
$707$	57.3230	2.15586
$708$	−17.2061	−0.646643
$709$	−16.3067	−0.612410	−0.306205	−	0.951966i	$-0.599059\pi$
$709$	−16.3067	−0.612410	−0.306205	+	0.951966i	$0.599059\pi$
$710$	−6.97816	−0.261886
$711$	7.36066	0.276046
$712$	−10.1800	−0.381510
$713$	10.3302	0.386870
$714$	9.90128	0.370546
$715$	−7.19488	−0.269073
$716$	30.5594	1.14206
$717$	20.4820	0.764915
$718$	8.83756	0.329815
$719$	−27.4968	−1.02546	−0.512729	−	0.858551i	$-0.671365\pi$
$719$	−27.4968	−1.02546	−0.512729	+	0.858551i	$0.671365\pi$
$720$	−5.91275	−0.220355
$721$	45.2410	1.68486
$722$	−0.779256	−0.0290009
$723$	0.815004	0.0303103
$724$	−31.2180	−1.16021
$725$	19.7919	0.735053
$726$	2.87460	0.106686
$727$	−15.2319	−0.564919	−0.282460	−	0.959279i	$-0.591150\pi$
$727$	−15.2319	−0.564919	−0.282460	+	0.959279i	$0.591150\pi$
$728$	−32.6201	−1.20898
$729$	2.54349	0.0942032
$730$	0.112642	0.00416905
$731$	15.8642	0.586758
$732$	−19.9972	−0.739118
$733$	6.76475	0.249862	0.124931	−	0.992165i	$-0.460129\pi$
$733$	6.76475	0.249862	0.124931	+	0.992165i	$0.460129\pi$
$734$	−5.35490	−0.197653
$735$	−11.2025	−0.413210
$736$	−7.05548	−0.260068
$737$	−14.1734	−0.522082
$738$	−10.4607	−0.385062
$739$	17.9519	0.660372	0.330186	−	0.943916i	$-0.392889\pi$
$739$	17.9519	0.660372	0.330186	+	0.943916i	$0.392889\pi$
$740$	−12.0822	−0.444151
$741$	−13.1084	−0.481551
$742$	−12.7043	−0.466390
$743$	−17.2096	−0.631357	−0.315679	−	0.948866i	$-0.602232\pi$
$743$	−17.2096	−0.631357	−0.315679	+	0.948866i	$0.602232\pi$
$744$	−10.8300	−0.397047
$745$	4.31559	0.158111
$746$	2.55195	0.0934336
$747$	5.76518	0.210937
$748$	−18.4714	−0.675380
$749$	42.2188	1.54264
$750$	3.46733	0.126609
$751$	4.98853	0.182034	0.0910170	−	0.995849i	$-0.470988\pi$
$751$	4.98853	0.182034	0.0910170	+	0.995849i	$0.470988\pi$
$752$	6.53032	0.238136
$753$	−2.05575	−0.0749156
$754$	9.12739	0.332400
$755$	0.0898146	0.00326869
$756$	35.3635	1.28616
$757$	−19.5585	−0.710864	−0.355432	−	0.934702i	$-0.615666\pi$
$757$	−19.5585	−0.710864	−0.355432	+	0.934702i	$0.615666\pi$
$758$	3.93335	0.142866
$759$	2.25349	0.0817966
$760$	7.35823	0.266911
$761$	−41.0235	−1.48710	−0.743550	−	0.668681i	$-0.766859\pi$
$761$	−41.0235	−1.48710	−0.743550	+	0.668681i	$0.766859\pi$
$762$	−4.50474	−0.163189
$763$	−14.9738	−0.542087
$764$	−23.3425	−0.844503
$765$	−12.1403	−0.438935
$766$	1.20131	0.0434053
$767$	46.1847	1.66763
$768$	−0.162852	−0.00587641
$769$	11.7068	0.422159	0.211079	−	0.977469i	$-0.432302\pi$
$769$	11.7068	0.422159	0.211079	+	0.977469i	$0.432302\pi$
$770$	−4.19589	−0.151209
$771$	−3.19765	−0.115161
$772$	44.9489	1.61775
$773$	−6.66278	−0.239643	−0.119822	−	0.992795i	$-0.538232\pi$
$773$	−6.66278	−0.239643	−0.119822	+	0.992795i	$0.538232\pi$
$774$	−3.34238	−0.120140
$775$	29.5283	1.06069
$776$	−9.68090	−0.347524
$777$	26.7962	0.961309
$778$	−13.9945	−0.501727
$779$	−38.3338	−1.37345
$780$	−5.32803	−0.190774
$781$	−28.8719	−1.03312
$782$	−3.75331	−0.134218
$783$	−21.1234	−0.754888
$784$	37.5980	1.34279
$785$	−9.74865	−0.347944
$786$	−5.61071	−0.200127
$787$	2.88890	0.102978	0.0514891	−	0.998674i	$-0.483603\pi$
$787$	2.88890	0.102978	0.0514891	+	0.998674i	$0.483603\pi$
$788$	26.4909	0.943698
$789$	−5.09364	−0.181338
$790$	−1.47739	−0.0525633
$791$	3.88896	0.138275
$792$	8.30778	0.295204
$793$	53.6767	1.90612
$794$	5.87762	0.208589
$795$	−4.42976	−0.157107
$796$	34.1574	1.21068
$797$	18.0912	0.640824	0.320412	−	0.947278i	$-0.396179\pi$
$797$	18.0912	0.640824	0.320412	+	0.947278i	$0.396179\pi$
$798$	−7.64455	−0.270614
$799$	13.4084	0.474355
$800$	−20.1676	−0.713033
$801$	−12.9678	−0.458193
$802$	−15.4528	−0.545656
$803$	0.466051	0.0164466
$804$	−10.4958	−0.370159
$805$	6.32700	0.222997
$806$	13.6175	0.479655
$807$	−16.7029	−0.587971
$808$	22.7809	0.801428
$809$	8.04121	0.282714	0.141357	−	0.989959i	$-0.454853\pi$
$809$	8.04121	0.282714	0.141357	+	0.989959i	$0.454853\pi$
$810$	1.62360	0.0570474
$811$	24.5111	0.860701	0.430350	−	0.902662i	$-0.358390\pi$
$811$	24.5111	0.860701	0.430350	+	0.902662i	$0.358390\pi$
$812$	−39.5008	−1.38621
$813$	−12.4842	−0.437839
$814$	6.73632	0.236108
$815$	7.21311	0.252664
$816$	−11.5870	−0.405626
$817$	−12.2484	−0.428517
$818$	−6.91507	−0.241780
$819$	−41.5532	−1.45199
$820$	−15.5811	−0.544115
$821$	−10.6539	−0.371823	−0.185912	−	0.982566i	$-0.559524\pi$
$821$	−10.6539	−0.371823	−0.185912	+	0.982566i	$0.559524\pi$
$822$	5.14574	0.179478
$823$	25.6473	0.894009	0.447004	−	0.894532i	$-0.352491\pi$
$823$	25.6473	0.894009	0.447004	+	0.894532i	$0.352491\pi$
$824$	17.9793	0.626339
$825$	6.44146	0.224263
$826$	26.9339	0.937150
$827$	18.0150	0.626442	0.313221	−	0.949680i	$-0.398592\pi$
$827$	18.0150	0.626442	0.313221	+	0.949680i	$0.398592\pi$
$828$	−5.86828	−0.203937
$829$	10.1189	0.351444	0.175722	−	0.984440i	$-0.443774\pi$
$829$	10.1189	0.351444	0.175722	+	0.984440i	$0.443774\pi$
$830$	−1.15716	−0.0401655
$831$	−2.66008	−0.0922771
$832$	10.9911	0.381047
$833$	77.1981	2.67476
$834$	−3.27125	−0.113274
$835$	17.1160	0.592325
$836$	14.2613	0.493238
$837$	−31.5148	−1.08931
$838$	15.1571	0.523593
$839$	−46.0365	−1.58936	−0.794679	−	0.607030i	$-0.792361\pi$
$839$	−46.0365	−1.58936	−0.794679	+	0.607030i	$0.792361\pi$
$840$	−6.63309	−0.228863
$841$	−5.40531	−0.186390
$842$	−13.3734	−0.460879
$843$	10.1705	0.350292
$844$	−49.2411	−1.69495
$845$	1.79557	0.0617696
$846$	−2.82498	−0.0971247
$847$	33.3928	1.14739
$848$	14.8673	0.510544
$849$	12.8865	0.442262
$850$	−10.7286	−0.367987
$851$	−10.1577	−0.348202
$852$	−21.3805	−0.732485
$853$	−55.0001	−1.88317	−0.941584	−	0.336780i	$-0.890662\pi$
$853$	−55.0001	−1.88317	−0.941584	+	0.336780i	$0.890662\pi$
$854$	31.3031	1.07117
$855$	9.37329	0.320560
$856$	16.7783	0.573469
$857$	−31.5202	−1.07671	−0.538354	−	0.842719i	$-0.680954\pi$
$857$	−31.5202	−1.07671	−0.538354	+	0.842719i	$0.680954\pi$
$858$	2.97059	0.101414
$859$	−37.2208	−1.26996	−0.634979	−	0.772529i	$-0.718991\pi$
$859$	−37.2208	−1.26996	−0.634979	+	0.772529i	$0.718991\pi$
$860$	−4.97846	−0.169764
$861$	34.5561	1.17767
$862$	−6.87180	−0.234054
$863$	30.3224	1.03218	0.516092	−	0.856533i	$-0.327386\pi$
$863$	30.3224	1.03218	0.516092	+	0.856533i	$0.327386\pi$
$864$	21.5244	0.732274
$865$	17.7900	0.604877
$866$	−8.64563	−0.293791
$867$	−9.93592	−0.337442
$868$	−58.9327	−2.00031
$869$	−6.11267	−0.207358
$870$	1.85599	0.0629241
$871$	28.1730	0.954605
$872$	−5.95075	−0.201518
$873$	−12.3320	−0.417376
$874$	2.89784	0.0980210
$875$	40.2783	1.36165
$876$	0.345125	0.0116607
$877$	27.0037	0.911849	0.455925	−	0.890018i	$-0.349309\pi$
$877$	27.0037	0.911849	0.455925	+	0.890018i	$0.349309\pi$
$878$	−1.23028	−0.0415200
$879$	−15.2526	−0.514457
$880$	4.91025	0.165525
$881$	−0.565506	−0.0190524	−0.00952619	−	0.999955i	$-0.503032\pi$
$881$	−0.565506	−0.0190524	−0.00952619	+	0.999955i	$0.503032\pi$
$882$	−16.2647	−0.547660
$883$	23.8838	0.803752	0.401876	−	0.915694i	$-0.368358\pi$
$883$	23.8838	0.803752	0.401876	+	0.915694i	$0.368358\pi$
$884$	36.7163	1.23490
$885$	9.39135	0.315687
$886$	−8.20600	−0.275686
$887$	−10.1717	−0.341533	−0.170767	−	0.985311i	$-0.554624\pi$
$887$	−10.1717	−0.341533	−0.170767	+	0.985311i	$0.554624\pi$
$888$	10.6491	0.357362
$889$	−52.3294	−1.75507
$890$	2.60282	0.0872468
$891$	6.71757	0.225047
$892$	0.682968	0.0228675
$893$	−10.3523	−0.346427
$894$	−1.78180	−0.0595924
$895$	−16.6798	−0.557544
$896$	52.0843	1.74001
$897$	−4.47937	−0.149562
$898$	−14.8975	−0.497135
$899$	35.2018	1.17405
$900$	−16.7741	−0.559136
$901$	30.5262	1.01697
$902$	8.68707	0.289248
$903$	11.0413	0.367432
$904$	1.54552	0.0514031
$905$	17.0393	0.566405
$906$	−0.0370823	−0.00123198
$907$	−44.1661	−1.46651	−0.733255	−	0.679954i	$-0.762000\pi$
$907$	−44.1661	−1.46651	−0.733255	+	0.679954i	$0.762000\pi$
$908$	−18.1146	−0.601154
$909$	29.0194	0.962514
$910$	8.34036	0.276480
$911$	−7.07316	−0.234344	−0.117172	−	0.993112i	$-0.537383\pi$
$911$	−7.07316	−0.234344	−0.117172	+	0.993112i	$0.537383\pi$
$912$	8.94605	0.296233
$913$	−4.78770	−0.158450
$914$	−15.9382	−0.527190
$915$	10.9148	0.360832
$916$	18.5672	0.613479
$917$	−65.1769	−2.15233
$918$	11.4503	0.377917
$919$	23.6016	0.778544	0.389272	−	0.921123i	$-0.372727\pi$
$919$	23.6016	0.778544	0.389272	+	0.921123i	$0.372727\pi$
$920$	2.51442	0.0828981
$921$	−4.26636	−0.140581
$922$	6.03976	0.198909
$923$	57.3899	1.88901
$924$	−12.8559	−0.422928
$925$	−29.0352	−0.954670
$926$	5.91530	0.194389
$927$	22.9030	0.752233
$928$	−24.0426	−0.789236
$929$	31.8496	1.04495	0.522475	−	0.852654i	$-0.325009\pi$
$929$	31.8496	1.04495	0.522475	+	0.852654i	$0.325009\pi$
$930$	2.76902	0.0907999
$931$	−59.6029	−1.95341
$932$	−45.2478	−1.48214
$933$	21.7506	0.712083
$934$	2.62290	0.0858238
$935$	10.0820	0.329716
$936$	−16.5137	−0.539768
$937$	44.1729	1.44307	0.721533	−	0.692380i	$-0.243438\pi$
$937$	44.1729	1.44307	0.721533	+	0.692380i	$0.243438\pi$
$938$	16.4299	0.536454
$939$	−5.08677	−0.166001
$940$	−4.20778	−0.137243
$941$	−34.5303	−1.12566	−0.562828	−	0.826574i	$-0.690287\pi$
$941$	−34.5303	−1.12566	−0.562828	+	0.826574i	$0.690287\pi$
$942$	4.02498	0.131141
$943$	−13.0993	−0.426571
$944$	−31.5194	−1.02587
$945$	−19.3020	−0.627893
$946$	2.77569	0.0902454
$947$	−3.46191	−0.112497	−0.0562485	−	0.998417i	$-0.517914\pi$
$947$	−3.46191	−0.112497	−0.0562485	+	0.998417i	$0.517914\pi$
$948$	−4.52662	−0.147018
$949$	−0.926389	−0.0300719
$950$	8.28329	0.268745
$951$	−5.61966	−0.182230
$952$	45.7097	1.48146
$953$	60.2596	1.95200	0.976000	−	0.217771i	$-0.0698785\pi$
$953$	60.2596	1.95200	0.976000	+	0.217771i	$0.0698785\pi$
$954$	−6.43148	−0.208227
$955$	12.7407	0.412280
$956$	44.2936	1.43256
$957$	7.67911	0.248230
$958$	−12.3664	−0.399541
$959$	59.7755	1.93025
$960$	2.23496	0.0721331
$961$	21.5188	0.694156
$962$	−13.3901	−0.431713
$963$	21.3730	0.688735
$964$	1.76250	0.0567662
$965$	−24.5338	−0.789772
$966$	−2.61227	−0.0840483
$967$	−39.9168	−1.28364	−0.641819	−	0.766856i	$-0.721820\pi$
$967$	−39.9168	−1.28364	−0.641819	+	0.766856i	$0.721820\pi$
$968$	13.2707	0.426536
$969$	18.3685	0.590081
$970$	2.47522	0.0794746
$971$	43.7104	1.40273	0.701366	−	0.712801i	$-0.252574\pi$
$971$	43.7104	1.40273	0.701366	+	0.712801i	$0.252574\pi$
$972$	27.9681	0.897078
$973$	−38.0006	−1.21824
$974$	−5.08020	−0.162780
$975$	−12.8040	−0.410055
$976$	−36.6325	−1.17258
$977$	−0.955388	−0.0305656	−0.0152828	−	0.999883i	$-0.504865\pi$
$977$	−0.955388	−0.0305656	−0.0152828	+	0.999883i	$0.504865\pi$
$978$	−2.97812	−0.0952298
$979$	10.7691	0.344182
$980$	−24.2261	−0.773874
$981$	−7.58037	−0.242023
$982$	16.7090	0.533205
$983$	−48.7488	−1.55485	−0.777423	−	0.628978i	$-0.783474\pi$
$983$	−48.7488	−1.55485	−0.777423	+	0.628978i	$0.783474\pi$
$984$	13.7330	0.437792
$985$	−14.4591	−0.460707
$986$	−12.7899	−0.407315
$987$	9.33211	0.297044
$988$	−28.3478	−0.901865
$989$	−4.18547	−0.133090
$990$	−2.12414	−0.0675097
$991$	0.488986	0.0155332	0.00776658	−	0.999970i	$-0.497528\pi$
$991$	0.488986	0.0155332	0.00776658	+	0.999970i	$0.497528\pi$
$992$	−35.8700	−1.13887
$993$	11.0594	0.350959
$994$	33.4685	1.06156
$995$	−18.6437	−0.591044
$996$	−3.54544	−0.112342
$997$	39.5339	1.25205	0.626026	−	0.779802i	$-0.284680\pi$
$997$	39.5339	1.25205	0.626026	+	0.779802i	$0.284680\pi$
$998$	7.78153	0.246320
$999$	30.9885	0.980432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.a.a.1.6	✓	7
3.2	odd	2		2169.2.a.e.1.2		7
4.3	odd	2		3856.2.a.j.1.5		7
5.4	even	2		6025.2.a.f.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.a.1.6	✓	7	1.1	even	1	trivial
2169.2.a.e.1.2		7	3.2	odd	2
3856.2.a.j.1.5		7	4.3	odd	2
6025.2.a.f.1.2		7	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)

\(f(q)\)	\(=\)	\(q+0.487343 q^{2} -0.815004 q^{3} -1.76250 q^{4} +0.961999 q^{5} -0.397187 q^{6} -4.61392 q^{7} -1.83363 q^{8} -2.33577 q^{9} +O(q^{10})\)	\(q+0.487343 q^{2} -0.815004 q^{3} -1.76250 q^{4} +0.961999 q^{5} -0.397187 q^{6} -4.61392 q^{7} -1.83363 q^{8} -2.33577 q^{9} +0.468824 q^{10} +1.93974 q^{11} +1.43644 q^{12} -3.85571 q^{13} -2.24856 q^{14} -0.784033 q^{15} +2.63139 q^{16} +5.40289 q^{17} -1.13832 q^{18} -4.17145 q^{19} -1.69552 q^{20} +3.76036 q^{21} +0.945321 q^{22} -1.42545 q^{23} +1.49441 q^{24} -4.07456 q^{25} -1.87905 q^{26} +4.34867 q^{27} +8.13202 q^{28} -4.85744 q^{29} -0.382093 q^{30} -7.24699 q^{31} +4.94964 q^{32} -1.58090 q^{33} +2.63306 q^{34} -4.43859 q^{35} +4.11678 q^{36} +7.12597 q^{37} -2.03293 q^{38} +3.14242 q^{39} -1.76395 q^{40} +9.18955 q^{41} +1.83259 q^{42} +2.93624 q^{43} -3.41879 q^{44} -2.24701 q^{45} -0.694685 q^{46} +2.48170 q^{47} -2.14459 q^{48} +14.2883 q^{49} -1.98571 q^{50} -4.40338 q^{51} +6.79568 q^{52} +5.64997 q^{53} +2.11930 q^{54} +1.86603 q^{55} +8.46022 q^{56} +3.39975 q^{57} -2.36724 q^{58} -11.9783 q^{59} +1.38186 q^{60} -13.9214 q^{61} -3.53177 q^{62} +10.7771 q^{63} -2.85060 q^{64} -3.70919 q^{65} -0.770440 q^{66} -7.30682 q^{67} -9.52258 q^{68} +1.16175 q^{69} -2.16312 q^{70} -14.8844 q^{71} +4.28293 q^{72} +0.240264 q^{73} +3.47279 q^{74} +3.32078 q^{75} +7.35217 q^{76} -8.94983 q^{77} +1.53144 q^{78} -3.15128 q^{79} +2.53139 q^{80} +3.46313 q^{81} +4.47847 q^{82} -2.46821 q^{83} -6.62763 q^{84} +5.19758 q^{85} +1.43096 q^{86} +3.95883 q^{87} -3.55677 q^{88} +5.55181 q^{89} -1.09506 q^{90} +17.7900 q^{91} +2.51235 q^{92} +5.90632 q^{93} +1.20944 q^{94} -4.01293 q^{95} -4.03398 q^{96} +5.27964 q^{97} +6.96330 q^{98} -4.53079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 7 * q - 4 * q^2 - 3 * q^3 + 2 * q^4 - 8 * q^5 - 5 * q^6 - 7 * q^7 - 6 * q^8 - 2 * q^9	\( 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9} + 3 q^{10} - 18 q^{11} + q^{12} - q^{13} - 6 q^{14} - 11 q^{15} + 4 q^{16} - 2 q^{17} + 8 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} + 10 q^{22} - 22 q^{23} - 3 q^{24} + 5 q^{25} + 8 q^{26} + 3 q^{27} + 9 q^{28} - 16 q^{29} + 29 q^{30} - 18 q^{31} - 6 q^{32} + 4 q^{33} + 11 q^{34} + 7 q^{35} - 7 q^{36} + 8 q^{37} + 16 q^{38} - 9 q^{39} + 14 q^{40} - 15 q^{41} + 19 q^{42} + 14 q^{43} - 4 q^{44} + 3 q^{45} + 11 q^{46} - 10 q^{47} + 31 q^{48} + 6 q^{49} - 4 q^{50} + 13 q^{51} + 27 q^{52} + 15 q^{53} + 16 q^{54} + 29 q^{55} + 13 q^{56} + 14 q^{57} + 17 q^{58} - 18 q^{59} + 15 q^{60} + 4 q^{61} + 13 q^{62} - 16 q^{63} + 2 q^{64} - 7 q^{65} + 16 q^{66} + 18 q^{67} - 15 q^{68} + 26 q^{69} + 8 q^{70} - 50 q^{71} + 30 q^{72} + 10 q^{74} + 16 q^{75} - 20 q^{76} + 17 q^{77} - 32 q^{78} - 15 q^{79} - 11 q^{80} - 9 q^{81} + 45 q^{82} - 24 q^{83} + 6 q^{84} - 2 q^{85} - 23 q^{86} + 12 q^{87} + 8 q^{88} - 13 q^{89} - 39 q^{90} - 12 q^{91} - 10 q^{92} + 14 q^{93} - 32 q^{94} - 41 q^{95} - 15 q^{96} + q^{97} + 9 q^{98} - 20 q^{99}+O(q^{100}) \) 7 * q - 4 * q^2 - 3 * q^3 + 2 * q^4 - 8 * q^5 - 5 * q^6 - 7 * q^7 - 6 * q^8 - 2 * q^9 + 3 * q^10 - 18 * q^11 + q^12 - q^13 - 6 * q^14 - 11 * q^15 + 4 * q^16 - 2 * q^17 + 8 * q^18 - 6 * q^19 - 8 * q^20 - 2 * q^21 + 10 * q^22 - 22 * q^23 - 3 * q^24 + 5 * q^25 + 8 * q^26 + 3 * q^27 + 9 * q^28 - 16 * q^29 + 29 * q^30 - 18 * q^31 - 6 * q^32 + 4 * q^33 + 11 * q^34 + 7 * q^35 - 7 * q^36 + 8 * q^37 + 16 * q^38 - 9 * q^39 + 14 * q^40 - 15 * q^41 + 19 * q^42 + 14 * q^43 - 4 * q^44 + 3 * q^45 + 11 * q^46 - 10 * q^47 + 31 * q^48 + 6 * q^49 - 4 * q^50 + 13 * q^51 + 27 * q^52 + 15 * q^53 + 16 * q^54 + 29 * q^55 + 13 * q^56 + 14 * q^57 + 17 * q^58 - 18 * q^59 + 15 * q^60 + 4 * q^61 + 13 * q^62 - 16 * q^63 + 2 * q^64 - 7 * q^65 + 16 * q^66 + 18 * q^67 - 15 * q^68 + 26 * q^69 + 8 * q^70 - 50 * q^71 + 30 * q^72 + 10 * q^74 + 16 * q^75 - 20 * q^76 + 17 * q^77 - 32 * q^78 - 15 * q^79 - 11 * q^80 - 9 * q^81 + 45 * q^82 - 24 * q^83 + 6 * q^84 - 2 * q^85 - 23 * q^86 + 12 * q^87 + 8 * q^88 - 13 * q^89 - 39 * q^90 - 12 * q^91 - 10 * q^92 + 14 * q^93 - 32 * q^94 - 41 * q^95 - 15 * q^96 + q^97 + 9 * q^98 - 20 * q^99

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