LMFDB - Embedded newform 1339.2.a.f.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.50096 q^{2} +2.99924 q^{3} +4.25481 q^{4} +4.07294 q^{5} -7.50098 q^{6} -1.09357 q^{7} -5.63921 q^{8} +5.99543 q^{9} +O(q^{10})$	\(q-2.50096 q^{2} +2.99924 q^{3} +4.25481 q^{4} +4.07294 q^{5} -7.50098 q^{6} -1.09357 q^{7} -5.63921 q^{8} +5.99543 q^{9} -10.1863 q^{10} +3.69645 q^{11} +12.7612 q^{12} +1.00000 q^{13} +2.73497 q^{14} +12.2157 q^{15} +5.59382 q^{16} -6.18952 q^{17} -14.9944 q^{18} -0.160967 q^{19} +17.3296 q^{20} -3.27987 q^{21} -9.24469 q^{22} -4.76439 q^{23} -16.9133 q^{24} +11.5889 q^{25} -2.50096 q^{26} +8.98402 q^{27} -4.65293 q^{28} -5.14569 q^{29} -30.5511 q^{30} +6.88459 q^{31} -2.71152 q^{32} +11.0865 q^{33} +15.4798 q^{34} -4.45404 q^{35} +25.5095 q^{36} -5.59797 q^{37} +0.402572 q^{38} +2.99924 q^{39} -22.9682 q^{40} +11.0728 q^{41} +8.20283 q^{42} -4.47298 q^{43} +15.7277 q^{44} +24.4191 q^{45} +11.9156 q^{46} +8.77010 q^{47} +16.7772 q^{48} -5.80411 q^{49} -28.9833 q^{50} -18.5639 q^{51} +4.25481 q^{52} +0.346274 q^{53} -22.4687 q^{54} +15.0554 q^{55} +6.16686 q^{56} -0.482777 q^{57} +12.8692 q^{58} +6.68172 q^{59} +51.9757 q^{60} +8.34773 q^{61} -17.2181 q^{62} -6.55641 q^{63} -4.40623 q^{64} +4.07294 q^{65} -27.7270 q^{66} -9.72242 q^{67} -26.3353 q^{68} -14.2896 q^{69} +11.1394 q^{70} -9.43799 q^{71} -33.8095 q^{72} -13.7985 q^{73} +14.0003 q^{74} +34.7578 q^{75} -0.684883 q^{76} -4.04232 q^{77} -7.50098 q^{78} -2.33254 q^{79} +22.7833 q^{80} +8.95892 q^{81} -27.6926 q^{82} +1.69204 q^{83} -13.9552 q^{84} -25.2096 q^{85} +11.1867 q^{86} -15.4331 q^{87} -20.8451 q^{88} -10.1464 q^{89} -61.0712 q^{90} -1.09357 q^{91} -20.2716 q^{92} +20.6485 q^{93} -21.9337 q^{94} -0.655608 q^{95} -8.13249 q^{96} -1.94543 q^{97} +14.5159 q^{98} +22.1618 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.50096	−1.76845	−0.884224	−	0.467063i	$-0.845312\pi$
$2$	−2.50096	−1.76845	−0.884224	+	0.467063i	$0.845312\pi$
$3$	2.99924	1.73161	0.865806	−	0.500380i	$-0.166807\pi$
$3$	2.99924	1.73161	0.865806	+	0.500380i	$0.166807\pi$
$4$	4.25481	2.12741
$5$	4.07294	1.82148	0.910738	−	0.412985i	$-0.135514\pi$
$5$	4.07294	1.82148	0.910738	+	0.412985i	$0.135514\pi$
$6$	−7.50098	−3.06226
$7$	−1.09357	−0.413330	−0.206665	−	0.978412i	$-0.566261\pi$
$7$	−1.09357	−0.413330	−0.206665	+	0.978412i	$0.566261\pi$
$8$	−5.63921	−1.99376
$9$	5.99543	1.99848
$10$	−10.1863	−3.22118
$11$	3.69645	1.11452	0.557261	−	0.830337i	$-0.311852\pi$
$11$	3.69645	1.11452	0.557261	+	0.830337i	$0.311852\pi$
$12$	12.7612	3.68384
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.73497	0.730952
$15$	12.2157	3.15409
$16$	5.59382	1.39845
$17$	−6.18952	−1.50118	−0.750590	−	0.660768i	$-0.770231\pi$
$17$	−6.18952	−1.50118	−0.750590	+	0.660768i	$0.770231\pi$
$18$	−14.9944	−3.53420
$19$	−0.160967	−0.0369283	−0.0184641	−	0.999830i	$-0.505878\pi$
$19$	−0.160967	−0.0369283	−0.0184641	+	0.999830i	$0.505878\pi$
$20$	17.3296	3.87502
$21$	−3.27987	−0.715726
$22$	−9.24469	−1.97097
$23$	−4.76439	−0.993445	−0.496722	−	0.867910i	$-0.665463\pi$
$23$	−4.76439	−0.993445	−0.496722	+	0.867910i	$0.665463\pi$
$24$	−16.9133	−3.45242
$25$	11.5889	2.31777
$26$	−2.50096	−0.490479
$27$	8.98402	1.72898
$28$	−4.65293	−0.879321
$29$	−5.14569	−0.955530	−0.477765	−	0.878488i	$-0.658553\pi$
$29$	−5.14569	−0.955530	−0.477765	+	0.878488i	$0.658553\pi$
$30$	−30.5511	−5.57784
$31$	6.88459	1.23651	0.618254	−	0.785978i	$-0.287840\pi$
$31$	6.88459	1.23651	0.618254	+	0.785978i	$0.287840\pi$
$32$	−2.71152	−0.479333
$33$	11.0865	1.92992
$34$	15.4798	2.65476
$35$	−4.45404	−0.752870
$36$	25.5095	4.25158
$37$	−5.59797	−0.920300	−0.460150	−	0.887841i	$-0.652204\pi$
$37$	−5.59797	−0.920300	−0.460150	+	0.887841i	$0.652204\pi$
$38$	0.402572	0.0653057
$39$	2.99924	0.480263
$40$	−22.9682	−3.63159
$41$	11.0728	1.72928	0.864638	−	0.502396i	$-0.167548\pi$
$41$	11.0728	1.72928	0.864638	+	0.502396i	$0.167548\pi$
$42$	8.20283	1.26572
$43$	−4.47298	−0.682122	−0.341061	−	0.940041i	$-0.610786\pi$
$43$	−4.47298	−0.682122	−0.341061	+	0.940041i	$0.610786\pi$
$44$	15.7277	2.37104
$45$	24.4191	3.64018
$46$	11.9156	1.75685
$47$	8.77010	1.27925	0.639626	−	0.768687i	$-0.279089\pi$
$47$	8.77010	1.27925	0.639626	+	0.768687i	$0.279089\pi$
$48$	16.7772	2.42158
$49$	−5.80411	−0.829159
$50$	−28.9833	−4.09886
$51$	−18.5639	−2.59946
$52$	4.25481	0.590037
$53$	0.346274	0.0475643	0.0237822	−	0.999717i	$-0.492429\pi$
$53$	0.346274	0.0475643	0.0237822	+	0.999717i	$0.492429\pi$
$54$	−22.4687	−3.05760
$55$	15.0554	2.03007
$56$	6.16686	0.824081
$57$	−0.482777	−0.0639454
$58$	12.8692	1.68981
$59$	6.68172	0.869886	0.434943	−	0.900458i	$-0.356768\pi$
$59$	6.68172	0.869886	0.434943	+	0.900458i	$0.356768\pi$
$60$	51.9757	6.71003
$61$	8.34773	1.06882	0.534409	−	0.845226i	$-0.320534\pi$
$61$	8.34773	1.06882	0.534409	+	0.845226i	$0.320534\pi$
$62$	−17.2181	−2.18670
$63$	−6.55641	−0.826030
$64$	−4.40623	−0.550779
$65$	4.07294	0.505186
$66$	−27.7270	−3.41296
$67$	−9.72242	−1.18778	−0.593891	−	0.804545i	$-0.702409\pi$
$67$	−9.72242	−1.18778	−0.593891	+	0.804545i	$0.702409\pi$
$68$	−26.3353	−3.19362
$69$	−14.2896	−1.72026
$70$	11.1394	1.33141
$71$	−9.43799	−1.12008	−0.560042	−	0.828464i	$-0.689215\pi$
$71$	−9.43799	−1.12008	−0.560042	+	0.828464i	$0.689215\pi$
$72$	−33.8095	−3.98449
$73$	−13.7985	−1.61499	−0.807495	−	0.589874i	$-0.799177\pi$
$73$	−13.7985	−1.61499	−0.807495	+	0.589874i	$0.799177\pi$
$74$	14.0003	1.62750
$75$	34.7578	4.01348
$76$	−0.684883	−0.0785615
$77$	−4.04232	−0.460665
$78$	−7.50098	−0.849319
$79$	−2.33254	−0.262432	−0.131216	−	0.991354i	$-0.541888\pi$
$79$	−2.33254	−0.262432	−0.131216	+	0.991354i	$0.541888\pi$
$80$	22.7833	2.54725
$81$	8.95892	0.995435
$82$	−27.6926	−3.05813
$83$	1.69204	0.185726	0.0928630	−	0.995679i	$-0.470398\pi$
$83$	1.69204	0.185726	0.0928630	+	0.995679i	$0.470398\pi$
$84$	−13.9552	−1.52264
$85$	−25.2096	−2.73436
$86$	11.1867	1.20630
$87$	−15.4331	−1.65461
$88$	−20.8451	−2.22209
$89$	−10.1464	−1.07551	−0.537756	−	0.843100i	$-0.680728\pi$
$89$	−10.1464	−1.07551	−0.537756	+	0.843100i	$0.680728\pi$
$90$	−61.0712	−6.43746
$91$	−1.09357	−0.114637
$92$	−20.2716	−2.11346
$93$	20.6485	2.14115
$94$	−21.9337	−2.26229
$95$	−0.655608	−0.0672640
$96$	−8.13249	−0.830019
$97$	−1.94543	−0.197528	−0.0987641	−	0.995111i	$-0.531489\pi$
$97$	−1.94543	−0.197528	−0.0987641	+	0.995111i	$0.531489\pi$
$98$	14.5159	1.46632
$99$	22.1618	2.22735
$100$	49.3085	4.93085
$101$	10.7952	1.07416	0.537079	−	0.843532i	$-0.319528\pi$
$101$	10.7952	1.07416	0.537079	+	0.843532i	$0.319528\pi$
$102$	46.4275	4.59701
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−5.63921	−0.552970
$105$	−13.3587	−1.30368
$106$	−0.866017	−0.0841150
$107$	11.1157	1.07459	0.537296	−	0.843394i	$-0.319446\pi$
$107$	11.1157	1.07459	0.537296	+	0.843394i	$0.319446\pi$
$108$	38.2253	3.67823
$109$	−7.25876	−0.695263	−0.347632	−	0.937631i	$-0.613014\pi$
$109$	−7.25876	−0.695263	−0.347632	+	0.937631i	$0.613014\pi$
$110$	−37.6531	−3.59008
$111$	−16.7896	−1.59360
$112$	−6.11722	−0.578023
$113$	−3.93235	−0.369924	−0.184962	−	0.982746i	$-0.559216\pi$
$113$	−3.93235	−0.369924	−0.184962	+	0.982746i	$0.559216\pi$
$114$	1.20741	0.113084
$115$	−19.4051	−1.80954
$116$	−21.8939	−2.03280
$117$	5.99543	0.554278
$118$	−16.7107	−1.53835
$119$	6.76866	0.620482
$120$	−68.8870	−6.28850
$121$	2.66375	0.242159
$122$	−20.8774	−1.89015
$123$	33.2099	2.99443
$124$	29.2926	2.63056
$125$	26.8361	2.40029
$126$	16.3973	1.46079
$127$	−9.34191	−0.828960	−0.414480	−	0.910058i	$-0.636037\pi$
$127$	−9.34191	−0.828960	−0.414480	+	0.910058i	$0.636037\pi$
$128$	16.4429	1.45336
$129$	−13.4155	−1.18117
$130$	−10.1863	−0.893396
$131$	6.59312	0.576044	0.288022	−	0.957624i	$-0.407002\pi$
$131$	6.59312	0.576044	0.288022	+	0.957624i	$0.407002\pi$
$132$	47.1712	4.10572
$133$	0.176028	0.0152636
$134$	24.3154	2.10053
$135$	36.5914	3.14929
$136$	34.9040	2.99299
$137$	−12.4061	−1.05993	−0.529964	−	0.848020i	$-0.677794\pi$
$137$	−12.4061	−1.05993	−0.529964	+	0.848020i	$0.677794\pi$
$138$	35.7376	3.04219
$139$	−23.2414	−1.97131	−0.985656	−	0.168769i	$-0.946021\pi$
$139$	−23.2414	−1.97131	−0.985656	+	0.168769i	$0.946021\pi$
$140$	−18.9511	−1.60166
$141$	26.3036	2.21517
$142$	23.6041	1.98081
$143$	3.69645	0.309113
$144$	33.5374	2.79478
$145$	−20.9581	−1.74047
$146$	34.5095	2.85603
$147$	−17.4079	−1.43578
$148$	−23.8183	−1.95785
$149$	17.9910	1.47388	0.736942	−	0.675956i	$-0.236269\pi$
$149$	17.9910	1.47388	0.736942	+	0.675956i	$0.236269\pi$
$150$	−86.9279	−7.09763
$151$	3.36836	0.274113	0.137056	−	0.990563i	$-0.456236\pi$
$151$	3.36836	0.274113	0.137056	+	0.990563i	$0.456236\pi$
$152$	0.907725	0.0736262
$153$	−37.1089	−3.00007
$154$	10.1097	0.814662
$155$	28.0405	2.25227
$156$	12.7612	1.02171
$157$	3.80262	0.303482	0.151741	−	0.988420i	$-0.451512\pi$
$157$	3.80262	0.303482	0.151741	+	0.988420i	$0.451512\pi$
$158$	5.83360	0.464097
$159$	1.03856	0.0823629
$160$	−11.0439	−0.873094
$161$	5.21019	0.410620
$162$	−22.4059	−1.76038
$163$	2.31381	0.181232	0.0906158	−	0.995886i	$-0.471116\pi$
$163$	2.31381	0.181232	0.0906158	+	0.995886i	$0.471116\pi$
$164$	47.1126	3.67887
$165$	45.1548	3.51530
$166$	−4.23174	−0.328447
$167$	−21.9694	−1.70004	−0.850022	−	0.526747i	$-0.823411\pi$
$167$	−21.9694	−1.70004	−0.850022	+	0.526747i	$0.823411\pi$
$168$	18.4959	1.42699
$169$	1.00000	0.0769231
$170$	63.0482	4.83558
$171$	−0.965065	−0.0738004
$172$	−19.0317	−1.45115
$173$	7.79937	0.592975	0.296488	−	0.955037i	$-0.404185\pi$
$173$	7.79937	0.592975	0.296488	+	0.955037i	$0.404185\pi$
$174$	38.5977	2.92609
$175$	−12.6732	−0.958004
$176$	20.6773	1.55861
$177$	20.0401	1.50630
$178$	25.3757	1.90199
$179$	−12.9199	−0.965682	−0.482841	−	0.875708i	$-0.660395\pi$
$179$	−12.9199	−0.965682	−0.482841	+	0.875708i	$0.660395\pi$
$180$	103.899	7.74414
$181$	5.84633	0.434554	0.217277	−	0.976110i	$-0.430282\pi$
$181$	5.84633	0.434554	0.217277	+	0.976110i	$0.430282\pi$
$182$	2.73497	0.202730
$183$	25.0368	1.85078
$184$	26.8674	1.98069
$185$	−22.8002	−1.67630
$186$	−51.6412	−3.78652
$187$	−22.8793	−1.67310
$188$	37.3152	2.72149
$189$	−9.82463	−0.714637
$190$	1.63965	0.118953
$191$	−17.8034	−1.28821	−0.644106	−	0.764936i	$-0.722770\pi$
$191$	−17.8034	−1.28821	−0.644106	+	0.764936i	$0.722770\pi$
$192$	−13.2153	−0.953735
$193$	25.3223	1.82274	0.911371	−	0.411585i	$-0.135025\pi$
$193$	25.3223	1.82274	0.911371	+	0.411585i	$0.135025\pi$
$194$	4.86544	0.349318
$195$	12.2157	0.874786
$196$	−24.6954	−1.76396
$197$	13.4677	0.959531	0.479766	−	0.877397i	$-0.340722\pi$
$197$	13.4677	0.959531	0.479766	+	0.877397i	$0.340722\pi$
$198$	−55.4259	−3.93895
$199$	8.56432	0.607108	0.303554	−	0.952814i	$-0.401827\pi$
$199$	8.56432	0.607108	0.303554	+	0.952814i	$0.401827\pi$
$200$	−65.3520	−4.62109
$201$	−29.1598	−2.05678
$202$	−26.9983	−1.89959
$203$	5.62716	0.394949
$204$	−78.9858	−5.53011
$205$	45.0987	3.14983
$206$	2.50096	0.174250
$207$	−28.5646	−1.98538
$208$	5.59382	0.387862
$209$	−0.595005	−0.0411574
$210$	33.4097	2.30549
$211$	−10.4692	−0.720727	−0.360363	−	0.932812i	$-0.617347\pi$
$211$	−10.4692	−0.720727	−0.360363	+	0.932812i	$0.617347\pi$
$212$	1.47333	0.101189
$213$	−28.3068	−1.93955
$214$	−27.7998	−1.90036
$215$	−18.2182	−1.24247
$216$	−50.6627	−3.44716
$217$	−7.52876	−0.511086
$218$	18.1539	1.22954
$219$	−41.3850	−2.79654
$220$	64.0581	4.31879
$221$	−6.18952	−0.416352
$222$	41.9903	2.81820
$223$	5.88428	0.394041	0.197020	−	0.980399i	$-0.436873\pi$
$223$	5.88428	0.394041	0.197020	+	0.980399i	$0.436873\pi$
$224$	2.96523	0.198123
$225$	69.4803	4.63202
$226$	9.83465	0.654191
$227$	−6.63392	−0.440309	−0.220154	−	0.975465i	$-0.570656\pi$
$227$	−6.63392	−0.440309	−0.220154	+	0.975465i	$0.570656\pi$
$228$	−2.05413	−0.136038
$229$	−9.55310	−0.631287	−0.315643	−	0.948878i	$-0.602220\pi$
$229$	−9.55310	−0.631287	−0.315643	+	0.948878i	$0.602220\pi$
$230$	48.5314	3.20007
$231$	−12.1239	−0.797693
$232$	29.0176	1.90510
$233$	3.24405	0.212525	0.106262	−	0.994338i	$-0.466112\pi$
$233$	3.24405	0.212525	0.106262	+	0.994338i	$0.466112\pi$
$234$	−14.9944	−0.980212
$235$	35.7201	2.33012
$236$	28.4295	1.85060
$237$	−6.99585	−0.454430
$238$	−16.9282	−1.09729
$239$	19.5076	1.26184	0.630921	−	0.775847i	$-0.282677\pi$
$239$	19.5076	1.26184	0.630921	+	0.775847i	$0.282677\pi$
$240$	68.3326	4.41085
$241$	−4.11036	−0.264772	−0.132386	−	0.991198i	$-0.542264\pi$
$241$	−4.11036	−0.264772	−0.132386	+	0.991198i	$0.542264\pi$
$242$	−6.66194	−0.428245
$243$	−0.0821253	−0.00526834
$244$	35.5181	2.27381
$245$	−23.6398	−1.51029
$246$	−83.0566	−5.29550
$247$	−0.160967	−0.0102421
$248$	−38.8236	−2.46530
$249$	5.07485	0.321605
$250$	−67.1160	−4.24479
$251$	2.74675	0.173373	0.0866866	−	0.996236i	$-0.472372\pi$
$251$	2.74675	0.173373	0.0866866	+	0.996236i	$0.472372\pi$
$252$	−27.8963	−1.75730
$253$	−17.6113	−1.10722
$254$	23.3638	1.46597
$255$	−75.6095	−4.73485
$256$	−32.3105	−2.01941
$257$	19.8461	1.23797	0.618984	−	0.785404i	$-0.287545\pi$
$257$	19.8461	1.23797	0.618984	+	0.785404i	$0.287545\pi$
$258$	33.5517	2.08884
$259$	6.12176	0.380388
$260$	17.3296	1.07474
$261$	−30.8506	−1.90961
$262$	−16.4891	−1.01870
$263$	25.6996	1.58471	0.792354	−	0.610062i	$-0.208856\pi$
$263$	25.6996	1.58471	0.792354	+	0.610062i	$0.208856\pi$
$264$	−62.5193	−3.84780
$265$	1.41035	0.0866373
$266$	−0.440239	−0.0269928
$267$	−30.4314	−1.86237
$268$	−41.3671	−2.52690
$269$	27.2848	1.66358	0.831792	−	0.555088i	$-0.187315\pi$
$269$	27.2848	1.66358	0.831792	+	0.555088i	$0.187315\pi$
$270$	−91.5137	−5.56935
$271$	−30.7936	−1.87058	−0.935289	−	0.353886i	$-0.884860\pi$
$271$	−30.7936	−1.87058	−0.935289	+	0.353886i	$0.884860\pi$
$272$	−34.6231	−2.09933
$273$	−3.27987	−0.198507
$274$	31.0273	1.87443
$275$	42.8377	2.58321
$276$	−60.7994	−3.65969
$277$	−18.0346	−1.08359	−0.541797	−	0.840509i	$-0.682256\pi$
$277$	−18.0346	−1.08359	−0.541797	+	0.840509i	$0.682256\pi$
$278$	58.1259	3.48616
$279$	41.2761	2.47113
$280$	25.1173	1.50104
$281$	20.8548	1.24409	0.622047	−	0.782980i	$-0.286301\pi$
$281$	20.8548	1.24409	0.622047	+	0.782980i	$0.286301\pi$
$282$	−65.7844	−3.91741
$283$	−24.9490	−1.48307	−0.741533	−	0.670916i	$-0.765901\pi$
$283$	−24.9490	−1.48307	−0.741533	+	0.670916i	$0.765901\pi$
$284$	−40.1569	−2.38287
$285$	−1.96633	−0.116475
$286$	−9.24469	−0.546650
$287$	−12.1088	−0.714761
$288$	−16.2567	−0.957937
$289$	21.3102	1.25354
$290$	52.4154	3.07794
$291$	−5.83480	−0.342042
$292$	−58.7100	−3.43574
$293$	23.3744	1.36555	0.682774	−	0.730630i	$-0.260774\pi$
$293$	23.3744	1.36555	0.682774	+	0.730630i	$0.260774\pi$
$294$	43.5365	2.53910
$295$	27.2143	1.58448
$296$	31.5681	1.83486
$297$	33.2090	1.92698
$298$	−44.9949	−2.60649
$299$	−4.76439	−0.275532
$300$	147.888	8.53831
$301$	4.89150	0.281941
$302$	−8.42414	−0.484755
$303$	32.3773	1.86003
$304$	−0.900419	−0.0516425
$305$	33.9998	1.94683
$306$	92.8079	5.30548
$307$	10.5409	0.601603	0.300801	−	0.953687i	$-0.402746\pi$
$307$	10.5409	0.601603	0.300801	+	0.953687i	$0.402746\pi$
$308$	−17.1993	−0.980022
$309$	−2.99924	−0.170621
$310$	−70.1283	−3.98302
$311$	−5.94134	−0.336903	−0.168451	−	0.985710i	$-0.553877\pi$
$311$	−5.94134	−0.336903	−0.168451	+	0.985710i	$0.553877\pi$
$312$	−16.9133	−0.957529
$313$	20.8312	1.17745	0.588723	−	0.808335i	$-0.299631\pi$
$313$	20.8312	1.17745	0.588723	+	0.808335i	$0.299631\pi$
$314$	−9.51022	−0.536693
$315$	−26.7039	−1.50459
$316$	−9.92454	−0.558299
$317$	−16.9244	−0.950570	−0.475285	−	0.879832i	$-0.657655\pi$
$317$	−16.9244	−0.950570	−0.475285	+	0.879832i	$0.657655\pi$
$318$	−2.59739	−0.145655
$319$	−19.0208	−1.06496
$320$	−17.9463	−1.00323
$321$	33.3385	1.86077
$322$	−13.0305	−0.726160
$323$	0.996307	0.0554360
$324$	38.1185	2.11770
$325$	11.5889	0.642835
$326$	−5.78675	−0.320499
$327$	−21.7708	−1.20393
$328$	−62.4416	−3.44776
$329$	−9.59070	−0.528753
$330$	−112.931	−6.21662
$331$	3.32474	0.182744	0.0913720	−	0.995817i	$-0.470875\pi$
$331$	3.32474	0.182744	0.0913720	+	0.995817i	$0.470875\pi$
$332$	7.19934	0.395115
$333$	−33.5622	−1.83920
$334$	54.9447	3.00644
$335$	−39.5988	−2.16352
$336$	−18.3470	−1.00091
$337$	19.0374	1.03703	0.518516	−	0.855068i	$-0.326485\pi$
$337$	19.0374	1.03703	0.518516	+	0.855068i	$0.326485\pi$
$338$	−2.50096	−0.136034
$339$	−11.7940	−0.640565
$340$	−107.262	−5.81710
$341$	25.4485	1.37812
$342$	2.41359	0.130512
$343$	14.0022	0.756046
$344$	25.2240	1.35999
$345$	−58.2005	−3.13341
$346$	−19.5059	−1.04865
$347$	−16.9833	−0.911712	−0.455856	−	0.890054i	$-0.650667\pi$
$347$	−16.9833	−0.911712	−0.455856	+	0.890054i	$0.650667\pi$
$348$	−65.6652	−3.52002
$349$	1.60919	0.0861379	0.0430690	−	0.999072i	$-0.486286\pi$
$349$	1.60919	0.0861379	0.0430690	+	0.999072i	$0.486286\pi$
$350$	31.6952	1.69418
$351$	8.98402	0.479531
$352$	−10.0230	−0.534228
$353$	−6.07436	−0.323305	−0.161653	−	0.986848i	$-0.551682\pi$
$353$	−6.07436	−0.323305	−0.161653	+	0.986848i	$0.551682\pi$
$354$	−50.1195	−2.66382
$355$	−38.4404	−2.04020
$356$	−43.1709	−2.28805
$357$	20.3008	1.07443
$358$	32.3123	1.70776
$359$	−34.1088	−1.80019	−0.900097	−	0.435690i	$-0.856504\pi$
$359$	−34.1088	−1.80019	−0.900097	+	0.435690i	$0.856504\pi$
$360$	−137.704	−7.25765
$361$	−18.9741	−0.998636
$362$	−14.6215	−0.768486
$363$	7.98922	0.419325
$364$	−4.65293	−0.243880
$365$	−56.2004	−2.94167
$366$	−62.6162	−3.27300
$367$	5.38423	0.281055	0.140527	−	0.990077i	$-0.455120\pi$
$367$	5.38423	0.281055	0.140527	+	0.990077i	$0.455120\pi$
$368$	−26.6512	−1.38929
$369$	66.3860	3.45592
$370$	57.0225	2.96446
$371$	−0.378674	−0.0196598
$372$	87.8556	4.55510
$373$	−1.14583	−0.0593288	−0.0296644	−	0.999560i	$-0.509444\pi$
$373$	−1.14583	−0.0593288	−0.0296644	+	0.999560i	$0.509444\pi$
$374$	57.2202	2.95879
$375$	80.4878	4.15637
$376$	−49.4564	−2.55052
$377$	−5.14569	−0.265016
$378$	24.5710	1.26380
$379$	17.6535	0.906800	0.453400	−	0.891307i	$-0.350211\pi$
$379$	17.6535	0.906800	0.453400	+	0.891307i	$0.350211\pi$
$380$	−2.78949	−0.143098
$381$	−28.0186	−1.43544
$382$	44.5258	2.27814
$383$	−14.7023	−0.751251	−0.375626	−	0.926771i	$-0.622572\pi$
$383$	−14.7023	−0.751251	−0.375626	+	0.926771i	$0.622572\pi$
$384$	49.3161	2.51665
$385$	−16.4641	−0.839090
$386$	−63.3302	−3.22342
$387$	−26.8174	−1.36321
$388$	−8.27743	−0.420223
$389$	−27.8711	−1.41312	−0.706561	−	0.707652i	$-0.749755\pi$
$389$	−27.8711	−1.41312	−0.706561	+	0.707652i	$0.749755\pi$
$390$	−30.5511	−1.54701
$391$	29.4893	1.49134
$392$	32.7306	1.65314
$393$	19.7743	0.997483
$394$	−33.6821	−1.69688
$395$	−9.50032	−0.478013
$396$	94.2945	4.73847
$397$	−13.5629	−0.680704	−0.340352	−	0.940298i	$-0.610546\pi$
$397$	−13.5629	−0.680704	−0.340352	+	0.940298i	$0.610546\pi$
$398$	−21.4190	−1.07364
$399$	0.527950	0.0264306
$400$	64.8260	3.24130
$401$	−9.86825	−0.492797	−0.246399	−	0.969169i	$-0.579247\pi$
$401$	−9.86825	−0.492797	−0.246399	+	0.969169i	$0.579247\pi$
$402$	72.9277	3.63730
$403$	6.88459	0.342946
$404$	45.9314	2.28517
$405$	36.4892	1.81316
$406$	−14.0733	−0.698447
$407$	−20.6926	−1.02570
$408$	104.685	5.18270
$409$	−34.5834	−1.71004	−0.855019	−	0.518597i	$-0.826455\pi$
$409$	−34.5834	−1.71004	−0.855019	+	0.518597i	$0.826455\pi$
$410$	−112.790	−5.57031
$411$	−37.2090	−1.83538
$412$	−4.25481	−0.209620
$413$	−7.30692	−0.359550
$414$	71.4390	3.51104
$415$	6.89160	0.338295
$416$	−2.71152	−0.132943
$417$	−69.7066	−3.41354
$418$	1.48809	0.0727847
$419$	15.1996	0.742549	0.371274	−	0.928523i	$-0.378921\pi$
$419$	15.1996	0.742549	0.371274	+	0.928523i	$0.378921\pi$
$420$	−56.8389	−2.77345
$421$	17.1175	0.834256	0.417128	−	0.908848i	$-0.363037\pi$
$421$	17.1175	0.834256	0.417128	+	0.908848i	$0.363037\pi$
$422$	26.1830	1.27457
$423$	52.5806	2.55655
$424$	−1.95271	−0.0948319
$425$	−71.7295	−3.47939
$426$	70.7942	3.42999
$427$	−9.12881	−0.441774
$428$	47.2951	2.28609
$429$	11.0865	0.535263
$430$	45.5630	2.19724
$431$	24.1326	1.16243	0.581213	−	0.813751i	$-0.302578\pi$
$431$	24.1326	1.16243	0.581213	+	0.813751i	$0.302578\pi$
$432$	50.2550	2.41789
$433$	−16.2723	−0.781996	−0.390998	−	0.920392i	$-0.627870\pi$
$433$	−16.2723	−0.781996	−0.390998	+	0.920392i	$0.627870\pi$
$434$	18.8292	0.903828
$435$	−62.8583	−3.01383
$436$	−30.8847	−1.47911
$437$	0.766909	0.0366862
$438$	103.502	4.94553
$439$	−17.3381	−0.827502	−0.413751	−	0.910390i	$-0.635782\pi$
$439$	−17.3381	−0.827502	−0.413751	+	0.910390i	$0.635782\pi$
$440$	−84.9007	−4.04748
$441$	−34.7981	−1.65705
$442$	15.4798	0.736297
$443$	19.7454	0.938132	0.469066	−	0.883163i	$-0.344591\pi$
$443$	19.7454	0.938132	0.469066	+	0.883163i	$0.344591\pi$
$444$	−71.4368	−3.39024
$445$	−41.3256	−1.95902
$446$	−14.7164	−0.696840
$447$	53.9594	2.55219
$448$	4.81851	0.227653
$449$	−2.28953	−0.108050	−0.0540248	−	0.998540i	$-0.517205\pi$
$449$	−2.28953	−0.108050	−0.0540248	+	0.998540i	$0.517205\pi$
$450$	−173.768	−8.19148
$451$	40.9299	1.92732
$452$	−16.7314	−0.786979
$453$	10.1025	0.474657
$454$	16.5912	0.778663
$455$	−4.45404	−0.208809
$456$	2.72248	0.127492
$457$	29.0390	1.35839	0.679193	−	0.733960i	$-0.262330\pi$
$457$	29.0390	1.35839	0.679193	+	0.733960i	$0.262330\pi$
$458$	23.8920	1.11640
$459$	−55.6068	−2.59550
$460$	−82.5651	−3.84962
$461$	3.72193	0.173347	0.0866737	−	0.996237i	$-0.472376\pi$
$461$	3.72193	0.173347	0.0866737	+	0.996237i	$0.472376\pi$
$462$	30.3214	1.41068
$463$	25.2682	1.17431	0.587157	−	0.809473i	$-0.300247\pi$
$463$	25.2682	1.17431	0.587157	+	0.809473i	$0.300247\pi$
$464$	−28.7840	−1.33627
$465$	84.1003	3.90006
$466$	−8.11325	−0.375839
$467$	−22.2997	−1.03191	−0.515954	−	0.856616i	$-0.672562\pi$
$467$	−22.2997	−1.03191	−0.515954	+	0.856616i	$0.672562\pi$
$468$	25.5095	1.17918
$469$	10.6321	0.490946
$470$	−89.3347	−4.12070
$471$	11.4050	0.525514
$472$	−37.6796	−1.73435
$473$	−16.5341	−0.760240
$474$	17.4964	0.803635
$475$	−1.86542	−0.0855914
$476$	28.7994	1.32002
$477$	2.07606	0.0950563
$478$	−48.7878	−2.23150
$479$	−7.29665	−0.333393	−0.166696	−	0.986008i	$-0.553310\pi$
$479$	−7.29665	−0.333393	−0.166696	+	0.986008i	$0.553310\pi$
$480$	−33.1232	−1.51186
$481$	−5.59797	−0.255245
$482$	10.2799	0.468235
$483$	15.6266	0.711035
$484$	11.3338	0.515171
$485$	−7.92361	−0.359793
$486$	0.205392	0.00931679
$487$	−8.31005	−0.376564	−0.188282	−	0.982115i	$-0.560292\pi$
$487$	−8.31005	−0.376564	−0.188282	+	0.982115i	$0.560292\pi$
$488$	−47.0746	−2.13097
$489$	6.93967	0.313823
$490$	59.1223	2.67087
$491$	−13.9962	−0.631639	−0.315820	−	0.948819i	$-0.602279\pi$
$491$	−13.9962	−0.631639	−0.315820	+	0.948819i	$0.602279\pi$
$492$	141.302	6.37038
$493$	31.8494	1.43442
$494$	0.402572	0.0181126
$495$	90.2638	4.05706
$496$	38.5111	1.72920
$497$	10.3211	0.462964
$498$	−12.6920	−0.568742
$499$	27.9772	1.25243	0.626215	−	0.779650i	$-0.284603\pi$
$499$	27.9772	1.25243	0.626215	+	0.779650i	$0.284603\pi$
$500$	114.183	5.10640
$501$	−65.8915	−2.94381
$502$	−6.86952	−0.306602
$503$	−14.2183	−0.633961	−0.316980	−	0.948432i	$-0.602669\pi$
$503$	−14.2183	−0.633961	−0.316980	+	0.948432i	$0.602669\pi$
$504$	36.9730	1.64691
$505$	43.9681	1.95655
$506$	44.0453	1.95805
$507$	2.99924	0.133201
$508$	−39.7481	−1.76354
$509$	38.6235	1.71196	0.855979	−	0.517011i	$-0.172955\pi$
$509$	38.6235	1.71196	0.855979	+	0.517011i	$0.172955\pi$
$510$	189.097	8.37334
$511$	15.0896	0.667524
$512$	47.9217	2.11786
$513$	−1.44613	−0.0638481
$514$	−49.6344	−2.18928
$515$	−4.07294	−0.179475
$516$	−57.0806	−2.51283
$517$	32.4183	1.42575
$518$	−15.3103	−0.672696
$519$	23.3922	1.02680
$520$	−22.9682	−1.00722
$521$	−39.3599	−1.72439	−0.862194	−	0.506578i	$-0.830910\pi$
$521$	−39.3599	−1.72439	−0.862194	+	0.506578i	$0.830910\pi$
$522$	77.1563	3.37704
$523$	15.0207	0.656809	0.328404	−	0.944537i	$-0.393489\pi$
$523$	15.0207	0.656809	0.328404	+	0.944537i	$0.393489\pi$
$524$	28.0525	1.22548
$525$	−38.0100	−1.65889
$526$	−64.2738	−2.80247
$527$	−42.6123	−1.85622
$528$	62.0161	2.69890
$529$	−0.300557	−0.0130677
$530$	−3.52724	−0.153213
$531$	40.0598	1.73845
$532$	0.748966	0.0324718
$533$	11.0728	0.479615
$534$	76.1077	3.29350
$535$	45.2734	1.95734
$536$	54.8267	2.36815
$537$	−38.7500	−1.67219
$538$	−68.2383	−2.94196
$539$	−21.4546	−0.924115
$540$	155.690	6.69981
$541$	37.7790	1.62425	0.812123	−	0.583486i	$-0.198312\pi$
$541$	37.7790	1.62425	0.812123	+	0.583486i	$0.198312\pi$
$542$	77.0136	3.30802
$543$	17.5345	0.752479
$544$	16.7830	0.719566
$545$	−29.5645	−1.26640
$546$	8.20283	0.351049
$547$	−31.2936	−1.33802	−0.669008	−	0.743255i	$-0.733281\pi$
$547$	−31.2936	−1.33802	−0.669008	+	0.743255i	$0.733281\pi$
$548$	−52.7858	−2.25490
$549$	50.0483	2.13601
$550$	−107.135	−4.56827
$551$	0.828284	0.0352861
$552$	80.5818	3.42979
$553$	2.55079	0.108471
$554$	45.1038	1.91628
$555$	−68.3833	−2.90271
$556$	−98.8879	−4.19378
$557$	13.9595	0.591483	0.295742	−	0.955268i	$-0.404433\pi$
$557$	13.9595	0.591483	0.295742	+	0.955268i	$0.404433\pi$
$558$	−103.230	−4.37007
$559$	−4.47298	−0.189187
$560$	−24.9151	−1.05285
$561$	−68.6204	−2.89716
$562$	−52.1572	−2.20012
$563$	−35.6025	−1.50047	−0.750234	−	0.661172i	$-0.770059\pi$
$563$	−35.6025	−1.50047	−0.750234	+	0.661172i	$0.770059\pi$
$564$	111.917	4.71256
$565$	−16.0162	−0.673808
$566$	62.3966	2.62273
$567$	−9.79718	−0.411443
$568$	53.2228	2.23318
$569$	−15.7489	−0.660227	−0.330114	−	0.943941i	$-0.607087\pi$
$569$	−15.7489	−0.660227	−0.330114	+	0.943941i	$0.607087\pi$
$570$	4.91771	0.205980
$571$	25.3214	1.05967	0.529833	−	0.848102i	$-0.322255\pi$
$571$	25.3214	1.05967	0.529833	+	0.848102i	$0.322255\pi$
$572$	15.7277	0.657609
$573$	−53.3968	−2.23068
$574$	30.2837	1.26402
$575$	−55.2139	−2.30258
$576$	−26.4173	−1.10072
$577$	−20.4794	−0.852570	−0.426285	−	0.904589i	$-0.640178\pi$
$577$	−20.4794	−0.852570	−0.426285	+	0.904589i	$0.640178\pi$
$578$	−53.2960	−2.21682
$579$	75.9478	3.15628
$580$	−89.1728	−3.70270
$581$	−1.85037	−0.0767661
$582$	14.5926	0.604883
$583$	1.27998	0.0530115
$584$	77.8125	3.21991
$585$	24.4191	1.00960
$586$	−58.4585	−2.41490
$587$	−10.2805	−0.424322	−0.212161	−	0.977235i	$-0.568050\pi$
$587$	−10.2805	−0.424322	−0.212161	+	0.977235i	$0.568050\pi$
$588$	−74.0674	−3.05449
$589$	−1.10819	−0.0456621
$590$	−68.0619	−2.80206
$591$	40.3927	1.66154
$592$	−31.3140	−1.28700
$593$	12.9857	0.533259	0.266629	−	0.963799i	$-0.414090\pi$
$593$	12.9857	0.533259	0.266629	+	0.963799i	$0.414090\pi$
$594$	−83.0544	−3.40776
$595$	27.5684	1.13019
$596$	76.5485	3.13555
$597$	25.6864	1.05128
$598$	11.9156	0.487264
$599$	12.6324	0.516145	0.258073	−	0.966126i	$-0.416913\pi$
$599$	12.6324	0.516145	0.258073	+	0.966126i	$0.416913\pi$
$600$	−196.006	−8.00192
$601$	29.9151	1.22026	0.610131	−	0.792301i	$-0.291117\pi$
$601$	29.9151	1.22026	0.610131	+	0.792301i	$0.291117\pi$
$602$	−12.2335	−0.498599
$603$	−58.2901	−2.37376
$604$	14.3317	0.583150
$605$	10.8493	0.441087
$606$	−80.9744	−3.28936
$607$	20.0802	0.815030	0.407515	−	0.913198i	$-0.366395\pi$
$607$	20.0802	0.815030	0.407515	+	0.913198i	$0.366395\pi$
$608$	0.436464	0.0177010
$609$	16.8772	0.683898
$610$	−85.0324	−3.44286
$611$	8.77010	0.354800
$612$	−157.891	−6.38238
$613$	−12.6159	−0.509552	−0.254776	−	0.967000i	$-0.582002\pi$
$613$	−12.6159	−0.509552	−0.254776	+	0.967000i	$0.582002\pi$
$614$	−26.3625	−1.06390
$615$	135.262	5.45429
$616$	22.7955	0.918456
$617$	46.4365	1.86946	0.934732	−	0.355354i	$-0.115640\pi$
$617$	46.4365	1.86946	0.934732	+	0.355354i	$0.115640\pi$
$618$	7.50098	0.301734
$619$	−25.8298	−1.03819	−0.519093	−	0.854717i	$-0.673730\pi$
$619$	−25.8298	−1.03819	−0.519093	+	0.854717i	$0.673730\pi$
$620$	119.307	4.79150
$621$	−42.8034	−1.71764
$622$	14.8591	0.595795
$623$	11.0957	0.444541
$624$	16.7772	0.671626
$625$	51.3575	2.05430
$626$	−52.0979	−2.08225
$627$	−1.78456	−0.0712686
$628$	16.1795	0.645631
$629$	34.6488	1.38154
$630$	66.7854	2.66080
$631$	−24.7938	−0.987024	−0.493512	−	0.869739i	$-0.664287\pi$
$631$	−24.7938	−0.987024	−0.493512	+	0.869739i	$0.664287\pi$
$632$	13.1537	0.523226
$633$	−31.3995	−1.24802
$634$	42.3274	1.68103
$635$	−38.0491	−1.50993
$636$	4.41887	0.175220
$637$	−5.80411	−0.229967
$638$	47.5703	1.88332
$639$	−56.5848	−2.23846
$640$	66.9708	2.64725
$641$	43.1003	1.70236	0.851180	−	0.524874i	$-0.175888\pi$
$641$	43.1003	1.70236	0.851180	+	0.524874i	$0.175888\pi$
$642$	−83.3784	−3.29068
$643$	−32.4009	−1.27777	−0.638883	−	0.769304i	$-0.720603\pi$
$643$	−32.4009	−1.27777	−0.638883	+	0.769304i	$0.720603\pi$
$644$	22.1684	0.873557
$645$	−54.6406	−2.15147
$646$	−2.49173	−0.0980357
$647$	0.985159	0.0387306	0.0193653	−	0.999812i	$-0.493835\pi$
$647$	0.985159	0.0387306	0.0193653	+	0.999812i	$0.493835\pi$
$648$	−50.5212	−1.98466
$649$	24.6987	0.969507
$650$	−28.9833	−1.13682
$651$	−22.5806	−0.885002
$652$	9.84483	0.385553
$653$	10.9705	0.429310	0.214655	−	0.976690i	$-0.431137\pi$
$653$	10.9705	0.429310	0.214655	+	0.976690i	$0.431137\pi$
$654$	54.4478	2.12908
$655$	26.8534	1.04925
$656$	61.9391	2.41831
$657$	−82.7279	−3.22752
$658$	23.9860	0.935071
$659$	−37.3158	−1.45362	−0.726809	−	0.686839i	$-0.758998\pi$
$659$	−37.3158	−1.45362	−0.726809	+	0.686839i	$0.758998\pi$
$660$	192.125	7.47847
$661$	−17.6210	−0.685378	−0.342689	−	0.939449i	$-0.611338\pi$
$661$	−17.6210	−0.685378	−0.342689	+	0.939449i	$0.611338\pi$
$662$	−8.31504	−0.323173
$663$	−18.5639	−0.720961
$664$	−9.54179	−0.370293
$665$	0.716952	0.0278022
$666$	83.9379	3.25253
$667$	24.5161	0.949266
$668$	−93.4758	−3.61669
$669$	17.6484	0.682325
$670$	99.0352	3.82607
$671$	30.8570	1.19122
$672$	8.89343	0.343072
$673$	−19.0270	−0.733436	−0.366718	−	0.930332i	$-0.619519\pi$
$673$	−19.0270	−0.733436	−0.366718	+	0.930332i	$0.619519\pi$
$674$	−47.6118	−1.83394
$675$	104.115	4.00737
$676$	4.25481	0.163647
$677$	−16.5325	−0.635395	−0.317698	−	0.948192i	$-0.602910\pi$
$677$	−16.5325	−0.635395	−0.317698	+	0.948192i	$0.602910\pi$
$678$	29.4965	1.13281
$679$	2.12746	0.0816443
$680$	142.162	5.45167
$681$	−19.8967	−0.762444
$682$	−63.6459	−2.43713
$683$	16.7028	0.639115	0.319558	−	0.947567i	$-0.396466\pi$
$683$	16.7028	0.639115	0.319558	+	0.947567i	$0.396466\pi$
$684$	−4.10617	−0.157003
$685$	−50.5295	−1.93063
$686$	−35.0189	−1.33703
$687$	−28.6520	−1.09314
$688$	−25.0210	−0.953917
$689$	0.346274	0.0131920
$690$	145.557	5.54127
$691$	−42.0709	−1.60045	−0.800227	−	0.599698i	$-0.795288\pi$
$691$	−42.0709	−1.60045	−0.800227	+	0.599698i	$0.795288\pi$
$692$	33.1849	1.26150
$693$	−24.2355	−0.920629
$694$	42.4746	1.61231
$695$	−94.6610	−3.59069
$696$	87.0307	3.29889
$697$	−68.5351	−2.59595
$698$	−4.02452	−0.152330
$699$	9.72969	0.368011
$700$	−53.9222	−2.03807
$701$	2.85794	0.107943	0.0539715	−	0.998542i	$-0.482812\pi$
$701$	2.85794	0.107943	0.0539715	+	0.998542i	$0.482812\pi$
$702$	−22.4687	−0.848026
$703$	0.901086	0.0339851
$704$	−16.2874	−0.613855
$705$	107.133	4.03487
$706$	15.1917	0.571749
$707$	−11.8052	−0.443982
$708$	85.2668	3.20452
$709$	−8.83010	−0.331621	−0.165811	−	0.986158i	$-0.553024\pi$
$709$	−8.83010	−0.331621	−0.165811	+	0.986158i	$0.553024\pi$
$710$	96.1380	3.60800
$711$	−13.9846	−0.524464
$712$	57.2175	2.14432
$713$	−32.8009	−1.22840
$714$	−50.7716	−1.90008
$715$	15.0554	0.563041
$716$	−54.9720	−2.05440
$717$	58.5080	2.18502
$718$	85.3048	3.18355
$719$	8.33897	0.310991	0.155496	−	0.987837i	$-0.450303\pi$
$719$	8.33897	0.310991	0.155496	+	0.987837i	$0.450303\pi$
$720$	136.596	5.09062
$721$	1.09357	0.0407266
$722$	47.4535	1.76604
$723$	−12.3280	−0.458482
$724$	24.8750	0.924474
$725$	−59.6327	−2.21470
$726$	−19.9807	−0.741555
$727$	−13.8865	−0.515023	−0.257512	−	0.966275i	$-0.582903\pi$
$727$	−13.8865	−0.515023	−0.257512	+	0.966275i	$0.582903\pi$
$728$	6.16686	0.228559
$729$	−27.1231	−1.00456
$730$	140.555	5.20218
$731$	27.6856	1.02399
$732$	106.527	3.93736
$733$	−3.55119	−0.131166	−0.0655830	−	0.997847i	$-0.520891\pi$
$733$	−3.55119	−0.131166	−0.0655830	+	0.997847i	$0.520891\pi$
$734$	−13.4658	−0.497030
$735$	−70.9014	−2.61524
$736$	12.9187	0.476191
$737$	−35.9384	−1.32381
$738$	−166.029	−6.11161
$739$	28.0428	1.03157	0.515785	−	0.856718i	$-0.327500\pi$
$739$	28.0428	1.03157	0.515785	+	0.856718i	$0.327500\pi$
$740$	−97.0107	−3.56618
$741$	−0.482777	−0.0177353
$742$	0.947049	0.0347672
$743$	2.85655	0.104797	0.0523983	−	0.998626i	$-0.483313\pi$
$743$	2.85655	0.104797	0.0523983	+	0.998626i	$0.483313\pi$
$744$	−116.441	−4.26895
$745$	73.2765	2.68464
$746$	2.86568	0.104920
$747$	10.1445	0.371169
$748$	−97.3471	−3.55936
$749$	−12.1557	−0.444161
$750$	−201.297	−7.35032
$751$	23.6551	0.863188	0.431594	−	0.902068i	$-0.357951\pi$
$751$	23.6551	0.863188	0.431594	+	0.902068i	$0.357951\pi$
$752$	49.0584	1.78898
$753$	8.23815	0.300215
$754$	12.8692	0.468668
$755$	13.7191	0.499290
$756$	−41.8020	−1.52032
$757$	−26.2190	−0.952945	−0.476473	−	0.879189i	$-0.658085\pi$
$757$	−26.2190	−0.952945	−0.476473	+	0.879189i	$0.658085\pi$
$758$	−44.1508	−1.60363
$759$	−52.8206	−1.91727
$760$	3.69711	0.134108
$761$	39.0493	1.41554	0.707769	−	0.706444i	$-0.249702\pi$
$761$	39.0493	1.41554	0.707769	+	0.706444i	$0.249702\pi$
$762$	70.0735	2.53850
$763$	7.93795	0.287373
$764$	−75.7504	−2.74055
$765$	−151.142	−5.46456
$766$	36.7699	1.32855
$767$	6.68172	0.241263
$768$	−96.9069	−3.49683
$769$	−8.59490	−0.309940	−0.154970	−	0.987919i	$-0.549528\pi$
$769$	−8.59490	−0.309940	−0.154970	+	0.987919i	$0.549528\pi$
$770$	41.1762	1.48389
$771$	59.5233	2.14368
$772$	107.742	3.87772
$773$	−12.8443	−0.461977	−0.230988	−	0.972957i	$-0.574196\pi$
$773$	−12.8443	−0.461977	−0.230988	+	0.972957i	$0.574196\pi$
$774$	67.0694	2.41076
$775$	79.7846	2.86595
$776$	10.9707	0.393824
$777$	18.3606	0.658683
$778$	69.7047	2.49903
$779$	−1.78235	−0.0638592
$780$	51.9757	1.86103
$781$	−34.8871	−1.24836
$782$	−73.7517	−2.63736
$783$	−46.2289	−1.65209
$784$	−32.4671	−1.15954
$785$	15.4879	0.552786
$786$	−49.4549	−1.76400
$787$	−18.4602	−0.658035	−0.329017	−	0.944324i	$-0.606717\pi$
$787$	−18.4602	−0.658035	−0.329017	+	0.944324i	$0.606717\pi$
$788$	57.3024	2.04131
$789$	77.0793	2.74410
$790$	23.7599	0.845341
$791$	4.30029	0.152901
$792$	−124.975	−4.44080
$793$	8.34773	0.296437
$794$	33.9204	1.20379
$795$	4.22998	0.150022
$796$	36.4396	1.29157
$797$	4.00625	0.141909	0.0709543	−	0.997480i	$-0.477396\pi$
$797$	4.00625	0.141909	0.0709543	+	0.997480i	$0.477396\pi$
$798$	−1.32038	−0.0467410
$799$	−54.2828	−1.92039
$800$	−31.4234	−1.11099
$801$	−60.8319	−2.14939
$802$	24.6801	0.871486
$803$	−51.0054	−1.79994
$804$	−124.070	−4.37560
$805$	21.2208	0.747935
$806$	−17.2181	−0.606482
$807$	81.8336	2.88068
$808$	−60.8762	−2.14162
$809$	−48.1990	−1.69459	−0.847293	−	0.531125i	$-0.821769\pi$
$809$	−48.1990	−1.69459	−0.847293	+	0.531125i	$0.821769\pi$
$810$	−91.2580	−3.20648
$811$	29.7982	1.04636	0.523179	−	0.852223i	$-0.324746\pi$
$811$	29.7982	1.04636	0.523179	+	0.852223i	$0.324746\pi$
$812$	23.9425	0.840217
$813$	−92.3573	−3.23911
$814$	51.7515	1.81389
$815$	9.42402	0.330109
$816$	−103.843	−3.63523
$817$	0.720000	0.0251896
$818$	86.4917	3.02411
$819$	−6.55641	−0.229100
$820$	191.887	6.70098
$821$	−13.6639	−0.476874	−0.238437	−	0.971158i	$-0.576635\pi$
$821$	−13.6639	−0.476874	−0.238437	+	0.971158i	$0.576635\pi$
$822$	93.0582	3.24578
$823$	45.0918	1.57180	0.785900	−	0.618354i	$-0.212200\pi$
$823$	45.0918	1.57180	0.785900	+	0.618354i	$0.212200\pi$
$824$	5.63921	0.196451
$825$	128.480	4.47311
$826$	18.2743	0.635845
$827$	−30.9871	−1.07753	−0.538764	−	0.842457i	$-0.681109\pi$
$827$	−30.9871	−1.07753	−0.538764	+	0.842457i	$0.681109\pi$
$828$	−121.537	−4.22371
$829$	4.92223	0.170956	0.0854780	−	0.996340i	$-0.472758\pi$
$829$	4.92223	0.170956	0.0854780	+	0.996340i	$0.472758\pi$
$830$	−17.2356	−0.598258
$831$	−54.0900	−1.87636
$832$	−4.40623	−0.152759
$833$	35.9247	1.24472
$834$	174.333	6.03668
$835$	−89.4801	−3.09659
$836$	−2.53164	−0.0875585
$837$	61.8513	2.13789
$838$	−38.0136	−1.31316
$839$	38.8616	1.34165	0.670825	−	0.741615i	$-0.265940\pi$
$839$	38.8616	1.34165	0.670825	+	0.741615i	$0.265940\pi$
$840$	75.3326	2.59922
$841$	−2.52190	−0.0869622
$842$	−42.8103	−1.47534
$843$	62.5486	2.15429
$844$	−44.5444	−1.53328
$845$	4.07294	0.140113
$846$	−131.502	−4.52113
$847$	−2.91299	−0.100091
$848$	1.93699	0.0665166
$849$	−74.8281	−2.56809
$850$	179.393	6.15313
$851$	26.6709	0.914268
$852$	−120.440	−4.12621
$853$	−35.6628	−1.22107	−0.610535	−	0.791989i	$-0.709046\pi$
$853$	−35.6628	−1.22107	−0.610535	+	0.791989i	$0.709046\pi$
$854$	22.8308	0.781255
$855$	−3.93065	−0.134426
$856$	−62.6835	−2.14248
$857$	22.0292	0.752504	0.376252	−	0.926517i	$-0.377213\pi$
$857$	22.0292	0.752504	0.376252	+	0.926517i	$0.377213\pi$
$858$	−27.7270	−0.946585
$859$	−10.0125	−0.341622	−0.170811	−	0.985304i	$-0.554639\pi$
$859$	−10.0125	−0.341622	−0.170811	+	0.985304i	$0.554639\pi$
$860$	−77.5150	−2.64324
$861$	−36.3172	−1.23769
$862$	−60.3547	−2.05569
$863$	41.1138	1.39953	0.699765	−	0.714374i	$-0.253288\pi$
$863$	41.1138	1.39953	0.699765	+	0.714374i	$0.253288\pi$
$864$	−24.3603	−0.828756
$865$	31.7664	1.08009
$866$	40.6964	1.38292
$867$	63.9144	2.17065
$868$	−32.0335	−1.08729
$869$	−8.62213	−0.292486
$870$	157.206	5.32979
$871$	−9.72242	−0.329431
$872$	40.9337	1.38619
$873$	−11.6637	−0.394756
$874$	−1.91801	−0.0648776
$875$	−29.3471	−0.992112
$876$	−176.085	−5.94937
$877$	29.0383	0.980554	0.490277	−	0.871567i	$-0.336896\pi$
$877$	29.0383	0.980554	0.490277	+	0.871567i	$0.336896\pi$
$878$	43.3619	1.46339
$879$	70.1054	2.36460
$880$	84.2174	2.83897
$881$	−6.83128	−0.230152	−0.115076	−	0.993357i	$-0.536711\pi$
$881$	−6.83128	−0.230152	−0.115076	+	0.993357i	$0.536711\pi$
$882$	87.0289	2.93041
$883$	32.2239	1.08442	0.542211	−	0.840242i	$-0.317587\pi$
$883$	32.2239	1.08442	0.542211	+	0.840242i	$0.317587\pi$
$884$	−26.3353	−0.885751
$885$	81.6221	2.74370
$886$	−49.3825	−1.65904
$887$	13.1840	0.442675	0.221337	−	0.975197i	$-0.428958\pi$
$887$	13.1840	0.442675	0.221337	+	0.975197i	$0.428958\pi$
$888$	94.6803	3.17726
$889$	10.2160	0.342634
$890$	103.354	3.46442
$891$	33.1162	1.10943
$892$	25.0365	0.838285
$893$	−1.41169	−0.0472406
$894$	−134.950	−4.51342
$895$	−52.6222	−1.75897
$896$	−17.9814	−0.600716
$897$	−14.2896	−0.477114
$898$	5.72603	0.191080
$899$	−35.4259	−1.18152
$900$	295.626	9.85419
$901$	−2.14327	−0.0714026
$902$	−102.364	−3.40836
$903$	14.6708	0.488213
$904$	22.1753	0.737540
$905$	23.8118	0.791530
$906$	−25.2660	−0.839406
$907$	17.7021	0.587789	0.293895	−	0.955838i	$-0.405048\pi$
$907$	17.7021	0.587789	0.293895	+	0.955838i	$0.405048\pi$
$908$	−28.2261	−0.936717
$909$	64.7217	2.14668
$910$	11.1394	0.369267
$911$	23.1761	0.767859	0.383930	−	0.923362i	$-0.374571\pi$
$911$	23.1761	0.767859	0.383930	+	0.923362i	$0.374571\pi$
$912$	−2.70057	−0.0894248
$913$	6.25456	0.206996
$914$	−72.6253	−2.40223
$915$	101.974	3.37115
$916$	−40.6467	−1.34300
$917$	−7.21002	−0.238096
$918$	139.071	4.59001
$919$	22.7951	0.751941	0.375971	−	0.926632i	$-0.377309\pi$
$919$	22.7951	0.751941	0.375971	+	0.926632i	$0.377309\pi$
$920$	109.429	3.60778
$921$	31.6148	1.04174
$922$	−9.30840	−0.306556
$923$	−9.43799	−0.310655
$924$	−51.5849	−1.69702
$925$	−64.8741	−2.13305
$926$	−63.1949	−2.07671
$927$	−5.99543	−0.196916
$928$	13.9526	0.458018
$929$	28.3039	0.928621	0.464311	−	0.885672i	$-0.346302\pi$
$929$	28.3039	0.928621	0.464311	+	0.885672i	$0.346302\pi$
$930$	−210.332	−6.89705
$931$	0.934268	0.0306194
$932$	13.8028	0.452127
$933$	−17.8195	−0.583385
$934$	55.7708	1.82488
$935$	−93.1860	−3.04751
$936$	−33.8095	−1.10510
$937$	−45.4517	−1.48484	−0.742421	−	0.669934i	$-0.766323\pi$
$937$	−45.4517	−1.48484	−0.742421	+	0.669934i	$0.766323\pi$
$938$	−26.5905	−0.868212
$939$	62.4776	2.03888
$940$	151.983	4.95712
$941$	−6.97700	−0.227444	−0.113722	−	0.993513i	$-0.536277\pi$
$941$	−6.97700	−0.227444	−0.113722	+	0.993513i	$0.536277\pi$
$942$	−28.5234	−0.929343
$943$	−52.7550	−1.71794
$944$	37.3764	1.21650
$945$	−40.0152	−1.30169
$946$	41.3513	1.34445
$947$	13.8237	0.449211	0.224605	−	0.974450i	$-0.427891\pi$
$947$	13.8237	0.449211	0.224605	+	0.974450i	$0.427891\pi$
$948$	−29.7661	−0.966757
$949$	−13.7985	−0.447918
$950$	4.66535	0.151364
$951$	−50.7604	−1.64602
$952$	−38.1699	−1.23709
$953$	−2.71098	−0.0878172	−0.0439086	−	0.999036i	$-0.513981\pi$
$953$	−2.71098	−0.0878172	−0.0439086	+	0.999036i	$0.513981\pi$
$954$	−5.19215	−0.168102
$955$	−72.5124	−2.34645
$956$	83.0013	2.68445
$957$	−57.0479	−1.84410
$958$	18.2487	0.589587
$959$	13.5669	0.438100
$960$	−53.8253	−1.73720
$961$	16.3976	0.528953
$962$	14.0003	0.451388
$963$	66.6432	2.14755
$964$	−17.4888	−0.563278
$965$	103.136	3.32008
$966$	−39.0815	−1.25743
$967$	−42.1100	−1.35417	−0.677083	−	0.735907i	$-0.736756\pi$
$967$	−42.1100	−1.35417	−0.677083	+	0.735907i	$0.736756\pi$
$968$	−15.0214	−0.482807
$969$	2.98816	0.0959936
$970$	19.8167	0.636275
$971$	−4.11166	−0.131950	−0.0659748	−	0.997821i	$-0.521016\pi$
$971$	−4.11166	−0.131950	−0.0659748	+	0.997821i	$0.521016\pi$
$972$	−0.349428	−0.0112079
$973$	25.4161	0.814802
$974$	20.7831	0.665935
$975$	34.7578	1.11314
$976$	46.6957	1.49469
$977$	15.0596	0.481798	0.240899	−	0.970550i	$-0.422558\pi$
$977$	15.0596	0.481798	0.240899	+	0.970550i	$0.422558\pi$
$978$	−17.3559	−0.554979
$979$	−37.5055	−1.19868
$980$	−100.583	−3.21301
$981$	−43.5194	−1.38947
$982$	35.0040	1.11702
$983$	−37.8658	−1.20773	−0.603866	−	0.797086i	$-0.706374\pi$
$983$	−37.8658	−1.20773	−0.603866	+	0.797086i	$0.706374\pi$
$984$	−187.277	−5.97018
$985$	54.8530	1.74776
$986$	−79.6540	−2.53670
$987$	−28.7648	−0.915594
$988$	−0.684883	−0.0217890
$989$	21.3110	0.677651
$990$	−225.747	−7.17469
$991$	−19.1612	−0.608676	−0.304338	−	0.952564i	$-0.598435\pi$
$991$	−19.1612	−0.608676	−0.304338	+	0.952564i	$0.598435\pi$
$992$	−18.6677	−0.592700
$993$	9.97168	0.316442
$994$	−25.8126	−0.818727
$995$	34.8820	1.10583
$996$	21.5925	0.684186
$997$	45.7610	1.44927	0.724633	−	0.689135i	$-0.242010\pi$
$997$	45.7610	1.44927	0.724633	+	0.689135i	$0.242010\pi$
$998$	−69.9699	−2.21486
$999$	−50.2923	−1.59118

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.f.1.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.f.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.50096 q^{2} +2.99924 q^{3} +4.25481 q^{4} +4.07294 q^{5} -7.50098 q^{6} -1.09357 q^{7} -5.63921 q^{8} +5.99543 q^{9} +O(q^{10})\)	\(q-2.50096 q^{2} +2.99924 q^{3} +4.25481 q^{4} +4.07294 q^{5} -7.50098 q^{6} -1.09357 q^{7} -5.63921 q^{8} +5.99543 q^{9} -10.1863 q^{10} +3.69645 q^{11} +12.7612 q^{12} +1.00000 q^{13} +2.73497 q^{14} +12.2157 q^{15} +5.59382 q^{16} -6.18952 q^{17} -14.9944 q^{18} -0.160967 q^{19} +17.3296 q^{20} -3.27987 q^{21} -9.24469 q^{22} -4.76439 q^{23} -16.9133 q^{24} +11.5889 q^{25} -2.50096 q^{26} +8.98402 q^{27} -4.65293 q^{28} -5.14569 q^{29} -30.5511 q^{30} +6.88459 q^{31} -2.71152 q^{32} +11.0865 q^{33} +15.4798 q^{34} -4.45404 q^{35} +25.5095 q^{36} -5.59797 q^{37} +0.402572 q^{38} +2.99924 q^{39} -22.9682 q^{40} +11.0728 q^{41} +8.20283 q^{42} -4.47298 q^{43} +15.7277 q^{44} +24.4191 q^{45} +11.9156 q^{46} +8.77010 q^{47} +16.7772 q^{48} -5.80411 q^{49} -28.9833 q^{50} -18.5639 q^{51} +4.25481 q^{52} +0.346274 q^{53} -22.4687 q^{54} +15.0554 q^{55} +6.16686 q^{56} -0.482777 q^{57} +12.8692 q^{58} +6.68172 q^{59} +51.9757 q^{60} +8.34773 q^{61} -17.2181 q^{62} -6.55641 q^{63} -4.40623 q^{64} +4.07294 q^{65} -27.7270 q^{66} -9.72242 q^{67} -26.3353 q^{68} -14.2896 q^{69} +11.1394 q^{70} -9.43799 q^{71} -33.8095 q^{72} -13.7985 q^{73} +14.0003 q^{74} +34.7578 q^{75} -0.684883 q^{76} -4.04232 q^{77} -7.50098 q^{78} -2.33254 q^{79} +22.7833 q^{80} +8.95892 q^{81} -27.6926 q^{82} +1.69204 q^{83} -13.9552 q^{84} -25.2096 q^{85} +11.1867 q^{86} -15.4331 q^{87} -20.8451 q^{88} -10.1464 q^{89} -61.0712 q^{90} -1.09357 q^{91} -20.2716 q^{92} +20.6485 q^{93} -21.9337 q^{94} -0.655608 q^{95} -8.13249 q^{96} -1.94543 q^{97} +14.5159 q^{98} +22.1618 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9}+O(q^{10}) \) 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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