LMFDB - Embedded newform 983.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, 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("983.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.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:	$7.84929451869$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56280 q^{2} +2.68242 q^{3} +4.56793 q^{4} +0.599683 q^{5} -6.87450 q^{6} +3.67314 q^{7} -6.58109 q^{8} +4.19537 q^{9} +O(q^{10})$	\(q-2.56280 q^{2} +2.68242 q^{3} +4.56793 q^{4} +0.599683 q^{5} -6.87450 q^{6} +3.67314 q^{7} -6.58109 q^{8} +4.19537 q^{9} -1.53687 q^{10} -3.79853 q^{11} +12.2531 q^{12} +4.06912 q^{13} -9.41351 q^{14} +1.60860 q^{15} +7.73014 q^{16} -2.47410 q^{17} -10.7519 q^{18} +2.95317 q^{19} +2.73931 q^{20} +9.85290 q^{21} +9.73487 q^{22} -0.908231 q^{23} -17.6532 q^{24} -4.64038 q^{25} -10.4283 q^{26} +3.20650 q^{27} +16.7786 q^{28} +10.2352 q^{29} -4.12252 q^{30} +5.72213 q^{31} -6.64861 q^{32} -10.1893 q^{33} +6.34062 q^{34} +2.20272 q^{35} +19.1642 q^{36} +4.66358 q^{37} -7.56839 q^{38} +10.9151 q^{39} -3.94657 q^{40} -2.80398 q^{41} -25.2510 q^{42} -10.4786 q^{43} -17.3514 q^{44} +2.51590 q^{45} +2.32761 q^{46} +4.32201 q^{47} +20.7355 q^{48} +6.49195 q^{49} +11.8924 q^{50} -6.63658 q^{51} +18.5875 q^{52} +8.49429 q^{53} -8.21760 q^{54} -2.27792 q^{55} -24.1733 q^{56} +7.92165 q^{57} -26.2306 q^{58} -3.47269 q^{59} +7.34798 q^{60} -10.4819 q^{61} -14.6647 q^{62} +15.4102 q^{63} +1.57875 q^{64} +2.44018 q^{65} +26.1130 q^{66} -7.02249 q^{67} -11.3015 q^{68} -2.43626 q^{69} -5.64512 q^{70} -3.14636 q^{71} -27.6101 q^{72} -3.30238 q^{73} -11.9518 q^{74} -12.4474 q^{75} +13.4899 q^{76} -13.9525 q^{77} -27.9732 q^{78} +2.22385 q^{79} +4.63564 q^{80} -3.98496 q^{81} +7.18604 q^{82} -9.34072 q^{83} +45.0074 q^{84} -1.48368 q^{85} +26.8545 q^{86} +27.4550 q^{87} +24.9985 q^{88} -2.47798 q^{89} -6.44773 q^{90} +14.9464 q^{91} -4.14874 q^{92} +15.3491 q^{93} -11.0764 q^{94} +1.77097 q^{95} -17.8343 q^{96} +4.55314 q^{97} -16.6376 q^{98} -15.9363 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * 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 $

$2$	−2.56280	−1.81217	−0.906086	−	0.423094i	$-0.860944\pi$
$2$	−2.56280	−1.81217	−0.906086	+	0.423094i	$0.860944\pi$
$3$	2.68242	1.54870	0.774348	−	0.632760i	$-0.218078\pi$
$3$	2.68242	1.54870	0.774348	+	0.632760i	$0.218078\pi$
$4$	4.56793	2.28397
$5$	0.599683	0.268186	0.134093	−	0.990969i	$-0.457188\pi$
$5$	0.599683	0.268186	0.134093	+	0.990969i	$0.457188\pi$
$6$	−6.87450	−2.80650
$7$	3.67314	1.38832	0.694158	−	0.719823i	$-0.255777\pi$
$7$	3.67314	1.38832	0.694158	+	0.719823i	$0.255777\pi$
$8$	−6.58109	−2.32677
$9$	4.19537	1.39846
$10$	−1.53687	−0.486000
$11$	−3.79853	−1.14530	−0.572650	−	0.819800i	$-0.694085\pi$
$11$	−3.79853	−1.14530	−0.572650	+	0.819800i	$0.694085\pi$
$12$	12.2531	3.53717
$13$	4.06912	1.12857	0.564286	−	0.825580i	$-0.309152\pi$
$13$	4.06912	1.12857	0.564286	+	0.825580i	$0.309152\pi$
$14$	−9.41351	−2.51587
$15$	1.60860	0.415339
$16$	7.73014	1.93254
$17$	−2.47410	−0.600058	−0.300029	−	0.953930i	$-0.596996\pi$
$17$	−2.47410	−0.600058	−0.300029	+	0.953930i	$0.596996\pi$
$18$	−10.7519	−2.53425
$19$	2.95317	0.677505	0.338752	−	0.940876i	$-0.389995\pi$
$19$	2.95317	0.677505	0.338752	+	0.940876i	$0.389995\pi$
$20$	2.73931	0.612529
$21$	9.85290	2.15008
$22$	9.73487	2.07548
$23$	−0.908231	−0.189379	−0.0946896	−	0.995507i	$-0.530186\pi$
$23$	−0.908231	−0.189379	−0.0946896	+	0.995507i	$0.530186\pi$
$24$	−17.6532	−3.60345
$25$	−4.64038	−0.928076
$26$	−10.4283	−2.04516
$27$	3.20650	0.617090
$28$	16.7786	3.17087
$29$	10.2352	1.90062	0.950310	−	0.311305i	$-0.100766\pi$
$29$	10.2352	1.90062	0.950310	+	0.311305i	$0.100766\pi$
$30$	−4.12252	−0.752666
$31$	5.72213	1.02772	0.513862	−	0.857873i	$-0.328214\pi$
$31$	5.72213	1.02772	0.513862	+	0.857873i	$0.328214\pi$
$32$	−6.64861	−1.17532
$33$	−10.1893	−1.77372
$34$	6.34062	1.08741
$35$	2.20272	0.372328
$36$	19.1642	3.19403
$37$	4.66358	0.766687	0.383344	−	0.923606i	$-0.374772\pi$
$37$	4.66358	0.766687	0.383344	+	0.923606i	$0.374772\pi$
$38$	−7.56839	−1.22775
$39$	10.9151	1.74781
$40$	−3.94657	−0.624007
$41$	−2.80398	−0.437908	−0.218954	−	0.975735i	$-0.570265\pi$
$41$	−2.80398	−0.437908	−0.218954	+	0.975735i	$0.570265\pi$
$42$	−25.2510	−3.89631
$43$	−10.4786	−1.59797	−0.798986	−	0.601350i	$-0.794630\pi$
$43$	−10.4786	−1.59797	−0.798986	+	0.601350i	$0.794630\pi$
$44$	−17.3514	−2.61583
$45$	2.51590	0.375048
$46$	2.32761	0.343188
$47$	4.32201	0.630430	0.315215	−	0.949020i	$-0.397923\pi$
$47$	4.32201	0.630430	0.315215	+	0.949020i	$0.397923\pi$
$48$	20.7355	2.99291
$49$	6.49195	0.927421
$50$	11.8924	1.68183
$51$	−6.63658	−0.929307
$52$	18.5875	2.57762
$53$	8.49429	1.16678	0.583391	−	0.812192i	$-0.301726\pi$
$53$	8.49429	1.16678	0.583391	+	0.812192i	$0.301726\pi$
$54$	−8.21760	−1.11827
$55$	−2.27792	−0.307154
$56$	−24.1733	−3.23029
$57$	7.92165	1.04925
$58$	−26.2306	−3.44425
$59$	−3.47269	−0.452105	−0.226053	−	0.974115i	$-0.572582\pi$
$59$	−3.47269	−0.452105	−0.226053	+	0.974115i	$0.572582\pi$
$60$	7.34798	0.948621
$61$	−10.4819	−1.34207	−0.671033	−	0.741428i	$-0.734149\pi$
$61$	−10.4819	−1.34207	−0.671033	+	0.741428i	$0.734149\pi$
$62$	−14.6647	−1.86241
$63$	15.4102	1.94150
$64$	1.57875	0.197344
$65$	2.44018	0.302668
$66$	26.1130	3.21429
$67$	−7.02249	−0.857934	−0.428967	−	0.903320i	$-0.641122\pi$
$67$	−7.02249	−0.857934	−0.428967	+	0.903320i	$0.641122\pi$
$68$	−11.3015	−1.37051
$69$	−2.43626	−0.293291
$70$	−5.64512	−0.674721
$71$	−3.14636	−0.373404	−0.186702	−	0.982417i	$-0.559780\pi$
$71$	−3.14636	−0.373404	−0.186702	+	0.982417i	$0.559780\pi$
$72$	−27.6101	−3.25389
$73$	−3.30238	−0.386514	−0.193257	−	0.981148i	$-0.561905\pi$
$73$	−3.30238	−0.386514	−0.193257	+	0.981148i	$0.561905\pi$
$74$	−11.9518	−1.38937
$75$	−12.4474	−1.43731
$76$	13.4899	1.54740
$77$	−13.9525	−1.59004
$78$	−27.9732	−3.16734
$79$	2.22385	0.250203	0.125102	−	0.992144i	$-0.460074\pi$
$79$	2.22385	0.250203	0.125102	+	0.992144i	$0.460074\pi$
$80$	4.63564	0.518280
$81$	−3.98496	−0.442773
$82$	7.18604	0.793565
$83$	−9.34072	−1.02528	−0.512639	−	0.858604i	$-0.671332\pi$
$83$	−9.34072	−1.02528	−0.512639	+	0.858604i	$0.671332\pi$
$84$	45.0074	4.91071
$85$	−1.48368	−0.160927
$86$	26.8545	2.89580
$87$	27.4550	2.94348
$88$	24.9985	2.66485
$89$	−2.47798	−0.262665	−0.131332	−	0.991338i	$-0.541926\pi$
$89$	−2.47798	−0.262665	−0.131332	+	0.991338i	$0.541926\pi$
$90$	−6.44773	−0.679651
$91$	14.9464	1.56681
$92$	−4.14874	−0.432536
$93$	15.3491	1.59163
$94$	−11.0764	−1.14245
$95$	1.77097	0.181698
$96$	−17.8343	−1.82021
$97$	4.55314	0.462301	0.231151	−	0.972918i	$-0.425751\pi$
$97$	4.55314	0.462301	0.231151	+	0.972918i	$0.425751\pi$
$98$	−16.6376	−1.68065
$99$	−15.9363	−1.60165
$100$	−21.1969	−2.11969
$101$	15.2209	1.51453	0.757267	−	0.653105i	$-0.226534\pi$
$101$	15.2209	1.51453	0.757267	+	0.653105i	$0.226534\pi$
$102$	17.0082	1.68406
$103$	−19.5444	−1.92576	−0.962882	−	0.269921i	$-0.913002\pi$
$103$	−19.5444	−1.92576	−0.962882	+	0.269921i	$0.913002\pi$
$104$	−26.7793	−2.62592
$105$	5.90862	0.576622
$106$	−21.7692	−2.11441
$107$	17.8154	1.72228	0.861142	−	0.508365i	$-0.169750\pi$
$107$	17.8154	1.72228	0.861142	+	0.508365i	$0.169750\pi$
$108$	14.6471	1.40941
$109$	11.3245	1.08469	0.542345	−	0.840156i	$-0.317536\pi$
$109$	11.3245	1.08469	0.542345	+	0.840156i	$0.317536\pi$
$110$	5.83784	0.556616
$111$	12.5097	1.18737
$112$	28.3939	2.68297
$113$	−3.46818	−0.326259	−0.163129	−	0.986605i	$-0.552159\pi$
$113$	−3.46818	−0.326259	−0.163129	+	0.986605i	$0.552159\pi$
$114$	−20.3016	−1.90142
$115$	−0.544651	−0.0507890
$116$	46.7535	4.34095
$117$	17.0715	1.57826
$118$	8.89979	0.819292
$119$	−9.08772	−0.833070
$120$	−10.5864	−0.966398
$121$	3.42884	0.311713
$122$	26.8629	2.43205
$123$	−7.52145	−0.678187
$124$	26.1383	2.34729
$125$	−5.78117	−0.517084
$126$	−39.4932	−3.51833
$127$	12.0461	1.06892	0.534458	−	0.845195i	$-0.320516\pi$
$127$	12.0461	1.06892	0.534458	+	0.845195i	$0.320516\pi$
$128$	9.25120	0.817698
$129$	−28.1080	−2.47477
$130$	−6.25370	−0.548486
$131$	17.9567	1.56889	0.784444	−	0.620200i	$-0.212949\pi$
$131$	17.9567	1.56889	0.784444	+	0.620200i	$0.212949\pi$
$132$	−46.5438	−4.05112
$133$	10.8474	0.940590
$134$	17.9972	1.55472
$135$	1.92288	0.165495
$136$	16.2823	1.39619
$137$	−0.850064	−0.0726259	−0.0363129	−	0.999340i	$-0.511561\pi$
$137$	−0.850064	−0.0726259	−0.0363129	+	0.999340i	$0.511561\pi$
$138$	6.24363	0.531493
$139$	−5.47081	−0.464028	−0.232014	−	0.972712i	$-0.574532\pi$
$139$	−5.47081	−0.464028	−0.232014	+	0.972712i	$0.574532\pi$
$140$	10.0619	0.850384
$141$	11.5934	0.976344
$142$	8.06348	0.676672
$143$	−15.4567	−1.29255
$144$	32.4308	2.70257
$145$	6.13785	0.509721
$146$	8.46332	0.700430
$147$	17.4141	1.43629
$148$	21.3029	1.75109
$149$	2.72231	0.223020	0.111510	−	0.993763i	$-0.464431\pi$
$149$	2.72231	0.223020	0.111510	+	0.993763i	$0.464431\pi$
$150$	31.9003	2.60465
$151$	6.69925	0.545177	0.272589	−	0.962131i	$-0.412120\pi$
$151$	6.69925	0.545177	0.272589	+	0.962131i	$0.412120\pi$
$152$	−19.4351	−1.57640
$153$	−10.3798	−0.839156
$154$	35.7575	2.88142
$155$	3.43146	0.275622
$156$	49.8594	3.99195
$157$	−19.4337	−1.55098	−0.775489	−	0.631361i	$-0.782496\pi$
$157$	−19.4337	−1.55098	−0.775489	+	0.631361i	$0.782496\pi$
$158$	−5.69929	−0.453411
$159$	22.7853	1.80699
$160$	−3.98706	−0.315204
$161$	−3.33606	−0.262918
$162$	10.2126	0.802380
$163$	12.4089	0.971942	0.485971	−	0.873975i	$-0.338466\pi$
$163$	12.4089	0.971942	0.485971	+	0.873975i	$0.338466\pi$
$164$	−12.8084	−1.00017
$165$	−6.11033	−0.475688
$166$	23.9384	1.85798
$167$	−22.7643	−1.76155	−0.880777	−	0.473531i	$-0.842979\pi$
$167$	−22.7643	−1.76155	−0.880777	+	0.473531i	$0.842979\pi$
$168$	−64.8428	−5.00273
$169$	3.55775	0.273673
$170$	3.80236	0.291628
$171$	12.3897	0.947462
$172$	−47.8655	−3.64971
$173$	8.19393	0.622973	0.311487	−	0.950251i	$-0.399173\pi$
$173$	8.19393	0.622973	0.311487	+	0.950251i	$0.399173\pi$
$174$	−70.3615	−5.33409
$175$	−17.0448	−1.28846
$176$	−29.3632	−2.21333
$177$	−9.31520	−0.700173
$178$	6.35055	0.475994
$179$	−20.5998	−1.53970	−0.769851	−	0.638224i	$-0.779670\pi$
$179$	−20.5998	−1.53970	−0.769851	+	0.638224i	$0.779670\pi$
$180$	11.4924	0.856596
$181$	−19.3507	−1.43833	−0.719164	−	0.694841i	$-0.755475\pi$
$181$	−19.3507	−1.43833	−0.719164	+	0.694841i	$0.755475\pi$
$182$	−38.3047	−2.83934
$183$	−28.1168	−2.07845
$184$	5.97715	0.440641
$185$	2.79667	0.205615
$186$	−39.3367	−2.88431
$187$	9.39795	0.687246
$188$	19.7426	1.43988
$189$	11.7779	0.856717
$190$	−4.53863	−0.329267
$191$	−22.3684	−1.61852	−0.809259	−	0.587452i	$-0.800131\pi$
$191$	−22.3684	−1.61852	−0.809259	+	0.587452i	$0.800131\pi$
$192$	4.23487	0.305625
$193$	21.1188	1.52017	0.760083	−	0.649826i	$-0.225158\pi$
$193$	21.1188	1.52017	0.760083	+	0.649826i	$0.225158\pi$
$194$	−11.6688	−0.837769
$195$	6.54560	0.468740
$196$	29.6548	2.11820
$197$	2.34581	0.167132	0.0835660	−	0.996502i	$-0.473369\pi$
$197$	2.34581	0.167132	0.0835660	+	0.996502i	$0.473369\pi$
$198$	40.8414	2.90247
$199$	9.46902	0.671241	0.335621	−	0.941997i	$-0.391054\pi$
$199$	9.46902	0.671241	0.335621	+	0.941997i	$0.391054\pi$
$200$	30.5388	2.15942
$201$	−18.8373	−1.32868
$202$	−39.0081	−2.74460
$203$	37.5951	2.63866
$204$	−30.3154	−2.12251
$205$	−1.68150	−0.117441
$206$	50.0883	3.48982
$207$	−3.81037	−0.264839
$208$	31.4549	2.18100
$209$	−11.2177	−0.775946
$210$	−15.1426	−1.04494
$211$	−6.83354	−0.470440	−0.235220	−	0.971942i	$-0.575581\pi$
$211$	−6.83354	−0.470440	−0.235220	+	0.971942i	$0.575581\pi$
$212$	38.8014	2.66489
$213$	−8.43985	−0.578289
$214$	−45.6574	−3.12107
$215$	−6.28384	−0.428554
$216$	−21.1022	−1.43583
$217$	21.0182	1.42681
$218$	−29.0224	−1.96565
$219$	−8.85836	−0.598592
$220$	−10.4054	−0.701530
$221$	−10.0674	−0.677208
$222$	−32.0598	−2.15171
$223$	27.4293	1.83680	0.918402	−	0.395650i	$-0.129481\pi$
$223$	27.4293	1.83680	0.918402	+	0.395650i	$0.129481\pi$
$224$	−24.4213	−1.63171
$225$	−19.4681	−1.29788
$226$	8.88824	0.591237
$227$	9.60589	0.637565	0.318783	−	0.947828i	$-0.396726\pi$
$227$	9.60589	0.637565	0.318783	+	0.947828i	$0.396726\pi$
$228$	36.1856	2.39645
$229$	−12.8028	−0.846030	−0.423015	−	0.906123i	$-0.639028\pi$
$229$	−12.8028	−0.846030	−0.423015	+	0.906123i	$0.639028\pi$
$230$	1.39583	0.0920383
$231$	−37.4266	−2.46249
$232$	−67.3585	−4.42230
$233$	4.79602	0.314198	0.157099	−	0.987583i	$-0.449786\pi$
$233$	4.79602	0.314198	0.157099	+	0.987583i	$0.449786\pi$
$234$	−43.7508	−2.86008
$235$	2.59184	0.169073
$236$	−15.8630	−1.03259
$237$	5.96531	0.387489
$238$	23.2900	1.50967
$239$	−2.00493	−0.129688	−0.0648441	−	0.997895i	$-0.520655\pi$
$239$	−2.00493	−0.129688	−0.0648441	+	0.997895i	$0.520655\pi$
$240$	12.4347	0.802658
$241$	−14.8318	−0.955399	−0.477700	−	0.878523i	$-0.658529\pi$
$241$	−14.8318	−0.955399	−0.477700	+	0.878523i	$0.658529\pi$
$242$	−8.78744	−0.564878
$243$	−20.3088	−1.30281
$244$	−47.8804	−3.06523
$245$	3.89311	0.248722
$246$	19.2760	1.22899
$247$	12.0168	0.764612
$248$	−37.6578	−2.39127
$249$	−25.0557	−1.58784
$250$	14.8160	0.937045
$251$	−4.30174	−0.271524	−0.135762	−	0.990742i	$-0.543348\pi$
$251$	−4.30174	−0.271524	−0.135762	+	0.990742i	$0.543348\pi$
$252$	70.3927	4.43432
$253$	3.44995	0.216896
$254$	−30.8717	−1.93706
$255$	−3.97984	−0.249228
$256$	−26.8664	−1.67915
$257$	−31.9995	−1.99607	−0.998037	−	0.0626200i	$-0.980054\pi$
$257$	−31.9995	−1.99607	−0.998037	+	0.0626200i	$0.980054\pi$
$258$	72.0351	4.48471
$259$	17.1300	1.06440
$260$	11.1466	0.691282
$261$	42.9403	2.65794
$262$	−46.0195	−2.84309
$263$	−0.772458	−0.0476318	−0.0238159	−	0.999716i	$-0.507582\pi$
$263$	−0.772458	−0.0476318	−0.0238159	+	0.999716i	$0.507582\pi$
$264$	67.0564	4.12704
$265$	5.09389	0.312915
$266$	−27.7997	−1.70451
$267$	−6.64697	−0.406788
$268$	−32.0783	−1.95949
$269$	−0.303030	−0.0184760	−0.00923802	−	0.999957i	$-0.502941\pi$
$269$	−0.303030	−0.0184760	−0.00923802	+	0.999957i	$0.502941\pi$
$270$	−4.92796	−0.299906
$271$	14.7208	0.894226	0.447113	−	0.894478i	$-0.352452\pi$
$271$	14.7208	0.894226	0.447113	+	0.894478i	$0.352452\pi$
$272$	−19.1252	−1.15963
$273$	40.0926	2.42652
$274$	2.17854	0.131611
$275$	17.6266	1.06293
$276$	−11.1287	−0.669866
$277$	−19.4337	−1.16766	−0.583828	−	0.811877i	$-0.698446\pi$
$277$	−19.4337	−1.16766	−0.583828	+	0.811877i	$0.698446\pi$
$278$	14.0206	0.840899
$279$	24.0065	1.43723
$280$	−14.4963	−0.866320
$281$	−25.7531	−1.53630	−0.768149	−	0.640271i	$-0.778822\pi$
$281$	−25.7531	−1.53630	−0.768149	+	0.640271i	$0.778822\pi$
$282$	−29.7116	−1.76930
$283$	−4.96265	−0.294999	−0.147499	−	0.989062i	$-0.547122\pi$
$283$	−4.96265	−0.294999	−0.147499	+	0.989062i	$0.547122\pi$
$284$	−14.3724	−0.852842
$285$	4.75048	0.281394
$286$	39.6124	2.34233
$287$	−10.2994	−0.607955
$288$	−27.8934	−1.64363
$289$	−10.8788	−0.639931
$290$	−15.7301	−0.923701
$291$	12.2134	0.715964
$292$	−15.0850	−0.882785
$293$	1.00505	0.0587157	0.0293579	−	0.999569i	$-0.490654\pi$
$293$	1.00505	0.0587157	0.0293579	+	0.999569i	$0.490654\pi$
$294$	−44.6289	−2.60281
$295$	−2.08251	−0.121249
$296$	−30.6914	−1.78390
$297$	−12.1800	−0.706754
$298$	−6.97673	−0.404151
$299$	−3.69570	−0.213728
$300$	−56.8591	−3.28276
$301$	−38.4893	−2.21849
$302$	−17.1688	−0.987954
$303$	40.8288	2.34555
$304$	22.8285	1.30930
$305$	−6.28580	−0.359924
$306$	26.6013	1.52069
$307$	19.0909	1.08958	0.544788	−	0.838574i	$-0.316610\pi$
$307$	19.0909	1.08958	0.544788	+	0.838574i	$0.316610\pi$
$308$	−63.7342	−3.63160
$309$	−52.4262	−2.98242
$310$	−8.79415	−0.499474
$311$	9.90259	0.561524	0.280762	−	0.959777i	$-0.409413\pi$
$311$	9.90259	0.561524	0.280762	+	0.959777i	$0.409413\pi$
$312$	−71.8332	−4.06675
$313$	−5.62871	−0.318154	−0.159077	−	0.987266i	$-0.550852\pi$
$313$	−5.62871	−0.318154	−0.159077	+	0.987266i	$0.550852\pi$
$314$	49.8046	2.81064
$315$	9.24123	0.520685
$316$	10.1584	0.571456
$317$	33.9826	1.90865	0.954326	−	0.298766i	$-0.0965749\pi$
$317$	33.9826	1.90865	0.954326	+	0.298766i	$0.0965749\pi$
$318$	−58.3940	−3.27457
$319$	−38.8786	−2.17678
$320$	0.946749	0.0529249
$321$	47.7885	2.66729
$322$	8.54965	0.476453
$323$	−7.30645	−0.406542
$324$	−18.2030	−1.01128
$325$	−18.8823	−1.04740
$326$	−31.8016	−1.76133
$327$	30.3771	1.67986
$328$	18.4533	1.01891
$329$	15.8753	0.875236
$330$	15.6595	0.862029
$331$	18.1347	0.996775	0.498387	−	0.866954i	$-0.333926\pi$
$331$	18.1347	0.996775	0.498387	+	0.866954i	$0.333926\pi$
$332$	−42.6678	−2.34170
$333$	19.5655	1.07218
$334$	58.3403	3.19224
$335$	−4.21127	−0.230086
$336$	76.1643	4.15510
$337$	6.94214	0.378162	0.189081	−	0.981961i	$-0.439449\pi$
$337$	6.94214	0.378162	0.189081	+	0.981961i	$0.439449\pi$
$338$	−9.11780	−0.495943
$339$	−9.30311	−0.505276
$340$	−6.77734	−0.367553
$341$	−21.7357	−1.17705
$342$	−31.7522	−1.71696
$343$	−1.86614	−0.100762
$344$	68.9606	3.71811
$345$	−1.46098	−0.0786566
$346$	−20.9994	−1.12893
$347$	−22.9467	−1.23185	−0.615923	−	0.787806i	$-0.711217\pi$
$347$	−22.9467	−1.23185	−0.615923	+	0.787806i	$0.711217\pi$
$348$	125.412	6.72281
$349$	−1.29797	−0.0694790	−0.0347395	−	0.999396i	$-0.511060\pi$
$349$	−1.29797	−0.0694790	−0.0347395	+	0.999396i	$0.511060\pi$
$350$	43.6823	2.33492
$351$	13.0476	0.696431
$352$	25.2549	1.34609
$353$	15.9023	0.846396	0.423198	−	0.906037i	$-0.360907\pi$
$353$	15.9023	0.846396	0.423198	+	0.906037i	$0.360907\pi$
$354$	23.8730	1.26883
$355$	−1.88682	−0.100142
$356$	−11.3192	−0.599918
$357$	−24.3771	−1.29017
$358$	52.7931	2.79020
$359$	12.5263	0.661115	0.330557	−	0.943786i	$-0.392763\pi$
$359$	12.5263	0.661115	0.330557	+	0.943786i	$0.392763\pi$
$360$	−16.5573	−0.872648
$361$	−10.2788	−0.540988
$362$	49.5920	2.60650
$363$	9.19760	0.482749
$364$	68.2744	3.57855
$365$	−1.98038	−0.103658
$366$	72.0576	3.76651
$367$	4.20867	0.219691	0.109845	−	0.993949i	$-0.464964\pi$
$367$	4.20867	0.219691	0.109845	+	0.993949i	$0.464964\pi$
$368$	−7.02075	−0.365982
$369$	−11.7638	−0.612396
$370$	−7.16730	−0.372610
$371$	31.2007	1.61986
$372$	70.1138	3.63523
$373$	2.04200	0.105731	0.0528654	−	0.998602i	$-0.483165\pi$
$373$	2.04200	0.105731	0.0528654	+	0.998602i	$0.483165\pi$
$374$	−24.0851	−1.24541
$375$	−15.5075	−0.800806
$376$	−28.4435	−1.46686
$377$	41.6481	2.14499
$378$	−30.1844	−1.55252
$379$	−22.6545	−1.16369	−0.581843	−	0.813301i	$-0.697668\pi$
$379$	−22.6545	−1.16369	−0.581843	+	0.813301i	$0.697668\pi$
$380$	8.08967	0.414991
$381$	32.3126	1.65543
$382$	57.3256	2.93303
$383$	−8.31424	−0.424838	−0.212419	−	0.977179i	$-0.568134\pi$
$383$	−8.31424	−0.424838	−0.212419	+	0.977179i	$0.568134\pi$
$384$	24.8156	1.26637
$385$	−8.36710	−0.426427
$386$	−54.1233	−2.75480
$387$	−43.9616	−2.23470
$388$	20.7984	1.05588
$389$	−31.9848	−1.62169	−0.810847	−	0.585258i	$-0.800993\pi$
$389$	−31.9848	−1.62169	−0.810847	+	0.585258i	$0.800993\pi$
$390$	−16.7750	−0.849437
$391$	2.24706	0.113639
$392$	−42.7241	−2.15789
$393$	48.1675	2.42973
$394$	−6.01183	−0.302872
$395$	1.33361	0.0671011
$396$	−72.7958	−3.65813
$397$	27.5133	1.38085	0.690427	−	0.723402i	$-0.257422\pi$
$397$	27.5133	1.38085	0.690427	+	0.723402i	$0.257422\pi$
$398$	−24.2672	−1.21640
$399$	29.0973	1.45669
$400$	−35.8708	−1.79354
$401$	−20.4682	−1.02213	−0.511066	−	0.859541i	$-0.670749\pi$
$401$	−20.4682	−1.02213	−0.511066	+	0.859541i	$0.670749\pi$
$402$	48.2761	2.40779
$403$	23.2840	1.15986
$404$	69.5280	3.45915
$405$	−2.38971	−0.118746
$406$	−96.3487	−4.78171
$407$	−17.7147	−0.878087
$408$	43.6759	2.16228
$409$	−5.67557	−0.280639	−0.140319	−	0.990106i	$-0.544813\pi$
$409$	−5.67557	−0.280639	−0.140319	+	0.990106i	$0.544813\pi$
$410$	4.30935	0.212823
$411$	−2.28023	−0.112475
$412$	−89.2774	−4.39838
$413$	−12.7557	−0.627665
$414$	9.76521	0.479934
$415$	−5.60147	−0.274966
$416$	−27.0540	−1.32643
$417$	−14.6750	−0.718639
$418$	28.7488	1.40615
$419$	−39.1036	−1.91033	−0.955167	−	0.296068i	$-0.904324\pi$
$419$	−39.1036	−1.91033	−0.955167	+	0.296068i	$0.904324\pi$
$420$	26.9902	1.31699
$421$	23.0244	1.12214	0.561071	−	0.827768i	$-0.310389\pi$
$421$	23.0244	1.12214	0.561071	+	0.827768i	$0.310389\pi$
$422$	17.5130	0.852519
$423$	18.1324	0.881629
$424$	−55.9017	−2.71483
$425$	11.4808	0.556899
$426$	21.6296	1.04796
$427$	−38.5013	−1.86321
$428$	81.3797	3.93364
$429$	−41.4613	−2.00177
$430$	16.1042	0.776614
$431$	−26.7776	−1.28983	−0.644917	−	0.764253i	$-0.723108\pi$
$431$	−26.7776	−1.28983	−0.644917	+	0.764253i	$0.723108\pi$
$432$	24.7867	1.19255
$433$	13.1380	0.631373	0.315686	−	0.948864i	$-0.397765\pi$
$433$	13.1380	0.631373	0.315686	+	0.948864i	$0.397765\pi$
$434$	−53.8653	−2.58562
$435$	16.4643	0.789402
$436$	51.7296	2.47740
$437$	−2.68216	−0.128305
$438$	22.7022	1.08475
$439$	−31.7294	−1.51436	−0.757180	−	0.653206i	$-0.773424\pi$
$439$	−31.7294	−1.51436	−0.757180	+	0.653206i	$0.773424\pi$
$440$	14.9912	0.714676
$441$	27.2362	1.29696
$442$	25.8008	1.22722
$443$	−15.9969	−0.760036	−0.380018	−	0.924979i	$-0.624082\pi$
$443$	−15.9969	−0.760036	−0.380018	+	0.924979i	$0.624082\pi$
$444$	57.1433	2.71190
$445$	−1.48600	−0.0704432
$446$	−70.2958	−3.32860
$447$	7.30238	0.345391
$448$	5.79896	0.273975
$449$	33.8803	1.59891	0.799454	−	0.600727i	$-0.205122\pi$
$449$	33.8803	1.59891	0.799454	+	0.600727i	$0.205122\pi$
$450$	49.8929	2.35197
$451$	10.6510	0.501537
$452$	−15.8424	−0.745164
$453$	17.9702	0.844313
$454$	−24.6180	−1.15538
$455$	8.96313	0.420198
$456$	−52.1331	−2.44136
$457$	18.4754	0.864242	0.432121	−	0.901816i	$-0.357765\pi$
$457$	18.4754	0.864242	0.432121	+	0.901816i	$0.357765\pi$
$458$	32.8109	1.53315
$459$	−7.93320	−0.370290
$460$	−2.48793	−0.116000
$461$	15.3544	0.715125	0.357562	−	0.933889i	$-0.383608\pi$
$461$	15.3544	0.715125	0.357562	+	0.933889i	$0.383608\pi$
$462$	95.9167	4.46245
$463$	6.56160	0.304943	0.152472	−	0.988308i	$-0.451277\pi$
$463$	6.56160	0.304943	0.152472	+	0.988308i	$0.451277\pi$
$464$	79.1192	3.67302
$465$	9.20462	0.426854
$466$	−12.2912	−0.569380
$467$	−20.1726	−0.933476	−0.466738	−	0.884396i	$-0.654571\pi$
$467$	−20.1726	−0.933476	−0.466738	+	0.884396i	$0.654571\pi$
$468$	77.9814	3.60469
$469$	−25.7946	−1.19108
$470$	−6.64235	−0.306389
$471$	−52.1293	−2.40199
$472$	22.8541	1.05194
$473$	39.8033	1.83016
$474$	−15.2879	−0.702196
$475$	−13.7038	−0.628776
$476$	−41.5121	−1.90270
$477$	35.6367	1.63169
$478$	5.13823	0.235017
$479$	−18.1324	−0.828490	−0.414245	−	0.910165i	$-0.635954\pi$
$479$	−18.1324	−0.828490	−0.414245	+	0.910165i	$0.635954\pi$
$480$	−10.6950	−0.488156
$481$	18.9767	0.865261
$482$	38.0109	1.73135
$483$	−8.94871	−0.407180
$484$	15.6627	0.711942
$485$	2.73044	0.123983
$486$	52.0474	2.36092
$487$	6.02254	0.272908	0.136454	−	0.990646i	$-0.456429\pi$
$487$	6.02254	0.272908	0.136454	+	0.990646i	$0.456429\pi$
$488$	68.9821	3.12267
$489$	33.2860	1.50524
$490$	−9.97726	−0.450727
$491$	2.59121	0.116940	0.0584698	−	0.998289i	$-0.481378\pi$
$491$	2.59121	0.116940	0.0584698	+	0.998289i	$0.481378\pi$
$492$	−34.3575	−1.54896
$493$	−25.3228	−1.14048
$494$	−30.7967	−1.38561
$495$	−9.55671	−0.429542
$496$	44.2328	1.98611
$497$	−11.5570	−0.518403
$498$	64.2128	2.87744
$499$	−7.19070	−0.321900	−0.160950	−	0.986963i	$-0.551456\pi$
$499$	−7.19070	−0.321900	−0.160950	+	0.986963i	$0.551456\pi$
$500$	−26.4080	−1.18100
$501$	−61.0634	−2.72811
$502$	11.0245	0.492047
$503$	29.5445	1.31733	0.658663	−	0.752438i	$-0.271122\pi$
$503$	29.5445	1.31733	0.658663	+	0.752438i	$0.271122\pi$
$504$	−101.416	−4.51742
$505$	9.12771	0.406178
$506$	−8.84151	−0.393053
$507$	9.54338	0.423836
$508$	55.0257	2.44137
$509$	−29.3239	−1.29976	−0.649880	−	0.760037i	$-0.725181\pi$
$509$	−29.3239	−1.29976	−0.649880	+	0.760037i	$0.725181\pi$
$510$	10.1995	0.451643
$511$	−12.1301	−0.536603
$512$	50.3509	2.22521
$513$	9.46934	0.418082
$514$	82.0083	3.61723
$515$	−11.7204	−0.516464
$516$	−128.395	−5.65229
$517$	−16.4173	−0.722031
$518$	−43.9006	−1.92888
$519$	21.9796	0.964796
$520$	−16.0591	−0.704237
$521$	33.3379	1.46056	0.730280	−	0.683148i	$-0.239390\pi$
$521$	33.3379	1.46056	0.730280	+	0.683148i	$0.239390\pi$
$522$	−110.047	−4.81664
$523$	27.1224	1.18598	0.592991	−	0.805209i	$-0.297947\pi$
$523$	27.1224	1.18598	0.592991	+	0.805209i	$0.297947\pi$
$524$	82.0252	3.58329
$525$	−45.7212	−1.99544
$526$	1.97965	0.0863170
$527$	−14.1571	−0.616694
$528$	−78.7644	−3.42778
$529$	−22.1751	−0.964135
$530$	−13.0546	−0.567056
$531$	−14.5692	−0.632250
$532$	49.5503	2.14828
$533$	−11.4097	−0.494211
$534$	17.0348	0.737170
$535$	10.6836	0.461893
$536$	46.2156	1.99621
$537$	−55.2573	−2.38453
$538$	0.776604	0.0334818
$539$	−24.6599	−1.06218
$540$	8.78359	0.377986
$541$	−29.6293	−1.27386	−0.636932	−	0.770920i	$-0.719797\pi$
$541$	−29.6293	−1.27386	−0.636932	+	0.770920i	$0.719797\pi$
$542$	−37.7265	−1.62049
$543$	−51.9067	−2.22753
$544$	16.4493	0.705259
$545$	6.79112	0.290899
$546$	−102.749	−4.39727
$547$	−26.1575	−1.11842	−0.559208	−	0.829027i	$-0.688895\pi$
$547$	−26.1575	−1.11842	−0.559208	+	0.829027i	$0.688895\pi$
$548$	−3.88304	−0.165875
$549$	−43.9753	−1.87682
$550$	−45.1735	−1.92620
$551$	30.2262	1.28768
$552$	16.0332	0.682420
$553$	8.16853	0.347361
$554$	49.8046	2.11599
$555$	7.50184	0.318435
$556$	−24.9903	−1.05982
$557$	−17.8460	−0.756159	−0.378080	−	0.925773i	$-0.623415\pi$
$557$	−17.8460	−0.756159	−0.378080	+	0.925773i	$0.623415\pi$
$558$	−61.5237	−2.60451
$559$	−42.6387	−1.80342
$560$	17.0273	0.719536
$561$	25.2093	1.06434
$562$	65.9999	2.78404
$563$	−13.2697	−0.559252	−0.279626	−	0.960109i	$-0.590210\pi$
$563$	−13.2697	−0.559252	−0.279626	+	0.960109i	$0.590210\pi$
$564$	52.9580	2.22994
$565$	−2.07981	−0.0874982
$566$	12.7183	0.534588
$567$	−14.6373	−0.614709
$568$	20.7065	0.868824
$569$	39.9248	1.67373	0.836867	−	0.547407i	$-0.184385\pi$
$569$	39.9248	1.67373	0.836867	+	0.547407i	$0.184385\pi$
$570$	−12.1745	−0.509935
$571$	−29.4171	−1.23107	−0.615533	−	0.788111i	$-0.711059\pi$
$571$	−29.4171	−1.23107	−0.615533	+	0.788111i	$0.711059\pi$
$572$	−70.6051	−2.95215
$573$	−60.0014	−2.50659
$574$	26.3953	1.10172
$575$	4.21454	0.175758
$576$	6.62344	0.275977
$577$	−25.0574	−1.04315	−0.521577	−	0.853204i	$-0.674656\pi$
$577$	−25.0574	−1.04315	−0.521577	+	0.853204i	$0.674656\pi$
$578$	27.8802	1.15966
$579$	56.6495	2.35427
$580$	28.0373	1.16418
$581$	−34.3098	−1.42341
$582$	−31.3006	−1.29745
$583$	−32.2659	−1.33631
$584$	21.7332	0.899328
$585$	10.2375	0.423268
$586$	−2.57574	−0.106403
$587$	−8.62682	−0.356067	−0.178033	−	0.984024i	$-0.556974\pi$
$587$	−8.62682	−0.356067	−0.178033	+	0.984024i	$0.556974\pi$
$588$	79.5466	3.28045
$589$	16.8984	0.696288
$590$	5.33706	0.219723
$591$	6.29244	0.258836
$592$	36.0501	1.48165
$593$	−12.9147	−0.530344	−0.265172	−	0.964201i	$-0.585429\pi$
$593$	−12.9147	−0.530344	−0.265172	+	0.964201i	$0.585429\pi$
$594$	31.2148	1.28076
$595$	−5.44975	−0.223418
$596$	12.4353	0.509371
$597$	25.3999	1.03955
$598$	9.47134	0.387312
$599$	12.3563	0.504866	0.252433	−	0.967614i	$-0.418769\pi$
$599$	12.3563	0.504866	0.252433	+	0.967614i	$0.418769\pi$
$600$	81.9178	3.34428
$601$	−44.7608	−1.82583	−0.912915	−	0.408150i	$-0.866174\pi$
$601$	−44.7608	−1.82583	−0.912915	+	0.408150i	$0.866174\pi$
$602$	98.6404	4.02028
$603$	−29.4620	−1.19978
$604$	30.6017	1.24517
$605$	2.05622	0.0835972
$606$	−104.636	−4.25055
$607$	25.2760	1.02592	0.512960	−	0.858412i	$-0.328549\pi$
$607$	25.2760	1.02592	0.512960	+	0.858412i	$0.328549\pi$
$608$	−19.6345	−0.796284
$609$	100.846	4.08648
$610$	16.1092	0.652244
$611$	17.5868	0.711485
$612$	−47.4141	−1.91660
$613$	−16.7267	−0.675587	−0.337793	−	0.941220i	$-0.609680\pi$
$613$	−16.7267	−0.675587	−0.337793	+	0.941220i	$0.609680\pi$
$614$	−48.9262	−1.97450
$615$	−4.51049	−0.181880
$616$	91.8229	3.69965
$617$	22.2299	0.894943	0.447471	−	0.894298i	$-0.352325\pi$
$617$	22.2299	0.894943	0.447471	+	0.894298i	$0.352325\pi$
$618$	134.358	5.40466
$619$	−20.8087	−0.836374	−0.418187	−	0.908361i	$-0.637334\pi$
$619$	−20.8087	−0.836374	−0.418187	+	0.908361i	$0.637334\pi$
$620$	15.6747	0.629511
$621$	−2.91224	−0.116864
$622$	−25.3783	−1.01758
$623$	−9.10195	−0.364662
$624$	84.3752	3.37771
$625$	19.7350	0.789401
$626$	14.4253	0.576549
$627$	−30.0906	−1.20170
$628$	−88.7718	−3.54238
$629$	−11.5382	−0.460057
$630$	−23.6834	−0.943570
$631$	−12.3371	−0.491130	−0.245565	−	0.969380i	$-0.578974\pi$
$631$	−12.3371	−0.491130	−0.245565	+	0.969380i	$0.578974\pi$
$632$	−14.6354	−0.582164
$633$	−18.3304	−0.728569
$634$	−87.0905	−3.45881
$635$	7.22383	0.286669
$636$	104.082	4.12710
$637$	26.4165	1.04666
$638$	99.6379	3.94470
$639$	−13.2002	−0.522190
$640$	5.54779	0.219296
$641$	8.07077	0.318776	0.159388	−	0.987216i	$-0.449048\pi$
$641$	8.07077	0.318776	0.159388	+	0.987216i	$0.449048\pi$
$642$	−122.472	−4.83359
$643$	4.96567	0.195827	0.0979135	−	0.995195i	$-0.468783\pi$
$643$	4.96567	0.195827	0.0979135	+	0.995195i	$0.468783\pi$
$644$	−15.2389	−0.600496
$645$	−16.8559	−0.663700
$646$	18.7250	0.736724
$647$	23.0283	0.905335	0.452667	−	0.891679i	$-0.350473\pi$
$647$	23.0283	0.905335	0.452667	+	0.891679i	$0.350473\pi$
$648$	26.2254	1.03023
$649$	13.1911	0.517796
$650$	48.3914	1.89807
$651$	56.3795	2.20969
$652$	56.6831	2.21988
$653$	14.7975	0.579072	0.289536	−	0.957167i	$-0.406499\pi$
$653$	14.7975	0.579072	0.289536	+	0.957167i	$0.406499\pi$
$654$	−77.8503	−3.04419
$655$	10.7684	0.420754
$656$	−21.6752	−0.846273
$657$	−13.8547	−0.540524
$658$	−40.6853	−1.58608
$659$	8.38371	0.326583	0.163291	−	0.986578i	$-0.447789\pi$
$659$	8.38371	0.326583	0.163291	+	0.986578i	$0.447789\pi$
$660$	−27.9116	−1.08646
$661$	7.22819	0.281144	0.140572	−	0.990070i	$-0.455106\pi$
$661$	7.22819	0.281144	0.140572	+	0.990070i	$0.455106\pi$
$662$	−46.4756	−1.80633
$663$	−27.0050	−1.04879
$664$	61.4722	2.38558
$665$	6.50501	0.252254
$666$	−50.1423	−1.94297
$667$	−9.29588	−0.359938
$668$	−103.986	−4.02333
$669$	73.5769	2.84465
$670$	10.7926	0.416956
$671$	39.8157	1.53707
$672$	−65.5080	−2.52703
$673$	−19.5356	−0.753041	−0.376521	−	0.926408i	$-0.622880\pi$
$673$	−19.5356	−0.753041	−0.376521	+	0.926408i	$0.622880\pi$
$674$	−17.7913	−0.685295
$675$	−14.8794	−0.572707
$676$	16.2516	0.625060
$677$	43.7864	1.68285	0.841424	−	0.540375i	$-0.181718\pi$
$677$	43.7864	1.68285	0.841424	+	0.540375i	$0.181718\pi$
$678$	23.8420	0.915646
$679$	16.7243	0.641820
$680$	9.76421	0.374440
$681$	25.7670	0.987395
$682$	55.7041	2.13302
$683$	−36.7342	−1.40560	−0.702798	−	0.711389i	$-0.748066\pi$
$683$	−36.7342	−1.40560	−0.702798	+	0.711389i	$0.748066\pi$
$684$	56.5952	2.16397
$685$	−0.509769	−0.0194773
$686$	4.78254	0.182598
$687$	−34.3424	−1.31024
$688$	−81.0010	−3.08814
$689$	34.5643	1.31680
$690$	3.74420	0.142539
$691$	−22.3560	−0.850462	−0.425231	−	0.905085i	$-0.639807\pi$
$691$	−22.3560	−0.850462	−0.425231	+	0.905085i	$0.639807\pi$
$692$	37.4293	1.42285
$693$	−58.5361	−2.22360
$694$	58.8079	2.23232
$695$	−3.28075	−0.124446
$696$	−180.684	−6.84880
$697$	6.93733	0.262770
$698$	3.32645	0.125908
$699$	12.8649	0.486597
$700$	−77.8593	−2.94281
$701$	−1.15609	−0.0436649	−0.0218324	−	0.999762i	$-0.506950\pi$
$701$	−1.15609	−0.0436649	−0.0218324	+	0.999762i	$0.506950\pi$
$702$	−33.4384	−1.26205
$703$	13.7724	0.519434
$704$	−5.99693	−0.226018
$705$	6.95239	0.261842
$706$	−40.7545	−1.53381
$707$	55.9084	2.10265
$708$	−42.5512	−1.59917
$709$	37.5680	1.41090	0.705448	−	0.708761i	$-0.250746\pi$
$709$	37.5680	1.41090	0.705448	+	0.708761i	$0.250746\pi$
$710$	4.83553	0.181474
$711$	9.32990	0.349899
$712$	16.3078	0.611160
$713$	−5.19701	−0.194630
$714$	62.4735	2.33801
$715$	−9.26912	−0.346645
$716$	−94.0985	−3.51663
$717$	−5.37806	−0.200848
$718$	−32.1025	−1.19805
$719$	35.2488	1.31456	0.657278	−	0.753648i	$-0.271708\pi$
$719$	35.2488	1.31456	0.657278	+	0.753648i	$0.271708\pi$
$720$	19.4482	0.724793
$721$	−71.7892	−2.67357
$722$	26.3424	0.980362
$723$	−39.7851	−1.47962
$724$	−88.3927	−3.28509
$725$	−47.4950	−1.76392
$726$	−23.5716	−0.874824
$727$	−49.4073	−1.83241	−0.916207	−	0.400705i	$-0.868765\pi$
$727$	−49.4073	−1.83241	−0.916207	+	0.400705i	$0.868765\pi$
$728$	−98.3639	−3.64561
$729$	−42.5219	−1.57488
$730$	5.07531	0.187846
$731$	25.9251	0.958875
$732$	−128.435	−4.74711
$733$	19.9811	0.738020	0.369010	−	0.929425i	$-0.379697\pi$
$733$	19.9811	0.738020	0.369010	+	0.929425i	$0.379697\pi$
$734$	−10.7860	−0.398117
$735$	10.4430	0.385194
$736$	6.03847	0.222581
$737$	26.6751	0.982592
$738$	30.1481	1.10977
$739$	51.1606	1.88197	0.940986	−	0.338444i	$-0.109901\pi$
$739$	51.1606	1.88197	0.940986	+	0.338444i	$0.109901\pi$
$740$	12.7750	0.469618
$741$	32.2342	1.18415
$742$	−79.9611	−2.93547
$743$	−14.8650	−0.545345	−0.272673	−	0.962107i	$-0.587908\pi$
$743$	−14.8650	−0.545345	−0.272673	+	0.962107i	$0.587908\pi$
$744$	−101.014	−3.70336
$745$	1.63252	0.0598110
$746$	−5.23323	−0.191602
$747$	−39.1878	−1.43381
$748$	42.9292	1.56965
$749$	65.4386	2.39107
$750$	39.7427	1.45120
$751$	31.1122	1.13530	0.567650	−	0.823270i	$-0.307853\pi$
$751$	31.1122	1.13530	0.567650	+	0.823270i	$0.307853\pi$
$752$	33.4097	1.21833
$753$	−11.5391	−0.420507
$754$	−106.736	−3.88708
$755$	4.01743	0.146209
$756$	53.8007	1.95671
$757$	38.2899	1.39167	0.695835	−	0.718202i	$-0.255034\pi$
$757$	38.2899	1.39167	0.695835	+	0.718202i	$0.255034\pi$
$758$	58.0590	2.10880
$759$	9.25420	0.335906
$760$	−11.6549	−0.422768
$761$	10.9821	0.398101	0.199050	−	0.979989i	$-0.436214\pi$
$761$	10.9821	0.398101	0.199050	+	0.979989i	$0.436214\pi$
$762$	−82.8108	−2.99992
$763$	41.5965	1.50589
$764$	−102.177	−3.69664
$765$	−6.22458	−0.225050
$766$	21.3077	0.769879
$767$	−14.1308	−0.510233
$768$	−72.0671	−2.60050
$769$	39.2645	1.41592	0.707958	−	0.706255i	$-0.249617\pi$
$769$	39.2645	1.41592	0.707958	+	0.706255i	$0.249617\pi$
$770$	21.4432	0.772759
$771$	−85.8361	−3.09131
$772$	96.4693	3.47201
$773$	26.8576	0.965999	0.483000	−	0.875621i	$-0.339547\pi$
$773$	26.8576	0.965999	0.483000	+	0.875621i	$0.339547\pi$
$774$	112.665	4.04965
$775$	−26.5528	−0.953806
$776$	−29.9646	−1.07567
$777$	45.9498	1.64844
$778$	81.9706	2.93879
$779$	−8.28064	−0.296685
$780$	29.8998	1.07059
$781$	11.9515	0.427660
$782$	−5.75875	−0.205932
$783$	32.8190	1.17285
$784$	50.1837	1.79227
$785$	−11.6541	−0.415951
$786$	−123.444	−4.40309
$787$	−4.69292	−0.167284	−0.0836422	−	0.996496i	$-0.526655\pi$
$787$	−4.69292	−0.167284	−0.0836422	+	0.996496i	$0.526655\pi$
$788$	10.7155	0.381724
$789$	−2.07206	−0.0737672
$790$	−3.41777	−0.121599
$791$	−12.7391	−0.452950
$792$	104.878	3.72668
$793$	−42.6520	−1.51462
$794$	−70.5111	−2.50235
$795$	13.6639	0.484610
$796$	43.2538	1.53309
$797$	28.2005	0.998912	0.499456	−	0.866339i	$-0.333533\pi$
$797$	28.2005	0.998912	0.499456	+	0.866339i	$0.333533\pi$
$798$	−74.5706	−2.63977
$799$	−10.6931	−0.378294
$800$	30.8521	1.09078
$801$	−10.3960	−0.367326
$802$	52.4558	1.85228
$803$	12.5442	0.442675
$804$	−86.0473	−3.03466
$805$	−2.00058	−0.0705111
$806$	−59.6723	−2.10187
$807$	−0.812853	−0.0286138
$808$	−100.170	−3.52397
$809$	−43.9703	−1.54591	−0.772956	−	0.634459i	$-0.781223\pi$
$809$	−43.9703	−1.54591	−0.772956	+	0.634459i	$0.781223\pi$
$810$	6.12435	0.215188
$811$	24.2837	0.852716	0.426358	−	0.904555i	$-0.359796\pi$
$811$	24.2837	0.852716	0.426358	+	0.904555i	$0.359796\pi$
$812$	171.732	6.02661
$813$	39.4874	1.38488
$814$	45.3993	1.59125
$815$	7.44143	0.260662
$816$	−51.3017	−1.79592
$817$	−30.9451	−1.08263
$818$	14.5453	0.508565
$819$	62.7060	2.19112
$820$	−7.68098	−0.268231
$821$	−4.89454	−0.170821	−0.0854103	−	0.996346i	$-0.527220\pi$
$821$	−4.89454	−0.170821	−0.0854103	+	0.996346i	$0.527220\pi$
$822$	5.84377	0.203825
$823$	−25.5266	−0.889801	−0.444901	−	0.895580i	$-0.646761\pi$
$823$	−25.5266	−0.889801	−0.444901	+	0.895580i	$0.646761\pi$
$824$	128.623	4.48081
$825$	47.2820	1.64615
$826$	32.6902	1.13744
$827$	−33.1573	−1.15299	−0.576495	−	0.817100i	$-0.695580\pi$
$827$	−33.1573	−1.15299	−0.576495	+	0.817100i	$0.695580\pi$
$828$	−17.4055	−0.604883
$829$	−0.405866	−0.0140963	−0.00704816	−	0.999975i	$-0.502244\pi$
$829$	−0.405866	−0.0140963	−0.00704816	+	0.999975i	$0.502244\pi$
$830$	14.3554	0.498285
$831$	−52.1292	−1.80834
$832$	6.42412	0.222716
$833$	−16.0617	−0.556506
$834$	37.6091	1.30230
$835$	−13.6514	−0.472425
$836$	−51.2418	−1.77224
$837$	18.3480	0.634199
$838$	100.214	3.46185
$839$	−40.4891	−1.39784	−0.698920	−	0.715200i	$-0.746336\pi$
$839$	−40.4891	−1.39784	−0.698920	+	0.715200i	$0.746336\pi$
$840$	−38.8852	−1.34167
$841$	75.7583	2.61236
$842$	−59.0070	−2.03351
$843$	−69.0805	−2.37926
$844$	−31.2152	−1.07447
$845$	2.13352	0.0733954
$846$	−46.4698	−1.59766
$847$	12.5946	0.432756
$848$	65.6621	2.25485
$849$	−13.3119	−0.456863
$850$	−29.4229	−1.00920
$851$	−4.23561	−0.145195
$852$	−38.5527	−1.32079
$853$	−50.5623	−1.73122	−0.865610	−	0.500719i	$-0.833069\pi$
$853$	−50.5623	−1.73122	−0.865610	+	0.500719i	$0.833069\pi$
$854$	98.6711	3.37646
$855$	7.42988	0.254096
$856$	−117.245	−4.00735
$857$	−21.9312	−0.749155	−0.374578	−	0.927196i	$-0.622212\pi$
$857$	−21.9312	−0.749155	−0.374578	+	0.927196i	$0.622212\pi$
$858$	106.257	3.62755
$859$	−5.83842	−0.199204	−0.0996022	−	0.995027i	$-0.531757\pi$
$859$	−5.83842	−0.199204	−0.0996022	+	0.995027i	$0.531757\pi$
$860$	−28.7042	−0.978803
$861$	−27.6273	−0.941537
$862$	68.6257	2.33740
$863$	40.4519	1.37700	0.688499	−	0.725237i	$-0.258270\pi$
$863$	40.4519	1.37700	0.688499	+	0.725237i	$0.258270\pi$
$864$	−21.3187	−0.725278
$865$	4.91376	0.167073
$866$	−33.6701	−1.14416
$867$	−29.1816	−0.991058
$868$	96.0096	3.25878
$869$	−8.44738	−0.286558
$870$	−42.1946	−1.43053
$871$	−28.5754	−0.968239
$872$	−74.5276	−2.52382
$873$	19.1021	0.646509
$874$	6.87385	0.232511
$875$	−21.2351	−0.717876
$876$	−40.4644	−1.36716
$877$	47.4882	1.60356	0.801782	−	0.597617i	$-0.203885\pi$
$877$	47.4882	1.60356	0.801782	+	0.597617i	$0.203885\pi$
$878$	81.3160	2.74428
$879$	2.69597	0.0909328
$880$	−17.6086	−0.593586
$881$	−5.50533	−0.185479	−0.0927396	−	0.995690i	$-0.529562\pi$
$881$	−5.50533	−0.185479	−0.0927396	+	0.995690i	$0.529562\pi$
$882$	−69.8008	−2.35031
$883$	17.4272	0.586473	0.293236	−	0.956040i	$-0.405268\pi$
$883$	17.4272	0.586473	0.293236	+	0.956040i	$0.405268\pi$
$884$	−45.9873	−1.54672
$885$	−5.58617	−0.187777
$886$	40.9969	1.37732
$887$	−45.2779	−1.52028	−0.760141	−	0.649758i	$-0.774870\pi$
$887$	−45.2779	−1.52028	−0.760141	+	0.649758i	$0.774870\pi$
$888$	−82.3273	−2.76272
$889$	44.2469	1.48399
$890$	3.80832	0.127655
$891$	15.1370	0.507108
$892$	125.295	4.19520
$893$	12.7636	0.427119
$894$	−18.7145	−0.625907
$895$	−12.3534	−0.412927
$896$	33.9809	1.13522
$897$	−9.91343	−0.331000
$898$	−86.8283	−2.89750
$899$	58.5668	1.95331
$900$	−88.9291	−2.96430
$901$	−21.0157	−0.700136
$902$	−27.2964	−0.908870
$903$	−103.245	−3.43576
$904$	22.8244	0.759128
$905$	−11.6043	−0.385740
$906$	−46.0540	−1.53004
$907$	−15.0010	−0.498100	−0.249050	−	0.968491i	$-0.580118\pi$
$907$	−15.0010	−0.498100	−0.249050	+	0.968491i	$0.580118\pi$
$908$	43.8791	1.45618
$909$	63.8573	2.11801
$910$	−22.9707	−0.761471
$911$	−2.70593	−0.0896516	−0.0448258	−	0.998995i	$-0.514273\pi$
$911$	−2.70593	−0.0896516	−0.0448258	+	0.998995i	$0.514273\pi$
$912$	61.2355	2.02771
$913$	35.4810	1.17425
$914$	−47.3487	−1.56615
$915$	−16.8611	−0.557412
$916$	−58.4822	−1.93230
$917$	65.9576	2.17811
$918$	20.3312	0.671029
$919$	46.3393	1.52859	0.764296	−	0.644866i	$-0.223087\pi$
$919$	46.3393	1.52859	0.764296	+	0.644866i	$0.223087\pi$
$920$	3.58440	0.118174
$921$	51.2099	1.68742
$922$	−39.3502	−1.29593
$923$	−12.8029	−0.421413
$924$	−170.962	−5.62424
$925$	−21.6408	−0.711544
$926$	−16.8161	−0.552610
$927$	−81.9960	−2.69310
$928$	−68.0495	−2.23383
$929$	−38.0328	−1.24782	−0.623908	−	0.781497i	$-0.714456\pi$
$929$	−38.0328	−1.24782	−0.623908	+	0.781497i	$0.714456\pi$
$930$	−23.5896	−0.773533
$931$	19.1719	0.628332
$932$	21.9079	0.717617
$933$	26.5629	0.869630
$934$	51.6983	1.69162
$935$	5.63579	0.184310
$936$	−112.349	−3.67224
$937$	−12.0111	−0.392385	−0.196192	−	0.980565i	$-0.562858\pi$
$937$	−12.0111	−0.392385	−0.196192	+	0.980565i	$0.562858\pi$
$938$	66.1063	2.15845
$939$	−15.0986	−0.492723
$940$	11.8393	0.386156
$941$	47.7145	1.55545	0.777724	−	0.628606i	$-0.216374\pi$
$941$	47.7145	1.55545	0.777724	+	0.628606i	$0.216374\pi$
$942$	133.597	4.35282
$943$	2.54666	0.0829308
$944$	−26.8444	−0.873709
$945$	7.06301	0.229760
$946$	−102.008	−3.31656
$947$	11.0504	0.359091	0.179545	−	0.983750i	$-0.442537\pi$
$947$	11.0504	0.359091	0.179545	+	0.983750i	$0.442537\pi$
$948$	27.2491	0.885011
$949$	−13.4378	−0.436208
$950$	35.1202	1.13945
$951$	91.1556	2.95592
$952$	59.8071	1.93836
$953$	30.9775	1.00346	0.501729	−	0.865025i	$-0.332697\pi$
$953$	30.9775	1.00346	0.501729	+	0.865025i	$0.332697\pi$
$954$	−91.3298	−2.95691
$955$	−13.4139	−0.434065
$956$	−9.15839	−0.296203
$957$	−104.289	−3.37117
$958$	46.4697	1.50137
$959$	−3.12240	−0.100828
$960$	2.53958	0.0819645
$961$	1.74273	0.0562170
$962$	−48.6333	−1.56800
$963$	74.7424	2.40854
$964$	−67.7506	−2.18210
$965$	12.6646	0.407688
$966$	22.9337	0.737881
$967$	−1.11655	−0.0359059	−0.0179529	−	0.999839i	$-0.505715\pi$
$967$	−1.11655	−0.0359059	−0.0179529	+	0.999839i	$0.505715\pi$
$968$	−22.5655	−0.725284
$969$	−19.5990	−0.629610
$970$	−6.99757	−0.224678
$971$	23.1430	0.742694	0.371347	−	0.928494i	$-0.378896\pi$
$971$	23.1430	0.742694	0.371347	+	0.928494i	$0.378896\pi$
$972$	−92.7693	−2.97558
$973$	−20.0951	−0.644218
$974$	−15.4346	−0.494555
$975$	−50.6502	−1.62210
$976$	−81.0263	−2.59359
$977$	5.23774	0.167570	0.0837852	−	0.996484i	$-0.473299\pi$
$977$	5.23774	0.167570	0.0837852	+	0.996484i	$0.473299\pi$
$978$	−85.3052	−2.72776
$979$	9.41267	0.300830
$980$	17.7835	0.568072
$981$	47.5105	1.51689
$982$	−6.64074	−0.211915
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	49.4994	1.57798
$985$	1.40674	0.0448225
$986$	64.8972	2.06675
$987$	42.5843	1.35547
$988$	54.8920	1.74635
$989$	9.51699	0.302623
$990$	24.4919	0.778404
$991$	−37.6272	−1.19527	−0.597633	−	0.801770i	$-0.703892\pi$
$991$	−37.6272	−1.19527	−0.597633	+	0.801770i	$0.703892\pi$
$992$	−38.0442	−1.20790
$993$	48.6450	1.54370
$994$	29.6183	0.939435
$995$	5.67841	0.180018
$996$	−114.453	−3.62658
$997$	−6.86766	−0.217501	−0.108750	−	0.994069i	$-0.534685\pi$
$997$	−6.86766	−0.217501	−0.108750	+	0.994069i	$0.534685\pi$
$998$	18.4283	0.583338
$999$	14.9537	0.473115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.b.1.3	✓	54
3.2	odd	2		8847.2.a.g.1.52		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.3	✓	54	1.1	even	1	trivial
8847.2.a.g.1.52		54	3.2	odd	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56280 q^{2} +2.68242 q^{3} +4.56793 q^{4} +0.599683 q^{5} -6.87450 q^{6} +3.67314 q^{7} -6.58109 q^{8} +4.19537 q^{9} +O(q^{10})\)	\(q-2.56280 q^{2} +2.68242 q^{3} +4.56793 q^{4} +0.599683 q^{5} -6.87450 q^{6} +3.67314 q^{7} -6.58109 q^{8} +4.19537 q^{9} -1.53687 q^{10} -3.79853 q^{11} +12.2531 q^{12} +4.06912 q^{13} -9.41351 q^{14} +1.60860 q^{15} +7.73014 q^{16} -2.47410 q^{17} -10.7519 q^{18} +2.95317 q^{19} +2.73931 q^{20} +9.85290 q^{21} +9.73487 q^{22} -0.908231 q^{23} -17.6532 q^{24} -4.64038 q^{25} -10.4283 q^{26} +3.20650 q^{27} +16.7786 q^{28} +10.2352 q^{29} -4.12252 q^{30} +5.72213 q^{31} -6.64861 q^{32} -10.1893 q^{33} +6.34062 q^{34} +2.20272 q^{35} +19.1642 q^{36} +4.66358 q^{37} -7.56839 q^{38} +10.9151 q^{39} -3.94657 q^{40} -2.80398 q^{41} -25.2510 q^{42} -10.4786 q^{43} -17.3514 q^{44} +2.51590 q^{45} +2.32761 q^{46} +4.32201 q^{47} +20.7355 q^{48} +6.49195 q^{49} +11.8924 q^{50} -6.63658 q^{51} +18.5875 q^{52} +8.49429 q^{53} -8.21760 q^{54} -2.27792 q^{55} -24.1733 q^{56} +7.92165 q^{57} -26.2306 q^{58} -3.47269 q^{59} +7.34798 q^{60} -10.4819 q^{61} -14.6647 q^{62} +15.4102 q^{63} +1.57875 q^{64} +2.44018 q^{65} +26.1130 q^{66} -7.02249 q^{67} -11.3015 q^{68} -2.43626 q^{69} -5.64512 q^{70} -3.14636 q^{71} -27.6101 q^{72} -3.30238 q^{73} -11.9518 q^{74} -12.4474 q^{75} +13.4899 q^{76} -13.9525 q^{77} -27.9732 q^{78} +2.22385 q^{79} +4.63564 q^{80} -3.98496 q^{81} +7.18604 q^{82} -9.34072 q^{83} +45.0074 q^{84} -1.48368 q^{85} +26.8545 q^{86} +27.4550 q^{87} +24.9985 q^{88} -2.47798 q^{89} -6.44773 q^{90} +14.9464 q^{91} -4.14874 q^{92} +15.3491 q^{93} -11.0764 q^{94} +1.77097 q^{95} -17.8343 q^{96} +4.55314 q^{97} -16.6376 q^{98} -15.9363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * q^99

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