LMFDB - Embedded newform 983.2.a.b.1.52

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			1.52
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)

$f(q)$	$=$	$q+2.73579 q^{2} -3.15625 q^{3} +5.48453 q^{4} +3.19952 q^{5} -8.63484 q^{6} +1.97538 q^{7} +9.53294 q^{8} +6.96195 q^{9} +O(q^{10})$	\(q+2.73579 q^{2} -3.15625 q^{3} +5.48453 q^{4} +3.19952 q^{5} -8.63484 q^{6} +1.97538 q^{7} +9.53294 q^{8} +6.96195 q^{9} +8.75320 q^{10} -1.74324 q^{11} -17.3106 q^{12} -6.04331 q^{13} +5.40421 q^{14} -10.0985 q^{15} +15.1110 q^{16} +4.47925 q^{17} +19.0464 q^{18} -5.10863 q^{19} +17.5479 q^{20} -6.23480 q^{21} -4.76913 q^{22} -1.36326 q^{23} -30.0884 q^{24} +5.23692 q^{25} -16.5332 q^{26} -12.5049 q^{27} +10.8340 q^{28} +8.35922 q^{29} -27.6273 q^{30} -6.98733 q^{31} +22.2747 q^{32} +5.50210 q^{33} +12.2543 q^{34} +6.32026 q^{35} +38.1830 q^{36} -0.981249 q^{37} -13.9761 q^{38} +19.0742 q^{39} +30.5008 q^{40} +0.601549 q^{41} -17.0571 q^{42} +2.85478 q^{43} -9.56084 q^{44} +22.2749 q^{45} -3.72960 q^{46} +8.35619 q^{47} -47.6942 q^{48} -3.09788 q^{49} +14.3271 q^{50} -14.1376 q^{51} -33.1447 q^{52} -2.52473 q^{53} -34.2108 q^{54} -5.57752 q^{55} +18.8312 q^{56} +16.1241 q^{57} +22.8691 q^{58} +5.94179 q^{59} -55.3855 q^{60} -11.1152 q^{61} -19.1158 q^{62} +13.7525 q^{63} +30.7167 q^{64} -19.3357 q^{65} +15.0526 q^{66} -12.2920 q^{67} +24.5666 q^{68} +4.30281 q^{69} +17.2909 q^{70} +5.43629 q^{71} +66.3678 q^{72} +9.88442 q^{73} -2.68449 q^{74} -16.5290 q^{75} -28.0184 q^{76} -3.44355 q^{77} +52.1830 q^{78} -11.0029 q^{79} +48.3480 q^{80} +18.5828 q^{81} +1.64571 q^{82} +2.20132 q^{83} -34.1949 q^{84} +14.3314 q^{85} +7.81006 q^{86} -26.3838 q^{87} -16.6182 q^{88} -6.22607 q^{89} +60.9393 q^{90} -11.9378 q^{91} -7.47687 q^{92} +22.0538 q^{93} +22.8608 q^{94} -16.3452 q^{95} -70.3045 q^{96} +7.27235 q^{97} -8.47515 q^{98} -12.1363 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.73579	1.93449	0.967247	−	0.253838i	$-0.0816929\pi$
$2$	2.73579	1.93449	0.967247	+	0.253838i	$0.0816929\pi$
$3$	−3.15625	−1.82226	−0.911132	−	0.412114i	$-0.864791\pi$
$3$	−3.15625	−1.82226	−0.911132	+	0.412114i	$0.864791\pi$
$4$	5.48453	2.74227
$5$	3.19952	1.43087	0.715434	−	0.698680i	$-0.246229\pi$
$5$	3.19952	1.43087	0.715434	+	0.698680i	$0.246229\pi$
$6$	−8.63484	−3.52516
$7$	1.97538	0.746623	0.373311	−	0.927706i	$-0.378222\pi$
$7$	1.97538	0.746623	0.373311	+	0.927706i	$0.378222\pi$
$8$	9.53294	3.37040
$9$	6.96195	2.32065
$10$	8.75320	2.76801
$11$	−1.74324	−0.525606	−0.262803	−	0.964850i	$-0.584647\pi$
$11$	−1.74324	−0.525606	−0.262803	+	0.964850i	$0.584647\pi$
$12$	−17.3106	−4.99713
$13$	−6.04331	−1.67611	−0.838056	−	0.545584i	$-0.816308\pi$
$13$	−6.04331	−1.67611	−0.838056	+	0.545584i	$0.816308\pi$
$14$	5.40421	1.44434
$15$	−10.0985	−2.60742
$16$	15.1110	3.77776
$17$	4.47925	1.08638	0.543188	−	0.839611i	$-0.317217\pi$
$17$	4.47925	1.08638	0.543188	+	0.839611i	$0.317217\pi$
$18$	19.0464	4.48928
$19$	−5.10863	−1.17200	−0.586000	−	0.810311i	$-0.699298\pi$
$19$	−5.10863	−1.17200	−0.586000	+	0.810311i	$0.699298\pi$
$20$	17.5479	3.92382
$21$	−6.23480	−1.36054
$22$	−4.76913	−1.01678
$23$	−1.36326	−0.284260	−0.142130	−	0.989848i	$-0.545395\pi$
$23$	−1.36326	−0.284260	−0.142130	+	0.989848i	$0.545395\pi$
$24$	−30.0884	−6.14176
$25$	5.23692	1.04738
$26$	−16.5332	−3.24243
$27$	−12.5049	−2.40657
$28$	10.8340	2.04744
$29$	8.35922	1.55227	0.776134	−	0.630568i	$-0.217178\pi$
$29$	8.35922	1.55227	0.776134	+	0.630568i	$0.217178\pi$
$30$	−27.6273	−5.04404
$31$	−6.98733	−1.25496	−0.627481	−	0.778632i	$-0.715914\pi$
$31$	−6.98733	−1.25496	−0.627481	+	0.778632i	$0.715914\pi$
$32$	22.2747	3.93764
$33$	5.50210	0.957793
$34$	12.2543	2.10159
$35$	6.32026	1.06832
$36$	38.1830	6.36383
$37$	−0.981249	−0.161316	−0.0806582	−	0.996742i	$-0.525702\pi$
$37$	−0.981249	−0.161316	−0.0806582	+	0.996742i	$0.525702\pi$
$38$	−13.9761	−2.26723
$39$	19.0742	3.05432
$40$	30.5008	4.82260
$41$	0.601549	0.0939462	0.0469731	−	0.998896i	$-0.485042\pi$
$41$	0.601549	0.0939462	0.0469731	+	0.998896i	$0.485042\pi$
$42$	−17.0571	−2.63196
$43$	2.85478	0.435349	0.217675	−	0.976021i	$-0.430153\pi$
$43$	2.85478	0.435349	0.217675	+	0.976021i	$0.430153\pi$
$44$	−9.56084	−1.44135
$45$	22.2749	3.32054
$46$	−3.72960	−0.549900
$47$	8.35619	1.21888	0.609438	−	0.792834i	$-0.291395\pi$
$47$	8.35619	1.21888	0.609438	+	0.792834i	$0.291395\pi$
$48$	−47.6942	−6.88407
$49$	−3.09788	−0.442555
$50$	14.3271	2.02616
$51$	−14.1376	−1.97967
$52$	−33.1447	−4.59635
$53$	−2.52473	−0.346799	−0.173399	−	0.984852i	$-0.555475\pi$
$53$	−2.52473	−0.346799	−0.173399	+	0.984852i	$0.555475\pi$
$54$	−34.2108	−4.65550
$55$	−5.57752	−0.752073
$56$	18.8312	2.51642
$57$	16.1241	2.13569
$58$	22.8691	3.00285
$59$	5.94179	0.773555	0.386777	−	0.922173i	$-0.373588\pi$
$59$	5.94179	0.773555	0.386777	+	0.922173i	$0.373588\pi$
$60$	−55.3855	−7.15024
$61$	−11.1152	−1.42316	−0.711579	−	0.702607i	$-0.752019\pi$
$61$	−11.1152	−1.42316	−0.711579	+	0.702607i	$0.752019\pi$
$62$	−19.1158	−2.42772
$63$	13.7525	1.73265
$64$	30.7167	3.83959
$65$	−19.3357	−2.39830
$66$	15.0526	1.85284
$67$	−12.2920	−1.50171	−0.750856	−	0.660466i	$-0.770359\pi$
$67$	−12.2920	−1.50171	−0.750856	+	0.660466i	$0.770359\pi$
$68$	24.5666	2.97913
$69$	4.30281	0.517997
$70$	17.2909	2.06666
$71$	5.43629	0.645169	0.322585	−	0.946541i	$-0.395448\pi$
$71$	5.43629	0.645169	0.322585	+	0.946541i	$0.395448\pi$
$72$	66.3678	7.82152
$73$	9.88442	1.15688	0.578442	−	0.815724i	$-0.303661\pi$
$73$	9.88442	1.15688	0.578442	+	0.815724i	$0.303661\pi$
$74$	−2.68449	−0.312065
$75$	−16.5290	−1.90861
$76$	−28.0184	−3.21394
$77$	−3.44355	−0.392429
$78$	52.1830	5.90856
$79$	−11.0029	−1.23792	−0.618960	−	0.785423i	$-0.712446\pi$
$79$	−11.0029	−1.23792	−0.618960	+	0.785423i	$0.712446\pi$
$80$	48.3480	5.40547
$81$	18.5828	2.06476
$82$	1.64571	0.181738
$83$	2.20132	0.241627	0.120813	−	0.992675i	$-0.461450\pi$
$83$	2.20132	0.241627	0.120813	+	0.992675i	$0.461450\pi$
$84$	−34.1949	−3.73097
$85$	14.3314	1.55446
$86$	7.81006	0.842180
$87$	−26.3838	−2.82864
$88$	−16.6182	−1.77150
$89$	−6.22607	−0.659962	−0.329981	−	0.943988i	$-0.607042\pi$
$89$	−6.22607	−0.659962	−0.329981	+	0.943988i	$0.607042\pi$
$90$	60.9393	6.42357
$91$	−11.9378	−1.25142
$92$	−7.47687	−0.779517
$93$	22.0538	2.28687
$94$	22.8608	2.35791
$95$	−16.3452	−1.67698
$96$	−70.3045	−7.17543
$97$	7.27235	0.738396	0.369198	−	0.929351i	$-0.379632\pi$
$97$	7.27235	0.738396	0.369198	+	0.929351i	$0.379632\pi$
$98$	−8.47515	−0.856119
$99$	−12.1363	−1.21975
$100$	28.7220	2.87220
$101$	−1.50416	−0.149670	−0.0748348	−	0.997196i	$-0.523843\pi$
$101$	−1.50416	−0.149670	−0.0748348	+	0.997196i	$0.523843\pi$
$102$	−38.6776	−3.82965
$103$	−10.7360	−1.05785	−0.528927	−	0.848667i	$-0.677405\pi$
$103$	−10.7360	−1.05785	−0.528927	+	0.848667i	$0.677405\pi$
$104$	−57.6105	−5.64917
$105$	−19.9483	−1.94676
$106$	−6.90713	−0.670880
$107$	−14.8128	−1.43201	−0.716005	−	0.698095i	$-0.754031\pi$
$107$	−14.8128	−1.43201	−0.716005	+	0.698095i	$0.754031\pi$
$108$	−68.5836	−6.59946
$109$	−3.15749	−0.302433	−0.151216	−	0.988501i	$-0.548319\pi$
$109$	−3.15749	−0.302433	−0.151216	+	0.988501i	$0.548319\pi$
$110$	−15.2589	−1.45488
$111$	3.09707	0.293961
$112$	29.8500	2.82056
$113$	−2.33181	−0.219358	−0.109679	−	0.993967i	$-0.534982\pi$
$113$	−2.33181	−0.219358	−0.109679	+	0.993967i	$0.534982\pi$
$114$	44.1122	4.13149
$115$	−4.36179	−0.406739
$116$	45.8464	4.25673
$117$	−42.0732	−3.88967
$118$	16.2555	1.49644
$119$	8.84820	0.811113
$120$	−96.2683	−8.78805
$121$	−7.96112	−0.723738
$122$	−30.4089	−2.75309
$123$	−1.89864	−0.171195
$124$	−38.3222	−3.44144
$125$	0.758019	0.0677993
$126$	37.6238	3.35180
$127$	11.6696	1.03551	0.517757	−	0.855528i	$-0.326767\pi$
$127$	11.6696	1.03551	0.517757	+	0.855528i	$0.326767\pi$
$128$	39.4850	3.49002
$129$	−9.01040	−0.793321
$130$	−52.8983	−4.63949
$131$	17.3567	1.51646	0.758231	−	0.651986i	$-0.226064\pi$
$131$	17.3567	1.51646	0.758231	+	0.651986i	$0.226064\pi$
$132$	30.1765	2.62652
$133$	−10.0915	−0.875042
$134$	−33.6284	−2.90505
$135$	−40.0097	−3.44349
$136$	42.7004	3.66153
$137$	−3.51859	−0.300613	−0.150307	−	0.988639i	$-0.548026\pi$
$137$	−3.51859	−0.300613	−0.150307	+	0.988639i	$0.548026\pi$
$138$	11.7716	1.00206
$139$	−2.59449	−0.220061	−0.110031	−	0.993928i	$-0.535095\pi$
$139$	−2.59449	−0.220061	−0.110031	+	0.993928i	$0.535095\pi$
$140$	34.6637	2.92961
$141$	−26.3743	−2.22111
$142$	14.8725	1.24808
$143$	10.5349	0.880975
$144$	105.202	8.76684
$145$	26.7455	2.22109
$146$	27.0417	2.23798
$147$	9.77771	0.806452
$148$	−5.38169	−0.442372
$149$	−1.70848	−0.139964	−0.0699821	−	0.997548i	$-0.522294\pi$
$149$	−1.70848	−0.139964	−0.0699821	+	0.997548i	$0.522294\pi$
$150$	−45.2199	−3.69219
$151$	−2.28494	−0.185945	−0.0929727	−	0.995669i	$-0.529637\pi$
$151$	−2.28494	−0.185945	−0.0929727	+	0.995669i	$0.529637\pi$
$152$	−48.7002	−3.95011
$153$	31.1843	2.52110
$154$	−9.42083	−0.759152
$155$	−22.3561	−1.79568
$156$	104.613	8.37576
$157$	−20.6016	−1.64418	−0.822091	−	0.569356i	$-0.807193\pi$
$157$	−20.6016	−1.64418	−0.822091	+	0.569356i	$0.807193\pi$
$158$	−30.1015	−2.39475
$159$	7.96870	0.631959
$160$	71.2682	5.63425
$161$	−2.69296	−0.212235
$162$	50.8387	3.99427
$163$	18.5998	1.45685	0.728425	−	0.685125i	$-0.240253\pi$
$163$	18.5998	1.45685	0.728425	+	0.685125i	$0.240253\pi$
$164$	3.29922	0.257625
$165$	17.6041	1.37048
$166$	6.02235	0.467425
$167$	−11.2740	−0.872408	−0.436204	−	0.899848i	$-0.643677\pi$
$167$	−11.2740	−0.872408	−0.436204	+	0.899848i	$0.643677\pi$
$168$	−59.4359	−4.58558
$169$	23.5216	1.80935
$170$	39.2077	3.00710
$171$	−35.5660	−2.71980
$172$	15.6571	1.19384
$173$	7.83219	0.595470	0.297735	−	0.954649i	$-0.403769\pi$
$173$	7.83219	0.595470	0.297735	+	0.954649i	$0.403769\pi$
$174$	−72.1806	−5.47199
$175$	10.3449	0.782000
$176$	−26.3421	−1.98561
$177$	−18.7538	−1.40962
$178$	−17.0332	−1.27669
$179$	1.48171	0.110749	0.0553743	−	0.998466i	$-0.482365\pi$
$179$	1.48171	0.110749	0.0553743	+	0.998466i	$0.482365\pi$
$180$	122.167	9.10581
$181$	−19.5370	−1.45217	−0.726086	−	0.687604i	$-0.758663\pi$
$181$	−19.5370	−1.45217	−0.726086	+	0.687604i	$0.758663\pi$
$182$	−32.6593	−2.42087
$183$	35.0824	2.59337
$184$	−12.9959	−0.958072
$185$	−3.13952	−0.230822
$186$	60.3345	4.42394
$187$	−7.80839	−0.571006
$188$	45.8298	3.34248
$189$	−24.7019	−1.79680
$190$	−44.7169	−3.24410
$191$	3.77214	0.272942	0.136471	−	0.990644i	$-0.456424\pi$
$191$	3.77214	0.272942	0.136471	+	0.990644i	$0.456424\pi$
$192$	−96.9498	−6.99675
$193$	6.40449	0.461005	0.230503	−	0.973072i	$-0.425963\pi$
$193$	6.40449	0.461005	0.230503	+	0.973072i	$0.425963\pi$
$194$	19.8956	1.42842
$195$	61.0283	4.37033
$196$	−16.9904	−1.21360
$197$	11.0655	0.788385	0.394193	−	0.919028i	$-0.371024\pi$
$197$	11.0655	0.788385	0.394193	+	0.919028i	$0.371024\pi$
$198$	−33.2024	−2.35959
$199$	10.2861	0.729162	0.364581	−	0.931172i	$-0.381212\pi$
$199$	10.2861	0.729162	0.364581	+	0.931172i	$0.381212\pi$
$200$	49.9232	3.53010
$201$	38.7968	2.73652
$202$	−4.11507	−0.289535
$203$	16.5126	1.15896
$204$	−77.5383	−5.42877
$205$	1.92467	0.134425
$206$	−29.3715	−2.04641
$207$	−9.49097	−0.659668
$208$	−91.3206	−6.33194
$209$	8.90556	0.616010
$210$	−54.5744	−3.76599
$211$	−13.1111	−0.902606	−0.451303	−	0.892371i	$-0.649041\pi$
$211$	−13.1111	−0.902606	−0.451303	+	0.892371i	$0.649041\pi$
$212$	−13.8470	−0.951014
$213$	−17.1583	−1.17567
$214$	−40.5248	−2.77022
$215$	9.13390	0.622927
$216$	−119.209	−8.11111
$217$	−13.8026	−0.936983
$218$	−8.63823	−0.585054
$219$	−31.1978	−2.10815
$220$	−30.5901	−2.06238
$221$	−27.0695	−1.82089
$222$	8.47293	0.568666
$223$	13.0094	0.871175	0.435587	−	0.900146i	$-0.356541\pi$
$223$	13.0094	0.871175	0.435587	+	0.900146i	$0.356541\pi$
$224$	44.0009	2.93993
$225$	36.4591	2.43061
$226$	−6.37934	−0.424347
$227$	−15.6290	−1.03733	−0.518667	−	0.854977i	$-0.673571\pi$
$227$	−15.6290	−1.03733	−0.518667	+	0.854977i	$0.673571\pi$
$228$	88.4333	5.85664
$229$	−18.6033	−1.22934	−0.614669	−	0.788785i	$-0.710711\pi$
$229$	−18.6033	−1.22934	−0.614669	+	0.788785i	$0.710711\pi$
$230$	−11.9329	−0.786834
$231$	10.8687	0.715110
$232$	79.6879	5.23177
$233$	28.2739	1.85228	0.926142	−	0.377174i	$-0.123104\pi$
$233$	28.2739	1.85228	0.926142	+	0.377174i	$0.123104\pi$
$234$	−115.103	−7.52454
$235$	26.7358	1.74405
$236$	32.5879	2.12129
$237$	34.7279	2.25582
$238$	24.2068	1.56909
$239$	−29.3504	−1.89852	−0.949261	−	0.314490i	$-0.898166\pi$
$239$	−29.3504	−1.89852	−0.949261	+	0.314490i	$0.898166\pi$
$240$	−152.599	−9.85020
$241$	19.2529	1.24019	0.620093	−	0.784529i	$-0.287095\pi$
$241$	19.2529	1.24019	0.620093	+	0.784529i	$0.287095\pi$
$242$	−21.7799	−1.40007
$243$	−21.1375	−1.35597
$244$	−60.9617	−3.90267
$245$	−9.91173	−0.633237
$246$	−5.19428	−0.331175
$247$	30.8730	1.96440
$248$	−66.6098	−4.22973
$249$	−6.94794	−0.440308
$250$	2.07378	0.131157
$251$	16.6835	1.05305	0.526525	−	0.850159i	$-0.323495\pi$
$251$	16.6835	1.05305	0.526525	+	0.850159i	$0.323495\pi$
$252$	75.4259	4.75138
$253$	2.37649	0.149409
$254$	31.9257	2.00319
$255$	−45.2336	−2.83264
$256$	46.5893	2.91183
$257$	21.7077	1.35409	0.677044	−	0.735943i	$-0.263261\pi$
$257$	21.7077	1.35409	0.677044	+	0.735943i	$0.263261\pi$
$258$	−24.6505	−1.53467
$259$	−1.93834	−0.120442
$260$	−106.047	−6.57676
$261$	58.1964	3.60227
$262$	47.4842	2.93359
$263$	2.66252	0.164178	0.0820891	−	0.996625i	$-0.473841\pi$
$263$	2.66252	0.164178	0.0820891	+	0.996625i	$0.473841\pi$
$264$	52.4512	3.22815
$265$	−8.07793	−0.496223
$266$	−27.6081	−1.69276
$267$	19.6511	1.20263
$268$	−67.4161	−4.11809
$269$	11.1387	0.679136	0.339568	−	0.940581i	$-0.389719\pi$
$269$	11.1387	0.679136	0.339568	+	0.940581i	$0.389719\pi$
$270$	−109.458	−6.66140
$271$	−6.03334	−0.366499	−0.183250	−	0.983066i	$-0.558662\pi$
$271$	−6.03334	−0.366499	−0.183250	+	0.983066i	$0.558662\pi$
$272$	67.6860	4.10407
$273$	37.6788	2.28042
$274$	−9.62611	−0.581534
$275$	−9.12919	−0.550511
$276$	23.5989	1.42049
$277$	18.6122	1.11830	0.559149	−	0.829067i	$-0.311128\pi$
$277$	18.6122	1.11830	0.559149	+	0.829067i	$0.311128\pi$
$278$	−7.09796	−0.425707
$279$	−48.6454	−2.91232
$280$	60.2506	3.60066
$281$	−7.12161	−0.424840	−0.212420	−	0.977178i	$-0.568134\pi$
$281$	−7.12161	−0.424840	−0.212420	+	0.977178i	$0.568134\pi$
$282$	−72.1544	−4.29673
$283$	−3.27269	−0.194541	−0.0972706	−	0.995258i	$-0.531011\pi$
$283$	−3.27269	−0.194541	−0.0972706	+	0.995258i	$0.531011\pi$
$284$	29.8155	1.76923
$285$	51.5895	3.05590
$286$	28.8213	1.70424
$287$	1.18829	0.0701424
$288$	155.075	9.13788
$289$	3.06364	0.180214
$290$	73.1700	4.29669
$291$	−22.9534	−1.34555
$292$	54.2114	3.17248
$293$	−24.2517	−1.41680	−0.708399	−	0.705813i	$-0.750582\pi$
$293$	−24.2517	−1.41680	−0.708399	+	0.705813i	$0.750582\pi$
$294$	26.7497	1.56008
$295$	19.0109	1.10685
$296$	−9.35419	−0.543701
$297$	21.7990	1.26491
$298$	−4.67404	−0.270760
$299$	8.23863	0.476452
$300$	−90.6541	−5.23391
$301$	5.63926	0.325042
$302$	−6.25110	−0.359710
$303$	4.74752	0.272738
$304$	−77.1966	−4.42753
$305$	−35.5633	−2.03635
$306$	85.3135	4.87705
$307$	23.3261	1.33129	0.665646	−	0.746267i	$-0.268156\pi$
$307$	23.3261	1.33129	0.665646	+	0.746267i	$0.268156\pi$
$308$	−18.8863	−1.07615
$309$	33.8857	1.92769
$310$	−61.1615	−3.47374
$311$	−18.4975	−1.04890	−0.524449	−	0.851442i	$-0.675729\pi$
$311$	−18.4975	−1.04890	−0.524449	+	0.851442i	$0.675729\pi$
$312$	181.833	10.2943
$313$	−20.8115	−1.17633	−0.588167	−	0.808740i	$-0.700150\pi$
$313$	−20.8115	−1.17633	−0.588167	+	0.808740i	$0.700150\pi$
$314$	−56.3615	−3.18066
$315$	44.0013	2.47919
$316$	−60.3456	−3.39470
$317$	31.4795	1.76807	0.884033	−	0.467425i	$-0.154818\pi$
$317$	31.4795	1.76807	0.884033	+	0.467425i	$0.154818\pi$
$318$	21.8007	1.22252
$319$	−14.5721	−0.815882
$320$	98.2787	5.49395
$321$	46.7531	2.60950
$322$	−7.36737	−0.410568
$323$	−22.8828	−1.27323
$324$	101.918	5.66212
$325$	−31.6483	−1.75553
$326$	50.8851	2.81827
$327$	9.96585	0.551113
$328$	5.73453	0.316636
$329$	16.5066	0.910040
$330$	48.1610	2.65118
$331$	−10.5876	−0.581946	−0.290973	−	0.956731i	$-0.593979\pi$
$331$	−10.5876	−0.581946	−0.290973	+	0.956731i	$0.593979\pi$
$332$	12.0732	0.662605
$333$	−6.83140	−0.374359
$334$	−30.8433	−1.68767
$335$	−39.3286	−2.14875
$336$	−94.2142	−5.13980
$337$	28.2835	1.54070	0.770349	−	0.637622i	$-0.220082\pi$
$337$	28.2835	1.54070	0.770349	+	0.637622i	$0.220082\pi$
$338$	64.3501	3.50018
$339$	7.35979	0.399729
$340$	78.6012	4.26275
$341$	12.1806	0.659615
$342$	−97.3010	−5.26144
$343$	−19.9471	−1.07704
$344$	27.2144	1.46730
$345$	13.7669	0.741186
$346$	21.4272	1.15193
$347$	−7.76097	−0.416631	−0.208315	−	0.978062i	$-0.566798\pi$
$347$	−7.76097	−0.416631	−0.208315	+	0.978062i	$0.566798\pi$
$348$	−144.703	−7.75689
$349$	−11.5173	−0.616508	−0.308254	−	0.951304i	$-0.599745\pi$
$349$	−11.5173	−0.616508	−0.308254	+	0.951304i	$0.599745\pi$
$350$	28.3014	1.51277
$351$	75.5710	4.03368
$352$	−38.8300	−2.06965
$353$	0.942796	0.0501800	0.0250900	−	0.999685i	$-0.492013\pi$
$353$	0.942796	0.0501800	0.0250900	+	0.999685i	$0.492013\pi$
$354$	−51.3064	−2.72690
$355$	17.3935	0.923152
$356$	−34.1471	−1.80979
$357$	−27.9272	−1.47806
$358$	4.05365	0.214242
$359$	−5.72791	−0.302308	−0.151154	−	0.988510i	$-0.548299\pi$
$359$	−5.72791	−0.302308	−0.151154	+	0.988510i	$0.548299\pi$
$360$	212.345	11.1916
$361$	7.09809	0.373584
$362$	−53.4490	−2.80922
$363$	25.1273	1.31884
$364$	−65.4734	−3.43174
$365$	31.6254	1.65535
$366$	95.9781	5.01686
$367$	−2.88340	−0.150512	−0.0752561	−	0.997164i	$-0.523977\pi$
$367$	−2.88340	−0.150512	−0.0752561	+	0.997164i	$0.523977\pi$
$368$	−20.6003	−1.07387
$369$	4.18795	0.218016
$370$	−8.58907	−0.446524
$371$	−4.98730	−0.258928
$372$	120.955	6.27121
$373$	−12.2052	−0.631963	−0.315981	−	0.948765i	$-0.602334\pi$
$373$	−12.2052	−0.631963	−0.315981	+	0.948765i	$0.602334\pi$
$374$	−21.3621	−1.10461
$375$	−2.39250	−0.123548
$376$	79.6590	4.10810
$377$	−50.5174	−2.60178
$378$	−67.5792	−3.47590
$379$	20.8899	1.07304	0.536520	−	0.843888i	$-0.319739\pi$
$379$	20.8899	1.07304	0.536520	+	0.843888i	$0.319739\pi$
$380$	−89.6455	−4.59872
$381$	−36.8324	−1.88698
$382$	10.3198	0.528005
$383$	25.6189	1.30906	0.654531	−	0.756035i	$-0.272866\pi$
$383$	25.6189	1.30906	0.654531	+	0.756035i	$0.272866\pi$
$384$	−124.625	−6.35974
$385$	−11.0177	−0.561515
$386$	17.5213	0.891812
$387$	19.8748	1.01029
$388$	39.8855	2.02488
$389$	12.0513	0.611025	0.305513	−	0.952188i	$-0.401172\pi$
$389$	12.0513	0.611025	0.305513	+	0.952188i	$0.401172\pi$
$390$	166.961	8.45437
$391$	−6.10640	−0.308814
$392$	−29.5319	−1.49159
$393$	−54.7822	−2.76339
$394$	30.2729	1.52513
$395$	−35.2039	−1.77130
$396$	−66.5621	−3.34487
$397$	7.01417	0.352031	0.176015	−	0.984387i	$-0.443679\pi$
$397$	7.01417	0.352031	0.176015	+	0.984387i	$0.443679\pi$
$398$	28.1406	1.41056
$399$	31.8513	1.59456
$400$	79.1352	3.95676
$401$	12.2067	0.609574	0.304787	−	0.952421i	$-0.401415\pi$
$401$	12.2067	0.609574	0.304787	+	0.952421i	$0.401415\pi$
$402$	106.140	5.29377
$403$	42.2266	2.10346
$404$	−8.24962	−0.410434
$405$	59.4561	2.95440
$406$	45.1750	2.24200
$407$	1.71055	0.0847888
$408$	−134.773	−6.67227
$409$	−29.6163	−1.46443	−0.732216	−	0.681073i	$-0.761514\pi$
$409$	−29.6163	−1.46443	−0.732216	+	0.681073i	$0.761514\pi$
$410$	5.26548	0.260044
$411$	11.1056	0.547797
$412$	−58.8822	−2.90092
$413$	11.7373	0.577553
$414$	−25.9653	−1.27612
$415$	7.04318	0.345736
$416$	−134.613	−6.59993
$417$	8.18886	0.401010
$418$	24.3637	1.19167
$419$	11.3503	0.554498	0.277249	−	0.960798i	$-0.410577\pi$
$419$	11.3503	0.554498	0.277249	+	0.960798i	$0.410577\pi$
$420$	−109.407	−5.33853
$421$	−26.2981	−1.28169	−0.640846	−	0.767670i	$-0.721416\pi$
$421$	−26.2981	−1.28169	−0.640846	+	0.767670i	$0.721416\pi$
$422$	−35.8692	−1.74609
$423$	58.1753	2.82858
$424$	−24.0681	−1.16885
$425$	23.4574	1.13785
$426$	−46.9415	−2.27433
$427$	−21.9567	−1.06256
$428$	−81.2415	−3.92695
$429$	−33.2509	−1.60537
$430$	24.9884	1.20505
$431$	−2.04096	−0.0983097	−0.0491548	−	0.998791i	$-0.515653\pi$
$431$	−2.04096	−0.0983097	−0.0491548	+	0.998791i	$0.515653\pi$
$432$	−188.962	−9.09144
$433$	19.5051	0.937353	0.468677	−	0.883370i	$-0.344731\pi$
$433$	19.5051	0.937353	0.468677	+	0.883370i	$0.344731\pi$
$434$	−37.7610	−1.81259
$435$	−84.4156	−4.04742
$436$	−17.3174	−0.829351
$437$	6.96441	0.333153
$438$	−85.3504	−4.07820
$439$	23.1807	1.10635	0.553176	−	0.833064i	$-0.313416\pi$
$439$	23.1807	1.10635	0.553176	+	0.833064i	$0.313416\pi$
$440$	−53.1702	−2.53479
$441$	−21.5673	−1.02701
$442$	−74.0563	−3.52250
$443$	−9.73470	−0.462510	−0.231255	−	0.972893i	$-0.574283\pi$
$443$	−9.73470	−0.462510	−0.231255	+	0.972893i	$0.574283\pi$
$444$	16.9860	0.806119
$445$	−19.9204	−0.944319
$446$	35.5910	1.68528
$447$	5.39240	0.255052
$448$	60.6771	2.86672
$449$	40.2616	1.90006	0.950032	−	0.312152i	$-0.101050\pi$
$449$	40.2616	1.90006	0.950032	+	0.312152i	$0.101050\pi$
$450$	99.7444	4.70200
$451$	−1.04864	−0.0493787
$452$	−12.7889	−0.601539
$453$	7.21184	0.338842
$454$	−42.7576	−2.00671
$455$	−38.1953	−1.79062
$456$	153.710	7.19815
$457$	26.5334	1.24118	0.620591	−	0.784135i	$-0.286893\pi$
$457$	26.5334	1.24118	0.620591	+	0.784135i	$0.286893\pi$
$458$	−50.8946	−2.37815
$459$	−56.0126	−2.61444
$460$	−23.9224	−1.11539
$461$	10.6186	0.494556	0.247278	−	0.968945i	$-0.420464\pi$
$461$	10.6186	0.494556	0.247278	+	0.968945i	$0.420464\pi$
$462$	29.7345	1.38338
$463$	7.46465	0.346912	0.173456	−	0.984842i	$-0.444507\pi$
$463$	7.46465	0.346912	0.173456	+	0.984842i	$0.444507\pi$
$464$	126.316	5.86409
$465$	70.5615	3.27221
$466$	77.3514	3.58323
$467$	7.11760	0.329363	0.164682	−	0.986347i	$-0.447340\pi$
$467$	7.11760	0.329363	0.164682	+	0.986347i	$0.447340\pi$
$468$	−230.752	−10.6665
$469$	−24.2814	−1.12121
$470$	73.1434	3.37385
$471$	65.0237	2.99614
$472$	56.6427	2.60719
$473$	−4.97655	−0.228822
$474$	95.0080	4.36386
$475$	−26.7535	−1.22753
$476$	48.5283	2.22429
$477$	−17.5771	−0.804798
$478$	−80.2965	−3.67268
$479$	12.7798	0.583926	0.291963	−	0.956430i	$-0.405692\pi$
$479$	12.7798	0.583926	0.291963	+	0.956430i	$0.405692\pi$
$480$	−224.941	−10.2671
$481$	5.92999	0.270384
$482$	52.6717	2.39913
$483$	8.49968	0.386749
$484$	−43.6630	−1.98468
$485$	23.2680	1.05655
$486$	−57.8276	−2.62311
$487$	−35.8295	−1.62359	−0.811796	−	0.583941i	$-0.801510\pi$
$487$	−35.8295	−1.62359	−0.811796	+	0.583941i	$0.801510\pi$
$488$	−105.961	−4.79661
$489$	−58.7058	−2.65477
$490$	−27.1164	−1.22499
$491$	−3.86452	−0.174403	−0.0872016	−	0.996191i	$-0.527792\pi$
$491$	−3.86452	−0.174403	−0.0872016	+	0.996191i	$0.527792\pi$
$492$	−10.4132	−0.469462
$493$	37.4430	1.68635
$494$	84.4620	3.80013
$495$	−38.8304	−1.74530
$496$	−105.586	−4.74094
$497$	10.7387	0.481698
$498$	−19.0081	−0.851773
$499$	14.1035	0.631359	0.315680	−	0.948866i	$-0.397767\pi$
$499$	14.1035	0.631359	0.315680	+	0.948866i	$0.397767\pi$
$500$	4.15738	0.185924
$501$	35.5836	1.58976
$502$	45.6424	2.03712
$503$	23.1174	1.03075	0.515377	−	0.856964i	$-0.327652\pi$
$503$	23.1174	1.03075	0.515377	+	0.856964i	$0.327652\pi$
$504$	131.101	5.83972
$505$	−4.81259	−0.214158
$506$	6.50158	0.289031
$507$	−74.2401	−3.29712
$508$	64.0025	2.83965
$509$	40.9665	1.81581	0.907904	−	0.419177i	$-0.137681\pi$
$509$	40.9665	1.81581	0.907904	+	0.419177i	$0.137681\pi$
$510$	−123.750	−5.47973
$511$	19.5255	0.863756
$512$	48.4882	2.14290
$513$	63.8829	2.82050
$514$	59.3876	2.61947
$515$	−34.3502	−1.51365
$516$	−49.4178	−2.17550
$517$	−14.5668	−0.640648
$518$	−5.30288	−0.232995
$519$	−24.7204	−1.08510
$520$	−184.326	−8.08322
$521$	14.6827	0.643261	0.321631	−	0.946865i	$-0.395769\pi$
$521$	14.6827	0.643261	0.321631	+	0.946865i	$0.395769\pi$
$522$	159.213	6.96857
$523$	−23.8931	−1.04477	−0.522385	−	0.852710i	$-0.674958\pi$
$523$	−23.8931	−1.04477	−0.522385	+	0.852710i	$0.674958\pi$
$524$	95.1933	4.15854
$525$	−32.6511	−1.42501
$526$	7.28409	0.317602
$527$	−31.2980	−1.36336
$528$	83.1424	3.61831
$529$	−21.1415	−0.919196
$530$	−22.0995	−0.959941
$531$	41.3664	1.79515
$532$	−55.3470	−2.39960
$533$	−3.63535	−0.157464
$534$	53.7611	2.32647
$535$	−47.3939	−2.04902
$536$	−117.179	−5.06137
$537$	−4.67667	−0.201813
$538$	30.4730	1.31379
$539$	5.40034	0.232609
$540$	−219.434	−9.44295
$541$	22.9082	0.984901	0.492450	−	0.870340i	$-0.336101\pi$
$541$	22.9082	0.984901	0.492450	+	0.870340i	$0.336101\pi$
$542$	−16.5059	−0.708990
$543$	61.6637	2.64624
$544$	99.7737	4.27776
$545$	−10.1025	−0.432742
$546$	103.081	4.41147
$547$	−7.07732	−0.302604	−0.151302	−	0.988488i	$-0.548347\pi$
$547$	−7.07732	−0.302604	−0.151302	+	0.988488i	$0.548347\pi$
$548$	−19.2978	−0.824361
$549$	−77.3835	−3.30265
$550$	−24.9755	−1.06496
$551$	−42.7042	−1.81926
$552$	41.0184	1.74586
$553$	−21.7348	−0.924259
$554$	50.9190	2.16334
$555$	9.90914	0.420620
$556$	−14.2295	−0.603467
$557$	−5.68615	−0.240930	−0.120465	−	0.992718i	$-0.538439\pi$
$557$	−5.68615	−0.240930	−0.120465	+	0.992718i	$0.538439\pi$
$558$	−133.083	−5.63387
$559$	−17.2523	−0.729694
$560$	95.5056	4.03585
$561$	24.6453	1.04052
$562$	−19.4832	−0.821850
$563$	9.41048	0.396604	0.198302	−	0.980141i	$-0.436457\pi$
$563$	9.41048	0.396604	0.198302	+	0.980141i	$0.436457\pi$
$564$	−144.650	−6.09088
$565$	−7.46067	−0.313873
$566$	−8.95338	−0.376339
$567$	36.7081	1.54160
$568$	51.8239	2.17448
$569$	−14.0015	−0.586973	−0.293486	−	0.955963i	$-0.594816\pi$
$569$	−14.0015	−0.586973	−0.293486	+	0.955963i	$0.594816\pi$
$570$	141.138	5.91161
$571$	−8.66028	−0.362422	−0.181211	−	0.983444i	$-0.558002\pi$
$571$	−8.66028	−0.362422	−0.181211	+	0.983444i	$0.558002\pi$
$572$	57.7791	2.41587
$573$	−11.9058	−0.497373
$574$	3.25090	0.135690
$575$	−7.13930	−0.297729
$576$	213.848	8.91034
$577$	−23.8354	−0.992279	−0.496139	−	0.868243i	$-0.665250\pi$
$577$	−23.8354	−0.992279	−0.496139	+	0.868243i	$0.665250\pi$
$578$	8.38148	0.348623
$579$	−20.2142	−0.840073
$580$	146.686	6.09082
$581$	4.34845	0.180404
$582$	−62.7956	−2.60296
$583$	4.40121	0.182280
$584$	94.2276	3.89916
$585$	−134.614	−5.56560
$586$	−66.3474	−2.74079
$587$	0.447487	0.0184698	0.00923488	−	0.999957i	$-0.497060\pi$
$587$	0.447487	0.0184698	0.00923488	+	0.999957i	$0.497060\pi$
$588$	53.6261	2.21150
$589$	35.6957	1.47081
$590$	52.0096	2.14120
$591$	−34.9256	−1.43665
$592$	−14.8277	−0.609414
$593$	0.117855	0.00483973	0.00241986	−	0.999997i	$-0.499230\pi$
$593$	0.117855	0.00483973	0.00241986	+	0.999997i	$0.499230\pi$
$594$	59.6375	2.44696
$595$	28.3100	1.16060
$596$	−9.37021	−0.383819
$597$	−32.4655	−1.32873
$598$	22.5391	0.921694
$599$	−34.1299	−1.39451	−0.697256	−	0.716823i	$-0.745596\pi$
$599$	−34.1299	−1.39451	−0.697256	+	0.716823i	$0.745596\pi$
$600$	−157.570	−6.43278
$601$	0.393978	0.0160707	0.00803535	−	0.999968i	$-0.497442\pi$
$601$	0.393978	0.0160707	0.00803535	+	0.999968i	$0.497442\pi$
$602$	15.4278	0.628791
$603$	−85.5765	−3.48495
$604$	−12.5318	−0.509912
$605$	−25.4718	−1.03557
$606$	12.9882	0.527609
$607$	11.7543	0.477093	0.238546	−	0.971131i	$-0.423329\pi$
$607$	11.7543	0.477093	0.238546	+	0.971131i	$0.423329\pi$
$608$	−113.793	−4.61492
$609$	−52.1180	−2.11193
$610$	−97.2937	−3.93931
$611$	−50.4990	−2.04297
$612$	171.031	6.91352
$613$	−20.0979	−0.811747	−0.405873	−	0.913929i	$-0.633033\pi$
$613$	−20.0979	−0.811747	−0.405873	+	0.913929i	$0.633033\pi$
$614$	63.8153	2.57538
$615$	−6.07474	−0.244957
$616$	−32.8272	−1.32264
$617$	−34.9091	−1.40539	−0.702695	−	0.711492i	$-0.748020\pi$
$617$	−34.9091	−1.40539	−0.702695	+	0.711492i	$0.748020\pi$
$618$	92.7040	3.72910
$619$	25.1577	1.01117	0.505586	−	0.862776i	$-0.331276\pi$
$619$	25.1577	1.01117	0.505586	+	0.862776i	$0.331276\pi$
$620$	−122.613	−4.92424
$621$	17.0475	0.684093
$622$	−50.6053	−2.02909
$623$	−12.2988	−0.492743
$624$	288.231	11.5385
$625$	−23.7593	−0.950371
$626$	−56.9357	−2.27561
$627$	−28.1082	−1.12253
$628$	−112.990	−4.50879
$629$	−4.39526	−0.175250
$630$	120.378	4.79598
$631$	−9.85062	−0.392147	−0.196073	−	0.980589i	$-0.562819\pi$
$631$	−9.85062	−0.392147	−0.196073	+	0.980589i	$0.562819\pi$
$632$	−104.890	−4.17229
$633$	41.3820	1.64479
$634$	86.1212	3.42031
$635$	37.3372	1.48168
$636$	43.7046	1.73300
$637$	18.7215	0.741771
$638$	−39.8662	−1.57832
$639$	37.8472	1.49721
$640$	126.333	4.99376
$641$	−17.0042	−0.671626	−0.335813	−	0.941929i	$-0.609011\pi$
$641$	−17.0042	−0.671626	−0.335813	+	0.941929i	$0.609011\pi$
$642$	127.906	5.04807
$643$	48.9420	1.93008	0.965042	−	0.262093i	$-0.0844129\pi$
$643$	48.9420	1.93008	0.965042	+	0.262093i	$0.0844129\pi$
$644$	−14.7696	−0.582005
$645$	−28.8289	−1.13514
$646$	−62.6025	−2.46306
$647$	23.6765	0.930818	0.465409	−	0.885096i	$-0.345907\pi$
$647$	23.6765	0.930818	0.465409	+	0.885096i	$0.345907\pi$
$648$	177.149	6.95907
$649$	−10.3579	−0.406585
$650$	−86.5830	−3.39607
$651$	43.5646	1.70743
$652$	102.011	3.99507
$653$	33.7683	1.32145	0.660727	−	0.750626i	$-0.270248\pi$
$653$	33.7683	1.32145	0.660727	+	0.750626i	$0.270248\pi$
$654$	27.2644	1.06612
$655$	55.5331	2.16986
$656$	9.09002	0.354906
$657$	68.8148	2.68472
$658$	45.1586	1.76047
$659$	1.94141	0.0756265	0.0378133	−	0.999285i	$-0.487961\pi$
$659$	1.94141	0.0756265	0.0378133	+	0.999285i	$0.487961\pi$
$660$	96.5501	3.75821
$661$	−19.1516	−0.744912	−0.372456	−	0.928050i	$-0.621484\pi$
$661$	−19.1516	−0.744912	−0.372456	+	0.928050i	$0.621484\pi$
$662$	−28.9654	−1.12577
$663$	85.4381	3.31814
$664$	20.9851	0.814379
$665$	−32.2879	−1.25207
$666$	−18.6893	−0.724194
$667$	−11.3958	−0.441248
$668$	−61.8326	−2.39237
$669$	−41.0610	−1.58751
$670$	−107.595	−4.15675
$671$	19.3765	0.748020
$672$	−138.878	−5.35734
$673$	5.03795	0.194199	0.0970993	−	0.995275i	$-0.469044\pi$
$673$	5.03795	0.194199	0.0970993	+	0.995275i	$0.469044\pi$
$674$	77.3775	2.98047
$675$	−65.4872	−2.52060
$676$	129.005	4.96173
$677$	−23.3646	−0.897974	−0.448987	−	0.893538i	$-0.648215\pi$
$677$	−23.3646	−0.897974	−0.448987	+	0.893538i	$0.648215\pi$
$678$	20.1348	0.773273
$679$	14.3656	0.551303
$680$	136.621	5.23916
$681$	49.3291	1.89030
$682$	33.3235	1.27602
$683$	42.0690	1.60973	0.804864	−	0.593460i	$-0.202238\pi$
$683$	42.0690	1.60973	0.804864	+	0.593460i	$0.202238\pi$
$684$	−195.063	−7.45841
$685$	−11.2578	−0.430138
$686$	−54.5711	−2.08353
$687$	58.7167	2.24018
$688$	43.1386	1.64464
$689$	15.2577	0.581274
$690$	37.6634	1.43382
$691$	−15.7916	−0.600740	−0.300370	−	0.953823i	$-0.597110\pi$
$691$	−15.7916	−0.600740	−0.300370	+	0.953823i	$0.597110\pi$
$692$	42.9559	1.63294
$693$	−23.9738	−0.910691
$694$	−21.2324	−0.805970
$695$	−8.30111	−0.314879
$696$	−251.515	−9.53367
$697$	2.69449	0.102061
$698$	−31.5089	−1.19263
$699$	−89.2396	−3.37535
$700$	56.7369	2.14445
$701$	12.5326	0.473352	0.236676	−	0.971589i	$-0.423942\pi$
$701$	12.5326	0.473352	0.236676	+	0.971589i	$0.423942\pi$
$702$	206.746	7.80314
$703$	5.01284	0.189063
$704$	−53.5465	−2.01811
$705$	−84.3849	−3.17812
$706$	2.57929	0.0970728
$707$	−2.97129	−0.111747
$708$	−102.856	−3.86556
$709$	1.63159	0.0612756	0.0306378	−	0.999531i	$-0.490246\pi$
$709$	1.63159	0.0612756	0.0306378	+	0.999531i	$0.490246\pi$
$710$	47.5850	1.78583
$711$	−76.6014	−2.87278
$712$	−59.3527	−2.22434
$713$	9.52558	0.356736
$714$	−76.4028	−2.85930
$715$	33.7067	1.26056
$716$	8.12651	0.303702
$717$	92.6374	3.45961
$718$	−15.6703	−0.584812
$719$	21.8909	0.816392	0.408196	−	0.912894i	$-0.366158\pi$
$719$	21.8909	0.816392	0.408196	+	0.912894i	$0.366158\pi$
$720$	336.596	12.5442
$721$	−21.2077	−0.789818
$722$	19.4189	0.722695
$723$	−60.7669	−2.25995
$724$	−107.151	−3.98224
$725$	43.7766	1.62582
$726$	68.7430	2.55129
$727$	45.1107	1.67306	0.836532	−	0.547917i	$-0.184579\pi$
$727$	45.1107	1.67306	0.836532	+	0.547917i	$0.184579\pi$
$728$	−113.802	−4.21780
$729$	10.9667	0.406174
$730$	86.5203	3.20226
$731$	12.7872	0.472953
$732$	192.411	7.11171
$733$	7.76315	0.286738	0.143369	−	0.989669i	$-0.454206\pi$
$733$	7.76315	0.286738	0.143369	+	0.989669i	$0.454206\pi$
$734$	−7.88836	−0.291165
$735$	31.2839	1.15393
$736$	−30.3663	−1.11932
$737$	21.4280	0.789309
$738$	11.4573	0.421751
$739$	42.3497	1.55786	0.778929	−	0.627112i	$-0.215763\pi$
$739$	42.3497	1.55786	0.778929	+	0.627112i	$0.215763\pi$
$740$	−17.2188	−0.632976
$741$	−97.4431	−3.57966
$742$	−13.6442	−0.500894
$743$	21.0862	0.773579	0.386790	−	0.922168i	$-0.373584\pi$
$743$	21.0862	0.773579	0.386790	+	0.922168i	$0.373584\pi$
$744$	210.237	7.70768
$745$	−5.46631	−0.200270
$746$	−33.3909	−1.22253
$747$	15.3255	0.560731
$748$	−42.8254	−1.56585
$749$	−29.2609	−1.06917
$750$	−6.54538	−0.239003
$751$	−10.0364	−0.366235	−0.183118	−	0.983091i	$-0.558619\pi$
$751$	−10.0364	−0.366235	−0.183118	+	0.983091i	$0.558619\pi$
$752$	126.271	4.60461
$753$	−52.6573	−1.91894
$754$	−138.205	−5.03312
$755$	−7.31069	−0.266063
$756$	−135.478	−4.92730
$757$	17.4490	0.634193	0.317097	−	0.948393i	$-0.397292\pi$
$757$	17.4490	0.634193	0.317097	+	0.948393i	$0.397292\pi$
$758$	57.1502	2.07579
$759$	−7.50082	−0.272263
$760$	−155.817	−5.65209
$761$	−26.2549	−0.951738	−0.475869	−	0.879516i	$-0.657866\pi$
$761$	−26.2549	−0.951738	−0.475869	+	0.879516i	$0.657866\pi$
$762$	−100.766	−3.65035
$763$	−6.23724	−0.225803
$764$	20.6884	0.748481
$765$	99.7746	3.60736
$766$	70.0877	2.53237
$767$	−35.9080	−1.29656
$768$	−147.048	−5.30612
$769$	−42.5100	−1.53295	−0.766474	−	0.642275i	$-0.777991\pi$
$769$	−42.5100	−1.53295	−0.766474	+	0.642275i	$0.777991\pi$
$770$	−30.1421	−1.08625
$771$	−68.5149	−2.46750
$772$	35.1256	1.26420
$773$	13.9431	0.501498	0.250749	−	0.968052i	$-0.419323\pi$
$773$	13.9431	0.501498	0.250749	+	0.968052i	$0.419323\pi$
$774$	54.3732	1.95440
$775$	−36.5921	−1.31443
$776$	69.3269	2.48869
$777$	6.11789	0.219478
$778$	32.9698	1.18202
$779$	−3.07309	−0.110105
$780$	334.712	11.9846
$781$	−9.47675	−0.339105
$782$	−16.7058	−0.597398
$783$	−104.531	−3.73564
$784$	−46.8122	−1.67186
$785$	−65.9150	−2.35261
$786$	−149.872	−5.34577
$787$	−5.11775	−0.182428	−0.0912140	−	0.995831i	$-0.529075\pi$
$787$	−5.11775	−0.182428	−0.0912140	+	0.995831i	$0.529075\pi$
$788$	60.6892	2.16196
$789$	−8.40360	−0.299176
$790$	−96.3103	−3.42657
$791$	−4.60621	−0.163778
$792$	−115.695	−4.11104
$793$	67.1727	2.38537
$794$	19.1893	0.681002
$795$	25.4960	0.904250
$796$	56.4144	1.99955
$797$	0.631455	0.0223673	0.0111836	−	0.999937i	$-0.496440\pi$
$797$	0.631455	0.0223673	0.0111836	+	0.999937i	$0.496440\pi$
$798$	87.1383	3.08466
$799$	37.4294	1.32416
$800$	116.651	4.12422
$801$	−43.3456	−1.53154
$802$	33.3950	1.17922
$803$	−17.2309	−0.608065
$804$	212.782	7.50426
$805$	−8.61618	−0.303681
$806$	115.523	4.06912
$807$	−35.1565	−1.23757
$808$	−14.3391	−0.504447
$809$	−21.6963	−0.762800	−0.381400	−	0.924410i	$-0.624558\pi$
$809$	−21.6963	−0.762800	−0.381400	+	0.924410i	$0.624558\pi$
$810$	162.659	5.71527
$811$	10.4185	0.365843	0.182922	−	0.983127i	$-0.441445\pi$
$811$	10.4185	0.365843	0.182922	+	0.983127i	$0.441445\pi$
$812$	90.5640	3.17817
$813$	19.0427	0.667858
$814$	4.67970	0.164023
$815$	59.5105	2.08456
$816$	−213.634	−7.47869
$817$	−14.5840	−0.510229
$818$	−81.0239	−2.83293
$819$	−83.1105	−2.90411
$820$	10.5559	0.368628
$821$	−47.5196	−1.65844	−0.829222	−	0.558919i	$-0.811216\pi$
$821$	−47.5196	−1.65844	−0.829222	+	0.558919i	$0.811216\pi$
$822$	30.3824	1.05971
$823$	−8.88490	−0.309708	−0.154854	−	0.987937i	$-0.549491\pi$
$823$	−8.88490	−0.309708	−0.154854	+	0.987937i	$0.549491\pi$
$824$	−102.346	−3.56539
$825$	28.8141	1.00318
$826$	32.1107	1.11727
$827$	1.55110	0.0539369	0.0269684	−	0.999636i	$-0.491415\pi$
$827$	1.55110	0.0539369	0.0269684	+	0.999636i	$0.491415\pi$
$828$	−52.0535	−1.80899
$829$	50.9145	1.76834	0.884168	−	0.467170i	$-0.154726\pi$
$829$	50.9145	1.76834	0.884168	+	0.467170i	$0.154726\pi$
$830$	19.2686	0.668824
$831$	−58.7449	−2.03784
$832$	−185.631	−6.43558
$833$	−13.8762	−0.480781
$834$	22.4030	0.775752
$835$	−36.0714	−1.24830
$836$	48.8428	1.68926
$837$	87.3759	3.02015
$838$	31.0520	1.07267
$839$	29.0101	1.00154	0.500771	−	0.865580i	$-0.333050\pi$
$839$	29.0101	1.00154	0.500771	+	0.865580i	$0.333050\pi$
$840$	−190.166	−6.56136
$841$	40.8766	1.40954
$842$	−71.9461	−2.47942
$843$	22.4776	0.774170
$844$	−71.9083	−2.47519
$845$	75.2578	2.58895
$846$	159.155	5.47187
$847$	−15.7262	−0.540359
$848$	−38.1513	−1.31012
$849$	10.3294	0.354505
$850$	64.1746	2.20117
$851$	1.33770	0.0458558
$852$	−94.1054	−3.22400
$853$	17.3095	0.592665	0.296333	−	0.955085i	$-0.404236\pi$
$853$	17.3095	0.592665	0.296333	+	0.955085i	$0.404236\pi$
$854$	−60.0690	−2.05552
$855$	−113.794	−3.89167
$856$	−141.210	−4.82645
$857$	−15.0528	−0.514194	−0.257097	−	0.966386i	$-0.582766\pi$
$857$	−15.0528	−0.514194	−0.257097	+	0.966386i	$0.582766\pi$
$858$	−90.9674	−3.10558
$859$	−16.5107	−0.563338	−0.281669	−	0.959512i	$-0.590888\pi$
$859$	−16.5107	−0.563338	−0.281669	+	0.959512i	$0.590888\pi$
$860$	50.0952	1.70823
$861$	−3.75054	−0.127818
$862$	−5.58364	−0.190179
$863$	15.5630	0.529771	0.264886	−	0.964280i	$-0.414666\pi$
$863$	15.5630	0.529771	0.264886	+	0.964280i	$0.414666\pi$
$864$	−278.543	−9.47622
$865$	25.0592	0.852039
$866$	53.3617	1.81330
$867$	−9.66964	−0.328398
$868$	−75.7009	−2.56946
$869$	19.1806	0.650658
$870$	−230.943	−7.82970
$871$	74.2846	2.51704
$872$	−30.1002	−1.01932
$873$	50.6297	1.71356
$874$	19.0532	0.644482
$875$	1.49737	0.0506205
$876$	−171.105	−5.78110
$877$	−14.3603	−0.484915	−0.242457	−	0.970162i	$-0.577953\pi$
$877$	−14.3603	−0.484915	−0.242457	+	0.970162i	$0.577953\pi$
$878$	63.4173	2.14023
$879$	76.5444	2.58178
$880$	−84.2821	−2.84115
$881$	26.1160	0.879871	0.439936	−	0.898029i	$-0.355001\pi$
$881$	26.1160	0.879871	0.439936	+	0.898029i	$0.355001\pi$
$882$	−59.0035	−1.98675
$883$	20.5881	0.692843	0.346422	−	0.938079i	$-0.387397\pi$
$883$	20.5881	0.692843	0.346422	+	0.938079i	$0.387397\pi$
$884$	−148.463	−4.99336
$885$	−60.0031	−2.01698
$886$	−26.6321	−0.894722
$887$	39.0889	1.31248	0.656239	−	0.754553i	$-0.272146\pi$
$887$	39.0889	1.31248	0.656239	+	0.754553i	$0.272146\pi$
$888$	29.5242	0.990767
$889$	23.0520	0.773138
$890$	−54.4980	−1.82678
$891$	−32.3943	−1.08525
$892$	71.3506	2.38899
$893$	−42.6887	−1.42852
$894$	14.7525	0.493396
$895$	4.74077	0.158467
$896$	77.9979	2.60573
$897$	−26.0032	−0.868222
$898$	110.147	3.67566
$899$	−58.4087	−1.94804
$900$	199.961	6.66537
$901$	−11.3089	−0.376754
$902$	−2.86886	−0.0955227
$903$	−17.7989	−0.592312
$904$	−22.2290	−0.739326
$905$	−62.5089	−2.07787
$906$	19.7301	0.655487
$907$	−40.2796	−1.33746	−0.668732	−	0.743504i	$-0.733163\pi$
$907$	−40.2796	−1.33746	−0.668732	+	0.743504i	$0.733163\pi$
$908$	−85.7177	−2.84464
$909$	−10.4719	−0.347331
$910$	−104.494	−3.46395
$911$	37.1143	1.22965	0.614827	−	0.788662i	$-0.289226\pi$
$911$	37.1143	1.22965	0.614827	+	0.788662i	$0.289226\pi$
$912$	243.652	8.06813
$913$	−3.83743	−0.127000
$914$	72.5898	2.40106
$915$	112.247	3.71077
$916$	−102.030	−3.37117
$917$	34.2860	1.13222
$918$	−153.238	−5.05762
$919$	−9.42904	−0.311035	−0.155518	−	0.987833i	$-0.549705\pi$
$919$	−9.42904	−0.311035	−0.155518	+	0.987833i	$0.549705\pi$
$920$	−41.5807	−1.37087
$921$	−73.6232	−2.42597
$922$	29.0502	0.956716
$923$	−32.8532	−1.08138
$924$	59.6099	1.96102
$925$	−5.13872	−0.168960
$926$	20.4217	0.671099
$927$	−74.7437	−2.45491
$928$	186.199	6.11228
$929$	7.34040	0.240831	0.120415	−	0.992724i	$-0.461577\pi$
$929$	7.34040	0.240831	0.120415	+	0.992724i	$0.461577\pi$
$930$	193.041	6.33007
$931$	15.8259	0.518674
$932$	155.069	5.07946
$933$	58.3829	1.91137
$934$	19.4722	0.637151
$935$	−24.9831	−0.817034
$936$	−401.081	−13.1097
$937$	20.6805	0.675602	0.337801	−	0.941217i	$-0.390317\pi$
$937$	20.6805	0.675602	0.337801	+	0.941217i	$0.390317\pi$
$938$	−66.4288	−2.16898
$939$	65.6863	2.14359
$940$	146.633	4.78265
$941$	−24.7382	−0.806443	−0.403221	−	0.915102i	$-0.632110\pi$
$941$	−24.7382	−0.806443	−0.403221	+	0.915102i	$0.632110\pi$
$942$	177.891	5.79601
$943$	−0.820071	−0.0267052
$944$	89.7865	2.92230
$945$	−79.0342	−2.57098
$946$	−13.6148	−0.442655
$947$	18.9216	0.614870	0.307435	−	0.951569i	$-0.400529\pi$
$947$	18.9216	0.614870	0.307435	+	0.951569i	$0.400529\pi$
$948$	190.466	6.18605
$949$	−59.7346	−1.93907
$950$	−73.1918	−2.37466
$951$	−99.3574	−3.22188
$952$	84.3494	2.73378
$953$	−19.3449	−0.626644	−0.313322	−	0.949647i	$-0.601442\pi$
$953$	−19.3449	−0.626644	−0.313322	+	0.949647i	$0.601442\pi$
$954$	−48.0871	−1.55688
$955$	12.0690	0.390545
$956$	−160.973	−5.20625
$957$	45.9933	1.48675
$958$	34.9629	1.12960
$959$	−6.95054	−0.224445
$960$	−310.193	−10.0114
$961$	17.8228	0.574929
$962$	16.2232	0.523057
$963$	−103.126	−3.32319
$964$	105.593	3.40092
$965$	20.4913	0.659638
$966$	23.2533	0.748163
$967$	56.6446	1.82157	0.910783	−	0.412885i	$-0.135479\pi$
$967$	56.6446	1.82157	0.910783	+	0.412885i	$0.135479\pi$
$968$	−75.8929	−2.43929
$969$	72.2240	2.32017
$970$	63.6564	2.04388
$971$	−19.9813	−0.641229	−0.320615	−	0.947210i	$-0.603889\pi$
$971$	−19.9813	−0.641229	−0.320615	+	0.947210i	$0.603889\pi$
$972$	−115.929	−3.71843
$973$	−5.12509	−0.164303
$974$	−98.0220	−3.14083
$975$	99.8901	3.19904
$976$	−167.962	−5.37634
$977$	21.9272	0.701512	0.350756	−	0.936467i	$-0.385925\pi$
$977$	21.9272	0.701512	0.350756	+	0.936467i	$0.385925\pi$
$978$	−160.607	−5.13563
$979$	10.8535	0.346880
$980$	−54.3612	−1.73650
$981$	−21.9823	−0.701840
$982$	−10.5725	−0.337382
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	−18.0996	−0.576995
$985$	35.4043	1.12808
$986$	102.436	3.26223
$987$	−52.0991	−1.65833
$988$	169.324	5.38692
$989$	−3.89181	−0.123752
$990$	−106.232	−3.37627
$991$	20.7985	0.660686	0.330343	−	0.943861i	$-0.392836\pi$
$991$	20.7985	0.660686	0.330343	+	0.943861i	$0.392836\pi$
$992$	−155.640	−4.94159
$993$	33.4171	1.06046
$994$	29.3789	0.931842
$995$	32.9105	1.04333
$996$	−38.1062	−1.20744
$997$	58.8900	1.86506	0.932532	−	0.361087i	$-0.117594\pi$
$997$	58.8900	1.86506	0.932532	+	0.361087i	$0.117594\pi$
$998$	38.5842	1.22136
$999$	12.2704	0.388219

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.52	✓	54	1.1	even	1	trivial
8847.2.a.g.1.3		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)

\(f(q)\)	\(=\)	\(q+2.73579 q^{2} -3.15625 q^{3} +5.48453 q^{4} +3.19952 q^{5} -8.63484 q^{6} +1.97538 q^{7} +9.53294 q^{8} +6.96195 q^{9} +O(q^{10})\)	\(q+2.73579 q^{2} -3.15625 q^{3} +5.48453 q^{4} +3.19952 q^{5} -8.63484 q^{6} +1.97538 q^{7} +9.53294 q^{8} +6.96195 q^{9} +8.75320 q^{10} -1.74324 q^{11} -17.3106 q^{12} -6.04331 q^{13} +5.40421 q^{14} -10.0985 q^{15} +15.1110 q^{16} +4.47925 q^{17} +19.0464 q^{18} -5.10863 q^{19} +17.5479 q^{20} -6.23480 q^{21} -4.76913 q^{22} -1.36326 q^{23} -30.0884 q^{24} +5.23692 q^{25} -16.5332 q^{26} -12.5049 q^{27} +10.8340 q^{28} +8.35922 q^{29} -27.6273 q^{30} -6.98733 q^{31} +22.2747 q^{32} +5.50210 q^{33} +12.2543 q^{34} +6.32026 q^{35} +38.1830 q^{36} -0.981249 q^{37} -13.9761 q^{38} +19.0742 q^{39} +30.5008 q^{40} +0.601549 q^{41} -17.0571 q^{42} +2.85478 q^{43} -9.56084 q^{44} +22.2749 q^{45} -3.72960 q^{46} +8.35619 q^{47} -47.6942 q^{48} -3.09788 q^{49} +14.3271 q^{50} -14.1376 q^{51} -33.1447 q^{52} -2.52473 q^{53} -34.2108 q^{54} -5.57752 q^{55} +18.8312 q^{56} +16.1241 q^{57} +22.8691 q^{58} +5.94179 q^{59} -55.3855 q^{60} -11.1152 q^{61} -19.1158 q^{62} +13.7525 q^{63} +30.7167 q^{64} -19.3357 q^{65} +15.0526 q^{66} -12.2920 q^{67} +24.5666 q^{68} +4.30281 q^{69} +17.2909 q^{70} +5.43629 q^{71} +66.3678 q^{72} +9.88442 q^{73} -2.68449 q^{74} -16.5290 q^{75} -28.0184 q^{76} -3.44355 q^{77} +52.1830 q^{78} -11.0029 q^{79} +48.3480 q^{80} +18.5828 q^{81} +1.64571 q^{82} +2.20132 q^{83} -34.1949 q^{84} +14.3314 q^{85} +7.81006 q^{86} -26.3838 q^{87} -16.6182 q^{88} -6.22607 q^{89} +60.9393 q^{90} -11.9378 q^{91} -7.47687 q^{92} +22.0538 q^{93} +22.8608 q^{94} -16.3452 q^{95} -70.3045 q^{96} +7.27235 q^{97} -8.47515 q^{98} -12.1363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 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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