LMFDB - Embedded newform 1339.2.a.c.1.1

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:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.17009$ of defining polynomial
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)

$f(q)$	$=$	$q-2.17009 q^{2} -2.70928 q^{3} +2.70928 q^{4} -4.17009 q^{5} +5.87936 q^{6} -1.70928 q^{7} -1.53919 q^{8} +4.34017 q^{9} +O(q^{10})$	\(q-2.17009 q^{2} -2.70928 q^{3} +2.70928 q^{4} -4.17009 q^{5} +5.87936 q^{6} -1.70928 q^{7} -1.53919 q^{8} +4.34017 q^{9} +9.04945 q^{10} -4.63090 q^{11} -7.34017 q^{12} +1.00000 q^{13} +3.70928 q^{14} +11.2979 q^{15} -2.07838 q^{16} -4.41855 q^{17} -9.41855 q^{18} -4.80098 q^{19} -11.2979 q^{20} +4.63090 q^{21} +10.0494 q^{22} +7.60197 q^{23} +4.17009 q^{24} +12.3896 q^{25} -2.17009 q^{26} -3.63090 q^{27} -4.63090 q^{28} -3.29072 q^{29} -24.5174 q^{30} +5.75872 q^{31} +7.58864 q^{32} +12.5464 q^{33} +9.58864 q^{34} +7.12783 q^{35} +11.7587 q^{36} +7.58864 q^{37} +10.4186 q^{38} -2.70928 q^{39} +6.41855 q^{40} -5.26180 q^{41} -10.0494 q^{42} +6.34017 q^{43} -12.5464 q^{44} -18.0989 q^{45} -16.4969 q^{46} +8.38962 q^{47} +5.63090 q^{48} -4.07838 q^{49} -26.8865 q^{50} +11.9711 q^{51} +2.70928 q^{52} +2.04945 q^{53} +7.87936 q^{54} +19.3112 q^{55} +2.63090 q^{56} +13.0072 q^{57} +7.14116 q^{58} -11.7721 q^{59} +30.6092 q^{60} +10.1278 q^{61} -12.4969 q^{62} -7.41855 q^{63} -12.3112 q^{64} -4.17009 q^{65} -27.2267 q^{66} -4.68035 q^{67} -11.9711 q^{68} -20.5958 q^{69} -15.4680 q^{70} +8.52359 q^{71} -6.68035 q^{72} -15.6875 q^{73} -16.4680 q^{74} -33.5669 q^{75} -13.0072 q^{76} +7.91548 q^{77} +5.87936 q^{78} +13.0205 q^{79} +8.66701 q^{80} -3.18342 q^{81} +11.4186 q^{82} +0.326842 q^{83} +12.5464 q^{84} +18.4257 q^{85} -13.7587 q^{86} +8.91548 q^{87} +7.12783 q^{88} +1.06505 q^{89} +39.2762 q^{90} -1.70928 q^{91} +20.5958 q^{92} -15.6020 q^{93} -18.2062 q^{94} +20.0205 q^{95} -20.5597 q^{96} +4.73820 q^{97} +8.85043 q^{98} -20.0989 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - q^{3} + q^{4} - 7 q^{5} + 5 q^{6} + 2 q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q - q^2 - q^3 + q^4 - 7 * q^5 + 5 * q^6 + 2 * q^7 - 3 * q^8 + 2 * q^9	\( 3 q - q^{2} - q^{3} + q^{4} - 7 q^{5} + 5 q^{6} + 2 q^{7} - 3 q^{8} + 2 q^{9} + 9 q^{10} - 10 q^{11} - 11 q^{12} + 3 q^{13} + 4 q^{14} + 7 q^{15} - 3 q^{16} + q^{17} - 14 q^{18} - 5 q^{19} - 7 q^{20} + 10 q^{21} + 12 q^{22} + 4 q^{23} + 7 q^{24} + 8 q^{25} - q^{26} - 7 q^{27} - 10 q^{28} - 17 q^{29} - 23 q^{30} - 8 q^{31} + 3 q^{32} + 2 q^{33} + 9 q^{34} + 10 q^{36} + 3 q^{37} + 17 q^{38} - q^{39} + 5 q^{40} - 8 q^{41} - 12 q^{42} + 8 q^{43} - 2 q^{44} - 18 q^{45} - 32 q^{46} - 4 q^{47} + 13 q^{48} - 9 q^{49} - 34 q^{50} + 21 q^{51} + q^{52} - 12 q^{53} + 11 q^{54} + 32 q^{55} + 4 q^{56} + 5 q^{57} + q^{58} - 11 q^{59} + 39 q^{60} + 9 q^{61} - 20 q^{62} - 8 q^{63} - 11 q^{64} - 7 q^{65} - 24 q^{66} + 8 q^{67} - 21 q^{68} - 8 q^{69} - 14 q^{70} + 10 q^{71} + 2 q^{72} + 9 q^{73} - 17 q^{74} - 32 q^{75} - 5 q^{76} - 8 q^{77} + 5 q^{78} + 6 q^{79} + 3 q^{80} - 5 q^{81} + 20 q^{82} - 11 q^{83} + 2 q^{84} + 7 q^{85} - 16 q^{86} - 5 q^{87} - q^{89} + 42 q^{90} + 2 q^{91} + 8 q^{92} - 28 q^{93} - 30 q^{94} + 27 q^{95} - 27 q^{96} + 22 q^{97} - q^{98} - 24 q^{99}+O(q^{100}) \) 3 * q - q^2 - q^3 + q^4 - 7 * q^5 + 5 * q^6 + 2 * q^7 - 3 * q^8 + 2 * q^9 + 9 * q^10 - 10 * q^11 - 11 * q^12 + 3 * q^13 + 4 * q^14 + 7 * q^15 - 3 * q^16 + q^17 - 14 * q^18 - 5 * q^19 - 7 * q^20 + 10 * q^21 + 12 * q^22 + 4 * q^23 + 7 * q^24 + 8 * q^25 - q^26 - 7 * q^27 - 10 * q^28 - 17 * q^29 - 23 * q^30 - 8 * q^31 + 3 * q^32 + 2 * q^33 + 9 * q^34 + 10 * q^36 + 3 * q^37 + 17 * q^38 - q^39 + 5 * q^40 - 8 * q^41 - 12 * q^42 + 8 * q^43 - 2 * q^44 - 18 * q^45 - 32 * q^46 - 4 * q^47 + 13 * q^48 - 9 * q^49 - 34 * q^50 + 21 * q^51 + q^52 - 12 * q^53 + 11 * q^54 + 32 * q^55 + 4 * q^56 + 5 * q^57 + q^58 - 11 * q^59 + 39 * q^60 + 9 * q^61 - 20 * q^62 - 8 * q^63 - 11 * q^64 - 7 * q^65 - 24 * q^66 + 8 * q^67 - 21 * q^68 - 8 * q^69 - 14 * q^70 + 10 * q^71 + 2 * q^72 + 9 * q^73 - 17 * q^74 - 32 * q^75 - 5 * q^76 - 8 * q^77 + 5 * q^78 + 6 * q^79 + 3 * q^80 - 5 * q^81 + 20 * q^82 - 11 * q^83 + 2 * q^84 + 7 * q^85 - 16 * q^86 - 5 * q^87 - q^89 + 42 * q^90 + 2 * q^91 + 8 * q^92 - 28 * q^93 - 30 * q^94 + 27 * q^95 - 27 * q^96 + 22 * q^97 - q^98 - 24 * 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 $

$2$	−2.17009	−1.53448	−0.767241	−	0.641358i	$-0.778371\pi$
$2$	−2.17009	−1.53448	−0.767241	+	0.641358i	$0.778371\pi$
$3$	−2.70928	−1.56420	−0.782100	−	0.623152i	$-0.785852\pi$
$3$	−2.70928	−1.56420	−0.782100	+	0.623152i	$0.785852\pi$
$4$	2.70928	1.35464
$5$	−4.17009	−1.86492	−0.932460	−	0.361274i	$-0.882342\pi$
$5$	−4.17009	−1.86492	−0.932460	+	0.361274i	$0.882342\pi$
$6$	5.87936	2.40024
$7$	−1.70928	−0.646045	−0.323023	−	0.946391i	$-0.604699\pi$
$7$	−1.70928	−0.646045	−0.323023	+	0.946391i	$0.604699\pi$
$8$	−1.53919	−0.544185
$9$	4.34017	1.44672
$10$	9.04945	2.86169
$11$	−4.63090	−1.39627	−0.698134	−	0.715967i	$-0.745986\pi$
$11$	−4.63090	−1.39627	−0.698134	+	0.715967i	$0.745986\pi$
$12$	−7.34017	−2.11893
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.70928	0.991346
$15$	11.2979	2.91711
$16$	−2.07838	−0.519594
$17$	−4.41855	−1.07166	−0.535828	−	0.844327i	$-0.680000\pi$
$17$	−4.41855	−1.07166	−0.535828	+	0.844327i	$0.680000\pi$
$18$	−9.41855	−2.21997
$19$	−4.80098	−1.10142	−0.550711	−	0.834696i	$-0.685643\pi$
$19$	−4.80098	−1.10142	−0.550711	+	0.834696i	$0.685643\pi$
$20$	−11.2979	−2.52629
$21$	4.63090	1.01054
$22$	10.0494	2.14255
$23$	7.60197	1.58512	0.792560	−	0.609794i	$-0.208748\pi$
$23$	7.60197	1.58512	0.792560	+	0.609794i	$0.208748\pi$
$24$	4.17009	0.851215
$25$	12.3896	2.47792
$26$	−2.17009	−0.425589
$27$	−3.63090	−0.698767
$28$	−4.63090	−0.875157
$29$	−3.29072	−0.611072	−0.305536	−	0.952180i	$-0.598836\pi$
$29$	−3.29072	−0.611072	−0.305536	+	0.952180i	$0.598836\pi$
$30$	−24.5174	−4.47625
$31$	5.75872	1.03430	0.517149	−	0.855896i	$-0.326993\pi$
$31$	5.75872	1.03430	0.517149	+	0.855896i	$0.326993\pi$
$32$	7.58864	1.34149
$33$	12.5464	2.18404
$34$	9.58864	1.64444
$35$	7.12783	1.20482
$36$	11.7587	1.95979
$37$	7.58864	1.24756	0.623782	−	0.781598i	$-0.285595\pi$
$37$	7.58864	1.24756	0.623782	+	0.781598i	$0.285595\pi$
$38$	10.4186	1.69011
$39$	−2.70928	−0.433831
$40$	6.41855	1.01486
$41$	−5.26180	−0.821754	−0.410877	−	0.911691i	$-0.634777\pi$
$41$	−5.26180	−0.821754	−0.410877	+	0.911691i	$0.634777\pi$
$42$	−10.0494	−1.55066
$43$	6.34017	0.966867	0.483434	−	0.875381i	$-0.339389\pi$
$43$	6.34017	0.966867	0.483434	+	0.875381i	$0.339389\pi$
$44$	−12.5464	−1.89144
$45$	−18.0989	−2.69802
$46$	−16.4969	−2.43234
$47$	8.38962	1.22375	0.611876	−	0.790954i	$-0.290415\pi$
$47$	8.38962	1.22375	0.611876	+	0.790954i	$0.290415\pi$
$48$	5.63090	0.812750
$49$	−4.07838	−0.582625
$50$	−26.8865	−3.80233
$51$	11.9711	1.67629
$52$	2.70928	0.375709
$53$	2.04945	0.281513	0.140757	−	0.990044i	$-0.455046\pi$
$53$	2.04945	0.281513	0.140757	+	0.990044i	$0.455046\pi$
$54$	7.87936	1.07225
$55$	19.3112	2.60393
$56$	2.63090	0.351568
$57$	13.0072	1.72284
$58$	7.14116	0.937680
$59$	−11.7721	−1.53259	−0.766295	−	0.642488i	$-0.777902\pi$
$59$	−11.7721	−1.53259	−0.766295	+	0.642488i	$0.777902\pi$
$60$	30.6092	3.95163
$61$	10.1278	1.29674	0.648368	−	0.761327i	$-0.275452\pi$
$61$	10.1278	1.29674	0.648368	+	0.761327i	$0.275452\pi$
$62$	−12.4969	−1.58711
$63$	−7.41855	−0.934650
$64$	−12.3112	−1.53891
$65$	−4.17009	−0.517236
$66$	−27.2267	−3.35138
$67$	−4.68035	−0.571795	−0.285898	−	0.958260i	$-0.592292\pi$
$67$	−4.68035	−0.571795	−0.285898	+	0.958260i	$0.592292\pi$
$68$	−11.9711	−1.45171
$69$	−20.5958	−2.47945
$70$	−15.4680	−1.84878
$71$	8.52359	1.01156	0.505782	−	0.862661i	$-0.331204\pi$
$71$	8.52359	1.01156	0.505782	+	0.862661i	$0.331204\pi$
$72$	−6.68035	−0.787286
$73$	−15.6875	−1.83609	−0.918043	−	0.396480i	$-0.870232\pi$
$73$	−15.6875	−1.83609	−0.918043	+	0.396480i	$0.870232\pi$
$74$	−16.4680	−1.91437
$75$	−33.5669	−3.87597
$76$	−13.0072	−1.49203
$77$	7.91548	0.902053
$78$	5.87936	0.665707
$79$	13.0205	1.46492	0.732461	−	0.680809i	$-0.238371\pi$
$79$	13.0205	1.46492	0.732461	+	0.680809i	$0.238371\pi$
$80$	8.66701	0.969002
$81$	−3.18342	−0.353713
$82$	11.4186	1.26097
$83$	0.326842	0.0358756	0.0179378	−	0.999839i	$-0.494290\pi$
$83$	0.326842	0.0358756	0.0179378	+	0.999839i	$0.494290\pi$
$84$	12.5464	1.36892
$85$	18.4257	1.99855
$86$	−13.7587	−1.48364
$87$	8.91548	0.955840
$88$	7.12783	0.759829
$89$	1.06505	0.112895	0.0564474	−	0.998406i	$-0.482023\pi$
$89$	1.06505	0.112895	0.0564474	+	0.998406i	$0.482023\pi$
$90$	39.2762	4.14007
$91$	−1.70928	−0.179181
$92$	20.5958	2.14726
$93$	−15.6020	−1.61785
$94$	−18.2062	−1.87783
$95$	20.0205	2.05406
$96$	−20.5597	−2.09837
$97$	4.73820	0.481092	0.240546	−	0.970638i	$-0.422674\pi$
$97$	4.73820	0.481092	0.240546	+	0.970638i	$0.422674\pi$
$98$	8.85043	0.894029
$99$	−20.0989	−2.02002
$100$	33.5669	3.35669
$101$	−14.4969	−1.44250	−0.721249	−	0.692676i	$-0.756432\pi$
$101$	−14.4969	−1.44250	−0.721249	+	0.692676i	$0.756432\pi$
$102$	−25.9783	−2.57223
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.53919	−0.150930
$105$	−19.3112	−1.88458
$106$	−4.44748	−0.431977
$107$	7.07838	0.684293	0.342146	−	0.939647i	$-0.388846\pi$
$107$	7.07838	0.684293	0.342146	+	0.939647i	$0.388846\pi$
$108$	−9.83710	−0.946576
$109$	3.21235	0.307687	0.153844	−	0.988095i	$-0.450835\pi$
$109$	3.21235	0.307687	0.153844	+	0.988095i	$0.450835\pi$
$110$	−41.9071	−3.99568
$111$	−20.5597	−1.95144
$112$	3.55252	0.335682
$113$	0.340173	0.0320008	0.0160004	−	0.999872i	$-0.494907\pi$
$113$	0.340173	0.0320008	0.0160004	+	0.999872i	$0.494907\pi$
$114$	−28.2267	−2.64367
$115$	−31.7009	−2.95612
$116$	−8.91548	−0.827781
$117$	4.34017	0.401249
$118$	25.5464	2.35173
$119$	7.55252	0.692338
$120$	−17.3896	−1.58745
$121$	10.4452	0.949565
$122$	−21.9783	−1.98982
$123$	14.2557	1.28539
$124$	15.6020	1.40110
$125$	−30.8154	−2.75621
$126$	16.0989	1.43420
$127$	−15.0989	−1.33981	−0.669905	−	0.742447i	$-0.733665\pi$
$127$	−15.0989	−1.33981	−0.669905	+	0.742447i	$0.733665\pi$
$128$	11.5392	1.01993
$129$	−17.1773	−1.51237
$130$	9.04945	0.793689
$131$	−0.183417	−0.0160253	−0.00801263	−	0.999968i	$-0.502551\pi$
$131$	−0.183417	−0.0160253	−0.00801263	+	0.999968i	$0.502551\pi$
$132$	33.9916	2.95859
$133$	8.20620	0.711568
$134$	10.1568	0.877410
$135$	15.1412	1.30314
$136$	6.80098	0.583180
$137$	−7.95055	−0.679261	−0.339631	−	0.940559i	$-0.610302\pi$
$137$	−7.95055	−0.679261	−0.339631	+	0.940559i	$0.610302\pi$
$138$	44.6947	3.80467
$139$	9.75872	0.827724	0.413862	−	0.910340i	$-0.364180\pi$
$139$	9.75872	0.827724	0.413862	+	0.910340i	$0.364180\pi$
$140$	19.3112	1.63210
$141$	−22.7298	−1.91419
$142$	−18.4969	−1.55223
$143$	−4.63090	−0.387255
$144$	−9.02052	−0.751710
$145$	13.7226	1.13960
$146$	34.0433	2.81744
$147$	11.0494	0.911343
$148$	20.5597	1.69000
$149$	−19.8082	−1.62275	−0.811374	−	0.584527i	$-0.801280\pi$
$149$	−19.8082	−1.62275	−0.811374	+	0.584527i	$0.801280\pi$
$150$	72.8431	5.94761
$151$	20.5958	1.67606	0.838032	−	0.545621i	$-0.183706\pi$
$151$	20.5958	1.67606	0.838032	+	0.545621i	$0.183706\pi$
$152$	7.38962	0.599377
$153$	−19.1773	−1.55039
$154$	−17.1773	−1.38418
$155$	−24.0144	−1.92888
$156$	−7.34017	−0.587684
$157$	0.133969	0.0106919	0.00534595	−	0.999986i	$-0.498298\pi$
$157$	0.133969	0.0106919	0.00534595	+	0.999986i	$0.498298\pi$
$158$	−28.2557	−2.24790
$159$	−5.55252	−0.440343
$160$	−31.6453	−2.50178
$161$	−12.9939	−1.02406
$162$	6.90829	0.542767
$163$	−18.3268	−1.43547	−0.717735	−	0.696317i	$-0.754821\pi$
$163$	−18.3268	−1.43547	−0.717735	+	0.696317i	$0.754821\pi$
$164$	−14.2557	−1.11318
$165$	−52.3195	−4.07307
$166$	−0.709275	−0.0550504
$167$	14.5597	1.12666	0.563332	−	0.826231i	$-0.309519\pi$
$167$	14.5597	1.12666	0.563332	+	0.826231i	$0.309519\pi$
$168$	−7.12783	−0.549924
$169$	1.00000	0.0769231
$170$	−39.9854	−3.06674
$171$	−20.8371	−1.59345
$172$	17.1773	1.30975
$173$	17.1773	1.30596	0.652982	−	0.757373i	$-0.273518\pi$
$173$	17.1773	1.30596	0.652982	+	0.757373i	$0.273518\pi$
$174$	−19.3474	−1.46672
$175$	−21.1773	−1.60085
$176$	9.62475	0.725493
$177$	31.8937	2.39728
$178$	−2.31124	−0.173235
$179$	−12.8865	−0.963186	−0.481593	−	0.876395i	$-0.659942\pi$
$179$	−12.8865	−0.963186	−0.481593	+	0.876395i	$0.659942\pi$
$180$	−49.0349	−3.65485
$181$	−1.21235	−0.0901130	−0.0450565	−	0.998984i	$-0.514347\pi$
$181$	−1.21235	−0.0901130	−0.0450565	+	0.998984i	$0.514347\pi$
$182$	3.70928	0.274950
$183$	−27.4391	−2.02835
$184$	−11.7009	−0.862599
$185$	−31.6453	−2.32661
$186$	33.8576	2.48256
$187$	20.4619	1.49632
$188$	22.7298	1.65774
$189$	6.20620	0.451435
$190$	−43.4463	−3.15192
$191$	6.89269	0.498738	0.249369	−	0.968409i	$-0.419777\pi$
$191$	6.89269	0.498738	0.249369	+	0.968409i	$0.419777\pi$
$192$	33.3545	2.40716
$193$	3.22568	0.232189	0.116095	−	0.993238i	$-0.462962\pi$
$193$	3.22568	0.232189	0.116095	+	0.993238i	$0.462962\pi$
$194$	−10.2823	−0.738227
$195$	11.2979	0.809060
$196$	−11.0494	−0.789246
$197$	8.77432	0.625145	0.312572	−	0.949894i	$-0.398809\pi$
$197$	8.77432	0.625145	0.312572	+	0.949894i	$0.398809\pi$
$198$	43.6163	3.09968
$199$	−20.6020	−1.46043	−0.730217	−	0.683215i	$-0.760581\pi$
$199$	−20.6020	−1.46043	−0.730217	+	0.683215i	$0.760581\pi$
$200$	−19.0700	−1.34845
$201$	12.6803	0.894403
$202$	31.4596	2.21349
$203$	5.62475	0.394780
$204$	32.4329	2.27076
$205$	21.9421	1.53251
$206$	−2.17009	−0.151197
$207$	32.9939	2.29323
$208$	−2.07838	−0.144110
$209$	22.2329	1.53788
$210$	41.9071	2.89186
$211$	−4.85762	−0.334412	−0.167206	−	0.985922i	$-0.553475\pi$
$211$	−4.85762	−0.334412	−0.167206	+	0.985922i	$0.553475\pi$
$212$	5.55252	0.381349
$213$	−23.0928	−1.58229
$214$	−15.3607	−1.05004
$215$	−26.4391	−1.80313
$216$	5.58864	0.380259
$217$	−9.84324	−0.668203
$218$	−6.97107	−0.472140
$219$	42.5018	2.87201
$220$	52.3195	3.52738
$221$	−4.41855	−0.297224
$222$	44.6163	2.99445
$223$	−5.05664	−0.338617	−0.169309	−	0.985563i	$-0.554153\pi$
$223$	−5.05664	−0.338617	−0.169309	+	0.985563i	$0.554153\pi$
$224$	−12.9711	−0.866666
$225$	53.7731	3.58487
$226$	−0.738205	−0.0491047
$227$	16.9360	1.12408	0.562041	−	0.827109i	$-0.310016\pi$
$227$	16.9360	1.12408	0.562041	+	0.827109i	$0.310016\pi$
$228$	35.2401	2.33383
$229$	−1.75872	−0.116220	−0.0581099	−	0.998310i	$-0.518507\pi$
$229$	−1.75872	−0.116220	−0.0581099	+	0.998310i	$0.518507\pi$
$230$	68.7936	4.53612
$231$	−21.4452	−1.41099
$232$	5.06505	0.332537
$233$	23.9916	1.57174	0.785871	−	0.618391i	$-0.212215\pi$
$233$	23.9916	1.57174	0.785871	+	0.618391i	$0.212215\pi$
$234$	−9.41855	−0.615710
$235$	−34.9854	−2.28220
$236$	−31.8937	−2.07611
$237$	−35.2762	−2.29143
$238$	−16.3896	−1.06238
$239$	−12.3535	−0.799082	−0.399541	−	0.916715i	$-0.630830\pi$
$239$	−12.3535	−0.799082	−0.399541	+	0.916715i	$0.630830\pi$
$240$	−23.4813	−1.51571
$241$	3.00719	0.193710	0.0968550	−	0.995299i	$-0.469122\pi$
$241$	3.00719	0.193710	0.0968550	+	0.995299i	$0.469122\pi$
$242$	−22.6670	−1.45709
$243$	19.5174	1.25204
$244$	27.4391	1.75661
$245$	17.0072	1.08655
$246$	−30.9360	−1.97241
$247$	−4.80098	−0.305479
$248$	−8.86376	−0.562850
$249$	−0.885505	−0.0561166
$250$	66.8720	4.22936
$251$	16.6781	1.05271	0.526355	−	0.850265i	$-0.323558\pi$
$251$	16.6781	1.05271	0.526355	+	0.850265i	$0.323558\pi$
$252$	−20.0989	−1.26611
$253$	−35.2039	−2.21325
$254$	32.7659	2.05592
$255$	−49.9204	−3.12614
$256$	−0.418551	−0.0261594
$257$	−16.1217	−1.00564	−0.502821	−	0.864390i	$-0.667705\pi$
$257$	−16.1217	−1.00564	−0.502821	+	0.864390i	$0.667705\pi$
$258$	37.2762	2.32071
$259$	−12.9711	−0.805983
$260$	−11.2979	−0.700667
$261$	−14.2823	−0.884053
$262$	0.398032	0.0245905
$263$	5.30510	0.327127	0.163563	−	0.986533i	$-0.447701\pi$
$263$	5.30510	0.327127	0.163563	+	0.986533i	$0.447701\pi$
$264$	−19.3112	−1.18852
$265$	−8.54638	−0.525000
$266$	−17.8082	−1.09189
$267$	−2.88550	−0.176590
$268$	−12.6803	−0.774575
$269$	25.3340	1.54464	0.772322	−	0.635232i	$-0.219095\pi$
$269$	25.3340	1.54464	0.772322	+	0.635232i	$0.219095\pi$
$270$	−32.8576	−1.99965
$271$	13.4947	0.819742	0.409871	−	0.912143i	$-0.365574\pi$
$271$	13.4947	0.819742	0.409871	+	0.912143i	$0.365574\pi$
$272$	9.18342	0.556826
$273$	4.63090	0.280275
$274$	17.2534	1.04232
$275$	−57.3751	−3.45985
$276$	−55.7998	−3.35875
$277$	3.07838	0.184962	0.0924809	−	0.995714i	$-0.470520\pi$
$277$	3.07838	0.184962	0.0924809	+	0.995714i	$0.470520\pi$
$278$	−21.1773	−1.27013
$279$	24.9939	1.49634
$280$	−10.9711	−0.655647
$281$	8.64423	0.515671	0.257836	−	0.966189i	$-0.416991\pi$
$281$	8.64423	0.515671	0.257836	+	0.966189i	$0.416991\pi$
$282$	49.3256	2.93730
$283$	−1.04945	−0.0623832	−0.0311916	−	0.999513i	$-0.509930\pi$
$283$	−1.04945	−0.0623832	−0.0311916	+	0.999513i	$0.509930\pi$
$284$	23.0928	1.37030
$285$	−54.2411	−3.21297
$286$	10.0494	0.594236
$287$	8.99386	0.530891
$288$	32.9360	1.94077
$289$	2.52359	0.148446
$290$	−29.7792	−1.74870
$291$	−12.8371	−0.752524
$292$	−42.5018	−2.48723
$293$	11.2123	0.655032	0.327516	−	0.944846i	$-0.393788\pi$
$293$	11.2123	0.655032	0.327516	+	0.944846i	$0.393788\pi$
$294$	−23.9783	−1.39844
$295$	49.0905	2.85816
$296$	−11.6803	−0.678906
$297$	16.8143	0.975666
$298$	42.9854	2.49008
$299$	7.60197	0.439633
$300$	−90.9420	−5.25054
$301$	−10.8371	−0.624640
$302$	−44.6947	−2.57189
$303$	39.2762	2.25636
$304$	9.97826	0.572292
$305$	−42.2339	−2.41831
$306$	41.6163	2.37905
$307$	−2.21008	−0.126136	−0.0630679	−	0.998009i	$-0.520088\pi$
$307$	−2.21008	−0.126136	−0.0630679	+	0.998009i	$0.520088\pi$
$308$	21.4452	1.22195
$309$	−2.70928	−0.154125
$310$	52.1133	2.95983
$311$	−5.65142	−0.320462	−0.160231	−	0.987080i	$-0.551224\pi$
$311$	−5.65142	−0.320462	−0.160231	+	0.987080i	$0.551224\pi$
$312$	4.17009	0.236085
$313$	−29.3318	−1.65793	−0.828965	−	0.559301i	$-0.811070\pi$
$313$	−29.3318	−1.65793	−0.828965	+	0.559301i	$0.811070\pi$
$314$	−0.290725	−0.0164065
$315$	30.9360	1.74305
$316$	35.2762	1.98444
$317$	−1.40417	−0.0788663	−0.0394332	−	0.999222i	$-0.512555\pi$
$317$	−1.40417	−0.0788663	−0.0394332	+	0.999222i	$0.512555\pi$
$318$	12.0494	0.675700
$319$	15.2390	0.853221
$320$	51.3390	2.86993
$321$	−19.1773	−1.07037
$322$	28.1978	1.57140
$323$	21.2134	1.18034
$324$	−8.62475	−0.479153
$325$	12.3896	0.687253
$326$	39.7708	2.20270
$327$	−8.70313	−0.481284
$328$	8.09890	0.447187
$329$	−14.3402	−0.790599
$330$	113.538	6.25005
$331$	−3.39576	−0.186648	−0.0933240	−	0.995636i	$-0.529749\pi$
$331$	−3.39576	−0.186648	−0.0933240	+	0.995636i	$0.529749\pi$
$332$	0.885505	0.0485984
$333$	32.9360	1.80488
$334$	−31.5958	−1.72885
$335$	19.5174	1.06635
$336$	−9.62475	−0.525073
$337$	29.9132	1.62948	0.814738	−	0.579829i	$-0.196881\pi$
$337$	29.9132	1.62948	0.814738	+	0.579829i	$0.196881\pi$
$338$	−2.17009	−0.118037
$339$	−0.921622	−0.0500556
$340$	49.9204	2.70731
$341$	−26.6681	−1.44416
$342$	45.2183	2.44513
$343$	18.9360	1.02245
$344$	−9.75872	−0.526155
$345$	85.8864	4.62397
$346$	−37.2762	−2.00398
$347$	−6.05786	−0.325203	−0.162601	−	0.986692i	$-0.551988\pi$
$347$	−6.05786	−0.325203	−0.162601	+	0.986692i	$0.551988\pi$
$348$	24.1545	1.29482
$349$	14.3451	0.767875	0.383938	−	0.923359i	$-0.374568\pi$
$349$	14.3451	0.767875	0.383938	+	0.923359i	$0.374568\pi$
$350$	45.9565	2.45648
$351$	−3.63090	−0.193803
$352$	−35.1422	−1.87309
$353$	−16.2918	−0.867123	−0.433562	−	0.901124i	$-0.642743\pi$
$353$	−16.2918	−0.867123	−0.433562	+	0.901124i	$0.642743\pi$
$354$	−69.2122	−3.67859
$355$	−35.5441	−1.88649
$356$	2.88550	0.152931
$357$	−20.4619	−1.08296
$358$	27.9649	1.47799
$359$	10.8722	0.573811	0.286906	−	0.957959i	$-0.407373\pi$
$359$	10.8722	0.573811	0.286906	+	0.957959i	$0.407373\pi$
$360$	27.8576	1.46823
$361$	4.04945	0.213129
$362$	2.63090	0.138277
$363$	−28.2990	−1.48531
$364$	−4.63090	−0.242725
$365$	65.4184	3.42415
$366$	59.5452	3.11248
$367$	17.7093	0.924417	0.462208	−	0.886771i	$-0.347057\pi$
$367$	17.7093	0.924417	0.462208	+	0.886771i	$0.347057\pi$
$368$	−15.7998	−0.823620
$369$	−22.8371	−1.18885
$370$	68.6730	3.57014
$371$	−3.50307	−0.181870
$372$	−42.2700	−2.19160
$373$	−21.8166	−1.12962	−0.564810	−	0.825221i	$-0.691051\pi$
$373$	−21.8166	−1.12962	−0.564810	+	0.825221i	$0.691051\pi$
$374$	−44.4040	−2.29608
$375$	83.4873	4.31127
$376$	−12.9132	−0.665948
$377$	−3.29072	−0.169481
$378$	−13.4680	−0.692719
$379$	34.5464	1.77453	0.887264	−	0.461262i	$-0.152603\pi$
$379$	34.5464	1.77453	0.887264	+	0.461262i	$0.152603\pi$
$380$	54.2411	2.78251
$381$	40.9071	2.09573
$382$	−14.9577	−0.765305
$383$	21.1506	1.08075	0.540373	−	0.841426i	$-0.318283\pi$
$383$	21.1506	1.08075	0.540373	+	0.841426i	$0.318283\pi$
$384$	−31.2628	−1.59538
$385$	−33.0082	−1.68226
$386$	−7.00000	−0.356291
$387$	27.5174	1.39879
$388$	12.8371	0.651705
$389$	−25.0700	−1.27110	−0.635549	−	0.772061i	$-0.719226\pi$
$389$	−25.0700	−1.27110	−0.635549	+	0.772061i	$0.719226\pi$
$390$	−24.5174	−1.24149
$391$	−33.5897	−1.69870
$392$	6.27739	0.317056
$393$	0.496928	0.0250667
$394$	−19.0410	−0.959274
$395$	−54.2967	−2.73196
$396$	−54.4534	−2.73639
$397$	−36.0010	−1.80684	−0.903420	−	0.428756i	$-0.858952\pi$
$397$	−36.0010	−1.80684	−0.903420	+	0.428756i	$0.858952\pi$
$398$	44.7081	2.24101
$399$	−22.2329	−1.11304
$400$	−25.7503	−1.28752
$401$	−7.17727	−0.358416	−0.179208	−	0.983811i	$-0.557354\pi$
$401$	−7.17727	−0.358416	−0.179208	+	0.983811i	$0.557354\pi$
$402$	−27.5174	−1.37245
$403$	5.75872	0.286862
$404$	−39.2762	−1.95406
$405$	13.2751	0.659646
$406$	−12.2062	−0.605784
$407$	−35.1422	−1.74193
$408$	−18.4257	−0.912210
$409$	19.5669	0.967521	0.483760	−	0.875200i	$-0.339271\pi$
$409$	19.5669	0.967521	0.483760	+	0.875200i	$0.339271\pi$
$410$	−47.6163	−2.35160
$411$	21.5402	1.06250
$412$	2.70928	0.133476
$413$	20.1217	0.990123
$414$	−71.5995	−3.51892
$415$	−1.36296	−0.0669050
$416$	7.58864	0.372064
$417$	−26.4391	−1.29473
$418$	−48.2472	−2.35985
$419$	−16.7877	−0.820131	−0.410065	−	0.912056i	$-0.634494\pi$
$419$	−16.7877	−0.820131	−0.410065	+	0.912056i	$0.634494\pi$
$420$	−52.3195	−2.55293
$421$	−6.89496	−0.336040	−0.168020	−	0.985784i	$-0.553737\pi$
$421$	−6.89496	−0.336040	−0.168020	+	0.985784i	$0.553737\pi$
$422$	10.5415	0.513150
$423$	36.4124	1.77043
$424$	−3.15449	−0.153195
$425$	−54.7442	−2.65548
$426$	50.1133	2.42800
$427$	−17.3112	−0.837750
$428$	19.1773	0.926969
$429$	12.5464	0.605745
$430$	57.3751	2.76687
$431$	20.6765	0.995951	0.497975	−	0.867191i	$-0.334077\pi$
$431$	20.6765	0.995951	0.497975	+	0.867191i	$0.334077\pi$
$432$	7.54638	0.363075
$433$	−13.3919	−0.643573	−0.321787	−	0.946812i	$-0.604283\pi$
$433$	−13.3919	−0.643573	−0.321787	+	0.946812i	$0.604283\pi$
$434$	21.3607	1.02535
$435$	−37.1783	−1.78256
$436$	8.70313	0.416804
$437$	−36.4969	−1.74588
$438$	−92.2327	−4.40705
$439$	5.44521	0.259886	0.129943	−	0.991521i	$-0.458521\pi$
$439$	5.44521	0.259886	0.129943	+	0.991521i	$0.458521\pi$
$440$	−29.7237	−1.41702
$441$	−17.7009	−0.842898
$442$	9.58864	0.456085
$443$	37.3051	1.77242	0.886209	−	0.463285i	$-0.153329\pi$
$443$	37.3051	1.77242	0.886209	+	0.463285i	$0.153329\pi$
$444$	−55.7019	−2.64350
$445$	−4.44134	−0.210540
$446$	10.9733	0.519603
$447$	53.6658	2.53830
$448$	21.0433	0.994203
$449$	18.9977	0.896558	0.448279	−	0.893894i	$-0.352037\pi$
$449$	18.9977	0.896558	0.448279	+	0.893894i	$0.352037\pi$
$450$	−116.692	−5.50093
$451$	24.3668	1.14739
$452$	0.921622	0.0433495
$453$	−55.7998	−2.62170
$454$	−36.7526	−1.72488
$455$	7.12783	0.334158
$456$	−20.0205	−0.937547
$457$	−26.6309	−1.24574	−0.622870	−	0.782325i	$-0.714034\pi$
$457$	−26.6309	−1.24574	−0.622870	+	0.782325i	$0.714034\pi$
$458$	3.81658	0.178337
$459$	16.0433	0.748837
$460$	−85.8864	−4.00447
$461$	14.9444	0.696030	0.348015	−	0.937489i	$-0.386856\pi$
$461$	14.9444	0.696030	0.348015	+	0.937489i	$0.386856\pi$
$462$	46.5380	2.16514
$463$	7.18115	0.333736	0.166868	−	0.985979i	$-0.446635\pi$
$463$	7.18115	0.333736	0.166868	+	0.985979i	$0.446635\pi$
$464$	6.83937	0.317510
$465$	65.0616	3.01716
$466$	−52.0638	−2.41181
$467$	−20.3896	−0.943519	−0.471760	−	0.881727i	$-0.656381\pi$
$467$	−20.3896	−0.943519	−0.471760	+	0.881727i	$0.656381\pi$
$468$	11.7587	0.543547
$469$	8.00000	0.369406
$470$	75.9214	3.50200
$471$	−0.362959	−0.0167243
$472$	18.1194	0.834014
$473$	−29.3607	−1.35001
$474$	76.5523	3.51617
$475$	−59.4824	−2.72924
$476$	20.4619	0.937868
$477$	8.89496	0.407272
$478$	26.8082	1.22618
$479$	10.6947	0.488654	0.244327	−	0.969693i	$-0.421433\pi$
$479$	10.6947	0.488654	0.244327	+	0.969693i	$0.421433\pi$
$480$	85.7358	3.91328
$481$	7.58864	0.346012
$482$	−6.52586	−0.297245
$483$	35.2039	1.60183
$484$	28.2990	1.28632
$485$	−19.7587	−0.897197
$486$	−42.3545	−1.92124
$487$	−39.3295	−1.78219	−0.891095	−	0.453817i	$-0.850062\pi$
$487$	−39.3295	−1.78219	−0.891095	+	0.453817i	$0.850062\pi$
$488$	−15.5886	−0.705664
$489$	49.6525	2.24536
$490$	−36.9071	−1.66729
$491$	−17.3074	−0.781071	−0.390535	−	0.920588i	$-0.627710\pi$
$491$	−17.3074	−0.781071	−0.390535	+	0.920588i	$0.627710\pi$
$492$	38.6225	1.74124
$493$	14.5402	0.654859
$494$	10.4186	0.468753
$495$	83.8141	3.76717
$496$	−11.9688	−0.537415
$497$	−14.5692	−0.653516
$498$	1.92162	0.0861100
$499$	−22.5380	−1.00894	−0.504469	−	0.863430i	$-0.668312\pi$
$499$	−22.5380	−1.00894	−0.504469	+	0.863430i	$0.668312\pi$
$500$	−83.4873	−3.73367
$501$	−39.4463	−1.76233
$502$	−36.1929	−1.61537
$503$	−21.8394	−0.973769	−0.486885	−	0.873466i	$-0.661867\pi$
$503$	−21.8394	−0.973769	−0.486885	+	0.873466i	$0.661867\pi$
$504$	11.4186	0.508623
$505$	60.4534	2.69014
$506$	76.3956	3.39620
$507$	−2.70928	−0.120323
$508$	−40.9071	−1.81496
$509$	−43.7770	−1.94038	−0.970190	−	0.242345i	$-0.922083\pi$
$509$	−43.7770	−1.94038	−0.970190	+	0.242345i	$0.922083\pi$
$510$	108.332	4.79700
$511$	26.8143	1.18620
$512$	−22.1701	−0.979789
$513$	17.4319	0.769636
$514$	34.9854	1.54314
$515$	−4.17009	−0.183756
$516$	−46.5380	−2.04872
$517$	−38.8515	−1.70869
$518$	28.1483	1.23677
$519$	−46.5380	−2.04279
$520$	6.41855	0.281472
$521$	−8.39803	−0.367924	−0.183962	−	0.982933i	$-0.558892\pi$
$521$	−8.39803	−0.367924	−0.183962	+	0.982933i	$0.558892\pi$
$522$	30.9939	1.35656
$523$	31.6781	1.38519	0.692593	−	0.721329i	$-0.256468\pi$
$523$	31.6781	1.38519	0.692593	+	0.721329i	$0.256468\pi$
$524$	−0.496928	−0.0217084
$525$	57.3751	2.50405
$526$	−11.5125	−0.501970
$527$	−25.4452	−1.10841
$528$	−26.0761	−1.13482
$529$	34.7899	1.51261
$530$	18.5464	0.805603
$531$	−51.0928	−2.21724
$532$	22.2329	0.963917
$533$	−5.26180	−0.227914
$534$	6.26180	0.270974
$535$	−29.5174	−1.27615
$536$	7.20394	0.311163
$537$	34.9132	1.50662
$538$	−54.9770	−2.37023
$539$	18.8865	0.813501
$540$	41.0216	1.76529
$541$	−2.48255	−0.106733	−0.0533666	−	0.998575i	$-0.516995\pi$
$541$	−2.48255	−0.106733	−0.0533666	+	0.998575i	$0.516995\pi$
$542$	−29.2846	−1.25788
$543$	3.28458	0.140955
$544$	−33.5308	−1.43762
$545$	−13.3958	−0.573812
$546$	−10.0494	−0.430077
$547$	−21.5525	−0.921519	−0.460760	−	0.887525i	$-0.652423\pi$
$547$	−21.5525	−0.921519	−0.460760	+	0.887525i	$0.652423\pi$
$548$	−21.5402	−0.920153
$549$	43.9565	1.87602
$550$	124.509	5.30908
$551$	15.7987	0.673048
$552$	31.7009	1.34928
$553$	−22.2557	−0.946407
$554$	−6.68035	−0.283821
$555$	85.7358	3.63928
$556$	26.4391	1.12127
$557$	−4.58986	−0.194479	−0.0972393	−	0.995261i	$-0.531001\pi$
$557$	−4.58986	−0.194479	−0.0972393	+	0.995261i	$0.531001\pi$
$558$	−54.2388	−2.29611
$559$	6.34017	0.268161
$560$	−14.8143	−0.626019
$561$	−55.4368	−2.34054
$562$	−18.7587	−0.791289
$563$	7.97107	0.335941	0.167970	−	0.985792i	$-0.446279\pi$
$563$	7.97107	0.335941	0.167970	+	0.985792i	$0.446279\pi$
$564$	−61.5813	−2.59304
$565$	−1.41855	−0.0596789
$566$	2.27739	0.0957260
$567$	5.44134	0.228515
$568$	−13.1194	−0.550478
$569$	−21.9688	−0.920980	−0.460490	−	0.887665i	$-0.652326\pi$
$569$	−21.9688	−0.920980	−0.460490	+	0.887665i	$0.652326\pi$
$570$	117.708	4.93024
$571$	3.85166	0.161187	0.0805934	−	0.996747i	$-0.474318\pi$
$571$	3.85166	0.161187	0.0805934	+	0.996747i	$0.474318\pi$
$572$	−12.5464	−0.524590
$573$	−18.6742	−0.780126
$574$	−19.5174	−0.814643
$575$	94.1855	3.92781
$576$	−53.4329	−2.22637
$577$	−5.48133	−0.228191	−0.114095	−	0.993470i	$-0.536397\pi$
$577$	−5.48133	−0.228191	−0.114095	+	0.993470i	$0.536397\pi$
$578$	−5.47641	−0.227789
$579$	−8.73925	−0.363191
$580$	37.1783	1.54375
$581$	−0.558663	−0.0231772
$582$	27.8576	1.15474
$583$	−9.49079	−0.393068
$584$	24.1461	0.999172
$585$	−18.0989	−0.748297
$586$	−24.3318	−1.00514
$587$	18.7877	0.775449	0.387725	−	0.921775i	$-0.373261\pi$
$587$	18.7877	0.775449	0.387725	+	0.921775i	$0.373261\pi$
$588$	29.9360	1.23454
$589$	−27.6475	−1.13920
$590$	−106.531	−4.38580
$591$	−23.7721	−0.977852
$592$	−15.7721	−0.648227
$593$	31.7370	1.30328	0.651641	−	0.758528i	$-0.274081\pi$
$593$	31.7370	1.30328	0.651641	+	0.758528i	$0.274081\pi$
$594$	−36.4885	−1.49714
$595$	−31.4947	−1.29116
$596$	−53.6658	−2.19824
$597$	55.8164	2.28441
$598$	−16.4969	−0.674610
$599$	37.3857	1.52754	0.763770	−	0.645488i	$-0.223346\pi$
$599$	37.3857	1.52754	0.763770	+	0.645488i	$0.223346\pi$
$600$	51.6658	2.10925
$601$	−25.0928	−1.02355	−0.511777	−	0.859118i	$-0.671013\pi$
$601$	−25.0928	−1.02355	−0.511777	+	0.859118i	$0.671013\pi$
$602$	23.5174	0.958500
$603$	−20.3135	−0.827230
$604$	55.7998	2.27046
$605$	−43.5574	−1.77086
$606$	−85.2327	−3.46234
$607$	−37.6514	−1.52822	−0.764112	−	0.645084i	$-0.776822\pi$
$607$	−37.6514	−1.52822	−0.764112	+	0.645084i	$0.776822\pi$
$608$	−36.4329	−1.47755
$609$	−15.2390	−0.617516
$610$	91.6512	3.71085
$611$	8.38962	0.339408
$612$	−51.9565	−2.10022
$613$	11.3691	0.459194	0.229597	−	0.973286i	$-0.426259\pi$
$613$	11.3691	0.459194	0.229597	+	0.973286i	$0.426259\pi$
$614$	4.79606	0.193553
$615$	−59.4473	−2.39715
$616$	−12.1834	−0.490884
$617$	−22.1701	−0.892534	−0.446267	−	0.894900i	$-0.647247\pi$
$617$	−22.1701	−0.892534	−0.446267	+	0.894900i	$0.647247\pi$
$618$	5.87936	0.236503
$619$	−11.5525	−0.464335	−0.232167	−	0.972676i	$-0.574582\pi$
$619$	−11.5525	−0.464335	−0.232167	+	0.972676i	$0.574582\pi$
$620$	−65.0616	−2.61293
$621$	−27.6020	−1.10763
$622$	12.2641	0.491744
$623$	−1.82046	−0.0729351
$624$	5.63090	0.225416
$625$	66.5546	2.66218
$626$	63.6525	2.54406
$627$	−60.2350	−2.40555
$628$	0.362959	0.0144837
$629$	−33.5308	−1.33696
$630$	−67.1338	−2.67467
$631$	−15.5981	−0.620950	−0.310475	−	0.950582i	$-0.600488\pi$
$631$	−15.5981	−0.620950	−0.310475	+	0.950582i	$0.600488\pi$
$632$	−20.0410	−0.797190
$633$	13.1606	0.523088
$634$	3.04718	0.121019
$635$	62.9637	2.49864
$636$	−15.0433	−0.596506
$637$	−4.07838	−0.161591
$638$	−33.0700	−1.30925
$639$	36.9939	1.46345
$640$	−48.1194	−1.90209
$641$	13.3028	0.525430	0.262715	−	0.964873i	$-0.415382\pi$
$641$	13.3028	0.525430	0.262715	+	0.964873i	$0.415382\pi$
$642$	41.6163	1.64247
$643$	6.88163	0.271385	0.135692	−	0.990751i	$-0.456674\pi$
$643$	6.88163	0.271385	0.135692	+	0.990751i	$0.456674\pi$
$644$	−35.2039	−1.38723
$645$	71.6307	2.82046
$646$	−46.0349	−1.81122
$647$	3.29299	0.129461	0.0647304	−	0.997903i	$-0.479381\pi$
$647$	3.29299	0.129461	0.0647304	+	0.997903i	$0.479381\pi$
$648$	4.89988	0.192485
$649$	54.5152	2.13991
$650$	−26.8865	−1.05458
$651$	26.6681	1.04520
$652$	−49.6525	−1.94454
$653$	24.9216	0.975258	0.487629	−	0.873051i	$-0.337862\pi$
$653$	24.9216	0.975258	0.487629	+	0.873051i	$0.337862\pi$
$654$	18.8865	0.738523
$655$	0.764867	0.0298858
$656$	10.9360	0.426979
$657$	−68.0866	−2.65631
$658$	31.1194	1.21316
$659$	10.2062	0.397577	0.198789	−	0.980042i	$-0.436299\pi$
$659$	10.2062	0.397577	0.198789	+	0.980042i	$0.436299\pi$
$660$	−141.748	−5.51753
$661$	−26.4163	−1.02747	−0.513737	−	0.857948i	$-0.671739\pi$
$661$	−26.4163	−1.02747	−0.513737	+	0.857948i	$0.671739\pi$
$662$	7.36910	0.286408
$663$	11.9711	0.464918
$664$	−0.503072	−0.0195230
$665$	−34.2206	−1.32702
$666$	−71.4740	−2.76956
$667$	−25.0160	−0.968623
$668$	39.4463	1.52622
$669$	13.6998	0.529666
$670$	−42.3545	−1.63630
$671$	−46.9009	−1.81059
$672$	35.1422	1.35564
$673$	14.1857	0.546818	0.273409	−	0.961898i	$-0.411849\pi$
$673$	14.1857	0.546818	0.273409	+	0.961898i	$0.411849\pi$
$674$	−64.9143	−2.50040
$675$	−44.9854	−1.73149
$676$	2.70928	0.104203
$677$	6.45959	0.248262	0.124131	−	0.992266i	$-0.460386\pi$
$677$	6.45959	0.248262	0.124131	+	0.992266i	$0.460386\pi$
$678$	2.00000	0.0768095
$679$	−8.09890	−0.310807
$680$	−28.3607	−1.08758
$681$	−45.8843	−1.75829
$682$	57.8720	2.21603
$683$	0.366835	0.0140365	0.00701827	−	0.999975i	$-0.497766\pi$
$683$	0.366835	0.0140365	0.00701827	+	0.999975i	$0.497766\pi$
$684$	−56.4534	−2.15855
$685$	33.1545	1.26677
$686$	−41.0928	−1.56893
$687$	4.76487	0.181791
$688$	−13.1773	−0.502379
$689$	2.04945	0.0780778
$690$	−186.381	−7.09540
$691$	35.6430	1.35592	0.677962	−	0.735097i	$-0.262863\pi$
$691$	35.6430	1.35592	0.677962	+	0.735097i	$0.262863\pi$
$692$	46.5380	1.76911
$693$	34.3545	1.30502
$694$	13.1461	0.499018
$695$	−40.6947	−1.54364
$696$	−13.7226	−0.520154
$697$	23.2495	0.880638
$698$	−31.1301	−1.17829
$699$	−64.9998	−2.45852
$700$	−57.3751	−2.16857
$701$	40.9709	1.54745	0.773725	−	0.633522i	$-0.218391\pi$
$701$	40.9709	1.54745	0.773725	+	0.633522i	$0.218391\pi$
$702$	7.87936	0.297387
$703$	−36.4329	−1.37409
$704$	57.0121	2.14872
$705$	94.7852	3.56982
$706$	35.3545	1.33059
$707$	24.7792	0.931919
$708$	86.4089	3.24745
$709$	−19.7321	−0.741053	−0.370527	−	0.928822i	$-0.620823\pi$
$709$	−19.7321	−0.741053	−0.370527	+	0.928822i	$0.620823\pi$
$710$	77.1338	2.89478
$711$	56.5113	2.11934
$712$	−1.63931	−0.0614357
$713$	43.7776	1.63949
$714$	44.4040	1.66178
$715$	19.3112	0.722200
$716$	−34.9132	−1.30477
$717$	33.4690	1.24992
$718$	−23.5936	−0.880504
$719$	−19.3652	−0.722201	−0.361101	−	0.932527i	$-0.617599\pi$
$719$	−19.3652	−0.722201	−0.361101	+	0.932527i	$0.617599\pi$
$720$	37.6163	1.40188
$721$	−1.70928	−0.0636567
$722$	−8.78765	−0.327043
$723$	−8.14730	−0.303001
$724$	−3.28458	−0.122071
$725$	−40.7708	−1.51419
$726$	61.4112	2.27918
$727$	16.6332	0.616890	0.308445	−	0.951242i	$-0.400191\pi$
$727$	16.6332	0.616890	0.308445	+	0.951242i	$0.400191\pi$
$728$	2.63090	0.0975076
$729$	−43.3279	−1.60474
$730$	−141.964	−5.25431
$731$	−28.0144	−1.03615
$732$	−74.3400	−2.74769
$733$	15.6248	0.577113	0.288557	−	0.957463i	$-0.406825\pi$
$733$	15.6248	0.577113	0.288557	+	0.957463i	$0.406825\pi$
$734$	−38.4307	−1.41850
$735$	−46.0772	−1.69958
$736$	57.6886	2.12643
$737$	21.6742	0.798380
$738$	49.5585	1.82427
$739$	−1.69982	−0.0625289	−0.0312644	−	0.999511i	$-0.509953\pi$
$739$	−1.69982	−0.0625289	−0.0312644	+	0.999511i	$0.509953\pi$
$740$	−85.7358	−3.15171
$741$	13.0072	0.477831
$742$	7.60197	0.279077
$743$	−32.3812	−1.18795	−0.593976	−	0.804483i	$-0.702442\pi$
$743$	−32.3812	−1.18795	−0.593976	+	0.804483i	$0.702442\pi$
$744$	24.0144	0.880410
$745$	82.6018	3.02630
$746$	47.3439	1.73338
$747$	1.41855	0.0519021
$748$	55.4368	2.02697
$749$	−12.0989	−0.442084
$750$	−181.175	−6.61556
$751$	−17.3607	−0.633501	−0.316750	−	0.948509i	$-0.602592\pi$
$751$	−17.3607	−0.633501	−0.316750	+	0.948509i	$0.602592\pi$
$752$	−17.4368	−0.635855
$753$	−45.1855	−1.64665
$754$	7.14116	0.260066
$755$	−85.8864	−3.12573
$756$	16.8143	0.611531
$757$	24.4596	0.888999	0.444499	−	0.895779i	$-0.353382\pi$
$757$	24.4596	0.888999	0.444499	+	0.895779i	$0.353382\pi$
$758$	−74.9686	−2.72298
$759$	95.3772	3.46197
$760$	−30.8154	−1.11779
$761$	39.2411	1.42249	0.711244	−	0.702945i	$-0.248132\pi$
$761$	39.2411	1.42249	0.711244	+	0.702945i	$0.248132\pi$
$762$	−88.7719	−3.21587
$763$	−5.49079	−0.198780
$764$	18.6742	0.675609
$765$	79.9709	2.89135
$766$	−45.8987	−1.65839
$767$	−11.7721	−0.425064
$768$	1.13397	0.0409186
$769$	−29.9204	−1.07896	−0.539479	−	0.841999i	$-0.681379\pi$
$769$	−29.9204	−1.07896	−0.539479	+	0.841999i	$0.681379\pi$
$770$	71.6307	2.58139
$771$	43.6781	1.57303
$772$	8.73925	0.314532
$773$	1.94602	0.0699934	0.0349967	−	0.999387i	$-0.488858\pi$
$773$	1.94602	0.0699934	0.0349967	+	0.999387i	$0.488858\pi$
$774$	−59.7152	−2.14642
$775$	71.3484	2.56291
$776$	−7.29299	−0.261803
$777$	35.1422	1.26072
$778$	54.4040	1.95048
$779$	25.2618	0.905098
$780$	30.6092	1.09598
$781$	−39.4719	−1.41241
$782$	72.8925	2.60663
$783$	11.9483	0.426997
$784$	8.47641	0.302729
$785$	−0.558663	−0.0199395
$786$	−1.07838	−0.0384645
$787$	47.8443	1.70546	0.852732	−	0.522348i	$-0.174944\pi$
$787$	47.8443	1.70546	0.852732	+	0.522348i	$0.174944\pi$
$788$	23.7721	0.846844
$789$	−14.3730	−0.511692
$790$	117.829	4.19215
$791$	−0.581449	−0.0206740
$792$	30.9360	1.09926
$793$	10.1278	0.359650
$794$	78.1254	2.77257
$795$	23.1545	0.821205
$796$	−55.8164	−1.97836
$797$	−30.5936	−1.08368	−0.541840	−	0.840482i	$-0.682272\pi$
$797$	−30.5936	−1.08368	−0.541840	+	0.840482i	$0.682272\pi$
$798$	48.2472	1.70793
$799$	−37.0700	−1.31144
$800$	94.0203	3.32412
$801$	4.62249	0.163328
$802$	15.5753	0.549983
$803$	72.6474	2.56367
$804$	34.3545	1.21159
$805$	54.1855	1.90979
$806$	−12.4969	−0.440186
$807$	−68.6369	−2.41613
$808$	22.3135	0.784987
$809$	−51.0265	−1.79400	−0.896998	−	0.442035i	$-0.854257\pi$
$809$	−51.0265	−1.79400	−0.896998	+	0.442035i	$0.854257\pi$
$810$	−28.8082	−1.01222
$811$	−20.0410	−0.703736	−0.351868	−	0.936050i	$-0.614453\pi$
$811$	−20.0410	−0.703736	−0.351868	+	0.936050i	$0.614453\pi$
$812$	15.2390	0.534784
$813$	−36.5608	−1.28224
$814$	76.2616	2.67297
$815$	76.4245	2.67703
$816$	−24.8804	−0.870988
$817$	−30.4391	−1.06493
$818$	−42.4619	−1.48464
$819$	−7.41855	−0.259225
$820$	59.4473	2.07599
$821$	−36.9093	−1.28814	−0.644072	−	0.764965i	$-0.722756\pi$
$821$	−36.9093	−1.28814	−0.644072	+	0.764965i	$0.722756\pi$
$822$	−46.7442	−1.63039
$823$	22.9672	0.800586	0.400293	−	0.916387i	$-0.368908\pi$
$823$	22.9672	0.800586	0.400293	+	0.916387i	$0.368908\pi$
$824$	−1.53919	−0.0536202
$825$	155.445	5.41190
$826$	−43.6658	−1.51933
$827$	−5.90707	−0.205409	−0.102704	−	0.994712i	$-0.532750\pi$
$827$	−5.90707	−0.205409	−0.102704	+	0.994712i	$0.532750\pi$
$828$	89.3894	3.10650
$829$	46.9360	1.63015	0.815077	−	0.579352i	$-0.196694\pi$
$829$	46.9360	1.63015	0.815077	+	0.579352i	$0.196694\pi$
$830$	2.95774	0.102665
$831$	−8.34017	−0.289317
$832$	−12.3112	−0.426816
$833$	18.0205	0.624374
$834$	57.3751	1.98674
$835$	−60.7152	−2.10114
$836$	60.2350	2.08327
$837$	−20.9093	−0.722732
$838$	36.4307	1.25848
$839$	13.6525	0.471335	0.235668	−	0.971834i	$-0.424272\pi$
$839$	13.6525	0.471335	0.235668	+	0.971834i	$0.424272\pi$
$840$	29.7237	1.02556
$841$	−18.1711	−0.626591
$842$	14.9627	0.515647
$843$	−23.4196	−0.806614
$844$	−13.1606	−0.453008
$845$	−4.17009	−0.143455
$846$	−79.0181	−2.71670
$847$	−17.8537	−0.613462
$848$	−4.25953	−0.146273
$849$	2.84324	0.0975799
$850$	118.800	4.07479
$851$	57.6886	1.97754
$852$	−62.5646	−2.14343
$853$	−25.9506	−0.888530	−0.444265	−	0.895895i	$-0.646535\pi$
$853$	−25.9506	−0.888530	−0.444265	+	0.895895i	$0.646535\pi$
$854$	37.5669	1.28551
$855$	86.8925	2.97166
$856$	−10.8950	−0.372382
$857$	44.8636	1.53251	0.766255	−	0.642536i	$-0.222118\pi$
$857$	44.8636	1.53251	0.766255	+	0.642536i	$0.222118\pi$
$858$	−27.2267	−0.929505
$859$	−46.0722	−1.57196	−0.785982	−	0.618249i	$-0.787842\pi$
$859$	−46.0722	−1.57196	−0.785982	+	0.618249i	$0.787842\pi$
$860$	−71.6307	−2.44259
$861$	−24.3668	−0.830420
$862$	−44.8697	−1.52827
$863$	19.4224	0.661147	0.330574	−	0.943780i	$-0.392758\pi$
$863$	19.4224	0.661147	0.330574	+	0.943780i	$0.392758\pi$
$864$	−27.5536	−0.937391
$865$	−71.6307	−2.43552
$866$	29.0616	0.987552
$867$	−6.83710	−0.232200
$868$	−26.6681	−0.905173
$869$	−60.2967	−2.04543
$870$	80.6802	2.73531
$871$	−4.68035	−0.158587
$872$	−4.94441	−0.167439
$873$	20.5646	0.696007
$874$	79.2015	2.67903
$875$	52.6719	1.78064
$876$	115.149	3.89053
$877$	−15.9821	−0.539678	−0.269839	−	0.962905i	$-0.586971\pi$
$877$	−15.9821	−0.539678	−0.269839	+	0.962905i	$0.586971\pi$
$878$	−11.8166	−0.398790
$879$	−30.3773	−1.02460
$880$	−40.1361	−1.35299
$881$	0.805905	0.0271516	0.0135758	−	0.999908i	$-0.495679\pi$
$881$	0.805905	0.0271516	0.0135758	+	0.999908i	$0.495679\pi$
$882$	38.4124	1.29341
$883$	−33.6209	−1.13143	−0.565716	−	0.824600i	$-0.691400\pi$
$883$	−33.6209	−1.13143	−0.565716	+	0.824600i	$0.691400\pi$
$884$	−11.9711	−0.402631
$885$	−133.000	−4.47073
$886$	−80.9553	−2.71975
$887$	28.9216	0.971093	0.485547	−	0.874211i	$-0.338621\pi$
$887$	28.9216	0.971093	0.485547	+	0.874211i	$0.338621\pi$
$888$	31.6453	1.06195
$889$	25.8082	0.865578
$890$	9.63809	0.323069
$891$	14.7421	0.493878
$892$	−13.6998	−0.458704
$893$	−40.2784	−1.34787
$894$	−116.459	−3.89499
$895$	53.7380	1.79626
$896$	−19.7237	−0.658921
$897$	−20.5958	−0.687675
$898$	−41.2267	−1.37575
$899$	−18.9504	−0.632030
$900$	145.686	4.85620
$901$	−9.05559	−0.301685
$902$	−52.8781	−1.76065
$903$	29.3607	0.977063
$904$	−0.523590	−0.0174144
$905$	5.05559	0.168054
$906$	121.090	4.02296
$907$	39.5813	1.31427	0.657137	−	0.753771i	$-0.271767\pi$
$907$	39.5813	1.31427	0.657137	+	0.753771i	$0.271767\pi$
$908$	45.8843	1.52272
$909$	−62.9192	−2.08690
$910$	−15.4680	−0.512759
$911$	−48.7114	−1.61388	−0.806940	−	0.590634i	$-0.798878\pi$
$911$	−48.7114	−1.61388	−0.806940	+	0.590634i	$0.798878\pi$
$912$	−27.0338	−0.895180
$913$	−1.51357	−0.0500919
$914$	57.7914	1.91157
$915$	114.423	3.78272
$916$	−4.76487	−0.157436
$917$	0.313511	0.0103530
$918$	−34.8154	−1.14908
$919$	1.11118	0.0366545	0.0183273	−	0.999832i	$-0.494166\pi$
$919$	1.11118	0.0366545	0.0183273	+	0.999832i	$0.494166\pi$
$920$	48.7936	1.60868
$921$	5.98771	0.197302
$922$	−32.4307	−1.06805
$923$	8.52359	0.280557
$924$	−58.1010	−1.91138
$925$	94.0203	3.09137
$926$	−15.5837	−0.512113
$927$	4.34017	0.142550
$928$	−24.9721	−0.819750
$929$	−51.1650	−1.67867	−0.839334	−	0.543615i	$-0.817055\pi$
$929$	−51.1650	−1.67867	−0.839334	+	0.543615i	$0.817055\pi$
$930$	−141.189	−4.62978
$931$	19.5802	0.641716
$932$	64.9998	2.12914
$933$	15.3112	0.501268
$934$	44.2472	1.44781
$935$	−85.3277	−2.79051
$936$	−6.68035	−0.218354
$937$	2.51971	0.0823155	0.0411577	−	0.999153i	$-0.486895\pi$
$937$	2.51971	0.0823155	0.0411577	+	0.999153i	$0.486895\pi$
$938$	−17.3607	−0.566847
$939$	79.4678	2.59333
$940$	−94.7852	−3.09155
$941$	−23.0784	−0.752334	−0.376167	−	0.926552i	$-0.622758\pi$
$941$	−23.0784	−0.752334	−0.376167	+	0.926552i	$0.622758\pi$
$942$	0.787653	0.0256631
$943$	−40.0000	−1.30258
$944$	24.4668	0.796326
$945$	−25.8804	−0.841890
$946$	63.7152	2.07156
$947$	−11.5174	−0.374267	−0.187133	−	0.982335i	$-0.559920\pi$
$947$	−11.5174	−0.374267	−0.187133	+	0.982335i	$0.559920\pi$
$948$	−95.5729	−3.10406
$949$	−15.6875	−0.509239
$950$	129.082	4.18797
$951$	3.80430	0.123363
$952$	−11.6248	−0.376760
$953$	22.2967	0.722261	0.361130	−	0.932515i	$-0.382391\pi$
$953$	22.2967	0.722261	0.361130	+	0.932515i	$0.382391\pi$
$954$	−19.3028	−0.624952
$955$	−28.7431	−0.930106
$956$	−33.4690	−1.08247
$957$	−41.2867	−1.33461
$958$	−23.2085	−0.749832
$959$	13.5897	0.438834
$960$	−139.091	−4.48915
$961$	2.16290	0.0697709
$962$	−16.4680	−0.530950
$963$	30.7214	0.989983
$964$	8.14730	0.262407
$965$	−13.4514	−0.433014
$966$	−76.3956	−2.45799
$967$	21.6787	0.697141	0.348571	−	0.937283i	$-0.386667\pi$
$967$	21.6787	0.697141	0.348571	+	0.937283i	$0.386667\pi$
$968$	−16.0772	−0.516739
$969$	−57.4729	−1.84630
$970$	42.8781	1.37673
$971$	41.7419	1.33956	0.669781	−	0.742559i	$-0.266388\pi$
$971$	41.7419	1.33956	0.669781	+	0.742559i	$0.266388\pi$
$972$	52.8781	1.69607
$973$	−16.6803	−0.534747
$974$	85.3484	2.73474
$975$	−33.5669	−1.07500
$976$	−21.0494	−0.673776
$977$	−27.3835	−0.876075	−0.438038	−	0.898957i	$-0.644326\pi$
$977$	−27.3835	−0.876075	−0.438038	+	0.898957i	$0.644326\pi$
$978$	−107.750	−3.44547
$979$	−4.93212	−0.157631
$980$	46.0772	1.47188
$981$	13.9421	0.445138
$982$	37.5585	1.19854
$983$	−24.1617	−0.770638	−0.385319	−	0.922783i	$-0.625909\pi$
$983$	−24.1617	−0.770638	−0.385319	+	0.922783i	$0.625909\pi$
$984$	−21.9421	−0.699490
$985$	−36.5897	−1.16584
$986$	−31.5536	−1.00487
$987$	38.8515	1.23666
$988$	−13.0072	−0.413814
$989$	48.1978	1.53260
$990$	−181.884	−5.78065
$991$	−6.39350	−0.203096	−0.101548	−	0.994831i	$-0.532380\pi$
$991$	−6.39350	−0.203096	−0.101548	+	0.994831i	$0.532380\pi$
$992$	43.7009	1.38750
$993$	9.20006	0.291955
$994$	31.6163	1.00281
$995$	85.9120	2.72359
$996$	−2.39908	−0.0760177
$997$	42.5074	1.34622	0.673112	−	0.739541i	$-0.264957\pi$
$997$	42.5074	1.34622	0.673112	+	0.739541i	$0.264957\pi$
$998$	48.9093	1.54820
$999$	−27.5536	−0.871756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.c.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.c.1.1	✓	3	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)

\(f(q)\)	\(=\)	\(q-2.17009 q^{2} -2.70928 q^{3} +2.70928 q^{4} -4.17009 q^{5} +5.87936 q^{6} -1.70928 q^{7} -1.53919 q^{8} +4.34017 q^{9} +O(q^{10})\)	\(q-2.17009 q^{2} -2.70928 q^{3} +2.70928 q^{4} -4.17009 q^{5} +5.87936 q^{6} -1.70928 q^{7} -1.53919 q^{8} +4.34017 q^{9} +9.04945 q^{10} -4.63090 q^{11} -7.34017 q^{12} +1.00000 q^{13} +3.70928 q^{14} +11.2979 q^{15} -2.07838 q^{16} -4.41855 q^{17} -9.41855 q^{18} -4.80098 q^{19} -11.2979 q^{20} +4.63090 q^{21} +10.0494 q^{22} +7.60197 q^{23} +4.17009 q^{24} +12.3896 q^{25} -2.17009 q^{26} -3.63090 q^{27} -4.63090 q^{28} -3.29072 q^{29} -24.5174 q^{30} +5.75872 q^{31} +7.58864 q^{32} +12.5464 q^{33} +9.58864 q^{34} +7.12783 q^{35} +11.7587 q^{36} +7.58864 q^{37} +10.4186 q^{38} -2.70928 q^{39} +6.41855 q^{40} -5.26180 q^{41} -10.0494 q^{42} +6.34017 q^{43} -12.5464 q^{44} -18.0989 q^{45} -16.4969 q^{46} +8.38962 q^{47} +5.63090 q^{48} -4.07838 q^{49} -26.8865 q^{50} +11.9711 q^{51} +2.70928 q^{52} +2.04945 q^{53} +7.87936 q^{54} +19.3112 q^{55} +2.63090 q^{56} +13.0072 q^{57} +7.14116 q^{58} -11.7721 q^{59} +30.6092 q^{60} +10.1278 q^{61} -12.4969 q^{62} -7.41855 q^{63} -12.3112 q^{64} -4.17009 q^{65} -27.2267 q^{66} -4.68035 q^{67} -11.9711 q^{68} -20.5958 q^{69} -15.4680 q^{70} +8.52359 q^{71} -6.68035 q^{72} -15.6875 q^{73} -16.4680 q^{74} -33.5669 q^{75} -13.0072 q^{76} +7.91548 q^{77} +5.87936 q^{78} +13.0205 q^{79} +8.66701 q^{80} -3.18342 q^{81} +11.4186 q^{82} +0.326842 q^{83} +12.5464 q^{84} +18.4257 q^{85} -13.7587 q^{86} +8.91548 q^{87} +7.12783 q^{88} +1.06505 q^{89} +39.2762 q^{90} -1.70928 q^{91} +20.5958 q^{92} -15.6020 q^{93} -18.2062 q^{94} +20.0205 q^{95} -20.5597 q^{96} +4.73820 q^{97} +8.85043 q^{98} -20.0989 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - q^{3} + q^{4} - 7 q^{5} + 5 q^{6} + 2 q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q - q^2 - q^3 + q^4 - 7 * q^5 + 5 * q^6 + 2 * q^7 - 3 * q^8 + 2 * q^9	\( 3 q - q^{2} - q^{3} + q^{4} - 7 q^{5} + 5 q^{6} + 2 q^{7} - 3 q^{8} + 2 q^{9} + 9 q^{10} - 10 q^{11} - 11 q^{12} + 3 q^{13} + 4 q^{14} + 7 q^{15} - 3 q^{16} + q^{17} - 14 q^{18} - 5 q^{19} - 7 q^{20} + 10 q^{21} + 12 q^{22} + 4 q^{23} + 7 q^{24} + 8 q^{25} - q^{26} - 7 q^{27} - 10 q^{28} - 17 q^{29} - 23 q^{30} - 8 q^{31} + 3 q^{32} + 2 q^{33} + 9 q^{34} + 10 q^{36} + 3 q^{37} + 17 q^{38} - q^{39} + 5 q^{40} - 8 q^{41} - 12 q^{42} + 8 q^{43} - 2 q^{44} - 18 q^{45} - 32 q^{46} - 4 q^{47} + 13 q^{48} - 9 q^{49} - 34 q^{50} + 21 q^{51} + q^{52} - 12 q^{53} + 11 q^{54} + 32 q^{55} + 4 q^{56} + 5 q^{57} + q^{58} - 11 q^{59} + 39 q^{60} + 9 q^{61} - 20 q^{62} - 8 q^{63} - 11 q^{64} - 7 q^{65} - 24 q^{66} + 8 q^{67} - 21 q^{68} - 8 q^{69} - 14 q^{70} + 10 q^{71} + 2 q^{72} + 9 q^{73} - 17 q^{74} - 32 q^{75} - 5 q^{76} - 8 q^{77} + 5 q^{78} + 6 q^{79} + 3 q^{80} - 5 q^{81} + 20 q^{82} - 11 q^{83} + 2 q^{84} + 7 q^{85} - 16 q^{86} - 5 q^{87} - q^{89} + 42 q^{90} + 2 q^{91} + 8 q^{92} - 28 q^{93} - 30 q^{94} + 27 q^{95} - 27 q^{96} + 22 q^{97} - q^{98} - 24 q^{99}+O(q^{100}) \) 3 * q - q^2 - q^3 + q^4 - 7 * q^5 + 5 * q^6 + 2 * q^7 - 3 * q^8 + 2 * q^9 + 9 * q^10 - 10 * q^11 - 11 * q^12 + 3 * q^13 + 4 * q^14 + 7 * q^15 - 3 * q^16 + q^17 - 14 * q^18 - 5 * q^19 - 7 * q^20 + 10 * q^21 + 12 * q^22 + 4 * q^23 + 7 * q^24 + 8 * q^25 - q^26 - 7 * q^27 - 10 * q^28 - 17 * q^29 - 23 * q^30 - 8 * q^31 + 3 * q^32 + 2 * q^33 + 9 * q^34 + 10 * q^36 + 3 * q^37 + 17 * q^38 - q^39 + 5 * q^40 - 8 * q^41 - 12 * q^42 + 8 * q^43 - 2 * q^44 - 18 * q^45 - 32 * q^46 - 4 * q^47 + 13 * q^48 - 9 * q^49 - 34 * q^50 + 21 * q^51 + q^52 - 12 * q^53 + 11 * q^54 + 32 * q^55 + 4 * q^56 + 5 * q^57 + q^58 - 11 * q^59 + 39 * q^60 + 9 * q^61 - 20 * q^62 - 8 * q^63 - 11 * q^64 - 7 * q^65 - 24 * q^66 + 8 * q^67 - 21 * q^68 - 8 * q^69 - 14 * q^70 + 10 * q^71 + 2 * q^72 + 9 * q^73 - 17 * q^74 - 32 * q^75 - 5 * q^76 - 8 * q^77 + 5 * q^78 + 6 * q^79 + 3 * q^80 - 5 * q^81 + 20 * q^82 - 11 * q^83 + 2 * q^84 + 7 * q^85 - 16 * q^86 - 5 * q^87 - q^89 + 42 * q^90 + 2 * q^91 + 8 * q^92 - 28 * q^93 - 30 * q^94 + 27 * q^95 - 27 * q^96 + 22 * q^97 - q^98 - 24 * q^99

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