LMFDB - Embedded newform 1511.2.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1511,2,Mod(1,1511)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1511, 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("1511.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1511 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1511.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:	$12.0653957454$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	1511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23663 q^{2} +2.94834 q^{3} +3.00251 q^{4} -1.14900 q^{5} -6.59433 q^{6} -0.894921 q^{7} -2.24225 q^{8} +5.69268 q^{9} +O(q^{10})$	\(q-2.23663 q^{2} +2.94834 q^{3} +3.00251 q^{4} -1.14900 q^{5} -6.59433 q^{6} -0.894921 q^{7} -2.24225 q^{8} +5.69268 q^{9} +2.56989 q^{10} +1.44593 q^{11} +8.85241 q^{12} -2.17076 q^{13} +2.00161 q^{14} -3.38764 q^{15} -0.989945 q^{16} -5.56829 q^{17} -12.7324 q^{18} -7.39024 q^{19} -3.44989 q^{20} -2.63853 q^{21} -3.23401 q^{22} -2.96908 q^{23} -6.61090 q^{24} -3.67980 q^{25} +4.85518 q^{26} +7.93893 q^{27} -2.68701 q^{28} -3.80442 q^{29} +7.57690 q^{30} -0.0594530 q^{31} +6.69864 q^{32} +4.26308 q^{33} +12.4542 q^{34} +1.02827 q^{35} +17.0923 q^{36} +0.869567 q^{37} +16.5292 q^{38} -6.40012 q^{39} +2.57635 q^{40} -0.928704 q^{41} +5.90141 q^{42} -5.42711 q^{43} +4.34142 q^{44} -6.54090 q^{45} +6.64073 q^{46} +1.79766 q^{47} -2.91869 q^{48} -6.19912 q^{49} +8.23034 q^{50} -16.4172 q^{51} -6.51772 q^{52} +5.79505 q^{53} -17.7564 q^{54} -1.66137 q^{55} +2.00664 q^{56} -21.7889 q^{57} +8.50909 q^{58} +2.85523 q^{59} -10.1714 q^{60} +6.09963 q^{61} +0.132974 q^{62} -5.09450 q^{63} -13.0025 q^{64} +2.49420 q^{65} -9.53493 q^{66} -3.30484 q^{67} -16.7188 q^{68} -8.75384 q^{69} -2.29985 q^{70} +5.48171 q^{71} -12.7644 q^{72} -2.68259 q^{73} -1.94490 q^{74} -10.8493 q^{75} -22.1893 q^{76} -1.29399 q^{77} +14.3147 q^{78} -5.07917 q^{79} +1.13745 q^{80} +6.32859 q^{81} +2.07717 q^{82} +6.13147 q^{83} -7.92221 q^{84} +6.39796 q^{85} +12.1384 q^{86} -11.2167 q^{87} -3.24213 q^{88} +2.85167 q^{89} +14.6296 q^{90} +1.94266 q^{91} -8.91469 q^{92} -0.175288 q^{93} -4.02070 q^{94} +8.49139 q^{95} +19.7498 q^{96} +10.1996 q^{97} +13.8651 q^{98} +8.23121 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 5 q^{2} - 4 q^{3} + 19 q^{4} - 8 q^{5} - 8 q^{6} - 15 q^{7} - 12 q^{8} - q^{9}+O(q^{10}) $ 39 * q - 5 * q^2 - 4 * q^3 + 19 * q^4 - 8 * q^5 - 8 * q^6 - 15 * q^7 - 12 * q^8 - q^9	\( 39 q - 5 q^{2} - 4 q^{3} + 19 q^{4} - 8 q^{5} - 8 q^{6} - 15 q^{7} - 12 q^{8} - q^{9} - 13 q^{10} - 13 q^{11} - 8 q^{12} - 24 q^{13} - 12 q^{14} - 16 q^{15} - 13 q^{16} - 26 q^{17} - 17 q^{18} - 40 q^{19} - 15 q^{20} - 26 q^{21} - 26 q^{22} - 8 q^{23} - 16 q^{24} - 35 q^{25} - 3 q^{26} - 10 q^{27} - 31 q^{28} - 30 q^{29} - 16 q^{30} - 21 q^{31} - 9 q^{32} - 25 q^{33} - 27 q^{34} - 2 q^{35} - 23 q^{36} - 27 q^{37} + q^{38} - 29 q^{39} - 36 q^{40} - 35 q^{41} - 6 q^{42} - 48 q^{43} - 17 q^{44} - 22 q^{45} - 31 q^{46} - 3 q^{47} + q^{48} - 64 q^{49} + 12 q^{50} - 27 q^{51} - 28 q^{52} - 14 q^{53} + q^{54} - 31 q^{55} - 12 q^{56} - 36 q^{57} - 19 q^{58} - 9 q^{59} - 6 q^{60} - 87 q^{61} + 32 q^{62} - 9 q^{63} - 52 q^{64} - 35 q^{65} + 5 q^{66} - 24 q^{67} - 13 q^{68} - 35 q^{69} - 8 q^{70} - 21 q^{71} - 11 q^{72} - 69 q^{73} - 23 q^{74} - 4 q^{75} - 58 q^{76} - 3 q^{77} + q^{78} - 72 q^{79} + 13 q^{80} - 73 q^{81} + 18 q^{82} - 11 q^{83} - 32 q^{84} - 70 q^{85} + 20 q^{86} - 9 q^{87} - 24 q^{88} - 25 q^{89} + 33 q^{90} - 32 q^{91} + 17 q^{92} - 19 q^{93} - 29 q^{94} - 9 q^{95} + 5 q^{96} - 56 q^{97} + 37 q^{98} - 19 q^{99}+O(q^{100}) \) 39 * q - 5 * q^2 - 4 * q^3 + 19 * q^4 - 8 * q^5 - 8 * q^6 - 15 * q^7 - 12 * q^8 - q^9 - 13 * q^10 - 13 * q^11 - 8 * q^12 - 24 * q^13 - 12 * q^14 - 16 * q^15 - 13 * q^16 - 26 * q^17 - 17 * q^18 - 40 * q^19 - 15 * q^20 - 26 * q^21 - 26 * q^22 - 8 * q^23 - 16 * q^24 - 35 * q^25 - 3 * q^26 - 10 * q^27 - 31 * q^28 - 30 * q^29 - 16 * q^30 - 21 * q^31 - 9 * q^32 - 25 * q^33 - 27 * q^34 - 2 * q^35 - 23 * q^36 - 27 * q^37 + q^38 - 29 * q^39 - 36 * q^40 - 35 * q^41 - 6 * q^42 - 48 * q^43 - 17 * q^44 - 22 * q^45 - 31 * q^46 - 3 * q^47 + q^48 - 64 * q^49 + 12 * q^50 - 27 * q^51 - 28 * q^52 - 14 * q^53 + q^54 - 31 * q^55 - 12 * q^56 - 36 * q^57 - 19 * q^58 - 9 * q^59 - 6 * q^60 - 87 * q^61 + 32 * q^62 - 9 * q^63 - 52 * q^64 - 35 * q^65 + 5 * q^66 - 24 * q^67 - 13 * q^68 - 35 * q^69 - 8 * q^70 - 21 * q^71 - 11 * q^72 - 69 * q^73 - 23 * q^74 - 4 * q^75 - 58 * q^76 - 3 * q^77 + q^78 - 72 * q^79 + 13 * q^80 - 73 * q^81 + 18 * q^82 - 11 * q^83 - 32 * q^84 - 70 * q^85 + 20 * q^86 - 9 * q^87 - 24 * q^88 - 25 * q^89 + 33 * q^90 - 32 * q^91 + 17 * q^92 - 19 * q^93 - 29 * q^94 - 9 * q^95 + 5 * q^96 - 56 * q^97 + 37 * q^98 - 19 * 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 $

$2$	−2.23663	−1.58154	−0.790768	−	0.612116i	$-0.790319\pi$
$2$	−2.23663	−1.58154	−0.790768	+	0.612116i	$0.790319\pi$
$3$	2.94834	1.70222	0.851111	−	0.524986i	$-0.175929\pi$
$3$	2.94834	1.70222	0.851111	+	0.524986i	$0.175929\pi$
$4$	3.00251	1.50126
$5$	−1.14900	−0.513849	−0.256924	−	0.966432i	$-0.582709\pi$
$5$	−1.14900	−0.513849	−0.256924	+	0.966432i	$0.582709\pi$
$6$	−6.59433	−2.69213
$7$	−0.894921	−0.338248	−0.169124	−	0.985595i	$-0.554094\pi$
$7$	−0.894921	−0.338248	−0.169124	+	0.985595i	$0.554094\pi$
$8$	−2.24225	−0.792755
$9$	5.69268	1.89756
$10$	2.56989	0.812670
$11$	1.44593	0.435964	0.217982	−	0.975953i	$-0.430053\pi$
$11$	1.44593	0.435964	0.217982	+	0.975953i	$0.430053\pi$
$12$	8.85241	2.55547
$13$	−2.17076	−0.602060	−0.301030	−	0.953615i	$-0.597330\pi$
$13$	−2.17076	−0.602060	−0.301030	+	0.953615i	$0.597330\pi$
$14$	2.00161	0.534952
$15$	−3.38764	−0.874685
$16$	−0.989945	−0.247486
$17$	−5.56829	−1.35051	−0.675254	−	0.737585i	$-0.735966\pi$
$17$	−5.56829	−1.35051	−0.675254	+	0.737585i	$0.735966\pi$
$18$	−12.7324	−3.00106
$19$	−7.39024	−1.69544	−0.847718	−	0.530447i	$-0.822024\pi$
$19$	−7.39024	−1.69544	−0.847718	+	0.530447i	$0.822024\pi$
$20$	−3.44989	−0.771419
$21$	−2.63853	−0.575774
$22$	−3.23401	−0.689492
$23$	−2.96908	−0.619096	−0.309548	−	0.950884i	$-0.600178\pi$
$23$	−2.96908	−0.619096	−0.309548	+	0.950884i	$0.600178\pi$
$24$	−6.61090	−1.34944
$25$	−3.67980	−0.735959
$26$	4.85518	0.952179
$27$	7.93893	1.52785
$28$	−2.68701	−0.507798
$29$	−3.80442	−0.706464	−0.353232	−	0.935536i	$-0.614917\pi$
$29$	−3.80442	−0.706464	−0.353232	+	0.935536i	$0.614917\pi$
$30$	7.57690	1.38335
$31$	−0.0594530	−0.0106781	−0.00533904	−	0.999986i	$-0.501699\pi$
$31$	−0.0594530	−0.0106781	−0.00533904	+	0.999986i	$0.501699\pi$
$32$	6.69864	1.18416
$33$	4.26308	0.742107
$34$	12.4542	2.13588
$35$	1.02827	0.173809
$36$	17.0923	2.84872
$37$	0.869567	0.142956	0.0714780	−	0.997442i	$-0.477228\pi$
$37$	0.869567	0.142956	0.0714780	+	0.997442i	$0.477228\pi$
$38$	16.5292	2.68139
$39$	−6.40012	−1.02484
$40$	2.57635	0.407356
$41$	−0.928704	−0.145039	−0.0725196	−	0.997367i	$-0.523104\pi$
$41$	−0.928704	−0.145039	−0.0725196	+	0.997367i	$0.523104\pi$
$42$	5.90141	0.910607
$43$	−5.42711	−0.827627	−0.413814	−	0.910362i	$-0.635803\pi$
$43$	−5.42711	−0.827627	−0.413814	+	0.910362i	$0.635803\pi$
$44$	4.34142	0.654493
$45$	−6.54090	−0.975059
$46$	6.64073	0.979122
$47$	1.79766	0.262215	0.131108	−	0.991368i	$-0.458147\pi$
$47$	1.79766	0.262215	0.131108	+	0.991368i	$0.458147\pi$
$48$	−2.91869	−0.421277
$49$	−6.19912	−0.885588
$50$	8.23034	1.16395
$51$	−16.4172	−2.29886
$52$	−6.51772	−0.903846
$53$	5.79505	0.796012	0.398006	−	0.917383i	$-0.369702\pi$
$53$	5.79505	0.796012	0.398006	+	0.917383i	$0.369702\pi$
$54$	−17.7564	−2.41635
$55$	−1.66137	−0.224019
$56$	2.00664	0.268148
$57$	−21.7889	−2.88601
$58$	8.50909	1.11730
$59$	2.85523	0.371719	0.185860	−	0.982576i	$-0.440493\pi$
$59$	2.85523	0.371719	0.185860	+	0.982576i	$0.440493\pi$
$60$	−10.1714	−1.31313
$61$	6.09963	0.780977	0.390489	−	0.920608i	$-0.372306\pi$
$61$	6.09963	0.780977	0.390489	+	0.920608i	$0.372306\pi$
$62$	0.132974	0.0168878
$63$	−5.09450	−0.641847
$64$	−13.0025	−1.62531
$65$	2.49420	0.309368
$66$	−9.53493	−1.17367
$67$	−3.30484	−0.403751	−0.201875	−	0.979411i	$-0.564704\pi$
$67$	−3.30484	−0.403751	−0.201875	+	0.979411i	$0.564704\pi$
$68$	−16.7188	−2.02746
$69$	−8.75384	−1.05384
$70$	−2.29985	−0.274885
$71$	5.48171	0.650559	0.325280	−	0.945618i	$-0.394542\pi$
$71$	5.48171	0.650559	0.325280	+	0.945618i	$0.394542\pi$
$72$	−12.7644	−1.50430
$73$	−2.68259	−0.313973	−0.156987	−	0.987601i	$-0.550178\pi$
$73$	−2.68259	−0.313973	−0.156987	+	0.987601i	$0.550178\pi$
$74$	−1.94490	−0.226090
$75$	−10.8493	−1.25277
$76$	−22.1893	−2.54528
$77$	−1.29399	−0.147464
$78$	14.3147	1.62082
$79$	−5.07917	−0.571451	−0.285725	−	0.958312i	$-0.592235\pi$
$79$	−5.07917	−0.571451	−0.285725	+	0.958312i	$0.592235\pi$
$80$	1.13745	0.127170
$81$	6.32859	0.703176
$82$	2.07717	0.229385
$83$	6.13147	0.673017	0.336508	−	0.941681i	$-0.390754\pi$
$83$	6.13147	0.673017	0.336508	+	0.941681i	$0.390754\pi$
$84$	−7.92221	−0.864384
$85$	6.39796	0.693957
$86$	12.1384	1.30892
$87$	−11.2167	−1.20256
$88$	−3.24213	−0.345612
$89$	2.85167	0.302277	0.151138	−	0.988513i	$-0.451706\pi$
$89$	2.85167	0.302277	0.151138	+	0.988513i	$0.451706\pi$
$90$	14.6296	1.54209
$91$	1.94266	0.203646
$92$	−8.91469	−0.929421
$93$	−0.175288	−0.0181765
$94$	−4.02070	−0.414703
$95$	8.49139	0.871198
$96$	19.7498	2.01571
$97$	10.1996	1.03561	0.517807	−	0.855497i	$-0.326748\pi$
$97$	10.1996	1.03561	0.517807	+	0.855497i	$0.326748\pi$
$98$	13.8651	1.40059
$99$	8.23121	0.827268
$100$	−11.0486	−1.10486
$101$	2.69873	0.268534	0.134267	−	0.990945i	$-0.457132\pi$
$101$	2.69873	0.268534	0.134267	+	0.990945i	$0.457132\pi$
$102$	36.7191	3.63574
$103$	4.76540	0.469549	0.234774	−	0.972050i	$-0.424565\pi$
$103$	4.76540	0.469549	0.234774	+	0.972050i	$0.424565\pi$
$104$	4.86738	0.477285
$105$	3.03167	0.295861
$106$	−12.9614	−1.25892
$107$	−12.5815	−1.21630	−0.608149	−	0.793823i	$-0.708088\pi$
$107$	−12.5815	−1.21630	−0.608149	+	0.793823i	$0.708088\pi$
$108$	23.8367	2.29369
$109$	−11.2373	−1.07634	−0.538170	−	0.842836i	$-0.680884\pi$
$109$	−11.2373	−1.07634	−0.538170	+	0.842836i	$0.680884\pi$
$110$	3.71588	0.354295
$111$	2.56377	0.243343
$112$	0.885923	0.0837118
$113$	7.62990	0.717760	0.358880	−	0.933384i	$-0.383159\pi$
$113$	7.62990	0.717760	0.358880	+	0.933384i	$0.383159\pi$
$114$	48.7337	4.56433
$115$	3.41147	0.318122
$116$	−11.4228	−1.06058
$117$	−12.3574	−1.14244
$118$	−6.38609	−0.587887
$119$	4.98318	0.456807
$120$	7.59593	0.693410
$121$	−8.90929	−0.809936
$122$	−13.6426	−1.23514
$123$	−2.73813	−0.246889
$124$	−0.178508	−0.0160305
$125$	9.97309	0.892021
$126$	11.3945	1.01510
$127$	9.95195	0.883093	0.441546	−	0.897238i	$-0.354430\pi$
$127$	9.95195	0.883093	0.441546	+	0.897238i	$0.354430\pi$
$128$	15.6845	1.38632
$129$	−16.0010	−1.40881
$130$	−5.57860	−0.489276
$131$	2.64336	0.230952	0.115476	−	0.993310i	$-0.463161\pi$
$131$	2.64336	0.230952	0.115476	+	0.993310i	$0.463161\pi$
$132$	12.8000	1.11409
$133$	6.61368	0.573479
$134$	7.39171	0.638546
$135$	−9.12184	−0.785083
$136$	12.4855	1.07062
$137$	−1.08861	−0.0930058	−0.0465029	−	0.998918i	$-0.514808\pi$
$137$	−1.08861	−0.0930058	−0.0465029	+	0.998918i	$0.514808\pi$
$138$	19.5791	1.66668
$139$	−9.38934	−0.796393	−0.398197	−	0.917300i	$-0.630364\pi$
$139$	−9.38934	−0.796393	−0.398197	+	0.917300i	$0.630364\pi$
$140$	3.08738	0.260931
$141$	5.30010	0.446349
$142$	−12.2606	−1.02888
$143$	−3.13876	−0.262476
$144$	−5.63544	−0.469620
$145$	4.37129	0.363016
$146$	5.99995	0.496560
$147$	−18.2771	−1.50747
$148$	2.61089	0.214613
$149$	3.20110	0.262244	0.131122	−	0.991366i	$-0.458142\pi$
$149$	3.20110	0.262244	0.131122	+	0.991366i	$0.458142\pi$
$150$	24.2658	1.98130
$151$	−4.17360	−0.339643	−0.169821	−	0.985475i	$-0.554319\pi$
$151$	−4.17360	−0.339643	−0.169821	+	0.985475i	$0.554319\pi$
$152$	16.5707	1.34407
$153$	−31.6985	−2.56267
$154$	2.89418	0.233220
$155$	0.0683116	0.00548692
$156$	−19.2164	−1.53855
$157$	−14.5307	−1.15967	−0.579837	−	0.814732i	$-0.696884\pi$
$157$	−14.5307	−1.15967	−0.579837	+	0.814732i	$0.696884\pi$
$158$	11.3602	0.903770
$159$	17.0858	1.35499
$160$	−7.69674	−0.608481
$161$	2.65709	0.209408
$162$	−14.1547	−1.11210
$163$	22.9953	1.80113	0.900566	−	0.434719i	$-0.143152\pi$
$163$	22.9953	1.80113	0.900566	+	0.434719i	$0.143152\pi$
$164$	−2.78844	−0.217741
$165$	−4.89828	−0.381331
$166$	−13.7138	−1.06440
$167$	−1.59567	−0.123476	−0.0617382	−	0.998092i	$-0.519664\pi$
$167$	−1.59567	−0.123476	−0.0617382	+	0.998092i	$0.519664\pi$
$168$	5.91624	0.456448
$169$	−8.28782	−0.637524
$170$	−14.3099	−1.09752
$171$	−42.0703	−3.21719
$172$	−16.2950	−1.24248
$173$	20.5278	1.56070	0.780349	−	0.625344i	$-0.215041\pi$
$173$	20.5278	1.56070	0.780349	+	0.625344i	$0.215041\pi$
$174$	25.0876	1.90189
$175$	3.29313	0.248937
$176$	−1.43139	−0.107895
$177$	8.41818	0.632749
$178$	−6.37814	−0.478062
$179$	−23.9736	−1.79187	−0.895936	−	0.444184i	$-0.853494\pi$
$179$	−23.9736	−1.79187	−0.895936	+	0.444184i	$0.853494\pi$
$180$	−19.6391	−1.46381
$181$	−23.8278	−1.77111	−0.885555	−	0.464535i	$-0.846221\pi$
$181$	−23.8278	−1.77111	−0.885555	+	0.464535i	$0.846221\pi$
$182$	−4.34500	−0.322073
$183$	17.9837	1.32940
$184$	6.65741	0.490791
$185$	−0.999133	−0.0734577
$186$	0.392053	0.0287467
$187$	−8.05134	−0.588772
$188$	5.39749	0.393653
$189$	−7.10472	−0.516792
$190$	−18.9921	−1.37783
$191$	9.85053	0.712760	0.356380	−	0.934341i	$-0.384011\pi$
$191$	9.85053	0.712760	0.356380	+	0.934341i	$0.384011\pi$
$192$	−38.3357	−2.76664
$193$	−6.57684	−0.473411	−0.236706	−	0.971581i	$-0.576068\pi$
$193$	−6.57684	−0.473411	−0.236706	+	0.971581i	$0.576068\pi$
$194$	−22.8128	−1.63786
$195$	7.35374	0.526612
$196$	−18.6129	−1.32949
$197$	−5.07128	−0.361314	−0.180657	−	0.983546i	$-0.557822\pi$
$197$	−5.07128	−0.361314	−0.180657	+	0.983546i	$0.557822\pi$
$198$	−18.4102	−1.30835
$199$	−8.56644	−0.607259	−0.303629	−	0.952790i	$-0.598198\pi$
$199$	−8.56644	−0.607259	−0.303629	+	0.952790i	$0.598198\pi$
$200$	8.25102	0.583435
$201$	−9.74378	−0.687273
$202$	−6.03606	−0.424696
$203$	3.40466	0.238960
$204$	−49.2928	−3.45118
$205$	1.06708	0.0745282
$206$	−10.6584	−0.742608
$207$	−16.9020	−1.17477
$208$	2.14893	0.149001
$209$	−10.6858	−0.739149
$210$	−6.78073	−0.467915
$211$	23.3794	1.60950	0.804751	−	0.593613i	$-0.202299\pi$
$211$	23.3794	1.60950	0.804751	+	0.593613i	$0.202299\pi$
$212$	17.3997	1.19502
$213$	16.1619	1.10740
$214$	28.1401	1.92362
$215$	6.23576	0.425275
$216$	−17.8011	−1.21121
$217$	0.0532058	0.00361184
$218$	25.1337	1.70227
$219$	−7.90917	−0.534452
$220$	−4.98829	−0.336311
$221$	12.0874	0.813086
$222$	−5.73422	−0.384855
$223$	−13.9386	−0.933399	−0.466700	−	0.884416i	$-0.654557\pi$
$223$	−13.9386	−0.933399	−0.466700	+	0.884416i	$0.654557\pi$
$224$	−5.99475	−0.400541
$225$	−20.9479	−1.39653
$226$	−17.0653	−1.13516
$227$	−12.3563	−0.820114	−0.410057	−	0.912060i	$-0.634491\pi$
$227$	−12.3563	−0.820114	−0.410057	+	0.912060i	$0.634491\pi$
$228$	−65.4214	−4.33264
$229$	18.8159	1.24339	0.621696	−	0.783259i	$-0.286444\pi$
$229$	18.8159	1.24339	0.621696	+	0.783259i	$0.286444\pi$
$230$	−7.63020	−0.503121
$231$	−3.81512	−0.251017
$232$	8.53046	0.560052
$233$	26.7335	1.75137	0.875685	−	0.482884i	$-0.160411\pi$
$233$	26.7335	1.75137	0.875685	+	0.482884i	$0.160411\pi$
$234$	27.6390	1.80682
$235$	−2.06551	−0.134739
$236$	8.57286	0.558046
$237$	−14.9751	−0.972736
$238$	−11.1455	−0.722457
$239$	−6.62600	−0.428600	−0.214300	−	0.976768i	$-0.568747\pi$
$239$	−6.62600	−0.428600	−0.214300	+	0.976768i	$0.568747\pi$
$240$	3.35358	0.216472
$241$	−24.5672	−1.58251	−0.791257	−	0.611483i	$-0.790573\pi$
$241$	−24.5672	−1.58251	−0.791257	+	0.611483i	$0.790573\pi$
$242$	19.9268	1.28094
$243$	−5.15800	−0.330886
$244$	18.3142	1.17245
$245$	7.12279	0.455058
$246$	6.12418	0.390464
$247$	16.0424	1.02075
$248$	0.133308	0.00846510
$249$	18.0776	1.14562
$250$	−22.3061	−1.41076
$251$	−12.8331	−0.810021	−0.405010	−	0.914312i	$-0.632732\pi$
$251$	−12.8331	−0.810021	−0.405010	+	0.914312i	$0.632732\pi$
$252$	−15.2963	−0.963577
$253$	−4.29307	−0.269903
$254$	−22.2588	−1.39664
$255$	18.8633	1.18127
$256$	−9.07537	−0.567210
$257$	22.8393	1.42468	0.712339	−	0.701836i	$-0.247636\pi$
$257$	22.8393	1.42468	0.712339	+	0.701836i	$0.247636\pi$
$258$	35.7882	2.22808
$259$	−0.778194	−0.0483546
$260$	7.48887	0.464440
$261$	−21.6574	−1.34056
$262$	−5.91223	−0.365259
$263$	−17.8301	−1.09945	−0.549726	−	0.835345i	$-0.685268\pi$
$263$	−17.8301	−1.09945	−0.549726	+	0.835345i	$0.685268\pi$
$264$	−9.55889	−0.588309
$265$	−6.65852	−0.409030
$266$	−14.7924	−0.906977
$267$	8.40769	0.514542
$268$	−9.92283	−0.606133
$269$	17.9939	1.09711	0.548554	−	0.836115i	$-0.315178\pi$
$269$	17.9939	1.09711	0.548554	+	0.836115i	$0.315178\pi$
$270$	20.4022	1.24164
$271$	27.0078	1.64061	0.820303	−	0.571929i	$-0.193805\pi$
$271$	27.0078	1.64061	0.820303	+	0.571929i	$0.193805\pi$
$272$	5.51230	0.334232
$273$	5.72760	0.346650
$274$	2.43481	0.147092
$275$	−5.32072	−0.320852
$276$	−26.2835	−1.58208
$277$	−13.1150	−0.788004	−0.394002	−	0.919110i	$-0.628910\pi$
$277$	−13.1150	−0.788004	−0.394002	+	0.919110i	$0.628910\pi$
$278$	21.0005	1.25952
$279$	−0.338447	−0.0202623
$280$	−2.30563	−0.137788
$281$	−10.3734	−0.618824	−0.309412	−	0.950928i	$-0.600132\pi$
$281$	−10.3734	−0.618824	−0.309412	+	0.950928i	$0.600132\pi$
$282$	−11.8544	−0.705917
$283$	−9.54707	−0.567515	−0.283757	−	0.958896i	$-0.591581\pi$
$283$	−9.54707	−0.567515	−0.283757	+	0.958896i	$0.591581\pi$
$284$	16.4589	0.976656
$285$	25.0355	1.48297
$286$	7.02024	0.415115
$287$	0.831117	0.0490593
$288$	38.1332	2.24702
$289$	14.0058	0.823871
$290$	−9.77695	−0.574122
$291$	30.0719	1.76285
$292$	−8.05450	−0.471354
$293$	−1.12599	−0.0657809	−0.0328904	−	0.999459i	$-0.510471\pi$
$293$	−1.12599	−0.0657809	−0.0328904	+	0.999459i	$0.510471\pi$
$294$	40.8790	2.38411
$295$	−3.28066	−0.191007
$296$	−1.94979	−0.113329
$297$	11.4791	0.666086
$298$	−7.15967	−0.414749
$299$	6.44515	0.372732
$300$	−32.5751	−1.88072
$301$	4.85684	0.279944
$302$	9.33479	0.537157
$303$	7.95677	0.457104
$304$	7.31593	0.419597
$305$	−7.00848	−0.401304
$306$	70.8978	4.05296
$307$	−30.8631	−1.76145	−0.880726	−	0.473626i	$-0.842945\pi$
$307$	−30.8631	−1.76145	−0.880726	+	0.473626i	$0.842945\pi$
$308$	−3.88523	−0.221381
$309$	14.0500	0.799276
$310$	−0.152788	−0.00867776
$311$	−23.1446	−1.31241	−0.656204	−	0.754583i	$-0.727839\pi$
$311$	−23.1446	−1.31241	−0.656204	+	0.754583i	$0.727839\pi$
$312$	14.3507	0.812446
$313$	−8.62409	−0.487462	−0.243731	−	0.969843i	$-0.578371\pi$
$313$	−8.62409	−0.487462	−0.243731	+	0.969843i	$0.578371\pi$
$314$	32.4998	1.83407
$315$	5.85359	0.329812
$316$	−15.2503	−0.857894
$317$	1.13753	0.0638899	0.0319449	−	0.999490i	$-0.489830\pi$
$317$	1.13753	0.0638899	0.0319449	+	0.999490i	$0.489830\pi$
$318$	−38.2145	−2.14296
$319$	−5.50092	−0.307993
$320$	14.9399	0.835164
$321$	−37.0944	−2.07041
$322$	−5.94293	−0.331187
$323$	41.1509	2.28970
$324$	19.0017	1.05565
$325$	7.98794	0.443091
$326$	−51.4320	−2.84856
$327$	−33.1314	−1.83217
$328$	2.08238	0.114980
$329$	−1.60876	−0.0886940
$330$	10.9556	0.603089
$331$	9.17704	0.504416	0.252208	−	0.967673i	$-0.418843\pi$
$331$	9.17704	0.504416	0.252208	+	0.967673i	$0.418843\pi$
$332$	18.4098	1.01037
$333$	4.95017	0.271268
$334$	3.56891	0.195282
$335$	3.79727	0.207467
$336$	2.61200	0.142496
$337$	−15.2995	−0.833415	−0.416707	−	0.909041i	$-0.636816\pi$
$337$	−15.2995	−0.833415	−0.416707	+	0.909041i	$0.636816\pi$
$338$	18.5368	1.00827
$339$	22.4955	1.22179
$340$	19.2100	1.04181
$341$	−0.0859648	−0.00465526
$342$	94.0956	5.08811
$343$	11.8122	0.637797
$344$	12.1689	0.656105
$345$	10.0582	0.541514
$346$	−45.9130	−2.46830
$347$	−20.4366	−1.09710	−0.548548	−	0.836119i	$-0.684819\pi$
$347$	−20.4366	−1.09710	−0.548548	+	0.836119i	$0.684819\pi$
$348$	−33.6783	−1.80535
$349$	22.2159	1.18919	0.594594	−	0.804026i	$-0.297313\pi$
$349$	22.2159	1.18919	0.594594	+	0.804026i	$0.297313\pi$
$350$	−7.36551	−0.393703
$351$	−17.2335	−0.919855
$352$	9.68575	0.516252
$353$	−4.50796	−0.239935	−0.119967	−	0.992778i	$-0.538279\pi$
$353$	−4.50796	−0.239935	−0.119967	+	0.992778i	$0.538279\pi$
$354$	−18.8283	−1.00072
$355$	−6.29849	−0.334289
$356$	8.56218	0.453795
$357$	14.6921	0.777587
$358$	53.6201	2.83391
$359$	20.2152	1.06692	0.533458	−	0.845827i	$-0.320892\pi$
$359$	20.2152	1.06692	0.533458	+	0.845827i	$0.320892\pi$
$360$	14.6663	0.772983
$361$	35.6156	1.87451
$362$	53.2940	2.80107
$363$	−26.2676	−1.37869
$364$	5.83285	0.305724
$365$	3.08229	0.161335
$366$	−40.2230	−2.10249
$367$	7.21338	0.376535	0.188268	−	0.982118i	$-0.439713\pi$
$367$	7.21338	0.376535	0.188268	+	0.982118i	$0.439713\pi$
$368$	2.93922	0.153218
$369$	−5.28682	−0.275221
$370$	2.23469	0.116176
$371$	−5.18612	−0.269250
$372$	−0.526303	−0.0272875
$373$	−19.3386	−1.00132	−0.500658	−	0.865645i	$-0.666908\pi$
$373$	−19.3386	−1.00132	−0.500658	+	0.865645i	$0.666908\pi$
$374$	18.0079	0.931165
$375$	29.4040	1.51842
$376$	−4.03080	−0.207873
$377$	8.25848	0.425333
$378$	15.8906	0.817326
$379$	11.9005	0.611289	0.305645	−	0.952146i	$-0.401128\pi$
$379$	11.9005	0.611289	0.305645	+	0.952146i	$0.401128\pi$
$380$	25.4955	1.30789
$381$	29.3417	1.50322
$382$	−22.0320	−1.12726
$383$	−8.28373	−0.423279	−0.211639	−	0.977348i	$-0.567880\pi$
$383$	−8.28373	−0.423279	−0.211639	+	0.977348i	$0.567880\pi$
$384$	46.2430	2.35983
$385$	1.48680	0.0757742
$386$	14.7100	0.748717
$387$	−30.8948	−1.57047
$388$	30.6245	1.55472
$389$	6.65559	0.337452	0.168726	−	0.985663i	$-0.446035\pi$
$389$	6.65559	0.337452	0.168726	+	0.985663i	$0.446035\pi$
$390$	−16.4476	−0.832856
$391$	16.5327	0.836093
$392$	13.9000	0.702054
$393$	7.79353	0.393131
$394$	11.3426	0.571431
$395$	5.83596	0.293639
$396$	24.7143	1.24194
$397$	26.1595	1.31291	0.656455	−	0.754365i	$-0.272055\pi$
$397$	26.1595	1.31291	0.656455	+	0.754365i	$0.272055\pi$
$398$	19.1600	0.960402
$399$	19.4993	0.976188
$400$	3.64280	0.182140
$401$	−7.74487	−0.386760	−0.193380	−	0.981124i	$-0.561945\pi$
$401$	−7.74487	−0.386760	−0.193380	+	0.981124i	$0.561945\pi$
$402$	21.7932	1.08695
$403$	0.129058	0.00642884
$404$	8.10298	0.403138
$405$	−7.27155	−0.361326
$406$	−7.61496	−0.377924
$407$	1.25733	0.0623236
$408$	36.8114	1.82244
$409$	−9.82582	−0.485855	−0.242928	−	0.970044i	$-0.578108\pi$
$409$	−9.82582	−0.485855	−0.242928	+	0.970044i	$0.578108\pi$
$410$	−2.38667	−0.117869
$411$	−3.20957	−0.158317
$412$	14.3082	0.704913
$413$	−2.55521	−0.125733
$414$	37.8036	1.85794
$415$	−7.04507	−0.345829
$416$	−14.5411	−0.712937
$417$	−27.6829	−1.35564
$418$	23.9001	1.16899
$419$	−14.3415	−0.700628	−0.350314	−	0.936632i	$-0.613925\pi$
$419$	−14.3415	−0.700628	−0.350314	+	0.936632i	$0.613925\pi$
$420$	9.10263	0.444163
$421$	24.7353	1.20553	0.602763	−	0.797920i	$-0.294067\pi$
$421$	24.7353	1.20553	0.602763	+	0.797920i	$0.294067\pi$
$422$	−52.2910	−2.54548
$423$	10.2335	0.497570
$424$	−12.9940	−0.631042
$425$	20.4902	0.993919
$426$	−36.1482	−1.75139
$427$	−5.45869	−0.264164
$428$	−37.7761	−1.82597
$429$	−9.25411	−0.446793
$430$	−13.9471	−0.672588
$431$	−12.3299	−0.593910	−0.296955	−	0.954891i	$-0.595971\pi$
$431$	−12.3299	−0.593910	−0.296955	+	0.954891i	$0.595971\pi$
$432$	−7.85910	−0.378121
$433$	−21.3023	−1.02372	−0.511862	−	0.859068i	$-0.671044\pi$
$433$	−21.3023	−1.02372	−0.511862	+	0.859068i	$0.671044\pi$
$434$	−0.119002	−0.00571226
$435$	12.8880	0.617933
$436$	−33.7402	−1.61586
$437$	21.9422	1.04964
$438$	17.6899	0.845255
$439$	26.9381	1.28569	0.642843	−	0.765998i	$-0.277755\pi$
$439$	26.9381	1.28569	0.642843	+	0.765998i	$0.277755\pi$
$440$	3.72521	0.177592
$441$	−35.2896	−1.68046
$442$	−27.0350	−1.28592
$443$	12.8475	0.610402	0.305201	−	0.952288i	$-0.401276\pi$
$443$	12.8475	0.610402	0.305201	+	0.952288i	$0.401276\pi$
$444$	7.69777	0.365320
$445$	−3.27657	−0.155325
$446$	31.1755	1.47620
$447$	9.43792	0.446398
$448$	11.6362	0.549759
$449$	35.9251	1.69541	0.847705	−	0.530468i	$-0.177984\pi$
$449$	35.9251	1.69541	0.847705	+	0.530468i	$0.177984\pi$
$450$	46.8527	2.20866
$451$	−1.34284	−0.0632318
$452$	22.9089	1.07754
$453$	−12.3052	−0.578147
$454$	27.6364	1.29704
$455$	−2.23211	−0.104643
$456$	48.8561	2.28790
$457$	10.2426	0.479130	0.239565	−	0.970880i	$-0.422995\pi$
$457$	10.2426	0.479130	0.239565	+	0.970880i	$0.422995\pi$
$458$	−42.0842	−1.96647
$459$	−44.2062	−2.06337
$460$	10.2430	0.477582
$461$	−21.6611	−1.00886	−0.504428	−	0.863454i	$-0.668297\pi$
$461$	−21.6611	−1.00886	−0.504428	+	0.863454i	$0.668297\pi$
$462$	8.53302	0.396992
$463$	35.0774	1.63018	0.815092	−	0.579332i	$-0.196686\pi$
$463$	35.0774	1.63018	0.815092	+	0.579332i	$0.196686\pi$
$464$	3.76617	0.174840
$465$	0.201405	0.00933996
$466$	−59.7929	−2.76985
$467$	−30.8897	−1.42940	−0.714702	−	0.699429i	$-0.753438\pi$
$467$	−30.8897	−1.42940	−0.714702	+	0.699429i	$0.753438\pi$
$468$	−37.1033	−1.71510
$469$	2.95757	0.136568
$470$	4.61978	0.213095
$471$	−42.8413	−1.97402
$472$	−6.40214	−0.294682
$473$	−7.84722	−0.360815
$474$	33.4937	1.53842
$475$	27.1946	1.24777
$476$	14.9621	0.685784
$477$	32.9894	1.51048
$478$	14.8199	0.677847
$479$	−24.1508	−1.10348	−0.551739	−	0.834017i	$-0.686035\pi$
$479$	−24.1508	−1.10348	−0.551739	+	0.834017i	$0.686035\pi$
$480$	−22.6926	−1.03577
$481$	−1.88762	−0.0860680
$482$	54.9478	2.50280
$483$	7.83400	0.356459
$484$	−26.7503	−1.21592
$485$	−11.7194	−0.532149
$486$	11.5365	0.523308
$487$	−9.02426	−0.408928	−0.204464	−	0.978874i	$-0.565545\pi$
$487$	−9.02426	−0.408928	−0.204464	+	0.978874i	$0.565545\pi$
$488$	−13.6769	−0.619123
$489$	67.7979	3.06593
$490$	−15.9310	−0.719691
$491$	−1.92635	−0.0869349	−0.0434675	−	0.999055i	$-0.513840\pi$
$491$	−1.92635	−0.0869349	−0.0434675	+	0.999055i	$0.513840\pi$
$492$	−8.22127	−0.370643
$493$	21.1841	0.954085
$494$	−35.8809	−1.61436
$495$	−9.45767	−0.425091
$496$	0.0588552	0.00264268
$497$	−4.90570	−0.220051
$498$	−40.4330	−1.81185
$499$	−35.5457	−1.59124	−0.795621	−	0.605795i	$-0.792855\pi$
$499$	−35.5457	−1.59124	−0.795621	+	0.605795i	$0.792855\pi$
$500$	29.9443	1.33915
$501$	−4.70456	−0.210184
$502$	28.7030	1.28108
$503$	35.8337	1.59775	0.798874	−	0.601498i	$-0.205429\pi$
$503$	35.8337	1.59775	0.798874	+	0.601498i	$0.205429\pi$
$504$	11.4231	0.508827
$505$	−3.10085	−0.137986
$506$	9.60202	0.426862
$507$	−24.4353	−1.08521
$508$	29.8809	1.32575
$509$	11.5311	0.511108	0.255554	−	0.966795i	$-0.417742\pi$
$509$	11.5311	0.511108	0.255554	+	0.966795i	$0.417742\pi$
$510$	−42.1903	−1.86822
$511$	2.40070	0.106201
$512$	−11.0707	−0.489260
$513$	−58.6706	−2.59037
$514$	−51.0831	−2.25318
$515$	−5.47545	−0.241277
$516$	−48.0431	−2.11498
$517$	2.59929	0.114316
$518$	1.74053	0.0764746
$519$	60.5228	2.65665
$520$	−5.59262	−0.245253
$521$	−19.3302	−0.846870	−0.423435	−	0.905927i	$-0.639176\pi$
$521$	−19.3302	−0.846870	−0.423435	+	0.905927i	$0.639176\pi$
$522$	48.4395	2.12014
$523$	18.7171	0.818444	0.409222	−	0.912435i	$-0.365800\pi$
$523$	18.7171	0.818444	0.409222	+	0.912435i	$0.365800\pi$
$524$	7.93673	0.346718
$525$	9.70925	0.423746
$526$	39.8793	1.73882
$527$	0.331051	0.0144208
$528$	−4.22022	−0.183661
$529$	−14.1846	−0.616721
$530$	14.8926	0.646895
$531$	16.2539	0.705360
$532$	19.8577	0.860939
$533$	2.01599	0.0873222
$534$	−18.8049	−0.813767
$535$	14.4561	0.624993
$536$	7.41028	0.320075
$537$	−70.6822	−3.05016
$538$	−40.2457	−1.73512
$539$	−8.96348	−0.386084
$540$	−27.3884	−1.17861
$541$	4.38640	0.188586	0.0942931	−	0.995544i	$-0.469941\pi$
$541$	4.38640	0.188586	0.0942931	+	0.995544i	$0.469941\pi$
$542$	−60.4064	−2.59468
$543$	−70.2525	−3.01482
$544$	−37.2999	−1.59922
$545$	12.9117	0.553076
$546$	−12.8105	−0.548240
$547$	−24.2838	−1.03830	−0.519150	−	0.854683i	$-0.673752\pi$
$547$	−24.2838	−1.03830	−0.519150	+	0.854683i	$0.673752\pi$
$548$	−3.26855	−0.139626
$549$	34.7232	1.48195
$550$	11.9005	0.507438
$551$	28.1156	1.19776
$552$	19.6283	0.835435
$553$	4.54545	0.193292
$554$	29.3334	1.24626
$555$	−2.94578	−0.125041
$556$	−28.1916	−1.19559
$557$	43.1132	1.82677	0.913383	−	0.407101i	$-0.133460\pi$
$557$	43.1132	1.82677	0.913383	+	0.407101i	$0.133460\pi$
$558$	0.756981	0.0320456
$559$	11.7809	0.498281
$560$	−1.01793	−0.0430152
$561$	−23.7381	−1.00222
$562$	23.2014	0.978692
$563$	15.8840	0.669431	0.334716	−	0.942319i	$-0.391360\pi$
$563$	15.8840	0.669431	0.334716	+	0.942319i	$0.391360\pi$
$564$	15.9136	0.670084
$565$	−8.76676	−0.368820
$566$	21.3533	0.897545
$567$	−5.66359	−0.237848
$568$	−12.2914	−0.515734
$569$	−34.2177	−1.43448	−0.717241	−	0.696825i	$-0.754595\pi$
$569$	−34.2177	−1.43448	−0.717241	+	0.696825i	$0.754595\pi$
$570$	−55.9951	−2.34537
$571$	−1.73284	−0.0725170	−0.0362585	−	0.999342i	$-0.511544\pi$
$571$	−1.73284	−0.0725170	−0.0362585	+	0.999342i	$0.511544\pi$
$572$	−9.42416	−0.394044
$573$	29.0427	1.21328
$574$	−1.85890	−0.0775890
$575$	10.9256	0.455629
$576$	−74.0190	−3.08412
$577$	39.9638	1.66371	0.831857	−	0.554989i	$-0.187278\pi$
$577$	39.9638	1.66371	0.831857	+	0.554989i	$0.187278\pi$
$578$	−31.3258	−1.30298
$579$	−19.3907	−0.805851
$580$	13.1248	0.544979
$581$	−5.48719	−0.227647
$582$	−67.2597	−2.78801
$583$	8.37923	0.347032
$584$	6.01503	0.248904
$585$	14.1987	0.587044
$586$	2.51842	0.104035
$587$	3.31145	0.136678	0.0683391	−	0.997662i	$-0.478230\pi$
$587$	3.31145	0.136678	0.0683391	+	0.997662i	$0.478230\pi$
$588$	−54.8771	−2.26309
$589$	0.439372	0.0181040
$590$	7.33762	0.302085
$591$	−14.9518	−0.615037
$592$	−0.860823	−0.0353796
$593$	−11.6592	−0.478785	−0.239392	−	0.970923i	$-0.576948\pi$
$593$	−11.6592	−0.478785	−0.239392	+	0.970923i	$0.576948\pi$
$594$	−25.6746	−1.05344
$595$	−5.72567	−0.234730
$596$	9.61134	0.393696
$597$	−25.2567	−1.03369
$598$	−14.4154	−0.589490
$599$	−28.5754	−1.16756	−0.583779	−	0.811912i	$-0.698427\pi$
$599$	−28.5754	−1.16756	−0.583779	+	0.811912i	$0.698427\pi$
$600$	24.3268	0.993136
$601$	8.15344	0.332586	0.166293	−	0.986076i	$-0.446820\pi$
$601$	8.15344	0.332586	0.166293	+	0.986076i	$0.446820\pi$
$602$	−10.8630	−0.442741
$603$	−18.8134	−0.766141
$604$	−12.5313	−0.509891
$605$	10.2368	0.416184
$606$	−17.7963	−0.722927
$607$	−23.3632	−0.948282	−0.474141	−	0.880449i	$-0.657241\pi$
$607$	−23.3632	−0.948282	−0.474141	+	0.880449i	$0.657241\pi$
$608$	−49.5045	−2.00767
$609$	10.0381	0.406764
$610$	15.6754	0.634677
$611$	−3.90228	−0.157869
$612$	−95.1751	−3.84722
$613$	31.0801	1.25531	0.627656	−	0.778491i	$-0.284015\pi$
$613$	31.0801	1.25531	0.627656	+	0.778491i	$0.284015\pi$
$614$	69.0294	2.78580
$615$	3.14611	0.126864
$616$	2.90145	0.116903
$617$	25.9028	1.04281	0.521403	−	0.853310i	$-0.325409\pi$
$617$	25.9028	1.04281	0.521403	+	0.853310i	$0.325409\pi$
$618$	−31.4246	−1.26408
$619$	22.8635	0.918962	0.459481	−	0.888188i	$-0.348035\pi$
$619$	22.8635	0.918962	0.459481	+	0.888188i	$0.348035\pi$
$620$	0.205106	0.00823727
$621$	−23.5713	−0.945884
$622$	51.7659	2.07562
$623$	−2.55202	−0.102245
$624$	6.33576	0.253634
$625$	6.93989	0.277596
$626$	19.2889	0.770939
$627$	−31.5052	−1.25820
$628$	−43.6285	−1.74097
$629$	−4.84200	−0.193063
$630$	−13.0923	−0.521610
$631$	−32.3376	−1.28734	−0.643670	−	0.765303i	$-0.722589\pi$
$631$	−32.3376	−1.28734	−0.643670	+	0.765303i	$0.722589\pi$
$632$	11.3888	0.453020
$633$	68.9302	2.73973
$634$	−2.54423	−0.101044
$635$	−11.4348	−0.453776
$636$	51.3002	2.03419
$637$	13.4568	0.533177
$638$	12.3035	0.487101
$639$	31.2056	1.23448
$640$	−18.0215	−0.712361
$641$	−13.9599	−0.551381	−0.275691	−	0.961246i	$-0.588906\pi$
$641$	−13.9599	−0.551381	−0.275691	+	0.961246i	$0.588906\pi$
$642$	82.9665	3.27443
$643$	−21.7974	−0.859605	−0.429802	−	0.902923i	$-0.641417\pi$
$643$	−21.7974	−0.859605	−0.429802	+	0.902923i	$0.641417\pi$
$644$	7.97795	0.314375
$645$	18.3851	0.723913
$646$	−92.0394	−3.62124
$647$	5.51197	0.216698	0.108349	−	0.994113i	$-0.465444\pi$
$647$	5.51197	0.216698	0.108349	+	0.994113i	$0.465444\pi$
$648$	−14.1903	−0.557446
$649$	4.12846	0.162056
$650$	−17.8661	−0.700765
$651$	0.156869	0.00614816
$652$	69.0437	2.70396
$653$	26.1756	1.02433	0.512165	−	0.858887i	$-0.328844\pi$
$653$	26.1756	1.02433	0.512165	+	0.858887i	$0.328844\pi$
$654$	74.1027	2.89764
$655$	−3.03723	−0.118674
$656$	0.919366	0.0358952
$657$	−15.2711	−0.595783
$658$	3.59821	0.140273
$659$	3.09183	0.120441	0.0602203	−	0.998185i	$-0.480820\pi$
$659$	3.09183	0.120441	0.0602203	+	0.998185i	$0.480820\pi$
$660$	−14.7072	−0.572475
$661$	−31.0796	−1.20886	−0.604429	−	0.796659i	$-0.706599\pi$
$661$	−31.0796	−1.20886	−0.604429	+	0.796659i	$0.706599\pi$
$662$	−20.5256	−0.797752
$663$	35.6377	1.38405
$664$	−13.7483	−0.533537
$665$	−7.59912	−0.294681
$666$	−11.0717	−0.429019
$667$	11.2956	0.437369
$668$	−4.79101	−0.185370
$669$	−41.0957	−1.58885
$670$	−8.49308	−0.328116
$671$	8.81962	0.340478
$672$	−17.6745	−0.681810
$673$	8.87424	0.342077	0.171038	−	0.985264i	$-0.445288\pi$
$673$	8.87424	0.342077	0.171038	+	0.985264i	$0.445288\pi$
$674$	34.2192	1.31808
$675$	−29.2137	−1.12443
$676$	−24.8843	−0.957087
$677$	12.7851	0.491373	0.245687	−	0.969349i	$-0.420987\pi$
$677$	12.7851	0.491373	0.245687	+	0.969349i	$0.420987\pi$
$678$	−50.3141	−1.93230
$679$	−9.12786	−0.350295
$680$	−14.3458	−0.550137
$681$	−36.4304	−1.39602
$682$	0.192271	0.00736246
$683$	−20.4015	−0.780640	−0.390320	−	0.920679i	$-0.627636\pi$
$683$	−20.4015	−0.780640	−0.390320	+	0.920679i	$0.627636\pi$
$684$	−126.316	−4.82983
$685$	1.25081	0.0477909
$686$	−26.4195	−1.00870
$687$	55.4756	2.11653
$688$	5.37254	0.204826
$689$	−12.5796	−0.479246
$690$	−22.4964	−0.856423
$691$	15.2249	0.579184	0.289592	−	0.957150i	$-0.406480\pi$
$691$	15.2249	0.579184	0.289592	+	0.957150i	$0.406480\pi$
$692$	61.6349	2.34301
$693$	−7.36629	−0.279822
$694$	45.7092	1.73510
$695$	10.7884	0.409226
$696$	25.1507	0.953334
$697$	5.17129	0.195877
$698$	−49.6886	−1.88074
$699$	78.8193	2.98122
$700$	9.88766	0.373718
$701$	−29.6600	−1.12024	−0.560121	−	0.828411i	$-0.689245\pi$
$701$	−29.6600	−1.12024	−0.560121	+	0.828411i	$0.689245\pi$
$702$	38.5449	1.45478
$703$	−6.42630	−0.242373
$704$	−18.8007	−0.708576
$705$	−6.08982	−0.229356
$706$	10.0826	0.379465
$707$	−2.41515	−0.0908312
$708$	25.2757	0.949918
$709$	−10.0381	−0.376989	−0.188494	−	0.982074i	$-0.560361\pi$
$709$	−10.0381	−0.376989	−0.188494	+	0.982074i	$0.560361\pi$
$710$	14.0874	0.528690
$711$	−28.9141	−1.08436
$712$	−6.39416	−0.239631
$713$	0.176521	0.00661075
$714$	−32.8607	−1.22978
$715$	3.60644	0.134873
$716$	−71.9811	−2.69006
$717$	−19.5357	−0.729573
$718$	−45.2138	−1.68737
$719$	−4.31179	−0.160803	−0.0804013	−	0.996763i	$-0.525620\pi$
$719$	−4.31179	−0.160803	−0.0804013	+	0.996763i	$0.525620\pi$
$720$	6.47513	0.241314
$721$	−4.26466	−0.158824
$722$	−79.6589	−2.96460
$723$	−72.4324	−2.69379
$724$	−71.5434	−2.65889
$725$	13.9995	0.519929
$726$	58.7509	2.18045
$727$	−9.05149	−0.335701	−0.167851	−	0.985812i	$-0.553683\pi$
$727$	−9.05149	−0.335701	−0.167851	+	0.985812i	$0.553683\pi$
$728$	−4.35592	−0.161441
$729$	−34.1933	−1.26642
$730$	−6.89395	−0.255157
$731$	30.2197	1.11772
$732$	53.9964	1.99577
$733$	37.4585	1.38356	0.691780	−	0.722109i	$-0.256827\pi$
$733$	37.4585	1.38356	0.691780	+	0.722109i	$0.256827\pi$
$734$	−16.1337	−0.595504
$735$	21.0004	0.774610
$736$	−19.8888	−0.733110
$737$	−4.77856	−0.176021
$738$	11.8246	0.435271
$739$	4.97123	0.182870	0.0914349	−	0.995811i	$-0.470855\pi$
$739$	4.97123	0.182870	0.0914349	+	0.995811i	$0.470855\pi$
$740$	−2.99991	−0.110279
$741$	47.2984	1.73755
$742$	11.5994	0.425828
$743$	44.5097	1.63290	0.816452	−	0.577413i	$-0.195938\pi$
$743$	44.5097	1.63290	0.816452	+	0.577413i	$0.195938\pi$
$744$	0.393038	0.0144095
$745$	−3.67807	−0.134754
$746$	43.2533	1.58362
$747$	34.9045	1.27709
$748$	−24.1742	−0.883898
$749$	11.2594	0.411411
$750$	−65.7659	−2.40143
$751$	−21.1806	−0.772890	−0.386445	−	0.922312i	$-0.626297\pi$
$751$	−21.1806	−0.772890	−0.386445	+	0.922312i	$0.626297\pi$
$752$	−1.77958	−0.0648947
$753$	−37.8364	−1.37884
$754$	−18.4712	−0.672680
$755$	4.79547	0.174525
$756$	−21.3320	−0.775838
$757$	31.9305	1.16053	0.580266	−	0.814427i	$-0.302949\pi$
$757$	31.9305	1.16053	0.580266	+	0.814427i	$0.302949\pi$
$758$	−26.6171	−0.966776
$759$	−12.6574	−0.459435
$760$	−19.0398	−0.690646
$761$	23.2934	0.844387	0.422193	−	0.906506i	$-0.361260\pi$
$761$	23.2934	0.844387	0.422193	+	0.906506i	$0.361260\pi$
$762$	−65.6265	−2.37740
$763$	10.0565	0.364071
$764$	29.5764	1.07003
$765$	36.4216	1.31683
$766$	18.5276	0.669431
$767$	−6.19801	−0.223797
$768$	−26.7572	−0.965518
$769$	−4.29186	−0.154768	−0.0773842	−	0.997001i	$-0.524657\pi$
$769$	−4.29186	−0.154768	−0.0773842	+	0.997001i	$0.524657\pi$
$770$	−3.32542	−0.119840
$771$	67.3379	2.42512
$772$	−19.7470	−0.710711
$773$	10.4474	0.375768	0.187884	−	0.982191i	$-0.439837\pi$
$773$	10.4474	0.375768	0.187884	+	0.982191i	$0.439837\pi$
$774$	69.1003	2.48376
$775$	0.218775	0.00785863
$776$	−22.8701	−0.820988
$777$	−2.29438	−0.0823103
$778$	−14.8861	−0.533693
$779$	6.86334	0.245905
$780$	22.0797	0.790580
$781$	7.92616	0.283620
$782$	−36.9775	−1.32231
$783$	−30.2031	−1.07937
$784$	6.13678	0.219171
$785$	16.6958	0.595897
$786$	−17.4312	−0.621751
$787$	31.8294	1.13460	0.567299	−	0.823512i	$-0.307989\pi$
$787$	31.8294	1.13460	0.567299	+	0.823512i	$0.307989\pi$
$788$	−15.2266	−0.542425
$789$	−52.5691	−1.87151
$790$	−13.0529	−0.464401
$791$	−6.82816	−0.242781
$792$	−18.4564	−0.655820
$793$	−13.2408	−0.470195
$794$	−58.5092	−2.07641
$795$	−19.6316	−0.696260
$796$	−25.7208	−0.911651
$797$	−55.9430	−1.98160	−0.990802	−	0.135321i	$-0.956794\pi$
$797$	−55.9430	−1.98160	−0.990802	+	0.135321i	$0.956794\pi$
$798$	−43.6128	−1.54388
$799$	−10.0099	−0.354124
$800$	−24.6496	−0.871496
$801$	16.2337	0.573589
$802$	17.3224	0.611676
$803$	−3.87883	−0.136881
$804$	−29.2558	−1.03177
$805$	−3.05300	−0.107604
$806$	−0.288655	−0.0101674
$807$	53.0521	1.86752
$808$	−6.05123	−0.212881
$809$	−19.5828	−0.688494	−0.344247	−	0.938879i	$-0.611866\pi$
$809$	−19.5828	−0.688494	−0.344247	+	0.938879i	$0.611866\pi$
$810$	16.2638	0.571450
$811$	19.2244	0.675059	0.337530	−	0.941315i	$-0.390409\pi$
$811$	19.2244	0.675059	0.337530	+	0.941315i	$0.390409\pi$
$812$	10.2225	0.358741
$813$	79.6280	2.79268
$814$	−2.81218	−0.0985670
$815$	−26.4216	−0.925510
$816$	16.2521	0.568937
$817$	40.1077	1.40319
$818$	21.9767	0.768398
$819$	11.0589	0.386430
$820$	3.20393	0.111886
$821$	−45.9240	−1.60276	−0.801379	−	0.598157i	$-0.795900\pi$
$821$	−45.9240	−1.60276	−0.801379	+	0.598157i	$0.795900\pi$
$822$	7.17863	0.250383
$823$	39.9665	1.39314	0.696572	−	0.717487i	$-0.254708\pi$
$823$	39.9665	1.39314	0.696572	+	0.717487i	$0.254708\pi$
$824$	−10.6852	−0.372237
$825$	−15.6873	−0.546161
$826$	5.71505	0.198852
$827$	11.4044	0.396568	0.198284	−	0.980145i	$-0.436463\pi$
$827$	11.4044	0.396568	0.198284	+	0.980145i	$0.436463\pi$
$828$	−50.7485	−1.76363
$829$	−36.3235	−1.26157	−0.630783	−	0.775959i	$-0.717266\pi$
$829$	−36.3235	−1.26157	−0.630783	+	0.775959i	$0.717266\pi$
$830$	15.7572	0.546941
$831$	−38.6674	−1.34136
$832$	28.2252	0.978533
$833$	34.5184	1.19599
$834$	61.9164	2.14399
$835$	1.83342	0.0634482
$836$	−32.0841	−1.10965
$837$	−0.471994	−0.0163145
$838$	32.0766	1.10807
$839$	−4.45454	−0.153788	−0.0768940	−	0.997039i	$-0.524500\pi$
$839$	−4.45454	−0.153788	−0.0768940	+	0.997039i	$0.524500\pi$
$840$	−6.79776	−0.234545
$841$	−14.5264	−0.500909
$842$	−55.3237	−1.90658
$843$	−30.5842	−1.05338
$844$	70.1968	2.41627
$845$	9.52271	0.327591
$846$	−22.8885	−0.786925
$847$	7.97312	0.273959
$848$	−5.73678	−0.197002
$849$	−28.1480	−0.966036
$850$	−45.8289	−1.57192
$851$	−2.58181	−0.0885034
$852$	48.5264	1.66249
$853$	−42.5696	−1.45756	−0.728778	−	0.684750i	$-0.759911\pi$
$853$	−42.5696	−1.45756	−0.728778	+	0.684750i	$0.759911\pi$
$854$	12.2091	0.417785
$855$	48.3388	1.65315
$856$	28.2108	0.964226
$857$	−1.58783	−0.0542393	−0.0271196	−	0.999632i	$-0.508634\pi$
$857$	−1.58783	−0.0542393	−0.0271196	+	0.999632i	$0.508634\pi$
$858$	20.6980	0.706619
$859$	−25.8743	−0.882818	−0.441409	−	0.897306i	$-0.645521\pi$
$859$	−25.8743	−0.882818	−0.441409	+	0.897306i	$0.645521\pi$
$860$	18.7229	0.638447
$861$	2.45041	0.0835098
$862$	27.5774	0.939291
$863$	50.2412	1.71023	0.855115	−	0.518438i	$-0.173486\pi$
$863$	50.2412	1.71023	0.855115	+	0.518438i	$0.173486\pi$
$864$	53.1800	1.80922
$865$	−23.5864	−0.801963
$866$	47.6454	1.61906
$867$	41.2938	1.40241
$868$	0.159751	0.00542230
$869$	−7.34411	−0.249132
$870$	−28.8257	−0.977283
$871$	7.17401	0.243082
$872$	25.1969	0.853274
$873$	58.0632	1.96514
$874$	−49.0766	−1.66004
$875$	−8.92513	−0.301725
$876$	−23.7474	−0.802349
$877$	−47.8389	−1.61540	−0.807702	−	0.589590i	$-0.799289\pi$
$877$	−47.8389	−1.61540	−0.807702	+	0.589590i	$0.799289\pi$
$878$	−60.2506	−2.03336
$879$	−3.31979	−0.111974
$880$	1.64467	0.0554417
$881$	27.8273	0.937526	0.468763	−	0.883324i	$-0.344700\pi$
$881$	27.8273	0.937526	0.468763	+	0.883324i	$0.344700\pi$
$882$	78.9298	2.65770
$883$	−2.66793	−0.0897830	−0.0448915	−	0.998992i	$-0.514294\pi$
$883$	−2.66793	−0.0897830	−0.0448915	+	0.998992i	$0.514294\pi$
$884$	36.2925	1.22065
$885$	−9.67249	−0.325137
$886$	−28.7350	−0.965372
$887$	1.01884	0.0342094	0.0171047	−	0.999854i	$-0.494555\pi$
$887$	1.01884	0.0342094	0.0171047	+	0.999854i	$0.494555\pi$
$888$	−5.74862	−0.192911
$889$	−8.90621	−0.298705
$890$	7.32848	0.245651
$891$	9.15068	0.306559
$892$	−41.8509	−1.40127
$893$	−13.2851	−0.444570
$894$	−21.1091	−0.705995
$895$	27.5457	0.920751
$896$	−14.0364	−0.468922
$897$	19.0025	0.634473
$898$	−80.3511	−2.68135
$899$	0.226185	0.00754368
$900$	−62.8964	−2.09655
$901$	−32.2685	−1.07502
$902$	3.00343	0.100003
$903$	14.3196	0.476526
$904$	−17.1081	−0.569008
$905$	27.3782	0.910082
$906$	27.5221	0.914361
$907$	41.7622	1.38669	0.693346	−	0.720605i	$-0.256136\pi$
$907$	41.7622	1.38669	0.693346	+	0.720605i	$0.256136\pi$
$908$	−37.0998	−1.23120
$909$	15.3630	0.509559
$910$	4.99241	0.165497
$911$	−2.26682	−0.0751031	−0.0375515	−	0.999295i	$-0.511956\pi$
$911$	−2.26682	−0.0751031	−0.0375515	+	0.999295i	$0.511956\pi$
$912$	21.5698	0.714248
$913$	8.86567	0.293411
$914$	−22.9090	−0.757761
$915$	−20.6633	−0.683109
$916$	56.4950	1.86665
$917$	−2.36560	−0.0781191
$918$	98.8730	3.26329
$919$	15.5618	0.513338	0.256669	−	0.966499i	$-0.417375\pi$
$919$	15.5618	0.513338	0.256669	+	0.966499i	$0.417375\pi$
$920$	−7.64937	−0.252192
$921$	−90.9949	−2.99838
$922$	48.4478	1.59554
$923$	−11.8995	−0.391675
$924$	−11.4550	−0.376840
$925$	−3.19983	−0.105210
$926$	−78.4551	−2.57819
$927$	27.1279	0.890997
$928$	−25.4845	−0.836568
$929$	−47.1723	−1.54767	−0.773837	−	0.633385i	$-0.781665\pi$
$929$	−47.1723	−1.54767	−0.773837	+	0.633385i	$0.781665\pi$
$930$	−0.450469	−0.0147715
$931$	45.8129	1.50146
$932$	80.2676	2.62925
$933$	−68.2380	−2.23401
$934$	69.0888	2.26065
$935$	9.25100	0.302540
$936$	27.7084	0.905678
$937$	30.8837	1.00892	0.504462	−	0.863434i	$-0.331691\pi$
$937$	30.8837	1.00892	0.504462	+	0.863434i	$0.331691\pi$
$938$	−6.61500	−0.215987
$939$	−25.4267	−0.829769
$940$	−6.20172	−0.202278
$941$	35.1275	1.14512	0.572562	−	0.819862i	$-0.305950\pi$
$941$	35.1275	1.14512	0.572562	+	0.819862i	$0.305950\pi$
$942$	95.8202	3.12199
$943$	2.75739	0.0897931
$944$	−2.82652	−0.0919954
$945$	8.16333	0.265553
$946$	17.5513	0.570643
$947$	3.44703	0.112013	0.0560067	−	0.998430i	$-0.482163\pi$
$947$	3.44703	0.112013	0.0560067	+	0.998430i	$0.482163\pi$
$948$	−44.9629	−1.46033
$949$	5.82324	0.189030
$950$	−60.8242	−1.97340
$951$	3.35381	0.108755
$952$	−11.1735	−0.362136
$953$	−33.8504	−1.09652	−0.548261	−	0.836307i	$-0.684710\pi$
$953$	−33.8504	−1.09652	−0.548261	+	0.836307i	$0.684710\pi$
$954$	−73.7851	−2.38888
$955$	−11.3183	−0.366251
$956$	−19.8947	−0.643439
$957$	−16.2186	−0.524272
$958$	54.0164	1.74519
$959$	0.974216	0.0314591
$960$	44.0477	1.42163
$961$	−30.9965	−0.999886
$962$	4.22190	0.136120
$963$	−71.6224	−2.30800
$964$	−73.7634	−2.37576
$965$	7.55679	0.243262
$966$	−17.5218	−0.563753
$967$	−41.0612	−1.32044	−0.660219	−	0.751073i	$-0.729537\pi$
$967$	−41.0612	−1.32044	−0.660219	+	0.751073i	$0.729537\pi$
$968$	19.9768	0.642080
$969$	121.327	3.89758
$970$	26.2119	0.841613
$971$	−7.65000	−0.245500	−0.122750	−	0.992438i	$-0.539171\pi$
$971$	−7.65000	−0.245500	−0.122750	+	0.992438i	$0.539171\pi$
$972$	−15.4870	−0.496744
$973$	8.40272	0.269379
$974$	20.1839	0.646735
$975$	23.5511	0.754240
$976$	−6.03829	−0.193281
$977$	−18.0638	−0.577914	−0.288957	−	0.957342i	$-0.593308\pi$
$977$	−18.0638	−0.577914	−0.288957	+	0.957342i	$0.593308\pi$
$978$	−151.639	−4.84888
$979$	4.12331	0.131782
$980$	21.3863	0.683159
$981$	−63.9705	−2.04242
$982$	4.30853	0.137491
$983$	−19.1548	−0.610943	−0.305471	−	0.952201i	$-0.598814\pi$
$983$	−19.1548	−0.610943	−0.305471	+	0.952201i	$0.598814\pi$
$984$	6.13957	0.195722
$985$	5.82691	0.185661
$986$	−47.3810	−1.50892
$987$	−4.74317	−0.150977
$988$	48.1675	1.53241
$989$	16.1135	0.512380
$990$	21.1533	0.672296
$991$	0.904242	0.0287242	0.0143621	−	0.999897i	$-0.495428\pi$
$991$	0.904242	0.0287242	0.0143621	+	0.999897i	$0.495428\pi$
$992$	−0.398254	−0.0126446
$993$	27.0570	0.858628
$994$	10.9722	0.348018
$995$	9.84285	0.312039
$996$	54.2783	1.71987
$997$	−23.8669	−0.755872	−0.377936	−	0.925832i	$-0.623366\pi$
$997$	−23.8669	−0.755872	−0.377936	+	0.925832i	$0.623366\pi$
$998$	79.5025	2.51661
$999$	6.90343	0.218415

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1511.2.a.a.1.5	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1511.2.a.a.1.5	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1511 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1511.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23663 q^{2} +2.94834 q^{3} +3.00251 q^{4} -1.14900 q^{5} -6.59433 q^{6} -0.894921 q^{7} -2.24225 q^{8} +5.69268 q^{9} +O(q^{10})\)	\(q-2.23663 q^{2} +2.94834 q^{3} +3.00251 q^{4} -1.14900 q^{5} -6.59433 q^{6} -0.894921 q^{7} -2.24225 q^{8} +5.69268 q^{9} +2.56989 q^{10} +1.44593 q^{11} +8.85241 q^{12} -2.17076 q^{13} +2.00161 q^{14} -3.38764 q^{15} -0.989945 q^{16} -5.56829 q^{17} -12.7324 q^{18} -7.39024 q^{19} -3.44989 q^{20} -2.63853 q^{21} -3.23401 q^{22} -2.96908 q^{23} -6.61090 q^{24} -3.67980 q^{25} +4.85518 q^{26} +7.93893 q^{27} -2.68701 q^{28} -3.80442 q^{29} +7.57690 q^{30} -0.0594530 q^{31} +6.69864 q^{32} +4.26308 q^{33} +12.4542 q^{34} +1.02827 q^{35} +17.0923 q^{36} +0.869567 q^{37} +16.5292 q^{38} -6.40012 q^{39} +2.57635 q^{40} -0.928704 q^{41} +5.90141 q^{42} -5.42711 q^{43} +4.34142 q^{44} -6.54090 q^{45} +6.64073 q^{46} +1.79766 q^{47} -2.91869 q^{48} -6.19912 q^{49} +8.23034 q^{50} -16.4172 q^{51} -6.51772 q^{52} +5.79505 q^{53} -17.7564 q^{54} -1.66137 q^{55} +2.00664 q^{56} -21.7889 q^{57} +8.50909 q^{58} +2.85523 q^{59} -10.1714 q^{60} +6.09963 q^{61} +0.132974 q^{62} -5.09450 q^{63} -13.0025 q^{64} +2.49420 q^{65} -9.53493 q^{66} -3.30484 q^{67} -16.7188 q^{68} -8.75384 q^{69} -2.29985 q^{70} +5.48171 q^{71} -12.7644 q^{72} -2.68259 q^{73} -1.94490 q^{74} -10.8493 q^{75} -22.1893 q^{76} -1.29399 q^{77} +14.3147 q^{78} -5.07917 q^{79} +1.13745 q^{80} +6.32859 q^{81} +2.07717 q^{82} +6.13147 q^{83} -7.92221 q^{84} +6.39796 q^{85} +12.1384 q^{86} -11.2167 q^{87} -3.24213 q^{88} +2.85167 q^{89} +14.6296 q^{90} +1.94266 q^{91} -8.91469 q^{92} -0.175288 q^{93} -4.02070 q^{94} +8.49139 q^{95} +19.7498 q^{96} +10.1996 q^{97} +13.8651 q^{98} +8.23121 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 5 q^{2} - 4 q^{3} + 19 q^{4} - 8 q^{5} - 8 q^{6} - 15 q^{7} - 12 q^{8} - q^{9}+O(q^{10}) \) 39 * q - 5 * q^2 - 4 * q^3 + 19 * q^4 - 8 * q^5 - 8 * q^6 - 15 * q^7 - 12 * q^8 - q^9	\( 39 q - 5 q^{2} - 4 q^{3} + 19 q^{4} - 8 q^{5} - 8 q^{6} - 15 q^{7} - 12 q^{8} - q^{9} - 13 q^{10} - 13 q^{11} - 8 q^{12} - 24 q^{13} - 12 q^{14} - 16 q^{15} - 13 q^{16} - 26 q^{17} - 17 q^{18} - 40 q^{19} - 15 q^{20} - 26 q^{21} - 26 q^{22} - 8 q^{23} - 16 q^{24} - 35 q^{25} - 3 q^{26} - 10 q^{27} - 31 q^{28} - 30 q^{29} - 16 q^{30} - 21 q^{31} - 9 q^{32} - 25 q^{33} - 27 q^{34} - 2 q^{35} - 23 q^{36} - 27 q^{37} + q^{38} - 29 q^{39} - 36 q^{40} - 35 q^{41} - 6 q^{42} - 48 q^{43} - 17 q^{44} - 22 q^{45} - 31 q^{46} - 3 q^{47} + q^{48} - 64 q^{49} + 12 q^{50} - 27 q^{51} - 28 q^{52} - 14 q^{53} + q^{54} - 31 q^{55} - 12 q^{56} - 36 q^{57} - 19 q^{58} - 9 q^{59} - 6 q^{60} - 87 q^{61} + 32 q^{62} - 9 q^{63} - 52 q^{64} - 35 q^{65} + 5 q^{66} - 24 q^{67} - 13 q^{68} - 35 q^{69} - 8 q^{70} - 21 q^{71} - 11 q^{72} - 69 q^{73} - 23 q^{74} - 4 q^{75} - 58 q^{76} - 3 q^{77} + q^{78} - 72 q^{79} + 13 q^{80} - 73 q^{81} + 18 q^{82} - 11 q^{83} - 32 q^{84} - 70 q^{85} + 20 q^{86} - 9 q^{87} - 24 q^{88} - 25 q^{89} + 33 q^{90} - 32 q^{91} + 17 q^{92} - 19 q^{93} - 29 q^{94} - 9 q^{95} + 5 q^{96} - 56 q^{97} + 37 q^{98} - 19 q^{99}+O(q^{100}) \) 39 * q - 5 * q^2 - 4 * q^3 + 19 * q^4 - 8 * q^5 - 8 * q^6 - 15 * q^7 - 12 * q^8 - q^9 - 13 * q^10 - 13 * q^11 - 8 * q^12 - 24 * q^13 - 12 * q^14 - 16 * q^15 - 13 * q^16 - 26 * q^17 - 17 * q^18 - 40 * q^19 - 15 * q^20 - 26 * q^21 - 26 * q^22 - 8 * q^23 - 16 * q^24 - 35 * q^25 - 3 * q^26 - 10 * q^27 - 31 * q^28 - 30 * q^29 - 16 * q^30 - 21 * q^31 - 9 * q^32 - 25 * q^33 - 27 * q^34 - 2 * q^35 - 23 * q^36 - 27 * q^37 + q^38 - 29 * q^39 - 36 * q^40 - 35 * q^41 - 6 * q^42 - 48 * q^43 - 17 * q^44 - 22 * q^45 - 31 * q^46 - 3 * q^47 + q^48 - 64 * q^49 + 12 * q^50 - 27 * q^51 - 28 * q^52 - 14 * q^53 + q^54 - 31 * q^55 - 12 * q^56 - 36 * q^57 - 19 * q^58 - 9 * q^59 - 6 * q^60 - 87 * q^61 + 32 * q^62 - 9 * q^63 - 52 * q^64 - 35 * q^65 + 5 * q^66 - 24 * q^67 - 13 * q^68 - 35 * q^69 - 8 * q^70 - 21 * q^71 - 11 * q^72 - 69 * q^73 - 23 * q^74 - 4 * q^75 - 58 * q^76 - 3 * q^77 + q^78 - 72 * q^79 + 13 * q^80 - 73 * q^81 + 18 * q^82 - 11 * q^83 - 32 * q^84 - 70 * q^85 + 20 * q^86 - 9 * q^87 - 24 * q^88 - 25 * q^89 + 33 * q^90 - 32 * q^91 + 17 * q^92 - 19 * q^93 - 29 * q^94 - 9 * q^95 + 5 * q^96 - 56 * q^97 + 37 * q^98 - 19 * q^99

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