LMFDB - Embedded newform 1339.2.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35134 q^{2} +1.07411 q^{3} +3.52878 q^{4} +3.29713 q^{5} -2.52560 q^{6} +3.84969 q^{7} -3.59467 q^{8} -1.84628 q^{9} +O(q^{10})$	\(q-2.35134 q^{2} +1.07411 q^{3} +3.52878 q^{4} +3.29713 q^{5} -2.52560 q^{6} +3.84969 q^{7} -3.59467 q^{8} -1.84628 q^{9} -7.75266 q^{10} -3.17489 q^{11} +3.79031 q^{12} +1.00000 q^{13} -9.05191 q^{14} +3.54149 q^{15} +1.39472 q^{16} +0.572034 q^{17} +4.34122 q^{18} -6.09326 q^{19} +11.6348 q^{20} +4.13500 q^{21} +7.46524 q^{22} +8.94736 q^{23} -3.86108 q^{24} +5.87106 q^{25} -2.35134 q^{26} -5.20546 q^{27} +13.5847 q^{28} +7.43606 q^{29} -8.32724 q^{30} -2.51047 q^{31} +3.90989 q^{32} -3.41019 q^{33} -1.34504 q^{34} +12.6929 q^{35} -6.51511 q^{36} +6.12858 q^{37} +14.3273 q^{38} +1.07411 q^{39} -11.8521 q^{40} +6.84247 q^{41} -9.72278 q^{42} -3.57444 q^{43} -11.2035 q^{44} -6.08742 q^{45} -21.0383 q^{46} +8.72782 q^{47} +1.49809 q^{48} +7.82010 q^{49} -13.8048 q^{50} +0.614429 q^{51} +3.52878 q^{52} +6.83570 q^{53} +12.2398 q^{54} -10.4680 q^{55} -13.8384 q^{56} -6.54485 q^{57} -17.4847 q^{58} -9.41964 q^{59} +12.4971 q^{60} -10.9831 q^{61} +5.90295 q^{62} -7.10760 q^{63} -11.9829 q^{64} +3.29713 q^{65} +8.01851 q^{66} +13.1766 q^{67} +2.01858 q^{68} +9.61049 q^{69} -29.8453 q^{70} +1.60879 q^{71} +6.63677 q^{72} +7.15707 q^{73} -14.4103 q^{74} +6.30619 q^{75} -21.5018 q^{76} -12.2223 q^{77} -2.52560 q^{78} -4.65959 q^{79} +4.59857 q^{80} -0.0524101 q^{81} -16.0889 q^{82} +2.45307 q^{83} +14.5915 q^{84} +1.88607 q^{85} +8.40470 q^{86} +7.98717 q^{87} +11.4127 q^{88} +0.362958 q^{89} +14.3136 q^{90} +3.84969 q^{91} +31.5733 q^{92} -2.69653 q^{93} -20.5220 q^{94} -20.0903 q^{95} +4.19966 q^{96} -2.74078 q^{97} -18.3877 q^{98} +5.86174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9}+O(q^{10}) $ 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9} + 5 q^{10} + 9 q^{11} + 15 q^{12} + 28 q^{13} + 20 q^{14} + 4 q^{15} + 32 q^{16} - 7 q^{17} + 10 q^{18} - 3 q^{19} + 53 q^{20} + 25 q^{21} - 14 q^{22} - 6 q^{23} + 10 q^{24} + 45 q^{25} + 6 q^{26} + 8 q^{27} - 12 q^{28} + 25 q^{29} - 43 q^{30} + q^{31} + 28 q^{32} + 17 q^{33} + 10 q^{34} + 11 q^{35} + 27 q^{36} + 18 q^{37} + 2 q^{38} + 5 q^{39} + 37 q^{40} + 56 q^{41} - 29 q^{42} - 30 q^{43} + 30 q^{44} + 38 q^{45} - 27 q^{46} + 40 q^{47} + 19 q^{48} + 36 q^{49} + 20 q^{50} - 18 q^{51} + 32 q^{52} + 51 q^{53} - 36 q^{54} - 5 q^{55} - 13 q^{56} + 31 q^{57} - 29 q^{58} + 29 q^{59} + 48 q^{60} + 16 q^{61} - 38 q^{62} - 23 q^{63} - 5 q^{64} + 27 q^{65} + 25 q^{66} - 2 q^{67} - 43 q^{68} + 38 q^{69} + 10 q^{70} + 34 q^{71} - 28 q^{72} + 14 q^{73} + 21 q^{74} + 19 q^{75} + 5 q^{76} + 34 q^{77} + 9 q^{78} + 3 q^{79} + 58 q^{80} + 4 q^{81} - 9 q^{82} + 38 q^{83} - 78 q^{84} - 27 q^{85} + 49 q^{86} + 8 q^{87} - 25 q^{88} + 125 q^{89} - 74 q^{90} + 6 q^{91} - 35 q^{92} + 36 q^{93} - q^{94} - 12 q^{95} + 26 q^{96} - 2 q^{97} + 18 q^{98} + 56 q^{99}+O(q^{100}) \) 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9 + 5 * q^10 + 9 * q^11 + 15 * q^12 + 28 * q^13 + 20 * q^14 + 4 * q^15 + 32 * q^16 - 7 * q^17 + 10 * q^18 - 3 * q^19 + 53 * q^20 + 25 * q^21 - 14 * q^22 - 6 * q^23 + 10 * q^24 + 45 * q^25 + 6 * q^26 + 8 * q^27 - 12 * q^28 + 25 * q^29 - 43 * q^30 + q^31 + 28 * q^32 + 17 * q^33 + 10 * q^34 + 11 * q^35 + 27 * q^36 + 18 * q^37 + 2 * q^38 + 5 * q^39 + 37 * q^40 + 56 * q^41 - 29 * q^42 - 30 * q^43 + 30 * q^44 + 38 * q^45 - 27 * q^46 + 40 * q^47 + 19 * q^48 + 36 * q^49 + 20 * q^50 - 18 * q^51 + 32 * q^52 + 51 * q^53 - 36 * q^54 - 5 * q^55 - 13 * q^56 + 31 * q^57 - 29 * q^58 + 29 * q^59 + 48 * q^60 + 16 * q^61 - 38 * q^62 - 23 * q^63 - 5 * q^64 + 27 * q^65 + 25 * q^66 - 2 * q^67 - 43 * q^68 + 38 * q^69 + 10 * q^70 + 34 * q^71 - 28 * q^72 + 14 * q^73 + 21 * q^74 + 19 * q^75 + 5 * q^76 + 34 * q^77 + 9 * q^78 + 3 * q^79 + 58 * q^80 + 4 * q^81 - 9 * q^82 + 38 * q^83 - 78 * q^84 - 27 * q^85 + 49 * q^86 + 8 * q^87 - 25 * q^88 + 125 * q^89 - 74 * q^90 + 6 * q^91 - 35 * q^92 + 36 * q^93 - q^94 - 12 * q^95 + 26 * q^96 - 2 * q^97 + 18 * q^98 + 56 * 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 $

$2$	−2.35134	−1.66265	−0.831323	−	0.555790i	$-0.812416\pi$
$2$	−2.35134	−1.66265	−0.831323	+	0.555790i	$0.812416\pi$
$3$	1.07411	0.620140	0.310070	−	0.950714i	$-0.399648\pi$
$3$	1.07411	0.620140	0.310070	+	0.950714i	$0.399648\pi$
$4$	3.52878	1.76439
$5$	3.29713	1.47452	0.737261	−	0.675608i	$-0.236119\pi$
$5$	3.29713	1.47452	0.737261	+	0.675608i	$0.236119\pi$
$6$	−2.52560	−1.03107
$7$	3.84969	1.45505	0.727523	−	0.686084i	$-0.240672\pi$
$7$	3.84969	1.45505	0.727523	+	0.686084i	$0.240672\pi$
$8$	−3.59467	−1.27091
$9$	−1.84628	−0.615427
$10$	−7.75266	−2.45161
$11$	−3.17489	−0.957266	−0.478633	−	0.878015i	$-0.658868\pi$
$11$	−3.17489	−0.957266	−0.478633	+	0.878015i	$0.658868\pi$
$12$	3.79031	1.09417
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−9.05191	−2.41922
$15$	3.54149	0.914409
$16$	1.39472	0.348680
$17$	0.572034	0.138739	0.0693693	−	0.997591i	$-0.477901\pi$
$17$	0.572034	0.138739	0.0693693	+	0.997591i	$0.477901\pi$
$18$	4.34122	1.02324
$19$	−6.09326	−1.39789	−0.698945	−	0.715175i	$-0.746347\pi$
$19$	−6.09326	−1.39789	−0.698945	+	0.715175i	$0.746347\pi$
$20$	11.6348	2.60163
$21$	4.13500	0.902331
$22$	7.46524	1.59159
$23$	8.94736	1.86565	0.932827	−	0.360324i	$-0.117334\pi$
$23$	8.94736	1.86565	0.932827	+	0.360324i	$0.117334\pi$
$24$	−3.86108	−0.788140
$25$	5.87106	1.17421
$26$	−2.35134	−0.461135
$27$	−5.20546	−1.00179
$28$	13.5847	2.56727
$29$	7.43606	1.38084	0.690421	−	0.723408i	$-0.257425\pi$
$29$	7.43606	1.38084	0.690421	+	0.723408i	$0.257425\pi$
$30$	−8.32724	−1.52034
$31$	−2.51047	−0.450893	−0.225447	−	0.974256i	$-0.572384\pi$
$31$	−2.51047	−0.450893	−0.225447	+	0.974256i	$0.572384\pi$
$32$	3.90989	0.691177
$33$	−3.41019	−0.593639
$34$	−1.34504	−0.230673
$35$	12.6929	2.14550
$36$	−6.51511	−1.08585
$37$	6.12858	1.00753	0.503766	−	0.863840i	$-0.331947\pi$
$37$	6.12858	1.00753	0.503766	+	0.863840i	$0.331947\pi$
$38$	14.3273	2.32420
$39$	1.07411	0.171996
$40$	−11.8521	−1.87398
$41$	6.84247	1.06861	0.534307	−	0.845290i	$-0.320573\pi$
$41$	6.84247	1.06861	0.534307	+	0.845290i	$0.320573\pi$
$42$	−9.72278	−1.50026
$43$	−3.57444	−0.545097	−0.272548	−	0.962142i	$-0.587866\pi$
$43$	−3.57444	−0.545097	−0.272548	+	0.962142i	$0.587866\pi$
$44$	−11.2035	−1.68899
$45$	−6.08742	−0.907460
$46$	−21.0383	−3.10192
$47$	8.72782	1.27308	0.636541	−	0.771243i	$-0.280364\pi$
$47$	8.72782	1.27308	0.636541	+	0.771243i	$0.280364\pi$
$48$	1.49809	0.216230
$49$	7.82010	1.11716
$50$	−13.8048	−1.95230
$51$	0.614429	0.0860373
$52$	3.52878	0.489353
$53$	6.83570	0.938955	0.469478	−	0.882944i	$-0.344442\pi$
$53$	6.83570	0.938955	0.469478	+	0.882944i	$0.344442\pi$
$54$	12.2398	1.66562
$55$	−10.4680	−1.41151
$56$	−13.8384	−1.84923
$57$	−6.54485	−0.866887
$58$	−17.4847	−2.29585
$59$	−9.41964	−1.22633	−0.613166	−	0.789954i	$-0.710104\pi$
$59$	−9.41964	−1.22633	−0.613166	+	0.789954i	$0.710104\pi$
$60$	12.4971	1.61337
$61$	−10.9831	−1.40624	−0.703121	−	0.711071i	$-0.748211\pi$
$61$	−10.9831	−1.40624	−0.703121	+	0.711071i	$0.748211\pi$
$62$	5.90295	0.749676
$63$	−7.10760	−0.895474
$64$	−11.9829	−1.49786
$65$	3.29713	0.408959
$66$	8.01851	0.987011
$67$	13.1766	1.60977	0.804887	−	0.593429i	$-0.202226\pi$
$67$	13.1766	1.60977	0.804887	+	0.593429i	$0.202226\pi$
$68$	2.01858	0.244789
$69$	9.61049	1.15697
$70$	−29.8453	−3.56720
$71$	1.60879	0.190928	0.0954642	−	0.995433i	$-0.469566\pi$
$71$	1.60879	0.190928	0.0954642	+	0.995433i	$0.469566\pi$
$72$	6.63677	0.782151
$73$	7.15707	0.837672	0.418836	−	0.908062i	$-0.362438\pi$
$73$	7.15707	0.837672	0.418836	+	0.908062i	$0.362438\pi$
$74$	−14.4103	−1.67517
$75$	6.30619	0.728176
$76$	−21.5018	−2.46642
$77$	−12.2223	−1.39287
$78$	−2.52560	−0.285968
$79$	−4.65959	−0.524245	−0.262122	−	0.965035i	$-0.584422\pi$
$79$	−4.65959	−0.524245	−0.262122	+	0.965035i	$0.584422\pi$
$80$	4.59857	0.514136
$81$	−0.0524101	−0.00582335
$82$	−16.0889	−1.77673
$83$	2.45307	0.269259	0.134630	−	0.990896i	$-0.457016\pi$
$83$	2.45307	0.269259	0.134630	+	0.990896i	$0.457016\pi$
$84$	14.5915	1.59206
$85$	1.88607	0.204573
$86$	8.40470	0.906302
$87$	7.98717	0.856315
$88$	11.4127	1.21660
$89$	0.362958	0.0384734	0.0192367	−	0.999815i	$-0.493876\pi$
$89$	0.362958	0.0384734	0.0192367	+	0.999815i	$0.493876\pi$
$90$	14.3136	1.50878
$91$	3.84969	0.403557
$92$	31.5733	3.29174
$93$	−2.69653	−0.279617
$94$	−20.5220	−2.11668
$95$	−20.0903	−2.06122
$96$	4.19966	0.428626
$97$	−2.74078	−0.278284	−0.139142	−	0.990272i	$-0.544434\pi$
$97$	−2.74078	−0.278284	−0.139142	+	0.990272i	$0.544434\pi$
$98$	−18.3877	−1.85744
$99$	5.86174	0.589127
$100$	20.7177	2.07177
$101$	−0.403874	−0.0401870	−0.0200935	−	0.999798i	$-0.506396\pi$
$101$	−0.403874	−0.0401870	−0.0200935	+	0.999798i	$0.506396\pi$
$102$	−1.44473	−0.143049
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−3.59467	−0.352486
$105$	13.6336	1.33051
$106$	−16.0730	−1.56115
$107$	4.79213	0.463273	0.231636	−	0.972802i	$-0.425592\pi$
$107$	4.79213	0.463273	0.231636	+	0.972802i	$0.425592\pi$
$108$	−18.3689	−1.76755
$109$	14.7825	1.41591	0.707954	−	0.706259i	$-0.249619\pi$
$109$	14.7825	1.41591	0.707954	+	0.706259i	$0.249619\pi$
$110$	24.6139	2.34684
$111$	6.58279	0.624811
$112$	5.36923	0.507345
$113$	−18.8128	−1.76976	−0.884879	−	0.465821i	$-0.845759\pi$
$113$	−18.8128	−1.76976	−0.884879	+	0.465821i	$0.845759\pi$
$114$	15.3891	1.44133
$115$	29.5006	2.75095
$116$	26.2402	2.43634
$117$	−1.84628	−0.170689
$118$	22.1487	2.03896
$119$	2.20215	0.201871
$120$	−12.7305	−1.16213
$121$	−0.920059	−0.0836417
$122$	25.8249	2.33808
$123$	7.34959	0.662690
$124$	−8.85889	−0.795551
$125$	2.87201	0.256881
$126$	16.7124	1.48885
$127$	−15.2389	−1.35223	−0.676115	−	0.736796i	$-0.736338\pi$
$127$	−15.2389	−1.35223	−0.676115	+	0.736796i	$0.736338\pi$
$128$	20.3560	1.79924
$129$	−3.83935	−0.338036
$130$	−7.75266	−0.679953
$131$	−2.39049	−0.208858	−0.104429	−	0.994532i	$-0.533301\pi$
$131$	−2.39049	−0.208858	−0.104429	+	0.994532i	$0.533301\pi$
$132$	−12.0338	−1.04741
$133$	−23.4572	−2.03399
$134$	−30.9825	−2.67648
$135$	−17.1631	−1.47716
$136$	−2.05627	−0.176324
$137$	6.88797	0.588479	0.294240	−	0.955732i	$-0.404934\pi$
$137$	6.88797	0.588479	0.294240	+	0.955732i	$0.404934\pi$
$138$	−22.5975	−1.92362
$139$	10.6688	0.904919	0.452459	−	0.891785i	$-0.350547\pi$
$139$	10.6688	0.904919	0.452459	+	0.891785i	$0.350547\pi$
$140$	44.7905	3.78549
$141$	9.37467	0.789489
$142$	−3.78281	−0.317446
$143$	−3.17489	−0.265498
$144$	−2.57504	−0.214587
$145$	24.5176	2.03608
$146$	−16.8287	−1.39275
$147$	8.39967	0.692793
$148$	21.6264	1.77768
$149$	−16.1847	−1.32590	−0.662952	−	0.748662i	$-0.730697\pi$
$149$	−16.1847	−1.32590	−0.662952	+	0.748662i	$0.730697\pi$
$150$	−14.8280	−1.21070
$151$	−6.85088	−0.557517	−0.278758	−	0.960361i	$-0.589923\pi$
$151$	−6.85088	−0.557517	−0.278758	+	0.960361i	$0.589923\pi$
$152$	21.9033	1.77659
$153$	−1.05613	−0.0853834
$154$	28.7388	2.31584
$155$	−8.27734	−0.664852
$156$	3.79031	0.303468
$157$	−14.5276	−1.15943	−0.579713	−	0.814821i	$-0.696835\pi$
$157$	−14.5276	−1.15943	−0.579713	+	0.814821i	$0.696835\pi$
$158$	10.9563	0.871633
$159$	7.34232	0.582284
$160$	12.8914	1.01916
$161$	34.4446	2.71461
$162$	0.123234	0.00968216
$163$	13.3625	1.04663	0.523316	−	0.852139i	$-0.324695\pi$
$163$	13.3625	1.04663	0.523316	+	0.852139i	$0.324695\pi$
$164$	24.1456	1.88545
$165$	−11.2439	−0.875333
$166$	−5.76799	−0.447683
$167$	−10.1112	−0.782426	−0.391213	−	0.920300i	$-0.627944\pi$
$167$	−10.1112	−0.782426	−0.391213	+	0.920300i	$0.627944\pi$
$168$	−14.8640	−1.14678
$169$	1.00000	0.0769231
$170$	−4.43478	−0.340132
$171$	11.2499	0.860299
$172$	−12.6134	−0.961762
$173$	13.9233	1.05857	0.529286	−	0.848443i	$-0.322460\pi$
$173$	13.9233	1.05857	0.529286	+	0.848443i	$0.322460\pi$
$174$	−18.7805	−1.42375
$175$	22.6018	1.70853
$176$	−4.42808	−0.333779
$177$	−10.1178	−0.760498
$178$	−0.853435	−0.0639677
$179$	3.73881	0.279452	0.139726	−	0.990190i	$-0.455378\pi$
$179$	3.73881	0.279452	0.139726	+	0.990190i	$0.455378\pi$
$180$	−21.4812	−1.60111
$181$	0.727646	0.0540855	0.0270428	−	0.999634i	$-0.491391\pi$
$181$	0.727646	0.0540855	0.0270428	+	0.999634i	$0.491391\pi$
$182$	−9.05191	−0.670972
$183$	−11.7971	−0.872066
$184$	−32.1628	−2.37107
$185$	20.2067	1.48563
$186$	6.34044	0.464904
$187$	−1.81614	−0.132810
$188$	30.7985	2.24621
$189$	−20.0394	−1.45765
$190$	47.2390	3.42708
$191$	4.13220	0.298996	0.149498	−	0.988762i	$-0.452234\pi$
$191$	4.13220	0.298996	0.149498	+	0.988762i	$0.452234\pi$
$192$	−12.8710	−0.928884
$193$	−6.98974	−0.503132	−0.251566	−	0.967840i	$-0.580946\pi$
$193$	−6.98974	−0.503132	−0.251566	+	0.967840i	$0.580946\pi$
$194$	6.44449	0.462687
$195$	3.54149	0.253611
$196$	27.5954	1.97110
$197$	21.7552	1.54999	0.774997	−	0.631965i	$-0.217752\pi$
$197$	21.7552	1.54999	0.774997	+	0.631965i	$0.217752\pi$
$198$	−13.7829	−0.979509
$199$	−7.55420	−0.535503	−0.267752	−	0.963488i	$-0.586281\pi$
$199$	−7.55420	−0.535503	−0.267752	+	0.963488i	$0.586281\pi$
$200$	−21.1045	−1.49232
$201$	14.1531	0.998284
$202$	0.949644	0.0668167
$203$	28.6265	2.00919
$204$	2.16818	0.151803
$205$	22.5605	1.57569
$206$	2.35134	0.163825
$207$	−16.5193	−1.14817
$208$	1.39472	0.0967064
$209$	19.3454	1.33815
$210$	−32.0573	−2.21216
$211$	−25.8211	−1.77760	−0.888798	−	0.458300i	$-0.848459\pi$
$211$	−25.8211	−1.77760	−0.888798	+	0.458300i	$0.848459\pi$
$212$	24.1217	1.65668
$213$	1.72802	0.118402
$214$	−11.2679	−0.770259
$215$	−11.7854	−0.803756
$216$	18.7119	1.27318
$217$	−9.66452	−0.656070
$218$	−34.7586	−2.35415
$219$	7.68751	0.519473
$220$	−36.9394	−2.49045
$221$	0.572034	0.0384791
$222$	−15.4783	−1.03884
$223$	16.8212	1.12643	0.563214	−	0.826311i	$-0.309565\pi$
$223$	16.8212	1.12643	0.563214	+	0.826311i	$0.309565\pi$
$224$	15.0519	1.00569
$225$	−10.8396	−0.722642
$226$	44.2352	2.94248
$227$	−5.14443	−0.341448	−0.170724	−	0.985319i	$-0.554611\pi$
$227$	−5.14443	−0.341448	−0.170724	+	0.985319i	$0.554611\pi$
$228$	−23.0953	−1.52953
$229$	−13.1862	−0.871368	−0.435684	−	0.900100i	$-0.643493\pi$
$229$	−13.1862	−0.871368	−0.435684	+	0.900100i	$0.643493\pi$
$230$	−69.3659	−4.57385
$231$	−13.1282	−0.863771
$232$	−26.7302	−1.75492
$233$	−20.0214	−1.31164	−0.655822	−	0.754916i	$-0.727678\pi$
$233$	−20.0214	−1.31164	−0.655822	+	0.754916i	$0.727678\pi$
$234$	4.34122	0.283795
$235$	28.7767	1.87719
$236$	−33.2398	−2.16373
$237$	−5.00493	−0.325105
$238$	−5.17799	−0.335640
$239$	−21.0866	−1.36398	−0.681990	−	0.731362i	$-0.738885\pi$
$239$	−21.0866	−1.36398	−0.681990	+	0.731362i	$0.738885\pi$
$240$	4.93939	0.318836
$241$	−23.0715	−1.48617	−0.743083	−	0.669199i	$-0.766637\pi$
$241$	−23.0715	−1.48617	−0.743083	+	0.669199i	$0.766637\pi$
$242$	2.16337	0.139067
$243$	15.5601	0.998179
$244$	−38.7569	−2.48116
$245$	25.7839	1.64727
$246$	−17.2814	−1.10182
$247$	−6.09326	−0.387705
$248$	9.02430	0.573044
$249$	2.63488	0.166978
$250$	−6.75307	−0.427101
$251$	−2.10612	−0.132937	−0.0664685	−	0.997789i	$-0.521173\pi$
$251$	−2.10612	−0.132937	−0.0664685	+	0.997789i	$0.521173\pi$
$252$	−25.0811	−1.57996
$253$	−28.4069	−1.78593
$254$	35.8317	2.24828
$255$	2.02585	0.126864
$256$	−23.8981	−1.49363
$257$	−18.3683	−1.14578	−0.572891	−	0.819632i	$-0.694178\pi$
$257$	−18.3683	−1.14578	−0.572891	+	0.819632i	$0.694178\pi$
$258$	9.02760	0.562034
$259$	23.5931	1.46600
$260$	11.6348	0.721562
$261$	−13.7290	−0.849807
$262$	5.62084	0.347256
$263$	−7.86367	−0.484895	−0.242447	−	0.970165i	$-0.577950\pi$
$263$	−7.86367	−0.484895	−0.242447	+	0.970165i	$0.577950\pi$
$264$	12.2585	0.754460
$265$	22.5382	1.38451
$266$	55.1556	3.38181
$267$	0.389858	0.0238589
$268$	46.4972	2.84027
$269$	27.2094	1.65899	0.829493	−	0.558518i	$-0.188630\pi$
$269$	27.2094	1.65899	0.829493	+	0.558518i	$0.188630\pi$
$270$	40.3561	2.45599
$271$	−11.2562	−0.683764	−0.341882	−	0.939743i	$-0.611064\pi$
$271$	−11.2562	−0.683764	−0.341882	+	0.939743i	$0.611064\pi$
$272$	0.797826	0.0483753
$273$	4.13500	0.250262
$274$	−16.1959	−0.978432
$275$	−18.6400	−1.12403
$276$	33.9133	2.04134
$277$	−17.6802	−1.06230	−0.531151	−	0.847277i	$-0.678240\pi$
$277$	−17.6802	−1.06230	−0.531151	+	0.847277i	$0.678240\pi$
$278$	−25.0860	−1.50456
$279$	4.63503	0.277492
$280$	−45.6269	−2.72673
$281$	9.31846	0.555893	0.277946	−	0.960597i	$-0.410346\pi$
$281$	9.31846	0.555893	0.277946	+	0.960597i	$0.410346\pi$
$282$	−22.0430	−1.31264
$283$	−10.0094	−0.594997	−0.297499	−	0.954722i	$-0.596152\pi$
$283$	−10.0094	−0.594997	−0.297499	+	0.954722i	$0.596152\pi$
$284$	5.67707	0.336872
$285$	−21.5792	−1.27824
$286$	7.46524	0.441429
$287$	26.3414	1.55488
$288$	−7.21875	−0.425369
$289$	−16.6728	−0.980752
$290$	−57.6492	−3.38528
$291$	−2.94391	−0.172575
$292$	25.2557	1.47798
$293$	29.6354	1.73132	0.865658	−	0.500635i	$-0.166900\pi$
$293$	29.6354	1.73132	0.865658	+	0.500635i	$0.166900\pi$
$294$	−19.7504	−1.15187
$295$	−31.0578	−1.80825
$296$	−22.0302	−1.28048
$297$	16.5268	0.958980
$298$	38.0557	2.20451
$299$	8.94736	0.517439
$300$	22.2531	1.28479
$301$	−13.7605	−0.793140
$302$	16.1087	0.926952
$303$	−0.433807	−0.0249215
$304$	−8.49839	−0.487416
$305$	−36.2127	−2.07353
$306$	2.48333	0.141962
$307$	−15.2911	−0.872709	−0.436354	−	0.899775i	$-0.643731\pi$
$307$	−15.2911	−0.872709	−0.436354	+	0.899775i	$0.643731\pi$
$308$	−43.1299	−2.45756
$309$	−1.07411	−0.0611042
$310$	19.4628	1.10541
$311$	−9.25059	−0.524553	−0.262276	−	0.964993i	$-0.584473\pi$
$311$	−9.25059	−0.524553	−0.262276	+	0.964993i	$0.584473\pi$
$312$	−3.86108	−0.218591
$313$	18.3211	1.03557	0.517784	−	0.855511i	$-0.326757\pi$
$313$	18.3211	1.03557	0.517784	+	0.855511i	$0.326757\pi$
$314$	34.1592	1.92772
$315$	−23.4347	−1.32039
$316$	−16.4427	−0.924972
$317$	−24.9843	−1.40326	−0.701629	−	0.712543i	$-0.747543\pi$
$317$	−24.9843	−1.40326	−0.701629	+	0.712543i	$0.747543\pi$
$318$	−17.2643	−0.968131
$319$	−23.6087	−1.32183
$320$	−39.5092	−2.20863
$321$	5.14730	0.287294
$322$	−80.9907	−4.51344
$323$	−3.48555	−0.193941
$324$	−0.184944	−0.0102747
$325$	5.87106	0.325668
$326$	−31.4197	−1.74018
$327$	15.8781	0.878060
$328$	−24.5964	−1.35811
$329$	33.5994	1.85239
$330$	26.4381	1.45537
$331$	16.2533	0.893363	0.446682	−	0.894693i	$-0.352606\pi$
$331$	16.2533	0.893363	0.446682	+	0.894693i	$0.352606\pi$
$332$	8.65634	0.475078
$333$	−11.3151	−0.620062
$334$	23.7748	1.30090
$335$	43.4448	2.37365
$336$	5.76717	0.314625
$337$	−30.8760	−1.68193	−0.840963	−	0.541093i	$-0.818011\pi$
$337$	−30.8760	−1.68193	−0.840963	+	0.541093i	$0.818011\pi$
$338$	−2.35134	−0.127896
$339$	−20.2071	−1.09750
$340$	6.65552	0.360946
$341$	7.97047	0.431625
$342$	−26.4522	−1.43037
$343$	3.15712	0.170468
$344$	12.8489	0.692767
$345$	31.6870	1.70597
$346$	−32.7385	−1.76003
$347$	−5.46159	−0.293194	−0.146597	−	0.989196i	$-0.546832\pi$
$347$	−5.46159	−0.293194	−0.146597	+	0.989196i	$0.546832\pi$
$348$	28.1850	1.51087
$349$	13.5973	0.727846	0.363923	−	0.931429i	$-0.381437\pi$
$349$	13.5973	0.727846	0.363923	+	0.931429i	$0.381437\pi$
$350$	−53.1443	−2.84068
$351$	−5.20546	−0.277847
$352$	−12.4135	−0.661640
$353$	20.4991	1.09106	0.545529	−	0.838092i	$-0.316329\pi$
$353$	20.4991	1.09106	0.545529	+	0.838092i	$0.316329\pi$
$354$	23.7903	1.26444
$355$	5.30439	0.281528
$356$	1.28080	0.0678821
$357$	2.36536	0.125188
$358$	−8.79121	−0.464630
$359$	−17.4771	−0.922407	−0.461204	−	0.887294i	$-0.652582\pi$
$359$	−17.4771	−0.922407	−0.461204	+	0.887294i	$0.652582\pi$
$360$	21.8823	1.15330
$361$	18.1278	0.954096
$362$	−1.71094	−0.0899250
$363$	−0.988248	−0.0518696
$364$	13.5847	0.712031
$365$	23.5978	1.23516
$366$	27.7389	1.44994
$367$	−5.87892	−0.306877	−0.153439	−	0.988158i	$-0.549035\pi$
$367$	−5.87892	−0.306877	−0.153439	+	0.988158i	$0.549035\pi$
$368$	12.4791	0.650516
$369$	−12.6331	−0.657654
$370$	−47.5128	−2.47007
$371$	26.3153	1.36622
$372$	−9.51545	−0.493353
$373$	10.0200	0.518814	0.259407	−	0.965768i	$-0.416473\pi$
$373$	10.0200	0.518814	0.259407	+	0.965768i	$0.416473\pi$
$374$	4.27037	0.220815
$375$	3.08487	0.159302
$376$	−31.3736	−1.61797
$377$	7.43606	0.382976
$378$	47.1193	2.42356
$379$	11.1175	0.571069	0.285534	−	0.958368i	$-0.407829\pi$
$379$	11.1175	0.571069	0.285534	+	0.958368i	$0.407829\pi$
$380$	−70.8941	−3.63679
$381$	−16.3683	−0.838572
$382$	−9.71619	−0.497124
$383$	−15.7579	−0.805190	−0.402595	−	0.915378i	$-0.631892\pi$
$383$	−15.7579	−0.805190	−0.402595	+	0.915378i	$0.631892\pi$
$384$	21.8647	1.11578
$385$	−40.2987	−2.05381
$386$	16.4352	0.836531
$387$	6.59941	0.335467
$388$	−9.67160	−0.491001
$389$	11.7861	0.597580	0.298790	−	0.954319i	$-0.403417\pi$
$389$	11.7861	0.597580	0.298790	+	0.954319i	$0.403417\pi$
$390$	−8.32724	−0.421666
$391$	5.11819	0.258838
$392$	−28.1107	−1.41980
$393$	−2.56765	−0.129521
$394$	−51.1537	−2.57709
$395$	−15.3633	−0.773010
$396$	20.6848	1.03945
$397$	−13.9140	−0.698325	−0.349163	−	0.937062i	$-0.613534\pi$
$397$	−13.9140	−0.698325	−0.349163	+	0.937062i	$0.613534\pi$
$398$	17.7625	0.890352
$399$	−25.1956	−1.26136
$400$	8.18848	0.409424
$401$	−37.7773	−1.88651	−0.943255	−	0.332070i	$-0.892253\pi$
$401$	−37.7773	−1.88651	−0.943255	+	0.332070i	$0.892253\pi$
$402$	−33.2787	−1.65979
$403$	−2.51047	−0.125055
$404$	−1.42518	−0.0709055
$405$	−0.172803	−0.00858665
$406$	−67.3105	−3.34056
$407$	−19.4576	−0.964476
$408$	−2.20867	−0.109345
$409$	32.7322	1.61850	0.809250	−	0.587464i	$-0.199874\pi$
$409$	32.7322	1.61850	0.809250	+	0.587464i	$0.199874\pi$
$410$	−53.0473	−2.61982
$411$	7.39846	0.364939
$412$	−3.52878	−0.173850
$413$	−36.2627	−1.78437
$414$	38.8425	1.90901
$415$	8.08809	0.397029
$416$	3.90989	0.191698
$417$	11.4595	0.561176
$418$	−45.4876	−2.22487
$419$	33.3304	1.62830	0.814149	−	0.580656i	$-0.197204\pi$
$419$	33.3304	1.62830	0.814149	+	0.580656i	$0.197204\pi$
$420$	48.1101	2.34753
$421$	30.8934	1.50565	0.752827	−	0.658218i	$-0.228690\pi$
$421$	30.8934	1.50565	0.752827	+	0.658218i	$0.228690\pi$
$422$	60.7140	2.95551
$423$	−16.1140	−0.783489
$424$	−24.5721	−1.19333
$425$	3.35845	0.162909
$426$	−4.06317	−0.196861
$427$	−42.2815	−2.04614
$428$	16.9104	0.817394
$429$	−3.41019	−0.164646
$430$	27.7114	1.33636
$431$	−2.38509	−0.114886	−0.0574428	−	0.998349i	$-0.518295\pi$
$431$	−2.38509	−0.114886	−0.0574428	+	0.998349i	$0.518295\pi$
$432$	−7.26015	−0.349304
$433$	12.4280	0.597253	0.298626	−	0.954370i	$-0.403472\pi$
$433$	12.4280	0.597253	0.298626	+	0.954370i	$0.403472\pi$
$434$	22.7245	1.09081
$435$	26.3347	1.26265
$436$	52.1642	2.49821
$437$	−54.5186	−2.60798
$438$	−18.0759	−0.863700
$439$	−29.0656	−1.38722	−0.693612	−	0.720349i	$-0.743982\pi$
$439$	−29.0656	−1.38722	−0.693612	+	0.720349i	$0.743982\pi$
$440$	37.6291	1.79390
$441$	−14.4381	−0.687528
$442$	−1.34504	−0.0639772
$443$	−29.4931	−1.40126	−0.700630	−	0.713525i	$-0.747098\pi$
$443$	−29.4931	−1.40126	−0.700630	+	0.713525i	$0.747098\pi$
$444$	23.2292	1.10241
$445$	1.19672	0.0567299
$446$	−39.5522	−1.87285
$447$	−17.3842	−0.822245
$448$	−46.1304	−2.17946
$449$	−16.7784	−0.791823	−0.395912	−	0.918289i	$-0.629571\pi$
$449$	−16.7784	−0.791823	−0.395912	+	0.918289i	$0.629571\pi$
$450$	25.4876	1.20150
$451$	−21.7241	−1.02295
$452$	−66.3861	−3.12254
$453$	−7.35862	−0.345738
$454$	12.0963	0.567707
$455$	12.6929	0.595053
$456$	23.5266	1.10173
$457$	6.41777	0.300211	0.150105	−	0.988670i	$-0.452039\pi$
$457$	6.41777	0.300211	0.150105	+	0.988670i	$0.452039\pi$
$458$	31.0051	1.44878
$459$	−2.97769	−0.138987
$460$	104.101	4.85374
$461$	−0.148337	−0.00690874	−0.00345437	−	0.999994i	$-0.501100\pi$
$461$	−0.148337	−0.00690874	−0.00345437	+	0.999994i	$0.501100\pi$
$462$	30.8688	1.43615
$463$	−13.0598	−0.606941	−0.303470	−	0.952841i	$-0.598145\pi$
$463$	−13.0598	−0.606941	−0.303470	+	0.952841i	$0.598145\pi$
$464$	10.3712	0.481471
$465$	−8.89080	−0.412301
$466$	47.0770	2.18080
$467$	−4.82412	−0.223234	−0.111617	−	0.993751i	$-0.535603\pi$
$467$	−4.82412	−0.223234	−0.111617	+	0.993751i	$0.535603\pi$
$468$	−6.51511	−0.301161
$469$	50.7257	2.34229
$470$	−67.6638	−3.12110
$471$	−15.6043	−0.719007
$472$	33.8605	1.55856
$473$	11.3485	0.521802
$474$	11.7683	0.540534
$475$	−35.7739	−1.64142
$476$	7.77090	0.356179
$477$	−12.6206	−0.577858
$478$	49.5817	2.26781
$479$	−6.51605	−0.297726	−0.148863	−	0.988858i	$-0.547561\pi$
$479$	−6.51605	−0.297726	−0.148863	+	0.988858i	$0.547561\pi$
$480$	13.8468	0.632019
$481$	6.12858	0.279439
$482$	54.2489	2.47097
$483$	36.9974	1.68344
$484$	−3.24668	−0.147577
$485$	−9.03670	−0.410335
$486$	−36.5869	−1.65962
$487$	17.3409	0.785790	0.392895	−	0.919583i	$-0.371474\pi$
$487$	17.3409	0.785790	0.392895	+	0.919583i	$0.371474\pi$
$488$	39.4806	1.78720
$489$	14.3528	0.649058
$490$	−60.6265	−2.73883
$491$	−38.3445	−1.73046	−0.865232	−	0.501372i	$-0.832829\pi$
$491$	−38.3445	−1.73046	−0.865232	+	0.501372i	$0.832829\pi$
$492$	25.9351	1.16924
$493$	4.25367	0.191576
$494$	14.3273	0.644616
$495$	19.3269	0.868680
$496$	−3.50140	−0.157217
$497$	6.19335	0.277810
$498$	−6.19548	−0.277626
$499$	34.3180	1.53629	0.768143	−	0.640279i	$-0.221181\pi$
$499$	34.3180	1.53629	0.768143	+	0.640279i	$0.221181\pi$
$500$	10.1347	0.453237
$501$	−10.8605	−0.485214
$502$	4.95219	0.221027
$503$	18.5242	0.825952	0.412976	−	0.910742i	$-0.364489\pi$
$503$	18.5242	0.825952	0.412976	+	0.910742i	$0.364489\pi$
$504$	25.5495	1.13806
$505$	−1.33163	−0.0592566
$506$	66.7942	2.96936
$507$	1.07411	0.0477031
$508$	−53.7746	−2.38586
$509$	26.3904	1.16973	0.584867	−	0.811129i	$-0.301147\pi$
$509$	26.3904	1.16973	0.584867	+	0.811129i	$0.301147\pi$
$510$	−4.76346	−0.210929
$511$	27.5525	1.21885
$512$	15.4803	0.684139
$513$	31.7182	1.40039
$514$	43.1900	1.90503
$515$	−3.29713	−0.145289
$516$	−13.5482	−0.596427
$517$	−27.7099	−1.21868
$518$	−55.4753	−2.43745
$519$	14.9553	0.656463
$520$	−11.8521	−0.519749
$521$	21.4729	0.940747	0.470373	−	0.882467i	$-0.344119\pi$
$521$	21.4729	0.940747	0.470373	+	0.882467i	$0.344119\pi$
$522$	32.2816	1.41293
$523$	−22.2783	−0.974164	−0.487082	−	0.873356i	$-0.661939\pi$
$523$	−22.2783	−0.974164	−0.487082	+	0.873356i	$0.661939\pi$
$524$	−8.43550	−0.368506
$525$	24.2769	1.05953
$526$	18.4901	0.806208
$527$	−1.43607	−0.0625563
$528$	−4.75626	−0.206990
$529$	57.0553	2.48067
$530$	−52.9948	−2.30195
$531$	17.3913	0.754718
$532$	−82.7751	−3.58876
$533$	6.84247	0.296380
$534$	−0.916686	−0.0396689
$535$	15.8003	0.683106
$536$	−47.3654	−2.04587
$537$	4.01591	0.173299
$538$	−63.9784	−2.75830
$539$	−24.8280	−1.06942
$540$	−60.5646	−2.60629
$541$	29.0463	1.24880	0.624399	−	0.781106i	$-0.285344\pi$
$541$	29.0463	1.24880	0.624399	+	0.781106i	$0.285344\pi$
$542$	26.4671	1.13686
$543$	0.781575	0.0335406
$544$	2.23659	0.0958929
$545$	48.7398	2.08779
$546$	−9.72278	−0.416096
$547$	22.5205	0.962907	0.481454	−	0.876472i	$-0.340109\pi$
$547$	22.5205	0.962907	0.481454	+	0.876472i	$0.340109\pi$
$548$	24.3061	1.03831
$549$	20.2779	0.865438
$550$	43.8289	1.86887
$551$	−45.3098	−1.93026
$552$	−34.5465	−1.47040
$553$	−17.9380	−0.762800
$554$	41.5721	1.76623
$555$	21.7043	0.921297
$556$	37.6480	1.59663
$557$	27.6415	1.17121	0.585605	−	0.810597i	$-0.300857\pi$
$557$	27.6415	1.17121	0.585605	+	0.810597i	$0.300857\pi$
$558$	−10.8985	−0.461370
$559$	−3.57444	−0.151183
$560$	17.7031	0.748091
$561$	−1.95075	−0.0823606
$562$	−21.9108	−0.924253
$563$	17.3916	0.732969	0.366485	−	0.930424i	$-0.380561\pi$
$563$	17.3916	0.732969	0.366485	+	0.930424i	$0.380561\pi$
$564$	33.0811	1.39297
$565$	−62.0282	−2.60955
$566$	23.5355	0.989269
$567$	−0.201763	−0.00847324
$568$	−5.78307	−0.242652
$569$	2.67483	0.112135	0.0560675	−	0.998427i	$-0.482144\pi$
$569$	2.67483	0.112135	0.0560675	+	0.998427i	$0.482144\pi$
$570$	50.7400	2.12527
$571$	−40.5136	−1.69544	−0.847720	−	0.530444i	$-0.822025\pi$
$571$	−40.5136	−1.69544	−0.847720	+	0.530444i	$0.822025\pi$
$572$	−11.2035	−0.468441
$573$	4.43845	0.185419
$574$	−61.9374	−2.58522
$575$	52.5306	2.19068
$576$	22.1238	0.921824
$577$	32.5873	1.35663	0.678313	−	0.734773i	$-0.262711\pi$
$577$	32.5873	1.35663	0.678313	+	0.734773i	$0.262711\pi$
$578$	39.2033	1.63064
$579$	−7.50777	−0.312012
$580$	86.5173	3.59244
$581$	9.44355	0.391785
$582$	6.92211	0.286931
$583$	−21.7026	−0.898830
$584$	−25.7273	−1.06460
$585$	−6.08742	−0.251684
$586$	−69.6827	−2.87857
$587$	30.6880	1.26663	0.633315	−	0.773894i	$-0.281694\pi$
$587$	30.6880	1.26663	0.633315	+	0.773894i	$0.281694\pi$
$588$	29.6406	1.22236
$589$	15.2969	0.630299
$590$	73.0272	3.00648
$591$	23.3675	0.961212
$592$	8.54764	0.351306
$593$	−14.2670	−0.585874	−0.292937	−	0.956132i	$-0.594633\pi$
$593$	−14.2670	−0.585874	−0.292937	+	0.956132i	$0.594633\pi$
$594$	−38.8600	−1.59444
$595$	7.26078	0.297663
$596$	−57.1123	−2.33941
$597$	−8.11407	−0.332087
$598$	−21.0383	−0.860318
$599$	43.6998	1.78553	0.892763	−	0.450527i	$-0.148764\pi$
$599$	43.6998	1.78553	0.892763	+	0.450527i	$0.148764\pi$
$600$	−22.6687	−0.925445
$601$	−13.8084	−0.563257	−0.281629	−	0.959523i	$-0.590875\pi$
$601$	−13.8084	−0.563257	−0.281629	+	0.959523i	$0.590875\pi$
$602$	32.3555	1.31871
$603$	−24.3276	−0.990697
$604$	−24.1752	−0.983676
$605$	−3.03355	−0.123331
$606$	1.02003	0.0414357
$607$	−45.3079	−1.83899	−0.919495	−	0.393102i	$-0.871402\pi$
$607$	−45.3079	−1.83899	−0.919495	+	0.393102i	$0.871402\pi$
$608$	−23.8240	−0.966190
$609$	30.7481	1.24598
$610$	85.1482	3.44755
$611$	8.72782	0.353090
$612$	−3.72686	−0.150650
$613$	20.2109	0.816312	0.408156	−	0.912912i	$-0.366172\pi$
$613$	20.2109	0.816312	0.408156	+	0.912912i	$0.366172\pi$
$614$	35.9545	1.45101
$615$	24.2326	0.977151
$616$	43.9353	1.77020
$617$	30.5178	1.22860	0.614300	−	0.789073i	$-0.289439\pi$
$617$	30.5178	1.22860	0.614300	+	0.789073i	$0.289439\pi$
$618$	2.52560	0.101595
$619$	−18.8750	−0.758650	−0.379325	−	0.925264i	$-0.623844\pi$
$619$	−18.8750	−0.758650	−0.379325	+	0.925264i	$0.623844\pi$
$620$	−29.2089	−1.17306
$621$	−46.5751	−1.86899
$622$	21.7512	0.872145
$623$	1.39727	0.0559806
$624$	1.49809	0.0599715
$625$	−19.8859	−0.795437
$626$	−43.0790	−1.72178
$627$	20.7792	0.829842
$628$	−51.2646	−2.04568
$629$	3.50575	0.139784
$630$	55.1028	2.19535
$631$	−26.3902	−1.05058	−0.525289	−	0.850924i	$-0.676043\pi$
$631$	−26.3902	−1.05058	−0.525289	+	0.850924i	$0.676043\pi$
$632$	16.7497	0.666267
$633$	−27.7348	−1.10236
$634$	58.7464	2.33312
$635$	−50.2445	−1.99389
$636$	25.9094	1.02737
$637$	7.82010	0.309844
$638$	55.5119	2.19774
$639$	−2.97028	−0.117502
$640$	67.1165	2.65301
$641$	−25.7141	−1.01565	−0.507823	−	0.861462i	$-0.669549\pi$
$641$	−25.7141	−1.01565	−0.507823	+	0.861462i	$0.669549\pi$
$642$	−12.1030	−0.477668
$643$	5.33703	0.210472	0.105236	−	0.994447i	$-0.466440\pi$
$643$	5.33703	0.210472	0.105236	+	0.994447i	$0.466440\pi$
$644$	121.547	4.78963
$645$	−12.6588	−0.498441
$646$	8.19570	0.322455
$647$	−39.3599	−1.54740	−0.773698	−	0.633555i	$-0.781595\pi$
$647$	−39.3599	−1.54740	−0.773698	+	0.633555i	$0.781595\pi$
$648$	0.188397	0.00740094
$649$	29.9063	1.17393
$650$	−13.8048	−0.541470
$651$	−10.3808	−0.406855
$652$	47.1533	1.84666
$653$	−4.28667	−0.167750	−0.0838751	−	0.996476i	$-0.526730\pi$
$653$	−4.28667	−0.167750	−0.0838751	+	0.996476i	$0.526730\pi$
$654$	−37.3347	−1.45990
$655$	−7.88175	−0.307965
$656$	9.54332	0.372604
$657$	−13.2140	−0.515525
$658$	−79.0034	−3.07987
$659$	−15.6171	−0.608354	−0.304177	−	0.952615i	$-0.598382\pi$
$659$	−15.6171	−0.608354	−0.304177	+	0.952615i	$0.598382\pi$
$660$	−39.6771	−1.54443
$661$	−20.0060	−0.778144	−0.389072	−	0.921207i	$-0.627204\pi$
$661$	−20.0060	−0.778144	−0.389072	+	0.921207i	$0.627204\pi$
$662$	−38.2170	−1.48535
$663$	0.614429	0.0238624
$664$	−8.81798	−0.342204
$665$	−77.3413	−2.99917
$666$	26.6055	1.03094
$667$	66.5331	2.57617
$668$	−35.6801	−1.38050
$669$	18.0678	0.698543
$670$	−102.153	−3.94653
$671$	34.8701	1.34615
$672$	16.1674	0.623671
$673$	41.9374	1.61657	0.808284	−	0.588792i	$-0.200396\pi$
$673$	41.9374	1.61657	0.808284	+	0.588792i	$0.200396\pi$
$674$	72.5999	2.79644
$675$	−30.5616	−1.17632
$676$	3.52878	0.135722
$677$	−3.67273	−0.141154	−0.0705772	−	0.997506i	$-0.522484\pi$
$677$	−3.67273	−0.141154	−0.0705772	+	0.997506i	$0.522484\pi$
$678$	47.5136	1.82475
$679$	−10.5511	−0.404916
$680$	−6.77980	−0.259993
$681$	−5.52570	−0.211745
$682$	−18.7412	−0.717639
$683$	−14.4680	−0.553601	−0.276800	−	0.960927i	$-0.589274\pi$
$683$	−14.4680	−0.553601	−0.276800	+	0.960927i	$0.589274\pi$
$684$	39.6983	1.51790
$685$	22.7105	0.867725
$686$	−7.42344	−0.283428
$687$	−14.1635	−0.540370
$688$	−4.98533	−0.190064
$689$	6.83570	0.260419
$690$	−74.5068	−2.83643
$691$	−17.8220	−0.677980	−0.338990	−	0.940790i	$-0.610085\pi$
$691$	−17.8220	−0.677980	−0.338990	+	0.940790i	$0.610085\pi$
$692$	49.1324	1.86773
$693$	22.5659	0.857207
$694$	12.8420	0.487477
$695$	35.1765	1.33432
$696$	−28.7112	−1.08830
$697$	3.91412	0.148258
$698$	−31.9718	−1.21015
$699$	−21.5052	−0.813402
$700$	79.7566	3.01452
$701$	27.1487	1.02539	0.512696	−	0.858570i	$-0.328647\pi$
$701$	27.1487	1.02539	0.512696	+	0.858570i	$0.328647\pi$
$702$	12.2398	0.461960
$703$	−37.3430	−1.40842
$704$	38.0444	1.43385
$705$	30.9095	1.16412
$706$	−48.2003	−1.81404
$707$	−1.55479	−0.0584739
$708$	−35.7033	−1.34181
$709$	−36.0929	−1.35550	−0.677748	−	0.735294i	$-0.737044\pi$
$709$	−36.0929	−1.35550	−0.677748	+	0.735294i	$0.737044\pi$
$710$	−12.4724	−0.468081
$711$	8.60291	0.322634
$712$	−1.30471	−0.0488962
$713$	−22.4621	−0.841211
$714$	−5.56175	−0.208143
$715$	−10.4680	−0.391482
$716$	13.1934	0.493062
$717$	−22.6494	−0.845858
$718$	41.0946	1.53364
$719$	−37.6803	−1.40524	−0.702620	−	0.711565i	$-0.747987\pi$
$719$	−37.6803	−1.40524	−0.702620	+	0.711565i	$0.747987\pi$
$720$	−8.49025	−0.316413
$721$	−3.84969	−0.143370
$722$	−42.6246	−1.58632
$723$	−24.7814	−0.921631
$724$	2.56770	0.0954279
$725$	43.6576	1.62140
$726$	2.32370	0.0862407
$727$	29.5255	1.09504	0.547521	−	0.836792i	$-0.315572\pi$
$727$	29.5255	1.09504	0.547521	+	0.836792i	$0.315572\pi$
$728$	−13.8384	−0.512884
$729$	16.8705	0.624834
$730$	−55.4863	−2.05364
$731$	−2.04470	−0.0756259
$732$	−41.6293	−1.53866
$733$	−32.2582	−1.19148	−0.595742	−	0.803176i	$-0.703142\pi$
$733$	−32.2582	−1.19148	−0.595742	+	0.803176i	$0.703142\pi$
$734$	13.8233	0.510228
$735$	27.6948	1.02154
$736$	34.9832	1.28950
$737$	−41.8342	−1.54098
$738$	29.7047	1.09344
$739$	−22.6684	−0.833872	−0.416936	−	0.908936i	$-0.636896\pi$
$739$	−22.6684	−0.833872	−0.416936	+	0.908936i	$0.636896\pi$
$740$	71.3050	2.62123
$741$	−6.54485	−0.240431
$742$	−61.8761	−2.27154
$743$	−30.3828	−1.11463	−0.557317	−	0.830299i	$-0.688169\pi$
$743$	−30.3828	−1.11463	−0.557317	+	0.830299i	$0.688169\pi$
$744$	9.69313	0.355367
$745$	−53.3631	−1.95507
$746$	−23.5603	−0.862603
$747$	−4.52905	−0.165709
$748$	−6.40877	−0.234328
$749$	18.4482	0.674083
$750$	−7.25356	−0.264863
$751$	9.74523	0.355608	0.177804	−	0.984066i	$-0.443101\pi$
$751$	9.74523	0.355608	0.177804	+	0.984066i	$0.443101\pi$
$752$	12.1728	0.443898
$753$	−2.26221	−0.0824395
$754$	−17.4847	−0.636754
$755$	−22.5882	−0.822070
$756$	−70.7145	−2.57186
$757$	18.8457	0.684959	0.342480	−	0.939525i	$-0.388733\pi$
$757$	18.8457	0.684959	0.342480	+	0.939525i	$0.388733\pi$
$758$	−26.1410	−0.949485
$759$	−30.5123	−1.10752
$760$	72.2179	2.61962
$761$	−9.39047	−0.340404	−0.170202	−	0.985409i	$-0.554442\pi$
$761$	−9.39047	−0.340404	−0.170202	+	0.985409i	$0.554442\pi$
$762$	38.4873	1.39425
$763$	56.9080	2.06021
$764$	14.5816	0.527545
$765$	−3.48221	−0.125900
$766$	37.0521	1.33875
$767$	−9.41964	−0.340123
$768$	−25.6692	−0.926259
$769$	−50.1846	−1.80970	−0.904851	−	0.425729i	$-0.860018\pi$
$769$	−50.1846	−1.80970	−0.904851	+	0.425729i	$0.860018\pi$
$770$	94.7557	3.41476
$771$	−19.7296	−0.710545
$772$	−24.6652	−0.887721
$773$	−18.1704	−0.653545	−0.326772	−	0.945103i	$-0.605961\pi$
$773$	−18.1704	−0.653545	−0.326772	+	0.945103i	$0.605961\pi$
$774$	−15.5174	−0.557763
$775$	−14.7391	−0.529445
$776$	9.85219	0.353673
$777$	25.3417	0.909128
$778$	−27.7131	−0.993563
$779$	−41.6930	−1.49381
$780$	12.4971	0.447469
$781$	−5.10774	−0.182769
$782$	−12.0346	−0.430356
$783$	−38.7081	−1.38331
$784$	10.9068	0.389530
$785$	−47.8993	−1.70960
$786$	6.03742	0.215348
$787$	27.1092	0.966338	0.483169	−	0.875527i	$-0.339486\pi$
$787$	27.1092	0.966338	0.483169	+	0.875527i	$0.339486\pi$
$788$	76.7692	2.73479
$789$	−8.44647	−0.300702
$790$	36.1242	1.28524
$791$	−72.4233	−2.57508
$792$	−21.0710	−0.748726
$793$	−10.9831	−0.390021
$794$	32.7166	1.16107
$795$	24.2086	0.858590
$796$	−26.6571	−0.944836
$797$	30.2172	1.07035	0.535174	−	0.844742i	$-0.320246\pi$
$797$	30.2172	1.07035	0.535174	+	0.844742i	$0.320246\pi$
$798$	59.2434	2.09719
$799$	4.99260	0.176626
$800$	22.9552	0.811589
$801$	−0.670121	−0.0236776
$802$	88.8272	3.13660
$803$	−22.7229	−0.801875
$804$	49.9432	1.76136
$805$	113.568	4.00275
$806$	5.90295	0.207923
$807$	29.2260	1.02880
$808$	1.45179	0.0510740
$809$	−41.7701	−1.46856	−0.734280	−	0.678847i	$-0.762480\pi$
$809$	−41.7701	−1.46856	−0.734280	+	0.678847i	$0.762480\pi$
$810$	0.406318	0.0142766
$811$	40.3449	1.41670	0.708350	−	0.705862i	$-0.249440\pi$
$811$	40.3449	1.41670	0.708350	+	0.705862i	$0.249440\pi$
$812$	101.017	3.54499
$813$	−12.0904	−0.424029
$814$	45.7513	1.60358
$815$	44.0579	1.54328
$816$	0.856956	0.0299995
$817$	21.7800	0.761985
$818$	−76.9643	−2.69099
$819$	−7.10760	−0.248360
$820$	79.6110	2.78014
$821$	−44.9582	−1.56905	−0.784527	−	0.620095i	$-0.787094\pi$
$821$	−44.9582	−1.56905	−0.784527	+	0.620095i	$0.787094\pi$
$822$	−17.3963	−0.606765
$823$	−16.6142	−0.579134	−0.289567	−	0.957158i	$-0.593511\pi$
$823$	−16.6142	−0.579134	−0.289567	+	0.957158i	$0.593511\pi$
$824$	3.59467	0.125226
$825$	−20.0215	−0.697058
$826$	85.2657	2.96677
$827$	25.8709	0.899621	0.449810	−	0.893124i	$-0.351492\pi$
$827$	25.8709	0.899621	0.449810	+	0.893124i	$0.351492\pi$
$828$	−58.2931	−2.02582
$829$	21.3917	0.742963	0.371482	−	0.928440i	$-0.378850\pi$
$829$	21.3917	0.742963	0.371482	+	0.928440i	$0.378850\pi$
$830$	−19.0178	−0.660118
$831$	−18.9906	−0.658775
$832$	−11.9829	−0.415432
$833$	4.47336	0.154993
$834$	−26.9452	−0.933037
$835$	−33.3379	−1.15370
$836$	68.2658	2.36102
$837$	13.0681	0.451701
$838$	−78.3710	−2.70728
$839$	−18.3267	−0.632709	−0.316355	−	0.948641i	$-0.602459\pi$
$839$	−18.3267	−0.632709	−0.316355	+	0.948641i	$0.602459\pi$
$840$	−49.0084	−1.69095
$841$	26.2950	0.906723
$842$	−72.6409	−2.50337
$843$	10.0091	0.344731
$844$	−91.1168	−3.13637
$845$	3.29713	0.113425
$846$	37.8894	1.30266
$847$	−3.54194	−0.121702
$848$	9.53388	0.327395
$849$	−10.7512	−0.368981
$850$	−7.89683	−0.270859
$851$	54.8346	1.87971
$852$	6.09782	0.208908
$853$	−20.7221	−0.709512	−0.354756	−	0.934959i	$-0.615436\pi$
$853$	−20.7221	−0.709512	−0.354756	+	0.934959i	$0.615436\pi$
$854$	99.4180	3.40201
$855$	37.0923	1.26853
$856$	−17.2261	−0.588777
$857$	10.6925	0.365249	0.182625	−	0.983183i	$-0.441541\pi$
$857$	10.6925	0.365249	0.182625	+	0.983183i	$0.441541\pi$
$858$	8.01851	0.273747
$859$	11.4620	0.391079	0.195539	−	0.980696i	$-0.437354\pi$
$859$	11.4620	0.391079	0.195539	+	0.980696i	$0.437354\pi$
$860$	−41.5880	−1.41814
$861$	28.2936	0.964244
$862$	5.60814	0.191014
$863$	24.1749	0.822923	0.411461	−	0.911427i	$-0.365018\pi$
$863$	24.1749	0.822923	0.411461	+	0.911427i	$0.365018\pi$
$864$	−20.3527	−0.692415
$865$	45.9071	1.56089
$866$	−29.2225	−0.993020
$867$	−17.9085	−0.608203
$868$	−34.1039	−1.15756
$869$	14.7937	0.501842
$870$	−61.9218	−2.09935
$871$	13.1766	0.446471
$872$	−53.1382	−1.79949
$873$	5.06024	0.171263
$874$	128.192	4.33615
$875$	11.0564	0.373773
$876$	27.1275	0.916553
$877$	−24.9783	−0.843458	−0.421729	−	0.906722i	$-0.638577\pi$
$877$	−24.9783	−0.843458	−0.421729	+	0.906722i	$0.638577\pi$
$878$	68.3429	2.30646
$879$	31.8318	1.07366
$880$	−14.6000	−0.492165
$881$	−6.75946	−0.227732	−0.113866	−	0.993496i	$-0.536323\pi$
$881$	−6.75946	−0.227732	−0.113866	+	0.993496i	$0.536323\pi$
$882$	33.9488	1.14312
$883$	−2.44509	−0.0822838	−0.0411419	−	0.999153i	$-0.513100\pi$
$883$	−2.44509	−0.0822838	−0.0411419	+	0.999153i	$0.513100\pi$
$884$	2.01858	0.0678922
$885$	−33.3596	−1.12137
$886$	69.3482	2.32980
$887$	52.5597	1.76478	0.882390	−	0.470518i	$-0.155933\pi$
$887$	52.5597	1.76478	0.882390	+	0.470518i	$0.155933\pi$
$888$	−23.6630	−0.794077
$889$	−58.6649	−1.96756
$890$	−2.81389	−0.0943217
$891$	0.166397	0.00557449
$892$	59.3581	1.98746
$893$	−53.1809	−1.77963
$894$	40.8761	1.36710
$895$	12.3274	0.412058
$896$	78.3644	2.61797
$897$	9.61049	0.320885
$898$	39.4517	1.31652
$899$	−18.6680	−0.622612
$900$	−38.2506	−1.27502
$901$	3.91025	0.130269
$902$	51.0807	1.70080
$903$	−14.7803	−0.491858
$904$	67.6257	2.24920
$905$	2.39914	0.0797502
$906$	17.3026	0.574840
$907$	−28.2366	−0.937581	−0.468791	−	0.883309i	$-0.655310\pi$
$907$	−28.2366	−0.937581	−0.468791	+	0.883309i	$0.655310\pi$
$908$	−18.1536	−0.602447
$909$	0.745665	0.0247321
$910$	−29.8453	−0.989362
$911$	−15.1339	−0.501409	−0.250704	−	0.968064i	$-0.580662\pi$
$911$	−15.1339	−0.501409	−0.250704	+	0.968064i	$0.580662\pi$
$912$	−9.12823	−0.302266
$913$	−7.78823	−0.257753
$914$	−15.0903	−0.499144
$915$	−38.8965	−1.28588
$916$	−46.5311	−1.53743
$917$	−9.20263	−0.303898
$918$	7.00156	0.231086
$919$	−58.4891	−1.92938	−0.964689	−	0.263390i	$-0.915159\pi$
$919$	−58.4891	−1.92938	−0.964689	+	0.263390i	$0.915159\pi$
$920$	−106.045	−3.49620
$921$	−16.4244	−0.541201
$922$	0.348790	0.0114868
$923$	1.60879	0.0529540
$924$	−46.3265	−1.52403
$925$	35.9813	1.18306
$926$	30.7080	1.00913
$927$	1.84628	0.0606398
$928$	29.0742	0.954406
$929$	−51.7097	−1.69654	−0.848269	−	0.529565i	$-0.822355\pi$
$929$	−51.7097	−1.69654	−0.848269	+	0.529565i	$0.822355\pi$
$930$	20.9053	0.685510
$931$	−47.6499	−1.56166
$932$	−70.6510	−2.31425
$933$	−9.93619	−0.325296
$934$	11.3431	0.371158
$935$	−5.98807	−0.195831
$936$	6.63677	0.216930
$937$	−13.3445	−0.435944	−0.217972	−	0.975955i	$-0.569944\pi$
$937$	−13.3445	−0.435944	−0.217972	+	0.975955i	$0.569944\pi$
$938$	−119.273	−3.89440
$939$	19.6789	0.642197
$940$	101.547	3.31209
$941$	−30.2618	−0.986507	−0.493253	−	0.869886i	$-0.664192\pi$
$941$	−30.2618	−0.986507	−0.493253	+	0.869886i	$0.664192\pi$
$942$	36.6909	1.19545
$943$	61.2221	1.99366
$944$	−13.1377	−0.427597
$945$	−66.0724	−2.14934
$946$	−26.6840	−0.867572
$947$	−33.0810	−1.07499	−0.537494	−	0.843268i	$-0.680629\pi$
$947$	−33.0810	−1.07499	−0.537494	+	0.843268i	$0.680629\pi$
$948$	−17.6613	−0.573612
$949$	7.15707	0.232328
$950$	84.1165	2.72910
$951$	−26.8360	−0.870216
$952$	−7.91601	−0.256559
$953$	−46.2741	−1.49896	−0.749482	−	0.662024i	$-0.769698\pi$
$953$	−46.2741	−1.49896	−0.749482	+	0.662024i	$0.769698\pi$
$954$	29.6753	0.960773
$955$	13.6244	0.440875
$956$	−74.4100	−2.40659
$957$	−25.3584	−0.819721
$958$	15.3214	0.495013
$959$	26.5165	0.856264
$960$	−42.4373	−1.36966
$961$	−24.6975	−0.796695
$962$	−14.4103	−0.464608
$963$	−8.84762	−0.285111
$964$	−81.4142	−2.62218
$965$	−23.0461	−0.741879
$966$	−86.9932	−2.79896
$967$	−7.17593	−0.230762	−0.115381	−	0.993321i	$-0.536809\pi$
$967$	−7.17593	−0.230762	−0.115381	+	0.993321i	$0.536809\pi$
$968$	3.30731	0.106301
$969$	−3.74388	−0.120271
$970$	21.2483	0.682242
$971$	6.61245	0.212204	0.106102	−	0.994355i	$-0.466163\pi$
$971$	6.61245	0.212204	0.106102	+	0.994355i	$0.466163\pi$
$972$	54.9080	1.76118
$973$	41.0717	1.31670
$974$	−40.7742	−1.30649
$975$	6.30619	0.201960
$976$	−15.3183	−0.490328
$977$	1.31793	0.0421644	0.0210822	−	0.999778i	$-0.493289\pi$
$977$	1.31793	0.0421644	0.0210822	+	0.999778i	$0.493289\pi$
$978$	−33.7483	−1.07915
$979$	−1.15235	−0.0368293
$980$	90.9856	2.90643
$981$	−27.2926	−0.871387
$982$	90.1608	2.87715
$983$	42.3545	1.35090	0.675449	−	0.737407i	$-0.263950\pi$
$983$	42.3545	1.35090	0.675449	+	0.737407i	$0.263950\pi$
$984$	−26.4194	−0.842218
$985$	71.7297	2.28550
$986$	−10.0018	−0.318523
$987$	36.0895	1.14874
$988$	−21.5018	−0.684062
$989$	−31.9818	−1.01696
$990$	−45.4441	−1.44431
$991$	35.7721	1.13634	0.568170	−	0.822911i	$-0.307652\pi$
$991$	35.7721	1.13634	0.568170	+	0.822911i	$0.307652\pi$
$992$	−9.81565	−0.311647
$993$	17.4579	0.554010
$994$	−14.5626	−0.461899
$995$	−24.9072	−0.789611
$996$	9.29789	0.294615
$997$	−42.1811	−1.33589	−0.667945	−	0.744211i	$-0.732826\pi$
$997$	−42.1811	−1.33589	−0.667945	+	0.744211i	$0.732826\pi$
$998$	−80.6932	−2.55430
$999$	−31.9020	−1.00934

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.f.1.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.f.1.3	✓	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q-2.35134 q^{2} +1.07411 q^{3} +3.52878 q^{4} +3.29713 q^{5} -2.52560 q^{6} +3.84969 q^{7} -3.59467 q^{8} -1.84628 q^{9} +O(q^{10})\)	\(q-2.35134 q^{2} +1.07411 q^{3} +3.52878 q^{4} +3.29713 q^{5} -2.52560 q^{6} +3.84969 q^{7} -3.59467 q^{8} -1.84628 q^{9} -7.75266 q^{10} -3.17489 q^{11} +3.79031 q^{12} +1.00000 q^{13} -9.05191 q^{14} +3.54149 q^{15} +1.39472 q^{16} +0.572034 q^{17} +4.34122 q^{18} -6.09326 q^{19} +11.6348 q^{20} +4.13500 q^{21} +7.46524 q^{22} +8.94736 q^{23} -3.86108 q^{24} +5.87106 q^{25} -2.35134 q^{26} -5.20546 q^{27} +13.5847 q^{28} +7.43606 q^{29} -8.32724 q^{30} -2.51047 q^{31} +3.90989 q^{32} -3.41019 q^{33} -1.34504 q^{34} +12.6929 q^{35} -6.51511 q^{36} +6.12858 q^{37} +14.3273 q^{38} +1.07411 q^{39} -11.8521 q^{40} +6.84247 q^{41} -9.72278 q^{42} -3.57444 q^{43} -11.2035 q^{44} -6.08742 q^{45} -21.0383 q^{46} +8.72782 q^{47} +1.49809 q^{48} +7.82010 q^{49} -13.8048 q^{50} +0.614429 q^{51} +3.52878 q^{52} +6.83570 q^{53} +12.2398 q^{54} -10.4680 q^{55} -13.8384 q^{56} -6.54485 q^{57} -17.4847 q^{58} -9.41964 q^{59} +12.4971 q^{60} -10.9831 q^{61} +5.90295 q^{62} -7.10760 q^{63} -11.9829 q^{64} +3.29713 q^{65} +8.01851 q^{66} +13.1766 q^{67} +2.01858 q^{68} +9.61049 q^{69} -29.8453 q^{70} +1.60879 q^{71} +6.63677 q^{72} +7.15707 q^{73} -14.4103 q^{74} +6.30619 q^{75} -21.5018 q^{76} -12.2223 q^{77} -2.52560 q^{78} -4.65959 q^{79} +4.59857 q^{80} -0.0524101 q^{81} -16.0889 q^{82} +2.45307 q^{83} +14.5915 q^{84} +1.88607 q^{85} +8.40470 q^{86} +7.98717 q^{87} +11.4127 q^{88} +0.362958 q^{89} +14.3136 q^{90} +3.84969 q^{91} +31.5733 q^{92} -2.69653 q^{93} -20.5220 q^{94} -20.0903 q^{95} +4.19966 q^{96} -2.74078 q^{97} -18.3877 q^{98} +5.86174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9}+O(q^{10}) \) 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9} + 5 q^{10} + 9 q^{11} + 15 q^{12} + 28 q^{13} + 20 q^{14} + 4 q^{15} + 32 q^{16} - 7 q^{17} + 10 q^{18} - 3 q^{19} + 53 q^{20} + 25 q^{21} - 14 q^{22} - 6 q^{23} + 10 q^{24} + 45 q^{25} + 6 q^{26} + 8 q^{27} - 12 q^{28} + 25 q^{29} - 43 q^{30} + q^{31} + 28 q^{32} + 17 q^{33} + 10 q^{34} + 11 q^{35} + 27 q^{36} + 18 q^{37} + 2 q^{38} + 5 q^{39} + 37 q^{40} + 56 q^{41} - 29 q^{42} - 30 q^{43} + 30 q^{44} + 38 q^{45} - 27 q^{46} + 40 q^{47} + 19 q^{48} + 36 q^{49} + 20 q^{50} - 18 q^{51} + 32 q^{52} + 51 q^{53} - 36 q^{54} - 5 q^{55} - 13 q^{56} + 31 q^{57} - 29 q^{58} + 29 q^{59} + 48 q^{60} + 16 q^{61} - 38 q^{62} - 23 q^{63} - 5 q^{64} + 27 q^{65} + 25 q^{66} - 2 q^{67} - 43 q^{68} + 38 q^{69} + 10 q^{70} + 34 q^{71} - 28 q^{72} + 14 q^{73} + 21 q^{74} + 19 q^{75} + 5 q^{76} + 34 q^{77} + 9 q^{78} + 3 q^{79} + 58 q^{80} + 4 q^{81} - 9 q^{82} + 38 q^{83} - 78 q^{84} - 27 q^{85} + 49 q^{86} + 8 q^{87} - 25 q^{88} + 125 q^{89} - 74 q^{90} + 6 q^{91} - 35 q^{92} + 36 q^{93} - q^{94} - 12 q^{95} + 26 q^{96} - 2 q^{97} + 18 q^{98} + 56 q^{99}+O(q^{100}) \) 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9 + 5 * q^10 + 9 * q^11 + 15 * q^12 + 28 * q^13 + 20 * q^14 + 4 * q^15 + 32 * q^16 - 7 * q^17 + 10 * q^18 - 3 * q^19 + 53 * q^20 + 25 * q^21 - 14 * q^22 - 6 * q^23 + 10 * q^24 + 45 * q^25 + 6 * q^26 + 8 * q^27 - 12 * q^28 + 25 * q^29 - 43 * q^30 + q^31 + 28 * q^32 + 17 * q^33 + 10 * q^34 + 11 * q^35 + 27 * q^36 + 18 * q^37 + 2 * q^38 + 5 * q^39 + 37 * q^40 + 56 * q^41 - 29 * q^42 - 30 * q^43 + 30 * q^44 + 38 * q^45 - 27 * q^46 + 40 * q^47 + 19 * q^48 + 36 * q^49 + 20 * q^50 - 18 * q^51 + 32 * q^52 + 51 * q^53 - 36 * q^54 - 5 * q^55 - 13 * q^56 + 31 * q^57 - 29 * q^58 + 29 * q^59 + 48 * q^60 + 16 * q^61 - 38 * q^62 - 23 * q^63 - 5 * q^64 + 27 * q^65 + 25 * q^66 - 2 * q^67 - 43 * q^68 + 38 * q^69 + 10 * q^70 + 34 * q^71 - 28 * q^72 + 14 * q^73 + 21 * q^74 + 19 * q^75 + 5 * q^76 + 34 * q^77 + 9 * q^78 + 3 * q^79 + 58 * q^80 + 4 * q^81 - 9 * q^82 + 38 * q^83 - 78 * q^84 - 27 * q^85 + 49 * q^86 + 8 * q^87 - 25 * q^88 + 125 * q^89 - 74 * q^90 + 6 * q^91 - 35 * q^92 + 36 * q^93 - q^94 - 12 * q^95 + 26 * q^96 - 2 * q^97 + 18 * q^98 + 56 * q^99

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